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<header id="title-block-header">
-<h1 class="title">Function Reference</h1>
+<h1 class="title">Thun Function Reference</h1>
</header>
<nav id="TOC" role="doc-toc">
<ul>
-<li><a href="#section">&</a></li>
-<li><a href="#section-1">&&</a></li>
-<li><a href="#section-2">*</a></li>
-<li><a href="#section-3">•</a></li>
-<li><a href="#section-4">^</a></li>
-<li><a href="#section-5">=</a></li>
-<li><a href="#section-6">!=</a></li>
-<li><a href="#section-7">!-</a></li>
-<li><a href="#section-8">></a></li>
-<li><a href="#section-9">>=</a></li>
-<li><a href="#section-10">>></a></li>
-<li><a href="#section-11">-</a></li>
-<li><a href="#section-12">–</a></li>
-<li><a href="#section-13"><</a></li>
-<li><a href="#section-14"><=</a></li>
-<li><a href="#section-15"><></a></li>
-<li><a href="#section-16"><{}</a></li>
-<li><a href="#section-17"><<</a></li>
-<li><a href="#section-18"><<{}</a></li>
-<li><a href="#section-19">%</a></li>
-<li><a href="#section-20">+</a></li>
-<li><a href="#section-21">++</a></li>
-<li><a href="#section-22">?</a></li>
-<li><a href="#section-23">/</a></li>
-<li><a href="#section-24">//</a></li>
-<li><a href="#floor">/floor</a></li>
-<li><a href="#section-25">||</a></li>
<li><a href="#abs">abs</a></li>
<li><a href="#add">add</a></li>
+<li><a href="#section">&&</a></li>
+<li><a href="#section-1">&</a></li>
<li><a href="#anamorphism">anamorphism</a></li>
<li><a href="#and">and</a></li>
<li><a href="#app1">app1</a></li>
<li><a href="#app2">app2</a></li>
<li><a href="#app3">app3</a></li>
<li><a href="#appn">appN</a></li>
+<li><a href="#section-2">*</a></li>
<li><a href="#at">at</a></li>
<li><a href="#average">average</a></li>
-<li><a href="#b">b</a></li>
<li><a href="#binary">binary</a></li>
+<li><a href="#b">b</a></li>
<li><a href="#bool">bool</a></li>
<li><a href="#branch">branch</a></li>
+<li><a href="#section-3">•</a></li>
<li><a href="#ccccons">ccccons</a></li>
<li><a href="#ccons">ccons</a></li>
<li><a href="#choice">choice</a></li>
+<li><a href="#section-4">^</a></li>
<li><a href="#clear">clear</a></li>
<li><a href="#cleave">cleave</a></li>
<li><a href="#clop">clop</a></li>
<li><a href="#cond">cond</a></li>
<li><a href="#cons">cons</a></li>
<li><a href="#dinfrirst">dinfrirst</a></li>
-<li><a href="#dip">dip</a></li>
-<li><a href="#dipd">dipd</a></li>
<li><a href="#dipdd">dipdd</a></li>
+<li><a href="#dipd">dipd</a></li>
+<li><a href="#dip">dip</a></li>
<li><a href="#disenstacken">disenstacken</a></li>
<li><a href="#div">div</a></li>
<li><a href="#divmod">divmod</a></li>
<li><a href="#down_to_zero">down_to_zero</a></li>
<li><a href="#drop">drop</a></li>
-<li><a href="#dup">dup</a></li>
-<li><a href="#dupd">dupd</a></li>
<li><a href="#dupdd">dupdd</a></li>
-<li><a href="#dupdip">dupdip</a></li>
<li><a href="#dupdipd">dupdipd</a></li>
+<li><a href="#dupdip">dupdip</a></li>
+<li><a href="#dupd">dupd</a></li>
+<li><a href="#dup">dup</a></li>
<li><a href="#enstacken">enstacken</a></li>
<li><a href="#eq">eq</a></li>
+<li><a href="#section-5">=</a></li>
+<li><a href="#section-6">!=</a></li>
+<li><a href="#section-7">!-</a></li>
<li><a href="#first">first</a></li>
<li><a href="#first_two">first_two</a></li>
<li><a href="#flatten">flatten</a></li>
-<li><a href="#floor-1">floor</a></li>
<li><a href="#floordiv">floordiv</a></li>
+<li><a href="#floor">floor</a></li>
<li><a href="#fork">fork</a></li>
<li><a href="#fourth">fourth</a></li>
-<li><a href="#gcd">gcd</a></li>
<li><a href="#gcd2">gcd2</a></li>
+<li><a href="#gcd">gcd</a></li>
<li><a href="#ge">ge</a></li>
<li><a href="#genrec">genrec</a></li>
<li><a href="#getitem">getitem</a></li>
<li><a href="#grabn">grabN</a></li>
<li><a href="#grba">grba</a></li>
+<li><a href="#section-8">>=</a></li>
+<li><a href="#section-9">>></a></li>
+<li><a href="#section-10">></a></li>
<li><a href="#gt">gt</a></li>
<li><a href="#help">help</a></li>
+<li><a href="#section-11">–</a></li>
+<li><a href="#section-12">-</a></li>
<li><a href="#hypot">hypot</a></li>
-<li><a href="#i">i</a></li>
<li><a href="#id">id</a></li>
<li><a href="#ifte">ifte</a></li>
<li><a href="#ii">ii</a></li>
+<li><a href="#i">i</a></li>
<li><a href="#infra">infra</a></li>
<li><a href="#infrst">infrst</a></li>
<li><a href="#inscribe">inscribe</a></li>
<li><a href="#le">le</a></li>
+<li><a href="#section-13"><=</a></li>
+<li><a href="#section-14"><></a></li>
+<li><a href="#section-15"><{}</a></li>
+<li><a href="#section-16"><<{}</a></li>
+<li><a href="#section-17"><<</a></li>
+<li><a href="#section-18"><</a></li>
<li><a href="#loop">loop</a></li>
<li><a href="#lshift">lshift</a></li>
<li><a href="#lt">lt</a></li>
<li><a href="#mod">mod</a></li>
<li><a href="#modulus">modulus</a></li>
<li><a href="#mul">mul</a></li>
-<li><a href="#ne">ne</a></li>
<li><a href="#neg">neg</a></li>
+<li><a href="#ne">ne</a></li>
<li><a href="#not">not</a></li>
<li><a href="#nulco">nulco</a></li>
<li><a href="#nullary">nullary</a></li>
<li><a href="#or">or</a></li>
<li><a href="#over">over</a></li>
<li><a href="#pam">pam</a></li>
+<li><a href="#section-19">%</a></li>
<li><a href="#pick">pick</a></li>
+<li><a href="#section-20">+</a></li>
+<li><a href="#section-21">++</a></li>
<li><a href="#pm">pm</a></li>
-<li><a href="#pop">pop</a></li>
-<li><a href="#popd">popd</a></li>
<li><a href="#popdd">popdd</a></li>
-<li><a href="#popop">popop</a></li>
-<li><a href="#popopd">popopd</a></li>
+<li><a href="#popd">popd</a></li>
+<li><a href="#pop">pop</a></li>
<li><a href="#popopdd">popopdd</a></li>
+<li><a href="#popopd">popopd</a></li>
+<li><a href="#popop">popop</a></li>
<li><a href="#popopop">popopop</a></li>
<li><a href="#pow">pow</a></li>
<li><a href="#pred">pred</a></li>
<li><a href="#primrec">primrec</a></li>
<li><a href="#product">product</a></li>
+<li><a href="#section-22">?</a></li>
<li><a href="#quoted">quoted</a></li>
<li><a href="#range">range</a></li>
<li><a href="#range_to_zero">range_to_zero</a></li>
<li><a href="#reco">reco</a></li>
-<li><a href="#rem">rem</a></li>
<li><a href="#remainder">remainder</a></li>
+<li><a href="#rem">rem</a></li>
<li><a href="#remove">remove</a></li>
<li><a href="#rest">rest</a></li>
<li><a href="#reverse">reverse</a></li>
<li><a href="#rolldown">rolldown</a></li>
-<li><a href="#rollup">rollup</a></li>
<li><a href="#roll">roll></a></li>
<li><a href="#roll-1">roll<</a></li>
+<li><a href="#rollup">rollup</a></li>
<li><a href="#round">round</a></li>
<li><a href="#rrest">rrest</a></li>
<li><a href="#rshift">rshift</a></li>
<li><a href="#shift">shift</a></li>
<li><a href="#shunt">shunt</a></li>
<li><a href="#size">size</a></li>
+<li><a href="#floor-1">/floor</a></li>
+<li><a href="#section-23">/</a></li>
+<li><a href="#section-24">//</a></li>
<li><a href="#sort">sort</a></li>
<li><a href="#spiral_next">spiral_next</a></li>
<li><a href="#split_at">split_at</a></li>
<li><a href="#split_list">split_list</a></li>
<li><a href="#sqr">sqr</a></li>
<li><a href="#sqrt">sqrt</a></li>
-<li><a href="#stack">stack</a></li>
<li><a href="#stackd">stackd</a></li>
+<li><a href="#stack">stack</a></li>
<li><a href="#step">step</a></li>
<li><a href="#step_zero">step_zero</a></li>
<li><a href="#stuncons">stuncons</a></li>
<li><a href="#succ">succ</a></li>
<li><a href="#sum">sum</a></li>
<li><a href="#swaack">swaack</a></li>
-<li><a href="#swap">swap</a></li>
<li><a href="#swapd">swapd</a></li>
+<li><a href="#swap">swap</a></li>
<li><a href="#swoncat">swoncat</a></li>
<li><a href="#swons">swons</a></li>
<li><a href="#tailrec">tailrec</a></li>
<li><a href="#unit">unit</a></li>
<li><a href="#unquoted">unquoted</a></li>
<li><a href="#unswons">unswons</a></li>
+<li><a href="#section-25">||</a></li>
<li><a href="#void">void</a></li>
<li><a href="#warranty">warranty</a></li>
<li><a href="#while">while</a></li>
<li><a href="#zip">zip</a></li>
</ul>
</nav>
+<p><a href="/">Home</a></p>
<p>Version -10.0.0</p>
<p>Each function, combinator, or definition should be documented here.</p>
<hr />
-<h2 id="section">&</h2>
-<p>See <a href="#and">and</a>.</p>
+<h2 id="abs">abs</h2>
+<p>Function</p>
+<p>Return the absolute value of the argument.</p>
+<h3 id="definition">Definition</h3>
+<blockquote>
+<p><a href="#dup">dup</a> 0 < [] [<a href="#neg">neg</a>] <a href="#branch">branch</a></p>
+</blockquote>
+<hr />
+<h2 id="add">add</h2>
+<p>Basis Function</p>
+<p>Add two numbers together: a + b.</p>
<hr />
-<h2 id="section-1">&&</h2>
+<h2 id="section">&&</h2>
<p>Combinator</p>
<p>Short-circuiting Boolean AND</p>
<p>Accept two quoted programs, run the first and expect a Boolean value, if it’s <code>true</code> pop it and run the second program (which should also return a Boolean value) otherwise pop the second program (leaving <code>false</code> on the stack.)</p>
[A] [B] &&
---------------- false
false</code></pre>
-<h3 id="definition">Definition</h3>
+<h3 id="definition-1">Definition</h3>
<pre><code>nulco [nullary [false]] dip branch</code></pre>
<h3 id="derivation">Derivation</h3>
<p>TODO: this is derived in one of the notebooks I think, look it up and link to it, or copy the content here.</p>
<h3 id="crosslinks">Crosslinks</h3>
<p><a href="#section-25">||</a></p>
<hr />
-<h2 id="section-2">*</h2>
-<p>See <a href="#mul">mul</a>.</p>
-<hr />
-<h2 id="section-3">•</h2>
-<p>See <a href="#id">id</a>.</p>
-<hr />
-<h2 id="section-4">^</h2>
-<p>See <a href="#xor">xor</a>.</p>
-<hr />
-<h2 id="section-5">=</h2>
-<p>See <a href="#eq">eq</a>.</p>
-<hr />
-<h2 id="section-6">!=</h2>
-<p>See <a href="#ne">ne</a>.</p>
-<hr />
-<h2 id="section-7">!-</h2>
-<p>Function</p>
-<p>Not negative.</p>
-<pre><code> n !-
------------ n < 0
- false
-
-
- n !-
----------- n >= 0
- true</code></pre>
-<h3 id="definition-1">Definition</h3>
-<pre><code>0 \>=</code></pre>
-<h3 id="discussion-1">Discussion</h3>
-<p>Return a Boolean value indicating if a number is greater than or equal to zero.</p>
-<hr />
-<h2 id="section-8">></h2>
-<p>See <a href="#gt">gt</a>.</p>
-<hr />
-<h2 id="section-9">>=</h2>
-<p>See <a href="#ge">ge</a>.</p>
-<hr />
-<h2 id="section-10">>></h2>
-<p>See <a href="#rshift">rshift</a>.</p>
-<hr />
-<h2 id="section-11">-</h2>
-<p>See <a href="#sub">sub</a>.</p>
-<hr />
-<h2 id="section-12">–</h2>
-<p>See <a href="#pred">pred</a>.</p>
-<hr />
-<h2 id="section-13"><</h2>
-<p>See <a href="#lt">lt</a>.</p>
-<hr />
-<h2 id="section-14"><=</h2>
-<p>See <a href="#le">le</a>.</p>
-<hr />
-<h2 id="section-15"><></h2>
-<p>See <a href="#ne">ne</a>.</p>
-<hr />
-<h2 id="section-16"><{}</h2>
-<p>Function</p>
-<pre><code> ... a <{}
-----------------
- ... [] a</code></pre>
-<h3 id="definition-2">Definition</h3>
-<pre><code>[] swap</code></pre>
-<h3 id="discussion-2">Discussion</h3>
-<p>Tuck an empty list just under the first item on the stack.</p>
-<h3 id="crosslinks-1">Crosslinks</h3>
-<p><a href="#section-18"><<{}</a></p>
-<hr />
-<h2 id="section-17"><<</h2>
-<p>See <a href="#lshift">lshift</a>.</p>
-<hr />
-<h2 id="section-18"><<{}</h2>
-<p>Function</p>
-<pre><code> ... b a <{}
------------------
- ... [] b a</code></pre>
-<h3 id="definition-3">Definition</h3>
-<pre><code>[] rollup</code></pre>
-<h3 id="discussion-3">Discussion</h3>
-<p>Tuck an empty list just under the first two items on the stack.</p>
-<h3 id="crosslinks-2">Crosslinks</h3>
-<p><a href="#section-16"><{}</a></p>
-<hr />
-<h2 id="section-19">%</h2>
-<p>See <a href="#mod">mod</a>.</p>
-<hr />
-<h2 id="section-20">+</h2>
-<p>See <a href="#add">add</a>.</p>
-<hr />
-<h2 id="section-21">++</h2>
-<p>See <a href="#succ">succ</a>.</p>
-<hr />
-<h2 id="section-22">?</h2>
-<p>Function</p>
-<p>Is the item on the top of the stack “truthy”?</p>
-<h3 id="definition-4">Definition</h3>
-<blockquote>
-<p><a href="#dup">dup</a> <a href="#bool">bool</a></p>
-</blockquote>
-<h3 id="discussion-4">Discussion</h3>
-<p>You often want to test the truth value of an item on the stack without consuming the item.</p>
-<h3 id="crosslinks-3">Crosslinks</h3>
-<p><a href="#bool">bool</a></p>
-<hr />
-<h2 id="section-23">/</h2>
-<p>See <a href="#floordiv">floordiv</a>.</p>
-<hr />
-<h2 id="section-24">//</h2>
-<p>See <a href="#floordiv">floordiv</a>.</p>
-<hr />
-<h2 id="floor">/floor</h2>
-<p>See <a href="#floordiv">floordiv</a>.</p>
-<hr />
-<h2 id="section-25">||</h2>
-<p>Combinator</p>
-<p>Short-circuiting Boolean OR</p>
-<h3 id="definition-5">Definition</h3>
-<blockquote>
-<p><a href="#nulco">nulco</a> [<a href="#nullary">nullary</a>] <a href="#dip">dip</a> [true] <a href="#branch">branch</a></p>
