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<div class="section" id="function-reference">
<h1>Function Reference<a class="headerlink" href="#function-reference" title="Permalink to this headline"></a></h1>
<div class="section" id="module-joy.library">
<span id="joy-library"></span><h2><code class="docutils literal notranslate"><span class="pre">joy.library</span></code><a class="headerlink" href="#module-joy.library" title="Permalink to this headline"></a></h2>
<p>This module contains the Joy function infrastructure and a library of
functions. Its main export is a Python function initialize() that
returns a dictionary of Joy functions suitable for use with the joy()
function.</p>
<dl class="function">
<dt id="joy.library.BinaryBuiltinWrapper">
<code class="descclassname">joy.library.</code><code class="descname">BinaryBuiltinWrapper</code><span class="sig-paren">(</span><em>f</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#BinaryBuiltinWrapper"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.BinaryBuiltinWrapper" title="Permalink to this definition"></a></dt>
<dd><p>Wrap functions that take two arguments and return a single result.</p>
</dd></dl>
<dl class="class">
<dt id="joy.library.DefinitionWrapper">
<em class="property">class </em><code class="descclassname">joy.library.</code><code class="descname">DefinitionWrapper</code><span class="sig-paren">(</span><em>name</em>, <em>body_text</em>, <em>doc=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#DefinitionWrapper"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.DefinitionWrapper" title="Permalink to this definition"></a></dt>
<dd><p>Provide implementation of defined functions, and some helper methods.</p>
<dl class="classmethod">
<dt id="joy.library.DefinitionWrapper.add_def">
<em class="property">classmethod </em><code class="descname">add_def</code><span class="sig-paren">(</span><em>definition</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#DefinitionWrapper.add_def"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.DefinitionWrapper.add_def" title="Permalink to this definition"></a></dt>
<dd><p>Add the definition to the dictionary.</p>
</dd></dl>
<dl class="classmethod">
<dt id="joy.library.DefinitionWrapper.add_definitions">
<em class="property">classmethod </em><code class="descname">add_definitions</code><span class="sig-paren">(</span><em>defs</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#DefinitionWrapper.add_definitions"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.DefinitionWrapper.add_definitions" title="Permalink to this definition"></a></dt>
<dd><p>Scan multi-line string defs for definitions and add them to the
dictionary.</p>
</dd></dl>
<dl class="classmethod">
<dt id="joy.library.DefinitionWrapper.parse_definition">
<em class="property">classmethod </em><code class="descname">parse_definition</code><span class="sig-paren">(</span><em>defi</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#DefinitionWrapper.parse_definition"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.DefinitionWrapper.parse_definition" title="Permalink to this definition"></a></dt>
<dd><p>Given some text describing a Joy function definition parse it and
return a DefinitionWrapper.</p>
</dd></dl>
</dd></dl>
<dl class="function">
<dt id="joy.library.FunctionWrapper">
<code class="descclassname">joy.library.</code><code class="descname">FunctionWrapper</code><span class="sig-paren">(</span><em>f</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#FunctionWrapper"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.FunctionWrapper" title="Permalink to this definition"></a></dt>
<dd><p>Set name attribute.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.SimpleFunctionWrapper">
<code class="descclassname">joy.library.</code><code class="descname">SimpleFunctionWrapper</code><span class="sig-paren">(</span><em>f</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#SimpleFunctionWrapper"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.SimpleFunctionWrapper" title="Permalink to this definition"></a></dt>
<dd><p>Wrap functions that take and return just a stack.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.UnaryBuiltinWrapper">
<code class="descclassname">joy.library.</code><code class="descname">UnaryBuiltinWrapper</code><span class="sig-paren">(</span><em>f</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#UnaryBuiltinWrapper"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.UnaryBuiltinWrapper" title="Permalink to this definition"></a></dt>
<dd><p>Wrap functions that take one argument and return a single result.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.add_aliases">
<code class="descclassname">joy.library.</code><code class="descname">add_aliases</code><span class="sig-paren">(</span><em>D</em>, <em>A</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#add_aliases"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.add_aliases" title="Permalink to this definition"></a></dt>
<dd><p>Given a dict and a iterable of (name, [alias, …]) pairs, create
additional entries in the dict mapping each alias to the named function
if it’s in the dict. Aliases for functions not in the dict are ignored.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.app1">
<code class="descclassname">joy.library.</code><code class="descname">app1</code><span class="sig-paren">(</span><em>S</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#app1"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.app1" title="Permalink to this definition"></a></dt>
<dd><p>Given a quoted program on TOS and anything as the second stack item run
the program and replace the two args with the first result of the
program.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">app1</span>
<span class="o">-----------------------------------</span>
<span class="o">...</span> <span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="n">first</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.app2">
<code class="descclassname">joy.library.</code><code class="descname">app2</code><span class="sig-paren">(</span><em>S</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#app2"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.app2" title="Permalink to this definition"></a></dt>
