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Simon Forman
2020-05-17 16:40:58 -07:00
parent ef6411205d
commit 56da4690d0
84 changed files with 7456 additions and 7972 deletions
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docs/sphinx_docs/_build/html/_modules/index.html
+18 -50
View File
@@ -1,18 +1,19 @@
<!DOCTYPE html>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Overview: module code &#8212; Thun 0.3.0 documentation</title>
<link rel="stylesheet" href="../_static/alabaster.css" type="text/css" />
<link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
<script id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script>
<script src="../_static/jquery.js"></script>
<script src="../_static/underscore.js"></script>
<script src="../_static/doctools.js"></script>
<script src="../_static/language_data.js"></script>
<script async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
<script type="text/javascript" src="../_static/documentation_options.js"></script>
<script type="text/javascript" src="../_static/jquery.js"></script>
<script type="text/javascript" src="../_static/underscore.js"></script>
<script type="text/javascript" src="../_static/doctools.js"></script>
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<link rel="index" title="Index" href="../genindex.html" />
<link rel="search" title="Search" href="../search.html" />
@@ -27,12 +28,10 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<h1>All modules for which code is available</h1>
<ul><li><a href="builtins.html">builtins</a></li>
<ul><li><a href="__builtin__.html">__builtin__</a></li>
<li><a href="joy/joy.html">joy.joy</a></li>
<li><a href="joy/library.html">joy.library</a></li>
<li><a href="joy/parser.html">joy.parser</a></li>
@@ -40,38 +39,13 @@
<li><a href="joy/utils/pretty_print.html">joy.utils.pretty_print</a></li>
<li><a href="joy/utils/stack.html">joy.utils.stack</a></li>
<li><a href="joy/utils/types.html">joy.utils.types</a></li>
<li><a href="past/types/basestring.html">past.types.basestring</a></li>
</ul>
</div>
</div>
</div>
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
<div class="sphinxsidebarwrapper">
<h1 class="logo"><a href="../index.html">Thun</a></h1>
<h3>Navigation</h3>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../notebooks/Intro.html">Thun: Joy in Python</a></li>
<li class="toctree-l1"><a class="reference internal" href="../joy.html">Joy Interpreter</a></li>
<li class="toctree-l1"><a class="reference internal" href="../stack.html">Stack or Quote or Sequence or List…</a></li>
<li class="toctree-l1"><a class="reference internal" href="../parser.html">Parsing Text into Joy Expressions</a></li>
<li class="toctree-l1"><a class="reference internal" href="../pretty.html">Tracing Joy Execution</a></li>
<li class="toctree-l1"><a class="reference internal" href="../library.html">Function Reference</a></li>
<li class="toctree-l1"><a class="reference internal" href="../lib.html">Functions Grouped by, er, Function with Examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="../types.html">Type Inference of Joy Expressions</a></li>
<li class="toctree-l1"><a class="reference internal" href="../notebooks/index.html">Essays about Programming in Joy</a></li>
</ul>
<div class="relations">
<div class="sphinxsidebarwrapper"><div class="relations">
<h3>Related Topics</h3>
<ul>
<li><a href="../index.html">Documentation overview</a><ul>
@@ -79,23 +53,17 @@
</ul>
</div>
<div id="searchbox" style="display: none" role="search">
<h3 id="searchlabel">Quick search</h3>
<h3>Quick search</h3>
<div class="searchformwrapper">
<form class="search" action="../search.html" method="get">
<input type="text" name="q" aria-labelledby="searchlabel" />
<input type="text" name="q" />
<input type="submit" value="Go" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
</div>
<script>$('#searchbox').show(0);</script>
<script type="text/javascript">$('#searchbox').show(0);</script>
</div>
</div>
<div class="clearer"></div>
@@ -106,7 +74,7 @@
</a>
<br />
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 3.0.2.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
</div>
</body>
docs/sphinx_docs/_build/html/_modules/joy/joy.html
+22 -53
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@@ -1,18 +1,19 @@
<!DOCTYPE html>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>joy.joy &#8212; Thun 0.3.0 documentation</title>
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
<script id="documentation_options" data-url_root="../../" src="../../_static/documentation_options.js"></script>
<script src="../../_static/jquery.js"></script>
<script src="../../_static/underscore.js"></script>
<script src="../../_static/doctools.js"></script>
<script src="../../_static/language_data.js"></script>
<script async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
<script type="text/javascript" src="../../_static/documentation_options.js"></script>
<script type="text/javascript" src="../../_static/jquery.js"></script>
<script type="text/javascript" src="../../_static/underscore.js"></script>
<script type="text/javascript" src="../../_static/doctools.js"></script>
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<link rel="index" title="Index" href="../../genindex.html" />
<link rel="search" title="Search" href="../../search.html" />
@@ -27,8 +28,6 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<h1>Source code for joy.joy</h1><div class="highlight"><pre>
@@ -57,11 +56,11 @@
<span class="sd">match the behaviour of the original version(s) written in C.</span>
<span class="sd">&#39;&#39;&#39;</span>
<span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">print_function</span>
<span class="kn">from</span> <span class="nn">builtins</span> <span class="kn">import</span> <span class="nb">input</span>
<span class="kn">from</span> <span class="nn">traceback</span> <span class="kn">import</span> <span class="n">print_exc</span><span class="p">,</span> <span class="n">format_exc</span>
<span class="kn">from</span> <span class="nn">.parser</span> <span class="kn">import</span> <span class="n">text_to_expression</span><span class="p">,</span> <span class="n">ParseError</span><span class="p">,</span> <span class="n">Symbol</span>
<span class="kn">from</span> <span class="nn">.utils.stack</span> <span class="kn">import</span> <span class="n">stack_to_string</span>
<span class="kn">from</span> <span class="nn">__future__</span> <span class="k">import</span> <span class="n">print_function</span>
<span class="kn">from</span> <span class="nn">builtins</span> <span class="k">import</span> <span class="nb">input</span>
<span class="kn">from</span> <span class="nn">traceback</span> <span class="k">import</span> <span class="n">print_exc</span><span class="p">,</span> <span class="n">format_exc</span>
<span class="kn">from</span> <span class="nn">.parser</span> <span class="k">import</span> <span class="n">text_to_expression</span><span class="p">,</span> <span class="n">ParseError</span><span class="p">,</span> <span class="n">Symbol</span>
<span class="kn">from</span> <span class="nn">.utils.stack</span> <span class="k">import</span> <span class="n">stack_to_string</span>
<div class="viewcode-block" id="joy"><a class="viewcode-back" href="../../joy.html#joy.joy.joy">[docs]</a><span class="k">def</span> <span class="nf">joy</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">,</span> <span class="n">viewer</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
@@ -146,34 +145,10 @@
</pre></div>
</div>
</div>
</div>
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
<div class="sphinxsidebarwrapper">
<h1 class="logo"><a href="../../index.html">Thun</a></h1>
<h3>Navigation</h3>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../../notebooks/Intro.html">Thun: Joy in Python</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../joy.html">Joy Interpreter</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../stack.html">Stack or Quote or Sequence or List…</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../parser.html">Parsing Text into Joy Expressions</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../pretty.html">Tracing Joy Execution</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../library.html">Function Reference</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../lib.html">Functions Grouped by, er, Function with Examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../types.html">Type Inference of Joy Expressions</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../notebooks/index.html">Essays about Programming in Joy</a></li>
</ul>
<div class="relations">
<div class="sphinxsidebarwrapper"><div class="relations">
<h3>Related Topics</h3>
<ul>
<li><a href="../../index.html">Documentation overview</a><ul>
@@ -183,23 +158,17 @@
</ul>
</div>
<div id="searchbox" style="display: none" role="search">
<h3 id="searchlabel">Quick search</h3>
<h3>Quick search</h3>
<div class="searchformwrapper">
<form class="search" action="../../search.html" method="get">
<input type="text" name="q" aria-labelledby="searchlabel" />
<input type="text" name="q" />
<input type="submit" value="Go" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
</div>
<script>$('#searchbox').show(0);</script>
<script type="text/javascript">$('#searchbox').show(0);</script>
</div>
</div>
<div class="clearer"></div>
@@ -210,7 +179,7 @@
</a>
<br />
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 3.0.2.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
</div>
</body>
docs/sphinx_docs/_build/html/_modules/joy/library.html
+129 -113
View File
@@ -1,18 +1,19 @@
<!DOCTYPE html>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>joy.library &#8212; Thun 0.3.0 documentation</title>
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
<script id="documentation_options" data-url_root="../../" src="../../_static/documentation_options.js"></script>
<script src="../../_static/jquery.js"></script>
<script src="../../_static/underscore.js"></script>
<script src="../../_static/doctools.js"></script>
<script src="../../_static/language_data.js"></script>
<script async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
<script type="text/javascript" src="../../_static/documentation_options.js"></script>
<script type="text/javascript" src="../../_static/jquery.js"></script>
<script type="text/javascript" src="../../_static/underscore.js"></script>
<script type="text/javascript" src="../../_static/doctools.js"></script>
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<link rel="index" title="Index" href="../../genindex.html" />
<link rel="search" title="Search" href="../../search.html" />
@@ -27,8 +28,6 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<h1>Source code for joy.library</h1><div class="highlight"><pre>
@@ -57,29 +56,29 @@
<span class="sd">returns a dictionary of Joy functions suitable for use with the joy()</span>
<span class="sd">function.</span>
<span class="sd">&#39;&#39;&#39;</span>
<span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">print_function</span>
<span class="kn">from</span> <span class="nn">builtins</span> <span class="kn">import</span> <span class="nb">map</span><span class="p">,</span> <span class="nb">object</span><span class="p">,</span> <span class="nb">range</span><span class="p">,</span> <span class="nb">zip</span>
<span class="kn">from</span> <span class="nn">logging</span> <span class="kn">import</span> <span class="n">getLogger</span>
<span class="kn">from</span> <span class="nn">__future__</span> <span class="k">import</span> <span class="n">print_function</span>
<span class="kn">from</span> <span class="nn">builtins</span> <span class="k">import</span> <span class="nb">map</span><span class="p">,</span> <span class="nb">object</span><span class="p">,</span> <span class="nb">range</span><span class="p">,</span> <span class="nb">zip</span>
<span class="kn">from</span> <span class="nn">logging</span> <span class="k">import</span> <span class="n">getLogger</span>
<span class="n">_log</span> <span class="o">=</span> <span class="n">getLogger</span><span class="p">(</span><span class="vm">__name__</span><span class="p">)</span>
<span class="n">_log</span><span class="o">.</span><span class="n">info</span><span class="p">(</span><span class="s1">&#39;Loading library.&#39;</span><span class="p">)</span>
<span class="kn">from</span> <span class="nn">inspect</span> <span class="kn">import</span> <span class="n">getdoc</span>
<span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">wraps</span>
<span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">count</span>
<span class="kn">from</span> <span class="nn">inspect</span> <span class="kn">import</span> <span class="n">getmembers</span><span class="p">,</span> <span class="n">isfunction</span>
<span class="kn">from</span> <span class="nn">inspect</span> <span class="k">import</span> <span class="n">getdoc</span>
<span class="kn">from</span> <span class="nn">functools</span> <span class="k">import</span> <span class="n">wraps</span>
<span class="kn">from</span> <span class="nn">itertools</span> <span class="k">import</span> <span class="n">count</span>
<span class="kn">from</span> <span class="nn">inspect</span> <span class="k">import</span> <span class="n">getmembers</span><span class="p">,</span> <span class="n">isfunction</span>
<span class="kn">import</span> <span class="nn">operator</span><span class="o">,</span> <span class="nn">math</span>
<span class="kn">from</span> <span class="nn">.parser</span> <span class="kn">import</span> <span class="n">text_to_expression</span><span class="p">,</span> <span class="n">Symbol</span>
<span class="kn">from</span> <span class="nn">.utils.stack</span> <span class="kn">import</span> <span class="n">expression_to_string</span><span class="p">,</span> <span class="n">list_to_stack</span><span class="p">,</span> <span class="n">iter_stack</span><span class="p">,</span> <span class="n">pick</span><span class="p">,</span> <span class="n">concat</span>
<span class="kn">from</span> <span class="nn">.parser</span> <span class="k">import</span> <span class="n">text_to_expression</span><span class="p">,</span> <span class="n">Symbol</span>
<span class="kn">from</span> <span class="nn">.utils.stack</span> <span class="k">import</span> <span class="n">expression_to_string</span><span class="p">,</span> <span class="n">list_to_stack</span><span class="p">,</span> <span class="n">iter_stack</span><span class="p">,</span> <span class="n">pick</span><span class="p">,</span> <span class="n">concat</span>
<span class="kn">import</span> <span class="nn">sys</span>
<span class="k">if</span> <span class="n">sys</span><span class="o">.</span><span class="n">version_info</span><span class="o">.</span><span class="n">major</span> <span class="o">&lt;</span> <span class="mi">3</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">.utils.brutal_hackery</span> <span class="kn">import</span> <span class="n">rename_code_object</span>
<span class="kn">from</span> <span class="nn">.utils.brutal_hackery</span> <span class="k">import</span> <span class="n">rename_code_object</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">rename_code_object</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">_</span><span class="p">:</span> <span class="k">lambda</span> <span class="n">f</span><span class="p">:</span> <span class="n">f</span>
<span class="kn">from</span> <span class="nn">.utils</span> <span class="kn">import</span> <span class="n">generated_library</span> <span class="k">as</span> <span class="n">genlib</span>
<span class="kn">from</span> <span class="nn">.utils.types</span> <span class="kn">import</span> <span class="p">(</span>
<span class="kn">from</span> <span class="nn">.utils</span> <span class="k">import</span> <span class="n">generated_library</span> <span class="k">as</span> <span class="n">genlib</span>
<span class="kn">from</span> <span class="nn">.utils.types</span> <span class="k">import</span> <span class="p">(</span>
<span class="n">compose</span><span class="p">,</span>
<span class="n">ef</span><span class="p">,</span>
<span class="n">stack_effect</span><span class="p">,</span>
@@ -136,6 +135,7 @@
<span class="n">Ss</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">StackStarJoyType</span><span class="p">,</span> <span class="n">_R</span><span class="p">))</span>
<span class="c1"># &quot;sec&quot;: stack effect comment, like in Forth.</span>
<span class="n">sec0</span> <span class="o">=</span> <span class="n">stack_effect</span><span class="p">(</span><span class="n">t1</span><span class="p">)()</span>
<span class="n">sec1</span> <span class="o">=</span> <span class="n">stack_effect</span><span class="p">(</span><span class="n">s0</span><span class="p">,</span> <span class="n">i1</span><span class="p">)(</span><span class="n">s1</span><span class="p">)</span>
<span class="n">sec2</span> <span class="o">=</span> <span class="n">stack_effect</span><span class="p">(</span><span class="n">s0</span><span class="p">,</span> <span class="n">i1</span><span class="p">)(</span><span class="n">a1</span><span class="p">)</span>
@@ -147,6 +147,7 @@
<span class="n">sec_unary_math</span> <span class="o">=</span> <span class="n">stack_effect</span><span class="p">(</span><span class="n">n1</span><span class="p">)(</span><span class="n">n2</span><span class="p">)</span>
<span class="n">sec_Ns_math</span> <span class="o">=</span> <span class="n">stack_effect</span><span class="p">((</span><span class="n">Ns</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">s1</span><span class="p">),)(</span><span class="n">n0</span><span class="p">)</span>
<span class="c1"># This is the main dict we&#39;re building.</span>
<span class="n">_dictionary</span> <span class="o">=</span> <span class="p">{}</span>
@@ -256,43 +257,43 @@
<span class="n">definitions</span> <span class="o">=</span> <span class="p">(</span><span class="s1">&#39;&#39;&#39;</span><span class="se">\</span>
<span class="s1">? == dup truthy</span>
<span class="s1">*fraction == [uncons] dip uncons [swap] dip concat [*] infra [*] dip cons</span>
<span class="s1">*fraction0 == concat [[swap] dip * [*] dip] infra</span>
<span class="s1">anamorphism == [pop []] swap [dip swons] genrec</span>
<span class="s1">average == [sum 1.0 *] [size] cleave /</span>
<span class="s1">binary == nullary [popop] dip</span>
<span class="s1">cleave == fork [popd] dip</span>
<span class="s1">codireco == cons dip rest cons</span>
<span class="s1">dinfrirst == dip infra first</span>
<span class="s1">unstack == ? [uncons ?] loop pop</span>
<span class="s1">down_to_zero == [0 &gt;] [dup --] while</span>
<span class="s1">dupdipd == dup dipd</span>
<span class="s1">enstacken == stack [clear] dip</span>
<span class="s1">flatten == [] swap [concat] step</span>
<span class="s1">fork == [i] app2</span>
<span class="s1">gcd == 1 [tuck modulus dup 0 &gt;] loop pop</span>
<span class="s1">ifte == [nullary not] dipd branch</span>
<span class="s1">ii == [dip] dupdip i</span>
<span class="s1">least_fraction == dup [gcd] infra [div] concat map</span>
<span class="s1">make_generator == [codireco] ccons</span>
<span class="s1">nullary == [stack] dinfrirst</span>
<span class="s1">of == swap at</span>
<span class="s1">pam == [i] map</span>
<span class="s1">tailrec == [i] genrec</span>
<span class="s1">product == 1 swap [*] step</span>
<span class="s1">quoted == [unit] dip</span>
<span class="s1">range == [0 &lt;=] [1 - dup] anamorphism</span>
<span class="s1">range_to_zero == unit [down_to_zero] infra</span>
<span class="s1">run == [] swap infra</span>
<span class="s1">size == 0 swap [pop ++] step</span>
<span class="s1">sqr == dup mul</span>
<span class="s1">step_zero == 0 roll&gt; step</span>
<span class="s1">swoncat == swap concat</span>
<span class="s1">ternary == unary [popop] dip</span>
<span class="s1">unary == nullary popd</span>
<span class="s1">unquoted == [i] dip</span>
<span class="s1">while == swap [nullary] cons dup dipd concat loop</span>
<span class="s1">? dup truthy</span>
<span class="s1">*fraction [uncons] dip uncons [swap] dip concat [*] infra [*] dip cons</span>
<span class="s1">*fraction0 concat [[swap] dip * [*] dip] infra</span>
<span class="s1">anamorphism [pop []] swap [dip swons] genrec</span>
<span class="s1">average [sum 1.0 *] [size] cleave /</span>
<span class="s1">binary nullary [popop] dip</span>
<span class="s1">cleave fork [popd] dip</span>
<span class="s1">codireco cons dip rest cons</span>
<span class="s1">dinfrirst dip infra first</span>
<span class="s1">unstack ? [uncons ?] loop pop</span>
<span class="s1">down_to_zero [0 &gt;] [dup --] while</span>
<span class="s1">dupdipd dup dipd</span>
<span class="s1">enstacken stack [clear] dip</span>
<span class="s1">flatten [] swap [concat] step</span>
<span class="s1">fork [i] app2</span>
<span class="s1">gcd 1 [tuck modulus dup 0 &gt;] loop pop</span>
<span class="s1">ifte [nullary not] dipd branch</span>
<span class="s1">ii [dip] dupdip i</span>
<span class="s1">least_fraction dup [gcd] infra [div] concat map</span>
<span class="s1">make_generator [codireco] ccons</span>
<span class="s1">nullary [stack] dinfrirst</span>
<span class="s1">of swap at</span>
<span class="s1">pam [i] map</span>
<span class="s1">tailrec [i] genrec</span>
<span class="s1">product 1 swap [*] step</span>
<span class="s1">quoted [unit] dip</span>
<span class="s1">range [0 &lt;=] [1 - dup] anamorphism</span>
<span class="s1">range_to_zero unit [down_to_zero] infra</span>
<span class="s1">run [] swap infra</span>
<span class="s1">size 0 swap [pop ++] step</span>
<span class="s1">sqr dup mul</span>
<span class="s1">step_zero 0 roll&gt; step</span>
<span class="s1">swoncat swap concat</span>
<span class="s1">ternary unary [popop] dip</span>
<span class="s1">unary nullary popd</span>
<span class="s1">unquoted [i] dip</span>
<span class="s1">while swap [nullary] cons dup dipd concat loop</span>
<span class="s1">&#39;&#39;&#39;</span>
<span class="c1">#</span>
<span class="c1">#</span>
@@ -389,14 +390,14 @@
<span class="sd"> Provide implementation of defined functions, and some helper methods.</span>
<span class="sd"> &#39;&#39;&#39;</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">body_text</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">body_text</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">=</span> <span class="n">name</span>
<span class="bp">self</span><span class="o">.</span><span class="n">body</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="n">body_text</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_body</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">iter_stack</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">body</span><span class="p">))</span>
<span class="bp">self</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> <span class="n">doc</span> <span class="ow">or</span> <span class="n">body_text</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_compiled</span> <span class="o">=</span> <span class="kc">None</span>
<span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">):</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_compiled</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_compiled</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">)</span> <span class="c1"># pylint: disable=E1102</span>
<span class="n">expression</span> <span class="o">=</span> <span class="n">list_to_stack</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_body</span><span class="p">,</span> <span class="n">expression</span><span class="p">)</span>
@@ -408,10 +409,7 @@
<span class="sd"> Given some text describing a Joy function definition parse it and</span>
<span class="sd"> return a DefinitionWrapper.</span>
<span class="sd"> &#39;&#39;&#39;</span>
<span class="n">name</span><span class="p">,</span> <span class="n">proper</span><span class="p">,</span> <span class="n">body_text</span> <span class="o">=</span> <span class="p">(</span><span class="n">n</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">defi</span><span class="o">.</span><span class="n">partition</span><span class="p">(</span><span class="s1">&#39;==&#39;</span><span class="p">))</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">proper</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;Definition </span><span class="si">%r</span><span class="s1"> failed&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">defi</span><span class="p">,))</span>
<span class="k">return</span> <span class="n">class_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">body_text</span><span class="p">)</span></div>
<span class="k">return</span> <span class="n">class_</span><span class="p">(</span><span class="o">*</span><span class="p">(</span><span class="n">n</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">defi</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="kc">None</span><span class="p">,</span> <span class="mi">1</span><span class="p">)))</span></div>
<div class="viewcode-block" id="DefinitionWrapper.add_definitions"><a class="viewcode-back" href="../../library.html#joy.library.DefinitionWrapper.add_definitions">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">add_definitions</span><span class="p">(</span><span class="n">class_</span><span class="p">,</span> <span class="n">defs</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">):</span>
@@ -440,7 +438,11 @@
<span class="k">def</span> <span class="nf">_text_to_defs</span><span class="p">(</span><span class="n">text</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span><span class="n">line</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span> <span class="k">for</span> <span class="n">line</span> <span class="ow">in</span> <span class="n">text</span><span class="o">.</span><span class="n">splitlines</span><span class="p">()</span> <span class="k">if</span> <span class="s1">&#39;==&#39;</span> <span class="ow">in</span> <span class="n">line</span><span class="p">)</span>
<span class="k">return</span> <span class="p">(</span>
<span class="n">line</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span>
<span class="k">for</span> <span class="n">line</span> <span class="ow">in</span> <span class="n">text</span><span class="o">.</span><span class="n">splitlines</span><span class="p">()</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">line</span><span class="o">.</span><span class="n">startswith</span><span class="p">(</span><span class="s1">&#39;#&#39;</span><span class="p">)</span>
<span class="p">)</span>
<span class="c1">#</span>
@@ -948,16 +950,17 @@
<span class="c1"># could change the word in the dictionary to use different semantics.</span>
<span class="n">S_choice</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;choice&#39;</span><span class="p">)</span>
<span class="n">S_first</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;first&#39;</span><span class="p">)</span>
<span class="n">S_getitem</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;getitem&#39;</span><span class="p">)</span>
<span class="n">S_genrec</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;genrec&#39;</span><span class="p">)</span>
<span class="n">S_loop</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;loop&#39;</span><span class="p">)</span>
<span class="n">S_getitem</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;getitem&#39;</span><span class="p">)</span>
<span class="n">S_i</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;i&#39;</span><span class="p">)</span>
<span class="n">S_ifte</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;ifte&#39;</span><span class="p">)</span>
<span class="n">S_infra</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;infra&#39;</span><span class="p">)</span>
<span class="n">S_loop</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;loop&#39;</span><span class="p">)</span>
<span class="n">S_pop</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;pop&#39;</span><span class="p">)</span>
<span class="n">S_primrec</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;primrec&#39;</span><span class="p">)</span>
<span class="n">S_step</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;step&#39;</span><span class="p">)</span>
<span class="n">S_times</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;times&#39;</span><span class="p">)</span>
<span class="n">S_swaack</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;swaack&#39;</span><span class="p">)</span>
<span class="n">S_times</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;times&#39;</span><span class="p">)</span>
<div class="viewcode-block" id="i"><a class="viewcode-back" href="../../library.html#joy.library.i">[docs]</a><span class="nd">@inscribe</span>
@@ -1059,9 +1062,9 @@
<span class="sd"> General Recursion Combinator.</span>
<span class="sd"> ::</span>
<span class="sd"> [if] [then] [rec1] [rec2] genrec</span>
<span class="sd"> ---------------------------------------------------------------------</span>
<span class="sd"> [if] [then] [rec1 [[if] [then] [rec1] [rec2] genrec] rec2] ifte</span>
<span class="sd"> [if] [then] [rec1] [rec2] genrec</span>
<span class="sd"> ---------------------------------------------------------------------</span>
<span class="sd"> [if] [then] [rec1 [[if] [then] [rec1] [rec2] genrec] rec2] ifte</span>
<span class="sd"> From &quot;Recursion Theory and Joy&quot; (j05cmp.html) by Manfred von Thun:</span>
<span class="sd"> &quot;The genrec combinator takes four program parameters in addition to</span>
@@ -1096,14 +1099,14 @@
<span class="sd"> ::</span>
<span class="sd"> F == [I] [T] [R1] [R2] genrec</span>
<span class="sd"> == [I] [T] [R1 [F] R2] ifte</span>
<span class="sd"> == [I] [T] [R1 [F] R2] ifte</span>
<span class="sd"> Primitive recursive functions are those where R2 == i.</span>
<span class="sd"> ::</span>
<span class="sd"> P == [I] [T] [R] tailrec</span>
<span class="sd"> == [I] [T] [R [P] i] ifte</span>
<span class="sd"> == [I] [T] [R P] ifte</span>
<span class="sd"> == [I] [T] [R [P] i] ifte</span>
<span class="sd"> == [I] [T] [R P] ifte</span>
<span class="sd"> &#39;&#39;&#39;</span>
<span class="p">(</span><span class="n">rec2</span><span class="p">,</span> <span class="p">(</span><span class="n">rec1</span><span class="p">,</span> <span class="n">stack</span><span class="p">))</span> <span class="o">=</span> <span class="n">stack</span>
@@ -1138,6 +1141,49 @@
<span class="k">return</span> <span class="n">stack</span><span class="p">,</span> <span class="p">(</span><span class="n">S_infra</span><span class="p">,</span> <span class="n">expression</span><span class="p">),</span> <span class="n">dictionary</span></div>
<div class="viewcode-block" id="primrec"><a class="viewcode-back" href="../../library.html#joy.library.primrec">[docs]</a><span class="nd">@inscribe</span>
<span class="nd">@FunctionWrapper</span>
<span class="k">def</span> <span class="nf">primrec</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">):</span>
<span class="sd">&#39;&#39;&#39;</span>
<span class="sd"> From the &quot;Overview of the language JOY&quot;:</span>
<span class="sd"> &gt; The primrec combinator expects two quoted programs in addition to a</span>
<span class="sd"> data parameter. For an integer data parameter it works like this: If</span>
<span class="sd"> the data parameter is zero, then the first quotation has to produce</span>
<span class="sd"> the value to be returned. If the data parameter is positive then the</span>
<span class="sd"> second has to combine the data parameter with the result of applying</span>
<span class="sd"> the function to its predecessor.</span>
<span class="sd"> 5 [1] [*] primrec</span>
<span class="sd"> &gt; Then primrec tests whether the top element on the stack (initially</span>
<span class="sd"> the 5) is equal to zero. If it is, it pops it off and executes one of</span>
<span class="sd"> the quotations, the [1] which leaves 1 on the stack as the result.</span>
<span class="sd"> Otherwise it pushes a decremented copy of the top element and</span>
<span class="sd"> recurses. On the way back from the recursion it uses the other</span>
<span class="sd"> quotation, [*], to multiply what is now a factorial on top of the</span>
<span class="sd"> stack by the second element on the stack.</span>
<span class="sd"> n [Base] [Recur] primrec</span>
<span class="sd"> 0 [Base] [Recur] primrec</span>
<span class="sd"> ------------------------------</span>
<span class="sd"> Base</span>
<span class="sd"> n [Base] [Recur] primrec</span>
<span class="sd"> ------------------------------------------ n &gt; 0</span>
<span class="sd"> n (n-1) [Base] [Recur] primrec Recur</span>
<span class="sd"> &#39;&#39;&#39;</span>
<span class="n">recur</span><span class="p">,</span> <span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">stack</span><span class="p">))</span> <span class="o">=</span> <span class="n">stack</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">expression</span> <span class="o">=</span> <span class="n">concat</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="n">expression</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">expression</span> <span class="o">=</span> <span class="n">S_primrec</span><span class="p">,</span> <span class="n">concat</span><span class="p">(</span><span class="n">recur</span><span class="p">,</span> <span class="n">expression</span><span class="p">)</span>
<span class="n">stack</span> <span class="o">=</span> <span class="n">recur</span><span class="p">,</span> <span class="p">(</span><span class="n">base</span><span class="p">,</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">n</span><span class="p">,</span> <span class="n">stack</span><span class="p">)))</span>
<span class="k">return</span> <span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span></div>
<span class="c1">#def cleave(S, expression, dictionary):</span>
<span class="c1"># &#39;&#39;&#39;</span>
<span class="c1"># The cleave combinator expects two quotations, and below that an item X.</span>
@@ -1671,34 +1717,10 @@
</pre></div>
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@@ -1708,23 +1730,17 @@
</ul>
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<h3 id="searchlabel">Quick search</h3>
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@@ -1735,7 +1751,7 @@
</a>
<br />
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 3.0.2.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
</div>
</body>
docs/sphinx_docs/_build/html/_modules/joy/parser.html
+20 -51
View File
@@ -1,18 +1,19 @@
<!DOCTYPE html>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>joy.parser &#8212; Thun 0.3.0 documentation</title>
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
<script id="documentation_options" data-url_root="../../" src="../../_static/documentation_options.js"></script>
<script src="../../_static/jquery.js"></script>
<script src="../../_static/underscore.js"></script>
<script src="../../_static/doctools.js"></script>
<script src="../../_static/language_data.js"></script>
<script async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
<script type="text/javascript" src="../../_static/documentation_options.js"></script>
<script type="text/javascript" src="../../_static/jquery.js"></script>
<script type="text/javascript" src="../../_static/underscore.js"></script>
<script type="text/javascript" src="../../_static/doctools.js"></script>
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<link rel="index" title="Index" href="../../genindex.html" />
<link rel="search" title="Search" href="../../search.html" />
@@ -27,8 +28,6 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<h1>Source code for joy.parser</h1><div class="highlight"><pre>
@@ -70,12 +69,12 @@
<span class="sd">around square brackets.</span>
<span class="sd">&#39;&#39;&#39;</span>
<span class="kn">from</span> <span class="nn">re</span> <span class="kn">import</span> <span class="n">Scanner</span>
<span class="kn">from</span> <span class="nn">.utils.stack</span> <span class="kn">import</span> <span class="n">list_to_stack</span>
<span class="kn">from</span> <span class="nn">re</span> <span class="k">import</span> <span class="n">Scanner</span>
<span class="kn">from</span> <span class="nn">.utils.stack</span> <span class="k">import</span> <span class="n">list_to_stack</span>
<span class="c1">#TODO: explain the details of float lits and strings.</span>
<span class="n">FLOAT</span> <span class="o">=</span> <span class="sa">r</span><span class="s1">&#39;-?\d+\.\d*&#39;</span>
<span class="n">FLOAT</span> <span class="o">=</span> <span class="sa">r</span><span class="s1">&#39;-?\d+\.\d*(e(-|\+)\d+)+&#39;</span>
<span class="n">INT</span> <span class="o">=</span> <span class="sa">r</span><span class="s1">&#39;-?\d+&#39;</span>
<span class="n">SYMBOL</span> <span class="o">=</span> <span class="sa">r</span><span class="s1">&#39;[•\w!@$%^&amp;*()_+&lt;&gt;?|\/;:`~,.=-]+&#39;</span>
<span class="n">BRACKETS</span> <span class="o">=</span> <span class="sa">r</span><span class="s1">&#39;\[|\]&#39;</span>
@@ -159,34 +158,10 @@
</pre></div>
</div>
</div>
</div>
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
<div class="sphinxsidebarwrapper">
<h1 class="logo"><a href="../../index.html">Thun</a></h1>
<h3>Navigation</h3>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../../notebooks/Intro.html">Thun: Joy in Python</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../joy.html">Joy Interpreter</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../stack.html">Stack or Quote or Sequence or List…</a></li>
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@@ -196,23 +171,17 @@
</ul>
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<div id="searchbox" style="display: none" role="search">
<h3 id="searchlabel">Quick search</h3>
<h3>Quick search</h3>
<div class="searchformwrapper">
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@@ -223,7 +192,7 @@
</a>
<br />
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 3.0.2.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
</div>
</body>
docs/sphinx_docs/_build/html/_modules/joy/utils/pretty_print.html
+25 -56
View File
@@ -1,18 +1,19 @@
<!DOCTYPE html>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>joy.utils.pretty_print &#8212; Thun 0.3.0 documentation</title>
<link rel="stylesheet" href="../../../_static/alabaster.css" type="text/css" />
<link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
<script id="documentation_options" data-url_root="../../../" src="../../../_static/documentation_options.js"></script>
<script src="../../../_static/jquery.js"></script>
<script src="../../../_static/underscore.js"></script>
<script src="../../../_static/doctools.js"></script>
<script src="../../../_static/language_data.js"></script>
<script async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
<script type="text/javascript" src="../../../_static/documentation_options.js"></script>
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<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<link rel="index" title="Index" href="../../../genindex.html" />
<link rel="search" title="Search" href="../../../search.html" />
@@ -27,8 +28,6 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<h1>Source code for joy.utils.pretty_print</h1><div class="highlight"><pre>
@@ -73,12 +72,12 @@
<span class="sd">&#39;&#39;&#39;</span>
<span class="c1"># (Kinda clunky and hacky. This should be swapped out in favor of much</span>
<span class="c1"># smarter stuff.)</span>
<span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">print_function</span>
<span class="kn">from</span> <span class="nn">builtins</span> <span class="kn">import</span> <span class="nb">object</span>
<span class="kn">from</span> <span class="nn">traceback</span> <span class="kn">import</span> <span class="n">print_exc</span>
<span class="kn">from</span> <span class="nn">.stack</span> <span class="kn">import</span> <span class="n">expression_to_string</span><span class="p">,</span> <span class="n">stack_to_string</span>
<span class="kn">from</span> <span class="nn">..joy</span> <span class="kn">import</span> <span class="n">joy</span>
<span class="kn">from</span> <span class="nn">..library</span> <span class="kn">import</span> <span class="n">inscribe</span><span class="p">,</span> <span class="n">FunctionWrapper</span>
<span class="kn">from</span> <span class="nn">__future__</span> <span class="k">import</span> <span class="n">print_function</span>
<span class="kn">from</span> <span class="nn">builtins</span> <span class="k">import</span> <span class="nb">object</span>
<span class="kn">from</span> <span class="nn">traceback</span> <span class="k">import</span> <span class="n">print_exc</span>
<span class="kn">from</span> <span class="nn">.stack</span> <span class="k">import</span> <span class="n">expression_to_string</span><span class="p">,</span> <span class="n">stack_to_string</span>
<span class="kn">from</span> <span class="nn">..joy</span> <span class="k">import</span> <span class="n">joy</span>
<span class="kn">from</span> <span class="nn">..library</span> <span class="k">import</span> <span class="n">inscribe</span><span class="p">,</span> <span class="n">FunctionWrapper</span>
<div class="viewcode-block" id="trace"><a class="viewcode-back" href="../../../pretty.html#joy.utils.pretty_print.trace">[docs]</a><span class="nd">@inscribe</span>
@@ -115,7 +114,7 @@
<span class="sd"> trace.</span>
<span class="sd"> &#39;&#39;&#39;</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">history</span> <span class="o">=</span> <span class="p">[]</span>
<div class="viewcode-block" id="TracePrinter.viewer"><a class="viewcode-back" href="../../../pretty.html#joy.utils.pretty_print.TracePrinter.viewer">[docs]</a> <span class="k">def</span> <span class="nf">viewer</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">):</span>
@@ -128,7 +127,7 @@
<span class="sd"> &#39;&#39;&#39;</span>
<span class="bp">self</span><span class="o">.</span><span class="n">history</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">))</span></div>
<span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="s1">&#39;</span><span class="se">\n</span><span class="s1">&#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">go</span><span class="p">())</span>
<div class="viewcode-block" id="TracePrinter.go"><a class="viewcode-back" href="../../../pretty.html#joy.utils.pretty_print.TracePrinter.go">[docs]</a> <span class="k">def</span> <span class="nf">go</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
@@ -163,34 +162,10 @@
</pre></div>
</div>
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<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
<div class="sphinxsidebarwrapper">
<h1 class="logo"><a href="../../../index.html">Thun</a></h1>
<h3>Navigation</h3>
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@@ -200,23 +175,17 @@
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<h3 id="searchlabel">Quick search</h3>
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<div class="searchformwrapper">
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@@ -227,7 +196,7 @@
</a>
<br />
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 3.0.2.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
</div>
</body>
docs/sphinx_docs/_build/html/_modules/joy/utils/stack.html
+20 -51
View File
@@ -1,18 +1,19 @@
<!DOCTYPE html>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>joy.utils.stack &#8212; Thun 0.3.0 documentation</title>
<link rel="stylesheet" href="../../../_static/alabaster.css" type="text/css" />
<link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
<script id="documentation_options" data-url_root="../../../" src="../../../_static/documentation_options.js"></script>
<script src="../../../_static/jquery.js"></script>
<script src="../../../_static/underscore.js"></script>
<script src="../../../_static/doctools.js"></script>
<script src="../../../_static/language_data.js"></script>
<script async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
<script type="text/javascript" src="../../../_static/documentation_options.js"></script>
<script type="text/javascript" src="../../../_static/jquery.js"></script>
<script type="text/javascript" src="../../../_static/underscore.js"></script>
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<link rel="index" title="Index" href="../../../genindex.html" />
<link rel="search" title="Search" href="../../../search.html" />
@@ -27,8 +28,6 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<h1>Source code for joy.utils.stack</h1><div class="highlight"><pre>
@@ -59,8 +58,8 @@
<span class="sd">There is no &quot;Stack&quot; Python class, instead we use the `cons list`_, a </span>
<span class="sd">venerable two-tuple recursive sequence datastructure, where the</span>
<span class="sd">empty tuple ``()`` is the empty stack and ``(head, rest)`` gives the recursive</span>
<span class="sd">form of a stack with one or more items on it::</span>
<span class="sd">empty tuple ``()`` is the empty stack and ``(head, rest)`` gives the</span>
<span class="sd">recursive form of a stack with one or more items on it::</span>
<span class="sd"> stack := () | (item, stack)</span>
@@ -106,7 +105,7 @@
<span class="sd">&#39;&#39;&#39;</span>
<span class="kn">from</span> <span class="nn">builtins</span> <span class="kn">import</span> <span class="nb">map</span>
<span class="kn">from</span> <span class="nn">builtins</span> <span class="k">import</span> <span class="nb">map</span>
<div class="viewcode-block" id="list_to_stack"><a class="viewcode-back" href="../../../stack.html#joy.utils.stack.list_to_stack">[docs]</a><span class="k">def</span> <span class="nf">list_to_stack</span><span class="p">(</span><span class="n">el</span><span class="p">,</span> <span class="n">stack</span><span class="o">=</span><span class="p">()):</span>
<span class="sd">&#39;&#39;&#39;Convert a Python list (or other sequence) to a Joy stack::</span>
@@ -232,34 +231,10 @@
</pre></div>
</div>
</div>
</div>
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
<div class="sphinxsidebarwrapper">
<h1 class="logo"><a href="../../../index.html">Thun</a></h1>
<h3>Navigation</h3>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../../../notebooks/Intro.html">Thun: Joy in Python</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../joy.html">Joy Interpreter</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../stack.html">Stack or Quote or Sequence or List…</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../parser.html">Parsing Text into Joy Expressions</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../pretty.html">Tracing Joy Execution</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../library.html">Function Reference</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../lib.html">Functions Grouped by, er, Function with Examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../types.html">Type Inference of Joy Expressions</a></li>
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@@ -269,23 +244,17 @@
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<div id="searchbox" style="display: none" role="search">
<h3 id="searchlabel">Quick search</h3>
<h3>Quick search</h3>
<div class="searchformwrapper">
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@@ -296,7 +265,7 @@
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 3.0.2.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
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docs/sphinx_docs/_build/html/_static/alabaster.css
+6 -66
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@@ -3,7 +3,7 @@
/* -- page layout ----------------------------------------------------------- */
body {
font-family: Georgia, serif;
font-family: 'goudy old style', 'minion pro', 'bell mt', Georgia, 'Hiragino Mincho Pro', serif;
font-size: 17px;
background-color: #fff;
color: #000;
@@ -107,7 +107,7 @@ div.sphinxsidebarwrapper p.blurb {
div.sphinxsidebar h3,
div.sphinxsidebar h4 {
font-family: Georgia, serif;
font-family: 'Garamond', 'Georgia', serif;
color: #444;
font-size: 24px;
font-weight: normal;
@@ -151,7 +151,7 @@ div.sphinxsidebar ul li.toctree-l2 > a {
div.sphinxsidebar input {
border: 1px solid #CCC;
font-family: Georgia, serif;
font-family: 'goudy old style', 'minion pro', 'bell mt', Georgia, 'Hiragino Mincho Pro', serif;
font-size: 1em;
}
@@ -166,19 +166,6 @@ div.sphinxsidebar hr {
width: 50%;
}
div.sphinxsidebar .badge {
border-bottom: none;
}
div.sphinxsidebar .badge:hover {
border-bottom: none;
}
/* To address an issue with donation coming after search */
div.sphinxsidebar h3.donation {
margin-top: 10px;
}
/* -- body styles ----------------------------------------------------------- */
a {
@@ -197,7 +184,7 @@ div.body h3,
div.body h4,
div.body h5,
div.body h6 {
font-family: Georgia, serif;
font-family: 'Garamond', 'Georgia', serif;
font-weight: normal;
margin: 30px 0px 10px 0px;
padding: 0;
@@ -238,7 +225,7 @@ div.admonition tt.xref, div.admonition code.xref, div.admonition a tt {
}
div.admonition p.admonition-title {
font-family: Georgia, serif;
font-family: 'Garamond', 'Georgia', serif;
font-weight: normal;
font-size: 24px;
margin: 0 0 10px 0;
@@ -327,7 +314,7 @@ p.admonition-title:after {
}
pre, tt, code {
font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace;
font-family: 'Consolas', 'Menlo', 'Deja Vu Sans Mono', 'Bitstream Vera Sans Mono', monospace;
font-size: 0.9em;
}
@@ -651,51 +638,4 @@ table.docutils.citation, table.docutils.citation td, table.docutils.citation th
-moz-box-shadow: none;
-webkit-box-shadow: none;
box-shadow: none;
}
/* relbar */
.related {
line-height: 30px;
width: 100%;
font-size: 0.9rem;
}
.related.top {
border-bottom: 1px solid #EEE;
margin-bottom: 20px;
}
.related.bottom {
border-top: 1px solid #EEE;
}
.related ul {
padding: 0;
margin: 0;
list-style: none;
}
.related li {
display: inline;
}
nav#rellinks {
float: right;
}
nav#rellinks li+li:before {
content: "|";
}
nav#breadcrumbs li+li:before {
content: "\00BB";
}
/* Hide certain items when printing */
@media print {
div.related {
display: none;
}
}
docs/sphinx_docs/_build/html/_static/basic.css
+2 -105
View File
@@ -4,7 +4,7 @@
*
* Sphinx stylesheet -- basic theme.
