sforman/Thun
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

Bunches of new docs.

Browse Source 
Type inference!

A new treatment of recursion combinator patterns.
This commit is contained in:
Simon Forman
2018-06-21 21:13:50 -07:00
parent 049cfd22b7
commit ca05ea404a
32 changed files with 42303 additions and 1064 deletions
Download Patch File Download Diff File Expand all files Collapse all files
docs/Quadratic.html
+128 -198
View File
@@ -11771,14 +11771,6 @@ div#notebook {
<div tabindex="-1" id="notebook" class="border-box-sizing">
<div class="container" id="notebook-container">
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h1 id="Quadratic-formula"><a href="https://en.wikipedia.org/wiki/Quadratic_formula">Quadratic formula</a><a class="anchor-link" href="#Quadratic-formula">&#182;</a></h1>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[1]:</div>
@@ -11791,6 +11783,14 @@ div#notebook {
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h1 id="Quadratic-formula"><a href="https://en.wikipedia.org/wiki/Quadratic_formula">Quadratic formula</a><a class="anchor-link" href="#Quadratic-formula">&#182;</a></h1>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
@@ -11806,9 +11806,9 @@ div#notebook {
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<pre><code> -b +/- sqrt(b^2 - 4 * a * c)
-----------------------------
2 * a</code></pre>
<pre><code> -b ± sqrt(b^2 - 4 * a * c)
--------------------------------
2 * a</code></pre>
</div>
</div>
@@ -11826,11 +11826,61 @@ div#notebook {
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<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
<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><p>This math translates to Joy code in a straightforward manner. We are going to use named variables to keep track of the arguments, then write a definition without them.</p>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h3 id="-b"><code>-b</code><a class="anchor-link" href="#-b">&#182;</a></h3>
<pre><code>b neg</code></pre>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h3 id="sqrt(b^2---4-*-a-*-c)"><code>sqrt(b^2 - 4 * a * c)</code><a class="anchor-link" href="#sqrt(b^2---4-*-a-*-c)">&#182;</a></h3>
<pre><code>b sqr 4 a c * * - sqrt</code></pre>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h3 id="/2a"><code>/2a</code><a class="anchor-link" href="#/2a">&#182;</a></h3>
<pre><code>a 2 * /</code></pre>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h3 id="&#177;"><code>&#177;</code><a class="anchor-link" href="#&#177;">&#182;</a></h3><p>There is a function <code>pm</code> that accepts two values on the stack and replaces them with their sum and difference.</p>
<pre><code>pm == [+] [-] cleave popdd</code></pre>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h3 id="Putting-Them-Together">Putting Them Together<a class="anchor-link" href="#Putting-Them-Together">&#182;</a></h3>
<pre><code>b neg b sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
</code></pre>
<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>
<p>We use <code>app2</code> to compute both roots by using a quoted program <code>[2a /]</code> built with <code>cons</code>.</p>
</div>
</div>
@@ -11839,48 +11889,16 @@ div#notebook {
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h3 id="Check-it.">Check it.<a class="anchor-link" href="#Check-it.">&#182;</a></h3><p>Evaluating by hand:</p>
<h2 id="Derive-a-definition.">Derive a definition.<a class="anchor-link" href="#Derive-a-definition.">&#182;</a></h2><p>Working backwards we use <code>dip</code> and <code>dipd</code> to extract the code from the variables:</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
-b b^2 4ac - sqrt [+] [-] cleave a 2 * [truediv] cons app2
-b b^2-4ac sqrt [+] [-] cleave a 2 * [truediv] cons app2
-b sqrt(b^2-4ac) [+] [-] cleave a 2 * [truediv] cons app2
-b -b+sqrt(b^2-4ac) -b-sqrt(b^2-4ac) a 2 * [truediv] cons app2
-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
<pre><code>b neg b sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
b [neg] dupdip sqr 4 a c * * - sqrt pm a 2 * [/] cons app2
b a c [[neg] dupdip sqr 4] dipd * * - sqrt pm a 2 * [/] cons app2
