Cleaning up docs.

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Simon Forman
2018-06-07 12:37:32 -07:00
parent 956d849c8a
commit 507d045a3d
19 changed files with 921 additions and 658 deletions
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@@ -135,9 +135,10 @@ interesting aspects. Its quite a treasure trove.</p>
<li class="toctree-l2"><a class="reference internal" href="notebooks/Replacing.html">Replacing Functions in the Dictionary</a></li>
<li class="toctree-l2"><a class="reference internal" href="notebooks/Ordered_Binary_Trees.html">Treating Trees I: Ordered Binary Trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="notebooks/Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="notebooks/Generator Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
<li class="toctree-l2"><a class="reference internal" href="notebooks/Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
<li class="toctree-l2"><a class="reference internal" href="notebooks/Newton-Raphson.html">Newtons method</a></li>
<li class="toctree-l2"><a class="reference internal" href="notebooks/Quadratic.html">Quadratic formula</a></li>
<li class="toctree-l2"><a class="reference internal" href="notebooks/Zipper.html">Traversing Datastructures with Zippers</a></li>
<li class="toctree-l2"><a class="reference internal" href="notebooks/NoUpdates.html">No Updates</a></li>
<li class="toctree-l2"><a class="reference internal" href="notebooks/Categorical.html">Categorical Programming</a></li>
</ul>
@@ -34,18 +34,25 @@
<div class="section" id="quadratic-formula">
<h1><a class="reference external" href="https://en.wikipedia.org/wiki/Quadratic_formula">Quadratic formula</a><a class="headerlink" href="#quadratic-formula" title="Permalink to this headline"></a></h1>
<p><a class="reference external" href="https://en.wikipedia.org/wiki/Quadratic_formula">The Quadratic formula</a></p>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="k">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
</pre></div>
</div>
<p>Cf.
<a class="reference external" href="http://www.kevinalbrecht.com/code/joy-mirror/jp-quadratic.html">jp-quadratic.html</a></p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="n">b</span> <span class="o">+/-</span> <span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">a</span> <span class="o">*</span> <span class="n">c</span><span class="p">)</span>
<span class="o">-----------------------------</span>
<span class="mi">2</span> <span class="o">*</span> <span class="n">a</span>
</pre></div>
</div>
<p><span class="math notranslate nohighlight">\(\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)</span></p>
<p>In
<a class="reference external" href="http://www.kevinalbrecht.com/code/joy-mirror/jp-quadratic.html">jp-quadratic.html</a>
a Joy function for the Quadratic formula is derived (along with one of my favorite combinators <code class="docutils literal notranslate"><span class="pre">[i]</span> <span class="pre">map</span></code>,
which I like to call <code class="docutils literal notranslate"><span class="pre">pam</span></code>) starting with a version written in Scheme. Here we investigate a different approach.</p>
<div class="section" id="write-a-program-with-variable-names">
<h2>Write a program with variable names.<a class="headerlink" href="#write-a-program-with-variable-names" title="Permalink to this headline"></a></h2>
<div class="section" id="write-a-straightforward-program-with-variable-names">
<h2>Write a straightforward program with variable names.<a class="headerlink" href="#write-a-straightforward-program-with-variable-names" title="Permalink to this headline"></a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="n">neg</span> <span class="n">b</span> <span class="n">sqr</span> <span class="mi">4</span> <span class="n">a</span> <span class="n">c</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="p">]</span> <span class="n">cleave</span> <span class="n">a</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
</pre></div>
</div>
<p>We use <code class="docutils literal notranslate"><span class="pre">cleave</span></code> to compute the sum and difference (“plus-or-minus”) and then <code class="docutils literal notranslate"><span class="pre">app2</span></code> to finish computing both roots using a quoted program <code class="docutils literal notranslate"><span class="pre">[2a</span> <span class="pre">truediv]</span></code> built with <code class="docutils literal notranslate"><span class="pre">cons</span></code>.</p>
<p>We use <code class="docutils literal notranslate"><span class="pre">cleave</span></code> to compute the sum and difference and then <code class="docutils literal notranslate"><span class="pre">app2</span></code> to
finish computing both roots using a quoted program <code class="docutils literal notranslate"><span class="pre">[2a</span> <span class="pre">truediv]</span></code>
built with <code class="docutils literal notranslate"><span class="pre">cons</span></code>.</p>
<div class="section" id="check-it">
<h3>Check it.<a class="headerlink" href="#check-it" title="Permalink to this headline"></a></h3>
<p>Evaluating by hand:</p>
@@ -62,12 +69,14 @@ which I like to call <code class="docutils literal notranslate"><span class="pre
<span class="o">-</span><span class="n">b</span> <span class="o">-</span><span class="n">b</span><span class="o">+</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span> <span class="o">-</span><span class="n">b</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span>
</pre></div>
</div>
