Minor docs cleanup.

diff --git a/docs/Generator Programs.html b/docs/Generator Programs.html
index 142e939..aaa6ffe 100644 (file)
--- a/docs/Generator Programs.html
+++ b/docs/Generator Programs.html
@@ -11799,10 +11799,16 @@ div#notebook {
 <div class="text_cell_render border-box-sizing rendered_html">
 <p>Consider the <code>x</code> combinator:</p>
 
-<pre><code>x == dup i
+<pre><code>x == dup i</code></pre>
 
-</code></pre>
-<p>We can apply it to a quoted program consisting of some value <code>a</code> and a function <code>B</code>:</p>
+</div>
+</div>
+</div>
+<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>We can apply it to a quoted program consisting of some value <code>a</code> and some function <code>B</code>:</p>
 
 <pre><code>[a B] x
 [a B] a B</code></pre>
@@ -11844,7 +11850,7 @@ b [B]        cons
 </div>
 <div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
-<p>Putting it together, this is the definition of <code>B</code>:</p>
+<p>Altogether, this is the definition of <code>B</code>:</p>
 
 <pre><code>B == swap [C] dip rest cons</code></pre>
 
@@ -11855,7 +11861,7 @@ b [B]        cons
 </div>
 <div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
-<p>We can create a quoted program that generates the Natural numbers (0, 1, 2, ...) by using <code>0</code> for <code>a</code> and <code>[dup ++]</code> for <code>[C]</code>:</p>
+<p>We can make a generator for the Natural numbers (0, 1, 2, ...) by using <code>0</code> for <code>a</code> and <code>[dup ++]</code> for <code>[C]</code>:</p>
 
 <pre><code>[0 swap [dup ++] dip rest cons]
 
@@ -11951,7 +11957,7 @@ b [B]        cons
 </div>
 <div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
-<h3 id="direco"><code>direco</code><a class="anchor-link" href="#direco">&#182;</a></h3>
+<h2 id="direco"><code>direco</code><a class="anchor-link" href="#direco">&#182;</a></h2>
 </div>
 </div>
 </div>
@@ -12015,7 +12021,7 @@ b [B]        cons
 </div>
 <div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
-<h1 id="Making-Generators">Making Generators<a class="anchor-link" href="#Making-Generators">&#182;</a></h1><p>We want to define a function that accepts <code>a</code> and <code>[C]</code> and builds our quoted program:</p>
+<h2 id="Making-Generators">Making Generators<a class="anchor-link" href="#Making-Generators">&#182;</a></h2><p>We want to define a function that accepts <code>a</code> and <code>[C]</code> and builds our quoted program:</p>
 
 <pre><code>         a [C] G
 -------------------------
@@ -12212,7 +12218,7 @@ G == [direco] cons [swap] swoncat cons</code></pre>
 </div>
 <div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
-<h1 id="Generating-Multiples-of-Three-and-Five">Generating Multiples of Three and Five<a class="anchor-link" href="#Generating-Multiples-of-Three-and-Five">&#182;</a></h1><p>Look at the treatment of the Project Euler Problem One in <a href="./Developing a Program.ipynb">Developing a Program.ipynb</a> and you'll see that we might be interested in generating an endless cycle of:</p>
+<h2 id="Generating-Multiples-of-Three-and-Five">Generating Multiples of Three and Five<a class="anchor-link" href="#Generating-Multiples-of-Three-and-Five">&#182;</a></h2><p>Look at the treatment of the Project Euler Problem One in <a href="./Developing a Program.ipynb">Developing a Program.ipynb</a> and you'll see that we might be interested in generating an endless cycle of:</p>
 
 <pre><code>3 2 1 3 1 2 3
 
@@ -12570,7 +12576,7 @@ G == [direco] cons [swap] swoncat cons</code></pre>
 </div>
 <div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
-<h1 id="Project-Euler-Problem-One">Project Euler Problem One<a class="anchor-link" href="#Project-Euler-Problem-One">&#182;</a></h1>
+<h2 id="Project-Euler-Problem-One">Project Euler Problem One<a class="anchor-link" href="#Project-Euler-Problem-One">&#182;</a></h2>
 </div>
 </div>
 </div>
@@ -12631,7 +12637,7 @@ G == [direco] cons [swap] swoncat cons</code></pre>
 </div>
 <div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
-<h1 id="A-generator-for-the-Fibonacci-Sequence.">A generator for the Fibonacci Sequence.<a class="anchor-link" href="#A-generator-for-the-Fibonacci-Sequence.">&#182;</a></h1><p>Consider:</p>
+<h2 id="A-generator-for-the-Fibonacci-Sequence.">A generator for the Fibonacci Sequence.<a class="anchor-link" href="#A-generator-for-the-Fibonacci-Sequence.">&#182;</a></h2><p>Consider:</p>
 
 <pre><code>[b a F] x
 [b a F] b a F</code></pre>
@@ -12818,7 +12824,7 @@ fib_gen == [1 1 F]</code></pre>
 </div>
 <div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
-<h3 id="Project-Euler-Problem-Two">Project Euler Problem Two<a class="anchor-link" href="#Project-Euler-Problem-Two">&#182;</a></h3>
+<h2 id="Project-Euler-Problem-Two">Project Euler Problem Two<a class="anchor-link" href="#Project-Euler-Problem-Two">&#182;</a></h2>
 <pre><code>By considering the terms in the Fibonacci sequence whose values do not exceed four million,
 find the sum of the even-valued terms.
 
@@ -13115,7 +13121,7 @@ o + e = o
 </div>
 <div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
-<h1 id="How-to-compile-these?">How to compile these?<a class="anchor-link" href="#How-to-compile-these?">&#182;</a></h1><p>You would probably start with a special version of <code>G</code>, and perhaps modifications to the default <code>x</code>?</p>
+<h2 id="How-to-compile-these?">How to compile these?<a class="anchor-link" href="#How-to-compile-these?">&#182;</a></h2><p>You would probably start with a special version of <code>G</code>, and perhaps modifications to the default <code>x</code>?</p>
 
 </div>
 </div>
@@ -13124,7 +13130,7 @@ o + e = o
 </div>
 <div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
-<h1 id="An-Interesting-Variation">An Interesting Variation<a class="anchor-link" href="#An-Interesting-Variation">&#182;</a></h1>
+<h2 id="An-Interesting-Variation">An Interesting Variation<a class="anchor-link" href="#An-Interesting-Variation">&#182;</a></h2>
 </div>
 </div>
 </div>

diff --git a/docs/Generator Programs.ipynb b/docs/Generator Programs.ipynb
index 0ed86be..dcb3f61 100644 (file)
--- a/docs/Generator Programs.ipynb
+++ b/docs/Generator Programs.ipynb
@@ -24,9 +24,14 @@
    "source": [
     "Consider the `x` combinator:\n",
     "\n",
-    "    x == dup i\n",
-    "\n",
-    "We can apply it to a quoted program consisting of some value `a` and a function `B`:\n",
+    "    x == dup i"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can apply it to a quoted program consisting of some value `a` and some function `B`:\n",
     "\n",
     "    [a B] x\n",
     "    [a B] a B"
@@ -62,7 +67,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Putting it together, this is the definition of `B`:\n",
+    "Altogether, this is the definition of `B`:\n",
     "\n",
     "    B == swap [C] dip rest cons"
    ]
@@ -71,7 +76,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We can create a quoted program that generates the Natural numbers (0, 1, 2, ...) by using `0` for `a` and `[dup ++]` for `[C]`:\n",
+    "We can make a generator for the Natural numbers (0, 1, 2, ...) by using `0` for `a` and `[dup ++]` for `[C]`:\n",
     "\n",
     "    [0 swap [dup ++] dip rest cons]\n",
     "\n",
@@ -136,7 +141,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### `direco`"
+    "## `direco`"
    ]
   },
   {
@@ -181,7 +186,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Making Generators\n",
+    "## Making Generators\n",
     "We want to define a function that accepts `a` and `[C]` and builds our quoted program:\n",
     "\n",
     "             a [C] G\n",
@@ -310,8 +315,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Generating Multiples of Three and Five\n",
-    "Look at the treatment of the Project Euler Problem One in [Developing a Program.ipynb](./Developing a Program.ipynb) and you'll see that we might be interested in generating an endless cycle of:\n",
+    "## Generating Multiples of Three and Five\n",
+    "Look at the treatment of the Project Euler Problem One in the \"Developing a Program\" notebook and you'll see that we might be interested in generating an endless cycle of:\n",
     "\n",
     "    3 2 1 3 1 2 3\n",
     "\n",
@@ -541,7 +546,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Project Euler Problem One"
+    "## Project Euler Problem One"
    ]
   },
   {
@@ -581,7 +586,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# A generator for the Fibonacci Sequence.\n",
+    "## A generator for the Fibonacci Sequence.\n",
     "Consider:\n",
     "\n",
     "    [b a F] x\n",
@@ -725,7 +730,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Project Euler Problem Two\n",
+    "## Project Euler Problem Two\n",
     "    By considering the terms in the Fibonacci sequence whose values do not exceed four million,\n",
     "    find the sum of the even-valued terms.\n",
     "\n",
@@ -921,7 +926,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# How to compile these?\n",
+    "## How to compile these?\n",
     "You would probably start with a special version of `G`, and perhaps modifications to the default `x`?"
    ]
   },
@@ -929,7 +934,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# An Interesting Variation"
+    "## An Interesting Variation"
    ]
   },
   {

diff --git a/docs/Generator Programs.md b/docs/Generator Programs.md
index 6190a1b..d22f64f 100644 (file)
--- a/docs/Generator Programs.md
+++ b/docs/Generator Programs.md
@@ -12,7 +12,7 @@ Consider the `x` combinator:
 
     x == dup i
 
-We can apply it to a quoted program consisting of some value `a` and a function `B`:
+We can apply it to a quoted program consisting of some value `a` and some function `B`:
 
