sforman
/
Thun
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
Thun/docs/sphinx_docs/_build/html/notebooks/Zipper.html

395 lines
66 KiB
HTML
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
<title>Traversing Datastructures with Zippers &#8212; Thun 0.4.1 documentation</title>
<link rel="stylesheet" type="text/css" href="../_static/pygments.css" />
<link rel="stylesheet" type="text/css" href="../_static/alabaster.css" />
<script data-url_root="../" id="documentation_options" src="../_static/documentation_options.js"></script>
<script src="../_static/jquery.js"></script>
<script src="../_static/underscore.js"></script>
<script src="../_static/doctools.js"></script>
<link rel="index" title="Index" href="../genindex.html" />
<link rel="search" title="Search" href="../search.html" />
<link rel="next" title="The Blissful Elegance of Typing Joy" href="Types.html" />
<link rel="prev" title="Newton’s method" href="Newton-Raphson.html" />
<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
<meta name="viewport" content="width=device-width, initial-scale=0.9, maximum-scale=0.9" />
</head><body>
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<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="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import J, V, define
</pre></div>
</div>
<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
<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>J(&#39;[1 [2 [3 4 25 6] 7] 8]&#39;)
</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>
</pre></div>
</div>
</section>
<section id="zipper-in-joy">
<h2>Zipper in Joy<a class="headerlink" href="#zipper-in-joy" title="Permalink to this headline"></a></h2>
<p>Zippers work by keeping track of the current item, the already-seen
items, and the yet-to-be seen items as you traverse a datastructure (the
datastructure used to keep track of these items is the zipper.)</p>
<p>In Joy we can do this with the following words:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">z</span><span class="o">-</span><span class="n">down</span> <span class="o">==</span> <span class="p">[]</span> <span class="n">swap</span> <span class="n">uncons</span> <span class="n">swap</span>
<span class="n">z</span><span class="o">-</span><span class="n">up</span> <span class="o">==</span> <span class="n">swons</span> <span class="n">swap</span> <span class="n">shunt</span>
<span class="n">z</span><span class="o">-</span><span class="n">right</span> <span class="o">==</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">cons</span> <span class="n">dip</span> <span class="n">uncons</span> <span class="n">swap</span>
<span class="n">z</span><span class="o">-</span><span class="n">left</span> <span class="o">==</span> <span class="n">swons</span> <span class="p">[</span><span class="n">uncons</span> <span class="n">swap</span><span class="p">]</span> <span class="n">dip</span> <span class="n">swap</span>
</pre></div>
</div>
<p>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.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define(&#39;z-down == [] swap uncons swap&#39;)
define(&#39;z-up == swons swap shunt&#39;)
define(&#39;z-right == [swons] cons dip uncons swap&#39;)
define(&#39;z-left == swons [uncons swap] dip swap&#39;)
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[1 [2 [3 4 25 6] 7] 8] z-down&#39;)
</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>
<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="o">.</span> <span class="n">z</span><span class="o">-</span><span class="n">down</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="o">.</span> <span class="p">[]</span> <span class="n">swap</span> <span class="n">uncons</span> <span class="n">swap</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="o">.</span> <span class="n">swap</span> <span class="n">uncons</span> <span class="n">swap</span>
<span class="p">[]</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="o">.</span> <span class="n">uncons</span> <span class="n">swap</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="o">.</span> <span class="n">swap</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="o">.</span>
</pre></div>
</div>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V(&#39;[] [[2 [3 4 25 6] 7] 8] 1 z-right&#39;)
</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>
<span class="p">[]</span> <span class="o">.</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>
<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="o">.</span> <span class="mi">1</span> <span class="n">z</span><span class="o">-</span><span class="n">right</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="o">.</span> <span class="n">z</span><span class="o">-</span><span class="n">right</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="o">.</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">cons</span> <span class="n">dip</span> <span class="n">uncons</span> <span class="n">swap</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="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="o">.</span> <span class="n">cons</span> <span class="n">dip</span> <span class="n">uncons</span> <span class="n">swap</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="p">[</span><span class="mi">1</span> <span class="n">swons</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span> <span class="n">uncons</span> <span class="n">swap</span>
<span class="p">[]</span> <span class="o">.</span> <span class="mi">1</span> <span class="n">swons</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">uncons</span> <span class="n">swap</span>
<span class="p">[]</span> <span class="mi">1</span> <span class="o">.</span> <span class="n">swons</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">uncons</span> <span class="n">swap</span>
<span class="p">[]</span> <span class="mi">1</span> <span class="o">.</span> <span class="n">swap</span> <span class="n">cons</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">uncons</span> <span class="n">swap</span>
<span class="mi">1</span> <span class="p">[]</span> <span class="o">.</span> <span class="n">cons</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">uncons</span> <span class="n">swap</span>
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</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">uncons</span> <span class="n">swap</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="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="o">.</span> <span class="n">uncons</span> <span class="n">swap</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="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="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="o">.</span> <span class="n">swap</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">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>J(&#39;[1] [8] [2 [3 4 25 6] 7] z-down&#39;)
</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>J(&#39;[1] [8] [] [[3 4 25 6] 7] 2 z-right&#39;)
</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>J(&#39;[1] [8] [2] [7] [3 4 25 6] z-down&#39;)
</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>J(&#39;[1] [8] [2] [7] [] [4 25 6] 3 z-right&#39;)
</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>J(&#39;[1] [8] [2] [7] [3] [25 6] 4 z-right&#39;)
</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>J(&#39;[1] [8] [2] [7] [4 3] [6] 25 sqr&#39;)
</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>V(&#39;[1] [8] [2] [7] [4 3] [6] 625 z-up&#39;)
