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

The Hylos notebook is not ready for public yet.

This commit is contained in:
Simon Forman 2018-06-08 13:05:59 -07:00
parent f5fe7d9726
commit b98e9f2107
18 changed files with 463 additions and 2825 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

4
docs/3._Developing_a_Program.ipynb
View File

@ -157,7 +157,7 @@
"cell_type": "code",
"execution_count": 6,
"metadata": {
"scrolled": true
"scrolled": false
},
"outputs": [
{
@ -1113,7 +1113,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.13"
"version": "2.7.12"
}
},
"nbformat": 4,

793
docs/Hylo-,_Ana-,_Cata-,_and_Para-morphisms_-_Recursion_Combinators.html
View File

@ -12526,7 +12526,7 @@ range_sum == [0 &lt;=] [pop 0] [1 - dup] [dip +] genrec</code></pre>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[8]:</div>
<div class="prompt input_prompt">In&nbsp;[10]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">defs</span> <span class="o">=</span> <span class="s1">&#39;&#39;&#39;</span>
@ -12548,7 +12548,7 @@ range_sum == [0 &lt;=] [pop 0] [1 - dup] [dip +] genrec</code></pre>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[9]:</div>
<div class="prompt input_prompt">In&nbsp;[11]:</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;10 range&#39;</span><span class="p">)</span>
@ -12579,7 +12579,7 @@ range_sum == [0 &lt;=] [pop 0] [1 - dup] [dip +] genrec</code></pre>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[10]:</div>
<div class="prompt input_prompt">In&nbsp;[12]:</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;[9 8 7 6 5 4 3 2 1 0] sum&#39;</span><span class="p">)</span>
@ -12610,7 +12610,7 @@ range_sum == [0 &lt;=] [pop 0] [1 - dup] [dip +] genrec</code></pre>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[11]:</div>
<div class="prompt input_prompt">In&nbsp;[13]:</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;10 range sum&#39;</span><span class="p">)</span>
@ -13127,7 +13127,7 @@ range_sum == [0 &lt;=] [pop 0] [1 - dup] [dip +] genrec</code></pre>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[12]:</div>
<div class="prompt input_prompt">In&nbsp;[14]:</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;10 range_sum&#39;</span><span class="p">)</span>
@ -14390,789 +14390,6 @@ False [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 2] . swaac
</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="Tree-with-node-and-list-of-trees.">Tree with node and list of trees.<a class="anchor-link" href="#Tree-with-node-and-list-of-trees.">&#182;</a></h1>
<pre><code>tree = [] | [node [tree*]]</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="treestep"><code>treestep</code><a class="anchor-link" href="#treestep">&#182;</a></h3>
<pre><code>tree z [C] [N] treestep
[] z [C] [N] treestep
---------------------------
z
[node [tree*]] z [C] [N] treestep
--------------------------------------- w/ K == z [C] [N] treestep
node N [tree*] [K] map C</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="Derive-the-recursive-form.">Derive the recursive form.<a class="anchor-link" href="#Derive-the-recursive-form.">&#182;</a></h3>
<pre><code>K == [not] [pop z] [J] ifte
[node [tree*]] J
------------------------------
node N [tree*] [K] map C
J == .. [N] .. [K] .. [C] ..
[node [tree*]] uncons [N] dip
node [[tree*]] [N] dip
node N [[tree*]]
node N [[tree*]] i [K] map
node N [tree*] [K] map
node N [K.tree*]
J == uncons [N] dip i [K] map [C] i
K == [not] [pop z] [uncons [N] dip i [K] map [C] i] ifte
K == [not] [pop z] [uncons [N] dip i] [map [C] i] genrec</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="Extract-the-givens-to-parameterize-the-program.">Extract the givens to parameterize the program.<a class="anchor-link" href="#Extract-the-givens-to-parameterize-the-program.">&#182;</a></h3>
<pre><code>[not] [pop z] [uncons [N] dip unquote] [map [C] i] genrec
[not] [z] [pop] swoncat [uncons [N] dip unquote] [map [C] i] genrec
[not] z unit [pop] swoncat [uncons [N] dip unquote] [map [C] i] genrec
z [not] swap unit [pop] swoncat [uncons [N] dip unquote] [map [C] i] genrec
\............TS0............/
z TS0 [uncons [N] dip unquote] [map [C] i] genrec
z [uncons [N] dip unquote] [TS0] dip [map [C] i] genrec
z [[N] dip unquote] [uncons] swoncat [TS0] dip [map [C] i] genrec
z [N] [dip unquote] cons [uncons] swoncat [TS0] dip [map [C] i] genrec
\...........TS1.................../
z [N] TS1 [TS0] dip [map [C] i] genrec
z [N] [map [C] i] [TS1 [TS0] dip] dip genrec
z [N] [map C ] [TS1 [TS0] dip] dip genrec
z [N] [C] [map] swoncat [TS1 [TS0] dip] dip genrec
z [C] [N] swap [map] swoncat [TS1 [TS0] dip] dip genrec</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">
<pre><code> TS0 == [not] swap unit [pop] swoncat
TS1 == [dip i] cons [uncons] swoncat
treestep == swap [map] swoncat [TS1 [TS0] dip] dip genrec</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">
<pre><code> [] 0 [C] [N] treestep
---------------------------
0
[n [tree*]] 0 [sum +] [] treestep
--------------------------------------------------
n [tree*] [0 [sum +] [] treestep] map sum +</code></pre>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[40]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">&#39;&#39;&#39;</span>
<span class="s1"> TS0 == [not] swap unit [pop] swoncat</span>
<span class="s1"> TS1 == [dip i] cons [uncons] swoncat</span>
<span class="s1">treestep == swap [map] swoncat [TS1 [TS0] dip] dip genrec</span>
<span class="s1">&#39;&#39;&#39;</span><span class="p">,</span> <span class="n">D</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;[31]:</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;[] 0 [sum +] [] treestep&#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> . [] 0 [sum +] [] treestep
[] . 0 [sum +] [] treestep
[] 0 . [sum +] [] treestep
[] 0 [sum +] . [] treestep
[] 0 [sum +] [] . treestep
[] 0 [sum +] [] . swap [map] swoncat [TS1 [TS0] dip] dip genrec
[] 0 [] [sum +] . [map] swoncat [TS1 [TS0] dip] dip genrec
[] 0 [] [sum +] [map] . swoncat [TS1 [TS0] dip] dip genrec
[] 0 [] [sum +] [map] . swap concat [TS1 [TS0] dip] dip genrec
[] 0 [] [map] [sum +] . concat [TS1 [TS0] dip] dip genrec
[] 0 [] [map sum +] . [TS1 [TS0] dip] dip genrec
[] 0 [] [map sum +] [TS1 [TS0] dip] . dip genrec
[] 0 [] . TS1 [TS0] dip [map sum +] genrec
[] 0 [] . [dip i] cons [uncons] swoncat [TS0] dip [map sum +] genrec
[] 0 [] [dip i] . cons [uncons] swoncat [TS0] dip [map sum +] genrec
[] 0 [[] dip i] . [uncons] swoncat [TS0] dip [map sum +] genrec
[] 0 [[] dip i] [uncons] . swoncat [TS0] dip [map sum +] genrec
[] 0 [[] dip i] [uncons] . swap concat [TS0] dip [map sum +] genrec
[] 0 [uncons] [[] dip i] . concat [TS0] dip [map sum +] genrec
[] 0 [uncons [] dip i] . [TS0] dip [map sum +] genrec
[] 0 [uncons [] dip i] [TS0] . dip [map sum +] genrec
[] 0 . TS0 [uncons [] dip i] [map sum +] genrec
[] 0 . [not] swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] 0 [not] . swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] [not] 0 . unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] [not] 0 . [] cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] [not] 0 [] . cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] [not] [0] . [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] [not] [0] [pop] . swoncat [uncons [] dip i] [map sum +] genrec
[] [not] [0] [pop] . swap concat [uncons [] dip i] [map sum +] genrec
[] [not] [pop] [0] . concat [uncons [] dip i] [map sum +] genrec
[] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec
[] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec
[] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec
[] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte
[] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[]] [not] . infra first choice i
[] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] []] swaack first choice i
True . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] []] swaack first choice i
True [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] []] . swaack first choice i
[] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [True] . first choice i
[] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] True . choice i
[] [pop 0] . i
[] . pop 0
. 0
0 .
</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;[32]:</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;[23 []] 0 [sum +] [] treestep&#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> . [23 []] 0 [sum +] [] treestep
[23 []] . 0 [sum +] [] treestep
[23 []] 0 . [sum +] [] treestep
[23 []] 0 [sum +] . [] treestep
[23 []] 0 [sum +] [] . treestep
[23 []] 0 [sum +] [] . swap [map] swoncat [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [sum +] . [map] swoncat [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [sum +] [map] . swoncat [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [sum +] [map] . swap concat [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [map] [sum +] . concat [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [map sum +] . [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [map sum +] [TS1 [TS0] dip] . dip genrec
[23 []] 0 [] . TS1 [TS0] dip [map sum +] genrec
[23 []] 0 [] . [dip i] cons [uncons] swoncat [TS0] dip [map sum +] genrec
[23 []] 0 [] [dip i] . cons [uncons] swoncat [TS0] dip [map sum +] genrec
[23 []] 0 [[] dip i] . [uncons] swoncat [TS0] dip [map sum +] genrec
[23 []] 0 [[] dip i] [uncons] . swoncat [TS0] dip [map sum +] genrec
[23 []] 0 [[] dip i] [uncons] . swap concat [TS0] dip [map sum +] genrec
[23 []] 0 [uncons] [[] dip i] . concat [TS0] dip [map sum +] genrec
[23 []] 0 [uncons [] dip i] . [TS0] dip [map sum +] genrec
[23 []] 0 [uncons [] dip i] [TS0] . dip [map sum +] genrec
[23 []] 0 . TS0 [uncons [] dip i] [map sum +] genrec
[23 []] 0 . [not] swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] 0 [not] . swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] 0 . unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] 0 . [] cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] 0 [] . cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] [0] . [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] [0] [pop] . swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] [0] [pop] . swap concat [uncons [] dip i] [map sum +] genrec
[23 []] [not] [pop] [0] . concat [uncons [] dip i] [map sum +] genrec
[23 []] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec
[23 []] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec
[23 []] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec
[23 []] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte
[23 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[23 []]] [not] . infra first choice i
[23 []] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 []]] swaack first choice i
False . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 []]] swaack first choice i
False [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 []]] . swaack first choice i
[23 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [False] . first choice i
[23 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] False . choice i
[23 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . i
[23 []] . uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[]] . [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[]] [] . dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 . [[]] i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[]] . i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 . [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum +
23 [] . sum +
23 [] . 0 [+] catamorphism +
23 [] 0 . [+] catamorphism +
23 [] 0 [+] . catamorphism +
23 [] 0 [+] . [[] =] roll&gt; [uncons swap] swap hylomorphism +
23 [] 0 [+] [[] =] . roll&gt; [uncons swap] swap hylomorphism +
23 [] [[] =] 0 [+] . [uncons swap] swap hylomorphism +
23 [] [[] =] 0 [+] [uncons swap] . swap hylomorphism +
23 [] [[] =] 0 [uncons swap] [+] . hylomorphism +
23 [] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec +
23 [] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec +
23 [] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec +
23 [] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec +
23 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec +
23 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec +
23 [] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec +
23 [] [[] =] [pop 0] [uncons swap] [dip +] . genrec +
23 [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[] 23] [[] =] . infra first choice i +
23 [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i +
23 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i +
23 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i +
23 True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] . swaack first choice i +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True 23] . first choice i +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i +
23 [] [pop 0] . i +
23 [] . pop 0 +
23 . 0 +
23 0 . +
23 .
</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;[33]:</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;[23 [[2 []] [3 []]]] 0 [sum +] [] treestep&#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> . [23 [[2 []] [3 []]]] 0 [sum +] [] treestep
[23 [[2 []] [3 []]]] . 0 [sum +] [] treestep
[23 [[2 []] [3 []]]] 0 . [sum +] [] treestep
[23 [[2 []] [3 []]]] 0 [sum +] . [] treestep
[23 [[2 []] [3 []]]] 0 [sum +] [] . treestep
[23 [[2 []] [3 []]]] 0 [sum +] [] . swap [map] swoncat [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [sum +] . [map] swoncat [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [sum +] [map] . swoncat [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [sum +] [map] . swap concat [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [map] [sum +] . concat [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [map sum +] . [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [map sum +] [TS1 [TS0] dip] . dip genrec
[23 [[2 []] [3 []]]] 0 [] . TS1 [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [] . [dip i] cons [uncons] swoncat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [] [dip i] . cons [uncons] swoncat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [[] dip i] . [uncons] swoncat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [[] dip i] [uncons] . swoncat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [[] dip i] [uncons] . swap concat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [uncons] [[] dip i] . concat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [uncons [] dip i] . [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [uncons [] dip i] [TS0] . dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 . TS0 [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] 0 . [not] swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [not] . swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] 0 . unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] 0 . [] cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] 0 [] . cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [0] . [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [0] [pop] . swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [0] [pop] . swap concat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [pop] [0] . concat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec
[23 [[2 []] [3 []]]] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte
[23 [[2 []] [3 []]]] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[23 [[2 []] [3 []]]]] [not] . infra first choice i
[23 [[2 []] [3 []]]] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 [[2 []] [3 []]]]] swaack first choice i
False . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 [[2 []] [3 []]]]] swaack first choice i
False [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 [[2 []] [3 []]]]] . swaack first choice i
[23 [[2 []] [3 []]]] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [False] . first choice i
[23 [[2 []] [3 []]]] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] False . choice i
[23 [[2 []] [3 []]]] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . i
[23 [[2 []] [3 []]]] . uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[[2 []] [3 []]]] . [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[[2 []] [3 []]]] [] . dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 . [[[2 []] [3 []]]] i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[[2 []] [3 []]]] . i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 . [[2 []] [3 []]] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[2 []] [3 []]] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[2 []] [3 []]] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum +
23 [] [[[3 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first] . infra sum +
. [[3 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
[[3 []] 23] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
[[3 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . infra first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] . [not] [pop 0] [uncons [] dip i] [map sum +] genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [not] . [pop 0] [uncons [] dip i] [map sum +] genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[3 []] 23] [not] . infra first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [3 []] 23] swaack first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 False . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [3 []] 23] swaack first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 False [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [3 []] 23] . swaack first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [False 23] . first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] False . choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] . uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [[]] . [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [[]] [] . dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 . [[]] i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [[]] . i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 . [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . 0 [+] catamorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] 0 . [+] catamorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] 0 [+] . catamorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] 0 [+] . [[] =] roll&gt; [uncons swap] swap hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] 0 [+] [[] =] . roll&gt; [uncons swap] swap hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [+] . [uncons swap] swap hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [+] [uncons swap] . swap hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [uncons swap] [+] . hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] [dip +] . genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[] 3 23] [[] =] . infra first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 3 23] swaack first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 3 23] swaack first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 3 23] swaack first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 3 23] . swaack first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True 3 23] . first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [pop 0] . i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . pop 0 + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 . 0 + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 0 . + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 . [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
[3 23] . first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
3 . [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
3 [[2 []] 23] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
3 [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . infra first [23] swaack sum +
23 [2 []] . [not] [pop 0] [uncons [] dip i] [map sum +] genrec [3] swaack first [23] swaack sum +
23 [2 []] [not] . [pop 0] [uncons [] dip i] [map sum +] genrec [3] swaack first [23] swaack sum +
23 [2 []] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec [3] swaack first [23] swaack sum +
23 [2 []] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec [3] swaack first [23] swaack sum +
23 [2 []] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec [3] swaack first [23] swaack sum +
23 [2 []] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte [3] swaack first [23] swaack sum +
23 [2 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[2 []] 23] [not] . infra first choice i [3] swaack first [23] swaack sum +
23 [2 []] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [2 []] 23] swaack first choice i [3] swaack first [23] swaack sum +
23 False . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [2 []] 23] swaack first choice i [3] swaack first [23] swaack sum +
23 False [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [2 []] 23] . swaack first choice i [3] swaack first [23] swaack sum +
23 [2 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [False 23] . first choice i [3] swaack first [23] swaack sum +
23 [2 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] False . choice i [3] swaack first [23] swaack sum +
23 [2 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . i [3] swaack first [23] swaack sum +
23 [2 []] . uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 [[]] . [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 [[]] [] . dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 . [[]] i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 [[]] . i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 . [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 [] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum + [3] swaack first [23] swaack sum +
23 2 [] . sum + [3] swaack first [23] swaack sum +
23 2 [] . 0 [+] catamorphism + [3] swaack first [23] swaack sum +
23 2 [] 0 . [+] catamorphism + [3] swaack first [23] swaack sum +
23 2 [] 0 [+] . catamorphism + [3] swaack first [23] swaack sum +
23 2 [] 0 [+] . [[] =] roll&gt; [uncons swap] swap hylomorphism + [3] swaack first [23] swaack sum +
23 2 [] 0 [+] [[] =] . roll&gt; [uncons swap] swap hylomorphism + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [+] . [uncons swap] swap hylomorphism + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [+] [uncons swap] . swap hylomorphism + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [uncons swap] [+] . hylomorphism + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] [dip +] . genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte + [3] swaack first [23] swaack sum +
23 2 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[] 2 23] [[] =] . infra first choice i + [3] swaack first [23] swaack sum +
23 2 [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 2 23] swaack first choice i + [3] swaack first [23] swaack sum +
23 2 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 2 23] swaack first choice i + [3] swaack first [23] swaack sum +
23 2 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 2 23] swaack first choice i + [3] swaack first [23] swaack sum +
23 2 True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 2 23] . swaack first choice i + [3] swaack first [23] swaack sum +
23 2 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True 2 23] . first choice i + [3] swaack first [23] swaack sum +
23 2 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i + [3] swaack first [23] swaack sum +
23 2 [] [pop 0] . i + [3] swaack first [23] swaack sum +
23 2 [] . pop 0 + [3] swaack first [23] swaack sum +
23 2 . 0 + [3] swaack first [23] swaack sum +
23 2 0 . + [3] swaack first [23] swaack sum +
23 2 . [3] swaack first [23] swaack sum +
23 2 [3] . swaack first [23] swaack sum +
3 [2 23] . first [23] swaack sum +
3 2 . [23] swaack sum +
3 2 [23] . swaack sum +
23 [2 3] . sum +
23 [2 3] . 0 [+] catamorphism +
23 [2 3] 0 . [+] catamorphism +
23 [2 3] 0 [+] . catamorphism +
23 [2 3] 0 [+] . [[] =] roll&gt; [uncons swap] swap hylomorphism +
23 [2 3] 0 [+] [[] =] . roll&gt; [uncons swap] swap hylomorphism +
23 [2 3] [[] =] 0 [+] . [uncons swap] swap hylomorphism +
23 [2 3] [[] =] 0 [+] [uncons swap] . swap hylomorphism +
23 [2 3] [[] =] 0 [uncons swap] [+] . hylomorphism +
23 [2 3] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec +
23 [2 3] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec +
23 [2 3] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] [dip +] . genrec +
23 [2 3] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte +
23 [2 3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[2 3] 23] [[] =] . infra first choice i +
23 [2 3] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 3] 23] swaack first choice i +
23 [2 3] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 3] 23] swaack first choice i +
23 False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 3] 23] swaack first choice i +
23 False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 3] 23] . swaack first choice i +
23 [2 3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False 23] . first choice i +
23 [2 3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i +
23 [2 3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i +
23 [2 3] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + +
23 2 [3] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + +
23 [3] 2 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + +
23 [3] 2 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + +
23 [3] . [[] =] [pop 0] [uncons swap] [dip +] genrec 2 + +
23 [3] [[] =] . [pop 0] [uncons swap] [dip +] genrec 2 + +
23 [3] [[] =] [pop 0] . [uncons swap] [dip +] genrec 2 + +
23 [3] [[] =] [pop 0] [uncons swap] . [dip +] genrec 2 + +
23 [3] [[] =] [pop 0] [uncons swap] [dip +] . genrec 2 + +
23 [3] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 2 + +
23 [3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[3] 23] [[] =] . infra first choice i 2 + +
23 [3] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3] 23] swaack first choice i 2 + +
23 [3] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3] 23] swaack first choice i 2 + +
23 False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3] 23] swaack first choice i 2 + +
23 False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3] 23] . swaack first choice i 2 + +
23 [3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False 23] . first choice i 2 + +
23 [3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i 2 + +
23 [3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i 2 + +
23 [3] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 2 + +
23 3 [] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 2 + +
23 [] 3 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 2 + +
23 [] 3 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + 2 + +
23 [] . [[] =] [pop 0] [uncons swap] [dip +] genrec 3 + 2 + +
23 [] [[] =] . [pop 0] [uncons swap] [dip +] genrec 3 + 2 + +
23 [] [[] =] [pop 0] . [uncons swap] [dip +] genrec 3 + 2 + +
23 [] [[] =] [pop 0] [uncons swap] . [dip +] genrec 3 + 2 + +
23 [] [[] =] [pop 0] [uncons swap] [dip +] . genrec 3 + 2 + +
23 [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 3 + 2 + +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[] 23] [[] =] . infra first choice i 3 + 2 + +
23 [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i 3 + 2 + +
23 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i 3 + 2 + +
23 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i 3 + 2 + +
23 True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] . swaack first choice i 3 + 2 + +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True 23] . first choice i 3 + 2 + +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i 3 + 2 + +
23 [] [pop 0] . i 3 + 2 + +
23 [] . pop 0 3 + 2 + +
23 . 0 3 + 2 + +
23 0 . 3 + 2 + +
23 0 3 . + 2 + +
23 3 . 2 + +
23 3 2 . + +
23 5 . +
28 .
</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;[34]:</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;[23 [[2 [[23 [[2 []] [3 []]]][23 [[2 []] [3 []]]]]] [3 [[23 [[2 []] [3 []]]][23 [[2 []] [3 []]]]]]]] 0 [sum +] [] treestep&#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>140
</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;[35]:</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;[] [] [unit cons] [23 +] treestep&#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>[]
</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;[36]:</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;[23 []] [] [unit cons] [23 +] treestep&#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>[46 []]
</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;[37]:</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;[23 [[2 []] [3 []]]] [] [unit cons] [23 +] treestep&#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>[46 [[25 []] [26 []]]]
</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;[38]:</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;treemap == [] [unit cons] roll&lt; treestep&#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;[39]:</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;[23 [[2 []] [3 []]]] [23 +] treemap&#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>[46 [[25 []] [26 []]]]
</pre>
</div>
</div>
</div>
</div>
</div>
</div>
</div>

