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diff --git a/docs/sphinx_docs/_build/doctrees/stack.doctree b/docs/sphinx_docs/_build/doctrees/stack.doctree
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diff --git a/docs/sphinx_docs/_build/doctrees/types.doctree b/docs/sphinx_docs/_build/doctrees/types.doctree
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diff --git a/docs/sphinx_docs/_build/html/_modules/index.html b/docs/sphinx_docs/_build/html/_modules/index.html
index a09f508..9ee35ef 100644 (file)
--- a/docs/sphinx_docs/_build/html/_modules/index.html
+++ b/docs/sphinx_docs/_build/html/_modules/index.html
@@ -102,7 +102,7 @@
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/_modules/joy/library.html b/docs/sphinx_docs/_build/html/_modules/joy/library.html
index 389391f..da257c6 100644 (file)
--- a/docs/sphinx_docs/_build/html/_modules/joy/library.html
+++ b/docs/sphinx_docs/_build/html/_modules/joy/library.html
@@ -94,7 +94,7 @@
 
 <span class="si">%s</span><span class="s1"></span>
 
-<span class="s1">---- end (</span><span class="si">%s</span><span class="s1">)</span>
+<span class="s1">---- end ( </span><span class="si">%s</span><span class="s1"> )</span>
 <span class="s1">&#39;&#39;&#39;</span>
 
 
@@ -260,15 +260,6 @@
     <span class="k">return</span> <span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span></div>
 
 
-<div class="viewcode-block" id="parse"><a class="viewcode-back" href="../../library.html#joy.library.parse">[docs]</a><span class="nd">@inscribe</span>
-<span class="nd">@SimpleFunctionWrapper</span>
-<span class="k">def</span> <span class="nf">parse</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
-    <span class="sd">&#39;&#39;&#39;Parse the string on the stack to a Joy expression.&#39;&#39;&#39;</span>
-    <span class="n">text</span><span class="p">,</span> <span class="n">stack</span> <span class="o">=</span> <span class="n">stack</span>
-    <span class="n">expression</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="n">text</span><span class="p">)</span>
-    <span class="k">return</span> <span class="n">expression</span><span class="p">,</span> <span class="n">stack</span></div>
-
-
 <span class="c1"># @inscribe</span>
 <span class="c1"># @SimpleFunctionWrapper</span>
 <span class="c1"># def infer_(stack):</span>
@@ -373,19 +364,18 @@
 <span class="sd">    Use a Boolean value to select one of two items.</span>
 <span class="sd">    ::</span>
 
-<span class="sd">           A B False choice</span>
+<span class="sd">           A B false choice</span>
 <span class="sd">        ----------------------</span>
 <span class="sd">           A</span>
 
 
-<span class="sd">           A B True choice</span>
+<span class="sd">           A B true choice</span>
 <span class="sd">        ---------------------</span>
 <span class="sd">             B</span>
 
-<span class="sd">    Currently Python semantics are used to evaluate the &quot;truthiness&quot; of the</span>
-<span class="sd">    Boolean value (so empty string, zero, etc. are counted as false, etc.)</span>
 <span class="sd">    &#39;&#39;&#39;</span>
     <span class="p">(</span><span class="n">if_</span><span class="p">,</span> <span class="p">(</span><span class="n">then</span><span class="p">,</span> <span class="p">(</span><span class="n">else_</span><span class="p">,</span> <span class="n">stack</span><span class="p">)))</span> <span class="o">=</span> <span class="n">stack</span>
+    <span class="k">assert</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">if_</span><span class="p">,</span> <span class="nb">bool</span><span class="p">),</span> <span class="nb">repr</span><span class="p">(</span><span class="n">if_</span><span class="p">)</span>
     <span class="k">return</span> <span class="n">then</span> <span class="k">if</span> <span class="n">if_</span> <span class="k">else</span> <span class="n">else_</span><span class="p">,</span> <span class="n">stack</span></div>
 
 
@@ -396,12 +386,12 @@
 <span class="sd">    Use a Boolean value to select one of two items from a sequence.</span>
 <span class="sd">    ::</span>
 
-<span class="sd">           [A B] False select</span>
+<span class="sd">           [A B] false select</span>
 <span class="sd">        ------------------------</span>
 <span class="sd">            A</span>
 
 
-<span class="sd">           [A B] True select</span>
+<span class="sd">           [A B] true select</span>
 <span class="sd">        -----------------------</span>
 <span class="sd">              B</span>
 
@@ -625,9 +615,9 @@
 
 <span class="sd">    Return the tuple (x//y, x%y).  Invariant: q * y + r == x.</span>
 <span class="sd">    &#39;&#39;&#39;</span>
-    <span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span> <span class="o">=</span> <span class="n">S</span>
-    <span class="n">d</span><span class="p">,</span> <span class="n">m</span> <span class="o">=</span> <span class="nb">divmod</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
-    <span class="k">return</span> <span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span></div>
+    <span class="n">y</span><span class="p">,</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span> <span class="o">=</span> <span class="n">S</span>
+    <span class="n">q</span><span class="p">,</span> <span class="n">r</span> <span class="o">=</span> <span class="nb">divmod</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
+    <span class="k">return</span> <span class="n">r</span><span class="p">,</span> <span class="p">(</span><span class="n">q</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span></div>
 
 
 <div class="viewcode-block" id="sqrt"><a class="viewcode-back" href="../../library.html#joy.library.sqrt">[docs]</a><span class="k">def</span> <span class="nf">sqrt</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
@@ -1482,7 +1472,7 @@
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/_modules/joy/parser.html b/docs/sphinx_docs/_build/html/_modules/joy/parser.html
index 46f58ec..153d3de 100644 (file)
--- a/docs/sphinx_docs/_build/html/_modules/joy/parser.html
+++ b/docs/sphinx_docs/_build/html/_modules/joy/parser.html
@@ -71,6 +71,11 @@
 <span class="sd">&#39;&#39;&#39;</span>
 <span class="kn">from</span> <span class="nn">re</span> <span class="kn">import</span> <span class="n">Scanner</span>
 <span class="kn">from</span> <span class="nn">.utils.stack</span> <span class="kn">import</span> <span class="n">list_to_stack</span>
+<span class="kn">from</span> <span class="nn">.utils.snippets</span> <span class="kn">import</span> <span class="p">(</span>
+    <span class="n">pat</span> <span class="k">as</span> <span class="n">SNIPPETS</span><span class="p">,</span>
+    <span class="n">from_string</span><span class="p">,</span>
+    <span class="n">Snippet</span><span class="p">,</span>
+    <span class="p">)</span>
 
 
 <span class="n">BRACKETS</span> <span class="o">=</span> <span class="sa">r</span><span class="s1">&#39;\[|\]&#39;</span>
@@ -79,6 +84,7 @@
 
 
 <span class="n">token_scanner</span> <span class="o">=</span> <span class="n">Scanner</span><span class="p">([</span>
+    <span class="p">(</span><span class="n">SNIPPETS</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">_</span><span class="p">,</span> <span class="n">token</span><span class="p">:</span> <span class="n">from_string</span><span class="p">(</span><span class="n">token</span><span class="p">)),</span>
     <span class="p">(</span><span class="n">BRACKETS</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">_</span><span class="p">,</span> <span class="n">token</span><span class="p">:</span> <span class="n">token</span><span class="p">),</span>
     <span class="p">(</span><span class="n">BLANKS</span><span class="p">,</span> <span class="kc">None</span><span class="p">),</span>
     <span class="p">(</span><span class="n">WORDS</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">_</span><span class="p">,</span> <span class="n">token</span><span class="p">:</span> <span class="n">token</span><span class="p">),</span>
@@ -138,20 +144,16 @@
             <span class="n">v</span> <span class="o">=</span> <span class="n">frame</span>
             <span class="k">try</span><span class="p">:</span> <span class="n">frame</span> <span class="o">=</span> <span class="n">stack</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
             <span class="k">except</span> <span class="ne">IndexError</span><span class="p">:</span>
-                <span class="k">raise</span> <span class="n">ParseError</span><span class="p">(</span><span class="s1">&#39;Extra closing bracket.&#39;</span><span class="p">)</span>
+                <span class="k">raise</span> <span class="n">ParseError</span><span class="p">(</span><span class="s1">&#39;Extra closing bracket.&#39;</span><span class="p">)</span> <span class="kn">from</span> <span class="bp">None</span>
             <span class="n">frame</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">list_to_stack</span><span class="p">(</span><span class="n">v</span><span class="p">))</span>
-        <span class="k">elif</span> <span class="n">tok</span> <span class="o">==</span> <span class="s1">&#39;true&#39;</span><span class="p">:</span>
-            <span class="n">frame</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
-        <span class="k">elif</span> <span class="n">tok</span> <span class="o">==</span> <span class="s1">&#39;false&#39;</span><span class="p">:</span>
-            <span class="n">frame</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="n">tok</span> <span class="o">==</span> <span class="s1">&#39;true&#39;</span><span class="p">:</span> <span class="n">frame</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="n">tok</span> <span class="o">==</span> <span class="s1">&#39;false&#39;</span><span class="p">:</span> <span class="n">frame</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">tok</span><span class="p">,</span> <span class="n">Snippet</span><span class="p">):</span> <span class="n">frame</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">tok</span><span class="p">)</span>
         <span class="k">else</span><span class="p">:</span>
-            <span class="k">try</span><span class="p">:</span>
-                <span class="n">thing</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">tok</span><span class="p">)</span>
-            <span class="k">except</span> <span class="ne">ValueError</span><span class="p">:</span>
-                <span class="n">thing</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="n">tok</span><span class="p">)</span>
+            <span class="k">try</span><span class="p">:</span> <span class="n">thing</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">tok</span><span class="p">)</span>
+            <span class="k">except</span> <span class="ne">ValueError</span><span class="p">:</span> <span class="n">thing</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="n">tok</span><span class="p">)</span>
             <span class="n">frame</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">thing</span><span class="p">)</span>
-    <span class="k">if</span> <span class="n">stack</span><span class="p">:</span>
-        <span class="k">raise</span> <span class="n">ParseError</span><span class="p">(</span><span class="s1">&#39;Unclosed bracket.&#39;</span><span class="p">)</span>
+    <span class="k">if</span> <span class="n">stack</span><span class="p">:</span> <span class="k">raise</span> <span class="n">ParseError</span><span class="p">(</span><span class="s1">&#39;Unclosed bracket.&#39;</span><span class="p">)</span>
     <span class="k">return</span> <span class="n">list_to_stack</span><span class="p">(</span><span class="n">frame</span><span class="p">)</span>
 </pre></div>
 
@@ -220,7 +222,7 @@
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/_modules/joy/utils/stack.html b/docs/sphinx_docs/_build/html/_modules/joy/utils/stack.html
index 945bc10..b9fa764 100644 (file)
--- a/docs/sphinx_docs/_build/html/_modules/joy/utils/stack.html
+++ b/docs/sphinx_docs/_build/html/_modules/joy/utils/stack.html
@@ -104,6 +104,7 @@
 
 <span class="sd">&#39;&#39;&#39;</span>
 <span class="kn">from</span> <span class="nn">.errors</span> <span class="kn">import</span> <span class="n">NotAListError</span>
+<span class="kn">from</span> <span class="nn">.snippets</span> <span class="kn">import</span> <span class="n">Snippet</span><span class="p">,</span> <span class="n">to_string</span> <span class="k">as</span> <span class="n">snip_to_string</span>
 
 
 <div class="viewcode-block" id="list_to_stack"><a class="viewcode-back" href="../../../stack.html#joy.utils.stack.list_to_stack">[docs]</a><span class="k">def</span> <span class="nf">list_to_stack</span><span class="p">(</span><span class="n">el</span><span class="p">,</span> <span class="n">stack</span><span class="o">=</span><span class="p">()):</span>
@@ -162,24 +163,28 @@
     <span class="k">return</span> <span class="n">_to_string</span><span class="p">(</span><span class="n">expression</span><span class="p">,</span> <span class="n">iter_stack</span><span class="p">)</span></div>
 
 
-<span class="n">_JOY_BOOL_LITS</span> <span class="o">=</span> <span class="s1">&#39;false&#39;</span><span class="p">,</span> <span class="s1">&#39;true&#39;</span>
+<span class="n">JOY_BOOL_LITERALS</span> <span class="o">=</span> <span class="s1">&#39;false&#39;</span><span class="p">,</span> <span class="s1">&#39;true&#39;</span>
 
 
 <span class="k">def</span> <span class="nf">_joy_repr</span><span class="p">(</span><span class="n">thing</span><span class="p">):</span>
-        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">thing</span><span class="p">,</span> <span class="nb">bool</span><span class="p">):</span>
-                <span class="k">return</span> <span class="n">_JOY_BOOL_LITS</span><span class="p">[</span><span class="n">thing</span><span class="p">]</span>
-        <span class="k">return</span> <span class="nb">repr</span><span class="p">(</span><span class="n">thing</span><span class="p">)</span>
+    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">thing</span><span class="p">,</span> <span class="nb">bool</span><span class="p">):</span> <span class="k">return</span> <span class="n">JOY_BOOL_LITERALS</span><span class="p">[</span><span class="n">thing</span><span class="p">]</span>
+    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">thing</span><span class="p">,</span> <span class="n">Snippet</span><span class="p">):</span> <span class="k">return</span> <span class="n">snip_to_string</span><span class="p">(</span><span class="n">thing</span><span class="p">)</span>
+    <span class="k">return</span> <span class="nb">repr</span><span class="p">(</span><span class="n">thing</span><span class="p">)</span>
 
 
 <span class="k">def</span> <span class="nf">_to_string</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">f</span><span class="p">):</span>
     <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span> <span class="k">return</span> <span class="n">_joy_repr</span><span class="p">(</span><span class="n">stack</span><span class="p">)</span>
     <span class="k">if</span> <span class="ow">not</span> <span class="n">stack</span><span class="p">:</span> <span class="k">return</span> <span class="s1">&#39;&#39;</span>  <span class="c1"># shortcut</span>
+    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">Snippet</span><span class="p">):</span> <span class="k">return</span> <span class="n">snip_to_string</span><span class="p">(</span><span class="n">stack</span><span class="p">)</span>
     <span class="k">return</span> <span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">_s</span><span class="p">,</span> <span class="n">f</span><span class="p">(</span><span class="n">stack</span><span class="p">)))</span>
 
 
 <span class="n">_s</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">s</span><span class="p">:</span> <span class="p">(</span>
     <span class="s1">&#39;[</span><span class="si">%s</span><span class="s1">]&#39;</span> <span class="o">%</span> <span class="n">expression_to_string</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
         <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)</span>
+        <span class="ow">and</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">Snippet</span><span class="p">)</span>
+        <span class="c1"># Is it worth making a non-tuple class for Snippet?</span>
+        <span class="c1"># Doing this check on each tuple seems a bit much.</span>
     <span class="k">else</span> <span class="n">_joy_repr</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
     <span class="p">)</span>
 
@@ -351,7 +356,7 @@
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/_static/basic.css b/docs/sphinx_docs/_build/html/_static/basic.css
index 603f6a8..ac9a52a 100644 (file)
--- a/docs/sphinx_docs/_build/html/_static/basic.css
+++ b/docs/sphinx_docs/_build/html/_static/basic.css
@@ -66,6 +66,10 @@ div.sphinxsidebar ul {
     list-style: none;
 }
 
+div.sphinxsidebar li {
+       padding-bottom: 0.5em;
+}
+
 div.sphinxsidebar ul ul,
 div.sphinxsidebar ul.want-points {
     margin-left: 20px;

diff --git a/docs/sphinx_docs/_build/html/_static/doctools.js b/docs/sphinx_docs/_build/html/_static/doctools.js
index 8cbf1b1..e509e48 100644 (file)
--- a/docs/sphinx_docs/_build/html/_static/doctools.js
+++ b/docs/sphinx_docs/_build/html/_static/doctools.js
@@ -4,7 +4,7 @@
  *
  * Sphinx JavaScript utilities for all documentation.
  *
- * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
@@ -264,6 +264,9 @@ var Documentation = {
   hideSearchWords : function() {
     $('#searchbox .highlight-link').fadeOut(300);
     $('span.highlighted').removeClass('highlighted');
+    var url = new URL(window.location);
+    url.searchParams.delete('highlight');
+    window.history.replaceState({}, '', url);
   },
 
   /**

diff --git a/docs/sphinx_docs/_build/html/_static/language_data.js b/docs/sphinx_docs/_build/html/_static/language_data.js
index 863704b..ebe2f03 100644 (file)
--- a/docs/sphinx_docs/_build/html/_static/language_data.js
+++ b/docs/sphinx_docs/_build/html/_static/language_data.js
@@ -5,7 +5,7 @@
  * This script contains the language-specific data used by searchtools.js,
  * namely the list of stopwords, stemmer, scorer and splitter.
  *
- * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */

diff --git a/docs/sphinx_docs/_build/html/_static/pygments.css b/docs/sphinx_docs/_build/html/_static/pygments.css
index f346859..691aeb8 100644 (file)
--- a/docs/sphinx_docs/_build/html/_static/pygments.css
+++ b/docs/sphinx_docs/_build/html/_static/pygments.css
@@ -1,7 +1,7 @@
-pre { line-height: 125%; margin: 0; }
-td.linenos pre { color: #000000; background-color: #f0f0f0; padding-left: 5px; padding-right: 5px; }
-span.linenos { color: #000000; background-color: #f0f0f0; padding-left: 5px; padding-right: 5px; }
-td.linenos pre.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
+pre { line-height: 125%; }
+td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
+span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
+td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
 span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
 .highlight .hll { background-color: #ffffcc }
 .highlight { background: #eeffcc; }

diff --git a/docs/sphinx_docs/_build/html/_static/searchtools.js b/docs/sphinx_docs/_build/html/_static/searchtools.js
index 002e9c4..2d77859 100644 (file)
--- a/docs/sphinx_docs/_build/html/_static/searchtools.js
+++ b/docs/sphinx_docs/_build/html/_static/searchtools.js
@@ -4,7 +4,7 @@
  *
  * Sphinx JavaScript utilities for the full-text search.
  *
- * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */

diff --git a/docs/sphinx_docs/_build/html/genindex.html b/docs/sphinx_docs/_build/html/genindex.html
index ce6c14b..f1bedb1 100644 (file)
--- a/docs/sphinx_docs/_build/html/genindex.html
+++ b/docs/sphinx_docs/_build/html/genindex.html
@@ -326,8 +326,6 @@
 <h2 id="P">P</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="library.html#joy.library.parse">parse() (in module joy.library)</a>
-</li>
       <li><a href="parser.html#joy.parser.ParseError">ParseError</a>
 </li>
       <li><a href="stack.html#joy.utils.stack.pick">pick() (in module joy.utils.stack)</a>
@@ -570,7 +568,7 @@
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/index.html b/docs/sphinx_docs/_build/html/index.html
index a8eb5af..ca81a00 100644 (file)
--- a/docs/sphinx_docs/_build/html/index.html
+++ b/docs/sphinx_docs/_build/html/index.html
@@ -256,7 +256,7 @@ interesting aspects.  It’s quite a treasure trove.</p>
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/joy.html b/docs/sphinx_docs/_build/html/joy.html
index 4a5a08e..20854d5 100644 (file)
--- a/docs/sphinx_docs/_build/html/joy.html
+++ b/docs/sphinx_docs/_build/html/joy.html
@@ -191,7 +191,7 @@ on every iteration, its return value is ignored.</p>
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/lib.html b/docs/sphinx_docs/_build/html/lib.html
index 03f9a10..1e59f3a 100644 (file)
--- a/docs/sphinx_docs/_build/html/lib.html
+++ b/docs/sphinx_docs/_build/html/lib.html
@@ -1333,7 +1333,7 @@ soley of containers, without strings or numbers or anything else.)</p>
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/library.html b/docs/sphinx_docs/_build/html/library.html
index 1325405..63e7a53 100644 (file)
--- a/docs/sphinx_docs/_build/html/library.html
+++ b/docs/sphinx_docs/_build/html/library.html
@@ -150,18 +150,16 @@ program.</p>
 <dt class="sig sig-object py" id="joy.library.choice">
 <span class="sig-prename descclassname"><span class="pre">joy.library.</span></span><span class="sig-name descname"><span class="pre">choice</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#choice"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.library.choice" title="Permalink to this definition">¶</a></dt>
 <dd><p>Use a Boolean value to select one of two items.</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>   <span class="n">A</span> <span class="n">B</span> <span class="kc">False</span> <span class="n">choice</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>   <span class="n">A</span> <span class="n">B</span> <span class="n">false</span> <span class="n">choice</span>
 <span class="o">----------------------</span>
    <span class="n">A</span>
 
 
-   <span class="n">A</span> <span class="n">B</span> <span class="kc">True</span> <span class="n">choice</span>
+   <span class="n">A</span> <span class="n">B</span> <span class="n">true</span> <span class="n">choice</span>
 <span class="o">---------------------</span>
      <span class="n">B</span>
 </pre></div>
 </div>
-<p>Currently Python semantics are used to evaluate the “truthiness” of the
-Boolean value (so empty string, zero, etc. are counted as false, etc.)</p>
 </dd></dl>
 
 <dl class="py function">
@@ -449,7 +447,7 @@ with the list as its stack.  Does not affect the rest of the stack.</p>
 
 <dl class="py function">
 <dt class="sig sig-object py" id="joy.library.inscribe">
-<span class="sig-prename descclassname"><span class="pre">joy.library.</span></span><span class="sig-name descname"><span class="pre">inscribe</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">function</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">d={'!=':</span> <span class="pre">&lt;function</span> <span class="pre">ne&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'%':</span> <span class="pre">&lt;function</span> <span class="pre">mod&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'&amp;':</span> <span class="pre">&lt;function</span> <span class="pre">and_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'*':</span> <span class="pre">&lt;function</span> <span class="pre">mul&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'+':</span> <span class="pre">&lt;function</span> <span class="pre">add&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'++':</span> <span class="pre">&lt;function</span> <span class="pre">succ&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'-':</span> <span class="pre">&lt;function</span> <span class="pre">sub&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'--':</span> <span class="pre">&lt;function</span> <span class="pre">pred&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'/':</span> <span class="pre">&lt;function</span> <span class="pre">floordiv&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'//':</span> <span class="pre">&lt;function</span> <span class="pre">floordiv&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'/floor':</span> <span class="pre">&lt;function</span> <span class="pre">floordiv&gt;</span></span></em>, <em 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class="pre">&lt;function</span> <span class="pre">app3&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'at':</span> <span class="pre">&lt;function</span> <span class="pre">getitem&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'b':</span> <span class="pre">&lt;function</span> <span class="pre">b&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'bool':</span> <span class="pre">&lt;function</span> <span class="pre">bool&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'branch':</span> <span class="pre">&lt;function</span> <span class="pre">branch&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'ccons':</span> <span class="pre">&lt;function</span> <span class="pre">ccons&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'choice':</span> <span class="pre">&lt;function</span> <span 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class="pre">&lt;function</span> <span class="pre">first_two&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'floor':</span> <span class="pre">&lt;function</span> <span class="pre">floor&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'floordiv':</span> <span class="pre">&lt;function</span> <span class="pre">floordiv&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'fourth':</span> <span class="pre">&lt;function</span> <span class="pre">fourth&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'gcd2':</span> <span class="pre">&lt;function</span> <span class="pre">gcd2&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'ge':</span> <span class="pre">&lt;function</span> <span class="pre">ge&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'genrec':</span> <span class="pre">&lt;function</span> <span class="pre">genrec&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'getitem':</span> <span class="pre">&lt;function</span> <span class="pre">getitem&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'gt':</span> <span class="pre">&lt;function</span> <span class="pre">gt&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'help':</span> <span class="pre">&lt;function</span> <span class="pre">help_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'i':</span> <span class="pre">&lt;function</span> <span class="pre">i&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'id':</span> <span class="pre">&lt;function</span> <span class="pre">id_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'ifte':</span> <span class="pre">&lt;function</span> <span class="pre">ifte&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'ii':</span> <span class="pre">&lt;function</span> <span class="pre">ii&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'infra':</span> <span class="pre">&lt;function</span> <span class="pre">infra&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'inscribe':</span> <span class="pre">&lt;function</span> <span class="pre">inscribe_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'le':</span> <span class="pre">&lt;function</span> <span class="pre">le&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'loop':</span> <span class="pre">&lt;function</span> <span class="pre">loop&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'lshift':</span> <span class="pre">&lt;function</span> <span class="pre">lshift&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'lt':</span> <span class="pre">&lt;function</span> <span class="pre">lt&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'map':</span> <span class="pre">&lt;function</span> <span class="pre">map_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'max':</span> <span class="pre">&lt;function</span> <span class="pre">max_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'min':</span> <span class="pre">&lt;function</span> <span class="pre">min_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'mod':</span> <span class="pre">&lt;function</span> <span class="pre">mod&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'modulus':</span> <span class="pre">&lt;function</span> <span class="pre">mod&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'mul':</span> <span class="pre">&lt;function</span> <span class="pre">mul&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'ne':</span> <span class="pre">&lt;function</span> <span class="pre">ne&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'neg':</span> <span class="pre">&lt;function</span> <span class="pre">neg&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'not':</span> <span class="pre">&lt;function</span> <span class="pre">not_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'or':</span> <span class="pre">&lt;function</span> <span class="pre">or_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'over':</span> <span class="pre">&lt;function</span> <span class="pre">over&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'parse':</span> <span class="pre">&lt;function</span> <span class="pre">parse&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'pick':</span> <span class="pre">&lt;function</span> <span class="pre">getitem&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'pm':</span> <span class="pre">&lt;function</span> <span class="pre">pm&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'pop':</span> <span class="pre">&lt;function</span> <span class="pre">pop&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'popd':</span> <span class="pre">&lt;function</span> <span class="pre">popd&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'popdd':</span> <span class="pre">&lt;function</span> <span class="pre">popdd&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'popop':</span> <span class="pre">&lt;function</span> <span class="pre">popop&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'popopd':</span> <span class="pre">&lt;function</span> <span class="pre">popopd&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'popopdd':</span> <span class="pre">&lt;function</span> <span class="pre">popopdd&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'pow':</span> <span class="pre">&lt;function</span> <span class="pre">pow&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'pred':</span> <span class="pre">&lt;function</span> <span class="pre">pred&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'primrec':</span> <span class="pre">&lt;function</span> <span class="pre">primrec&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'rem':</span> <span class="pre">&lt;function</span> <span class="pre">mod&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'remainder':</span> <span class="pre">&lt;function</span> <span class="pre">mod&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'remove':</span> <span class="pre">&lt;function</span> <span class="pre">remove&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'rest':</span> <span class="pre">&lt;function</span> <span class="pre">rest&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'reverse':</span> <span class="pre">&lt;function</span> <span class="pre">reverse&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'roll&lt;':</span> <span class="pre">&lt;function</span> <span class="pre">rolldown&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'roll&gt;':</span> <span class="pre">&lt;function</span> <span class="pre">rollup&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'rolldown':</span> <span class="pre">&lt;function</span> <span class="pre">rolldown&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'rollup':</span> <span class="pre">&lt;function</span> <span class="pre">rollup&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'round':</span> <span class="pre">&lt;function</span> <span class="pre">round&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'rrest':</span> <span class="pre">&lt;function</span> <span class="pre">rrest&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'rshift':</span> <span class="pre">&lt;function</span> <span class="pre">rshift&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'second':</span> <span class="pre">&lt;function</span> <span class="pre">second&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'select':</span> <span class="pre">&lt;function</span> <span class="pre">select&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'sharing':</span> <span class="pre">&lt;function</span> <span class="pre">sharing&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'shunt':</span> <span class="pre">&lt;function</span> <span class="pre">shunt&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'sort':</span> <span class="pre">&lt;function</span> <span class="pre">sort_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'sqrt':</span> <span class="pre">&lt;function</span> <span class="pre">sqrt&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'stack':</span> <span class="pre">&lt;function</span> <span class="pre">stack&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'step':</span> <span class="pre">&lt;function</span> <span class="pre">step&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'stuncons':</span> <span class="pre">&lt;function</span> <span class="pre">stuncons&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'stununcons':</span> <span class="pre">&lt;function</span> <span class="pre">stununcons&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'sub':</span> <span class="pre">&lt;function</span> <span class="pre">sub&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'succ':</span> <span class="pre">&lt;function</span> <span class="pre">succ&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'sum':</span> <span class="pre">&lt;function</span> <span class="pre">sum_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'swaack':</span> <span class="pre">&lt;function</span> <span class="pre">swaack&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'swap':</span> <span class="pre">&lt;function</span> <span class="pre">swap&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'swons':</span> <span class="pre">&lt;function</span> <span class="pre">swons&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'take':</span> <span class="pre">&lt;function</span> <span class="pre">take&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'third':</span> <span class="pre">&lt;function</span> <span class="pre">third&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'times':</span> <span class="pre">&lt;function</span> <span class="pre">times&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'truthy':</span> <span class="pre">&lt;function</span> <span class="pre">bool&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'tuck':</span> <span class="pre">&lt;function</span> <span class="pre">tuck&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'uncons':</span> <span class="pre">&lt;function</span> <span class="pre">uncons&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'unique':</span> <span class="pre">&lt;function</span> <span class="pre">unique&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'unit':</span> <span class="pre">&lt;function</span> <span class="pre">unit&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'unswons':</span> <span class="pre">&lt;function</span> <span class="pre">unswons&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'void':</span> <span class="pre">&lt;function</span> <span class="pre">void&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'warranty':</span> <span class="pre">&lt;function</span> <span class="pre">warranty&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'words':</span> <span class="pre">&lt;function</span> <span class="pre">words&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'x':</span> <span class="pre">&lt;function</span> <span class="pre">x&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'xor':</span> <span class="pre">&lt;function</span> <span class="pre">xor&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'zip':</span> <span class="pre">&lt;function</span> <span class="pre">zip_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'•':</span> <span class="pre">&lt;function</span> <span class="pre">id_&gt;}</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#inscribe"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.library.inscribe" title="Permalink to this definition">¶</a></dt>
+<span class="sig-prename descclassname"><span class="pre">joy.library.</span></span><span class="sig-name descname"><span class="pre">inscribe</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">function</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">d={'!=':</span> <span class="pre">&lt;function</span> <span class="pre">ne&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'%':</span> <span class="pre">&lt;function</span> <span class="pre">mod&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'&amp;':</span> <span class="pre">&lt;function</span> <span class="pre">and_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'*':</span> <span class="pre">&lt;function</span> <span class="pre">mul&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'+':</span> <span class="pre">&lt;function</span> <span class="pre">add&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'++':</span> <span class="pre">&lt;function</span> <span class="pre">succ&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'-':</span> <span class="pre">&lt;function</span> <span class="pre">sub&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'--':</span> <span class="pre">&lt;function</span> <span class="pre">pred&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'/':</span> <span class="pre">&lt;function</span> <span class="pre">floordiv&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'//':</span> <span class="pre">&lt;function</span> <span class="pre">floordiv&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'/floor':</span> <span class="pre">&lt;function</span> <span class="pre">floordiv&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'&lt;':</span> <span class="pre">&lt;function</span> <span class="pre">lt&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'&lt;&lt;':</span> <span class="pre">&lt;function</span> <span class="pre">lshift&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'&lt;=':</span> <span class="pre">&lt;function</span> <span class="pre">le&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'&lt;&gt;':</span> <span class="pre">&lt;function</span> <span class="pre">ne&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'=':</span> <span class="pre">&lt;function</span> <span class="pre">eq&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'&gt;':</span> <span class="pre">&lt;function</span> <span class="pre">gt&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'&gt;=':</span> <span class="pre">&lt;function</span> <span class="pre">ge&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'&gt;&gt;':</span> <span class="pre">&lt;function</span> <span class="pre">rshift&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'^':</span> <span class="pre">&lt;function</span> <span class="pre">xor&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'_Tree_add_Ee':</span> <span class="pre">&lt;function</span> <span class="pre">_Tree_add_Ee&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'_Tree_delete_R0':</span> <span class="pre">&lt;function</span> <span class="pre">_Tree_delete_R0&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'_Tree_delete_clear_stuff':</span> <span class="pre">&lt;function</span> <span class="pre">_Tree_delete_clear_stuff&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'_Tree_get_E':</span> <span class="pre">&lt;function</span> <span class="pre">_Tree_get_E&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'abs':</span> <span class="pre">&lt;function</span> <span class="pre">abs&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'add':</span> <span class="pre">&lt;function</span> <span class="pre">add&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'and':</span> <span class="pre">&lt;function</span> <span class="pre">and_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'app1':</span> <span class="pre">&lt;function</span> <span class="pre">app1&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'app2':</span> <span class="pre">&lt;function</span> <span class="pre">app2&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'app3':</span> <span class="pre">&lt;function</span> <span class="pre">app3&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'at':</span> <span class="pre">&lt;function</span> <span class="pre">getitem&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'b':</span> <span class="pre">&lt;function</span> <span class="pre">b&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'bool':</span> <span class="pre">&lt;function</span> <span class="pre">bool&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'branch':</span> <span class="pre">&lt;function</span> <span class="pre">branch&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'ccons':</span> <span class="pre">&lt;function</span> <span class="pre">ccons&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'choice':</span> <span class="pre">&lt;function</span> <span class="pre">choice&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'clear':</span> <span class="pre">&lt;function</span> <span class="pre">clear&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'cmp':</span> <span class="pre">&lt;function</span> <span class="pre">cmp_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'concat':</span> <span class="pre">&lt;function</span> <span class="pre">concat_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'cond':</span> <span class="pre">&lt;function</span> <span class="pre">cond&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'cons':</span> <span class="pre">&lt;function</span> <span class="pre">cons&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'dip':</span> <span class="pre">&lt;function</span> <span class="pre">dip&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'dipd':</span> <span class="pre">&lt;function</span> <span class="pre">dipd&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'dipdd':</span> <span class="pre">&lt;function</span> <span class="pre">dipdd&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'disenstacken':</span> <span class="pre">&lt;function</span> <span class="pre">disenstacken&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'div':</span> <span class="pre">&lt;function</span> <span class="pre">floordiv&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'divmod':</span> <span class="pre">&lt;function</span> <span class="pre">divmod_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'drop':</span> <span class="pre">&lt;function</span> <span class="pre">drop&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'dup':</span> <span class="pre">&lt;function</span> <span class="pre">dup&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'dupd':</span> <span class="pre">&lt;function</span> <span class="pre">dupd&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'dupdd':</span> <span class="pre">&lt;function</span> <span class="pre">dupdd&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'dupdip':</span> <span class="pre">&lt;function</span> <span class="pre">dupdip&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'eq':</span> <span class="pre">&lt;function</span> <span class="pre">eq&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'first':</span> <span class="pre">&lt;function</span> <span class="pre">first&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'first_two':</span> <span class="pre">&lt;function</span> <span class="pre">first_two&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'floor':</span> <span class="pre">&lt;function</span> <span class="pre">floor&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'floordiv':</span> <span class="pre">&lt;function</span> <span class="pre">floordiv&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'fourth':</span> <span class="pre">&lt;function</span> <span class="pre">fourth&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'gcd2':</span> <span class="pre">&lt;function</span> <span class="pre">gcd2&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'ge':</span> <span class="pre">&lt;function</span> <span class="pre">ge&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'genrec':</span> <span class="pre">&lt;function</span> <span class="pre">genrec&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'getitem':</span> <span class="pre">&lt;function</span> <span class="pre">getitem&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'gt':</span> <span class="pre">&lt;function</span> <span class="pre">gt&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'help':</span> <span class="pre">&lt;function</span> <span class="pre">help_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'i':</span> <span class="pre">&lt;function</span> <span class="pre">i&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'id':</span> <span class="pre">&lt;function</span> <span class="pre">id_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'ifte':</span> <span class="pre">&lt;function</span> <span class="pre">ifte&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'ii':</span> <span class="pre">&lt;function</span> <span class="pre">ii&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'infra':</span> <span class="pre">&lt;function</span> <span class="pre">infra&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'inscribe':</span> <span class="pre">&lt;function</span> <span class="pre">inscribe_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'le':</span> <span class="pre">&lt;function</span> <span class="pre">le&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'loop':</span> <span class="pre">&lt;function</span> <span class="pre">loop&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'lshift':</span> <span class="pre">&lt;function</span> <span class="pre">lshift&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'lt':</span> <span class="pre">&lt;function</span> <span class="pre">lt&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'map':</span> <span class="pre">&lt;function</span> <span class="pre">map_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'max':</span> <span class="pre">&lt;function</span> <span class="pre">max_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'min':</span> <span class="pre">&lt;function</span> <span class="pre">min_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'mod':</span> <span class="pre">&lt;function</span> <span class="pre">mod&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'modulus':</span> <span class="pre">&lt;function</span> <span class="pre">mod&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'mul':</span> <span class="pre">&lt;function</span> <span class="pre">mul&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'ne':</span> <span class="pre">&lt;function</span> <span class="pre">ne&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'neg':</span> <span class="pre">&lt;function</span> <span class="pre">neg&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'not':</span> <span class="pre">&lt;function</span> <span class="pre">not_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'or':</span> <span class="pre">&lt;function</span> <span class="pre">or_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'over':</span> <span class="pre">&lt;function</span> <span class="pre">over&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'pick':</span> <span class="pre">&lt;function</span> <span class="pre">getitem&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'pm':</span> <span class="pre">&lt;function</span> <span class="pre">pm&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'pop':</span> <span class="pre">&lt;function</span> <span class="pre">pop&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'popd':</span> <span class="pre">&lt;function</span> <span class="pre">popd&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'popdd':</span> <span class="pre">&lt;function</span> <span class="pre">popdd&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'popop':</span> <span class="pre">&lt;function</span> <span class="pre">popop&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'popopd':</span> <span class="pre">&lt;function</span> <span class="pre">popopd&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'popopdd':</span> <span class="pre">&lt;function</span> <span class="pre">popopdd&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'pow':</span> <span class="pre">&lt;function</span> <span class="pre">pow&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'pred':</span> <span class="pre">&lt;function</span> <span class="pre">pred&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'primrec':</span> <span class="pre">&lt;function</span> <span class="pre">primrec&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'rem':</span> <span class="pre">&lt;function</span> <span class="pre">mod&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'remainder':</span> <span class="pre">&lt;function</span> <span class="pre">mod&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'remove':</span> <span class="pre">&lt;function</span> <span class="pre">remove&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'rest':</span> <span class="pre">&lt;function</span> <span class="pre">rest&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'reverse':</span> <span class="pre">&lt;function</span> <span class="pre">reverse&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'roll&lt;':</span> <span class="pre">&lt;function</span> <span class="pre">rolldown&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'roll&gt;':</span> <span class="pre">&lt;function</span> <span class="pre">rollup&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'rolldown':</span> <span class="pre">&lt;function</span> <span class="pre">rolldown&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'rollup':</span> <span class="pre">&lt;function</span> <span class="pre">rollup&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'round':</span> <span class="pre">&lt;function</span> <span class="pre">round&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'rrest':</span> <span class="pre">&lt;function</span> <span class="pre">rrest&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'rshift':</span> <span class="pre">&lt;function</span> <span class="pre">rshift&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'second':</span> <span class="pre">&lt;function</span> <span class="pre">second&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'select':</span> <span class="pre">&lt;function</span> <span class="pre">select&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'sharing':</span> <span class="pre">&lt;function</span> <span class="pre">sharing&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'shunt':</span> <span class="pre">&lt;function</span> <span class="pre">shunt&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'sort':</span> <span class="pre">&lt;function</span> <span class="pre">sort_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'sqrt':</span> <span class="pre">&lt;function</span> <span class="pre">sqrt&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'stack':</span> <span class="pre">&lt;function</span> <span class="pre">stack&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'step':</span> <span class="pre">&lt;function</span> <span class="pre">step&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'stuncons':</span> <span class="pre">&lt;function</span> <span class="pre">stuncons&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'stununcons':</span> <span class="pre">&lt;function</span> <span class="pre">stununcons&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'sub':</span> <span class="pre">&lt;function</span> <span class="pre">sub&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'succ':</span> <span class="pre">&lt;function</span> <span class="pre">succ&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'sum':</span> <span class="pre">&lt;function</span> <span class="pre">sum_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'swaack':</span> <span class="pre">&lt;function</span> <span class="pre">swaack&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'swap':</span> <span class="pre">&lt;function</span> <span class="pre">swap&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'swons':</span> <span class="pre">&lt;function</span> <span class="pre">swons&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'take':</span> <span class="pre">&lt;function</span> <span class="pre">take&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'third':</span> <span class="pre">&lt;function</span> <span class="pre">third&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'times':</span> <span class="pre">&lt;function</span> <span class="pre">times&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'truthy':</span> <span class="pre">&lt;function</span> <span class="pre">bool&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'tuck':</span> <span class="pre">&lt;function</span> <span class="pre">tuck&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'uncons':</span> <span class="pre">&lt;function</span> <span class="pre">uncons&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'unique':</span> <span class="pre">&lt;function</span> <span class="pre">unique&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'unit':</span> <span class="pre">&lt;function</span> <span class="pre">unit&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'unswons':</span> <span class="pre">&lt;function</span> <span class="pre">unswons&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'void':</span> <span class="pre">&lt;function</span> <span class="pre">void&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'warranty':</span> <span class="pre">&lt;function</span> <span class="pre">warranty&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'words':</span> <span class="pre">&lt;function</span> <span class="pre">words&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'x':</span> <span class="pre">&lt;function</span> <span class="pre">x&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'xor':</span> <span class="pre">&lt;function</span> <span class="pre">xor&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'zip':</span> <span class="pre">&lt;function</span> <span class="pre">zip_&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">'•':</span> <span class="pre">&lt;function</span> <span class="pre">id_&gt;}</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#inscribe"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.library.inscribe" title="Permalink to this definition">¶</a></dt>
 <dd><p>A decorator to inscribe functions into the default dictionary.</p>
 </dd></dl>
 
@@ -499,12 +497,6 @@ new list with the results in place of the program and original list.</p>
 </dd></dl>
 
 <dl class="py function">
-<dt class="sig sig-object py" id="joy.library.parse">
-<span class="sig-prename descclassname"><span class="pre">joy.library.</span></span><span class="sig-name descname"><span class="pre">parse</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#parse"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.library.parse" title="Permalink to this definition">¶</a></dt>
-<dd><p>Parse the string on the stack to a Joy expression.</p>
-</dd></dl>
-
-<dl class="py function">
 <dt class="sig sig-object py" id="joy.library.pm">
 <span class="sig-prename descclassname"><span class="pre">joy.library.</span></span><span class="sig-name descname"><span class="pre">pm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#pm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.library.pm" title="Permalink to this definition">¶</a></dt>
 <dd><p>Plus or minus</p>
@@ -580,12 +572,12 @@ empty or the item isn’t in the list then the list is unchanged.</p>
 <dt class="sig sig-object py" id="joy.library.select">
 <span class="sig-prename descclassname"><span class="pre">joy.library.</span></span><span class="sig-name descname"><span class="pre">select</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#select"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.library.select" title="Permalink to this definition">¶</a></dt>
 <dd><p>Use a Boolean value to select one of two items from a sequence.</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>   <span class="p">[</span><span class="n">A</span> <span class="n">B</span><span class="p">]</span> <span class="kc">False</span> <span class="n">select</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>   <span class="p">[</span><span class="n">A</span> <span class="n">B</span><span class="p">]</span> <span class="n">false</span> <span class="n">select</span>
 <span class="o">------------------------</span>
     <span class="n">A</span>
 