-</blockquote>
-<h3 id="discussion-5">Discussion</h3>
-<p>Accept two quoted programs, run the first and expect a Boolean value, if it’s <code>false</code> pop it and run the second program (which should also return a Boolean value) otherwise pop the second program (leaving <code>true</code> on the stack.)</p>
-<pre><code> [A] [B] ||
----------------- A -> false
- B
-
-
- [A] [B] ||
----------------- A -> true
- true</code></pre>
-<h3 id="crosslinks-4">Crosslinks</h3>
-<p><a href="#section-1">&&</a></p>
-<hr />
-<h2 id="abs">abs</h2>
-<p>Function</p>
-<p>Return the absolute value of the argument.</p>
-<h3 id="definition-6">Definition</h3>
-<blockquote>
-<p><a href="#dup">dup</a> 0 < [] [<a href="#neg">neg</a>] <a href="#branch">branch</a></p>
-</blockquote>
-<hr />
-<h2 id="add">add</h2>
-<p>Basis Function</p>
-<p>Add two numbers together: a + b.</p>
+<h2 id="section-1">&</h2>
+<p>See <a href="#and">and</a>.</p>
<hr />
<h2 id="anamorphism">anamorphism</h2>
<p>Combinator</p>
<pre><code> [P] [G] anamorphism
-----------------------------------------
[P] [pop []] [G] [dip swons] genrec</code></pre>
-<h3 id="definition-7">Definition</h3>
+<h3 id="definition-2">Definition</h3>
<blockquote>
<p>[<a href="#pop">pop</a> []] <a href="#swap">swap</a> [<a href="#dip">dip</a> <a href="#swons">swons</a>] <a href="#genrec">genrec</a></p>
</blockquote>
<blockquote>
<p>[0 <=] [-- dup] anamorphism</p>
</blockquote>
-<h3 id="discussion-6">Discussion</h3>
+<h3 id="discussion-1">Discussion</h3>
<p>See the <a href="https://joypy.osdn.io/notebooks/Recursion_Combinators.html">Recursion Combinators notebook</a>.</p>
<hr />
<h2 id="and">and</h2>
<p>Basis Function</p>
<p>Logical bit-wise AND.</p>
-<h3 id="crosslinks-5">Crosslinks</h3>
+<h3 id="crosslinks-1">Crosslinks</h3>
<p><a href="#or">or</a> <a href="#xor">xor</a></p>
<hr />
<h2 id="app1">app1</h2>
---------------------------------
... [x ...] [Q] infra first</code></pre>
<p>This is the same effect as the <a href="#unary">unary</a> combinator.</p>
-<h3 id="definition-8">Definition</h3>
+<h3 id="definition-3">Definition</h3>
<blockquote>
<p><a href="#nullary">nullary</a> <a href="#popd">popd</a></p>
</blockquote>
-<h3 id="discussion-7">Discussion</h3>
+<h3 id="discussion-2">Discussion</h3>
<p>Just a specialization of <code>nullary</code> really. Its parallelizable cousins are more useful.</p>
-<h3 id="crosslinks-6">Crosslinks</h3>
+<h3 id="crosslinks-2">Crosslinks</h3>
<p><a href="#app2">app2</a> <a href="#app3">app3</a> <a href="#appN">appN</a> <a href="#unary">unary</a></p>
<hr />
<h2 id="app2">app2</h2>
-----------------------------------
... [y ...] [Q] . infra first
[x ...] [Q] infra first</code></pre>
-<h3 id="definition-9">Definition</h3>
+<h3 id="definition-4">Definition</h3>
<blockquote>
<p>[<a href="#grba">grba</a> <a href="#swap">swap</a> <a href="#grba">grba</a> <a href="#swap">swap</a>] <a href="#dip">dip</a> [<a href="#infrst">infrst</a>] <a href="#cons">cons</a> <a href="#ii">ii</a></p>
</blockquote>
-<h3 id="discussion-8">Discussion</h3>
+<h3 id="discussion-3">Discussion</h3>
<p>Unlike <a href="#app1">app1</a>, which is essentially an alias for <a href="#unary">unary</a>, this function is not the same as <a href="#binary">binary</a>. Instead of running one program using exactly two items from the stack and pushing one result (as <a href="#binary">binary</a> does) this function takes two items from the stack and runs the program twice, separately for each of the items, then puts both results onto the stack.</p>
<p>This is not currently implemented as parallel processes but it can (and should) be done.</p>
-<h3 id="crosslinks-7">Crosslinks</h3>
+<h3 id="crosslinks-3">Crosslinks</h3>
<p><a href="#app1">app1</a> <a href="#app3">app3</a> <a href="#appN">appN</a> <a href="#unary">unary</a></p>
<hr />
<h2 id="app3">app3</h2>
... [z ...] [Q] . infra first
[y ...] [Q] infra first
[x ...] [Q] infra first</code></pre>
-<h3 id="definition-10">Definition</h3>
+<h3 id="definition-5">Definition</h3>
<blockquote>
<p>3 <a href="#appn">appN</a></p>
</blockquote>
-<h3 id="discussion-9">Discussion</h3>
+<h3 id="discussion-4">Discussion</h3>
<p>See <a href="#app2">app2</a>.</p>
-<h3 id="crosslinks-8">Crosslinks</h3>
+<h3 id="crosslinks-4">Crosslinks</h3>
<p><a href="#app1">app1</a> <a href="#app2">app2</a> <a href="#appN">appN</a> <a href="#unary">unary</a></p>
<hr />
<h2 id="appn">appN</h2>
[x2 ...] [Q] infra first
[x1 ...] [Q] infra first
[x0 ...] [Q] infra first</code></pre>
-<h3 id="definition-11">Definition</h3>
+<h3 id="definition-6">Definition</h3>
<blockquote>
<p>[<a href="#grabn">grabN</a>] <a href="#codi">codi</a> <a href="#map">map</a> <a href="#disenstacken">disenstacken</a></p>
</blockquote>
-<h3 id="discussion-10">Discussion</h3>
+<h3 id="discussion-5">Discussion</h3>
<p>This function takes a quoted function <code>Q</code> and an integer and runs the function that many times on that many stack items. See also <a href="#app2">app2</a>.</p>
-<h3 id="crosslinks-9">Crosslinks</h3>
+<h3 id="crosslinks-5">Crosslinks</h3>
<p><a href="#app1">app1</a> <a href="#app2">app2</a> <a href="#app3">app3</a> <a href="#unary">unary</a></p>
<hr />
+<h2 id="section-2">*</h2>
+<p>See <a href="#mul">mul</a>.</p>
+<hr />
<h2 id="at">at</h2>
<p>See <a href="#getitem">getitem</a>.</p>
<hr />
<h2 id="average">average</h2>
<p>Function</p>
<p>Compute the average of a list of numbers. (Currently broken until I can figure out what to do about “numeric tower” in Thun.)</p>
-<h3 id="definition-12">Definition</h3>
+<h3 id="definition-7">Definition</h3>
<blockquote>
<p>[<a href="#sum">sum</a>] [<a href="#size">size</a>] <a href="#cleave">cleave</a> <a href="#section-23">/</a></p>
</blockquote>
-<h3 id="discussion-11">Discussion</h3>
+<h3 id="discussion-6">Discussion</h3>
<p>Theoretically this function would compute the sum and the size in two separate threads, then divide. This works but a compiled version would probably do better to sum and count the list once, in one thread, eh?</p>
<p>As an exercise in Functional Programming in Joy it would be fun to convert this into a catamorphism. See the <a href="https://joypy.osdn.io/notebooks/Recursion_Combinators.html">Recursion Combinators notebook</a>.</p>
<hr />
-<h2 id="b">b</h2>
-<p>Combinator</p>
-<p>Run two quoted programs</p>
-<pre><code> [P] [Q] b
----------------
- P Q</code></pre>
-<h3 id="definition-13">Definition</h3>
-<blockquote>
-<p>[<a href="#i">i</a>] <a href="#dip">dip</a> <a href="#i">i</a></p>
-</blockquote>
-<h3 id="discussion-12">Discussion</h3>
-<p>This combinator may seem trivial but it comes in handy.</p>
-<h3 id="crosslinks-10">Crosslinks</h3>
-<p><a href="#dupdip">dupdip</a> <a href="#ii">ii</a></p>
-<hr />
<h2 id="binary">binary</h2>
<p>Combinator</p>
<p>Run a quoted program using exactly two stack values and leave the first item of the result on the stack.</p>
<pre><code> ... y x [P] binary
-----------------------
... a</code></pre>
-<h3 id="definition-14">Definition</h3>
+<h3 id="definition-8">Definition</h3>
<blockquote>
<p><a href="#unary">unary</a> <a href="#popd">popd</a></p>
</blockquote>
-<h3 id="discussion-13">Discussion</h3>
+<h3 id="discussion-7">Discussion</h3>
<p>Runs any other quoted function and returns its first result while consuming exactly two items from the stack.</p>
-<h3 id="crosslinks-11">Crosslinks</h3>
+<h3 id="crosslinks-6">Crosslinks</h3>
<p><a href="#nullary">nullary</a> <a href="#ternary">ternary</a> <a href="#unary">unary</a></p>
<hr />
+<h2 id="b">b</h2>
+<p>Combinator</p>
+<p>Run two quoted programs</p>
+<pre><code> [P] [Q] b
+---------------
+ P Q</code></pre>
+<h3 id="definition-9">Definition</h3>
+<blockquote>
+<p>[<a href="#i">i</a>] <a href="#dip">dip</a> <a href="#i">i</a></p>
+</blockquote>
+<h3 id="discussion-8">Discussion</h3>
+<p>This combinator may seem trivial but it comes in handy.</p>
+<h3 id="crosslinks-7">Crosslinks</h3>
+<p><a href="#dupdip">dupdip</a> <a href="#ii">ii</a></p>
+<hr />
<h2 id="bool">bool</h2>
<p>Basis Function</p>
<p>Convert the item on the top of the stack to a Boolean value.</p>
-<h3 id="discussion-14">Discussion</h3>
+<h3 id="discussion-9">Discussion</h3>
<p>For integers 0 is <code>false</code> and any other number is <code>true</code>; for lists the empty list is <code>false</code> and all other lists are <code>true</code>.</p>
-<h3 id="crosslinks-12">Crosslinks</h3>
+<h3 id="crosslinks-8">Crosslinks</h3>
<p><a href="#not">not</a></p>
<hr />
<h2 id="branch">branch</h2>
true [F] [T] branch
-------------------------
T</code></pre>
-<h3 id="definition-15">Definition</h3>
+<h3 id="definition-10">Definition</h3>
<blockquote>
<p><a href="#rolldown">rolldown</a> <a href="#choice">choice</a> <a href="#i">i</a></p>
</blockquote>
-<h3 id="discussion-15">Discussion</h3>
+<h3 id="discussion-10">Discussion</h3>
<p>This is one of the fundamental operations (although it can be defined in terms of <a href="#choice">choice</a> as above). The more common “if..then..else” construct <a href="#ifte">ifte</a> adds a predicate function that is evaluated <a href="#nullary">nullary</a>.</p>
-<h3 id="crosslinks-13">Crosslinks</h3>
+<h3 id="crosslinks-9">Crosslinks</h3>
<p><a href="#choice">choice</a> <a href="#ifte">ifte</a> <a href="#select">select</a></p>
<hr />
+<h2 id="section-3">•</h2>
+<p>See <a href="#id">id</a>.</p>
+<hr />
<h2 id="ccccons">ccccons</h2>
<p>Function</p>
<pre><code> a b c d [...] ccccons
---------------------------
[a b c d ...]</code></pre>
<p>Do <a href="#cons">cons</a> four times.</p>
-<h3 id="definition-16">Definition</h3>
+<h3 id="definition-11">Definition</h3>
<blockquote>
<p><a href="#ccons">ccons</a> <a href="#ccons">ccons</a></p>
</blockquote>
-<h3 id="crosslinks-14">Crosslinks</h3>
+<h3 id="crosslinks-10">Crosslinks</h3>
<p><a href="#ccons">ccons</a> <a href="#cons">cons</a> <a href="#times">times</a></p>
<hr />
<h2 id="ccons">ccons</h2>
---------------------
[a b ...]</code></pre>
<p>Do <a href="#cons">cons</a> two times.</p>
-<h3 id="definition-17">Definition</h3>
+<h3 id="definition-12">Definition</h3>
<blockquote>
<p><a href="#cons">cons</a> <a href="#cons">cons</a></p>
</blockquote>
-<h3 id="crosslinks-15">Crosslinks</h3>
+<h3 id="crosslinks-11">Crosslinks</h3>
<p><a href="#cons">cons</a> <a href="#ccons">ccons</a></p>
<hr />
<h2 id="choice">choice</h2>
a b true choice
---------------------
b</code></pre>
-<h3 id="definition-18">Definition</h3>
+<h3 id="definition-13">Definition</h3>
<blockquote>
<p>[<a href="#pop">pop</a>] [<a href="#popd">popd</a>] <a href="#branch">branch</a></p>
</blockquote>
-<h3 id="discussion-16">Discussion</h3>
+<h3 id="discussion-11">Discussion</h3>
<p>It’s a matter of taste whether you implement this in terms of <a href="#branch">branch</a> or the other way around.</p>
-<h3 id="crosslinks-16">Crosslinks</h3>
+<h3 id="crosslinks-12">Crosslinks</h3>
<p><a href="#branch">branch</a> <a href="#select">select</a></p>
<hr />
+<h2 id="section-4">^</h2>
+<p>See <a href="#xor">xor</a>.</p>
+<hr />
<h2 id="clear">clear</h2>
<p>Basis Function</p>
<p>Clear everything from the stack.</p>
-<h3 id="definition-19">Definition</h3>
+<h3 id="definition-14">Definition</h3>
<blockquote>
<p><a href="#stack">stack</a> <a href="#bool">bool</a> [<a href="#pop">pop</a> <a href="#stack">stack</a> <a href="#bool">bool</a>] <a href="#loop">loop</a></p>
</blockquote>
-<h3 id="crosslinks-17">Crosslinks</h3>
+<h3 id="crosslinks-13">Crosslinks</h3>
<p><a href="#stack">stack</a> <a href="#swaack">swaack</a></p>
<hr />
<h2 id="cleave">cleave</h2>
<pre><code> 1 2 3 [+] [-] cleave
--------------------------
1 2 5 -1</code></pre>
-<h3 id="discussion-17">Discussion</h3>
+<h3 id="discussion-12">Discussion</h3>
<p>One of a handful of useful parallel combinators.</p>
-<h3 id="crosslinks-18">Crosslinks</h3>
+<h3 id="crosslinks-14">Crosslinks</h3>
<p><a href="#clop">clop</a> <a href="#fork">fork</a> <a href="#map">map</a></p>
<hr />
<h2 id="clop">clop</h2>
<pre><code> ... x y [A] [B] clop
--------------------------
... a b</code></pre>
-<h3 id="definition-20">Definition</h3>
+<h3 id="definition-15">Definition</h3>
<blockquote>
<p><a href="#cleave">cleave</a> <a href="#popdd">popdd</a></p>
</blockquote>
-<h3 id="discussion-18">Discussion</h3>
+<h3 id="discussion-13">Discussion</h3>
<p>Like <a href="#cleave">cleave</a> but consumes an additional item from the stack.</p>
<pre><code> 1 2 3 4 [+] [-] clop