<p>(Eventually well be able to use e.g. Sympy versions of the Joy commands to do this sort of thing symbolically. This is part of what is meant by a “categorical” language.)</p>
<p>(Eventually well be able to use e.g. Sympy versions of the Joy commands
to do this sort of thing symbolically. This is part of what is meant by
a “categorical” language.)</p>
</div>
<div class="section" id="cleanup">
<h3>Cleanup<a class="headerlink" href="#cleanup" title="Permalink to this headline"></a></h3>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="n">b</span> <span class="o">-</span><span class="n">b</span><span class="o">+</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span> <span class="o">-</span><span class="n">b</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span> <span class="n">roll</span><span class="o">&lt;</span> <span class="n">pop</span>
<span class="o">-</span><span class="n">b</span><span class="o">+</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span> <span class="o">-</span><span class="n">b</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span> <span class="o">-</span><span class="n">b</span> <span class="n">pop</span>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="n">b</span> <span class="o">-</span><span class="n">b</span><span class="o">+</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span> <span class="o">-</span><span class="n">b</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span> <span class="n">roll</span><span class="o">&lt;</span> <span class="n">pop</span>
<span class="o">-</span><span class="n">b</span><span class="o">+</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span> <span class="o">-</span><span class="n">b</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span> <span class="o">-</span><span class="n">b</span> <span class="n">pop</span>
<span class="o">-</span><span class="n">b</span><span class="o">+</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span> <span class="o">-</span><span class="n">b</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span>
</pre></div>
</div>
@@ -82,9 +91,6 @@ which I like to call <code class="docutils literal notranslate"><span class="pre
<span class="n">b</span> <span class="n">a</span> <span class="n">c</span> <span class="n">over</span> <span class="p">[[[</span><span class="n">neg</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">sqr</span> <span class="mi">4</span><span class="p">]</span> <span class="n">dipd</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="p">]</span> <span class="n">cleave</span><span class="p">]</span> <span class="n">dip</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span> <span class="n">roll</span><span class="o">&lt;</span> <span class="n">pop</span>
</pre></div>
</div>
<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="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 [+] [-] cleave] dip 2 * [truediv] cons app2 roll&lt; pop&#39;</span><span class="p">)</span>
</pre></div>
</div>
@@ -94,10 +100,11 @@ which I like to call <code class="docutils literal notranslate"><span class="pre
<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>
</pre></div>
</div>
</div>
<div class="section" id="simplify">
<h3>Simplify<a class="headerlink" href="#simplify" title="Permalink to this headline"></a></h3>
<h2>Simplify<a class="headerlink" href="#simplify" title="Permalink to this headline"></a></h2>
<p>We can define a <code class="docutils literal notranslate"><span class="pre">pm</span></code> plus-or-minus function:</p>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;pm == [+] [-] cleave popdd&#39;</span><span class="p">)</span>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">pm</span> <span class="o">==</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="p">]</span> <span class="n">cleave</span> <span class="n">popdd</span>
</pre></div>
</div>
<p>Then <code class="docutils literal notranslate"><span class="pre">quadratic</span></code> becomes:</p>
@@ -110,25 +117,17 @@ which I like to call <code class="docutils literal notranslate"><span class="pre
<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>
</pre></div>
</div>
</div>
<div class="section" id="define-a-native-pm-function">
<h3>Define a “native” <code class="docutils literal notranslate"><span class="pre">pm</span></code> function.<a class="headerlink" href="#define-a-native-pm-function" title="Permalink to this headline"></a></h3>
<p>The definition of <code class="docutils literal notranslate"><span class="pre">pm</span></code> above is pretty elegant, but the implementation
takes a lot of steps relative to what its accomplishing. Since we are
likely to use <code class="docutils literal notranslate"><span class="pre">pm</span></code> more than once in the future, lets write a
primitive in Python and add it to the dictionary.</p>
<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">notebook_preamble</span> <span class="k">import</span> <span class="n">D</span>
<span class="nd">@SimpleFunctionWrapper</span>
<span class="k">def</span> <span class="nf">pm</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
primitive in Python and add it to the dictionary. (This has been done
already.)</p>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">pm</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
<span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span> <span class="o">=</span> <span class="n">stack</span>