*
* :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
* :copyright: Copyright 2007-2018 by the Sphinx team, see AUTHORS.
* :license: BSD, see LICENSE for details.
*
*/
@@ -81,10 +81,6 @@ div.sphinxsidebar input {
font-size: 1em;
}
div.sphinxsidebar #searchbox form.search {
overflow: hidden;
}
div.sphinxsidebar #searchbox input[type="text"] {
float: left;
width: 80%;
@@ -231,16 +227,6 @@ a.headerlink {
visibility: hidden;
}
a.brackets:before,
span.brackets > a:before{
content: "[";
}
a.brackets:after,
span.brackets > a:after {
content: "]";
}
h1:hover > a.headerlink,
h2:hover > a.headerlink,
h3:hover > a.headerlink,
@@ -289,12 +275,6 @@ img.align-center, .figure.align-center, object.align-center {
margin-right: auto;
}
img.align-default, .figure.align-default {
display: block;
margin-left: auto;
margin-right: auto;
}
.align-left {
text-align: left;
}
@@ -303,10 +283,6 @@ img.align-default, .figure.align-default {
text-align: center;
}
.align-default {
text-align: center;
}
.align-right {
text-align: right;
}
@@ -378,11 +354,6 @@ table.align-center {
margin-right: auto;
}
table.align-default {
margin-left: auto;
margin-right: auto;
}
table caption span.caption-number {
font-style: italic;
}
@@ -416,16 +387,6 @@ table.citation td {
border-bottom: none;
}
th > p:first-child,
td > p:first-child {
margin-top: 0px;
}
th > p:last-child,
td > p:last-child {
margin-bottom: 0px;
}
/* -- figures --------------------------------------------------------------- */
div.figure {
@@ -466,13 +427,6 @@ table.field-list td, table.field-list th {
hyphens: manual;
}
/* -- hlist styles ---------------------------------------------------------- */
table.hlist td {
vertical-align: top;
}
/* -- other body styles ----------------------------------------------------- */
ol.arabic {
@@ -495,58 +449,11 @@ ol.upperroman {
list-style: upper-roman;
}
li > p:first-child {
margin-top: 0px;
}
li > p:last-child {
margin-bottom: 0px;
}
dl.footnote > dt,
dl.citation > dt {
float: left;
}
dl.footnote > dd,
dl.citation > dd {
margin-bottom: 0em;
}
dl.footnote > dd:after,
dl.citation > dd:after {
content: "";
clear: both;
}
dl.field-list {
display: grid;
grid-template-columns: fit-content(30%) auto;
}
dl.field-list > dt {
font-weight: bold;
word-break: break-word;
padding-left: 0.5em;
padding-right: 5px;
}
dl.field-list > dt:after {
content: ":";
}
dl.field-list > dd {
padding-left: 0.5em;
margin-top: 0em;
margin-left: 0em;
margin-bottom: 0em;
}
dl {
margin-bottom: 15px;
}
dd > p:first-child {
dd p {
margin-top: 0px;
}
@@ -619,12 +526,6 @@ dl.glossary dt {
font-style: oblique;
}
.classifier:before {
font-style: normal;
margin: 0.5em;
content: ":";
}
abbr, acronym {
border-bottom: dotted 1px;
cursor: help;
@@ -672,10 +573,6 @@ div.code-block-caption + div > div.highlight > pre {
margin-top: 0;
}
div.doctest > div.highlight span.gp { /* gp: Generic.Prompt */
user-select: none;
}
div.code-block-caption span.caption-number {
padding: 0.1em 0.3em;
font-style: italic;
docs/sphinx_docs/_build/html/_static/doctools.js
+8 -10
View File
@@ -4,7 +4,7 @@
*
* Sphinx JavaScript utilities for all documentation.
*
* :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
* :copyright: Copyright 2007-2018 by the Sphinx team, see AUTHORS.
* :license: BSD, see LICENSE for details.
*
*/
@@ -87,13 +87,14 @@ jQuery.fn.highlightText = function(text, className) {
node.nextSibling));
node.nodeValue = val.substr(0, pos);
if (isInSVG) {
var bbox = span.getBBox();
var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect");
var bbox = node.parentElement.getBBox();
rect.x.baseVal.value = bbox.x;
rect.x.baseVal.value = bbox.x;
rect.y.baseVal.value = bbox.y;
rect.width.baseVal.value = bbox.width;
rect.height.baseVal.value = bbox.height;
rect.setAttribute('class', className);
var parentOfText = node.parentNode.parentNode;
addItems.push({
"parent": node.parentNode,
"target": rect});
@@ -149,9 +150,7 @@ var Documentation = {
this.fixFirefoxAnchorBug();
this.highlightSearchWords();
this.initIndexTable();
if (DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) {
this.initOnKeyListeners();
}
},
/**
@@ -283,11 +282,10 @@ var Documentation = {
},
initOnKeyListeners: function() {
$(document).keydown(function(event) {
$(document).keyup(function(event) {
var activeElementType = document.activeElement.tagName;
// don't navigate when in search box or textarea
if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT'
&& !event.altKey && !event.ctrlKey && !event.metaKey && !event.shiftKey) {
if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT') {
switch (event.keyCode) {
case 37: // left
var prevHref = $('link[rel="prev"]').prop('href');
@@ -312,4 +310,4 @@ _ = Documentation.gettext;
$(document).ready(function() {
Documentation.init();
});
});
docs/sphinx_docs/_build/html/_static/documentation_options.js
+2 -5
View File
@@ -1,12 +1,9 @@
var DOCUMENTATION_OPTIONS = {
URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
URL_ROOT: '',
VERSION: '0.3.0',
LANGUAGE: 'None',
COLLAPSE_INDEX: false,
BUILDER: 'html',
FILE_SUFFIX: '.html',
LINK_SUFFIX: '.html',
HAS_SOURCE: true,
SOURCELINK_SUFFIX: '.txt',
NAVIGATION_WITH_KEYS: false
SOURCELINK_SUFFIX: '.txt'
};
docs/sphinx_docs/_build/html/_static/jquery.js
Vendored
+4 -2
View File
File diff suppressed because one or more lines are too long
docs/sphinx_docs/_build/html/_static/searchtools.js
+335 -89
View File
@@ -1,54 +1,331 @@
/*
* searchtools.js
* searchtools.js_t
* ~~~~~~~~~~~~~~~~
*
* Sphinx JavaScript utilities for the full-text search.
*
* :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
* :copyright: Copyright 2007-2018 by the Sphinx team, see AUTHORS.
* :license: BSD, see LICENSE for details.
*
*/
if (!Scorer) {
/**
* Simple result scoring code.
*/
var Scorer = {
// Implement the following function to further tweak the score for each result
// The function takes a result array [filename, title, anchor, descr, score]
// and returns the new score.
/*
score: function(result) {
return result[4];
},
*/
// query matches the full name of an object
objNameMatch: 11,
// or matches in the last dotted part of the object name
objPartialMatch: 6,
// Additive scores depending on the priority of the object
objPrio: {0: 15, // used to be importantResults
1: 5, // used to be objectResults
2: -5}, // used to be unimportantResults
// Used when the priority is not in the mapping.
objPrioDefault: 0,
/* Non-minified version JS is _stemmer.js if file is provided */
/**
* Porter Stemmer
*/
var Stemmer = function() {
// query found in title
title: 15,
partialTitle: 7,
// query found in terms
term: 5,
partialTerm: 2
var step2list = {
ational: 'ate',
tional: 'tion',
enci: 'ence',
anci: 'ance',
izer: 'ize',
bli: 'ble',
alli: 'al',
entli: 'ent',
eli: 'e',
ousli: 'ous',
ization: 'ize',
ation: 'ate',
ator: 'ate',
alism: 'al',
iveness: 'ive',
fulness: 'ful',
ousness: 'ous',
aliti: 'al',
iviti: 'ive',
biliti: 'ble',
logi: 'log'
};
}
if (!splitQuery) {
function splitQuery(query) {
return query.split(/\s+/);
var step3list = {
icate: 'ic',
ative: '',
alize: 'al',
iciti: 'ic',
ical: 'ic',
ful: '',
ness: ''
};
var c = "[^aeiou]"; // consonant
var v = "[aeiouy]"; // vowel
var C = c + "[^aeiouy]*"; // consonant sequence
var V = v + "[aeiou]*"; // vowel sequence
var mgr0 = "^(" + C + ")?" + V + C; // [C]VC... is m>0
var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$"; // [C]VC[V] is m=1
var mgr1 = "^(" + C + ")?" + V + C + V + C; // [C]VCVC... is m>1
var s_v = "^(" + C + ")?" + v; // vowel in stem
this.stemWord = function (w) {
var stem;
var suffix;
var firstch;
var origword = w;
if (w.length < 3)
return w;
var re;
var re2;
var re3;
var re4;
firstch = w.substr(0,1);
if (firstch == "y")
w = firstch.toUpperCase() + w.substr(1);
// Step 1a
re = /^(.+?)(ss|i)es$/;
re2 = /^(.+?)([^s])s$/;
if (re.test(w))
w = w.replace(re,"$1$2");
else if (re2.test(w))
w = w.replace(re2,"$1$2");
// Step 1b
re = /^(.+?)eed$/;
re2 = /^(.+?)(ed|ing)$/;
if (re.test(w)) {
var fp = re.exec(w);
re = new RegExp(mgr0);
if (re.test(fp[1])) {
re = /.$/;
w = w.replace(re,"");
}
}
else if (re2.test(w)) {
var fp = re2.exec(w);
stem = fp[1];
re2 = new RegExp(s_v);
if (re2.test(stem)) {
w = stem;
re2 = /(at|bl|iz)$/;
re3 = new RegExp("([^aeiouylsz])\\1$");
re4 = new RegExp("^" + C + v + "[^aeiouwxy]$");
if (re2.test(w))
w = w + "e";
else if (re3.test(w)) {
re = /.$/;
w = w.replace(re,"");
}
else if (re4.test(w))
w = w + "e";
}
}
// Step 1c
re = /^(.+?)y$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
re = new RegExp(s_v);
if (re.test(stem))
w = stem + "i";
}
// Step 2
re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
suffix = fp[2];
re = new RegExp(mgr0);
if (re.test(stem))
w = stem + step2list[suffix];
}
// Step 3
re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
suffix = fp[2];
re = new RegExp(mgr0);
if (re.test(stem))
w = stem + step3list[suffix];
}
// Step 4
re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/;
re2 = /^(.+?)(s|t)(ion)$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
re = new RegExp(mgr1);
if (re.test(stem))
w = stem;
}
else if (re2.test(w)) {
var fp = re2.exec(w);
stem = fp[1] + fp[2];
re2 = new RegExp(mgr1);
if (re2.test(stem))
w = stem;
}
// Step 5
re = /^(.+?)e$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
re = new RegExp(mgr1);
re2 = new RegExp(meq1);
re3 = new RegExp("^" + C + v + "[^aeiouwxy]$");
if (re.test(stem) || (re2.test(stem) && !(re3.test(stem))))
w = stem;
}
re = /ll$/;
re2 = new RegExp(mgr1);
if (re.test(w) && re2.test(w)) {
re = /.$/;
w = w.replace(re,"");
}
// and turn initial Y back to y
if (firstch == "y")
w = firstch.toLowerCase() + w.substr(1);
return w;
}
}
/**
* Simple result scoring code.
*/
var Scorer = {
// Implement the following function to further tweak the score for each result
// The function takes a result array [filename, title, anchor, descr, score]
// and returns the new score.
/*
score: function(result) {
return result[4];
},
*/
// query matches the full name of an object
objNameMatch: 11,
// or matches in the last dotted part of the object name
objPartialMatch: 6,
// Additive scores depending on the priority of the object
objPrio: {0: 15, // used to be importantResults
1: 5, // used to be objectResults
2: -5}, // used to be unimportantResults
// Used when the priority is not in the mapping.
objPrioDefault: 0,
// query found in title
title: 15,
// query found in terms
term: 5
};
var splitChars = (function() {
var result = {};
var singles = [96, 180, 187, 191, 215, 247, 749, 885, 903, 907, 909, 930, 1014, 1648,
1748, 1809, 2416, 2473, 2481, 2526, 2601, 2609, 2612, 2615, 2653, 2702,
2706, 2729, 2737, 2740, 2857, 2865, 2868, 2910, 2928, 2948, 2961, 2971,
2973, 3085, 3089, 3113, 3124, 3213, 3217, 3241, 3252, 3295, 3341, 3345,
3369, 3506, 3516, 3633, 3715, 3721, 3736, 3744, 3748, 3750, 3756, 3761,
3781, 3912, 4239, 4347, 4681, 4695, 4697, 4745, 4785, 4799, 4801, 4823,
4881, 5760, 5901, 5997, 6313, 7405, 8024, 8026, 8028, 8030, 8117, 8125,
8133, 8181, 8468, 8485, 8487, 8489, 8494, 8527, 11311, 11359, 11687, 11695,
11703, 11711, 11719, 11727, 11735, 12448, 12539, 43010, 43014, 43019, 43587,
43696, 43713, 64286, 64297, 64311, 64317, 64319, 64322, 64325, 65141];
var i, j, start, end;
for (i = 0; i < singles.length; i++) {
result[singles[i]] = true;
}
var ranges = [[0, 47], [58, 64], [91, 94], [123, 169], [171, 177], [182, 184], [706, 709],
[722, 735], [741, 747], [751, 879], [888, 889], [894, 901], [1154, 1161],
[1318, 1328], [1367, 1368], [1370, 1376], [1416, 1487], [1515, 1519], [1523, 1568],
[1611, 1631], [1642, 1645], [1750, 1764], [1767, 1773], [1789, 1790], [1792, 1807],
[1840, 1868], [1958, 1968], [1970, 1983], [2027, 2035], [2038, 2041], [2043, 2047],
[2070, 2073], [2075, 2083], [2085, 2087], [2089, 2307], [2362, 2364], [2366, 2383],
[2385, 2391], [2402, 2405], [2419, 2424], [2432, 2436], [2445, 2446], [2449, 2450],
[2483, 2485], [2490, 2492], [2494, 2509], [2511, 2523], [2530, 2533], [2546, 2547],
[2554, 2564], [2571, 2574], [2577, 2578], [2618, 2648], [2655, 2661], [2672, 2673],
[2677, 2692], [2746, 2748], [2750, 2767], [2769, 2783], [2786, 2789], [2800, 2820],
[2829, 2830], [2833, 2834], [2874, 2876], [2878, 2907], [2914, 2917], [2930, 2946],
[2955, 2957], [2966, 2968], [2976, 2978], [2981, 2983], [2987, 2989], [3002, 3023],
[3025, 3045], [3059, 3076], [3130, 3132], [3134, 3159], [3162, 3167], [3170, 3173],
[3184, 3191], [3199, 3204], [3258, 3260], [3262, 3293], [3298, 3301], [3312, 3332],
[3386, 3388], [3390, 3423], [3426, 3429], [3446, 3449], [3456, 3460], [3479, 3481],
[3518, 3519], [3527, 3584], [3636, 3647], [3655, 3663], [3674, 3712], [3717, 3718],
[3723, 3724], [3726, 3731], [3752, 3753], [3764, 3772], [3774, 3775], [3783, 3791],
[3802, 3803], [3806, 3839], [3841, 3871], [3892, 3903], [3949, 3975], [3980, 4095],
[4139, 4158], [4170, 4175], [4182, 4185], [4190, 4192], [4194, 4196], [4199, 4205],
[4209, 4212], [4226, 4237], [4250, 4255], [4294, 4303], [4349, 4351], [4686, 4687],
[4702, 4703], [4750, 4751], [4790, 4791], [4806, 4807], [4886, 4887], [4955, 4968],
[4989, 4991], [5008, 5023], [5109, 5120], [5741, 5742], [5787, 5791], [5867, 5869],
[5873, 5887], [5906, 5919], [5938, 5951], [5970, 5983], [6001, 6015], [6068, 6102],
[6104, 6107], [6109, 6111], [6122, 6127], [6138, 6159], [6170, 6175], [6264, 6271],
[6315, 6319], [6390, 6399], [6429, 6469], [6510, 6511], [6517, 6527], [6572, 6592],
[6600, 6607], [6619, 6655], [6679, 6687], [6741, 6783], [6794, 6799], [6810, 6822],
[6824, 6916], [6964, 6980], [6988, 6991], [7002, 7042], [7073, 7085], [7098, 7167],
[7204, 7231], [7242, 7244], [7294, 7400], [7410, 7423], [7616, 7679], [7958, 7959],
[7966, 7967], [8006, 8007], [8014, 8015], [8062, 8063], [8127, 8129], [8141, 8143],
[8148, 8149], [8156, 8159], [8173, 8177], [8189, 8303], [8306, 8307], [8314, 8318],
[8330, 8335], [8341, 8449], [8451, 8454], [8456, 8457], [8470, 8472], [8478, 8483],
[8506, 8507], [8512, 8516], [8522, 8525], [8586, 9311], [9372, 9449], [9472, 10101],
[10132, 11263], [11493, 11498], [11503, 11516], [11518, 11519], [11558, 11567],
[11622, 11630], [11632, 11647], [11671, 11679], [11743, 11822], [11824, 12292],
[12296, 12320], [12330, 12336], [12342, 12343], [12349, 12352], [12439, 12444],
[12544, 12548], [12590, 12592], [12687, 12689], [12694, 12703], [12728, 12783],
[12800, 12831], [12842, 12880], [12896, 12927], [12938, 12976], [12992, 13311],
[19894, 19967], [40908, 40959], [42125, 42191], [42238, 42239], [42509, 42511],
[42540, 42559], [42592, 42593], [42607, 42622], [42648, 42655], [42736, 42774],
[42784, 42785], [42889, 42890], [42893, 43002], [43043, 43055], [43062, 43071],
[43124, 43137], [43188, 43215], [43226, 43249], [43256, 43258], [43260, 43263],
[43302, 43311], [43335, 43359], [43389, 43395], [43443, 43470], [43482, 43519],
[43561, 43583], [43596, 43599], [43610, 43615], [43639, 43641], [43643, 43647],
[43698, 43700], [43703, 43704], [43710, 43711], [43715, 43738], [43742, 43967],
[44003, 44015], [44026, 44031], [55204, 55215], [55239, 55242], [55292, 55295],
[57344, 63743], [64046, 64047], [64110, 64111], [64218, 64255], [64263, 64274],
[64280, 64284], [64434, 64466], [64830, 64847], [64912, 64913], [64968, 65007],
[65020, 65135], [65277, 65295], [65306, 65312], [65339, 65344], [65371, 65381],
[65471, 65473], [65480, 65481], [65488, 65489], [65496, 65497]];
for (i = 0; i < ranges.length; i++) {
start = ranges[i][0];
end = ranges[i][1];
for (j = start; j <= end; j++) {
result[j] = true;
}
}
return result;
})();
function splitQuery(query) {
var result = [];
var start = -1;
for (var i = 0; i < query.length; i++) {
if (splitChars[query.charCodeAt(i)]) {
if (start !== -1) {
result.push(query.slice(start, i));
start = -1;
}
} else if (start === -1) {
start = i;
}
}
if (start !== -1) {
result.push(query.slice(start));
}
return result;
}
/**
* Search Module
*/
@@ -58,19 +335,6 @@ var Search = {
_queued_query : null,
_pulse_status : -1,
htmlToText : function(htmlString) {
var htmlElement = document.createElement('span');
htmlElement.innerHTML = htmlString;
$(htmlElement).find('.headerlink').remove();
docContent = $(htmlElement).find('[role=main]')[0];
if(docContent === undefined) {
console.warn("Content block not found. Sphinx search tries to obtain it " +
"via '[role=main]'. Could you check your theme or template.");
return "";
}
return docContent.textContent || docContent.innerText;
},
init : function() {
var params = $.getQueryParameters();
if (params.q) {
@@ -135,7 +399,7 @@ var Search = {
this.out = $('#search-results');
this.title = $('<h2>' + _('Searching') + '</h2>').appendTo(this.out);
this.dots = $('<span></span>').appendTo(this.title);
this.status = $('<p class="search-summary">&nbsp;</p>').appendTo(this.out);
this.status = $('<p style="display: none"></p>').appendTo(this.out);
this.output = $('<ul class="search"/>').appendTo(this.out);
$('#search-progress').text(_('Preparing search...'));
@@ -153,6 +417,7 @@ var Search = {
*/
query : function(query) {
var i;
var stopwords = ["a","and","are","as","at","be","but","by","for","if","in","into","is","it","near","no","not","of","on","or","such","that","the","their","then","there","these","they","this","to","was","will","with"];
// stem the searchterms and add them to the correct list
var stemmer = new Stemmer();
@@ -250,9 +515,7 @@ var Search = {
if (results.length) {
var item = results.pop();
var listItem = $('<li style="display:none"></li>');
var requestUrl = "";
var linkUrl = "";
if (DOCUMENTATION_OPTIONS.BUILDER === 'dirhtml') {
if (DOCUMENTATION_OPTIONS.FILE_SUFFIX === '') {
// dirhtml builder
var dirname = item[0] + '/';
if (dirname.match(/\/index\/$/)) {
@@ -260,17 +523,15 @@ var Search = {
} else if (dirname == 'index/') {
dirname = '';
}
requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + dirname;
linkUrl = requestUrl;
listItem.append($('<a/>').attr('href',
DOCUMENTATION_OPTIONS.URL_ROOT + dirname +
highlightstring + item[2]).html(item[1]));
} else {
// normal html builders
requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + item[0] + DOCUMENTATION_OPTIONS.FILE_SUFFIX;
linkUrl = item[0] + DOCUMENTATION_OPTIONS.LINK_SUFFIX;
}
listItem.append($('<a/>').attr('href',
linkUrl +
listItem.append($('<a/>').attr('href',
item[0] + DOCUMENTATION_OPTIONS.FILE_SUFFIX +
highlightstring + item[2]).html(item[1]));
}
if (item[3]) {
listItem.append($('<span> (' + item[3] + ')</span>'));
Search.output.append(listItem);
@@ -278,7 +539,11 @@ var Search = {
displayNextItem();
});
} else if (DOCUMENTATION_OPTIONS.HAS_SOURCE) {
$.ajax({url: requestUrl,
var suffix = DOCUMENTATION_OPTIONS.SOURCELINK_SUFFIX;
if (suffix === undefined) {
suffix = '.txt';
}
$.ajax({url: DOCUMENTATION_OPTIONS.URL_ROOT + '_sources/' + item[5] + (item[5].slice(-suffix.length) === suffix ? '' : suffix),
dataType: "text",
complete: function(jqxhr, textstatus) {
var data = jqxhr.responseText;
@@ -328,13 +593,12 @@ var Search = {
for (var prefix in objects) {
for (var name in objects[prefix]) {
var fullname = (prefix ? prefix + '.' : '') + name;
var fullnameLower = fullname.toLowerCase()
if (fullnameLower.indexOf(object) > -1) {
if (fullname.toLowerCase().indexOf(object) > -1) {
var score = 0;
var parts = fullnameLower.split('.');
var parts = fullname.split('.');
// check for different match types: exact matches of full name or
// "last name" (i.e. last dotted part)
if (fullnameLower == object || parts[parts.length - 1] == object) {
if (fullname == object || parts[parts.length - 1] == object) {
score += Scorer.objNameMatch;
// matches in last name
} else if (parts[parts.length - 1].indexOf(object) > -1) {
@@ -401,19 +665,6 @@ var Search = {
{files: terms[word], score: Scorer.term},
{files: titleterms[word], score: Scorer.title}
];
// add support for partial matches
if (word.length > 2) {
for (var w in terms) {
if (w.match(word) && !terms[word]) {
_o.push({files: terms[w], score: Scorer.partialTerm})
}
}
for (var w in titleterms) {
if (w.match(word) && !titleterms[word]) {
_o.push({files: titleterms[w], score: Scorer.partialTitle})
}
}
}
// no match but word was a required one
if ($u.every(_o, function(o){return o.files === undefined;})) {
@@ -433,7 +684,7 @@ var Search = {
for (j = 0; j < _files.length; j++) {
file = _files[j];
if (!(file in scoreMap))
scoreMap[file] = {};
scoreMap[file] = {}
scoreMap[file][word] = o.score;
}
});
@@ -441,7 +692,7 @@ var Search = {
// create the mapping
for (j = 0; j < files.length; j++) {
file = files[j];
if (file in fileMap && fileMap[file].indexOf(word) === -1)
if (file in fileMap)
fileMap[file].push(word);
else
fileMap[file] = [word];
@@ -453,12 +704,8 @@ var Search = {
var valid = true;
// check if all requirements are matched
var filteredTermCount = // as search terms with length < 3 are discarded: ignore
searchterms.filter(function(term){return term.length > 2}).length
if (
fileMap[file].length != searchterms.length &&
fileMap[file].length != filteredTermCount
) continue;
if (fileMap[file].length != searchterms.length)
continue;
// ensure that none of the excluded terms is in the search result
for (i = 0; i < excluded.length; i++) {
@@ -489,8 +736,7 @@ var Search = {
* words. the first one is used to find the occurrence, the
* latter for highlighting it.
*/
makeSearchSummary : function(htmlText, keywords, hlwords) {
var text = Search.htmlToText(htmlText);
makeSearchSummary : function(text, keywords, hlwords) {
var textLower = text.toLowerCase();
var start = 0;
$.each(keywords, function() {
@@ -512,4 +758,4 @@ var Search = {
$(document).ready(function() {
Search.init();
});
});
docs/sphinx_docs/_build/html/genindex.html
+32 -141
View File
@@ -1,19 +1,20 @@
<!DOCTYPE html>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Index &#8212; Thun 0.3.0 documentation</title>
<link rel="stylesheet" href="_static/alabaster.css" type="text/css" />
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
<script id="documentation_options" data-url_root="./" src="_static/documentation_options.js"></script>
<script src="_static/jquery.js"></script>
<script src="_static/underscore.js"></script>
<script src="_static/doctools.js"></script>
<script src="_static/language_data.js"></script>
<script async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
<script type="text/javascript" src="_static/documentation_options.js"></script>
<script type="text/javascript" src="_static/jquery.js"></script>
<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<link rel="index" title="Index" href="#" />
<link rel="search" title="Search" href="search.html" />
@@ -28,8 +29,6 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
@@ -87,8 +86,6 @@
<li><a href="library.html#joy.library.DefinitionWrapper.add_definitions">add_definitions() (joy.library.DefinitionWrapper class method)</a>
</li>
<li><a href="types.html#joy.utils.types.AnyJoyType">AnyJoyType (class in joy.utils.types)</a>
</li>
<li><a href="types.html#joy.utils.types.AnyStarJoyType">AnyStarJoyType (class in joy.utils.types)</a>
</li>
<li><a href="library.html#joy.library.app1">app1() (in module joy.library)</a>
</li>
@@ -197,8 +194,6 @@
<li><a href="library.html#joy.utils.generated_library.first_two">first_two() (in module joy.utils.generated_library)</a>
</li>
<li><a href="types.html#joy.utils.types.FloatJoyType">FloatJoyType (class in joy.utils.types)</a>
</li>
<li><a href="types.html#joy.utils.types.FloatStarJoyType">FloatStarJoyType (class in joy.utils.types)</a>
</li>
</ul></td>
<td style="width: 33%; vertical-align: top;"><ul>
@@ -257,8 +252,6 @@
<li><a href="library.html#joy.library.inscribe_">inscribe_() (in module joy.library)</a>
</li>
<li><a href="types.html#joy.utils.types.IntJoyType">IntJoyType (class in joy.utils.types)</a>
</li>
<li><a href="types.html#joy.utils.types.IntStarJoyType">IntStarJoyType (class in joy.utils.types)</a>
</li>
<li><a href="stack.html#joy.utils.stack.iter_stack">iter_stack() (in module joy.utils.stack)</a>
</li>
@@ -270,57 +263,22 @@
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="joy.html#joy.joy.joy">joy() (in module joy.joy)</a>
</li>
<li>
joy.joy
<ul>
<li><a href="joy.html#module-joy.joy">module</a>
<li><a href="joy.html#module-joy.joy">joy.joy (module)</a>
</li>
</ul></li>
<li>
joy.library
<ul>
<li><a href="library.html#module-joy.library">module</a>
<li><a href="library.html#module-joy.library">joy.library (module)</a>
</li>
</ul></li>
<li>
joy.parser
<ul>
<li><a href="parser.html#module-joy.parser">module</a>
<li><a href="parser.html#module-joy.parser">joy.parser (module)</a>
</li>
</ul></li>
<li>
joy.utils.generated_library
<ul>
<li><a href="library.html#module-joy.utils.generated_library">module</a>
</li>
</ul></li>
</ul></td>
<td style="width: 33%; vertical-align: top;"><ul>
<li>
joy.utils.pretty_print
<ul>
<li><a href="pretty.html#module-joy.utils.pretty_print">module</a>
<li><a href="library.html#module-joy.utils.generated_library">joy.utils.generated_library (module)</a>
</li>
</ul></li>
<li>
joy.utils.stack
<ul>
<li><a href="stack.html#module-joy.utils.stack">module</a>
<li><a href="pretty.html#module-joy.utils.pretty_print">joy.utils.pretty_print (module)</a>
</li>
</ul></li>
<li>
joy.utils.types
<ul>
<li><a href="types.html#module-joy.utils.types">module</a>
<li><a href="stack.html#module-joy.utils.stack">joy.utils.stack (module)</a>
</li>
<li><a href="types.html#module-joy.utils.types">joy.utils.types (module)</a>
</li>
</ul></li>
<li><a href="types.html#joy.utils.types.JoyTypeError">JoyTypeError</a>
</li>
</ul></td>
@@ -329,22 +287,8 @@
<h2 id="K">K</h2>
<table style="width: 100%" class="indextable genindextable"><tr>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="types.html#joy.utils.types.AnyStarJoyType.kind">kind (joy.utils.types.AnyStarJoyType attribute)</a>
<ul>
<li><a href="types.html#joy.utils.types.FloatStarJoyType.kind">(joy.utils.types.FloatStarJoyType attribute)</a>
<li><a href="types.html#joy.utils.types.KleeneStar.kind">kind (joy.utils.types.KleeneStar attribute)</a>
</li>
<li><a href="types.html#joy.utils.types.IntStarJoyType.kind">(joy.utils.types.IntStarJoyType attribute)</a>
</li>
<li><a href="types.html#joy.utils.types.KleeneStar.kind">(joy.utils.types.KleeneStar attribute)</a>
</li>
<li><a href="types.html#joy.utils.types.NumberStarJoyType.kind">(joy.utils.types.NumberStarJoyType attribute)</a>
</li>
<li><a href="types.html#joy.utils.types.StackStarJoyType.kind">(joy.utils.types.StackStarJoyType attribute)</a>
</li>
<li><a href="types.html#joy.utils.types.TextStarJoyType.kind">(joy.utils.types.TextStarJoyType attribute)</a>
</li>
</ul></li>
</ul></td>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="types.html#joy.utils.types.KleeneStar">KleeneStar (class in joy.utils.types)</a>
@@ -371,29 +315,12 @@
</li>
<li><a href="library.html#joy.library.max_">max_() (in module joy.library)</a>
</li>
</ul></td>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="types.html#joy.utils.types.meta_compose">meta_compose() (in module joy.utils.types)</a>
</li>
<li><a href="library.html#joy.library.min_">min_() (in module joy.library)</a>
</li>
<li>
module
<ul>
<li><a href="joy.html#module-joy.joy">joy.joy</a>
</li>
<li><a href="library.html#module-joy.library">joy.library</a>
</li>
<li><a href="parser.html#module-joy.parser">joy.parser</a>
</li>
<li><a href="library.html#module-joy.utils.generated_library">joy.utils.generated_library</a>
</li>
<li><a href="pretty.html#module-joy.utils.pretty_print">joy.utils.pretty_print</a>
</li>
<li><a href="stack.html#module-joy.utils.stack">joy.utils.stack</a>
</li>
<li><a href="types.html#module-joy.utils.types">joy.utils.types</a>
</li>
</ul></li>
</ul></td>
</tr></table>
@@ -401,10 +328,6 @@
<table style="width: 100%" class="indextable genindextable"><tr>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="types.html#joy.utils.types.NumberJoyType">NumberJoyType (class in joy.utils.types)</a>
</li>
</ul></td>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="types.html#joy.utils.types.NumberStarJoyType">NumberStarJoyType (class in joy.utils.types)</a>
</li>
</ul></td>
</tr></table>
@@ -432,10 +355,10 @@
</li>
<li><a href="types.html#joy.utils.types.poly_compose">poly_compose() (in module joy.utils.types)</a>
</li>
</ul></td>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="library.html#joy.utils.generated_library.pop">pop() (in module joy.utils.generated_library)</a>
</li>
</ul></td>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="library.html#joy.utils.generated_library.popd">popd() (in module joy.utils.generated_library)</a>
</li>
<li><a href="library.html#joy.utils.generated_library.popdd">popdd() (in module joy.utils.generated_library)</a>
@@ -447,6 +370,8 @@
<li><a href="library.html#joy.utils.generated_library.popopdd">popopdd() (in module joy.utils.generated_library)</a>
</li>
<li><a href="library.html#joy.library.pred">pred() (in module joy.library)</a>
</li>
<li><a href="library.html#joy.library.primrec">primrec() (in module joy.library)</a>
</li>
</ul></td>
</tr></table>
@@ -504,8 +429,6 @@
</li>
</ul></td>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="types.html#joy.utils.types.StackStarJoyType">StackStarJoyType (class in joy.utils.types)</a>
</li>
<li><a href="library.html#joy.library.step">step() (in module joy.library)</a>
</li>
<li><a href="library.html#joy.utils.generated_library.stuncons">stuncons() (in module joy.utils.generated_library)</a>
@@ -537,8 +460,6 @@
<li><a href="parser.html#joy.parser.text_to_expression">text_to_expression() (in module joy.parser)</a>
</li>
<li><a href="types.html#joy.utils.types.TextJoyType">TextJoyType (class in joy.utils.types)</a>
</li>
<li><a href="types.html#joy.utils.types.TextStarJoyType">TextStarJoyType (class in joy.utils.types)</a>
</li>
<li><a href="library.html#joy.utils.generated_library.third">third() (in module joy.utils.generated_library)</a>
</li>
@@ -628,34 +549,10 @@
</div>
</div>
</div>
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
<div class="sphinxsidebarwrapper">
<h1 class="logo"><a href="index.html">Thun</a></h1>
<h3>Navigation</h3>
<ul>
<li class="toctree-l1"><a class="reference internal" href="notebooks/Intro.html">Thun: Joy in Python</a></li>
<li class="toctree-l1"><a class="reference internal" href="joy.html">Joy Interpreter</a></li>
<li class="toctree-l1"><a class="reference internal" href="stack.html">Stack or Quote or Sequence or List…</a></li>
<li class="toctree-l1"><a class="reference internal" href="parser.html">Parsing Text into Joy Expressions</a></li>
<li class="toctree-l1"><a class="reference internal" href="pretty.html">Tracing Joy Execution</a></li>
<li class="toctree-l1"><a class="reference internal" href="library.html">Function Reference</a></li>
<li class="toctree-l1"><a class="reference internal" href="lib.html">Functions Grouped by, er, Function with Examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="types.html">Type Inference of Joy Expressions</a></li>
<li class="toctree-l1"><a class="reference internal" href="notebooks/index.html">Essays about Programming in Joy</a></li>
</ul>
<div class="relations">
<div class="sphinxsidebarwrapper"><div class="relations">
<h3>Related Topics</h3>
<ul>
<li><a href="index.html">Documentation overview</a><ul>
@@ -663,23 +560,17 @@
</ul>
</div>
<div id="searchbox" style="display: none" role="search">
<h3 id="searchlabel">Quick search</h3>
<h3>Quick search</h3>
<div class="searchformwrapper">
<form class="search" action="search.html" method="get">
<input type="text" name="q" aria-labelledby="searchlabel" />
<input type="text" name="q" />
<input type="submit" value="Go" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
</div>
<script>$('#searchbox').show(0);</script>
<script type="text/javascript">$('#searchbox').show(0);</script>
</div>
</div>
<div class="clearer"></div>
@@ -690,7 +581,7 @@
</a>
<br />
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 3.0.2.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
</div>
</body>
docs/sphinx_docs/_build/html/index.html
+44 -56
View File
@@ -1,18 +1,19 @@
<!DOCTYPE html>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Thun 0.3.0 Documentation &#8212; Thun 0.3.0 documentation</title>
<link rel="stylesheet" href="_static/alabaster.css" type="text/css" />
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
<script id="documentation_options" data-url_root="./" src="_static/documentation_options.js"></script>
<script src="_static/jquery.js"></script>
<script src="_static/underscore.js"></script>
<script src="_static/doctools.js"></script>
<script src="_static/language_data.js"></script>
<script async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
<script type="text/javascript" src="_static/documentation_options.js"></script>
<script type="text/javascript" src="_static/jquery.js"></script>
<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
<link rel="next" title="Thun: Joy in Python" href="notebooks/Intro.html" />
@@ -28,8 +29,6 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<div class="section" id="thun-release-documentation">
@@ -44,10 +43,10 @@ between Thun and the originals, other than being written in Python, is
that it works by the “Continuation-Passing Style”.</p>
<p>Joy is:</p>
<ul class="simple">
<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Purely_functional_programming">Purely Functional</a></p></li>
<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Stack-oriented_programming_language">Stack-based</a></p></li>
<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Concatenative_programming_language">Concatinative</a> ( See also <a class="reference external" href="http://www.concatenative.org/wiki/view/Concatenative%20language">concatenative.org</a>)</p></li>
<li><p><a class="reference internal" href="notebooks/Categorical.html"><span class="doc">Categorical</span></a></p></li>
<li><a class="reference external" href="https://en.wikipedia.org/wiki/Purely_functional_programming">Purely Functional</a></li>
<li><a class="reference external" href="https://en.wikipedia.org/wiki/Stack-oriented_programming_language">Stack-based</a></li>
<li><a class="reference external" href="https://en.wikipedia.org/wiki/Concatenative_programming_language">Concatinative</a> ( See also <a class="reference external" href="http://www.concatenative.org/wiki/view/Concatenative%20language">concatenative.org</a>)</li>
<li><a class="reference internal" href="notebooks/Categorical.html"><span class="doc">Categorical</span></a></li>
</ul>
<p>I hope that this package is useful in the sense that it provides an
additional joy interpreter (the binary in the archive from La Trobe seems
@@ -69,10 +68,10 @@ itself.</p>
<div class="section" id="project-hosted-on-osdn">
<h2>Project Hosted on <a class="reference external" href="https://osdn.net/projects/joypy/">OSDN</a><a class="headerlink" href="#project-hosted-on-osdn" title="Permalink to this headline"></a></h2>
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@@ -161,41 +160,29 @@ interesting aspects. It’s quite a treasure trove.</p>
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@@ -204,24 +191,25 @@ interesting aspects. It’s quite a treasure trove.</p>
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@@ -232,7 +220,7 @@ interesting aspects. It’s quite a treasure trove.</p>
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 3.0.2.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
</div>
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docs/sphinx_docs/_build/html/joy.html
+79 -86
View File
@@ -1,18 +1,19 @@
<!DOCTYPE html>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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@@ -29,8 +30,6 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<div class="section" id="joy-interpreter">
@@ -40,9 +39,9 @@
<p>This module implements an interpreter for a dialect of Joy that
attempts to stay very close to the spirit of Joy but does not precisely
match the behaviour of the original version(s) written in C.</p>
<dl class="py function">
<dl class="function">
<dt id="joy.joy.joy">
<code class="sig-prename descclassname">joy.joy.</code><code class="sig-name descname">joy</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">stack</span></em>, <em class="sig-param"><span class="n">expression</span></em>, <em class="sig-param"><span class="n">dictionary</span></em>, <em class="sig-param"><span class="n">viewer</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/joy.html#joy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.joy.joy" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.joy.</code><code class="descname">joy</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em>, <em>viewer=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/joy.html#joy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.joy.joy" title="Permalink to this definition"></a></dt>
<dd><p>Evaluate a Joy expression on a stack.</p>
<p>This function iterates through a sequence of terms which are either
literals (strings, numbers, sequences of terms) or function symbols.