</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>
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</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>
<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="o">.</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>
<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="o">.</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>
<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="o">.</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>
<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="o">.</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>
<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="o">.</span> <span class="mi">625</span> <span class="n">z</span><span class="o">-</span><span class="n">up</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="o">.</span> <span class="n">z</span><span class="o">-</span><span class="n">up</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="o">.</span> <span class="n">swons</span> <span class="n">swap</span> <span class="n">shunt</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="o">.</span> <span class="n">swap</span> <span class="n">cons</span> <span class="n">swap</span> <span class="n">shunt</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="mi">625</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="o">.</span> <span class="n">cons</span> <span class="n">swap</span> <span class="n">shunt</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">625</span> <span class="mi">6</span><span class="p">]</span> <span class="o">.</span> <span class="n">swap</span> <span class="n">shunt</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">625</span> <span class="mi">6</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="o">.</span> <span class="n">shunt</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">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>J(&#39;[1] [8] [2] [7] [3 4 625 6] z-up&#39;)
</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>J(&#39;[1] [8] [2 [3 4 625 6] 7] z-up&#39;)
</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>
</pre></div>
</div>
</section>
<section id="dip-and-infra">
<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>V(&#39;[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra&#39;)
</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>
<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="o">.</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>
<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="o">.</span> <span class="n">infra</span>
<span class="mi">8</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">1</span> <span class="o">.</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">swaack</span>
<span class="mi">8</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">1</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="o">.</span> <span class="n">dip</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">8</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> <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="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">8</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="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="o">.</span> <span class="n">infra</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">7</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">2</span> <span class="o">.</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="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">7</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">2</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="o">.</span> <span class="n">dip</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">7</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="o">.</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="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">7</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="p">[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">6</span> <span class="mi">25</span> <span class="mi">4</span> <span class="mi">3</span> <span class="o">.</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="mi">7</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">6</span> <span class="mi">25</span> <span class="mi">4</span> <span class="mi">3</span> <span class="p">[</span><span class="n">sqr</span><span class="p">]</span> <span class="o">.</span> <span class="n">dipd</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">6</span> <span class="mi">25</span> <span class="o">.</span> <span class="n">sqr</span> <span class="mi">4</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">6</span> <span class="mi">25</span> <span class="o">.</span> <span class="n">dup</span> <span class="n">mul</span> <span class="mi">4</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">6</span> <span class="mi">25</span> <span class="mi">25</span> <span class="o">.</span> <span class="n">mul</span> <span class="mi">4</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">6</span> <span class="mi">625</span> <span class="o">.</span> <span class="mi">4</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">6</span> <span class="mi">625</span> <span class="mi">4</span> <span class="o">.</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">6</span> <span class="mi">625</span> <span class="mi">4</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">6</span> <span class="mi">625</span> <span class="mi">4</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="o">.</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">7</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> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">7</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">2</span> <span class="o">.</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">7</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">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="o">.</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">8</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="o">.</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">8</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">1</span> <span class="o">.</span> <span class="p">[]</span> <span class="n">swaack</span>
<span class="mi">8</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">1</span> <span class="p">[]</span> <span class="o">.</span> <span class="n">swaack</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> <span class="o">.</span>
</pre></div>
</div>
<p>If you read the trace carefully you’ll see that about half of it is 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 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 <code class="docutils literal notranslate"><span class="pre">sqr</span></code> has run the rest of the pending expression rebuilds the
datastructure.</p>
</section>
<section id="z">
<h2><code class="docutils literal notranslate"><span class="pre">Z</span></code><a class="headerlink" href="#z" title="Permalink to this headline"></a></h2>
<p>Imagine a function <code class="docutils literal notranslate"><span class="pre">Z</span></code> that accepts a sequence of <code class="docutils literal notranslate"><span class="pre">dip</span></code> and
<code class="docutils literal notranslate"><span class="pre">infra</span></code> combinators, a quoted program <code class="docutils literal notranslate"><span class="pre">[Q]</span></code>, and a datastructure to