--------------------------
1 2 7 -1</code></pre>
-<h3 id="crosslinks-19">Crosslinks</h3>
+<h3 id="crosslinks-15">Crosslinks</h3>
<p><a href="#cleave">cleave</a> <a href="#fork">fork</a> <a href="#map">map</a></p>
<hr />
<h2 id="cmp">cmp</h2>
a b [G] [E] [L] cmp
------------------------- a < b
L</code></pre>
-<h3 id="discussion-19">Discussion</h3>
-<p>This is useful sometimes, and you can <a href="#dup">dup</a> or <a href="#dupd">dupd</a> with two quoted programs to handle the cases when you just want to deal with <a href="#section-14"><=</a> or <a href="#section-9">>=</a> and not all three possibilities, e.g.:</p>
+<h3 id="discussion-14">Discussion</h3>
+<p>This is useful sometimes, and you can <a href="#dup">dup</a> or <a href="#dupd">dupd</a> with two quoted programs to handle the cases when you just want to deal with <a href="#section-13"><=</a> or <a href="#section-8">>=</a> and not all three possibilities, e.g.:</p>
<pre><code>[G] [EL] dup cmp
[GE] [L] dupd cmp</code></pre>
<p>Or even:</p>
<pre><code>[GL] [E] over cmp</code></pre>
-<h3 id="crosslinks-20">Crosslinks</h3>
+<h3 id="crosslinks-16">Crosslinks</h3>
<p>TODO: link to tree notebooks where this was used.</p>
<hr />
<h2 id="codi">codi</h2>
<pre><code> a b [F] . codi
--------------------
b . F a</code></pre>
-<h3 id="definition-21">Definition</h3>
+<h3 id="definition-16">Definition</h3>
<blockquote>
<p><a href="#cons">cons</a> <a href="#dip">dip</a></p>
</blockquote>
-<h3 id="discussion-20">Discussion</h3>
+<h3 id="discussion-15">Discussion</h3>
<p>This is one of those weirdly specific functions that turns out to be useful in a few places.</p>
-<h3 id="crosslinks-21">Crosslinks</h3>
+<h3 id="crosslinks-17">Crosslinks</h3>
<p><a href="#appn">appN</a> <a href="#codireco">codireco</a></p>
<hr />
<h2 id="codireco">codireco</h2>
<p>Combinator</p>
<p>This is part of the <a href="#make_generator">make_generator</a> function. You would not use this combinator directly.</p>
-<h3 id="definition-22">Definition</h3>
+<h3 id="definition-17">Definition</h3>
<blockquote>
<p><a href="#codi">codi</a> <a href="#reco">reco</a></p>
</blockquote>
-<h3 id="discussion-21">Discussion</h3>
+<h3 id="discussion-16">Discussion</h3>
<p>See <a href="#make_generator">make_generator</a> and the <a href="https://joypy.osdn.io/notebooks/Generator_Programs.html#an-interesting-variation">“Using <code>x</code> to Generate Values” notebook</a> as well as <a href="https://www.kevinalbrecht.com/code/joy-mirror/j05cmp.html">Recursion Theory and Joy</a> by Manfred von Thun.</p>
-<h3 id="crosslinks-22">Crosslinks</h3>
+<h3 id="crosslinks-18">Crosslinks</h3>
<p><a href="#make_generator">make_generator</a></p>
<hr />
<h2 id="concat">concat</h2>
<pre><code> [a b c] [d e f] concat
----------------------------
[a b c d e f]</code></pre>
-<h3 id="crosslinks-23">Crosslinks</h3>
+<h3 id="crosslinks-19">Crosslinks</h3>
<p><a href="#first">first</a> <a href="#first_two">first_two</a> <a href="#flatten">flatten</a> <a href="#fourth">fourth</a> <a href="#getitem">getitem</a> <a href="#remove">remove</a> <a href="#rest">rest</a> <a href="#reverse">reverse</a> <a href="#rrest">rrest</a> <a href="#second">second</a> <a href="#shift">shift</a> <a href="#shunt">shunt</a> <a href="#size">size</a> <a href="#sort">sort</a> <a href="#split_at">split_at</a> <a href="#split_list">split_list</a> <a href="#swaack">swaack</a> <a href="#third">third</a> <a href="#zip">zip</a></p>
<hr />
<h2 id="cond">cond</h2>
[Default]
]
cond</code></pre>
-<h3 id="discussion-22">Discussion</h3>
+<h3 id="discussion-17">Discussion</h3>
<p>It works by rewriting into a chain of nested <span class="title-ref">ifte</span> expressions, e.g.:</p>
<pre><code> [[[B0] T0] [[B1] T1] [D]] cond
-----------------------------------------
[B0] [T0] [[B1] [T1] [D] ifte] ifte</code></pre>
-<h3 id="crosslinks-24">Crosslinks</h3>
+<h3 id="crosslinks-20">Crosslinks</h3>
<p><a href="#ifte">ifte</a></p>
<hr />
<h2 id="cons">cons</h2>
<pre><code> a [...] cons
------------------
[a ...]</code></pre>
-<h3 id="discussion-23">Discussion</h3>
+<h3 id="discussion-18">Discussion</h3>
<p>Cons is a <a href="https://en.wikipedia.org/wiki/Cons#Lists">venerable old function from Lisp</a>. Its inverse operation is <a href="#uncons">uncons</a>.</p>
-<h3 id="crosslinks-25">Crosslinks</h3>
+<h3 id="crosslinks-21">Crosslinks</h3>
<p><a href="#uncons">uncons</a></p>
<hr />
<h2 id="dinfrirst">dinfrirst</h2>
<p>Combinator</p>
<p>Specialist function (that means I forgot what it does and why.)</p>
-<h3 id="definition-23">Definition</h3>
+<h3 id="definition-18">Definition</h3>
<blockquote>
<p><a href="#dip">dip</a> <a href="#infrst">infrst</a></p>
</blockquote>
<hr />
-<h2 id="dip">dip</h2>
-<p>Basis Combinator</p>
-<p>The <code>dip</code> combinator expects a quoted program on the stack and below it some item, it hoists the item into the expression and runs the program on the rest of the stack.</p>
-<pre><code> ... x [Q] . dip
----------------------
- ... . Q x</code></pre>
-<h3 id="discussion-24">Discussion</h3>
-<p>This along with <a href="#infra">infra</a> are enough to update any datastructure. See the <a href="https://joypy.osdn.io/notebooks/Zipper.html">“Traversing Datastructures with Zippers” notebook</a>.</p>
-<p>Note that the item that was on the top of the stack (<code>x</code> in the example above) will not be treated specially by the interpreter when it is reached again. This is something of a footgun. My advice is to avoid putting bare unquoted symbols onto the stack, but then you can’t use symbols as “atoms” and also use <code>dip</code> and <code>infra</code> to operate on compound datastructures with atoms in them. This is a kind of side-effect of the Continuation-Passing Style. The <code>dip</code> combinator could “set aside” the item and replace it after running <code>Q</code> but that means that there is an “extra space” where the item resides while <code>Q</code> runs. One of the nice things about CPS is that the whole state is recorded in the stack and pending expression (not counting modifications to the dictionary.)</p>
-<h3 id="crosslinks-26">Crosslinks</h3>
-<p><a href="#dipd">dipd</a> <a href="#dipdd">dipdd</a> <a href="#dupdip">dupdip</a> <a href="#dupdipd">dupdipd</a> <a href="#infra">infra</a></p>
-<hr />
-<h2 id="dipd">dipd</h2>
-<p>Combinator</p>
-<p>Like <a href="#dip">dip</a> but expects two items.</p>
-<pre><code> ... y x [Q] . dipd
--------------------------
- ... . Q y x</code></pre>
-<h3 id="discussion-25">Discussion</h3>
-<p>See <a href="#dip">dip</a>.</p>
-<h3 id="crosslinks-27">Crosslinks</h3>
-<p><a href="#dip">dip</a> <a href="#dipdd">dipdd</a> <a href="#dupdip">dupdip</a> <a href="#dupdipd">dupdipd</a> <a href="#infra">infra</a></p>
-<hr />
<h2 id="dipdd">dipdd</h2>
<p>Combinator</p>
<p>Like <a href="#dip">dip</a> but expects three items. :</p>
<pre><code> ... z y x [Q] . dip
-----------------------------
... . Q z y x</code></pre>
-<h3 id="discussion-26">Discussion</h3>
+<h3 id="discussion-19">Discussion</h3>
<p>See <a href="#dip">dip</a>.</p>
-<h3 id="crosslinks-28">Crosslinks</h3>
+<h3 id="crosslinks-22">Crosslinks</h3>
<p><a href="#dip">dip</a> <a href="#dipd">dipd</a> <a href="#dupdip">dupdip</a> <a href="#dupdipd">dupdipd</a> <a href="#infra">infra</a></p>
<hr />
+<h2 id="dipd">dipd</h2>
+<p>Combinator</p>
+<p>Like <a href="#dip">dip</a> but expects two items.</p>
+<pre><code> ... y x [Q] . dipd
+-------------------------
+ ... . Q y x</code></pre>
+<h3 id="discussion-20">Discussion</h3>
+<p>See <a href="#dip">dip</a>.</p>
+<h3 id="crosslinks-23">Crosslinks</h3>
+<p><a href="#dip">dip</a> <a href="#dipdd">dipdd</a> <a href="#dupdip">dupdip</a> <a href="#dupdipd">dupdipd</a> <a href="#infra">infra</a></p>
+<hr />
+<h2 id="dip">dip</h2>
+<p>Basis Combinator</p>
+<p>The <code>dip</code> combinator expects a quoted program on the stack and below it some item, it hoists the item into the expression and runs the program on the rest of the stack.</p>
+<pre><code> ... x [Q] . dip
+---------------------
+ ... . Q x</code></pre>
+<h3 id="discussion-21">Discussion</h3>
+<p>This along with <a href="#infra">infra</a> are enough to update any datastructure. See the <a href="https://joypy.osdn.io/notebooks/Zipper.html">“Traversing Datastructures with Zippers” notebook</a>.</p>
+<p>Note that the item that was on the top of the stack (<code>x</code> in the example above) will not be treated specially by the interpreter when it is reached again. This is something of a footgun. My advice is to avoid putting bare unquoted symbols onto the stack, but then you can’t use symbols as “atoms” and also use <code>dip</code> and <code>infra</code> to operate on compound datastructures with atoms in them. This is a kind of side-effect of the Continuation-Passing Style. The <code>dip</code> combinator could “set aside” the item and replace it after running <code>Q</code> but that means that there is an “extra space” where the item resides while <code>Q</code> runs. One of the nice things about CPS is that the whole state is recorded in the stack and pending expression (not counting modifications to the dictionary.)</p>
+<h3 id="crosslinks-24">Crosslinks</h3>
+<p><a href="#dipd">dipd</a> <a href="#dipdd">dipdd</a> <a href="#dupdip">dupdip</a> <a href="#dupdipd">dupdipd</a> <a href="#infra">infra</a></p>
+<hr />
<h2 id="disenstacken">disenstacken</h2>
<p>Function</p>
<p>The <code>disenstacken</code> function expects a list on top of the stack and makes that the stack discarding the rest of the stack.</p>
<pre><code> 1 2 3 [4 5 6] disenstacken
--------------------------------
6 5 4</code></pre>
-<h3 id="definition-24">Definition</h3>
+<h3 id="definition-19">Definition</h3>
<blockquote>
<p>[<a href="#clear">clear</a>] <a href="#dip">dip</a> <a href="#reverse">reverse</a> <a href="#unstack">unstack</a></p>
</blockquote>
-<h3 id="discussion-27">Discussion</h3>
+<h3 id="discussion-22">Discussion</h3>
<p>Note that the order of the list is not changed, it just looks that way because the stack is printed with the top on the right while lists are printed with the top or head on the left.</p>
-<h3 id="crosslinks-29">Crosslinks</h3>
+<h3 id="crosslinks-25">Crosslinks</h3>
<p><a href="#enstacken">enstacken</a> <a href="#stack">stack</a> <a href="#unstack">unstack</a></p>
<hr />
<h2 id="div">div</h2>
q r
(x/y) (x%y)</code></pre>
<p>Invariant: <code>qy + r = x</code>.</p>
-<h3 id="definition-25">Definition</h3>
+<h3 id="definition-20">Definition</h3>
<blockquote>
<p>[<a href="#floordiv">floordiv</a>] [<a href="#mod">mod</a>] <a href="#clop">clop</a></p>
</blockquote>
<pre><code> 3 down_to_zero
--------------------
3 2 1 0</code></pre>
-<h3 id="definition-26">Definition</h3>
+<h3 id="definition-21">Definition</h3>
<blockquote>
-<p>[0 >] [<a href="#dup">dup</a> <a href="#section-1
2">–</a>] <a href="#while">while</a></p>
+<p>[0 >] [<a href="#dup">dup</a> <a href="#section-1
1">–</a>] <a href="#while">while</a></p>
</blockquote>
-<h3 id="crosslinks-30">Crosslinks</h3>
+<h3 id="crosslinks-26">Crosslinks</h3>
<p><a href="#range">range</a></p>
<hr />
<h2 id="drop">drop</h2>
<pre><code> [a b c d] 2 drop
----------------------
[c d]</code></pre>
-<h3 id="definition-27">Definition</h3>
+<h3 id="definition-22">Definition</h3>
<blockquote>
<p>[<a href="#rest">rest</a>] <a href="#times">times</a></p>
</blockquote>
-<h3 id="crosslinks-31">Crosslinks</h3>
+<h3 id="crosslinks-27">Crosslinks</h3>
<p><a href="#take">take</a></p>
<hr />
-<h2 id="dup">dup</h2>
-<p>Basis Function</p>
-<p>“Dup”licate the top item on the stack.</p>
-<pre><code> a dup
------------
- a a</code></pre>
-<h3 id="crosslinks-32">Crosslinks</h3>
-<p><a href="#dupd">dupd</a> <a href="#dupdd">dupdd</a> <a href="#dupdip">dupdip</a> <a href="#dupdipd">dupdipd</a></p>
-<hr />
-<h2 id="dupd">dupd</h2>
-<p>Function</p>
-<p><a href="#dup">dup</a> the second item down on the stack.</p>
-<pre><code> a b dupd
---------------
- a a b</code></pre>
-<h3 id="definition-28">Definition</h3>
-<blockquote>
-<p>[<a href="#dup">dup</a>] <a href="#dip">dip</a></p>
-</blockquote>
-<h3 id="crosslinks-33">Crosslinks</h3>
-<p><a href="#dup">dup</a> <a href="#dupdd">dupdd</a> <a href="#dupdip">dupdip</a> <a href="#dupdipd">dupdipd</a></p>
-<hr />
<h2 id="dupdd">dupdd</h2>
<p>Function</p>
<p><a href="#dup">dup</a> the third item down on the stack.</p>
<pre><code> a b c dupdd
-----------------
a a b c</code></pre>