 
-   <span class="p">[</span><span class="n">A</span> <span class="n">B</span><span class="p">]</span> <span class="kc">True</span> <span class="n">select</span>
+   <span class="p">[</span><span class="n">A</span> <span class="n">B</span><span class="p">]</span> <span class="n">true</span> <span class="n">select</span>
 <span class="o">-----------------------</span>
       <span class="n">B</span>
 </pre></div>
@@ -748,7 +740,7 @@ from each list.  The smallest list sets the length of the result list.</p>
 <dl class="py function">
 <dt class="sig sig-object py" id="joy.utils.generated_library.ccons">
 <span class="sig-prename descclassname"><span class="pre">joy.utils.generated_library.</span></span><span class="sig-name descname"><span class="pre">ccons</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#ccons"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.utils.generated_library.ccons" title="Permalink to this definition">¶</a></dt>
-<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="p">[</span><span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">...</span><span class="mi">1</span><span class="p">])</span>
+<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="p">[</span><span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">..</span><span class="mf">.1</span><span class="p">])</span>
 </pre></div>
 </div>
 </dd></dl>
@@ -756,7 +748,7 @@ from each list.  The smallest list sets the length of the result list.</p>
 <dl class="py function">
 <dt class="sig sig-object py" id="joy.utils.generated_library.cons">
 <span class="sig-prename descclassname"><span class="pre">joy.utils.generated_library.</span></span><span class="sig-name descname"><span class="pre">cons</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#cons"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.utils.generated_library.cons" title="Permalink to this definition">¶</a></dt>
-<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">...</span><span class="mi">0</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">...</span><span class="mi">0</span><span class="p">])</span>
+<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">..</span><span class="mf">.0</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">..</span><span class="mf">.0</span><span class="p">])</span>
 </pre></div>
 </div>
 </dd></dl>
@@ -788,7 +780,7 @@ from each list.  The smallest list sets the length of the result list.</p>
 <dl class="py function">
 <dt class="sig sig-object py" id="joy.utils.generated_library.first">
 <span class="sig-prename descclassname"><span class="pre">joy.utils.generated_library.</span></span><span class="sig-name descname"><span class="pre">first</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#first"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.utils.generated_library.first" title="Permalink to this definition">¶</a></dt>
-<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span>
+<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span>
 </pre></div>
 </div>
 </dd></dl>
@@ -796,7 +788,7 @@ from each list.  The smallest list sets the length of the result list.</p>
 <dl class="py function">
 <dt class="sig sig-object py" id="joy.utils.generated_library.first_two">
 <span class="sig-prename descclassname"><span class="pre">joy.utils.generated_library.</span></span><span class="sig-name descname"><span class="pre">first_two</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#first_two"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.utils.generated_library.first_two" title="Permalink to this definition">¶</a></dt>
-<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a2</span><span class="p">)</span>
+<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a2</span><span class="p">)</span>
 </pre></div>
 </div>
 </dd></dl>
@@ -804,7 +796,7 @@ from each list.  The smallest list sets the length of the result list.</p>
 <dl class="py function">
 <dt class="sig sig-object py" id="joy.utils.generated_library.fourth">
 <span class="sig-prename descclassname"><span class="pre">joy.utils.generated_library.</span></span><span class="sig-name descname"><span class="pre">fourth</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#fourth"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.utils.generated_library.fourth" title="Permalink to this definition">¶</a></dt>
-<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="n">a4</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a4</span><span class="p">)</span>
+<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="n">a4</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a4</span><span class="p">)</span>
 </pre></div>
 </div>
 </dd></dl>
@@ -868,7 +860,7 @@ from each list.  The smallest list sets the length of the result list.</p>
 <dl class="py function">
 <dt class="sig sig-object py" id="joy.utils.generated_library.rest">
 <span class="sig-prename descclassname"><span class="pre">joy.utils.generated_library.</span></span><span class="sig-name descname"><span class="pre">rest</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#rest"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.utils.generated_library.rest" title="Permalink to this definition">¶</a></dt>
-<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="o">...</span><span class="mi">0</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">...</span><span class="mi">0</span><span class="p">])</span>
+<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="o">..</span><span class="mf">.0</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">..</span><span class="mf">.0</span><span class="p">])</span>
 </pre></div>
 </div>
 </dd></dl>
@@ -892,7 +884,7 @@ from each list.  The smallest list sets the length of the result list.</p>
 <dl class="py function">
 <dt class="sig sig-object py" id="joy.utils.generated_library.rrest">
 <span class="sig-prename descclassname"><span class="pre">joy.utils.generated_library.</span></span><span class="sig-name descname"><span class="pre">rrest</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#rrest"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.utils.generated_library.rrest" title="Permalink to this definition">¶</a></dt>
-<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">...</span><span class="mi">1</span><span class="p">])</span>
+<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">..</span><span class="mf">.1</span><span class="p">])</span>
 </pre></div>
 </div>
 </dd></dl>
@@ -900,7 +892,7 @@ from each list.  The smallest list sets the length of the result list.</p>
 <dl class="py function">
 <dt class="sig sig-object py" id="joy.utils.generated_library.second">
 <span class="sig-prename descclassname"><span class="pre">joy.utils.generated_library.</span></span><span class="sig-name descname"><span class="pre">second</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#second"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.utils.generated_library.second" title="Permalink to this definition">¶</a></dt>
-<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a2</span><span class="p">)</span>
+<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a2</span><span class="p">)</span>
 </pre></div>
 </div>
 </dd></dl>
@@ -932,7 +924,7 @@ from each list.  The smallest list sets the length of the result list.</p>
 <dl class="py function">
 <dt class="sig sig-object py" id="joy.utils.generated_library.swaack">
 <span class="sig-prename descclassname"><span class="pre">joy.utils.generated_library.</span></span><span class="sig-name descname"><span class="pre">swaack</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#swaack"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.utils.generated_library.swaack" title="Permalink to this definition">¶</a></dt>
-<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">...</span><span class="mi">0</span><span class="p">])</span>
+<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">..</span><span class="mf">.0</span><span class="p">])</span>
 </pre></div>
 </div>
 </dd></dl>
@@ -948,7 +940,7 @@ from each list.  The smallest list sets the length of the result list.</p>
 <dl class="py function">
 <dt class="sig sig-object py" id="joy.utils.generated_library.swons">
 <span class="sig-prename descclassname"><span class="pre">joy.utils.generated_library.</span></span><span class="sig-name descname"><span class="pre">swons</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#swons"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.utils.generated_library.swons" title="Permalink to this definition">¶</a></dt>
-<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">...</span><span class="mi">1</span><span class="p">])</span>
+<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">..</span><span class="mf">.1</span><span class="p">])</span>
 </pre></div>
 </div>
 </dd></dl>
@@ -956,7 +948,7 @@ from each list.  The smallest list sets the length of the result list.</p>
 <dl class="py function">
 <dt class="sig sig-object py" id="joy.utils.generated_library.third">
 <span class="sig-prename descclassname"><span class="pre">joy.utils.generated_library.</span></span><span class="sig-name descname"><span class="pre">third</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#third"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.utils.generated_library.third" title="Permalink to this definition">¶</a></dt>
-<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a3</span><span class="p">)</span>
+<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a3</span><span class="p">)</span>
 </pre></div>
 </div>
 </dd></dl>
@@ -972,7 +964,7 @@ from each list.  The smallest list sets the length of the result list.</p>
 <dl class="py function">
 <dt class="sig sig-object py" id="joy.utils.generated_library.uncons">
 <span class="sig-prename descclassname"><span class="pre">joy.utils.generated_library.</span></span><span class="sig-name descname"><span class="pre">uncons</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#uncons"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.utils.generated_library.uncons" title="Permalink to this definition">¶</a></dt>
-<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="o">...</span><span class="mi">0</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="p">[</span><span class="o">...</span><span class="mi">0</span><span class="p">])</span>
+<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="o">..</span><span class="mf">.0</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="p">[</span><span class="o">..</span><span class="mf">.0</span><span class="p">])</span>
 </pre></div>
 </div>
 </dd></dl>
@@ -988,7 +980,7 @@ from each list.  The smallest list sets the length of the result list.</p>
 <dl class="py function">
 <dt class="sig sig-object py" id="joy.utils.generated_library.unswons">
 <span class="sig-prename descclassname"><span class="pre">joy.utils.generated_library.</span></span><span class="sig-name descname"><span class="pre">unswons</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stack</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#unswons"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#joy.utils.generated_library.unswons" title="Permalink to this definition">¶</a></dt>
-<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a1</span><span class="p">)</span>
+<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="n">a1</span><span class="p">)</span>
 </pre></div>
 </div>
 </dd></dl>
@@ -1066,7 +1058,7 @@ from each list.  The smallest list sets the length of the result list.</p>
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/Categorical.html b/docs/sphinx_docs/_build/html/notebooks/Categorical.html
index 420e11c..7b2020f 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/Categorical.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Categorical.html
@@ -80,6 +80,7 @@
 <li class="toctree-l2"><a class="reference internal" href="Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
 <li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
 <li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html">Square Spiral Example Joy Code</a></li>
 <li class="toctree-l2"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a></li>
 <li class="toctree-l2"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a></li>
 <li class="toctree-l2"><a class="reference internal" href="TypeChecking.html">Type Checking</a></li>
@@ -130,7 +131,7 @@
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/Derivatives_of_Regular_Expressions.html b/docs/sphinx_docs/_build/html/notebooks/Derivatives_of_Regular_Expressions.html
index 34e24eb..fc0fd9c 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/Derivatives_of_Regular_Expressions.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Derivatives_of_Regular_Expressions.html
@@ -96,15 +96,15 @@ R∘λ = λ∘R = R
 </section>
 <section id="implementation">
 <h2>Implementation<a class="headerlink" href="#implementation" title="Permalink to this headline">¶</a></h2>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">partial</span> <span class="k">as</span> <span class="n">curry</span>
-<span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">product</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from functools import partial as curry
+from itertools import product
 </pre></div>
 </div>
 <section id="and">
 <h3><code class="docutils literal notranslate"><span class="pre">ϕ</span></code> and <code class="docutils literal notranslate"><span class="pre">λ</span></code><a class="headerlink" href="#and" title="Permalink to this headline">¶</a></h3>
 <p>The empty set and the set of just the empty string.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">phi</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">()</span>   <span class="c1"># ϕ</span>
-<span class="n">y</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;&#39;</span><span class="p">})</span> <span class="c1"># λ</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>phi = frozenset()   # ϕ
+y = frozenset({&#39;&#39;}) # λ
 </pre></div>
 </div>
 </section>
@@ -115,7 +115,7 @@ illustrate the algorithm and because you can represent any other
 alphabet with two symbols (if you had to.)</p>
 <p>I chose the names <code class="docutils literal notranslate"><span class="pre">O</span></code> and <code class="docutils literal notranslate"><span class="pre">l</span></code> (uppercase “o” and lowercase “L”) to
 look like <code class="docutils literal notranslate"><span class="pre">0</span></code> and <code class="docutils literal notranslate"><span class="pre">1</span></code> (zero and one) respectively.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">syms</span> <span class="o">=</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;0&#39;</span><span class="p">}),</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;1&#39;</span><span class="p">})</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>syms = O, l = frozenset({&#39;0&#39;}), frozenset({&#39;1&#39;})
 </pre></div>
 </div>
 </section>
@@ -133,7 +133,7 @@ expression</em> is one of:</p>
 </pre></div>
 </div>
 <p>Where <code class="docutils literal notranslate"><span class="pre">R</span></code> and <code class="docutils literal notranslate"><span class="pre">S</span></code> stand for <em>regular expressions</em>.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">AND</span><span class="p">,</span> <span class="n">CONS</span><span class="p">,</span> <span class="n">KSTAR</span><span class="p">,</span> <span class="n">NOT</span><span class="p">,</span> <span class="n">OR</span> <span class="o">=</span> <span class="s1">&#39;and cons * not or&#39;</span><span class="o">.</span><span class="n">split</span><span class="p">()</span>  <span class="c1"># Tags are just strings.</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>AND, CONS, KSTAR, NOT, OR = &#39;and cons * not or&#39;.split()  # Tags are just strings.
 </pre></div>
 </div>
 <p>Because they are formed of <code class="docutils literal notranslate"><span class="pre">frozenset</span></code>, <code class="docutils literal notranslate"><span class="pre">tuple</span></code> and <code class="docutils literal notranslate"><span class="pre">str</span></code> objects
@@ -141,36 +141,36 @@ only, these datastructures are immutable.</p>
 </section>
 <section id="string-representation-of-re-datastructures">
 <h3>String Representation of RE Datastructures<a class="headerlink" href="#string-representation-of-re-datastructures" title="Permalink to this headline">¶</a></h3>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
-    <span class="sd">&#39;&#39;&#39;</span>
-<span class="sd">    Return a nice string repr for a regular expression datastructure.</span>
-<span class="sd">    &#39;&#39;&#39;</span>
-    <span class="k">if</span> <span class="n">re</span> <span class="o">==</span> <span class="n">I</span><span class="p">:</span> <span class="k">return</span> <span class="s1">&#39;.&#39;</span>
-    <span class="k">if</span> <span class="n">re</span> <span class="ow">in</span> <span class="n">syms</span><span class="p">:</span> <span class="k">return</span> <span class="nb">next</span><span class="p">(</span><span class="nb">iter</span><span class="p">(</span><span class="n">re</span><span class="p">))</span>
-    <span class="k">if</span> <span class="n">re</span> <span class="o">==</span> <span class="n">y</span><span class="p">:</span> <span class="k">return</span> <span class="s1">&#39;^&#39;</span>
-    <span class="k">if</span> <span class="n">re</span> <span class="o">==</span> <span class="n">phi</span><span class="p">:</span> <span class="k">return</span> <span class="s1">&#39;X&#39;</span>
-
-    <span class="k">assert</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">re</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">),</span> <span class="nb">repr</span><span class="p">(</span><span class="n">re</span><span class="p">)</span>
-    <span class="n">tag</span> <span class="o">=</span> <span class="n">re</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
-
-    <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">KSTAR</span><span class="p">:</span>
-        <span class="n">body</span> <span class="o">=</span> <span class="n">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
-        <span class="k">if</span> <span class="ow">not</span> <span class="n">body</span><span class="p">:</span> <span class="k">return</span> <span class="n">body</span>
-        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">body</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span> <span class="k">return</span> <span class="s1">&#39;(&#39;</span> <span class="o">+</span> <span class="n">body</span> <span class="o">+</span> <span class="s2">&quot;)*&quot;</span>
-        <span class="k">return</span> <span class="n">body</span> <span class="o">+</span> <span class="s1">&#39;*&#39;</span>
-
-    <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">NOT</span><span class="p">:</span>
-        <span class="n">body</span> <span class="o">=</span> <span class="n">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
-        <span class="k">if</span> <span class="ow">not</span> <span class="n">body</span><span class="p">:</span> <span class="k">return</span> <span class="n">body</span>
-        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">body</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span> <span class="k">return</span> <span class="s1">&#39;(&#39;</span> <span class="o">+</span> <span class="n">body</span> <span class="o">+</span> <span class="s2">&quot;)&#39;&quot;</span>
-        <span class="k">return</span> <span class="n">body</span> <span class="o">+</span> <span class="s2">&quot;&#39;&quot;</span>
-
-    <span class="n">r</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
-    <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">CONS</span><span class="p">:</span> <span class="k">return</span> <span class="n">r</span> <span class="o">+</span> <span class="n">s</span>
-    <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">OR</span><span class="p">:</span>   <span class="k">return</span> <span class="s1">&#39;</span><span class="si">%s</span><span class="s1"> | </span><span class="si">%s</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">s</span><span class="p">)</span>
-    <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">AND</span><span class="p">:</span>  <span class="k">return</span> <span class="s1">&#39;(</span><span class="si">%s</span><span class="s1">) &amp; (</span><span class="si">%s</span><span class="s1">)&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">s</span><span class="p">)</span>
-
-    <span class="k">raise</span> <span class="ne">ValueError</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def stringy(re):
+    &#39;&#39;&#39;
+    Return a nice string repr for a regular expression datastructure.
+    &#39;&#39;&#39;
+    if re == I: return &#39;.&#39;
+    if re in syms: return next(iter(re))
+    if re == y: return &#39;^&#39;
+    if re == phi: return &#39;X&#39;
+
+    assert isinstance(re, tuple), repr(re)
+    tag = re[0]
+
+    if tag == KSTAR:
+        body = stringy(re[1])
+        if not body: return body
+        if len(body) &gt; 1: return &#39;(&#39; + body + &quot;)*&quot;
+        return body + &#39;*&#39;
+
+    if tag == NOT:
+        body = stringy(re[1])
+        if not body: return body
+        if len(body) &gt; 1: return &#39;(&#39; + body + &quot;)&#39;&quot;
+        return body + &quot;&#39;&quot;
+
+    r, s = stringy(re[1]), stringy(re[2])
+    if tag == CONS: return r + s
+    if tag == OR:   return &#39;%s | %s&#39; % (r, s)
+    if tag == AND:  return &#39;(%s) &amp; (%s)&#39; % (r, s)
+
+    raise ValueError
 </pre></div>
 </div>
 </section>
@@ -180,10 +180,10 @@ only, these datastructures are immutable.</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">I</span> <span class="o">=</span> <span class="p">(</span><span class="mi">0</span><span class="o">|</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">I</span> <span class="o">=</span> <span class="p">(</span><span class="n">KSTAR</span><span class="p">,</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>I = (KSTAR, (OR, O, l))
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">I</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print stringy(I)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">.</span>
@@ -193,57 +193,57 @@ only, these datastructures are immutable.</p>
 <section id="id1">
 <h3><code class="docutils literal notranslate"><span class="pre">(.111.)</span> <span class="pre">&amp;</span> <span class="pre">(.01</span> <span class="pre">+</span> <span class="pre">11*)'</span></code><a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h3>
 <p>The example expression from Brzozowski:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">+</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="mf">.111</span><span class="o">.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">(</span><span class="mf">.01</span> <span class="o">+</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;</span>
    <span class="n">a</span>    <span class="o">&amp;</span>  <span class="p">(</span><span class="n">b</span>  <span class="o">+</span>  <span class="n">c</span><span class="p">)</span><span class="s1">&#39;</span>
 </pre></div>
 </div>
 <p>Note that it contains one of everything.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">I</span><span class="p">))))</span>
-<span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
-<span class="n">c</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">KSTAR</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
-<span class="n">it</span> <span class="o">=</span> <span class="p">(</span><span class="n">AND</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">NOT</span><span class="p">,</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">)))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>a = (CONS, I, (CONS, l, (CONS, l, (CONS, l, I))))
+b = (CONS, I, (CONS, O, l))
+c = (CONS, l, (KSTAR, l))
+it = (AND, a, (NOT, (OR, b, c)))
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print stringy(it)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="mf">.111</span><span class="o">.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
 </pre></div>
 </div>
 </section>
 <section id="nully">
 <h3><code class="docutils literal notranslate"><span class="pre">nully()</span></code><a class="headerlink" href="#nully" title="Permalink to this headline">¶</a></h3>
 <p>Let’s get that auxiliary predicate function <code class="docutils literal notranslate"><span class="pre">δ</span></code> out of the way.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">nully</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
-    <span class="sd">&#39;&#39;&#39;</span>
-<span class="sd">    δ - Return λ if λ ⊆ R otherwise ϕ.</span>
-<span class="sd">    &#39;&#39;&#39;</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def nully(R):
+    &#39;&#39;&#39;
+    δ - Return λ if λ ⊆ R otherwise ϕ.
+    &#39;&#39;&#39;
 
-    <span class="c1"># δ(a) → ϕ</span>
-    <span class="c1"># δ(ϕ) → ϕ</span>
-    <span class="k">if</span> <span class="n">R</span> <span class="ow">in</span> <span class="n">syms</span> <span class="ow">or</span> <span class="n">R</span> <span class="o">==</span> <span class="n">phi</span><span class="p">:</span>
-        <span class="k">return</span> <span class="n">phi</span>
+    # δ(a) → ϕ
+    # δ(ϕ) → ϕ
+    if R in syms or R == phi:
+        return phi
 
-    <span class="c1"># δ(λ) → λ</span>
-    <span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="n">y</span><span class="p">:</span>
-        <span class="k">return</span> <span class="n">y</span>
+    # δ(λ) → λ
+    if R == y:
+        return y
 
-    <span class="n">tag</span> <span class="o">=</span> <span class="n">R</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+    tag = R[0]
 
-    <span class="c1"># δ(R*) → λ</span>
-    <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">KSTAR</span><span class="p">:</span>
-        <span class="k">return</span> <span class="n">y</span>
+    # δ(R*) → λ
+    if tag == KSTAR:
+        return y
 
-    <span class="c1"># δ(¬R) δ(R)≟ϕ → λ</span>
-    <span class="c1"># δ(¬R) δ(R)≟λ → ϕ</span>
-    <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">NOT</span><span class="p">:</span>
-        <span class="k">return</span> <span class="n">phi</span> <span class="k">if</span> <span class="n">nully</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="k">else</span> <span class="n">y</span>
+    # δ(¬R) δ(R)≟ϕ → λ
+    # δ(¬R) δ(R)≟λ → ϕ
+    if tag == NOT:
+        return phi if nully(R[1]) else y
 
-    <span class="c1"># δ(R∘S) → δ(R) ∧ δ(S)</span>
-    <span class="c1"># δ(R ∧ S) → δ(R) ∧ δ(S)</span>
-    <span class="c1"># δ(R ∨ S) → δ(R) ∨ δ(S)</span>
-    <span class="n">r</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">nully</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">nully</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
-    <span class="k">return</span> <span class="n">r</span> <span class="o">&amp;</span> <span class="n">s</span> <span class="k">if</span> <span class="n">tag</span> <span class="ow">in</span> <span class="p">{</span><span class="n">AND</span><span class="p">,</span> <span class="n">CONS</span><span class="p">}</span> <span class="k">else</span> <span class="n">r</span> <span class="o">|</span> <span class="n">s</span>
+    # δ(R∘S) → δ(R) ∧ δ(S)
+    # δ(R ∧ S) → δ(R) ∧ δ(S)
+    # δ(R ∨ S) → δ(R) ∨ δ(S)
+    r, s = nully(R[1]), nully(R[2])
+    return r &amp; s if tag in {AND, CONS} else r | s
 </pre></div>
 </div>
 </section>
@@ -252,71 +252,71 @@ only, these datastructures are immutable.</p>
 <p>This is the straightforward version with no “compaction”. It works fine,
 but does waaaay too much work because the expressions grow each
 derivation.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def D(symbol):
 
-    <span class="k">def</span> <span class="nf">derv</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
+    def derv(R):
 
-        <span class="c1"># ∂a(a) → λ</span>
-        <span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="p">{</span><span class="n">symbol</span><span class="p">}:</span>
-            <span class="k">return</span> <span class="n">y</span>
+        # ∂a(a) → λ
+        if R == {symbol}:
+            return y
 
-        <span class="c1"># ∂a(λ) → ϕ</span>
-        <span class="c1"># ∂a(ϕ) → ϕ</span>
-        <span class="c1"># ∂a(¬a) → ϕ</span>
-        <span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="n">y</span> <span class="ow">or</span> <span class="n">R</span> <span class="o">==</span> <span class="n">phi</span> <span class="ow">or</span> <span class="n">R</span> <span class="ow">in</span> <span class="n">syms</span><span class="p">:</span>
-            <span class="k">return</span> <span class="n">phi</span>
+        # ∂a(λ) → ϕ
+        # ∂a(ϕ) → ϕ
+        # ∂a(¬a) → ϕ
+        if R == y or R == phi or R in syms:
+            return phi
 
-        <span class="n">tag</span> <span class="o">=</span> <span class="n">R</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+        tag = R[0]
 
-        <span class="c1"># ∂a(R*) → ∂a(R)∘R*</span>
-        <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">KSTAR</span><span class="p">:</span>
-            <span class="k">return</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">R</span><span class="p">)</span>
+        # ∂a(R*) → ∂a(R)∘R*
+        if tag == KSTAR:
+            return (CONS, derv(R[1]), R)
 
-        <span class="c1"># ∂a(¬R) → ¬∂a(R)</span>
-        <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">NOT</span><span class="p">:</span>
-            <span class="k">return</span> <span class="p">(</span><span class="n">NOT</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">]))</span>
+        # ∂a(¬R) → ¬∂a(R)
+        if tag == NOT:
+            return (NOT, derv(R[1]))
 
-        <span class="n">r</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span>
+        r, s = R[1:]
 
-        <span class="c1"># ∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S)</span>
-        <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">CONS</span><span class="p">:</span>
-            <span class="n">A</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">r</span><span class="p">),</span> <span class="n">s</span><span class="p">)</span>  <span class="c1"># A = ∂a(R)∘S</span>
-            <span class="c1"># A ∨ δ(R) ∘ ∂a(S)</span>
-            <span class="c1"># A ∨  λ   ∘ ∂a(S) → A ∨ ∂a(S)</span>
-            <span class="c1"># A ∨  ϕ   ∘ ∂a(S) → A ∨ ϕ → A</span>
-            <span class="k">return</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">A</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">s</span><span class="p">))</span> <span class="k">if</span> <span class="n">nully</span><span class="p">(</span><span class="n">r</span><span class="p">)</span> <span class="k">else</span> <span class="n">A</span>
+        # ∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S)
+        if tag == CONS:
+            A = (CONS, derv(r), s)  # A = ∂a(R)∘S
+            # A ∨ δ(R) ∘ ∂a(S)
+            # A ∨  λ   ∘ ∂a(S) → A ∨ ∂a(S)
+            # A ∨  ϕ   ∘ ∂a(S) → A ∨ ϕ → A
+            return (OR, A, derv(s)) if nully(r) else A
 
-        <span class="c1"># ∂a(R ∧ S) → ∂a(R) ∧ ∂a(S)</span>
-        <span class="c1"># ∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)</span>
-        <span class="k">return</span> <span class="p">(</span><span class="n">tag</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">r</span><span class="p">),</span> <span class="n">derv</span><span class="p">(</span><span class="n">s</span><span class="p">))</span>
+        # ∂a(R ∧ S) → ∂a(R) ∧ ∂a(S)
+        # ∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)
+        return (tag, derv(r), derv(s))
 
-    <span class="k">return</span> <span class="n">derv</span>
+    return derv
 </pre></div>
 </div>
 </section>
 <section id="compaction-rules">
 <h3>Compaction Rules<a class="headerlink" href="#compaction-rules" title="Permalink to this headline">¶</a></h3>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">_compaction_rule</span><span class="p">(</span><span class="n">relation</span><span class="p">,</span> <span class="n">one</span><span class="p">,</span> <span class="n">zero</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
-    <span class="k">return</span> <span class="p">(</span>
-        <span class="n">b</span> <span class="k">if</span> <span class="n">a</span> <span class="o">==</span> <span class="n">one</span> <span class="k">else</span>  <span class="c1"># R*1 = 1*R = R</span>
-        <span class="n">a</span> <span class="k">if</span> <span class="n">b</span> <span class="o">==</span> <span class="n">one</span> <span class="k">else</span>
-        <span class="n">zero</span> <span class="k">if</span> <span class="n">a</span> <span class="o">==</span> <span class="n">zero</span> <span class="ow">or</span> <span class="n">b</span> <span class="o">==</span> <span class="n">zero</span> <span class="k">else</span>  <span class="c1"># R*0 = 0*R = 0</span>
-        <span class="p">(</span><span class="n">relation</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
-        <span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def _compaction_rule(relation, one, zero, a, b):
+    return (
+        b if a == one else  # R*1 = 1*R = R
+        a if b == one else
+        zero if a == zero or b == zero else  # R*0 = 0*R = 0
+        (relation, a, b)
+        )
 </pre></div>
 </div>
 <p>An elegant symmetry.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># R ∧ I = I ∧ R = R</span>
-<span class="c1"># R ∧ ϕ = ϕ ∧ R = ϕ</span>
-<span class="n">_and</span> <span class="o">=</span> <span class="n">curry</span><span class="p">(</span><span class="n">_compaction_rule</span><span class="p">,</span> <span class="n">AND</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span># R ∧ I = I ∧ R = R
+# R ∧ ϕ = ϕ ∧ R = ϕ
+_and = curry(_compaction_rule, AND, I, phi)
 
-<span class="c1"># R ∨ ϕ = ϕ ∨ R = R</span>
-<span class="c1"># R ∨ I = I ∨ R = I</span>
-<span class="n">_or</span> <span class="o">=</span> <span class="n">curry</span><span class="p">(</span><span class="n">_compaction_rule</span><span class="p">,</span> <span class="n">OR</span><span class="p">,</span> <span class="n">phi</span><span class="p">,</span> <span class="n">I</span><span class="p">)</span>
+# R ∨ ϕ = ϕ ∨ R = R
+# R ∨ I = I ∨ R = I
+_or = curry(_compaction_rule, OR, phi, I)
 
-<span class="c1"># R∘λ = λ∘R = R</span>
-<span class="c1"># R∘ϕ = ϕ∘R = ϕ</span>
-<span class="n">_cons</span> <span class="o">=</span> <span class="n">curry</span><span class="p">(</span><span class="n">_compaction_rule</span><span class="p">,</span> <span class="n">CONS</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
+# R∘λ = λ∘R = R
+# R∘ϕ = ϕ∘R = ϕ
+_cons = curry(_compaction_rule, CONS, y, phi)
 </pre></div>
 </div>
 </section>
@@ -325,21 +325,21 @@ derivation.</p>
 <p>We can save re-processing by remembering results we have already
 computed. RE datastructures are immutable and the <code class="docutils literal notranslate"><span class="pre">derv()</span></code> functions
 are <em>pure</em> so this is fine.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">Memo</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>class Memo(object):
 
-    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">):</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">f</span> <span class="o">=</span> <span class="n">f</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">calls</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hits</span> <span class="o">=</span> <span class="mi">0</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">mem</span> <span class="o">=</span> <span class="p">{}</span>
+    def __init__(self, f):
+        self.f = f
+        self.calls = self.hits = 0
+        self.mem = {}
 
-    <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">):</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">calls</span> <span class="o">+=</span> <span class="mi">1</span>
-        <span class="k">try</span><span class="p">:</span>
-            <span class="n">result</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">mem</span><span class="p">[</span><span class="n">key</span><span class="p">]</span>
-            <span class="bp">self</span><span class="o">.</span><span class="n">hits</span> <span class="o">+=</span> <span class="mi">1</span>
-        <span class="k">except</span> <span class="ne">KeyError</span><span class="p">:</span>
-            <span class="n">result</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">mem</span><span class="p">[</span><span class="n">key</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">f</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
-        <span class="k">return</span> <span class="n">result</span>
+    def __call__(self, key):
+        self.calls += 1
+        try:
+            result = self.mem[key]
+            self.hits += 1
+        except KeyError:
+            result = self.mem[key] = self.f(key)
+        return result
 </pre></div>
 </div>
 </section>
@@ -347,47 +347,47 @@ are <em>pure</em> so this is fine.</p>
 <h3>With “Compaction”<a class="headerlink" href="#with-compaction" title="Permalink to this headline">¶</a></h3>
 <p>This version uses the rules above to perform compaction. It keeps the
 expressions from growing too large.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D_compaction</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def D_compaction(symbol):
 
-    <span class="nd">@Memo</span>
-    <span class="k">def</span> <span class="nf">derv</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
+    @Memo
+    def derv(R):
 
-        <span class="c1"># ∂a(a) → λ</span>
-        <span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="p">{</span><span class="n">symbol</span><span class="p">}:</span>
-            <span class="k">return</span> <span class="n">y</span>
+        # ∂a(a) → λ
+        if R == {symbol}:
+            return y
 
-        <span class="c1"># ∂a(λ) → ϕ</span>
-        <span class="c1"># ∂a(ϕ) → ϕ</span>
-        <span class="c1"># ∂a(¬a) → ϕ</span>
-        <span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="n">y</span> <span class="ow">or</span> <span class="n">R</span> <span class="o">==</span> <span class="n">phi</span> <span class="ow">or</span> <span class="n">R</span> <span class="ow">in</span> <span class="n">syms</span><span class="p">:</span>
-            <span class="k">return</span> <span class="n">phi</span>
+        # ∂a(λ) → ϕ
+        # ∂a(ϕ) → ϕ
+        # ∂a(¬a) → ϕ
+        if R == y or R == phi or R in syms:
+            return phi
 
-        <span class="n">tag</span> <span class="o">=</span> <span class="n">R</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+        tag = R[0]
 
-        <span class="c1"># ∂a(R*) → ∂a(R)∘R*</span>
-        <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">KSTAR</span><span class="p">:</span>
-            <span class="k">return</span> <span class="n">_cons</span><span class="p">(</span><span class="n">derv</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">R</span><span class="p">)</span>
+        # ∂a(R*) → ∂a(R)∘R*
+        if tag == KSTAR:
+            return _cons(derv(R[1]), R)
 
-        <span class="c1"># ∂a(¬R) → ¬∂a(R)</span>
-        <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">NOT</span><span class="p">:</span>
-            <span class="k">return</span> <span class="p">(</span><span class="n">NOT</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">]))</span>
+        # ∂a(¬R) → ¬∂a(R)
+        if tag == NOT:
+            return (NOT, derv(R[1]))
 
-        <span class="n">r</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">R</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span>
+        r, s = R[1:]
 
-        <span class="c1"># ∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S)</span>
-        <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">CONS</span><span class="p">:</span>
-            <span class="n">A</span> <span class="o">=</span> <span class="n">_cons</span><span class="p">(</span><span class="n">derv</span><span class="p">(</span><span class="n">r</span><span class="p">),</span> <span class="n">s</span><span class="p">)</span>  <span class="c1"># A = ∂a(r)∘s</span>
-            <span class="c1"># A ∨ δ(R) ∘ ∂a(S)</span>
-            <span class="c1"># A ∨  λ   ∘ ∂a(S) → A ∨ ∂a(S)</span>
-            <span class="c1"># A ∨  ϕ   ∘ ∂a(S) → A ∨ ϕ → A</span>
-            <span class="k">return</span> <span class="n">_or</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">derv</span><span class="p">(</span><span class="n">s</span><span class="p">))</span> <span class="k">if</span> <span class="n">nully</span><span class="p">(</span><span class="n">r</span><span class="p">)</span> <span class="k">else</span> <span class="n">A</span>
+        # ∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S)
+        if tag == CONS:
+            A = _cons(derv(r), s)  # A = ∂a(r)∘s
+            # A ∨ δ(R) ∘ ∂a(S)
+            # A ∨  λ   ∘ ∂a(S) → A ∨ ∂a(S)
+            # A ∨  ϕ   ∘ ∂a(S) → A ∨ ϕ → A
+            return _or(A, derv(s)) if nully(r) else A
 
-        <span class="c1"># ∂a(R ∧ S) → ∂a(R) ∧ ∂a(S)</span>
-        <span class="c1"># ∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)</span>
-        <span class="n">dr</span><span class="p">,</span> <span class="n">ds</span> <span class="o">=</span> <span class="n">derv</span><span class="p">(</span><span class="n">r</span><span class="p">),</span> <span class="n">derv</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
-        <span class="k">return</span> <span class="n">_and</span><span class="p">(</span><span class="n">dr</span><span class="p">,</span> <span class="n">ds</span><span class="p">)</span> <span class="k">if</span> <span class="n">tag</span> <span class="o">==</span> <span class="n">AND</span> <span class="k">else</span> <span class="n">_or</span><span class="p">(</span><span class="n">dr</span><span class="p">,</span> <span class="n">ds</span><span class="p">)</span>
+        # ∂a(R ∧ S) → ∂a(R) ∧ ∂a(S)
+        # ∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)
+        dr, ds = derv(r), derv(s)
+        return _and(dr, ds) if tag == AND else _or(dr, ds)
 
-    <span class="k">return</span> <span class="n">derv</span>
+    return derv
 </pre></div>
 </div>
 </section>
@@ -395,59 +395,59 @@ expressions from growing too large.</p>
 <section id="lets-try-it-out">
 <h2>Let’s try it out…<a class="headerlink" href="#lets-try-it-out" title="Permalink to this headline">¶</a></h2>
 <p>(FIXME: redo.)</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">o</span><span class="p">,</span> <span class="n">z</span> <span class="o">=</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;0&#39;</span><span class="p">),</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;1&#39;</span><span class="p">)</span>
-<span class="n">REs</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
-<span class="n">N</span> <span class="o">=</span> <span class="mi">5</span>
-<span class="n">names</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">product</span><span class="p">(</span><span class="o">*</span><span class="p">(</span><span class="n">N</span> <span class="o">*</span> <span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)])))</span>
-<span class="n">dervs</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">product</span><span class="p">(</span><span class="o">*</span><span class="p">(</span><span class="n">N</span> <span class="o">*</span> <span class="p">[(</span><span class="n">o</span><span class="p">,</span> <span class="n">z</span><span class="p">)])))</span>
-<span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">ds</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">names</span><span class="p">,</span> <span class="n">dervs</span><span class="p">):</span>
-    <span class="n">R</span> <span class="o">=</span> <span class="n">it</span>
-    <span class="n">ds</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">ds</span><span class="p">)</span>
-    <span class="k">while</span> <span class="n">ds</span><span class="p">:</span>
-        <span class="n">R</span> <span class="o">=</span> <span class="n">ds</span><span class="o">.</span><span class="n">pop</span><span class="p">()(</span><span class="n">R</span><span class="p">)</span>
-        <span class="k">if</span> <span class="n">R</span> <span class="o">==</span> <span class="n">phi</span> <span class="ow">or</span> <span class="n">R</span> <span class="o">==</span> <span class="n">I</span><span class="p">:</span>
-            <span class="k">break</span>
-        <span class="n">REs</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">R</span><span class="p">)</span>
-
-<span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">it</span><span class="p">)</span> <span class="p">;</span> <span class="nb">print</span>
-<span class="nb">print</span> <span class="n">o</span><span class="o">.</span><span class="n">hits</span><span class="p">,</span> <span class="s1">&#39;/&#39;</span><span class="p">,</span> <span class="n">o</span><span class="o">.</span><span class="n">calls</span>
-<span class="nb">print</span> <span class="n">z</span><span class="o">.</span><span class="n">hits</span><span class="p">,</span> <span class="s1">&#39;/&#39;</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">calls</span>
-<span class="nb">print</span>
-<span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">stringy</span><span class="p">,</span> <span class="n">REs</span><span class="p">),</span> <span class="n">key</span><span class="o">=</span><span class="k">lambda</span> <span class="n">n</span><span class="p">:</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">n</span><span class="p">),</span> <span class="n">n</span><span class="p">)):</span>
-    <span class="nb">print</span> <span class="n">s</span>
-</pre></div>
-</div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>o, z = D_compaction(&#39;0&#39;), D_compaction(&#39;1&#39;)
+REs = set()
+N = 5
+names = list(product(*(N * [(0, 1)])))
+dervs = list(product(*(N * [(o, z)])))
+for name, ds in zip(names, dervs):
+    R = it
+    ds = list(ds)
+    while ds:
+        R = ds.pop()(R)
+        if R == phi or R == I:
+            break
+        REs.add(R)
+
+print stringy(it) ; print
+print o.hits, &#39;/&#39;, o.calls
+print z.hits, &#39;/&#39;, z.calls
+print
+for s in sorted(map(stringy, REs), key=lambda n: (len(n), n)):
+    print s
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="mf">.111</span><span class="o">.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
 
 <span class="mi">92</span> <span class="o">/</span> <span class="mi">122</span>
 <span class="mi">92</span> <span class="o">/</span> <span class="mi">122</span>
 
-<span class="p">(</span><span class="o">.</span><span class="mi">01</span><span class="p">)</span><span class="s1">&#39;</span>
-<span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="p">)</span><span class="s1">&#39;</span>
-<span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="o">^</span><span class="p">)</span><span class="s1">&#39;</span>
-<span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;</span>
-<span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="p">)</span><span class="s1">&#39;)</span>
-<span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="o">^</span><span class="p">)</span><span class="s1">&#39;)</span>
-<span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span><span class="p">)</span><span class="s1">&#39;)</span>
-<span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
-<span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
+<span class="p">(</span><span class="mf">.01</span><span class="p">)</span><span class="s1">&#39;</span>
+<span class="p">(</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">1</span><span class="p">)</span><span class="s1">&#39;</span>
+<span class="p">(</span><span class="mf">.01</span> <span class="o">|</span> <span class="o">^</span><span class="p">)</span><span class="s1">&#39;</span>
+<span class="p">(</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;</span>
+<span class="p">(</span><span class="mf">.111</span><span class="o">.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">1</span><span class="p">)</span><span class="s1">&#39;)</span>
+<span class="p">(</span><span class="mf">.111</span><span class="o">.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span> <span class="o">|</span> <span class="o">^</span><span class="p">)</span><span class="s1">&#39;)</span>
+<span class="p">(</span><span class="mf">.111</span><span class="o">.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span><span class="p">)</span><span class="s1">&#39;)</span>
+<span class="p">(</span><span class="mf">.111</span><span class="o">.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
+<span class="p">(</span><span class="mf">.111</span><span class="o">.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
 </pre></div>
 </div>
 <p>Should match:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="mf">.111</span><span class="o">.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
 
 <span class="mi">92</span> <span class="o">/</span> <span class="mi">122</span>
 <span class="mi">92</span> <span class="o">/</span> <span class="mi">122</span>
 
-<span class="p">(</span><span class="o">.</span><span class="mi">01</span>     <span class="p">)</span><span class="s1">&#39;</span>
-<span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span> <span class="p">)</span><span class="s1">&#39;</span>
-<span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="o">^</span> <span class="p">)</span><span class="s1">&#39;</span>
-<span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;</span>
-<span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span>            <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span> <span class="p">)</span><span class="s1">&#39;)</span>
-<span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span>      <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="o">^</span> <span class="p">)</span><span class="s1">&#39;)</span>
-<span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span>      <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
-<span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span>     <span class="p">)</span><span class="s1">&#39;)</span>
-<span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
+<span class="p">(</span><span class="mf">.01</span>     <span class="p">)</span><span class="s1">&#39;</span>
+<span class="p">(</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">1</span> <span class="p">)</span><span class="s1">&#39;</span>
+<span class="p">(</span><span class="mf">.01</span> <span class="o">|</span> <span class="o">^</span> <span class="p">)</span><span class="s1">&#39;</span>
+<span class="p">(</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;</span>
+<span class="p">(</span><span class="mf">.111</span><span class="o">.</span><span class="p">)</span>            <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">1</span> <span class="p">)</span><span class="s1">&#39;)</span>
+<span class="p">(</span><span class="mf">.111</span><span class="o">.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span>      <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span> <span class="o">|</span> <span class="o">^</span> <span class="p">)</span><span class="s1">&#39;)</span>
+<span class="p">(</span><span class="mf">.111</span><span class="o">.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span>      <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
+<span class="p">(</span><span class="mf">.111</span><span class="o">.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span>     <span class="p">)</span><span class="s1">&#39;)</span>
+<span class="p">(</span><span class="mf">.111</span><span class="o">.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
 </pre></div>
 </div>
 </section>
@@ -495,7 +495,7 @@ for now.</p>
 <h2>State Machine<a class="headerlink" href="#state-machine" title="Permalink to this headline">¶</a></h2>
 <p>We can drive the regular expressions to flesh out the underlying state
 machine transition table.</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">.</span><span class="mf">111.</span> <span class="o">&amp;</span> <span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">+</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">.111</span><span class="o">.</span> <span class="o">&amp;</span> <span class="p">(</span><span class="mf">.01</span> <span class="o">+</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;</span>
 </pre></div>
 </div>
 <p>Says, “Three or more 1’s and not ending in 01 nor composed of all 1’s.”</p>
@@ -540,60 +540,60 @@ a --1--&gt; ∂1(a)
 </div>
 <p>And so on, each new unique RE is a new state in the FSM table.</p>
 <p>Here are the derived REs at each state:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
-<span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="p">)</span><span class="s1">&#39;)</span>
-<span class="n">c</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
-<span class="n">d</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="o">^</span><span class="p">)</span><span class="s1">&#39;)</span>
-<span class="n">e</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
-<span class="n">f</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mf">111.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span><span class="p">)</span><span class="s1">&#39;)</span>
-<span class="n">g</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;</span>
-<span class="n">h</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mi">01</span><span class="p">)</span><span class="s1">&#39;</span>
-<span class="n">i</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">1</span><span class="p">)</span><span class="s1">&#39;</span>
-<span class="n">j</span> <span class="o">=</span> <span class="p">(</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="o">^</span><span class="p">)</span><span class="s1">&#39;</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="mf">.111</span><span class="o">.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
+<span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="mf">.111</span><span class="o">.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">1</span><span class="p">)</span><span class="s1">&#39;)</span>
+<span class="n">c</span> <span class="o">=</span> <span class="p">(</span><span class="mf">.111</span><span class="o">.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
+<span class="n">d</span> <span class="o">=</span> <span class="p">(</span><span class="mf">.111</span><span class="o">.</span> <span class="o">|</span> <span class="mf">11.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span> <span class="o">|</span> <span class="o">^</span><span class="p">)</span><span class="s1">&#39;)</span>
+<span class="n">e</span> <span class="o">=</span> <span class="p">(</span><span class="mf">.111</span><span class="o">.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
+<span class="n">f</span> <span class="o">=</span> <span class="p">(</span><span class="mf">.111</span><span class="o">.</span> <span class="o">|</span> <span class="mf">11.</span> <span class="o">|</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="mf">.01</span><span class="p">)</span><span class="s1">&#39;)</span>
+<span class="n">g</span> <span class="o">=</span> <span class="p">(</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">1</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;</span>
+<span class="n">h</span> <span class="o">=</span> <span class="p">(</span><span class="mf">.01</span><span class="p">)</span><span class="s1">&#39;</span>
+<span class="n">i</span> <span class="o">=</span> <span class="p">(</span><span class="mf">.01</span> <span class="o">|</span> <span class="mi">1</span><span class="p">)</span><span class="s1">&#39;</span>
+<span class="n">j</span> <span class="o">=</span> <span class="p">(</span><span class="mf">.01</span> <span class="o">|</span> <span class="o">^</span><span class="p">)</span><span class="s1">&#39;</span>
 </pre></div>
 </div>
 <p>You can see the one-way nature of the <code class="docutils literal notranslate"><span class="pre">g</span></code> state and the <code class="docutils literal notranslate"><span class="pre">hij</span></code> “trap”
 in the way that the <code class="docutils literal notranslate"><span class="pre">.111.</span></code> on the left-hand side of the <code class="docutils literal notranslate"><span class="pre">&amp;</span></code>
 disappears once it has been matched.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
-<span class="kn">from</span> <span class="nn">pprint</span> <span class="kn">import</span> <span class="n">pprint</span>
-<span class="kn">from</span> <span class="nn">string</span> <span class="kn">import</span> <span class="n">ascii_lowercase</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from collections import defaultdict
+from pprint import pprint
+from string import ascii_lowercase
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">d0</span><span class="p">,</span> <span class="n">d1</span> <span class="o">=</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;0&#39;</span><span class="p">),</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;1&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>d0, d1 = D_compaction(&#39;0&#39;), D_compaction(&#39;1&#39;)
 </pre></div>
 </div>
 </section>
 <section id="explore">
 <h3><code class="docutils literal notranslate"><span class="pre">explore()</span></code><a class="headerlink" href="#explore" title="Permalink to this headline">¶</a></h3>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">explore</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def explore(re):
 
-    <span class="c1"># Don&#39;t have more than 26 states...</span>
-    <span class="n">names</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="nb">iter</span><span class="p">(</span><span class="n">ascii_lowercase</span><span class="p">)</span><span class="o">.</span><span class="n">next</span><span class="p">)</span>
+    # Don&#39;t have more than 26 states...
+    names = defaultdict(iter(ascii_lowercase).next)
 
-    <span class="n">table</span><span class="p">,</span> <span class="n">accepting</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(),</span> <span class="nb">set</span><span class="p">()</span>
+    table, accepting = dict(), set()
 
-    <span class="n">to_check</span> <span class="o">=</span> <span class="p">{</span><span class="n">re</span><span class="p">}</span>
-    <span class="k">while</span> <span class="n">to_check</span><span class="p">:</span>
+    to_check = {re}
+    while to_check:
 
-        <span class="n">re</span> <span class="o">=</span> <span class="n">to_check</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
-        <span class="n">state_name</span> <span class="o">=</span> <span class="n">names</span><span class="p">[</span><span class="n">re</span><span class="p">]</span>
+        re = to_check.pop()
+        state_name = names[re]
 