@@ -50,56 +49,68 @@ Literals are put onto the stack and functions are looked up in the
disctionary and executed.</p>
<p>The viewer is a function that is called with the stack and expression
on every iteration, its return value is ignored.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>stack</strong> (<em>stack</em>) – The stack.</p></li>
<li><p><strong>expression</strong> (<em>stack</em>) – The expression to evaluate.</p></li>
<li><p><strong>dictionary</strong> (<em>dict</em>) – A <code class="docutils literal notranslate"><span class="pre">dict</span></code> mapping names to Joy functions.</p></li>
<li><p><strong>viewer</strong> (<em>function</em>) – Optional viewer function.</p></li>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>stack</strong> (<em>stack</em>) – The stack.</li>
<li><strong>expression</strong> (<em>stack</em>) – The expression to evaluate.</li>
<li><strong>dictionary</strong> (<em>dict</em>) – A <code class="docutils literal notranslate"><span class="pre">dict</span></code> mapping names to Joy functions.</li>
<li><strong>viewer</strong> (<em>function</em>) – Optional viewer function.</li>
</ul>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>(stack, (), dictionary)</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">(stack, (), dictionary)</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.joy.repl">
<code class="sig-prename descclassname">joy.joy.</code><code class="sig-name descname">repl</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">stack</span><span class="o">=</span><span class="default_value">()</span></em>, <em class="sig-param"><span class="n">dictionary</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/joy.html#repl"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.joy.repl" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.joy.</code><code class="descname">repl</code><span class="sig-paren">(</span><em>stack=()</em>, <em>dictionary=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/joy.html#repl"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.joy.repl" title="Permalink to this definition"></a></dt>
<dd><p>Read-Evaluate-Print Loop</p>
<p>Accept input and run it on the stack, loop.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>stack</strong> (<em>stack</em>) – The stack.</p></li>
<li><p><strong>dictionary</strong> (<em>dict</em>) – A <code class="docutils literal notranslate"><span class="pre">dict</span></code> mapping names to Joy functions.</p></li>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>stack</strong> (<em>stack</em>) – The stack.</li>
<li><strong>dictionary</strong> (<em>dict</em>) – A <code class="docutils literal notranslate"><span class="pre">dict</span></code> mapping names to Joy functions.</li>
</ul>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>stack</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">stack</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.joy.run">
<code class="sig-prename descclassname">joy.joy.</code><code class="sig-name descname">run</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">text</span></em>, <em class="sig-param"><span class="n">stack</span></em>, <em class="sig-param"><span class="n">dictionary</span></em>, <em class="sig-param"><span class="n">viewer</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/joy.html#run"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.joy.run" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.joy.</code><code class="descname">run</code><span class="sig-paren">(</span><em>text</em>, <em>stack</em>, <em>dictionary</em>, <em>viewer=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/joy.html#run"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.joy.run" title="Permalink to this definition"></a></dt>
<dd><p>Return the stack resulting from running the Joy code text on the stack.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>text</strong> (<em>str</em>) – Joy code.</p></li>
<li><p><strong>stack</strong> (<em>stack</em>) – The stack.</p></li>
<li><p><strong>dictionary</strong> (<em>dict</em>) – A <code class="docutils literal notranslate"><span class="pre">dict</span></code> mapping names to Joy functions.</p></li>
<li><p><strong>viewer</strong> (<em>function</em>) – Optional viewer function.</p></li>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>text</strong> (<em>str</em>) – Joy code.</li>
<li><strong>stack</strong> (<em>stack</em>) – The stack.</li>
<li><strong>dictionary</strong> (<em>dict</em>) – A <code class="docutils literal notranslate"><span class="pre">dict</span></code> mapping names to Joy functions.</li>
<li><strong>viewer</strong> (<em>function</em>) – Optional viewer function.</li>
</ul>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>(stack, (), dictionary)</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">(stack, (), dictionary)</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
</div>
@@ -107,36 +118,17 @@ on every iteration, its return value is ignored.</p>
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@@ -146,24 +138,25 @@ on every iteration, its return value is ignored.</p>
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@@ -174,7 +167,7 @@ on every iteration, its return value is ignored.</p>
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@@ -1,18 +1,19 @@
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@@ -29,8 +30,6 @@
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@@ -40,58 +39,16 @@
<p>In Manfred von Thun’s article <a class="reference external" href="http://www.kevinalbrecht.com/code/joy-mirror/j08cnt.html">Joy compared with other functional languages</a> he asks, “Could the language of categories be used for writing programs? Any lambda expression can be translated into a categorical expression, so the language of categories is expressively complete. But this does not make it a suitable language for writing programs. As it stands it is a very low-level language.”</p>
<p>In <a class="reference external" href="http://conal.net/papers/compiling-to-categories/">Compiling to categories</a> Conal Elliott give a taste of what this might mean.</p>
<blockquote>
<div><p>It is well-known that the simply typed lambda-calculus is modeled by any cartesian closed category (CCC). This correspondence suggests giving typed functional programs a variety of interpretations, each corresponding to a different category. A convenient way to realize this idea is as a collection of meaning-preserving transformations added to an existing compiler, such as GHC for Haskell. This paper describes such an implementation and demonstrates its use for a variety of interpretations including hardware circuits, automatic differentiation, incremental computation, and interval analysis. Each such interpretation is a category easily defined in Haskell (outside of the compiler). The general technique appears to provide a compelling alternative to deeply embedded domain-specific languages.</p>
</div></blockquote>
<div>It is well-known that the simply typed lambda-calculus is modeled by any cartesian closed category (CCC). This correspondence suggests giving typed functional programs a variety of interpretations, each corresponding to a different category. A convenient way to realize this idea is as a collection of meaning-preserving transformations added to an existing compiler, such as GHC for Haskell. This paper describes such an implementation and demonstrates its use for a variety of interpretations including hardware circuits, automatic differentiation, incremental computation, and interval analysis. Each such interpretation is a category easily defined in Haskell (outside of the compiler). The general technique appears to provide a compelling alternative to deeply embedded domain-specific languages.</div></blockquote>
<p>What he’s doing is translating lambda forms into a kind of “point-free” style that is very close to Joy code (although more verbose) and then showing how to instantiate that code over different categories to get several different kinds of program out of the same code.</p>
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@@ -130,7 +88,7 @@
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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@@ -1,18 +1,19 @@
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@@ -28,14 +29,12 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<div class="section" id="re">
<h1>∂RE<a class="headerlink" href="#re" title="Permalink to this headline"></a></h1>
<div class="section" id="brzozowski-s-derivatives-of-regular-expressions">
<h2>Brzozowski’s Derivatives of Regular Expressions<a class="headerlink" href="#brzozowski-s-derivatives-of-regular-expressions" title="Permalink to this headline"></a></h2>
<div class="section" id="brzozowskis-derivatives-of-regular-expressions">
<h2>Brzozowski’s Derivatives of Regular Expressions<a class="headerlink" href="#brzozowskis-derivatives-of-regular-expressions" title="Permalink to this headline"></a></h2>
<p>Legend:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>∧ intersection
∨ union
@@ -96,14 +95,14 @@ R∘λ = λ∘R = R
</div>
<div class="section" id="implementation">
<h2>Implementation<a class="headerlink" href="#implementation" title="Permalink to this headline"></a></h2>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">partial</span> <span class="k">as</span> <span class="n">curry</span>
<span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">product</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">functools</span> <span class="k">import</span> <span class="n">partial</span> <span class="k">as</span> <span class="n">curry</span>
<span class="kn">from</span> <span class="nn">itertools</span> <span class="k">import</span> <span class="n">product</span>
</pre></div>
</div>
<div class="section" id="and">
<h3><code class="docutils literal notranslate"><span class="pre">ϕ</span></code> and <code class="docutils literal notranslate"><span class="pre">λ</span></code><a class="headerlink" href="#and" title="Permalink to this headline"></a></h3>
<p>The empty set and the set of just the empty string.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">phi</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">()</span> <span class="c1"># ϕ</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">phi</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">()</span> <span class="c1"># ϕ</span>
<span class="n">y</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;&#39;</span><span class="p">})</span> <span class="c1"># λ</span>
</pre></div>
</div>
@@ -115,7 +114,7 @@ illustrate the algorithm and because you can represent any other
alphabet with two symbols (if you had to.)</p>
<p>I chose the names <code class="docutils literal notranslate"><span class="pre">O</span></code> and <code class="docutils literal notranslate"><span class="pre">l</span></code> (uppercase “o” and lowercase “L”) to
look like <code class="docutils literal notranslate"><span class="pre">0</span></code> and <code class="docutils literal notranslate"><span class="pre">1</span></code> (zero and one) respectively.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">syms</span> <span class="o">=</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;0&#39;</span><span class="p">}),</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;1&#39;</span><span class="p">})</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">syms</span> <span class="o">=</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;0&#39;</span><span class="p">}),</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;1&#39;</span><span class="p">})</span>
</pre></div>
</div>
</div>
@@ -133,7 +132,7 @@ expression</em> is one of:</p>
</pre></div>
</div>
<p>Where <code class="docutils literal notranslate"><span class="pre">R</span></code> and <code class="docutils literal notranslate"><span class="pre">S</span></code> stand for <em>regular expressions</em>.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">AND</span><span class="p">,</span> <span class="n">CONS</span><span class="p">,</span> <span class="n">KSTAR</span><span class="p">,</span> <span class="n">NOT</span><span class="p">,</span> <span class="n">OR</span> <span class="o">=</span> <span class="s1">&#39;and cons * not or&#39;</span><span class="o">.</span><span class="n">split</span><span class="p">()</span> <span class="c1"># Tags are just strings.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">AND</span><span class="p">,</span> <span class="n">CONS</span><span class="p">,</span> <span class="n">KSTAR</span><span class="p">,</span> <span class="n">NOT</span><span class="p">,</span> <span class="n">OR</span> <span class="o">=</span> <span class="s1">&#39;and cons * not or&#39;</span><span class="o">.</span><span class="n">split</span><span class="p">()</span> <span class="c1"># Tags are just strings.</span>
</pre></div>
</div>
<p>Because they are formed of <code class="docutils literal notranslate"><span class="pre">frozenset</span></code>, <code class="docutils literal notranslate"><span class="pre">tuple</span></code> and <code class="docutils literal notranslate"><span class="pre">str</span></code> objects
@@ -141,7 +140,7 @@ only, these datastructures are immutable.</p>
</div>
<div class="section" id="string-representation-of-re-datastructures">
<h3>String Representation of RE Datastructures<a class="headerlink" href="#string-representation-of-re-datastructures" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
<span class="sd">&#39;&#39;&#39;</span>
<span class="sd"> Return a nice string repr for a regular expression datastructure.</span>
<span class="sd"> &#39;&#39;&#39;</span>
@@ -180,10 +179,10 @@ only, these datastructures are immutable.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">I</span> <span class="o">=</span> <span class="p">(</span><span class="mi">0</span><span class="o">|</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">I</span> <span class="o">=</span> <span class="p">(</span><span class="n">KSTAR</span><span class="p">,</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">I</span> <span class="o">=</span> <span class="p">(</span><span class="n">KSTAR</span><span class="p">,</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">I</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">I</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">.</span>
@@ -198,13 +197,13 @@ only, these datastructures are immutable.</p>
</pre></div>
</div>
<p>Note that it contains one of everything.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">I</span><span class="p">))))</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">I</span><span class="p">))))</span>
<span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
<span class="n">c</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">KSTAR</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
<span class="n">it</span> <span class="o">=</span> <span class="p">(</span><span class="n">AND</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">NOT</span><span class="p">,</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">)))</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">&#39;)</span>
@@ -214,7 +213,7 @@ only, these datastructures are immutable.</p>
<div class="section" id="nully">
<h3><code class="docutils literal notranslate"><span class="pre">nully()</span></code><a class="headerlink" href="#nully" title="Permalink to this headline"></a></h3>
<p>Let’s get that auxiliary predicate function <code class="docutils literal notranslate"><span class="pre">δ</span></code> out of the way.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">nully</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">nully</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
<span class="sd">&#39;&#39;&#39;</span>
<span class="sd"> δ - Return λ if λ ⊆ R otherwise ϕ.</span>
<span class="sd"> &#39;&#39;&#39;</span>
@@ -252,7 +251,7 @@ only, these datastructures are immutable.</p>
<p>This is the straightforward version with no “compaction”. It works fine,
but does waaaay too much work because the expressions grow each
derivation.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">derv</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
@@ -296,7 +295,7 @@ derivation.</p>
</div>
<div class="section" id="compaction-rules">
<h3>Compaction Rules<a class="headerlink" href="#compaction-rules" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">_compaction_rule</span><span class="p">(</span><span class="n">relation</span><span class="p">,</span> <span class="n">one</span><span class="p">,</span> <span class="n">zero</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">_compaction_rule</span><span class="p">(</span><span class="n">relation</span><span class="p">,</span> <span class="n">one</span><span class="p">,</span> <span class="n">zero</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span>
<span class="n">b</span> <span class="k">if</span> <span class="n">a</span> <span class="o">==</span> <span class="n">one</span> <span class="k">else</span> <span class="c1"># R*1 = 1*R = R</span>
<span class="n">a</span> <span class="k">if</span> <span class="n">b</span> <span class="o">==</span> <span class="n">one</span> <span class="k">else</span>
@@ -306,7 +305,7 @@ derivation.</p>
</pre></div>
</div>
<p>An elegant symmetry.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># R ∧ I = I ∧ R = R</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># R ∧ I = I ∧ R = R</span>
<span class="c1"># R ∧ ϕ = ϕ ∧ R = ϕ</span>
<span class="n">_and</span> <span class="o">=</span> <span class="n">curry</span><span class="p">(</span><span class="n">_compaction_rule</span><span class="p">,</span> <span class="n">AND</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
@@ -325,14 +324,14 @@ derivation.</p>
<p>We can save re-processing by remembering results we have already
computed. RE datastructures are immutable and the <code class="docutils literal notranslate"><span class="pre">derv()</span></code> functions
are <em>pure</em> so this is fine.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">Memo</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">Memo</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">f</span> <span class="o">=</span> <span class="n">f</span>
<span class="bp">self</span><span class="o">.</span><span class="n">calls</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hits</span> <span class="o">=</span> <span class="mi">0</span>
<span class="bp">self</span><span class="o">.</span><span class="n">mem</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">calls</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">result</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">mem</span><span class="p">[</span><span class="n">key</span><span class="p">]</span>
@@ -347,7 +346,7 @@ are <em>pure</em> so this is fine.</p>
<h3>With “Compaction”<a class="headerlink" href="#with-compaction" title="Permalink to this headline"></a></h3>
<p>This version uses the rules above to perform compaction. It keeps the
expressions from growing too large.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D_compaction</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D_compaction</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span>
<span class="nd">@Memo</span>
<span class="k">def</span> <span class="nf">derv</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
@@ -392,10 +391,10 @@ expressions from growing too large.</p>
</div>
</div>
</div>
<div class="section" id="let-s-try-it-out">
<h2>Let’s try it out…<a class="headerlink" href="#let-s-try-it-out" title="Permalink to this headline"></a></h2>
<div class="section" id="lets-try-it-out">
<h2>Let’s try it out…<a class="headerlink" href="#lets-try-it-out" title="Permalink to this headline"></a></h2>
<p>(FIXME: redo.)</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">o</span><span class="p">,</span> <span class="n">z</span> <span class="o">=</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;0&#39;</span><span class="p">),</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;1&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">o</span><span class="p">,</span> <span class="n">z</span> <span class="o">=</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;0&#39;</span><span class="p">),</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;1&#39;</span><span class="p">)</span>
<span class="n">REs</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="n">N</span> <span class="o">=</span> <span class="mi">5</span>
<span class="n">names</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">product</span><span class="p">(</span><span class="o">*</span><span class="p">(</span><span class="n">N</span> <span class="o">*</span> <span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)])))</span>
@@ -453,7 +452,7 @@ expressions from growing too large.</p>
</div>
<div class="section" id="larger-alphabets">
<h2>Larger Alphabets<a class="headerlink" href="#larger-alphabets" title="Permalink to this headline"></a></h2>
<p>We could parse larger alphabets by defining patterns for e.g. each byte
<p>We could parse larger alphabets by defining patterns for e.g.&nbsp;each byte
of the ASCII code. Or we can generalize this code. If you study the code
above you’ll see that we never use the “set-ness” of the symbols <code class="docutils literal notranslate"><span class="pre">O</span></code>
and <code class="docutils literal notranslate"><span class="pre">l</span></code>. The only time Python set operators (<code class="docutils literal notranslate"><span class="pre">&amp;</span></code> and <code class="docutils literal notranslate"><span class="pre">|</span></code>) appear
@@ -499,8 +498,8 @@ machine transition table.</p>
</pre></div>
</div>
<p>Says, “Three or more 1’s and not ending in 01 nor composed of all 1’s.”</p>
<div class="figure align-default" id="id2">
<img alt="omg.svg" src="notebooks/attachment:omg.svg" /><p class="caption"><span class="caption-text">omg.svg</span><a class="headerlink" href="#id2" title="Permalink to this image"></a></p>
<div class="figure" id="id2">
<img alt="omg.svg" src="notebooks/attachment:omg.svg" /><p class="caption"><span class="caption-text">omg.svg</span></p>
</div>
<p>Start at <code class="docutils literal notranslate"><span class="pre">a</span></code> and follow the transition arrows according to their
labels. Accepting states have a double outline. (Graphic generated with
@@ -553,18 +552,18 @@ a --1--&gt; ∂1(a)
<p>You can see the one-way nature of the <code class="docutils literal notranslate"><span class="pre">g</span></code> state and the <code class="docutils literal notranslate"><span class="pre">hij</span></code> “trap”
in the way that the <code class="docutils literal notranslate"><span class="pre">.111.</span></code> on the left-hand side of the <code class="docutils literal notranslate"><span class="pre">&amp;</span></code>
disappears once it has been matched.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
<span class="kn">from</span> <span class="nn">pprint</span> <span class="kn">import</span> <span class="n">pprint</span>
<span class="kn">from</span> <span class="nn">string</span> <span class="kn">import</span> <span class="n">ascii_lowercase</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="k">import</span> <span class="n">defaultdict</span>
<span class="kn">from</span> <span class="nn">pprint</span> <span class="k">import</span> <span class="n">pprint</span>
<span class="kn">from</span> <span class="nn">string</span> <span class="k">import</span> <span class="n">ascii_lowercase</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">d0</span><span class="p">,</span> <span class="n">d1</span> <span class="o">=</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;0&#39;</span><span class="p">),</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;1&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">d0</span><span class="p">,</span> <span class="n">d1</span> <span class="o">=</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;0&#39;</span><span class="p">),</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">&#39;1&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="section" id="explore">
<h3><code class="docutils literal notranslate"><span class="pre">explore()</span></code><a class="headerlink" href="#explore" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">explore</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">explore</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
<span class="c1"># Don&#39;t have more than 26 states...</span>
<span class="n">names</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="nb">iter</span><span class="p">(</span><span class="n">ascii_lowercase</span><span class="p">)</span><span class="o">.</span><span class="n">next</span><span class="p">)</span>
@@ -590,7 +589,7 @@ disappears once it has been matched.</p>
<span class="k">return</span> <span class="n">table</span><span class="p">,</span> <span class="n">accepting</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span> <span class="o">=</span> <span class="n">explore</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span> <span class="o">=</span> <span class="n">explore</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>
<span class="n">table</span>
</pre></div>
</div>
@@ -616,7 +615,7 @@ disappears once it has been matched.</p>
<span class="p">(</span><span class="s1">&#39;j&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">):</span> <span class="s1">&#39;h&#39;</span><span class="p">}</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">accepting</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">accepting</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="s1">&#39;h&#39;</span><span class="p">,</span> <span class="s1">&#39;i&#39;</span><span class="p">}</span>
@@ -627,7 +626,7 @@ disappears once it has been matched.</p>
<h3>Generate Diagram<a class="headerlink" href="#generate-diagram" title="Permalink to this headline"></a></h3>
<p>Once we have the FSM table and the set of accepting states we can
generate the diagram above.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">_template</span> <span class="o">=</span> <span class="s1">&#39;&#39;&#39;</span><span class="se">\</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">_template</span> <span class="o">=</span> <span class="s1">&#39;&#39;&#39;</span><span class="se">\</span>
<span class="s1">digraph finite_state_machine {</span>
<span class="s1"> rankdir=LR;</span>
<span class="s1"> size=&quot;8,5&quot;</span>
@@ -651,7 +650,7 @@ generate the diagram above.</p>
<span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">make_graph</span><span class="p">(</span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">make_graph</span><span class="p">(</span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">digraph</span> <span class="n">finite_state_machine</span> <span class="p">{</span>
@@ -697,7 +696,7 @@ hard-code the information in the table into a little patch of branches.</p>
<h4>Trampoline Function<a class="headerlink" href="#trampoline-function" title="Permalink to this headline"></a></h4>
<p>Python has no GOTO statement but we can fake it with a “trampoline”
function.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">trampoline</span><span class="p">(</span><span class="n">input_</span><span class="p">,</span> <span class="n">jump_from</span><span class="p">,</span> <span class="n">accepting</span><span class="p">):</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">trampoline</span><span class="p">(</span><span class="n">input_</span><span class="p">,</span> <span class="n">jump_from</span><span class="p">,</span> <span class="n">accepting</span><span class="p">):</span>
<span class="n">I</span> <span class="o">=</span> <span class="nb">iter</span><span class="p">(</span><span class="n">input_</span><span class="p">)</span>
<span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
<span class="k">try</span><span class="p">:</span>
@@ -712,7 +711,7 @@ function.</p>
<h4>Stream Functions<a class="headerlink" href="#stream-functions" title="Permalink to this headline"></a></h4>
<p>Little helpers to process the iterator of our data (a “stream” of “1”
and “0” characters, not bits.)</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">getch</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="nb">int</span><span class="p">(</span><span class="nb">next</span><span class="p">(</span><span class="n">I</span><span class="p">))</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">getch</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="nb">int</span><span class="p">(</span><span class="nb">next</span><span class="p">(</span><span class="n">I</span><span class="p">))</span>
<span class="k">def</span> <span class="nf">_1</span><span class="p">(</span><span class="n">I</span><span class="p">):</span>
@@ -733,7 +732,7 @@ and “0” characters, not bits.)</p>
code. (You have to imagine that these are GOTO statements in C or
branches in assembly and that the state names are branch destination
labels.)</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">c</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">c</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
<span class="n">b</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">_0</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="ow">or</span> <span class="n">d</span>
<span class="n">c</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">e</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
<span class="n">d</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">f</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
@@ -748,11 +747,11 @@ labels.)</p>
<p>Note that the implementations of <code class="docutils literal notranslate"><span class="pre">h</span></code> and <code class="docutils literal notranslate"><span class="pre">g</span></code> are identical ergo
<code class="docutils literal notranslate"><span class="pre">h</span> <span class="pre">=</span> <span class="pre">g</span></code> and we could eliminate one in the code but <code class="docutils literal notranslate"><span class="pre">h</span></code> is an
accepting state and <code class="docutils literal notranslate"><span class="pre">g</span></code> isn’t.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">acceptable</span><span class="p">(</span><span class="n">input_</span><span class="p">):</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">acceptable</span><span class="p">(</span><span class="n">input_</span><span class="p">):</span>
<span class="k">return</span> <span class="n">trampoline</span><span class="p">(</span><span class="n">input_</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="p">{</span><span class="n">h</span><span class="p">,</span> <span class="n">i</span><span class="p">})</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="o">**</span><span class="mi">5</span><span class="p">):</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="o">**</span><span class="mi">5</span><span class="p">):</span>
<span class="n">s</span> <span class="o">=</span> <span class="nb">bin</span><span class="p">(</span><span class="n">n</span><span class="p">)[</span><span class="mi">2</span><span class="p">:]</span>
<span class="nb">print</span> <span class="s1">&#39;</span><span class="si">%05s</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">s</span><span class="p">,</span> <span class="n">acceptable</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
</pre></div>
@@ -822,7 +821,7 @@ derivative-with-respect-to-N of some other state/RE:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="o">=</span> <span class="n">d10</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
</pre></div>
</div>
<p>‘’’</p>
<p>’’’</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">j</span> <span class="o">=</span> <span class="n">d1</span><span class="p">(</span><span class="n">d0</span><span class="p">(</span><span class="n">j</span><span class="p">))</span>
</pre></div>
</div>
@@ -843,50 +842,46 @@ derivative-with-respect-to-N of some other state/RE:</p>
</div>
</div>
</div>
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<li class="toctree-l2"><a class="reference internal" href="Developing.html">Developing a Program in Joy</a></li>
<li class="toctree-l2"><a class="reference internal" href="Quadratic.html">Quadratic formula</a></li>
<li class="toctree-l2"><a class="reference internal" href="Replacing.html">Replacing Functions in the Dictionary</a></li>
<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html">Recursion Combinators</a></li>
<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html">Treating Trees I: Ordered Binary Trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a></li>
<li class="toctree-l2"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a></li>
<li class="toctree-l2"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a></li>
<li class="toctree-l2"><a class="reference internal" href="TypeChecking.html">Type Checking</a></li>
<li class="toctree-l2"><a class="reference internal" href="NoUpdates.html">No Updates</a></li>
<li class="toctree-l2"><a class="reference internal" href="Categorical.html">Categorical Programming</a></li>
<li class="toctree-l2"><a class="reference internal" href="The_Four_Operations.html">The Four Fundamental Operations of Definite Action</a></li>
<li class="toctree-l2 current"><a class="current reference internal" href="#">∂RE</a></li>
<h3><a href="../index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">∂RE</a><ul>
<li><a class="reference internal" href="#brzozowskis-derivatives-of-regular-expressions">Brzozowski’s Derivatives of Regular Expressions</a></li>
<li><a class="reference internal" href="#implementation">Implementation</a><ul>
<li><a class="reference internal" href="#and"><code class="docutils literal notranslate"><span class="pre">ϕ</span></code> and <code class="docutils literal notranslate"><span class="pre">λ</span></code></a></li>
<li><a class="reference internal" href="#two-letter-alphabet">Two-letter Alphabet</a></li>
<li><a class="reference internal" href="#representing-regular-expressions">Representing Regular Expressions</a></li>
<li><a class="reference internal" href="#string-representation-of-re-datastructures">String Representation of RE Datastructures</a></li>
<li><a class="reference internal" href="#i"><code class="docutils literal notranslate"><span class="pre">I</span></code></a></li>
<li><a class="reference internal" href="#id1"><code class="docutils literal notranslate"><span class="pre">(.111.)</span> <span class="pre">&amp;</span> <span class="pre">(.01</span> <span class="pre">+</span> <span class="pre">11*)'</span></code></a></li>
<li><a class="reference internal" href="#nully"><code class="docutils literal notranslate"><span class="pre">nully()</span></code></a></li>
<li><a class="reference internal" href="#no-compaction">No “Compaction”</a></li>
<li><a class="reference internal" href="#compaction-rules">Compaction Rules</a></li>
<li><a class="reference internal" href="#memoizing">Memoizing</a></li>
<li><a class="reference internal" href="#with-compaction">With “Compaction”</a></li>
</ul>
</li>
<li><a class="reference internal" href="#lets-try-it-out">Let’s try it out…</a></li>
<li><a class="reference internal" href="#larger-alphabets">Larger Alphabets</a></li>
<li><a class="reference internal" href="#state-machine">State Machine</a><ul>
<li><a class="reference internal" href="#re-to-fsm">RE to FSM</a></li>
<li><a class="reference internal" href="#explore"><code class="docutils literal notranslate"><span class="pre">explore()</span></code></a></li>
<li><a class="reference internal" href="#generate-diagram">Generate Diagram</a></li>
<li><a class="reference internal" href="#drive-a-fsm">Drive a FSM</a><ul>
<li><a class="reference internal" href="#trampoline-function">Trampoline Function</a></li>
<li><a class="reference internal" href="#stream-functions">Stream Functions</a></li>
<li><a class="reference internal" href="#a-finite-state-machine">A Finite State Machine</a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference internal" href="#reversing-the-derivatives-to-generate-matching-strings">Reversing the Derivatives to Generate Matching Strings</a></li>
</ul>
</li>
</ul>
<div class="relations">
<h3>Related Topics</h3>
<ul>
@@ -897,24 +892,25 @@ derivative-with-respect-to-N of some other state/RE:</p>
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@@ -925,7 +921,7 @@ derivative-with-respect-to-N of some other state/RE:</p>
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<br />
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 3.0.2.
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@@ -1,18 +1,19 @@
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@@ -29,8 +30,6 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<div class="section" id="thun-joy-in-python">
@@ -39,18 +38,18 @@
model and method of Joy. Python seems like a great implementation
language for Joy for several reasons.</p>
<ul class="simple">
<li><p>We can lean on the Python immutable types for our basic semantics and types: ints, floats, strings, and tuples, which enforces functional purity.</p></li>
<li><p>We get garbage collection for free.</p></li>
<li><p>Compilation via Cython.</p></li>
<li><p>Python is a “glue language” with loads of libraries which we can wrap in Joy functions.</p></li>
<li>We can lean on the Python immutable types for our basic semantics and types: ints, floats, strings, and tuples, which enforces functional purity.</li>
<li>We get garbage collection for free.</li>
<li>Compilation via Cython.</li>
<li>Python is a “glue language” with loads of libraries which we can wrap in Joy functions.</li>
</ul>
<div class="section" id="read-eval-print-loop-repl">
<h2><a class="reference external" href="https://en.wikipedia.org/wiki/Read%E2%80%93eval%E2%80%93print_loop">Read-Eval-Print Loop (REPL)</a><a class="headerlink" href="#read-eval-print-loop-repl" title="Permalink to this headline"></a></h2>
<p>The main way to interact with the Joy interpreter is through a simple
<a class="reference external" href="https://en.wikipedia.org/wiki/Read%E2%80%93eval%E2%80%93print_loop">REPL</a>
that you start by running the package:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>$ python -m joy
Joypy - Copyright © 2017 Simon Forman
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>$ python3 -m joy
Thun - Copyright © 2017 Simon Forman
This program comes with ABSOLUTELY NO WARRANTY; for details type &quot;warranty&quot;.
This is free software, and you are welcome to redistribute it
under certain conditions; type &quot;sharing&quot; for details.
@@ -58,7 +57,7 @@ Type &quot;words&quot; to see a list of all words, and &quot;[&lt;name&gt;] help
docs for a word.
&lt;-top
&lt;-top
joy? _
</pre></div>
@@ -67,7 +66,14 @@ joy? _
You can enter Joy notation at the prompt and a <a class="reference internal" href="../pretty.html"><span class="doc">trace of evaluation</span></a> will
be printed followed by the stack and prompt again:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>joy? 23 sqr 18 +
. 23 sqr 18 +
547 &lt;-top
joy?