     [a B] x
     [a B] a B
@@ -33,11 +33,11 @@ Now discard the quoted `a` with `rest` then `cons` `b`:
     b [B]        cons
     [b B]
 
-Putting it together, this is the definition of `B`:
+Altogether, this is the definition of `B`:
 
     B == swap [C] dip rest cons
 
-We can create a quoted program that generates the Natural numbers (0, 1, 2, ...) by using `0` for `a` and `[dup ++]` for `[C]`:
+We can make a generator for the Natural numbers (0, 1, 2, ...) by using `0` for `a` and `[dup ++]` for `[C]`:
 
     [0 swap [dup ++] dip rest cons]
 
@@ -72,7 +72,7 @@ J('[0 swap [dup ++] dip rest cons] x x x x x pop')
     0 1 2 3 4
 
 
-### `direco`
+## `direco`
 
 
 ```python
@@ -99,7 +99,7 @@ V('[0 swap [dup ++] direco] x')
              0 [1 swap [dup ++] direco] . 
 
 
-# Making Generators
+## Making Generators
 We want to define a function that accepts `a` and `[C]` and builds our quoted program:
 
              a [C] G
@@ -163,7 +163,7 @@ J('23 [dup ++] G 5 [x] times')
     23 24 25 26 27 [28 swap [dup ++] direco]
 
 
-# Generating Multiples of Three and Five
+## Generating Multiples of Three and Five
 Look at the treatment of the Project Euler Problem One in [Developing a Program.ipynb](./Developing a Program.ipynb) and you'll see that we might be interested in generating an endless cycle of:
 
     3 2 1 3 1 2 3
@@ -273,7 +273,7 @@ J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times pop enstacken sum')
     999
 
 
-# Project Euler Problem One
+## Project Euler Problem One
 
 
 ```python
@@ -290,7 +290,7 @@ J('0 0 0 [PE1.1.check PE1.1] G 466 [x [PE1.2] dip] times popop')
     233168
 
 
-# A generator for the Fibonacci Sequence.
+## A generator for the Fibonacci Sequence.
 Consider:
 
     [b a F] x
@@ -362,7 +362,7 @@ J('fib_gen 10 [x] times')
     1 2 3 5 8 13 21 34 55 89 [144 89 fib]
 
 
-### Project Euler Problem Two
+## Project Euler Problem Two
     By considering the terms in the Fibonacci sequence whose values do not exceed four million,
     find the sum of the even-valued terms.
 
@@ -463,10 +463,10 @@ J('0 [1 0 fib] PE2.2 [pop >4M] [popop] [[PE2.1] dip PE2.2] primrec')
     4613732
 
 
-# How to compile these?
+## How to compile these?
 You would probably start with a special version of `G`, and perhaps modifications to the default `x`?
 
-# An Interesting Variation
+## An Interesting Variation
 
 
 ```python

diff --git a/docs/Generator Programs.rst b/docs/Generator Programs.rst
index 4ae0294..d5ee3ca 100644 (file)
--- a/docs/Generator Programs.rst
+++ b/docs/Generator Programs.rst
@@ -14,8 +14,8 @@ Consider the ``x`` combinator:
 
     x == dup i
 
-We can apply it to a quoted program consisting of some value ``a`` and a
-function ``B``:
+We can apply it to a quoted program consisting of some value ``a`` and
+some function ``B``:
 
 ::
 
@@ -43,14 +43,14 @@ Now discard the quoted ``a`` with ``rest`` then ``cons`` ``b``:
     b [B]        cons
     [b B]
 
-Putting it together, this is the definition of ``B``:
+Altogether, this is the definition of ``B``:
 
 ::
 
     B == swap [C] dip rest cons
 
-We can create a quoted program that generates the Natural numbers (0, 1,
-2, ...) by using ``0`` for ``a`` and ``[dup ++]`` for ``[C]``:
+We can make a generator for the Natural numbers (0, 1, 2, ...) by using
+``0`` for ``a`` and ``[dup ++]`` for ``[C]``:
 
 ::
 
@@ -93,7 +93,7 @@ After one application of ``x`` the quoted program contains ``1`` and
 
 
 ``direco``
-~~~~~~~~~~
+----------
 
 .. code:: ipython2
 
@@ -122,7 +122,7 @@ After one application of ``x`` the quoted program contains ``1`` and
 
 
 Making Generators
-=================
+-----------------
 
 We want to define a function that accepts ``a`` and ``[C]`` and builds
 our quoted program:
@@ -206,7 +206,7 @@ with the ``x`` combinator.
 
 
 Generating Multiples of Three and Five
-======================================
+--------------------------------------
 
 Look at the treatment of the Project Euler Problem One in `Developing a
 Program.ipynb <./Developing%20a%20Program.ipynb>`__ and you'll see that
@@ -351,7 +351,7 @@ If we drive our generator 466 times and sum the stack we get 999.
 
 
 Project Euler Problem One
-=========================
+-------------------------
 
 .. code:: ipython2
 
@@ -370,7 +370,7 @@ Now we can add ``PE1.2`` to the quoted program given to ``G``.
 
 
 A generator for the Fibonacci Sequence.
-=======================================
+---------------------------------------
 
 Consider:
 
@@ -466,7 +466,7 @@ Putting it all together:
 
 
 Project Euler Problem Two
-~~~~~~~~~~~~~~~~~~~~~~~~~
+-------------------------
 
 ::
 
@@ -589,13 +589,13 @@ Replace ``x`` with our new driver function ``PE2.2`` and start our
 
 
 How to compile these?
-=====================
+---------------------
 
 You would probably start with a special version of ``G``, and perhaps
 modifications to the default ``x``?
 
 An Interesting Variation
-========================
+------------------------
 
 .. code:: ipython2
 

diff --git a/docs/sphinx_docs/_build/html/_modules/joy/library.html b/docs/sphinx_docs/_build/html/_modules/joy/library.html
index b3c1333..b0d5920 100644 (file)
--- a/docs/sphinx_docs/_build/html/_modules/joy/library.html
+++ b/docs/sphinx_docs/_build/html/_modules/joy/library.html
@@ -1177,14 +1177,17 @@
 <span class="nd">@FunctionWrapper</span>
 <span class="k">def</span> <span class="nf">cond</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="sd">&#39;&#39;&#39;</span>
-<span class="sd">  like a case statement; works by rewriting into a chain of ifte.</span>
+<span class="sd">  This combinator works like a case statement.  It expects a single quote</span>
+<span class="sd">  on the stack that must contain zero or more condition quotes and a </span>
+<span class="sd">  default quote.  Each condition clause should contain a quoted predicate</span>
+<span class="sd">  followed by the function expression to run if that predicate returns</span>
+<span class="sd">  true.  If no predicates return true the default function runs.</span>
 
-<span class="sd">  [..[[Bi] Ti]..[D]] -&gt; ...</span>
+<span class="sd">  It works by rewriting into a chain of nested `ifte` expressions, e.g.::</span>
 
-
-<span class="sd">        [[[B0] T0] [[B1] T1] [D]] cond</span>
-<span class="sd">  -----------------------------------------</span>
-<span class="sd">     [B0] [T0] [[B1] [T1] [D] ifte] ifte</span>
+<span class="sd">            [[[B0] T0] [[B1] T1] [D]] cond</span>
+<span class="sd">      -----------------------------------------</span>
+<span class="sd">         [B0] [T0] [[B1] [T1] [D] ifte] ifte</span>
 
 <span class="sd">  &#39;&#39;&#39;</span>
   <span class="n">conditions</span><span class="p">,</span> <span class="n">stack</span> <span class="o">=</span> <span class="n">stack</span>
@@ -1433,9 +1436,10 @@
 <div class="viewcode-block" id="cmp_"><a class="viewcode-back" href="../../library.html#joy.library.cmp_">[docs]</a><span class="nd">@inscribe</span>
 <span class="nd">@FunctionWrapper</span>
 <span class="k">def</span> <span class="nf">cmp_</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="sd">&#39;&#39;&#39;</span>
-<span class="sd">    cmp takes two values and three quoted programs on the stack and runs</span>
-<span class="sd">    one of the three depending on the results of comparing the two values:</span>
+  <span class="sd">&#39;&#39;&#39;</span>
+<span class="sd">  cmp takes two values and three quoted programs on the stack and runs</span>
+<span class="sd">  one of the three depending on the results of comparing the two values:</span>
+<span class="sd">  ::</span>
 
 <span class="sd">           a b [G] [E] [L] cmp</span>
 <span class="sd">        ------------------------- a &gt; b</span>
@@ -1448,10 +1452,10 @@
 <span class="sd">           a b [G] [E] [L] cmp</span>
 <span class="sd">        ------------------------- a &lt; b</span>
 <span class="sd">                        L</span>
-<span class="sd">    &#39;&#39;&#39;</span>
-    <span class="n">L</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">G</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> <span class="o">=</span> <span class="n">stack</span>
-    <span class="n">expression</span> <span class="o">=</span> <span class="n">pushback</span><span class="p">(</span><span class="n">G</span> <span class="k">if</span> <span class="n">a</span> <span class="o">&gt;</span> <span class="n">b</span> <span class="k">else</span> <span class="n">L</span> <span class="k">if</span> <span class="n">a</span> <span class="o">&lt;</span> <span class="n">b</span> <span class="k">else</span> <span class="n">E</span><span class="p">,</span> <span class="n">expression</span><span class="p">)</span>
-    <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>
+<span class="sd">  &#39;&#39;&#39;</span>
+  <span class="n">L</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">G</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> <span class="o">=</span> <span class="n">stack</span>
+  <span class="n">expression</span> <span class="o">=</span> <span class="n">pushback</span><span class="p">(</span><span class="n">G</span> <span class="k">if</span> <span class="n">a</span> <span class="o">&gt;</span> <span class="n">b</span> <span class="k">else</span> <span class="n">L</span> <span class="k">if</span> <span class="n">a</span> <span class="o">&lt;</span> <span class="n">b</span> <span class="k">else</span> <span class="n">E</span><span class="p">,</span> <span class="n">expression</span><span class="p">)</span>
+  <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>
 
 
 <span class="c1">#def nullary(S, expression, dictionary):</span>

diff --git a/docs/sphinx_docs/_build/html/index.html b/docs/sphinx_docs/_build/html/index.html
index e06d2e9..f8fe488 100644 (file)
--- a/docs/sphinx_docs/_build/html/index.html
+++ b/docs/sphinx_docs/_build/html/index.html
@@ -135,6 +135,7 @@ interesting aspects.  It’s quite a treasure trove.</p>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/Replacing.html">Replacing Functions in the Dictionary</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/Ordered_Binary_Trees.html">Treating Trees I: Ordered Binary Trees</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/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="notebooks/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="notebooks/Newton-Raphson.html">Newton’s method</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/Quadratic.html">Quadratic formula</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/NoUpdates.html">No Updates</a></li>

diff --git a/docs/sphinx_docs/_build/html/library.html b/docs/sphinx_docs/_build/html/library.html
index 304a854..cc1198d 100644 (file)
--- a/docs/sphinx_docs/_build/html/library.html
+++ b/docs/sphinx_docs/_build/html/library.html
@@ -198,24 +198,19 @@ Boolean value (so empty string, zero, etc. are counted as false, etc.)</p>
 <code class="descclassname">joy.library.</code><code class="descname">cmp_</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#cmp_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.cmp_" title="Permalink to this definition">¶</a></dt>
 <dd><p>cmp takes two values and three quoted programs on the stack and runs
 one of the three depending on the results of comparing the two values:</p>
-<blockquote>
-<div><blockquote>
-<div>a b [G] [E] [L] cmp</div></blockquote>
-<dl class="docutils">
-<dt>————————- a &gt; b</dt>
-<dd><blockquote class="first">
-<div>G</div></blockquote>
-<p class="last">a b [G] [E] [L] cmp</p>
-</dd>
-<dt>————————- a = b</dt>
-<dd><blockquote class="first">
-<div>E</div></blockquote>
-<p class="last">a b [G] [E] [L] cmp</p>
-</dd>
-<dt>————————- a &lt; b</dt>
-<dd>L</dd>
-</dl>
-</div></blockquote>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>   <span class="n">a</span> <span class="n">b</span> <span class="p">[</span><span class="n">G</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">L</span><span class="p">]</span> <span class="nb">cmp</span>
+<span class="o">-------------------------</span> <span class="n">a</span> <span class="o">&gt;</span> <span class="n">b</span>
+        <span class="n">G</span>
+
+   <span class="n">a</span> <span class="n">b</span> <span class="p">[</span><span class="n">G</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">L</span><span class="p">]</span> <span class="nb">cmp</span>
+<span class="o">-------------------------</span> <span class="n">a</span> <span class="o">=</span> <span class="n">b</span>
+            <span class="n">E</span>
+
+   <span class="n">a</span> <span class="n">b</span> <span class="p">[</span><span class="n">G</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">L</span><span class="p">]</span> <span class="nb">cmp</span>
+<span class="o">-------------------------</span> <span class="n">a</span> <span class="o">&lt;</span> <span class="n">b</span>
+                <span class="n">L</span>
+</pre></div>
+</div>
 </dd></dl>
 
 <dl class="function">
@@ -227,12 +222,17 @@ one of the three depending on the results of comparing the two values:</p>
 <dl class="function">
 <dt id="joy.library.cond">
 <code class="descclassname">joy.library.</code><code class="descname">cond</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#cond"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.cond" title="Permalink to this definition">¶</a></dt>
-<dd><p>like a case statement; works by rewriting into a chain of ifte.</p>
-<p>[..[[Bi] Ti]..[D]] -&gt; …</p>
-<blockquote>
-<div>[[[B0] T0] [[B1] T1] [D]] cond</div></blockquote>
-<blockquote>
-<div>[B0] [T0] [[B1] [T1] [D] ifte] ifte</div></blockquote>
+<dd><p>This combinator works like a case statement.  It expects a single quote
+on the stack that must contain zero or more condition quotes and a 
+default quote.  Each condition clause should contain a quoted predicate
+followed by the function expression to run if that predicate returns