-        <span class="k">if</span> <span class="p">(</span><span class="n">state_name</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="ow">in</span> <span class="n">table</span><span class="p">:</span>
-            <span class="k">continue</span>
+        if (state_name, 0) in table:
+            continue
 
-        <span class="k">if</span> <span class="n">nully</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
-            <span class="n">accepting</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">state_name</span><span class="p">)</span>
+        if nully(re):
+            accepting.add(state_name)
 
-        <span class="n">o</span><span class="p">,</span> <span class="n">i</span> <span class="o">=</span> <span class="n">d0</span><span class="p">(</span><span class="n">re</span><span class="p">),</span> <span class="n">d1</span><span class="p">(</span><span class="n">re</span><span class="p">)</span>
-        <span class="n">table</span><span class="p">[</span><span class="n">state_name</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">names</span><span class="p">[</span><span class="n">o</span><span class="p">]</span> <span class="p">;</span> <span class="n">to_check</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">o</span><span class="p">)</span>
-        <span class="n">table</span><span class="p">[</span><span class="n">state_name</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">names</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="p">;</span> <span class="n">to_check</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+        o, i = d0(re), d1(re)
+        table[state_name, 0] = names[o] ; to_check.add(o)
+        table[state_name, 1] = names[i] ; to_check.add(i)
 
-    <span class="k">return</span> <span class="n">table</span><span class="p">,</span> <span class="n">accepting</span>
+    return table, accepting
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span> <span class="o">=</span> <span class="n">explore</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>
-<span class="n">table</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>table, accepting = explore(it)
+table
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{(</span><span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="mi">0</span><span class="p">):</span> <span class="s1">&#39;b&#39;</span><span class="p">,</span>
@@ -618,7 +618,7 @@ disappears once it has been matched.</p>
  <span class="p">(</span><span class="s1">&#39;j&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">):</span> <span class="s1">&#39;h&#39;</span><span class="p">}</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">accepting</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>accepting
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="s1">&#39;h&#39;</span><span class="p">,</span> <span class="s1">&#39;i&#39;</span><span class="p">}</span>
@@ -629,31 +629,31 @@ disappears once it has been matched.</p>
 <h3>Generate Diagram<a class="headerlink" href="#generate-diagram" title="Permalink to this headline">¶</a></h3>
 <p>Once we have the FSM table and the set of accepting states we can
 generate the diagram above.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">_template</span> <span class="o">=</span> <span class="s1">&#39;&#39;&#39;</span><span class="se">\</span>
-<span class="s1">digraph finite_state_machine {</span>
-<span class="s1">  rankdir=LR;</span>
-<span class="s1">  size=&quot;8,5&quot;</span>
-<span class="s1">  node [shape = doublecircle]; </span><span class="si">%s</span><span class="s1">;</span>
-<span class="s1">  node [shape = circle];</span>
-<span class="si">%s</span><span class="s1"></span>
-<span class="s1">}</span>
-<span class="s1">&#39;&#39;&#39;</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>_template = &#39;&#39;&#39;\
+digraph finite_state_machine {
+  rankdir=LR;
+  size=&quot;8,5&quot;
+  node [shape = doublecircle]; %s;
+  node [shape = circle];
+%s
+}
+&#39;&#39;&#39;
 
-<span class="k">def</span> <span class="nf">link</span><span class="p">(</span><span class="n">fr</span><span class="p">,</span> <span class="n">nm</span><span class="p">,</span> <span class="n">label</span><span class="p">):</span>
-    <span class="k">return</span> <span class="s1">&#39;  </span><span class="si">%s</span><span class="s1"> -&gt; </span><span class="si">%s</span><span class="s1"> [ label = &quot;</span><span class="si">%s</span><span class="s1">&quot; ];&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">fr</span><span class="p">,</span> <span class="n">nm</span><span class="p">,</span> <span class="n">label</span><span class="p">)</span>
+def link(fr, nm, label):
+    return &#39;  %s -&gt; %s [ label = &quot;%s&quot; ];&#39; % (fr, nm, label)
 
 
-<span class="k">def</span> <span class="nf">make_graph</span><span class="p">(</span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span><span class="p">):</span>
-    <span class="k">return</span> <span class="n">_template</span> <span class="o">%</span> <span class="p">(</span>
-        <span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">accepting</span><span class="p">),</span>
-        <span class="s1">&#39;</span><span class="se">\n</span><span class="s1">&#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span>
-          <span class="n">link</span><span class="p">(</span><span class="n">from_</span><span class="p">,</span> <span class="n">to</span><span class="p">,</span> <span class="n">char</span><span class="p">)</span>
-          <span class="k">for</span> <span class="p">(</span><span class="n">from_</span><span class="p">,</span> <span class="n">char</span><span class="p">),</span> <span class="p">(</span><span class="n">to</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">table</span><span class="o">.</span><span class="n">iteritems</span><span class="p">())</span>
-          <span class="p">)</span>
-        <span class="p">)</span>
+def make_graph(table, accepting):
+    return _template % (
+        &#39; &#39;.join(accepting),
+        &#39;\n&#39;.join(
+          link(from_, to, char)
+          for (from_, char), (to) in sorted(table.iteritems())
+          )
+        )
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">make_graph</span><span class="p">(</span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print make_graph(table, accepting)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">digraph</span> <span class="n">finite_state_machine</span> <span class="p">{</span>
@@ -699,14 +699,14 @@ hard-code the information in the table into a little patch of branches.</p>
 <h4>Trampoline Function<a class="headerlink" href="#trampoline-function" title="Permalink to this headline">¶</a></h4>
 <p>Python has no GOTO statement but we can fake it with a “trampoline”
 function.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">trampoline</span><span class="p">(</span><span class="n">input_</span><span class="p">,</span> <span class="n">jump_from</span><span class="p">,</span> <span class="n">accepting</span><span class="p">):</span>
-    <span class="n">I</span> <span class="o">=</span> <span class="nb">iter</span><span class="p">(</span><span class="n">input_</span><span class="p">)</span>
-    <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
-        <span class="k">try</span><span class="p">:</span>
-            <span class="n">bounce_to</span> <span class="o">=</span> <span class="n">jump_from</span><span class="p">(</span><span class="n">I</span><span class="p">)</span>
-        <span class="k">except</span> <span class="ne">StopIteration</span><span class="p">:</span>
-            <span class="k">return</span> <span class="n">jump_from</span> <span class="ow">in</span> <span class="n">accepting</span>
-        <span class="n">jump_from</span> <span class="o">=</span> <span class="n">bounce_to</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def trampoline(input_, jump_from, accepting):
+    I = iter(input_)
+    while True:
+        try:
+            bounce_to = jump_from(I)
+        except StopIteration:
+            return jump_from in accepting
+        jump_from = bounce_to
 </pre></div>
 </div>
 </section>
@@ -714,17 +714,17 @@ function.</p>
 <h4>Stream Functions<a class="headerlink" href="#stream-functions" title="Permalink to this headline">¶</a></h4>
 <p>Little helpers to process the iterator of our data (a “stream” of “1”
 and “0” characters, not bits.)</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">getch</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="nb">int</span><span class="p">(</span><span class="nb">next</span><span class="p">(</span><span class="n">I</span><span class="p">))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>getch = lambda I: int(next(I))
 
 
-<span class="k">def</span> <span class="nf">_1</span><span class="p">(</span><span class="n">I</span><span class="p">):</span>
-    <span class="sd">&#39;&#39;&#39;Loop on ones.&#39;&#39;&#39;</span>
-    <span class="k">while</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">):</span> <span class="k">pass</span>
+def _1(I):
+    &#39;&#39;&#39;Loop on ones.&#39;&#39;&#39;
+    while getch(I): pass
 
 
-<span class="k">def</span> <span class="nf">_0</span><span class="p">(</span><span class="n">I</span><span class="p">):</span>
-    <span class="sd">&#39;&#39;&#39;Loop on zeros.&#39;&#39;&#39;</span>
-    <span class="k">while</span> <span class="ow">not</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">):</span> <span class="k">pass</span>
+def _0(I):
+    &#39;&#39;&#39;Loop on zeros.&#39;&#39;&#39;
+    while not getch(I): pass
 </pre></div>
 </div>
 </section>
@@ -735,28 +735,28 @@ and “0” characters, not bits.)</p>
 code. (You have to imagine that these are GOTO statements in C or
 branches in assembly and that the state names are branch destination
 labels.)</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">c</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
-<span class="n">b</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">_0</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="ow">or</span> <span class="n">d</span>
-<span class="n">c</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">e</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
-<span class="n">d</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">f</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
-<span class="n">e</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">g</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
-<span class="n">f</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">h</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
-<span class="n">g</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">_1</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="ow">or</span> <span class="n">i</span>
-<span class="n">h</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">_1</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="ow">or</span> <span class="n">i</span>
-<span class="n">i</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">_0</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="ow">or</span> <span class="n">j</span>
-<span class="n">j</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">h</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">i</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>a = lambda I: c if getch(I) else b
+b = lambda I: _0(I) or d
+c = lambda I: e if getch(I) else b
+d = lambda I: f if getch(I) else b
+e = lambda I: g if getch(I) else b
+f = lambda I: h if getch(I) else b
+g = lambda I: _1(I) or i
+h = lambda I: _1(I) or i
+i = lambda I: _0(I) or j
+j = lambda I: h if getch(I) else i
 </pre></div>
 </div>
 <p>Note that the implementations of <code class="docutils literal notranslate"><span class="pre">h</span></code> and <code class="docutils literal notranslate"><span class="pre">g</span></code> are identical ergo
 <code class="docutils literal notranslate"><span class="pre">h</span> <span class="pre">=</span> <span class="pre">g</span></code> and we could eliminate one in the code but <code class="docutils literal notranslate"><span class="pre">h</span></code> is an
 accepting state and <code class="docutils literal notranslate"><span class="pre">g</span></code> isn’t.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">acceptable</span><span class="p">(</span><span class="n">input_</span><span class="p">):</span>
-    <span class="k">return</span> <span class="n">trampoline</span><span class="p">(</span><span class="n">input_</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="p">{</span><span class="n">h</span><span class="p">,</span> <span class="n">i</span><span class="p">})</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def acceptable(input_):
+    return trampoline(input_, a, {h, i})
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="o">**</span><span class="mi">5</span><span class="p">):</span>
-    <span class="n">s</span> <span class="o">=</span> <span class="nb">bin</span><span class="p">(</span><span class="n">n</span><span class="p">)[</span><span class="mi">2</span><span class="p">:]</span>
-    <span class="nb">print</span> <span class="s1">&#39;</span><span class="si">%05s</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">s</span><span class="p">,</span> <span class="n">acceptable</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for n in range(2**5):
+    s = bin(n)[2:]
+    print &#39;%05s&#39; % s, acceptable(s)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>    <span class="mi">0</span> <span class="kc">False</span>
@@ -928,7 +928,7 @@ derivative-with-respect-to-N of some other state/RE:</p>
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/Developing.html b/docs/sphinx_docs/_build/html/notebooks/Developing.html
index 164db0d..6a2808e 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/Developing.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Developing.html
@@ -13,7 +13,7 @@
     <script src="../_static/jquery.js"></script>
     <script src="../_static/underscore.js"></script>
     <script src="../_static/doctools.js"></script>
-    <script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
+    <script async="async" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
     <link rel="next" title="Quadratic formula" href="Quadratic.html" />
@@ -113,7 +113,7 @@ these differences to the counter one-by-one in a loop.</p>
 go we need a function that will accept the sum, the counter, and the
 next term to add, and that adds the term to the counter and a copy of
 the counter to the running sum. This function will do that:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="o">==</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">PE1</span><span class="mf">.1</span> <span class="o">==</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span>
 </pre></div>
 </div>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;PE1.1 == + [+] dupdip&#39;</span><span class="p">)</span>
@@ -122,10 +122,10 @@ the counter to the running sum. This function will do that:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;0 0 3 PE1.1&#39;</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>        <span class="o">.</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span>
-      <span class="mi">0</span> <span class="o">.</span> <span class="mi">0</span> <span class="mi">3</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span>
-    <span class="mi">0</span> <span class="mi">0</span> <span class="o">.</span> <span class="mi">3</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span>
-  <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>        <span class="o">.</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="n">PE1</span><span class="mf">.1</span>
+      <span class="mi">0</span> <span class="o">.</span> <span class="mi">0</span> <span class="mi">3</span> <span class="n">PE1</span><span class="mf">.1</span>
+    <span class="mi">0</span> <span class="mi">0</span> <span class="o">.</span> <span class="mi">3</span> <span class="n">PE1</span><span class="mf">.1</span>
+  <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span>
   <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span>
     <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span>
 <span class="mi">0</span> <span class="mi">3</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span>
@@ -137,73 +137,73 @@ the counter to the running sum. This function will do that:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;0 0 [3 2 1 3 1 2 3] [PE1.1] step&#39;</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                            <span class="o">.</span> <span class="mi">0</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                          <span class="mi">0</span> <span class="o">.</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                        <span class="mi">0</span> <span class="mi">0</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-        <span class="mi">0</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-<span class="mi">0</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
-              <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                      <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                      <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                        <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                    <span class="mi">0</span> <span class="mi">3</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                        <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                          <span class="mi">3</span> <span class="o">.</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                        <span class="mi">3</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-          <span class="mi">3</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-  <span class="mi">3</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
-              <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                      <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                      <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                        <span class="mi">3</span> <span class="mi">5</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                    <span class="mi">3</span> <span class="mi">5</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                        <span class="mi">3</span> <span class="mi">5</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">5</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                          <span class="mi">8</span> <span class="o">.</span> <span class="mi">5</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                        <span class="mi">8</span> <span class="mi">5</span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-            <span class="mi">8</span> <span class="mi">5</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-    <span class="mi">8</span> <span class="mi">5</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
-              <span class="mi">8</span> <span class="mi">5</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                      <span class="mi">8</span> <span class="mi">5</span> <span class="mi">1</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                      <span class="mi">8</span> <span class="mi">5</span> <span class="mi">1</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                        <span class="mi">8</span> <span class="mi">6</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                    <span class="mi">8</span> <span class="mi">6</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                        <span class="mi">8</span> <span class="mi">6</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">6</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                         <span class="mi">14</span> <span class="o">.</span> <span class="mi">6</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                       <span class="mi">14</span> <span class="mi">6</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-             <span class="mi">14</span> <span class="mi">6</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-     <span class="mi">14</span> <span class="mi">6</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
-             <span class="mi">14</span> <span class="mi">6</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                     <span class="mi">14</span> <span class="mi">6</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                     <span class="mi">14</span> <span class="mi">6</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                       <span class="mi">14</span> <span class="mi">9</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                   <span class="mi">14</span> <span class="mi">9</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                       <span class="mi">14</span> <span class="mi">9</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">9</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                         <span class="mi">23</span> <span class="o">.</span> <span class="mi">9</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                       <span class="mi">23</span> <span class="mi">9</span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-               <span class="mi">23</span> <span class="mi">9</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-       <span class="mi">23</span> <span class="mi">9</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
-             <span class="mi">23</span> <span class="mi">9</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                     <span class="mi">23</span> <span class="mi">9</span> <span class="mi">1</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                     <span class="mi">23</span> <span class="mi">9</span> <span class="mi">1</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                      <span class="mi">23</span> <span class="mi">10</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                  <span class="mi">23</span> <span class="mi">10</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                      <span class="mi">23</span> <span class="mi">10</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">10</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                         <span class="mi">33</span> <span class="o">.</span> <span class="mi">10</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                      <span class="mi">33</span> <span class="mi">10</span> <span class="o">.</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                <span class="mi">33</span> <span class="mi">10</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-        <span class="mi">33</span> <span class="mi">10</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
-            <span class="mi">33</span> <span class="mi">10</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                    <span class="mi">33</span> <span class="mi">10</span> <span class="mi">2</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                    <span class="mi">33</span> <span class="mi">10</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                      <span class="mi">33</span> <span class="mi">12</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                  <span class="mi">33</span> <span class="mi">12</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                      <span class="mi">33</span> <span class="mi">12</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">12</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                         <span class="mi">45</span> <span class="o">.</span> <span class="mi">12</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                      <span class="mi">45</span> <span class="mi">12</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-                  <span class="mi">45</span> <span class="mi">12</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">step</span>
-          <span class="mi">45</span> <span class="mi">12</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
-            <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span>
-                    <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                            <span class="o">.</span> <span class="mi">0</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                          <span class="mi">0</span> <span class="o">.</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                        <span class="mi">0</span> <span class="mi">0</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+        <span class="mi">0</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+<span class="mi">0</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
+              <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                      <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                      <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                        <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                    <span class="mi">0</span> <span class="mi">3</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                        <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                          <span class="mi">3</span> <span class="o">.</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                        <span class="mi">3</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+          <span class="mi">3</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+  <span class="mi">3</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
+              <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                      <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                      <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                        <span class="mi">3</span> <span class="mi">5</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                    <span class="mi">3</span> <span class="mi">5</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                        <span class="mi">3</span> <span class="mi">5</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">5</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                          <span class="mi">8</span> <span class="o">.</span> <span class="mi">5</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                        <span class="mi">8</span> <span class="mi">5</span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+            <span class="mi">8</span> <span class="mi">5</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+    <span class="mi">8</span> <span class="mi">5</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
+              <span class="mi">8</span> <span class="mi">5</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                      <span class="mi">8</span> <span class="mi">5</span> <span class="mi">1</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                      <span class="mi">8</span> <span class="mi">5</span> <span class="mi">1</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                        <span class="mi">8</span> <span class="mi">6</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                    <span class="mi">8</span> <span class="mi">6</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                        <span class="mi">8</span> <span class="mi">6</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">6</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                         <span class="mi">14</span> <span class="o">.</span> <span class="mi">6</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                       <span class="mi">14</span> <span class="mi">6</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+             <span class="mi">14</span> <span class="mi">6</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+     <span class="mi">14</span> <span class="mi">6</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
+             <span class="mi">14</span> <span class="mi">6</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                     <span class="mi">14</span> <span class="mi">6</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                     <span class="mi">14</span> <span class="mi">6</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                       <span class="mi">14</span> <span class="mi">9</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                   <span class="mi">14</span> <span class="mi">9</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                       <span class="mi">14</span> <span class="mi">9</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">9</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                         <span class="mi">23</span> <span class="o">.</span> <span class="mi">9</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                       <span class="mi">23</span> <span class="mi">9</span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+               <span class="mi">23</span> <span class="mi">9</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+       <span class="mi">23</span> <span class="mi">9</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
+             <span class="mi">23</span> <span class="mi">9</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                     <span class="mi">23</span> <span class="mi">9</span> <span class="mi">1</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                     <span class="mi">23</span> <span class="mi">9</span> <span class="mi">1</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                      <span class="mi">23</span> <span class="mi">10</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                  <span class="mi">23</span> <span class="mi">10</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                      <span class="mi">23</span> <span class="mi">10</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">10</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                         <span class="mi">33</span> <span class="o">.</span> <span class="mi">10</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                      <span class="mi">33</span> <span class="mi">10</span> <span class="o">.</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                <span class="mi">33</span> <span class="mi">10</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+        <span class="mi">33</span> <span class="mi">10</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
+            <span class="mi">33</span> <span class="mi">10</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                    <span class="mi">33</span> <span class="mi">10</span> <span class="mi">2</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                    <span class="mi">33</span> <span class="mi">10</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                      <span class="mi">33</span> <span class="mi">12</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                  <span class="mi">33</span> <span class="mi">12</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                      <span class="mi">33</span> <span class="mi">12</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">12</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                         <span class="mi">45</span> <span class="o">.</span> <span class="mi">12</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                      <span class="mi">45</span> <span class="mi">12</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+                  <span class="mi">45</span> <span class="mi">12</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">step</span>
+          <span class="mi">45</span> <span class="mi">12</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
+            <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span>
+                    <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span>
                     <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span>
                       <span class="mi">45</span> <span class="mi">15</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span>
                   <span class="mi">45</span> <span class="mi">15</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span>
@@ -279,15 +279,15 @@ integer terms from the list.</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;0 0 14811 PE1.2&#39;</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                      <span class="o">.</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">2</span>
-                    <span class="mi">0</span> <span class="o">.</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">2</span>
-                  <span class="mi">0</span> <span class="mi">0</span> <span class="o">.</span> <span class="mi">14811</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">2</span>
-            <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">2</span>
-            <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
-<span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
-            <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
-          <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
-                <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                      <span class="o">.</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="n">PE1</span><span class="mf">.2</span>
+                    <span class="mi">0</span> <span class="o">.</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="n">PE1</span><span class="mf">.2</span>
+                  <span class="mi">0</span> <span class="mi">0</span> <span class="o">.</span> <span class="mi">14811</span> <span class="n">PE1</span><span class="mf">.2</span>
+            <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.2</span>
+            <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
+<span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
+            <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
+          <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
+                <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
                 <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
                   <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
               <span class="mi">0</span> <span class="mi">3</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
@@ -302,15 +302,15 @@ integer terms from the list.</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;3 3 3702 PE1.2&#39;</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                     <span class="o">.</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">2</span>
-                   <span class="mi">3</span> <span class="o">.</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">2</span>
-                 <span class="mi">3</span> <span class="mi">3</span> <span class="o">.</span> <span class="mi">3702</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">2</span>
-            <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">2</span>
-            <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
-<span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
-            <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
-          <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
-               <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                     <span class="o">.</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="n">PE1</span><span class="mf">.2</span>
+                   <span class="mi">3</span> <span class="o">.</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="n">PE1</span><span class="mf">.2</span>
+                 <span class="mi">3</span> <span class="mi">3</span> <span class="o">.</span> <span class="mi">3702</span> <span class="n">PE1</span><span class="mf">.2</span>
+            <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.2</span>
+            <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
+<span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
+            <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
+          <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
+               <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
                <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
                  <span class="mi">3</span> <span class="mi">5</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
              <span class="mi">3</span> <span class="mi">5</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
@@ -325,127 +325,127 @@ integer terms from the list.</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;0 0 14811 7 [PE1.2] times pop&#39;</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                      <span class="o">.</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="mi">7</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                    <span class="mi">0</span> <span class="o">.</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="mi">7</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                  <span class="mi">0</span> <span class="mi">0</span> <span class="o">.</span> <span class="mi">14811</span> <span class="mi">7</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-            <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="o">.</span> <span class="mi">7</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-          <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="mi">7</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-  <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="mi">7</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span> <span class="n">pop</span>
-    <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-            <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">2</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-            <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-<span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-            <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-          <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                  <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-              <span class="mi">0</span> <span class="mi">3</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                  <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">3</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                    <span class="mi">3</span> <span class="o">.</span> <span class="mi">3</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                  <span class="mi">3</span> <span class="mi">3</span> <span class="o">.</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-            <span class="mi">3</span> <span class="mi">3</span> <span class="mi">14811</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-          <span class="mi">3</span> <span class="mi">3</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="o">.</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-           <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="mi">6</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-   <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span> <span class="n">pop</span>
-     <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">2</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
- <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-           <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                  <span class="mi">3</span> <span class="mi">5</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-              <span class="mi">3</span> <span class="mi">5</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                  <span class="mi">3</span> <span class="mi">5</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">5</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                    <span class="mi">8</span> <span class="o">.</span> <span class="mi">5</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                  <span class="mi">8</span> <span class="mi">5</span> <span class="o">.</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">8</span> <span class="mi">5</span> <span class="mi">3702</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-           <span class="mi">8</span> <span class="mi">5</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-              <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="o">.</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-            <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="mi">5</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-    <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span> <span class="n">pop</span>
-      <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-              <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">2</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-              <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-  <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-              <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-            <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                <span class="mi">8</span> <span class="mi">5</span> <span class="mi">1</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                <span class="mi">8</span> <span class="mi">5</span> <span class="mi">1</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                  <span class="mi">8</span> <span class="mi">6</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-              <span class="mi">8</span> <span class="mi">6</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                  <span class="mi">8</span> <span class="mi">6</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">6</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                   <span class="mi">14</span> <span class="o">.</span> <span class="mi">6</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                 <span class="mi">14</span> <span class="mi">6</span> <span class="o">.</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">14</span> <span class="mi">6</span> <span class="mi">925</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-           <span class="mi">14</span> <span class="mi">6</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="o">.</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-           <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="mi">4</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-   <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span> <span class="n">pop</span>
-     <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">2</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
- <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-           <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-               <span class="mi">14</span> <span class="mi">6</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-               <span class="mi">14</span> <span class="mi">6</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                 <span class="mi">14</span> <span class="mi">9</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">14</span> <span class="mi">9</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                 <span class="mi">14</span> <span class="mi">9</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">9</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                   <span class="mi">23</span> <span class="o">.</span> <span class="mi">9</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                 <span class="mi">23</span> <span class="mi">9</span> <span class="o">.</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">23</span> <span class="mi">9</span> <span class="mi">231</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-           <span class="mi">23</span> <span class="mi">9</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-              <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="o">.</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-            <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-    <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span> <span class="n">pop</span>
-      <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-              <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">2</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-              <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-  <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-              <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-            <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-               <span class="mi">23</span> <span class="mi">9</span> <span class="mi">1</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-               <span class="mi">23</span> <span class="mi">9</span> <span class="mi">1</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                <span class="mi">23</span> <span class="mi">10</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-            <span class="mi">23</span> <span class="mi">10</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                <span class="mi">23</span> <span class="mi">10</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">10</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                   <span class="mi">33</span> <span class="o">.</span> <span class="mi">10</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                <span class="mi">33</span> <span class="mi">10</span> <span class="o">.</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">33</span> <span class="mi">10</span> <span class="mi">57</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-           <span class="mi">33</span> <span class="mi">10</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="o">.</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-           <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-   <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span> <span class="n">pop</span>
-     <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">2</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
- <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-           <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-              <span class="mi">33</span> <span class="mi">10</span> <span class="mi">2</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-              <span class="mi">33</span> <span class="mi">10</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                <span class="mi">33</span> <span class="mi">12</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-            <span class="mi">33</span> <span class="mi">12</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                <span class="mi">33</span> <span class="mi">12</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">12</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                   <span class="mi">45</span> <span class="o">.</span> <span class="mi">12</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-                <span class="mi">45</span> <span class="mi">12</span> <span class="o">.</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-             <span class="mi">45</span> <span class="mi">12</span> <span class="mi">14</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-           <span class="mi">45</span> <span class="mi">12</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-              <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="o">.</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-            <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-    <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span> <span class="n">pop</span>
-      <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="n">pop</span>
-              <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">2</span> <span class="n">pop</span>
-              <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="n">pop</span>
-  <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="n">pop</span>
-              <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="n">pop</span>
-            <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="n">pop</span>
-              <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="n">pop</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                      <span class="o">.</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="mi">7</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                    <span class="mi">0</span> <span class="o">.</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="mi">7</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                  <span class="mi">0</span> <span class="mi">0</span> <span class="o">.</span> <span class="mi">14811</span> <span class="mi">7</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+            <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="o">.</span> <span class="mi">7</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+          <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="mi">7</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+  <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="mi">7</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span> <span class="n">pop</span>
+    <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+            <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.2</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+            <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+<span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+            <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+          <span class="mi">0</span> <span class="mi">0</span> <span class="mi">14811</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                <span class="mi">0</span> <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                  <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+              <span class="mi">0</span> <span class="mi">3</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                  <span class="mi">0</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">3</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                    <span class="mi">3</span> <span class="o">.</span> <span class="mi">3</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                  <span class="mi">3</span> <span class="mi">3</span> <span class="o">.</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+            <span class="mi">3</span> <span class="mi">3</span> <span class="mi">14811</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+          <span class="mi">3</span> <span class="mi">3</span> <span class="mi">14811</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">&gt;&gt;</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="o">.</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+           <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="mi">6</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+   <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="mi">6</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span> <span class="n">pop</span>
+     <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.2</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+ <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+           <span class="mi">3</span> <span class="mi">3</span> <span class="mi">3702</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                  <span class="mi">3</span> <span class="mi">5</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+              <span class="mi">3</span> <span class="mi">5</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                  <span class="mi">3</span> <span class="mi">5</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">5</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                    <span class="mi">8</span> <span class="o">.</span> <span class="mi">5</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                  <span class="mi">8</span> <span class="mi">5</span> <span class="o">.</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">8</span> <span class="mi">5</span> <span class="mi">3702</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+           <span class="mi">8</span> <span class="mi">5</span> <span class="mi">3702</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">&gt;&gt;</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+              <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="o">.</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+            <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="mi">5</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+    <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="mi">5</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span> <span class="n">pop</span>
+      <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+              <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.2</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+              <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+  <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+              <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+            <span class="mi">8</span> <span class="mi">5</span> <span class="mi">925</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                <span class="mi">8</span> <span class="mi">5</span> <span class="mi">1</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                <span class="mi">8</span> <span class="mi">5</span> <span class="mi">1</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                  <span class="mi">8</span> <span class="mi">6</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+              <span class="mi">8</span> <span class="mi">6</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                  <span class="mi">8</span> <span class="mi">6</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">6</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                   <span class="mi">14</span> <span class="o">.</span> <span class="mi">6</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                 <span class="mi">14</span> <span class="mi">6</span> <span class="o">.</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">14</span> <span class="mi">6</span> <span class="mi">925</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+           <span class="mi">14</span> <span class="mi">6</span> <span class="mi">925</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">&gt;&gt;</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="o">.</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+           <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="mi">4</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+   <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span> <span class="n">pop</span>
+     <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.2</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+ <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+           <span class="mi">14</span> <span class="mi">6</span> <span class="mi">231</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+               <span class="mi">14</span> <span class="mi">6</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+               <span class="mi">14</span> <span class="mi">6</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                 <span class="mi">14</span> <span class="mi">9</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">14</span> <span class="mi">9</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                 <span class="mi">14</span> <span class="mi">9</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">9</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                   <span class="mi">23</span> <span class="o">.</span> <span class="mi">9</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                 <span class="mi">23</span> <span class="mi">9</span> <span class="o">.</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">23</span> <span class="mi">9</span> <span class="mi">231</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+           <span class="mi">23</span> <span class="mi">9</span> <span class="mi">231</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">&gt;&gt;</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+              <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="o">.</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+            <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+    <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span> <span class="n">pop</span>
+      <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+              <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.2</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+              <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+  <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+              <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+            <span class="mi">23</span> <span class="mi">9</span> <span class="mi">57</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+               <span class="mi">23</span> <span class="mi">9</span> <span class="mi">1</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+               <span class="mi">23</span> <span class="mi">9</span> <span class="mi">1</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                <span class="mi">23</span> <span class="mi">10</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+            <span class="mi">23</span> <span class="mi">10</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                <span class="mi">23</span> <span class="mi">10</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">10</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                   <span class="mi">33</span> <span class="o">.</span> <span class="mi">10</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                <span class="mi">33</span> <span class="mi">10</span> <span class="o">.</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">33</span> <span class="mi">10</span> <span class="mi">57</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+           <span class="mi">33</span> <span class="mi">10</span> <span class="mi">57</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">&gt;&gt;</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="o">.</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+           <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+   <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="mi">2</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span> <span class="n">pop</span>
+     <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.2</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+ <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+           <span class="mi">33</span> <span class="mi">10</span> <span class="mi">14</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+              <span class="mi">33</span> <span class="mi">10</span> <span class="mi">2</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+              <span class="mi">33</span> <span class="mi">10</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                <span class="mi">33</span> <span class="mi">12</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+            <span class="mi">33</span> <span class="mi">12</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                <span class="mi">33</span> <span class="mi">12</span> <span class="o">.</span> <span class="o">+</span> <span class="mi">12</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                   <span class="mi">45</span> <span class="o">.</span> <span class="mi">12</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+                <span class="mi">45</span> <span class="mi">12</span> <span class="o">.</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+             <span class="mi">45</span> <span class="mi">12</span> <span class="mi">14</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+           <span class="mi">45</span> <span class="mi">12</span> <span class="mi">14</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">&gt;&gt;</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+              <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="o">.</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+            <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">.</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+    <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="mi">1</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span> <span class="n">pop</span>
+      <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="n">pop</span>
+              <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.2</span> <span class="n">pop</span>
+              <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="n">pop</span>
+  <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="n">pop</span>
+              <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="o">.</span> <span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="n">pop</span>
+            <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="n">pop</span>
+              <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="n">pop</span>
               <span class="mi">45</span> <span class="mi">12</span> <span class="mi">3</span> <span class="o">.</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="n">pop</span>
                 <span class="mi">45</span> <span class="mi">15</span> <span class="o">.</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="n">pop</span>
             <span class="mi">45</span> <span class="mi">15</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="mi">3</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span> <span class="n">pop</span>
@@ -471,10 +471,10 @@ integer terms from the list.</p>
 </section>
 <section id="let-s-refactor">
 <h3>Let’s refactor<a class="headerlink" href="#let-s-refactor" title="Permalink to this headline">¶</a></h3>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>  <span class="mi">14811</span> <span class="mi">7</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-  <span class="mi">14811</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-  <span class="mi">14811</span> <span class="n">n</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-<span class="n">n</span> <span class="mi">14811</span> <span class="n">swap</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>  <span class="mi">14811</span> <span class="mi">7</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+  <span class="mi">14811</span> <span class="mi">4</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+  <span class="mi">14811</span> <span class="n">n</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+<span class="n">n</span> <span class="mi">14811</span> <span class="n">swap</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
 </pre></div>
 </div>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;PE1.3 == 14811 swap [PE1.2] times pop&#39;</span><span class="p">)</span>
@@ -493,10 +493,10 @@ integer terms from the list.</p>
 <p>Here’s our joy program all in one place. It doesn’t make so much sense,
 but if you have read through the above description of how it was derived
 I hope it’s clear.</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span> <span class="o">==</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span>
-<span class="n">PE1</span><span class="o">.</span><span class="mi">2</span> <span class="o">==</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
-<span class="n">PE1</span><span class="o">.</span><span class="mi">3</span> <span class="o">==</span> <span class="mi">14811</span> <span class="n">swap</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
-<span class="n">PE1</span> <span class="o">==</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">66</span> <span class="p">[</span><span class="mi">7</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">3</span><span class="p">]</span> <span class="n">times</span> <span class="mi">4</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">3</span> <span class="n">pop</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">PE1</span><span class="mf">.1</span> <span class="o">==</span> <span class="o">+</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">dupdip</span>
+<span class="n">PE1</span><span class="mf">.2</span> <span class="o">==</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">dupdip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
+<span class="n">PE1</span><span class="mf">.3</span> <span class="o">==</span> <span class="mi">14811</span> <span class="n">swap</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.2</span><span class="p">]</span> <span class="n">times</span> <span class="n">pop</span>
+<span class="n">PE1</span> <span class="o">==</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">66</span> <span class="p">[</span><span class="mi">7</span> <span class="n">PE1</span><span class="mf">.3</span><span class="p">]</span> <span class="n">times</span> <span class="mi">4</span> <span class="n">PE1</span><span class="mf">.3</span> <span class="n">pop</span>
 </pre></div>
 </div>
 </section>
@@ -697,6 +697,7 @@ is just:</p>
 <li class="toctree-l2"><a class="reference internal" href="Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
 <li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
 <li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html">Square Spiral Example Joy Code</a></li>
 <li class="toctree-l2"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a></li>
 <li class="toctree-l2"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a></li>
 <li class="toctree-l2"><a class="reference internal" href="TypeChecking.html">Type Checking</a></li>
@@ -747,7 +748,7 @@ is just:</p>
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/Generator_Programs.html b/docs/sphinx_docs/_build/html/notebooks/Generator_Programs.html
index 938d607..166daab 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/Generator_Programs.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Generator_Programs.html
@@ -36,7 +36,7 @@
   <section id="using-x-to-generate-values">
 <h1>Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values<a class="headerlink" href="#using-x-to-generate-values" title="Permalink to this headline">¶</a></h1>
 <p>Cf. jp-reprod.html</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import J, V, define
 </pre></div>
 </div>
 <p>Consider the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator:</p>
@@ -76,7 +76,7 @@ function <code class="docutils literal notranslate"><span class="pre">C</span></
 </pre></div>
 </div>
 <p>Let’s try it:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[0 swap [dup ++] dip rest cons] x&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[0 swap [dup ++] dip rest cons] x&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                                           <span class="o">.</span> <span class="p">[</span><span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">dip</span> <span class="n">rest</span> <span class="n">cons</span><span class="p">]</span> <span class="n">x</span>
@@ -95,7 +95,7 @@ function <code class="docutils literal notranslate"><span class="pre">C</span></
 </div>
 <p>After one application of <code class="docutils literal notranslate"><span class="pre">x</span></code> the quoted program contains <code class="docutils literal notranslate"><span class="pre">1</span></code> and
 <code class="docutils literal notranslate"><span class="pre">0</span></code> is below it on the stack.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[0 swap [dup ++] dip rest cons] x x x x x pop&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[0 swap [dup ++] dip rest cons] x x x x x pop&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span>
@@ -103,10 +103,10 @@ function <code class="docutils literal notranslate"><span class="pre">C</span></
 </div>
 <section id="direco">
 <h2><code class="docutils literal notranslate"><span class="pre">direco</span></code><a class="headerlink" href="#direco" title="Permalink to this headline">¶</a></h2>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;direco == dip rest cons&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;direco == dip rest cons&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[0 swap [dup ++] direco] x&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[0 swap [dup ++] direco] x&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                                    <span class="o">.</span> <span class="p">[</span><span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">direco</span><span class="p">]</span> <span class="n">x</span>
@@ -147,17 +147,17 @@ our quoted program:</p>
 <span class="n">G</span> <span class="o">==</span> <span class="p">[</span><span class="n">direco</span><span class="p">]</span> <span class="n">cons</span> <span class="p">[</span><span class="n">swap</span><span class="p">]</span> <span class="n">swoncat</span> <span class="n">cons</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;G == [direco] cons [swap] swoncat cons&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;G == [direco] cons [swap] swoncat cons&#39;)
 </pre></div>
 </div>
 <p>Let’s try it out:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;0 [dup ++] G&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;0 [dup ++] G&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">direco</span><span class="p">]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;0 [dup ++] G x x x pop&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;0 [dup ++] G x x x pop&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span>
@@ -165,7 +165,7 @@ our quoted program:</p>
 </div>
 <section id="powers-of-2">
 <h3>Powers of 2<a class="headerlink" href="#powers-of-2" title="Permalink to this headline">¶</a></h3>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;1 [dup 1 &lt;&lt;] G x x x x x x x x x pop&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 [dup 1 &lt;&lt;] G x x x x x x x x x pop&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">4</span> <span class="mi">8</span> <span class="mi">16</span> <span class="mi">32</span> <span class="mi">64</span> <span class="mi">128</span> <span class="mi">256</span>
@@ -176,7 +176,7 @@ our quoted program:</p>
 <h3><code class="docutils literal notranslate"><span class="pre">[x]</span> <span class="pre">times</span></code><a class="headerlink" href="#x-times" title="Permalink to this headline">¶</a></h3>
 <p>If we have one of these quoted programs we can drive it using <code class="docutils literal notranslate"><span class="pre">times</span></code>
 with the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 [dup ++] G 5 [x] times&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 [dup ++] G 5 [x] times&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span> <span class="mi">24</span> <span class="mi">25</span> <span class="mi">26</span> <span class="mi">27</span> <span class="p">[</span><span class="mi">28</span> <span class="n">swap</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">direco</span><span class="p">]</span>
@@ -200,14 +200,14 @@ int:</p>
 </div>
 <p>And pick them off by masking with 3 (binary 11) and then shifting the
 int right two bits.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;PE1.1 == dup [3 &amp;] dip 2 &gt;&gt;&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;PE1.1 == dup [3 &amp;] dip 2 &gt;&gt;&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;14811 PE1.1&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;14811 PE1.1&#39;)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                  <span class="o">.</span> <span class="mi">14811</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span>
-            <span class="mi">14811</span> <span class="o">.</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                  <span class="o">.</span> <span class="mi">14811</span> <span class="n">PE1</span><span class="mf">.1</span>
+            <span class="mi">14811</span> <span class="o">.</span> <span class="n">PE1</span><span class="mf">.1</span>
             <span class="mi">14811</span> <span class="o">.</span> <span class="n">dup</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span><span class="p">]</span> <span class="n">dip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
       <span class="mi">14811</span> <span class="mi">14811</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span><span class="p">]</span> <span class="n">dip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
 <span class="mi">14811</span> <span class="mi">14811</span> <span class="p">[</span><span class="mi">3</span> <span class="o">&amp;</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span> <span class="mi">2</span> <span class="o">&gt;&gt;</span>
@@ -220,36 +220,36 @@ int right two bits.</p>
 </pre></div>
 </div>
 <p>If we plug <code class="docutils literal notranslate"><span class="pre">14811</span></code> and <code class="docutils literal notranslate"><span class="pre">[PE1.1]</span></code> into our generator form…</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;14811 [PE1.1] G&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;14811 [PE1.1] G&#39;)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">14811</span> <span class="n">swap</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">direco</span><span class="p">]</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">14811</span> <span class="n">swap</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">direco</span><span class="p">]</span>
 </pre></div>
 </div>
 <p>…we get a generator that works for seven cycles before it reaches zero:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[14811 swap [PE1.1] direco] 7 [x] times&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[14811 swap [PE1.1] direco] 7 [x] times&#39;)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">direco</span><span class="p">]</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">direco</span><span class="p">]</span>
 </pre></div>
 </div>
 <section id="reset-at-zero">
 <h3>Reset at Zero<a class="headerlink" href="#reset-at-zero" title="Permalink to this headline">¶</a></h3>
 <p>We need a function that checks if the int has reached zero and resets it
 if so.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;PE1.1.check == dup [pop 14811] [] branch&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;PE1.1.check == dup [pop 14811] [] branch&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;14811 [PE1.1.check PE1.1] G&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;14811 [PE1.1.check PE1.1] G&#39;)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">14811</span> <span class="n">swap</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mf">1.</span><span class="n">check</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">direco</span><span class="p">]</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">14811</span> <span class="n">swap</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="o">.</span><span class="n">check</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">direco</span><span class="p">]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[14811 swap [PE1.1.check PE1.1] direco] 21 [x] times&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[14811 swap [PE1.1.check PE1.1] direco] 21 [x] times&#39;)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mf">1.</span><span class="n">check</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">direco</span><span class="p">]</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="o">.</span><span class="n">check</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">direco</span><span class="p">]</span>
 </pre></div>
 </div>
 <p>(It would be more efficient to reset the int every seven cycles but
@@ -262,20 +262,20 @@ say.)</p>
 <p>In the PE1 problem we are asked to sum all the multiples of three and
 five less than 1000. It’s worked out that we need to use all seven
 numbers sixty-six times and then four more.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;7 66 * 4 +&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;7 66 * 4 +&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">466</span>
 </pre></div>
 </div>
 <p>If we drive our generator 466 times and sum the stack we get 999.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times&#39;)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">57</span> <span class="n">swap</span> <span class="p">[</span><span class="n">PE1</span><span class="o">.</span><span class="mf">1.</span><span class="n">check</span> <span class="n">PE1</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">direco</span><span class="p">]</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">57</span> <span class="n">swap</span> <span class="p">[</span><span class="n">PE1</span><span class="mf">.1</span><span class="o">.</span><span class="n">check</span> <span class="n">PE1</span><span class="mf">.1</span><span class="p">]</span> <span class="n">direco</span><span class="p">]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times pop enstacken sum&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times pop enstacken sum&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">999</span>
@@ -285,11 +285,11 @@ numbers sixty-six times and then four more.</p>
 </section>
 <section id="project-euler-problem-one">
 <h2>Project Euler Problem One<a class="headerlink" href="#project-euler-problem-one" title="Permalink to this headline">¶</a></h2>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;PE1.2 == + dup [+] dip&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;PE1.2 == + dup [+] dip&#39;)
 </pre></div>
 </div>
 <p>Now we can add <code class="docutils literal notranslate"><span class="pre">PE1.2</span></code> to the quoted program given to <code class="docutils literal notranslate"><span class="pre">G</span></code>.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;0 0 0 [PE1.1.check PE1.1] G 466 [x [PE1.2] dip] times popop&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;0 0 0 [PE1.1.check PE1.1] G 466 [x [PE1.2] dip] times popop&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">233168</span>
@@ -351,13 +351,13 @@ numbers sixty-six times and then four more.</p>
 <span class="n">fib_gen</span> <span class="o">==</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">1</span> <span class="n">F</span><span class="p">]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;fib == + [popdd over] cons infra uncons&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;fib == + [popdd over] cons infra uncons&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;fib_gen == [1 1 fib]&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;fib_gen == [1 1 fib]&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;fib_gen 10 [x] times&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;fib_gen 10 [x] times&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">5</span> <span class="mi">8</span> <span class="mi">13</span> <span class="mi">21</span> <span class="mi">34</span> <span class="mi">55</span> <span class="mi">89</span> <span class="p">[</span><span class="mi">144</span> <span class="mi">89</span> <span class="n">fib</span><span class="p">]</span>
@@ -373,21 +373,21 @@ not exceed four million, find the sum of the even-valued terms.</p>
 <p>Now that we have a generator for the Fibonacci sequence, we need a
 function that adds a term in the sequence to a sum if it is even, and
 <code class="docutils literal notranslate"><span class="pre">pop</span></code>s it otherwise.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;PE2.1 == dup 2 % [+] [pop] branch&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;PE2.1 == dup 2 % [+] [pop] branch&#39;)
 </pre></div>
 </div>
 <p>And a predicate function that detects when the terms in the series
 “exceed four million”.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;&gt;4M == 4000000 &gt;&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;&gt;4M == 4000000 &gt;&#39;)
 </pre></div>
 </div>
 <p>Now it’s straightforward to define <code class="docutils literal notranslate"><span class="pre">PE2</span></code> as a recursive function that
 generates terms in the Fibonacci sequence until they exceed four million
 and sums the even ones.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;PE2 == 0 fib_gen x [pop &gt;4M] [popop] [[PE2.1] dip x] primrec&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;PE2 == 0 fib_gen x [pop &gt;4M] [popop] [[PE2.1] dip x] primrec&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;PE2&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;PE2&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">4613732</span>
@@ -400,8 +400,8 @@ and sums the even ones.</p>
 <span class="n">even</span> <span class="o">==</span> <span class="n">dup</span> <span class="mi">2</span> <span class="o">%</span>
 <span class="o">&gt;</span><span class="mi">4</span><span class="n">M</span> <span class="o">==</span> <span class="mi">4000000</span> <span class="o">&gt;</span>
 