</pre></div>
</div>
<p>There is a <cite>trace</cite> combinator:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>joy? 23 [sqr 18 +] trace
23 . sqr 18 +
23 . dup mul 18 +
23 23 . mul 18 +
@@ -150,19 +156,19 @@ like that.</p>
</div>
<div class="section" id="examples">
<h3>Examples<a class="headerlink" href="#examples" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;1 2 3 4 5&#39;</span><span class="p">)</span> <span class="c1"># A simple sequence.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;1 2 3 4 5&#39;</span><span class="p">)</span> <span class="c1"># A simple sequence.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="p">())))))</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[1 2 3] 4 5&#39;</span><span class="p">)</span> <span class="c1"># Three items, the first is a list with three items</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[1 2 3] 4 5&#39;</span><span class="p">)</span> <span class="c1"># Three items, the first is a list with three items</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">()))),</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="p">())))</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;1 23 [&quot;four&quot; [-5.0] cons] 8888&#39;</span><span class="p">)</span> <span class="c1"># A mixed bag. cons is</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;1 23 [&quot;four&quot; [-5.0] cons] 8888&#39;</span><span class="p">)</span> <span class="c1"># A mixed bag. cons is</span>
<span class="c1"># a Symbol, no lookup at</span>
<span class="c1"># parse-time. Haiku docs.</span>
</pre></div>
@@ -170,13 +176,13 @@ like that.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">23</span><span class="p">,</span> <span class="p">((</span><span class="s1">&#39;four&#39;</span><span class="p">,</span> <span class="p">((</span><span class="o">-</span><span class="mf">5.0</span><span class="p">,</span> <span class="p">()),</span> <span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="p">()))),</span> <span class="p">(</span><span class="mi">8888</span><span class="p">,</span> <span class="p">()))))</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[][][][][]&#39;</span><span class="p">)</span> <span class="c1"># Five empty lists.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[][][][][]&#39;</span><span class="p">)</span> <span class="c1"># Five empty lists.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((),</span> <span class="p">((),</span> <span class="p">((),</span> <span class="p">((),</span> <span class="p">((),</span> <span class="p">())))))</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[[[[[]]]]]&#39;</span><span class="p">)</span> <span class="c1"># Five nested lists.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[[[[[]]]]]&#39;</span><span class="p">)</span> <span class="c1"># Five nested lists.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((((((),</span> <span class="p">()),</span> <span class="p">()),</span> <span class="p">()),</span> <span class="p">()),</span> <span class="p">())</span>
@@ -192,7 +198,7 @@ the Joy system. There are simple functions such as addition <code class="docutil
<code class="docutils literal notranslate"><span class="pre">+</span></code>, the library module supports aliases), and combinators which
provide control-flow and higher-order operations.</p>
<p>Many of the functions are defined in Python, like <code class="docutils literal notranslate"><span class="pre">dip</span></code>:</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">inspect</span><span class="o">.</span><span class="n">getsource</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">dip</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">inspect</span><span class="o">.</span><span class="n">getsource</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">dip</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">dip</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">):</span>
@@ -205,10 +211,11 @@ provide control-flow and higher-order operations.</p>
When the interpreter executes a definition function that function just
pushes its body expression onto the pending expression (the
continuation) and returns control to the interpreter.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">definitions</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">definitions</span>
</pre></div>
</div>
<pre class="literal-block">second == rest first
<pre class="literal-block">
second == rest first
third == rest rest first
product == 1 swap [*] step
swons == swap cons
@@ -241,7 +248,8 @@ anamorphism == [pop []] swap [dip swons] genrec
range == [0 &lt;=] [1 - dup] anamorphism
while == swap [nullary] cons dup dipd concat loop
dudipd == dup dipd
primrec == [i] genrec</pre>
primrec == [i] genrec
</pre>
<p>Currently, there’s no function to add new definitions to the dictionary
from “within” Joy code itself. Adding new definitions remains a
meta-interpreter action. You have to do it yourself, in Python, and wash
@@ -290,41 +298,37 @@ developing structured processes.</p>
</div>
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<li class="toctree-l1 current"><a class="current reference internal" href="#">Thun: Joy in Python</a><ul>
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<li class="toctree-l2"><a class="reference internal" href="#the-stack">The Stack</a></li>
<li class="toctree-l2"><a class="reference internal" href="#purely-functional-datastructures">Purely Functional Datastructures</a></li>
<li class="toctree-l2"><a class="reference internal" href="#the-joy-function">The <code class="docutils literal notranslate"><span class="pre">joy()</span></code> function</a></li>
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<h3><a href="../index.html">Table Of Contents</a></h3>
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<li><a class="reference internal" href="#">Thun: Joy in Python</a><ul>
<li><a class="reference internal" href="#read-eval-print-loop-repl">Read-Eval-Print Loop (REPL)</a></li>
<li><a class="reference internal" href="#the-stack">The Stack</a></li>
<li><a class="reference internal" href="#purely-functional-datastructures">Purely Functional Datastructures</a></li>
<li><a class="reference internal" href="#the-joy-function">The <code class="docutils literal notranslate"><span class="pre">joy()</span></code> function</a><ul>
<li><a class="reference internal" href="#an-interpreter">An Interpreter</a></li>
<li><a class="reference internal" href="#continuation-passing-style">Continuation-Passing Style</a></li>
<li><a class="reference internal" href="#view-function">View function</a></li>
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<li><a class="reference internal" href="#symbols">Symbols</a></li>
<li><a class="reference internal" href="#token-regular-expressions">Token Regular Expressions</a></li>
<li><a class="reference internal" href="#examples">Examples</a></li>
</ul>
</li>
<li><a class="reference internal" href="#library">Library</a><ul>
<li><a class="reference internal" href="#there-should-be-only-one">“There should be only one.”</a></li>
<li><a class="reference internal" href="#literary-code-library">Literary Code Library</a></li>
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@@ -334,24 +338,25 @@ developing structured processes.</p>
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@@ -362,7 +367,7 @@ developing structured processes.</p>
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docs/sphinx_docs/_build/html/notebooks/Newton-Raphson.html
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@@ -29,17 +30,15 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<div class="section" id="newton-s-method">
<h1><a class="reference external" href="https://en.wikipedia.org/wiki/Newton%27s_method">Newton’s method</a><a class="headerlink" href="#newton-s-method" title="Permalink to this headline"></a></h1>
<div class="section" id="newtons-method">
<h1><a class="reference external" href="https://en.wikipedia.org/wiki/Newton%27s_method">Newton’s method</a><a class="headerlink" href="#newtons-method" title="Permalink to this headline"></a></h1>
<p>Let’s use the Newton-Raphson method for finding the root of an equation
to write a function that can compute the square root of a number.</p>
<p>Cf. <a class="reference external" href="https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf">“Why Functional Programming Matters” by John
Hughes</a></p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="k">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
</pre></div>
</div>
<div class="section" id="a-generator-for-approximations">
@@ -91,10 +90,10 @@ function we’re writing. If we let 1 be the initial approximation:</p>
<span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">make_generator</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 gsra&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 gsra&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span>
@@ -102,7 +101,7 @@ function we’re writing. If we let 1 be the initial approximation:</p>
</div>
<p>Let’s drive the generator a few time (with the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator) and
square the approximation to see how well it works…</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 gsra 6 [x popd] times first sqr&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 gsra 6 [x popd] times first sqr&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">23.0000000001585</span>
@@ -115,11 +114,10 @@ square the approximation to see how well it works…</p>
<p>From <a class="reference external" href="https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf">“Why Functional Programming Matters” by John
Hughes</a>:</p>
<blockquote>
<div><p>The remainder of a square root finder is a function <em>within</em>, which
<div>The remainder of a square root finder is a function <em>within</em>, which
takes a tolerance and a list of approximations and looks down the
list for two successive approximations that differ by no more than
the given tolerance.</p>
</div></blockquote>
the given tolerance.</div></blockquote>
<p>(And note that by “list” he means a lazily-evaluated list.)</p>
<p>Using the <em>output</em> <code class="docutils literal notranslate"><span class="pre">[a</span> <span class="pre">G]</span></code> of the above generator for square root
approximations, and further assuming that the first term a has been
@@ -144,7 +142,7 @@ generated already and epsilon ε is handy on the stack…</p>
<span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">a</span><span class="o">-</span><span class="n">b</span><span class="p">)</span><span class="o">&lt;=</span><span class="n">ε</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_P == [first - abs] dip &lt;=&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_P == [first - abs] dip &lt;=&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
@@ -156,7 +154,7 @@ generated already and epsilon ε is handy on the stack…</p>
<span class="n">b</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_B == roll&lt; popop first&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_B == roll&lt; popop first&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
@@ -166,9 +164,9 @@ generated already and epsilon ε is handy on the stack…</p>
</pre></div>
</div>
<ol class="arabic simple">
<li><p>Discard a.</p></li>
<li><p>Use <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator to generate next term from <code class="docutils literal notranslate"><span class="pre">G</span></code>.</p></li>
<li><p>Run <code class="docutils literal notranslate"><span class="pre">within</span></code> with <code class="docutils literal notranslate"><span class="pre">i</span></code> (it is a <code class="docutils literal notranslate"><span class="pre">primrec</span></code> function.)</p></li>
<li>Discard a.</li>
<li>Use <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator to generate next term from <code class="docutils literal notranslate"><span class="pre">G</span></code>.</li>
<li>Run <code class="docutils literal notranslate"><span class="pre">within</span></code> with <code class="docutils literal notranslate"><span class="pre">i</span></code> (it is a <code class="docutils literal notranslate"><span class="pre">primrec</span></code> function.)</li>
</ol>
<p>Pretty straightforward:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">R0</span> <span class="p">[</span><span class="n">within</span><span class="p">]</span> <span class="n">R1</span>
@@ -181,7 +179,7 @@ generated already and epsilon ε is handy on the stack…</p>
<span class="n">b</span> <span class="p">[</span><span class="n">c</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">within</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_R == [popd x] dip&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_R == [popd x] dip&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
@@ -193,31 +191,31 @@ generated already and epsilon ε is handy on the stack…</p>
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="o">...</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec&#39;</span><span class="p">)</span>
<span class="n">define</span><span class="p">(</span><span class="s1">&#39;sqrt == gsra within&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>Try it out…</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;36 sqrt&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;36 sqrt&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">6.0</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 sqrt&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 sqrt&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span>
</pre></div>
</div>
<p>Check it.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span><span class="o">**</span><span class="mi">2</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span><span class="o">**</span><span class="mi">2</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">22.999999999999996</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">sqrt</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="k">import</span> <span class="n">sqrt</span>
<span class="n">sqrt</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span>
</pre></div>
@@ -231,50 +229,28 @@ generated already and epsilon ε is handy on the stack…</p>
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<li><a class="reference internal" href="#">Newton’s method</a><ul>
<li><a class="reference internal" href="#a-generator-for-approximations">A Generator for Approximations</a><ul>
<li><a class="reference internal" href="#a-function-to-compute-the-next-approximation">A Function to Compute the Next Approximation</a></li>
<li><a class="reference internal" href="#make-it-into-a-generator">Make it into a Generator</a></li>
</ul>
</li>
<li><a class="reference internal" href="#finding-consecutive-approximations-within-a-tolerance">Finding Consecutive Approximations within a Tolerance</a><ul>
<li><a class="reference internal" href="#predicate">Predicate</a></li>
<li><a class="reference internal" href="#base-case">Base-Case</a></li>
<li><a class="reference internal" href="#recur">Recur</a></li>
<li><a class="reference internal" href="#setting-up">Setting up</a></li>
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@@ -286,24 +262,25 @@ generated already and epsilon ε is handy on the stack…</p>
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@@ -314,7 +291,7 @@ generated already and epsilon ε is handy on the stack…</p>
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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@@ -1,18 +1,19 @@
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@@ -29,82 +30,39 @@
<div class="document">
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<div class="section" id="no-updates">
<h1>No Updates<a class="headerlink" href="#no-updates" title="Permalink to this headline"></a></h1>
<p>DRAFT</p>
<ol class="arabic simple">
<li><p>Joy doesn’t need to change.</p></li>
<li>Joy doesn’t need to change.</li>
</ol>
<blockquote>
<div><ol class="upperalpha simple">
<li><p>The interpreter doesn’t need to change, <code class="docutils literal notranslate"><span class="pre">viewer</span></code> function can customize mainloop. Or use a sub-interpreter (Joy in Joy.) The base interpreter remains static.</p></li>
<li><p>Once a function has been named and defined <em>never change that name</em>. It’s just not allowed. If you need to change a function <code class="docutils literal notranslate"><span class="pre">foo</span></code> you have to call it <code class="docutils literal notranslate"><span class="pre">foo_II</span></code> or something. Once a function (name mapped to behavior) is released to the public <em>that’s it</em>, it’s done.</p></li>
<li><p>The language evolves by adding new definitions and refactoring, always choosing new names for new functions.</p></li>
<li>The interpreter doesn’t need to change, <code class="docutils literal notranslate"><span class="pre">viewer</span></code> function can customize mainloop. Or use a sub-interpreter (Joy in Joy.) The base interpreter remains static.</li>
<li>Once a function has been named and defined <em>never change that name</em>. It’s just not allowed. If you need to change a function <code class="docutils literal notranslate"><span class="pre">foo</span></code> you have to call it <code class="docutils literal notranslate"><span class="pre">foo_II</span></code> or something. Once a function (name mapped to behavior) is released to the public <em>that’s it</em>, it’s done.</li>
<li>The language evolves by adding new definitions and refactoring, always choosing new names for new functions.</li>
</ol>
</div></blockquote>
<ol class="arabic simple" start="2">
<li><p>Following <a class="reference external" href="https://semver.org">Semantic Versioning</a> there will never be a version 2.0.</p></li>
<li>Following <a class="reference external" href="https://semver.org">Semantic Versioning</a> there will never be a version 2.0.</li>
</ol>
<blockquote>
<div><ol class="upperalpha simple">
<li><p><a class="reference external" href="https://semver.org/#spec-item-8">Major version must be incremented if any backwards incompatible changes are introduced to the public API.</a></p></li>
<li><p>We never implement any backwards incompatible changes, so…</p></li>
<li><p>We could see e.g. Thun version 1.273.3!</p></li>
<li><a class="reference external" href="https://semver.org/#spec-item-8">Major version must be incremented if any backwards incompatible changes are introduced to the public API.</a></li>
<li>We never implement any backwards incompatible changes, so…</li>
<li>We could see e.g. Thun version 1.273.3!</li>
</ol>
</div></blockquote>
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@@ -115,24 +73,25 @@
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@@ -143,7 +102,7 @@
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docs/sphinx_docs/_build/html/notebooks/Ordered_Binary_Trees.html
+152 -116
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@@ -1,18 +1,19 @@
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@@ -29,8 +30,6 @@
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<div class="section" id="treating-trees-i-ordered-binary-trees">
@@ -63,7 +62,7 @@ the Sufficiently Smart Compiler can be modified to use an optimized
implementation under the hood. (Where does the “type” come from? It has
a contingent existence predicated on the disciplined use of these
functions on otherwise undistinguished Joy datastructures.)</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span><span class="p">,</span> <span class="n">DefinitionWrapper</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="k">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span><span class="p">,</span> <span class="n">DefinitionWrapper</span>
</pre></div>
</div>
<div class="section" id="adding-nodes-to-the-tree">
@@ -100,10 +99,10 @@ functions on otherwise undistinguished Joy datastructures.)</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Tree</span><span class="o">-</span><span class="n">new</span> <span class="o">==</span> <span class="n">swap</span> <span class="p">[[]</span> <span class="p">[]]</span> <span class="n">cons</span> <span class="n">cons</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-new == swap [[] []] cons cons&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-new == swap [[] []] cons cons&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&quot;v&quot; &quot;k&quot; Tree-new&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&quot;v&quot; &quot;k&quot; Tree-new&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;k&#39;</span> <span class="s1">&#39;v&#39;</span> <span class="p">[]</span> <span class="p">[]]</span>
@@ -159,18 +158,18 @@ comparison operator:</p>
<span class="n">P</span> <span class="o">==</span> <span class="n">pop</span> <span class="n">roll</span><span class="o">&gt;</span> <span class="n">pop</span> <span class="n">first</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;P == pop roll&gt; pop first&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;P == pop roll&gt; pop first&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;old_key&quot; 23 [] []] 17 &quot;new_key&quot; [&quot;...&quot;] P&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;old_key&quot; 23 [] []] 17 &quot;new_key&quot; [&quot;...&quot;] P&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;new_key&#39;</span> <span class="s1">&#39;old_key&#39;</span>
</pre></div>
</div>
</div>
<div class="section" id="if-the-key-we-re-adding-is-greater-than-the-node-s-key">
<h4>If the key we’re adding is greater than the node’s key.<a class="headerlink" href="#if-the-key-we-re-adding-is-greater-than-the-node-s-key" title="Permalink to this headline"></a></h4>
<div class="section" id="if-the-key-were-adding-is-greater-than-the-nodes-key">
<h4>If the key we’re adding is greater than the node’s key.<a class="headerlink" href="#if-the-key-were-adding-is-greater-than-the-nodes-key" title="Permalink to this headline"></a></h4>
<p>Here the parentheses are meant to signify that the expression is not
literal, the code in the parentheses is meant to have been evaluated:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">key_n</span> <span class="n">value_n</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">value</span> <span class="n">key</span> <span class="p">[</span><span class="n">Tree</span><span class="o">-</span><span class="n">add</span><span class="p">]</span> <span class="n">T</span>
@@ -217,24 +216,24 @@ stack:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">T</span> <span class="o">==</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="n">dipdd</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;T == cons cons [dipdd] cons infra&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;T == cons cons [dipdd] cons infra&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;old_k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;new_key&quot; [&quot;Tree-add&quot;] T&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;old_k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;new_key&quot; [&quot;Tree-add&quot;] T&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;old_k&#39;</span> <span class="s1">&#39;old_value&#39;</span> <span class="s1">&#39;left&#39;</span> <span class="s1">&#39;Tree-add&#39;</span> <span class="s1">&#39;new_key&#39;</span> <span class="s1">&#39;new_value&#39;</span> <span class="s1">&#39;right&#39;</span><span class="p">]</span>
</pre></div>
</div>
</div>
<div class="section" id="if-the-key-we-re-adding-is-less-than-the-node-s-key">
<h4>If the key we’re adding is less than the node’s key.<a class="headerlink" href="#if-the-key-we-re-adding-is-less-than-the-node-s-key" title="Permalink to this headline"></a></h4>
<div class="section" id="if-the-key-were-adding-is-less-than-the-nodes-key">
<h4>If the key we’re adding is less than the node’s key.<a class="headerlink" href="#if-the-key-were-adding-is-less-than-the-nodes-key" title="Permalink to this headline"></a></h4>
<p>This is very very similar to the above:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">key_n</span> <span class="n">value_n</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">value</span> <span class="n">key</span> <span class="p">[</span><span class="n">Tree</span><span class="o">-</span><span class="n">add</span><span class="p">]</span> <span class="n">E</span>
<span class="p">[</span><span class="n">key_n</span> <span class="n">value_n</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">value</span> <span class="n">key</span> <span class="p">[</span><span class="n">Tree</span><span class="o">-</span><span class="n">add</span><span class="p">]</span> <span class="p">[</span><span class="n">P</span> <span class="o">&lt;</span><span class="p">]</span> <span class="p">[</span><span class="n">Te</span><span class="p">]</span> <span class="p">[</span><span class="n">Ee</span><span class="p">]</span> <span class="n">ifte</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;E == [P &lt;] [Te] [Ee] ifte&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;E == [P &lt;] [Te] [Ee] ifte&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>In this case <code class="docutils literal notranslate"><span class="pre">Te</span></code> works that same as <code class="docutils literal notranslate"><span class="pre">T</span></code> but on the left child tree
@@ -243,10 +242,10 @@ instead of the right, so the only difference is that it must use
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Te</span> <span class="o">==</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="n">dipd</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Te == cons cons [dipd] cons infra&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Te == cons cons [dipd] cons infra&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;old_k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;new_key&quot; [&quot;Tree-add&quot;] Te&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;old_k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;new_key&quot; [&quot;Tree-add&quot;] Te&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;old_k&#39;</span> <span class="s1">&#39;old_value&#39;</span> <span class="s1">&#39;Tree-add&#39;</span> <span class="s1">&#39;new_key&#39;</span> <span class="s1">&#39;new_value&#39;</span> <span class="s1">&#39;left&#39;</span> <span class="s1">&#39;right&#39;</span><span class="p">]</span>
@@ -274,10 +273,10 @@ instead of the right, so the only difference is that it must use
<span class="p">[</span><span class="n">key</span> <span class="n">new_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Ee == pop swap roll&lt; rest rest cons cons&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Ee == pop swap roll&lt; rest rest cons cons&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;k&quot; [&quot;Tree-add&quot;] Ee&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;k&quot; &quot;old_value&quot; &quot;left&quot; &quot;right&quot;] &quot;new_value&quot; &quot;k&quot; [&quot;Tree-add&quot;] Ee&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;k&#39;</span> <span class="s1">&#39;new_value&#39;</span> <span class="s1">&#39;left&#39;</span> <span class="s1">&#39;right&#39;</span><span class="p">]</span>
@@ -302,43 +301,43 @@ instead of the right, so the only difference is that it must use
<span class="n">Tree</span><span class="o">-</span><span class="n">add</span> <span class="o">==</span> <span class="p">[</span><span class="n">popop</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[[</span><span class="n">pop</span><span class="p">]</span> <span class="n">dipd</span> <span class="n">Tree</span><span class="o">-</span><span class="n">new</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="n">R</span><span class="p">]</span> <span class="n">genrec</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-add == [popop not] [[pop] dipd Tree-new] [] [[P &gt;] [T] [E] ifte] genrec&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-add == [popop not] [[pop] dipd Tree-new] [] [[P &gt;] [T] [E] ifte] genrec&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="section" id="examples">
<h3>Examples<a class="headerlink" href="#examples" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] 23 &quot;b&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Initial</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] 23 &quot;b&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Initial</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[]]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;b&quot; 23 [] []] 88 &quot;c&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Greater than</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;b&quot; 23 [] []] 88 &quot;c&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Greater than</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;b&quot; 23 [] []] 88 &quot;a&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Less than</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;b&quot; 23 [] []] 88 &quot;a&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Less than</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[]]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;b&quot; 23 [] []] 88 &quot;b&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Equal to</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;b&quot; 23 [] []] 88 &quot;b&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Equal to</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] 23 &quot;b&quot; Tree-add 88 &quot;a&quot; Tree-add 44 &quot;c&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Series.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] 23 &quot;b&quot; Tree-add 88 &quot;a&quot; Tree-add 44 &quot;c&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Series.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [[23 &quot;b&quot;] [88 &quot;a&quot;] [44 &quot;c&quot;]] [i Tree-add] step&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [[23 &quot;b&quot;] [88 &quot;a&quot;] [44 &quot;c&quot;]] [i Tree-add] step&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
@@ -365,19 +364,19 @@ values:</p>
<span class="n">L</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;1 0 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;1 0 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;G&#39;</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;1 1 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;1 1 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;E&#39;</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;0 1 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;0 1 [&#39;G&#39;] [&#39;E&#39;] [&#39;L&#39;] cmp&quot;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;L&#39;</span>
@@ -414,7 +413,7 @@ node key (by throwing everything else away):</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">P</span> <span class="o">==</span> <span class="n">over</span> <span class="p">[</span><span class="n">popop</span> <span class="n">popop</span> <span class="n">first</span><span class="p">]</span> <span class="n">nullary</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;P == over [popop popop first] nullary&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;P == over [popop popop first] nullary&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>Using <code class="docutils literal notranslate"><span class="pre">cmp</span></code> to simplify <cite>our code above at
@@ -434,10 +433,10 @@ to understand:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Tree</span><span class="o">-</span><span class="n">add</span> <span class="o">==</span> <span class="p">[</span><span class="n">popop</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[[</span><span class="n">pop</span><span class="p">]</span> <span class="n">dipd</span> <span class="n">Tree</span><span class="o">-</span><span class="n">new</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="n">P</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">Ee</span><span class="p">]</span> <span class="p">[</span><span class="n">Te</span><span class="p">]</span> <span class="nb">cmp</span><span class="p">]</span> <span class="n">genrec</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] 23 &quot;b&quot; Tree-add 88 &quot;a&quot; Tree-add 44 &quot;c&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Still works.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] 23 &quot;b&quot; Tree-add 88 &quot;a&quot; Tree-add 44 &quot;c&quot; Tree-add&#39;</span><span class="p">)</span> <span class="c1"># Still works.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
@@ -545,22 +544,22 @@ with an interesting situation:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Tree</span><span class="o">-</span><span class="nb">iter</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="n">roll</span><span class="o">&lt;</span> <span class="p">[</span><span class="n">dupdip</span> <span class="n">rest</span> <span class="n">rest</span><span class="p">]</span> <span class="n">cons</span> <span class="p">[</span><span class="n">step</span><span class="p">]</span> <span class="n">genrec</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-iter == [not] [pop] roll&lt; [dupdip rest rest] cons [step] genrec&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Tree-iter == [not] [pop] roll&lt; [dupdip rest rest] cons [step] genrec&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="section" id="id1">
<h3>Examples<a class="headerlink" href="#id1" title="Permalink to this headline"></a></h3>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [foo] Tree-iter&#39;</span><span class="p">)</span> <span class="c1"># It doesn&#39;t matter what F is as it won&#39;t be used.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [foo] Tree-iter&#39;</span><span class="p">)</span> <span class="c1"># It doesn&#39;t matter what F is as it won&#39;t be used.</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;b&#39; 23 [&#39;a&#39; 88 [] []] [&#39;c&#39; 44 [] []]] [first] Tree-iter&quot;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;b&#39; 23 [&#39;a&#39; 88 [] []] [&#39;c&#39; 44 [] []]] [first] Tree-iter&quot;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;b&#39;</span> <span class="s1">&#39;a&#39;</span> <span class="s1">&#39;c&#39;</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;b&#39; 23 [&#39;a&#39; 88 [] []] [&#39;c&#39; 44 [] []]] [second] Tree-iter&quot;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;b&#39; 23 [&#39;a&#39; 88 [] []] [&#39;c&#39; 44 [] []]] [second] Tree-iter&quot;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span> <span class="mi">88</span> <span class="mi">44</span>
@@ -571,20 +570,20 @@ with an interesting situation:</p>
<div class="section" id="interlude-a-set-like-datastructure">
<h2>Interlude: A Set-like Datastructure<a class="headerlink" href="#interlude-a-set-like-datastructure" title="Permalink to this headline"></a></h2>
<p>We can use this to make a set-like datastructure by just setting values
to e.g. 0 and ignoring them. It’s set-like in that duplicate items added
to e.g.&nbsp;0 and ignoring them. It’s set-like in that duplicate items added
to it will only occur once within it, and we can query it in
<cite>:math:`O(log_2 N)</cite> &lt;<a class="reference external" href="https://en.wikipedia.org/wiki/Binary_search_tree#cite_note-2">https://en.wikipedia.org/wiki/Binary_search_tree#cite_note-2</a>&gt;`__
time.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [3 9 5 2 8 6 7 8 4] [0 swap Tree-add] step&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [3 9 5 2 8 6 7 8 4] [0 swap Tree-add] step&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">9</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <span class="p">[]]]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;to_set == [] swap [0 swap Tree-add] step&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;to_set == [] swap [0 swap Tree-add] step&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[3 9 5 2 8 6 7 8 4] to_set&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[3 9 5 2 8 6 7 8 4] to_set&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">9</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <span class="p">[]]]</span>
@@ -592,10 +591,10 @@ time.</p>
</div>
<p>And with that we can write a little program <code class="docutils literal notranslate"><span class="pre">unique</span></code> to remove
duplicate items from a list.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;unique == [to_set [first] Tree-iter] cons run&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;unique == [to_set [first] Tree-iter] cons run&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[3 9 3 5 2 9 8 8 8 6 2 7 8 4 3] unique&#39;</span><span class="p">)</span> <span class="c1"># Filter duplicate items.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[3 9 3 5 2 9 8 8 8 6 2 7 8 4 3] unique&#39;</span><span class="p">)</span> <span class="c1"># Filter duplicate items.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">7</span> <span class="mi">6</span> <span class="mi">8</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">9</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span>
@@ -641,8 +640,8 @@ when they run:</p>
</pre></div>
</div>
<p>If <code class="docutils literal notranslate"><span class="pre">F</span></code> needs items from the stack below the left stuff it should have
<code class="docutils literal notranslate"><span class="pre">cons</span></code>’d them before beginning maybe? For functions like <code class="docutils literal notranslate"><span class="pre">first</span></code> it
works fine as-is.</p>
<code class="docutils literal notranslate"><span class="pre">cons</span></code>’d them before beginning maybe? For functions like <code class="docutils literal notranslate"><span class="pre">first</span></code>
it works fine as-is.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">left</span> <span class="n">Tree</span><span class="o">-</span><span class="nb">iter</span><span class="o">-</span><span class="n">order</span> <span class="p">[</span><span class="n">key</span> <span class="n">value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">first</span> <span class="p">[</span><span class="n">key</span> <span class="n">value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">Tree</span><span class="o">-</span><span class="nb">iter</span><span class="o">-</span><span class="n">order</span><span class="p">]</span>
<span class="n">left</span> <span class="n">Tree</span><span class="o">-</span><span class="nb">iter</span><span class="o">-</span><span class="n">order</span> <span class="n">key</span> <span class="p">[</span><span class="n">key</span> <span class="n">value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">Tree</span><span class="o">-</span><span class="nb">iter</span><span class="o">-</span><span class="n">order</span><span class="p">]</span>
</pre></div>
@@ -679,7 +678,7 @@ right side:</p>
</pre></div>
</div>
<p>Now we can sort sequences.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1">#define(&#39;Tree-iter-order == [not] [pop] [dup third] [[cons dip] dupdip [[first] dupdip] dip [rest rest rest first] dip i] genrec&#39;)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1">#define(&#39;Tree-iter-order == [not] [pop] [dup third] [[cons dip] dupdip [[first] dupdip] dip [rest rest rest first] dip i] genrec&#39;)</span>
<span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
@@ -695,7 +694,7 @@ right side:</p>
<span class="s1">&#39;&#39;&#39;</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[3 9 5 2 8 6 7 8 4] to_set Tree-iter-order&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[3 9 5 2 8 6 7 8 4] to_set Tree-iter-order&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span> <span class="mi">9</span>
@@ -835,7 +834,7 @@ because there’s no value to discard.</p>
<span class="n">Tree</span><span class="o">-</span><span class="n">get</span> <span class="o">==</span> <span class="p">[</span><span class="n">pop</span> <span class="ow">not</span><span class="p">]</span> <span class="n">swap</span> <span class="p">[]</span> <span class="p">[</span><span class="n">P</span> <span class="p">[</span><span class="n">T</span><span class="o">&gt;</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="o">&lt;</span><span class="p">]</span> <span class="nb">cmp</span><span class="p">]</span> <span class="n">genrec</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># I don&#39;t want to deal with name conflicts with the above so I&#39;m inlining everything here.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># I don&#39;t want to deal with name conflicts with the above so I&#39;m inlining everything here.</span>
<span class="c1"># The original Joy system has &quot;hide&quot; which is a meta-command which allows you to use named</span>
<span class="c1"># definitions that are only in scope for a given definition. I don&#39;t want to implement</span>
<span class="c1"># that (yet) so...</span>
@@ -852,19 +851,19 @@ because there’s no value to discard.</p>
<span class="s1">&#39;&#39;&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;gary&quot; 23 [] []] &quot;mike&quot; [popd &quot; not in tree&quot; +] Tree-get&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;gary&quot; 23 [] []] &quot;mike&quot; [popd &quot; not in tree&quot; +] Tree-get&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;mike not in tree&#39;</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;gary&quot; 23 [] []] &quot;gary&quot; [popop &quot;err&quot;] Tree-get&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[&quot;gary&quot; 23 [] []] &quot;gary&quot; [popop &quot;err&quot;] Tree-get&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
<span class="s1"> [] [[0 &#39;a&#39;] [1 &#39;b&#39;] [2 &#39;c&#39;]] [i Tree-add] step</span>
@@ -876,7 +875,7 @@ because there’s no value to discard.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
<span class="s1"> [] [[0 &#39;a&#39;] [1 &#39;b&#39;] [2 &#39;c&#39;]] [i Tree-add] step</span>
@@ -1175,7 +1174,7 @@ E == [
</div>
<p>By the standards of the code I’ve written so far, this is a <em>huge</em> Joy
program.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
<span class="s1">first_two == uncons uncons pop</span>
<span class="s1">fourth == rest rest rest first</span>
<span class="s1">?fourth == [] [fourth] [] ifte</span>
@@ -1193,43 +1192,43 @@ program.</p>
<span class="s1">&#39;&#39;&#39;</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;c&#39; Tree-Delete &quot;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;c&#39; Tree-Delete &quot;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;b&#39; Tree-Delete &quot;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;b&#39; Tree-Delete &quot;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;a&#39; Tree-Delete &quot;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;a&#39; Tree-Delete &quot;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;der&#39; Tree-Delete &quot;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[&#39;a&#39; 23 [] [&#39;b&#39; 88 [] [&#39;c&#39; 44 [] []]]] &#39;der&#39; Tree-Delete &quot;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;a&#39;</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;b&#39;</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">&#39;c&#39;</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [4 2 3 1 6 7 5 ] [0 swap Tree-add] step&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] [4 2 3 1 6 7 5 ] [0 swap Tree-add] step&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 3 Tree-Delete &quot;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 3 Tree-Delete &quot;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 4 Tree-Delete &quot;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">&quot;[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 4 Tree-Delete &quot;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]]</span>
@@ -1289,50 +1288,86 @@ Tree-delete == [pop not] [pop] [_Tree_delete_R0] [_Tree_delete_R1] genrec
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<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html">∂RE</a></li>
<h3><a href="../index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">Treating Trees I: Ordered Binary Trees</a><ul>
<li><a class="reference internal" href="#adding-nodes-to-the-tree">Adding Nodes to the Tree</a><ul>
<li><a class="reference internal" href="#adding-to-an-empty-node">Adding to an empty node.</a><ul>
<li><a class="reference internal" href="#tree-new"><code class="docutils literal notranslate"><span class="pre">Tree-new</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#adding-to-a-non-empty-node">Adding to a non-empty node.</a><ul>
<li><a class="reference internal" href="#a-predicate-to-compare-keys">A predicate to compare keys.</a></li>
<li><a class="reference internal" href="#if-the-key-were-adding-is-greater-than-the-nodes-key">If the key we’re adding is greater than the node’s key.</a></li>
<li><a class="reference internal" href="#if-the-key-were-adding-is-less-than-the-nodes-key">If the key we’re adding is less than the node’s key.</a></li>
<li><a class="reference internal" href="#else-the-keys-must-be-equal">Else the keys must be equal.</a></li>
</ul>
</li>
<li><a class="reference internal" href="#now-we-can-define-tree-add">Now we can define <code class="docutils literal notranslate"><span class="pre">Tree-add</span></code></a></li>
<li><a class="reference internal" href="#examples">Examples</a></li>
</ul>
</li>
<li><a class="reference internal" href="#interlude-cmp-combinator">Interlude: <code class="docutils literal notranslate"><span class="pre">cmp</span></code> combinator</a><ul>
<li><a class="reference internal" href="#redefine-tree-add">Redefine <code class="docutils literal notranslate"><span class="pre">Tree-add</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#a-function-to-traverse-this-structure">A Function to Traverse this Structure</a><ul>
<li><a class="reference internal" href="#base-case">Base case <code class="docutils literal notranslate"><span class="pre">[]</span></code></a></li>
<li><a class="reference internal" href="#node-case-key-value-left-right">Node case <code class="docutils literal notranslate"><span class="pre">[key</span> <span class="pre">value</span> <span class="pre">left</span> <span class="pre">right]</span></code></a><ul>
<li><a class="reference internal" href="#processing-the-current-node">Processing the current node.</a></li>
<li><a class="reference internal" href="#recur">Recur</a></li>
</ul>
</li>
<li><a class="reference internal" href="#putting-it-together">Putting it together</a></li>
<li><a class="reference internal" href="#parameterizing-the-f-per-node-processing-function">Parameterizing the <code class="docutils literal notranslate"><span class="pre">F</span></code> per-node processing function.</a></li>
<li><a class="reference internal" href="#tree-iter"><code class="docutils literal notranslate"><span class="pre">Tree-iter</span></code></a></li>
<li><a class="reference internal" href="#id1">Examples</a></li>
</ul>
</li>
<li><a class="reference internal" href="#interlude-a-set-like-datastructure">Interlude: A Set-like Datastructure</a></li>
<li><a class="reference internal" href="#a-version-of-tree-iter-that-does-in-order-traversal">A Version of <code class="docutils literal notranslate"><span class="pre">Tree-iter</span></code> that does In-Order Traversal</a><ul>
<li><a class="reference internal" href="#process-the-left-child">Process the left child.</a></li>
<li><a class="reference internal" href="#process-the-current-node">Process the current node.</a></li>
<li><a class="reference internal" href="#process-the-right-child">Process the right child.</a></li>
<li><a class="reference internal" href="#defining-tree-iter-order">Defining <code class="docutils literal notranslate"><span class="pre">Tree-iter-order</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#getting-values-by-key">Getting values by key</a><ul>
<li><a class="reference internal" href="#the-base-case">The base case <code class="docutils literal notranslate"><span class="pre">[]</span></code></a></li>
<li><a class="reference internal" href="#id2">Node case <code class="docutils literal notranslate"><span class="pre">[key</span> <span class="pre">value</span> <span class="pre">left</span> <span class="pre">right]</span></code></a><ul>
<li><a class="reference internal" href="#predicate">Predicate</a></li>
<li><a class="reference internal" href="#branches">Branches</a></li>
<li><a class="reference internal" href="#greater-than-and-less-than">Greater than and less than</a></li>
<li><a class="reference internal" href="#equal-keys">Equal keys</a></li>
</ul>
</li>
<li><a class="reference internal" href="#tree-get"><code class="docutils literal notranslate"><span class="pre">Tree-get</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#tree-delete">Tree-delete</a><ul>
<li><a class="reference internal" href="#id3">Base case</a></li>
<li><a class="reference internal" href="#id4">Recur</a></li>
<li><a class="reference internal" href="#compare-keys">Compare Keys</a></li>
<li><a class="reference internal" href="#greater-than-case-and-less-than-case">Greater than case and less than case</a></li>
<li><a class="reference internal" href="#the-else-case">The else case</a><ul>
<li><a class="reference internal" href="#one-or-more-child-nodes-are">One or more child nodes are <code class="docutils literal notranslate"><span class="pre">[]</span></code></a></li>
<li><a class="reference internal" href="#both-child-nodes-are-non-empty">Both child nodes are non-empty.</a></li>
<li><a class="reference internal" href="#we-have-to-we-find-the-highest-right-most-node-in-our-lower-left-sub-tree">We have to we find the highest (right-most) node in our lower (left) sub-tree:</a></li>
<li><a class="reference internal" href="#found-right-most-node-in-our-left-sub-tree">Found right-most node in our left sub-tree</a></li>
<li><a class="reference internal" href="#replace-current-node-key-and-value-recursively-delete-rightmost">Replace current node key and value, recursively delete rightmost</a></li>
</ul>
</li>
<li><a class="reference internal" href="#refactoring">Refactoring</a></li>
</ul>
</li>
<li><a class="reference internal" href="#appendix-the-source-code">Appendix: The source code.</a></li>
</ul>
</li>
</ul>
<div class="relations">
<h3>Related Topics</h3>
<ul>
@@ -1344,24 +1379,25 @@ Tree-delete == [pop not] [pop] [_Tree_delete_R0] [_Tree_delete_R1] genrec
</ul></li>
</ul>
</div>
<div role="note" aria-label="source link">
<h3>This Page</h3>
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@@ -1372,7 +1408,7 @@ Tree-delete == [pop not] [pop] [_Tree_delete_R0] [_Tree_delete_R1] genrec
</a>
<br />
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 3.0.2.