<dd><p>Like app1 with two items.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">y</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">app2</span>
<span class="o">-----------------------------------</span>
<span class="o">...</span> <span class="p">[</span><span class="n">y</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="n">first</span>
<span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.app3">
<code class="descclassname">joy.library.</code><code class="descname">app3</code><span class="sig-paren">(</span><em>S</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#app3"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.app3" title="Permalink to this definition"></a></dt>
<dd><p>Like app1 with three items.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">z</span> <span class="n">y</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">app3</span>
<span class="o">-----------------------------------</span>
<span class="o">...</span> <span class="p">[</span><span class="n">z</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="n">first</span>
<span class="p">[</span><span class="n">y</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
<span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.b">
<code class="descclassname">joy.library.</code><code class="descname">b</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#b"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.b" title="Permalink to this definition"></a></dt>
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="o">==</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">dip</span> <span class="n">i</span>
<span class="o">...</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">b</span> <span class="o">==</span> <span class="o">...</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="n">i</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">i</span>
<span class="o">...</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">b</span> <span class="o">==</span> <span class="o">...</span> <span class="n">P</span> <span class="n">Q</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.branch">
<code class="descclassname">joy.library.</code><code class="descname">branch</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#branch"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.branch" title="Permalink to this definition"></a></dt>
<dd><p>Use a Boolean value to select one of two quoted programs to run.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">branch</span> <span class="o">==</span> <span class="n">roll</span><span class="o">&lt;</span> <span class="n">choice</span> <span class="n">i</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="kc">False</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="n">branch</span>
<span class="o">--------------------------</span>
<span class="n">F</span>
<span class="kc">True</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="n">branch</span>
<span class="o">-------------------------</span>
<span class="n">T</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.choice">
<code class="descclassname">joy.library.</code><code class="descname">choice</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#choice"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.choice" title="Permalink to this definition"></a></dt>
<dd><p>Use a Boolean value to select one of two items.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">A</span> <span class="n">B</span> <span class="kc">False</span> <span class="n">choice</span>
<span class="o">----------------------</span>
<span class="n">A</span>
<span class="n">A</span> <span class="n">B</span> <span class="kc">True</span> <span class="n">choice</span>
<span class="o">---------------------</span>
<span class="n">B</span>
</pre></div>
</div>
<p>Currently Python semantics are used to evaluate the “truthiness” of the
Boolean value (so empty string, zero, etc. are counted as false, etc.)</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.clear">
<code class="descclassname">joy.library.</code><code class="descname">clear</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#clear"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.clear" title="Permalink to this definition"></a></dt>
<dd><p>Clear everything from the stack.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">clear</span>
<span class="o">---------------</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.cmp_">
<code class="descclassname">joy.library.</code><code class="descname">cmp_</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#cmp_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.cmp_" title="Permalink to this definition"></a></dt>
<dd><p>cmp takes two values and three quoted programs on the stack and runs
one of the three depending on the results of comparing the two values:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">a</span> <span class="n">b</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">L</span><span class="p">]</span> <span class="nb">cmp</span>
<span class="o">-------------------------</span> <span class="n">a</span> <span class="o">&gt;</span> <span class="n">b</span>
<span class="n">G</span>
<span class="n">a</span> <span class="n">b</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">L</span><span class="p">]</span> <span class="nb">cmp</span>
<span class="o">-------------------------</span> <span class="n">a</span> <span class="o">=</span> <span class="n">b</span>
<span class="n">E</span>
<span class="n">a</span> <span class="n">b</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">L</span><span class="p">]</span> <span class="nb">cmp</span>
<span class="o">-------------------------</span> <span class="n">a</span> <span class="o">&lt;</span> <span class="n">b</span>
<span class="n">L</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.concat">
<code class="descclassname">joy.library.</code><code class="descname">concat</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#concat"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.concat" title="Permalink to this definition"></a></dt>
<dd><p>Concatinate the two lists on the top of the stack.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.cond">
<code class="descclassname">joy.library.</code><code class="descname">cond</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#cond"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.cond" title="Permalink to this definition"></a></dt>
<dd><p>This combinator works like a case statement. It expects a single quote
on the stack that must contain zero or more condition quotes and a
default quote. Each condition clause should contain a quoted predicate
followed by the function expression to run if that predicate returns
true. If no predicates return true the default function runs.</p>
<p>It works by rewriting into a chain of nested <cite>ifte</cite> expressions, e.g.:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[[[</span><span class="n">B0</span><span class="p">]</span> <span class="n">T0</span><span class="p">]</span> <span class="p">[[</span><span class="n">B1</span><span class="p">]</span> <span class="n">T1</span><span class="p">]</span> <span class="p">[</span><span class="n">D</span><span class="p">]]</span> <span class="n">cond</span>
<span class="o">-----------------------------------------</span>
<span class="p">[</span><span class="n">B0</span><span class="p">]</span> <span class="p">[</span><span class="n">T0</span><span class="p">]</span> <span class="p">[[</span><span class="n">B1</span><span class="p">]</span> <span class="p">[</span><span class="n">T1</span><span class="p">]</span> <span class="p">[</span><span class="n">D</span><span class="p">]</span> <span class="n">ifte</span><span class="p">]</span> <span class="n">ifte</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.cons">
<code class="descclassname">joy.library.</code><code class="descname">cons</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#cons"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.cons" title="Permalink to this definition"></a></dt>
<dd><p>The cons operator expects a list on top of the stack and the potential
member below. The effect is to add the potential member into the
aggregate.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.dip">
<code class="descclassname">joy.library.</code><code class="descname">dip</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#dip"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.dip" title="Permalink to this definition"></a></dt>
<dd><p>The dip 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>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dip</span>
<span class="o">-------------------</span>
<span class="o">...</span> <span class="n">Q</span> <span class="n">x</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.dipd">
<code class="descclassname">joy.library.</code><code class="descname">dipd</code><span class="sig-paren">(</span><em>S</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#dipd"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.dipd" title="Permalink to this definition"></a></dt>
<dd><p>Like dip but expects two items.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">y</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dip</span>
<span class="o">---------------------</span>
<span class="o">...</span> <span class="n">Q</span> <span class="n">y</span> <span class="n">x</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.dipdd">
<code class="descclassname">joy.library.</code><code class="descname">dipdd</code><span class="sig-paren">(</span><em>S</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#dipdd"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.dipdd" title="Permalink to this definition"></a></dt>
<dd><p>Like dip but expects three items.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">z</span> <span class="n">y</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dip</span>
<span class="o">-----------------------</span>
<span class="o">...</span> <span class="n">Q</span> <span class="n">z</span> <span class="n">y</span> <span class="n">x</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.divmod_">
<code class="descclassname">joy.library.</code><code class="descname">divmod_</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#divmod_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.divmod_" title="Permalink to this definition"></a></dt>
<dd><p>divmod(x, y) -&gt; (quotient, remainder)</p>
<p>Return the tuple (x//y, x%y). Invariant: div*y + mod == x.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.drop">
<code class="descclassname">joy.library.</code><code class="descname">drop</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#drop"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.drop" title="Permalink to this definition"></a></dt>
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">drop</span> <span class="o">==</span> <span class="p">[</span><span class="n">rest</span><span class="p">]</span> <span class="n">times</span>
</pre></div>
</div>
<p>Expects an integer and a quote on the stack and returns the quote with
n items removed off the top.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="mi">2</span> <span class="n">drop</span>
<span class="o">----------------------</span>
<span class="p">[</span><span class="n">c</span> <span class="n">d</span><span class="p">]</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.dup">
<code class="descclassname">joy.library.</code><code class="descname">dup</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#dup"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.dup" title="Permalink to this definition"></a></dt>
<dd><p>Duplicate the top item on the stack.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.dupd">
<code class="descclassname">joy.library.</code><code class="descname">dupd</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#dupd"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.dupd" title="Permalink to this definition"></a></dt>
<dd><p>Duplicate the second item on the stack.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.dupdip">
<code class="descclassname">joy.library.</code><code class="descname">dupdip</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#dupdip"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.dupdip" title="Permalink to this definition"></a></dt>
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">dupdip</span> <span class="o">==</span> <span class="n">dup</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">dip</span>