-<span class="n">PE2</span><span class="o">.</span><span class="mi">1</span> <span class="o">==</span> <span class="n">even</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="n">branch</span>
-<span class="n">PE2</span> <span class="o">==</span> <span class="mi">0</span> <span class="n">fib_gen</span> <span class="n">x</span> <span class="p">[</span><span class="n">pop</span> <span class="o">&gt;</span><span class="mi">4</span><span class="n">M</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span><span class="p">]</span> <span class="p">[[</span><span class="n">PE2</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span> <span class="n">dip</span> <span class="n">x</span><span class="p">]</span> <span class="n">primrec</span>
+<span class="n">PE2</span><span class="mf">.1</span> <span class="o">==</span> <span class="n">even</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="n">branch</span>
+<span class="n">PE2</span> <span class="o">==</span> <span class="mi">0</span> <span class="n">fib_gen</span> <span class="n">x</span> <span class="p">[</span><span class="n">pop</span> <span class="o">&gt;</span><span class="mi">4</span><span class="n">M</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span><span class="p">]</span> <span class="p">[[</span><span class="n">PE2</span><span class="mf">.1</span><span class="p">]</span> <span class="n">dip</span> <span class="n">x</span><span class="p">]</span> <span class="n">primrec</span>
 </pre></div>
 </div>
 <section id="even-valued-fibonacci-terms">
@@ -418,23 +418,23 @@ and sums the even ones.</p>
 </pre></div>
 </div>
 <p>Every third term is even.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 0 fib] x x x&#39;</span><span class="p">)</span>  <span class="c1"># To start the sequence with 1 1 2 3 instead of 1 2 3.</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 0 fib] x x x&#39;)  # To start the sequence with 1 1 2 3 instead of 1 2 3.
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">1</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="n">fib</span><span class="p">]</span>
 </pre></div>
 </div>
 <p>Drive the generator three times and <code class="docutils literal notranslate"><span class="pre">popop</span></code> the two odd terms.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 0 fib] x x x [popop] dipd&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 0 fib] x x x [popop] dipd&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="n">fib</span><span class="p">]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;PE2.2 == x x x [popop] dipd&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;PE2.2 == x x x [popop] dipd&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 0 fib] 10 [PE2.2] times&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 0 fib] 10 [PE2.2] times&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span> <span class="mi">8</span> <span class="mi">34</span> <span class="mi">144</span> <span class="mi">610</span> <span class="mi">2584</span> <span class="mi">10946</span> <span class="mi">46368</span> <span class="mi">196418</span> <span class="mi">832040</span> <span class="p">[</span><span class="mi">1346269</span> <span class="mi">832040</span> <span class="n">fib</span><span class="p">]</span>
@@ -442,7 +442,7 @@ and sums the even ones.</p>
 </div>
 <p>Replace <code class="docutils literal notranslate"><span class="pre">x</span></code> with our new driver function <code class="docutils literal notranslate"><span class="pre">PE2.2</span></code> and start our
 <code class="docutils literal notranslate"><span class="pre">fib</span></code> generator at <code class="docutils literal notranslate"><span class="pre">1</span> <span class="pre">0</span></code>.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;0 [1 0 fib] PE2.2 [pop &gt;4M] [popop] [[PE2.1] dip PE2.2] primrec&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;0 [1 0 fib] PE2.2 [pop &gt;4M] [popop] [[PE2.1] dip PE2.2] primrec&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">4613732</span>
@@ -457,10 +457,10 @@ modifications to the default <code class="docutils literal notranslate"><span cl
 </section>
 <section id="an-interesting-variation">
 <h2>An Interesting Variation<a class="headerlink" href="#an-interesting-variation" title="Permalink to this headline">¶</a></h2>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;codireco == cons dip rest cons&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;codireco == cons dip rest cons&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[0 [dup ++] codireco] x&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[0 [dup ++] codireco] x&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                                 <span class="o">.</span> <span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="n">x</span>
@@ -479,10 +479,10 @@ modifications to the default <code class="docutils literal notranslate"><span cl
          <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="o">.</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;G == [codireco] cons cons&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;G == [codireco] cons cons&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;230 [dup ++] G 5 [x] times pop&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;230 [dup ++] G 5 [x] times pop&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">230</span> <span class="mi">231</span> <span class="mi">232</span> <span class="mi">233</span> <span class="mi">234</span>
@@ -577,7 +577,7 @@ modifications to the default <code class="docutils literal notranslate"><span cl
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/Intro.html b/docs/sphinx_docs/_build/html/notebooks/Intro.html
index 658704d..d56d9e0 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/Intro.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Intro.html
@@ -369,7 +369,7 @@ developing structured processes.</p>
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/Newton-Raphson.html b/docs/sphinx_docs/_build/html/notebooks/Newton-Raphson.html
index 4a8ff3a..5d23612 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/Newton-Raphson.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Newton-Raphson.html
@@ -13,7 +13,7 @@
     <script src="../_static/jquery.js"></script>
     <script src="../_static/underscore.js"></script>
     <script src="../_static/doctools.js"></script>
-    <script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
+    <script async="async" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
     <link rel="next" title="Square Spiral Example Joy Code" href="Square_Spiral.html" />
@@ -40,7 +40,7 @@
 to write a function that can compute the square root of a number.</p>
 <p>Cf. <a class="reference external" href="https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf">“Why Functional Programming Matters” by John
 Hughes</a></p>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import J, V, define
 </pre></div>
 </div>
 <section id="a-generator-for-approximations">
@@ -92,10 +92,10 @@ function we’re writing. If we let 1 be the initial approximation:</p>
 <span class="mi">1</span>   <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span>                    <span class="n">make_generator</span>
 </pre></div>
 </div>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define(&#39;gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 gsra&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 gsra&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span>
@@ -103,7 +103,7 @@ function we’re writing. If we let 1 be the initial approximation:</p>
 </div>
 <p>Let’s drive the generator a few time (with the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator) and
 square the approximation to see how well it works…</p>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 gsra 6 [x popd] times first sqr&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 gsra 6 [x popd] times first sqr&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">23.0000000001585</span>
@@ -145,7 +145,7 @@ generated already and epsilon ε is handy on the stack…</p>
 <span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">a</span><span class="o">-</span><span class="n">b</span><span class="p">)</span><span class="o">&lt;=</span><span class="n">ε</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_P [first - abs] dip &lt;=&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define(&#39;_within_P [first - abs] dip &lt;=&#39;)
 </pre></div>
 </div>
 </section>
@@ -157,7 +157,7 @@ generated already and epsilon ε is handy on the stack…</p>
    <span class="n">b</span>
 </pre></div>
 </div>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_B roll&lt; popop first&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define(&#39;_within_B roll&lt; popop first&#39;)
 </pre></div>
 </div>
 </section>
@@ -182,7 +182,7 @@ generated already and epsilon ε is handy on the stack…</p>
 <span class="n">b</span> <span class="p">[</span><span class="n">c</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">within</span>
 </pre></div>
 </div>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_R [popd x] dip&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define(&#39;_within_R [popd x] dip&#39;)
 </pre></div>
 </div>
 </section>
@@ -194,33 +194,33 @@ generated already and epsilon ε is handy on the stack…</p>
 <span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="o">...</span>
 </pre></div>
 </div>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec&#39;</span><span class="p">)</span>
-<span class="n">define</span><span class="p">(</span><span class="s1">&#39;sqrt gsra within&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define(&#39;within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec&#39;)
+define(&#39;sqrt gsra within&#39;)
 </pre></div>
 </div>
 <p>Try it out…</p>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;36 sqrt&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J(&#39;36 sqrt&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">6.0</span>
 </pre></div>
 </div>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 sqrt&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J(&#39;23 sqrt&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span>
 </pre></div>
 </div>
 <p>Check it.</p>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span><span class="o">**</span><span class="mi">2</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>4.795831523312719**2
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">22.999999999999996</span>
 </pre></div>
 </div>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">sqrt</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>from math import sqrt
 
-<span class="n">sqrt</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span>
+sqrt(23)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span>
@@ -316,7 +316,7 @@ generated already and epsilon ε is handy on the stack…</p>
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/NoUpdates.html b/docs/sphinx_docs/_build/html/notebooks/NoUpdates.html
index 65498ab..797a302 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/NoUpdates.html
+++ b/docs/sphinx_docs/_build/html/notebooks/NoUpdates.html
@@ -93,6 +93,7 @@
 <li class="toctree-l2"><a class="reference internal" href="Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
 <li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
 <li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html">Square Spiral Example Joy Code</a></li>
 <li class="toctree-l2"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a></li>
 <li class="toctree-l2"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a></li>
 <li class="toctree-l2"><a class="reference internal" href="TypeChecking.html">Type Checking</a></li>
@@ -143,7 +144,7 @@
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/Ordered_Binary_Trees.html b/docs/sphinx_docs/_build/html/notebooks/Ordered_Binary_Trees.html
index 05fa302..6d63e16 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/Ordered_Binary_Trees.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Ordered_Binary_Trees.html
@@ -63,7 +63,7 @@ the Sufficiently Smart Compiler can be modified to use an optimized
 implementation under the hood. (Where does the “type” come from? It has
 a contingent existence predicated on the disciplined use of these
 functions on otherwise undistinguished Joy datastructures.)</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span><span class="p">,</span> <span class="n">DefinitionWrapper</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import D, J, V, define, DefinitionWrapper
 </pre></div>
 </div>
 <section id="adding-nodes-to-the-tree">
@@ -100,10 +100,10 @@ functions on otherwise undistinguished Joy datastructures.)</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Tree</span><span class="o">-</span><span class="n">new</span> <span class="o">==</span> <span class="n">swap</span> <span class="p">[[]</span> <span class="p">[]]</span> <span class="n">cons</span> <span class="n">cons</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-new == swap [[] []] cons cons&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;Tree-new == swap [[] []] cons cons&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&quot;v&quot; &quot;k&quot; Tree-new&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;&quot;v&quot; &quot;k&quot; Tree-new&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;k&#39;</span> <span class="s1">&#39;v&#39;</span> <span class="p">[]</span> <span class="p">[]]</span>
@@ -159,10 +159,10 @@ comparison operator:</p>
 <span class="n">P</span>   <span class="o">==</span> <span class="n">pop</span> <span class="n">roll</span><span class="o">&gt;</span> <span class="n">pop</span> <span class="n">first</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;P == pop roll&gt; pop first&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;P == pop roll&gt; pop first&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;old_key&quot; 23 [] []] 17 &quot;new_key&quot; [&quot;...&quot;] P&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[&quot;old_key&quot; 23 [] []] 17 &quot;new_key&quot; [&quot;...&quot;] P&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;new_key&#39;</span> <span class="s1">&#39;old_key&#39;</span>
@@ -217,10 +217,10 @@ stack:</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">T</span> <span class="o">==</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="n">dipdd</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;T == cons cons [dipdd] cons infra&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;T == cons cons [dipdd] cons infra&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;old_k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;new_key&quot; [&quot;Tree-add&quot;] T&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[&quot;old_k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;new_key&quot; [&quot;Tree-add&quot;] T&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;old_k&#39;</span> <span class="s1">&#39;old_value&#39;</span> <span class="s1">&#39;left&#39;</span> <span class="s1">&#39;Tree-add&#39;</span> <span class="s1">&#39;new_key&#39;</span> <span class="s1">&#39;new_value&#39;</span> <span class="s1">&#39;right&#39;</span><span class="p">]</span>
@@ -234,7 +234,7 @@ stack:</p>
 <span class="p">[</span><span class="n">key_n</span> <span class="n">value_n</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">value</span> <span class="n">key</span> <span class="p">[</span><span class="n">Tree</span><span class="o">-</span><span class="n">add</span><span class="p">]</span> <span class="p">[</span><span class="n">P</span> <span class="o">&lt;</span><span class="p">]</span> <span class="p">[</span><span class="n">Te</span><span class="p">]</span> <span class="p">[</span><span class="n">Ee</span><span class="p">]</span> <span class="n">ifte</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;E == [P &lt;] [Te] [Ee] ifte&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;E == [P &lt;] [Te] [Ee] ifte&#39;)
 </pre></div>
 </div>
 <p>In this case <code class="docutils literal notranslate"><span class="pre">Te</span></code> works that same as <code class="docutils literal notranslate"><span class="pre">T</span></code> but on the left child tree
@@ -243,10 +243,10 @@ instead of the right, so the only difference is that it must use
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Te</span> <span class="o">==</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="n">dipd</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Te == cons cons [dipd] cons infra&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;Te == cons cons [dipd] cons infra&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;old_k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;new_key&quot; [&quot;Tree-add&quot;] Te&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[&quot;old_k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;new_key&quot; [&quot;Tree-add&quot;] Te&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;old_k&#39;</span> <span class="s1">&#39;old_value&#39;</span> <span class="s1">&#39;Tree-add&#39;</span> <span class="s1">&#39;new_key&#39;</span> <span class="s1">&#39;new_value&#39;</span> <span class="s1">&#39;left&#39;</span> <span class="s1">&#39;right&#39;</span><span class="p">]</span>
@@ -274,10 +274,10 @@ instead of the right, so the only difference is that it must use
               <span class="p">[</span><span class="n">key</span> <span class="n">new_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Ee == pop swap roll&lt; rest rest cons cons&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;Ee == pop swap roll&lt; rest rest cons cons&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;k&quot; [&quot;Tree-add&quot;] Ee&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[&quot;k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;k&quot; [&quot;Tree-add&quot;] Ee&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;k&#39;</span> <span class="s1">&#39;new_value&#39;</span> <span class="s1">&#39;left&#39;</span> <span class="s1">&#39;right&#39;</span><span class="p">]</span>
@@ -302,43 +302,43 @@ instead of the right, so the only difference is that it must use
 <span class="n">Tree</span><span class="o">-</span><span class="n">add</span> <span class="o">==</span> <span class="p">[</span><span class="n">popop</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[[</span><span class="n">pop</span><span class="p">]</span> <span class="n">dipd</span> <span class="n">Tree</span><span class="o">-</span><span class="n">new</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="n">R</span><span class="p">]</span> <span class="n">genrec</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-add == [popop not] [[pop] dipd Tree-new] [] [[P &gt;] [T] [E] ifte] genrec&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;Tree-add == [popop not] [[pop] dipd Tree-new] [] [[P &gt;] [T] [E] ifte] genrec&#39;)
 </pre></div>
 </div>
 </section>
 <section id="examples">
 <h3>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h3>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] 23 &quot;b&quot; Tree-add&#39;</span><span class="p">)</span>  <span class="c1"># Initial</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] 23 &quot;b&quot; Tree-add&#39;)  # Initial
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[]]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;b&quot; 23 [] []] 88 &quot;c&quot; Tree-add&#39;</span><span class="p">)</span>  <span class="c1"># Greater than</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[&quot;b&quot; 23 [] []] 88 &quot;c&quot; Tree-add&#39;)  # Greater than
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;b&quot; 23 [] []] 88 &quot;a&quot; Tree-add&#39;</span><span class="p">)</span>  <span class="c1"># Less than</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[&quot;b&quot; 23 [] []] 88 &quot;a&quot; Tree-add&#39;)  # Less than
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[]]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;b&quot; 23 [] []] 88 &quot;b&quot; Tree-add&#39;</span><span class="p">)</span>  <span class="c1"># Equal to</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[&quot;b&quot; 23 [] []] 88 &quot;b&quot; Tree-add&#39;)  # Equal to
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] 23 &quot;b&quot; Tree-add 88 &quot;a&quot; Tree-add 44 &quot;c&quot; Tree-add&#39;</span><span class="p">)</span>  <span class="c1"># Series.</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] 23 &quot;b&quot; Tree-add 88 &quot;a&quot; Tree-add 44 &quot;c&quot; Tree-add&#39;)  # Series.
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [[23 &quot;b&quot;] [88 &quot;a&quot;] [44 &quot;c&quot;]] [i Tree-add] step&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] [[23 &quot;b&quot;] [88 &quot;a&quot;] [44 &quot;c&quot;]] [i Tree-add] step&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
@@ -365,19 +365,19 @@ values:</p>
                 <span class="n">L</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;1 0 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;1 0 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;G&#39;</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;1 1 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;1 1 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;E&#39;</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;0 1 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;0 1 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;L&#39;</span>
@@ -414,7 +414,7 @@ node key (by throwing everything else away):</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">P</span> <span class="o">==</span> <span class="n">over</span> <span class="p">[</span><span class="n">popop</span> <span class="n">popop</span> <span class="n">first</span><span class="p">]</span> <span class="n">nullary</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;P == over [popop popop first] nullary&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;P == over [popop popop first] nullary&#39;)
 </pre></div>
 </div>
 <p>Using <code class="docutils literal notranslate"><span class="pre">cmp</span></code> to simplify <cite>our code above at
@@ -434,10 +434,10 @@ to understand:</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Tree</span><span class="o">-</span><span class="n">add</span> <span class="o">==</span> <span class="p">[</span><span class="n">popop</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[[</span><span class="n">pop</span><span class="p">]</span> <span class="n">dipd</span> <span class="n">Tree</span><span class="o">-</span><span class="n">new</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="n">P</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">Ee</span><span class="p">]</span> <span class="p">[</span><span class="n">Te</span><span class="p">]</span> <span class="n">cmp</span><span class="p">]</span> <span class="n">genrec</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] 23 &quot;b&quot; Tree-add 88 &quot;a&quot; Tree-add 44 &quot;c&quot; Tree-add&#39;</span><span class="p">)</span>  <span class="c1"># Still works.</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] 23 &quot;b&quot; Tree-add 88 &quot;a&quot; Tree-add 44 &quot;c&quot; Tree-add&#39;)  # Still works.
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
@@ -545,22 +545,22 @@ with an interesting situation:</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Tree</span><span class="o">-</span><span class="nb">iter</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="n">roll</span><span class="o">&lt;</span> <span class="p">[</span><span class="n">dupdip</span> <span class="n">rest</span> <span class="n">rest</span><span class="p">]</span> <span class="n">cons</span> <span class="p">[</span><span class="n">step</span><span class="p">]</span> <span class="n">genrec</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-iter == [not] [pop] roll&lt; [dupdip rest rest] cons [step] genrec&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;Tree-iter == [not] [pop] roll&lt; [dupdip rest rest] cons [step] genrec&#39;)
 </pre></div>
 </div>
 </section>
 <section id="id1">
 <h3>Examples<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h3>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [foo] Tree-iter&#39;</span><span class="p">)</span>  <span class="c1">#  It doesn&#39;t matter what F is as it won&#39;t be used.</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] [foo] Tree-iter&#39;)  #  It doesn&#39;t matter what F is as it won&#39;t be used.
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;b&#39; 23 [&#39;a&#39; 88 [] []] [&#39;c&#39; 44 [] []]] [first] Tree-iter&quot;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;[&#39;b&#39; 23 [&#39;a&#39; 88 [] []] [&#39;c&#39; 44 [] []]] [first] Tree-iter&quot;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;b&#39;</span> <span class="s1">&#39;a&#39;</span> <span class="s1">&#39;c&#39;</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;b&#39; 23 [&#39;a&#39; 88 [] []] [&#39;c&#39; 44 [] []]] [second] Tree-iter&quot;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;[&#39;b&#39; 23 [&#39;a&#39; 88 [] []] [&#39;c&#39; 44 [] []]] [second] Tree-iter&quot;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span> <span class="mi">88</span> <span class="mi">44</span>
@@ -575,16 +575,16 @@ to e.g. 0 and ignoring them. It’s set-like in that duplicate items added
 to it will only occur once within it, and we can query it in
 <cite>:math:`O(log_2 N)</cite> &lt;<a class="reference external" href="https://en.wikipedia.org/wiki/Binary_search_tree#cite_note-2">https://en.wikipedia.org/wiki/Binary_search_tree#cite_note-2</a>&gt;`__
 time.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [3 9 5 2 8 6 7 8 4] [0 swap Tree-add] step&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] [3 9 5 2 8 6 7 8 4] [0 swap Tree-add] step&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">9</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <span class="p">[]]]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;to_set == [] swap [0 swap Tree-add] step&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;to_set == [] swap [0 swap Tree-add] step&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[3 9 5 2 8 6 7 8 4] to_set&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[3 9 5 2 8 6 7 8 4] to_set&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">9</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <span class="p">[]]]</span>
@@ -592,10 +592,10 @@ time.</p>
 </div>
 <p>And with that we can write a little program <code class="docutils literal notranslate"><span class="pre">unique</span></code> to remove
 duplicate items from a list.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;unique == [to_set [first] Tree-iter] cons run&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;unique == [to_set [first] Tree-iter] cons run&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[3 9 3 5 2 9 8 8 8 6 2 7 8 4 3] unique&#39;</span><span class="p">)</span>  <span class="c1"># Filter duplicate items.</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[3 9 3 5 2 9 8 8 8 6 2 7 8 4 3] unique&#39;)  # Filter duplicate items.
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">7</span> <span class="mi">6</span> <span class="mi">8</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">9</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span>
@@ -679,23 +679,23 @@ right side:</p>
 </pre></div>
 </div>
 <p>Now we can sort sequences.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1">#define(&#39;Tree-iter-order == [not] [pop] [dup third] [[cons dip] dupdip [[first] dupdip] dip [rest rest rest first] dip i] genrec&#39;)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>#define(&#39;Tree-iter-order == [not] [pop] [dup third] [[cons dip] dupdip [[first] dupdip] dip [rest rest rest first] dip i] genrec&#39;)
 
 
-<span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
+DefinitionWrapper.add_definitions(&#39;&#39;&#39;
 
-<span class="s1">fourth == rest rest rest first</span>
+fourth == rest rest rest first
 
-<span class="s1">proc_left == [cons dip] dupdip</span>
-<span class="s1">proc_current == [[first] dupdip] dip</span>
-<span class="s1">proc_right == [fourth] dip i</span>
+proc_left == [cons dip] dupdip
+proc_current == [[first] dupdip] dip
+proc_right == [fourth] dip i
 
-<span class="s1">Tree-iter-order == [not] [pop] [dup third] [proc_left proc_current proc_right] genrec</span>
+Tree-iter-order == [not] [pop] [dup third] [proc_left proc_current proc_right] genrec
 
-<span class="s1">&#39;&#39;&#39;</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
+&#39;&#39;&#39;, D)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[3 9 5 2 8 6 7 8 4] to_set Tree-iter-order&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[3 9 5 2 8 6 7 8 4] to_set Tree-iter-order&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span> <span class="mi">9</span>
@@ -835,54 +835,54 @@ because there’s no value to discard.</p>
 <span class="n">Tree</span><span class="o">-</span><span class="n">get</span> <span class="o">==</span> <span class="p">[</span><span class="n">pop</span> <span class="ow">not</span><span class="p">]</span> <span class="n">swap</span> <span class="p">[]</span> <span class="p">[</span><span class="n">P</span> <span class="p">[</span><span class="n">T</span><span class="o">&gt;</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="o">&lt;</span><span class="p">]</span> <span class="n">cmp</span><span class="p">]</span> <span class="n">genrec</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># I don&#39;t want to deal with name conflicts with the above so I&#39;m inlining everything here.</span>
-<span class="c1"># The original Joy system has &quot;hide&quot; which is a meta-command which allows you to use named</span>
-<span class="c1"># definitions that are only in scope for a given definition.  I don&#39;t want to implement</span>
-<span class="c1"># that (yet) so...</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span># I don&#39;t want to deal with name conflicts with the above so I&#39;m inlining everything here.
+# The original Joy system has &quot;hide&quot; which is a meta-command which allows you to use named
+# definitions that are only in scope for a given definition.  I don&#39;t want to implement
+# that (yet) so...
 
 
-<span class="n">define</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
-<span class="s1">Tree-get == [pop not] swap [] [</span>
-<span class="s1">  over [pop popop first] nullary</span>
-<span class="s1">  [[fourth] dipd i]</span>
-<span class="s1">  [popop second]</span>
-<span class="s1">  [[third] dipd i]</span>
-<span class="s1">  cmp</span>
-<span class="s1">  ] genrec</span>
-<span class="s1">&#39;&#39;&#39;</span><span class="p">)</span>
+define(&#39;&#39;&#39;
+Tree-get == [pop not] swap [] [
+  over [pop popop first] nullary
+  [[fourth] dipd i]
+  [popop second]
+  [[third] dipd i]
+  cmp
+  ] genrec
+&#39;&#39;&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;gary&quot; 23 [] []] &quot;mike&quot; [popd &quot; not in tree&quot; +] Tree-get&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[&quot;gary&quot; 23 [] []] &quot;mike&quot; [popd &quot; not in tree&quot; +] Tree-get&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;mike not in tree&#39;</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;gary&quot; 23 [] []] &quot;gary&quot; [popop &quot;err&quot;] Tree-get&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[&quot;gary&quot; 23 [] []] &quot;gary&quot; [popop &quot;err&quot;] Tree-get&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;&#39;&#39;
 
-<span class="s1">    [] [[0 &#39;a&#39;] [1 &#39;b&#39;] [2 &#39;c&#39;]] [i Tree-add] step</span>
+    [] [[0 &#39;a&#39;] [1 &#39;b&#39;] [2 &#39;c&#39;]] [i Tree-add] step
 
-<span class="s1">    &#39;c&#39; [popop &#39;not found&#39;] Tree-get</span>
+    &#39;c&#39; [popop &#39;not found&#39;] Tree-get
 
-<span class="s1">&#39;&#39;&#39;</span><span class="p">)</span>
+&#39;&#39;&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;&#39;&#39;
 
-<span class="s1">    [] [[0 &#39;a&#39;] [1 &#39;b&#39;] [2 &#39;c&#39;]] [i Tree-add] step</span>
+    [] [[0 &#39;a&#39;] [1 &#39;b&#39;] [2 &#39;c&#39;]] [i Tree-add] step
 
-<span class="s1">    &#39;d&#39; [popop &#39;not found&#39;] Tree-get</span>
+    &#39;d&#39; [popop &#39;not found&#39;] Tree-get
 
-<span class="s1">&#39;&#39;&#39;</span><span class="p">)</span>
+&#39;&#39;&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;not found&#39;</span>
@@ -1160,11 +1160,11 @@ E == [
 <span class="n">W</span> <span class="o">==</span> <span class="n">dup</span> <span class="n">W</span><span class="o">.</span><span class="n">rightmost</span> <span class="n">W</span><span class="o">.</span><span class="n">unpack</span> <span class="n">over</span>
 <span class="n">E</span><span class="o">.</span><span class="n">clear_stuff</span> <span class="o">==</span> <span class="n">roll</span><span class="o">&gt;</span> <span class="n">popop</span> <span class="n">rest</span>
 <span class="n">E</span><span class="o">.</span><span class="n">delete</span> <span class="o">==</span> <span class="n">cons</span> <span class="n">dipd</span>
-<span class="n">E</span><span class="o">.</span><span class="mi">0</span> <span class="o">==</span> <span class="n">E</span><span class="o">.</span><span class="n">clear_stuff</span> <span class="p">[</span><span class="n">W</span><span class="p">]</span> <span class="n">dip</span> <span class="n">E</span><span class="o">.</span><span class="n">delete</span> <span class="n">swap</span>
+<span class="n">E</span><span class="mf">.0</span> <span class="o">==</span> <span class="n">E</span><span class="o">.</span><span class="n">clear_stuff</span> <span class="p">[</span><span class="n">W</span><span class="p">]</span> <span class="n">dip</span> <span class="n">E</span><span class="o">.</span><span class="n">delete</span> <span class="n">swap</span>
 <span class="n">E</span> <span class="o">==</span> <span class="p">[</span>
     <span class="p">[[</span><span class="n">pop</span> <span class="n">third</span> <span class="ow">not</span><span class="p">]</span> <span class="n">pop</span> <span class="n">fourth</span><span class="p">]</span>
     <span class="p">[[</span><span class="n">pop</span> <span class="n">fourth</span> <span class="ow">not</span><span class="p">]</span> <span class="n">pop</span> <span class="n">third</span><span class="p">]</span>
-    <span class="p">[[</span><span class="n">E</span><span class="o">.</span><span class="mi">0</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span><span class="p">]</span>
+    <span class="p">[[</span><span class="n">E</span><span class="mf">.0</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span><span class="p">]</span>
 <span class="p">]</span> <span class="n">cond</span>
 <span class="n">T</span><span class="o">&gt;</span> <span class="o">==</span> <span class="p">[</span><span class="n">dipd</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span>
 <span class="n">T</span><span class="o">&lt;</span> <span class="o">==</span> <span class="p">[</span><span class="n">dipdd</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span>
@@ -1175,61 +1175,61 @@ E == [
 </div>
 <p>By the standards of the code I’ve written so far, this is a <em>huge</em> Joy
 program.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
-<span class="s1">first_two == uncons uncons pop</span>
-<span class="s1">fourth == rest rest rest first</span>
-<span class="s1">?fourth == [] [fourth] [] ifte</span>
-<span class="s1">W.rightmost == [?fourth] [fourth] while</span>
-<span class="s1">E.clear_stuff == roll&gt; popop rest</span>
-<span class="s1">E.delete == cons dipd</span>
-<span class="s1">W == dup W.rightmost first_two over</span>
-<span class="s1">E.0 == E.clear_stuff [W] dip E.delete swap</span>
-<span class="s1">E == [[[pop third not] pop fourth] [[pop fourth not] pop third] [[E.0] cons infra]] cond</span>
-<span class="s1">T&gt; == [dipd] cons infra</span>
-<span class="s1">T&lt; == [dipdd] cons infra</span>
-<span class="s1">R0 == over first swap dup</span>
-<span class="s1">R1 == cons roll&gt; [T&gt;] [E] [T&lt;] cmp</span>
-<span class="s1">Tree-Delete == [pop not] [pop] [R0] [R1] genrec</span>
-<span class="s1">&#39;&#39;&#39;</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
-</pre></div>
-</div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;c&#39; Tree-Delete &quot;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>DefinitionWrapper.add_definitions(&#39;&#39;&#39;
+first_two == uncons uncons pop
+fourth == rest rest rest first
+?fourth == [] [fourth] [] ifte
+W.rightmost == [?fourth] [fourth] while
+E.clear_stuff == roll&gt; popop rest
+E.delete == cons dipd
+W == dup W.rightmost first_two over
+E.0 == E.clear_stuff [W] dip E.delete swap
+E == [[[pop third not] pop fourth] [[pop fourth not] pop third] [[E.0] cons infra]] cond
+T&gt; == [dipd] cons infra
+T&lt; == [dipdd] cons infra
+R0 == over first swap dup
+R1 == cons roll&gt; [T&gt;] [E] [T&lt;] cmp
+Tree-Delete == [pop not] [pop] [R0] [R1] genrec
+&#39;&#39;&#39;, D)
+</pre></div>
+</div>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;c&#39; Tree-Delete &quot;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;b&#39; Tree-Delete &quot;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;b&#39; Tree-Delete &quot;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;a&#39; Tree-Delete &quot;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;a&#39; Tree-Delete &quot;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;der&#39; Tree-Delete &quot;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;der&#39; Tree-Delete &quot;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [4 2 3 1 6 7 5 ] [0 swap Tree-add] step&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] [4 2 3 1 6 7 5 ] [0 swap Tree-add] step&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 3 Tree-Delete &quot;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 3 Tree-Delete &quot;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 4 Tree-Delete &quot;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&quot;[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 4 Tree-Delete &quot;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]]</span>
@@ -1373,7 +1373,7 @@ Tree-delete == [pop not] [pop] [_Tree_delete_R0] [_Tree_delete_R1] genrec
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/Quadratic.html b/docs/sphinx_docs/_build/html/notebooks/Quadratic.html
index 4c2d7c8..86fe364 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/Quadratic.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Quadratic.html
@@ -13,7 +13,7 @@
     <script src="../_static/jquery.js"></script>
     <script src="../_static/underscore.js"></script>
     <script src="../_static/doctools.js"></script>
-    <script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
+    <script async="async" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
     <link rel="next" title="Replacing Functions in the Dictionary" href="Replacing.html" />
@@ -34,7 +34,7 @@
 
           <div class="body" role="main">
             
-  <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
+  <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import J, V, define
 </pre></div>
 </div>
 <section id="quadratic-formula">
@@ -100,11 +100,11 @@ the variables:</p>
 </div>
 <p>The three arguments are to the left, so we can “chop off” everything to
 the right and say it’s the definition of the <code class="docutils literal notranslate"><span class="pre">quadratic</span></code> function:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2&#39;)
 </pre></div>
 </div>
 <p>Let’s try it out:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;3 1 1 quadratic&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;3 1 1 quadratic&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="mf">0.3819660112501051</span> <span class="o">-</span><span class="mf">2.618033988749895</span>
@@ -114,7 +114,7 @@ the right and say it’s the definition of the <code class="docutils literal not
 lines are the <code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">dipd</span></code> combinators building the main program
 by incorporating the values on the stack. Then that program runs and you
 get the results. This is pretty typical of Joy code.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;-5 1 4 quadratic&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;-5 1 4 quadratic&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                                                   <span class="o">.</span> <span class="o">-</span><span class="mi">5</span> <span class="mi">1</span> <span class="mi">4</span> <span class="n">quadratic</span>
@@ -253,7 +253,7 @@ get the results. This is pretty typical of Joy code.</p>
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/Recursion_Combinators.html b/docs/sphinx_docs/_build/html/notebooks/Recursion_Combinators.html
index d143e1a..385778c 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/Recursion_Combinators.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Recursion_Combinators.html
@@ -33,7 +33,7 @@
 
           <div class="body" role="main">
             
-  <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">DefinitionWrapper</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
+  <div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import D, DefinitionWrapper, J, V, define
 </pre></div>
 </div>
 <section id="recursion-combinators">
@@ -101,18 +101,18 @@ cons list”.</p></li>
 </ul>
 <p>It may be helpful to see this function implemented in imperative Python
 code.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">hylomorphism</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
-    <span class="sd">&#39;&#39;&#39;Return a hylomorphism function H.&#39;&#39;&#39;</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def hylomorphism(c, F, P, G):
+    &#39;&#39;&#39;Return a hylomorphism function H.&#39;&#39;&#39;
 
-    <span class="k">def</span> <span class="nf">H</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
-        <span class="k">if</span> <span class="n">P</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
-            <span class="n">result</span> <span class="o">=</span> <span class="n">c</span>
-        <span class="k">else</span><span class="p">:</span>
-            <span class="n">b</span><span class="p">,</span> <span class="n">aa</span> <span class="o">=</span> <span class="n">G</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
-            <span class="n">result</span> <span class="o">=</span> <span class="n">F</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">H</span><span class="p">(</span><span class="n">aa</span><span class="p">))</span>  <span class="c1"># b is stored in the stack frame during recursive call to H().</span>
-        <span class="k">return</span> <span class="n">result</span>
+    def H(a):
+        if P(a):
+            result = c
+        else:
+            b, aa = G(a)
+            result = F(b, H(aa))  # b is stored in the stack frame during recursive call to H().
+        return result
 
-    <span class="k">return</span> <span class="n">H</span>
+    return H
 </pre></div>
 </div>
 <p>Cf. <a class="reference external" href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.125">“Bananas, Lenses, &amp; Barbed
@@ -185,7 +185,7 @@ the left so we have a definition for <code class="docutils literal notranslate">
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">hylomorphism</span> <span class="o">==</span> <span class="p">[</span><span class="n">unit</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="n">swoncat</span><span class="p">]</span> <span class="n">dipd</span> <span class="p">[</span><span class="n">dip</span><span class="p">]</span> <span class="n">swoncat</span> <span class="n">genrec</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec&#39;)
 </pre></div>
 </div>
 <section id="example-finding-triangular-numbers">
@@ -200,17 +200,17 @@ of all positive integers less than that one. (In this case the types
 <li><p><code class="docutils literal notranslate"><span class="pre">[G]</span></code> is <code class="docutils literal notranslate"><span class="pre">[--</span> <span class="pre">dup]</span></code></p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">[F]</span></code> is <code class="docutils literal notranslate"><span class="pre">[+]</span></code></p></li>
 </ul>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;triangular_number == [1 &lt;=] 0 [-- dup] [+] hylomorphism&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;triangular_number == [1 &lt;=] 0 [-- dup] [+] hylomorphism&#39;)
 </pre></div>
 </div>
 <p>Let’s try it:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 triangular_number&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;5 triangular_number&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">10</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[0 1 2 3 4 5 6] [triangular_number] map&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[0 1 2 3 4 5 6] [triangular_number] map&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">6</span> <span class="mi">10</span> <span class="mi">15</span><span class="p">]</span>
@@ -372,10 +372,10 @@ values.</p>
    <span class="o">==</span> <span class="p">[</span><span class="mi">0</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="p">[]]</span> <span class="p">[</span><span class="o">--</span> <span class="n">dup</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">swons</span><span class="p">]</span> <span class="n">genrec</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;range == [0 &lt;=] [] [-- dup] [swons] hylomorphism&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;range == [0 &lt;=] [] [-- dup] [swons] hylomorphism&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 range&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;5 range&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">4</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span><span class="p">]</span>
@@ -388,10 +388,10 @@ values.</p>
    <span class="o">==</span> <span class="p">[]</span> <span class="n">swap</span> <span class="p">[</span><span class="mi">0</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="p">[</span><span class="o">--</span> <span class="n">dup</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">primrec</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;range_reverse == [] swap [0 &lt;=] [pop] [-- dup [swons] dip] primrec&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;range_reverse == [] swap [0 &lt;=] [pop] [-- dup [swons] dip] primrec&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 range_reverse&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;5 range_reverse&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span>
@@ -404,10 +404,10 @@ values.</p>
    <span class="o">==</span> <span class="p">[</span><span class="mi">0</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="p">[]]</span> <span class="p">[[</span><span class="o">--</span><span class="p">]</span> <span class="n">dupdip</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">swons</span><span class="p">]</span> <span class="n">genrec</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;ranger == [0 &lt;=] [pop []] [[--] dupdip] [dip swons] genrec&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;ranger == [0 &lt;=] [pop []] [[--] dupdip] [dip swons] genrec&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 ranger&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;5 ranger&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">5</span> <span class="mi">4</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span><span class="p">]</span>
@@ -420,10 +420,10 @@ values.</p>
    <span class="o">==</span> <span class="p">[]</span> <span class="n">swap</span> <span class="p">[</span><span class="mi">0</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="p">[[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dupdip</span> <span class="o">--</span><span class="p">]</span> <span class="n">primrec</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;ranger_reverse == [] swap [0 &lt;=] [pop] [[swons] dupdip --] primrec&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;ranger_reverse == [] swap [0 &lt;=] [pop] [[swons] dupdip --] primrec&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 ranger_reverse&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;5 ranger_reverse&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span><span class="p">]</span>
@@ -444,17 +444,17 @@ and makes some new value.</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">C</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="n">c</span> <span class="p">[</span><span class="n">uncons</span> <span class="n">swap</span><span class="p">]</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">hylomorphism</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;swuncons == uncons swap&#39;</span><span class="p">)</span>  <span class="c1"># Awkward name.</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;swuncons == uncons swap&#39;)  # Awkward name.
 </pre></div>
 </div>
 <p>An example of a catamorphism is the sum function.</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">sum</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="mi">0</span> <span class="p">[</span><span class="n">swuncons</span><span class="p">]</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">hylomorphism</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;sum == [not] 0 [swuncons] [+] hylomorphism&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;sum == [not] 0 [swuncons] [+] hylomorphism&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[5 4 3 2 1] sum&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[5 4 3 2 1] sum&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span>
@@ -464,7 +464,7 @@ and makes some new value.</p>
 <h3>The <code class="docutils literal notranslate"><span class="pre">step</span></code> combinator<a class="headerlink" href="#the-step-combinator" title="Permalink to this headline">¶</a></h3>
 <p>The <code class="docutils literal notranslate"><span class="pre">step</span></code> combinator will usually be better to use than
 <code class="docutils literal notranslate"><span class="pre">catamorphism</span></code>.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[step] help&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[step] help&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Run</span> <span class="n">a</span> <span class="n">quoted</span> <span class="n">program</span> <span class="n">on</span> <span class="n">each</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">a</span> <span class="n">sequence</span><span class="o">.</span>
@@ -488,10 +488,10 @@ and makes some new value.</p>
 <span class="n">on</span> <span class="n">top</span> <span class="n">of</span> <span class="n">the</span> <span class="n">stack</span><span class="o">.</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;sum == 0 swap [+] step&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;sum == 0 swap [+] step&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[5 4 3 2 1] sum&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[5 4 3 2 1] sum&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span>
@@ -512,10 +512,10 @@ and makes some new value.</p>
 <span class="n">P</span> <span class="o">==</span> <span class="mi">1</span> <span class="o">&lt;=</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;factorial == 1 swap [1 &lt;=] [pop] [[*] dupdip --] primrec&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;factorial == 1 swap [1 &lt;=] [pop] [[*] dupdip --] primrec&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 factorial&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;5 factorial&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">120</span>
@@ -544,10 +544,10 @@ pattern <code class="docutils literal notranslate"><span class="pre">H2</span></
 <span class="n">P</span> <span class="o">==</span> <span class="ow">not</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;tails == [] swap [not] [pop] [rest dup [swons] dip] primrec&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;tails == [] swap [not] [pop] [rest dup [swons] dip] primrec&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 2 3] tails&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 2 3] tails&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[]</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]]</span>
@@ -675,7 +675,7 @@ Wire”</a></p>
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/Replacing.html b/docs/sphinx_docs/_build/html/notebooks/Replacing.html
index 01108aa..f1fcbbc 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/Replacing.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Replacing.html
@@ -42,12 +42,12 @@ we can implement e.g. a function that adds new functions to the
 dictionary. However, there’s no function that does that. Adding a new
 function to the dictionary is a meta-interpreter action, you have to do
 it in Python, not Joy.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import D, J, V
 </pre></div>
 </div>
 <section id="a-long-trace">
 <h2>A long trace<a class="headerlink" href="#a-long-trace" title="Permalink to this headline">¶</a></h2>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[23 18] average&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[23 18] average&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                                  <span class="o">.</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="n">average</span>
@@ -105,30 +105,30 @@ it in Python, not Joy.</p>
 <p>An efficient <code class="docutils literal notranslate"><span class="pre">sum</span></code> function is already in the library. But for
 <code class="docutils literal notranslate"><span class="pre">size</span></code> we can use a “compiled” version hand-written in Python to speed
 up evaluation and make the trace more readable.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">SimpleFunctionWrapper</span>
-<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="kn">import</span> <span class="n">iter_stack</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from joy.library import SimpleFunctionWrapper
+from joy.utils.stack import iter_stack
 
 
-<span class="nd">@SimpleFunctionWrapper</span>
-<span class="k">def</span> <span class="nf">size</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
-    <span class="sd">&#39;&#39;&#39;Return the size of the sequence on the stack.&#39;&#39;&#39;</span>
-    <span class="n">sequence</span><span class="p">,</span> <span class="n">stack</span> <span class="o">=</span> <span class="n">stack</span>
-    <span class="n">n</span> <span class="o">=</span> <span class="mi">0</span>
-    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="n">iter_stack</span><span class="p">(</span><span class="n">sequence</span><span class="p">):</span>
-        <span class="n">n</span> <span class="o">+=</span> <span class="mi">1</span>
-    <span class="k">return</span> <span class="n">n</span><span class="p">,</span> <span class="n">stack</span>
+@SimpleFunctionWrapper
+def size(stack):
+    &#39;&#39;&#39;Return the size of the sequence on the stack.&#39;&#39;&#39;
+    sequence, stack = stack
+    n = 0
+    for _ in iter_stack(sequence):
+        n += 1
+    return n, stack
 </pre></div>
 </div>
 <p>Now we replace the old version in the dictionary with the new version,
 and re-evaluate the expression.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">D</span><span class="p">[</span><span class="s1">&#39;size&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">size</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>D[&#39;size&#39;] = size
 </pre></div>
 </div>
 </section>
 <section id="a-shorter-trace">
 <h2>A shorter trace<a class="headerlink" href="#a-shorter-trace" title="Permalink to this headline">¶</a></h2>
 <p>You can see that <code class="docutils literal notranslate"><span class="pre">size</span></code> now executes in a single step.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[23 18] average&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[23 18] average&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                                  <span class="o">.</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="n">average</span>
@@ -251,7 +251,7 @@ and re-evaluate the expression.</p>
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/Square_Spiral.html b/docs/sphinx_docs/_build/html/notebooks/Square_Spiral.html
index 474d0b8..a6033ad 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/Square_Spiral.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Square_Spiral.html
@@ -33,7 +33,7 @@
 