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docs/sphinx_docs/_build/html/notebooks/Quadratic.html
+39 -64
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@@ -1,18 +1,19 @@
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@@ -29,11 +30,9 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="k">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
</pre></div>
</div>
<div class="section" id="quadratic-formula">
@@ -99,11 +98,11 @@ the variables:</p>
</div>
<p>The three arguments are to the left, so we can “chop off” everything to
the right and say it’s the definition of the <code class="docutils literal notranslate"><span class="pre">quadratic</span></code> function:</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>Let’s try it out:</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;3 1 1 quadratic&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;3 1 1 quadratic&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="mf">0.3819660112501051</span> <span class="o">-</span><span class="mf">2.618033988749895</span>
@@ -113,7 +112,7 @@ the right and say it’s the definition of the <code class="docutils literal not
lines are the <code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">dipd</span></code> combinators building the main program
by incorporating the values on the stack. Then that program runs and you
get the results. This is pretty typical of Joy code.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;-5 1 4 quadratic&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;-5 1 4 quadratic&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="o">-</span><span class="mi">5</span> <span class="mi">1</span> <span class="mi">4</span> <span class="n">quadratic</span>
@@ -168,50 +167,25 @@ get the results. This is pretty typical of Joy code.</p>
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<h3><a href="../index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">Quadratic formula</a><ul>
<li><a class="reference internal" href="#write-a-straightforward-program-with-variable-names">Write a straightforward program with variable names.</a><ul>
<li><a class="reference internal" href="#b"><code class="docutils literal notranslate"><span class="pre">-b</span></code></a></li>
<li><a class="reference internal" href="#sqrt-b-2-4-a-c"><code class="docutils literal notranslate"><span class="pre">sqrt(b^2</span> <span class="pre">-</span> <span class="pre">4</span> <span class="pre">*</span> <span class="pre">a</span> <span class="pre">*</span> <span class="pre">c)</span></code></a></li>
<li><a class="reference internal" href="#a"><code class="docutils literal notranslate"><span class="pre">/2a</span></code></a></li>
<li><a class="reference internal" href="#id1"><code class="docutils literal notranslate"><span class="pre">±</span></code></a></li>
<li><a class="reference internal" href="#putting-them-together">Putting Them Together</a></li>
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<li><a class="reference internal" href="#derive-a-definition">Derive a definition.</a></li>
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@@ -223,24 +197,25 @@ get the results. This is pretty typical of Joy code.</p>
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@@ -251,7 +226,7 @@ get the results. This is pretty typical of Joy code.</p>
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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docs/sphinx_docs/_build/html/notebooks/Recursion_Combinators.html
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@@ -1,18 +1,19 @@
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@@ -29,11 +30,9 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">DefinitionWrapper</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="k">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">DefinitionWrapper</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
</pre></div>
</div>
<div class="section" id="recursion-combinators">
@@ -47,18 +46,16 @@ several generic specializations.</p>
</div>
<p>From “Recursion Theory and Joy” (j05cmp.html) by Manfred von Thun:</p>
<blockquote>
<div><p>“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>
</div></blockquote>
<div>“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.”</div></blockquote>
<div class="section" id="designing-recursive-functions">
<h2>Designing Recursive Functions<a class="headerlink" href="#designing-recursive-functions" title="Permalink to this headline"></a></h2>
<p>The way to design one of these is to fix your base case and test and
@@ -93,16 +90,16 @@ have to do to apply the quoted <code class="docutils literal notranslate"><span
is a recursive function <code class="docutils literal notranslate"><span class="pre">H</span> <span class="pre">::</span> <span class="pre">A</span> <span class="pre">-&gt;</span> <span class="pre">C</span></code> that converts a value of type
<code class="docutils literal notranslate"><span class="pre">A</span></code> into a value of type <code class="docutils literal notranslate"><span class="pre">C</span></code> by means of:</p>
<ul class="simple">
<li><p>A generator <code class="docutils literal notranslate"><span class="pre">G</span> <span class="pre">::</span> <span class="pre">A</span> <span class="pre">-&gt;</span> <span class="pre">(B,</span> <span class="pre">A)</span></code></p></li>
<li><p>A combiner <code class="docutils literal notranslate"><span class="pre">F</span> <span class="pre">::</span> <span class="pre">(B,</span> <span class="pre">C)</span> <span class="pre">-&gt;</span> <span class="pre">C</span></code></p></li>
<li><p>A predicate <code class="docutils literal notranslate"><span class="pre">P</span> <span class="pre">::</span> <span class="pre">A</span> <span class="pre">-&gt;</span> <span class="pre">Bool</span></code> to detect the base case</p></li>
<li><p>A base case value <code class="docutils literal notranslate"><span class="pre">c</span> <span class="pre">::</span> <span class="pre">C</span></code></p></li>
<li><p>Recursive calls (zero or more); it has a “call stack in the form of a
cons list”.</p></li>
<li>A generator <code class="docutils literal notranslate"><span class="pre">G</span> <span class="pre">::</span> <span class="pre">A</span> <span class="pre">-&gt;</span> <span class="pre">(B,</span> <span class="pre">A)</span></code></li>
<li>A combiner <code class="docutils literal notranslate"><span class="pre">F</span> <span class="pre">::</span> <span class="pre">(B,</span> <span class="pre">C)</span> <span class="pre">-&gt;</span> <span class="pre">C</span></code></li>
<li>A predicate <code class="docutils literal notranslate"><span class="pre">P</span> <span class="pre">::</span> <span class="pre">A</span> <span class="pre">-&gt;</span> <span class="pre">Bool</span></code> to detect the base case</li>
<li>A base case value <code class="docutils literal notranslate"><span class="pre">c</span> <span class="pre">::</span> <span class="pre">C</span></code></li>
<li>Recursive calls (zero or more); it has a “call stack in the form of a
cons list”.</li>
</ul>
<p>It may be helpful to see this function implemented in imperative Python
code.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">hylomorphism</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">hylomorphism</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
<span class="sd">&#39;&#39;&#39;Return a hylomorphism function H.&#39;&#39;&#39;</span>
<span class="k">def</span> <span class="nf">H</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
@@ -170,9 +167,9 @@ arguments out of the pieces given to the <code class="docutils literal notransla
</div>
<p>Working in reverse:</p>
<ul class="simple">
<li><p>Use <code class="docutils literal notranslate"><span class="pre">swoncat</span></code> twice to decouple <code class="docutils literal notranslate"><span class="pre">[c]</span></code> and <code class="docutils literal notranslate"><span class="pre">[F]</span></code>.</p></li>
<li><p>Use <code class="docutils literal notranslate"><span class="pre">unit</span></code> to dequote <code class="docutils literal notranslate"><span class="pre">c</span></code>.</p></li>
<li><p>Use <code class="docutils literal notranslate"><span class="pre">dipd</span></code> to untangle <code class="docutils literal notranslate"><span class="pre">[unit</span> <span class="pre">[pop]</span> <span class="pre">swoncat]</span></code> from the givens.</p></li>
<li>Use <code class="docutils literal notranslate"><span class="pre">swoncat</span></code> twice to decouple <code class="docutils literal notranslate"><span class="pre">[c]</span></code> and <code class="docutils literal notranslate"><span class="pre">[F]</span></code>.</li>
<li>Use <code class="docutils literal notranslate"><span class="pre">unit</span></code> to dequote <code class="docutils literal notranslate"><span class="pre">c</span></code>.</li>
<li>Use <code class="docutils literal notranslate"><span class="pre">dipd</span></code> to untangle <code class="docutils literal notranslate"><span class="pre">[unit</span> <span class="pre">[pop]</span> <span class="pre">swoncat]</span></code> from the givens.</li>
</ul>
<p>So:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">H</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">pop</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">F</span><span class="p">]</span> <span class="n">genrec</span>
@@ -186,7 +183,7 @@ the left so we have a definition for <code class="docutils literal notranslate">
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">hylomorphism</span> <span class="o">==</span> <span class="p">[</span><span class="n">unit</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="n">swoncat</span><span class="p">]</span> <span class="n">dipd</span> <span class="p">[</span><span class="n">dip</span><span class="p">]</span> <span class="n">swoncat</span> <span class="n">genrec</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="section" id="example-finding-triangular-numbers">
@@ -196,22 +193,22 @@ of all positive integers less than that one. (In this case the types
<code class="docutils literal notranslate"><span class="pre">A</span></code>, <code class="docutils literal notranslate"><span class="pre">B</span></code> and <code class="docutils literal notranslate"><span class="pre">C</span></code> are all <code class="docutils literal notranslate"><span class="pre">int</span></code>.)</p>
<p>To sum a range of integers from 0 to <em>n</em> - 1:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">[P]</span></code> is <code class="docutils literal notranslate"><span class="pre">[1</span> <span class="pre">&lt;=]</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">c</span></code> is <code class="docutils literal notranslate"><span class="pre">0</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">[G]</span></code> is <code class="docutils literal notranslate"><span class="pre">[--</span> <span class="pre">dup]</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">[F]</span></code> is <code class="docutils literal notranslate"><span class="pre">[+]</span></code></p></li>
<li><code class="docutils literal notranslate"><span class="pre">[P]</span></code> is <code class="docutils literal notranslate"><span class="pre">[1</span> <span class="pre">&lt;=]</span></code></li>
<li><code class="docutils literal notranslate"><span class="pre">c</span></code> is <code class="docutils literal notranslate"><span class="pre">0</span></code></li>
<li><code class="docutils literal notranslate"><span class="pre">[G]</span></code> is <code class="docutils literal notranslate"><span class="pre">[--</span> <span class="pre">dup]</span></code></li>
<li><code class="docutils literal notranslate"><span class="pre">[F]</span></code> is <code class="docutils literal notranslate"><span class="pre">[+]</span></code></li>
</ul>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;triangular_number == [1 &lt;=] 0 [-- dup] [+] hylomorphism&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;triangular_number == [1 &lt;=] 0 [-- dup] [+] hylomorphism&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>Let’s try it:</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 triangular_number&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 triangular_number&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">10</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[0 1 2 3 4 5 6] [triangular_number] map&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[0 1 2 3 4 5 6] [triangular_number] map&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">6</span> <span class="mi">10</span> <span class="mi">15</span><span class="p">]</span>
@@ -363,10 +360,8 @@ values.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">A</span> <span class="o">==</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">hylomorphism</span>
</pre></div>
</div>
<div class="section" id="range-et-al">
<h3><code class="docutils literal notranslate"><span class="pre">range</span></code> et. al.<a class="headerlink" href="#range-et-al" title="Permalink to this headline"></a></h3>
<p>An example of an anamorphism is the <code class="docutils literal notranslate"><span class="pre">range</span></code> function which generates
the list of integers from 0 to <em>n</em> - 1 given <em>n</em>.</p>
<div class="section" id="range-et-al-an-example-of-an-anamorphism-is-the-range-function-which-generates-the-list-of-integers-from-0-to-n-1-given-n">
<h3><code class="docutils literal notranslate"><span class="pre">range</span></code> et. al.&nbsp;An example of an anamorphism is the <code class="docutils literal notranslate"><span class="pre">range</span></code> function which generates the list of integers from 0 to <em>n</em> - 1 given <em>n</em>.<a class="headerlink" href="#range-et-al-an-example-of-an-anamorphism-is-the-range-function-which-generates-the-list-of-integers-from-0-to-n-1-given-n" title="Permalink to this headline"></a></h3>
<p>Each of the above variations can be used to make four slightly different
<code class="docutils literal notranslate"><span class="pre">range</span></code> functions.</p>
<div class="section" id="range-with-h1">
@@ -375,10 +370,10 @@ the list of integers from 0 to <em>n</em> - 1 given <em>n</em>.</p>
<span class="o">==</span> <span class="p">[</span><span class="mi">0</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="p">[]]</span> <span class="p">[</span><span class="o">--</span> <span class="n">dup</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">swons</span><span class="p">]</span> <span class="n">genrec</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;range == [0 &lt;=] [] [-- dup] [swons] hylomorphism&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;range == [0 &lt;=] [] [-- dup] [swons] hylomorphism&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 range&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 range&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">4</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span><span class="p">]</span>
@@ -391,10 +386,10 @@ the list of integers from 0 to <em>n</em> - 1 given <em>n</em>.</p>
<span class="o">==</span> <span class="p">[]</span> <span class="n">swap</span> <span class="p">[</span><span class="mi">0</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="p">[</span><span class="o">--</span> <span class="n">dup</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">primrec</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;range_reverse == [] swap [0 &lt;=] [pop] [-- dup [swons] dip] primrec&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;range_reverse == [] swap [0 &lt;=] [pop] [-- dup [swons] dip] primrec&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 range_reverse&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 range_reverse&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span>
@@ -407,10 +402,10 @@ the list of integers from 0 to <em>n</em> - 1 given <em>n</em>.</p>
<span class="o">==</span> <span class="p">[</span><span class="mi">0</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="p">[]]</span> <span class="p">[[</span><span class="o">--</span><span class="p">]</span> <span class="n">dupdip</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">swons</span><span class="p">]</span> <span class="n">genrec</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;ranger == [0 &lt;=] [pop []] [[--] dupdip] [dip swons] genrec&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;ranger == [0 &lt;=] [pop []] [[--] dupdip] [dip swons] genrec&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 ranger&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 ranger&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">5</span> <span class="mi">4</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span><span class="p">]</span>
@@ -423,10 +418,10 @@ the list of integers from 0 to <em>n</em> - 1 given <em>n</em>.</p>
<span class="o">==</span> <span class="p">[]</span> <span class="n">swap</span> <span class="p">[</span><span class="mi">0</span> <span class="o">&lt;=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="p">[[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dupdip</span> <span class="o">--</span><span class="p">]</span> <span class="n">primrec</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;ranger_reverse == [] swap [0 &lt;=] [pop] [[swons] dupdip --] primrec&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;ranger_reverse == [] swap [0 &lt;=] [pop] [[swons] dupdip --] primrec&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 ranger_reverse&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 ranger_reverse&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span><span class="p">]</span>
@@ -447,17 +442,17 @@ and makes some new value.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">C</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="n">c</span> <span class="p">[</span><span class="n">uncons</span> <span class="n">swap</span><span class="p">]</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">hylomorphism</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;swuncons == uncons swap&#39;</span><span class="p">)</span> <span class="c1"># Awkward name.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;swuncons == uncons swap&#39;</span><span class="p">)</span> <span class="c1"># Awkward name.</span>
</pre></div>
</div>
<p>An example of a catamorphism is the sum function.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">sum</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="mi">0</span> <span class="p">[</span><span class="n">swuncons</span><span class="p">]</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">hylomorphism</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;sum == [not] 0 [swuncons] [+] hylomorphism&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;sum == [not] 0 [swuncons] [+] hylomorphism&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[5 4 3 2 1] sum&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[5 4 3 2 1] sum&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span>
@@ -467,7 +462,7 @@ and makes some new value.</p>
<h3>The <code class="docutils literal notranslate"><span class="pre">step</span></code> combinator<a class="headerlink" href="#the-step-combinator" title="Permalink to this headline"></a></h3>
<p>The <code class="docutils literal notranslate"><span class="pre">step</span></code> combinator will usually be better to use than
<code class="docutils literal notranslate"><span class="pre">catamorphism</span></code>.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[step] help&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[step] help&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Run</span> <span class="n">a</span> <span class="n">quoted</span> <span class="n">program</span> <span class="n">on</span> <span class="n">each</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">a</span> <span class="n">sequence</span><span class="o">.</span>
@@ -491,10 +486,10 @@ and makes some new value.</p>
<span class="n">on</span> <span class="n">top</span> <span class="n">of</span> <span class="n">the</span> <span class="n">stack</span><span class="o">.</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;sum == 0 swap [+] step&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;sum == 0 swap [+] step&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[5 4 3 2 1] sum&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[5 4 3 2 1] sum&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span>
@@ -515,10 +510,10 @@ and makes some new value.</p>
<span class="n">P</span> <span class="o">==</span> <span class="mi">1</span> <span class="o">&lt;=</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;factorial == 1 swap [1 &lt;=] [pop] [[*] dupdip --] primrec&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;factorial == 1 swap [1 &lt;=] [pop] [[*] dupdip --] primrec&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 factorial&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;5 factorial&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">120</span>
@@ -547,10 +542,10 @@ pattern <code class="docutils literal notranslate"><span class="pre">H2</span></
<span class="n">P</span> <span class="o">==</span> <span class="ow">not</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;tails == [] swap [not] [pop] [rest dup [swons] dip] primrec&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;tails == [] swap [not] [pop] [rest dup [swons] dip] primrec&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 2 3] tails&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 2 3] tails&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[]</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]]</span>
@@ -594,50 +589,53 @@ Wire”</a></p>
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<h3><a href="../index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">Recursion Combinators</a><ul>
<li><a class="reference internal" href="#designing-recursive-functions">Designing Recursive Functions</a></li>
<li><a class="reference internal" href="#primitive-recursive-functions">Primitive Recursive Functions</a></li>
<li><a class="reference internal" href="#hylomorphism">Hylomorphism</a></li>
<li><a class="reference internal" href="#hylomorphism-in-joy">Hylomorphism in Joy</a></li>
<li><a class="reference internal" href="#derivation-of-hylomorphism-combinator">Derivation of <code class="docutils literal notranslate"><span class="pre">hylomorphism</span></code> combinator</a><ul>
<li><a class="reference internal" href="#example-finding-triangular-numbers">Example: Finding Triangular Numbers</a></li>
</ul>
</li>
<li><a class="reference internal" href="#four-specializations">Four Specializations</a><ul>
<li><a class="reference internal" href="#h1"><code class="docutils literal notranslate"><span class="pre">H1</span></code></a></li>
<li><a class="reference internal" href="#h2"><code class="docutils literal notranslate"><span class="pre">H2</span></code></a></li>
<li><a class="reference internal" href="#h3"><code class="docutils literal notranslate"><span class="pre">H3</span></code></a></li>
<li><a class="reference internal" href="#h4"><code class="docutils literal notranslate"><span class="pre">H4</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#anamorphism">Anamorphism</a><ul>
<li><a class="reference internal" href="#range-et-al-an-example-of-an-anamorphism-is-the-range-function-which-generates-the-list-of-integers-from-0-to-n-1-given-n"><code class="docutils literal notranslate"><span class="pre">range</span></code> et. al.&nbsp;An example of an anamorphism is the <code class="docutils literal notranslate"><span class="pre">range</span></code> function which generates the list of integers from 0 to <em>n</em> - 1 given <em>n</em>.</a><ul>
<li><a class="reference internal" href="#range-with-h1"><code class="docutils literal notranslate"><span class="pre">range</span></code> with <code class="docutils literal notranslate"><span class="pre">H1</span></code></a></li>
<li><a class="reference internal" href="#range-with-h2"><code class="docutils literal notranslate"><span class="pre">range</span></code> with <code class="docutils literal notranslate"><span class="pre">H2</span></code></a></li>
<li><a class="reference internal" href="#range-with-h3"><code class="docutils literal notranslate"><span class="pre">range</span></code> with <code class="docutils literal notranslate"><span class="pre">H3</span></code></a></li>
<li><a class="reference internal" href="#range-with-h4"><code class="docutils literal notranslate"><span class="pre">range</span></code> with <code class="docutils literal notranslate"><span class="pre">H4</span></code></a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference internal" href="#catamorphism">Catamorphism</a><ul>
<li><a class="reference internal" href="#the-step-combinator">The <code class="docutils literal notranslate"><span class="pre">step</span></code> combinator</a></li>
</ul>
</li>
<li><a class="reference internal" href="#example-factorial-function">Example: Factorial Function</a></li>
<li><a class="reference internal" href="#example-tails">Example: <code class="docutils literal notranslate"><span class="pre">tails</span></code></a></li>
<li><a class="reference internal" href="#conclusion-patterns-of-recursion">Conclusion: Patterns of Recursion</a><ul>
<li><a class="reference internal" href="#hylo-ana-cata">Hylo-, Ana-, Cata-</a></li>
<li><a class="reference internal" href="#para">Para-, ?-, ?-</a></li>
</ul>
</li>
<li><a class="reference internal" href="#appendix-fun-with-symbols">Appendix: Fun with Symbols</a></li>
</ul>
</li>
</ul>
<div class="relations">
<h3>Related Topics</h3>
<ul>
@@ -649,24 +647,25 @@ Wire”</a></p>
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@@ -677,7 +676,7 @@ Wire”</a></p>
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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docs/sphinx_docs/_build/html/notebooks/Replacing.html
+36 -67
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@@ -1,18 +1,19 @@
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@@ -29,8 +30,6 @@
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<div class="body" role="main">
<div class="section" id="replacing-functions-in-the-dictionary">
@@ -38,16 +37,16 @@
<p>For now, there is no way to define new functions from within the Joy
language. All functions (and the interpreter) all accept and return a
dictionary parameter (in addition to the stack and expression) so that
we can implement e.g. a function that adds new functions to the
we can implement e.g.&nbsp;a function that adds new functions to the
dictionary. However, there’s no function that does that. Adding a new
function to the dictionary is a meta-interpreter action, you have to do
it in Python, not Joy.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="k">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span>
</pre></div>
</div>
<div class="section" id="a-long-trace">
<h2>A long trace<a class="headerlink" href="#a-long-trace" title="Permalink to this headline"></a></h2>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[23 18] average&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[23 18] average&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="n">average</span>
@@ -105,8 +104,8 @@ it in Python, not Joy.</p>
<p>An efficient <code class="docutils literal notranslate"><span class="pre">sum</span></code> function is already in the library. But for
<code class="docutils literal notranslate"><span class="pre">size</span></code> we can use a “compiled” version hand-written in Python to speed
up evaluation and make the trace more readable.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">SimpleFunctionWrapper</span>
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="kn">import</span> <span class="n">iter_stack</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.library</span> <span class="k">import</span> <span class="n">SimpleFunctionWrapper</span>
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="k">import</span> <span class="n">iter_stack</span>
<span class="nd">@SimpleFunctionWrapper</span>
@@ -121,14 +120,14 @@ up evaluation and make the trace more readable.</p>
</div>
<p>Now we replace the old version in the dictionary with the new version,
and re-evaluate the expression.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">D</span><span class="p">[</span><span class="s1">&#39;size&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">size</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">D</span><span class="p">[</span><span class="s1">&#39;size&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">size</span>
</pre></div>
</div>
</div>
<div class="section" id="a-shorter-trace">
<h2>A shorter trace<a class="headerlink" href="#a-shorter-trace" title="Permalink to this headline"></a></h2>
<p>You can see that <code class="docutils literal notranslate"><span class="pre">size</span></code> now executes in a single step.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[23 18] average&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[23 18] average&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="n">average</span>
@@ -167,50 +166,19 @@ and re-evaluate the expression.</p>
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<li><a class="reference internal" href="#">Replacing Functions in the Dictionary</a><ul>
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@@ -222,24 +190,25 @@ and re-evaluate the expression.</p>
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@@ -250,7 +219,7 @@ and re-evaluate the expression.</p>
</a>
<br />
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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@@ -1,18 +1,19 @@
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@@ -29,8 +30,6 @@
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<div class="body" role="main">
<div class="section" id="the-four-fundamental-operations-of-definite-action">
@@ -38,10 +37,10 @@
<p>All definite actions (computer program) can be defined by four
fundamental patterns of combination:</p>
<ol class="arabic simple">
<li><p>Sequence</p></li>
<li><p>Branch</p></li>
<li><p>Loop</p></li>
<li><p>Parallel</p></li>
<li>Sequence</li>
<li>Branch</li>
<li>Loop</li>
<li>Parallel</li>
</ol>
<div class="section" id="sequence">
<h2>Sequence<a class="headerlink" href="#sequence" title="Permalink to this headline"></a></h2>
@@ -202,7 +201,7 @@ difficulty in this sort of thing is orchestrating the recombining
(“join” or “wait”) of the results of the functions after they finish.</p>
<p>The current implementaions and the following definitions <em>are not
actually parallel</em> (yet), but there is no reason they couldn’t be
reimplemented in terms of e.g. Python threads. I am not concerned with
reimplemented in terms of e.g.&nbsp;Python threads. I am not concerned with
performance of the system just yet, only the elegance of the code it
allows us to write.</p>
<div class="section" id="cleave">
@@ -267,7 +266,7 @@ value.)</p>
</pre></div>
</div>
<p>There is no reason why the implementation of <code class="docutils literal notranslate"><span class="pre">map</span></code> couldn’t distribute
the <code class="docutils literal notranslate"><span class="pre">Q</span></code> function over e.g. a pool of worker CPUs.</p>
the <code class="docutils literal notranslate"><span class="pre">Q</span></code> function over e.g.&nbsp;a pool of worker CPUs.</p>
</div>
<div class="section" id="pam">
<h3><code class="docutils literal notranslate"><span class="pre">pam</span></code><a class="headerlink" href="#pam" title="Permalink to this headline"></a></h3>
@@ -320,50 +319,37 @@ evaluation, yeah?)</p>
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<ul>
<li><a class="reference internal" href="#">The Four Fundamental Operations of Definite Action</a><ul>
<li><a class="reference internal" href="#sequence">Sequence</a></li>
<li><a class="reference internal" href="#branch">Branch</a><ul>
<li><a class="reference internal" href="#ifte"><code class="docutils literal notranslate"><span class="pre">ifte</span></code></a></li>
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<li><a class="reference internal" href="#first-to-finish">first-to-finish</a></li>
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@@ -375,24 +361,25 @@ evaluation, yeah?)</p>
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@@ -403,7 +390,7 @@ evaluation, yeah?)</p>
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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+71 -84
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@@ -1,18 +1,19 @@
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@@ -29,8 +30,6 @@
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@@ -148,10 +147,10 @@ the desired outcome.</p>
</div>
<div class="section" id="define-treestep">
<h2>Define <code class="docutils literal notranslate"><span class="pre">treestep</span></code><a class="headerlink" href="#define-treestep" title="Permalink to this headline"></a></h2>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span><span class="p">,</span> <span class="n">DefinitionWrapper</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="k">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span><span class="p">,</span> <span class="n">DefinitionWrapper</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
<span class="s1"> _treestep_0 == [[not] swap] dip</span>
<span class="s1"> _treestep_1 == [dip] cons [uncons] swoncat</span>
@@ -169,7 +168,7 @@ all nodes in a tree with this function:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">sumtree</span> <span class="o">==</span> <span class="p">[</span><span class="n">pop</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="nb">sum</span> <span class="o">+</span><span class="p">]</span> <span class="n">treestep</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;sumtree == [pop 0] [] [sum +] treestep&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;sumtree == [pop 0] [] [sum +] treestep&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>Running this function on an empty tree value gives zero:</p>
@@ -178,7 +177,7 @@ all nodes in a tree with this function:</p>
<span class="mi">0</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] sumtree&#39;</span><span class="p">)</span> <span class="c1"># Empty tree.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[] sumtree&#39;</span><span class="p">)</span> <span class="c1"># Empty tree.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span>
@@ -192,61 +191,61 @@ all nodes in a tree with this function:</p>
<span class="n">n</span><span class="o">+</span><span class="n">m</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23] sumtree&#39;</span><span class="p">)</span> <span class="c1"># No child trees.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23] sumtree&#39;</span><span class="p">)</span> <span class="c1"># No child trees.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 []] sumtree&#39;</span><span class="p">)</span> <span class="c1"># Child tree, empty.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 []] sumtree&#39;</span><span class="p">)</span> <span class="c1"># Child tree, empty.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [4]] [3]] sumtree&#39;</span><span class="p">)</span> <span class="c1"># Non-empty child trees.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [4]] [3]] sumtree&#39;</span><span class="p">)</span> <span class="c1"># Non-empty child trees.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">32</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] sumtree&#39;</span><span class="p">)</span> <span class="c1"># Etc...</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] sumtree&#39;</span><span class="p">)</span> <span class="c1"># Etc...</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">49</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep&#39;</span><span class="p">)</span> <span class="c1"># Alternate &quot;spelling&quot;.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep&#39;</span><span class="p">)</span> <span class="c1"># Alternate &quot;spelling&quot;.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">49</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep&#39;</span><span class="p">)</span> <span class="c1"># Replace each node.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep&#39;</span><span class="p">)</span> <span class="c1"># Replace each node.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">23</span> <span class="p">[</span><span class="mi">23</span> <span class="p">[</span><span class="mi">23</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span><span class="p">]]</span> <span class="p">[</span><span class="mi">23</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="p">[]]]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span><span class="p">]]</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[]]]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">6</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep&#39;</span><span class="p">)</span> <span class="c1"># Combine replace and sum into one function.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep&#39;</span><span class="p">)</span> <span class="c1"># Combine replace and sum into one function.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">6</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep&#39;</span><span class="p">)</span> <span class="c1"># Combine replace and sum into one function.</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep&#39;</span><span class="p">)</span> <span class="c1"># Combine replace and sum into one function.</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span>
@@ -277,7 +276,7 @@ all nodes in a tree with this function:</p>
</pre></div>
</div>
<p>This doesn’t quite work:</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] [&quot;B&quot;] [first] [i] treestep&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] [&quot;B&quot;] [first] [i] treestep&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="s1">&#39;B&#39;</span> <span class="s1">&#39;B&#39;</span>
@@ -299,7 +298,7 @@ depositing our results directly on the stack.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="n">first</span><span class="p">]</span> <span class="p">[</span><span class="n">flatten</span> <span class="n">cons</span><span class="p">]</span> <span class="n">treestep</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [first] [flatten cons] treestep&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [first] [flatten cons] treestep&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">9</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">8</span> <span class="mi">6</span> <span class="mi">7</span><span class="p">]</span>
@@ -322,7 +321,7 @@ depositing our results directly on the stack.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="n">i</span> <span class="n">roll</span><span class="o">&lt;</span> <span class="n">swons</span> <span class="n">concat</span><span class="p">]</span> <span class="p">[</span><span class="n">first</span><span class="p">]</span> <span class="n">treestep</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [uncons pop] [i roll&lt; swons concat] treestep&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [uncons pop] [i roll&lt; swons concat] treestep&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span> <span class="mi">9</span><span class="p">]</span>
@@ -343,7 +342,7 @@ non-empty node is:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">key</span> <span class="n">value</span><span class="p">]</span> <span class="n">N</span> <span class="p">[</span><span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">K</span><span class="p">]</span> <span class="n">C</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[&quot;key&quot; &quot;value&quot;] [&quot;left&quot;] [&quot;right&quot;] ] [&quot;B&quot;] [&quot;N&quot;] [&quot;C&quot;] treegrind&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[&quot;key&quot; &quot;value&quot;] [&quot;left&quot;] [&quot;right&quot;] ] [&quot;B&quot;] [&quot;N&quot;] [&quot;C&quot;] treegrind&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">&#39;key&#39;</span> <span class="s1">&#39;value&#39;</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[[</span><span class="s1">&#39;left&#39;</span><span class="p">]</span> <span class="p">[</span><span class="s1">&#39;right&#39;</span><span class="p">]]</span> <span class="p">[[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="s1">&#39;B&#39;</span><span class="p">]</span> <span class="p">[</span><span class="n">uncons</span> <span class="p">[</span><span class="s1">&#39;N&#39;</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="p">[</span><span class="s1">&#39;C&#39;</span><span class="p">]</span> <span class="n">genrec</span><span class="p">]</span> <span class="s1">&#39;C&#39;</span>
@@ -353,21 +352,21 @@ non-empty node is:</p>
<div class="section" id="treegrind-with-step">
<h2><code class="docutils literal notranslate"><span class="pre">treegrind</span></code> with <code class="docutils literal notranslate"><span class="pre">step</span></code><a class="headerlink" href="#treegrind-with-step" title="Permalink to this headline"></a></h2>
<p>Iteration through the nodes</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [&quot;N&quot;] [step] treegrind&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [&quot;N&quot;] [step] treegrind&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">9</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">&#39;N&#39;</span>
</pre></div>
</div>
<p>Sum the nodes’ keys.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [first +] [step] treegrind&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [first +] [step] treegrind&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">44</span>
</pre></div>
</div>
<p>Rebuild the tree using <code class="docutils literal notranslate"><span class="pre">map</span></code> (imitating <code class="docutils literal notranslate"><span class="pre">treestep</span></code>.)</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [[100 +] infra] [map cons] treegrind&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [[100 +] infra] [map cons] treegrind&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="mi">103</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">102</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[[</span><span class="mi">109</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">105</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">104</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[[</span><span class="mi">108</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">106</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">107</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <span class="p">[]]]</span>
@@ -449,7 +448,7 @@ equal):</p>
</pre></div>
</div>
<p>To me, that seems simpler than the <code class="docutils literal notranslate"><span class="pre">genrec</span></code> version.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
<span class="s1"> T&gt; == pop [first] dip i</span>
<span class="s1"> T&lt; == pop [second] dip i</span>
@@ -461,7 +460,7 @@ equal):</p>
<span class="s1">&#39;&#39;&#39;</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span><span class="se">\</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span><span class="se">\</span>
<span class="s1">[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]</span>
@@ -473,7 +472,7 @@ equal):</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span><span class="se">\</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span><span class="se">\</span>
<span class="s1">[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]</span>
@@ -490,50 +489,37 @@ equal):</p>
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<ul>
<li><a class="reference internal" href="#">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a><ul>
<li><a class="reference internal" href="#derive-the-recursive-function">Derive the recursive function.</a></li>
<li><a class="reference internal" href="#extract-the-givens-to-parameterize-the-program">Extract the givens to parameterize the program.</a><ul>
<li><a class="reference internal" href="#alternate-extract-the-givens-to-parameterize-the-program">(alternate) Extract the givens to parameterize the program.</a></li>
</ul>
</li>
<li><a class="reference internal" href="#define-treestep">Define <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
<li><a class="reference internal" href="#examples">Examples</a></li>
<li><a class="reference internal" href="#redefining-the-ordered-binary-tree-in-terms-of-treestep">Redefining the Ordered Binary Tree in terms of <code class="docutils literal notranslate"><span class="pre">treestep</span></code>.</a><ul>
<li><a class="reference internal" href="#traversal">Traversal</a></li>
<li><a class="reference internal" href="#in-order-traversal">In-order traversal</a></li>
</ul>
</li>
<li><a class="reference internal" href="#with-treegrind">With <code class="docutils literal notranslate"><span class="pre">treegrind</span></code>?</a></li>
<li><a class="reference internal" href="#treegrind-with-step"><code class="docutils literal notranslate"><span class="pre">treegrind</span></code> with <code class="docutils literal notranslate"><span class="pre">step</span></code></a></li>
<li><a class="reference internal" href="#do-we-have-the-flexibility-to-reimplement-tree-get">Do we have the flexibility to reimplement <code class="docutils literal notranslate"><span class="pre">Tree-get</span></code>?</a><ul>
<li><a class="reference internal" href="#the-predicate-p">The predicate <code class="docutils literal notranslate"><span class="pre">P</span></code></a></li>
<li><a class="reference internal" href="#e"><code class="docutils literal notranslate"><span class="pre">E</span></code></a></li>
<li><a class="reference internal" href="#t-and-t"><code class="docutils literal notranslate"><span class="pre">T&lt;</span></code> and <code class="docutils literal notranslate"><span class="pre">T&gt;</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#putting-it-together">Putting it together</a></li>
</ul>
</li>
</ul>
<div class="relations">
<h3>Related Topics</h3>
<ul>
@@ -545,24 +531,25 @@ equal):</p>
</ul></li>
</ul>
</div>
<div role="note" aria-label="source link">
<h3>This Page</h3>
<ul class="this-page-menu">
<li><a href="../_sources/notebooks/Treestep.rst.txt"
rel="nofollow">Show Source</a></li>
</ul>
</div>
<div id="searchbox" style="display: none" role="search">
<h3 id="searchlabel">Quick search</h3>
<h3>Quick search</h3>
<div class="searchformwrapper">
<form class="search" action="../search.html" method="get">
<input type="text" name="q" aria-labelledby="searchlabel" />
<input type="text" name="q" />
<input type="submit" value="Go" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
</div>
<script>$('#searchbox').show(0);</script>
<script type="text/javascript">$('#searchbox').show(0);</script>
</div>
</div>
<div class="clearer"></div>
@@ -573,7 +560,7 @@ equal):</p>
</a>
<br />
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 3.0.2.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
</div>
</body>
docs/sphinx_docs/_build/html/notebooks/TypeChecking.html
+45 -76
View File
@@ -1,18 +1,19 @@
<!DOCTYPE html>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Type Checking &#8212; Thun 0.3.0 documentation</title>
<link rel="stylesheet" href="../_static/alabaster.css" type="text/css" />
<link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
<script id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script>
<script src="../_static/jquery.js"></script>
<script src="../_static/underscore.js"></script>
<script src="../_static/doctools.js"></script>
<script src="../_static/language_data.js"></script>
<script async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
<script type="text/javascript" src="../_static/documentation_options.js"></script>
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<script type="text/javascript" src="../_static/underscore.js"></script>
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<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<link rel="index" title="Index" href="../genindex.html" />
<link rel="search" title="Search" href="../search.html" />
<link rel="next" title="No Updates" href="NoUpdates.html" />
@@ -29,13 +30,11 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<div class="section" id="type-checking">
<h1>Type Checking<a class="headerlink" href="#type-checking" title="Permalink to this headline"></a></h1>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">logging</span><span class="o">,</span> <span class="nn">sys</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">logging</span><span class="o">,</span> <span class="nn">sys</span>
<span class="n">logging</span><span class="o">.</span><span class="n">basicConfig</span><span class="p">(</span>
<span class="nb">format</span><span class="o">=</span><span class="s1">&#39;</span><span class="si">%(message)s</span><span class="s1">&#39;</span><span class="p">,</span>
@@ -44,7 +43,7 @@
<span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.utils.types</span> <span class="kn">import</span> <span class="p">(</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.utils.types</span> <span class="k">import</span> <span class="p">(</span>
<span class="n">doc_from_stack_effect</span><span class="p">,</span>
<span class="n">infer</span><span class="p">,</span>
<span class="n">reify</span><span class="p">,</span>
@@ -54,14 +53,14 @@
<span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">D</span> <span class="o">=</span> <span class="n">FUNCTIONS</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">D</span> <span class="o">=</span> <span class="n">FUNCTIONS</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="k">del</span> <span class="n">D</span><span class="p">[</span><span class="s1">&#39;product&#39;</span><span class="p">]</span>
<span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">D</span><span class="p">)</span>
</pre></div>
</div>
<div class="section" id="an-example">
<h2>An Example<a class="headerlink" href="#an-example" title="Permalink to this headline"></a></h2>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">rrest</span><span class="p">,</span> <span class="n">ccons</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">rrest</span><span class="p">,</span> <span class="n">ccons</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>25 (--) ∘ pop swap rolldown rrest ccons
@@ -72,31 +71,31 @@
40 ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) ∘
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a4</span> <span class="n">a5</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a3</span> <span class="o">...</span><span class="mi">1</span><span class="p">])</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.parser</span> <span class="kn">import</span> <span class="n">text_to_expression</span>
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="kn">import</span> <span class="n">stack_to_string</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.parser</span> <span class="k">import</span> <span class="n">text_to_expression</span>
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="k">import</span> <span class="n">stack_to_string</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;0 1 2 [3 4]&#39;</span><span class="p">)</span> <span class="c1"># reverse order</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;0 1 2 [3 4]&#39;</span><span class="p">)</span> <span class="c1"># reverse order</span>
<span class="nb">print</span> <span class="n">stack_to_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fi</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fi</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">u</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">a1</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">a2</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">a3</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="n">a4</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">a5</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(),</span> <span class="n">s1</span><span class="p">:</span> <span class="p">()}</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span>
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">g</span><span class="p">)</span>
</pre></div>
</div>
@@ -106,17 +105,17 @@
</div>
<div class="section" id="unification-works-in-reverse">
<h2>Unification Works “in Reverse”<a class="headerlink" href="#unification-works-in-reverse" title="Permalink to this headline"></a></h2>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[2 3]&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;[2 3]&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fo</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># output side, not input side</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fo</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># output side, not input side</span>
<span class="n">u</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">a2</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="n">a3</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(),</span> <span class="n">s1</span><span class="p">:</span> <span class="p">()}</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span>
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">g</span><span class="p">)</span>
</pre></div>
</div>
@@ -126,7 +125,7 @@
</div>
<div class="section" id="failing-a-check">
<h2>Failing a Check<a class="headerlink" href="#failing-a-check" title="Permalink to this headline"></a></h2>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>25 (--) ∘ dup mul
@@ -135,14 +134,14 @@
31 (i1 -- i2) ∘
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;&quot;two&quot;&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">&#39;&quot;two&quot;&#39;</span><span class="p">)</span>
<span class="nb">print</span> <span class="n">stack_to_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">&#39;two&#39;</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">try</span><span class="p">:</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">try</span><span class="p">:</span>
<span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fi</span><span class="p">)</span>
<span class="k">except</span> <span class="n">JoyTypeError</span><span class="p">,</span> <span class="n">err</span><span class="p">:</span>
<span class="nb">print</span> <span class="n">err</span>
@@ -156,50 +155,19 @@
</div>
</div>
</div>
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
<div class="sphinxsidebarwrapper">
<h1 class="logo"><a href="../index.html">Thun</a></h1>
<h3>Navigation</h3>
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<li class="toctree-l1"><a class="reference internal" href="Intro.html">Thun: Joy in Python</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../stack.html">Stack or Quote or Sequence or List…</a></li>
<li class="toctree-l1"><a class="reference internal" href="../parser.html">Parsing Text into Joy Expressions</a></li>
<li class="toctree-l1"><a class="reference internal" href="../pretty.html">Tracing Joy Execution</a></li>
<li class="toctree-l1"><a class="reference internal" href="../library.html">Function Reference</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html">Recursion Combinators</a></li>
<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html">Treating Trees I: Ordered Binary Trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a></li>
<li class="toctree-l2"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a></li>
<li class="toctree-l2"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a></li>
<li class="toctree-l2 current"><a class="current reference internal" href="#">Type Checking</a></li>
<li class="toctree-l2"><a class="reference internal" href="NoUpdates.html">No Updates</a></li>
<li class="toctree-l2"><a class="reference internal" href="Categorical.html">Categorical Programming</a></li>
<li class="toctree-l2"><a class="reference internal" href="The_Four_Operations.html">The Four Fundamental Operations of Definite Action</a></li>
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html">∂RE</a></li>
<h3><a href="../index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">Type Checking</a><ul>
<li><a class="reference internal" href="#an-example">An Example</a></li>
<li><a class="reference internal" href="#unification-works-in-reverse">Unification Works “in Reverse”</a></li>
<li><a class="reference internal" href="#failing-a-check">Failing a Check</a></li>
</ul>
</li>
</ul>
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@@ -211,24 +179,25 @@
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@@ -239,7 +208,7 @@
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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+268 -213
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@@ -1,18 +1,19 @@
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@@ -29,8 +30,6 @@
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<div class="section" id="traversing-datastructures-with-zippers">
@@ -42,18 +41,17 @@ the original paper: <a class="reference external" href="https://www.st.cs.uni-sa
Huet</a></p>
<p>Given a datastructure on the stack we can navigate through it, modify
it, and rebuild it using the “zipper” technique.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="k">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
</pre></div>
</div>
<div class="section" id="trees">
<h2>Trees<a class="headerlink" href="#trees" title="Permalink to this headline"></a></h2>
<p>In Joypy there aren’t any complex datastructures, just ints, floats,
strings, Symbols (strings that are names of functions) and sequences
(aka lists, aka quoted literals, aka aggregates, etc…), but we can
build
(aka lists, aka quoted literals, aka aggregates, etc…), but we can build
<a class="reference external" href="https://en.wikipedia.org/wiki/Tree_%28data_structure%29">trees</a> out
of sequences.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8]&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8]&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span>
@@ -76,13 +74,13 @@ datastructure used to keep track of these items is the zipper.)</p>
show the trace so you can see how it works. If we were going to use
these a lot it would make sense to write Python versions for efficiency,
but see below.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-down == [] swap uncons swap&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-down == [] swap uncons swap&#39;</span><span class="p">)</span>
<span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-up == swons swap shunt&#39;</span><span class="p">)</span>
<span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-right == [swons] cons dip uncons swap&#39;</span><span class="p">)</span>
<span class="n">define</span><span class="p">(</span><span class="s1">&#39;z-left == swons [uncons swap] dip swap&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8] z-down&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8] z-down&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="n">z</span><span class="o">-</span><span class="n">down</span>
@@ -94,7 +92,7 @@ but see below.</p>
<span class="p">[]</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="mi">1</span> <span class="o">.</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[] [[2 [3 4 25 6] 7] 8] 1 z-right&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[] [[2 [3 4 25 6] 7] 8] 1 z-right&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="mi">1</span> <span class="n">z</span><span class="o">-</span><span class="n">right</span>
@@ -114,43 +112,43 @@ but see below.</p>
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="o">.</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2 [3 4 25 6] 7] z-down&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2 [3 4 25 6] 7] z-down&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">2</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [] [[3 4 25 6] 7] 2 z-right&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [] [[3 4 25 6] 7] 2 z-right&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [3 4 25 6] z-down&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [3 4 25 6] z-down&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">3</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [] [4 25 6] 3 z-right&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [] [4 25 6] 3 z-right&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">4</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [3] [25 6] 4 z-right&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [3] [25 6] 4 z-right&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">25</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [4 3] [6] 25 sqr&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [4 3] [6] 25 sqr&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [4 3] [6] 625 z-up&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [4 3] [6] 625 z-up&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span> <span class="n">z</span><span class="o">-</span><span class="n">up</span>
@@ -169,13 +167,13 @@ but see below.</p>
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="o">.</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [3 4 625 6] z-up&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2] [7] [3 4 625 6] z-up&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2 [3 4 625 6] 7] z-up&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1] [8] [2 [3 4 625 6] 7] z-up&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span>
@@ -186,7 +184,7 @@ but see below.</p>
<h2><code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">infra</span></code><a class="headerlink" href="#dip-and-infra" title="Permalink to this headline"></a></h2>
<p>In Joy we have the <code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">infra</span></code> combinators which can “target”
or “address” any particular item in a Joy tree structure.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="p">[[[[[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span>
@@ -237,11 +235,11 @@ been embedded in a nested series of quoted programs, e.g.:</p>
</pre></div>
</div>
<p>The <code class="docutils literal notranslate"><span class="pre">Z</span></code> function isn’t hard to make.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Z == [[] cons cons] step i&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;Z == [[] cons cons] step i&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>Here it is in action in a simplified scenario.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;1 [2 3 4] Z&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;1 [2 3 4] Z&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="n">Z</span>
@@ -274,7 +272,7 @@ been embedded in a nested series of quoted programs, e.g.:</p>
</pre></div>
</div>
<p>And here it is doing the main thing.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z&#39;</span><span class="p">)</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span>
@@ -306,50 +304,22 @@ i d i d i d d Bingo!
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<li><a class="reference internal" href="#">Traversing Datastructures with Zippers</a><ul>
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<li><a class="reference internal" href="#dip-and-infra"><code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">infra</span></code></a></li>
<li><a class="reference internal" href="#z"><code class="docutils literal notranslate"><span class="pre">Z</span></code></a></li>
<li><a class="reference internal" href="#addressing">Addressing</a></li>
<li><a class="reference internal" href="#determining-the-right-path-for-an-item-in-a-tree">Determining the right “path” for an item in a tree.</a></li>
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@@ -361,24 +331,25 @@ i d i d i d d Bingo!
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@@ -389,7 +360,7 @@ i d i d i d d Bingo!
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@@ -1,18 +1,19 @@
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@@ -29,8 +30,6 @@
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@@ -120,7 +119,7 @@
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<li class="toctree-l1"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Types.html#part-i-poial-s-rules">Part I: Pöial’s Rules</a></li>
<li class="toctree-l2"><a class="reference internal" href="Types.html#part-i-poials-rules">Part I: Pöial’s Rules</a></li>
<li class="toctree-l2"><a class="reference internal" href="Types.html#part-ii-implementation">Part II: Implementation</a></li>
<li class="toctree-l2"><a class="reference internal" href="Types.html#part-iii-compiling-yin-functions">Part III: Compiling Yin Functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="Types.html#part-iv-types-and-subtypes-of-arguments">Part IV: Types and Subtypes of Arguments</a></li>
@@ -147,9 +146,9 @@
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<li class="toctree-l1"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html">∂RE</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#brzozowski-s-derivatives-of-regular-expressions">Brzozowski’s Derivatives of Regular Expressions</a></li>
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#brzozowskis-derivatives-of-regular-expressions">Brzozowski’s Derivatives of Regular Expressions</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#let-s-try-it-out">Let’s try it out…</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#larger-alphabets">Larger Alphabets</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#reversing-the-derivatives-to-generate-matching-strings">Reversing the Derivatives to Generate Matching Strings</a></li>
@@ -161,51 +160,10 @@
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@@ -214,24 +172,25 @@
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@@ -242,7 +201,7 @@
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@@ -29,8 +30,6 @@
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@@ -52,36 +51,37 @@ literal value (integer, float, string, or Joy expression) or a function
symbol. Function symbols are unquoted strings and cannot contain square
brackets. Terms must be separated by blanks, which can be omitted
around square brackets.</p>
<dl class="py exception">
<dl class="exception">
<dt id="joy.parser.ParseError">
<em class="property">exception </em><code class="sig-prename descclassname">joy.parser.</code><code class="sig-name descname">ParseError</code><a class="reference internal" href="_modules/joy/parser.html#ParseError"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.parser.ParseError" title="Permalink to this definition"></a></dt>
<em class="property">exception </em><code class="descclassname">joy.parser.</code><code class="descname">ParseError</code><a class="reference internal" href="_modules/joy/parser.html#ParseError"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.parser.ParseError" title="Permalink to this definition"></a></dt>
<dd><p>Raised when there is a error while parsing text.</p>
</dd></dl>
<dl class="py class">
<dl class="class">
<dt id="joy.parser.Symbol">
<em class="property">class </em><code class="sig-prename descclassname">joy.parser.</code><code class="sig-name descname">Symbol</code><a class="reference internal" href="_modules/joy/parser.html#Symbol"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.parser.Symbol" title="Permalink to this definition"></a></dt>
<em class="property">class </em><code class="descclassname">joy.parser.</code><code class="descname">Symbol</code><a class="reference internal" href="_modules/joy/parser.html#Symbol"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.parser.Symbol" title="Permalink to this definition"></a></dt>
<dd><p>A string class that represents Joy function names.</p>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.parser.text_to_expression">
<code class="sig-prename descclassname">joy.parser.</code><code class="sig-name descname">text_to_expression</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">text</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/parser.html#text_to_expression"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.parser.text_to_expression" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.parser.</code><code class="descname">text_to_expression</code><span class="sig-paren">(</span><em>text</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/parser.html#text_to_expression"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.parser.text_to_expression" title="Permalink to this definition"></a></dt>
<dd><p>Convert a string to a Joy expression.</p>
<p>When supplied with a string this function returns a Python datastructure
that represents the Joy datastructure described by the text expression.