<span class="o">...</span> <span class="n">a</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">dupdip</span>
<span class="o">...</span> <span class="n">a</span> <span class="n">dup</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">dip</span>
<span class="o">...</span> <span class="n">a</span> <span class="n">a</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">dip</span>
<span class="o">...</span> <span class="n">a</span> <span class="n">F</span> <span class="n">a</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.first">
<code class="descclassname">joy.library.</code><code class="descname">first</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#first"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.first" title="Permalink to this definition"></a></dt>
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">first</span> <span class="o">==</span> <span class="n">uncons</span> <span class="n">pop</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.floor">
<code class="descclassname">joy.library.</code><code class="descname">floor</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#floor"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.floor" title="Permalink to this definition"></a></dt>
<dd><p>Return the floor of x as a float.
This is the largest integral value &lt;= x.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.genrec">
<code class="descclassname">joy.library.</code><code class="descname">genrec</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#genrec"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.genrec" title="Permalink to this definition"></a></dt>
<dd><p>General Recursion Combinator.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="k">if</span><span class="p">]</span> <span class="p">[</span><span class="n">then</span><span class="p">]</span> <span class="p">[</span><span class="n">rec1</span><span class="p">]</span> <span class="p">[</span><span class="n">rec2</span><span class="p">]</span> <span class="n">genrec</span>
<span class="o">---------------------------------------------------------------------</span>
<span class="p">[</span><span class="k">if</span><span class="p">]</span> <span class="p">[</span><span class="n">then</span><span class="p">]</span> <span class="p">[</span><span class="n">rec1</span> <span class="p">[[</span><span class="k">if</span><span class="p">]</span> <span class="p">[</span><span class="n">then</span><span class="p">]</span> <span class="p">[</span><span class="n">rec1</span><span class="p">]</span> <span class="p">[</span><span class="n">rec2</span><span class="p">]</span> <span class="n">genrec</span><span class="p">]</span> <span class="n">rec2</span><span class="p">]</span> <span class="n">ifte</span>
</pre></div>
</div>
<p>From “Recursion Theory and Joy” (j05cmp.html) by Manfred von Thun:
“The genrec combinator takes four program parameters in addition to
whatever data parameters it needs. Fourth from the top is an if-part,
followed by a then-part. If the if-part yields true, then the then-part
is executed and the combinator terminates. The other two parameters are
the rec1-part and the rec2-part. If the if-part yields false, the
rec1-part is executed. Following that the four program parameters and
the combinator are again pushed onto the stack bundled up in a quoted
form. Then the rec2-part is executed, where it will find the bundled
form. Typically it will then execute the bundled form, either with i or
with app2, or some other combinator.”</p>
<p>The way to design one of these is to fix your base case [then] and the
test [if], and then treat rec1 and rec2 as an else-part “sandwiching”
a quotation of the whole function.</p>
<p>For example, given a (general recursive) function ‘F’:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">==</span> <span class="p">[</span><span class="n">I</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">R1</span><span class="p">]</span> <span class="p">[</span><span class="n">R2</span><span class="p">]</span> <span class="n">genrec</span>
</pre></div>
</div>
<p>If the [I] if-part fails you must derive R1 and R2 from:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">...</span> <span class="n">R1</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">R2</span>
</pre></div>
</div>
<p>Just set the stack arguments in front, and figure out what R1 and R2
have to do to apply the quoted [F] in the proper way. In effect, the
genrec combinator turns into an ifte combinator with a quoted copy of
the original definition in the else-part:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">==</span> <span class="p">[</span><span class="n">I</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">R1</span><span class="p">]</span> <span class="p">[</span><span class="n">R2</span><span class="p">]</span> <span class="n">genrec</span>
<span class="o">==</span> <span class="p">[</span><span class="n">I</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">R1</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">R2</span><span class="p">]</span> <span class="n">ifte</span>
</pre></div>
</div>
<p>Primitive recursive functions are those where R2 == i.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">P</span> <span class="o">==</span> <span class="p">[</span><span class="n">I</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">R</span><span class="p">]</span> <span class="n">primrec</span>
<span class="o">==</span> <span class="p">[</span><span class="n">I</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">R</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="n">i</span><span class="p">]</span> <span class="n">ifte</span>
<span class="o">==</span> <span class="p">[</span><span class="n">I</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">R</span> <span class="n">P</span><span class="p">]</span> <span class="n">ifte</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.getitem">
<code class="descclassname">joy.library.</code><code class="descname">getitem</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#getitem"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.getitem" title="Permalink to this definition"></a></dt>
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">getitem</span> <span class="o">==</span> <span class="n">drop</span> <span class="n">first</span>
</pre></div>
</div>
<p>Expects an integer and a quote on the stack and returns the item at the
nth position in the quote counting from 0.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="mi">0</span> <span class="n">getitem</span>
<span class="o">-------------------------</span>
<span class="n">a</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.help_">
<code class="descclassname">joy.library.</code><code class="descname">help_</code><span class="sig-paren">(</span><em>S</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#help_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.help_" title="Permalink to this definition"></a></dt>
<dd><p>Accepts a quoted symbol on the top of the stack and prints its docs.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.i">
<code class="descclassname">joy.library.</code><code class="descname">i</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#i"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.i" title="Permalink to this definition"></a></dt>
<dd><p>The i combinator expects a quoted program on the stack and unpacks it
onto the pending expression for evaluation.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">i</span>
<span class="o">-----------</span>
<span class="n">Q</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.id_">
<code class="descclassname">joy.library.</code><code class="descname">id_</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#id_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.id_" title="Permalink to this definition"></a></dt>
<dd><p>The identity function.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.ifte">
<code class="descclassname">joy.library.</code><code class="descname">ifte</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#ifte"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.ifte" title="Permalink to this definition"></a></dt>
<dd><p>If-Then-Else Combinator</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="p">[</span><span class="k">if</span><span class="p">]</span> <span class="p">[</span><span class="n">then</span><span class="p">]</span> <span class="p">[</span><span class="k">else</span><span class="p">]</span> <span class="n">ifte</span>
<span class="o">---------------------------------------------------</span>
<span class="o">...</span> <span class="p">[[</span><span class="k">else</span><span class="p">]</span> <span class="p">[</span><span class="n">then</span><span class="p">]]</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="k">if</span><span class="p">]</span> <span class="n">infra</span> <span class="n">select</span> <span class="n">i</span>
<span class="o">...</span> <span class="p">[</span><span class="k">if</span><span class="p">]</span> <span class="p">[</span><span class="n">then</span><span class="p">]</span> <span class="p">[</span><span class="k">else</span><span class="p">]</span> <span class="n">ifte</span>
<span class="o">-------------------------------------------------------</span>
<span class="o">...</span> <span class="p">[</span><span class="k">else</span><span class="p">]</span> <span class="p">[</span><span class="n">then</span><span class="p">]</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="k">if</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="n">choice</span> <span class="n">i</span>
</pre></div>
</div>
<p>Has the effect of grabbing a copy of the stack on which to run the
if-part using infra.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.infra">
<code class="descclassname">joy.library.</code><code class="descname">infra</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#infra"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.infra" title="Permalink to this definition"></a></dt>
<dd><p>Accept a quoted program and a list on the stack and run the program
with the list as its stack.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span>
<span class="o">-----------------------------</span>
<span class="n">c</span> <span class="n">b</span> <span class="n">a</span> <span class="o">.</span> <span class="n">Q</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">swaack</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.initialize">
<code class="descclassname">joy.library.</code><code class="descname">initialize</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#initialize"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.initialize" title="Permalink to this definition"></a></dt>
<dd><p>Return a dictionary of Joy functions for use with joy().</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.inscribe">
<code class="descclassname">joy.library.</code><code class="descname">inscribe</code><span class="sig-paren">(</span><em>function</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#inscribe"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.inscribe" title="Permalink to this definition"></a></dt>
<dd><p>A decorator to inscribe functions into the default dictionary.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.loop">
<code class="descclassname">joy.library.</code><code class="descname">loop</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#loop"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.loop" title="Permalink to this definition"></a></dt>
<dd><p>Basic loop combinator.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="kc">True</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
<span class="o">-----------------------</span>
<span class="o">...</span> <span class="n">Q</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
<span class="o">...</span> <span class="kc">False</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
<span class="o">------------------------</span>
<span class="o">...</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.map_">
<code class="descclassname">joy.library.</code><code class="descname">map_</code><span class="sig-paren">(</span><em>S</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#map_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.map_" title="Permalink to this definition"></a></dt>
<dd><p>Run the quoted program on TOS on the items in the list under it, push a
new list with the results (in place of the program and original list.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.max_">
<code class="descclassname">joy.library.</code><code class="descname">max_</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#max_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.max_" title="Permalink to this definition"></a></dt>
<dd><p>Given a list find the maximum.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.min_">
<code class="descclassname">joy.library.</code><code class="descname">min_</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#min_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.min_" title="Permalink to this definition"></a></dt>
<dd><p>Given a list find the minimum.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.over">
<code class="descclassname">joy.library.</code><code class="descname">over</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#over"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.over" title="Permalink to this definition"></a></dt>
<dd><p>Copy the second item down on the stack to the top of the stack.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">a</span> <span class="n">b</span> <span class="n">over</span>
<span class="o">--------------</span>
<span class="n">a</span> <span class="n">b</span> <span class="n">a</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.parse">
<code class="descclassname">joy.library.</code><code class="descname">parse</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#parse"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.parse" title="Permalink to this definition"></a></dt>
<dd><p>Parse the string on the stack to a Joy expression.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.pm">
<code class="descclassname">joy.library.</code><code class="descname">pm</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#pm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.pm" title="Permalink to this definition"></a></dt>
<dd><p>Plus or minus</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">a</span> <span class="n">b</span> <span class="n">pm</span>
<span class="o">-------------</span>
<span class="n">a</span><span class="o">+</span><span class="n">b</span> <span class="n">a</span><span class="o">-</span><span class="n">b</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.pop">
<code class="descclassname">joy.library.</code><code class="descname">pop</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#pop"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.pop" title="Permalink to this definition"></a></dt>
<dd><p>Pop and discard the top item from the stack.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.popd">
<code class="descclassname">joy.library.</code><code class="descname">popd</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#popd"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.popd" title="Permalink to this definition"></a></dt>
<dd><p>Pop and discard the second item from the stack.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.popdd">
<code class="descclassname">joy.library.</code><code class="descname">popdd</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#popdd"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.popdd" title="Permalink to this definition"></a></dt>
<dd><p>Pop and discard the third item from the stack.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.popop">
<code class="descclassname">joy.library.</code><code class="descname">popop</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#popop"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.popop" title="Permalink to this definition"></a></dt>
<dd><p>Pop and discard the first and second items from the stack.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.pred">
<code class="descclassname">joy.library.</code><code class="descname">pred</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#pred"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.pred" title="Permalink to this definition"></a></dt>
<dd><p>Decrement TOS.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.remove">
<code class="descclassname">joy.library.</code><code class="descname">remove</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#remove"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.remove" title="Permalink to this definition"></a></dt>
<dd><p>Expects an item on the stack and a quote under it and removes that item
from the the quote. The item is only removed once.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span><span class="p">]</span> <span class="mi">1</span> <span class="n">remove</span>
<span class="o">------------------------</span>
<span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span><span class="p">]</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.rest">
<code class="descclassname">joy.library.</code><code class="descname">rest</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#rest"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.rest" title="Permalink to this definition"></a></dt>
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">rest</span> <span class="o">==</span> <span class="n">uncons</span> <span class="n">popd</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.reverse">
<code class="descclassname">joy.library.</code><code class="descname">reverse</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#reverse"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.reverse" title="Permalink to this definition"></a></dt>
<dd><p>Reverse the list on the top of the stack.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">reverse</span> <span class="o">==</span> <span class="p">[]</span> <span class="n">swap</span> <span class="n">shunt</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.rolldown">
<code class="descclassname">joy.library.</code><code class="descname">rolldown</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#rolldown"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.rolldown" title="Permalink to this definition"></a></dt>
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">a</span> <span class="n">b</span> <span class="n">c</span>
<span class="o">-----------</span>
<span class="n">c</span> <span class="n">a</span> <span class="n">b</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.rollup">