730
docs/Hylo-,_Ana-,_Cata-,_and_Para-morphisms_-_Recursion_Combinators.ipynb
View File

@ -273,9 +273,7 @@
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -642,7 +640,7 @@
},
{
"cell_type": "code",
"execution_count": 8,
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
@ -660,7 +658,7 @@
},
{
"cell_type": "code",
"execution_count": 9,
"execution_count": 11,
"metadata": {},
"outputs": [
{
@ -677,7 +675,7 @@
},
{
"cell_type": "code",
"execution_count": 10,
"execution_count": 12,
"metadata": {},
"outputs": [
{
@ -694,10 +692,8 @@
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -1199,10 +1195,8 @@
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": true
},
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -1906,9 +1900,7 @@
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": true
},
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -2008,9 +2000,7 @@
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": true
},
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -2092,9 +2082,7 @@
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": true
},
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -2177,9 +2165,7 @@
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": true
},
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -2269,698 +2255,6 @@
"\n",
"\"Too much is always better than not enough.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Tree with node and list of trees.\n",
"\n",
" tree = [] | [node [tree*]]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### `treestep`\n",
"\n",
" tree z [C] [N] treestep\n",
"\n",
"\n",
" [] z [C] [N] treestep\n",
" ---------------------------\n",
" z\n",
"\n",
"\n",
" [node [tree*]] z [C] [N] treestep\n",
" --------------------------------------- w/ K == z [C] [N] treestep\n",
" node N [tree*] [K] map C"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Derive the recursive form.\n",
" K == [not] [pop z] [J] ifte\n",
"\n",
"\n",
" [node [tree*]] J\n",
" ------------------------------\n",
" node N [tree*] [K] map C\n",
"\n",
"\n",
" J == .. [N] .. [K] .. [C] ..\n",
"\n",
" [node [tree*]] uncons [N] dip\n",
" node [[tree*]] [N] dip\n",
" node N [[tree*]]\n",
"\n",
" node N [[tree*]] i [K] map\n",
" node N [tree*] [K] map\n",
" node N [K.tree*]\n",
"\n",
" J == uncons [N] dip i [K] map [C] i\n",
"\n",
" K == [not] [pop z] [uncons [N] dip i [K] map [C] i] ifte\n",
" K == [not] [pop z] [uncons [N] dip i] [map [C] i] genrec"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Extract the givens to parameterize the program.\n",
" [not] [pop z] [uncons [N] dip unquote] [map [C] i] genrec\n",
" [not] [z] [pop] swoncat [uncons [N] dip unquote] [map [C] i] genrec\n",
" [not] z unit [pop] swoncat [uncons [N] dip unquote] [map [C] i] genrec\n",
" z [not] swap unit [pop] swoncat [uncons [N] dip unquote] [map [C] i] genrec\n",
" \\............TS0............/\n",
" z TS0 [uncons [N] dip unquote] [map [C] i] genrec\n",
" z [uncons [N] dip unquote] [TS0] dip [map [C] i] genrec\n",
" z [[N] dip unquote] [uncons] swoncat [TS0] dip [map [C] i] genrec\n",
" z [N] [dip unquote] cons [uncons] swoncat [TS0] dip [map [C] i] genrec\n",
" \\...........TS1.................../\n",
" z [N] TS1 [TS0] dip [map [C] i] genrec\n",
" z [N] [map [C] i] [TS1 [TS0] dip] dip genrec\n",
" z [N] [map C ] [TS1 [TS0] dip] dip genrec\n",
" z [N] [C] [map] swoncat [TS1 [TS0] dip] dip genrec\n",
" z [C] [N] swap [map] swoncat [TS1 [TS0] dip] dip genrec"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" TS0 == [not] swap unit [pop] swoncat\n",
" TS1 == [dip i] cons [uncons] swoncat\n",
" treestep == swap [map] swoncat [TS1 [TS0] dip] dip genrec"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" [] 0 [C] [N] treestep\n",
" ---------------------------\n",
" 0\n",
"\n",
"\n",
" [n [tree*]] 0 [sum +] [] treestep\n",
" --------------------------------------------------\n",
" n [tree*] [0 [sum +] [] treestep] map sum +"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [],
"source": [
"DefinitionWrapper.add_definitions('''\n",
"\n",
" TS0 == [not] swap unit [pop] swoncat\n",
" TS1 == [dip i] cons [uncons] swoncat\n",
"treestep == swap [map] swoncat [TS1 [TS0] dip] dip genrec\n",
"\n",
"''', D)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" . [] 0 [sum +] [] treestep\n",
" [] . 0 [sum +] [] treestep\n",
" [] 0 . [sum +] [] treestep\n",
" [] 0 [sum +] . [] treestep\n",
" [] 0 [sum +] [] . treestep\n",
" [] 0 [sum +] [] . swap [map] swoncat [TS1 [TS0] dip] dip genrec\n",
" [] 0 [] [sum +] . [map] swoncat [TS1 [TS0] dip] dip genrec\n",
" [] 0 [] [sum +] [map] . swoncat [TS1 [TS0] dip] dip genrec\n",
" [] 0 [] [sum +] [map] . swap concat [TS1 [TS0] dip] dip genrec\n",
" [] 0 [] [map] [sum +] . concat [TS1 [TS0] dip] dip genrec\n",
" [] 0 [] [map sum +] . [TS1 [TS0] dip] dip genrec\n",
" [] 0 [] [map sum +] [TS1 [TS0] dip] . dip genrec\n",
" [] 0 [] . TS1 [TS0] dip [map sum +] genrec\n",
" [] 0 [] . [dip i] cons [uncons] swoncat [TS0] dip [map sum +] genrec\n",
" [] 0 [] [dip i] . cons [uncons] swoncat [TS0] dip [map sum +] genrec\n",
" [] 0 [[] dip i] . [uncons] swoncat [TS0] dip [map sum +] genrec\n",
" [] 0 [[] dip i] [uncons] . swoncat [TS0] dip [map sum +] genrec\n",
" [] 0 [[] dip i] [uncons] . swap concat [TS0] dip [map sum +] genrec\n",
" [] 0 [uncons] [[] dip i] . concat [TS0] dip [map sum +] genrec\n",
" [] 0 [uncons [] dip i] . [TS0] dip [map sum +] genrec\n",
" [] 0 [uncons [] dip i] [TS0] . dip [map sum +] genrec\n",
" [] 0 . TS0 [uncons [] dip i] [map sum +] genrec\n",
" [] 0 . [not] swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [] 0 [not] . swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [] [not] 0 . unit [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [] [not] 0 . [] cons [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [] [not] 0 [] . cons [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [] [not] [0] . [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [] [not] [0] [pop] . swoncat [uncons [] dip i] [map sum +] genrec\n",
" [] [not] [0] [pop] . swap concat [uncons [] dip i] [map sum +] genrec\n",
" [] [not] [pop] [0] . concat [uncons [] dip i] [map sum +] genrec\n",
" [] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec\n",
" [] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec\n",
" [] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec\n",
" [] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte\n",
"[] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[]] [not] . infra first choice i\n",
" [] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] []] swaack first choice i\n",
" True . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] []] swaack first choice i\n",
" True [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] []] . swaack first choice i\n",
" [] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [True] . first choice i\n",
" [] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] True . choice i\n",
" [] [pop 0] . i\n",
" [] . pop 0\n",
" . 0\n",
" 0 . \n"
]
}
],
"source": [
"V('[] 0 [sum +] [] treestep')"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" . [23 []] 0 [sum +] [] treestep\n",
" [23 []] . 0 [sum +] [] treestep\n",
" [23 []] 0 . [sum +] [] treestep\n",
" [23 []] 0 [sum +] . [] treestep\n",
" [23 []] 0 [sum +] [] . treestep\n",
" [23 []] 0 [sum +] [] . swap [map] swoncat [TS1 [TS0] dip] dip genrec\n",
" [23 []] 0 [] [sum +] . [map] swoncat [TS1 [TS0] dip] dip genrec\n",
" [23 []] 0 [] [sum +] [map] . swoncat [TS1 [TS0] dip] dip genrec\n",
" [23 []] 0 [] [sum +] [map] . swap concat [TS1 [TS0] dip] dip genrec\n",
" [23 []] 0 [] [map] [sum +] . concat [TS1 [TS0] dip] dip genrec\n",
" [23 []] 0 [] [map sum +] . [TS1 [TS0] dip] dip genrec\n",
" [23 []] 0 [] [map sum +] [TS1 [TS0] dip] . dip genrec\n",
" [23 []] 0 [] . TS1 [TS0] dip [map sum +] genrec\n",
" [23 []] 0 [] . [dip i] cons [uncons] swoncat [TS0] dip [map sum +] genrec\n",
" [23 []] 0 [] [dip i] . cons [uncons] swoncat [TS0] dip [map sum +] genrec\n",
" [23 []] 0 [[] dip i] . [uncons] swoncat [TS0] dip [map sum +] genrec\n",
" [23 []] 0 [[] dip i] [uncons] . swoncat [TS0] dip [map sum +] genrec\n",
" [23 []] 0 [[] dip i] [uncons] . swap concat [TS0] dip [map sum +] genrec\n",
" [23 []] 0 [uncons] [[] dip i] . concat [TS0] dip [map sum +] genrec\n",
" [23 []] 0 [uncons [] dip i] . [TS0] dip [map sum +] genrec\n",
" [23 []] 0 [uncons [] dip i] [TS0] . dip [map sum +] genrec\n",
" [23 []] 0 . TS0 [uncons [] dip i] [map sum +] genrec\n",
" [23 []] 0 . [not] swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [23 []] 0 [not] . swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [23 []] [not] 0 . unit [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [23 []] [not] 0 . [] cons [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [23 []] [not] 0 [] . cons [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [23 []] [not] [0] . [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [23 []] [not] [0] [pop] . swoncat [uncons [] dip i] [map sum +] genrec\n",
" [23 []] [not] [0] [pop] . swap concat [uncons [] dip i] [map sum +] genrec\n",
" [23 []] [not] [pop] [0] . concat [uncons [] dip i] [map sum +] genrec\n",
" [23 []] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec\n",
" [23 []] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec\n",
" [23 []] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec\n",
" [23 []] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte\n",
"[23 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[23 []]] [not] . infra first choice i\n",
" [23 []] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 []]] swaack first choice i\n",
" False . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 []]] swaack first choice i\n",
" False [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 []]] . swaack first choice i\n",
" [23 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [False] . first choice i\n",
" [23 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] False . choice i\n",
" [23 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . i\n",
" [23 []] . uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +\n",
" 23 [[]] . [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +\n",
" 23 [[]] [] . dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +\n",
" 23 . [[]] i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +\n",
" 23 [[]] . i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +\n",
" 23 . [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +\n",
" 23 [] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +\n",
" 23 [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum +\n",
" 23 [] . sum +\n",
" 23 [] . 0 [+] catamorphism +\n",
" 23 [] 0 . [+] catamorphism +\n",
" 23 [] 0 [+] . catamorphism +\n",
" 23 [] 0 [+] . [[] =] roll> [uncons swap] swap hylomorphism +\n",
" 23 [] 0 [+] [[] =] . roll> [uncons swap] swap hylomorphism +\n",
" 23 [] [[] =] 0 [+] . [uncons swap] swap hylomorphism +\n",
" 23 [] [[] =] 0 [+] [uncons swap] . swap hylomorphism +\n",
" 23 [] [[] =] 0 [uncons swap] [+] . hylomorphism +\n",
" 23 [] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec +\n",
" 23 [] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec +\n",
" 23 [] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +\n",
" 23 [] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +\n",
" 23 [] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +\n",
" 23 [] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +\n",
" 23 [] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec +\n",
" 23 [] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec +\n",
" 23 [] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec +\n",
" 23 [] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec +\n",
" 23 [] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec +\n",
" 23 [] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec +\n",
" 23 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec +\n",
" 23 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec +\n",
" 23 [] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec +\n",
" 23 [] [[] =] [pop 0] [uncons swap] [dip +] . genrec +\n",
" 23 [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte +\n",
" 23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[] 23] [[] =] . infra first choice i +\n",
" 23 [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i +\n",
" 23 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i +\n",
" 23 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i +\n",
" 23 True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] . swaack first choice i +\n",
" 23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True 23] . first choice i +\n",
" 23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i +\n",
" 23 [] [pop 0] . i +\n",
" 23 [] . pop 0 +\n",
" 23 . 0 +\n",
" 23 0 . +\n",
" 23 . \n"
]
}
],
"source": [
"V('[23 []] 0 [sum +] [] treestep')"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" . [23 [[2 []] [3 []]]] 0 [sum +] [] treestep\n",
" [23 [[2 []] [3 []]]] . 0 [sum +] [] treestep\n",
" [23 [[2 []] [3 []]]] 0 . [sum +] [] treestep\n",
" [23 [[2 []] [3 []]]] 0 [sum +] . [] treestep\n",
" [23 [[2 []] [3 []]]] 0 [sum +] [] . treestep\n",
" [23 [[2 []] [3 []]]] 0 [sum +] [] . swap [map] swoncat [TS1 [TS0] dip] dip genrec\n",
" [23 [[2 []] [3 []]]] 0 [] [sum +] . [map] swoncat [TS1 [TS0] dip] dip genrec\n",
" [23 [[2 []] [3 []]]] 0 [] [sum +] [map] . swoncat [TS1 [TS0] dip] dip genrec\n",
" [23 [[2 []] [3 []]]] 0 [] [sum +] [map] . swap concat [TS1 [TS0] dip] dip genrec\n",
" [23 [[2 []] [3 []]]] 0 [] [map] [sum +] . concat [TS1 [TS0] dip] dip genrec\n",
" [23 [[2 []] [3 []]]] 0 [] [map sum +] . [TS1 [TS0] dip] dip genrec\n",
" [23 [[2 []] [3 []]]] 0 [] [map sum +] [TS1 [TS0] dip] . dip genrec\n",
" [23 [[2 []] [3 []]]] 0 [] . TS1 [TS0] dip [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] 0 [] . [dip i] cons [uncons] swoncat [TS0] dip [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] 0 [] [dip i] . cons [uncons] swoncat [TS0] dip [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] 0 [[] dip i] . [uncons] swoncat [TS0] dip [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] 0 [[] dip i] [uncons] . swoncat [TS0] dip [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] 0 [[] dip i] [uncons] . swap concat [TS0] dip [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] 0 [uncons] [[] dip i] . concat [TS0] dip [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] 0 [uncons [] dip i] . [TS0] dip [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] 0 [uncons [] dip i] [TS0] . dip [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] 0 . TS0 [uncons [] dip i] [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] 0 . [not] swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] 0 [not] . swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] [not] 0 . unit [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] [not] 0 . [] cons [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] [not] 0 [] . cons [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] [not] [0] . [pop] swoncat [uncons [] dip i] [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] [not] [0] [pop] . swoncat [uncons [] dip i] [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] [not] [0] [pop] . swap concat [uncons [] dip i] [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] [not] [pop] [0] . concat [uncons [] dip i] [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec\n",
" [23 [[2 []] [3 []]]] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec\n",
" [23 [[2 []] [3 []]]] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte\n",