Any unbalanced square brackets will raise a ParseError.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>text</strong> (<em>str</em>) – Text to convert.</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>stack</p>
</dd>
<dt class="field-odd">Raises</dt>
<dd class="field-odd"><p><a class="reference internal" href="#joy.parser.ParseError" title="joy.parser.ParseError"><strong>ParseError</strong></a> – if the parse fails.</p>
</dd>
</dl>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>text</strong> (<em>str</em>) – Text to convert.</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body">stack</td>
</tr>
<tr class="field-odd field"><th class="field-name">Raises:</th><td class="field-body"><a class="reference internal" href="#joy.parser.ParseError" title="joy.parser.ParseError"><strong>ParseError</strong></a> – if the parse fails.</td>
</tr>
</tbody>
</table>
</dd></dl>
</div>
@@ -93,37 +93,18 @@ Any unbalanced square brackets will raise a ParseError.</p>
</div>
</div>
</div>
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
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<h3>Navigation</h3>
<ul class="current">
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<li class="toctree-l1"><a class="reference internal" href="joy.html">Joy Interpreter</a></li>
<li class="toctree-l1"><a class="reference internal" href="stack.html">Stack or Quote or Sequence or List…</a></li>
<li class="toctree-l1 current"><a class="current reference internal" href="#">Parsing Text into Joy Expressions</a><ul>
<li class="toctree-l2"><a class="reference internal" href="#module-joy.parser"><code class="docutils literal notranslate"><span class="pre">joy.parser</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="#parser-internals">Parser Internals</a></li>
<h3><a href="index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">Parsing Text into Joy Expressions</a><ul>
<li><a class="reference internal" href="#module-joy.parser"><code class="docutils literal notranslate"><span class="pre">joy.parser</span></code></a></li>
<li><a class="reference internal" href="#parser-internals">Parser Internals</a></li>
</ul>
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<li class="toctree-l1"><a class="reference internal" href="pretty.html">Tracing Joy Execution</a></li>
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<li class="toctree-l1"><a class="reference internal" href="lib.html">Functions Grouped by, er, Function with Examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="types.html">Type Inference of Joy Expressions</a></li>
<li class="toctree-l1"><a class="reference internal" href="notebooks/index.html">Essays about Programming in Joy</a></li>
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<ul>
@@ -133,24 +114,25 @@ Any unbalanced square brackets will raise a ParseError.</p>
</ul></li>
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<div role="note" aria-label="source link">
<h3>This Page</h3>
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@@ -161,7 +143,7 @@ Any unbalanced square brackets will raise a ParseError.</p>
</a>
<br />
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 3.0.2.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
</div>
</body>
docs/sphinx_docs/_build/html/pretty.html
+69 -77
View File
@@ -1,18 +1,19 @@
<!DOCTYPE html>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Tracing Joy Execution &#8212; Thun 0.3.0 documentation</title>
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<link rel="search" title="Search" href="search.html" />
<link rel="next" title="Function Reference" href="library.html" />
@@ -29,8 +30,6 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<div class="section" id="tracing-joy-execution">
@@ -54,60 +53,71 @@ joy?
<p>On each line the stack is printed with the top to the right, then a <code class="docutils literal notranslate"><span class="pre">.</span></code> to
represent the current locus of processing, then the pending expression to the
left.</p>
<dl class="py class">
<dl class="class">
<dt id="joy.utils.pretty_print.TracePrinter">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.pretty_print.</code><code class="sig-name descname">TracePrinter</code><a class="reference internal" href="_modules/joy/utils/pretty_print.html#TracePrinter"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.pretty_print.TracePrinter" title="Permalink to this definition"></a></dt>
<em class="property">class </em><code class="descclassname">joy.utils.pretty_print.</code><code class="descname">TracePrinter</code><a class="reference internal" href="_modules/joy/utils/pretty_print.html#TracePrinter"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.pretty_print.TracePrinter" title="Permalink to this definition"></a></dt>
<dd><p>This is what does the formatting. You instantiate it and pass the <code class="docutils literal notranslate"><span class="pre">viewer()</span></code>
method to the <a class="reference internal" href="joy.html#joy.joy.joy" title="joy.joy.joy"><code class="xref py py-func docutils literal notranslate"><span class="pre">joy.joy.joy()</span></code></a> function, then print it to see the
trace.</p>
<dl class="py method">
<dl class="method">
<dt id="joy.utils.pretty_print.TracePrinter.go">
<code class="sig-name descname">go</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/pretty_print.html#TracePrinter.go"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.pretty_print.TracePrinter.go" title="Permalink to this definition"></a></dt>
<code class="descname">go</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/pretty_print.html#TracePrinter.go"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.pretty_print.TracePrinter.go" title="Permalink to this definition"></a></dt>
<dd><p>Return a list of strings, one for each entry in the history, prefixed
with enough spaces to align all the interpreter dots.</p>
<p>This method is called internally by the <code class="docutils literal notranslate"><span class="pre">__str__()</span></code> method.</p>
<dl class="field-list simple">
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>list(str)</p>
</dd>
</dl>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body">list(str)</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="py method">
<dl class="method">
<dt id="joy.utils.pretty_print.TracePrinter.viewer">
<code class="sig-name descname">viewer</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">stack</span></em>, <em class="sig-param"><span class="n">expression</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/pretty_print.html#TracePrinter.viewer"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.pretty_print.TracePrinter.viewer" title="Permalink to this definition"></a></dt>
<code class="descname">viewer</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/pretty_print.html#TracePrinter.viewer"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.pretty_print.TracePrinter.viewer" title="Permalink to this definition"></a></dt>
<dd><p>Record the current stack and expression in the TracePrinter’s history.
Pass this method as the <code class="docutils literal notranslate"><span class="pre">viewer</span></code> argument to the <a class="reference internal" href="joy.html#joy.joy.joy" title="joy.joy.joy"><code class="xref py py-func docutils literal notranslate"><span class="pre">joy.joy.joy()</span></code></a> function.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>quote</strong> (<em>stack</em>) – A stack.</p></li>
<li><p><strong>expression</strong> (<em>stack</em>) – A stack.</p></li>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>quote</strong> (<em>stack</em>) – A stack.</li>
<li><strong>expression</strong> (<em>stack</em>) – A stack.</li>
</ul>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.pretty_print.trace">
<code class="sig-prename descclassname">joy.utils.pretty_print.</code><code class="sig-name descname">trace</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">stack</span></em>, <em class="sig-param"><span class="n">expression</span></em>, <em class="sig-param"><span class="n">dictionary</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/pretty_print.html#trace"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.pretty_print.trace" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.pretty_print.</code><code class="descname">trace</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/utils/pretty_print.html#trace"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.pretty_print.trace" title="Permalink to this definition"></a></dt>
<dd><p>Evaluate a Joy expression on a stack and print a trace.</p>
<p>This function is just like the <cite>i</cite> combinator but it also prints a
trace of the evaluation</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>stack</strong> (<em>stack</em>) – The stack.</p></li>
<li><p><strong>expression</strong> (<em>stack</em>) – The expression to evaluate.</p></li>
<li><p><strong>dictionary</strong> (<em>dict</em>) – A <code class="docutils literal notranslate"><span class="pre">dict</span></code> mapping names to Joy functions.</p></li>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>stack</strong> (<em>stack</em>) – The stack.</li>
<li><strong>expression</strong> (<em>stack</em>) – The expression to evaluate.</li>
<li><strong>dictionary</strong> (<em>dict</em>) – A <code class="docutils literal notranslate"><span class="pre">dict</span></code> mapping names to Joy functions.</li>
</ul>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>(stack, (), dictionary)</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">(stack, (), dictionary)</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
</div>
@@ -115,36 +125,17 @@ trace of the evaluation</p>
</div>
</div>
</div>
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<div class="sphinxsidebarwrapper">
<h1 class="logo"><a href="index.html">Thun</a></h1>
<h3>Navigation</h3>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="notebooks/Intro.html">Thun: Joy in Python</a></li>
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<li class="toctree-l1"><a class="reference internal" href="stack.html">Stack or Quote or Sequence or List…</a></li>
<li class="toctree-l1"><a class="reference internal" href="parser.html">Parsing Text into Joy Expressions</a></li>
<li class="toctree-l1 current"><a class="current reference internal" href="#">Tracing Joy Execution</a><ul>
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<h3><a href="index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">Tracing Joy Execution</a><ul>
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@@ -154,24 +145,25 @@ trace of the evaluation</p>
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@@ -182,7 +174,7 @@ trace of the evaluation</p>
</a>
<br />
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 3.0.2.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
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docs/sphinx_docs/_build/html/py-modindex.html
+17 -48
View File
@@ -1,18 +1,19 @@
<!DOCTYPE html>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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@@ -30,8 +31,6 @@
<div class="document">
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@@ -90,34 +89,10 @@
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<div class="sphinxsidebarwrapper">
<h1 class="logo"><a href="index.html">Thun</a></h1>
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<li class="toctree-l1"><a class="reference internal" href="notebooks/Intro.html">Thun: Joy in Python</a></li>
<li class="toctree-l1"><a class="reference internal" href="joy.html">Joy Interpreter</a></li>
<li class="toctree-l1"><a class="reference internal" href="stack.html">Stack or Quote or Sequence or List…</a></li>
<li class="toctree-l1"><a class="reference internal" href="parser.html">Parsing Text into Joy Expressions</a></li>
<li class="toctree-l1"><a class="reference internal" href="pretty.html">Tracing Joy Execution</a></li>
<li class="toctree-l1"><a class="reference internal" href="library.html">Function Reference</a></li>
<li class="toctree-l1"><a class="reference internal" href="lib.html">Functions Grouped by, er, Function with Examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="types.html">Type Inference of Joy Expressions</a></li>
<li class="toctree-l1"><a class="reference internal" href="notebooks/index.html">Essays about Programming in Joy</a></li>
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@@ -125,23 +100,17 @@
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<script>$('#searchbox').show(0);</script>
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@@ -152,7 +121,7 @@
</a>
<br />
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 3.0.2.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
</div>
</body>
docs/sphinx_docs/_build/html/search.html
+24 -52
View File
@@ -1,23 +1,27 @@
<!DOCTYPE html>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Search &#8212; Thun 0.3.0 documentation</title>
<link rel="stylesheet" href="_static/alabaster.css" type="text/css" />
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
<script id="documentation_options" data-url_root="./" src="_static/documentation_options.js"></script>
<script src="_static/jquery.js"></script>
<script src="_static/underscore.js"></script>
<script src="_static/doctools.js"></script>
<script src="_static/language_data.js"></script>
<script async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
<script src="_static/searchtools.js"></script>
<script type="text/javascript" src="_static/documentation_options.js"></script>
<script type="text/javascript" src="_static/jquery.js"></script>
<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<script type="text/javascript" src="_static/searchtools.js"></script>
<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="#" />
<script src="searchindex.js" defer></script>
<script type="text/javascript">
jQuery(function() { Search.loadIndex("searchindex.js"); });
</script>
<script type="text/javascript" id="searchindexloader"></script>
<link rel="stylesheet" href="_static/custom.css" type="text/css" />
@@ -32,24 +36,24 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<h1 id="search-documentation">Search</h1>
<div id="fallback" class="admonition warning">
<script>$('#fallback').hide();</script>
<script type="text/javascript">$('#fallback').hide();</script>
<p>
Please activate JavaScript to enable the search
functionality.
</p>
</div>
<p>
Searching for multiple words only shows matches that contain
all words.
From here you can search these documents. Enter your search
words into the box below and click "search". Note that the search
function will automatically search for all of the words. Pages
containing fewer words won't appear in the result list.
</p>
<form action="" method="get">
<input type="text" name="q" aria-labelledby="search-documentation" value="" />
<input type="text" name="q" value="" />
<input type="submit" value="search" />
<span id="search-progress" style="padding-left: 10px"></span>
</form>
@@ -59,48 +63,16 @@
</div>
</div>
</div>
</div>
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
<div class="sphinxsidebarwrapper">
<h1 class="logo"><a href="index.html">Thun</a></h1>
<h3>Navigation</h3>
<ul>
<li class="toctree-l1"><a class="reference internal" href="notebooks/Intro.html">Thun: Joy in Python</a></li>
<li class="toctree-l1"><a class="reference internal" href="joy.html">Joy Interpreter</a></li>
<li class="toctree-l1"><a class="reference internal" href="stack.html">Stack or Quote or Sequence or List…</a></li>
<li class="toctree-l1"><a class="reference internal" href="parser.html">Parsing Text into Joy Expressions</a></li>
<li class="toctree-l1"><a class="reference internal" href="pretty.html">Tracing Joy Execution</a></li>
<li class="toctree-l1"><a class="reference internal" href="library.html">Function Reference</a></li>
<li class="toctree-l1"><a class="reference internal" href="lib.html">Functions Grouped by, er, Function with Examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="types.html">Type Inference of Joy Expressions</a></li>
<li class="toctree-l1"><a class="reference internal" href="notebooks/index.html">Essays about Programming in Joy</a></li>
</ul>
<div class="relations">
<div class="sphinxsidebarwrapper"><div class="relations">
<h3>Related Topics</h3>
<ul>
<li><a href="index.html">Documentation overview</a><ul>
</ul></li>
</ul>
</div>
</div>
</div>
<div class="clearer"></div>
@@ -111,7 +83,7 @@
</a>
<br />
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 3.0.2.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
</div>
</body>
docs/sphinx_docs/_build/html/searchindex.js
+1 -1
View File
File diff suppressed because one or more lines are too long
docs/sphinx_docs/_build/html/stack.html
+123 -124
View File
@@ -1,18 +1,19 @@
<!DOCTYPE html>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Stack or Quote or Sequence or List… &#8212; Thun 0.3.0 documentation</title>
<link rel="stylesheet" href="_static/alabaster.css" type="text/css" />
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
<script id="documentation_options" data-url_root="./" src="_static/documentation_options.js"></script>
<script src="_static/jquery.js"></script>
<script src="_static/underscore.js"></script>
<script src="_static/doctools.js"></script>
<script src="_static/language_data.js"></script>
<script async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
<script type="text/javascript" src="_static/documentation_options.js"></script>
<script type="text/javascript" src="_static/jquery.js"></script>
<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
<link rel="next" title="Parsing Text into Joy Expressions" href="parser.html" />
@@ -29,8 +30,6 @@
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<div class="section" id="stack-or-quote-or-sequence-or-list">
@@ -43,9 +42,9 @@ permits certain operations such as iterating and pushing and popping
values from (at least) one end.</p>
<p>There is no “Stack” Python class, instead we use the <a class="reference external" href="https://en.wikipedia.org/wiki/Cons#Lists">cons list</a>, a
venerable two-tuple recursive sequence datastructure, where the
empty tuple <code class="docutils literal notranslate"><span class="pre">()</span></code> is the empty stack and <code class="docutils literal notranslate"><span class="pre">(head,</span> <span class="pre">rest)</span></code> gives the recursive
form of a stack with one or more items on it:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">stack</span> <span class="o">:=</span> <span class="p">()</span> <span class="o">|</span> <span class="p">(</span><span class="n">item</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span>
empty tuple <code class="docutils literal notranslate"><span class="pre">()</span></code> is the empty stack and <code class="docutils literal notranslate"><span class="pre">(head,</span> <span class="pre">rest)</span></code> gives the
recursive form of a stack with one or more items on it:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">stack</span> <span class="p">:</span><span class="o">=</span> <span class="p">()</span> <span class="o">|</span> <span class="p">(</span><span class="n">item</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span>
</pre></div>
</div>
<p>Putting some numbers onto a stack:</p>
@@ -81,119 +80,137 @@ iterable and another to iterate through a stack and yield its items
one-by-one in order. There are also two functions to generate string representations
of stacks. They only differ in that one prints the terms in stack from left-to-right while the other prints from right-to-left. In both functions <em>internal stacks</em> are
printed left-to-right. These functions are written to support <a class="reference internal" href="pretty.html"><span class="doc">Tracing Joy Execution</span></a>.</p>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.stack.concat">
<code class="sig-prename descclassname">joy.utils.stack.</code><code class="sig-name descname">concat</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">quote</span></em>, <em class="sig-param"><span class="n">expression</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/stack.html#concat"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.stack.concat" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.stack.</code><code class="descname">concat</code><span class="sig-paren">(</span><em>quote</em>, <em>expression</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/stack.html#concat"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.stack.concat" title="Permalink to this definition"></a></dt>
<dd><p>Concatinate quote onto expression.</p>
<p>In joy [1 2] [3 4] would become [1 2 3 4].</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>quote</strong> (<em>stack</em>) – A stack.</p></li>
<li><p><strong>expression</strong> (<em>stack</em>) – A stack.</p></li>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>quote</strong> (<em>stack</em>) – A stack.</li>
<li><strong>expression</strong> (<em>stack</em>) – A stack.</li>
</ul>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><p><strong>RuntimeError</strong> – if quote is larger than sys.getrecursionlimit().</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>stack</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Raises:</th><td class="field-body"><p class="first"><strong>RuntimeError</strong> – if quote is larger than sys.getrecursionlimit().</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">stack</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.stack.expression_to_string">
<code class="sig-prename descclassname">joy.utils.stack.</code><code class="sig-name descname">expression_to_string</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">expression</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/stack.html#expression_to_string"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.stack.expression_to_string" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.stack.</code><code class="descname">expression_to_string</code><span class="sig-paren">(</span><em>expression</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/stack.html#expression_to_string"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.stack.expression_to_string" title="Permalink to this definition"></a></dt>
<dd><p>Return a “pretty print” string for a expression.</p>
<p>The items are written left-to-right:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">top</span><span class="p">,</span> <span class="p">(</span><span class="n">second</span><span class="p">,</span> <span class="o">...</span><span class="p">))</span> <span class="o">-&gt;</span> <span class="s1">&#39;top second ...&#39;</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>expression</strong> (<em>stack</em>) – A stack.</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>str</p>
</dd>
</dl>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>expression</strong> (<em>stack</em>) – A stack.</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body">str</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.stack.iter_stack">
<code class="sig-prename descclassname">joy.utils.stack.</code><code class="sig-name descname">iter_stack</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">stack</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/stack.html#iter_stack"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.stack.iter_stack" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.stack.</code><code class="descname">iter_stack</code><span class="sig-paren">(</span><em>stack</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/stack.html#iter_stack"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.stack.iter_stack" title="Permalink to this definition"></a></dt>
<dd><p>Iterate through the items on the stack.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>stack</strong> (<em>stack</em>) – A stack.</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>iterator</p>
</dd>
</dl>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>stack</strong> (<em>stack</em>) – A stack.</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body">iterator</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.stack.list_to_stack">
<code class="sig-prename descclassname">joy.utils.stack.</code><code class="sig-name descname">list_to_stack</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">el</span></em>, <em class="sig-param"><span class="n">stack</span><span class="o">=</span><span class="default_value">()</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/stack.html#list_to_stack"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.stack.list_to_stack" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.stack.</code><code class="descname">list_to_stack</code><span class="sig-paren">(</span><em>el</em>, <em>stack=()</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/stack.html#list_to_stack"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.stack.list_to_stack" title="Permalink to this definition"></a></dt>
<dd><p>Convert a Python list (or other sequence) to a Joy stack:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">())))</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>el</strong> (<em>list</em>) – A Python list or other sequence (iterators and generators
won’t work because <code class="docutils literal notranslate"><span class="pre">reverse()</span></code> is called on <code class="docutils literal notranslate"><span class="pre">el</span></code>.)</p></li>
<li><p><strong>stack</strong> (<em>stack</em>) – A stack, optional, defaults to the empty stack.</p></li>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>el</strong> (<em>list</em>) – A Python list or other sequence (iterators and generators
won’t work because <code class="docutils literal notranslate"><span class="pre">reverse()</span></code> is called on <code class="docutils literal notranslate"><span class="pre">el</span></code>.)</li>
<li><strong>stack</strong> (<em>stack</em>) – A stack, optional, defaults to the empty stack.</li>
</ul>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>stack</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">stack</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.stack.pick">
<code class="sig-prename descclassname">joy.utils.stack.</code><code class="sig-name descname">pick</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">stack</span></em>, <em class="sig-param"><span class="n">n</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/stack.html#pick"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.stack.pick" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.stack.</code><code class="descname">pick</code><span class="sig-paren">(</span><em>stack</em>, <em>n</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/stack.html#pick"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.stack.pick" title="Permalink to this definition"></a></dt>
<dd><p>Return the nth item on the stack.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>stack</strong> (<em>stack</em>) – A stack.</p></li>
<li><p><strong>n</strong> (<em>int</em>) – An index into the stack.</p></li>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>stack</strong> (<em>stack</em>) – A stack.</li>
<li><strong>n</strong> (<em>int</em>) – An index into the stack.</li>
</ul>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><ul class="simple">
<li><p><strong>ValueError</strong> – if <code class="docutils literal notranslate"><span class="pre">n</span></code> is less than zero.</p></li>
<li><p><strong>IndexError</strong> – if <code class="docutils literal notranslate"><span class="pre">n</span></code> is equal to or greater than the length of <code class="docutils literal notranslate"><span class="pre">stack</span></code>.</p></li>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Raises:</th><td class="field-body"><ul class="first simple">
<li><strong>ValueError</strong> – if <code class="docutils literal notranslate"><span class="pre">n</span></code> is less than zero.</li>
<li><strong>IndexError</strong> – if <code class="docutils literal notranslate"><span class="pre">n</span></code> is equal to or greater than the length of <code class="docutils literal notranslate"><span class="pre">stack</span></code>.</li>
</ul>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>whatever</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">whatever</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.stack.stack_to_string">
<code class="sig-prename descclassname">joy.utils.stack.</code><code class="sig-name descname">stack_to_string</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">stack</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/stack.html#stack_to_string"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.stack.stack_to_string" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.stack.</code><code class="descname">stack_to_string</code><span class="sig-paren">(</span><em>stack</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/stack.html#stack_to_string"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.stack.stack_to_string" title="Permalink to this definition"></a></dt>
<dd><p>Return a “pretty print” string for a stack.</p>
<p>The items are written right-to-left:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">top</span><span class="p">,</span> <span class="p">(</span><span class="n">second</span><span class="p">,</span> <span class="o">...</span><span class="p">))</span> <span class="o">-&gt;</span> <span class="s1">&#39;... second top&#39;</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>stack</strong> (<em>stack</em>) – A stack.</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>str</p>
</dd>
</dl>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>stack</strong> (<em>stack</em>) – A stack.</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body">str</td>
</tr>
</tbody>
</table>
</dd></dl>
</div>
@@ -201,36 +218,17 @@ won’t work because <code class="docutils literal notranslate"><span class="pre
</div>
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@@ -240,24 +238,25 @@ won’t work because <code class="docutils literal notranslate"><span class="pre
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@@ -268,7 +267,7 @@ won’t work because <code class="docutils literal notranslate"><span class="pre
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<br />
<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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docs/sphinx_docs/_build/html/types.html
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@@ -1,18 +1,19 @@
<!DOCTYPE html>
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@@ -29,8 +30,6 @@
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<div class="section" id="type-inference-of-joy-expressions">
@@ -108,37 +107,26 @@ auto-compiled to Python):</p>
<span class="n">unswons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a1</span><span class="p">)</span> <span class="o">*</span>
</pre></div>
</div>
<span class="target" id="module-joy.utils.types"></span><dl class="py class">
<span class="target" id="module-joy.utils.types"></span><dl class="class">
<dt id="joy.utils.types.AnyJoyType">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">AnyJoyType</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">number</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#AnyJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.AnyJoyType" title="Permalink to this definition"></a></dt>
<em class="property">class </em><code class="descclassname">joy.utils.types.</code><code class="descname">AnyJoyType</code><span class="sig-paren">(</span><em>number</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#AnyJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.AnyJoyType" title="Permalink to this definition"></a></dt>
<dd><p>Joy type variable. Represents any Joy value.</p>
</dd></dl>
<dl class="py class">
<dt id="joy.utils.types.AnyStarJoyType">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">AnyStarJoyType</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">number</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#AnyStarJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.AnyStarJoyType" title="Permalink to this definition"></a></dt>
<dd><dl class="py attribute">
<dt id="joy.utils.types.AnyStarJoyType.kind">
<code class="sig-name descname">kind</code><a class="headerlink" href="#joy.utils.types.AnyStarJoyType.kind" title="Permalink to this definition"></a></dt>
<dd><p>alias of <a class="reference internal" href="#joy.utils.types.AnyJoyType" title="joy.utils.types.AnyJoyType"><code class="xref py py-class docutils literal notranslate"><span class="pre">AnyJoyType</span></code></a></p>
</dd></dl>
</dd></dl>
<dl class="py class">
<dl class="class">
<dt id="joy.utils.types.BooleanJoyType">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">BooleanJoyType</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">number</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#BooleanJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.BooleanJoyType" title="Permalink to this definition"></a></dt>
<dd><dl class="py attribute">
<em class="property">class </em><code class="descclassname">joy.utils.types.</code><code class="descname">BooleanJoyType</code><span class="sig-paren">(</span><em>number</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#BooleanJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.BooleanJoyType" title="Permalink to this definition"></a></dt>
<dd><dl class="attribute">
<dt id="joy.utils.types.BooleanJoyType.accept">
<code class="sig-name descname">accept</code><a class="headerlink" href="#joy.utils.types.BooleanJoyType.accept" title="Permalink to this definition"></a></dt>
<dd><p>alias of <code class="xref py py-class docutils literal notranslate"><span class="pre">builtins.bool</span></code></p>
<code class="descname">accept</code><a class="headerlink" href="#joy.utils.types.BooleanJoyType.accept" title="Permalink to this definition"></a></dt>
<dd><p>alias of <code class="xref py py-class docutils literal notranslate"><span class="pre">__builtin__.bool</span></code></p>
</dd></dl>
</dd></dl>
<dl class="py class">
<dl class="class">
<dt id="joy.utils.types.CombinatorJoyType">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">CombinatorJoyType</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">name</span></em>, <em class="sig-param"><span class="n">sec</span></em>, <em class="sig-param"><span class="n">number</span></em>, <em class="sig-param"><span class="n">expect</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#CombinatorJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.CombinatorJoyType" title="Permalink to this definition"></a></dt>
<em class="property">class </em><code class="descclassname">joy.utils.types.</code><code class="descname">CombinatorJoyType</code><span class="sig-paren">(</span><em>name</em>, <em>sec</em>, <em>number</em>, <em>expect=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#CombinatorJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.CombinatorJoyType" title="Permalink to this definition"></a></dt>
<dd><p>Represent combinators.</p>
<p>These type variables carry Joy functions that implement the
behaviour of Joy combinators and they can appear in expressions.
@@ -148,67 +136,44 @@ combinators themselves.</p>
guard against being used on invalid types.</p>
</dd></dl>
<dl class="py class">
<dl class="class">
<dt id="joy.utils.types.FloatJoyType">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">FloatJoyType</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">number</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#FloatJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.FloatJoyType" title="Permalink to this definition"></a></dt>
<dd><dl class="py attribute">
<em class="property">class </em><code class="descclassname">joy.utils.types.</code><code class="descname">FloatJoyType</code><span class="sig-paren">(</span><em>number</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#FloatJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.FloatJoyType" title="Permalink to this definition"></a></dt>
<dd><dl class="attribute">
<dt id="joy.utils.types.FloatJoyType.accept">
<code class="sig-name descname">accept</code><a class="headerlink" href="#joy.utils.types.FloatJoyType.accept" title="Permalink to this definition"></a></dt>
<dd><p>alias of <code class="xref py py-class docutils literal notranslate"><span class="pre">builtins.float</span></code></p>
<code class="descname">accept</code><a class="headerlink" href="#joy.utils.types.FloatJoyType.accept" title="Permalink to this definition"></a></dt>
<dd><p>alias of <code class="xref py py-class docutils literal notranslate"><span class="pre">__builtin__.float</span></code></p>
</dd></dl>
</dd></dl>
<dl class="py class">
<dt id="joy.utils.types.FloatStarJoyType">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">FloatStarJoyType</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">number</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#FloatStarJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.FloatStarJoyType" title="Permalink to this definition"></a></dt>
<dd><dl class="py attribute">
<dt id="joy.utils.types.FloatStarJoyType.kind">
<code class="sig-name descname">kind</code><a class="headerlink" href="#joy.utils.types.FloatStarJoyType.kind" title="Permalink to this definition"></a></dt>
<dd><p>alias of <a class="reference internal" href="#joy.utils.types.FloatJoyType" title="joy.utils.types.FloatJoyType"><code class="xref py py-class docutils literal notranslate"><span class="pre">FloatJoyType</span></code></a></p>
</dd></dl>
</dd></dl>
<dl class="py class">
<dl class="class">
<dt id="joy.utils.types.FunctionJoyType">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">FunctionJoyType</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">name</span></em>, <em class="sig-param"><span class="n">sec</span></em>, <em class="sig-param"><span class="n">number</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#FunctionJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.FunctionJoyType" title="Permalink to this definition"></a></dt>
<em class="property">class </em><code class="descclassname">joy.utils.types.</code><code class="descname">FunctionJoyType</code><span class="sig-paren">(</span><em>name</em>, <em>sec</em>, <em>number</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#FunctionJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.FunctionJoyType" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
<dl class="py class">
<dl class="class">
<dt id="joy.utils.types.IntJoyType">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">IntJoyType</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">number</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#IntJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.IntJoyType" title="Permalink to this definition"></a></dt>
<dd><dl class="py attribute">
<em class="property">class </em><code class="descclassname">joy.utils.types.</code><code class="descname">IntJoyType</code><span class="sig-paren">(</span><em>number</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#IntJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.IntJoyType" title="Permalink to this definition"></a></dt>
<dd><dl class="attribute">
<dt id="joy.utils.types.IntJoyType.accept">
<code class="sig-name descname">accept</code><a class="headerlink" href="#joy.utils.types.IntJoyType.accept" title="Permalink to this definition"></a></dt>
<dd><p>alias of <code class="xref py py-class docutils literal notranslate"><span class="pre">builtins.int</span></code></p>
<code class="descname">accept</code><a class="headerlink" href="#joy.utils.types.IntJoyType.accept" title="Permalink to this definition"></a></dt>
<dd><p>alias of <code class="xref py py-class docutils literal notranslate"><span class="pre">__builtin__.int</span></code></p>
</dd></dl>
</dd></dl>
<dl class="py class">
<dt id="joy.utils.types.IntStarJoyType">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">IntStarJoyType</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">number</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#IntStarJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.IntStarJoyType" title="Permalink to this definition"></a></dt>
<dd><dl class="py attribute">
<dt id="joy.utils.types.IntStarJoyType.kind">
<code class="sig-name descname">kind</code><a class="headerlink" href="#joy.utils.types.IntStarJoyType.kind" title="Permalink to this definition"></a></dt>
<dd><p>alias of <a class="reference internal" href="#joy.utils.types.IntJoyType" title="joy.utils.types.IntJoyType"><code class="xref py py-class docutils literal notranslate"><span class="pre">IntJoyType</span></code></a></p>
</dd></dl>
</dd></dl>
<dl class="py exception">
<dl class="exception">
<dt id="joy.utils.types.JoyTypeError">
<em class="property">exception </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">JoyTypeError</code><a class="reference internal" href="_modules/joy/utils/types.html#JoyTypeError"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.JoyTypeError" title="Permalink to this definition"></a></dt>
<em class="property">exception </em><code class="descclassname">joy.utils.types.</code><code class="descname">JoyTypeError</code><a class="reference internal" href="_modules/joy/utils/types.html#JoyTypeError"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.JoyTypeError" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
<dl class="py class">
<dl class="class">
<dt id="joy.utils.types.KleeneStar">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">KleeneStar</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">number</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#KleeneStar"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.KleeneStar" title="Permalink to this definition"></a></dt>
<em class="property">class </em><code class="descclassname">joy.utils.types.</code><code class="descname">KleeneStar</code><span class="sig-paren">(</span><em>number</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#KleeneStar"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.KleeneStar" title="Permalink to this definition"></a></dt>
<dd><p>A sequence of zero or more <cite>AnyJoyType</cite> variables would be:</p>
<blockquote>
<div><p>A*</p>
</div></blockquote>
<div>A*</div></blockquote>
<p>The <cite>A*</cite> works by splitting the universe into two alternate histories:</p>
<blockquote>
<div><p>A* → ∅</p>
@@ -218,118 +183,85 @@ guard against being used on invalid types.</p>
it turns into an <cite>AnyJoyType</cite> variable followed by itself again.</p>
<p>We have to return all universes (represented by their substitution
dicts, the “unifiers”) that don’t lead to type conflicts.</p>
<dl class="py attribute">
<dl class="attribute">
<dt id="joy.utils.types.KleeneStar.kind">
<code class="sig-name descname">kind</code><a class="headerlink" href="#joy.utils.types.KleeneStar.kind" title="Permalink to this definition"></a></dt>
<code class="descname">kind</code><a class="headerlink" href="#joy.utils.types.KleeneStar.kind" title="Permalink to this definition"></a></dt>
<dd><p>alias of <a class="reference internal" href="#joy.utils.types.AnyJoyType" title="joy.utils.types.AnyJoyType"><code class="xref py py-class docutils literal notranslate"><span class="pre">AnyJoyType</span></code></a></p>
</dd></dl>
</dd></dl>
<dl class="py class">
<dl class="class">
<dt id="joy.utils.types.NumberJoyType">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">NumberJoyType</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">number</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#NumberJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.NumberJoyType" title="Permalink to this definition"></a></dt>
<em class="property">class </em><code class="descclassname">joy.utils.types.</code><code class="descname">NumberJoyType</code><span class="sig-paren">(</span><em>number</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#NumberJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.NumberJoyType" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
<dl class="py class">
<dt id="joy.utils.types.NumberStarJoyType">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">NumberStarJoyType</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">number</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#NumberStarJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.NumberStarJoyType" title="Permalink to this definition"></a></dt>
<dd><dl class="py attribute">
<dt id="joy.utils.types.NumberStarJoyType.kind">
<code class="sig-name descname">kind</code><a class="headerlink" href="#joy.utils.types.NumberStarJoyType.kind" title="Permalink to this definition"></a></dt>
<dd><p>alias of <a class="reference internal" href="#joy.utils.types.NumberJoyType" title="joy.utils.types.NumberJoyType"><code class="xref py py-class docutils literal notranslate"><span class="pre">NumberJoyType</span></code></a></p>
</dd></dl>
</dd></dl>
<dl class="py class">
<dl class="class">
<dt id="joy.utils.types.StackJoyType">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">StackJoyType</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">number</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#StackJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.StackJoyType" title="Permalink to this definition"></a></dt>
<dd><dl class="py attribute">
<em class="property">class </em><code class="descclassname">joy.utils.types.</code><code class="descname">StackJoyType</code><span class="sig-paren">(</span><em>number</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#StackJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.StackJoyType" title="Permalink to this definition"></a></dt>
<dd><dl class="attribute">
<dt id="joy.utils.types.StackJoyType.accept">
<code class="sig-name descname">accept</code><a class="headerlink" href="#joy.utils.types.StackJoyType.accept" title="Permalink to this definition"></a></dt>
<dd><p>alias of <code class="xref py py-class docutils literal notranslate"><span class="pre">builtins.tuple</span></code></p>
<code class="descname">accept</code><a class="headerlink" href="#joy.utils.types.StackJoyType.accept" title="Permalink to this definition"></a></dt>
<dd><p>alias of <code class="xref py py-class docutils literal notranslate"><span class="pre">__builtin__.tuple</span></code></p>
</dd></dl>
</dd></dl>
<dl class="py class">
<dt id="joy.utils.types.StackStarJoyType">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">StackStarJoyType</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">number</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#StackStarJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.StackStarJoyType" title="Permalink to this definition"></a></dt>
<dd><dl class="py attribute">
<dt id="joy.utils.types.StackStarJoyType.kind">
<code class="sig-name descname">kind</code><a class="headerlink" href="#joy.utils.types.StackStarJoyType.kind" title="Permalink to this definition"></a></dt>
<dd><p>alias of <a class="reference internal" href="#joy.utils.types.StackJoyType" title="joy.utils.types.StackJoyType"><code class="xref py py-class docutils literal notranslate"><span class="pre">StackJoyType</span></code></a></p>
</dd></dl>
</dd></dl>
<dl class="py class">
<dl class="class">
<dt id="joy.utils.types.SymbolJoyType">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">SymbolJoyType</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">name</span></em>, <em class="sig-param"><span class="n">sec</span></em>, <em class="sig-param"><span class="n">number</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#SymbolJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.SymbolJoyType" title="Permalink to this definition"></a></dt>
<em class="property">class </em><code class="descclassname">joy.utils.types.</code><code class="descname">SymbolJoyType</code><span class="sig-paren">(</span><em>name</em>, <em>sec</em>, <em>number</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#SymbolJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.SymbolJoyType" title="Permalink to this definition"></a></dt>
<dd><p>Represent non-combinator functions.</p>
<p>These type variables carry the stack effect comments and can
appear in expressions (as in quoted programs.)</p>
</dd></dl>
<dl class="py class">
<dl class="class">
<dt id="joy.utils.types.TextJoyType">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">TextJoyType</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">number</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#TextJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.TextJoyType" title="Permalink to this definition"></a></dt>
<dd><dl class="py attribute">
<em class="property">class </em><code class="descclassname">joy.utils.types.</code><code class="descname">TextJoyType</code><span class="sig-paren">(</span><em>number</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#TextJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.TextJoyType" title="Permalink to this definition"></a></dt>
<dd><dl class="attribute">
<dt id="joy.utils.types.TextJoyType.accept">
<code class="sig-name descname">accept</code><a class="headerlink" href="#joy.utils.types.TextJoyType.accept" title="Permalink to this definition"></a></dt>
<dd><p>alias of <code class="xref py py-class docutils literal notranslate"><span class="pre">past.types.basestring.basestring</span></code></p>
<code class="descname">accept</code><a class="headerlink" href="#joy.utils.types.TextJoyType.accept" title="Permalink to this definition"></a></dt>
<dd><p>alias of <code class="xref py py-class docutils literal notranslate"><span class="pre">__builtin__.basestring</span></code></p>
</dd></dl>
</dd></dl>
<dl class="py class">
<dt id="joy.utils.types.TextStarJoyType">
<em class="property">class </em><code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">TextStarJoyType</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">number</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#TextStarJoyType"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.TextStarJoyType" title="Permalink to this definition"></a></dt>
<dd><dl class="py attribute">
<dt id="joy.utils.types.TextStarJoyType.kind">
<code class="sig-name descname">kind</code><a class="headerlink" href="#joy.utils.types.TextStarJoyType.kind" title="Permalink to this definition"></a></dt>
<dd><p>alias of <a class="reference internal" href="#joy.utils.types.TextJoyType" title="joy.utils.types.TextJoyType"><code class="xref py py-class docutils literal notranslate"><span class="pre">TextJoyType</span></code></a></p>
</dd></dl>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.types.compilable">
<code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">compilable</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">f</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#compilable"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.compilable" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.types.</code><code class="descname">compilable</code><span class="sig-paren">(</span><em>f</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#compilable"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.compilable" title="Permalink to this definition"></a></dt>
<dd><p>Return True if a stack effect represents a function that can be
automatically compiled (to Python), False otherwise.</p>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.types.compile_">
<code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">compile_</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">name</span></em>, <em class="sig-param"><span class="n">f</span></em>, <em class="sig-param"><span class="n">doc</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#compile_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.compile_" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.types.</code><code class="descname">compile_</code><span class="sig-paren">(</span><em>name</em>, <em>f</em>, <em>doc=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#compile_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.compile_" title="Permalink to this definition"></a></dt>
<dd><p>Return a string of Python code implementing the function described
by the stack effect. If no doc string is passed doc_from_stack_effect()
is used to generate one.</p>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.types.compose">
<code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">compose</code><span class="sig-paren">(</span><em class="sig-param"><span class="o">*</span><span class="n">functions</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#compose"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.compose" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.types.</code><code class="descname">compose</code><span class="sig-paren">(</span><em>*functions</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#compose"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.compose" title="Permalink to this definition"></a></dt>
<dd><p>Return the stack effect of the composition of some of stack effects.</p>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.types.delabel">
<code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">delabel</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">f</span></em>, <em class="sig-param"><span class="n">seen</span><span class="o">=</span><span class="default_value">None</span></em>, <em class="sig-param"><span class="n">c</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#delabel"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.delabel" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.types.</code><code class="descname">delabel</code><span class="sig-paren">(</span><em>f</em>, <em>seen=None</em>, <em>c=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#delabel"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.delabel" title="Permalink to this definition"></a></dt>
<dd><p>Fix up type variable numbers after relabel().</p>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.types.doc_from_stack_effect">
<code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">doc_from_stack_effect</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">inputs</span></em>, <em class="sig-param"><span class="n">outputs</span><span class="o">=</span><span class="default_value">'??', ()</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#doc_from_stack_effect"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.doc_from_stack_effect" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.types.</code><code class="descname">doc_from_stack_effect</code><span class="sig-paren">(</span><em>inputs</em>, <em>outputs=('??'</em>, <em>())</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#doc_from_stack_effect"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.doc_from_stack_effect" title="Permalink to this definition"></a></dt>
<dd><p>Return a crude string representation of a stack effect.</p>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.types.infer">
<code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">infer</code><span class="sig-paren">(</span><em class="sig-param"><span class="o">*</span><span class="n">expression</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#infer"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.infer" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.types.</code><code class="descname">infer</code><span class="sig-paren">(</span><em>*expression</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#infer"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.infer" title="Permalink to this definition"></a></dt>
<dd><p>Return a list of stack effects for a Joy expression.</p>
<p>For example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">h</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">cons</span><span class="p">,</span> <span class="n">cons</span><span class="p">)</span>
@@ -343,43 +275,43 @@ is used to generate one.</p>
</div>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.types.meta_compose">
<code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">meta_compose</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">F</span></em>, <em class="sig-param"><span class="n">G</span></em>, <em class="sig-param"><span class="n">e</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#meta_compose"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.meta_compose" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.types.</code><code class="descname">meta_compose</code><span class="sig-paren">(</span><em>F</em>, <em>G</em>, <em>e</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#meta_compose"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.meta_compose" title="Permalink to this definition"></a></dt>
<dd><p>Yield the stack effects of the composition of two lists of stack
effects. An expression is carried along and updated and yielded.</p>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.types.poly_compose">
<code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">poly_compose</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">f</span></em>, <em class="sig-param"><span class="n">g</span></em>, <em class="sig-param"><span class="n">e</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#poly_compose"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.poly_compose" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.types.</code><code class="descname">poly_compose</code><span class="sig-paren">(</span><em>f</em>, <em>g</em>, <em>e</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#poly_compose"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.poly_compose" title="Permalink to this definition"></a></dt>
<dd><p>Yield the stack effects of the composition of two stack effects. An
expression is carried along and updated and yielded.</p>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.types.reify">
<code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">reify</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">meaning</span></em>, <em class="sig-param"><span class="n">name</span></em>, <em class="sig-param"><span class="n">seen</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#reify"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.reify" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.types.</code><code class="descname">reify</code><span class="sig-paren">(</span><em>meaning</em>, <em>name</em>, <em>seen=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#reify"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.reify" title="Permalink to this definition"></a></dt>
<dd><p>Apply substitution dict to term, returning new term.</p>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.types.relabel">
<code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">relabel</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">left</span></em>, <em class="sig-param"><span class="n">right</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#relabel"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.relabel" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.types.</code><code class="descname">relabel</code><span class="sig-paren">(</span><em>left</em>, <em>right</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#relabel"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.relabel" title="Permalink to this definition"></a></dt>
<dd><p>Re-number type variables to avoid collisions between stack effects.</p>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.types.type_check">
<code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">type_check</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">name</span></em>, <em class="sig-param"><span class="n">stack</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#type_check"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.type_check" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.types.</code><code class="descname">type_check</code><span class="sig-paren">(</span><em>name</em>, <em>stack</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#type_check"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.type_check" title="Permalink to this definition"></a></dt>
<dd><p>Trinary predicate. True if named function type-checks, False if it
fails, None if it’s indeterminate (because I haven’t entered it into
the FUNCTIONS dict yet.)</p>
</dd></dl>
<dl class="py function">
<dl class="function">
<dt id="joy.utils.types.uni_unify">
<code class="sig-prename descclassname">joy.utils.types.</code><code class="sig-name descname">uni_unify</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">u</span></em>, <em class="sig-param"><span class="n">v</span></em>, <em class="sig-param"><span class="n">s</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#uni_unify"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.uni_unify" title="Permalink to this definition"></a></dt>
<code class="descclassname">joy.utils.types.</code><code class="descname">uni_unify</code><span class="sig-paren">(</span><em>u</em>, <em>v</em>, <em>s=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/types.html#uni_unify"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.types.uni_unify" title="Permalink to this definition"></a></dt>
<dd><p>Return a substitution dict representing a unifier for u and v.</p>
</dd></dl>
@@ -451,36 +383,17 @@ far.</p>
</div>
</div>
</div>
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<h1 class="logo"><a href="index.html">Thun</a></h1>
<h3>Navigation</h3>
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<li class="toctree-l1"><a class="reference internal" href="stack.html">Stack or Quote or Sequence or List…</a></li>
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<h3><a href="index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">Type Inference of Joy Expressions</a><ul>
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@@ -490,24 +403,25 @@ far.</p>
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@@ -518,7 +432,7 @@ far.</p>
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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docs/sphinx_docs/notebooks/Derivatives_of_Regular_Expressions.rst
+141 -141
View File
@@ -1,69 +1,69 @@
∂RE
===
Brzozowski's Derivatives of Regular Expressions
Brzozowski’s Derivatives of Regular Expressions
-----------------------------------------------
Legend:
::
∧ intersection
∨ union
∘ concatenation (see below)
¬ complement
ϕ empty set (aka ∅)
λ singleton set containing just the empty string
I set of all letters in alphabet
∧ intersection
∨ union
∘ concatenation (see below)
¬ complement
ϕ empty set (aka ∅)
λ singleton set containing just the empty string
I set of all letters in alphabet
Derivative of a set ``R`` of strings and a string ``a``:
::
∂a(R)
∂a(R)
∂a(a) → λ
∂a(λ) → ϕ
∂a(ϕ) → ϕ
∂a(¬a) → ϕ
∂a(R*) → ∂a(R)∘R*
∂a(¬R) → ¬∂a(R)
∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S)
∂a(R ∧ S) → ∂a(R) ∧ ∂a(S)
∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)
∂a(a) → λ
∂a(λ) → ϕ
∂a(ϕ) → ϕ
∂a(¬a) → ϕ
∂a(R*) → ∂a(R)∘R*
∂a(¬R) → ¬∂a(R)
∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S)
∂a(R ∧ S) → ∂a(R) ∧ ∂a(S)
∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)
∂ab(R) = ∂b(∂a(R))
∂ab(R) = ∂b(∂a(R))
Auxiliary predicate function ``δ`` (I call it ``nully``) returns either
``λ`` if ``λ ⊆ R`` or ``ϕ`` otherwise:
::
δ(a) → ϕ
δ(λ) → λ
δ(ϕ) → ϕ
δ(R*) → λ
δ(¬R) δ(R)≟ϕ → λ
δ(¬R) δ(R)≟λ → ϕ
δ(R∘S) → δ(R) ∧ δ(S)
δ(R ∧ S) → δ(R) ∧ δ(S)
δ(R ∨ S) → δ(R) ∨ δ(S)
δ(a) → ϕ
δ(λ) → λ
δ(ϕ) → ϕ
δ(R*) → λ
δ(¬R) δ(R)≟ϕ → λ
δ(¬R) δ(R)≟λ → ϕ
δ(R∘S) → δ(R) ∧ δ(S)
δ(R ∧ S) → δ(R) ∧ δ(S)
δ(R ∨ S) → δ(R) ∨ δ(S)
Some rules we will use later for "compaction":
Some rules we will use later for “compaction”:
::
R ∧ ϕ = ϕ ∧ R = ϕ
R ∧ ϕ = ϕ ∧ R = ϕ
R ∧ I = I ∧ R = R
R ∧ I = I ∧ R = R
R ∨ ϕ = ϕ ∨ R = R
R ∨ ϕ = ϕ ∨ R = R
R ∨ I = I ∨ R = I
R ∨ I = I ∨ R = I
R∘ϕ = ϕ∘R = ϕ
R∘ϕ = ϕ∘R = ϕ
R∘λ = λ∘R = R
R∘λ = λ∘R = R
Concatination of sets: for two sets A and B the set A∘B is defined as:
@@ -71,7 +71,7 @@ Concatination of sets: for two sets A and B the set A∘B is defined as:
E.g.:
{'a', 'b'}∘{'c', 'd'} → {'ac', 'ad', 'bc', 'bd'}
{‘a’, ‘b’}∘{‘c’, ‘d’} → {‘ac’, ‘ad’, ‘bc’, ‘bd’}
Implementation
--------------
@@ -94,11 +94,11 @@ The empty set and the set of just the empty string.