-<h3 id="definition-29">Definition</h3>
+<h3 id="definition-23">Definition</h3>
<blockquote>
<p>[<a href="#dup">dup</a>] <a href="#dipd">dipd</a></p>
</blockquote>
-<h3 id="crosslinks-34">Crosslinks</h3>
+<h3 id="crosslinks-28">Crosslinks</h3>
<p><a href="#dup">dup</a> <a href="#dupd">dupd</a> <a href="#dupdip">dupdip</a> <a href="#dupdipd">dupdipd</a></p>
<hr />
+<h2 id="dupdipd">dupdipd</h2>
+<p>Combinator</p>
+<p>Run a copy of program <code>F</code> under the next item down on the stack.</p>
+<pre><code> a [F] dupdipd
+-------------------
+ F a [F]</code></pre>
+<h3 id="definition-24">Definition</h3>
+<blockquote>
+<p><a href="#dup">dup</a> <a href="#dipd">dipd</a></p>
+</blockquote>
+<h3 id="crosslinks-29">Crosslinks</h3>
+<p><a href="#dupdip">dupdip</a></p>
+<hr />
<h2 id="dupdip">dupdip</h2>
<p>Combinator</p>
<p>Apply a function <code>F</code> and <a href="#dup">dup</a> the item under it on the stack.</p>
<pre><code> a [F] dupdip
------------------
a F a</code></pre>
-<h3 id="definition-30">Definition</h3>
+<h3 id="definition-25">Definition</h3>
<blockquote>
<p><a href="#dupd">dupd</a> <a href="#dip">dip</a></p>
</blockquote>
a dup [F] dip
a a [F] dip
a F a</code></pre>
-<h3 id="discussion-28">Discussion</h3>
+<h3 id="discussion-23">Discussion</h3>
<p>A very common and useful combinator.</p>
-<h3 id="crosslinks-35">Crosslinks</h3>
+<h3 id="crosslinks-30">Crosslinks</h3>
<p><a href="#dupdipd">dupdipd</a></p>
<hr />
-<h2 id="dupdipd">dupdipd</h2>
-<p>Combinator</p>
-<p>Run a copy of program <code>F</code> under the next item down on the stack.</p>
-<pre><code> a [F] dupdipd
--------------------
- F a [F]</code></pre>
-<h3 id="definition-31">Definition</h3>
+<h2 id="dupd">dupd</h2>
+<p>Function</p>
+<p><a href="#dup">dup</a> the second item down on the stack.</p>
+<pre><code> a b dupd
+--------------
+ a a b</code></pre>
+<h3 id="definition-26">Definition</h3>
<blockquote>
-<p><a href="#dup">dup</a> <a href="#dipd">dipd</a></p>
+<p>[<a href="#dup">dup</a>] <a href="#dip">dip</a></p>
</blockquote>
-<h3 id="crosslinks-36">Crosslinks</h3>
-<p><a href="#dupdip">dupdip</a></p>
+<h3 id="crosslinks-31">Crosslinks</h3>
+<p><a href="#dup">dup</a> <a href="#dupdd">dupdd</a> <a href="#dupdip">dupdip</a> <a href="#dupdipd">dupdipd</a></p>
+<hr />
+<h2 id="dup">dup</h2>
+<p>Basis Function</p>
+<p>“Dup”licate the top item on the stack.</p>
+<pre><code> a dup
+-----------
+ a a</code></pre>
+<h3 id="crosslinks-32">Crosslinks</h3>
+<p><a href="#dupd">dupd</a> <a href="#dupdd">dupdd</a> <a href="#dupdip">dupdip</a> <a href="#dupdipd">dupdipd</a></p>
<hr />
<h2 id="enstacken">enstacken</h2>
<p>Function</p>
<pre><code> ... a b c enstacken
-------------------------
[c b a ...]</code></pre>
-<h3 id="definition-32">Definition</h3>
+<h3 id="definition-27">Definition</h3>
<blockquote>
<p><a href="#stack">stack</a> [<a href="#clear">clear</a>] <a href="#dip">dip</a></p>
</blockquote>
-<h3 id="discussion-29">Discussion</h3>
+<h3 id="discussion-24">Discussion</h3>
<p>This is a destructive version of <a href="#stack">stack</a>. See the note under <a href="#disenstacken">disenstacken</a> about the apparent but illusory reversal of the stack.</p>
-<h3 id="crosslinks-37">Crosslinks</h3>
+<h3 id="crosslinks-33">Crosslinks</h3>
<p><a href="#stack">stack</a> [unstack] <a href="#disenstacken">disenstacken</a></p>
<hr />
<h2 id="eq">eq</h2>
-------------
Boolean
(a = b)</code></pre>
-<h3 id="crosslinks-38">Crosslinks</h3>
+<h3 id="crosslinks-34">Crosslinks</h3>
<p><a href="#cmp">cmp</a> <a href="#ge">ge</a> <a href="#gt">gt</a> <a href="#le">le</a> <a href="#lt">lt</a> <a href="#ne">ne</a></p>
<hr />
+<h2 id="section-5">=</h2>
+<p>See <a href="#eq">eq</a>.</p>
+<hr />
+<h2 id="section-6">!=</h2>
+<p>See <a href="#ne">ne</a>.</p>
+<hr />
+<h2 id="section-7">!-</h2>
+<p>Function</p>
+<p>Not negative.</p>
+<pre><code> n !-
+----------- n < 0
+ false
+
+
+ n !-
+---------- n >= 0
+ true</code></pre>
+<h3 id="definition-28">Definition</h3>
+<pre><code>0 \>=</code></pre>
+<h3 id="discussion-25">Discussion</h3>
+<p>Return a Boolean value indicating if a number is greater than or equal to zero.</p>
+<hr />
<h2 id="first">first</h2>
<p>Function</p>
<p>Replace a list with its first item.</p>
<pre><code> [a ...]
--------------
a</code></pre>
-<h3 id="definition-33">Definition</h3>
+<h3 id="definition-29">Definition</h3>
<blockquote>
<p><a href="#uncons">uncons</a> <a href="#pop">pop</a></p>
</blockquote>
-<h3 id="crosslinks-39">Crosslinks</h3>
+<h3 id="crosslinks-35">Crosslinks</h3>
<p><a href="#second">second</a> <a href="#third">third</a> <a href="#fourth">fourth</a> <a href="#rest">rest</a></p>
<hr />
<h2 id="first_two">first_two</h2>
<pre><code> [a b ...] first_two
-------------------------
a b</code></pre>
-<h3 id="definition-34">Definition</h3>
+<h3 id="definition-30">Definition</h3>
<blockquote>
<p><a href="#uncons">uncons</a> <a href="#first">first</a></p>
</blockquote>
-<h3 id="crosslinks-40">Crosslinks</h3>
+<h3 id="crosslinks-36">Crosslinks</h3>
<p><a href="#first">first</a> <a href="#second">second</a> <a href="#third">third</a> <a href="#fourth">fourth</a> <a href="#rest">rest</a></p>
<hr />
<h2 id="flatten">flatten</h2>
<pre><code> [[1 2] [3 [4] 5] [6 7]] flatten
-------------------------------------
[1 2 3 [4] 5 6 7]</code></pre>
-<h3 id="definition-35">Definition</h3>
+<h3 id="definition-31">Definition</h3>
<blockquote>
-<p><a href="#section-1
6"><{}</a> [<a href="#concat">concat</a>] <a href="#step">step</a></p>
+<p><a href="#section-1
5"><{}</a> [<a href="#concat">concat</a>] <a href="#step">step</a></p>
</blockquote>
-<h3 id="discussion-30">Discussion</h3>
+<h3 id="discussion-26">Discussion</h3>
<p>Note that only one “level” of lists is flattened. In the example above <code>[4]</code> is not unquoted.</p>
-<h3 id="crosslinks-41">Crosslinks</h3>
+<h3 id="crosslinks-37">Crosslinks</h3>
<p><a href="#concat">concat</a> <a href="#first">first</a> <a href="#first_two">first_two</a> <a href="#fourth">fourth</a> <a href="#getitem">getitem</a> <a href="#remove">remove</a> <a href="#rest">rest</a> <a href="#reverse">reverse</a> <a href="#rrest">rrest</a> <a href="#second">second</a> <a href="#shift">shift</a> <a href="#shunt">shunt</a> <a href="#size">size</a> <a href="#sort">sort</a> <a href="#split_at">split_at</a> <a href="#split_list">split_list</a> <a href="#swaack">swaack</a> <a href="#third">third</a> <a href="#zip">zip</a></p>
<hr />
-<h2 id="floor-1">floor</h2>
-<p>Basis Function</p>
-<p>Return the largest integer <= x.</p>
-<h3 id="discussion-31">Discussion</h3>
-<p>This function doesn’t make sense (yet) to have because there are (as yet) only integers in the system.</p>
-<hr />
<h2 id="floordiv">floordiv</h2>
<p>Basis Function</p>
<p>I don’t know why this is called “floor” div, I think it rounds its result down (not towards zero or up.)</p>
<pre><code> a b floordiv
------------------
(a/b)</code></pre>
-<h3 id="discussion-32">Discussion</h3>
+<h3 id="discussion-27">Discussion</h3>
<p>All the division commands need to be revisited when the “numeric tower” for Thun gets nailed down.</p>
-<h3 id="crosslinks-42">Crosslinks</h3>
+<h3 id="crosslinks-38">Crosslinks</h3>
<p><a href="#divmod">divmod</a></p>
<hr />
+<h2 id="floor">floor</h2>
+<p>Basis Function</p>
+<p>Return the largest integer <= x.</p>
+<h3 id="discussion-28">Discussion</h3>
+<p>This function doesn’t make sense (yet) to have because there are (as yet) only integers in the system.</p>
+<hr />
<h2 id="fork">fork</h2>
<p>Combinator</p>
<p>Run two quoted programs in parallel and replace them with their results.</p>
<pre><code> ... [F] [G] fork
----------------------
... f g</code></pre>
-<h3 id="definition-36">Definition</h3>
+<h3 id="definition-32">Definition</h3>
<blockquote>
<p>[<a href="#i">i</a>] <a href="#app2">app2</a></p>
</blockquote>
-<h3 id="discussion-33">Discussion</h3>
+<h3 id="discussion-29">Discussion</h3>
<p>The basic parallelism combinator, the two programs are run independently.</p>
-<h3 id="crosslinks-43">Crosslinks</h3>
+<h3 id="crosslinks-39">Crosslinks</h3>
<p><a href="#cleave">cleave</a> <a href="#clop">clop</a> <a href="#map">map</a></p>
<hr />
<h2 id="fourth">fourth</h2>
<pre><code> [a b c d ...] fourth
--------------------------
d</code></pre>
-<h3 id="definition-37">Definition</h3>
+<h3 id="definition-33">Definition</h3>
<blockquote>
<p><a href="#rest">rest</a> <a href="#third">third</a></p>
</blockquote>
-<h3 id="crosslinks-44">Crosslinks</h3>
+<h3 id="crosslinks-40">Crosslinks</h3>
<p><a href="#first">first</a> <a href="#second">second</a> <a href="#third">third</a> <a href="#rest">rest</a></p>
<hr />
+<h2 id="gcd2">gcd2</h2>
+<p>Function</p>
+<p>Compiled GCD function.</p>
+<h3 id="discussion-30">Discussion</h3>
+<p>See <a href="#gcd">gcd</a>.</p>
+<h3 id="crosslinks-41">Crosslinks</h3>
+<p><a href="#gcd">gcd</a></p>
+<hr />
<h2 id="gcd">gcd</h2>
<p>Function</p>
<p>Take two integers from the stack and replace them with their Greatest Common Denominator.</p>
-<h3 id="definition-38">Definition</h3>
+<h3 id="definition-34">Definition</h3>
<blockquote>
-<p>true [<a href="#tuck">tuck</a> <a href="#mod">mod</a> <a href="#dup">dup</a> 0 <a href="#section-
8">></a>] <a href="#loop">loop</a> <a href="#pop">pop</a></p>
+<p>true [<a href="#tuck">tuck</a> <a href="#mod">mod</a> <a href="#dup">dup</a> 0 <a href="#section-
10">></a>] <a href="#loop">loop</a> <a href="#pop">pop</a></p>
</blockquote>
-<h3 id="discussion-34">Discussion</h3>
+<h3 id="discussion-31">Discussion</h3>
<p>Euclid’s Algorithm</p>
<hr />
-<h2 id="gcd2">gcd2</h2>
-<p>Function</p>
-<p>Compiled GCD function.</p>
-<h3 id="discussion-35">Discussion</h3>
-<p>See <a href="#gcd">gcd</a>.</p>
-<h3 id="crosslinks-45">Crosslinks</h3>
-<p><a href="#gcd">gcd</a></p>
-<hr />
<h2 id="ge">ge</h2>
<p>Basis Function</p>
<p>Greater-than-or-equal-to comparison of two numbers.</p>
--------------
Boolean
(a >= b)</code></pre>
-<h3 id="crosslinks-46">Crosslinks</h3>
+<h3 id="crosslinks-42">Crosslinks</h3>
<p><a href="#cmp">cmp</a> <a href="#eq">eq</a> <a href="#gt">gt</a> <a href="#le">le</a> <a href="#lt">lt</a> <a href="#ne">ne</a></p>
<hr />
<h2 id="genrec">genrec</h2>
<pre><code> [if] [then] [rec1] [rec2] genrec
---------------------------------------------------------------------
[if] [then] [rec1 [[if] [then] [rec1] [rec2] genrec] rec2] ifte</code></pre>
-<h3 id="definition-39">Definition</h3>
+<h3 id="definition-35">Definition</h3>
<blockquote>
<p>[[<a href="#genrec">genrec</a>] <a href="#ccccons">ccccons</a>] <a href="#nullary">nullary</a> <a href="#swons">swons</a> <a href="#concat">concat</a> <a href="#ifte">ifte</a></p>
</blockquote>
<p>(Note that this definition includes the <code>genrec</code> symbol itself, it is self-referential. This is possible because the definition machinery does not check that symbols in defs are in the dictionary. <code>genrec</code> is the only self-referential definition.)</p>
-<h3 id="discussion-36">Discussion</h3>
+<h3 id="discussion-32">Discussion</h3>
<p>See the <a href="https://joypy.osdn.io/notebooks/Recursion_Combinators.html">Recursion Combinators notebook</a>.</p>
<p>From <a href="https://www.kevinalbrecht.com/code/joy-mirror/j05cmp.html">“Recursion Theory and Joy”</a> by Manfred von Thun:</p>
<blockquote>
<pre><code>P == [I] [T] [R] tailrec
== [I] [T] [R [P] i] ifte
== [I] [T] [R P] ifte</code></pre>
-<h3 id="crosslinks-47">Crosslinks</h3>
+<h3 id="crosslinks-43">Crosslinks</h3>
<p><a href="#anamorphism">anamorphism</a> <a href="#tailrec">tailrec</a> <a href="#x">x</a></p>
<hr />
<h2 id="getitem">getitem</h2>
<pre><code> [a b c d] 2 getitem
-------------------------
c</code></pre>
-<h3 id="definition-40">Definition</h3>
+<h3 id="definition-36">Definition</h3>
<blockquote>
<p><a href="#drop">drop</a> <a href="#first">first</a></p>
</blockquote>
-<h3 id="discussion-37">Discussion</h3>
+<h3 id="discussion-33">Discussion</h3>
<p>If the number isn’t a valid index into the quote <code>getitem</code> will cause some sort of problem (the exact nature of which is implementation-dependant.)</p>
-<h3 id="crosslinks-48">Crosslinks</h3>
+<h3 id="crosslinks-44">Crosslinks</h3>
<p><a href="#concat">concat</a> <a href="#first">first</a> <a href="#first_two">first_two</a> <a href="#flatten">flatten</a> <a href="#fourth">fourth</a> <a href="#remove">remove</a> <a href="#rest">rest</a> <a href="#reverse">reverse</a> <a href="#rrest">rrest</a> <a href="#second">second</a> <a href="#shift">shift</a> <a href="#shunt">shunt</a> <a href="#size">size</a> <a href="#sort">sort</a> <a href="#split_at">split_at</a> <a href="#split_list">split_list</a> <a href="#swaack">swaack</a> <a href="#third">third</a> <a href="#zip">zip</a></p>