" [23 [[2 []] [3 []]]] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[23 [[2 []] [3 []]]]] [not] . infra first choice i\n",
" [23 [[2 []] [3 []]]] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 [[2 []] [3 []]]]] swaack first choice i\n",
" False . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 [[2 []] [3 []]]]] swaack first choice i\n",
" False [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 [[2 []] [3 []]]]] . swaack first choice i\n",
" [23 [[2 []] [3 []]]] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [False] . first choice i\n",
" [23 [[2 []] [3 []]]] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] False . choice i\n",
" [23 [[2 []] [3 []]]] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . i\n",
" [23 [[2 []] [3 []]]] . uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +\n",
" 23 [[[2 []] [3 []]]] . [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +\n",
" 23 [[[2 []] [3 []]]] [] . dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +\n",
" 23 . [[[2 []] [3 []]]] i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +\n",
" 23 [[[2 []] [3 []]]] . i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +\n",
" 23 . [[2 []] [3 []]] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +\n",
" 23 [[2 []] [3 []]] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +\n",
" 23 [[2 []] [3 []]] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum +\n",
"23 [] [[[3 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first] . infra sum +\n",
" . [[3 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" [[3 []] 23] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" [[3 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . infra first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 [3 []] . [not] [pop 0] [uncons [] dip i] [map sum +] genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 [3 []] [not] . [pop 0] [uncons [] dip i] [map sum +] genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 [3 []] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 [3 []] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 [3 []] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 [3 []] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 [3 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[3 []] 23] [not] . infra first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 [3 []] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [3 []] 23] swaack first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 False . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [3 []] 23] swaack first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 False [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [3 []] 23] . swaack first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 [3 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [False 23] . first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 [3 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] False . choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 [3 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 [3 []] . uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [[]] . [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [[]] [] . dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 . [[]] i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [[]] . i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 . [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] . sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] . 0 [+] catamorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] 0 . [+] catamorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] 0 [+] . catamorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] 0 [+] . [[] =] roll> [uncons swap] swap hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] 0 [+] [[] =] . roll> [uncons swap] swap hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] 0 [+] . [uncons swap] swap hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] 0 [+] [uncons swap] . swap hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] 0 [uncons swap] [+] . hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] [pop 0] [uncons swap] [dip +] . genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[] 3 23] [[] =] . infra first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 3 23] swaack first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 3 23] swaack first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 3 23] swaack first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 3 23] . swaack first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True 3 23] . first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] [pop 0] . i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] . pop 0 + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 . 0 + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 0 . + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 . [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 23 3 [] . swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" [3 23] . first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 3 . [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 3 [[2 []] 23] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +\n",
" 3 [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . infra first [23] swaack sum +\n",
" 23 [2 []] . [not] [pop 0] [uncons [] dip i] [map sum +] genrec [3] swaack first [23] swaack sum +\n",
" 23 [2 []] [not] . [pop 0] [uncons [] dip i] [map sum +] genrec [3] swaack first [23] swaack sum +\n",
" 23 [2 []] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec [3] swaack first [23] swaack sum +\n",
" 23 [2 []] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec [3] swaack first [23] swaack sum +\n",
" 23 [2 []] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec [3] swaack first [23] swaack sum +\n",
" 23 [2 []] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte [3] swaack first [23] swaack sum +\n",
" 23 [2 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[2 []] 23] [not] . infra first choice i [3] swaack first [23] swaack sum +\n",
" 23 [2 []] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [2 []] 23] swaack first choice i [3] swaack first [23] swaack sum +\n",
" 23 False . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [2 []] 23] swaack first choice i [3] swaack first [23] swaack sum +\n",
" 23 False [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [2 []] 23] . swaack first choice i [3] swaack first [23] swaack sum +\n",
" 23 [2 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [False 23] . first choice i [3] swaack first [23] swaack sum +\n",
" 23 [2 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] False . choice i [3] swaack first [23] swaack sum +\n",
" 23 [2 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . i [3] swaack first [23] swaack sum +\n",
" 23 [2 []] . uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +\n",
" 23 2 [[]] . [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +\n",
" 23 2 [[]] [] . dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +\n",
" 23 2 . [[]] i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +\n",
" 23 2 [[]] . i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +\n",
" 23 2 . [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +\n",
" 23 2 [] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum + [3] swaack first [23] swaack sum +\n",
" 23 2 [] . sum + [3] swaack first [23] swaack sum +\n",
" 23 2 [] . 0 [+] catamorphism + [3] swaack first [23] swaack sum +\n",
" 23 2 [] 0 . [+] catamorphism + [3] swaack first [23] swaack sum +\n",
" 23 2 [] 0 [+] . catamorphism + [3] swaack first [23] swaack sum +\n",
" 23 2 [] 0 [+] . [[] =] roll> [uncons swap] swap hylomorphism + [3] swaack first [23] swaack sum +\n",
" 23 2 [] 0 [+] [[] =] . roll> [uncons swap] swap hylomorphism + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] 0 [+] . [uncons swap] swap hylomorphism + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] 0 [+] [uncons swap] . swap hylomorphism + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] 0 [uncons swap] [+] . hylomorphism + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] [pop 0] [uncons swap] [dip +] . genrec + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[] 2 23] [[] =] . infra first choice i + [3] swaack first [23] swaack sum +\n",
" 23 2 [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 2 23] swaack first choice i + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 2 23] swaack first choice i + [3] swaack first [23] swaack sum +\n",
" 23 2 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 2 23] swaack first choice i + [3] swaack first [23] swaack sum +\n",
" 23 2 True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 2 23] . swaack first choice i + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True 2 23] . first choice i + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i + [3] swaack first [23] swaack sum +\n",
" 23 2 [] [pop 0] . i + [3] swaack first [23] swaack sum +\n",
" 23 2 [] . pop 0 + [3] swaack first [23] swaack sum +\n",
" 23 2 . 0 + [3] swaack first [23] swaack sum +\n",
" 23 2 0 . + [3] swaack first [23] swaack sum +\n",
" 23 2 . [3] swaack first [23] swaack sum +\n",
" 23 2 [3] . swaack first [23] swaack sum +\n",
" 3 [2 23] . first [23] swaack sum +\n",
" 3 2 . [23] swaack sum +\n",
" 3 2 [23] . swaack sum +\n",
" 23 [2 3] . sum +\n",
" 23 [2 3] . 0 [+] catamorphism +\n",
" 23 [2 3] 0 . [+] catamorphism +\n",
" 23 [2 3] 0 [+] . catamorphism +\n",
" 23 [2 3] 0 [+] . [[] =] roll> [uncons swap] swap hylomorphism +\n",
" 23 [2 3] 0 [+] [[] =] . roll> [uncons swap] swap hylomorphism +\n",
" 23 [2 3] [[] =] 0 [+] . [uncons swap] swap hylomorphism +\n",
" 23 [2 3] [[] =] 0 [+] [uncons swap] . swap hylomorphism +\n",
" 23 [2 3] [[] =] 0 [uncons swap] [+] . hylomorphism +\n",
" 23 [2 3] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec +\n",
" 23 [2 3] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec +\n",
" 23 [2 3] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +\n",
" 23 [2 3] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +\n",
" 23 [2 3] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +\n",
" 23 [2 3] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +\n",
" 23 [2 3] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec +\n",
" 23 [2 3] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec +\n",
" 23 [2 3] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec +\n",
" 23 [2 3] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec +\n",
" 23 [2 3] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec +\n",
" 23 [2 3] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec +\n",
" 23 [2 3] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec +\n",
" 23 [2 3] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec +\n",
" 23 [2 3] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec +\n",
" 23 [2 3] [[] =] [pop 0] [uncons swap] [dip +] . genrec +\n",
" 23 [2 3] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte +\n",
" 23 [2 3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[2 3] 23] [[] =] . infra first choice i +\n",
" 23 [2 3] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 3] 23] swaack first choice i +\n",
" 23 [2 3] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 3] 23] swaack first choice i +\n",
" 23 False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 3] 23] swaack first choice i +\n",
" 23 False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 3] 23] . swaack first choice i +\n",
" 23 [2 3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False 23] . first choice i +\n",
" 23 [2 3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i +\n",
" 23 [2 3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i +\n",
" 23 [2 3] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + +\n",
" 23 2 [3] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + +\n",
" 23 [3] 2 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + +\n",
" 23 [3] 2 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + +\n",
" 23 [3] . [[] =] [pop 0] [uncons swap] [dip +] genrec 2 + +\n",
" 23 [3] [[] =] . [pop 0] [uncons swap] [dip +] genrec 2 + +\n",
" 23 [3] [[] =] [pop 0] . [uncons swap] [dip +] genrec 2 + +\n",
" 23 [3] [[] =] [pop 0] [uncons swap] . [dip +] genrec 2 + +\n",
" 23 [3] [[] =] [pop 0] [uncons swap] [dip +] . genrec 2 + +\n",
" 23 [3] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 2 + +\n",
" 23 [3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[3] 23] [[] =] . infra first choice i 2 + +\n",
" 23 [3] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3] 23] swaack first choice i 2 + +\n",
" 23 [3] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3] 23] swaack first choice i 2 + +\n",
" 23 False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3] 23] swaack first choice i 2 + +\n",
" 23 False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3] 23] . swaack first choice i 2 + +\n",
" 23 [3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False 23] . first choice i 2 + +\n",
" 23 [3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i 2 + +\n",
" 23 [3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i 2 + +\n",
" 23 [3] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 2 + +\n",
" 23 3 [] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 2 + +\n",
" 23 [] 3 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 2 + +\n",
" 23 [] 3 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + 2 + +\n",
" 23 [] . [[] =] [pop 0] [uncons swap] [dip +] genrec 3 + 2 + +\n",
" 23 [] [[] =] . [pop 0] [uncons swap] [dip +] genrec 3 + 2 + +\n",
" 23 [] [[] =] [pop 0] . [uncons swap] [dip +] genrec 3 + 2 + +\n",
" 23 [] [[] =] [pop 0] [uncons swap] . [dip +] genrec 3 + 2 + +\n",
" 23 [] [[] =] [pop 0] [uncons swap] [dip +] . genrec 3 + 2 + +\n",
" 23 [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 3 + 2 + +\n",
" 23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[] 23] [[] =] . infra first choice i 3 + 2 + +\n",
" 23 [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i 3 + 2 + +\n",
" 23 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i 3 + 2 + +\n",
" 23 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i 3 + 2 + +\n",
" 23 True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] . swaack first choice i 3 + 2 + +\n",
" 23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True 23] . first choice i 3 + 2 + +\n",
" 23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i 3 + 2 + +\n",
" 23 [] [pop 0] . i 3 + 2 + +\n",
" 23 [] . pop 0 3 + 2 + +\n",
" 23 . 0 3 + 2 + +\n",
" 23 0 . 3 + 2 + +\n",
" 23 0 3 . + 2 + +\n",
" 23 3 . 2 + +\n",
" 23 3 2 . + +\n",
" 23 5 . +\n",
" 28 . \n"
]
}
],
"source": [
"V('[23 [[2 []] [3 []]]] 0 [sum +] [] treestep')"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"140\n"
]
}
],
"source": [
"J('[23 [[2 [[23 [[2 []] [3 []]]][23 [[2 []] [3 []]]]]] [3 [[23 [[2 []] [3 []]]][23 [[2 []] [3 []]]]]]]] 0 [sum +] [] treestep')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[]\n"
]
}
],
"source": [
"J('[] [] [unit cons] [23 +] treestep')"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[46 []]\n"
]
}
],
"source": [
"J('[23 []] [] [unit cons] [23 +] treestep')"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[46 [[25 []] [26 []]]]\n"
]
}
],
"source": [
"J('[23 [[2 []] [3 []]]] [] [unit cons] [23 +] treestep')"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [],
"source": [
"define('treemap == [] [unit cons] roll< treestep')"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[46 [[25 []] [26 []]]]\n"
]
}
],
"source": [
"J('[23 [[2 []] [3 []]]] [23 +] treemap')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {

541
docs/Hylo-,_Ana-,_Cata-,_and_Para-morphisms_-_Recursion_Combinators.md
View File

@ -1906,544 +1906,3 @@ V('[2 1] [[] =] [pop c ] [uncons swap] [dip F] genrec')
I think they are having slightly too much fun with the symbols.
"Too much is always better than not enough."
# Tree with node and list of trees.
tree = [] | [node [tree*]]
### `treestep`
tree z [C] [N] treestep
[] z [C] [N] treestep
---------------------------
z
[node [tree*]] z [C] [N] treestep
--------------------------------------- w/ K == z [C] [N] treestep
node N [tree*] [K] map C
### Derive the recursive form.
K == [not] [pop z] [J] ifte
[node [tree*]] J
------------------------------
node N [tree*] [K] map C
J == .. [N] .. [K] .. [C] ..
[node [tree*]] uncons [N] dip
node [[tree*]] [N] dip
node N [[tree*]]
node N [[tree*]] i [K] map
node N [tree*] [K] map
node N [K.tree*]
J == uncons [N] dip i [K] map [C] i
K == [not] [pop z] [uncons [N] dip i [K] map [C] i] ifte
K == [not] [pop z] [uncons [N] dip i] [map [C] i] genrec
### Extract the givens to parameterize the program.
[not] [pop z] [uncons [N] dip unquote] [map [C] i] genrec
[not] [z] [pop] swoncat [uncons [N] dip unquote] [map [C] i] genrec
[not] z unit [pop] swoncat [uncons [N] dip unquote] [map [C] i] genrec
z [not] swap unit [pop] swoncat [uncons [N] dip unquote] [map [C] i] genrec
\............TS0............/
z TS0 [uncons [N] dip unquote] [map [C] i] genrec
z [uncons [N] dip unquote] [TS0] dip [map [C] i] genrec
z [[N] dip unquote] [uncons] swoncat [TS0] dip [map [C] i] genrec
z [N] [dip unquote] cons [uncons] swoncat [TS0] dip [map [C] i] genrec
\...........TS1.................../
z [N] TS1 [TS0] dip [map [C] i] genrec
z [N] [map [C] i] [TS1 [TS0] dip] dip genrec
z [N] [map C ] [TS1 [TS0] dip] dip genrec
z [N] [C] [map] swoncat [TS1 [TS0] dip] dip genrec
z [C] [N] swap [map] swoncat [TS1 [TS0] dip] dip genrec
TS0 == [not] swap unit [pop] swoncat
TS1 == [dip i] cons [uncons] swoncat
treestep == swap [map] swoncat [TS1 [TS0] dip] dip genrec
[] 0 [C] [N] treestep
---------------------------
0
[n [tree*]] 0 [sum +] [] treestep
--------------------------------------------------
n [tree*] [0 [sum +] [] treestep] map sum +
```python
DefinitionWrapper.add_definitions('''
TS0 == [not] swap unit [pop] swoncat
TS1 == [dip i] cons [uncons] swoncat
treestep == swap [map] swoncat [TS1 [TS0] dip] dip genrec
''', D)
```
```python
V('[] 0 [sum +] [] treestep')
```
. [] 0 [sum +] [] treestep
[] . 0 [sum +] [] treestep
[] 0 . [sum +] [] treestep
[] 0 [sum +] . [] treestep
[] 0 [sum +] [] . treestep
[] 0 [sum +] [] . swap [map] swoncat [TS1 [TS0] dip] dip genrec
[] 0 [] [sum +] . [map] swoncat [TS1 [TS0] dip] dip genrec
[] 0 [] [sum +] [map] . swoncat [TS1 [TS0] dip] dip genrec
[] 0 [] [sum +] [map] . swap concat [TS1 [TS0] dip] dip genrec
[] 0 [] [map] [sum +] . concat [TS1 [TS0] dip] dip genrec
[] 0 [] [map sum +] . [TS1 [TS0] dip] dip genrec
[] 0 [] [map sum +] [TS1 [TS0] dip] . dip genrec
[] 0 [] . TS1 [TS0] dip [map sum +] genrec
[] 0 [] . [dip i] cons [uncons] swoncat [TS0] dip [map sum +] genrec
[] 0 [] [dip i] . cons [uncons] swoncat [TS0] dip [map sum +] genrec
[] 0 [[] dip i] . [uncons] swoncat [TS0] dip [map sum +] genrec
[] 0 [[] dip i] [uncons] . swoncat [TS0] dip [map sum +] genrec
[] 0 [[] dip i] [uncons] . swap concat [TS0] dip [map sum +] genrec
[] 0 [uncons] [[] dip i] . concat [TS0] dip [map sum +] genrec
[] 0 [uncons [] dip i] . [TS0] dip [map sum +] genrec
[] 0 [uncons [] dip i] [TS0] . dip [map sum +] genrec
[] 0 . TS0 [uncons [] dip i] [map sum +] genrec
[] 0 . [not] swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] 0 [not] . swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] [not] 0 . unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] [not] 0 . [] cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] [not] 0 [] . cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] [not] [0] . [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] [not] [0] [pop] . swoncat [uncons [] dip i] [map sum +] genrec
[] [not] [0] [pop] . swap concat [uncons [] dip i] [map sum +] genrec
[] [not] [pop] [0] . concat [uncons [] dip i] [map sum +] genrec
[] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec
[] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec
[] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec
[] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte
[] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[]] [not] . infra first choice i
[] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] []] swaack first choice i
True . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] []] swaack first choice i
True [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] []] . swaack first choice i
[] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [True] . first choice i
[] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] True . choice i
[] [pop 0] . i
[] . pop 0
. 0
0 .
```python
V('[23 []] 0 [sum +] [] treestep')
```
. [23 []] 0 [sum +] [] treestep
[23 []] . 0 [sum +] [] treestep
[23 []] 0 . [sum +] [] treestep
[23 []] 0 [sum +] . [] treestep
[23 []] 0 [sum +] [] . treestep
[23 []] 0 [sum +] [] . swap [map] swoncat [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [sum +] . [map] swoncat [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [sum +] [map] . swoncat [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [sum +] [map] . swap concat [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [map] [sum +] . concat [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [map sum +] . [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [map sum +] [TS1 [TS0] dip] . dip genrec
[23 []] 0 [] . TS1 [TS0] dip [map sum +] genrec
[23 []] 0 [] . [dip i] cons [uncons] swoncat [TS0] dip [map sum +] genrec
[23 []] 0 [] [dip i] . cons [uncons] swoncat [TS0] dip [map sum +] genrec
[23 []] 0 [[] dip i] . [uncons] swoncat [TS0] dip [map sum +] genrec
[23 []] 0 [[] dip i] [uncons] . swoncat [TS0] dip [map sum +] genrec
[23 []] 0 [[] dip i] [uncons] . swap concat [TS0] dip [map sum +] genrec
[23 []] 0 [uncons] [[] dip i] . concat [TS0] dip [map sum +] genrec
[23 []] 0 [uncons [] dip i] . [TS0] dip [map sum +] genrec
[23 []] 0 [uncons [] dip i] [TS0] . dip [map sum +] genrec
[23 []] 0 . TS0 [uncons [] dip i] [map sum +] genrec
[23 []] 0 . [not] swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] 0 [not] . swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] 0 . unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] 0 . [] cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] 0 [] . cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] [0] . [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] [0] [pop] . swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] [0] [pop] . swap concat [uncons [] dip i] [map sum +] genrec
[23 []] [not] [pop] [0] . concat [uncons [] dip i] [map sum +] genrec
[23 []] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec
[23 []] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec
[23 []] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec
[23 []] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte
[23 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[23 []]] [not] . infra first choice i
[23 []] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 []]] swaack first choice i
False . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 []]] swaack first choice i
False [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 []]] . swaack first choice i
[23 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [False] . first choice i
[23 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] False . choice i
[23 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . i
[23 []] . uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[]] . [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[]] [] . dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 . [[]] i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[]] . i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 . [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum +
23 [] . sum +
23 [] . 0 [+] catamorphism +
23 [] 0 . [+] catamorphism +
23 [] 0 [+] . catamorphism +
23 [] 0 [+] . [[] =] roll> [uncons swap] swap hylomorphism +
23 [] 0 [+] [[] =] . roll> [uncons swap] swap hylomorphism +
23 [] [[] =] 0 [+] . [uncons swap] swap hylomorphism +
23 [] [[] =] 0 [+] [uncons swap] . swap hylomorphism +
23 [] [[] =] 0 [uncons swap] [+] . hylomorphism +
23 [] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec +
23 [] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec +
23 [] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec +
23 [] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec +
23 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec +
23 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec +
23 [] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec +
23 [] [[] =] [pop 0] [uncons swap] [dip +] . genrec +
23 [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[] 23] [[] =] . infra first choice i +
23 [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i +
23 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i +
23 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i +
23 True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] . swaack first choice i +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True 23] . first choice i +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i +
23 [] [pop 0] . i +
23 [] . pop 0 +
23 . 0 +
23 0 . +
23 .
```python
V('[23 [[2 []] [3 []]]] 0 [sum +] [] treestep')
```
. [23 [[2 []] [3 []]]] 0 [sum +] [] treestep
[23 [[2 []] [3 []]]] . 0 [sum +] [] treestep
[23 [[2 []] [3 []]]] 0 . [sum +] [] treestep
[23 [[2 []] [3 []]]] 0 [sum +] . [] treestep
[23 [[2 []] [3 []]]] 0 [sum +] [] . treestep
[23 [[2 []] [3 []]]] 0 [sum +] [] . swap [map] swoncat [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [sum +] . [map] swoncat [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [sum +] [map] . swoncat [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [sum +] [map] . swap concat [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [map] [sum +] . concat [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [map sum +] . [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [map sum +] [TS1 [TS0] dip] . dip genrec
[23 [[2 []] [3 []]]] 0 [] . TS1 [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [] . [dip i] cons [uncons] swoncat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [] [dip i] . cons [uncons] swoncat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [[] dip i] . [uncons] swoncat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [[] dip i] [uncons] . swoncat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [[] dip i] [uncons] . swap concat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [uncons] [[] dip i] . concat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [uncons [] dip i] . [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [uncons [] dip i] [TS0] . dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 . TS0 [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] 0 . [not] swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [not] . swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] 0 . unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] 0 . [] cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] 0 [] . cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [0] . [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [0] [pop] . swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [0] [pop] . swap concat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [pop] [0] . concat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec
[23 [[2 []] [3 []]]] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte
[23 [[2 []] [3 []]]] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[23 [[2 []] [3 []]]]] [not] . infra first choice i
[23 [[2 []] [3 []]]] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 [[2 []] [3 []]]]] swaack first choice i
False . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 [[2 []] [3 []]]]] swaack first choice i
False [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 [[2 []] [3 []]]]] . swaack first choice i
[23 [[2 []] [3 []]]] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [False] . first choice i
[23 [[2 []] [3 []]]] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] False . choice i
[23 [[2 []] [3 []]]] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . i
[23 [[2 []] [3 []]]] . uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[[2 []] [3 []]]] . [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[[2 []] [3 []]]] [] . dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 . [[[2 []] [3 []]]] i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[[2 []] [3 []]]] . i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 . [[2 []] [3 []]] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[2 []] [3 []]] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[2 []] [3 []]] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum +
23 [] [[[3 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first] . infra sum +
. [[3 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
[[3 []] 23] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
[[3 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . infra first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] . [not] [pop 0] [uncons [] dip i] [map sum +] genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [not] . [pop 0] [uncons [] dip i] [map sum +] genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[3 []] 23] [not] . infra first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [3 []] 23] swaack first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 False . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [3 []] 23] swaack first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 False [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [3 []] 23] . swaack first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [False 23] . first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] False . choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] . uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [[]] . [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [[]] [] . dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 . [[]] i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [[]] . i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 . [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . 0 [+] catamorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] 0 . [+] catamorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] 0 [+] . catamorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] 0 [+] . [[] =] roll> [uncons swap] swap hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] 0 [+] [[] =] . roll> [uncons swap] swap hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [+] . [uncons swap] swap hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [+] [uncons swap] . swap hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [uncons swap] [+] . hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] [dip +] . genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[] 3 23] [[] =] . infra first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 3 23] swaack first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 3 23] swaack first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 3 23] swaack first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 3 23] . swaack first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True 3 23] . first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [pop 0] . i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . pop 0 + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 . 0 + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 0 . + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 . [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
[3 23] . first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
3 . [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
3 [[2 []] 23] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
3 [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . infra first [23] swaack sum +
23 [2 []] . [not] [pop 0] [uncons [] dip i] [map sum +] genrec [3] swaack first [23] swaack sum +
23 [2 []] [not] . [pop 0] [uncons [] dip i] [map sum +] genrec [3] swaack first [23] swaack sum +
23 [2 []] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec [3] swaack first [23] swaack sum +
23 [2 []] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec [3] swaack first [23] swaack sum +
23 [2 []] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec [3] swaack first [23] swaack sum +
23 [2 []] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte [3] swaack first [23] swaack sum +
23 [2 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[2 []] 23] [not] . infra first choice i [3] swaack first [23] swaack sum +
23 [2 []] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [2 []] 23] swaack first choice i [3] swaack first [23] swaack sum +
23 False . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [2 []] 23] swaack first choice i [3] swaack first [23] swaack sum +
23 False [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [2 []] 23] . swaack first choice i [3] swaack first [23] swaack sum +
23 [2 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [False 23] . first choice i [3] swaack first [23] swaack sum +
23 [2 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] False . choice i [3] swaack first [23] swaack sum +
23 [2 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . i [3] swaack first [23] swaack sum +
23 [2 []] . uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 [[]] . [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 [[]] [] . dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 . [[]] i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 [[]] . i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 . [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 [] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum + [3] swaack first [23] swaack sum +
23 2 [] . sum + [3] swaack first [23] swaack sum +
23 2 [] . 0 [+] catamorphism + [3] swaack first [23] swaack sum +
23 2 [] 0 . [+] catamorphism + [3] swaack first [23] swaack sum +
23 2 [] 0 [+] . catamorphism + [3] swaack first [23] swaack sum +
23 2 [] 0 [+] . [[] =] roll> [uncons swap] swap hylomorphism + [3] swaack first [23] swaack sum +
23 2 [] 0 [+] [[] =] . roll> [uncons swap] swap hylomorphism + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [+] . [uncons swap] swap hylomorphism + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [+] [uncons swap] . swap hylomorphism + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [uncons swap] [+] . hylomorphism + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] [dip +] . genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte + [3] swaack first [23] swaack sum +
23 2 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[] 2 23] [[] =] . infra first choice i + [3] swaack first [23] swaack sum +
23 2 [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 2 23] swaack first choice i + [3] swaack first [23] swaack sum +
23 2 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 2 23] swaack first choice i + [3] swaack first [23] swaack sum +
23 2 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 2 23] swaack first choice i + [3] swaack first [23] swaack sum +
23 2 True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 2 23] . swaack first choice i + [3] swaack first [23] swaack sum +
23 2 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True 2 23] . first choice i + [3] swaack first [23] swaack sum +
23 2 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i + [3] swaack first [23] swaack sum +
23 2 [] [pop 0] . i + [3] swaack first [23] swaack sum +
23 2 [] . pop 0 + [3] swaack first [23] swaack sum +
23 2 . 0 + [3] swaack first [23] swaack sum +
23 2 0 . + [3] swaack first [23] swaack sum +
23 2 . [3] swaack first [23] swaack sum +
23 2 [3] . swaack first [23] swaack sum +
3 [2 23] . first [23] swaack sum +
3 2 . [23] swaack sum +
3 2 [23] . swaack sum +
23 [2 3] . sum +
23 [2 3] . 0 [+] catamorphism +
23 [2 3] 0 . [+] catamorphism +
23 [2 3] 0 [+] . catamorphism +
23 [2 3] 0 [+] . [[] =] roll> [uncons swap] swap hylomorphism +
23 [2 3] 0 [+] [[] =] . roll> [uncons swap] swap hylomorphism +
23 [2 3] [[] =] 0 [+] . [uncons swap] swap hylomorphism +
23 [2 3] [[] =] 0 [+] [uncons swap] . swap hylomorphism +
23 [2 3] [[] =] 0 [uncons swap] [+] . hylomorphism +
23 [2 3] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec +
23 [2 3] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec +
23 [2 3] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] [dip +] . genrec +
23 [2 3] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte +
23 [2 3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[2 3] 23] [[] =] . infra first choice i +
23 [2 3] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 3] 23] swaack first choice i +
23 [2 3] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 3] 23] swaack first choice i +
23 False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 3] 23] swaack first choice i +
23 False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 3] 23] . swaack first choice i +
23 [2 3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False 23] . first choice i +
23 [2 3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i +
23 [2 3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i +
23 [2 3] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + +
23 2 [3] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + +
23 [3] 2 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + +
23 [3] 2 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + +
23 [3] . [[] =] [pop 0] [uncons swap] [dip +] genrec 2 + +
23 [3] [[] =] . [pop 0] [uncons swap] [dip +] genrec 2 + +
23 [3] [[] =] [pop 0] . [uncons swap] [dip +] genrec 2 + +
23 [3] [[] =] [pop 0] [uncons swap] . [dip +] genrec 2 + +
23 [3] [[] =] [pop 0] [uncons swap] [dip +] . genrec 2 + +
23 [3] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 2 + +
23 [3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[3] 23] [[] =] . infra first choice i 2 + +
23 [3] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3] 23] swaack first choice i 2 + +
23 [3] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3] 23] swaack first choice i 2 + +
23 False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3] 23] swaack first choice i 2 + +
23 False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3] 23] . swaack first choice i 2 + +
23 [3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False 23] . first choice i 2 + +
23 [3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i 2 + +
23 [3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i 2 + +
23 [3] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 2 + +
23 3 [] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 2 + +
23 [] 3 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 2 + +
23 [] 3 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + 2 + +
23 [] . [[] =] [pop 0] [uncons swap] [dip +] genrec 3 + 2 + +
23 [] [[] =] . [pop 0] [uncons swap] [dip +] genrec 3 + 2 + +
23 [] [[] =] [pop 0] . [uncons swap] [dip +] genrec 3 + 2 + +
23 [] [[] =] [pop 0] [uncons swap] . [dip +] genrec 3 + 2 + +
23 [] [[] =] [pop 0] [uncons swap] [dip +] . genrec 3 + 2 + +
23 [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 3 + 2 + +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[] 23] [[] =] . infra first choice i 3 + 2 + +
23 [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i 3 + 2 + +
23 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i 3 + 2 + +
23 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i 3 + 2 + +
23 True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] . swaack first choice i 3 + 2 + +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True 23] . first choice i 3 + 2 + +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i 3 + 2 + +
23 [] [pop 0] . i 3 + 2 + +
23 [] . pop 0 3 + 2 + +
23 . 0 3 + 2 + +
23 0 . 3 + 2 + +
23 0 3 . + 2 + +
23 3 . 2 + +
23 3 2 . + +
23 5 . +
28 .
```python
J('[23 [[2 [[23 [[2 []] [3 []]]][23 [[2 []] [3 []]]]]] [3 [[23 [[2 []] [3 []]]][23 [[2 []] [3 []]]]]]]] 0 [sum +] [] treestep')
```
140
```python
J('[] [] [unit cons] [23 +] treestep')
```
[]
```python
J('[23 []] [] [unit cons] [23 +] treestep')
```
[46 []]
```python
J('[23 [[2 []] [3 []]]] [] [unit cons] [23 +] treestep')
```
[46 [[25 []] [26 []]]]
```python
define('treemap == [] [unit cons] roll< treestep')
```
```python
J('[23 [[2 []] [3 []]]] [23 +] treemap')
```
[46 [[25 []] [26 []]]]