b a c a [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2
b a c over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2
</code></pre>
<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>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<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>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<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
b a c a [[[neg] dupdip sqr 4] dipd * * - sqrt [+] [-] cleave] dip 2 * [truediv] cons app2 roll&lt; pop
b a c over [[[neg] dupdip sqr 4] dipd * * - sqrt [+] [-] cleave] dip 2 * [truediv] cons app2 roll&lt; pop</code></pre>
<p>The three arguments are to the left, so we can "chop off" everything to the right and say it's the definition of the <code>quadratic</code> function:</p>
</div>
</div>
@@ -11890,13 +11908,22 @@ b a c over [[[neg] dupdip sqr 4] dipd * * - sqrt [+] [-] cleave] dip 2 * [truedi
<div class="prompt input_prompt">In&nbsp;[2]:</div>
<div class="inner_cell">
<div class="input_area">
<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 [+] [-] cleave] dip 2 * [truediv] cons app2 roll&lt; pop&#39;</span><span class="p">)</span>
<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 * [/] cons app2&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Let's try it out:</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
@@ -11933,26 +11960,7 @@ b a c over [[[neg] dupdip sqr 4] dipd * * - sqrt [+] [-] cleave] dip 2 * [truedi
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<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>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<pre><code>pm == [+] [-] cleave popdd</code></pre>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Then <code>quadratic</code> becomes:</p>
<p>If you look at the Joy evaluation trace you can see that the first few lines are the <code>dip</code> and <code>dipd</code> combinators building the main program by incorporating the values on the stack. Then that program runs and you get the results. This is pretty typical of Joy code.</p>
</div>
</div>
@@ -11962,20 +11970,7 @@ b a c over [[[neg] dupdip sqr 4] dipd * * - sqrt [+] [-] cleave] dip 2 * [truedi
<div class="prompt input_prompt">In&nbsp;[4]:</div>
<div class="inner_cell">
<div class="input_area">
<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>
</pre></div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[5]:</div>
<div class="inner_cell">
<div class="input_area">
<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>
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;-5 1 4 quadratic&#39;</span><span class="p">)</span>
</pre></div>
</div>
@@ -11992,116 +11987,51 @@ b a c over [[[neg] dupdip sqr 4] dipd * * - sqrt [+] [-] cleave] dip 2 * [truedi
<div class="output_subarea output_stream output_stdout output_text">
<pre>-0.3819660112501051 -2.618033988749895
</pre>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<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>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[6]:</div>
<div class="inner_cell">
<div class="input_area">
<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>
</pre></div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>The resulting trace is short enough to fit on a page.</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[7]:</div>
<div class="inner_cell">
<div class="input_area">
<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>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area">
<div class="prompt"></div>
<div class="output_subarea output_stream output_stdout output_text">
<pre> . 3 1 1 quadratic
3 . 1 1 quadratic
3 1 . 1 quadratic
3 1 1 . quadratic
3 1 1 . over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [truediv] cons app2
3 1 1 1 . [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [truediv] cons app2
3 1 1 1 [[[neg] dupdip sqr 4] dipd * * - sqrt pm] . dip 2 * [truediv] cons app2
3 1 1 . [[neg] dupdip sqr 4] dipd * * - sqrt pm 1 2 * [truediv] cons app2
3 1 1 [[neg] dupdip sqr 4] . dipd * * - sqrt pm 1 2 * [truediv] cons app2