<hr />
<h2 id="grabn">grabN</h2>
<pre><code> a b c d e 3 grabN
-----------------------
a b [c d e]</code></pre>
-<h3 id="definition-41">Definition</h3>
+<h3 id="definition-37">Definition</h3>
<blockquote>
-<p><a href="#section-1
6"><{}</a> [<a href="#cons">cons</a>] <a href="#times">times</a></p>
+<p><a href="#section-1
5"><{}</a> [<a href="#cons">cons</a>] <a href="#times">times</a></p>
</blockquote>
<hr />
<h2 id="grba">grba</h2>
-------------------------------
... 1 2 3 [4 3 2 1 ...] 5</code></pre>
<p>It grabs the stack under the top item, and substitutes it for the second item down on the stack.</p>
-<h3 id="definition-42">Definition</h3>
+<h3 id="definition-38">Definition</h3>
<blockquote>
<p>[<a href="#stack">stack</a> <a href="#popd">popd</a>] <a href="#dip">dip</a></p>
</blockquote>
-<h3 id="discussion-38">Discussion</h3>
+<h3 id="discussion-34">Discussion</h3>
<p>This function “grabs” an item from the stack along with a copy of the stack. It’s part of the <a href="#app2">app2</a> definition.</p>
-<h3 id="crosslinks-49">Crosslinks</h3>
+<h3 id="crosslinks-45">Crosslinks</h3>
<p><a href="#app2">app2</a></p>
<hr />
+<h2 id="section-8">>=</h2>
+<p>See <a href="#ge">ge</a>.</p>
+<hr />
+<h2 id="section-9">>></h2>
+<p>See <a href="#rshift">rshift</a>.</p>
+<hr />
+<h2 id="section-10">></h2>
+<p>See <a href="#gt">gt</a>.</p>
+<hr />
<h2 id="gt">gt</h2>
<p>Basis Function</p>
<p>Greater-than comparison of two numbers.</p>
--------------
Boolean
(a > b)</code></pre>
-<h3 id="crosslinks-50">Crosslinks</h3>
+<h3 id="crosslinks-46">Crosslinks</h3>
<p><a href="#cmp">cmp</a> <a href="#eq">eq</a> <a href="#ge">ge</a> <a href="#le">le</a> <a href="#lt">lt</a> <a href="#ne">ne</a></p>
<hr />
<h2 id="help">help</h2>
<p>Accepts a quoted symbol on the top of the stack and prints its documentation.</p>
<pre><code> [foo] help
----------------</code></pre>
-<h3 id="discussion-39">Discussion</h3>
+<h3 id="discussion-35">Discussion</h3>
<p>Technically this is equivalent to <code>pop</code>, but it will only work if the item on the top of the stack is a quoted symbol.</p>
<hr />
+<h2 id="section-11">–</h2>
+<p>See <a href="#pred">pred</a>.</p>
+<hr />
+<h2 id="section-12">-</h2>
+<p>See <a href="#sub">sub</a>.</p>
+<hr />
<h2 id="hypot">hypot</h2>
<p>Function</p>
<pre><code> x y hypot
---------------------------
sqrt(sqr(x) + sqr(y))</code></pre>
-<h3 id="definition-43">Definition</h3>
+<h3 id="definition-39">Definition</h3>
<blockquote>
<p>[<a href="#sqr">sqr</a>] <a href="#ii">ii</a> <a href="#section-20">+</a> <a href="#sqrt">sqrt</a></p>
</blockquote>
-<h3 id="discussion-40">Discussion</h3>
+<h3 id="discussion-36">Discussion</h3>
<p>This is another function that has to wait on the numeric tower.</p>
-<h3 id="crosslinks-51">Crosslinks</h3>
+<h3 id="crosslinks-47">Crosslinks</h3>
<p><a href="#sqrt">sqrt</a></p>
<hr />
-<h2 id="i">i</h2>
-<p>Basis Combinator</p>
-<p>Append a quoted expression onto the pending expression.</p>
-<pre><code> [Q] . i
--------------
- . Q</code></pre>
-<h3 id="discussion-41">Discussion</h3>
-<p>This is a fundamental combinator. It is used in all kinds of places. For example, the <a href="#x">x</a> combinator can be defined as <code>dup i</code>.</p>
-<hr />
<h2 id="id">id</h2>
<p>Basis Function</p>
<p>The identity function.</p>
-<h3 id="discussion-42">Discussion</h3>
+<h3 id="discussion-37">Discussion</h3>
<p>Does nothing. It’s kind of a mathematical thing, but it occasionally comes in handy.</p>
<hr />
<h2 id="ifte">ifte</h2>
<pre><code> [if] [then] [else] ifte
---------------------------------------
[if] nullary [else] [then] branch</code></pre>
-<h3 id="definition-44">Definition</h3>
+<h3 id="definition-40">Definition</h3>
<blockquote>
<p>[<a href="#nullary">nullary</a>] <a href="#dipd">dipd</a> <a href="#swap">swap</a> <a href="#branch">branch</a></p>
</blockquote>
-<h3 id="crosslinks-52">Crosslinks</h3>
+<h3 id="crosslinks-48">Crosslinks</h3>
<p><a href="#branch">branch</a> <a href="#loop">loop</a> <a href="#while">while</a></p>
<hr />
<h2 id="ii">ii</h2>
<pre><code>... a [Q] ii
------------------
... Q a Q</code></pre>
-<h3 id="definition-45">Definition</h3>
+<h3 id="definition-41">Definition</h3>
<blockquote>
<p>[<a href="#dip">dip</a>] <a href="#dupdip">dupdip</a> <a href="#i">i</a></p>
</blockquote>
1 2 4 4 [++] • i
1 2 4 4 • ++
1 2 4 5 •</code></pre>
-<h3 id="discussion-43">Discussion</h3>
+<h3 id="discussion-38">Discussion</h3>
<p>In some cases (like the example above) this is the same effect as using <a href="#app2">app2</a> but most of the time it’s not:</p>
<pre><code> 1 2 3 4 [+] ii
--------------------
1 2 3 4 [+] app2
----------------------
1 2 5 6</code></pre>
-<h3 id="crosslinks-53">Crosslinks</h3>
+<h3 id="crosslinks-49">Crosslinks</h3>
<p><a href="#app2">app2</a> <a href="#b">b</a></p>
<hr />
+<h2 id="i">i</h2>
+<p>Basis Combinator</p>
+<p>Append a quoted expression onto the pending expression.</p>
+<pre><code> [Q] . i
+-------------
+ . Q</code></pre>
+<h3 id="discussion-39">Discussion</h3>
+<p>This is a fundamental combinator. It is used in all kinds of places. For example, the <a href="#x">x</a> combinator can be defined as <code>dup i</code>.</p>
+<hr />
<h2 id="infra">infra</h2>
<p>Combinator</p>
<p>Accept a quoted program and a list on the stack and run the program with the list as its stack. Does not affect the stack (below the list.)</p>
<pre><code> ... x y z [a b c] [Q] infra
---------------------------------
c b a Q [z y x ...] swaack</code></pre>
-<h3 id="definition-46">Definition</h3>
+<h3 id="definition-42">Definition</h3>
<blockquote>
<p><a href="#swons">swons</a> <a href="#swaack">swaack</a> [<a href="#i">i</a>] <a href="#dip">dip</a> <a href="#swaack">swaack</a></p>
</blockquote>
-<h3 id="discussion-44">Discussion</h3>
+<pre><code>... [a b c] [F] swons swaack [i] dip swaack
+... [[F] a b c] swaack [i] dip swaack
+
+c b a [F] [...] [i] dip swaack
+c b a [F] i [...] swaack
+c b a F [...] swaack
+d e [...] swaack
+... [e d]</code></pre>
+<h3 id="discussion-40">Discussion</h3>
<p>This is one of the more useful combinators. It allows a quoted expression to serve as a stack for a program, effectively running it in a kind of “pocket universe”. If the list represents a datastructure then <code>infra</code> lets you work on its internal structure.</p>
-<h3 id="crosslinks-54">Crosslinks</h3>
+<h3 id="crosslinks-50">Crosslinks</h3>
<p><a href="#swaack">swaack</a></p>
<hr />
<h2 id="infrst">infrst</h2>
<p>Combinator</p>
<p>Does <a href="#infra">infra</a> and then extracts the <a href="#first">first</a> item from the resulting list.</p>
-<h3 id="definition-47">Definition</h3>
+<h3 id="definition-43">Definition</h3>
<blockquote>
<p><a href="#infra">infra</a> <a href="#first">first</a></p>
</blockquote>
<p>Create a new Joy function definition in the Joy dictionary. A definition is given as a quote with a name followed by a Joy expression.</p>
<h3 id="example-8">Example</h3>
<pre><code>[sqr dup mul] inscribe</code></pre>
-<h3 id="discussion-45">Discussion</h3>
+<h3 id="discussion-41">Discussion</h3>
<p>This is the only function that modifies the dictionary. It’s provided as a convenience, for tinkering with new definitions before entering them into the <code>defs.txt</code> file. It can be abused, which you should avoid unless you know what you’re doing.</p>
<hr />
<h2 id="le">le</h2>
-------------
Boolean
(a <= b)</code></pre>
-<h3 id="crosslinks-55">Crosslinks</h3>
+<h3 id="crosslinks-51">Crosslinks</h3>
<p><a href="#cmp">cmp</a> <a href="#eq">eq</a> <a href="#ge">ge</a> <a href="#gt">gt</a> <a href="#lt">lt</a> <a href="#ne">ne</a></p>
<hr />
+<h2 id="section-13"><=</h2>
+<p>See <a href="#le">le</a>.</p>
+<hr />
+<h2 id="section-14"><></h2>
+<p>See <a href="#ne">ne</a>.</p>
+<hr />
+<h2 id="section-15"><{}</h2>
+<p>Function</p>
+<pre><code> ... a <{}
+----------------
+ ... [] a</code></pre>
+<h3 id="definition-44">Definition</h3>
+<pre><code>[] swap</code></pre>
+<h3 id="discussion-42">Discussion</h3>
+<p>Tuck an empty list just under the first item on the stack.</p>
+<h3 id="crosslinks-52">Crosslinks</h3>
+<p><a href="#section-18"><<{}</a></p>
+<hr />
+<h2 id="section-16"><<{}</h2>
+<p>Function</p>
+<pre><code> ... b a <{}
+-----------------
+ ... [] b a</code></pre>
+<h3 id="definition-45">Definition</h3>
+<pre><code>[] rollup</code></pre>
+<h3 id="discussion-43">Discussion</h3>
+<p>Tuck an empty list just under the first two items on the stack.</p>
+<h3 id="crosslinks-53">Crosslinks</h3>
+<p><a href="#section-16"><{}</a></p>
+<hr />
+<h2 id="section-17"><<</h2>
+<p>See <a href="#lshift">lshift</a>.</p>
+<hr />
+<h2 id="section-18"><</h2>
+<p>See <a href="#lt">lt</a>.</p>
+<hr />
<h2 id="loop">loop</h2>
<p>Basis Combinator</p>
<p>Expect a quoted program <code>Q</code> and a Boolean value on the stack. If the value is false discard the quoted program, otherwise run a copy of <code>Q</code> and <code>loop</code> again.</p>
true [Q] . loop
--------------------------
. Q [Q] loop</code></pre>
-<h3 id="discussion-46">Discussion</h3>
+<h3 id="discussion-44">Discussion</h3>
<p>This, along with <a href="#branch">branch</a> and <a href="#fork">fork</a>, is one of the four main combinators of all programming. The fourth, sequence, is implied by juxtaposition. That is to say, in Joy <code>F G</code> is like <code>G(F(...))</code> in a language bassed on function application. Or again, to quote the <a href="https://en.wikipedia.org/wiki/Joy_(programming_language)#Mathematical_purity">Joy Wikipedia entry</a>,</p>
<blockquote>
<p>In Joy, the meaning function is a homomorphism from the syntactic monoid onto the semantic monoid. That is, the syntactic relation of concatenation of symbols maps directly onto the semantic relation of composition of functions.</p>
</blockquote>
<p>Anyway, <a href="#branch">branch</a>, <a href="#fork">fork</a>, amd <a href="#loop">loop</a> are the fundamental combinators in Joy. Just as <a href="#branch">branch</a> has it’s more common and convenient form <a href="#ifte">ifte</a>, <a href="#loop">loop</a> has <a href="#while">while</a>.</p>
-<h3 id="crosslinks-56">Crosslinks</h3>
+<h3 id="crosslinks-54">Crosslinks</h3>
<p><a href="#branch">branch</a> <a href="#fork">fork</a> <a href="#while">while</a></p>
<hr />
<h2 id="lshift">lshift</h2>
<pre><code> a n lshift
----------------
(a×2ⁿ)</code></pre>
-<h3 id="crosslinks-57">Crosslinks</h3>
+<h3 id="crosslinks-55">Crosslinks</h3>
<p><a href="#rshift">rshift</a></p>
<hr />
<h2 id="lt">lt</h2>
-------------
Boolean
(a < b)</code></pre>
-<h3 id="crosslinks-58">Crosslinks</h3>
+<h3 id="crosslinks-56">Crosslinks</h3>
<p><a href="#cmp">cmp</a> <a href="#eq">eq</a> <a href="#ge">ge</a> <a href="#gt">gt</a> <a href="#le">le</a> <a href="#ne">ne</a></p>
<hr />
<h2 id="make_generator">make_generator</h2>
<pre><code> [230 [dup ++] codireco] 5 [x] times pop
---------------------------------------------
230 231 232 233 234</code></pre>
-<h3 id="definition-48">Definition</h3>
+<h3 id="definition-46">Definition</h3>
<blockquote>
<p>[<a href="#codireco">codireco</a>] <a href="#ccons">ccons</a></p>
</blockquote>
-<h3 id="discussion-47">Discussion</h3>
+<h3 id="discussion-45">Discussion</h3>
<p>See the <a href="https://joypy.osdn.io/notebooks/Generator_Programs.html#an-interesting-variation">“Using <code>x</code> to Generate Values” notebook</a>.</p>
-<h3 id="crosslinks-59">Crosslinks</h3>
+<h3 id="crosslinks-57">Crosslinks</h3>
<p><a href="#codireco">codireco</a></p>
<hr />
<h2 id="map">map</h2>
<pre><code> 5 [1 2 3] [++ *] map
--------------------------
5 [10 15 20]</code></pre>
-<h3 id="discussion-48">Discussion</h3>
+<h3 id="discussion-46">Discussion</h3>
<p>This is a common operation in many languages. In Joy it can be a parallelism combinator due to the “pure” nature of the language.</p>
-<h3 id="crosslinks-60">Crosslinks</h3>
+<h3 id="crosslinks-58">Crosslinks</h3>
<p><a href="#app1">app1</a> <a href="#app2">app2</a> <a href="#app3">app3</a> <a href="#appn">appN</a> <a href="#fork">fork</a></p>
<hr />
<h2 id="max">max</h2>
<pre><code> [1 2 3 4] max
-------------------
4</code></pre>
-<h3 id="crosslinks-61">Crosslinks</h3>
+<h3 id="crosslinks-59">Crosslinks</h3>