573
docs/Hylo-,_Ana-,_Cata-,_and_Para-morphisms_-_Recursion_Combinators.rst
View File

@ -2105,576 +2105,3 @@ Wire" <http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.125>`__
I think they are having slightly too much fun with the symbols.
"Too much is always better than not enough."
Tree with node and list of trees.
=================================
::
tree = [] | [node [tree*]]
``treestep``
~~~~~~~~~~~~
::
tree z [C] [N] treestep
[] z [C] [N] treestep
---------------------------
z
[node [tree*]] z [C] [N] treestep
--------------------------------------- w/ K == z [C] [N] treestep
node N [tree*] [K] map C
Derive the recursive form.
~~~~~~~~~~~~~~~~~~~~~~~~~~
::
K == [not] [pop z] [J] ifte
[node [tree*]] J
------------------------------
node N [tree*] [K] map C
J == .. [N] .. [K] .. [C] ..
[node [tree*]] uncons [N] dip
node [[tree*]] [N] dip
node N [[tree*]]
node N [[tree*]] i [K] map
node N [tree*] [K] map
node N [K.tree*]
J == uncons [N] dip i [K] map [C] i
K == [not] [pop z] [uncons [N] dip i [K] map [C] i] ifte
K == [not] [pop z] [uncons [N] dip i] [map [C] i] genrec
Extract the givens to parameterize the program.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
::
[not] [pop z] [uncons [N] dip unquote] [map [C] i] genrec
[not] [z] [pop] swoncat [uncons [N] dip unquote] [map [C] i] genrec
[not] z unit [pop] swoncat [uncons [N] dip unquote] [map [C] i] genrec
z [not] swap unit [pop] swoncat [uncons [N] dip unquote] [map [C] i] genrec
\............TS0............/
z TS0 [uncons [N] dip unquote] [map [C] i] genrec
z [uncons [N] dip unquote] [TS0] dip [map [C] i] genrec
z [[N] dip unquote] [uncons] swoncat [TS0] dip [map [C] i] genrec
z [N] [dip unquote] cons [uncons] swoncat [TS0] dip [map [C] i] genrec
\...........TS1.................../
z [N] TS1 [TS0] dip [map [C] i] genrec
z [N] [map [C] i] [TS1 [TS0] dip] dip genrec
z [N] [map C ] [TS1 [TS0] dip] dip genrec
z [N] [C] [map] swoncat [TS1 [TS0] dip] dip genrec
z [C] [N] swap [map] swoncat [TS1 [TS0] dip] dip genrec
::
TS0 == [not] swap unit [pop] swoncat
TS1 == [dip i] cons [uncons] swoncat
treestep == swap [map] swoncat [TS1 [TS0] dip] dip genrec
::
[] 0 [C] [N] treestep
---------------------------
0
[n [tree*]] 0 [sum +] [] treestep
--------------------------------------------------
n [tree*] [0 [sum +] [] treestep] map sum +
.. code:: ipython2
DefinitionWrapper.add_definitions('''
TS0 == [not] swap unit [pop] swoncat
TS1 == [dip i] cons [uncons] swoncat
treestep == swap [map] swoncat [TS1 [TS0] dip] dip genrec
''', D)
.. code:: ipython2
V('[] 0 [sum +] [] treestep')
.. parsed-literal::
. [] 0 [sum +] [] treestep
[] . 0 [sum +] [] treestep
[] 0 . [sum +] [] treestep
[] 0 [sum +] . [] treestep
[] 0 [sum +] [] . treestep
[] 0 [sum +] [] . swap [map] swoncat [TS1 [TS0] dip] dip genrec
[] 0 [] [sum +] . [map] swoncat [TS1 [TS0] dip] dip genrec
[] 0 [] [sum +] [map] . swoncat [TS1 [TS0] dip] dip genrec
[] 0 [] [sum +] [map] . swap concat [TS1 [TS0] dip] dip genrec
[] 0 [] [map] [sum +] . concat [TS1 [TS0] dip] dip genrec
[] 0 [] [map sum +] . [TS1 [TS0] dip] dip genrec
[] 0 [] [map sum +] [TS1 [TS0] dip] . dip genrec
[] 0 [] . TS1 [TS0] dip [map sum +] genrec
[] 0 [] . [dip i] cons [uncons] swoncat [TS0] dip [map sum +] genrec
[] 0 [] [dip i] . cons [uncons] swoncat [TS0] dip [map sum +] genrec
[] 0 [[] dip i] . [uncons] swoncat [TS0] dip [map sum +] genrec
[] 0 [[] dip i] [uncons] . swoncat [TS0] dip [map sum +] genrec
[] 0 [[] dip i] [uncons] . swap concat [TS0] dip [map sum +] genrec
[] 0 [uncons] [[] dip i] . concat [TS0] dip [map sum +] genrec
[] 0 [uncons [] dip i] . [TS0] dip [map sum +] genrec
[] 0 [uncons [] dip i] [TS0] . dip [map sum +] genrec
[] 0 . TS0 [uncons [] dip i] [map sum +] genrec
[] 0 . [not] swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] 0 [not] . swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] [not] 0 . unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] [not] 0 . [] cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] [not] 0 [] . cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] [not] [0] . [pop] swoncat [uncons [] dip i] [map sum +] genrec
[] [not] [0] [pop] . swoncat [uncons [] dip i] [map sum +] genrec
[] [not] [0] [pop] . swap concat [uncons [] dip i] [map sum +] genrec
[] [not] [pop] [0] . concat [uncons [] dip i] [map sum +] genrec
[] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec
[] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec
[] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec
[] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte
[] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[]] [not] . infra first choice i
[] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] []] swaack first choice i
True . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] []] swaack first choice i
True [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] []] . swaack first choice i
[] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [True] . first choice i
[] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] True . choice i
[] [pop 0] . i
[] . pop 0
. 0
0 .
.. code:: ipython2
V('[23 []] 0 [sum +] [] treestep')
.. parsed-literal::
. [23 []] 0 [sum +] [] treestep
[23 []] . 0 [sum +] [] treestep
[23 []] 0 . [sum +] [] treestep
[23 []] 0 [sum +] . [] treestep
[23 []] 0 [sum +] [] . treestep
[23 []] 0 [sum +] [] . swap [map] swoncat [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [sum +] . [map] swoncat [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [sum +] [map] . swoncat [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [sum +] [map] . swap concat [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [map] [sum +] . concat [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [map sum +] . [TS1 [TS0] dip] dip genrec
[23 []] 0 [] [map sum +] [TS1 [TS0] dip] . dip genrec
[23 []] 0 [] . TS1 [TS0] dip [map sum +] genrec
[23 []] 0 [] . [dip i] cons [uncons] swoncat [TS0] dip [map sum +] genrec
[23 []] 0 [] [dip i] . cons [uncons] swoncat [TS0] dip [map sum +] genrec
[23 []] 0 [[] dip i] . [uncons] swoncat [TS0] dip [map sum +] genrec
[23 []] 0 [[] dip i] [uncons] . swoncat [TS0] dip [map sum +] genrec
[23 []] 0 [[] dip i] [uncons] . swap concat [TS0] dip [map sum +] genrec
[23 []] 0 [uncons] [[] dip i] . concat [TS0] dip [map sum +] genrec
[23 []] 0 [uncons [] dip i] . [TS0] dip [map sum +] genrec
[23 []] 0 [uncons [] dip i] [TS0] . dip [map sum +] genrec
[23 []] 0 . TS0 [uncons [] dip i] [map sum +] genrec
[23 []] 0 . [not] swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] 0 [not] . swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] 0 . unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] 0 . [] cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] 0 [] . cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] [0] . [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] [0] [pop] . swoncat [uncons [] dip i] [map sum +] genrec
[23 []] [not] [0] [pop] . swap concat [uncons [] dip i] [map sum +] genrec
[23 []] [not] [pop] [0] . concat [uncons [] dip i] [map sum +] genrec
[23 []] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec
[23 []] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec
[23 []] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec
[23 []] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte
[23 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[23 []]] [not] . infra first choice i
[23 []] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 []]] swaack first choice i
False . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 []]] swaack first choice i
False [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 []]] . swaack first choice i
[23 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [False] . first choice i
[23 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] False . choice i
[23 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . i
[23 []] . uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[]] . [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[]] [] . dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 . [[]] i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[]] . i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 . [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum +
23 [] . sum +
23 [] . 0 [+] catamorphism +
23 [] 0 . [+] catamorphism +
23 [] 0 [+] . catamorphism +
23 [] 0 [+] . [[] =] roll> [uncons swap] swap hylomorphism +
23 [] 0 [+] [[] =] . roll> [uncons swap] swap hylomorphism +
23 [] [[] =] 0 [+] . [uncons swap] swap hylomorphism +
23 [] [[] =] 0 [+] [uncons swap] . swap hylomorphism +
23 [] [[] =] 0 [uncons swap] [+] . hylomorphism +
23 [] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec +
23 [] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec +
23 [] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec +
23 [] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec +
23 [] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec +
23 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec +
23 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec +
23 [] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec +
23 [] [[] =] [pop 0] [uncons swap] [dip +] . genrec +
23 [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[] 23] [[] =] . infra first choice i +
23 [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i +
23 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i +
23 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i +
23 True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] . swaack first choice i +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True 23] . first choice i +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i +
23 [] [pop 0] . i +
23 [] . pop 0 +
23 . 0 +
23 0 . +
23 .
.. code:: ipython2
V('[23 [[2 []] [3 []]]] 0 [sum +] [] treestep')
.. parsed-literal::
. [23 [[2 []] [3 []]]] 0 [sum +] [] treestep
[23 [[2 []] [3 []]]] . 0 [sum +] [] treestep
[23 [[2 []] [3 []]]] 0 . [sum +] [] treestep
[23 [[2 []] [3 []]]] 0 [sum +] . [] treestep
[23 [[2 []] [3 []]]] 0 [sum +] [] . treestep
[23 [[2 []] [3 []]]] 0 [sum +] [] . swap [map] swoncat [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [sum +] . [map] swoncat [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [sum +] [map] . swoncat [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [sum +] [map] . swap concat [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [map] [sum +] . concat [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [map sum +] . [TS1 [TS0] dip] dip genrec
[23 [[2 []] [3 []]]] 0 [] [map sum +] [TS1 [TS0] dip] . dip genrec
[23 [[2 []] [3 []]]] 0 [] . TS1 [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [] . [dip i] cons [uncons] swoncat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [] [dip i] . cons [uncons] swoncat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [[] dip i] . [uncons] swoncat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [[] dip i] [uncons] . swoncat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [[] dip i] [uncons] . swap concat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [uncons] [[] dip i] . concat [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [uncons [] dip i] . [TS0] dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [uncons [] dip i] [TS0] . dip [map sum +] genrec
[23 [[2 []] [3 []]]] 0 . TS0 [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] 0 . [not] swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] 0 [not] . swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] 0 . unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] 0 . [] cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] 0 [] . cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [0] . [pop] swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [0] [pop] . swoncat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [0] [pop] . swap concat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [pop] [0] . concat [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec
[23 [[2 []] [3 []]]] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec
[23 [[2 []] [3 []]]] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte
[23 [[2 []] [3 []]]] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[23 [[2 []] [3 []]]]] [not] . infra first choice i
[23 [[2 []] [3 []]]] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 [[2 []] [3 []]]]] swaack first choice i
False . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 [[2 []] [3 []]]]] swaack first choice i
False [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 [[2 []] [3 []]]]] . swaack first choice i
[23 [[2 []] [3 []]]] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [False] . first choice i
[23 [[2 []] [3 []]]] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] False . choice i
[23 [[2 []] [3 []]]] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . i
[23 [[2 []] [3 []]]] . uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[[2 []] [3 []]]] . [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[[2 []] [3 []]]] [] . dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 . [[[2 []] [3 []]]] i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[[2 []] [3 []]]] . i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 . [[2 []] [3 []]] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[2 []] [3 []]] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
23 [[2 []] [3 []]] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum +
23 [] [[[3 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first] . infra sum +
. [[3 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
[[3 []] 23] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
[[3 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . infra first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] . [not] [pop 0] [uncons [] dip i] [map sum +] genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [not] . [pop 0] [uncons [] dip i] [map sum +] genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[3 []] 23] [not] . infra first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [3 []] 23] swaack first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 False . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [3 []] 23] swaack first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 False [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [3 []] 23] . swaack first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [False 23] . first choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] False . choice i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . i [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 [3 []] . uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [[]] . [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [[]] [] . dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 . [[]] i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [[]] . i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 . [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . sum + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . 0 [+] catamorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] 0 . [+] catamorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] 0 [+] . catamorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] 0 [+] . [[] =] roll> [uncons swap] swap hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] 0 [+] [[] =] . roll> [uncons swap] swap hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [+] . [uncons swap] swap hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [+] [uncons swap] . swap hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [uncons swap] [+] . hylomorphism + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap] [dip +] . genrec + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[] 3 23] [[] =] . infra first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 3 23] swaack first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 3 23] swaack first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 3 23] swaack first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 3 23] . swaack first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True 3 23] . first choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] [pop 0] . i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . pop 0 + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 . 0 + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 0 . + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 . [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
23 3 [] . swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
[3 23] . first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
3 . [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
3 [[2 []] 23] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
3 [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . infra first [23] swaack sum +
23 [2 []] . [not] [pop 0] [uncons [] dip i] [map sum +] genrec [3] swaack first [23] swaack sum +
23 [2 []] [not] . [pop 0] [uncons [] dip i] [map sum +] genrec [3] swaack first [23] swaack sum +
23 [2 []] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec [3] swaack first [23] swaack sum +
23 [2 []] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec [3] swaack first [23] swaack sum +
23 [2 []] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec [3] swaack first [23] swaack sum +
23 [2 []] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte [3] swaack first [23] swaack sum +
23 [2 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [[2 []] 23] [not] . infra first choice i [3] swaack first [23] swaack sum +
23 [2 []] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [2 []] 23] swaack first choice i [3] swaack first [23] swaack sum +
23 False . [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [2 []] 23] swaack first choice i [3] swaack first [23] swaack sum +
23 False [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [2 []] 23] . swaack first choice i [3] swaack first [23] swaack sum +
23 [2 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] [False 23] . first choice i [3] swaack first [23] swaack sum +
23 [2 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [pop 0] False . choice i [3] swaack first [23] swaack sum +
23 [2 []] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . i [3] swaack first [23] swaack sum +
23 [2 []] . uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 [[]] . [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 [[]] [] . dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 . [[]] i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 [[]] . i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 . [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 [] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum + [3] swaack first [23] swaack sum +
23 2 [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum + [3] swaack first [23] swaack sum +
23 2 [] . sum + [3] swaack first [23] swaack sum +
23 2 [] . 0 [+] catamorphism + [3] swaack first [23] swaack sum +
23 2 [] 0 . [+] catamorphism + [3] swaack first [23] swaack sum +
23 2 [] 0 [+] . catamorphism + [3] swaack first [23] swaack sum +
23 2 [] 0 [+] . [[] =] roll> [uncons swap] swap hylomorphism + [3] swaack first [23] swaack sum +
23 2 [] 0 [+] [[] =] . roll> [uncons swap] swap hylomorphism + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [+] . [uncons swap] swap hylomorphism + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [+] [uncons swap] . swap hylomorphism + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [uncons swap] [+] . hylomorphism + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap] [dip +] . genrec + [3] swaack first [23] swaack sum +
23 2 [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte + [3] swaack first [23] swaack sum +
23 2 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[] 2 23] [[] =] . infra first choice i + [3] swaack first [23] swaack sum +
23 2 [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 2 23] swaack first choice i + [3] swaack first [23] swaack sum +
23 2 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 2 23] swaack first choice i + [3] swaack first [23] swaack sum +
23 2 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 2 23] swaack first choice i + [3] swaack first [23] swaack sum +
23 2 True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 2 23] . swaack first choice i + [3] swaack first [23] swaack sum +
23 2 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True 2 23] . first choice i + [3] swaack first [23] swaack sum +
23 2 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i + [3] swaack first [23] swaack sum +
23 2 [] [pop 0] . i + [3] swaack first [23] swaack sum +
23 2 [] . pop 0 + [3] swaack first [23] swaack sum +
23 2 . 0 + [3] swaack first [23] swaack sum +
23 2 0 . + [3] swaack first [23] swaack sum +
23 2 . [3] swaack first [23] swaack sum +
23 2 [3] . swaack first [23] swaack sum +
3 [2 23] . first [23] swaack sum +
3 2 . [23] swaack sum +
3 2 [23] . swaack sum +
23 [2 3] . sum +
23 [2 3] . 0 [+] catamorphism +
23 [2 3] 0 . [+] catamorphism +
23 [2 3] 0 [+] . catamorphism +
23 [2 3] 0 [+] . [[] =] roll> [uncons swap] swap hylomorphism +
23 [2 3] 0 [+] [[] =] . roll> [uncons swap] swap hylomorphism +
23 [2 3] [[] =] 0 [+] . [uncons swap] swap hylomorphism +
23 [2 3] [[] =] 0 [+] [uncons swap] . swap hylomorphism +
23 [2 3] [[] =] 0 [uncons swap] [+] . hylomorphism +
23 [2 3] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec +
23 [2 3] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec +
23 [2 3] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec +
23 [2 3] [[] =] [pop 0] [uncons swap] [dip +] . genrec +
23 [2 3] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte +
23 [2 3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[2 3] 23] [[] =] . infra first choice i +
23 [2 3] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 3] 23] swaack first choice i +
23 [2 3] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 3] 23] swaack first choice i +
23 False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 3] 23] swaack first choice i +
23 False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 3] 23] . swaack first choice i +
23 [2 3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False 23] . first choice i +
23 [2 3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i +
23 [2 3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i +
23 [2 3] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + +
23 2 [3] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + +
23 [3] 2 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + +
23 [3] 2 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + +
23 [3] . [[] =] [pop 0] [uncons swap] [dip +] genrec 2 + +
23 [3] [[] =] . [pop 0] [uncons swap] [dip +] genrec 2 + +
23 [3] [[] =] [pop 0] . [uncons swap] [dip +] genrec 2 + +
23 [3] [[] =] [pop 0] [uncons swap] . [dip +] genrec 2 + +
23 [3] [[] =] [pop 0] [uncons swap] [dip +] . genrec 2 + +
23 [3] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 2 + +
23 [3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[3] 23] [[] =] . infra first choice i 2 + +
23 [3] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3] 23] swaack first choice i 2 + +
23 [3] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3] 23] swaack first choice i 2 + +
23 False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3] 23] swaack first choice i 2 + +
23 False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3] 23] . swaack first choice i 2 + +
23 [3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False 23] . first choice i 2 + +
23 [3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i 2 + +
23 [3] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i 2 + +
23 [3] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 2 + +
23 3 [] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 2 + +
23 [] 3 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 2 + +
23 [] 3 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + 2 + +
23 [] . [[] =] [pop 0] [uncons swap] [dip +] genrec 3 + 2 + +
23 [] [[] =] . [pop 0] [uncons swap] [dip +] genrec 3 + 2 + +
23 [] [[] =] [pop 0] . [uncons swap] [dip +] genrec 3 + 2 + +
23 [] [[] =] [pop 0] [uncons swap] . [dip +] genrec 3 + 2 + +
23 [] [[] =] [pop 0] [uncons swap] [dip +] . genrec 3 + 2 + +
23 [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 3 + 2 + +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[] 23] [[] =] . infra first choice i 3 + 2 + +
23 [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i 3 + 2 + +
23 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i 3 + 2 + +
23 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i 3 + 2 + +
23 True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] . swaack first choice i 3 + 2 + +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True 23] . first choice i 3 + 2 + +
23 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i 3 + 2 + +
23 [] [pop 0] . i 3 + 2 + +
23 [] . pop 0 3 + 2 + +
23 . 0 3 + 2 + +
23 0 . 3 + 2 + +
23 0 3 . + 2 + +
23 3 . 2 + +
23 3 2 . + +
23 5 . +
28 .
.. code:: ipython2
J('[23 [[2 [[23 [[2 []] [3 []]]][23 [[2 []] [3 []]]]]] [3 [[23 [[2 []] [3 []]]][23 [[2 []] [3 []]]]]]]] 0 [sum +] [] treestep')
.. parsed-literal::
140
.. code:: ipython2
J('[] [] [unit cons] [23 +] treestep')
.. parsed-literal::
[]
.. code:: ipython2
J('[23 []] [] [unit cons] [23 +] treestep')
.. parsed-literal::
[46 []]
.. code:: ipython2
J('[23 [[2 []] [3 []]]] [] [unit cons] [23 +] treestep')
.. parsed-literal::
[46 [[25 []] [26 []]]]
.. code:: ipython2
define('treemap == [] [unit cons] roll< treestep')
.. code:: ipython2
J('[23 [[2 []] [3 []]]] [23 +] treemap')
.. parsed-literal::
[46 [[25 []] [26 []]]]

4
docs/Makefile
View File

@ -22,7 +22,9 @@ $(docs_md): %.md : %.ipynb
$(docs_rst): %.rst : %.ipynb
python -m nbconvert --to rst $<
move_us = Generator_Programs.rst Ordered_Binary_Trees.rst Quadratic.rst Replacing.rst Treestep.rst Zipper.rst
move_us = Generator_Programs.rst Newton-Raphson.rst Ordered_Binary_Trees.rst Quadratic.rst Replacing.rst Treestep.rst Zipper.rst
mov: $(move_us)
cp -v $? ./sphinx_docs/notebooks/

119
docs/Newton-Raphson.html
View File

@ -11867,21 +11867,6 @@ n+1 2 /
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<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;codireco == cons dip rest cons&#39;</span><span class="p">)</span>
<span class="n">define</span><span class="p">(</span><span class="s1">&#39;make_generator == [codireco] ccons&#39;</span><span class="p">)</span>
<span class="n">define</span><span class="p">(</span><span class="s1">&#39;ccons == cons cons&#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;[3]:</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;gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator&#39;</span><span class="p">)</span>
@ -11894,7 +11879,7 @@ n+1 2 /
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[4]:</div>
<div class="prompt input_prompt">In&nbsp;[3]:</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;23 gsra&#39;</span><span class="p">)</span>
@ -11934,7 +11919,7 @@ n+1 2 /
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[5]:</div>
<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">J</span><span class="p">(</span><span class="s1">&#39;23 gsra 6 [x popd] times first sqr&#39;</span><span class="p">)</span>
@ -11967,9 +11952,9 @@ n+1 2 /
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<h2 id="Finding-Consecutive-Approximations-within-a-Tolerance">Finding Consecutive Approximations within a Tolerance<a class="anchor-link" href="#Finding-Consecutive-Approximations-within-a-Tolerance">&#182;</a></h2><blockquote><p>The remainder of a square root finder is a function <em>within</em>, which takes a tolerance and a list of approximations and looks down the list for two successive approximations that differ by no more than the given tolerance.</p>
<h2 id="Finding-Consecutive-Approximations-within-a-Tolerance">Finding Consecutive Approximations within a Tolerance<a class="anchor-link" href="#Finding-Consecutive-Approximations-within-a-Tolerance">&#182;</a></h2><p>From <a href="https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf">"Why Functional Programming Matters" by John Hughes</a>:</p>
<blockquote><p>The remainder of a square root finder is a function <em>within</em>, which takes a tolerance and a list of approximations and looks down the list for two successive approximations that differ by no more than the given tolerance.</p>
</blockquote>
<p>From <a href="https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf">"Why Functional Programming Matters" by John Hughes</a></p>
<p>(And note that by “list” he means a lazily-evaluated list.)</p>
<p>Using the <em>output</em> <code>[a G]</code> of the above generator for square root approximations, and further assuming that the first term a has been generated already and epsilon ε is handy on the stack...</p>
@ -12002,7 +11987,7 @@ abs(a-b) ε &lt;=
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[6]:</div>
<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">define</span><span class="p">(</span><span class="s1">&#39;_within_P == [first - abs] dip &lt;=&#39;</span><span class="p">)</span>
@ -12028,7 +12013,7 @@ abs(a-b) ε &lt;=
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[7]:</div>
<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="n">define</span><span class="p">(</span><span class="s1">&#39;_within_B == roll&lt; popop first&#39;</span><span class="p">)</span>
@ -12049,8 +12034,8 @@ abs(a-b) ε &lt;=
</code></pre>
<ol>
<li>Discard a.</li>
<li>Use x combinator to generate next term from G.</li>
<li>Run within with <code>i</code> (it is a <code>primrec</code> function.)</li>
<li>Use <code>x</code> combinator to generate next term from <code>G</code>.</li>
<li>Run <code>within</code> with <code>i</code> (it is a <code>primrec</code> function.)</li>
</ol>
<p>Pretty straightforward:</p>
@ -12068,7 +12053,7 @@ b [c G] ε within</code></pre>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[8]:</div>
<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">define</span><span class="p">(</span><span class="s1">&#39;_within_R == [popd x] dip&#39;</span><span class="p">)</span>
@ -12093,7 +12078,7 @@ a [b G] ε ...</code></pre>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[9]:</div>
<div class="prompt input_prompt">In&nbsp;[8]:</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;within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec&#39;</span><span class="p">)</span>
@ -12104,6 +12089,46 @@ a [b G] ε ...</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>Try it out...</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[9]:</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;36 sqrt&#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>6.0
</pre>
</div>
</div>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
@ -12135,6 +12160,15 @@ a [b G] ε ...</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>Check it.</p>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
@ -12168,6 +12202,41 @@ a [b G] ε ...</code></pre>
</div>
</div>
</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[12]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">sqrt</span>
<span class="n">sqrt</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area">
<div class="prompt output_prompt">Out[12]:</div>
<div class="output_text output_subarea output_execute_result">
<pre>4.795831523312719</pre>
</div>
</div>
</div>
</div>
</div>
</div>
</div>