+true.  If no predicates return true the default function runs.</p>
+<p>It works by rewriting into a chain of nested <cite>ifte</cite> expressions, e.g.:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>      <span class="p">[[[</span><span class="n">B0</span><span class="p">]</span> <span class="n">T0</span><span class="p">]</span> <span class="p">[[</span><span class="n">B1</span><span class="p">]</span> <span class="n">T1</span><span class="p">]</span> <span class="p">[</span><span class="n">D</span><span class="p">]]</span> <span class="n">cond</span>
+<span class="o">-----------------------------------------</span>
+   <span class="p">[</span><span class="n">B0</span><span class="p">]</span> <span class="p">[</span><span class="n">T0</span><span class="p">]</span> <span class="p">[[</span><span class="n">B1</span><span class="p">]</span> <span class="p">[</span><span class="n">T1</span><span class="p">]</span> <span class="p">[</span><span class="n">D</span><span class="p">]</span> <span class="n">ifte</span><span class="p">]</span> <span class="n">ifte</span>
+</pre></div>
+</div>
 </dd></dl>
 
 <dl class="function">

diff --git a/docs/sphinx_docs/_build/html/notebooks/Generator Programs.html b/docs/sphinx_docs/_build/html/notebooks/Generator Programs.html
index 4c3cc83..690e8c4 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/Generator Programs.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Generator Programs.html
@@ -16,6 +16,8 @@
     <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
+    <link rel="next" title="Newton’s method" href="Newton-Raphson.html" />
+    <link rel="prev" title="Treating Trees II: treestep" href="Treestep.html" />
    
   <link rel="stylesheet" href="../_static/custom.css" type="text/css" />
   
@@ -36,33 +38,39 @@
 <div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="k">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>
 </pre></div>
 </div>
-<p>Consider the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">==</span> <span class="pre">dup</span> <span class="pre">i</span></code>:</p>
+<p>Consider the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">==</span> <span class="n">dup</span> <span class="n">i</span>
+</pre></div>
+</div>
+<p>We can apply it to a quoted program consisting of some value <code class="docutils literal notranslate"><span class="pre">a</span></code> and
+some function <code class="docutils literal notranslate"><span class="pre">B</span></code>:</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="n">x</span>
 <span class="p">[</span><span class="n">a</span> <span class="n">B</span><span class="p">]</span> <span class="n">a</span> <span class="n">B</span>
 </pre></div>
 </div>
-<p>Let <code class="docutils literal notranslate"><span class="pre">B</span></code> <code class="docutils literal notranslate"><span class="pre">swap</span></code> the <code class="docutils literal notranslate"><span class="pre">a</span></code> with the quote and run some function
-<code class="docutils literal notranslate"><span class="pre">[C]</span></code> on it.</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="n">a</span> <span class="n">B</span>
+<p>Let <code class="docutils literal notranslate"><span class="pre">B</span></code> function <code class="docutils literal notranslate"><span class="pre">swap</span></code> the <code class="docutils literal notranslate"><span class="pre">a</span></code> with the quote and run some
+function <code class="docutils literal notranslate"><span class="pre">C</span></code> on it to generate a new value <code class="docutils literal notranslate"><span class="pre">b</span></code>:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">B</span> <span class="o">==</span> <span class="n">swap</span> <span class="p">[</span><span class="n">C</span><span class="p">]</span> <span class="n">dip</span>
+
+<span class="p">[</span><span class="n">a</span> <span class="n">B</span><span class="p">]</span> <span class="n">a</span> <span class="n">B</span>
 <span class="p">[</span><span class="n">a</span> <span class="n">B</span><span class="p">]</span> <span class="n">a</span> <span class="n">swap</span> <span class="p">[</span><span class="n">C</span><span class="p">]</span> <span class="n">dip</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="p">[</span><span class="n">C</span><span class="p">]</span> <span class="n">dip</span>
 <span class="n">a</span> <span class="n">C</span> <span class="p">[</span><span class="n">a</span> <span class="n">B</span><span class="p">]</span>
+<span class="n">b</span> <span class="p">[</span><span class="n">a</span> <span class="n">B</span><span class="p">]</span>
 </pre></div>
 </div>
-<p>Now discard the quoted <code class="docutils literal notranslate"><span class="pre">a</span></code> with <code class="docutils literal notranslate"><span class="pre">rest</span></code> and <code class="docutils literal notranslate"><span class="pre">cons</span></code> the result of
-<code class="docutils literal notranslate"><span class="pre">C</span></code> on <code class="docutils literal notranslate"><span class="pre">a</span></code> whatever that is:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">aC</span> <span class="p">[</span><span class="n">a</span> <span class="n">B</span><span class="p">]</span> <span class="n">rest</span> <span class="n">cons</span>
-<span class="n">aC</span> <span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="n">cons</span>
-<span class="p">[</span><span class="n">aC</span> <span class="n">B</span><span class="p">]</span>
+<p>Now discard the quoted <code class="docutils literal notranslate"><span class="pre">a</span></code> with <code class="docutils literal notranslate"><span class="pre">rest</span></code> then <code class="docutils literal notranslate"><span class="pre">cons</span></code> <code class="docutils literal notranslate"><span class="pre">b</span></code>:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="p">[</span><span class="n">a</span> <span class="n">B</span><span class="p">]</span> <span class="n">rest</span> <span class="n">cons</span>
+<span class="n">b</span> <span class="p">[</span><span class="n">B</span><span class="p">]</span>        <span class="n">cons</span>
+<span class="p">[</span><span class="n">b</span> <span class="n">B</span><span class="p">]</span>
 </pre></div>
 </div>
 <p>Altogether, this is the definition of <code class="docutils literal notranslate"><span class="pre">B</span></code>:</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">B</span> <span class="o">==</span> <span class="n">swap</span> <span class="p">[</span><span class="n">C</span><span class="p">]</span> <span class="n">dip</span> <span class="n">rest</span> <span class="n">cons</span>
 </pre></div>
 </div>
-<p>We can create a quoted program that generates the Natural numbers
-(integers 0, 1, 2, …) by using <code class="docutils literal notranslate"><span class="pre">0</span></code> for <code class="docutils literal notranslate"><span class="pre">a</span></code> and <code class="docutils literal notranslate"><span class="pre">[dup</span> <span class="pre">++]</span></code> for
-<code class="docutils literal notranslate"><span class="pre">[C]</span></code>:</p>
+<p>We can make a generator for the Natural numbers (0, 1, 2, …) by using
+<code class="docutils literal notranslate"><span class="pre">0</span></code> for <code class="docutils literal notranslate"><span class="pre">a</span></code> and <code class="docutils literal notranslate"><span class="pre">[dup</span> <span class="pre">++]</span></code> for <code class="docutils literal notranslate"><span class="pre">[C]</span></code>:</p>
 <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">dip</span> <span class="n">rest</span> <span class="n">cons</span><span class="p">]</span>
 </pre></div>
 </div>
@@ -116,15 +124,13 @@
 </pre></div>
 </div>
 </div>
-</div>
-<div class="section" id="generating-generators">
-<h1>Generating Generators<a class="headerlink" href="#generating-generators" title="Permalink to this headline">¶</a></h1>
-<p>We want to go from:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="p">[</span><span class="n">C</span><span class="p">]</span> <span class="n">G</span>
-</pre></div>
-</div>
-<p>to:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">a</span> <span class="n">swap</span> <span class="p">[</span><span class="n">C</span><span class="p">]</span> <span class="n">direco</span><span class="p">]</span>
+<div class="section" id="making-generators">
+<h2>Making Generators<a class="headerlink" href="#making-generators" title="Permalink to this headline">¶</a></h2>
+<p>We want to define a function that accepts <code class="docutils literal notranslate"><span class="pre">a</span></code> and <code class="docutils literal notranslate"><span class="pre">[C]</span></code> and builds
+our quoted program:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>         <span class="n">a</span> <span class="p">[</span><span class="n">C</span><span class="p">]</span> <span class="n">G</span>
+<span class="o">-------------------------</span>
+   <span class="p">[</span><span class="n">a</span> <span class="n">swap</span> <span class="p">[</span><span class="n">C</span><span class="p">]</span> <span class="n">direco</span><span class="p">]</span>
 </pre></div>
 </div>
 <p>Working in reverse:</p>
@@ -140,107 +146,45 @@
 <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>
-<p>We can try it out:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></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">G</span>
-</pre></div>
-</div>
 <div class="code ipython2 highlight-default 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>
 </pre></div>
 </div>
-<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;0 [dup ++] G&#39;</span><span class="p">)</span>
+<p>Let’s try it out:</p>
+<div class="code ipython2 highlight-default 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>
 </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="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">G</span>
-                         <span class="mi">0</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">G</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="o">.</span> <span class="n">G</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="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>
-       <span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="p">[</span><span class="n">direco</span><span class="p">]</span> <span class="o">.</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>
-       <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">direco</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">swap</span><span class="p">]</span> <span class="n">swoncat</span> <span class="n">cons</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">direco</span><span class="p">]</span> <span class="p">[</span><span class="n">swap</span><span class="p">]</span> <span class="o">.</span> <span class="n">swoncat</span> <span class="n">cons</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">direco</span><span class="p">]</span> <span class="p">[</span><span class="n">swap</span><span class="p">]</span> <span class="o">.</span> <span class="n">swap</span> <span class="n">concat</span> <span class="n">cons</span>
-<span class="mi">0</span> <span class="p">[</span><span class="n">swap</span><span class="p">]</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="o">.</span> <span class="n">concat</span> <span class="n">cons</span>