           <div class="body" role="main">
             
-  <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
+  <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import J, V, define
 </pre></div>
 </div>
 <section id="square-spiral-example-joy-code">
@@ -99,8 +99,8 @@ to apply <code class="docutils literal notranslate"><span class="pre">abs</span>
 that each accept two quoted predicate programs, run the first, and
 conditionally run the second only if required (to compute the final
 Boolean value). They run their predicate arguments <code class="docutils literal notranslate"><span class="pre">nullary</span></code>.</p>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;&amp;&amp; [nullary] cons [nullary [0]] dip branch&#39;</span><span class="p">)</span>
-<span class="n">define</span><span class="p">(</span><span class="s1">&#39;|| [nullary] cons [nullary] dip [1] branch&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define(&#39;&amp;&amp; [nullary] cons [nullary [0]] dip branch&#39;)
+define(&#39;|| [nullary] cons [nullary] dip [1] branch&#39;)
 </pre></div>
 </div>
 <p>Given those, we can define <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">!=</span> <span class="pre">y</span> <span class="pre">||</span> <span class="pre">x</span> <span class="pre">&gt;=</span> <span class="pre">0</span></code> as:</p>
@@ -143,7 +143,7 @@ legible.</p>
 </section>
 <section id="not-negative">
 <h3>“Not Negative”<a class="headerlink" href="#not-negative" title="Permalink to this headline">¶</a></h3>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;!- 0 &gt;=&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define(&#39;!- 0 &gt;=&#39;)
 </pre></div>
 </div>
 </section>
@@ -169,29 +169,29 @@ of <code class="docutils literal notranslate"><span class="pre">ifte</span></cod
 branch
 </pre></div>
 </div>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;spiral_next [[[abs] ii &lt;=] [[&lt;&gt;] [pop !-] ||] &amp;&amp;] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define(&#39;spiral_next [[[abs] ii &lt;=] [[&lt;&gt;] [pop !-] ||] &amp;&amp;] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte&#39;)
 </pre></div>
 </div>
 <p>Let’s try it out:</p>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;0 0 spiral_next&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J(&#39;0 0 spiral_next&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">0</span>
 </pre></div>
 </div>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;1 0 spiral_next&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 0 spiral_next&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="o">-</span><span class="mi">1</span>
 </pre></div>
 </div>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;1 -1 spiral_next&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J(&#39;1 -1 spiral_next&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span> <span class="o">-</span><span class="mi">1</span>
 </pre></div>
 </div>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;0 -1 spiral_next&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J(&#39;0 -1 spiral_next&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="mi">1</span> <span class="o">-</span><span class="mi">1</span>
@@ -240,7 +240,7 @@ From:</p>
            <span class="p">[</span><span class="n">x</span><span class="s1">&#39; y&#39;</span><span class="p">]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[0 0] [spiral_next] infra&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J(&#39;[0 0] [spiral_next] infra&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">1</span><span class="p">]</span>
@@ -262,7 +262,7 @@ us out of the value and stepper function:</p>
 </pre></div>
 </div>
 <p>Here it is in action:</p>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[0 0] [dup [spiral_next] infra] make_generator x x x x pop&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J(&#39;[0 0] [dup [spiral_next] infra] make_generator x x x x pop&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span> <span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span> <span class="mi">0</span><span class="p">]</span>
@@ -290,13 +290,13 @@ pairs, where the next pair in the series can be generated at any time by
 using the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator on the generator (which is just a quoted
 expression containing a copy of the current pair and the “stepper
 function” to generate the next pair from that.)</p>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_spn_P [[abs] ii &lt;=] [[&lt;&gt;] [pop !-] ||] &amp;&amp;&#39;</span><span class="p">)</span>
-<span class="n">define</span><span class="p">(</span><span class="s1">&#39;_spn_T [!-] [[++]] [[--]] ifte dip&#39;</span><span class="p">)</span>
-<span class="n">define</span><span class="p">(</span><span class="s1">&#39;_spn_E [pop !-] [--] [++] ifte&#39;</span><span class="p">)</span>
-<span class="n">define</span><span class="p">(</span><span class="s1">&#39;spiral_next _spn_P [_spn_E] [_spn_T] branch&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define(&#39;_spn_P [[abs] ii &lt;=] [[&lt;&gt;] [pop !-] ||] &amp;&amp;&#39;)
+define(&#39;_spn_T [!-] [[++]] [[--]] ifte dip&#39;)
+define(&#39;_spn_E [pop !-] [--] [++] ifte&#39;)
+define(&#39;spiral_next _spn_P [_spn_E] [_spn_T] branch&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;23 18 spiral_next&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>V(&#39;23 18 spiral_next&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                                                               . 23 18 spiral_next
@@ -456,7 +456,7 @@ function” to generate the next pair from that.)</p>
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/The_Four_Operations.html b/docs/sphinx_docs/_build/html/notebooks/The_Four_Operations.html
index b2ae3a1..3be8e1e 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/The_Four_Operations.html
+++ b/docs/sphinx_docs/_build/html/notebooks/The_Four_Operations.html
@@ -404,7 +404,7 @@ evaluation, yeah?)</p>
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/Treestep.html b/docs/sphinx_docs/_build/html/notebooks/Treestep.html
index 5c37053..f5d8d63 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/Treestep.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Treestep.html
@@ -125,13 +125,13 @@ the desired outcome.</p>
 </pre></div>
 </div>
 <p>Extract a couple of auxiliary definitions:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">TS</span><span class="o">.</span><span class="mi">0</span> <span class="o">==</span> <span class="p">[[</span><span class="ow">not</span><span class="p">]</span> <span class="n">swap</span><span class="p">]</span> <span class="n">dip</span>
-<span class="n">TS</span><span class="o">.</span><span class="mi">1</span> <span class="o">==</span> <span class="p">[</span><span class="n">dip</span><span class="p">]</span> <span class="n">cons</span> <span class="p">[</span><span class="n">uncons</span><span class="p">]</span> <span class="n">swoncat</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">TS</span><span class="mf">.0</span> <span class="o">==</span> <span class="p">[[</span><span class="ow">not</span><span class="p">]</span> <span class="n">swap</span><span class="p">]</span> <span class="n">dip</span>
+<span class="n">TS</span><span class="mf">.1</span> <span class="o">==</span> <span class="p">[</span><span class="n">dip</span><span class="p">]</span> <span class="n">cons</span> <span class="p">[</span><span class="n">uncons</span><span class="p">]</span> <span class="n">swoncat</span>
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="p">[</span><span class="n">N</span><span class="p">]</span> <span class="n">TS</span><span class="o">.</span><span class="mi">1</span> <span class="n">TS</span><span class="o">.</span><span class="mi">0</span> <span class="p">[</span><span class="nb">map</span> <span class="n">C</span><span class="p">]</span>                         <span class="n">genrec</span>
-<span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="p">[</span><span class="n">N</span><span class="p">]</span>           <span class="p">[</span><span class="nb">map</span> <span class="n">C</span><span class="p">]</span>         <span class="p">[</span><span class="n">TS</span><span class="o">.</span><span class="mi">1</span> <span class="n">TS</span><span class="o">.</span><span class="mi">0</span><span class="p">]</span> <span class="n">dip</span> <span class="n">genrec</span>
-<span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="p">[</span><span class="n">N</span><span class="p">]</span> <span class="p">[</span><span class="n">C</span><span class="p">]</span>         <span class="p">[</span><span class="nb">map</span><span class="p">]</span> <span class="n">swoncat</span> <span class="p">[</span><span class="n">TS</span><span class="o">.</span><span class="mi">1</span> <span class="n">TS</span><span class="o">.</span><span class="mi">0</span><span class="p">]</span> <span class="n">dip</span> <span class="n">genrec</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="p">[</span><span class="n">N</span><span class="p">]</span> <span class="n">TS</span><span class="mf">.1</span> <span class="n">TS</span><span class="mf">.0</span> <span class="p">[</span><span class="nb">map</span> <span class="n">C</span><span class="p">]</span>                         <span class="n">genrec</span>
+<span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="p">[</span><span class="n">N</span><span class="p">]</span>           <span class="p">[</span><span class="nb">map</span> <span class="n">C</span><span class="p">]</span>         <span class="p">[</span><span class="n">TS</span><span class="mf">.1</span> <span class="n">TS</span><span class="mf">.0</span><span class="p">]</span> <span class="n">dip</span> <span class="n">genrec</span>
+<span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="p">[</span><span class="n">N</span><span class="p">]</span> <span class="p">[</span><span class="n">C</span><span class="p">]</span>         <span class="p">[</span><span class="nb">map</span><span class="p">]</span> <span class="n">swoncat</span> <span class="p">[</span><span class="n">TS</span><span class="mf">.1</span> <span class="n">TS</span><span class="mf">.0</span><span class="p">]</span> <span class="n">dip</span> <span class="n">genrec</span>
 </pre></div>
 </div>
 <p>The givens are all to the left so we have our definition.</p>
@@ -148,17 +148,17 @@ the desired outcome.</p>
 </section>
 <section id="define-treestep">
 <h2>Define <code class="docutils literal notranslate"><span class="pre">treestep</span></code><a class="headerlink" href="#define-treestep" title="Permalink to this headline">¶</a></h2>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span><span class="p">,</span> <span class="n">DefinitionWrapper</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import D, J, V, define, DefinitionWrapper
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>DefinitionWrapper.add_definitions(&#39;&#39;&#39;
 
-<span class="s1">    _treestep_0 == [[not] swap] dip</span>
-<span class="s1">    _treestep_1 == [dip] cons [uncons] swoncat</span>
-<span class="s1">    treegrind == [_treestep_1 _treestep_0] dip genrec</span>
-<span class="s1">    treestep == [map] swoncat treegrind</span>
+    _treestep_0 == [[not] swap] dip
+    _treestep_1 == [dip] cons [uncons] swoncat
+    treegrind == [_treestep_1 _treestep_0] dip genrec
+    treestep == [map] swoncat treegrind
 
-<span class="s1">&#39;&#39;&#39;</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
+&#39;&#39;&#39;, D)
 </pre></div>
 </div>
 </section>
@@ -169,7 +169,7 @@ all nodes in a tree with this function:</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">sumtree</span> <span class="o">==</span> <span class="p">[</span><span class="n">pop</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="nb">sum</span> <span class="o">+</span><span class="p">]</span> <span class="n">treestep</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;sumtree == [pop 0] [] [sum +] treestep&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;sumtree == [pop 0] [] [sum +] treestep&#39;)
 </pre></div>
 </div>
 <p>Running this function on an empty tree value gives zero:</p>
@@ -178,7 +178,7 @@ all nodes in a tree with this function:</p>
            <span class="mi">0</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] sumtree&#39;</span><span class="p">)</span>  <span class="c1"># Empty tree.</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[] sumtree&#39;)  # Empty tree.
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span>
@@ -192,61 +192,61 @@ all nodes in a tree with this function:</p>
 <span class="n">n</span><span class="o">+</span><span class="n">m</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23] sumtree&#39;</span><span class="p">)</span>  <span class="c1"># No child trees.</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23] sumtree&#39;)  # No child trees.
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 []] sumtree&#39;</span><span class="p">)</span>  <span class="c1"># Child tree, empty.</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 []] sumtree&#39;)  # Child tree, empty.
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [4]] [3]] sumtree&#39;</span><span class="p">)</span>  <span class="c1"># Non-empty child trees.</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 [2 [4]] [3]] sumtree&#39;)  # Non-empty child trees.
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">32</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] sumtree&#39;</span><span class="p">)</span>  <span class="c1"># Etc...</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 [2 [8] [9]] [3] [4 []]] sumtree&#39;)  # Etc...
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">49</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep&#39;</span><span class="p">)</span>  <span class="c1"># Alternate &quot;spelling&quot;.</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep&#39;)  # Alternate &quot;spelling&quot;.
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">49</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep&#39;</span><span class="p">)</span>  <span class="c1"># Replace each node.</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep&#39;)  # Replace each node.
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">23</span> <span class="p">[</span><span class="mi">23</span> <span class="p">[</span><span class="mi">23</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span><span class="p">]]</span> <span class="p">[</span><span class="mi">23</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="p">[]]]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span><span class="p">]]</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[]]]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">6</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep&#39;</span><span class="p">)</span>  <span class="c1"># Combine replace and sum into one function.</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep&#39;)  # Combine replace and sum into one function.
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">6</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep&#39;</span><span class="p">)</span>  <span class="c1"># Combine replace and sum into one function.</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep&#39;)  # Combine replace and sum into one function.
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span>
@@ -277,7 +277,7 @@ all nodes in a tree with this function:</p>
 </pre></div>
 </div>
 <p>This doesn’t quite work:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] [&quot;B&quot;] [first] [i] treestep&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] [&quot;B&quot;] [first] [i] treestep&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="s1">&#39;B&#39;</span> <span class="s1">&#39;B&#39;</span>
@@ -299,7 +299,7 @@ depositing our results directly on the stack.</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="n">first</span><span class="p">]</span> <span class="p">[</span><span class="n">flatten</span> <span class="n">cons</span><span class="p">]</span> <span class="n">treestep</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [] [first] [flatten cons] treestep&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [] [first] [flatten cons] treestep&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">9</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">8</span> <span class="mi">6</span> <span class="mi">7</span><span class="p">]</span>
@@ -322,7 +322,7 @@ depositing our results directly on the stack.</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="n">i</span> <span class="n">roll</span><span class="o">&lt;</span> <span class="n">swons</span> <span class="n">concat</span><span class="p">]</span> <span class="p">[</span><span class="n">first</span><span class="p">]</span> <span class="n">treestep</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [] [uncons pop] [i roll&lt; swons concat] treestep&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [] [uncons pop] [i roll&lt; swons concat] treestep&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span> <span class="mi">9</span><span class="p">]</span>
@@ -343,7 +343,7 @@ non-empty node is:</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">key</span> <span class="n">value</span><span class="p">]</span> <span class="n">N</span> <span class="p">[</span><span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">K</span><span class="p">]</span> <span class="n">C</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[&quot;key&quot; &quot;value&quot;] [&quot;left&quot;] [&quot;right&quot;] ] [&quot;B&quot;] [&quot;N&quot;] [&quot;C&quot;] treegrind&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[[&quot;key&quot; &quot;value&quot;] [&quot;left&quot;] [&quot;right&quot;] ] [&quot;B&quot;] [&quot;N&quot;] [&quot;C&quot;] treegrind&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;key&#39;</span> <span class="s1">&#39;value&#39;</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[[</span><span class="s1">&#39;left&#39;</span><span class="p">]</span> <span class="p">[</span><span class="s1">&#39;right&#39;</span><span class="p">]]</span> <span class="p">[[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="s1">&#39;B&#39;</span><span class="p">]</span> <span class="p">[</span><span class="n">uncons</span> <span class="p">[</span><span class="s1">&#39;N&#39;</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="p">[</span><span class="s1">&#39;C&#39;</span><span class="p">]</span> <span class="n">genrec</span><span class="p">]</span> <span class="s1">&#39;C&#39;</span>
@@ -353,21 +353,21 @@ non-empty node is:</p>
 <section id="treegrind-with-step">
 <h2><code class="docutils literal notranslate"><span class="pre">treegrind</span></code> with <code class="docutils literal notranslate"><span class="pre">step</span></code><a class="headerlink" href="#treegrind-with-step" title="Permalink to this headline">¶</a></h2>
 <p>Iteration through the nodes</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [pop] [&quot;N&quot;] [step] treegrind&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [pop] [&quot;N&quot;] [step] treegrind&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">9</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span>
 </pre></div>
 </div>
 <p>Sum the nodes’ keys.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [pop] [first +] [step] treegrind&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [pop] [first +] [step] treegrind&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">44</span>
 </pre></div>
 </div>
 <p>Rebuild the tree using <code class="docutils literal notranslate"><span class="pre">map</span></code> (imitating <code class="docutils literal notranslate"><span class="pre">treestep</span></code>.)</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [] [[100 +] infra] [map cons] treegrind&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [] [[100 +] infra] [map cons] treegrind&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="mi">103</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">102</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[[</span><span class="mi">109</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">105</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">104</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[[</span><span class="mi">108</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">106</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">107</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <span class="p">[]]]</span>
@@ -449,37 +449,37 @@ equal):</p>
 </pre></div>
 </div>
 <p>To me, that seems simpler than the <code class="docutils literal notranslate"><span class="pre">genrec</span></code> version.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>DefinitionWrapper.add_definitions(&#39;&#39;&#39;
 
-<span class="s1">    T&gt; == pop [first] dip i</span>
-<span class="s1">    T&lt; == pop [second] dip i</span>
-<span class="s1">    E == roll&gt; popop first</span>
-<span class="s1">    P == roll&lt; [roll&lt; uncons swap] dip</span>
+    T&gt; == pop [first] dip i
+    T&lt; == pop [second] dip i
+    E == roll&gt; popop first
+    P == roll&lt; [roll&lt; uncons swap] dip
 
-<span class="s1">    Tree-get == [P [T&gt;] [E] [T&lt;] cmp] treegrind</span>
+    Tree-get == [P [T&gt;] [E] [T&lt;] cmp] treegrind
 
-<span class="s1">&#39;&#39;&#39;</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
+&#39;&#39;&#39;, D)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span><span class="se">\</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;&#39;&#39;\
 
-<span class="s1">[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]</span>
+[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]
 
-<span class="s1">[] [5] Tree-get</span>
+[] [5] Tree-get
 
-<span class="s1">&#39;&#39;&#39;</span><span class="p">)</span>
+&#39;&#39;&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span><span class="se">\</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;&#39;&#39;\
 
-<span class="s1">[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]</span>
+[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]
 
-<span class="s1">[pop &quot;nope&quot;] [25] Tree-get</span>
+[pop &quot;nope&quot;] [25] Tree-get
 
-<span class="s1">&#39;&#39;&#39;</span><span class="p">)</span>
+&#39;&#39;&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;nope&#39;</span>
@@ -574,7 +574,7 @@ equal):</p>
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/TypeChecking.html b/docs/sphinx_docs/_build/html/notebooks/TypeChecking.html
index 142a672..09ebb68 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/TypeChecking.html
+++ b/docs/sphinx_docs/_build/html/notebooks/TypeChecking.html
@@ -35,33 +35,33 @@
             
   <section id="type-checking">
 <h1>Type Checking<a class="headerlink" href="#type-checking" title="Permalink to this headline">¶</a></h1>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">logging</span><span class="o">,</span> <span class="nn">sys</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>import logging, sys
 
-<span class="n">logging</span><span class="o">.</span><span class="n">basicConfig</span><span class="p">(</span>
-  <span class="nb">format</span><span class="o">=</span><span class="s1">&#39;</span><span class="si">%(message)s</span><span class="s1">&#39;</span><span class="p">,</span>
-  <span class="n">stream</span><span class="o">=</span><span class="n">sys</span><span class="o">.</span><span class="n">stdout</span><span class="p">,</span>
-  <span class="n">level</span><span class="o">=</span><span class="n">logging</span><span class="o">.</span><span class="n">INFO</span><span class="p">,</span>
-  <span class="p">)</span>
+logging.basicConfig(
+  format=&#39;%(message)s&#39;,
+  stream=sys.stdout,
+  level=logging.INFO,
+  )
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.utils.types</span> <span class="kn">import</span> <span class="p">(</span>
-    <span class="n">doc_from_stack_effect</span><span class="p">,</span>
-    <span class="n">infer</span><span class="p">,</span>
-    <span class="n">reify</span><span class="p">,</span>
-    <span class="n">unify</span><span class="p">,</span>
-    <span class="n">FUNCTIONS</span><span class="p">,</span>
-    <span class="n">JoyTypeError</span><span class="p">,</span>
-<span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from joy.utils.types import (
+    doc_from_stack_effect,
+    infer,
+    reify,
+    unify,
+    FUNCTIONS,
+    JoyTypeError,
+)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">D</span> <span class="o">=</span> <span class="n">FUNCTIONS</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
-<span class="k">del</span> <span class="n">D</span><span class="p">[</span><span class="s1">&#39;product&#39;</span><span class="p">]</span>
-<span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">D</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>D = FUNCTIONS.copy()
+del D[&#39;product&#39;]
+globals().update(D)
 </pre></div>
 </div>
 <section id="an-example">
 <h2>An Example<a class="headerlink" href="#an-example" title="Permalink to this headline">¶</a></h2>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">rrest</span><span class="p">,</span> <span class="n">ccons</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>fi, fo = infer(pop, swap, rolldown, rrest, ccons)[0]
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>25 (--) ∘ pop swap rolldown rrest ccons
@@ -72,32 +72,32 @@
 40 ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) ∘
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print doc_from_stack_effect(fi, fo)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a4</span> <span class="n">a5</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a3</span> <span class="o">...</span><span class="mi">1</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a4</span> <span class="n">a5</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a3</span> <span class="o">..</span><span class="mf">.1</span><span class="p">])</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.parser</span> <span class="kn">import</span> <span class="n">text_to_expression</span>
-<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="kn">import</span> <span class="n">stack_to_string</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from joy.parser import text_to_expression
+from joy.utils.stack import stack_to_string
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;0 1 2 [3 4]&#39;</span><span class="p">)</span>  <span class="c1"># reverse order</span>
-<span class="nb">print</span> <span class="n">stack_to_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>e = text_to_expression(&#39;0 1 2 [3 4]&#39;)  # reverse order
+print stack_to_string(e)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fi</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
-<span class="n">u</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>u = unify(e, fi)[0]
+u
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">a1</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">a2</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">a3</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="n">a4</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">a5</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(),</span> <span class="n">s1</span><span class="p">:</span> <span class="p">()}</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span>
-<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">g</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>g = reify(u, (fi, fo))
+print doc_from_stack_effect(*g)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">...</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="p">]</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="p">])</span>
@@ -106,18 +106,18 @@
 </section>
 <section id="unification-works-in-reverse">
 <h2>Unification Works “in Reverse”<a class="headerlink" href="#unification-works-in-reverse" title="Permalink to this headline">¶</a></h2>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[2 3]&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>e = text_to_expression(&#39;[2 3]&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fo</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>  <span class="c1"># output side, not input side</span>
-<span class="n">u</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>u = unify(e, fo)[0]  # output side, not input side
+u
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">a2</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="n">a3</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(),</span> <span class="n">s1</span><span class="p">:</span> <span class="p">()}</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span>
-<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">g</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>g = reify(u, (fi, fo))
+print doc_from_stack_effect(*g)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">...</span> <span class="p">[</span><span class="n">a4</span> <span class="n">a5</span> <span class="p">]</span> <span class="mi">3</span> <span class="mi">2</span> <span class="n">a1</span> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="p">])</span>
@@ -126,7 +126,7 @@
 </section>
 <section id="failing-a-check">
 <h2>Failing a Check<a class="headerlink" href="#failing-a-check" title="Permalink to this headline">¶</a></h2>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>fi, fo = infer(dup, mul)[0]
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>25 (--) ∘ dup mul
@@ -135,17 +135,17 @@
 31 (i1 -- i2) ∘
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;&quot;two&quot;&#39;</span><span class="p">)</span>
-<span class="nb">print</span> <span class="n">stack_to_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>e = text_to_expression(&#39;&quot;two&quot;&#39;)
+print stack_to_string(e)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;two&#39;</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">try</span><span class="p">:</span>
-    <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fi</span><span class="p">)</span>
-<span class="k">except</span> <span class="n">JoyTypeError</span><span class="p">,</span> <span class="n">err</span><span class="p">:</span>
-    <span class="nb">print</span> <span class="n">err</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>try:
+    unify(e, fi)
+except JoyTypeError, err:
+    print err
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Cannot</span> <span class="n">unify</span> <span class="s1">&#39;two&#39;</span> <span class="ow">and</span> <span class="n">f1</span><span class="o">.</span>
@@ -240,7 +240,7 @@
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/Types.html b/docs/sphinx_docs/_build/html/notebooks/Types.html
index 2330787..8a5b149 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/Types.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Types.html
@@ -182,8 +182,8 @@ terms in the forms:</p>
 <section id="compiling-popswaproll">
 <h3>Compiling <code class="docutils literal notranslate"><span class="pre">pop∘swap∘roll&lt;</span></code><a class="headerlink" href="#compiling-popswaproll" title="Permalink to this headline">¶</a></h3>
 <p>The simplest way to “compile” this function would be something like:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">poswrd</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">e</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
-    <span class="k">return</span> <span class="n">rolldown</span><span class="p">(</span><span class="o">*</span><span class="n">swap</span><span class="p">(</span><span class="o">*</span><span class="n">pop</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">e</span><span class="p">,</span> <span class="n">d</span><span class="p">)))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def poswrd(s, e, d):
+    return rolldown(*swap(*pop(s, e, d)))
 </pre></div>
 </div>
 <p>However, internally this function would still be allocating tuples
@@ -193,9 +193,9 @@ terms in the forms:</p>
 </pre></div>
 </div>
 <p>We should be able to directly write out a Python function like:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">poswrd</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
-    <span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span>
-    <span class="k">return</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">stack</span><span class="p">)))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def poswrd(stack):
+    (_, (a, (b, (c, stack)))) = stack
+    return (c, (b, (a, stack)))
 </pre></div>
 </div>
 <p>This eliminates the internal work of the first version. Because this
@@ -243,14 +243,14 @@ available index number for the right-side stack effect comment):</p>
 </pre></div>
 </div>
 <p>Re-label (the tails of the lists on each side each get their own label):</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">0</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span> <span class="p">[</span><span class="o">.</span><span class="mf">0.</span><span class="p">])</span> <span class="p">([</span><span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mf">.0</span><span class="o">.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">0</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span> <span class="p">[</span><span class="mf">.0</span><span class="o">.</span><span class="p">])</span> <span class="p">([</span><span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
 <p>Unify and update (note the opening square brackets have been omited in
 the substitution dict, this is deliberate and I’ll explain below):</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</span>   <span class="mi">2</span> <span class="mi">3</span> <span class="mi">0</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span> <span class="p">[</span><span class="o">.</span><span class="mf">0.</span><span class="p">]</span>  <span class="p">)</span> <span class="p">([</span><span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
-                                                    <span class="n">w</span><span class="o">/</span> <span class="p">{</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</span> <span class="p">:</span> <span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="p">}</span>
-<span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">0</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span> <span class="p">([</span><span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mf">.0</span><span class="o">.</span><span class="p">]</span>   <span class="mi">2</span> <span class="mi">3</span> <span class="mi">0</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span> <span class="p">[</span><span class="mf">.0</span><span class="o">.</span><span class="p">]</span>  <span class="p">)</span> <span class="p">([</span><span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
+                                                    <span class="n">w</span><span class="o">/</span> <span class="p">{</span> <span class="mf">.0</span><span class="o">.</span><span class="p">]</span> <span class="p">:</span> <span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="p">}</span>
+<span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">0</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span> <span class="p">([</span><span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
 <p>How do we find <code class="docutils literal notranslate"><span class="pre">.0.]</span></code> in <code class="docutils literal notranslate"><span class="pre">[4</span> <span class="pre">.0.]</span></code> and replace it with <code class="docutils literal notranslate"><span class="pre">5</span> <span class="pre">.1.]</span></code>
@@ -258,15 +258,15 @@ getting the result <code class="docutils literal notranslate"><span class="pre">
 underlying structure of the Joy list is a cons-list in Python it’s
 actually pretty easy. I’ll explain below.</p>
 <p>Next we unify and find our two terms are the same already: <code class="docutils literal notranslate"><span class="pre">[5</span> <span class="pre">.1.]</span></code>:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">0</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span> <span class="p">([</span><span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">0</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span> <span class="p">([</span><span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
 <p>Giving us:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">0</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span><span class="p">)</span> <span class="p">(</span><span class="o">--</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">0</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span><span class="p">)</span> <span class="p">(</span><span class="o">--</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
 <p>From here we apply the first rule and get:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">0</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">0</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
 <p>Cleaning up the labels:</p>
@@ -281,19 +281,19 @@ actually pretty easy. I’ll explain below.</p>
 </pre></div>
 </div>
 <p>Re-label:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span> <span class="p">(</span><span class="mi">6</span> <span class="p">[</span><span class="o">.</span><span class="mf">2.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="o">.</span><span class="mf">2.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span> <span class="p">(</span><span class="mi">6</span> <span class="p">[</span><span class="mf">.2</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="mf">.2</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
 <p>Unify:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span> <span class="p">(</span><span class="mi">6</span> <span class="p">[</span><span class="o">.</span><span class="mf">2.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="o">.</span><span class="mf">2.</span><span class="p">])</span>
-                                                     <span class="n">w</span><span class="o">/</span> <span class="p">{</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="p">:</span> <span class="o">.</span><span class="mf">2.</span><span class="p">]</span> <span class="p">}</span>
-<span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="o">.</span><span class="mf">2.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span>      <span class="p">)</span> <span class="p">(</span><span class="mi">6</span>       <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="o">.</span><span class="mf">2.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span> <span class="p">(</span><span class="mi">6</span> <span class="p">[</span><span class="mf">.2</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="mf">.2</span><span class="o">.</span><span class="p">])</span>
+                                                     <span class="n">w</span><span class="o">/</span> <span class="p">{</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="p">:</span> <span class="mf">.2</span><span class="o">.</span><span class="p">]</span> <span class="p">}</span>
+<span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="mf">.2</span><span class="o">.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">--</span> <span class="mi">3</span> <span class="mi">2</span>      <span class="p">)</span> <span class="p">(</span><span class="mi">6</span>       <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="mf">.2</span><span class="o">.</span><span class="p">])</span>
                                                      <span class="n">w</span><span class="o">/</span> <span class="p">{</span><span class="mi">2</span><span class="p">:</span> <span class="mi">6</span><span class="p">}</span>
-<span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="o">.</span><span class="mf">2.</span><span class="p">]</span> <span class="mi">6</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">--</span> <span class="mi">3</span>        <span class="p">)</span> <span class="p">(</span>        <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="o">.</span><span class="mf">2.</span><span class="p">])</span>
+<span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="mf">.2</span><span class="o">.</span><span class="p">]</span> <span class="mi">6</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">--</span> <span class="mi">3</span>        <span class="p">)</span> <span class="p">(</span>        <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="mf">.2</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
 <p>First rule:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="o">.</span><span class="mf">2.</span><span class="p">]</span> <span class="mi">6</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">--</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">6</span> <span class="o">.</span><span class="mf">2.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="mf">.2</span><span class="o">.</span><span class="p">]</span> <span class="mi">6</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">--</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">6</span> <span class="mf">.2</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
 <p>Re-label:</p>
@@ -309,19 +309,19 @@ actually pretty easy. I’ll explain below.</p>
 </pre></div>
 </div>
 <p>Re-label:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">--</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span> <span class="p">(</span><span class="mi">6</span> <span class="p">[</span><span class="o">.</span><span class="mf">2.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="o">.</span><span class="mf">2.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">--</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">2</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span> <span class="p">(</span><span class="mi">6</span> <span class="p">[</span><span class="mf">.2</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="mf">.2</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
 <p>Unify:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">--</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span> <span class="p">(</span><span class="mi">6</span> <span class="p">[</span><span class="o">.</span><span class="mf">2.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="o">.</span><span class="mf">2.</span><span class="p">]</span>  <span class="p">)</span>
-                                                       <span class="n">w</span><span class="o">/</span> <span class="p">{</span> <span class="o">.</span><span class="mf">2.</span><span class="p">]</span> <span class="p">:</span> <span class="mi">2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="p">}</span>
-<span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">--</span> <span class="mi">3</span>        <span class="p">)</span> <span class="p">(</span><span class="mi">6</span>       <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">--</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">2</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span> <span class="p">(</span><span class="mi">6</span> <span class="p">[</span><span class="mf">.2</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="mf">.2</span><span class="o">.</span><span class="p">]</span>  <span class="p">)</span>
+                                                       <span class="n">w</span><span class="o">/</span> <span class="p">{</span> <span class="mf">.2</span><span class="o">.</span><span class="p">]</span> <span class="p">:</span> <span class="mi">2</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="p">}</span>
+<span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span> <span class="o">--</span> <span class="mi">3</span>        <span class="p">)</span> <span class="p">(</span><span class="mi">6</span>       <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">2</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
                                                        <span class="n">w</span><span class="o">/</span> <span class="p">{</span><span class="mi">3</span><span class="p">:</span> <span class="mi">6</span><span class="p">}</span>
-<span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">6</span> <span class="mi">1</span> <span class="o">--</span>          <span class="p">)</span> <span class="p">(</span>        <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">6</span> <span class="mi">1</span> <span class="o">--</span>          <span class="p">)</span> <span class="p">(</span>        <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">2</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
 <p>First or second rule:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">6</span> <span class="mi">1</span> <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mi">4</span> <span class="mi">5</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">6</span> <span class="mi">1</span> <span class="o">--</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">2</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
 <p>Clean up the labels:</p>
@@ -335,9 +335,9 @@ actually pretty easy. I’ll explain below.</p>
 </div>
 <p>From this stack effect comment it should be possible to construct the
 following Python code:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
-    <span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">((</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span>
-    <span class="k">return</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def F(stack):
+    (_, (d, (c, ((a, (b, S0)), stack)))) = stack
+    return (d, (c, S0)), stack
 </pre></div>
 </div>
 </section>
@@ -348,96 +348,96 @@ following Python code:</p>
 <h3>Representing Stack Effect Comments in Python<a class="headerlink" href="#representing-stack-effect-comments-in-python" title="Permalink to this headline">¶</a></h3>
 <p>I’m going to use pairs of tuples of type descriptors, which will be
 integers or tuples of type descriptors:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">roll_dn</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>roll_dn = (1, 2, 3), (2, 3, 1)
 
-<span class="n">pop</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,),</span> <span class="p">()</span>
+pop = (1,), ()
 
-<span class="n">swap</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+swap = (1, 2), (2, 1)
 </pre></div>
 </div>
 </section>
 <section id="compose">
 <h3><code class="docutils literal notranslate"><span class="pre">compose()</span></code><a class="headerlink" href="#compose" title="Permalink to this headline">¶</a></h3>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def compose(f, g):
 
-    <span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">),</span> <span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">)</span> <span class="o">=</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span>
+    (f_in, f_out), (g_in, g_out) = f, g
 
-    <span class="c1"># First rule.</span>
-    <span class="c1">#</span>
-    <span class="c1">#       (a -- b) (-- d)</span>
-    <span class="c1">#    ---------------------</span>
-    <span class="c1">#         (a -- b d)</span>
+    # First rule.
+    #
+    #       (a -- b) (-- d)
+    #    ---------------------
+    #         (a -- b d)
 
-    <span class="k">if</span> <span class="ow">not</span> <span class="n">g_in</span><span class="p">:</span>
+    if not g_in:
 
-        <span class="n">fg_in</span><span class="p">,</span> <span class="n">fg_out</span> <span class="o">=</span> <span class="n">f_in</span><span class="p">,</span> <span class="n">f_out</span> <span class="o">+</span> <span class="n">g_out</span>
+        fg_in, fg_out = f_in, f_out + g_out
 
-    <span class="c1"># Second rule.</span>
-    <span class="c1">#</span>
-    <span class="c1">#       (a --) (c -- d)</span>
-    <span class="c1">#    ---------------------</span>
-    <span class="c1">#         (c a -- d)</span>
+    # Second rule.
+    #
+    #       (a --) (c -- d)
+    #    ---------------------
+    #         (c a -- d)
 
-    <span class="k">elif</span> <span class="ow">not</span> <span class="n">f_out</span><span class="p">:</span>
+    elif not f_out:
 
-        <span class="n">fg_in</span><span class="p">,</span> <span class="n">fg_out</span> <span class="o">=</span> <span class="n">g_in</span> <span class="o">+</span> <span class="n">f_in</span><span class="p">,</span> <span class="n">g_out</span>
+        fg_in, fg_out = g_in + f_in, g_out
 
-    <span class="k">else</span><span class="p">:</span> <span class="c1"># Unify, update, recur.</span>
+    else: # Unify, update, recur.
 
-        <span class="n">fo</span><span class="p">,</span> <span class="n">gi</span> <span class="o">=</span> <span class="n">f_out</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">g_in</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+        fo, gi = f_out[-1], g_in[-1]
 
-        <span class="n">s</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">gi</span><span class="p">,</span> <span class="n">fo</span><span class="p">)</span>
+        s = unify(gi, fo)
 
-        <span class="k">if</span> <span class="n">s</span> <span class="o">==</span> <span class="kc">False</span><span class="p">:</span>  <span class="c1"># s can also be the empty dict, which is ok.</span>
-            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;Cannot unify </span><span class="si">%r</span><span class="s1"> and </span><span class="si">%r</span><span class="s1">.&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">fo</span><span class="p">,</span> <span class="n">gi</span><span class="p">))</span>
+        if s == False:  # s can also be the empty dict, which is ok.
+            raise TypeError(&#39;Cannot unify %r and %r.&#39; % (fo, gi))
 
-        <span class="n">f_g</span> <span class="o">=</span> <span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]),</span> <span class="p">(</span><span class="n">g_in</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">g_out</span><span class="p">)</span>
+        f_g = (f_in, f_out[:-1]), (g_in[:-1], g_out)
 
-        <span class="k">if</span> <span class="n">s</span><span class="p">:</span> <span class="n">f_g</span> <span class="o">=</span> <span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">f_g</span><span class="p">)</span>
+        if s: f_g = update(s, f_g)
 
-        <span class="n">fg_in</span><span class="p">,</span> <span class="n">fg_out</span> <span class="o">=</span> <span class="n">compose</span><span class="p">(</span><span class="o">*</span><span class="n">f_g</span><span class="p">)</span>
+        fg_in, fg_out = compose(*f_g)
 
-    <span class="k">return</span> <span class="n">fg_in</span><span class="p">,</span> <span class="n">fg_out</span>
+    return fg_in, fg_out
 </pre></div>
 </div>
 </section>
 <section id="unify">
 <h3><code class="docutils literal notranslate"><span class="pre">unify()</span></code><a class="headerlink" href="#unify" title="Permalink to this headline">¶</a></h3>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
-    <span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-        <span class="n">s</span> <span class="o">=</span> <span class="p">{}</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def unify(u, v, s=None):
+    if s is None:
+        s = {}
 
-    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="nb">int</span><span class="p">):</span>
-        <span class="n">s</span><span class="p">[</span><span class="n">u</span><span class="p">]</span> <span class="o">=</span> <span class="n">v</span>
-    <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">int</span><span class="p">):</span>
-        <span class="n">s</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">=</span> <span class="n">u</span>
-    <span class="k">else</span><span class="p">:</span>
-        <span class="n">s</span> <span class="o">=</span> <span class="kc">False</span>
+    if isinstance(u, int):
+        s[u] = v
+    elif isinstance(v, int):
+        s[v] = u
+    else:
+        s = False
 
-    <span class="k">return</span> <span class="n">s</span>
+    return s
 </pre></div>
 </div>
 </section>
 <section id="update">
 <h3><code class="docutils literal notranslate"><span class="pre">update()</span></code><a class="headerlink" href="#update" title="Permalink to this headline">¶</a></h3>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">term</span><span class="p">):</span>
-    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-        <span class="k">return</span> <span class="n">s</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="n">term</span><span class="p">)</span>
-    <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">inner</span><span class="p">)</span> <span class="k">for</span> <span class="n">inner</span> <span class="ow">in</span> <span class="n">term</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def update(s, term):
+    if not isinstance(term, tuple):
+        return s.get(term, term)
+    return tuple(update(s, inner) for inner in term)
 </pre></div>
 </div>
 </section>
 <section id="relabel">
 <h3><code class="docutils literal notranslate"><span class="pre">relabel()</span></code><a class="headerlink" href="#relabel" title="Permalink to this headline">¶</a></h3>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">relabel</span><span class="p">(</span><span class="n">left</span><span class="p">,</span> <span class="n">right</span><span class="p">):</span>
-    <span class="k">return</span> <span class="n">left</span><span class="p">,</span> <span class="n">_1000</span><span class="p">(</span><span class="n">right</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def relabel(left, right):
+    return left, _1000(right)
 
-<span class="k">def</span> <span class="nf">_1000</span><span class="p">(</span><span class="n">right</span><span class="p">):</span>
-    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">right</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-        <span class="k">return</span> <span class="mi">1000</span> <span class="o">+</span> <span class="n">right</span>
-    <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_1000</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">right</span><span class="p">)</span>
+def _1000(right):
+    if not isinstance(right, tuple):
+        return 1000 + right
+    return tuple(_1000(n) for n in right)
 
-<span class="n">relabel</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">)</span>
+relabel(pop, swap)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(((</span><span class="mi">1</span><span class="p">,),</span> <span class="p">()),</span> <span class="p">((</span><span class="mi">1001</span><span class="p">,</span> <span class="mi">1002</span><span class="p">),</span> <span class="p">(</span><span class="mi">1002</span><span class="p">,</span> <span class="mi">1001</span><span class="p">)))</span>
@@ -446,21 +446,21 @@ integers or tuples of type descriptors:</p>
 </section>
 <section id="delabel">
 <h3><code class="docutils literal notranslate"><span class="pre">delabel()</span></code><a class="headerlink" href="#delabel" title="Permalink to this headline">¶</a></h3>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">delabel</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
-    <span class="n">s</span> <span class="o">=</span> <span class="p">{</span><span class="n">u</span><span class="p">:</span> <span class="n">i</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">u</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">sorted</span><span class="p">(</span><span class="n">_unique</span><span class="p">(</span><span class="n">f</span><span class="p">)))}</span>
-    <span class="k">return</span> <span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def delabel(f):
+    s = {u: i for i, u in enumerate(sorted(_unique(f)))}
+    return update(s, f)
 
-<span class="k">def</span> <span class="nf">_unique</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">seen</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
-    <span class="k">if</span> <span class="n">seen</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-        <span class="n">seen</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
-    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-        <span class="n">seen</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
-    <span class="k">else</span><span class="p">:</span>
-        <span class="k">for</span> <span class="n">inner</span> <span class="ow">in</span> <span class="n">f</span><span class="p">:</span>
-            <span class="n">_unique</span><span class="p">(</span><span class="n">inner</span><span class="p">,</span> <span class="n">seen</span><span class="p">)</span>
-    <span class="k">return</span> <span class="n">seen</span>
+def _unique(f, seen=None):
+    if seen is None:
+        seen = set()
+    if not isinstance(f, tuple):
+        seen.add(f)
+    else:
+        for inner in f:
+            _unique(inner, seen)
+    return seen
 
-<span class="n">delabel</span><span class="p">(</span><span class="n">relabel</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">))</span>
+delabel(relabel(pop, swap))
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(((</span><span class="mi">0</span><span class="p">,),</span> <span class="p">()),</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)))</span>
@@ -472,39 +472,39 @@ integers or tuples of type descriptors:</p>
 <p>At last we put it all together in a function <code class="docutils literal notranslate"><span class="pre">C()</span></code> that accepts two
 stack effect comments and returns their composition (or raises and
 exception if they can’t be composed due to type conflicts.)</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">C</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
-    <span class="n">f</span><span class="p">,</span> <span class="n">g</span> <span class="o">=</span> <span class="n">relabel</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">)</span>
-    <span class="n">fg</span> <span class="o">=</span> <span class="n">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">)</span>
-    <span class="k">return</span> <span class="n">delabel</span><span class="p">(</span><span class="n">fg</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def C(f, g):
+    f, g = relabel(f, g)
+    fg = compose(f, g)
+    return delabel(fg)
 </pre></div>
 </div>
 <p>Let’s try it out.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>C(pop, swap)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">C</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">),</span> <span class="n">roll_dn</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>C(C(pop, swap), roll_dn)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>C(swap, roll_dn)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">C</span><span class="p">(</span><span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>C(pop, C(swap, roll_dn))
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">poswrd</span> <span class="o">=</span> <span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">))</span>
-<span class="n">poswrd</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>poswrd = reduce(C, (pop, swap, roll_dn))
+poswrd
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
@@ -516,12 +516,12 @@ exception if they can’t be composed due to type conflicts.)</p>
 <p>Here’s that trick to represent functions like <code class="docutils literal notranslate"><span class="pre">rest</span></code> and <code class="docutils literal notranslate"><span class="pre">cons</span></code> that
 manipulate stacks. We use a cons-list of tuples and give the tails their
 own numbers. Then everything above already works.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">rest</span> <span class="o">=</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>rest = ((1, 2),), (2,)
 
-<span class="n">cons</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),)</span>
+cons = (1, 2), ((1, 2),)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">poswrd</span><span class="p">,</span> <span class="n">rest</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>C(poswrd, rest)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
@@ -542,9 +542,9 @@ own numbers. Then everything above already works.</p>
 <span class="p">}</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">=</span> <span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">cons</span><span class="p">,</span> <span class="n">cons</span><span class="p">))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>F = reduce(C, (pop, swap, roll_dn, rest, rest, cons, cons))
 
-<span class="n">F</span>
+F
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(((</span><span class="mi">3</span><span class="p">,</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">)),</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">)),))</span>
@@ -560,13 +560,13 @@ own numbers. Then everything above already works.</p>
 <h3>Dealing with <code class="docutils literal notranslate"><span class="pre">cons</span></code> and <code class="docutils literal notranslate"><span class="pre">uncons</span></code><a class="headerlink" href="#dealing-with-cons-and-uncons" title="Permalink to this headline">¶</a></h3>
 <p>However, if we try to compose e.g. <code class="docutils literal notranslate"><span class="pre">cons</span></code> and <code class="docutils literal notranslate"><span class="pre">uncons</span></code> it won’t
 work:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">uncons</span> <span class="o">=</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>uncons = ((1, 2),), (1, 2)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">try</span><span class="p">:</span>
-    <span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)</span>
-<span class="k">except</span> <span class="ne">Exception</span><span class="p">,</span> <span class="n">e</span><span class="p">:</span>
-    <span class="nb">print</span> <span class="n">e</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>try:
+    C(cons, uncons)
+except Exception, e:
+    print e
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Cannot</span> <span class="n">unify</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="mi">1001</span><span class="p">,</span> <span class="mi">1002</span><span class="p">)</span><span class="o">.</span>
@@ -577,36 +577,36 @@ work:</p>
 <p>The problem is that the <code class="docutils literal notranslate"><span class="pre">unify()</span></code> function as written doesn’t handle
 the case when both terms are tuples. We just have to add a clause to
 deal with this recursively:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
-    <span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-        <span class="n">s</span> <span class="o">=</span> <span class="p">{}</span>
-    <span class="k">elif</span> <span class="n">s</span><span class="p">:</span>
-        <span class="n">u</span> <span class="o">=</span> <span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">u</span><span class="p">)</span>
-        <span class="n">v</span> <span class="o">=</span> <span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def unify(u, v, s=None):
+    if s is None:
+        s = {}
+    elif s:
+        u = update(s, u)
+        v = update(s, v)
 
-    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="nb">int</span><span class="p">):</span>
-        <span class="n">s</span><span class="p">[</span><span class="n">u</span><span class="p">]</span> <span class="o">=</span> <span class="n">v</span>
+    if isinstance(u, int):
+        s[u] = v
 
-    <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">int</span><span class="p">):</span>
-        <span class="n">s</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">=</span> <span class="n">u</span>
+    elif isinstance(v, int):
+        s[v] = u
 
-    <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
+    elif isinstance(u, tuple) and isinstance(v, tuple):
 
-        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">u</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">2</span> <span class="ow">or</span> <span class="nb">len</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">2</span><span class="p">:</span>
-            <span class="c1"># Not a type error, caller passed in a bad value.</span>
-            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="nb">repr</span><span class="p">((</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)))</span>  <span class="c1"># FIXME this message sucks.</span>
+        if len(u) != 2 or len(v) != 2:
+            # Not a type error, caller passed in a bad value.
+            raise ValueError(repr((u, v)))  # FIXME this message sucks.
 