86
docs/Newton-Raphson.ipynb
View File

@ -87,17 +87,6 @@
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"define('codireco == cons dip rest cons')\n",
"define('make_generator == [codireco] ccons')\n",
"define('ccons == cons cons')"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"scrolled": true
},
@ -108,7 +97,7 @@
},
{
"cell_type": "code",
"execution_count": 4,
"execution_count": 3,
"metadata": {},
"outputs": [
{
@ -132,7 +121,7 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 4,
"metadata": {},
"outputs": [
{
@ -153,11 +142,11 @@
"source": [
"## Finding Consecutive Approximations within a Tolerance\n",
"\n",
"From [\"Why Functional Programming Matters\" by John Hughes](https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf):\n",
"\n",
"\n",
"> The remainder of a square root finder is a function _within_, which takes a tolerance and a list of approximations and looks down the list for two successive approximations that differ by no more than the given tolerance.\n",
"\n",
"From [\"Why Functional Programming Matters\" by John Hughes](https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf)\n",
"\n",
"(And note that by “list” he means a lazily-evaluated list.)\n",
"\n",
"Using the _output_ `[a G]` of the above generator for square root approximations, and further assuming that the first term a has been generated already and epsilon ε is handy on the stack...\n",
@ -189,7 +178,7 @@
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
@ -210,7 +199,7 @@
},
{
"cell_type": "code",
"execution_count": 7,
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
@ -226,8 +215,8 @@
" a [b G] ε R0 [within] R1\n",
"\n",
"1. Discard a.\n",
"2. Use x combinator to generate next term from G.\n",
"3. Run within with `i` (it is a `primrec` function.)\n",
"2. Use `x` combinator to generate next term from `G`.\n",
"3. Run `within` with `i` (it is a `primrec` function.)\n",
"\n",
"Pretty straightforward:\n",
"\n",
@ -243,7 +232,7 @@
},
{
"cell_type": "code",
"execution_count": 8,
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
@ -264,7 +253,7 @@
},
{
"cell_type": "code",
"execution_count": 9,
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
@ -272,6 +261,32 @@
"define('sqrt == gsra within')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Try it out..."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"6.0\n"
]
}
],
"source": [
"J('36 sqrt')"
]
},
{
"cell_type": "code",
"execution_count": 10,
@ -291,6 +306,13 @@
"J('23 sqrt')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Check it."
]
},
{
"cell_type": "code",
"execution_count": 11,
@ -312,6 +334,28 @@
"source": [
"4.795831523312719**2"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4.795831523312719"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from math import sqrt\n",
"\n",
"sqrt(23)"
]
}
],
"metadata": {

