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Cleaning up docs.

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Simon Forman
2018-06-07 12:37:32 -07:00
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<h1 id="Write-a-straightforward-program-with-variable-names.">Write a straightforward program with variable names.<a class="anchor-link" href="#Write-a-straightforward-program-with-variable-names.">&#182;</a></h1>
<h2 id="Write-a-straightforward-program-with-variable-names.">Write a straightforward program with variable names.<a class="anchor-link" href="#Write-a-straightforward-program-with-variable-names.">&#182;</a></h2>
<pre><code>b neg b sqr 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2
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<h3 id="Check-it.">Check it.<a class="anchor-link" href="#Check-it.">&#182;</a></h3>
<p>We use <code>cleave</code> to compute the sum and difference and then <code>app2</code> to finish computing both roots using a quoted program <code>[2a truediv]</code> built with <code>cons</code>.</p>
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<h3 id="Check-it.">Check it.<a class="anchor-link" href="#Check-it.">&#182;</a></h3><p>Evaluating by hand:</p>
<pre><code> b neg b sqr 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2
-b b sqr 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2
-b b^2 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2
@@ -11842,8 +11852,18 @@ div#notebook {
-b -b+sqrt(b^2-4ac) -b-sqrt(b^2-4ac) 2a [truediv] cons app2
-b -b+sqrt(b^2-4ac) -b-sqrt(b^2-4ac) [2a truediv] app2
-b -b+sqrt(b^2-4ac)/2a -b-sqrt(b^2-4ac)/2a
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<h3 id="Codicil">Codicil<a class="anchor-link" href="#Codicil">&#182;</a></h3>
<p>(Eventually we’ll 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>
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<h3 id="Cleanup">Cleanup<a class="anchor-link" href="#Cleanup">&#182;</a></h3>
<pre><code>-b -b+sqrt(b^2-4ac)/2a -b-sqrt(b^2-4ac)/2a roll&lt; pop
-b+sqrt(b^2-4ac)/2a -b-sqrt(b^2-4ac)/2a -b pop
-b+sqrt(b^2-4ac)/2a -b-sqrt(b^2-4ac)/2a</code></pre>
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<h1 id="Derive-a-definition.">Derive a definition.<a class="anchor-link" href="#Derive-a-definition.">&#182;</a></h1>
<h2 id="Derive-a-definition.">Derive a definition.<a class="anchor-link" href="#Derive-a-definition.">&#182;</a></h2>
<pre><code>b neg b sqr 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2 roll&lt; pop
b [neg] dupdip sqr 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2 roll&lt; pop
b a c [[neg] dupdip sqr 4] dipd * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2 roll&lt; pop
@@ -11913,23 +11933,20 @@ b a c over [[[neg] dupdip sqr 4] dipd * * - sqrt [+] [-] cleave] dip 2 * [truedi
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<h3 id="Simplify">Simplify<a class="anchor-link" href="#Simplify">&#182;</a></h3><p>We can define a <code>pm</code> plus-or-minus function:</p>
<h2 id="Simplify">Simplify<a class="anchor-link" href="#Simplify">&#182;</a></h2><p>We can define a <code>pm</code> plus-or-minus function:</p>
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<div class=" highlight hl-ipython2"><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>
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<pre><code>pm == [+] [-] cleave popdd</code></pre>
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<div class=" highlight hl-ipython2"><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 * [truediv] cons app2&#39;</span><span class="p">)</span>
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<div class=" highlight hl-ipython2"><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>
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<h3 id="Define-a-&quot;native&quot;-pm-function.">Define a "native" <code>pm</code> function.<a class="anchor-link" href="#Define-a-&quot;native&quot;-pm-function.">&#182;</a></h3><p>The definition of <code>pm</code> above is pretty elegant, but the implementation takes a lot of steps relative to what it's accomplishing. Since we are likely to use <code>pm</code> more than once in the future, let's write a primitive in Python and add it to the dictionary.</p>
<h3 id="Define-a-&quot;native&quot;-pm-function.">Define a "native" <code>pm</code> function.<a class="anchor-link" href="#Define-a-&quot;native&quot;-pm-function.">&#182;</a></h3><p>The definition of <code>pm</code> above is pretty elegant, but the implementation takes a lot of steps relative to what it's accomplishing. Since we are likely to use <code>pm</code> more than once in the future, let's write a primitive in Python and add it to the dictionary. (This has been done already.)</p>
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<div class=" highlight hl-ipython2"><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">notebook_preamble</span> <span class="kn">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>
<div class=" highlight hl-ipython2"><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>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;3 1 1 quadratic&#39;</span><span class="p">)</span>