-  <span class="mi">0</span> <span class="p">[</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="o">.</span> <span class="n">cons</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="o">.</span>
+<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="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;0 [dup ++] G x&#39;</span><span class="p">)</span>
+<div class="code ipython2 highlight-default 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>
 </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="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">G</span> <span class="n">x</span>
-                                  <span class="mi">0</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">G</span> <span class="n">x</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="o">.</span> <span class="n">G</span> <span class="n">x</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="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> <span class="n">x</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="p">[</span><span class="n">direco</span><span class="p">]</span> <span class="o">.</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> <span class="n">x</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">direco</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">swap</span><span class="p">]</span> <span class="n">swoncat</span> <span class="n">cons</span> <span class="n">x</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">direco</span><span class="p">]</span> <span class="p">[</span><span class="n">swap</span><span class="p">]</span> <span class="o">.</span> <span class="n">swoncat</span> <span class="n">cons</span> <span class="n">x</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">direco</span><span class="p">]</span> <span class="p">[</span><span class="n">swap</span><span class="p">]</span> <span class="o">.</span> <span class="n">swap</span> <span class="n">concat</span> <span class="n">cons</span> <span class="n">x</span>
-         <span class="mi">0</span> <span class="p">[</span><span class="n">swap</span><span class="p">]</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="o">.</span> <span class="n">concat</span> <span class="n">cons</span> <span class="n">x</span>
-           <span class="mi">0</span> <span class="p">[</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="o">.</span> <span class="n">cons</span> <span class="n">x</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="o">.</span> <span class="n">x</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="o">.</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="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="mi">0</span> <span class="o">.</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="mi">0</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="o">.</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="mi">0</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="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">direco</span>
-<span class="mi">0</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="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span> <span class="n">rest</span> <span class="n">cons</span>
-                                  <span class="mi">0</span> <span class="o">.</span> <span class="n">dup</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">rest</span> <span class="n">cons</span>
-                                <span class="mi">0</span> <span class="mi">0</span> <span class="o">.</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">rest</span> <span class="n">cons</span>
-                                <span class="mi">0</span> <span class="mi">1</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">rest</span> <span class="n">cons</span>
-       <span class="mi">0</span> <span class="mi">1</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="o">.</span> <span class="n">rest</span> <span class="n">cons</span>
-         <span class="mi">0</span> <span class="mi">1</span> <span class="p">[</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="o">.</span> <span class="n">cons</span>
-         <span class="mi">0</span> <span class="p">[</span><span class="mi">1</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="o">.</span>
+<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>
 </pre></div>
 </div>
 <div class="section" id="powers-of-2">
-<h2>Powers of 2<a class="headerlink" href="#powers-of-2" title="Permalink to this headline">¶</a></h2>
-<div class="code ipython2 highlight-default 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&#39;</span><span class="p">)</span>
+<h3>Powers of 2<a class="headerlink" href="#powers-of-2" title="Permalink to this headline">¶</a></h3>
+<div class="code ipython2 highlight-default 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>
 </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> <span class="p">[</span><span class="mi">512</span> <span class="n">swap</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">1</span> <span class="o">&lt;&lt;</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">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>
 </pre></div>
 </div>
 </div>
-</div>
-<div class="section" id="n-x-times">
-<h1><code class="docutils literal notranslate"><span class="pre">n</span> <span class="pre">[x]</span> <span class="pre">times</span></code><a class="headerlink" href="#n-x-times" title="Permalink to this headline">¶</a></h1>
+<div class="section" id="x-times">
+<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>
-<p>Let’s define a word <code class="docutils literal notranslate"><span class="pre">n_range</span></code> that takes a starting integer and a
-count and leaves that many consecutive integers on the stack. For
-example:</p>
-<div class="code ipython2 highlight-default 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 pop&#39;</span><span class="p">)</span>
-</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>
-</pre></div>
-</div>
-<p>We can use <code class="docutils literal notranslate"><span class="pre">dip</span></code> to untangle <code class="docutils literal notranslate"><span class="pre">[dup</span> <span class="pre">++]</span> <span class="pre">G</span></code> from the arguments.</p>
-<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 5 [[dup ++] G] dip [x] times pop&#39;</span><span class="p">)</span>
-</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>
+<div class="code ipython2 highlight-default 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>
 </pre></div>
 </div>
-<p>Now that the givens (arguments) are on the left we have the definition
-we’re looking for:</p>
-<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;n_range == [[dup ++] G] dip [x] times pop&#39;</span><span class="p">)</span>
+<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>
 </pre></div>
 </div>
-<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;450 10 n_range&#39;</span><span class="p">)</span>
-</pre></div>
-</div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">450</span> <span class="mi">451</span> <span class="mi">452</span> <span class="mi">453</span> <span class="mi">454</span> <span class="mi">455</span> <span class="mi">456</span> <span class="mi">457</span> <span class="mi">458</span> <span class="mi">459</span>
-</pre></div>
-</div>
-<p>This is better just using the <code class="docutils literal notranslate"><span class="pre">times</span></code> combinator though…</p>
-<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;450 9 [dup ++] times&#39;</span><span class="p">)</span>
-</pre></div>
-</div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">450</span> <span class="mi">451</span> <span class="mi">452</span> <span class="mi">453</span> <span class="mi">454</span> <span class="mi">455</span> <span class="mi">456</span> <span class="mi">457</span> <span class="mi">458</span> <span class="mi">459</span>
-</pre></div>
 </div>
 </div>
 <div class="section" id="generating-multiples-of-three-and-five">
-<h1>Generating Multiples of Three and Five<a class="headerlink" href="#generating-multiples-of-three-and-five" title="Permalink to this headline">¶</a></h1>
+<h2>Generating Multiples of Three and Five<a class="headerlink" href="#generating-multiples-of-three-and-five" title="Permalink to this headline">¶</a></h2>
 <p>Look at the treatment of the Project Euler Problem One in <a class="reference external" href="./Developing%20a%20Program.ipynb">Developing a
 Program.ipynb</a> and you’ll see that
 we might be interested in generating an endless cycle of:</p>
@@ -281,12 +225,6 @@ int right two bits.</p>
 <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>
 </pre></div>
 </div>
-<div class="code ipython2 highlight-default 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] x&#39;</span><span class="p">)</span>
-</pre></div>
-</div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="p">[</span><span class="mi">3702</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>
-</pre></div>
-</div>
 <p>…we get a generator that works for seven cycles before it reaches
 zero:</p>
 <div class="code ipython2 highlight-default 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>
@@ -296,21 +234,31 @@ zero:</p>
 </pre></div>
 </div>
 <div class="section" id="reset-at-zero">
-<h2>Reset at Zero<a class="headerlink" href="#reset-at-zero" title="Permalink to this headline">¶</a></h2>
+<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="code ipython2 highlight-default 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>
 </pre></div>
 </div>
+<div class="code ipython2 highlight-default 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>
+</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>
+</pre></div>
+</div>
 <div class="code ipython2 highlight-default 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>
 </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>
 </pre></div>
 </div>
+<p>(It would be more efficient to reset the int every seven cycles but
+that’s a little beyond the scope of this article. This solution does
+extra work, but not much, and we’re not using it “in production” as they
+say.)</p>
 </div>
 <div class="section" id="run-466-times">
-<h2>Run 466 times<a class="headerlink" href="#run-466-times" title="Permalink to this headline">¶</a></h2>
+<h3>Run 466 times<a class="headerlink" href="#run-466-times" title="Permalink to this headline">¶</a></h3>
 <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>
@@ -321,13 +269,13 @@ numbers sixty-six times and then four more.</p>
 </pre></div>
 </div>
 <p>If we drive our generator 466 times and sum the stack we get 999.</p>
-<div class="code ipython2 highlight-default 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] dip rest cons] 466 [x] times&#39;</span><span class="p">)</span>
+<div class="code ipython2 highlight-default 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>
 </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">dip</span> <span class="n">rest</span> <span class="n">cons</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="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>
 </pre></div>
 </div>
-<div class="code ipython2 highlight-default 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] dip rest cons] 466 [x] times pop enstacken sum&#39;</span><span class="p">)</span>
+<div class="code ipython2 highlight-default 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>
 </pre></div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">999</span>
@@ -336,18 +284,11 @@ numbers sixty-six times and then four more.</p>
 </div>
 </div>
 <div class="section" id="project-euler-problem-one">