Two-letter Alphabet
~~~~~~~~~~~~~~~~~~~
I'm only going to use two symbols (at first) becaase this is enough to
I’m only going to use two symbols (at first) becaase this is enough to
illustrate the algorithm and because you can represent any other
alphabet with two symbols (if you had to.)
I chose the names ``O`` and ``l`` (uppercase "o" and lowercase "L") to
I chose the names ``O`` and ``l`` (uppercase “o” and lowercase “L”) to
look like ``0`` and ``1`` (zero and one) respectively.
.. code:: ipython2
@@ -108,18 +108,18 @@ look like ``0`` and ``1`` (zero and one) respectively.
Representing Regular Expressions
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To represent REs in Python I'm going to use tagged tuples. A *regular
To represent REs in Python I’m going to use tagged tuples. A *regular
expression* is one of:
::
O
l
(KSTAR, R)
(NOT, R)
(AND, R, S)
(CONS, R, S)
(OR, R, S)
O
l
(KSTAR, R)
(NOT, R)
(AND, R, S)
(CONS, R, S)
(OR, R, S)
Where ``R`` and ``S`` stand for *regular expressions*.
@@ -169,11 +169,11 @@ String Representation of RE Datastructures
``I``
~~~~~
Match anything. Often spelled "."
Match anything. Often spelled “.”
::
I = (0|1)*
I = (0|1)*
.. code:: ipython2
@@ -196,8 +196,8 @@ The example expression from Brzozowski:
::
(.111.) & (.01 + 11*)'
a & (b + c)'
(.111.) & (.01 + 11*)'
a & (b + c)'
Note that it contains one of everything.
@@ -221,7 +221,7 @@ Note that it contains one of everything.
``nully()``
~~~~~~~~~~~
Let's get that auxiliary predicate function ``δ`` out of the way.
Let’s get that auxiliary predicate function ``δ`` out of the way.
.. code:: ipython2
@@ -256,10 +256,10 @@ Let's get that auxiliary predicate function ``δ`` out of the way.
r, s = nully(R[1]), nully(R[2])
return r & s if tag in {AND, CONS} else r | s
No "Compaction"
No “Compaction”
~~~~~~~~~~~~~~~
This is the straightforward version with no "compaction". It works fine,
This is the straightforward version with no “compaction”. It works fine,
but does waaaay too much work because the expressions grow each
derivation.
@@ -359,7 +359,7 @@ are *pure* so this is fine.
result = self.mem[key] = self.f(key)
return result
With "Compaction"
With “Compaction”
~~~~~~~~~~~~~~~~~
This version uses the rules above to perform compaction. It keeps the
@@ -409,8 +409,8 @@ expressions from growing too large.
return derv
Let's try it out...
-------------------
Let’s try it out…
-----------------
(FIXME: redo.)
@@ -460,27 +460,27 @@ Should match:
::
(.111.) & ((.01 | 11*)')
(.111.) & ((.01 | 11*)')
92 / 122
92 / 122
92 / 122
92 / 122
(.01 )'
(.01 | 1 )'
(.01 | ^ )'
(.01 | 1*)'
(.111.) & ((.01 | 1 )')
(.111. | 11.) & ((.01 | ^ )')
(.111. | 11.) & ((.01 | 1*)')
(.111. | 11. | 1.) & ((.01 )')
(.111. | 11. | 1.) & ((.01 | 1*)')
(.01 )'
(.01 | 1 )'
(.01 | ^ )'
(.01 | 1*)'
(.111.) & ((.01 | 1 )')
(.111. | 11.) & ((.01 | ^ )')
(.111. | 11.) & ((.01 | 1*)')
(.111. | 11. | 1.) & ((.01 )')
(.111. | 11. | 1.) & ((.01 | 1*)')
Larger Alphabets
----------------
We could parse larger alphabets by defining patterns for e.g. each byte
We could parse larger alphabets by defining patterns for e.g. each byte
of the ASCII code. Or we can generalize this code. If you study the code
above you'll see that we never use the "set-ness" of the symbols ``O``
above you’ll see that we never use the “set-ness” of the symbols ``O``
and ``l``. The only time Python set operators (``&`` and ``|``) appear
is in the ``nully()`` function, and there they operate on (recursively
computed) outputs of that function, never ``O`` and ``l``.
@@ -489,33 +489,33 @@ What if we try:
::
(OR, O, l)
(OR, O, l)
∂1((OR, O, l))
∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)
∂1(O) ∨ ∂1(l)
∂a(¬a) → ϕ
ϕ ∨ ∂1(l)
∂a(a) → λ
ϕ ∨ λ
ϕ ∨ R = R
λ
∂1((OR, O, l))
∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)
∂1(O) ∨ ∂1(l)
∂a(¬a) → ϕ
ϕ ∨ ∂1(l)
∂a(a) → λ
ϕ ∨ λ
ϕ ∨ R = R
λ
And compare it to:
::
{'0', '1')
{'0', '1')
∂1({'0', '1'))
∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)
∂1({'0')) ∨ ∂1({'1'))
∂a(¬a) → ϕ
ϕ ∨ ∂1({'1'))
∂a(a) → λ
ϕ ∨ λ
ϕ ∨ R = R
λ
∂1({'0', '1'))
∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)
∂1({'0')) ∨ ∂1({'1'))
∂a(¬a) → ϕ
ϕ ∨ ∂1({'1'))
∂a(a) → λ
ϕ ∨ λ
ϕ ∨ R = R
λ
This suggests that we should be able to alter the functions above to
detect sets and deal with them appropriately. Exercise for the Reader
@@ -529,9 +529,9 @@ machine transition table.
::
.111. & (.01 + 11*)'
.111. & (.01 + 11*)'
Says, "Three or more 1's and not ending in 01 nor composed of all 1's."
Says, “Three or more 1’s and not ending in 01 nor composed of all 1’s.”
.. figure:: attachment:omg.svg
:alt: omg.svg
@@ -540,32 +540,32 @@ Says, "Three or more 1's and not ending in 01 nor composed of all 1's."
Start at ``a`` and follow the transition arrows according to their
labels. Accepting states have a double outline. (Graphic generated with
`Dot from Graphviz <http://www.graphviz.org/>`__.) You'll see that only
`Dot from Graphviz <http://www.graphviz.org/>`__.) You’ll see that only
paths that lead to one of the accepting states will match the regular
expression. All other paths will terminate at one of the non-accepting
states.
There's a happy path to ``g`` along 111:
There’s a happy path to ``g`` along 111:
::
a→c→e→g
a→c→e→g
After you reach ``g`` you're stuck there eating 1's until you see a 0,
which takes you to the ``i→j→i|i→j→h→i`` "trap". You can't reach any
After you reach ``g`` you’re stuck there eating 1’s until you see a 0,
which takes you to the ``i→j→i|i→j→h→i`` “trap”. You can’t reach any
other states from those two loops.
If you see a 0 before you see 111 you will reach ``b``, which forms
another "trap" with ``d`` and ``f``. The only way out is another happy
another “trap” with ``d`` and ``f``. The only way out is another happy
path along 111 to ``h``:
::
b→d→f→h
b→d→f→h
Once you have reached ``h`` you can see as many 1's or as many 0' in a
row and still be either still at ``h`` (for 1's) or move to ``i`` (for
0's). If you find yourself at ``i`` you can see as many 0's, or
Once you have reached ``h`` you can see as many 1’s or as many 0’ in a
row and still be either still at ``h`` (for 1’s) or move to ``i`` (for
0’s). If you find yourself at ``i`` you can see as many 0’s, or
repetitions of 10, as there are, but if you see just a 1 you move to
``j``.
@@ -575,14 +575,14 @@ RE to FSM
So how do we get the state machine from the regular expression?
It turns out that each RE is effectively a state, and each arrow points
to the derivative RE in respect to the arrow's symbol.
to the derivative RE in respect to the arrow’s symbol.
If we label the initial RE ``a``, we can say:
::
a --0--> ∂0(a)
a --1--> ∂1(a)
a --0--> ∂0(a)
a --1--> ∂1(a)
And so on, each new unique RE is a new state in the FSM table.
@@ -590,18 +590,18 @@ Here are the derived REs at each state:
::
a = (.111.) & ((.01 | 11*)')
b = (.111.) & ((.01 | 1)')
c = (.111. | 11.) & ((.01 | 1*)')
d = (.111. | 11.) & ((.01 | ^)')
e = (.111. | 11. | 1.) & ((.01 | 1*)')
f = (.111. | 11. | 1.) & ((.01)')
g = (.01 | 1*)'
h = (.01)'
i = (.01 | 1)'
j = (.01 | ^)'
a = (.111.) & ((.01 | 11*)')
b = (.111.) & ((.01 | 1)')
c = (.111. | 11.) & ((.01 | 1*)')
d = (.111. | 11.) & ((.01 | ^)')
e = (.111. | 11. | 1.) & ((.01 | 1*)')
f = (.111. | 11. | 1.) & ((.01)')
g = (.01 | 1*)'
h = (.01)'
i = (.01 | 1)'
j = (.01 | ^)'
You can see the one-way nature of the ``g`` state and the ``hij`` "trap"
You can see the one-way nature of the ``g`` state and the ``hij`` “trap”
in the way that the ``.111.`` on the left-hand side of the ``&``
disappears once it has been matched.
@@ -764,16 +764,16 @@ Drive a FSM
There are *lots* of FSM libraries already. Once you have the state
transition table they should all be straightforward to use. State
Machine code is very simple. Just for fun, here is an implementation in
Python that imitates what "compiled" FSM code might look like in an
"unrolled" form. Most FSM code uses a little driver loop and a table
Python that imitates what “compiled” FSM code might look like in an
“unrolled” form. Most FSM code uses a little driver loop and a table
datastructure, the code below instead acts like JMP instructions
("jump", or GOTO in higher-level-but-still-low-level languages) to
(“jump”, or GOTO in higher-level-but-still-low-level languages) to
hard-code the information in the table into a little patch of branches.
Trampoline Function
^^^^^^^^^^^^^^^^^^^
Python has no GOTO statement but we can fake it with a "trampoline"
Python has no GOTO statement but we can fake it with a “trampoline”
function.
.. code:: ipython2
@@ -790,8 +790,8 @@ function.
Stream Functions
^^^^^^^^^^^^^^^^
Little helpers to process the iterator of our data (a "stream" of "1"
and "0" characters, not bits.)
Little helpers to process the iterator of our data (a “stream” of “1”
and “0” characters, not bits.)
.. code:: ipython2
@@ -831,7 +831,7 @@ labels.)
Note that the implementations of ``h`` and ``g`` are identical ergo
``h = g`` and we could eliminate one in the code but ``h`` is an
accepting state and ``g`` isn't.
accepting state and ``g`` isn’t.
.. code:: ipython2
@@ -885,7 +885,7 @@ Reversing the Derivatives to Generate Matching Strings
------------------------------------------------------
(UNFINISHED) Brzozowski also shewed how to go from the state machine to
strings and expressions...
strings and expressions…
Each of these states is just a name for a Brzozowskian RE, and so, other
than the initial state ``a``, they can can be described in terms of the
@@ -893,54 +893,54 @@ derivative-with-respect-to-N of some other state/RE:
::
c = d1(a)
b = d0(a)
b = d0(c)
...
i = d0(j)
j = d1(i)
c = d1(a)
b = d0(a)
b = d0(c)
...
i = d0(j)
j = d1(i)
Consider:
::
c = d1(a)
b = d0(c)
c = d1(a)
b = d0(c)
Substituting:
::
b = d0(d1(a))
b = d0(d1(a))
Unwrapping:
::
b = d10(a)
b = d10(a)
'''
’’’
::
j = d1(d0(j))
j = d1(d0(j))
Unwrapping:
::
j = d1(d0(j)) = d01(j)
j = d1(d0(j)) = d01(j)
We have a loop or "fixed point".
We have a loop or “fixed point”.
::
j = d01(j) = d0101(j) = d010101(j) = ...
j = d01(j) = d0101(j) = d010101(j) = ...
hmm...
hmm…
::
j = (01)*
j = (01)*
docs/sphinx_docs/notebooks/Generator_Programs.rst
+73 -74
View File
@@ -11,51 +11,51 @@ Consider the ``x`` combinator:
::
x == dup i
x == dup i
We can apply it to a quoted program consisting of some value ``a`` and
some function ``B``:
::
[a B] x
[a B] a B
[a B] x
[a B] a B
Let ``B`` function ``swap`` the ``a`` with the quote and run some
function ``C`` on it to generate a new value ``b``:
::
B == swap [C] dip
B == swap [C] dip
[a B] a B
[a B] a swap [C] dip
a [a B] [C] dip
a C [a B]
b [a B]
[a B] a B
[a B] a swap [C] dip
a [a B] [C] dip
a C [a B]
b [a B]
Now discard the quoted ``a`` with ``rest`` then ``cons`` ``b``:
::
b [a B] rest cons
b [B] cons
[b B]
b [a B] rest cons
b [B] cons
[b B]
Altogether, this is the definition of ``B``:
::
B == swap [C] dip rest cons
B == swap [C] dip rest cons
We can make a generator for the Natural numbers (0, 1, 2, ...) by using
We can make a generator for the Natural numbers (0, 1, 2, …) by using
``0`` for ``a`` and ``[dup ++]`` for ``[C]``:
::
[0 swap [dup ++] dip rest cons]
[0 swap [dup ++] dip rest cons]
Let's try it:
Let’s try it:
.. code:: ipython2
@@ -128,32 +128,32 @@ our quoted program:
::
a [C] G
-------------------------
[a swap [C] direco]
a [C] G
-------------------------
[a swap [C] direco]
Working in reverse:
::
[a swap [C] direco] cons
a [swap [C] direco] concat
a [swap] [[C] direco] swap
a [[C] direco] [swap]
a [C] [direco] cons [swap]
[a swap [C] direco] cons
a [swap [C] direco] concat
a [swap] [[C] direco] swap
a [[C] direco] [swap]
a [C] [direco] cons [swap]
Reading from the bottom up:
::
G == [direco] cons [swap] swap concat cons
G == [direco] cons [swap] swoncat cons
G == [direco] cons [swap] swap concat cons
G == [direco] cons [swap] swoncat cons
.. code:: ipython2
define('G == [direco] cons [swap] swoncat cons')
Let's try it out:
Let’s try it out:
.. code:: ipython2
@@ -208,20 +208,20 @@ Generating Multiples of Three and Five
--------------------------------------
Look at the treatment of the Project Euler Problem One in the
"Developing a Program" notebook and you'll see that we might be
“Developing a Program” notebook and you’ll see that we might be
interested in generating an endless cycle of:
::
3 2 1 3 1 2 3
3 2 1 3 1 2 3
To do this we want to encode the numbers as pairs of bits in a single
int:
::
3 2 1 3 1 2 3
0b 11 10 01 11 01 10 11 == 14811
3 2 1 3 1 2 3
0b 11 10 01 11 01 10 11 == 14811
And pick them off by masking with 3 (binary 11) and then shifting the
int right two bits.
@@ -250,7 +250,7 @@ int right two bits.
3 3702 .
If we plug ``14811`` and ``[PE1.1]`` into our generator form...
If we plug ``14811`` and ``[PE1.1]`` into our generator form…
.. code:: ipython2
@@ -262,8 +262,7 @@ If we plug ``14811`` and ``[PE1.1]`` into our generator form...
[14811 swap [PE1.1] direco]
...we get a generator that works for seven cycles before it reaches
zero:
…we get a generator that works for seven cycles before it reaches zero:
.. code:: ipython2
@@ -306,15 +305,15 @@ if so.
(It would be more efficient to reset the int every seven cycles but
that's a little beyond the scope of this article. This solution does
extra work, but not much, and we're not using it "in production" as they
that’s a little beyond the scope of this article. This solution does
extra work, but not much, and we’re not using it “in production” as they
say.)
Run 466 times
~~~~~~~~~~~~~
In the PE1 problem we are asked to sum all the multiples of three and
five less than 1000. It's worked out that we need to use all seven
five less than 1000. It’s worked out that we need to use all seven
numbers sixty-six times and then four more.
.. code:: ipython2
@@ -375,76 +374,76 @@ Consider:
::
[b a F] x
[b a F] b a F
[b a F] x
[b a F] b a F
The obvious first thing to do is just add ``b`` and ``a``:
::
[b a F] b a +
[b a F] b+a
[b a F] b a +
[b a F] b+a
From here we want to arrive at:
::
b [b+a b F]
b [b+a b F]
Let's start with ``swons``:
Let’s start with ``swons``:
::
[b a F] b+a swons
[b+a b a F]
[b a F] b+a swons
[b+a b a F]
Considering this quote as a stack:
::
F a b b+a
F a b b+a
We want to get it to:
::
F b b+a b
F b b+a b
So:
::
F a b b+a popdd over
F b b+a b
F a b b+a popdd over
F b b+a b
And therefore:
::
[b+a b a F] [popdd over] infra
[b b+a b F]
[b+a b a F] [popdd over] infra
[b b+a b F]
But we can just use ``cons`` to carry ``b+a`` into the quote:
::
[b a F] b+a [popdd over] cons infra
[b a F] [b+a popdd over] infra
[b b+a b F]
[b a F] b+a [popdd over] cons infra
[b a F] [b+a popdd over] infra
[b b+a b F]
Lastly:
::
[b b+a b F] uncons
b [b+a b F]
[b b+a b F] uncons
b [b+a b F]
Putting it all together:
::
F == + [popdd over] cons infra uncons
fib_gen == [1 1 F]
F == + [popdd over] cons infra uncons
fib_gen == [1 1 F]
.. code:: ipython2
@@ -467,8 +466,8 @@ Putting it all together:
Project Euler Problem Two
-------------------------
By considering the terms in the Fibonacci sequence whose values do
not exceed four million, find the sum of the even-valued terms.
By considering the terms in the Fibonacci sequence whose values do
not exceed four million, find the sum of the even-valued terms.
Now that we have a generator for the Fibonacci sequence, we need a
function that adds a term in the sequence to a sum if it is even, and
@@ -479,13 +478,13 @@ function that adds a term in the sequence to a sum if it is even, and
define('PE2.1 == dup 2 % [+] [pop] branch')
And a predicate function that detects when the terms in the series
"exceed four million".
“exceed four million”.
.. code:: ipython2
define('>4M == 4000000 >')
Now it's straightforward to define ``PE2`` as a recursive function that
Now it’s straightforward to define ``PE2`` as a recursive function that
generates terms in the Fibonacci sequence until they exceed four million
and sums the even ones.
@@ -503,18 +502,18 @@ and sums the even ones.
4613732
Here's the collected program definitions:
Here’s the collected program definitions:
::
fib == + swons [popdd over] infra uncons
fib_gen == [1 1 fib]
fib == + swons [popdd over] infra uncons
fib_gen == [1 1 fib]
even == dup 2 %
>4M == 4000000 >
even == dup 2 %
>4M == 4000000 >
PE2.1 == even [+] [pop] branch
PE2 == 0 fib_gen x [pop >4M] [popop] [[PE2.1] dip x] primrec
PE2.1 == even [+] [pop] branch
PE2 == 0 fib_gen x [pop >4M] [popop] [[PE2.1] dip x] primrec
Even-valued Fibonacci Terms
~~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -523,16 +522,16 @@ Using ``o`` for odd and ``e`` for even:
::
o + o = e
e + e = e
o + e = o
o + o = e
e + e = e
o + e = o
So the Fibonacci sequence considered in terms of just parity would be:
::
o o e o o e o o e o o e o o e o o e
1 1 2 3 5 8 . . .
o o e o o e o o e o o e o o e o o e
1 1 2 3 5 8 . . .
Every third term is even.
docs/sphinx_docs/notebooks/Intro.rst
+11 -4
View File
@@ -22,8 +22,8 @@ that you start by running the package:
::
$ python -m joy
Joypy - Copyright © 2017 Simon Forman
$ python3 -m joy
Thun - Copyright © 2017 Simon Forman
This program comes with ABSOLUTELY NO WARRANTY; for details type "warranty".
This is free software, and you are welcome to redistribute it
under certain conditions; type "sharing" for details.
@@ -31,7 +31,7 @@ that you start by running the package:
docs for a word.
<-top
<-top
joy? _
@@ -40,7 +40,14 @@ You can enter Joy notation at the prompt and a :doc:`trace of evaluation <../pre
be printed followed by the stack and prompt again::
joy? 23 sqr 18 +
. 23 sqr 18 +
547 <-top
joy?
There is a `trace` combinator::
joy? 23 [sqr 18 +] trace
23 . sqr 18 +
23 . dup mul 18 +
23 23 . mul 18 +
docs/sphinx_docs/notebooks/Newton-Raphson.rst
+57 -57
View File
@@ -1,10 +1,10 @@
`Newton's method <https://en.wikipedia.org/wiki/Newton%27s_method>`__
`Newton’s method <https://en.wikipedia.org/wiki/Newton%27s_method>`__
=====================================================================
Let's use the Newton-Raphson method for finding the root of an equation
Let’s use the Newton-Raphson method for finding the root of an equation
to write a function that can compute the square root of a number.
Cf. `"Why Functional Programming Matters" by John
Cf. `“Why Functional Programming Matters” by John
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__
.. code:: ipython2
@@ -20,9 +20,9 @@ computes the next approximation:
::
a F
---------
a'
a F
---------
a'
A Function to Compute the Next Approximation
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -34,17 +34,17 @@ square root:
::
a n over / + 2 /
a n a / + 2 /
a n/a + 2 /
a+n/a 2 /
(a+n/a)/2
a n over / + 2 /
a n a / + 2 /
a n/a + 2 /
a+n/a 2 /
(a+n/a)/2
The function we want has the argument ``n`` in it:
::
F == n over / + 2 /
F == n over / + 2 /
Make it into a Generator
~~~~~~~~~~~~~~~~~~~~~~~~
@@ -53,27 +53,27 @@ Our generator would be created by:
::
a [dup F] make_generator
a [dup F] make_generator
With n as part of the function F, but n is the input to the sqrt
function we’re writing. If we let 1 be the initial approximation:
::
1 n 1 / + 2 /
1 n/1 + 2 /
1 n + 2 /
n+1 2 /
(n+1)/2
1 n 1 / + 2 /
1 n/1 + 2 /
1 n + 2 /
n+1 2 /
(n+1)/2
The generator can be written as:
::
23 1 swap [over / + 2 /] cons [dup] swoncat make_generator
1 23 [over / + 2 /] cons [dup] swoncat make_generator
1 [23 over / + 2 /] [dup] swoncat make_generator
1 [dup 23 over / + 2 /] make_generator
23 1 swap [over / + 2 /] cons [dup] swoncat make_generator
1 23 [over / + 2 /] cons [dup] swoncat make_generator
1 [23 over / + 2 /] [dup] swoncat make_generator
1 [dup 23 over / + 2 /] make_generator
.. code:: ipython2
@@ -89,8 +89,8 @@ The generator can be written as:
[1 [dup 23 over / + 2 /] codireco]
Let's drive the generator a few time (with the ``x`` combinator) and
square the approximation to see how well it works...
Let’s drive the generator a few time (with the ``x`` combinator) and
square the approximation to see how well it works…
.. code:: ipython2
@@ -105,42 +105,42 @@ square the approximation to see how well it works...
Finding Consecutive Approximations within a Tolerance
-----------------------------------------------------
From `"Why Functional Programming Matters" by John
From `“Why Functional Programming Matters” by John
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__:
The remainder of a square root finder is a function *within*, which
takes a tolerance and a list of approximations and looks down the
list for two successive approximations that differ by no more than
the given tolerance.
The remainder of a square root finder is a function *within*, which
takes a tolerance and a list of approximations and looks down the
list for two successive approximations that differ by no more than
the given tolerance.
(And note that by “list” he means a lazily-evaluated list.)
Using the *output* ``[a G]`` of the above generator for square root
approximations, and further assuming that the first term a has been
generated already and epsilon ε is handy on the stack...
generated already and epsilon ε is handy on the stack…
::
a [b G] ε within
---------------------- a b - abs ε <=
b
a [b G] ε within
---------------------- a b - abs ε <=
b
a [b G] ε within
---------------------- a b - abs ε >
b [c G] ε within
a [b G] ε within
---------------------- a b - abs ε >
b [c G] ε within
Predicate
~~~~~~~~~
::
a [b G] ε [first - abs] dip <=
a [b G] first - abs ε <=
a b - abs ε <=
a-b abs ε <=
abs(a-b) ε <=
(abs(a-b)<=ε)
a [b G] ε [first - abs] dip <=
a [b G] first - abs ε <=
a b - abs ε <=
a-b abs ε <=
abs(a-b) ε <=
(abs(a-b)<=ε)
.. code:: ipython2
@@ -151,10 +151,10 @@ Base-Case
::
a [b G] ε roll< popop first
[b G] ε a popop first
[b G] first
b
a [b G] ε roll< popop first
[b G] ε a popop first
[b G] first
b
.. code:: ipython2
@@ -165,7 +165,7 @@ Recur
::
a [b G] ε R0 [within] R1
a [b G] ε R0 [within] R1
1. Discard a.
2. Use ``x`` combinator to generate next term from ``G``.
@@ -175,14 +175,14 @@ Pretty straightforward:
::
a [b G] ε R0 [within] R1
a [b G] ε [popd x] dip [within] i
a [b G] popd x ε [within] i
[b G] x ε [within] i
b [c G] ε [within] i
b [c G] ε within
a [b G] ε R0 [within] R1
a [b G] ε [popd x] dip [within] i
a [b G] popd x ε [within] i
[b G] x ε [within] i
b [c G] ε [within] i
b [c G] ε within
b [c G] ε within
b [c G] ε within
.. code:: ipython2
@@ -196,15 +196,15 @@ The recursive function we have defined so far needs a slight preamble:
::
[a G] x ε ...
a [b G] ε ...
[a G] x ε ...
a [b G] ε ...
.. code:: ipython2
define('within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec')
define('sqrt == gsra within')
Try it out...
Try it out…
.. code:: ipython2
docs/sphinx_docs/notebooks/Ordered_Binary_Trees.rst
+391 -391
View File
File diff suppressed because it is too large Load Diff
docs/sphinx_docs/notebooks/Quadratic.rst
+16 -16
View File
@@ -10,9 +10,9 @@ Cf.
::
-b ± sqrt(b^2 - 4 * a * c)
--------------------------------
2 * a
-b ± sqrt(b^2 - 4 * a * c)
--------------------------------
2 * a
:math:`\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}`
@@ -28,21 +28,21 @@ a definition without them.
::
b neg
b neg
``sqrt(b^2 - 4 * a * c)``
~~~~~~~~~~~~~~~~~~~~~~~~~
::
b sqr 4 a c * * - sqrt
b sqr 4 a c * * - sqrt
``/2a``
~~~~~~~
::
a 2 * /
a 2 * /
``±``
~~~~~
@@ -52,14 +52,14 @@ replaces them with their sum and difference.
::
pm == [+] [-] cleave popdd
pm == [+] [-] cleave popdd
Putting Them Together
~~~~~~~~~~~~~~~~~~~~~
::
b neg b sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
b neg b sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
We use ``app2`` to compute both roots by using a quoted program
``[2a /]`` built with ``cons``.
@@ -72,20 +72,20 @@ the variables:
::
b neg b sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
b [neg] dupdip sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
b a c [[neg] dupdip sqr 4] dipd * * - sqrt pm a 2 * [/] cons app2
b a c a [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2
b a c over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2
b neg b sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
b [neg] dupdip sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
b a c [[neg] dupdip sqr 4] dipd * * - sqrt pm a 2 * [/] cons app2
b a c a [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2
b a c over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2
The three arguments are to the left, so we can "chop off" everything to
the right and say it's the definition of the ``quadratic`` function:
The three arguments are to the left, so we can “chop off” everything to
the right and say it’s the definition of the ``quadratic`` function:
.. code:: ipython2
define('quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2')
Let's try it out:
Let’s try it out:
.. code:: ipython2
docs/sphinx_docs/notebooks/Recursion_Combinators.rst
+164 -168
View File
@@ -10,44 +10,43 @@ several generic specializations.
::
[if] [then] [rec1] [rec2] genrec
---------------------------------------------------------------------
[if] [then] [rec1 [[if] [then] [rec1] [rec2] genrec] rec2] ifte
[if] [then] [rec1] [rec2] genrec
---------------------------------------------------------------------
[if] [then] [rec1 [[if] [then] [rec1] [rec2] genrec] rec2] ifte
From "Recursion Theory and Joy" (j05cmp.html) by Manfred von Thun:
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."
“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.”
Designing Recursive Functions
-----------------------------
The way to design one of these is to fix your base case and test and
then treat ``R1`` and ``R2`` as an else-part "sandwiching" a quotation
then treat ``R1`` and ``R2`` as an else-part “sandwiching” a quotation
of the whole function.
For example, given a (general recursive) function ``F``:
::
F == [I] [T] [R1] [R2] genrec
== [I] [T] [R1 [F] R2] ifte
F == [I] [T] [R1] [R2] genrec
== [I] [T] [R1 [F] R2] ifte
If the ``[I]`` predicate is false you must derive ``R1`` and ``R2``
from:
::
... R1 [F] R2
... R1 [F] R2
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.
@@ -59,9 +58,9 @@ Primitive recursive functions are those where ``R2 == i``.
::
P == [I] [T] [R] primrec
== [I] [T] [R [P] i] ifte
== [I] [T] [R P] ifte
P == [I] [T] [R] primrec
== [I] [T] [R [P] i] ifte
== [I] [T] [R P] ifte
`Hylomorphism <https://en.wikipedia.org/wiki/Hylomorphism_%28computer_science%29>`__
------------------------------------------------------------------------------------
@@ -75,8 +74,8 @@ is a recursive function ``H :: A -> C`` that converts a value of type
- A combiner ``F :: (B, C) -> C``
- A predicate ``P :: A -> Bool`` to detect the base case
- A base case value ``c :: C``
- Recursive calls (zero or more); it has a "call stack in the form of a
cons list".
- Recursive calls (zero or more); it has a “call stack in the form of a
cons list”.
It may be helpful to see this function implemented in imperative Python
code.
@@ -96,12 +95,12 @@ code.
return H
Cf. `"Bananas, Lenses, & Barbed
Wire" <http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.125>`__
Cf. `“Bananas, Lenses, & Barbed
Wire” <http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.125>`__
Note that during evaluation of ``H()`` the intermediate ``b`` values are
stored in the Python call stack. This is what is meant by "call stack in
the form of a cons list".
stored in the Python call stack. This is what is meant by “call stack in
the form of a cons list”.
Hylomorphism in Joy
-------------------
@@ -111,7 +110,7 @@ hylomorphism combinator ``H`` from constituent parts.
::
H == [P] c [G] [F] hylomorphism
H == [P] c [G] [F] hylomorphism
The function ``H`` is recursive, so we start with ``ifte`` and set the
else-part to some function ``J`` that will contain a quoted copy of
@@ -120,37 +119,37 @@ with the base case value ``c``.)
::
H == [P] [pop c] [J] ifte
H == [P] [pop c] [J] ifte
The else-part ``J`` gets just the argument ``a`` on the stack.
::
a J
a G The first thing to do is use the generator G
aa b which produces b and a new aa
aa b [H] dip we recur with H on the new aa
aa H b F and run F on the result.
a J
a G The first thing to do is use the generator G
aa b which produces b and a new aa
aa b [H] dip we recur with H on the new aa
aa H b F and run F on the result.
This gives us a definition for ``J``.
::
J == G [H] dip F
J == G [H] dip F
Plug it in and convert to genrec.
::
H == [P] [pop c] [G [H] dip F] ifte
H == [P] [pop c] [G] [dip F] genrec
H == [P] [pop c] [G [H] dip F] ifte
H == [P] [pop c] [G] [dip F] genrec
This is the form of a hylomorphism in Joy, which nicely illustrates that
it is a simple specialization of the general recursion combinator.
::
H == [P] c [G] [F] hylomorphism == [P] [pop c] [G] [dip F] genrec
H == [P] c [G] [F] hylomorphism == [P] [pop c] [G] [dip F] genrec
Derivation of ``hylomorphism`` combinator
-----------------------------------------
@@ -160,9 +159,9 @@ arguments out of the pieces given to the ``hylomorphism`` combinator.
::
[P] c [G] [F] hylomorphism
------------------------------------------
[P] [pop c] [G] [dip F] genrec
[P] c [G] [F] hylomorphism
------------------------------------------
[P] [pop c] [G] [dip F] genrec
Working in reverse:
@@ -174,17 +173,17 @@ So:
::
H == [P] [pop c] [G] [dip F] genrec
[P] [c] [pop] swoncat [G] [F] [dip] swoncat genrec
[P] c unit [pop] swoncat [G] [F] [dip] swoncat genrec
[P] c [G] [F] [unit [pop] swoncat] dipd [dip] swoncat genrec
H == [P] [pop c] [G] [dip F] genrec
[P] [c] [pop] swoncat [G] [F] [dip] swoncat genrec
[P] c unit [pop] swoncat [G] [F] [dip] swoncat genrec
[P] c [G] [F] [unit [pop] swoncat] dipd [dip] swoncat genrec
At this point all of the arguments (givens) to the hylomorphism are to
the left so we have a definition for ``hylomorphism``:
::
hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec
hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec
.. code:: ipython2
@@ -193,7 +192,7 @@ the left so we have a definition for ``hylomorphism``:
Example: Finding `Triangular Numbers <https://en.wikipedia.org/wiki/Triangular_number>`__
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let's write a function that, given a positive integer, returns the sum
Let’s write a function that, given a positive integer, returns the sum
of all positive integers less than that one. (In this case the types
``A``, ``B`` and ``C`` are all ``int``.)
@@ -208,7 +207,7 @@ To sum a range of integers from 0 to *n* - 1:
define('triangular_number == [1 <=] 0 [-- dup] [+] hylomorphism')
Let's try it:
Let’s try it:
.. code:: ipython2
@@ -236,30 +235,30 @@ Four Specializations
There are at least four kinds of recursive combinator, depending on two
choices. The first choice is whether the combiner function ``F`` should
be evaluated during the recursion or pushed into the pending expression
to be "collapsed" at the end. The second choice is whether the combiner
to be “collapsed” at the end. The second choice is whether the combiner
needs to operate on the current value of the datastructure or the
generator's output, in other words, whether ``F`` or ``G`` should run
generator’s output, in other words, whether ``F`` or ``G`` should run
first in the recursive branch.