41
docs/Newton-Raphson.md
View File

@ -55,13 +55,6 @@ The generator can be written as:
1 [dup 23 over / + 2 /] make_generator
```python
define('codireco == cons dip rest cons')
define('make_generator == [codireco] ccons')
define('ccons == cons cons')
```
```python
define('gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
```
@ -86,11 +79,11 @@ J('23 gsra 6 [x popd] times first sqr')
## Finding Consecutive Approximations within a Tolerance
From ["Why Functional Programming Matters" by John Hughes](https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf):
> The remainder of a square root finder is a function _within_, which takes a tolerance and a list of approximations and looks down the list for two successive approximations that differ by no more than the given tolerance.
From ["Why Functional Programming Matters" by John Hughes](https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf)
(And note that by “list” he means a lazily-evaluated list.)
Using the _output_ `[a G]` of the above generator for square root approximations, and further assuming that the first term a has been generated already and epsilon ε is handy on the stack...
@ -137,8 +130,8 @@ define('_within_B == roll< popop first')
a [b G] ε R0 [within] R1
1. Discard a.
2. Use x combinator to generate next term from G.
3. Run within with `i` (it is a `primrec` function.)
2. Use `x` combinator to generate next term from `G`.
3. Run `within` with `i` (it is a `primrec` function.)
Pretty straightforward:
@ -169,6 +162,16 @@ define('within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec')
define('sqrt == gsra within')
```
Try it out...
```python
J('36 sqrt')
```
6.0
```python
J('23 sqrt')
@ -177,6 +180,8 @@ J('23 sqrt')
4.795831523312719
Check it.
```python
4.795831523312719**2
@ -188,3 +193,17 @@ J('23 sqrt')
22.999999999999996
```python
from math import sqrt
sqrt(23)
```
4.795831523312719

45
docs/Newton-Raphson.rst
View File

@ -76,12 +76,6 @@ The generator can be written as:
1 [23 over / + 2 /] [dup] swoncat make_generator
1 [dup 23 over / + 2 /] make_generator
.. code:: ipython2
define('codireco == cons dip rest cons')
define('make_generator == [codireco] ccons')
define('ccons == cons cons')
.. code:: ipython2
define('gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
@ -112,14 +106,14 @@ square the approximation to see how well it works...
Finding Consecutive Approximations within a Tolerance
-----------------------------------------------------
From `"Why Functional Programming Matters" by John
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__:
The remainder of a square root finder is a function *within*, which
takes a tolerance and a list of approximations and looks down the
list for two successive approximations that differ by no more than
the given tolerance.
From `"Why Functional Programming Matters" by John
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__
(And note that by “list” he means a lazily-evaluated list.)
Using the *output* ``[a G]`` of the above generator for square root
@ -175,8 +169,8 @@ Recur
a [b G] ε R0 [within] R1
1. Discard a.
2. Use x combinator to generate next term from G.
3. Run within with ``i`` (it is a ``primrec`` function.)
2. Use ``x`` combinator to generate next term from ``G``.
3. Run ``within`` with ``i`` (it is a ``primrec`` function.)
Pretty straightforward:
@ -211,6 +205,18 @@ The recursive function we have defined so far needs a slight preamble:
define('within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec')
define('sqrt == gsra within')
Try it out...
.. code:: ipython2
J('36 sqrt')
.. parsed-literal::
6.0
.. code:: ipython2
J('23 sqrt')
@ -221,6 +227,8 @@ The recursive function we have defined so far needs a slight preamble:
4.795831523312719
Check it.
.. code:: ipython2
4.795831523312719**2
@ -233,3 +241,18 @@ The recursive function we have defined so far needs a slight preamble:
22.999999999999996
.. code:: ipython2
from math import sqrt
sqrt(23)
.. parsed-literal::
4.795831523312719

3
docs/sphinx_docs/_build/html/_modules/joy/library.html
View File

@ -157,6 +157,9 @@
<span class="s1">dudipd == dup dipd</span>
<span class="s1">primrec == [i] genrec</span>
<span class="s1">step_zero == 0 roll&gt; step</span>
<span class="s1">codireco == cons dip rest cons</span>
<span class="s1">make_generator == [codireco] ccons</span>
<span class="s1">ccons == cons cons</span>
<span class="s1">&#39;&#39;&#39;</span>
<span class="c1">##Zipper</span>

132
docs/sphinx_docs/_build/html/notebooks/Newton-Raphson.html
View File

@ -17,7 +17,7 @@
<link rel="index" title="Index" href="../genindex.html" />
<link rel="search" title="Search" href="../search.html" />
<link rel="next" title="Quadratic formula" href="Quadratic.html" />
<link rel="prev" title="Treating Trees" href="Trees.html" />
<link rel="prev" title="Using x to Generate Values" href="Generator_Programs.html" />
<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
@ -34,16 +34,18 @@
<div class="section" id="newton-s-method">
<h1><a class="reference external" href="https://en.wikipedia.org/wiki/Newton%27s_method">Newton’s method</a><a class="headerlink" href="#newton-s-method" title="Permalink to this headline"></a></h1>
<p>Newton-Raphson for finding the root of an equation.</p>
<p>Let’s use the Newton-Raphson method for finding the root of an equation
to write a function that can compute the square root of a number.</p>
<p>Cf. <a class="reference external" href="https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf">“Why Functional Programming Matters” by John
Hughes</a></p>
<div class="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="https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf">“Why Functional Programming Matters” by John
Hughes</a></p>
<div class="section" id="a-generator-for-approximations">
<h2>A Generator for Approximations<a class="headerlink" href="#a-generator-for-approximations" title="Permalink to this headline"></a></h2>
<p>In <a class="reference internal" href="Generator Programs.html"><span class="doc">Using x to Generate Values</span></a> we derive a function (called <code class="docutils literal notranslate"><span class="pre">make_generator</span></code> in the dictionary) that accepts an initial value and a quoted program and returns a new quoted program that, when driven by the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator (<a class="reference internal" href="../library.html#joy.library.x" title="joy.library.x"><code class="xref py py-func docutils literal notranslate"><span class="pre">joy.library.x()</span></code></a>), acts like a lazy stream.</p>
<p>To make a generator that generates successive approximations let’s start by assuming an initial approximation and then derive the function that computes the next approximation:</p>
<p>To make a generator that generates successive approximations let’s start
by assuming an initial approximation and then derive the function that
computes the next approximation:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">a</span> <span class="n">F</span>
<span class="o">---------</span>
<span class="n">a</span><span class="s1">&#39;</span>
@ -51,7 +53,8 @@ Hughes</a></p>
</div>
<div class="section" id="a-function-to-compute-the-next-approximation">
<h3>A Function to Compute the Next Approximation<a class="headerlink" href="#a-function-to-compute-the-next-approximation" title="Permalink to this headline"></a></h3>
<p>Looking at the equation again:</p>
<p>This is the equation for computing the next approximate value of the
square root:</p>
<p><span class="math notranslate nohighlight">\(a_{i+1} = \frac{(a_i+\frac{n}{a_i})}{2}\)</span></p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="n">n</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span>
<span class="n">a</span> <span class="n">n</span> <span class="n">a</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span>
@ -71,7 +74,8 @@ Hughes</a></p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="p">[</span><span class="n">dup</span> <span class="n">F</span><span class="p">]</span> <span class="n">make_generator</span>
</pre></div>
</div>
<p>With <code class="docutils literal notranslate"><span class="pre">n</span></code> as part of the function <code class="docutils literal notranslate"><span class="pre">F</span></code>, but <code class="docutils literal notranslate"><span class="pre">n</span></code> is the input to the <code class="docutils literal notranslate"><span class="pre">sqrt</span></code> function we’re writing. If we let 1 be the initial approximation:</p>
<p>With n as part of the function F, but n is the input to the sqrt
function we’re writing. If we let 1 be the initial approximation:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="n">n</span> <span class="mi">1</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span>
<span class="mi">1</span> <span class="n">n</span><span class="o">/</span><span class="mi">1</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span>
<span class="mi">1</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span>
@ -80,48 +84,51 @@ Hughes</a></p>
</pre></div>
</div>
<p>The generator can be written as:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="n">swap</span> <span class="p">[</span><span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">cons</span> <span class="p">[</span><span class="n">dup</span><span class="p">]</span> <span class="n">swoncat</span> <span class="n">make_generator</span>
</pre></div>
</div>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span> <span class="mi">1</span> <span class="n">swap</span> <span class="p">[</span><span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">cons</span> <span class="p">[</span><span class="n">dup</span><span class="p">]</span> <span class="n">swoncat</span> <span class="n">make_generator</span>
<span class="mi">1</span> <span class="mi">23</span> <span class="p">[</span><span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">cons</span> <span class="p">[</span><span class="n">dup</span><span class="p">]</span> <span class="n">swoncat</span> <span class="n">make_generator</span>
<span class="mi">1</span> <span class="p">[</span><span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="p">[</span><span class="n">dup</span><span class="p">]</span> <span class="n">swoncat</span> <span class="n">make_generator</span>
<span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">make_generator</span>
<span class="o">.</span>
<span class="o">.</span>
<span class="o">.</span>
<span class="p">[</span><span class="mi">1</span> <span class="n">swap</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">direco</span><span class="p">]</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;gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="section" id="a-generator-of-square-root-approximations">
<h3>A Generator of Square Root Approximations<a class="headerlink" href="#a-generator-of-square-root-approximations" title="Permalink to this headline"></a></h3>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">gsra</span> <span class="o">==</span> <span class="mi">1</span> <span class="n">swap</span> <span class="p">[</span><span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">cons</span> <span class="p">[</span><span class="n">dup</span><span class="p">]</span> <span class="n">swoncat</span> <span class="n">make_generator</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 gsra&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span>
</pre></div>
</div>
<p>Let’s drive the generator a few time (with the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator) and
square the approximation to see how well it works…</p>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 gsra 6 [x popd] times first sqr&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">23.0000000001585</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="finding-consecutive-approximations-within-a-tolerance">
<h2>Finding Consecutive Approximations <code class="docutils literal notranslate"><span class="pre">within</span></code> a Tolerance<a class="headerlink" href="#finding-consecutive-approximations-within-a-tolerance" title="Permalink to this headline"></a></h2>
<blockquote>
<div>The remainder of a square root finder is a function <em>within</em>, which takes a tolerance and a list of approximations and looks down the list for two successive approximations that differ by no more than the given tolerance.</div></blockquote>
<h2>Finding Consecutive Approximations within a Tolerance<a class="headerlink" href="#finding-consecutive-approximations-within-a-tolerance" title="Permalink to this headline"></a></h2>
<p>From <a class="reference external" href="https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf">“Why Functional Programming Matters” by John
Hughes</a></p>
Hughes</a>:</p>
<blockquote>
<div>The remainder of a square root finder is a function <em>within</em>, which
takes a tolerance and a list of approximations and looks down the
list for two successive approximations that differ by no more than
the given tolerance.</div></blockquote>
<p>(And note that by “list” he means a lazily-evaluated list.)</p>
<p>Using the <em>output</em> <code class="docutils literal notranslate"><span class="pre">[a</span> <span class="pre">G]</span></code> of the above <a class="reference internal" href="Generator Programs.html"><span class="doc">generator</span></a> for square root approximations, and further assuming that the first term <code class="docutils literal notranslate"><span class="pre">a</span></code> has been generated already and epsilon <code class="docutils literal notranslate"><span class="pre">ε</span></code> is handy on the stack…</p>
<p>Using the <em>output</em> <code class="docutils literal notranslate"><span class="pre">[a</span> <span class="pre">G]</span></code> of the above generator for square root
approximations, and further assuming that the first term a has been
generated already and epsilon ε is handy on the stack…</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">within</span>
<span class="o">----------------------</span> <span class="n">a</span> <span class="n">b</span> <span class="o">-</span> <span class="nb">abs</span> <span class="n">ε</span> <span class="o">&lt;=</span>
<span class="n">b</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">within</span>
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">within</span>
<span class="o">----------------------</span> <span class="n">a</span> <span class="n">b</span> <span class="o">-</span> <span class="nb">abs</span> <span class="n">ε</span> <span class="o">&gt;</span>
<span class="o">.</span>
<span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">x</span> <span class="n">ε</span> <span class="o">...</span>
<span class="n">b</span> <span class="p">[</span><span class="n">c</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="o">...</span>
<span class="o">.</span>
<span class="o">----------------------</span>
<span class="n">b</span> <span class="p">[</span><span class="n">c</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">within</span>
</pre></div>
</div>
@ -135,7 +142,7 @@ Hughes</a></p>
<span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">a</span><span class="o">-</span><span class="n">b</span><span class="p">)</span><span class="o">&lt;=</span><span class="n">ε</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">P</span> <span class="o">==</span> <span class="p">[</span><span class="n">first</span> <span class="o">-</span> <span class="nb">abs</span><span class="p">]</span> <span class="n">dip</span> <span class="o">&lt;=</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_P == [first - abs] dip &lt;=&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
@ -147,7 +154,7 @@ Hughes</a></p>
<span class="n">b</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">B</span> <span class="o">==</span> <span class="n">roll</span><span class="o">&lt;</span> <span class="n">popop</span> <span class="n">first</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_B == roll&lt; popop first&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
@ -157,10 +164,11 @@ Hughes</a></p>
</pre></div>
</div>
<ol class="arabic simple">
<li>Discard <code class="docutils literal notranslate"><span class="pre">a</span></code>.</li>
<li>Discard a.</li>