<p><a href="#min">min</a> <a href="#size">size</a> <a href="#sum">sum</a></p>
<hr />
<h2 id="min">min</h2>
<pre><code> [1 2 3 4] min
-------------------
1 </code></pre>
-<h3 id="crosslinks-62">Crosslinks</h3>
+<h3 id="crosslinks-60">Crosslinks</h3>
<p><a href="#max">max</a> <a href="#size">size</a> <a href="#sum">sum</a></p>
<hr />
<h2 id="mod">mod</h2>
<pre><code> a b mod
-------------
(a%b)</code></pre>
-<h3 id="crosslinks-63">Crosslinks</h3>
+<h3 id="crosslinks-61">Crosslinks</h3>
<p><a href="#divmod">divmod</a> <a href="#mul">mul</a></p>
<hr />
<h2 id="modulus">modulus</h2>
<pre><code> a b mul
-------------
(a×b)</code></pre>
-<h3 id="crosslinks-64">Crosslinks</h3>
+<h3 id="crosslinks-62">Crosslinks</h3>
<p><a href="#div">div</a> <a href="#product">product</a></p>
<hr />
-<h2 id="ne">ne</h2>
-<p>Basis Function</p>
-<p>Not-Equal comparison of the two items on the top of the stack, replacing them with a Boolean value.</p>
-<pre><code> a b ne
--------------
- Boolean
- (a = b)</code></pre>
-<h3 id="crosslinks-65">Crosslinks</h3>
-<p><a href="#cmp">cmp</a> <a href="#eq">eq</a> <a href="#ge">ge</a> <a href="#gt">gt</a> <a href="#le">le</a> <a href="#lt">lt</a></p>
-<hr />
<h2 id="neg">neg</h2>
<p>Function</p>
<p>Invert the sign of a number.</p>
<pre><code> a neg
-----------
-a</code></pre>
-<h3 id="definition-49">Definition</h3>
+<h3 id="definition-47">Definition</h3>
<blockquote>
-<p>0 <a href="#swap">swap</a> <a href="#section-11">-</a></p>
+<p>0 <a href="#swap">swap</a> <a href="#section-12">-</a></p>
</blockquote>
<hr />
+<h2 id="ne">ne</h2>
+<p>Basis Function</p>
+<p>Not-Equal comparison of the two items on the top of the stack, replacing them with a Boolean value.</p>
+<pre><code> a b ne
+-------------
+ Boolean
+ (a = b)</code></pre>
+<h3 id="crosslinks-63">Crosslinks</h3>
+<p><a href="#cmp">cmp</a> <a href="#eq">eq</a> <a href="#ge">ge</a> <a href="#gt">gt</a> <a href="#le">le</a> <a href="#lt">lt</a></p>
+<hr />
<h2 id="not">not</h2>
<p>Function</p>
<p>Like <a href="#bool">bool</a> but convert the item on the top of the stack to the inverse Boolean value.</p>
false not
---------------
true</code></pre>
-<h3 id="definition-50">Definition</h3>
+<h3 id="definition-48">Definition</h3>
<blockquote>
<p><a href="#bool">bool</a> [true] [false] <a href="#branch">branch</a></p>
</blockquote>
-<h3 id="crosslinks-66">Crosslinks</h3>
+<h3 id="crosslinks-64">Crosslinks</h3>
<p><a href="#bool">bool</a></p>
<hr />
<h2 id="nulco">nulco</h2>
<pre><code> [F] nulco
-------------------
[[F] nullary]</code></pre>
-<h3 id="definition-51">Definition</h3>
+<h3 id="definition-49">Definition</h3>
<blockquote>
<p>[<a href="#nullary">nullary</a>] <a href="#cons">cons</a></p>
</blockquote>
-<h3 id="discussion-49">Discussion</h3>
-<p>Helper function for <a href="#section-25">||</a> and <a href="#section-1">&&</a>.</p>
-<h3 id="crosslinks-67">Crosslinks</h3>
-<p><a href="#section
-1">&&</a> <a href="#section-25">||</a></p>
+<h3 id="discussion-47">Discussion</h3>
+<p>Helper function for <a href="#section-25">||</a> and <a href="#section">&&</a>.</p>
+<h3 id="crosslinks-65">Crosslinks</h3>
+<p><a href="#section">&&</a> <a href="#section-25">||</a></p>
<hr />
<h2 id="nullary">nullary</h2>
<p>Combinator</p>
<pre><code> ... [P] nullary
---------------------
... a</code></pre>
-<h3 id="definition-52">Definition</h3>
+<h3 id="definition-50">Definition</h3>
<blockquote>
<p>[<a href="#stack">stack</a>] <a href="#dip">dip</a> <a href="#infra">infra</a> <a href="#first">first</a></p>
</blockquote>
... [...] [P] infra first
... [a ...] first
... a</code></pre>
-<h3 id="discussion-50">Discussion</h3>
+<h3 id="discussion-48">Discussion</h3>
<p>A very useful function that runs any other quoted function and returns it’s first result without disturbing the stack (under the quoted program.)</p>
-<h3 id="crosslinks-68">Crosslinks</h3>
+<h3 id="crosslinks-66">Crosslinks</h3>
<p><a href="#unary">unary</a> <a href="#binary">binary</a> <a href="#ternary">ternary</a></p>
<hr />
<h2 id="of">of</h2>
<pre><code> 2 [a b c d] of
--------------------
c</code></pre>
-<h3 id="definition-53">Definition</h3>
+<h3 id="definition-51">Definition</h3>
<blockquote>
<p><a href="#swap">swap</a> <a href="#getitem">getitem</a></p>
</blockquote>
-<h3 id="crosslinks-69">Crosslinks</h3>
+<h3 id="crosslinks-67">Crosslinks</h3>
<p><a href="#getitem">getitem</a></p>
<hr />
<h2 id="or">or</h2>
<p>Basis Function</p>
<p>Logical bit-wise OR.</p>
-<h3 id="crosslinks-70">Crosslinks</h3>
+<h3 id="crosslinks-68">Crosslinks</h3>
<p><a href="#and">and</a> <a href="#xor">xor</a></p>
<hr />
<h2 id="over">over</h2>
<pre><code> a b over
--------------
a b a</code></pre>
-<h3 id="definition-54">Definition</h3>
+<h3 id="definition-52">Definition</h3>
<p>There are many many ways to define this function.</p>
<blockquote>
<p><a href="#swap">swap</a> <a href="#tuck">tuck</a></p>
<p><a href="#unit">unit</a> <a href="#dupdipd">dupdipd</a> <a href="#first">first</a></p>
</blockquote>
<p>And so on…</p>
-<h3 id="discussion-51">Discussion</h3>
+<h3 id="discussion-49">Discussion</h3>
<p>A fine old word from Forth.</p>
-<h3 id="crosslinks-71">Crosslinks</h3>
+<h3 id="crosslinks-69">Crosslinks</h3>
<p><a href="#tuck">tuck</a></p>
<hr />
<h2 id="pam">pam</h2>
<pre><code> 5 7 [[+][-][*][/][%]] pam
-------------------------------
5 7 [12 -2 35 0 5]</code></pre>
-<h3 id="definition-55">Definition</h3>
+<h3 id="definition-53">Definition</h3>
<blockquote>
<p>[<a href="#i">i</a>] <a href="#map">map</a></p>
</blockquote>
-<h3 id="discussion-52">Discussion</h3>
+<h3 id="discussion-50">Discussion</h3>
<p>A specialization of <a href="#map">map</a> that runs a list of functions in parallel (if the underlying <a href="#map">map</a> function is so implemented, of course.)</p>
-<h3 id="crosslinks-72">Crosslinks</h3>
+<h3 id="crosslinks-70">Crosslinks</h3>
<p><a href="#map">map</a></p>
<hr />
+<h2 id="section-19">%</h2>
+<p>See <a href="#mod">mod</a>.</p>
+<hr />
<h2 id="pick">pick</h2>
<p>See <a href="#getitem">getitem</a>.</p>
<hr />
+<h2 id="section-20">+</h2>
+<p>See <a href="#add">add</a>.</p>
+<hr />
+<h2 id="section-21">++</h2>
+<p>See <a href="#succ">succ</a>.</p>
+<hr />
<h2 id="pm">pm</h2>
<p>Function</p>
<p>Plus or minus. Replace two numbers with their sum and difference.</p>
<pre><code> a b pm
-----------------
(a+b) (a-b)</code></pre>
-<h3 id="definition-56">Definition</h3>
+<h3 id="definition-54">Definition</h3>
<blockquote>
<p>[+] [-] <a href="#clop">clop</a></p>
</blockquote>
<hr />
-<h2 id="pop">pop</h2>
-<p>Basis Function</p>
-<p>Pop the top item from the stack and discard it.</p>
-<pre><code> a pop
------------</code></pre>
-<h3 id="crosslinks-73">Crosslinks</h3>
-<p><a href="#popd">popd</a> <a href="#popdd">popdd</a> <a href="#popop">popop</a> <a href="#popopd">popopd</a> <a href="#popopdd">popopdd</a> <a href="#popopop">popopop</a></p>
+<h2 id="popdd">popdd</h2>
+<p>Function</p>
+<p><a href="#pop">pop</a> the third item on the stack.</p>
+<pre><code> a b c popdd
+-----------------
+ b c</code></pre>
+<h3 id="definition-55">Definition</h3>
+<blockquote>
+<p><a href="#rolldown">rolldown</a> <a href="#pop">pop</a></p>
+</blockquote>
+<h3 id="crosslinks-71">Crosslinks</h3>
+<p><a href="#pop">pop</a> <a href="#popd">popd</a> <a href="#popop">popop</a> <a href="#popopd">popopd</a> <a href="#popopdd">popopdd</a> <a href="#popopop">popopop</a></p>
<hr />
<h2 id="popd">popd</h2>
<p>Function</p>
<pre><code> a b popd
--------------
b</code></pre>
-<h3 id="definition-57">Definition</h3>
+<h3 id="definition-56">Definition</h3>
<blockquote>
<p><a href="#swap">swap</a> <a href="#pop">pop</a></p>
</blockquote>
-<h3 id="crosslinks-74">Crosslinks</h3>
+<h3 id="crosslinks-72">Crosslinks</h3>
<p><a href="#pop">pop</a> <a href="#popdd">popdd</a> <a href="#popop">popop</a> <a href="#popopd">popopd</a> <a href="#popopdd">popopdd</a> <a href="#popopop">popopop</a></p>
<hr />
-<h2 id="popdd">popdd</h2>
-<p>Function</p>
-<p><a href="#pop">pop</a> the third item on the stack.</p>
-<pre><code> a b c popdd
------------------
- b c</code></pre>
-<h3 id="definition-58">Definition</h3>
-<blockquote>
-<p><a href="#rolldown">rolldown</a> <a href="#pop">pop</a></p>
-</blockquote>
-<h3 id="crosslinks-75">Crosslinks</h3>
-<p><a href="#pop">pop</a> <a href="#popd">popd</a> <a href="#popop">popop</a> <a href="#popopd">popopd</a> <a href="#popopdd">popopdd</a> <a href="#popopop">popopop</a></p>
+<h2 id="pop">pop</h2>
+<p>Basis Function</p>
+<p>Pop the top item from the stack and discard it.</p>
+<pre><code> a pop
+-----------</code></pre>
+<h3 id="crosslinks-73">Crosslinks</h3>
+<p><a href="#popd">popd</a> <a href="#popdd">popdd</a> <a href="#popop">popop</a> <a href="#popopd">popopd</a> <a href="#popopdd">popopdd</a> <a href="#popopop">popopop</a></p>
<hr />
-<h2 id="popop">popop</h2>
+<h2 id="popopdd">popopdd</h2>
<p>Function</p>
-<p><a href="#pop">pop</a> two items from the stack.</p>
-<pre><code> a b popop
----------------</code></pre>
-<h3 id="definition-59">Definition</h3>
+<pre><code> a b c d popopdd
+---------------------
+ c d</code></pre>
+<h3 id="definition-57">Definition</h3>
<blockquote>
-<p><a href="#pop">pop</a> <a href="#pop">pop</a></p>
+<p>[<a href="#popop">popop</a>] <a href="#dipd">dipd</a></p>
</blockquote>
-<h3 id="crosslinks-76">Crosslinks</h3>
-<p><a href="#pop">pop</a> <a href="#popd">popd</a> <a href="#popdd">popdd</a> <a href="#popop
d">popopd</a> <a href="#popopdd">popopdd</a> <a href="#popopop">popopop</a></p>
+<h3 id="crosslinks-74">Crosslinks</h3>
+<p><a href="#pop">pop</a> <a href="#popd">popd</a> <a href="#popdd">popdd</a> <a href="#popop
">popop</a> <a href="#popopd">popopd</a> <a href="#popopop">popopop</a></p>
<hr />
<h2 id="popopd">popopd</h2>
<p>Function</p>
<pre><code> a b c popopd
------------------
c</code></pre>
-<h3 id="definition-60">Definition</h3>
+<h3 id="definition-58">Definition</h3>
<blockquote>
<p><a href="#rollup">rollup</a> <a href="#popop">popop</a></p>
</blockquote>
-<h3 id="crosslinks-77">Crosslinks</h3>
+<h3 id="crosslinks-75">Crosslinks</h3>
<p><a href="#pop">pop</a> <a href="#popd">popd</a> <a href="#popdd">popdd</a> <a href="#popop">popop</a> <a href="#popopdd">popopdd</a> <a href="#popopop">popopop</a></p>
<hr />
-<h2 id="popopdd">popopdd</h2>
+<h2 id="popop">popop</h2>
<p>Function</p>
-<pre><code> a b c d popopdd
----------------------
- c d</code></pre>
-<h3 id="definition-61">Definition</h3>
+<p><a href="#pop">pop</a> two items from the stack.</p>
+<pre><code> a b popop
+---------------</code></pre>
+<h3 id="definition-59">Definition</h3>
<blockquote>
-<p>[<a href="#popop">popop</a>] <a href="#dipd">dipd</a></p>
+<p><a href="#pop">pop</a> <a href="#pop">pop</a></p>
</blockquote>
-<h3 id="crosslinks-78">Crosslinks</h3>
-<p><a href="#pop">pop</a> <a href="#popd">popd</a> <a href="#popdd">popdd</a> <a href="#popop
">popop</a> <a href="#popopd">popopd</a> <a href="#popopop">popopop</a></p>
+<h3 id="crosslinks-76">Crosslinks</h3>
+<p><a href="#pop">pop</a> <a href="#popd">popd</a> <a href="#popdd">popdd</a> <a href="#popop
d">popopd</a> <a href="#popopdd">popopdd</a> <a href="#popopop">popopop</a></p>
<hr />
<h2 id="popopop">popopop</h2>
<p>Function</p>
<p><a href="#pop">pop</a> three items from the stack.</p>
<pre><code> a b c popopop
-------------------</code></pre>
-<h3 id="definition-62">Definition</h3>
+<h3 id="definition-60">Definition</h3>
<blockquote>
<p><a href="#pop">pop</a> <a href="#popop">popop</a></p>
</blockquote>
-<h3 id="crosslinks-79">Crosslinks</h3>
+<h3 id="crosslinks-77">Crosslinks</h3>
<p><a href="#pop">pop</a> <a href="#popd">popd</a> <a href="#popdd">popdd</a> <a href="#popop">popop</a> <a href="#popopd">popopd</a> <a href="#popopdd">popopdd</a></p>
<hr />
<h2 id="pow">pow</h2>
<p>Basis Function</p>
-<p>Take two numbers <code>a</code> and <code>b</code> from the stack and raise <code>a</code> to the <code>n</code>th power. (<code>b</code> is on the top of the stack.)</p>
+<p>Take two numbers <code>a</code> and <code>n</code> from the stack and raise <code>a</code> to the <code>n</code>th power. (<code>n</code> is on the top of the stack.)</p>
<pre><code> a n pow
-------------
(aⁿ)</code></pre>
<h2 id="pred">pred</h2>
<p>Function</p>
<p>Predecessor. Decrement TOS.</p>
-<h3 id="definition-63">Definition</h3>
+<h3 id="definition-61">Definition</h3>
<blockquote>
<p>1 -</p>
</blockquote>
-<h3 id="crosslinks-80">Crosslinks</h3>