::
H1 == [P] [pop c] [G ] [dip F] genrec
H2 == c swap [P] [pop] [G [F] dip ] [i] genrec
H3 == [P] [pop c] [ [G] dupdip ] [dip F] genrec
H4 == c swap [P] [pop] [ [F] dupdip G] [i] genrec
H1 == [P] [pop c] [G ] [dip F] genrec
H2 == c swap [P] [pop] [G [F] dip ] [i] genrec
H3 == [P] [pop c] [ [G] dupdip ] [dip F] genrec
H4 == c swap [P] [pop] [ [F] dupdip G] [i] genrec
The working of the generator function ``G`` differs slightly for each.
Consider the recursive branches:
::
... a G [H1] dip F w/ a G == a′ b
... a G [H1] dip F w/ a G == a′ b
... c a G [F] dip H2 a G == b a′
... c a G [F] dip H2 a G == b a′
... a [G] dupdip [H3] dip F a G == a′
... a [G] dupdip [H3] dip F a G == a′
... c a [F] dupdip G H4 a G == a′
... c a [F] dupdip G H4 a G == a′
The following four sections illustrate how these work, omitting the
predicate evaluation.
@@ -269,31 +268,31 @@ predicate evaluation.
::
H1 == [P] [pop c] [G] [dip F] genrec
H1 == [P] [pop c] [G] [dip F] genrec
Iterate n times.
::
... a G [H1] dip F
... a′ b [H1] dip F
... a′ H1 b F
... a′ G [H1] dip F b F
... a″ b′ [H1] dip F b F
... a″ H1 b′ F b F
... a″ G [H1] dip F b′ F b F
... a‴ b″ [H1] dip F b′ F b F
... a‴ H1 b″ F b′ F b F
... a‴ pop c b″ F b′ F b F
... c b″ F b′ F b F
... d b′ F b F
... d′ b F
... d″
... a G [H1] dip F
... a′ b [H1] dip F
... a′ H1 b F
... a′ G [H1] dip F b F
... a″ b′ [H1] dip F b F
... a″ H1 b′ F b F
... a″ G [H1] dip F b′ F b F
... a‴ b″ [H1] dip F b′ F b F
... a‴ H1 b″ F b′ F b F
... a‴ pop c b″ F b′ F b F
... c b″ F b′ F b F
... d b′ F b F
... d′ b F
... d″
This form builds up a pending expression (continuation) that contains
the intermediate results along with the pending combiner functions. When
the base case is reached the last term is replaced by the identity value
``c`` and the continuation "collapses" into the final result using the
``c`` and the continuation “collapses” into the final result using the
combiner ``F``.
``H2``
@@ -307,53 +306,53 @@ reverse order.
::
H2 == c swap [P] [pop] [G [F] dip] primrec
H2 == c swap [P] [pop] [G [F] dip] primrec
... c a G [F] dip H2
... c b a′ [F] dip H2
... c b F a′ H2
... d a′ H2
... d a′ G [F] dip H2
... d b′ a″ [F] dip H2
... d b′ F a″ H2
... d′ a″ H2
... d′ a″ G [F] dip H2
... d′ b″ a‴ [F] dip H2
... d′ b″ F a‴ H2
... d″ a‴ H2
... d″ a‴ pop
... d″
... c a G [F] dip H2
... c b a′ [F] dip H2
... c b F a′ H2
... d a′ H2
... d a′ G [F] dip H2
... d b′ a″ [F] dip H2
... d b′ F a″ H2
... d′ a″ H2
... d′ a″ G [F] dip H2
... d′ b″ a‴ [F] dip H2
... d′ b″ F a‴ H2
... d″ a‴ H2
... d″ a‴ pop
... d″
``H3``
~~~~~~
If you examine the traces above you'll see that the combiner ``F`` only
gets to operate on the results of ``G``, it never "sees" the first value
If you examine the traces above you’ll see that the combiner ``F`` only
gets to operate on the results of ``G``, it never “sees” the first value
``a``. If the combiner and the generator both need to work on the
current value then ``dup`` must be used, and the generator must produce
one item instead of two (the b is instead the duplicate of a.)
::
H3 == [P] [pop c] [[G] dupdip] [dip F] genrec
H3 == [P] [pop c] [[G] dupdip] [dip F] genrec
... a [G] dupdip [H3] dip F
... a G a [H3] dip F
... a′ a [H3] dip F
... a′ H3 a F
... a′ [G] dupdip [H3] dip F a F
... a′ G a′ [H3] dip F a F
... a″ a′ [H3] dip F a F
... a″ H3 a′ F a F
... a″ [G] dupdip [H3] dip F a′ F a F
... a″ G a″ [H3] dip F a′ F a F
... a‴ a″ [H3] dip F a′ F a F
... a‴ H3 a″ F a′ F a F
... a‴ pop c a″ F a′ F a F
... c a″ F a′ F a F
... d a′ F a F
... d′ a F
... d″
... a [G] dupdip [H3] dip F
... a G a [H3] dip F
... a′ a [H3] dip F
... a′ H3 a F
... a′ [G] dupdip [H3] dip F a F
... a′ G a′ [H3] dip F a F
... a″ a′ [H3] dip F a F
... a″ H3 a′ F a F
... a″ [G] dupdip [H3] dip F a′ F a F
... a″ G a″ [H3] dip F a′ F a F
... a‴ a″ [H3] dip F a′ F a F
... a‴ H3 a″ F a′ F a F
... a‴ pop c a″ F a′ F a F
... c a″ F a′ F a F
... d a′ F a F
... d′ a F
... d″
``H4``
~~~~~~
@@ -364,22 +363,22 @@ the form:
::
H4 == c swap [P] [pop] [[F] dupdip G] primrec
H4 == c swap [P] [pop] [[F] dupdip G] primrec
... c a [F] dupdip G H4
... c a F a G H4
... d a G H4
... d a′ H4
... d a′ [F] dupdip G H4
... d a′ F a′ G H4
... d′ a′ G H4
... d′ a″ H4
... d′ a″ [F] dupdip G H4
... d′ a″ F a″ G H4
... d″ a″ G H4
... d″ a‴ H4
... d″ a‴ pop
... d″
... c a [F] dupdip G H4
... c a F a G H4
... d a G H4
... d a′ H4
... d a′ [F] dupdip G H4
... d a′ F a′ G H4
... d′ a′ G H4
... d′ a″ H4
... d′ a″ [F] dupdip G H4
... d′ a″ F a″ G H4
... d″ a″ G H4
... d″ a‴ H4
... d″ a‴ pop
... d″
Anamorphism
-----------
@@ -390,13 +389,10 @@ values.
::
A == [P] [] [G] [swons] hylomorphism
A == [P] [] [G] [swons] hylomorphism
``range`` et. al.
~~~~~~~~~~~~~~~~~
An example of an anamorphism is the ``range`` function which generates
the list of integers from 0 to *n* - 1 given *n*.
``range`` et. al. An example of an anamorphism is the ``range`` function which generates the list of integers from 0 to *n* - 1 given *n*.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Each of the above variations can be used to make four slightly different
``range`` functions.
@@ -406,8 +402,8 @@ Each of the above variations can be used to make four slightly different
::
H1 == [P] [pop c] [G] [dip F] genrec
== [0 <=] [pop []] [-- dup] [dip swons] genrec
H1 == [P] [pop c] [G] [dip F] genrec
== [0 <=] [pop []] [-- dup] [dip swons] genrec
.. code:: ipython2
@@ -428,8 +424,8 @@ Each of the above variations can be used to make four slightly different
::
H2 == c swap [P] [pop] [G [F] dip] primrec
== [] swap [0 <=] [pop] [-- dup [swons] dip] primrec
H2 == c swap [P] [pop] [G [F] dip] primrec
== [] swap [0 <=] [pop] [-- dup [swons] dip] primrec
.. code:: ipython2
@@ -450,8 +446,8 @@ Each of the above variations can be used to make four slightly different
::
H3 == [P] [pop c] [[G] dupdip] [dip F] genrec
== [0 <=] [pop []] [[--] dupdip] [dip swons] genrec
H3 == [P] [pop c] [[G] dupdip] [dip F] genrec
== [0 <=] [pop []] [[--] dupdip] [dip swons] genrec
.. code:: ipython2
@@ -472,8 +468,8 @@ Each of the above variations can be used to make four slightly different
::
H4 == c swap [P] [pop] [[F] dupdip G ] primrec
== [] swap [0 <=] [pop] [[swons] dupdip --] primrec
H4 == c swap [P] [pop] [[F] dupdip G ] primrec
== [] swap [0 <=] [pop] [[swons] dupdip --] primrec
.. code:: ipython2
@@ -503,7 +499,7 @@ and makes some new value.
::
C == [not] c [uncons swap] [F] hylomorphism
C == [not] c [uncons swap] [F] hylomorphism
.. code:: ipython2
@@ -513,7 +509,7 @@ An example of a catamorphism is the sum function.
::
sum == [not] 0 [swuncons] [+] hylomorphism
sum == [not] 0 [swuncons] [+] hylomorphism
.. code:: ipython2
@@ -585,16 +581,16 @@ For the Factorial function:
::
H4 == c swap [P] [pop] [[F] dupdip G] primrec
H4 == c swap [P] [pop] [[F] dupdip G] primrec
With:
::
c == 1
F == *
G == --
P == 1 <=
c == 1
F == *
G == --
P == 1 <=
.. code:: ipython2
@@ -613,31 +609,31 @@ With:
Example: ``tails``
------------------
An example of a paramorphism for lists given in the `"Bananas..."
An example of a paramorphism for lists given in the `“Bananas…”
paper <http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.125>`__
is ``tails`` which returns the list of "tails" of a list.
is ``tails`` which returns the list of “tails” of a list.
::
[1 2 3] tails
--------------------
[[] [3] [2 3]]
[1 2 3] tails
--------------------
[[] [3] [2 3]]
We can build as we go, and we want ``F`` to run after ``G``, so we use
pattern ``H2``:
::
H2 == c swap [P] [pop] [G [F] dip] primrec
H2 == c swap [P] [pop] [G [F] dip] primrec
We would use:
::
c == []
F == swons
G == rest dup
P == not
c == []
F == swons
G == rest dup
P == not
.. code:: ipython2
@@ -656,39 +652,39 @@ We would use:
Conclusion: Patterns of Recursion
---------------------------------
Our story so far...
Our story so far…
Hylo-, Ana-, Cata-
~~~~~~~~~~~~~~~~~~
::
H == [P ] [pop c ] [G ] [dip F ] genrec
A == [P ] [pop []] [G ] [dip swap cons] genrec
C == [not] [pop c ] [uncons swap] [dip F ] genrec
H == [P ] [pop c ] [G ] [dip F ] genrec
A == [P ] [pop []] [G ] [dip swap cons] genrec
C == [not] [pop c ] [uncons swap] [dip F ] genrec
Para-, ?-, ?-
~~~~~~~~~~~~~
::
P == c swap [P ] [pop] [[F ] dupdip G ] primrec
? == [] swap [P ] [pop] [[swap cons] dupdip G ] primrec
? == c swap [not] [pop] [[F ] dupdip uncons swap] primrec
P == c swap [P ] [pop] [[F ] dupdip G ] primrec
? == [] swap [P ] [pop] [[swap cons] dupdip G ] primrec
? == c swap [not] [pop] [[F ] dupdip uncons swap] primrec
Appendix: Fun with Symbols
--------------------------
::
|[ (c, F), (G, P) ]| == (|c, F|) • [(G, P)]
|[ (c, F), (G, P) ]| == (|c, F|) • [(G, P)]
`"Bananas, Lenses, & Barbed
Wire" <http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.125>`__
`“Bananas, Lenses, & Barbed
Wire” <http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.125>`__
::
(|...|) [(...)] [<...>]
(|...|) [(...)] [<...>]
I think they are having slightly too much fun with the symbols. However,
"Too much is always better than not enough."
“Too much is always better than not enough.”
docs/sphinx_docs/notebooks/Replacing.rst
+4 -4
View File
@@ -4,8 +4,8 @@ Replacing Functions in the Dictionary
For now, there is no way to define new functions from within the Joy
language. All functions (and the interpreter) all accept and return a
dictionary parameter (in addition to the stack and expression) so that
we can implement e.g. a function that adds new functions to the
dictionary. However, there's no function that does that. Adding a new
we can implement e.g. a function that adds new functions to the
dictionary. However, there’s no function that does that. Adding a new
function to the dictionary is a meta-interpreter action, you have to do
it in Python, not Joy.
@@ -74,8 +74,8 @@ Both ``sum`` and ``size`` each convert a sequence to a single value.
::
sum == 0 swap [+] step
size == 0 swap [pop ++] step
sum == 0 swap [+] step
size == 0 swap [pop ++] step
An efficient ``sum`` function is already in the library. But for
``size`` we can use a “compiled” version hand-written in Python to speed
docs/sphinx_docs/notebooks/The_Four_Operations.rst
+102 -102
View File
@@ -17,10 +17,10 @@ symbols together, juxtaposition:
::
foo bar
foo bar
Operations have inputs and outputs. The outputs of ``foo`` must be
compatible in "arity", type, and shape with the inputs of ``bar``.
compatible in “arity”, type, and shape with the inputs of ``bar``.
Branch
------
@@ -29,72 +29,72 @@ Do one thing or another.
::
boolean [F] [T] branch
boolean [F] [T] branch
t [F] [T] branch
----------------------
T
t [F] [T] branch
----------------------
T
f [F] [T] branch
----------------------
F
f [F] [T] branch
----------------------
F
branch == unit cons swap pick i
branch == unit cons swap pick i
boolean [F] [T] branch
boolean [F] [T] unit cons swap pick i
boolean [F] [[T]] cons swap pick i
boolean [[F] [T]] swap pick i
[[F] [T]] boolean pick i
[F-or-T] i
boolean [F] [T] branch
boolean [F] [T] unit cons swap pick i
boolean [F] [[T]] cons swap pick i
boolean [[F] [T]] swap pick i
[[F] [T]] boolean pick i
[F-or-T] i
Given some branch function ``G``:
::
G == [F] [T] branch
G == [F] [T] branch
Used in a sequence like so:
::
foo G bar
foo G bar
The inputs and outputs of ``F`` and ``T`` must be compatible with the
outputs for ``foo`` and the inputs of ``bar``, respectively.
::
foo F bar
foo F bar
foo T bar
foo T bar
``ifte``
~~~~~~~~
Often it will be easier on the programmer to write branching code with
the predicate specified in a quote. The ``ifte`` combinator provides
this (``T`` for "then" and ``E`` for "else"):
this (``T`` for “then” and ``E`` for “else”):
::
[P] [T] [E] ifte
[P] [T] [E] ifte
Defined in terms of ``branch``:
::
ifte == [nullary not] dip branch
ifte == [nullary not] dip branch
In this case, ``P`` must be compatible with the stack and return a
Boolean value, and ``T`` and ``E`` both must be compatible with the
preceeding and following functions, as described above for ``F`` and
``T``. (Note that in the current implementation we are depending on
Python for the underlying semantics, so the Boolean value doesn't *have*
to be Boolean because Python's rules for "truthiness" will be used to
Python for the underlying semantics, so the Boolean value doesn’t *have*
to be Boolean because Python’s rules for “truthiness” will be used to
evaluate it. I reflect this in the structure of the stack effect comment
of ``branch``, it will only accept Boolean values, and in the definition
of ``ifte`` above by including ``not`` in the quote, which also has the
@@ -107,17 +107,17 @@ Do one thing zero or more times.
::
boolean [Q] loop
boolean [Q] loop
t [Q] loop
----------------
Q [Q] loop
t [Q] loop
----------------
Q [Q] loop
... f [Q] loop
--------------------
...
... f [Q] loop
--------------------
...
The ``loop`` combinator generates a copy of itself in the true branch.
This is the hallmark of recursive defintions. In Thun there is no
@@ -128,21 +128,21 @@ constructs that do not need to be directly self-referential, unlike
::
loop == [] swap [dup dip loop] cons branch
loop == [] swap [dup dip loop] cons branch
boolean [Q] loop
boolean [Q] [] swap [dup dip loop] cons branch
boolean [] [Q] [dup dip loop] cons branch
boolean [] [[Q] dup dip loop] branch
boolean [Q] loop
boolean [Q] [] swap [dup dip loop] cons branch
boolean [] [Q] [dup dip loop] cons branch
boolean [] [[Q] dup dip loop] branch
In action the false branch does nothing while the true branch does:
::
t [] [[Q] dup dip loop] branch
[Q] dup dip loop
[Q] [Q] dip loop
Q [Q] loop
t [] [[Q] dup dip loop] branch
[Q] dup dip loop
[Q] [Q] dip loop
Q [Q] loop
Because ``loop`` expects and consumes a Boolean value, the ``Q``
function must be compatible with the previous stack *and itself* with a
@@ -150,15 +150,15 @@ boolean flag for the next iteration:
::
Q == G b
Q == G b
Q [Q] loop
G b [Q] loop
G Q [Q] loop
G G b [Q] loop
G G Q [Q] loop
G G G b [Q] loop
G G G
Q [Q] loop
G b [Q] loop
G Q [Q] loop
G G b [Q] loop
G G Q [Q] loop
G G G b [Q] loop
G G G
``while``
~~~~~~~~~
@@ -170,21 +170,21 @@ flag for the next iteration:
::
[P] [B] while
--------------------------------------
[P] nullary [B [P] nullary] loop
[P] [B] while
--------------------------------------
[P] nullary [B [P] nullary] loop
while == swap [nullary] cons dup dipd concat loop
while == swap [nullary] cons dup dipd concat loop
[P] [B] while
[P] [B] swap [nullary] cons dup dipd concat loop
[B] [P] [nullary] cons dup dipd concat loop
[B] [[P] nullary] dup dipd concat loop
[B] [[P] nullary] [[P] nullary] dipd concat loop
[P] nullary [B] [[P] nullary] concat loop
[P] nullary [B [P] nullary] loop
[P] [B] while
[P] [B] swap [nullary] cons dup dipd concat loop
[B] [P] [nullary] cons dup dipd concat loop
[B] [[P] nullary] dup dipd concat loop
[B] [[P] nullary] [[P] nullary] dipd concat loop
[P] nullary [B] [[P] nullary] concat loop
[P] nullary [B [P] nullary] loop
Parallel
--------
@@ -192,11 +192,11 @@ Parallel
The *parallel* operation indicates that two (or more) functions *do not
interfere* with each other and so can run in parallel. The main
difficulty in this sort of thing is orchestrating the recombining
("join" or "wait") of the results of the functions after they finish.
(“join” or “wait”) of the results of the functions after they finish.
The current implementaions and the following definitions *are not
actually parallel* (yet), but there is no reason they couldn't be
reimplemented in terms of e.g. Python threads. I am not concerned with
actually parallel* (yet), but there is no reason they couldn’t be
reimplemented in terms of e.g. Python threads. I am not concerned with
performance of the system just yet, only the elegance of the code it
allows us to write.
@@ -207,27 +207,27 @@ Joy has a few parallel combinators, the main one being ``cleave``:
::
... x [A] [B] cleave
---------------------------------------------------------
... [x ...] [A] infra first [x ...] [B] infra first
---------------------------------------------------------
... a b
... x [A] [B] cleave
---------------------------------------------------------
... [x ...] [A] infra first [x ...] [B] infra first
---------------------------------------------------------
... a b
The ``cleave`` combinator expects a value and two quotes and it executes
each quote in "separate universes" such that neither can affect the
each quote in “separate universes” such that neither can affect the
other, then it takes the first item from the stack in each universe and
replaces the value and quotes with their respective results.
(I think this corresponds to the "fork" operator, the little
(I think this corresponds to the “fork” operator, the little
upward-pointed triangle, that takes two functions ``A :: x -> a`` and
``B :: x -> b`` and returns a function ``F :: x -> (a, b)``, in Conal
Elliott's "Compiling to Categories" paper, et. al.)
Elliott’s “Compiling to Categories” paper, et. al.)
Just a thought, if you ``cleave`` two jobs and one requires more time to
finish than the other you'd like to be able to assign resources
finish than the other you’d like to be able to assign resources
accordingly so that they both finish at the same time.
"Apply" Functions
“Apply” Functions
~~~~~~~~~~~~~~~~~
There are also ``app2`` and ``app3`` which run a single quote on more
@@ -235,35 +235,35 @@ than one value:
::
... y x [Q] app2
---------------------------------------------------------
... [y ...] [Q] infra first [x ...] [Q] infra first
... y x [Q] app2
---------------------------------------------------------
... [y ...] [Q] infra first [x ...] [Q] infra first
... z y x [Q] app3
---------------------------------
... [z ...] [Q] infra first
[y ...] [Q] infra first
[x ...] [Q] infra first
... z y x [Q] app3
---------------------------------
... [z ...] [Q] infra first
[y ...] [Q] infra first
[x ...] [Q] infra first
Because the quoted program can be ``i`` we can define ``cleave`` in
terms of ``app2``:
::
cleave == [i] app2 [popd] dip
cleave == [i] app2 [popd] dip
(I'm not sure why ``cleave`` was specified to take that value, I may
(I’m not sure why ``cleave`` was specified to take that value, I may
make a combinator that does the same thing but without expecting a
value.)
::
clv == [i] app2
clv == [i] app2
[A] [B] clv
------------------
a b
[A] [B] clv
------------------
a b
``map``
~~~~~~~
@@ -273,10 +273,10 @@ The common ``map`` function in Joy should also be though of as a
::
[a b c ...] [Q] map
[a b c ...] [Q] map
There is no reason why the implementation of ``map`` couldn't distribute
the ``Q`` function over e.g. a pool of worker CPUs.
There is no reason why the implementation of ``map`` couldn’t distribute
the ``Q`` function over e.g. a pool of worker CPUs.
``pam``
~~~~~~~
@@ -285,16 +285,16 @@ One of my favorite combinators, the ``pam`` combinator is just:
::
pam == [i] map
pam == [i] map
This can be used to run any number of programs separately on the current
stack and combine their (first) outputs in a result list.
::
[[A] [B] [C] ...] [i] map
-------------------------------
[ a b c ...]
[[A] [B] [C] ...] [i] map
-------------------------------
[ a b c ...]
Handling Other Kinds of Join
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -302,7 +302,7 @@ Handling Other Kinds of Join
The ``cleave`` operators and others all have pretty brutal join
semantics: everything works and we always wait for every
sub-computation. We can imagine a few different potentially useful
patterns of "joining" results from parallel combinators.
patterns of “joining” results from parallel combinators.
first-to-finish
^^^^^^^^^^^^^^^
@@ -313,24 +313,24 @@ stack could be replaced by its output stack.
The other sub-programs would be cancelled.
"Fulminators"
“Fulminators”
^^^^^^^^^^^^^
Also known as "Futures" or "Promises" (by *everybody* else. "Fulinators"
Also known as “Futures” or “Promises” (by *everybody* else. “Fulinators”
is what I was going to call them when I was thinking about implementing
them in Thun.)
The runtime could be amended to permit "thunks" representing the results
The runtime could be amended to permit “thunks” representing the results
of in-progress computations to be left on the stack and picked up by
subsequent functions. These would themselves be able to leave behind
more "thunks", the values of which depend on the eventual resolution of
more “thunks”, the values of which depend on the eventual resolution of
the values of the previous thunks.
In this way you can create "chains" (and more complex shapes) out of
In this way you can create “chains” (and more complex shapes) out of
normal-looking code that consist of a kind of call-graph interspersed
with "asyncronous" ... events?
with “asyncronous” … events?
In any case, until I can find a rigorous theory that shows that this
sort of thing works perfectly in Joy code I'm not going to worry about
sort of thing works perfectly in Joy code I’m not going to worry about
it. (And I think the Categories can deal with it anyhow? Incremental
evaluation, yeah?)
docs/sphinx_docs/notebooks/Treestep.rst
+109 -109
View File
@@ -1,8 +1,8 @@
Treating Trees II: ``treestep``
===============================
Let's consider a tree structure, similar to one described `"Why
functional programming matters" by John
Let’s consider a tree structure, similar to one described `“Why
functional programming matters” by John
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__,
that consists of a node value followed by zero or more child trees. (The
asterisk is meant to indicate the `Kleene
@@ -10,7 +10,7 @@ star <https://en.wikipedia.org/wiki/Kleene_star>`__.)
::
tree = [] | [node tree*]
tree = [] | [node tree*]
In the spirit of ``step`` we are going to define a combinator
``treestep`` which expects a tree and three additional items: a
@@ -18,15 +18,15 @@ base-case function ``[B]``, and two quoted programs ``[N]`` and ``[C]``.
::
tree [B] [N] [C] treestep
tree [B] [N] [C] treestep
If the current tree node is empty then just execute ``B``:
::
[] [B] [N] [C] treestep
---------------------------
[] B
[] [B] [N] [C] treestep
---------------------------
[] B
Otherwise, evaluate ``N`` on the node value, ``map`` the whole function
(abbreviated here as ``K``) over the child trees recursively, and then
@@ -34,11 +34,11 @@ combine the result with ``C``.
::
[node tree*] [B] [N] [C] treestep
--------------------------------------- w/ K == [B] [N] [C] treestep
node N [tree*] [K] map C
[node tree*] [B] [N] [C] treestep
--------------------------------------- w/ K == [B] [N] [C] treestep
node N [tree*] [K] map C
(Later on we'll experiment with making ``map`` part of ``C`` so you can
(Later on we’ll experiment with making ``map`` part of ``C`` so you can
use other combinators.)
Derive the recursive function.
@@ -49,59 +49,59 @@ will produce.
::
K == [not] [B] [R0] [R1] genrec
== [not] [B] [R0 [K] R1] ifte
K == [not] [B] [R0] [R1] genrec
== [not] [B] [R0 [K] R1] ifte
So we just have to derive ``J``:
::
J == R0 [K] R1
J == R0 [K] R1
The behavior of ``J`` is to accept a (non-empty) tree node and arrive at
the desired outcome.
::
[node tree*] J
------------------------------
node N [tree*] [K] map C
[node tree*] J
------------------------------
node N [tree*] [K] map C
So ``J`` will have some form like:
::
J == ... [N] ... [K] ... [C] ...
J == ... [N] ... [K] ... [C] ...
Let's dive in. First, unquote the node and ``dip`` ``N``.
Let’s dive in. First, unquote the node and ``dip`` ``N``.
::
[node tree*] uncons [N] dip
node [tree*] [N] dip
node N [tree*]
[node tree*] uncons [N] dip
node [tree*] [N] dip
node N [tree*]
Next, ``map`` ``K`` over the child trees and combine with ``C``.
::
node N [tree*] [K] map C
node N [tree*] [K] map C
node N [K.tree*] C
node N [tree*] [K] map C
node N [tree*] [K] map C
node N [K.tree*] C
So:
::
J == uncons [N] dip [K] map C
J == uncons [N] dip [K] map C
Plug it in and convert to ``genrec``:
::
K == [not] [B] [J ] ifte
== [not] [B] [uncons [N] dip [K] map C] ifte
== [not] [B] [uncons [N] dip] [map C] genrec
K == [not] [B] [J ] ifte
== [not] [B] [uncons [N] dip [K] map C] ifte
== [not] [B] [uncons [N] dip] [map C] genrec
Extract the givens to parameterize the program.
-----------------------------------------------
@@ -110,26 +110,26 @@ Working backwards:
::
[not] [B] [uncons [N] dip] [map C] genrec
[B] [not] swap [uncons [N] dip] [map C] genrec
[B] [uncons [N] dip] [[not] swap] dip [map C] genrec
^^^^^^^^^^^^^^^^
[B] [[N] dip] [uncons] swoncat [[not] swap] dip [map C] genrec
[B] [N] [dip] cons [uncons] swoncat [[not] swap] dip [map C] genrec
^^^^^^^^^^^^^^^^^^^^^^^^^^^
[not] [B] [uncons [N] dip] [map C] genrec
[B] [not] swap [uncons [N] dip] [map C] genrec
[B] [uncons [N] dip] [[not] swap] dip [map C] genrec
^^^^^^^^^^^^^^^^
[B] [[N] dip] [uncons] swoncat [[not] swap] dip [map C] genrec
[B] [N] [dip] cons [uncons] swoncat [[not] swap] dip [map C] genrec
^^^^^^^^^^^^^^^^^^^^^^^^^^^
Extract a couple of auxiliary definitions:
::
TS.0 == [[not] swap] dip
TS.1 == [dip] cons [uncons] swoncat
TS.0 == [[not] swap] dip
TS.1 == [dip] cons [uncons] swoncat
::
[B] [N] TS.1 TS.0 [map C] genrec
[B] [N] [map C] [TS.1 TS.0] dip genrec
[B] [N] [C] [map] swoncat [TS.1 TS.0] dip genrec
[B] [N] TS.1 TS.0 [map C] genrec
[B] [N] [map C] [TS.1 TS.0] dip genrec
[B] [N] [C] [map] swoncat [TS.1 TS.0] dip genrec
The givens are all to the left so we have our definition.
@@ -140,10 +140,10 @@ Working backwards:
::
[not] [B] [uncons [N] dip] [map C] genrec
[not] [B] [N] [dip] cons [uncons] swoncat [map C] genrec
[B] [N] [not] roll> [dip] cons [uncons] swoncat [map C] genrec
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
[not] [B] [uncons [N] dip] [map C] genrec
[not] [B] [N] [dip] cons [uncons] swoncat [map C] genrec
[B] [N] [not] roll> [dip] cons [uncons] swoncat [map C] genrec
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Define ``treestep``
-------------------
@@ -171,7 +171,7 @@ all nodes in a tree with this function:
::
sumtree == [pop 0] [] [sum +] treestep
sumtree == [pop 0] [] [sum +] treestep
.. code:: ipython2
@@ -181,9 +181,9 @@ Running this function on an empty tree value gives zero:
::
[] [pop 0] [] [sum +] treestep
------------------------------------
0
[] [pop 0] [] [sum +] treestep
------------------------------------
0
.. code:: ipython2
@@ -199,11 +199,11 @@ Running it on a non-empty node:
::
[n tree*] [pop 0] [] [sum +] treestep
n [tree*] [[pop 0] [] [sum +] treestep] map sum +
n [ ... ] sum +
n m +
n+m
[n tree*] [pop 0] [] [sum +] treestep
n [tree*] [[pop 0] [] [sum +] treestep] map sum +
n [ ... ] sum +
n m +
n+m
.. code:: ipython2
@@ -310,7 +310,7 @@ Redefining the Ordered Binary Tree in terms of ``treestep``.
::
Tree = [] | [[key value] left right]
Tree = [] | [[key value] left right]
What kind of functions can we write for this with our ``treestep``?
@@ -318,26 +318,26 @@ The pattern for processing a non-empty node is:
::
node N [tree*] [K] map C
node N [tree*] [K] map C
Plugging in our BTree structure:
::
[key value] N [left right] [K] map C
[key value] N [left right] [K] map C
Traversal
~~~~~~~~~
::
[key value] first [left right] [K] map i
key [value] [left right] [K] map i
key [left right] [K] map i
key [lkey rkey ] i
key lkey rkey
[key value] first [left right] [K] map i
key [value] [left right] [K] map i
key [left right] [K] map i
key [lkey rkey ] i
key lkey rkey
This doesn't quite work:
This doesn’t quite work:
.. code:: ipython2
@@ -349,25 +349,25 @@ This doesn't quite work:
3 'B' 'B'
Doesn't work because ``map`` extracts the ``first`` item of whatever its
Doesn’t work because ``map`` extracts the ``first`` item of whatever its
mapped function produces. We have to return a list, rather than
depositing our results directly on the stack.
::
[key value] N [left right] [K] map C
[key value] N [left right] [K] map C
[key value] first [left right] [K] map flatten cons
key [left right] [K] map flatten cons
key [[lk] [rk] ] flatten cons
key [ lk rk ] cons
[key lk rk ]
[key value] first [left right] [K] map flatten cons
key [left right] [K] map flatten cons
key [[lk] [rk] ] flatten cons
key [ lk rk ] cons
[key lk rk ]
So:
::
[] [first] [flatten cons] treestep
[] [first] [flatten cons] treestep
.. code:: ipython2
@@ -388,18 +388,18 @@ From here:
::
key [[lk] [rk]] C
key [[lk] [rk]] i
key [lk] [rk] roll<
[lk] [rk] key swons concat
[lk] [key rk] concat
[lk key rk]
key [[lk] [rk]] C
key [[lk] [rk]] i
key [lk] [rk] roll<
[lk] [rk] key swons concat
[lk] [key rk] concat
[lk key rk]
So:
::
[] [i roll< swons concat] [first] treestep
[] [i roll< swons concat] [first] treestep
.. code:: ipython2
@@ -414,20 +414,20 @@ So:
With ``treegrind``?
-------------------
The ``treegrind`` function doesn't include the ``map`` combinator, so
The ``treegrind`` function doesn’t include the ``map`` combinator, so
the ``[C]`` function must arrange to use some combinator on the quoted
recursive copy ``[K]``. With this function, the pattern for processing a
non-empty node is:
::
node N [tree*] [K] C
node N [tree*] [K] C
Plugging in our BTree structure:
::
[key value] N [left right] [K] C
[key value] N [left right] [K] C
.. code:: ipython2
@@ -454,7 +454,7 @@ Iteration through the nodes
[3 0] 'N' [2 0] 'N' [9 0] 'N' [5 0] 'N' [4 0] 'N' [8 0] 'N' [6 0] 'N' [7 0] 'N'
Sum the nodes' keys.
Sum the nodes’ keys.
.. code:: ipython2
@@ -485,28 +485,28 @@ I think we do:
::
[B] [N] [C] treegrind
[B] [N] [C] treegrind
We'll start by saying that the base-case (the key is not in the tree) is
We’ll start by saying that the base-case (the key is not in the tree) is
user defined, and the per-node function is just the query key literal:
::
[B] [query_key] [C] treegrind
[B] [query_key] [C] treegrind
This means we just have to define ``C`` from:
::
[key value] query_key [left right] [K] C
[key value] query_key [left right] [K] C
Let's try ``cmp``:
Let’s try ``cmp``:
::
C == P [T>] [E] [T<] cmp
C == P [T>] [E] [T<] cmp
[key value] query_key [left right] [K] P [T>] [E] [T<] cmp
[key value] query_key [left right] [K] P [T>] [E] [T<] cmp
The predicate ``P``
~~~~~~~~~~~~~~~~~~~
@@ -516,16 +516,16 @@ equal):
::
[key value] query_key [left right] [K] P
[key value] query_key [left right] [K] roll<
[key value] [left right] [K] query_key [roll< uncons swap] dip
[key value] query_key [left right] [K] P
[key value] query_key [left right] [K] roll<
[key value] [left right] [K] query_key [roll< uncons swap] dip
[key value] [left right] [K] roll< uncons swap query_key
[left right] [K] [key value] uncons swap query_key
[left right] [K] key [value] swap query_key
[left right] [K] [value] key query_key
[key value] [left right] [K] roll< uncons swap query_key
[left right] [K] [key value] uncons swap query_key
[left right] [K] key [value] swap query_key
[left right] [K] [value] key query_key
P == roll< [roll< uncons swap] dip
P == roll< [roll< uncons swap] dip
(Possibly with a swap at the end? Or just swap ``T<`` and ``T>``.)
@@ -533,15 +533,15 @@ So now:
::
[left right] [K] [value] key query_key [T>] [E] [T<] cmp
[left right] [K] [value] key query_key [T>] [E] [T<] cmp
Becomes one of these three:
::
[left right] [K] [value] T>
[left right] [K] [value] E
[left right] [K] [value] T<
[left right] [K] [value] T>
[left right] [K] [value] E
[left right] [K] [value] T<
``E``
~~~~~
@@ -550,27 +550,27 @@ Easy.
::
E == roll> popop first
E == roll> popop first
``T<`` and ``T>``
~~~~~~~~~~~~~~~~~
::
T< == pop [first] dip i
T> == pop [second] dip i
T< == pop [first] dip i
T> == pop [second] dip i
Putting it together
-------------------
::
T> == pop [first] dip i
T< == pop [second] dip i
E == roll> popop first
P == roll< [roll< uncons swap] dip
T> == pop [first] dip i
T< == pop [second] dip i
E == roll> popop first
P == roll< [roll< uncons swap] dip
Tree-get == [P [T>] [E] [T<] cmp] treegrind
Tree-get == [P [T>] [E] [T<] cmp] treegrind
To me, that seems simpler than the ``genrec`` version.
docs/sphinx_docs/notebooks/TypeChecking.rst
+1 -1
View File
@@ -98,7 +98,7 @@ An Example
(... [3 4 ] 2 1 0 -- ... [1 2 ])
Unification Works "in Reverse"
Unification Works “in Reverse”
------------------------------
.. code:: ipython2
docs/sphinx_docs/notebooks/Types.rst
+292 -288
View File
File diff suppressed because it is too large Load Diff
docs/sphinx_docs/notebooks/Zipper.rst
+26 -27
View File
@@ -1,14 +1,14 @@
Traversing Datastructures with Zippers
======================================
This notebook is about using the "zipper" with joy datastructures. See
This notebook is about using the “zipper” with joy datastructures. See
the `Zipper wikipedia
entry <https://en.wikipedia.org/wiki/Zipper_%28data_structure%29>`__ or
the original paper: `"FUNCTIONAL PEARL The Zipper" by Gérard
the original paper: `“FUNCTIONAL PEARL The Zipper” by Gérard
Huet <https://www.st.cs.uni-saarland.de/edu/seminare/2005/advanced-fp/docs/huet-zipper.pdf>`__
Given a datastructure on the stack we can navigate through it, modify
it, and rebuild it using the "zipper" technique.
it, and rebuild it using the “zipper” technique.
.. code:: ipython2
@@ -17,10 +17,9 @@ it, and rebuild it using the "zipper" technique.
Trees
-----
In Joypy there aren't any complex datastructures, just ints, floats,
In Joypy there aren’t any complex datastructures, just ints, floats,
strings, Symbols (strings that are names of functions) and sequences
(aka lists, aka quoted literals, aka aggregates, etc...), but we can
build
(aka lists, aka quoted literals, aka aggregates, etc…), but we can build
`trees <https://en.wikipedia.org/wiki/Tree_%28data_structure%29>`__ out
of sequences.
@@ -45,12 +44,12 @@ In Joy we can do this with the following words:
::
z-down == [] swap uncons swap
z-up == swons swap shunt
z-right == [swons] cons dip uncons swap
z-left == swons [uncons swap] dip swap
z-down == [] swap uncons swap
z-up == swons swap shunt
z-right == [swons] cons dip uncons swap
z-left == swons [uncons swap] dip swap
Let's use them to change 25 into 625. The first time a word is used I
Let’s use them to change 25 into 625. The first time a word is used I
show the trace so you can see how it works. If we were going to use
these a lot it would make sense to write Python versions for efficiency,
but see below.
@@ -208,8 +207,8 @@ but see below.
``dip`` and ``infra``
---------------------
In Joy we have the ``dip`` and ``infra`` combinators which can "target"
or "address" any particular item in a Joy tree structure.
In Joy we have the ``dip`` and ``infra`` combinators which can “target”
or “address” any particular item in a Joy tree structure.
.. code:: ipython2
@@ -247,8 +246,8 @@ or "address" any particular item in a Joy tree structure.
[1 [2 [3 4 625 6] 7] 8] .
If you read the trace carefully you'll see that about half of it is the
``dip`` and ``infra`` combinators de-quoting programs and "digging" into
If you read the trace carefully you’ll see that about half of it is the
``dip`` and ``infra`` combinators de-quoting programs and “digging” into
the subject datastructure. Instead of maintaining temporary results on
the stack they are pushed into the pending expression (continuation).
When ``sqr`` has run the rest of the pending expression rebuilds the
@@ -264,12 +263,12 @@ been embedded in a nested series of quoted programs, e.g.:
::
[...] [Q] [dip dip infra dip infra dip infra] Z
-------------------------------------------------------------
[...] [[[[[[[Q] dip] dip] infra] dip] infra] dip] infra
[...] [Q] [dip dip infra dip infra dip infra] Z
-------------------------------------------------------------
[...] [[[[[[[Q] dip] dip] infra] dip] infra] dip] infra
The ``Z`` function isn't hard to make.
The ``Z`` function isn’t hard to make.
.. code:: ipython2
@@ -333,21 +332,21 @@ a string made from only two characters.
::
[...] [Q] 'ddididi' Zstr
-------------------------------------------------------------
[...] [[[[[[[Q] dip] dip] infra] dip] infra] dip] infra
[...] [Q] 'ddididi' Zstr
-------------------------------------------------------------
[...] [[[[[[[Q] dip] dip] infra] dip] infra] dip] infra
The string can be considered a name or address for an item in the
subject datastructure.
Determining the right "path" for an item in a tree.
Determining the right “path” for an item in a tree.
---------------------------------------------------
It's easy to read off (in reverse) the right sequence of "d" and "i"
It’s easy to read off (in reverse) the right sequence of “d” and “i”
from the subject datastructure:
::
[ n [ n [ n n x ...
i d i d i d d Bingo!
[ n [ n [ n n x ...
i d i d i d d Bingo!