<li>Use <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator to generate next term from <code class="docutils literal notranslate"><span class="pre">G</span></code>.</li>
<li>Run <code class="docutils literal notranslate"><span class="pre">within</span></code> with <code class="docutils literal notranslate"><span class="pre">i</span></code> (it is a <code class="docutils literal notranslate"><span class="pre">primrec</span></code> function.)</li>
</ol>
<p>Pretty straightforward:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">R0</span> <span class="p">[</span><span class="n">within</span><span class="p">]</span> <span class="n">R1</span>
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="p">[</span><span class="n">popd</span> <span class="n">x</span><span class="p">]</span> <span class="n">dip</span> <span class="p">[</span><span class="n">within</span><span class="p">]</span> <span class="n">i</span>
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">popd</span> <span class="n">x</span> <span class="n">ε</span> <span class="p">[</span><span class="n">within</span><span class="p">]</span> <span class="n">i</span>
@ -171,34 +179,51 @@ Hughes</a></p>
<span class="n">b</span> <span class="p">[</span><span class="n">c</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">within</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">R0</span> <span class="o">==</span> <span class="p">[</span><span class="n">popd</span> <span class="n">x</span><span class="p">]</span> <span class="n">dip</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;_within_R == [popd x] dip&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="section" id="setting-up">
<h3>Setting up<a class="headerlink" href="#setting-up" title="Permalink to this headline"></a></h3>
<p>The recursive function we have defined so far needs a slight preamble: <code class="docutils literal notranslate"><span class="pre">x</span></code> to prime the generator and the epsilon value to use:</p>
<p>The recursive function we have defined so far needs a slight preamble:
<code class="docutils literal notranslate"><span class="pre">x</span></code> to prime the generator and the epsilon value to use:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">a</span> <span class="n">G</span><span class="p">]</span> <span class="n">x</span> <span class="n">ε</span> <span class="o">...</span>
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="o">...</span>
</pre></div>
</div>
</div>
<div class="section" id="within">
<h3><code class="docutils literal notranslate"><span class="pre">within</span></code><a class="headerlink" href="#within" title="Permalink to this headline"></a></h3>
<p>Giving us the following definitions:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">_within_P</span> <span class="o">==</span> <span class="p">[</span><span class="n">first</span> <span class="o">-</span> <span class="nb">abs</span><span class="p">]</span> <span class="n">dip</span> <span class="o">&lt;=</span>
<span class="n">_within_B</span> <span class="o">==</span> <span class="n">roll</span><span class="o">&lt;</span> <span class="n">popop</span> <span class="n">first</span>
<span class="n">_within_R</span> <span class="o">==</span> <span class="p">[</span><span class="n">popd</span> <span class="n">x</span><span class="p">]</span> <span class="n">dip</span>
<span class="n">within</span> <span class="o">==</span> <span class="n">x</span> <span class="n">ε</span> <span class="p">[</span><span class="n">_within_P</span><span class="p">]</span> <span class="p">[</span><span class="n">_within_B</span><span class="p">]</span> <span class="p">[</span><span class="n">_within_R</span><span class="p">]</span> <span class="n">primrec</span>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">&#39;within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec&#39;</span><span class="p">)</span>
<span class="n">define</span><span class="p">(</span><span class="s1">&#39;sqrt == gsra within&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="finding-square-roots">
<h2>Finding Square Roots<a class="headerlink" href="#finding-square-roots" title="Permalink to this headline"></a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">sqrt</span> <span class="o">==</span> <span class="n">gsra</span> <span class="n">within</span>
<p>Try it out…</p>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;36 sqrt&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">6.0</span>
</pre></div>
</div>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">&#39;23 sqrt&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span>
</pre></div>
</div>
<p>Check it.</p>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span><span class="o">**</span><span class="mi">2</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">22.999999999999996</span>
</pre></div>
</div>
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="k">import</span> <span class="n">sqrt</span>
<span class="n">sqrt</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span>
</pre></div>
</div>
</div>
</div>
</div>
@ -214,18 +239,15 @@ Hughes</a></p>
<li><a class="reference internal" href="#a-generator-for-approximations">A Generator for Approximations</a><ul>
<li><a class="reference internal" href="#a-function-to-compute-the-next-approximation">A Function to Compute the Next Approximation</a></li>
<li><a class="reference internal" href="#make-it-into-a-generator">Make it into a Generator</a></li>
<li><a class="reference internal" href="#a-generator-of-square-root-approximations">A Generator of Square Root Approximations</a></li>
</ul>
</li>
<li><a class="reference internal" href="#finding-consecutive-approximations-within-a-tolerance">Finding Consecutive Approximations <code class="docutils literal notranslate"><span class="pre">within</span></code> a Tolerance</a><ul>
<li><a class="reference internal" href="#finding-consecutive-approximations-within-a-tolerance">Finding Consecutive Approximations within a Tolerance</a><ul>
<li><a class="reference internal" href="#predicate">Predicate</a></li>
<li><a class="reference internal" href="#base-case">Base-Case</a></li>
<li><a class="reference internal" href="#recur">Recur</a></li>
<li><a class="reference internal" href="#setting-up">Setting up</a></li>
<li><a class="reference internal" href="#within"><code class="docutils literal notranslate"><span class="pre">within</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#finding-square-roots">Finding Square Roots</a></li>
</ul>
</li>
</ul>
@ -234,7 +256,7 @@ Hughes</a></p>
<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="Trees.html" title="previous chapter">Treating Trees</a></li>
<li>Previous: <a href="Generator_Programs.html" title="previous chapter">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
<li>Next: <a href="Quadratic.html" title="next chapter">Quadratic formula</a></li>
</ul></li>
</ul></li>

4
docs/sphinx_docs/_build/html/notebooks/Quadratic.html
View File

@ -16,7 +16,7 @@
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<link rel="index" title="Index" href="../genindex.html" />
<link rel="search" title="Search" href="../search.html" />
<link rel="next" title="No Updates" href="NoUpdates.html" />
<link rel="next" title="Traversing Datastructures with Zippers" href="Zipper.html" />
<link rel="prev" title="Newton’s method" href="Newton-Raphson.html" />
<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
@ -213,7 +213,7 @@ already.)</p>
<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="NoUpdates.html" title="next chapter">No Updates</a></li>
<li>Next: <a href="Zipper.html" title="next chapter">Traversing Datastructures with Zippers</a></li>
</ul></li>
</ul></li>
</ul>

6
docs/sphinx_docs/_build/html/notebooks/Zipper.html
View File

@ -16,6 +16,8 @@
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<link rel="index" title="Index" href="../genindex.html" />
<link rel="search" title="Search" href="../search.html" />
<link rel="next" title="No Updates" href="NoUpdates.html" />
<link rel="prev" title="Quadratic formula" href="Quadratic.html" />
<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
@ -323,6 +325,10 @@ i d i d i d d Bingo!
<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="Quadratic.html" title="previous chapter">Quadratic formula</a></li>
<li>Next: <a href="NoUpdates.html" title="next chapter">No Updates</a></li>
</ul></li>
</ul></li>
</ul>
</div>

3
docs/sphinx_docs/_build/html/notebooks/index.html
View File

@ -86,8 +86,7 @@
</li>
<li class="toctree-l1"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html#a-generator-for-approximations">A Generator for Approximations</a></li>
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html#finding-consecutive-approximations-within-a-tolerance">Finding Consecutive Approximations <code class="docutils literal notranslate"><span class="pre">within</span></code> a Tolerance</a></li>
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html#finding-square-roots">Finding Square Roots</a></li>
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html#finding-consecutive-approximations-within-a-tolerance">Finding Consecutive Approximations within a Tolerance</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="Quadratic.html">Quadratic formula</a><ul>

BIN
docs/sphinx_docs/_build/html/objects.inv
View File

Binary file not shown.

2
docs/sphinx_docs/_build/html/searchindex.js
View File

File diff suppressed because one or more lines are too long

202
docs/sphinx_docs/notebooks/Newton-Raphson.rst
View File

@ -1,33 +1,35 @@
*********************************************************************
`Newton's method <https://en.wikipedia.org/wiki/Newton%27s_method>`__
*********************************************************************
Newton-Raphson for finding the root of an equation.
`Newton's method <https://en.wikipedia.org/wiki/Newton%27s_method>`__
=====================================================================
Let's use the Newton-Raphson method for finding the root of an equation
to write a function that can compute the square root of a number.
Cf. `"Why Functional Programming Matters" by John
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__
.. code:: ipython2
from notebook_preamble import J, V, define
Cf. `"Why Functional Programming Matters" by John
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__
A Generator for Approximations
==============================
------------------------------
In :doc:`Generator Programs` we derive a function (called ``make_generator`` in the dictionary) that accepts an initial value and a quoted program and returns a new quoted program that, when driven by the ``x`` combinator (:py:func:`joy.library.x`), acts like a lazy stream.
To make a generator that generates successive approximations let’s start
by assuming an initial approximation and then derive the function that
computes the next approximation:
To make a generator that generates successive approximations let's start by assuming an initial approximation and then derive the function that computes the next approximation::
::
a F
---------
a'
A Function to Compute the Next Approximation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Looking at the equation again:
This is the equation for computing the next approximate value of the
square root:
:math:`a_{i+1} = \frac{(a_i+\frac{n}{a_i})}{2}`
@ -39,19 +41,25 @@ Looking at the equation again:
a+n/a 2 /
(a+n/a)/2
The function we want has the argument ``n`` in it::
The function we want has the argument ``n`` in it:
::
F == n over / + 2 /
Make it into a Generator
^^^^^^^^^^^^^^^^^^^^^^^^
~~~~~~~~~~~~~~~~~~~~~~~~
Our generator would be created by::
Our generator would be created by:
::
a [dup F] make_generator
With ``n`` as part of the function ``F``, but ``n`` is the input to the ``sqrt`` function we're writing. If we let 1 be the initial approximation::
With n as part of the function F, but n is the input to the sqrt
function we’re writing. If we let 1 be the initial approximation:
::
1 n 1 / + 2 /
1 n/1 + 2 /
@ -59,41 +67,58 @@ With ``n`` as part of the function ``F``, but ``n`` is the input to the ``sqrt``
n+1 2 /
(n+1)/2
The generator can be written as::
The generator can be written as:
1 swap [over / + 2 /] cons [dup] swoncat make_generator
Example::
::
23 1 swap [over / + 2 /] cons [dup] swoncat make_generator
1 23 [over / + 2 /] cons [dup] swoncat make_generator
1 [23 over / + 2 /] [dup] swoncat make_generator
1 [dup 23 over / + 2 /] make_generator
.
.
.
[1 swap [dup 23 over / + 2 /] direco]
.. code:: ipython2
define('gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
.. code:: ipython2
J('23 gsra')
A Generator of Square Root Approximations
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. parsed-literal::
::
gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator
[1 [dup 23 over / + 2 /] codireco]
Finding Consecutive Approximations ``within`` a Tolerance
=========================================================
Let's drive the generator a few time (with the ``x`` combinator) and
square the approximation to see how well it works...
The remainder of a square root finder is a function *within*, which takes a tolerance and a list of approximations and looks down the list for two successive approximations that differ by no more than the given tolerance.
.. code:: ipython2
J('23 gsra 6 [x popd] times first sqr')
.. parsed-literal::
23.0000000001585
Finding Consecutive Approximations within a Tolerance
-----------------------------------------------------
From `"Why Functional Programming Matters" by John
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__:
(And note that by "list" he means a lazily-evaluated list.)
The remainder of a square root finder is a function *within*, which
takes a tolerance and a list of approximations and looks down the
list for two successive approximations that differ by no more than
the given tolerance.
Using the *output* ``[a G]`` of the above :doc:`generator <Generator Programs>` for square root approximations, and further assuming that the first term ``a`` has been generated already and epsilon ``ε`` is handy on the stack...
(And note that by “list” he means a lazily-evaluated list.)
Using the *output* ``[a G]`` of the above generator for square root
approximations, and further assuming that the first term a has been
generated already and epsilon ε is handy on the stack...
::
@ -101,21 +126,13 @@ Using the *output* ``[a G]`` of the above :doc:`generator <Generator Programs>`
---------------------- a b - abs ε <=
b
::
a [b G] ε within
---------------------- a b - abs ε >
.
[b G] x ε ...
b [c G] ε ...
.
----------------------
b [c G] ε within
Predicate
^^^^^^^^^^^^^
~~~~~~~~~
::
@ -126,14 +143,12 @@ Predicate
abs(a-b) ε <=
(abs(a-b)<=ε)
.. code:: ipython2
::
P == [first - abs] dip <=
define('_within_P == [first - abs] dip <=')
Base-Case
^^^^^^^^^^^^^
~~~~~~~~~
::
@ -142,23 +157,23 @@ Base-Case
[b G] first
b
::
B == roll< popop first
.. code:: ipython2
define('_within_B == roll< popop first')
Recur
^^^^^^^^^^^^^
~~~~~
::
a [b G] ε R0 [within] R1
1. Discard ``a``.
1. Discard a.
2. Use ``x`` combinator to generate next term from ``G``.
3. Run ``within`` with ``i`` (it is a ``primrec`` function.)
Pretty straightforward:
::
a [b G] ε R0 [within] R1
@ -170,35 +185,74 @@ Recur
b [c G] ε within
::
R0 == [popd x] dip
.. code:: ipython2
define('_within_R == [popd x] dip')
Setting up
^^^^^^^^^^
~~~~~~~~~~
The recursive function we have defined so far needs a slight preamble: ``x`` to prime the generator and the epsilon value to use::
The recursive function we have defined so far needs a slight preamble:
``x`` to prime the generator and the epsilon value to use:
::
[a G] x ε ...
a [b G] ε ...
.. code:: ipython2
``within``
^^^^^^^^^^
define('within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec')
define('sqrt == gsra within')
Giving us the following definitions::
Try it out...
_within_P == [first - abs] dip <=
_within_B == roll< popop first
_within_R == [popd x] dip
within == x ε [_within_P] [_within_B] [_within_R] primrec
.. code:: ipython2
J('36 sqrt')
Finding Square Roots
====================
.. parsed-literal::
::
6.0
.. code:: ipython2
J('23 sqrt')
.. parsed-literal::
4.795831523312719
Check it.
.. code:: ipython2
4.795831523312719**2
.. parsed-literal::
22.999999999999996
.. code:: ipython2
from math import sqrt
sqrt(23)
.. parsed-literal::
4.795831523312719
sqrt == gsra within