3 . [neg] dupdip sqr 4 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
3 [neg] . dupdip sqr 4 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
3 . neg 3 sqr 4 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
-3 . 3 sqr 4 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
-3 3 . sqr 4 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
-3 3 . dup mul 4 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
-3 3 3 . mul 4 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
-3 9 . 4 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
-3 9 4 . 1 1 * * - sqrt pm 1 2 * [truediv] cons app2
-3 9 4 1 . 1 * * - sqrt pm 1 2 * [truediv] cons app2
-3 9 4 1 1 . * * - sqrt pm 1 2 * [truediv] cons app2
-3 9 4 1 . * - sqrt pm 1 2 * [truediv] cons app2
-3 9 4 . - sqrt pm 1 2 * [truediv] cons app2
-3 5 . sqrt pm 1 2 * [truediv] cons app2
-3 2.23606797749979 . pm 1 2 * [truediv] cons app2
-0.7639320225002102 -5.23606797749979 . 1 2 * [truediv] cons app2
-0.7639320225002102 -5.23606797749979 1 . 2 * [truediv] cons app2
-0.7639320225002102 -5.23606797749979 1 2 . * [truediv] cons app2
-0.7639320225002102 -5.23606797749979 2 . [truediv] cons app2
-0.7639320225002102 -5.23606797749979 2 [truediv] . cons app2
-0.7639320225002102 -5.23606797749979 [2 truediv] . app2
[-0.7639320225002102] [2 truediv] . infra first [-5.23606797749979] [2 truediv] infra first
-0.7639320225002102 . 2 truediv [] swaack first [-5.23606797749979] [2 truediv] infra first
-0.7639320225002102 2 . truediv [] swaack first [-5.23606797749979] [2 truediv] infra first
-0.3819660112501051 . [] swaack first [-5.23606797749979] [2 truediv] infra first
-0.3819660112501051 [] . swaack first [-5.23606797749979] [2 truediv] infra first
[-0.3819660112501051] . first [-5.23606797749979] [2 truediv] infra first
-0.3819660112501051 . [-5.23606797749979] [2 truediv] infra first
-0.3819660112501051 [-5.23606797749979] . [2 truediv] infra first
-0.3819660112501051 [-5.23606797749979] [2 truediv] . infra first
-5.23606797749979 . 2 truediv [-0.3819660112501051] swaack first
-5.23606797749979 2 . truediv [-0.3819660112501051] swaack first
-2.618033988749895 . [-0.3819660112501051] swaack first
-2.618033988749895 [-0.3819660112501051] . swaack first
-0.3819660112501051 [-2.618033988749895] . first
-0.3819660112501051 -2.618033988749895 .
<pre> . -5 1 4 quadratic
-5 . 1 4 quadratic
-5 1 . 4 quadratic
-5 1 4 . quadratic
-5 1 4 . over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2
-5 1 4 1 . [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2
-5 1 4 1 [[[neg] dupdip sqr 4] dipd * * - sqrt pm] . dip 2 * [/] cons app2
-5 1 4 . [[neg] dupdip sqr 4] dipd * * - sqrt pm 1 2 * [/] cons app2
-5 1 4 [[neg] dupdip sqr 4] . dipd * * - sqrt pm 1 2 * [/] cons app2
-5 . [neg] dupdip sqr 4 1 4 * * - sqrt pm 1 2 * [/] cons app2
-5 [neg] . dupdip sqr 4 1 4 * * - sqrt pm 1 2 * [/] cons app2
-5 . neg -5 sqr 4 1 4 * * - sqrt pm 1 2 * [/] cons app2
5 . -5 sqr 4 1 4 * * - sqrt pm 1 2 * [/] cons app2
5 -5 . sqr 4 1 4 * * - sqrt pm 1 2 * [/] cons app2
5 -5 . dup mul 4 1 4 * * - sqrt pm 1 2 * [/] cons app2
5 -5 -5 . mul 4 1 4 * * - sqrt pm 1 2 * [/] cons app2
5 25 . 4 1 4 * * - sqrt pm 1 2 * [/] cons app2
5 25 4 . 1 4 * * - sqrt pm 1 2 * [/] cons app2
5 25 4 1 . 4 * * - sqrt pm 1 2 * [/] cons app2
5 25 4 1 4 . * * - sqrt pm 1 2 * [/] cons app2
5 25 4 4 . * - sqrt pm 1 2 * [/] cons app2
5 25 16 . - sqrt pm 1 2 * [/] cons app2
5 9 . sqrt pm 1 2 * [/] cons app2
5 3.0 . pm 1 2 * [/] cons app2
8.0 2.0 . 1 2 * [/] cons app2
8.0 2.0 1 . 2 * [/] cons app2
8.0 2.0 1 2 . * [/] cons app2
8.0 2.0 2 . [/] cons app2
8.0 2.0 2 [/] . cons app2
8.0 2.0 [2 /] . app2
[8.0] [2 /] . infra first [2.0] [2 /] infra first
8.0 . 2 / [] swaack first [2.0] [2 /] infra first
8.0 2 . / [] swaack first [2.0] [2 /] infra first
4.0 . [] swaack first [2.0] [2 /] infra first
4.0 [] . swaack first [2.0] [2 /] infra first
[4.0] . first [2.0] [2 /] infra first
4.0 . [2.0] [2 /] infra first
4.0 [2.0] . [2 /] infra first
4.0 [2.0] [2 /] . infra first
2.0 . 2 / [4.0] swaack first
2.0 2 . / [4.0] swaack first
1.0 . [4.0] swaack first
1.0 [4.0] . swaack first
4.0 [1.0] . first
4.0 1.0 .
</pre>
</div>
</div>