<code class="descclassname">joy.library.</code><code class="descname">rollup</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#rollup"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.rollup" title="Permalink to this definition"></a></dt>
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">a</span> <span class="n">b</span> <span class="n">c</span>
<span class="o">-----------</span>
<span class="n">b</span> <span class="n">c</span> <span class="n">a</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.select">
<code class="descclassname">joy.library.</code><code class="descname">select</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#select"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.select" title="Permalink to this definition"></a></dt>
<dd><p>Use a Boolean value to select one of two items from a sequence.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">A</span> <span class="n">B</span><span class="p">]</span> <span class="kc">False</span> <span class="n">select</span>
<span class="o">------------------------</span>
<span class="n">A</span>
<span class="p">[</span><span class="n">A</span> <span class="n">B</span><span class="p">]</span> <span class="kc">True</span> <span class="n">select</span>
<span class="o">-----------------------</span>
<span class="n">B</span>
</pre></div>
</div>
<p>The sequence can contain more than two items but not fewer.
Currently Python semantics are used to evaluate the “truthiness” of the
Boolean value (so empty string, zero, etc. are counted as false, etc.)</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.sharing">
<code class="descclassname">joy.library.</code><code class="descname">sharing</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#sharing"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.sharing" title="Permalink to this definition"></a></dt>
<dd><p>Print redistribution information.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.shunt">
<code class="descclassname">joy.library.</code><code class="descname">shunt</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#shunt"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.shunt" title="Permalink to this definition"></a></dt>
<dd><p>Like concat but reverses the top list into the second.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">shunt</span> <span class="o">==</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">step</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.sort_">
<code class="descclassname">joy.library.</code><code class="descname">sort_</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#sort_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.sort_" title="Permalink to this definition"></a></dt>
<dd><p>Given a list return it sorted.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.sqrt">
<code class="descclassname">joy.library.</code><code class="descname">sqrt</code><span class="sig-paren">(</span><em>a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#sqrt"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.sqrt" title="Permalink to this definition"></a></dt>
<dd><p>Return the square root of the number a.
Negative numbers return complex roots.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.stack_">
<code class="descclassname">joy.library.</code><code class="descname">stack_</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#stack_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.stack_" title="Permalink to this definition"></a></dt>
<dd><p>The stack operator pushes onto the stack a list containing all the
elements of the stack.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.step">
<code class="descclassname">joy.library.</code><code class="descname">step</code><span class="sig-paren">(</span><em>S</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.step" title="Permalink to this definition"></a></dt>
<dd><p>Run a quoted program on each item in a sequence.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="p">[]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
<span class="o">-----------------------</span>
<span class="o">...</span> <span class="o">.</span>
<span class="o">...</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
<span class="o">------------------------</span>
<span class="o">...</span> <span class="n">a</span> <span class="o">.</span> <span class="n">Q</span>
<span class="o">...</span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
<span class="o">----------------------------------------</span>
<span class="o">...</span> <span class="n">a</span> <span class="o">.</span> <span class="n">Q</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">step</span>
</pre></div>
</div>
<p>The step combinator executes the quotation on each member of the list
on top of the stack.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.succ">
<code class="descclassname">joy.library.</code><code class="descname">succ</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#succ"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.succ" title="Permalink to this definition"></a></dt>
<dd><p>Increment TOS.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.sum_">
<code class="descclassname">joy.library.</code><code class="descname">sum_</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#sum_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.sum_" title="Permalink to this definition"></a></dt>
<dd><p>Given a quoted sequence of numbers return the sum.</p>
<p>sum == 0 swap [+] step</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.swaack">
<code class="descclassname">joy.library.</code><code class="descname">swaack</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#swaack"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.swaack" title="Permalink to this definition"></a></dt>
<dd><p>swap stack</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.swap">
<code class="descclassname">joy.library.</code><code class="descname">swap</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#swap"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.swap" title="Permalink to this definition"></a></dt>
<dd><p>Swap the top two items on stack.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.take">
<code class="descclassname">joy.library.</code><code class="descname">take</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#take"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.take" title="Permalink to this definition"></a></dt>