-        <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">),</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">d</span><span class="p">)</span> <span class="o">=</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span>
-        <span class="n">s</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">s</span><span class="p">)</span>
-        <span class="k">if</span> <span class="n">s</span> <span class="o">!=</span> <span class="kc">False</span><span class="p">:</span>
-            <span class="n">s</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">d</span><span class="p">,</span> <span class="n">s</span><span class="p">)</span>
-    <span class="k">else</span><span class="p">:</span>
-        <span class="n">s</span> <span class="o">=</span> <span class="kc">False</span>
+        (a, b), (c, d) = u, v
+        s = unify(a, c, s)
+        if s != False:
+            s = unify(b, d, s)
+    else:
+        s = False
 
-    <span class="k">return</span> <span class="n">s</span>
+    return s
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>C(cons, uncons)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
@@ -618,13 +618,13 @@ deal with this recursively:</p>
 <section id="part-iii-compiling-yin-functions">
 <h2>Part III: Compiling Yin Functions<a class="headerlink" href="#part-iii-compiling-yin-functions" title="Permalink to this headline">¶</a></h2>
 <p>Now consider the Python function we would like to derive:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F_python</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
-    <span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">((</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span>
-    <span class="k">return</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def F_python(stack):
+    (_, (d, (c, ((a, (b, S0)), stack)))) = stack
+    return (d, (c, S0)), stack
 </pre></div>
 </div>
 <p>And compare it to the input stack effect comment tuple we just computed:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">F</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>F[0]
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">)),</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
@@ -646,7 +646,7 @@ stack effect comment tuple, just in the reverse order:</p>
 </div>
 <p>Eh?</p>
 <p>And the return tuple</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">F</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>F[1]
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">)),)</span>
@@ -666,21 +666,21 @@ effect.)</p>
 <h3>Python Identifiers<a class="headerlink" href="#python-identifiers" title="Permalink to this headline">¶</a></h3>
 <p>We want to substitute Python identifiers for the integers. I’m going to
 repurpose <code class="docutils literal notranslate"><span class="pre">joy.parser.Symbol</span></code> class for this:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
-<span class="kn">from</span> <span class="nn">joy.parser</span> <span class="kn">import</span> <span class="n">Symbol</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from collections import defaultdict
+from joy.parser import Symbol
 
 
-<span class="k">def</span> <span class="nf">_names_for</span><span class="p">():</span>
-    <span class="n">I</span> <span class="o">=</span> <span class="nb">iter</span><span class="p">(</span><span class="n">xrange</span><span class="p">(</span><span class="mi">1000</span><span class="p">))</span>
-    <span class="k">return</span> <span class="k">lambda</span><span class="p">:</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;a</span><span class="si">%i</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="nb">next</span><span class="p">(</span><span class="n">I</span><span class="p">))</span>
+def _names_for():
+    I = iter(xrange(1000))
+    return lambda: Symbol(&#39;a%i&#39; % next(I))
 
 
-<span class="k">def</span> <span class="nf">identifiers</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
-    <span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-        <span class="n">s</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="n">_names_for</span><span class="p">())</span>
-    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="nb">int</span><span class="p">):</span>
-        <span class="k">return</span> <span class="n">s</span><span class="p">[</span><span class="n">term</span><span class="p">]</span>
-    <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">identifiers</span><span class="p">(</span><span class="n">inner</span><span class="p">,</span> <span class="n">s</span><span class="p">)</span> <span class="k">for</span> <span class="n">inner</span> <span class="ow">in</span> <span class="n">term</span><span class="p">)</span>
+def identifiers(term, s=None):
+    if s is None:
+        s = defaultdict(_names_for())
+    if isinstance(term, int):
+        return s[term]
+    return tuple(identifiers(inner, s) for inner in term)
 </pre></div>
 </div>
 </section>
@@ -690,36 +690,36 @@ repurpose <code class="docutils literal notranslate"><span class="pre">joy.parse
 effect comment tuples to reasonable text format. There are some details
 in how this code works that related to stuff later in the notebook, so
 you should skip it for now and read it later if you’re interested.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">doc_from_stack_effect</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span><span class="p">):</span>
-    <span class="k">return</span> <span class="s1">&#39;(</span><span class="si">%s</span><span class="s1">--</span><span class="si">%s</span><span class="s1">)&#39;</span> <span class="o">%</span> <span class="p">(</span>
-        <span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">_to_str</span><span class="p">,</span> <span class="n">inputs</span> <span class="o">+</span> <span class="p">(</span><span class="s1">&#39;&#39;</span><span class="p">,))),</span>
-        <span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">_to_str</span><span class="p">,</span> <span class="p">(</span><span class="s1">&#39;&#39;</span><span class="p">,)</span> <span class="o">+</span> <span class="n">outputs</span><span class="p">))</span>
-    <span class="p">)</span>
-
-
-<span class="k">def</span> <span class="nf">_to_str</span><span class="p">(</span><span class="n">term</span><span class="p">):</span>
-    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-        <span class="k">try</span><span class="p">:</span>
-            <span class="n">t</span> <span class="o">=</span> <span class="n">term</span><span class="o">.</span><span class="n">prefix</span> <span class="o">==</span> <span class="s1">&#39;s&#39;</span>
-        <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
-            <span class="k">return</span> <span class="nb">str</span><span class="p">(</span><span class="n">term</span><span class="p">)</span>
-        <span class="k">return</span> <span class="s1">&#39;[.</span><span class="si">%i</span><span class="s1">.]&#39;</span> <span class="o">%</span> <span class="n">term</span><span class="o">.</span><span class="n">number</span> <span class="k">if</span> <span class="n">t</span> <span class="k">else</span> <span class="nb">str</span><span class="p">(</span><span class="n">term</span><span class="p">)</span>
-
-    <span class="n">a</span> <span class="o">=</span> <span class="p">[]</span>
-    <span class="k">while</span> <span class="n">term</span> <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-        <span class="n">item</span><span class="p">,</span> <span class="n">term</span> <span class="o">=</span> <span class="n">term</span>
-        <span class="n">a</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">_to_str</span><span class="p">(</span><span class="n">item</span><span class="p">))</span>
-
-    <span class="k">try</span><span class="p">:</span>
-        <span class="n">n</span> <span class="o">=</span> <span class="n">term</span><span class="o">.</span><span class="n">number</span>
-    <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
-        <span class="n">n</span> <span class="o">=</span> <span class="n">term</span>
-    <span class="k">else</span><span class="p">:</span>
-        <span class="k">if</span> <span class="n">term</span><span class="o">.</span><span class="n">prefix</span> <span class="o">!=</span> <span class="s1">&#39;s&#39;</span><span class="p">:</span>
-            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;Stack label: </span><span class="si">%s</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">term</span><span class="p">,))</span>
-
-    <span class="n">a</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s1">&#39;.</span><span class="si">%s</span><span class="s1">.&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">n</span><span class="p">,))</span>
-    <span class="k">return</span> <span class="s1">&#39;[</span><span class="si">%s</span><span class="s1">]&#39;</span> <span class="o">%</span> <span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def doc_from_stack_effect(inputs, outputs):
+    return &#39;(%s--%s)&#39; % (
+        &#39; &#39;.join(map(_to_str, inputs + (&#39;&#39;,))),
+        &#39; &#39;.join(map(_to_str, (&#39;&#39;,) + outputs))
+    )
+
+
+def _to_str(term):
+    if not isinstance(term, tuple):
+        try:
+            t = term.prefix == &#39;s&#39;
+        except AttributeError:
+            return str(term)
+        return &#39;[.%i.]&#39; % term.number if t else str(term)
+
+    a = []
+    while term and isinstance(term, tuple):
+        item, term = term
+        a.append(_to_str(item))
+
+    try:
+        n = term.number
+    except AttributeError:
+        n = term
+    else:
+        if term.prefix != &#39;s&#39;:
+            raise ValueError(&#39;Stack label: %s&#39; % (term,))
+
+    a.append(&#39;.%s.&#39; % (n,))
+    return &#39;[%s]&#39; % &#39; &#39;.join(a)
 </pre></div>
 </div>
 </section>
@@ -728,25 +728,25 @@ you should skip it for now and read it later if you’re interested.</p>
 <p>Now we can write a compiler function to emit Python source code. (The
 underscore suffix distiguishes it from the built-in <code class="docutils literal notranslate"><span class="pre">compile()</span></code>
 function.)</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
-    <span class="k">if</span> <span class="n">doc</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-        <span class="n">doc</span> <span class="o">=</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
-    <span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span> <span class="o">=</span> <span class="n">identifiers</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
-    <span class="n">i</span> <span class="o">=</span> <span class="n">o</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;stack&#39;</span><span class="p">)</span>
-    <span class="k">for</span> <span class="n">term</span> <span class="ow">in</span> <span class="n">inputs</span><span class="p">:</span>
-        <span class="n">i</span> <span class="o">=</span> <span class="n">term</span><span class="p">,</span> <span class="n">i</span>
-    <span class="k">for</span> <span class="n">term</span> <span class="ow">in</span> <span class="n">outputs</span><span class="p">:</span>
-        <span class="n">o</span> <span class="o">=</span> <span class="n">term</span><span class="p">,</span> <span class="n">o</span>
-    <span class="k">return</span> <span class="s1">&#39;&#39;&#39;def </span><span class="si">%s</span><span class="s1">(stack):</span>
-<span class="s1">    &quot;&quot;&quot;</span><span class="si">%s</span><span class="s1">&quot;&quot;&quot;</span>
-<span class="s1">    </span><span class="si">%s</span><span class="s1"> = stack</span>
-<span class="s1">    return </span><span class="si">%s</span><span class="s1">&#39;&#39;&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">doc</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">o</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def compile_(name, f, doc=None):
+    if doc is None:
+        doc = doc_from_stack_effect(*f)
+    inputs, outputs = identifiers(f)
+    i = o = Symbol(&#39;stack&#39;)
+    for term in inputs:
+        i = term, i
+    for term in outputs:
+        o = term, o
+    return &#39;&#39;&#39;def %s(stack):
+    &quot;&quot;&quot;%s&quot;&quot;&quot;
+    %s = stack
+    return %s&#39;&#39;&#39; % (name, doc, i, o)
 </pre></div>
 </div>
 <p>Here it is in action:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">source</span> <span class="o">=</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">&#39;F&#39;</span><span class="p">,</span> <span class="n">F</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>source = compile_(&#39;F&#39;, F)
 
-<span class="nb">print</span> <span class="n">source</span>
+print source
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
@@ -756,31 +756,31 @@ function.)</p>
 </pre></div>
 </div>
 <p>Compare:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F_python</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
-    <span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">((</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span>
-    <span class="k">return</span> <span class="p">((</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def F_python(stack):
+    (_, (d, (c, ((a, (b, S0)), stack)))) = stack
+    return ((d, (c, S0)), stack)
 </pre></div>
 </div>
 <p>Next steps:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">L</span> <span class="o">=</span> <span class="p">{}</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>L = {}
 
-<span class="nb">eval</span><span class="p">(</span><span class="nb">compile</span><span class="p">(</span><span class="n">source</span><span class="p">,</span> <span class="s1">&#39;__main__&#39;</span><span class="p">,</span> <span class="s1">&#39;single&#39;</span><span class="p">),</span> <span class="p">{},</span> <span class="n">L</span><span class="p">)</span>
+eval(compile(source, &#39;__main__&#39;, &#39;single&#39;), {}, L)
 
-<span class="n">L</span><span class="p">[</span><span class="s1">&#39;F&#39;</span><span class="p">]</span>
+L[&#39;F&#39;]
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">&lt;</span><span class="n">function</span> <span class="n">F</span><span class="o">&gt;</span>
 </pre></div>
 </div>
 <p>Let’s try it out:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span>
-<span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">SimpleFunctionWrapper</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import D, J, V
+from joy.library import SimpleFunctionWrapper
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">D</span><span class="p">[</span><span class="s1">&#39;F&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">SimpleFunctionWrapper</span><span class="p">(</span><span class="n">L</span><span class="p">[</span><span class="s1">&#39;F&#39;</span><span class="p">])</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>D[&#39;F&#39;] = SimpleFunctionWrapper(L[&#39;F&#39;])
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[4 5 ...] 2 3 1 F&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[4 5 ...] 2 3 1 F&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="o">...</span><span class="p">]</span>
@@ -800,33 +800,33 @@ this might be less helpful.</p>
 <h3>Compiling Library Functions<a class="headerlink" href="#compiling-library-functions" title="Permalink to this headline">¶</a></h3>
 <p>We can use <code class="docutils literal notranslate"><span class="pre">compile_()</span></code> to generate many primitives in the library
 from their stack effect comments:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">defs</span><span class="p">():</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def defs():
 
-    <span class="n">rolldown</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+    rolldown = (1, 2, 3), (2, 3, 1)
 
-    <span class="n">rollup</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+    rollup = (1, 2, 3), (3, 1, 2)
 
-    <span class="n">pop</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,),</span> <span class="p">()</span>
+    pop = (1,), ()
 
-    <span class="n">swap</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+    swap = (1, 2), (2, 1)
 
-    <span class="n">rest</span> <span class="o">=</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,)</span>
+    rest = ((1, 2),), (2,)
 
-    <span class="n">rrest</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">rest</span><span class="p">,</span> <span class="n">rest</span><span class="p">)</span>
+    rrest = C(rest, rest)
 
-    <span class="n">cons</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),)</span>
+    cons = (1, 2), ((1, 2),)
 
-    <span class="n">uncons</span> <span class="o">=</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+    uncons = ((1, 2),), (1, 2)
 
-    <span class="n">swons</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">swap</span><span class="p">,</span> <span class="n">cons</span><span class="p">)</span>
+    swons = C(swap, cons)
 
-    <span class="k">return</span> <span class="nb">locals</span><span class="p">()</span>
+    return locals()
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">defs</span><span class="p">()</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
-    <span class="nb">print</span>
-    <span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span><span class="p">)</span>
-    <span class="nb">print</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for name, stack_effect_comment in sorted(defs().items()):
+    print
+    print compile_(name, stack_effect_comment)
+    print
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">cons</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
@@ -966,57 +966,57 @@ and <code class="docutils literal notranslate"><span class="pre">t</span></code>
 Python class hierarchy of Joy types and use the <code class="docutils literal notranslate"><span class="pre">issubclass()</span></code> method
 to establish domain ordering, as well as other handy behaviour that will
 make it fairly easy to reuse most of the code above.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">AnyJoyType</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>class AnyJoyType(object):
 
-    <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;a&#39;</span>
+    prefix = &#39;a&#39;
 
-    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">number</span><span class="p">):</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">number</span> <span class="o">=</span> <span class="n">number</span>
+    def __init__(self, number):
+        self.number = number
 
-    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">prefix</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">number</span><span class="p">)</span>
+    def __repr__(self):
+        return self.prefix + str(self.number)
 
-    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-        <span class="k">return</span> <span class="p">(</span>
-            <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="p">)</span>
-            <span class="ow">and</span> <span class="n">other</span><span class="o">.</span><span class="n">prefix</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">prefix</span>
-            <span class="ow">and</span> <span class="n">other</span><span class="o">.</span><span class="n">number</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">number</span>
-        <span class="p">)</span>
+    def __eq__(self, other):
+        return (
+            isinstance(other, self.__class__)
+            and other.prefix == self.prefix
+            and other.number == self.number
+        )
 
-    <span class="k">def</span> <span class="fm">__ge__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-        <span class="k">return</span> <span class="nb">issubclass</span><span class="p">(</span><span class="n">other</span><span class="o">.</span><span class="vm">__class__</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="p">)</span>
+    def __ge__(self, other):
+        return issubclass(other.__class__, self.__class__)
 
-    <span class="k">def</span> <span class="fm">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">number</span> <span class="o">+</span> <span class="n">other</span><span class="p">)</span>
-    <span class="fm">__radd__</span> <span class="o">=</span> <span class="fm">__add__</span>
+    def __add__(self, other):
+        return self.__class__(self.number + other)
+    __radd__ = __add__
 
-    <span class="k">def</span> <span class="fm">__hash__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-        <span class="k">return</span> <span class="nb">hash</span><span class="p">(</span><span class="nb">repr</span><span class="p">(</span><span class="bp">self</span><span class="p">))</span>
+    def __hash__(self):
+        return hash(repr(self))
 
 
-<span class="k">class</span> <span class="nc">NumberJoyType</span><span class="p">(</span><span class="n">AnyJoyType</span><span class="p">):</span> <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;n&#39;</span>
-<span class="k">class</span> <span class="nc">FloatJoyType</span><span class="p">(</span><span class="n">NumberJoyType</span><span class="p">):</span> <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;f&#39;</span>
-<span class="k">class</span> <span class="nc">IntJoyType</span><span class="p">(</span><span class="n">FloatJoyType</span><span class="p">):</span> <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;i&#39;</span>
+class NumberJoyType(AnyJoyType): prefix = &#39;n&#39;
+class FloatJoyType(NumberJoyType): prefix = &#39;f&#39;
+class IntJoyType(FloatJoyType): prefix = &#39;i&#39;
 
 
-<span class="k">class</span> <span class="nc">StackJoyType</span><span class="p">(</span><span class="n">AnyJoyType</span><span class="p">):</span>
-    <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;s&#39;</span>
+class StackJoyType(AnyJoyType):
+    prefix = &#39;s&#39;
 
 
-<span class="n">_R</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
-<span class="n">A</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">AnyJoyType</span><span class="p">,</span> <span class="n">_R</span><span class="p">)</span>
-<span class="n">N</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">NumberJoyType</span><span class="p">,</span> <span class="n">_R</span><span class="p">)</span>
-<span class="n">S</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">StackJoyType</span><span class="p">,</span> <span class="n">_R</span><span class="p">)</span>
+_R = range(10)
+A = map(AnyJoyType, _R)
+N = map(NumberJoyType, _R)
+S = map(StackJoyType, _R)
 </pre></div>
 </div>
 <p>Mess with it a little:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">permutations</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from itertools import permutations
 </pre></div>
 </div>
 <p>“Any” types can be specialized to numbers and stacks, but not vice
 versa:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">permutations</span><span class="p">((</span><span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="mi">2</span><span class="p">):</span>
-    <span class="nb">print</span> <span class="n">a</span><span class="p">,</span> <span class="s1">&#39;&gt;=&#39;</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="s1">&#39;-&gt;&#39;</span><span class="p">,</span> <span class="n">a</span> <span class="o">&gt;=</span> <span class="n">b</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for a, b in permutations((A[0], N[0], S[0]), 2):
+    print a, &#39;&gt;=&#39;, b, &#39;-&gt;&#39;, a &gt;= b
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a0</span> <span class="o">&gt;=</span> <span class="n">n0</span> <span class="o">-&gt;</span> <span class="kc">True</span>
@@ -1030,8 +1030,8 @@ versa:</p>
 <p>Our crude <a class="reference external" href="https://en.wikipedia.org/wiki/Numerical_tower">Numerical
 Tower</a> of <em>numbers</em> &gt;
 <em>floats</em> &gt; <em>integers</em> works as well (but we’re not going to use it yet):</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">permutations</span><span class="p">((</span><span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">FloatJoyType</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="n">IntJoyType</span><span class="p">(</span><span class="mi">0</span><span class="p">)),</span> <span class="mi">2</span><span class="p">):</span>
-    <span class="nb">print</span> <span class="n">a</span><span class="p">,</span> <span class="s1">&#39;&gt;=&#39;</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="s1">&#39;-&gt;&#39;</span><span class="p">,</span> <span class="n">a</span> <span class="o">&gt;=</span> <span class="n">b</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for a, b in permutations((A[0], N[0], FloatJoyType(0), IntJoyType(0)), 2):
+    print a, &#39;&gt;=&#39;, b, &#39;-&gt;&#39;, a &gt;= b
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a0</span> <span class="o">&gt;=</span> <span class="n">n0</span> <span class="o">-&gt;</span> <span class="kc">True</span>
@@ -1051,18 +1051,18 @@ Tower</a> of <em>numbers</em> &gt;
 </section>
 <section id="typing-sqr">
 <h3>Typing <code class="docutils literal notranslate"><span class="pre">sqr</span></code><a class="headerlink" href="#typing-sqr" title="Permalink to this headline">¶</a></h3>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">dup</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>dup = (A[1],), (A[1], A[1])
 
-<span class="n">mul</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">2</span><span class="p">]),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">3</span><span class="p">],)</span>
+mul = (N[1], N[2]), (N[3],)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">dup</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>dup
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">a1</span><span class="p">,),</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">a1</span><span class="p">))</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">mul</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>mul
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">n1</span><span class="p">,</span> <span class="n">n2</span><span class="p">),</span> <span class="p">(</span><span class="n">n3</span><span class="p">,))</span>
@@ -1072,9 +1072,9 @@ Tower</a> of <em>numbers</em> &gt;
 <section id="modifying-the-inferencer">
 <h3>Modifying the Inferencer<a class="headerlink" href="#modifying-the-inferencer" title="Permalink to this headline">¶</a></h3>
 <p>Re-labeling still works fine:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">foo</span> <span class="o">=</span> <span class="n">relabel</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>foo = relabel(dup, mul)
 
-<span class="n">foo</span>
+foo
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(((</span><span class="n">a1</span><span class="p">,),</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">a1</span><span class="p">)),</span> <span class="p">((</span><span class="n">n1001</span><span class="p">,</span> <span class="n">n1002</span><span class="p">),</span> <span class="p">(</span><span class="n">n1003</span><span class="p">,)))</span>
@@ -1084,28 +1084,28 @@ Tower</a> of <em>numbers</em> &gt;
 <h4><code class="docutils literal notranslate"><span class="pre">delabel()</span></code> version 2<a class="headerlink" href="#delabel-version-2" title="Permalink to this headline">¶</a></h4>
 <p>The <code class="docutils literal notranslate"><span class="pre">delabel()</span></code> function needs an overhaul. It now has to keep track
 of how many labels of each domain it has “seen”.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">Counter</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from collections import Counter
 
 
-<span class="k">def</span> <span class="nf">delabel</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">seen</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
-    <span class="k">if</span> <span class="n">seen</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-        <span class="k">assert</span> <span class="n">c</span> <span class="ow">is</span> <span class="kc">None</span>
-        <span class="n">seen</span><span class="p">,</span> <span class="n">c</span> <span class="o">=</span> <span class="p">{},</span> <span class="n">Counter</span><span class="p">()</span>
+def delabel(f, seen=None, c=None):
+    if seen is None:
+        assert c is None
+        seen, c = {}, Counter()
 
-    <span class="k">try</span><span class="p">:</span>
-        <span class="k">return</span> <span class="n">seen</span><span class="p">[</span><span class="n">f</span><span class="p">]</span>
-    <span class="k">except</span> <span class="ne">KeyError</span><span class="p">:</span>
-        <span class="k">pass</span>
+    try:
+        return seen[f]
+    except KeyError:
+        pass
 
-    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-        <span class="n">seen</span><span class="p">[</span><span class="n">f</span><span class="p">]</span> <span class="o">=</span> <span class="n">f</span><span class="o">.</span><span class="vm">__class__</span><span class="p">(</span><span class="n">c</span><span class="p">[</span><span class="n">f</span><span class="o">.</span><span class="n">prefix</span><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
-        <span class="n">c</span><span class="p">[</span><span class="n">f</span><span class="o">.</span><span class="n">prefix</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
-        <span class="k">return</span> <span class="n">seen</span><span class="p">[</span><span class="n">f</span><span class="p">]</span>
+    if not isinstance(f, tuple):
+        seen[f] = f.__class__(c[f.prefix] + 1)
+        c[f.prefix] += 1
+        return seen[f]
 
-    <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">delabel</span><span class="p">(</span><span class="n">inner</span><span class="p">,</span> <span class="n">seen</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span> <span class="k">for</span> <span class="n">inner</span> <span class="ow">in</span> <span class="n">f</span><span class="p">)</span>
+    return tuple(delabel(inner, seen, c) for inner in f)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">delabel</span><span class="p">(</span><span class="n">foo</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>delabel(foo)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(((</span><span class="n">a1</span><span class="p">,),</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">a1</span><span class="p">)),</span> <span class="p">((</span><span class="n">n1</span><span class="p">,</span> <span class="n">n2</span><span class="p">),</span> <span class="p">(</span><span class="n">n3</span><span class="p">,)))</span>
@@ -1114,120 +1114,120 @@ of how many labels of each domain it has “seen”.</p>
 </section>
 <section id="unify-version-3">
 <h4><code class="docutils literal notranslate"><span class="pre">unify()</span></code> version 3<a class="headerlink" href="#unify-version-3" title="Permalink to this headline">¶</a></h4>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
-    <span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-        <span class="n">s</span> <span class="o">=</span> <span class="p">{}</span>
-    <span class="k">elif</span> <span class="n">s</span><span class="p">:</span>
-        <span class="n">u</span> <span class="o">=</span> <span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">u</span><span class="p">)</span>
-        <span class="n">v</span> <span class="o">=</span> <span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
-
-    <span class="k">if</span> <span class="n">u</span> <span class="o">==</span> <span class="n">v</span><span class="p">:</span>
-        <span class="k">return</span> <span class="n">s</span>
-
-    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">AnyJoyType</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">AnyJoyType</span><span class="p">):</span>
-        <span class="k">if</span> <span class="n">u</span> <span class="o">&gt;=</span> <span class="n">v</span><span class="p">:</span>
-            <span class="n">s</span><span class="p">[</span><span class="n">u</span><span class="p">]</span> <span class="o">=</span> <span class="n">v</span>
-            <span class="k">return</span> <span class="n">s</span>
-        <span class="k">if</span> <span class="n">v</span> <span class="o">&gt;=</span> <span class="n">u</span><span class="p">:</span>
-            <span class="n">s</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">=</span> <span class="n">u</span>
-            <span class="k">return</span> <span class="n">s</span>
-        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;Cannot unify </span><span class="si">%r</span><span class="s1"> and </span><span class="si">%r</span><span class="s1">.&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">))</span>
-
-    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">u</span><span class="p">)</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">2</span><span class="p">:</span>
-            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="nb">repr</span><span class="p">((</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)))</span>
-        <span class="k">for</span> <span class="n">uu</span><span class="p">,</span> <span class="n">vv</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
-            <span class="n">s</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">uu</span><span class="p">,</span> <span class="n">vv</span><span class="p">,</span> <span class="n">s</span><span class="p">)</span>
-            <span class="k">if</span> <span class="n">s</span> <span class="o">==</span> <span class="kc">False</span><span class="p">:</span> <span class="c1"># (instead of a substitution dict.)</span>
-                <span class="k">break</span>
-        <span class="k">return</span> <span class="n">s</span>
-
-    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-        <span class="k">if</span> <span class="ow">not</span> <span class="n">stacky</span><span class="p">(</span><span class="n">u</span><span class="p">):</span>
-            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;Cannot unify </span><span class="si">%r</span><span class="s1"> and </span><span class="si">%r</span><span class="s1">.&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">))</span>
-        <span class="n">s</span><span class="p">[</span><span class="n">u</span><span class="p">]</span> <span class="o">=</span> <span class="n">v</span>
-        <span class="k">return</span> <span class="n">s</span>
-
-    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-        <span class="k">if</span> <span class="ow">not</span> <span class="n">stacky</span><span class="p">(</span><span class="n">v</span><span class="p">):</span>
-            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;Cannot unify </span><span class="si">%r</span><span class="s1"> and </span><span class="si">%r</span><span class="s1">.&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">u</span><span class="p">))</span>
-        <span class="n">s</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">=</span> <span class="n">u</span>
-        <span class="k">return</span> <span class="n">s</span>
-
-    <span class="k">return</span> <span class="kc">False</span>
-
-
-<span class="k">def</span> <span class="nf">stacky</span><span class="p">(</span><span class="n">thing</span><span class="p">):</span>
-    <span class="k">return</span> <span class="n">thing</span><span class="o">.</span><span class="vm">__class__</span> <span class="ow">in</span> <span class="p">{</span><span class="n">AnyJoyType</span><span class="p">,</span> <span class="n">StackJoyType</span><span class="p">}</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def unify(u, v, s=None):
+    if s is None:
+        s = {}
+    elif s:
+        u = update(s, u)
+        v = update(s, v)
+
+    if u == v:
+        return s
+
+    if isinstance(u, AnyJoyType) and isinstance(v, AnyJoyType):
+        if u &gt;= v:
+            s[u] = v
+            return s
+        if v &gt;= u:
+            s[v] = u
+            return s
+        raise TypeError(&#39;Cannot unify %r and %r.&#39; % (u, v))
+
+    if isinstance(u, tuple) and isinstance(v, tuple):
+        if len(u) != len(v) != 2:
+            raise TypeError(repr((u, v)))
+        for uu, vv in zip(u, v):
+            s = unify(uu, vv, s)
+            if s == False: # (instead of a substitution dict.)
+                break
+        return s
+
+    if isinstance(v, tuple):
+        if not stacky(u):
+            raise TypeError(&#39;Cannot unify %r and %r.&#39; % (u, v))
+        s[u] = v
+        return s
+
+    if isinstance(u, tuple):
+        if not stacky(v):
+            raise TypeError(&#39;Cannot unify %r and %r.&#39; % (v, u))
+        s[v] = u
+        return s
+
+    return False
+
+
+def stacky(thing):
+    return thing.__class__ in {AnyJoyType, StackJoyType}
 </pre></div>
 </div>
 <p>Rewrite the stack effect comments:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">defs</span><span class="p">():</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def defs():
 
-    <span class="n">rolldown</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">3</span><span class="p">]),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+    rolldown = (A[1], A[2], A[3]), (A[2], A[3], A[1])
 
-    <span class="n">rollup</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">3</span><span class="p">]),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
+    rollup = (A[1], A[2], A[3]), (A[3], A[1], A[2])
 
-    <span class="n">pop</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],),</span> <span class="p">()</span>
+    pop = (A[1],), ()
 
-    <span class="n">popop</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],),</span> <span class="p">()</span>
+    popop = (A[2], A[1],), ()
 
-    <span class="n">popd</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],)</span>
+    popd = (A[2], A[1],), (A[1],)
 
-    <span class="n">popdd</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],)</span>
+    popdd = (A[3], A[2], A[1],), (A[2], A[1],)
 
-    <span class="n">swap</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">]),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+    swap = (A[1], A[2]), (A[2], A[1])
 
-    <span class="n">rest</span> <span class="o">=</span> <span class="p">((</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]),),</span> <span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">],)</span>
+    rest = ((A[1], S[1]),), (S[1],)
 
-    <span class="n">rrest</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">rest</span><span class="p">,</span> <span class="n">rest</span><span class="p">)</span>
+    rrest = C(rest, rest)
 
-    <span class="n">cons</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="p">((</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]),)</span>
+    cons = (A[1], S[1]), ((A[1], S[1]),)
 
-    <span class="n">ccons</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">cons</span><span class="p">)</span>
+    ccons = C(cons, cons)
 
-    <span class="n">uncons</span> <span class="o">=</span> <span class="p">((</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]),),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+    uncons = ((A[1], S[1]),), (A[1], S[1])
 
-    <span class="n">swons</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">swap</span><span class="p">,</span> <span class="n">cons</span><span class="p">)</span>
+    swons = C(swap, cons)
 
-    <span class="n">dup</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+    dup = (A[1],), (A[1], A[1])
 
-    <span class="n">dupd</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+    dupd = (A[2], A[1]), (A[2], A[2], A[1])
 
-    <span class="n">mul</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">2</span><span class="p">]),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">3</span><span class="p">],)</span>
+    mul = (N[1], N[2]), (N[3],)
 
-    <span class="n">sqrt</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)</span>
+    sqrt = C(dup, mul)
 
-    <span class="n">first</span> <span class="o">=</span> <span class="p">((</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]),),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],)</span>
+    first = ((A[1], S[1]),), (A[1],)
 
-    <span class="n">second</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">rest</span><span class="p">,</span> <span class="n">first</span><span class="p">)</span>
+    second = C(rest, first)
 
-    <span class="n">third</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">rest</span><span class="p">,</span> <span class="n">second</span><span class="p">)</span>
+    third = C(rest, second)
 
-    <span class="n">tuck</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+    tuck = (A[2], A[1]), (A[1], A[2], A[1])
 
-    <span class="n">over</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
+    over = (A[2], A[1]), (A[2], A[1], A[2])
 
-    <span class="n">succ</span> <span class="o">=</span> <span class="n">pred</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">],),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">2</span><span class="p">],)</span>
+    succ = pred = (N[1],), (N[2],)
 
-    <span class="n">divmod_</span> <span class="o">=</span> <span class="n">pm</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">4</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">3</span><span class="p">])</span>
+    divmod_ = pm = (N[2], N[1]), (N[4], N[3])
 
-    <span class="k">return</span> <span class="nb">locals</span><span class="p">()</span>
+    return locals()
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">DEFS</span> <span class="o">=</span> <span class="n">defs</span><span class="p">()</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>DEFS = defs()
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">DEFS</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
-    <span class="nb">print</span> <span class="n">name</span><span class="p">,</span> <span class="s1">&#39;=&#39;</span><span class="p">,</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack_effect_comment</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for name, stack_effect_comment in sorted(DEFS.items()):
+    print name, &#39;=&#39;, doc_from_stack_effect(*stack_effect_comment)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">ccons</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
-<span class="n">cons</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">ccons</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="n">a2</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
+<span class="n">cons</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 <span class="n">divmod_</span> <span class="o">=</span> <span class="p">(</span><span class="n">n2</span> <span class="n">n1</span> <span class="o">--</span> <span class="n">n4</span> <span class="n">n3</span><span class="p">)</span>
 <span class="n">dup</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a1</span><span class="p">)</span>
 <span class="n">dupd</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span>
-<span class="n">first</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span>
+<span class="n">first</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span>
 <span class="n">mul</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="n">n2</span> <span class="o">--</span> <span class="n">n3</span><span class="p">)</span>
 <span class="n">over</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a1</span> <span class="n">a2</span><span class="p">)</span>
 <span class="n">pm</span> <span class="o">=</span> <span class="p">(</span><span class="n">n2</span> <span class="n">n1</span> <span class="o">--</span> <span class="n">n4</span> <span class="n">n3</span><span class="p">)</span>
@@ -1236,68 +1236,68 @@ of how many labels of each domain it has “seen”.</p>
 <span class="n">popdd</span> <span class="o">=</span> <span class="p">(</span><span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span>
 <span class="n">popop</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span><span class="p">)</span>
 <span class="n">pred</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
-<span class="n">rest</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<span class="n">rest</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 <span class="n">rolldown</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a3</span> <span class="n">a1</span><span class="p">)</span>
 <span class="n">rollup</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">--</span> <span class="n">a3</span> <span class="n">a1</span> <span class="n">a2</span><span class="p">)</span>
-<span class="n">rrest</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
-<span class="n">second</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a2</span><span class="p">)</span>
+<span class="n">rrest</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
+<span class="n">second</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a2</span><span class="p">)</span>
 <span class="n">sqrt</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
 <span class="n">succ</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
 <span class="n">swap</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span>
-<span class="n">swons</span> <span class="o">=</span> <span class="p">([</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
-<span class="n">third</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a3</span><span class="p">)</span>
+<span class="n">swons</span> <span class="o">=</span> <span class="p">([</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
+<span class="n">third</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a3</span><span class="p">)</span>
 <span class="n">tuck</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span>
-<span class="n">uncons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<span class="n">uncons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">DEFS</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>globals().update(DEFS)
 </pre></div>
 </div>
 </section>
 <section id="compose-dup-and-mul">
 <h4>Compose <code class="docutils literal notranslate"><span class="pre">dup</span></code> and <code class="docutils literal notranslate"><span class="pre">mul</span></code><a class="headerlink" href="#compose-dup-and-mul" title="Permalink to this headline">¶</a></h4>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>C(dup, mul)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">n1</span><span class="p">,),</span> <span class="p">(</span><span class="n">n2</span><span class="p">,))</span>
 </pre></div>
 </div>
 <p>Revisit the <code class="docutils literal notranslate"><span class="pre">F</span></code> function, works fine.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">=</span> <span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">cons</span><span class="p">,</span> <span class="n">cons</span><span class="p">))</span>
-<span class="n">F</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>F = reduce(C, (pop, swap, rolldown, rest, rest, cons, cons))
+F
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(((</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">a3</span><span class="p">,</span> <span class="n">a4</span><span class="p">,</span> <span class="n">a5</span><span class="p">),</span> <span class="p">((</span><span class="n">a4</span><span class="p">,</span> <span class="p">(</span><span class="n">a3</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),))</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">F</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print doc_from_stack_effect(*F)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="n">a3</span> <span class="n">a4</span> <span class="n">a5</span> <span class="o">--</span> <span class="p">[</span><span class="n">a4</span> <span class="n">a3</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="n">a3</span> <span class="n">a4</span> <span class="n">a5</span> <span class="o">--</span> <span class="p">[</span><span class="n">a4</span> <span class="n">a3</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
 <p>Some otherwise inefficient functions are no longer to be feared. We can
 also get the effect of combinators in some limited cases.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">neato</span><span class="p">(</span><span class="o">*</span><span class="n">funcs</span><span class="p">):</span>
-    <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="n">funcs</span><span class="p">))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def neato(*funcs):
+    print doc_from_stack_effect(*reduce(C, funcs))
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># e.g. [swap] dip</span>
-<span class="n">neato</span><span class="p">(</span><span class="n">rollup</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span># e.g. [swap] dip
+neato(rollup, swap, rolldown)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a1</span> <span class="n">a3</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># e.g. [popop] dipd</span>
-<span class="n">neato</span><span class="p">(</span><span class="n">popdd</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">pop</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span># e.g. [popop] dipd
+neato(popdd, rolldown, pop)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="n">a4</span> <span class="o">--</span> <span class="n">a3</span> <span class="n">a4</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Reverse the order of the top three items.</span>
-<span class="n">neato</span><span class="p">(</span><span class="n">rollup</span><span class="p">,</span> <span class="n">swap</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span># Reverse the order of the top three items.
+neato(rollup, swap)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">--</span> <span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span>
@@ -1308,22 +1308,22 @@ also get the effect of combinators in some limited cases.</p>
 <h4><code class="docutils literal notranslate"><span class="pre">compile_()</span></code> version 2<a class="headerlink" href="#compile-version-2" title="Permalink to this headline">¶</a></h4>
 <p>Because the type labels represent themselves as valid Python identifiers
 the <code class="docutils literal notranslate"><span class="pre">compile_()</span></code> function doesn’t need to generate them anymore:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
-    <span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span> <span class="o">=</span> <span class="n">f</span>
-    <span class="k">if</span> <span class="n">doc</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-        <span class="n">doc</span> <span class="o">=</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span><span class="p">)</span>
-    <span class="n">i</span> <span class="o">=</span> <span class="n">o</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;stack&#39;</span><span class="p">)</span>
-    <span class="k">for</span> <span class="n">term</span> <span class="ow">in</span> <span class="n">inputs</span><span class="p">:</span>
-        <span class="n">i</span> <span class="o">=</span> <span class="n">term</span><span class="p">,</span> <span class="n">i</span>
-    <span class="k">for</span> <span class="n">term</span> <span class="ow">in</span> <span class="n">outputs</span><span class="p">:</span>
-        <span class="n">o</span> <span class="o">=</span> <span class="n">term</span><span class="p">,</span> <span class="n">o</span>
-    <span class="k">return</span> <span class="s1">&#39;&#39;&#39;def </span><span class="si">%s</span><span class="s1">(stack):</span>
-<span class="s1">    &quot;&quot;&quot;</span><span class="si">%s</span><span class="s1">&quot;&quot;&quot;</span>
-<span class="s1">    </span><span class="si">%s</span><span class="s1"> = stack</span>
-<span class="s1">    return </span><span class="si">%s</span><span class="s1">&#39;&#39;&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">doc</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">o</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def compile_(name, f, doc=None):
+    inputs, outputs = f
+    if doc is None:
+        doc = doc_from_stack_effect(inputs, outputs)
+    i = o = Symbol(&#39;stack&#39;)
+    for term in inputs:
+        i = term, i
+    for term in outputs:
+        o = term, o
+    return &#39;&#39;&#39;def %s(stack):
+    &quot;&quot;&quot;%s&quot;&quot;&quot;
+    %s = stack
+    return %s&#39;&#39;&#39; % (name, doc, i, o)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">&#39;F&#39;</span><span class="p">,</span> <span class="n">F</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print compile_(&#39;F&#39;, F)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
@@ -1334,7 +1334,7 @@ the <code class="docutils literal notranslate"><span class="pre">compile_()</spa
 </div>
 <p>But it cannot magically create new functions that involve e.g. math and
 such. Note that this is <em>not</em> a <code class="docutils literal notranslate"><span class="pre">sqr</span></code> function implementation:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">&#39;sqr&#39;</span><span class="p">,</span> <span class="n">C</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print compile_(&#39;sqr&#39;, C(dup, mul))
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">sqr</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
@@ -1356,38 +1356,38 @@ functions (at least) are already wrappers it should be straightforward.)</p>
 <p>The functions that <em>can</em> be compiled are the ones that have only
 <code class="docutils literal notranslate"><span class="pre">AnyJoyType</span></code> and <code class="docutils literal notranslate"><span class="pre">StackJoyType</span></code> labels in their stack effect
 comments. We can write a function to check that:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">imap</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from itertools import imap
 
 
-<span class="k">def</span> <span class="nf">compilable</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
-    <span class="k">return</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">all</span><span class="p">(</span><span class="n">imap</span><span class="p">(</span><span class="n">compilable</span><span class="p">,</span> <span class="n">f</span><span class="p">))</span> <span class="ow">or</span> <span class="n">stacky</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
+def compilable(f):
+    return isinstance(f, tuple) and all(imap(compilable, f)) or stacky(f)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">defs</span><span class="p">()</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
-    <span class="k">if</span> <span class="n">compilable</span><span class="p">(</span><span class="n">stack_effect_comment</span><span class="p">):</span>
-        <span class="nb">print</span> <span class="n">name</span><span class="p">,</span> <span class="s1">&#39;=&#39;</span><span class="p">,</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack_effect_comment</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for name, stack_effect_comment in sorted(defs().items()):
+    if compilable(stack_effect_comment):
+        print name, &#39;=&#39;, doc_from_stack_effect(*stack_effect_comment)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">ccons</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
-<span class="n">cons</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">ccons</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="n">a2</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
+<span class="n">cons</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 <span class="n">dup</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a1</span><span class="p">)</span>
 <span class="n">dupd</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span>
-<span class="n">first</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span>
+<span class="n">first</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span>
 <span class="n">over</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a1</span> <span class="n">a2</span><span class="p">)</span>
 <span class="n">pop</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="o">--</span><span class="p">)</span>
 <span class="n">popd</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span>
 <span class="n">popdd</span> <span class="o">=</span> <span class="p">(</span><span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span>
 <span class="n">popop</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span><span class="p">)</span>
-<span class="n">rest</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<span class="n">rest</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 <span class="n">rolldown</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a3</span> <span class="n">a1</span><span class="p">)</span>
 <span class="n">rollup</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">--</span> <span class="n">a3</span> <span class="n">a1</span> <span class="n">a2</span><span class="p">)</span>
-<span class="n">rrest</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
-<span class="n">second</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a2</span><span class="p">)</span>
+<span class="n">rrest</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
+<span class="n">second</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a2</span><span class="p">)</span>
 <span class="n">swap</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span>
-<span class="n">swons</span> <span class="o">=</span> <span class="p">([</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
-<span class="n">third</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a3</span><span class="p">)</span>
+<span class="n">swons</span> <span class="o">=</span> <span class="p">([</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
+<span class="n">third</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a3</span><span class="p">)</span>
 <span class="n">tuck</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span>
-<span class="n">uncons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<span class="n">uncons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
 </section>
@@ -1465,36 +1465,36 @@ first two rules’ <code class="docutils literal notranslate"><span class="pre">
 the “truthiness” of <code class="docutils literal notranslate"><span class="pre">StackJoyType</span></code> to false to let e.g.
 <code class="docutils literal notranslate"><span class="pre">joy.utils.stack.concat</span></code> work with our stack effect comment cons-list
 tuples.)</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
-    <span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">),</span> <span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">)</span> <span class="o">=</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span>
-    <span class="n">s</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">)</span>
-    <span class="k">if</span> <span class="n">s</span> <span class="o">==</span> <span class="kc">False</span><span class="p">:</span>  <span class="c1"># s can also be the empty dict, which is ok.</span>
-        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;Cannot unify </span><span class="si">%r</span><span class="s1"> and </span><span class="si">%r</span><span class="s1">.&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">f_out</span><span class="p">,</span> <span class="n">g_in</span><span class="p">))</span>
-    <span class="k">return</span> <span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def compose(f, g):
+    (f_in, f_out), (g_in, g_out) = f, g
+    s = unify(g_in, f_out)
+    if s == False:  # s can also be the empty dict, which is ok.
+        raise TypeError(&#39;Cannot unify %r and %r.&#39; % (f_out, g_in))
+    return update(s, (f_in, g_out))
 </pre></div>
 </div>
 <p>I don’t want to rewrite all the defs myself, so I’ll write a little
 conversion function instead. This is programmer’s laziness.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">sequence_to_stack</span><span class="p">(</span><span class="n">seq</span><span class="p">,</span> <span class="n">stack</span><span class="o">=</span><span class="n">StackJoyType</span><span class="p">(</span><span class="mi">23</span><span class="p">)):</span>
-    <span class="k">for</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">seq</span><span class="p">:</span> <span class="n">stack</span> <span class="o">=</span> <span class="n">item</span><span class="p">,</span> <span class="n">stack</span>
-    <span class="k">return</span> <span class="n">stack</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def sequence_to_stack(seq, stack=StackJoyType(23)):
+    for item in seq: stack = item, stack
+    return stack
 