+<h3 id="crosslinks-78">Crosslinks</h3>
<p><a href="#succ">succ</a></p>
<hr />
<h2 id="primrec">primrec</h2>
n [Base] [Recur] primrec
------------------------------------------ n > 0
n (n-1) [Base] [Recur] primrec Recur</code></pre>
-<h3 id="discussion-53">Discussion</h3>
+<h3 id="discussion-51">Discussion</h3>
<p>Simple and useful specialization of the <a href="#genrec">genrec</a> combinator from the <a href="https://www.kevinalbrecht.com/code/joy-mirror/index.html">original Joy system</a>.</p>
-<h3 id="crosslinks-81">Crosslinks</h3>
+<h3 id="crosslinks-79">Crosslinks</h3>
<p><a href="#genrec">genrec</a> <a href="#tailrec">tailrec</a></p>
<hr />
<h2 id="product">product</h2>
<p>Function</p>
<p>Just as <a href="#sum">sum</a> sums a list of numbers, this function multiplies them together.</p>
-<h3 id="definition-64">Definition</h3>
+<h3 id="definition-62">Definition</h3>
<blockquote>
<p>1 <a href="#swap">swap</a> [<a href="#mul">mul</a>] <a href="#step">step</a></p>
</blockquote>
<p>[1] [<a href="#mul">mul</a>] <a href="#primrec">primrec</a></p>
</blockquote>
<hr />
+<h2 id="section-22">?</h2>
+<p>Function</p>
+<p>Is the item on the top of the stack “truthy”?</p>
+<h3 id="definition-63">Definition</h3>
+<blockquote>
+<p><a href="#dup">dup</a> <a href="#bool">bool</a></p>
+</blockquote>
+<h3 id="discussion-52">Discussion</h3>
+<p>You often want to test the truth value of an item on the stack without consuming the item.</p>
+<h3 id="crosslinks-80">Crosslinks</h3>
+<p><a href="#bool">bool</a></p>
+<hr />
<h2 id="quoted">quoted</h2>
<p>Function</p>
<p>“Quote D” Wrap the second item on the stack in a list.</p>
<pre><code> a b quoted
----------------
[a] b</code></pre>
-<h3 id="definition-65">Definition</h3>
+<h3 id="definition-64">Definition</h3>
<blockquote>
<p>[<a href="#unit">unit</a>] <a href="#dip">dip</a></p>
</blockquote>
-<h3 id="discussion-54">Discussion</h3>
+<h3 id="discussion-53">Discussion</h3>
<p>This comes from the original Joy stuff.</p>
-<h3 id="crosslinks-82">Crosslinks</h3>
+<h3 id="crosslinks-81">Crosslinks</h3>
<p><a href="#unit">unit</a></p>
<hr />
<h2 id="range">range</h2>
-5 range
--------------
[]</code></pre>
-<h3 id="definition-66">Definition</h3>
+<h3 id="definition-65">Definition</h3>
<blockquote>
<p>[0 <=] [1 - <a href="#dup">dup</a>] <a href="#anamorphism">anamorphism</a></p>
</blockquote>
-<h3 id="discussion-55">Discussion</h3>
+<h3 id="discussion-54">Discussion</h3>
<p>If <code>n</code> is less than 1 the resulting list is empty.</p>
-<h3 id="crosslinks-83">Crosslinks</h3>
+<h3 id="crosslinks-82">Crosslinks</h3>
<p><a href="#range_to_zero">range_to_zero</a></p>
<hr />
<h2 id="range_to_zero">range_to_zero</h2>
<pre><code> 5 range_to_zero
---------------------
[0 1 2 3 4 5]</code></pre>
-<h3 id="definition-67">Definition</h3>
+<h3 id="definition-66">Definition</h3>
<blockquote>
<p><a href="#unit">unit</a> [<a href="#down_to_zero">down_to_zero</a>] <a href="#infra">infra</a></p>
</blockquote>
-<h3 id="discussion-56">Discussion</h3>
+<h3 id="discussion-55">Discussion</h3>
<p>Note that the order is reversed compared to <a href="#range">range</a>.</p>
-<h3 id="crosslinks-84">Crosslinks</h3>
+<h3 id="crosslinks-83">Crosslinks</h3>
<p><a href="#down_to_zero">down_to_zero</a> <a href="#range">range</a></p>
<hr />
<h2 id="reco">reco</h2>
<pre><code> a [b ...] reco
--------------------
[a ...]</code></pre>
-<h3 id="definition-68">Definition</h3>
+<h3 id="definition-67">Definition</h3>
<blockquote>
<p><a href="#rest">rest</a> <a href="#cons">cons</a></p>
</blockquote>
-<h3 id="crosslinks-85">Crosslinks</h3>
+<h3 id="crosslinks-84">Crosslinks</h3>
<p><a href="#codireco">codireco</a> <a href="#make_generator">make_generator</a></p>
<hr />
-<h2 id="rem">rem</h2>
+<h2 id="remainder">remainder</h2>
<p>See <a href="#mod">mod</a>.</p>
<hr />
-<h2 id="remainder">remainder</h2>
+<h2 id="rem">rem</h2>
<p>See <a href="#mod">mod</a>.</p>
<hr />
<h2 id="remove">remove</h2>
<pre><code> [1 2 3 1] 1 remove
------------------------
[2 3 1]</code></pre>
-<h3 id="definition-69">Definition</h3>
+<h3 id="definition-68">Definition</h3>
<p>See the <a href="https://osdn.net/projects/joypy/scm/git/Thun/blobs/master/docs/notebooks/Remove-Function.ipynb">“Remove Function” notebook</a>.</p>
<hr />
<h2 id="rest">rest</h2>
<pre><code> [a ...] rest
------------------
[...]</code></pre>
-<h3 id="crosslinks-86">Crosslinks</h3>
+<h3 id="crosslinks-85">Crosslinks</h3>
<p><a href="#first">first</a> <a href="#uncons">uncons</a></p>
<hr />
<h2 id="reverse">reverse</h2>
<pre><code> [1 2 3] reverse
---------------------
[3 2 1]</code></pre>
-<h3 id="definition-70">Definition</h3>
+<h3 id="definition-69">Definition</h3>
<blockquote>
-<p><a href="#section-1
6"><{}</a> <a href="#shunt">shunt</a></p>
+<p><a href="#section-1
5"><{}</a> <a href="#shunt">shunt</a></p>
</blockquote>
<hr />
<h2 id="rolldown">rolldown</h2>
<pre><code> a b c rolldown
--------------------
b c a</code></pre>
-<h3 id="definition-71">Definition</h3>
+<h3 id="definition-70">Definition</h3>
<blockquote>
<p><a href="#swapd">swapd</a> <a href="#swap">swap</a></p>
</blockquote>
-<h3 id="crosslinks-87">Crosslinks</h3>
+<h3 id="crosslinks-86">Crosslinks</h3>
<p><a href="#rollup">rollup</a></p>
<hr />
+<h2 id="roll">roll></h2>
+<p>See <a href="#rollup">rollup</a>.</p>
+<hr />
+<h2 id="roll-1">roll<</h2>
+<p>See <a href="#rolldown">rolldown</a>.</p>
+<hr />
<h2 id="rollup">rollup</h2>
<p>Function</p>
<pre><code> a b c rollup
------------------
c a b</code></pre>
-<h3 id="definition-72">Definition</h3>
+<h3 id="definition-71">Definition</h3>
<blockquote>
<p><a href="#swap">swap</a> <a href="#swapd">swapd</a></p>
</blockquote>
-<h3 id="crosslinks-88">Crosslinks</h3>
+<h3 id="crosslinks-87">Crosslinks</h3>
<p><a href="#rolldown">rolldown</a></p>
<hr />
-<h2 id="roll">roll></h2>
-<p>See <a href="#rollup">rollup</a>.</p>
-<hr />
-<h2 id="roll-1">roll<</h2>
-<p>See <a href="#rolldown">rolldown</a>.</p>
-<hr />
<h2 id="round">round</h2>
<p>Function</p>
<p>Round a number to a given precision in decimal digits.</p>
-<h3 id="discussion-57">Discussion</h3>
+<h3 id="discussion-56">Discussion</h3>
<p>Another one that won’t make sense until the “numeric tower” is nailed down.</p>
<hr />
<h2 id="rrest">rrest</h2>
<pre><code> [a b ...] rrest
---------------------
[...]</code></pre>
-<h3 id="definition-73">Definition</h3>
+<h3 id="definition-72">Definition</h3>
<blockquote>
<p><a href="#rest">rest</a> <a href="#rest">rest</a></p>
</blockquote>
-<h3 id="crosslinks-89">Crosslinks</h3>
+<h3 id="crosslinks-88">Crosslinks</h3>
<p><a href="#rest">rest</a></p>
<hr />
<h2 id="rshift">rshift</h2>
<pre><code> a n rshift
----------------
(a∕2ⁿ)</code></pre>
-<h3 id="crosslinks-90">Crosslinks</h3>
+<h3 id="crosslinks-89">Crosslinks</h3>
<p><a href="#lshift">lshift</a></p>
<hr />
<h2 id="run">run</h2>
<pre><code> [1 2 +] run
-----------------
[3]</code></pre>
-<h3 id="definition-74">Definition</h3>
+<h3 id="definition-73">Definition</h3>
<blockquote>
-<p><a href="#section-1
6"><{}</a> <a href="#infra">infra</a></p>
+<p><a href="#section-1
5"><{}</a> <a href="#infra">infra</a></p>
</blockquote>
<hr />
<h2 id="second">second</h2>
<pre><code> [a b ...] second
----------------------
b</code></pre>
-<h3 id="definition-75">Definition</h3>
+<h3 id="definition-74">Definition</h3>
<blockquote>
<p><a href="#rest">rest</a> <a href="#first">first</a></p>
</blockquote>
-<h3 id="crosslinks-91">Crosslinks</h3>
+<h3 id="crosslinks-90">Crosslinks</h3>
<p><a href="#first">first</a> <a href="#third">third</a> <a href="#fourth">fourth</a></p>
<hr />
<h2 id="select">select</h2>
[a b] true select
-----------------------
b</code></pre>
-<h3 id="discussion-58">Discussion</h3>
+<h3 id="discussion-57">Discussion</h3>
<p>The sequence can contain more than two items but not fewer.</p>
-<h3 id="crosslinks-92">Crosslinks</h3>
+<h3 id="crosslinks-91">Crosslinks</h3>
<p><a href="#choice">choice</a></p>
<hr />
<h2 id="sharing">sharing</h2>
<p>Function</p>
<p>Print redistribution information.</p>
-<h3 id="discussion-59">Discussion</h3>
+<h3 id="discussion-58">Discussion</h3>
<p>Mathematically this is a form of <a href="#id">id</a>, but it has the side-effect of printing out the GPL notice.</p>
-<h3 id="crosslinks-93">Crosslinks</h3>
+<h3 id="crosslinks-92">Crosslinks</h3>
<p><a href="#warranty">warranty</a></p>
<hr />
<h2 id="shift">shift</h2>
<pre><code> [x y z] [a b c] shift
---------------------------
[a x y z] [b c]</code></pre>
-<h3 id="definition-76">Definition</h3>
+<h3 id="definition-75">Definition</h3>
<blockquote>
<p><a href="#uncons">uncons</a> [<a href="#swons">swons</a>] <a href="#dip">dip</a></p>
</blockquote>
-<h3 id="crosslinks-94">Crosslinks</h3>
+<h3 id="crosslinks-93">Crosslinks</h3>
<p><a href="#shunt">shunt</a></p>
<hr />
<h2 id="shunt">shunt</h2>
<pre><code> [a b c] [d e f] shunt
---------------------------
[f e d a b c] </code></pre>
-<h3 id="definition-77">Definition</h3>
+<h3 id="definition-76">Definition</h3>
<blockquote>
<p>[<a href="#swons">swons</a>] <a href="#step">step</a></p>
</blockquote>
-<h3 id="discussion-60">Discussion</h3>
+<h3 id="discussion-59">Discussion</h3>
<p>This is more efficient than <a href="#concat">concat</a> so prefer it if you don’t need to preserve order.</p>
-<h3 id="crosslinks-95">Crosslinks</h3>
+<h3 id="crosslinks-94">Crosslinks</h3>
<p><a href="#concat">concat</a> <a href="#reverse">reverse</a> <a href="#shift">shift</a></p>
<hr />
<h2 id="size">size</h2>
<pre><code> [23 [cats] 4] size
------------------------
3</code></pre>
-<h3 id="definition-78">Definition</h3>
+<h3 id="definition-77">Definition</h3>
<blockquote>
<p>[<a href="#pop">pop</a> <a href="#section-21">++</a>] <a href="#step_zero">step_zero</a></p>
</blockquote>
<hr />
+<h2 id="floor-1">/floor</h2>
+<p>See <a href="#floordiv">floordiv</a>.</p>
+<hr />
+<h2 id="section-23">/</h2>
+<p>See <a href="#floordiv">floordiv</a>.</p>
+<hr />
+<h2 id="section-24">//</h2>
+<p>See <a href="#floordiv">floordiv</a>.</p>
+<hr />
<h2 id="sort">sort</h2>
<p>Function</p>
<p>Given a list return it sorted.</p>
<h2 id="spiral_next">spiral_next</h2>
<p>Function</p>
<p>Example code.</p>
-<h3 id="discussion-61">Discussion</h3>
+<h3 id="discussion-60">Discussion</h3>
<p>See the <a href="https://joypy.osdn.io/notebooks/Square_Spiral.html">“Square Spiral Example Joy Code” notebook</a>.</p>
<hr />
<h2 id="split_at">split_at</h2>
<pre><code> [1 2 3 4 5 6 7] 4 split_at
--------------------------------
[5 6 7] [4 3 2 1]</code></pre>
-<h3 id="definition-79">Definition</h3>
+<h3 id="definition-78">Definition</h3>
<blockquote>
<p>[<a href="#drop">drop</a>] [<a href="#take">take</a>] <a href="#clop">clop</a></p>
</blockquote>
-<h3 id="discussion-62">Discussion</h3>
+<h3 id="discussion-61">Discussion</h3>
<p>Take a list and a number <code>n</code> from the stack, take <code>n</code> items from the top of the list and <a href="#shunt">shunt</a> them onto a new list that replaces the number <code>n</code> on the top of the stack.</p>
-<h3 id="crosslinks-96">Crosslinks</h3>
+<h3 id="crosslinks-95">Crosslinks</h3>
<p><a href="#split_list">split_list</a></p>
<hr />
<h2 id="split_list">split_list</h2>
<pre><code> [1 2 3 4 5 6 7] 4 split_list
----------------------------------
[1 2 3 4] [5 6 7]</code></pre>
-<h3 id="definition-80">Definition</h3>
+<h3 id="definition-79">Definition</h3>
<blockquote>
<p>[<a href="#take">take</a> <a href="#reverse">reverse</a>] [<a href="#drop">drop</a>] <a href="#clop">clop</a></p>
</blockquote>
-<h3 id="discussion-63">Discussion</h3>
+<h3 id="discussion-62">Discussion</h3>
<p>Compare with <a href="#split_at">split_at</a>. This function does extra work to ensure that <a href="#concat">concat</a> would reconstruct the original list.</p>
-<h3 id="crosslinks-97">Crosslinks</h3>
+<h3 id="crosslinks-96">Crosslinks</h3>
<p><a href="#split_at">split_at</a></p>
<hr />
<h2 id="sqr">sqr</h2>
<pre><code> n sqr
------------
n²</code></pre>
-<h3 id="definition-81">Definition</h3>
+<h3 id="definition-80">Definition</h3>
<blockquote>
<p><a href="#dup">dup</a> <a href="#mul">mul</a></p>
</blockquote>
<h2 id="sqrt">sqrt</h2>
<p>Basis Function Combinator</p>
<p>Return the square root of the number a. Negative numbers return complex roots.</p>
-<h3 id="discussion-64">Discussion</h3>
+<h3 id="discussion-63">Discussion</h3>
<p>Another “numeric tower” hatch…</p>
<hr />
+<h2 id="stackd">stackd</h2>
+<p>Function</p>