-<h1>Project Euler Problem One<a class="headerlink" href="#project-euler-problem-one" title="Permalink to this headline">¶</a></h1>
+<h2>Project Euler Problem One<a class="headerlink" href="#project-euler-problem-one" title="Permalink to this headline">¶</a></h2>
 <div class="code ipython2 highlight-default 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>
 </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">times</span></code>.</p>
-<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;0 0 [0 swap [PE1.1.check PE1.1] direco] 466 [x [PE1.2] dip] times popop&#39;</span><span class="p">)</span>
-</pre></div>
-</div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">233168</span>
-</pre></div>
-</div>
-<p>Or using <code class="docutils literal notranslate"><span class="pre">G</span></code> we can write:</p>
+<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="code ipython2 highlight-default 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>
 </pre></div>
 </div>
@@ -356,7 +297,7 @@ numbers sixty-six times and then four more.</p>
 </div>
 </div>
 <div class="section" id="a-generator-for-the-fibonacci-sequence">
-<h1>A generator for the Fibonacci Sequence.<a class="headerlink" href="#a-generator-for-the-fibonacci-sequence" title="Permalink to this headline">¶</a></h1>
+<h2>A generator for the Fibonacci Sequence.<a class="headerlink" href="#a-generator-for-the-fibonacci-sequence" title="Permalink to this headline">¶</a></h2>
 <p>Consider:</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">b</span> <span class="n">a</span> <span class="n">F</span><span class="p">]</span> <span class="n">x</span>
 <span class="p">[</span><span class="n">b</span> <span class="n">a</span> <span class="n">F</span><span class="p">]</span> <span class="n">b</span> <span class="n">a</span> <span class="n">F</span>
@@ -394,21 +335,23 @@ numbers sixty-six times and then four more.</p>
 <span class="p">[</span><span class="n">b</span> <span class="n">b</span><span class="o">+</span><span class="n">a</span> <span class="n">b</span> <span class="n">F</span><span class="p">]</span>
 </pre></div>
 </div>
-<p>And lastly:</p>
+<p>But we can just use <code class="docutils literal notranslate"><span class="pre">cons</span></code> to carry <code class="docutils literal notranslate"><span class="pre">b+a</span></code> into the quote:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">b</span> <span class="n">a</span> <span class="n">F</span><span class="p">]</span> <span class="n">b</span><span class="o">+</span><span class="n">a</span> <span class="p">[</span><span class="n">popdd</span> <span class="n">over</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span>
+<span class="p">[</span><span class="n">b</span> <span class="n">a</span> <span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">b</span><span class="o">+</span><span class="n">a</span> <span class="n">popdd</span> <span class="n">over</span><span class="p">]</span>      <span class="n">infra</span>
+<span class="p">[</span><span class="n">b</span> <span class="n">b</span><span class="o">+</span><span class="n">a</span> <span class="n">b</span> <span class="n">F</span><span class="p">]</span>
+</pre></div>
+</div>
+<p>Lastly:</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">b</span> <span class="n">b</span><span class="o">+</span><span class="n">a</span> <span class="n">b</span> <span class="n">F</span><span class="p">]</span> <span class="n">uncons</span>
 <span class="n">b</span> <span class="p">[</span><span class="n">b</span><span class="o">+</span><span class="n">a</span> <span class="n">b</span> <span class="n">F</span><span class="p">]</span>
 </pre></div>
 </div>
-<p>Done.</p>
 <p>Putting it all together:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">==</span> <span class="o">+</span> <span class="n">swons</span> <span class="p">[</span><span class="n">popdd</span> <span class="n">over</span><span class="p">]</span> <span class="n">infra</span> <span class="n">uncons</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">==</span> <span class="o">+</span> <span class="p">[</span><span class="n">popdd</span> <span class="n">over</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span> <span class="n">uncons</span>
+<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>
-<p>And:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><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="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;fib == + swons [popdd over] infra uncons&#39;</span><span class="p">)</span>
+<div class="code ipython2 highlight-default 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>
 </pre></div>
 </div>
 <div class="code ipython2 highlight-default 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>
@@ -420,9 +363,11 @@ numbers sixty-six times and then four more.</p>
 <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>
 </pre></div>
 </div>
+</div>
 <div class="section" id="project-euler-problem-two">
 <h2>Project Euler Problem Two<a class="headerlink" href="#project-euler-problem-two" title="Permalink to this headline">¶</a></h2>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">By</span> <span class="n">considering</span> <span class="n">the</span> <span class="n">terms</span> <span class="ow">in</span> <span class="n">the</span> <span class="n">Fibonacci</span> <span class="n">sequence</span> <span class="n">whose</span> <span class="n">values</span> <span class="n">do</span> <span class="ow">not</span> <span class="n">exceed</span> <span class="n">four</span> <span class="n">million</span><span class="p">,</span> <span class="n">find</span> <span class="n">the</span> <span class="nb">sum</span> <span class="n">of</span> <span class="n">the</span> <span class="n">even</span><span class="o">-</span><span class="n">valued</span> <span class="n">terms</span><span class="o">.</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">By</span> <span class="n">considering</span> <span class="n">the</span> <span class="n">terms</span> <span class="ow">in</span> <span class="n">the</span> <span class="n">Fibonacci</span> <span class="n">sequence</span> <span class="n">whose</span> <span class="n">values</span> <span class="n">do</span> <span class="ow">not</span> <span class="n">exceed</span> <span class="n">four</span> <span class="n">million</span><span class="p">,</span>
+<span class="n">find</span> <span class="n">the</span> <span class="nb">sum</span> <span class="n">of</span> <span class="n">the</span> <span class="n">even</span><span class="o">-</span><span class="n">valued</span> <span class="n">terms</span><span class="o">.</span>
 </pre></div>
 </div>
 <p>Now that we have a generator for the Fibonacci sequence, we need a
@@ -459,9 +404,8 @@ and sums the even ones.</p>
 <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>
 </pre></div>
 </div>
-</div>
 <div class="section" id="even-valued-fibonacci-terms">
-<h2>Even-valued Fibonacci Terms<a class="headerlink" href="#even-valued-fibonacci-terms" title="Permalink to this headline">¶</a></h2>
+<h3>Even-valued Fibonacci Terms<a class="headerlink" href="#even-valued-fibonacci-terms" title="Permalink to this headline">¶</a></h3>
 <p>Using <code class="docutils literal notranslate"><span class="pre">o</span></code> for odd and <code class="docutils literal notranslate"><span class="pre">e</span></code> for even:</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">o</span> <span class="o">+</span> <span class="n">o</span> <span class="o">=</span> <span class="n">e</span>
 <span class="n">e</span> <span class="o">+</span> <span class="n">e</span> <span class="o">=</span> <span class="n">e</span>
@@ -507,10 +451,45 @@ and sums the even ones.</p>
 </div>
 </div>
 <div class="section" id="how-to-compile-these">
-<h1>How to compile these?<a class="headerlink" href="#how-to-compile-these" title="Permalink to this headline">¶</a></h1>
+<h2>How to compile these?<a class="headerlink" href="#how-to-compile-these" title="Permalink to this headline">¶</a></h2>
 <p>You would probably start with a special version of <code class="docutils literal notranslate"><span class="pre">G</span></code>, and perhaps
 modifications to the default <code class="docutils literal notranslate"><span class="pre">x</span></code>?</p>
 </div>
+<div class="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="code ipython2 highlight-default 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>
+</pre></div>
+</div>
+<div class="code ipython2 highlight-default 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>
+</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>
+           <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="o">.</span> <span class="n">x</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="o">.</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="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="mi">0</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">codireco</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="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">codireco</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="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">cons</span> <span class="n">dip</span> <span class="n">rest</span> <span class="n">cons</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="p">[</span><span class="mi">0</span> <span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span> <span class="n">rest</span> <span class="n">cons</span>
+                                 <span class="o">.</span> <span class="mi">0</span> <span class="n">dup</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">rest</span> <span class="n">cons</span>
+                               <span class="mi">0</span> <span class="o">.</span> <span class="n">dup</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">rest</span> <span class="n">cons</span>
+                             <span class="mi">0</span> <span class="mi">0</span> <span class="o">.</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">rest</span> <span class="n">cons</span>
+                             <span class="mi">0</span> <span class="mi">1</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">rest</span> <span class="n">cons</span>
+       <span class="mi">0</span> <span class="mi">1</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="o">.</span> <span class="n">rest</span> <span class="n">cons</span>
+         <span class="mi">0</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> <span class="n">cons</span>
+         <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="code ipython2 highlight-default 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>
+</pre></div>
+</div>
+<div class="code ipython2 highlight-default 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>
+</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>
+</pre></div>
+</div>
+</div>
+</div>
 
 
           </div>
@@ -522,30 +501,35 @@ modifications to the default <code class="docutils literal notranslate"><span cl
   <ul>
 <li><a class="reference internal" href="#">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a><ul>
 <li><a class="reference internal" href="#direco"><code class="docutils literal notranslate"><span class="pre">direco</span></code></a></li>
-</ul>
-</li>
-<li><a class="reference internal" href="#generating-generators">Generating Generators</a><ul>
+<li><a class="reference internal" href="#making-generators">Making Generators</a><ul>
 <li><a class="reference internal" href="#powers-of-2">Powers of 2</a></li>