-<span class="n">NEW_DEFS</span> <span class="o">=</span> <span class="p">{</span>
-    <span class="n">name</span><span class="p">:</span> <span class="p">(</span><span class="n">sequence_to_stack</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">sequence_to_stack</span><span class="p">(</span><span class="n">o</span><span class="p">))</span>
-    <span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">o</span><span class="p">)</span> <span class="ow">in</span> <span class="n">DEFS</span><span class="o">.</span><span class="n">iteritems</span><span class="p">()</span>
-<span class="p">}</span>
-<span class="n">NEW_DEFS</span><span class="p">[</span><span class="s1">&#39;stack&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
-<span class="n">NEW_DEFS</span><span class="p">[</span><span class="s1">&#39;swaack&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
-<span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">NEW_DEFS</span><span class="p">)</span>
+NEW_DEFS = {
+    name: (sequence_to_stack(i), sequence_to_stack(o))
+    for name, (i, o) in DEFS.iteritems()
+}
+NEW_DEFS[&#39;stack&#39;] = S[0], (S[0], S[0])
+NEW_DEFS[&#39;swaack&#39;] = (S[1], S[0]), (S[0], S[1])
+globals().update(NEW_DEFS)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>C(stack, uncons)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">),</span> <span class="p">(</span><span class="n">s1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">))))</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>reduce(C, (stack, uncons, uncons))
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="p">(</span><span class="n">s1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s1</span><span class="p">))))))</span>
@@ -1506,63 +1506,63 @@ conversion function instead. This is programmer’s laziness.</p>
 <section id="doc-from-stack-effect-version-2">
 <h3><code class="docutils literal notranslate"><span class="pre">doc_from_stack_effect()</span></code> version 2<a class="headerlink" href="#doc-from-stack-effect-version-2" title="Permalink to this headline">¶</a></h3>
 <p>Clunky junk, but it will suffice for now.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">doc_from_stack_effect</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span><span class="p">):</span>
-    <span class="n">switch</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span>  <span class="c1"># Do we need to display the &#39;...&#39; for the rest of the main stack?</span>
-    <span class="n">i</span><span class="p">,</span> <span class="n">o</span> <span class="o">=</span> <span class="n">_f</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">switch</span><span class="p">),</span> <span class="n">_f</span><span class="p">(</span><span class="n">outputs</span><span class="p">,</span> <span class="n">switch</span><span class="p">)</span>
-    <span class="k">if</span> <span class="n">switch</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
-        <span class="n">i</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s1">&#39;...&#39;</span><span class="p">)</span>
-        <span class="n">o</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s1">&#39;...&#39;</span><span class="p">)</span>
-    <span class="k">return</span> <span class="s1">&#39;(</span><span class="si">%s</span><span class="s1">--</span><span class="si">%s</span><span class="s1">)&#39;</span> <span class="o">%</span> <span class="p">(</span>
-        <span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">reversed</span><span class="p">([</span><span class="s1">&#39;&#39;</span><span class="p">]</span> <span class="o">+</span> <span class="n">i</span><span class="p">)),</span>
-        <span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">reversed</span><span class="p">(</span><span class="n">o</span> <span class="o">+</span> <span class="p">[</span><span class="s1">&#39;&#39;</span><span class="p">])),</span>
-    <span class="p">)</span>
-
-
-<span class="k">def</span> <span class="nf">_f</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="n">switch</span><span class="p">):</span>
-    <span class="n">a</span> <span class="o">=</span> <span class="p">[]</span>
-    <span class="k">while</span> <span class="n">term</span> <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-        <span class="n">item</span><span class="p">,</span> <span class="n">term</span> <span class="o">=</span> <span class="n">term</span>
-        <span class="n">a</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">item</span><span class="p">)</span>
-    <span class="k">assert</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="n">StackJoyType</span><span class="p">),</span> <span class="nb">repr</span><span class="p">(</span><span class="n">term</span><span class="p">)</span>
-    <span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="n">_to_str</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">term</span><span class="p">,</span> <span class="n">switch</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">a</span><span class="p">]</span>
-    <span class="k">return</span> <span class="n">a</span>
-
-
-<span class="k">def</span> <span class="nf">_to_str</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="n">stack</span><span class="p">,</span> <span class="n">switch</span><span class="p">):</span>
-    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-        <span class="k">if</span> <span class="n">term</span> <span class="o">==</span> <span class="n">stack</span><span class="p">:</span>
-            <span class="n">switch</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="kc">True</span>
-            <span class="k">return</span> <span class="s1">&#39;[...]&#39;</span>
-        <span class="k">return</span> <span class="p">(</span>
-            <span class="s1">&#39;[.</span><span class="si">%i</span><span class="s1">.]&#39;</span> <span class="o">%</span> <span class="n">term</span><span class="o">.</span><span class="n">number</span>
-            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="n">StackJoyType</span><span class="p">)</span>
-            <span class="k">else</span> <span class="nb">str</span><span class="p">(</span><span class="n">term</span><span class="p">)</span>
-        <span class="p">)</span>
-
-    <span class="n">a</span> <span class="o">=</span> <span class="p">[]</span>
-    <span class="k">while</span> <span class="n">term</span> <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-        <span class="n">item</span><span class="p">,</span> <span class="n">term</span> <span class="o">=</span> <span class="n">term</span>
-        <span class="n">a</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">_to_str</span><span class="p">(</span><span class="n">item</span><span class="p">,</span> <span class="n">stack</span><span class="p">,</span> <span class="n">switch</span><span class="p">))</span>
-    <span class="k">assert</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="n">StackJoyType</span><span class="p">),</span> <span class="nb">repr</span><span class="p">(</span><span class="n">term</span><span class="p">)</span>
-    <span class="k">if</span> <span class="n">term</span> <span class="o">==</span> <span class="n">stack</span><span class="p">:</span>
-        <span class="n">switch</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="kc">True</span>
-        <span class="n">end</span> <span class="o">=</span> <span class="s1">&#39;...&#39;</span>
-    <span class="k">else</span><span class="p">:</span>
-        <span class="n">end</span> <span class="o">=</span> <span class="s1">&#39;.</span><span class="si">%i</span><span class="s1">.&#39;</span> <span class="o">%</span> <span class="n">term</span><span class="o">.</span><span class="n">number</span>
-    <span class="n">a</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">end</span><span class="p">)</span>
-    <span class="k">return</span> <span class="s1">&#39;[</span><span class="si">%s</span><span class="s1">]&#39;</span> <span class="o">%</span> <span class="s1">&#39; &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
-</pre></div>
-</div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">NEW_DEFS</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
-    <span class="nb">print</span> <span class="n">name</span><span class="p">,</span> <span class="s1">&#39;=&#39;</span><span class="p">,</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack_effect_comment</span><span class="p">)</span>
-</pre></div>
-</div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">ccons</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
-<span class="n">cons</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def doc_from_stack_effect(inputs, outputs):
+    switch = [False]  # Do we need to display the &#39;...&#39; for the rest of the main stack?
+    i, o = _f(inputs, switch), _f(outputs, switch)
+    if switch[0]:
+        i.append(&#39;...&#39;)
+        o.append(&#39;...&#39;)
+    return &#39;(%s--%s)&#39; % (
+        &#39; &#39;.join(reversed([&#39;&#39;] + i)),
+        &#39; &#39;.join(reversed(o + [&#39;&#39;])),
+    )
+
+
+def _f(term, switch):
+    a = []
+    while term and isinstance(term, tuple):
+        item, term = term
+        a.append(item)
+    assert isinstance(term, StackJoyType), repr(term)
+    a = [_to_str(i, term, switch) for i in a]
+    return a
+
+
+def _to_str(term, stack, switch):
+    if not isinstance(term, tuple):
+        if term == stack:
+            switch[0] = True
+            return &#39;[...]&#39;
+        return (
+            &#39;[.%i.]&#39; % term.number
+            if isinstance(term, StackJoyType)
+            else str(term)
+        )
+
+    a = []
+    while term and isinstance(term, tuple):
+        item, term = term
+        a.append(_to_str(item, stack, switch))
+    assert isinstance(term, StackJoyType), repr(term)
+    if term == stack:
+        switch[0] = True
+        end = &#39;...&#39;
+    else:
+        end = &#39;.%i.&#39; % term.number
+    a.append(end)
+    return &#39;[%s]&#39; % &#39; &#39;.join(a)
+</pre></div>
+</div>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for name, stack_effect_comment in sorted(NEW_DEFS.items()):
+    print name, &#39;=&#39;, doc_from_stack_effect(*stack_effect_comment)
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">ccons</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="n">a2</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
+<span class="n">cons</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 <span class="n">divmod_</span> <span class="o">=</span> <span class="p">(</span><span class="n">n2</span> <span class="n">n1</span> <span class="o">--</span> <span class="n">n4</span> <span class="n">n3</span><span class="p">)</span>
 <span class="n">dup</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a1</span><span class="p">)</span>
 <span class="n">dupd</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span>
-<span class="n">first</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span>
+<span class="n">first</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span>
 <span class="n">mul</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="n">n2</span> <span class="o">--</span> <span class="n">n3</span><span class="p">)</span>
 <span class="n">over</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a1</span> <span class="n">a2</span><span class="p">)</span>
 <span class="n">pm</span> <span class="o">=</span> <span class="p">(</span><span class="n">n2</span> <span class="n">n1</span> <span class="o">--</span> <span class="n">n4</span> <span class="n">n3</span><span class="p">)</span>
@@ -1571,26 +1571,26 @@ conversion function instead. This is programmer’s laziness.</p>
 <span class="n">popdd</span> <span class="o">=</span> <span class="p">(</span><span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span>
 <span class="n">popop</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span><span class="p">)</span>
 <span class="n">pred</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
-<span class="n">rest</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<span class="n">rest</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 <span class="n">rolldown</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a3</span> <span class="n">a1</span><span class="p">)</span>
 <span class="n">rollup</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">--</span> <span class="n">a3</span> <span class="n">a1</span> <span class="n">a2</span><span class="p">)</span>
-<span class="n">rrest</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
-<span class="n">second</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a2</span><span class="p">)</span>
+<span class="n">rrest</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
+<span class="n">second</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a2</span><span class="p">)</span>
 <span class="n">sqrt</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
 <span class="n">stack</span> <span class="o">=</span> <span class="p">(</span><span class="o">...</span> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="o">...</span><span class="p">])</span>
 <span class="n">succ</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
-<span class="n">swaack</span> <span class="o">=</span> <span class="p">([</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">.</span><span class="mf">0.</span><span class="p">])</span>
+<span class="n">swaack</span> <span class="o">=</span> <span class="p">([</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="mf">.0</span><span class="o">.</span><span class="p">])</span>
 <span class="n">swap</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span>
-<span class="n">swons</span> <span class="o">=</span> <span class="p">([</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
-<span class="n">third</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a3</span><span class="p">)</span>
+<span class="n">swons</span> <span class="o">=</span> <span class="p">([</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
+<span class="n">third</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a3</span><span class="p">)</span>
 <span class="n">tuck</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span>
-<span class="n">uncons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<span class="n">uncons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack</span><span class="p">)</span>
-<span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">))</span>
-<span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)))</span>
-<span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">,</span> <span class="n">cons</span><span class="p">)))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print ; print doc_from_stack_effect(*stack)
+print ; print doc_from_stack_effect(*C(stack, uncons))
+print ; print doc_from_stack_effect(*reduce(C, (stack, uncons, uncons)))
+print ; print doc_from_stack_effect(*reduce(C, (stack, uncons, cons)))
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">...</span> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="o">...</span><span class="p">])</span>
@@ -1602,15 +1602,15 @@ conversion function instead. This is programmer’s laziness.</p>
 <span class="p">(</span><span class="o">...</span> <span class="n">a1</span> <span class="o">--</span> <span class="o">...</span> <span class="n">a1</span> <span class="p">[</span><span class="n">a1</span> <span class="o">...</span><span class="p">])</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">ccons</span><span class="p">,</span> <span class="n">stack</span><span class="p">))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print doc_from_stack_effect(*C(ccons, stack))
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">...</span> <span class="n">a2</span> <span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="p">[[</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">...</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">...</span> <span class="n">a2</span> <span class="n">a1</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="p">[[</span><span class="n">a2</span> <span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">...</span><span class="p">])</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">Q</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">ccons</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>Q = C(ccons, stack)
 
-<span class="n">Q</span>
+Q
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">s1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s2</span><span class="p">))),</span> <span class="p">(((</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">s2</span><span class="p">),</span> <span class="p">((</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">s2</span><span class="p">)))</span>
@@ -1620,17 +1620,17 @@ conversion function instead. This is programmer’s laziness.</p>
 <h4><code class="docutils literal notranslate"><span class="pre">compile_()</span></code> version 3<a class="headerlink" href="#compile-version-3" title="Permalink to this headline">¶</a></h4>
 <p>This makes the <code class="docutils literal notranslate"><span class="pre">compile_()</span></code> function pretty simple as the stack effect
 comments are now already in the form needed for the Python code:</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
-    <span class="n">i</span><span class="p">,</span> <span class="n">o</span> <span class="o">=</span> <span class="n">f</span>
-    <span class="k">if</span> <span class="n">doc</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-        <span class="n">doc</span> <span class="o">=</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">o</span><span class="p">)</span>
-    <span class="k">return</span> <span class="s1">&#39;&#39;&#39;def </span><span class="si">%s</span><span class="s1">(stack):</span>
-<span class="s1">    &quot;&quot;&quot;</span><span class="si">%s</span><span class="s1">&quot;&quot;&quot;</span>
-<span class="s1">    </span><span class="si">%s</span><span class="s1"> = stack</span>
-<span class="s1">    return </span><span class="si">%s</span><span class="s1">&#39;&#39;&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">doc</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">o</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def compile_(name, f, doc=None):
+    i, o = f
+    if doc is None:
+        doc = doc_from_stack_effect(i, o)
+    return &#39;&#39;&#39;def %s(stack):
+    &quot;&quot;&quot;%s&quot;&quot;&quot;
+    %s = stack
+    return %s&#39;&#39;&#39; % (name, doc, i, o)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">&#39;Q&#39;</span><span class="p">,</span> <span class="n">Q</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print compile_(&#39;Q&#39;, Q)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">Q</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
@@ -1639,35 +1639,35 @@ comments are now already in the form needed for the Python code:</p>
     <span class="k">return</span> <span class="p">(((</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">s2</span><span class="p">),</span> <span class="p">((</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">s2</span><span class="p">))</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">unstack</span> <span class="o">=</span> <span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
-<span class="n">enstacken</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>unstack = (S[1], S[0]), S[1]
+enstacken = S[0], (S[0], S[1])
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">unstack</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print doc_from_stack_effect(*unstack)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span><span class="p">)</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">enstacken</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print doc_from_stack_effect(*enstacken)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">--</span> <span class="p">[</span><span class="o">.</span><span class="mf">0.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">--</span> <span class="p">[</span><span class="mf">.0</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">unstack</span><span class="p">))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print doc_from_stack_effect(*C(cons, unstack))
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">enstacken</span><span class="p">))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print doc_from_stack_effect(*C(cons, enstacken))
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[[</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">.</span><span class="mf">2.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[[</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="mf">.2</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">unstack</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>C(cons, unstack)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">s1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s2</span><span class="p">)),</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">))</span>
@@ -1679,23 +1679,23 @@ comments are now already in the form needed for the Python code:</p>
 <section id="part-vi-multiple-stack-effects">
 <h2>Part VI: Multiple Stack Effects<a class="headerlink" href="#part-vi-multiple-stack-effects" title="Permalink to this headline">¶</a></h2>
 <p>…</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">IntJoyType</span><span class="p">(</span><span class="n">NumberJoyType</span><span class="p">):</span> <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;i&#39;</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>class IntJoyType(NumberJoyType): prefix = &#39;i&#39;
 
 
-<span class="n">F</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">FloatJoyType</span><span class="p">,</span> <span class="n">_R</span><span class="p">)</span>
-<span class="n">I</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">IntJoyType</span><span class="p">,</span> <span class="n">_R</span><span class="p">)</span>
+F = map(FloatJoyType, _R)
+I = map(IntJoyType, _R)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">muls</span> <span class="o">=</span> <span class="p">[</span>
-     <span class="p">((</span><span class="n">I</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">I</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span> <span class="p">(</span><span class="n">I</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span>
-     <span class="p">((</span><span class="n">F</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">I</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span> <span class="p">(</span><span class="n">F</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span>
-     <span class="p">((</span><span class="n">I</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">F</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span> <span class="p">(</span><span class="n">F</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span>
-     <span class="p">((</span><span class="n">F</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">F</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span> <span class="p">(</span><span class="n">F</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span>
-<span class="p">]</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>muls = [
+     ((I[2], (I[1], S[0])), (I[3], S[0])),
+     ((F[2], (I[1], S[0])), (F[3], S[0])),
+     ((I[2], (F[1], S[0])), (F[3], S[0])),
+     ((F[2], (F[1], S[0])), (F[3], S[0])),
+]
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">muls</span><span class="p">:</span>
-    <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for f in muls:
+    print doc_from_stack_effect(*f)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">i1</span> <span class="n">i2</span> <span class="o">--</span> <span class="n">i3</span><span class="p">)</span>
@@ -1704,42 +1704,42 @@ comments are now already in the form needed for the Python code:</p>
 <span class="p">(</span><span class="n">f1</span> <span class="n">f2</span> <span class="o">--</span> <span class="n">f3</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">muls</span><span class="p">:</span>
-    <span class="k">try</span><span class="p">:</span>
-        <span class="n">e</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span>
-    <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>
-        <span class="k">continue</span>
-    <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">dup</span><span class="p">),</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">),</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">e</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for f in muls:
+    try:
+        e = C(dup, f)
+    except TypeError:
+        continue
+    print doc_from_stack_effect(*dup), doc_from_stack_effect(*f), doc_from_stack_effect(*e)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a1</span><span class="p">)</span> <span class="p">(</span><span class="n">i1</span> <span class="n">i2</span> <span class="o">--</span> <span class="n">i3</span><span class="p">)</span> <span class="p">(</span><span class="n">i1</span> <span class="o">--</span> <span class="n">i2</span><span class="p">)</span>
 <span class="p">(</span><span class="n">a1</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a1</span><span class="p">)</span> <span class="p">(</span><span class="n">f1</span> <span class="n">f2</span> <span class="o">--</span> <span class="n">f3</span><span class="p">)</span> <span class="p">(</span><span class="n">f1</span> <span class="o">--</span> <span class="n">f2</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">product</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from itertools import product
 
 
-<span class="k">def</span> <span class="nf">meta_compose</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
-    <span class="k">for</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span> <span class="ow">in</span> <span class="n">product</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
-        <span class="k">try</span><span class="p">:</span>
-            <span class="k">yield</span> <span class="n">C</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">)</span>
-        <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>
-            <span class="k">pass</span>
+def meta_compose(F, G):
+    for f, g in product(F, G):
+        try:
+            yield C(f, g)
+        except TypeError:
+            pass
 
 
-<span class="k">def</span> <span class="nf">MC</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
-    <span class="k">return</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">meta_compose</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">)))</span>
+def MC(F, G):
+    return sorted(set(meta_compose(F, G)))
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="p">[</span><span class="n">mul</span><span class="p">]):</span>
-    <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for f in MC([dup], [mul]):
+    print doc_from_stack_effect(*f)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">n1</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="n">muls</span><span class="p">):</span>
-    <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for f in MC([dup], muls):
+    print doc_from_stack_effect(*f)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">f1</span> <span class="o">--</span> <span class="n">f2</span><span class="p">)</span>
@@ -1768,173 +1768,173 @@ to return all universes (represented by their substitution dicts, the
 “unifiers”) that don’t lead to type conflicts.</p>
 <p>Consider unifying two stacks (the lowercase letters are any type
 variables of the kinds we have defined so far):</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">a</span> <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</span> <span class="n">U</span> <span class="p">[</span><span class="n">c</span> <span class="n">d</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">a</span> <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="mf">.0</span><span class="o">.</span><span class="p">]</span> <span class="n">U</span> <span class="p">[</span><span class="n">c</span> <span class="n">d</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span>
                           <span class="n">w</span><span class="o">/</span> <span class="p">{</span><span class="n">c</span><span class="p">:</span> <span class="n">a</span><span class="p">}</span>
-<span class="p">[</span>  <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</span> <span class="n">U</span> <span class="p">[</span>  <span class="n">d</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span>
+<span class="p">[</span>  <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="mf">.0</span><span class="o">.</span><span class="p">]</span> <span class="n">U</span> <span class="p">[</span>  <span class="n">d</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span>
 </pre></div>
 </div>
 <p>Now we have to split universes to unify <code class="docutils literal notranslate"><span class="pre">A*</span></code>. In the first universe it
 disappears:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">b</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</span> <span class="n">U</span> <span class="p">[</span><span class="n">d</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span>
-                   <span class="n">w</span><span class="o">/</span> <span class="p">{</span><span class="n">d</span><span class="p">:</span> <span class="n">b</span><span class="p">,</span> <span class="o">.</span><span class="mf">1.</span><span class="p">:</span> <span class="o">.</span><span class="mf">0.</span><span class="p">}</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">b</span> <span class="mf">.0</span><span class="o">.</span><span class="p">]</span> <span class="n">U</span> <span class="p">[</span><span class="n">d</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span>
+                   <span class="n">w</span><span class="o">/</span> <span class="p">{</span><span class="n">d</span><span class="p">:</span> <span class="n">b</span><span class="p">,</span> <span class="mf">.1</span><span class="o">.</span><span class="p">:</span> <span class="mf">.0</span><span class="o">.</span><span class="p">}</span>
      <span class="p">[]</span> <span class="n">U</span> <span class="p">[]</span>
 </pre></div>
 </div>
 <p>While in the second it spawns an <code class="docutils literal notranslate"><span class="pre">A</span></code>, which we will label <code class="docutils literal notranslate"><span class="pre">e</span></code>:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">e</span> <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</span> <span class="n">U</span> <span class="p">[</span><span class="n">d</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">e</span> <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="mf">.0</span><span class="o">.</span><span class="p">]</span> <span class="n">U</span> <span class="p">[</span><span class="n">d</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span>
                         <span class="n">w</span><span class="o">/</span> <span class="p">{</span><span class="n">d</span><span class="p">:</span> <span class="n">e</span><span class="p">}</span>
-<span class="p">[</span>  <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</span> <span class="n">U</span> <span class="p">[</span>  <span class="o">.</span><span class="mf">1.</span><span class="p">]</span>
-                        <span class="n">w</span><span class="o">/</span> <span class="p">{</span><span class="o">.</span><span class="mf">1.</span><span class="p">:</span> <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="o">.</span><span class="mf">0.</span><span class="p">}</span>
-<span class="p">[</span>  <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</span> <span class="n">U</span> <span class="p">[</span>  <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</span>
+<span class="p">[</span>  <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="mf">.0</span><span class="o">.</span><span class="p">]</span> <span class="n">U</span> <span class="p">[</span>  <span class="mf">.1</span><span class="o">.</span><span class="p">]</span>
+                        <span class="n">w</span><span class="o">/</span> <span class="p">{</span><span class="mf">.1</span><span class="o">.</span><span class="p">:</span> <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="mf">.0</span><span class="o">.</span><span class="p">}</span>
+<span class="p">[</span>  <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="mf">.0</span><span class="o">.</span><span class="p">]</span> <span class="n">U</span> <span class="p">[</span>  <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="mf">.0</span><span class="o">.</span><span class="p">]</span>
 </pre></div>
 </div>
 <p>Giving us two unifiers:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">c</span><span class="p">:</span> <span class="n">a</span><span class="p">,</span>  <span class="n">d</span><span class="p">:</span> <span class="n">b</span><span class="p">,</span>  <span class="o">.</span><span class="mf">1.</span><span class="p">:</span>      <span class="o">.</span><span class="mf">0.</span><span class="p">}</span>
-<span class="p">{</span><span class="n">c</span><span class="p">:</span> <span class="n">a</span><span class="p">,</span>  <span class="n">d</span><span class="p">:</span> <span class="n">e</span><span class="p">,</span>  <span class="o">.</span><span class="mf">1.</span><span class="p">:</span> <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="o">.</span><span class="mf">0.</span><span class="p">}</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">c</span><span class="p">:</span> <span class="n">a</span><span class="p">,</span>  <span class="n">d</span><span class="p">:</span> <span class="n">b</span><span class="p">,</span>  <span class="mf">.1</span><span class="o">.</span><span class="p">:</span>      <span class="mf">.0</span><span class="o">.</span><span class="p">}</span>
+<span class="p">{</span><span class="n">c</span><span class="p">:</span> <span class="n">a</span><span class="p">,</span>  <span class="n">d</span><span class="p">:</span> <span class="n">e</span><span class="p">,</span>  <span class="mf">.1</span><span class="o">.</span><span class="p">:</span> <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="mf">.0</span><span class="o">.</span><span class="p">}</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">KleeneStar</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>class KleeneStar(object):
 
-    <span class="n">kind</span> <span class="o">=</span> <span class="n">AnyJoyType</span>
+    kind = AnyJoyType
 
-    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">number</span><span class="p">):</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">number</span> <span class="o">=</span> <span class="n">number</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">prefix</span> <span class="o">=</span> <span class="nb">repr</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
+    def __init__(self, number):
+        self.number = number
+        self.count = 0
+        self.prefix = repr(self)
 
-    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-        <span class="k">return</span> <span class="s1">&#39;</span><span class="si">%s%i</span><span class="s1">*&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">kind</span><span class="o">.</span><span class="n">prefix</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">number</span><span class="p">)</span>
+    def __repr__(self):
+        return &#39;%s%i*&#39; % (self.kind.prefix, self.number)
 
-    <span class="k">def</span> <span class="nf">another</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
-        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">kind</span><span class="p">(</span><span class="mi">10000</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">number</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">count</span><span class="p">)</span>
+    def another(self):
+        self.count += 1
+        return self.kind(10000 * self.number + self.count)
 
-    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-        <span class="k">return</span> <span class="p">(</span>
-            <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="p">)</span>
-            <span class="ow">and</span> <span class="n">other</span><span class="o">.</span><span class="n">number</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">number</span>
-        <span class="p">)</span>
+    def __eq__(self, other):
+        return (
+            isinstance(other, self.__class__)
+            and other.number == self.number
+        )
 
-    <span class="k">def</span> <span class="fm">__ge__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">kind</span> <span class="o">&gt;=</span> <span class="n">other</span><span class="o">.</span><span class="n">kind</span>
+    def __ge__(self, other):
+        return self.kind &gt;= other.kind
 
-    <span class="k">def</span> <span class="fm">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">number</span> <span class="o">+</span> <span class="n">other</span><span class="p">)</span>
-    <span class="fm">__radd__</span> <span class="o">=</span> <span class="fm">__add__</span>
+    def __add__(self, other):
+        return self.__class__(self.number + other)
+    __radd__ = __add__
 
-    <span class="k">def</span> <span class="fm">__hash__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-        <span class="k">return</span> <span class="nb">hash</span><span class="p">(</span><span class="nb">repr</span><span class="p">(</span><span class="bp">self</span><span class="p">))</span>
+    def __hash__(self):
+        return hash(repr(self))
 
-<span class="k">class</span> <span class="nc">AnyStarJoyType</span><span class="p">(</span><span class="n">KleeneStar</span><span class="p">):</span> <span class="n">kind</span> <span class="o">=</span> <span class="n">AnyJoyType</span>
-<span class="k">class</span> <span class="nc">NumberStarJoyType</span><span class="p">(</span><span class="n">KleeneStar</span><span class="p">):</span> <span class="n">kind</span> <span class="o">=</span> <span class="n">NumberJoyType</span>
-<span class="c1">#class FloatStarJoyType(KleeneStar): kind = FloatJoyType</span>
-<span class="c1">#class IntStarJoyType(KleeneStar): kind = IntJoyType</span>
-<span class="k">class</span> <span class="nc">StackStarJoyType</span><span class="p">(</span><span class="n">KleeneStar</span><span class="p">):</span> <span class="n">kind</span> <span class="o">=</span> <span class="n">StackJoyType</span>
+class AnyStarJoyType(KleeneStar): kind = AnyJoyType
+class NumberStarJoyType(KleeneStar): kind = NumberJoyType
+#class FloatStarJoyType(KleeneStar): kind = FloatJoyType
+#class IntStarJoyType(KleeneStar): kind = IntJoyType
+class StackStarJoyType(KleeneStar): kind = StackJoyType
 
 
-<span class="n">As</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">AnyStarJoyType</span><span class="p">,</span> <span class="n">_R</span><span class="p">)</span>
-<span class="n">Ns</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">NumberStarJoyType</span><span class="p">,</span> <span class="n">_R</span><span class="p">)</span>
-<span class="n">Ss</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">StackStarJoyType</span><span class="p">,</span> <span class="n">_R</span><span class="p">)</span>
+As = map(AnyStarJoyType, _R)
+Ns = map(NumberStarJoyType, _R)
+Ss = map(StackStarJoyType, _R)
 </pre></div>
 </div>
 <section id="unify-version-4">
 <h4><code class="docutils literal notranslate"><span class="pre">unify()</span></code> version 4<a class="headerlink" href="#unify-version-4" title="Permalink to this headline">¶</a></h4>
 <p>Can now return multiple results…</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
-    <span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-        <span class="n">s</span> <span class="o">=</span> <span class="p">{}</span>
-    <span class="k">elif</span> <span class="n">s</span><span class="p">:</span>
-        <span class="n">u</span> <span class="o">=</span> <span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">u</span><span class="p">)</span>
-        <span class="n">v</span> <span class="o">=</span> <span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
-
-    <span class="k">if</span> <span class="n">u</span> <span class="o">==</span> <span class="n">v</span><span class="p">:</span>
-        <span class="k">return</span> <span class="n">s</span><span class="p">,</span>
-
-    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">AnyJoyType</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">AnyJoyType</span><span class="p">):</span>
-        <span class="k">if</span> <span class="n">u</span> <span class="o">&gt;=</span> <span class="n">v</span><span class="p">:</span>
-            <span class="n">s</span><span class="p">[</span><span class="n">u</span><span class="p">]</span> <span class="o">=</span> <span class="n">v</span>
-            <span class="k">return</span> <span class="n">s</span><span class="p">,</span>
-        <span class="k">if</span> <span class="n">v</span> <span class="o">&gt;=</span> <span class="n">u</span><span class="p">:</span>
-            <span class="n">s</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">=</span> <span class="n">u</span>
-            <span class="k">return</span> <span class="n">s</span><span class="p">,</span>
-        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;Cannot unify </span><span class="si">%r</span><span class="s1"> and </span><span class="si">%r</span><span class="s1">.&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">))</span>
-
-    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">u</span><span class="p">)</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">2</span><span class="p">:</span>
-            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="nb">repr</span><span class="p">((</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)))</span>
-
-        <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">v</span>
-        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">KleeneStar</span><span class="p">):</span>
-            <span class="c1"># Two universes, in one the Kleene star disappears and unification</span>
-            <span class="c1"># continues without it...</span>
-            <span class="n">s0</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
-
-            <span class="c1"># In the other it spawns a new variable.</span>
-            <span class="n">s1</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">a</span><span class="o">.</span><span class="n">another</span><span class="p">(),</span> <span class="n">v</span><span class="p">))</span>
-
-            <span class="n">t</span> <span class="o">=</span> <span class="n">s0</span> <span class="o">+</span> <span class="n">s1</span>
-            <span class="k">for</span> <span class="n">sn</span> <span class="ow">in</span> <span class="n">t</span><span class="p">:</span>
-                <span class="n">sn</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
-            <span class="k">return</span> <span class="n">t</span>
-
-        <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">u</span>
-        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">KleeneStar</span><span class="p">):</span>
-            <span class="n">s0</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
-            <span class="n">s1</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="p">(</span><span class="n">a</span><span class="o">.</span><span class="n">another</span><span class="p">(),</span> <span class="n">u</span><span class="p">))</span>
-            <span class="n">t</span> <span class="o">=</span> <span class="n">s0</span> <span class="o">+</span> <span class="n">s1</span>
-            <span class="k">for</span> <span class="n">sn</span> <span class="ow">in</span> <span class="n">t</span><span class="p">:</span>
-                <span class="n">sn</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
-            <span class="k">return</span> <span class="n">t</span>
-
-        <span class="n">ses</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">v</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">s</span><span class="p">)</span>
-        <span class="n">results</span> <span class="o">=</span> <span class="p">()</span>
-        <span class="k">for</span> <span class="n">sn</span> <span class="ow">in</span> <span class="n">ses</span><span class="p">:</span>
-            <span class="n">results</span> <span class="o">+=</span> <span class="n">unify</span><span class="p">(</span><span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">sn</span><span class="p">)</span>
-        <span class="k">return</span> <span class="n">results</span>
-
-    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-        <span class="k">if</span> <span class="ow">not</span> <span class="n">stacky</span><span class="p">(</span><span class="n">u</span><span class="p">):</span>
-            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;Cannot unify </span><span class="si">%r</span><span class="s1"> and </span><span class="si">%r</span><span class="s1">.&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">))</span>
-        <span class="n">s</span><span class="p">[</span><span class="n">u</span><span class="p">]</span> <span class="o">=</span> <span class="n">v</span>
-        <span class="k">return</span> <span class="n">s</span><span class="p">,</span>
-
-    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-        <span class="k">if</span> <span class="ow">not</span> <span class="n">stacky</span><span class="p">(</span><span class="n">v</span><span class="p">):</span>
-            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;Cannot unify </span><span class="si">%r</span><span class="s1"> and </span><span class="si">%r</span><span class="s1">.&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">u</span><span class="p">))</span>
-        <span class="n">s</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">=</span> <span class="n">u</span>
-        <span class="k">return</span> <span class="n">s</span><span class="p">,</span>
-
-    <span class="k">return</span> <span class="p">()</span>
-
-
-<span class="k">def</span> <span class="nf">stacky</span><span class="p">(</span><span class="n">thing</span><span class="p">):</span>
-    <span class="k">return</span> <span class="n">thing</span><span class="o">.</span><span class="vm">__class__</span> <span class="ow">in</span> <span class="p">{</span><span class="n">AnyJoyType</span><span class="p">,</span> <span class="n">StackJoyType</span><span class="p">}</span>
-</pre></div>
-</div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">As</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
-<span class="n">a</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def unify(u, v, s=None):
+    if s is None:
+        s = {}
+    elif s:
+        u = update(s, u)
+        v = update(s, v)
+
+    if u == v:
+        return s,
+
+    if isinstance(u, AnyJoyType) and isinstance(v, AnyJoyType):
+        if u &gt;= v:
+            s[u] = v
+            return s,
+        if v &gt;= u:
+            s[v] = u
+            return s,
+        raise TypeError(&#39;Cannot unify %r and %r.&#39; % (u, v))
+
+    if isinstance(u, tuple) and isinstance(v, tuple):
+        if len(u) != len(v) != 2:
+            raise TypeError(repr((u, v)))
+
+        a, b = v
+        if isinstance(a, KleeneStar):
+            # Two universes, in one the Kleene star disappears and unification
+            # continues without it...
+            s0 = unify(u, b)
+
+            # In the other it spawns a new variable.
+            s1 = unify(u, (a.another(), v))
+
+            t = s0 + s1
+            for sn in t:
+                sn.update(s)
+            return t
+
+        a, b = u
+        if isinstance(a, KleeneStar):
+            s0 = unify(v, b)
+            s1 = unify(v, (a.another(), u))
+            t = s0 + s1
+            for sn in t:
+                sn.update(s)
+            return t
+
+        ses = unify(u[0], v[0], s)
+        results = ()
+        for sn in ses:
+            results += unify(u[1], v[1], sn)
+        return results
+
+    if isinstance(v, tuple):
+        if not stacky(u):
+            raise TypeError(&#39;Cannot unify %r and %r.&#39; % (u, v))
+        s[u] = v
+        return s,
+
+    if isinstance(u, tuple):
+        if not stacky(v):
+            raise TypeError(&#39;Cannot unify %r and %r.&#39; % (v, u))
+        s[v] = u
+        return s,
+
+    return ()
+
+
+def stacky(thing):
+    return thing.__class__ in {AnyJoyType, StackJoyType}
+</pre></div>
+</div>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>a = (As[1], S[1])
+a
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
-<span class="n">b</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>b = (A[1], S[2])
+b
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s2</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">a</span><span class="p">):</span>
-    <span class="nb">print</span> <span class="n">result</span><span class="p">,</span> <span class="s1">&#39;-&gt;&#39;</span><span class="p">,</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">a</span><span class="p">),</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for result in unify(b, a):
+    print result, &#39;-&gt;&#39;, update(result, a), update(result, b)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">s1</span><span class="p">:</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s2</span><span class="p">)}</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s2</span><span class="p">))</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s2</span><span class="p">)</span>
 <span class="p">{</span><span class="n">a1</span><span class="p">:</span> <span class="n">a10001</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">)}</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">)</span> <span class="p">(</span><span class="n">a10001</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">))</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
-    <span class="nb">print</span> <span class="n">result</span><span class="p">,</span> <span class="s1">&#39;-&gt;&#39;</span><span class="p">,</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">a</span><span class="p">),</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for result in unify(a, b):
+    print result, &#39;-&gt;&#39;, update(result, a), update(result, b)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">s1</span><span class="p">:</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s2</span><span class="p">)}</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s2</span><span class="p">))</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s2</span><span class="p">)</span>
@@ -1948,24 +1948,24 @@ disappears:</p>
 <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">)</span>       <span class="p">[</span><span class="n">a1</span><span class="o">*</span><span class="p">]</span>       <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">))</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a1</span><span class="o">*</span><span class="p">]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">sum_</span> <span class="o">=</span> <span class="p">((</span><span class="n">Ns</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>sum_ = ((Ns[1], S[1]), S[0]), (N[0], S[0])
 
-<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">sum_</span><span class="p">)</span>
+print doc_from_stack_effect(*sum_)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n0</span><span class="p">)</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">n1</span><span class="o">*</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n0</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">f</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]))),</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>f = (N[1], (N[2], (N[3], S[1]))), S[0]
 
-<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">f</span><span class="p">)</span>
+print doc_from_stack_effect(S[0], f)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">--</span> <span class="p">[</span><span class="n">n1</span> <span class="n">n2</span> <span class="n">n3</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">--</span> <span class="p">[</span><span class="n">n1</span> <span class="n">n2</span> <span class="n">n3</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">sum_</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">f</span><span class="p">):</span>
-    <span class="nb">print</span> <span class="n">result</span><span class="p">,</span> <span class="s1">&#39;-&gt;&#39;</span><span class="p">,</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">sum_</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for result in unify(sum_[0], f):
+    print result, &#39;-&gt;&#39;, update(result, sum_[1])
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">s1</span><span class="p">:</span> <span class="p">(</span><span class="n">n1</span><span class="p">,</span> <span class="p">(</span><span class="n">n2</span><span class="p">,</span> <span class="p">(</span><span class="n">n3</span><span class="p">,</span> <span class="n">s1</span><span class="p">)))}</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="n">n0</span><span class="p">,</span> <span class="n">s0</span><span class="p">)</span>
@@ -1978,88 +1978,88 @@ disappears:</p>
 <section id="compose-version-3">
 <h4><code class="docutils literal notranslate"><span class="pre">compose()</span></code> version 3<a class="headerlink" href="#compose-version-3" title="Permalink to this headline">¶</a></h4>
 <p>This function has to be modified to yield multiple results.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
-    <span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">),</span> <span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">)</span> <span class="o">=</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span>
-    <span class="n">s</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">)</span>
-    <span class="k">if</span> <span class="ow">not</span> <span class="n">s</span><span class="p">:</span>
-        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;Cannot unify </span><span class="si">%r</span><span class="s1"> and </span><span class="si">%r</span><span class="s1">.&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">f_out</span><span class="p">,</span> <span class="n">g_in</span><span class="p">))</span>
-    <span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">s</span><span class="p">:</span>
-        <span class="k">yield</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def compose(f, g):
+    (f_in, f_out), (g_in, g_out) = f, g
+    s = unify(g_in, f_out)
+    if not s:
+        raise TypeError(&#39;Cannot unify %r and %r.&#39; % (f_out, g_in))
+    for result in s:
+        yield update(result, (f_in, g_out))
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">meta_compose</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
-    <span class="k">for</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span> <span class="ow">in</span> <span class="n">product</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
-        <span class="k">try</span><span class="p">:</span>
-            <span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">C</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
-                <span class="k">yield</span> <span class="n">result</span>
-        <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>
-            <span class="k">pass</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def meta_compose(F, G):
+    for f, g in product(F, G):
+        try:
+            for result in C(f, g):
+                yield result
+        except TypeError:
+            pass
 
 
-<span class="k">def</span> <span class="nf">C</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
-    <span class="n">f</span><span class="p">,</span> <span class="n">g</span> <span class="o">=</span> <span class="n">relabel</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">)</span>
-    <span class="k">for</span> <span class="n">fg</span> <span class="ow">in</span> <span class="n">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
-        <span class="k">yield</span> <span class="n">delabel</span><span class="p">(</span><span class="n">fg</span><span class="p">)</span>
+def C(f, g):
+    f, g = relabel(f, g)
+    for fg in compose(f, g):
+        yield delabel(fg)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="n">muls</span><span class="p">):</span>
-    <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for f in MC([dup], muls):
+    print doc_from_stack_effect(*f)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">f1</span> <span class="o">--</span> <span class="n">f2</span><span class="p">)</span>
 <span class="p">(</span><span class="n">i1</span> <span class="o">--</span> <span class="n">i2</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="p">[</span><span class="n">sum_</span><span class="p">]):</span>
-    <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for f in MC([dup], [sum_]):
+    print doc_from_stack_effect(*f)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="n">n1</span><span class="p">)</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">n1</span><span class="o">*</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">n1</span><span class="o">*</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="n">n1</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">cons</span><span class="p">],</span> <span class="p">[</span><span class="n">sum_</span><span class="p">]):</span>
-    <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for f in MC([cons], [sum_]):
+    print doc_from_stack_effect(*f)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n1</span><span class="p">)</span>
-<span class="p">(</span><span class="n">n1</span> <span class="p">[</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n1</span><span class="p">)</span>
+<span class="p">(</span><span class="n">n1</span> <span class="p">[</span><span class="n">n1</span><span class="o">*</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">sum_</span> <span class="o">=</span> <span class="p">(((</span><span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">Ns</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])),</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]))</span>
-<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">cons</span><span class="p">),</span>
-<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">sum_</span><span class="p">),</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>sum_ = (((N[1], (Ns[1], S[1])), S[0]), (N[0], S[0]))
+print doc_from_stack_effect(*cons),
+print doc_from_stack_effect(*sum_),
 
-<span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">cons</span><span class="p">],</span> <span class="p">[</span><span class="n">sum_</span><span class="p">]):</span>
-    <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
+for f in MC([cons], [sum_]):
+    print doc_from_stack_effect(*f)
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span> <span class="p">([</span><span class="n">n1</span> <span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n0</span><span class="p">)</span> <span class="p">(</span><span class="n">n1</span> <span class="p">[</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="mf">.1</span><span class="o">.</span><span class="p">])</span> <span class="p">([</span><span class="n">n1</span> <span class="n">n1</span><span class="o">*</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n0</span><span class="p">)</span> <span class="p">(</span><span class="n">n1</span> <span class="p">[</span><span class="n">n1</span><span class="o">*</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">4</span><span class="p">],</span> <span class="p">(</span><span class="n">As</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])))</span>
-<span class="n">a</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>a = (A[4], (As[1], (A[3], S[1])))
+a
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a4</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="p">(</span><span class="n">a3</span><span class="p">,</span> <span class="n">s1</span><span class="p">)))</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">2</span><span class="p">]))</span>
-<span class="n">b</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>b = (A[1], (A[2], S[2]))
+b
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s2</span><span class="p">))</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">a</span><span class="p">):</span>
-    <span class="nb">print</span> <span class="n">result</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for result in unify(b, a):
+    print result
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">a1</span><span class="p">:</span> <span class="n">a4</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="n">s1</span><span class="p">,</span> <span class="n">a2</span><span class="p">:</span> <span class="n">a3</span><span class="p">}</span>
 <span class="p">{</span><span class="n">a1</span><span class="p">:</span> <span class="n">a4</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="p">(</span><span class="n">a3</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">a2</span><span class="p">:</span> <span class="n">a10003</span><span class="p">}</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
-    <span class="nb">print</span> <span class="n">result</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>for result in unify(a, b):
+    print result
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">s2</span><span class="p">:</span> <span class="n">s1</span><span class="p">,</span> <span class="n">a2</span><span class="p">:</span> <span class="n">a3</span><span class="p">,</span> <span class="n">a4</span><span class="p">:</span> <span class="n">a1</span><span class="p">}</span>
@@ -2075,11 +2075,11 @@ disappears:</p>
 have the quoted programs they expect available. In the most general
 case, the <code class="docutils literal notranslate"><span class="pre">i</span></code> combinator, you can’t say anything about its stack
 effect other than it expects one quote:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">i</span> <span class="p">(</span><span class="o">...</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="o">...</span> <span class="o">.</span><span class="mf">1.</span><span class="p">)</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">i</span> <span class="p">(</span><span class="o">...</span> <span class="p">[</span><span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="o">...</span> <span class="mf">.1</span><span class="o">.</span><span class="p">)</span>
 </pre></div>
 </div>
 <p>Or</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">i</span> <span class="p">(</span><span class="o">...</span> <span class="p">[</span><span class="n">A</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="o">...</span> <span class="n">A</span><span class="o">*</span><span class="p">)</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">i</span> <span class="p">(</span><span class="o">...</span> <span class="p">[</span><span class="n">A</span><span class="o">*</span> <span class="mf">.1</span><span class="o">.</span><span class="p">]</span> <span class="o">--</span> <span class="o">...</span> <span class="n">A</span><span class="o">*</span><span class="p">)</span>
 </pre></div>
 </div>
 <p>Consider the type of:</p>
@@ -2087,7 +2087,7 @@ effect other than it expects one quote:</p>
 </pre></div>
 </div>
 <p>Obviously it would be:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">..</span><span class="mi">1</span><span class="p">]</span> <span class="n">a2</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">..</span><span class="mi">1</span><span class="p">]</span> <span class="n">a2</span><span class="p">)</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">.1</span><span class="p">]</span> <span class="n">a2</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">.</span><span class="mf">.1</span><span class="p">]</span> <span class="n">a2</span><span class="p">)</span>
 </pre></div>
 </div>
 <p><code class="docutils literal notranslate"><span class="pre">dip</span></code> itself could have:</p>
@@ -2111,19 +2111,19 @@ stack effect we have to “split universes” again and return both.</p>
 <p>We need a type variable for Joy functions that can go in our expressions
 and be used by the hybrid inferencer/interpreter. They have to store a
 name and a list of stack effects.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">FunctionJoyType</span><span class="p">(</span><span class="n">AnyJoyType</span><span class="p">):</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>class FunctionJoyType(AnyJoyType):
 