<span class="n">p</span><span class="p">,</span> <span class="n">m</span><span class="p">,</span> <span class="o">=</span> <span class="n">b</span> <span class="o">+</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">-</span> <span class="n">a</span>
<span class="k">return</span> <span class="n">m</span><span class="p">,</span> <span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span>
<span class="n">D</span><span class="p">[</span><span class="s1">&#39;pm&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">pm</span>
</pre></div>
</div>
<p>The resulting trace is short enough to fit on a page.</p>
@@ -195,13 +194,13 @@ primitive in Python and add it to the dictionary.</p>
<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-program-with-variable-names">Write a program with variable names.</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="#check-it">Check it.</a></li>
<li><a class="reference internal" href="#cleanup">Cleanup</a></li>
</ul>
</li>
<li><a class="reference internal" href="#derive-a-definition">Derive a definition.</a><ul>
<li><a class="reference internal" href="#simplify">Simplify</a></li>
<li><a class="reference internal" href="#derive-a-definition">Derive a definition.</a></li>
<li><a class="reference internal" href="#simplify">Simplify</a><ul>
<li><a class="reference internal" href="#define-a-native-pm-function">Define a “native” <code class="docutils literal notranslate"><span class="pre">pm</span></code> function.</a></li>
</ul>
</li>
@@ -6,7 +6,7 @@
<head>
<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Preamble &#8212; Thun 0.2.0 documentation</title>
<title>Traversing Datastructures with Zippers &#8212; Thun 0.2.0 documentation</title>
<link rel="stylesheet" href="../_static/alabaster.css" type="text/css" />
<link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
<script type="text/javascript" src="../_static/documentation_options.js"></script>
@@ -30,15 +30,15 @@
<div class="bodywrapper">
<div class="body" role="main">
<p>This notebook is about using the “zipper” with joy datastructures. See
<div class="section" id="traversing-datastructures-with-zippers">
<h1>Traversing Datastructures with Zippers<a class="headerlink" href="#traversing-datastructures-with-zippers" title="Permalink to this headline"></a></h1>
<p>This notebook is about using the “zipper” with joy datastructures. See
the <a class="reference external" href="https://en.wikipedia.org/wiki/Zipper_%28data_structure%29">Zipper wikipedia
entry</a> or
the original paper: <a class="reference external" href="https://www.st.cs.uni-saarland.de/edu/seminare/2005/advanced-fp/docs/huet-zipper.pdf">“FUNCTIONAL PEARL The Zipper” by Gérard
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="section" id="preamble">
<h1>Preamble<a class="headerlink" href="#preamble" title="Permalink to this headline"></a></h1>
<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>
@@ -309,7 +309,7 @@ i d i d i d d Bingo!
<div class="sphinxsidebarwrapper">
<h3><a href="../index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">Preamble</a><ul>
<li><a class="reference internal" href="#">Traversing Datastructures with Zippers</a><ul>
<li><a class="reference internal" href="#trees">Trees</a></li>
<li><a class="reference internal" href="#zipper-in-joy">Zipper in Joy</a></li>
<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>
@@ -73,15 +73,15 @@
<li class="toctree-l2"><a class="reference internal" href="Treestep.html#putting-it-together">Putting it together</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="Generator Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Generator Programs.html#direco"><code class="docutils literal notranslate"><span class="pre">direco</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator Programs.html#making-generators">Making Generators</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator Programs.html#generating-multiples-of-three-and-five">Generating Multiples of Three and Five</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator Programs.html#project-euler-problem-one">Project Euler Problem One</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator Programs.html#a-generator-for-the-fibonacci-sequence">A generator for the Fibonacci Sequence.</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator Programs.html#project-euler-problem-two">Project Euler Problem Two</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator Programs.html#how-to-compile-these">How to compile these?</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator Programs.html#an-interesting-variation">An Interesting Variation</a></li>
<li class="toctree-l1"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html#direco"><code class="docutils literal notranslate"><span class="pre">direco</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html#making-generators">Making Generators</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html#generating-multiples-of-three-and-five">Generating Multiples of Three and Five</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html#project-euler-problem-one">Project Euler Problem One</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html#a-generator-for-the-fibonacci-sequence">A generator for the Fibonacci Sequence.</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html#project-euler-problem-two">Project Euler Problem Two</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html#how-to-compile-these">How to compile these?</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Zipper.html#trees">Trees</a></li>
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