+<li><a class="reference internal" href="#x-times"><code class="docutils literal notranslate"><span class="pre">[x]</span> <span class="pre">times</span></code></a></li>
 </ul>
 </li>
-<li><a class="reference internal" href="#n-x-times"><code class="docutils literal notranslate"><span class="pre">n</span> <span class="pre">[x]</span> <span class="pre">times</span></code></a></li>
 <li><a class="reference internal" href="#generating-multiples-of-three-and-five">Generating Multiples of Three and Five</a><ul>
 <li><a class="reference internal" href="#reset-at-zero">Reset at Zero</a></li>
 <li><a class="reference internal" href="#run-466-times">Run 466 times</a></li>
 </ul>
 </li>
 <li><a class="reference internal" href="#project-euler-problem-one">Project Euler Problem One</a></li>
-<li><a class="reference internal" href="#a-generator-for-the-fibonacci-sequence">A generator for the Fibonacci Sequence.</a><ul>
-<li><a class="reference internal" href="#project-euler-problem-two">Project Euler Problem Two</a></li>
+<li><a class="reference internal" href="#a-generator-for-the-fibonacci-sequence">A generator for the Fibonacci Sequence.</a></li>
+<li><a class="reference internal" href="#project-euler-problem-two">Project Euler Problem Two</a><ul>
 <li><a class="reference internal" href="#even-valued-fibonacci-terms">Even-valued Fibonacci Terms</a></li>
 </ul>
 </li>
 <li><a class="reference internal" href="#how-to-compile-these">How to compile these?</a></li>
+<li><a class="reference internal" href="#an-interesting-variation">An Interesting Variation</a></li>
+</ul>
+</li>
 </ul>
 <div class="relations">
 <h3>Related Topics</h3>
 <ul>
   <li><a href="../index.html">Documentation overview</a><ul>
+  <li><a href="index.html">Essays about Programming in Joy</a><ul>
+      <li>Previous: <a href="Treestep.html" title="previous chapter">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
+      <li>Next: <a href="Newton-Raphson.html" title="next chapter">Newton’s method</a></li>
+  </ul></li>
   </ul></li>
 </ul>
 </div>

diff --git a/docs/sphinx_docs/_build/html/notebooks/index.html b/docs/sphinx_docs/_build/html/notebooks/index.html
index 84ee6af..d6eeb83 100644 (file)
--- a/docs/sphinx_docs/_build/html/notebooks/index.html
+++ b/docs/sphinx_docs/_build/html/notebooks/index.html
@@ -73,6 +73,17 @@
 <li class="toctree-l2"><a class="reference internal" href="Treestep.html#putting-it-together">Putting it together</a></li>
 </ul>
 </li>
+<li class="toctree-l1"><a class="reference internal" href="Generator Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="Generator Programs.html#direco"><code class="docutils literal notranslate"><span class="pre">direco</span></code></a></li>
+<li class="toctree-l2"><a class="reference internal" href="Generator Programs.html#making-generators">Making Generators</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Generator Programs.html#generating-multiples-of-three-and-five">Generating Multiples of Three and Five</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Generator Programs.html#project-euler-problem-one">Project Euler Problem One</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Generator Programs.html#a-generator-for-the-fibonacci-sequence">A generator for the Fibonacci Sequence.</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Generator Programs.html#project-euler-problem-two">Project Euler Problem Two</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Generator Programs.html#how-to-compile-these">How to compile these?</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Generator Programs.html#an-interesting-variation">An Interesting Variation</a></li>
+</ul>
+</li>
 <li class="toctree-l1"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a><ul>
 <li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html#a-generator-for-approximations">A Generator for Approximations</a></li>
 <li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html#finding-consecutive-approximations-within-a-tolerance">Finding Consecutive Approximations <code class="docutils literal notranslate"><span class="pre">within</span></code> a Tolerance</a></li>

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index cde5b78..f42664a 100644 (file)
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\ No newline at end of file

diff --git a/docs/sphinx_docs/notebooks/Generator Programs.rst b/docs/sphinx_docs/notebooks/Generator Programs.rst
index f1b99a6..d5ee3ca 100644 (file)
--- a/docs/sphinx_docs/notebooks/Generator Programs.rst
+++ b/docs/sphinx_docs/notebooks/Generator Programs.rst
@@ -8,31 +8,40 @@ Cf. jp-reprod.html
 
     from notebook_preamble import J, V, define
 
-Consider the ``x`` combinator ``x == dup i``:
+Consider the ``x`` combinator:
+
+::
+
+    x == dup i
+
+We can apply it to a quoted program consisting of some value ``a`` and
+some function ``B``:
 
 ::
 
     [a B] x
     [a B] a B
 
-Let ``B`` ``swap`` the ``a`` with the quote and run some function
-``[C]`` on it.
+Let ``B`` function ``swap`` the ``a`` with the quote and run some
+function ``C`` on it to generate a new value ``b``:
 
 ::
 
+    B == swap [C] dip
+
     [a B] a B
     [a B] a swap [C] dip
     a [a B]      [C] dip
     a C [a B]
+    b [a B]
 
-Now discard the quoted ``a`` with ``rest`` and ``cons`` the result of
-``C`` on ``a`` whatever that is:
+Now discard the quoted ``a`` with ``rest`` then ``cons`` ``b``:
 
 ::
 
-    aC [a B] rest cons
-    aC [B] cons
-    [aC B]
+    b [a B] rest cons
+    b [B]        cons
+    [b B]
 
 Altogether, this is the definition of ``B``:
 
@@ -40,9 +49,8 @@ Altogether, this is the definition of ``B``:
 
     B == swap [C] dip rest cons
 
-We can create a quoted program that generates the Natural numbers
-(integers 0, 1, 2, ...) by using ``0`` for ``a`` and ``[dup ++]`` for
-``[C]``:
+We can make a generator for the Natural numbers (0, 1, 2, ...) by using
+``0`` for ``a`` and ``[dup ++]`` for ``[C]``:
 
 ::
 
@@ -85,7 +93,7 @@ After one application of ``x`` the quoted program contains ``1`` and
 
 
 ``direco``
-~~~~~~~~~~
+----------
 
 .. code:: ipython2
 
@@ -113,20 +121,17 @@ After one application of ``x`` the quoted program contains ``1`` and
              0 [1 swap [dup ++] direco] . 
 
 
-Generating Generators
-=====================
+Making Generators
+-----------------
 
-We want to go from:
+We want to define a function that accepts ``a`` and ``[C]`` and builds
+our quoted program:
 
 ::
 
-    a [C] G
-
-to:
-
-::
-
-    [a swap [C] direco]
+             a [C] G
+    -------------------------
+       [a swap [C] direco]
 
 Working in reverse:
 
@@ -145,65 +150,30 @@ Reading from the bottom up:
     G == [direco] cons [swap] swap concat cons
     G == [direco] cons [swap] swoncat cons
 
-We can try it out:
-
-::
-
-    0 [dup ++] G
-
 .. code:: ipython2
 
     define('G == [direco] cons [swap] swoncat cons')
 
+Let's try it out:
+
 .. code:: ipython2
 
-    V('0 [dup ++] G')
+    J('0 [dup ++] G')
 
 
 .. parsed-literal::
 
-                               . 0 [dup ++] G
-                             0 . [dup ++] G
-                    0 [dup ++] . G
-                    0 [dup ++] . [direco] cons [swap] swoncat cons
-           0 [dup ++] [direco] . cons [swap] swoncat cons
-           0 [[dup ++] direco] . [swap] swoncat cons
-    0 [[dup ++] direco] [swap] . swoncat cons
-    0 [[dup ++] direco] [swap] . swap concat cons
-    0 [swap] [[dup ++] direco] . concat cons
-      0 [swap [dup ++] direco] . cons
-      [0 swap [dup ++] direco] . 
+    [0 swap [dup ++] direco]
 
 
 .. code:: ipython2
 
-    V('0 [dup ++] G x')
+    J('0 [dup ++] G x x x pop')
 
 
 .. parsed-literal::
 
-                                        . 0 [dup ++] G x
-                                      0 . [dup ++] G x
-                             0 [dup ++] . G x
-                             0 [dup ++] . [direco] cons [swap] swoncat cons x
-                    0 [dup ++] [direco] . cons [swap] swoncat cons x
-                    0 [[dup ++] direco] . [swap] swoncat cons x
-             0 [[dup ++] direco] [swap] . swoncat cons x
-             0 [[dup ++] direco] [swap] . swap concat cons x
-             0 [swap] [[dup ++] direco] . concat cons x
-               0 [swap [dup ++] direco] . cons x
-               [0 swap [dup ++] direco] . x
-               [0 swap [dup ++] direco] . 0 swap [dup ++] direco
-             [0 swap [dup ++] direco] 0 . swap [dup ++] direco
-             0 [0 swap [dup ++] direco] . [dup ++] direco
-    0 [0 swap [dup ++] direco] [dup ++] . direco
-    0 [0 swap [dup ++] direco] [dup ++] . dip rest cons
-                                      0 . dup ++ [0 swap [dup ++] direco] rest cons
-                                    0 0 . ++ [0 swap [dup ++] direco] rest cons
-                                    0 1 . [0 swap [dup ++] direco] rest cons
-           0 1 [0 swap [dup ++] direco] . rest cons
-             0 1 [swap [dup ++] direco] . cons
-             0 [1 swap [dup ++] direco] . 
+    0 1 2
 
 
 Powers of 2
@@ -211,77 +181,32 @@ Powers of 2
 
 .. code:: ipython2
 
-    J('1 [dup 1 <<] G x x x x x x x x x')
+    J('1 [dup 1 <<] G x x x x x x x x x pop')
 
 
 .. parsed-literal::
 
-    1 2 4 8 16 32 64 128 256 [512 swap [dup 1 <<] direco]
+    1 2 4 8 16 32 64 128 256
 
 
-``n [x] times``
-===============
+``[x] times``
+~~~~~~~~~~~~~
 
 If we have one of these quoted programs we can drive it using ``times``
 with the ``x`` combinator.
 
-Let's define a word ``n_range`` that takes a starting integer and a
-count and leaves that many consecutive integers on the stack. For
-example:
-
-.. code:: ipython2
-
-    J('23 [dup ++] G 5 [x] times pop')
-
-
-.. parsed-literal::
-
-    23 24 25 26 27
-
-
-We can use ``dip`` to untangle ``[dup ++] G`` from the arguments.
-
-.. code:: ipython2
-
-    J('23 5 [[dup ++] G] dip [x] times pop')
-
-
-.. parsed-literal::
-
-    23 24 25 26 27
-
-
-Now that the givens (arguments) are on the left we have the definition
-we're looking for:
-
-.. code:: ipython2
-
-    define('n_range == [[dup ++] G] dip [x] times pop')
-
-.. code:: ipython2
-
-    J('450 10 n_range')
-
-
-.. parsed-literal::
-
-    450 451 452 453 454 455 456 457 458 459
-
-
-This is better just using the ``times`` combinator though...
-
 .. code:: ipython2
 
-    J('450 9 [dup ++] times')
+    J('23 [dup ++] G 5 [x] times')
 
 
 .. parsed-literal::
 
-    450 451 452 453 454 455 456 457 458 459
+    23 24 25 26 27 [28 swap [dup ++] direco]
 
 
 Generating Multiples of Three and Five
-======================================
+--------------------------------------
 
 Look at the treatment of the Project Euler Problem One in `Developing a
 Program.ipynb <./Developing%20a%20Program.ipynb>`__ and you'll see that
@@ -338,16 +263,6 @@ If we plug ``14811`` and ``[PE1.1]`` into our generator form...
     [14811 swap [PE1.1] direco]
 
 
-.. code:: ipython2
-
-    J('[14811 swap [PE1.1] direco] x')
-
-
-.. parsed-literal::
-
-    3 [3702 swap [PE1.1] direco]
-
-
 ...we get a generator that works for seven cycles before it reaches
 zero:
 
@@ -373,6 +288,16 @@ if so.
 
 .. code:: ipython2
 
+    J('14811 [PE1.1.check PE1.1] G')
+
+
+.. parsed-literal::
+
+    [14811 swap [PE1.1.check PE1.1] direco]
+
+
+.. code:: ipython2
+
     J('[14811 swap [PE1.1.check PE1.1] direco] 21 [x] times')
 
 
@@ -381,6 +306,11 @@ if so.
     3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 [0 swap [PE1.1.check PE1.1] direco]
 
 
+(It would be more efficient to reset the int every seven cycles but
+that's a little beyond the scope of this article. This solution does
+extra work, but not much, and we're not using it "in production" as they
+say.)
+
 Run 466 times
 ~~~~~~~~~~~~~
 