+<p>Grab the stack under the top item and put it onto the stack.</p>
+<h3 id="example-26">Example</h3>
+<pre><code> ... 1 2 3 stackd
+------------------------
+ ... 1 2 [2 1 ...] 3</code></pre>
+<h3 id="definition-81">Definition</h3>
+<blockquote>
+<p>[<a href="#stack">stack</a>] <a href="#dip">dip</a></p>
+</blockquote>
+<hr />
<h2 id="stack">stack</h2>
<p>Function</p>
<p>Put the stack onto the stack.</p>
<blockquote>
<p>[] <a href="#swaack">swaack</a> <a href="#dup">dup</a> <a href="#swaack">swaack</a> <a href="#first">first</a></p>
</blockquote>
-<h3 id="discussion-65">Discussion</h3>
+<h3 id="discussion-64">Discussion</h3>
<p>This function forms a pair with [unstack], and together they form the complement to the “destructive” pair <a href="#enstacken">enstacken</a> and <a href="#disenstacken">disenstacken</a>.</p>
-<h3 id="crosslinks-98">Crosslinks</h3>
+<h3 id="crosslinks-97">Crosslinks</h3>
<p>[unstack] <a href="#enstacken">enstacken</a> <a href="#disenstacken">disenstacken</a></p>
<hr />
-<h2 id="stackd">stackd</h2>
-<p>Function</p>
-<p>Grab the stack under the top item and put it onto the stack.</p>
-<h3 id="example-26">Example</h3>
-<pre><code> ... 1 2 3 stackd
-------------------------
- ... 1 2 [2 1 ...] 3</code></pre>
-<h3 id="definition-83">Definition</h3>
-<blockquote>
-<p>[<a href="#stack">stack</a>] <a href="#dip">dip</a></p>
-</blockquote>
-<hr />
<h2 id="step">step</h2>
<p>Combinator</p>
<p>Run a quoted program on each item in a sequence.</p>
... [a b c] [Q] . step
----------------------------------------
... a . Q [b c] [Q] step</code></pre>
-<h3 id="discussion-66">Discussion</h3>
+<h3 id="discussion-65">Discussion</h3>
<p>See the <a href="https://joypy.osdn.io/notebooks/Recursion_Combinators.html">Recursion Combinators notebook</a>.</p>
-<h3 id="crosslinks-99">Crosslinks</h3>
+<h3 id="crosslinks-98">Crosslinks</h3>
<p><a href="#step_zero">step_zero</a></p>
<hr />
<h2 id="step_zero">step_zero</h2>
<pre><code> [...] [F] step_zero
-------------------------
0 [...] [F] step</code></pre>
-<h3 id="definition-84">Definition</h3>
+<h3 id="definition-83">Definition</h3>
<blockquote>
<p>0 <a href="#roll">roll></a> <a href="#step">step</a></p>
</blockquote>
-<h3 id="discussion-67">Discussion</h3>
+<h3 id="discussion-66">Discussion</h3>
<p><a href="#size">size</a> and <a href="#sum">sum</a> can both be defined in terms of this specialization of <a href="#step">step</a>.</p>
-<h3 id="crosslinks-100">Crosslinks</h3>
+<h3 id="crosslinks-99">Crosslinks</h3>
<p><a href="#step">step</a></p>
<hr />
<h2 id="stuncons">stuncons</h2>
<pre><code> 1 2 3 stuncons
--------------------
1 2 3 3 [2 1]</code></pre>
-<h3 id="definition-85">Definition</h3>
+<h3 id="definition-84">Definition</h3>
<blockquote>
<p><a href="#stack">stack</a> <a href="#uncons">uncons</a></p>
</blockquote>
<pre><code> 1 2 3 stununcons
----------------------
1 2 3 3 2 [1]</code></pre>
-<h3 id="definition-86">Definition</h3>
+<h3 id="definition-85">Definition</h3>
<blockquote>
<p><a href="#stack">stack</a> <a href="#uncons">uncons</a> <a href="#uncons">uncons</a></p>
</blockquote>
-<h3 id="crosslinks-101">Crosslinks</h3>
+<h3 id="crosslinks-100">Crosslinks</h3>
<p><a href="#stuncons">stuncons</a></p>
<hr />
<h2 id="sub">sub</h2>
<pre><code> a b sub
-------------
(a-b)</code></pre>
-<h3 id="crosslinks-102">Crosslinks</h3>
+<h3 id="crosslinks-101">Crosslinks</h3>
<p><a href="#add">add</a></p>
<hr />
<h2 id="succ">succ</h2>
<p>Function</p>
<p>Successor. Increment TOS.</p>
-<h3 id="definition-87">Definition</h3>
+<h3 id="definition-86">Definition</h3>
<blockquote>
<p>1 +</p>
</blockquote>
-<h3 id="crosslinks-103">Crosslinks</h3>
+<h3 id="crosslinks-102">Crosslinks</h3>
<p><a href="#pred">pred</a></p>
<hr />
<h2 id="sum">sum</h2>
<pre><code> [1 2 3 4 5] sum
---------------------
15</code></pre>
-<h3 id="definition-88">Definition</h3>
+<h3 id="definition-87">Definition</h3>
<blockquote>
<p>[+] <a href="#step_zero">step_zero</a></p>
</blockquote>
-<h3 id="crosslinks-104">Crosslinks</h3>
+<h3 id="crosslinks-103">Crosslinks</h3>
<p><a href="#size">size</a></p>
<hr />
<h2 id="swaack">swaack</h2>
<pre><code> 1 2 3 [4 5 6] swaack
--------------------------
6 5 4 [3 2 1]</code></pre>
-<h3 id="discussion-68">Discussion</h3>
+<h3 id="discussion-67">Discussion</h3>
<p>This function works as a kind of “context switch”. It’s used in the definition of <a href="#infra">infra</a>.</p>
-<h3 id="crosslinks-105">Crosslinks</h3>
+<h3 id="crosslinks-104">Crosslinks</h3>
<p><a href="#infra">infra</a></p>
<hr />
-<h2 id="swap">swap</h2>
-<p>Basis Function</p>
-<p>Swap the top two items on the stack.</p>
-<pre><code> a b swap
---------------
- b a</code></pre>
-<h3 id="crosslinks-106">Crosslinks</h3>
-<p><a href="#swapd">swapd</a></p>
-<hr />
<h2 id="swapd">swapd</h2>
<p>Function</p>
<p>Swap the second and third items on the stack.</p>
<pre><code> a b c swapd
-----------------
b a c</code></pre>
-<h3 id="definition-89">Definition</h3>
+<h3 id="definition-88">Definition</h3>
<blockquote>
<p>[<a href="#swap">swap</a>] <a href="#dip">dip</a></p>
</blockquote>
-<h3 id="crosslinks-107">Crosslinks</h3>
+<h3 id="crosslinks-105">Crosslinks</h3>
<p><a href="#over">over</a> <a href="#tuck">tuck</a></p>
<hr />
+<h2 id="swap">swap</h2>
+<p>Basis Function</p>
+<p>Swap the top two items on the stack.</p>
+<pre><code> a b swap
+--------------
+ b a</code></pre>
+<h3 id="crosslinks-106">Crosslinks</h3>
+<p><a href="#swapd">swapd</a></p>
+<hr />
<h2 id="swoncat">swoncat</h2>
<p>Function</p>
<p><a href="#concat">concat</a> two lists, but <a href="#swap">swap</a> the lists first.</p>
-<h3 id="definition-90">Definition</h3>
+<h3 id="definition-89">Definition</h3>
<blockquote>
<p><a href="#swap">swap</a> <a href="#concat">concat</a></p>
</blockquote>
-<h3 id="crosslinks-108">Crosslinks</h3>
+<h3 id="crosslinks-107">Crosslinks</h3>
<p><a href="#concat">concat</a></p>
<hr />
<h2 id="swons">swons</h2>
<pre><code> [...] a swons
-------------------
[a ...]</code></pre>
-<h3 id="definition-91">Definition</h3>
+<h3 id="definition-90">Definition</h3>
<blockquote>
<p><a href="#swap">swap</a> <a href="#cons">cons</a></p>
</blockquote>
<h2 id="tailrec">tailrec</h2>
<p>Combinator</p>
<p>A specialization of the <a href="#genrec">genrec</a> combinator.</p>
-<h3 id="definition-92">Definition</h3>
+<h3 id="definition-91">Definition</h3>
<blockquote>
<p>[<a href="#i">i</a>] <a href="#genrec">genrec</a></p>
</blockquote>
-<h3 id="discussion-69">Discussion</h3>
+<h3 id="discussion-68">Discussion</h3>
<p>Some recursive functions do not need to store additional data or pending actions per-call. These are called <a href="https://en.wikipedia.org/wiki/Tail_recursive">“tail recursive” functions</a>. In Joy, they appear as <a href="#genrec">genrec</a> definitions that have <a href="#i">i</a> for the second half of their recursive branch.</p>
<p>See the <a href="https://joypy.osdn.io/notebooks/Recursion_Combinators.html">Recursion Combinators notebook</a>.</p>
-<h3 id="crosslinks-109">Crosslinks</h3>
+<h3 id="crosslinks-108">Crosslinks</h3>
<p><a href="#genrec">genrec</a></p>
<hr />
<h2 id="take">take</h2>
<pre><code> [a b c d] 2 take
----------------------
[b a]</code></pre>
-<h3 id="definition-93">Definition</h3>
+<h3 id="definition-92">Definition</h3>
<blockquote>
-<p><a href="#section-1
8"><<{}</a> [<a href="#shift">shift</a>] <a href="#times">times</a> <a href="#pop">pop</a></p>
+<p><a href="#section-1
6"><<{}</a> [<a href="#shift">shift</a>] <a href="#times">times</a> <a href="#pop">pop</a></p>
</blockquote>
<hr />
<h2 id="ternary">ternary</h2>
<pre><code> ... z y x [P] ternary
-------------------------
... a</code></pre>
-<h3 id="definition-94">Definition</h3>
+<h3 id="definition-93">Definition</h3>
<blockquote>
<p><a href="#binary">binary</a> <a href="#popd">popd</a></p>
</blockquote>
-<h3 id="discussion-70">Discussion</h3>
+<h3 id="discussion-69">Discussion</h3>
<p>Runs any other quoted function and returns its first result while consuming exactly three items from the stack.</p>
-<h3 id="crosslinks-110">Crosslinks</h3>
+<h3 id="crosslinks-109">Crosslinks</h3>
<p><a href="#binary">binary</a> <a href="#nullary">nullary</a> <a href="#unary">unary</a></p>
<hr />
<h2 id="third">third</h2>
<pre><code> [a b c ...] third
-----------------------
c</code></pre>
-<h3 id="definition-95">Definition</h3>
+<h3 id="definition-94">Definition</h3>
<blockquote>
<p><a href="#rest">rest</a> <a href="#second">second</a></p>
</blockquote>
-<h3 id="crosslinks-111">Crosslinks</h3>
+<h3 id="crosslinks-110">Crosslinks</h3>
<p><a href="#first">first</a> <a href="#second">second</a> <a href="#fourth">fourth</a> <a href="#rest">rest</a></p>
<hr />
<h2 id="times">times</h2>
... n [Q] . times
------------------------------------- w/ n > 1
... . Q (n-1) [Q] times</code></pre>
-<h3 id="definition-96">Definition</h3>
+<h3 id="definition-95">Definition</h3>
<blockquote>
<p>[-- dip] cons [swap] infra [0 >] swap while pop :</p>
</blockquote>
-<h3 id="discussion-71">Discussion</h3>
+<h3 id="discussion-70">Discussion</h3>
<p>This works by building a little <a href="#while">while</a> program and running it:</p>
<pre><code> 1 3 [++] • [-- dip] cons [swap] infra [0 >] swap while pop
1 3 [++] [-- dip] • cons [swap] infra [0 >] swap while pop
<pre><code> a b tuck
--------------
b a b</code></pre>
-<h3 id="definition-97">Definition</h3>
+<h3 id="definition-96">Definition</h3>
<blockquote>
<p><a href="#dup">dup</a> [<a href="#swap">swap</a>] <a href="#dip">dip</a></p>
</blockquote>
-<h3 id="crosslinks-112">Crosslinks</h3>
+<h3 id="crosslinks-111">Crosslinks</h3>
<p><a href="#over">over</a></p>
<hr />
<h2 id="unary">unary</h2>
<pre><code> ... x [P] unary
---------------------
... a</code></pre>
-<h3 id="definition-98">Definition</h3>
+<h3 id="definition-97">Definition</h3>
<blockquote>
<p><a href="#nullary">nullary</a> <a href="#popd">popd</a></p>
</blockquote>
-<h3 id="discussion-72">Discussion</h3>
+<h3 id="discussion-71">Discussion</h3>
<p>Runs any other quoted function and returns its first result while consuming exactly one item from the stack.</p>
-<h3 id="crosslinks-113">Crosslinks</h3>
+<h3 id="crosslinks-112">Crosslinks</h3>
<p><a href="#binary">binary</a> <a href="#nullary">nullary</a> <a href="#ternary">ternary</a></p>
<hr />
<h2 id="uncons">uncons</h2>
<pre><code> [a ...] uncons
--------------------
a [...]</code></pre>
-<h3 id="discussion-73">Discussion</h3>
+<h3 id="discussion-72">Discussion</h3>
<p>This is the inverse of <a href="#cons">cons</a>.</p>
-<h3 id="crosslinks-114">Crosslinks</h3>
+<h3 id="crosslinks-113">Crosslinks</h3>
<p><a href="#cons">cons</a></p>
<hr />
<h2 id="unique">unique</h2>
<pre><code> a unit
------------
[a]</code></pre>
-<h3 id="definition-99">Definition</h3>
+<h3 id="definition-98">Definition</h3>
<blockquote>
<p>[] <a href="#cons">cons</a></p>
</blockquote>
<pre><code> 1 2 [3 4] 5 unquoted
--------------------------
1 2 3 4 5</code></pre>
-<h3 id="definition-100">Definition</h3>
+<h3 id="definition-99">Definition</h3>
<blockquote>
<p>[<a href="#i">i</a>] <a href="#dip">dip</a></p>
</blockquote>
-<h3 id="crosslinks-115">Crosslinks</h3>
+<h3 id="crosslinks-114">Crosslinks</h3>
<p><a href="#unit">unit</a></p>
<hr />
<h2 id="unswons">unswons</h2>
<pre><code> [a ...] unswons
---------------------
[...] a</code></pre>
-<h3 id="definition-101">Definition</h3>
+<h3 id="definition-100">Definition</h3>
<blockquote>
<p><a href="#uncons">uncons</a> <a href="#swap">swap</a></p>
</blockquote>
<hr />
+<h2 id="section-25">||</h2>
+<p>Combinator</p>
+<p>Short-circuiting Boolean OR</p>
+<h3 id="definition-101">Definition</h3>
+<blockquote>
+<p><a href="#nulco">nulco</a> [<a href="#nullary">nullary</a>] <a href="#dip">dip</a> [true] <a href="#branch">branch</a></p>
+</blockquote>
+<h3 id="discussion-73">Discussion</h3>
+<p>Accept two quoted programs, run the first and expect a Boolean value, if it’s <code>false</code> pop it and run the second program (which should also return a Boolean value) otherwise pop the second program (leaving <code>true</code> on the stack.)</p>
+<pre><code> [A] [B] ||
+---------------- A -> false
+ B
+
+
+ [A] [B] ||
+---------------- A -> true
+ true</code></pre>
+<h3 id="crosslinks-115">Crosslinks</h3>
+<p><a href="#section-1">&&</a></p>
+<hr />
<h2 id="void">void</h2>
<p>Basis Function</p>
<p>True if the form on TOS is void otherwise False.</p>
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