-    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">sec</span><span class="p">,</span> <span class="n">number</span><span class="p">):</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="n">name</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">stack_effects</span> <span class="o">=</span> <span class="n">sec</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">number</span> <span class="o">=</span> <span class="n">number</span>
+    def __init__(self, name, sec, number):
+        self.name = name
+        self.stack_effects = sec
+        self.number = number
 
-    <span class="k">def</span> <span class="fm">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-        <span class="k">return</span> <span class="bp">self</span>
-    <span class="fm">__radd__</span> <span class="o">=</span> <span class="fm">__add__</span>
+    def __add__(self, other):
+        return self
+    __radd__ = __add__
 
-    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">name</span>
+    def __repr__(self):
+        return self.name
 </pre></div>
 </div>
 </section>
@@ -2131,47 +2131,47 @@ name and a list of stack effects.</p>
 <h4>Specialized for Simple Functions and Combinators<a class="headerlink" href="#specialized-for-simple-functions-and-combinators" title="Permalink to this headline">¶</a></h4>
 <p>For non-combinator functions the stack effects list contains stack
 effect comments (represented by pairs of cons-lists as described above.)</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">SymbolJoyType</span><span class="p">(</span><span class="n">FunctionJoyType</span><span class="p">):</span>
-    <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;F&#39;</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>class SymbolJoyType(FunctionJoyType):
+    prefix = &#39;F&#39;
 </pre></div>
 </div>
 <p>For combinators the list contains Python functions.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">CombinatorJoyType</span><span class="p">(</span><span class="n">FunctionJoyType</span><span class="p">):</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>class CombinatorJoyType(FunctionJoyType):
 
-    <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;C&#39;</span>
+    prefix = &#39;C&#39;
 
-    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">sec</span><span class="p">,</span> <span class="n">number</span><span class="p">,</span> <span class="n">expect</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
-        <span class="nb">super</span><span class="p">(</span><span class="n">CombinatorJoyType</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">sec</span><span class="p">,</span> <span class="n">number</span><span class="p">)</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">expect</span> <span class="o">=</span> <span class="n">expect</span>
+    def __init__(self, name, sec, number, expect=None):
+        super(CombinatorJoyType, self).__init__(name, sec, number)
+        self.expect = expect
 
-    <span class="k">def</span> <span class="nf">enter_guard</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">):</span>
-        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">expect</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-            <span class="k">return</span> <span class="n">f</span>
-        <span class="n">g</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">expect</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">expect</span>
-        <span class="n">new_f</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">,</span> <span class="p">()))</span>
-        <span class="k">assert</span> <span class="nb">len</span><span class="p">(</span><span class="n">new_f</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">,</span> <span class="nb">repr</span><span class="p">(</span><span class="n">new_f</span><span class="p">)</span>
-        <span class="k">return</span> <span class="n">new_f</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span>
+    def enter_guard(self, f):
+        if self.expect is None:
+            return f
+        g = self.expect, self.expect
+        new_f = list(compose(f, g, ()))
+        assert len(new_f) == 1, repr(new_f)
+        return new_f[0][1]
 </pre></div>
 </div>
 <p>For simple combinators that have only one effect (like <code class="docutils literal notranslate"><span class="pre">dip</span></code>) you only
 need one function and it can be the combinator itself.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">joy.library</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>import joy.library
 
-<span class="n">dip</span> <span class="o">=</span> <span class="n">CombinatorJoyType</span><span class="p">(</span><span class="s1">&#39;dip&#39;</span><span class="p">,</span> <span class="p">[</span><span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">dip</span><span class="p">],</span> <span class="mi">23</span><span class="p">)</span>
+dip = CombinatorJoyType(&#39;dip&#39;, [joy.library.dip], 23)
 </pre></div>
 </div>
 <p>For combinators that can have more than one effect (like <code class="docutils literal notranslate"><span class="pre">branch</span></code>) you
 have to write functions that each implement the action of one of the
 effects.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">branch_true</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">):</span>
-    <span class="p">(</span><span class="n">then</span><span class="p">,</span> <span class="p">(</span><span class="n">else_</span><span class="p">,</span> <span class="p">(</span><span class="n">flag</span><span class="p">,</span> <span class="n">stack</span><span class="p">)))</span> <span class="o">=</span> <span class="n">stack</span>
-    <span class="k">return</span> <span class="n">stack</span><span class="p">,</span> <span class="n">concat</span><span class="p">(</span><span class="n">then</span><span class="p">,</span> <span class="n">expression</span><span class="p">),</span> <span class="n">dictionary</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def branch_true(stack, expression, dictionary):
+    (then, (else_, (flag, stack))) = stack
+    return stack, concat(then, expression), dictionary
 
-<span class="k">def</span> <span class="nf">branch_false</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">):</span>
-    <span class="p">(</span><span class="n">then</span><span class="p">,</span> <span class="p">(</span><span class="n">else_</span><span class="p">,</span> <span class="p">(</span><span class="n">flag</span><span class="p">,</span> <span class="n">stack</span><span class="p">)))</span> <span class="o">=</span> <span class="n">stack</span>
-    <span class="k">return</span> <span class="n">stack</span><span class="p">,</span> <span class="n">concat</span><span class="p">(</span><span class="n">else_</span><span class="p">,</span> <span class="n">expression</span><span class="p">),</span> <span class="n">dictionary</span>
+def branch_false(stack, expression, dictionary):
+    (then, (else_, (flag, stack))) = stack
+    return stack, concat(else_, expression), dictionary
 
-<span class="n">branch</span> <span class="o">=</span> <span class="n">CombinatorJoyType</span><span class="p">(</span><span class="s1">&#39;branch&#39;</span><span class="p">,</span> <span class="p">[</span><span class="n">branch_true</span><span class="p">,</span> <span class="n">branch_false</span><span class="p">],</span> <span class="mi">100</span><span class="p">)</span>
+branch = CombinatorJoyType(&#39;branch&#39;, [branch_true, branch_false], 100)
 </pre></div>
 </div>
 <p>You can also provide an optional stack effect, input-side only, that
@@ -2189,54 +2189,54 @@ that expression.</p>
 updated along with the stack effects after doing unification or we risk
 losing useful information. This was a straightforward, if awkward,
 modification to the call structure of <code class="docutils literal notranslate"><span class="pre">meta_compose()</span></code> et. al.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">ID</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>  <span class="c1"># Identity function.</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>ID = S[0], S[0]  # Identity function.
 
 
-<span class="k">def</span> <span class="nf">infer</span><span class="p">(</span><span class="o">*</span><span class="n">expression</span><span class="p">):</span>
-    <span class="k">return</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">_infer</span><span class="p">(</span><span class="n">list_to_stack</span><span class="p">(</span><span class="n">expression</span><span class="p">))))</span>
+def infer(*expression):
+    return sorted(set(_infer(list_to_stack(expression))))
 
 
-<span class="k">def</span> <span class="nf">_infer</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">F</span><span class="o">=</span><span class="n">ID</span><span class="p">):</span>
-    <span class="n">_log_it</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">F</span><span class="p">)</span>
-    <span class="k">if</span> <span class="ow">not</span> <span class="n">e</span><span class="p">:</span>
-        <span class="k">return</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span>
+def _infer(e, F=ID):
+    _log_it(e, F)
+    if not e:
+        return [F]
 
-    <span class="n">n</span><span class="p">,</span> <span class="n">e</span> <span class="o">=</span> <span class="n">e</span>
+    n, e = e
 
-    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">SymbolJoyType</span><span class="p">):</span>
-        <span class="n">eFG</span> <span class="o">=</span> <span class="n">meta_compose</span><span class="p">([</span><span class="n">F</span><span class="p">],</span> <span class="n">n</span><span class="o">.</span><span class="n">stack_effects</span><span class="p">,</span> <span class="n">e</span><span class="p">)</span>
-        <span class="n">res</span> <span class="o">=</span> <span class="n">flatten</span><span class="p">(</span><span class="n">_infer</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">Fn</span><span class="p">)</span> <span class="k">for</span> <span class="n">e</span><span class="p">,</span> <span class="n">Fn</span> <span class="ow">in</span> <span class="n">eFG</span><span class="p">)</span>
+    if isinstance(n, SymbolJoyType):
+        eFG = meta_compose([F], n.stack_effects, e)
+        res = flatten(_infer(e, Fn) for e, Fn in eFG)
 
-    <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">CombinatorJoyType</span><span class="p">):</span>
-        <span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">n</span><span class="o">.</span><span class="n">enter_guard</span><span class="p">(</span><span class="n">F</span><span class="p">)</span>
-        <span class="n">res</span> <span class="o">=</span> <span class="n">flatten</span><span class="p">(</span><span class="n">_interpret</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">,</span> <span class="n">e</span><span class="p">)</span> <span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">n</span><span class="o">.</span><span class="n">stack_effects</span><span class="p">)</span>
+    elif isinstance(n, CombinatorJoyType):
+        fi, fo = n.enter_guard(F)
+        res = flatten(_interpret(f, fi, fo, e) for f in n.stack_effects)
 
-    <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">Symbol</span><span class="p">):</span>
-        <span class="k">assert</span> <span class="n">n</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">FUNCTIONS</span><span class="p">,</span> <span class="nb">repr</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
-        <span class="n">func</span> <span class="o">=</span> <span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">_dictionary</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
-        <span class="n">res</span> <span class="o">=</span> <span class="n">_interpret</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">F</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">F</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">e</span><span class="p">)</span>
+    elif isinstance(n, Symbol):
+        assert n not in FUNCTIONS, repr(n)
+        func = joy.library._dictionary[n]
+        res = _interpret(func, F[0], F[1], e)
 
-    <span class="k">else</span><span class="p">:</span>
-        <span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">F</span>
-        <span class="n">res</span> <span class="o">=</span> <span class="n">_infer</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">fo</span><span class="p">)))</span>
+    else:
+        fi, fo = F
+        res = _infer(e, (fi, (n, fo)))
 
-    <span class="k">return</span> <span class="n">res</span>
+    return res
 
 
-<span class="k">def</span> <span class="nf">_interpret</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">,</span> <span class="n">e</span><span class="p">):</span>
-    <span class="n">new_fo</span><span class="p">,</span> <span class="n">ee</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="n">fo</span><span class="p">,</span> <span class="n">e</span><span class="p">,</span> <span class="p">{})</span>
-    <span class="n">ee</span> <span class="o">=</span> <span class="n">update</span><span class="p">(</span><span class="n">FUNCTIONS</span><span class="p">,</span> <span class="n">ee</span><span class="p">)</span>  <span class="c1"># Fix Symbols.</span>
-    <span class="n">new_F</span> <span class="o">=</span> <span class="n">fi</span><span class="p">,</span> <span class="n">new_fo</span>
-    <span class="k">return</span> <span class="n">_infer</span><span class="p">(</span><span class="n">ee</span><span class="p">,</span> <span class="n">new_F</span><span class="p">)</span>
+def _interpret(f, fi, fo, e):
+    new_fo, ee, _ = f(fo, e, {})
+    ee = update(FUNCTIONS, ee)  # Fix Symbols.
+    new_F = fi, new_fo
+    return _infer(ee, new_F)
 
 
-<span class="k">def</span> <span class="nf">_log_it</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">F</span><span class="p">):</span>
-    <span class="n">_log</span><span class="o">.</span><span class="n">info</span><span class="p">(</span>
-        <span class="sa">u</span><span class="s1">&#39;</span><span class="si">%3i</span><span class="s1"> </span><span class="si">%s</span><span class="s1"> ∘ </span><span class="si">%s</span><span class="s1">&#39;</span><span class="p">,</span>
-        <span class="nb">len</span><span class="p">(</span><span class="n">inspect_stack</span><span class="p">()),</span>
-        <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">F</span><span class="p">),</span>
-        <span class="n">expression_to_string</span><span class="p">(</span><span class="n">e</span><span class="p">),</span>
-        <span class="p">)</span>
+def _log_it(e, F):
+    _log.info(
+        u&#39;%3i %s ∘ %s&#39;,
+        len(inspect_stack()),
+        doc_from_stack_effect(*F),
+        expression_to_string(e),
+        )
 </pre></div>
 </div>
 </section>
@@ -2249,18 +2249,18 @@ module (FIXME link to its docs here!) should be explained… There is
 cruft to convert the definitions in <code class="docutils literal notranslate"><span class="pre">DEFS</span></code> to the new
 <code class="docutils literal notranslate"><span class="pre">SymbolJoyType</span></code> objects, and some combinators. Here is an example of
 output from the current code :</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span><span class="o">/</span><span class="mi">0</span>  <span class="c1"># (Don&#39;t try to run this cell!  It&#39;s not going to work.  This is &quot;read only&quot; code heh..)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>1/0  # (Don&#39;t try to run this cell!  It&#39;s not going to work.  This is &quot;read only&quot; code heh..)
 
-<span class="n">logging</span><span class="o">.</span><span class="n">basicConfig</span><span class="p">(</span><span class="nb">format</span><span class="o">=</span><span class="s1">&#39;</span><span class="si">%(message)s</span><span class="s1">&#39;</span><span class="p">,</span> <span class="n">stream</span><span class="o">=</span><span class="n">sys</span><span class="o">.</span><span class="n">stdout</span><span class="p">,</span> <span class="n">level</span><span class="o">=</span><span class="n">logging</span><span class="o">.</span><span class="n">INFO</span><span class="p">)</span>
+logging.basicConfig(format=&#39;%(message)s&#39;, stream=sys.stdout, level=logging.INFO)
 
-<span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">FUNCTIONS</span><span class="p">)</span>
+globals().update(FUNCTIONS)
 
-<span class="n">h</span> <span class="o">=</span> <span class="n">infer</span><span class="p">((</span><span class="n">pred</span><span class="p">,</span> <span class="n">s2</span><span class="p">),</span> <span class="p">(</span><span class="n">mul</span><span class="p">,</span> <span class="n">s3</span><span class="p">),</span> <span class="p">(</span><span class="n">div</span><span class="p">,</span> <span class="n">s4</span><span class="p">),</span> <span class="p">(</span><span class="n">nullary</span><span class="p">,</span> <span class="p">(</span><span class="nb">bool</span><span class="p">,</span> <span class="n">s5</span><span class="p">)),</span> <span class="n">dipd</span><span class="p">,</span> <span class="n">branch</span><span class="p">)</span>
+h = infer((pred, s2), (mul, s3), (div, s4), (nullary, (bool, s5)), dipd, branch)
 
-<span class="nb">print</span> <span class="s1">&#39;-&#39;</span> <span class="o">*</span> <span class="mi">40</span>
+print &#39;-&#39; * 40
 
-<span class="k">for</span> <span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="ow">in</span> <span class="n">h</span><span class="p">:</span>
-    <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">)</span>
+for fi, fo in h:
+    print doc_from_stack_effect(fi, fo)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">---------------------------------------------------------------------------</span>
@@ -2366,14 +2366,14 @@ relational</em> nature of the stack effect comments to “compute in reverse”
 as it were. There’s a working demo of this at the end of the <code class="docutils literal notranslate"><span class="pre">types</span></code>
 module. But if you’re interested in all that you should just use Prolog!</p>
 <p>Anyhow, type <em>checking</em> is a few easy steps away.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">_ge</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-    <span class="k">return</span> <span class="p">(</span><span class="nb">issubclass</span><span class="p">(</span><span class="n">other</span><span class="o">.</span><span class="vm">__class__</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="p">)</span>
-            <span class="ow">or</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">&#39;accept&#39;</span><span class="p">)</span>
-            <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">accept</span><span class="p">))</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def _ge(self, other):
+    return (issubclass(other.__class__, self.__class__)
+            or hasattr(self, &#39;accept&#39;)
+            and isinstance(other, self.accept))
 
-<span class="n">AnyJoyType</span><span class="o">.</span><span class="fm">__ge__</span> <span class="o">=</span> <span class="n">_ge</span>
-<span class="n">AnyJoyType</span><span class="o">.</span><span class="n">accept</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">,</span> <span class="nb">int</span><span class="p">,</span> <span class="nb">float</span><span class="p">,</span> <span class="n">long</span><span class="p">,</span> <span class="nb">str</span><span class="p">,</span> <span class="n">unicode</span><span class="p">,</span> <span class="nb">bool</span><span class="p">,</span> <span class="n">Symbol</span>
-<span class="n">StackJoyType</span><span class="o">.</span><span class="n">accept</span> <span class="o">=</span> <span class="nb">tuple</span>
+AnyJoyType.__ge__ = _ge
+AnyJoyType.accept = tuple, int, float, long, str, unicode, bool, Symbol
+StackJoyType.accept = tuple
 </pre></div>
 </div>
 </section>
@@ -2465,7 +2465,7 @@ module. But if you’re interested in all that you should just use Prolog!</p>
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/notebooks/Zipper.html b/docs/sphinx_docs/_build/html/notebooks/Zipper.html
index 72ff9f1..7eec7cd 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/Zipper.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Zipper.html
@@ -42,7 +42,7 @@ the original paper: <a class="reference external" href="https://www.st.cs.uni-sa
 Huet</a></p>
 <p>Given a datastructure on the stack we can navigate through it, modify
 it, and rebuild it using the “zipper” technique.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import J, V, define
 </pre></div>
 </div>
 <section id="trees">
@@ -52,7 +52,7 @@ strings, Symbols (strings that are names of functions) and sequences
 (aka lists, aka quoted literals, aka aggregates, etc…), but we can build
 <a class="reference external" href="https://en.wikipedia.org/wiki/Tree_%28data_structure%29">trees</a> out
 of sequences.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8]&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 [2 [3 4 25 6] 7] 8]&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span>
@@ -75,13 +75,13 @@ datastructure used to keep track of these items is the zipper.)</p>
 show the trace so you can see how it works. If we were going to use
 these a lot it would make sense to write Python versions for efficiency,
 but see below.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-down == [] swap uncons swap&#39;</span><span class="p">)</span>
-<span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-up == swons swap shunt&#39;</span><span class="p">)</span>
-<span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-right == [swons] cons dip uncons swap&#39;</span><span class="p">)</span>
-<span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-left == swons [uncons swap] dip swap&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;z-down == [] swap uncons swap&#39;)
+define(&#39;z-up == swons swap shunt&#39;)
+define(&#39;z-right == [swons] cons dip uncons swap&#39;)
+define(&#39;z-left == swons [uncons swap] dip swap&#39;)
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8] z-down&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[1 [2 [3 4 25 6] 7] 8] z-down&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                          <span class="o">.</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="n">z</span><span class="o">-</span><span class="n">down</span>
@@ -93,7 +93,7 @@ but see below.</p>
 <span class="p">[]</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="mi">1</span> <span class="o">.</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[] [[2 [3 4 25 6] 7] 8] 1 z-right&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[] [[2 [3 4 25 6] 7] 8] 1 z-right&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                                  <span class="o">.</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="mi">1</span> <span class="n">z</span><span class="o">-</span><span class="n">right</span>
@@ -113,43 +113,43 @@ but see below.</p>
          <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="o">.</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2 [3 4 25 6] 7] z-down&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1] [8] [2 [3 4 25 6] 7] z-down&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">2</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [] [[3 4 25 6] 7] 2 z-right&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1] [8] [] [[3 4 25 6] 7] 2 z-right&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [3 4 25 6] z-down&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1] [8] [2] [7] [3 4 25 6] z-down&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">3</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [] [4 25 6] 3 z-right&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1] [8] [2] [7] [] [4 25 6] 3 z-right&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">4</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [3] [25 6] 4 z-right&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1] [8] [2] [7] [3] [25 6] 4 z-right&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">25</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [4 3] [6] 25 sqr&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1] [8] [2] [7] [4 3] [6] 25 sqr&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [4 3] [6] 625 z-up&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[1] [8] [2] [7] [4 3] [6] 625 z-up&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                              <span class="o">.</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span> <span class="n">z</span><span class="o">-</span><span class="n">up</span>
@@ -168,13 +168,13 @@ but see below.</p>
   <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="o">.</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [3 4 625 6] z-up&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1] [8] [2] [7] [3 4 625 6] z-up&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span>
 </pre></div>
 </div>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2 [3 4 625 6] 7] z-up&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1] [8] [2 [3 4 625 6] 7] z-up&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span>
@@ -185,7 +185,7 @@ but see below.</p>
 <h2><code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">infra</span></code><a class="headerlink" href="#dip-and-infra" title="Permalink to this headline">¶</a></h2>
 <p>In Joy we have the <code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">infra</span></code> combinators which can “target”
 or “address” any particular item in a Joy tree structure.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                                                                <span class="o">.</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="p">[[[[[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span>
@@ -236,11 +236,11 @@ been embedded in a nested series of quoted programs, e.g.:</p>
 </pre></div>
 </div>
 <p>The <code class="docutils literal notranslate"><span class="pre">Z</span></code> function isn’t hard to make.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Z == [[] cons cons] step i&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;Z == [[] cons cons] step i&#39;)
 </pre></div>
 </div>
 <p>Here it is in action in a simplified scenario.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;1 [2 3 4] Z&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;1 [2 3 4] Z&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                             <span class="o">.</span> <span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="n">Z</span>
@@ -273,7 +273,7 @@ been embedded in a nested series of quoted programs, e.g.:</p>
 </pre></div>
 </div>
 <p>And here it is doing the main thing.</p>
-<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z&#39;</span><span class="p">)</span>
+<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z&#39;)
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span>
@@ -389,7 +389,7 @@ i d i d i d d Bingo!
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-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
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diff --git a/docs/sphinx_docs/_build/html/notebooks/index.html b/docs/sphinx_docs/_build/html/notebooks/index.html
index e742b6c..26bd28c 100644 (file)
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-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
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diff --git a/docs/sphinx_docs/_build/html/objects.inv b/docs/sphinx_docs/_build/html/objects.inv
index 136209a..10dedf8 100644 (file)
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diff --git a/docs/sphinx_docs/_build/html/parser.html b/docs/sphinx_docs/_build/html/parser.html
index 99c6be7..1de95b8 100644 (file)
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-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
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diff --git a/docs/sphinx_docs/_build/html/pretty.html b/docs/sphinx_docs/_build/html/pretty.html
index b43aaef..8d609eb 100644 (file)
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-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
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diff --git a/docs/sphinx_docs/_build/html/py-modindex.html b/docs/sphinx_docs/_build/html/py-modindex.html
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-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
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   </body>

diff --git a/docs/sphinx_docs/_build/html/search.html b/docs/sphinx_docs/_build/html/search.html
index cb9bd5d..3c0ea74 100644 (file)
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@@ -120,7 +120,7 @@
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-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
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index a270cf5..24de0c6 100644 (file)
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,17,18,19,20,21,24,25],txt:[],type:[0,1,4,8,11,13,16,21,22,23,24],typeerror:19,typeless:19,typic:[2,3,12,13],u:[18,19],uh:19,ui:8,ulam:[0,15],unari:8,unarybuiltinwrapp:3,unbalanc:[11,22],unbound:25,unchang:[3,11],uncompil:19,uncon:[3,7,8,11,13,17,20,25],under:[2,3,8,11],underli:[5,16,19],underscor:19,understand:[0,11],undistinguish:11,undocu:8,unfinish:5,unfortun:24,unicod:19,unif:[19,21],unifi:18,union:5,uniqu:[3,5,11,19],unit:[3,8,13,16,25],univers:[0,8,16,19],unknownsymbolerror:1,unlik:16,unnecessari:21,unnecesssari:19,unpack:[2,3,11,24],unpair:6,unquot:[8,15,17,22],unread:[0,15],unrol:5,unstack:19,unswon:[3,25],untangl:13,until:[5,7,16],unus:6,unusu:11,unwrap:5,up:[1,2,3,6,7,8,11,13,14,15,16,19,20,24],updat:[0,18,21,25],uppercas:5,upward:16,us:[0,1,2,3,4,5,6,8,9,10,11,12,13,14,15,16,17,20,21,22,24,25],usag:8,user:17,usual:[0,2,13],util:[0,3,14,18,19],uu:19,v0:25,v:[2,6,7,9,11,12,13,14,15,17,20,21],valid:19,valu:[0,1,2,3,6,8,9,12,13,14,15,16,17,19,21,22,24,25],value_n:11,valueerror:[5,19,24],variabl:[19,21],variant:11,variat:[13,16,21],varieti:[4,8],variou:0,ve:[11,15,19],vener:24,verbos:4,veri:[0,1,4,5,8,11,15,24],versa:[2,19],version:[0,1,2,5,7,10,17,20,21],vi:21,via:8,vice:[2,19],view:[11,21],viewer:[1,8,10,23],vii:21,visibl:19,von:[0,2,3,4,13],vs:19,vv:19,w:[3,11,13,17,19],wa:[2,6,8,11,15,16,19,24],waaaai:5,wai:[0,2,3,4,5,6,8,13,14,15,16,19],wait:16,want:[2,6,7,9,11,13,19],warranti:[3,8],wash:8,wast:8,we:[2,5,6,7,8,9,10,12,13,14,15,16,19,20,21,24],web:24,websit:[0,6],welcom:8,well:[0,4,8,9,11,19,22],went:19,were:[8,19,20],what:[2,3,4,5,8,11,13,16,17,19,23],whatev:[2,3,13,17,24],when:[6,7,8,11,13,16,19,20,22,24,25],where:[2,3,5,8,11,13,15,19,21,24],whether:[3,13],which:[0,1,3,5,6,8,9,11,15,16,17,19,20,22,24,25],whole:[2,3,6,13,17,19],whose:7,why:[9,16,17],wiki:11,wikipedia:[0,11,20],wildli:8,wind:8,wire:13,within:[8,11,14,21],without:[2,8,11,12,15,16,19],won:[11,19,24],word:[0,3,6,8,13,20],work:[0,3,5,6,7,8,9,11,12,13,15,16,17,20,21,24,25],worker:16,worri:16,worth:6,would:[2,6,7,8,9,11,13,16,19,20,24],wrap:[3,8],wrapper:19,write:[4,5,9,11,13,15,16,17,19,20,21,24],written:[0,1,9,11,14,19,24],wrong:2,wrote:19,x:[0,3,5,6,8,9,16,20,21],xor:3,xrang:19,y:[2,3,5,15,16],yang:19,yeah:16,year:[8,19],yet:[11,16,19,20],yield:[2,3,13,19,24],yin:21,you:[0,2,3,5,6,7,8,10,11,12,13,14,15,16,17,19,20,23,24,25],your:[2,3,8,13,19],yourself:[5,8,11],z:[3,5,16,19,21],zero:[3,5,11,13,16,17,19,22,24],zerodivisionerror:19,zip:[3,5,6,19],zip_:3,zipper:[0,21],zstr:20},titles:["Thun 0.4.1 Documentation","Joy Interpreter","Functions Grouped by, er, Function with Examples","Function Reference","Categorical Programming","\u2202RE","Developing a Program in Joy","Using <code class=\"docutils literal notranslate\"><span class=\"pre\">x</span></code> to Generate Values","Thun: Joy in Python","Newton\u2019s method","No Updates","Treating Trees I: Ordered Binary Trees","Quadratic formula","Recursion Combinators","Replacing Functions in the Dictionary","Square Spiral Example Joy Code","The Four Fundamental Operations of Definite Action","Treating Trees II: <code class=\"docutils literal notranslate\"><span class=\"pre\">treestep</span></code>","Type Checking","The Blissful Elegance of Typing Joy","Traversing Datastructures with Zippers","Essays about Programming in Joy","Parsing Text into Joy Expressions","Tracing Joy Execution","Stack or Quote or Sequence or List\u2026","Type Inference of Joy Expressions"],titleterms:{"0":[0,13],"01":5,"1":[0,13],"11":5,"111":5,"2":[7,12,19],"2a":12,"3":[6,19],"4":[0,12,19],"466":7,"5":6,"\u03bb":5,"\u03d5":5,"boolean":15,"case":[9,11],"do":17,"function":[2,3,5,8,9,11,13,14,16,17,19],"long":14,"new":11,"p\u00f6ial":19,"try":5,"void":2,"while":[2,16],A:[5,6,7,9,11,14],If:11,In:[11,17],No:[5,10],Not:15,One:[7,11],The:[6,8,11,13,15,16,17,19],There:8,With:[5,17],about:21,action:16,ad:11,add:[2,11],address:20,al:13,alphabet:5,altern:17,an:[6,7,8,11,13,18,19,20],ana:13,analysi:6,anamorph:[2,13],app1:2,app2:2,app3:2,appendix:[11,13,19],appli:16,approxim:9,ar:11,argument:19,auto:3,averag:2,b:[2,12],base:[9,11],binari:[2,11,17],bliss:19,both:11,branch:[2,11,15,16],brzozowski:5,c:[12,19],can:11,cata:13,catamorph:13,categor:4,chatter:2,check:18,child:11,choic:2,clear:2,cleav:[2,16],cmp:11,code:[0,8,11,15],combin:[2,11,13,19],comment:19,compact:5,compar:11,comparison:2,compil:[7,19],compile_:19,compos:19,comput:9,con:[2,19],concat:2,conclus:[13,15,19],consecut:9,continu:8,current:11,datastructur:[5,8,11,20],deal:19,decrement:15,defin:[11,17],definit:[12,16],delabel:19,delet:11,deriv:[5,12,13,17],design:13,determin:20,develop:6,diagram:5,dialect:0,dictionari:14,dip:[2,20],dipd:2,dipdd:2,direco:7,disenstacken:2,distinguish:19,div:2,doc_from_stack_effect:19,document:0,doe:11,down_to_zero:2,drive:5,drop:2,dup:[2,19],dupd:2,dupdip:2,e:17,effect:19,eleg:19,els:11,empti:11,enstacken:2,equal:11,er:2,essai:21,et:13,euler:[6,7],eval:8,even:7,exampl:[0,2,8,11,13,15,17,18],execut:23,explor:5,express:[5,8,22,25],extract:17,f:11,factori:13,fail:18,fibonacci:7,filter:6,find:[9,11,13],finish:16,finit:5,first:[2,6,15,16,19],five:7,flatten:2,flexibl:17,floordiv:2,form:15,formula:12,found:11,four:[13,16],from:13,fsm:5,fulmin:16,fun:13,fundament:16,further:6,gcd:2,gener:[3,5,6,7,9,13,15],genrec:2,get:[11,17],getitem:2,given:[13,17],greater:11,group:2,h1:13,h2:13,h3:13,h4:13,handl:16,have:[11,17],help:2,highest:11,host:0,how:[6,7],hybrid:19,hylo:13,hylomorph:13,i:[2,5,11,19],identifi:19,ift:[2,16],ii:[17,19],iii:19,implement:[5,19],increment:15,indic:0,infer:[19,25],inferenc:19,inform:0,infra:[2,20],integ:[6,13],interest:7,interlud:11,intern:22,interpret:[1,8,19],item:20,iter:[6,11],iv:19,joi:[0,1,3,6,8,13,15,19,20,21,22,23,24,25],join:16,just:6,kei:11,kind:16,languag:0,larger:5,least_fract:2,left:11,less:11,let:[5,6],letter:5,librari:[3,8,19],like:11,list:[2,13,24],literari:8,littl:6,logic:[2,19],loop:[2,8,16],lower:11,lshift:2,machin:5,make:[7,9],mani:6,map:[2,16],match:5,math:2,memoiz:5,method:9,min:2,miscellan:2,mod:2,modifi:19,modulu:2,more:11,most:11,mul:[2,19],multipl:[6,7,19],must:11,n:13,name:12,ne:2,neg:[2,15],newton:9,next:9,node:11,non:11,now:11,nullari:2,nulli:5,number:[13,19],one:8,onli:8,oper:16,order:[11,17],origin:15,osdn:0,other:16,our:11,out:5,over:2,p:17,pack:6,pam:[2,16],para:13,paradigm:19,parallel:16,parameter:[11,17],pars:[2,22],parser:[8,22],part:19,pass:8,path:20,pattern:13,per:11,piec:15,pop:[2,19],popd:2,popop:2,pow:2,power:7,pred:2,predic:[6,9,11,15,17],pretty_print:23,primit:13,primrec:2,print:8,problem:[6,7],process:11,product:2,program:[4,6,12,17,21],progress:19,project:[0,6,7],pure:8,put:[11,12,15,17],python:[8,14,19],quadrat:12,quick:0,quot:[2,24],rang:[2,6,13],range_to_zero:2,re:[5,11],read:8,recur:[9,11],recurs:[11,13,17],redefin:[11,17],refactor:[6,11],refer:3,regular:[5,8],reimplement:17,relabel:19,rem:2,remaind:2,remov:2,render:6,repl:8,replac:[11,14],repres:[5,19],represent:5,reset:7,rest:[2,19],revers:[2,5,18],right:[11,20],rightmost:11,roll:[2,19],rolldown:2,rollup:2,rshift:2,rule:[5,19],run:[2,7],s:[5,6,9,11,19],second:[2,19],select:2,sequenc:[7,16,19,24],set:[9,11],shorter:14,should:8,shunt:2,simpl:19,simplest:6,size:[2,14],sourc:11,special:[13,19],spiral:15,sqr:[2,19],sqrt:[2,12],squar:15,stack:[2,8,19,24],start:0,state:5,step:[2,13,17],straightforward:12,stream:5,string:5,structur:11,style:8,sub:[2,11],subtyp:19,succ:2,sum:[2,6],swaack:2,swap:[2,19],swon:2,swoncat:2,symbol:[8,13],t:17,tabl:0,tail:13,take:2,term:[6,7,17],ternari:2,text:22,than:11,them:12,thi:11,third:[2,19],three:7,thun:[0,8],time:[2,7],togeth:[11,12,15,17],token:8,toler:9,trace:[14,23],traceprint:8,trampolin:5,translat:15,travers:[11,17,20],treat:[11,17],tree:[11,17,20],treegrind:17,treestep:17,triangular:13,truediv:2,truthi:2,tuck:2,turn:15,two:[5,7],type:[18,19,25],unari:2,unbound:19,uncon:[2,19],unif:18,unifi:19,unit:2,unnecessari:6,unquot:2,unstack:2,up:9,updat:[10,19],us:[7,19],util:[23,24,25],v:19,valu:[7,11],variabl:12,variat:7,version:[6,11,14,19],vi:19,view:8,vii:19,we:[11,17],which:13,within:9,word:2,work:[18,19],write:12,x:[2,7,15],xor:2,yin:19,z:20,zero:7,zip:2,zipper:20}})
\ No newline at end of file

diff --git a/docs/sphinx_docs/_build/html/stack.html b/docs/sphinx_docs/_build/html/stack.html
index ab153d5..2d6ad97 100644 (file)
--- a/docs/sphinx_docs/_build/html/stack.html
+++ b/docs/sphinx_docs/_build/html/stack.html
@@ -280,7 +280,7 @@ won’t work because <code class="docutils literal notranslate"><span class="pre
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
   </body>

diff --git a/docs/sphinx_docs/_build/html/types.html b/docs/sphinx_docs/_build/html/types.html
index a7e9539..e0f9ec1 100644 (file)
--- a/docs/sphinx_docs/_build/html/types.html
+++ b/docs/sphinx_docs/_build/html/types.html
@@ -49,25 +49,25 @@ information is available.)</p>
 <h2><code class="docutils literal notranslate"><span class="pre">joy.utils.types</span></code><a class="headerlink" href="#joy-utils-types" title="Permalink to this headline">¶</a></h2>
 <p>Curently (asterix after name indicates a function that can be
 auto-compiled to Python):</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">_Tree_add_Ee</span> <span class="o">=</span> <span class="p">([</span><span class="n">a4</span> <span class="n">a5</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a3</span> <span class="o">...</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span>
-<span class="n">_Tree_delete_R0</span> <span class="o">=</span> <span class="p">([</span><span class="n">a2</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a2</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a2</span> <span class="n">a1</span> <span class="n">a1</span><span class="p">)</span> <span class="o">*</span>
-<span class="n">_Tree_delete_clear_stuff</span> <span class="o">=</span> <span class="p">(</span><span class="n">a3</span> <span class="n">a2</span> <span class="p">[</span><span class="n">a1</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">...</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span>
-<span class="n">_Tree_get_E</span> <span class="o">=</span> <span class="p">([</span><span class="n">a3</span> <span class="n">a4</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a4</span><span class="p">)</span> <span class="o">*</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">_Tree_add_Ee</span> <span class="o">=</span> <span class="p">([</span><span class="n">a4</span> <span class="n">a5</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a3</span> <span class="o">..</span><span class="mf">.1</span><span class="p">])</span> <span class="o">*</span>
+<span class="n">_Tree_delete_R0</span> <span class="o">=</span> <span class="p">([</span><span class="n">a2</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a2</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="n">a2</span> <span class="n">a1</span> <span class="n">a1</span><span class="p">)</span> <span class="o">*</span>
+<span class="n">_Tree_delete_clear_stuff</span> <span class="o">=</span> <span class="p">(</span><span class="n">a3</span> <span class="n">a2</span> <span class="p">[</span><span class="n">a1</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">..</span><span class="mf">.1</span><span class="p">])</span> <span class="o">*</span>
+<span class="n">_Tree_get_E</span> <span class="o">=</span> <span class="p">([</span><span class="n">a3</span> <span class="n">a4</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a4</span><span class="p">)</span> <span class="o">*</span>
 <span class="n">add</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="n">n2</span> <span class="o">--</span> <span class="n">n3</span><span class="p">)</span>
 <span class="ow">and</span> <span class="o">=</span> <span class="p">(</span><span class="n">b1</span> <span class="n">b2</span> <span class="o">--</span> <span class="n">b3</span><span class="p">)</span>
 <span class="nb">bool</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="o">--</span> <span class="n">b1</span><span class="p">)</span>
-<span class="n">ccons</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="p">[</span><span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">...</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span>
-<span class="n">cons</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">...</span><span class="mi">0</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">...</span><span class="mi">0</span><span class="p">])</span> <span class="o">*</span>
+<span class="n">ccons</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="p">[</span><span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">..</span><span class="mf">.1</span><span class="p">])</span> <span class="o">*</span>
+<span class="n">cons</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">..</span><span class="mf">.0</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">..</span><span class="mf">.0</span><span class="p">])</span> <span class="o">*</span>
 <span class="n">div</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="n">n2</span> <span class="o">--</span> <span class="n">n3</span><span class="p">)</span>
 <span class="nb">divmod</span> <span class="o">=</span> <span class="p">(</span><span class="n">n2</span> <span class="n">n1</span> <span class="o">--</span> <span class="n">n4</span> <span class="n">n3</span><span class="p">)</span>
 <span class="n">dup</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a1</span><span class="p">)</span> <span class="o">*</span>
 <span class="n">dupd</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span> <span class="o">*</span>
 <span class="n">dupdd</span> <span class="o">=</span> <span class="p">(</span><span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a3</span> <span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span> <span class="o">*</span>
 <span class="n">eq</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="n">n2</span> <span class="o">--</span> <span class="n">b1</span><span class="p">)</span>
-<span class="n">first</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span> <span class="o">*</span>
-<span class="n">first_two</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a2</span><span class="p">)</span> <span class="o">*</span>
+<span class="n">first</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span> <span class="o">*</span>
+<span class="n">first_two</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a2</span><span class="p">)</span> <span class="o">*</span>
 <span class="n">floordiv</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="n">n2</span> <span class="o">--</span> <span class="n">n3</span><span class="p">)</span>
-<span class="n">fourth</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="n">a4</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a4</span><span class="p">)</span> <span class="o">*</span>
+<span class="n">fourth</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="n">a4</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a4</span><span class="p">)</span> <span class="o">*</span>
 <span class="n">ge</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="n">n2</span> <span class="o">--</span> <span class="n">b1</span><span class="p">)</span>
 <span class="n">gt</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="n">n2</span> <span class="o">--</span> <span class="n">b1</span><span class="p">)</span>
 <span class="n">le</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="n">n2</span> <span class="o">--</span> <span class="n">b1</span><span class="p">)</span>
@@ -88,27 +88,27 @@ auto-compiled to Python):</p>
 <span class="n">popopdd</span> <span class="o">=</span> <span class="p">(</span><span class="n">a4</span> <span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span> <span class="o">*</span>
 <span class="nb">pow</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="n">n2</span> <span class="o">--</span> <span class="n">n3</span><span class="p">)</span>
 <span class="n">pred</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
-<span class="n">rest</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">...</span><span class="mi">0</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">...</span><span class="mi">0</span><span class="p">])</span> <span class="o">*</span>
+<span class="n">rest</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">..</span><span class="mf">.0</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">..</span><span class="mf">.0</span><span class="p">])</span> <span class="o">*</span>
 <span class="n">rolldown</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a3</span> <span class="n">a1</span><span class="p">)</span> <span class="o">*</span>
 <span class="n">rollup</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">--</span> <span class="n">a3</span> <span class="n">a1</span> <span class="n">a2</span><span class="p">)</span> <span class="o">*</span>
-<span class="n">rrest</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">...</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span>
+<span class="n">rrest</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">..</span><span class="mf">.1</span><span class="p">])</span> <span class="o">*</span>
 <span class="n">rshift</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="n">n2</span> <span class="o">--</span> <span class="n">n3</span><span class="p">)</span>
-<span class="n">second</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a2</span><span class="p">)</span> <span class="o">*</span>
+<span class="n">second</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a2</span><span class="p">)</span> <span class="o">*</span>
 <span class="n">sqrt</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
 <span class="n">stack</span> <span class="o">=</span> <span class="p">(</span><span class="o">...</span> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="o">...</span><span class="p">])</span> <span class="o">*</span>
 <span class="n">stuncons</span> <span class="o">=</span> <span class="p">(</span><span class="o">...</span> <span class="n">a1</span> <span class="o">--</span> <span class="o">...</span> <span class="n">a1</span> <span class="n">a1</span> <span class="p">[</span><span class="o">...</span><span class="p">])</span> <span class="o">*</span>
 <span class="n">stununcons</span> <span class="o">=</span> <span class="p">(</span><span class="o">...</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="o">...</span> <span class="n">a2</span> <span class="n">a1</span> <span class="n">a1</span> <span class="n">a2</span> <span class="p">[</span><span class="o">...</span><span class="p">])</span> <span class="o">*</span>
 <span class="n">sub</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="n">n2</span> <span class="o">--</span> <span class="n">n3</span><span class="p">)</span>
 <span class="n">succ</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
-<span class="n">swaack</span> <span class="o">=</span> <span class="p">([</span><span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">...</span><span class="mi">0</span><span class="p">])</span> <span class="o">*</span>
+<span class="n">swaack</span> <span class="o">=</span> <span class="p">([</span><span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">..</span><span class="mf">.0</span><span class="p">])</span> <span class="o">*</span>
 <span class="n">swap</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span> <span class="o">*</span>
-<span class="n">swons</span> <span class="o">=</span> <span class="p">([</span><span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">...</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span>
-<span class="n">third</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a3</span><span class="p">)</span> <span class="o">*</span>
+<span class="n">swons</span> <span class="o">=</span> <span class="p">([</span><span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">..</span><span class="mf">.1</span><span class="p">])</span> <span class="o">*</span>
+<span class="n">third</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a3</span><span class="p">)</span> <span class="o">*</span>
 <span class="n">truediv</span> <span class="o">=</span> <span class="p">(</span><span class="n">n1</span> <span class="n">n2</span> <span class="o">--</span> <span class="n">n3</span><span class="p">)</span>
 <span class="n">tuck</span> <span class="o">=</span> <span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a2</span> <span class="n">a1</span><span class="p">)</span> <span class="o">*</span>
-<span class="n">uncons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">...</span><span class="mi">0</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="p">[</span><span class="o">...</span><span class="mi">0</span><span class="p">])</span> <span class="o">*</span>
+<span class="n">uncons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">..</span><span class="mf">.0</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="p">[</span><span class="o">..</span><span class="mf">.0</span><span class="p">])</span> <span class="o">*</span>
 <span class="n">unit</span> <span class="o">=</span> <span class="p">(</span><span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="p">])</span> <span class="o">*</span>
-<span class="n">unswons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a1</span><span class="p">)</span> <span class="o">*</span>
+<span class="n">unswons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">..</span><span class="mf">.1</span><span class="p">]</span> <span class="n">a1</span><span class="p">)</span> <span class="o">*</span>
 </pre></div>
 </div>
 <p>Example output of the <code class="docutils literal notranslate"><span class="pre">infer()</span></code> function.  The first number on each
@@ -246,7 +246,7 @@ far.</p>
 </a>
 <br />
 <span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
+      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.4.0.
     </div>
 
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