@@ -402,17 +332,17 @@ If we drive our generator 466 times and sum the stack we get 999.
 
 .. code:: ipython2
 
-    J('[14811 swap [PE1.1.check PE1.1] dip rest cons] 466 [x] times')
+    J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times')
 
 
 .. parsed-literal::
 
-    3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 [57 swap [PE1.1.check PE1.1] dip rest cons]
+    3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 [57 swap [PE1.1.check PE1.1] direco]
 
 
 .. code:: ipython2
 
-    J('[14811 swap [PE1.1.check PE1.1] dip rest cons] 466 [x] times pop enstacken sum')
+    J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times pop enstacken sum')
 
 
 .. parsed-literal::
@@ -421,25 +351,13 @@ If we drive our generator 466 times and sum the stack we get 999.
 
 
 Project Euler Problem One
-=========================
+-------------------------
 
 .. code:: ipython2
 
     define('PE1.2 == + dup [+] dip')
 
-Now we can add ``PE1.2`` to the quoted program given to ``times``.
-
-.. code:: ipython2
-
-    J('0 0 [0 swap [PE1.1.check PE1.1] direco] 466 [x [PE1.2] dip] times popop')
-
-
-.. parsed-literal::
-
-    233168
-
-
-Or using ``G`` we can write:
+Now we can add ``PE1.2`` to the quoted program given to ``G``.
 
 .. code:: ipython2
 
@@ -452,7 +370,7 @@ Or using ``G`` we can write:
 
 
 A generator for the Fibonacci Sequence.
-=======================================
+---------------------------------------
 
 Consider:
 
@@ -507,30 +425,31 @@ And therefore:
     [b+a b a F] [popdd over] infra
     [b b+a b F]
 
-And lastly:
+But we can just use ``cons`` to carry ``b+a`` into the quote:
 
 ::
 
-    [b b+a b F] uncons
-    b [b+a b F]
-
-Done.
+    [b a F] b+a [popdd over] cons infra
+    [b a F] [b+a popdd over]      infra
+    [b b+a b F]
 
-Putting it all together:
+Lastly:
 
 ::
 
-    F == + swons [popdd over] infra uncons
+    [b b+a b F] uncons
+    b [b+a b F]
 
-And:
+Putting it all together:
 
 ::
 
+    F == + [popdd over] cons infra uncons
     fib_gen == [1 1 F]
 
 .. code:: ipython2
 
-    define('fib == + swons [popdd over] infra uncons')
+    define('fib == + [popdd over] cons infra uncons')
 
 .. code:: ipython2
 
@@ -547,11 +466,12 @@ And:
 
 
 Project Euler Problem Two
-~~~~~~~~~~~~~~~~~~~~~~~~~
+-------------------------
 
 ::
 
-    By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.
+    By considering the terms in the Fibonacci sequence whose values do not exceed four million,
+    find the sum of the even-valued terms.
 
 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
@@ -669,7 +589,51 @@ Replace ``x`` with our new driver function ``PE2.2`` and start our
 
 
 How to compile these?
-=====================
+---------------------
 
 You would probably start with a special version of ``G``, and perhaps
 modifications to the default ``x``?
+
+An Interesting Variation
+------------------------
+
+.. code:: ipython2
+
+    define('codireco == cons dip rest cons')
+
+.. code:: ipython2
+
+    V('[0 [dup ++] codireco] x')
+
+
+.. parsed-literal::
+
+                                     . [0 [dup ++] codireco] x
+               [0 [dup ++] codireco] . x
+               [0 [dup ++] codireco] . 0 [dup ++] codireco
+             [0 [dup ++] codireco] 0 . [dup ++] codireco
+    [0 [dup ++] codireco] 0 [dup ++] . codireco
+    [0 [dup ++] codireco] 0 [dup ++] . cons dip rest cons
+    [0 [dup ++] codireco] [0 dup ++] . dip rest cons
+                                     . 0 dup ++ [0 [dup ++] codireco] rest cons
+                                   0 . dup ++ [0 [dup ++] codireco] rest cons
+                                 0 0 . ++ [0 [dup ++] codireco] rest cons
+                                 0 1 . [0 [dup ++] codireco] rest cons
+           0 1 [0 [dup ++] codireco] . rest cons
+             0 1 [[dup ++] codireco] . cons
+             0 [1 [dup ++] codireco] . 
+
+
+.. code:: ipython2
+
+    define('G == [codireco] cons cons')
+
+.. code:: ipython2
+
+    J('230 [dup ++] G 5 [x] times pop')
+
+
+.. parsed-literal::
+
+    230 231 232 233 234
+

diff --git a/docs/sphinx_docs/notebooks/index.rst b/docs/sphinx_docs/notebooks/index.rst
index 00fa66a..c5abc23 100644 (file)
--- a/docs/sphinx_docs/notebooks/index.rst
+++ b/docs/sphinx_docs/notebooks/index.rst
@@ -12,6 +12,7 @@ These essays are adapted from Jupyter notebooks.  I hope to have those hosted so
    Replacing
    Ordered_Binary_Trees
    Treestep
+   Generator Programs
    Newton-Raphson
    Quadratic
    NoUpdates

diff --git a/joy/library.py b/joy/library.py
index 98f44d8..3157dc8 100644 (file)
--- a/joy/library.py
+++ b/joy/library.py
@@ -1144,14 +1144,17 @@ def ifte(stack, expression, dictionary):
 @FunctionWrapper
 def cond(stack, expression, dictionary):
   '''
-  like a case statement; works by rewriting into a chain of ifte.
+  This combinator works like a case statement.  It expects a single quote
+  on the stack that must contain zero or more condition quotes and a 
+  default quote.  Each condition clause should contain a quoted predicate
+  followed by the function expression to run if that predicate returns
+  true.  If no predicates return true the default function runs.
 
-  [..[[Bi] Ti]..[D]] -> ...
+  It works by rewriting into a chain of nested `ifte` expressions, e.g.::
 
-
-        [[[B0] T0] [[B1] T1] [D]] cond
-  -----------------------------------------
-     [B0] [T0] [[B1] [T1] [D] ifte] ifte
+            [[[B0] T0] [[B1] T1] [D]] cond
+      -----------------------------------------
+         [B0] [T0] [[B1] [T1] [D] ifte] ifte
 
   '''
   conditions, stack = stack
@@ -1400,9 +1403,10 @@ def loop(stack, expression, dictionary):
 @inscribe
 @FunctionWrapper
 def cmp_(stack, expression, dictionary):
-    '''
-    cmp takes two values and three quoted programs on the stack and runs
-    one of the three depending on the results of comparing the two values:
+  '''
+  cmp takes two values and three quoted programs on the stack and runs
+  one of the three depending on the results of comparing the two values:
+  ::
 
            a b [G] [E] [L] cmp
         ------------------------- a > b
@@ -1415,10 +1419,10 @@ def cmp_(stack, expression, dictionary):
            a b [G] [E] [L] cmp
         ------------------------- a < b
                         L
-    '''
-    L, (E, (G, (b, (a, stack)))) = stack
-    expression = pushback(G if a > b else L if a < b else E, expression)
-    return stack, expression, dictionary
+  '''
+  L, (E, (G, (b, (a, stack)))) = stack
+  expression = pushback(G if a > b else L if a < b else E, expression)
+  return stack, expression, dictionary
 
 
 #def nullary(S, expression, dictionary):