<dd><p>Expects an integer and a quote on the stack and returns the quote with
just the top n items in reverse order (because that’s easier and you can
use reverse if needed.)</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="mi">2</span> <span class="n">take</span>
<span class="o">----------------------</span>
<span class="p">[</span><span class="n">b</span> <span class="n">a</span><span class="p">]</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.times">
<code class="descclassname">joy.library.</code><code class="descname">times</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#times"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.times" title="Permalink to this definition"></a></dt>
<dd><p>times == [– dip] cons [swap] infra [0 &gt;] swap while pop</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">n</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span>
<span class="o">---------------------</span> <span class="n">w</span><span class="o">/</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">0</span>
<span class="o">...</span> <span class="o">.</span>
<span class="o">...</span> <span class="mi">1</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span>
<span class="o">---------------------------------</span>
<span class="o">...</span> <span class="o">.</span> <span class="n">Q</span>
<span class="o">...</span> <span class="n">n</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span>
<span class="o">---------------------------------</span> <span class="n">w</span><span class="o">/</span> <span class="n">n</span> <span class="o">&gt;</span> <span class="mi">1</span>
<span class="o">...</span> <span class="o">.</span> <span class="n">Q</span> <span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">times</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.tuck">
<code class="descclassname">joy.library.</code><code class="descname">tuck</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#tuck"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.tuck" title="Permalink to this definition"></a></dt>
<dd><p>Copy the item at TOS under the second item of the stack.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">a</span> <span class="n">b</span> <span class="n">tuck</span>
<span class="o">--------------</span>
<span class="n">b</span> <span class="n">a</span> <span class="n">b</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.uncons">
<code class="descclassname">joy.library.</code><code class="descname">uncons</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#uncons"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.uncons" title="Permalink to this definition"></a></dt>
<dd><p>Inverse of cons, removes an item from the top of the list on the stack
and places it under the remaining list.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.unique">
<code class="descclassname">joy.library.</code><code class="descname">unique</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#unique"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.unique" title="Permalink to this definition"></a></dt>
<dd><p>Given a list remove duplicate items.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.unstack">
<code class="descclassname">joy.library.</code><code class="descname">unstack</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#unstack"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.unstack" title="Permalink to this definition"></a></dt>
<dd><p>The unstack operator expects a list on top of the stack and makes that
the stack discarding the rest of the stack.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.void">
<code class="descclassname">joy.library.</code><code class="descname">void</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#void"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.void" title="Permalink to this definition"></a></dt>
<dd><p>True if the form on TOS is void otherwise False.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.warranty">
<code class="descclassname">joy.library.</code><code class="descname">warranty</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#warranty"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.warranty" title="Permalink to this definition"></a></dt>
<dd><p>Print warranty information.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.words">
<code class="descclassname">joy.library.</code><code class="descname">words</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#words"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.words" title="Permalink to this definition"></a></dt>
<dd><p>Print all the words in alphabetical order.</p>
</dd></dl>
<dl class="function">
<dt id="joy.library.x">
<code class="descclassname">joy.library.</code><code class="descname">x</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#x"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.x" title="Permalink to this definition"></a></dt>
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">==</span> <span class="n">dup</span> <span class="n">i</span>
<span class="o">...</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">x</span> <span class="o">=</span> <span class="o">...</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dup</span> <span class="n">i</span>
<span class="o">...</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">x</span> <span class="o">=</span> <span class="o">...</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">i</span>
<span class="o">...</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">x</span> <span class="o">=</span> <span class="o">...</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">Q</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="joy.library.zip_">
<code class="descclassname">joy.library.</code><code class="descname">zip_</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#zip_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.zip_" title="Permalink to this definition"></a></dt>
<dd><p>Replace the two lists on the top of the stack with a list of the pairs
from each list. The smallest list sets the length of the result list.</p>
</dd></dl>
</div>
</div>
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