work on. It would effectively execute the quoted program as if it had
been embedded in a nested series of quoted programs, e.g.:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">dip</span> <span class="n">infra</span> <span class="n">dip</span> <span class="n">infra</span> <span class="n">dip</span> <span class="n">infra</span><span class="p">]</span> <span class="n">Z</span>
<span class="o">-------------------------------------------------------------</span>
<span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[[[[[[[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dip</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><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span>
</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>define(&#39;Z == [[] cons cons] step i&#39;)
</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>V(&#39;1 [2 3 4] Z&#39;)
</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>
<span class="mi">1</span> <span class="o">.</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>
<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="o">.</span> <span class="n">Z</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="o">.</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</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="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span> <span class="n">i</span>
<span class="mi">1</span> <span class="mi">2</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
<span class="mi">1</span> <span class="mi">2</span> <span class="o">.</span> <span class="p">[]</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
<span class="mi">1</span> <span class="mi">2</span> <span class="p">[]</span> <span class="o">.</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
<span class="mi">1</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">cons</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
<span class="p">[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
<span class="p">[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="o">.</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
<span class="p">[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span> <span class="n">i</span>
<span class="p">[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
<span class="p">[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[]</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
<span class="p">[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span> <span class="p">[]</span> <span class="o">.</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
<span class="p">[</span><span class="mi">1</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="o">.</span> <span class="n">cons</span> <span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</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="o">.</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</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="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span> <span class="n">i</span>
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="mi">4</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="n">i</span>
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="mi">4</span> <span class="o">.</span> <span class="p">[]</span> <span class="n">cons</span> <span class="n">cons</span> <span class="n">i</span>
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="mi">4</span> <span class="p">[]</span> <span class="o">.</span> <span class="n">cons</span> <span class="n">cons</span> <span class="n">i</span>
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</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="o">.</span> <span class="n">cons</span> <span class="n">i</span>
<span class="p">[[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="mi">4</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span>
<span class="o">.</span> <span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="mi">4</span>
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="mi">4</span>
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="mi">4</span> <span class="o">.</span>
</pre></div>
</div>
<p>And here it is doing the main thing.</p>
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J(&#39;[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z&#39;)
</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>
</pre></div>
</div>
</section>
<section id="addressing">
<h2>Addressing<a class="headerlink" href="#addressing" title="Permalink to this headline"></a></h2>
<p>Because we are only using two combinators we could replace the list with
a string made from only two characters.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="s1">&#39;ddididi&#39;</span> <span class="n">Zstr</span>
<span class="o">-------------------------------------------------------------</span>
<span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[[[[[[[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dip</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><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span>
</pre></div>
</div>
<p>The string can be considered a name or address for an item in the
subject datastructure.</p>
</section>
<section id="determining-the-right-path-for-an-item-in-a-tree">
<h2>Determining the right “path” for an item in a tree.<a class="headerlink" href="#determining-the-right-path-for-an-item-in-a-tree" title="Permalink to this headline"></a></h2>
<p>It’s easy to read off (in reverse) the right sequence of “d” and “i”
from the subject datastructure:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>[ n [ n [ n n x ...
i d i d i d d Bingo!
</pre></div>
</div>
</section>
</section>
</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 class="current">
<li class="toctree-l1"><a class="reference internal" href="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 current"><a class="reference internal" href="index.html">Essays about Programming in Joy</a><ul class="current">
<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 current"><a class="current reference internal" href="#">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"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html">∂RE</a></li>
</ul>
</li>
</ul>
<div class="relations">
<h3>Related Topics</h3>
<ul>
<li><a href="../index.html">Documentation overview</a><ul>
<li><a href="index.html">Essays about Programming in Joy</a><ul>
<li>Previous: <a href="Newton-Raphson.html" title="previous chapter">Newton’s method</a></li>
<li>Next: <a href="Types.html" title="next chapter">The Blissful Elegance of Typing Joy</a></li>
</ul></li>
</ul></li>
</ul>
</div>
<div id="searchbox" style="display: none" role="search">
<h3 id="searchlabel">Quick search</h3>
<div class="searchformwrapper">
<form class="search" action="../search.html" method="get">
<input type="text" name="q" aria-labelledby="searchlabel" autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false"/>
<input type="submit" value="Go" />
</form>
</div>
</div>
<script>$('#searchbox').show(0);</script>
</div>
</div>
<div class="clearer"></div>
</div>
<div class="footer" role="contentinfo">
<a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">
<img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" />
</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> 4.3.0.
</div>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink