The Hylos notebook is not ready for public yet.
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Simon Forman
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f5fe7d9726
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@ -157,7 +157,7 @@
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 6,
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"execution_count": 6,
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"metadata": {
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"name": "python",
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"name": "python",
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"nbconvert_exporter": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython2",
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"pygments_lexer": "ipython2",
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"version": "2.7.13"
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"version": "2.7.12"
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}
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"nbformat": 4,
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@ -12526,7 +12526,7 @@ range_sum == [0 <=] [pop 0] [1 - dup] [dip +] genrec</code></pre>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">defs</span> <span class="o">=</span> <span class="s1">'''</span>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">defs</span> <span class="o">=</span> <span class="s1">'''</span>
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@ -12548,7 +12548,7 @@ range_sum == [0 <=] [pop 0] [1 - dup] [dip +] genrec</code></pre>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'10 range'</span><span class="p">)</span>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'10 range'</span><span class="p">)</span>
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@ -12579,7 +12579,7 @@ range_sum == [0 <=] [pop 0] [1 - dup] [dip +] genrec</code></pre>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[9 8 7 6 5 4 3 2 1 0] sum'</span><span class="p">)</span>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[9 8 7 6 5 4 3 2 1 0] sum'</span><span class="p">)</span>
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@ -12610,7 +12610,7 @@ range_sum == [0 <=] [pop 0] [1 - dup] [dip +] genrec</code></pre>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'10 range sum'</span><span class="p">)</span>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'10 range sum'</span><span class="p">)</span>
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@ -13127,7 +13127,7 @@ range_sum == [0 <=] [pop 0] [1 - dup] [dip +] genrec</code></pre>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'10 range_sum'</span><span class="p">)</span>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'10 range_sum'</span><span class="p">)</span>
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@ -14390,789 +14390,6 @@ False [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 2] . swaac
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<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.">¶</a></h1>
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<pre><code>tree = [] | [node [tree*]]</code></pre>
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<h3 id="treestep"><code>treestep</code><a class="anchor-link" href="#treestep">¶</a></h3>
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<pre><code>tree z [C] [N] treestep
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[] z [C] [N] treestep
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---------------------------
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z
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[node [tree*]] z [C] [N] treestep
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--------------------------------------- w/ K == z [C] [N] treestep
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node N [tree*] [K] map C</code></pre>
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<h3 id="Derive-the-recursive-form.">Derive the recursive form.<a class="anchor-link" href="#Derive-the-recursive-form.">¶</a></h3>
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<pre><code>K == [not] [pop z] [J] ifte
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[node [tree*]] J
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------------------------------
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node N [tree*] [K] map C
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J == .. [N] .. [K] .. [C] ..
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[node [tree*]] uncons [N] dip
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node [[tree*]] [N] dip
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node N [[tree*]]
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node N [[tree*]] i [K] map
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node N [tree*] [K] map
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node N [K.tree*]
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J == uncons [N] dip i [K] map [C] i
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K == [not] [pop z] [uncons [N] dip i [K] map [C] i] ifte
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K == [not] [pop z] [uncons [N] dip i] [map [C] i] genrec</code></pre>
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<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.">¶</a></h3>
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<pre><code>[not] [pop z] [uncons [N] dip unquote] [map [C] i] genrec
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[not] [z] [pop] swoncat [uncons [N] dip unquote] [map [C] i] genrec
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[not] z unit [pop] swoncat [uncons [N] dip unquote] [map [C] i] genrec
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z [not] swap unit [pop] swoncat [uncons [N] dip unquote] [map [C] i] genrec
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\............TS0............/
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z TS0 [uncons [N] dip unquote] [map [C] i] genrec
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z [uncons [N] dip unquote] [TS0] dip [map [C] i] genrec
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z [[N] dip unquote] [uncons] swoncat [TS0] dip [map [C] i] genrec
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z [N] [dip unquote] cons [uncons] swoncat [TS0] dip [map [C] i] genrec
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\...........TS1.................../
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z [N] TS1 [TS0] dip [map [C] i] genrec
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z [N] [map [C] i] [TS1 [TS0] dip] dip genrec
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z [N] [map C ] [TS1 [TS0] dip] dip genrec
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z [N] [C] [map] swoncat [TS1 [TS0] dip] dip genrec
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z [C] [N] swap [map] swoncat [TS1 [TS0] dip] dip genrec</code></pre>
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<pre><code> TS0 == [not] swap unit [pop] swoncat
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TS1 == [dip i] cons [uncons] swoncat
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treestep == swap [map] swoncat [TS1 [TS0] dip] dip genrec</code></pre>
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<pre><code> [] 0 [C] [N] treestep
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0
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[n [tree*]] 0 [sum +] [] treestep
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--------------------------------------------------
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n [tree*] [0 [sum +] [] treestep] map sum +</code></pre>
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<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">'''</span>
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<span class="s1"> TS0 == [not] swap unit [pop] swoncat</span>
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<span class="s1"> TS1 == [dip i] cons [uncons] swoncat</span>
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<span class="s1">treestep == swap [map] swoncat [TS1 [TS0] dip] dip genrec</span>
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<span class="s1">'''</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[] 0 [sum +] [] treestep'</span><span class="p">)</span>
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<pre> . [] 0 [sum +] [] treestep
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[] . 0 [sum +] [] treestep
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[] [not] [pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] . ifte
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[23 []] 0 [sum +] [] treestep'</span><span class="p">)</span>
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<pre> . [23 []] 0 [sum +] [] treestep
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[23 []] . 0 [sum +] [] treestep
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[23 []] 0 . [sum +] [] treestep
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[23 []] 0 [sum +] . [] treestep
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[23 []] 0 [sum +] [] . treestep
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[23 []] 0 [sum +] [] . swap [map] swoncat [TS1 [TS0] dip] dip genrec
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||||||
[23 []] 0 [] [sum +] . [map] swoncat [TS1 [TS0] dip] dip genrec
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[23 []] 0 [] [sum +] [map] . swoncat [TS1 [TS0] dip] dip genrec
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[23 []] 0 [] [sum +] [map] . swap concat [TS1 [TS0] dip] dip genrec
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[23 []] 0 [] [map] [sum +] . concat [TS1 [TS0] dip] dip genrec
|
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||||||
[23 []] 0 [] [map sum +] . [TS1 [TS0] dip] dip genrec
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||||||
[23 []] 0 [] [map sum +] [TS1 [TS0] dip] . dip genrec
|
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||||||
[23 []] 0 [] . TS1 [TS0] dip [map sum +] genrec
|
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||||||
[23 []] 0 [] . [dip i] cons [uncons] swoncat [TS0] dip [map sum +] genrec
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||||||
[23 []] 0 [] [dip i] . cons [uncons] swoncat [TS0] dip [map sum +] genrec
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||||||
[23 []] 0 [[] dip i] . [uncons] swoncat [TS0] dip [map sum +] genrec
|
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||||||
[23 []] 0 [[] dip i] [uncons] . swoncat [TS0] dip [map sum +] genrec
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||||||
[23 []] 0 [[] dip i] [uncons] . swap concat [TS0] dip [map sum +] genrec
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||||||
[23 []] 0 [uncons] [[] dip i] . concat [TS0] dip [map sum +] genrec
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||||||
[23 []] 0 [uncons [] dip i] . [TS0] dip [map sum +] genrec
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||||||
[23 []] 0 [uncons [] dip i] [TS0] . dip [map sum +] genrec
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||||||
[23 []] 0 . TS0 [uncons [] dip i] [map sum +] genrec
|
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||||||
[23 []] 0 . [not] swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
|
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||||||
[23 []] 0 [not] . swap unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
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|
||||||
[23 []] [not] 0 . unit [pop] swoncat [uncons [] dip i] [map sum +] genrec
|
|
||||||
[23 []] [not] 0 . [] cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
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||||||
[23 []] [not] 0 [] . cons [pop] swoncat [uncons [] dip i] [map sum +] genrec
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||||||
[23 []] [not] [0] . [pop] swoncat [uncons [] dip i] [map sum +] genrec
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||||||
[23 []] [not] [0] [pop] . swoncat [uncons [] dip i] [map sum +] genrec
|
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||||||
[23 []] [not] [0] [pop] . swap concat [uncons [] dip i] [map sum +] genrec
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||||||
[23 []] [not] [pop] [0] . concat [uncons [] dip i] [map sum +] genrec
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|
||||||
[23 []] [not] [pop 0] . [uncons [] dip i] [map sum +] genrec
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||||||
[23 []] [not] [pop 0] [uncons [] dip i] . [map sum +] genrec
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|
||||||
[23 []] [not] [pop 0] [uncons [] dip i] [map sum +] . genrec
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||||||
[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
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||||||
[23 []] . not [[pop 0] [uncons [] dip i [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +] [23 []]] swaack first choice i
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||||||
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
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||||||
[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 +
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||||||
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 +
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||||||
23 . [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
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||||||
23 [] . [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] map sum +
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||||||
23 [] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] . map sum +
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|
||||||
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 +
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||||||
23 [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i +
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||||||
23 True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [] 23] swaack first choice i +
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|
||||||
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 .
|
|
||||||
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|
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|
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|
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|
||||||
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<div class="prompt input_prompt">In [33]:</div>
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|
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<div class="inner_cell">
|
|
||||||
<div class="input_area">
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[23 [[2 []] [3 []]]] 0 [sum +] [] treestep'</span><span class="p">)</span>
|
|
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</pre></div>
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<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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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||||||
23 3 [] [pop 0] . i + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
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|
||||||
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 +
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|
||||||
23 3 0 . + [] swaack first [[2 []] 23] [[not] [pop 0] [uncons [] dip i] [map sum +] genrec] infra first [23] swaack sum +
|
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||||||
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 +
|
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||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 .
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
<div class="cell border-box-sizing code_cell rendered">
|
|
||||||
<div class="input">
|
|
||||||
<div class="prompt input_prompt">In [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">'[23 [[2 [[23 [[2 []] [3 []]]][23 [[2 []] [3 []]]]]] [3 [[23 [[2 []] [3 []]]][23 [[2 []] [3 []]]]]]]] 0 [sum +] [] treestep'</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 [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">'[] [] [unit cons] [23 +] treestep'</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 [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">'[23 []] [] [unit cons] [23 +] treestep'</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 [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">'[23 [[2 []] [3 []]]] [] [unit cons] [23 +] treestep'</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 [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">'treemap == [] [unit cons] roll< treestep'</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 [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">'[23 [[2 []] [3 []]]] [23 +] treemap'</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>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
|
||||||
|
|
@ -273,9 +273,7 @@
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 9,
|
"execution_count": 9,
|
||||||
"metadata": {
|
"metadata": {},
|
||||||
"collapsed": true
|
|
||||||
},
|
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
|
|
@ -642,7 +640,7 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 8,
|
"execution_count": 10,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [],
|
"outputs": [],
|
||||||
"source": [
|
"source": [
|
||||||
|
|
@ -660,7 +658,7 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 9,
|
"execution_count": 11,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
|
|
@ -677,7 +675,7 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 10,
|
"execution_count": 12,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
|
|
@ -694,10 +692,8 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 11,
|
"execution_count": 13,
|
||||||
"metadata": {
|
"metadata": {},
|
||||||
"collapsed": true
|
|
||||||
},
|
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
|
|
@ -1199,10 +1195,8 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 12,
|
"execution_count": 14,
|
||||||
"metadata": {
|
"metadata": {},
|
||||||
"collapsed": true
|
|
||||||
},
|
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
|
|
@ -1906,9 +1900,7 @@
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 26,
|
"execution_count": 26,
|
||||||
"metadata": {
|
"metadata": {},
|
||||||
"collapsed": true
|
|
||||||
},
|
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
|
|
@ -2008,9 +2000,7 @@
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 27,
|
"execution_count": 27,
|
||||||
"metadata": {
|
"metadata": {},
|
||||||
"collapsed": true
|
|
||||||
},
|
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
|
|
@ -2092,9 +2082,7 @@
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 28,
|
"execution_count": 28,
|
||||||
"metadata": {
|
"metadata": {},
|
||||||
"collapsed": true
|
|
||||||
},
|
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
|
|
@ -2177,9 +2165,7 @@
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 29,
|
"execution_count": 29,
|
||||||
"metadata": {
|
"metadata": {},
|
||||||
"collapsed": true
|
|
||||||
},
|
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
|
|
@ -2269,698 +2255,6 @@
|
||||||
"\n",
|
"\n",
|
||||||
"\"Too much is always better than not enough.\""
|
"\"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": {
|
"metadata": {
|
||||||
|
|
|
||||||
|
|
@ -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.
|
I think they are having slightly too much fun with the symbols.
|
||||||
|
|
||||||
"Too much is always better than not enough."
|
"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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 +
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|
||||||
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 []]]]
|
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -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.
|
I think they are having slightly too much fun with the symbols.
|
||||||
|
|
||||||
"Too much is always better than not enough."
|
"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 []]]]
|
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -22,7 +22,9 @@ $(docs_md): %.md : %.ipynb
|
||||||
$(docs_rst): %.rst : %.ipynb
|
$(docs_rst): %.rst : %.ipynb
|
||||||
python -m nbconvert --to rst $<
|
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)
|
mov: $(move_us)
|
||||||
cp -v $? ./sphinx_docs/notebooks/
|
cp -v $? ./sphinx_docs/notebooks/
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -11867,21 +11867,6 @@ n+1 2 /
|
||||||
<div class="cell border-box-sizing code_cell rendered">
|
<div class="cell border-box-sizing code_cell rendered">
|
||||||
<div class="input">
|
<div class="input">
|
||||||
<div class="prompt input_prompt">In [2]:</div>
|
<div class="prompt input_prompt">In [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">'codireco == cons dip rest cons'</span><span class="p">)</span>
|
|
||||||
<span class="n">define</span><span class="p">(</span><span class="s1">'make_generator == [codireco] ccons'</span><span class="p">)</span>
|
|
||||||
<span class="n">define</span><span class="p">(</span><span class="s1">'ccons == cons cons'</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 [3]:</div>
|
|
||||||
<div class="inner_cell">
|
<div class="inner_cell">
|
||||||
<div class="input_area">
|
<div class="input_area">
|
||||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator'</span><span class="p">)</span>
|
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator'</span><span class="p">)</span>
|
||||||
|
|
@ -11894,7 +11879,7 @@ n+1 2 /
|
||||||
</div>
|
</div>
|
||||||
<div class="cell border-box-sizing code_cell rendered">
|
<div class="cell border-box-sizing code_cell rendered">
|
||||||
<div class="input">
|
<div class="input">
|
||||||
<div class="prompt input_prompt">In [4]:</div>
|
<div class="prompt input_prompt">In [3]:</div>
|
||||||
<div class="inner_cell">
|
<div class="inner_cell">
|
||||||
<div class="input_area">
|
<div class="input_area">
|
||||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra'</span><span class="p">)</span>
|
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra'</span><span class="p">)</span>
|
||||||
|
|
@ -11934,7 +11919,7 @@ n+1 2 /
|
||||||
</div>
|
</div>
|
||||||
<div class="cell border-box-sizing code_cell rendered">
|
<div class="cell border-box-sizing code_cell rendered">
|
||||||
<div class="input">
|
<div class="input">
|
||||||
<div class="prompt input_prompt">In [5]:</div>
|
<div class="prompt input_prompt">In [4]:</div>
|
||||||
<div class="inner_cell">
|
<div class="inner_cell">
|
||||||
<div class="input_area">
|
<div class="input_area">
|
||||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra 6 [x popd] times first sqr'</span><span class="p">)</span>
|
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra 6 [x popd] times first sqr'</span><span class="p">)</span>
|
||||||
|
|
@ -11967,9 +11952,9 @@ n+1 2 /
|
||||||
</div>
|
</div>
|
||||||
<div class="inner_cell">
|
<div class="inner_cell">
|
||||||
<div class="text_cell_render border-box-sizing rendered_html">
|
<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">¶</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">¶</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>
|
</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>(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>
|
<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 <=
|
||||||
</div>
|
</div>
|
||||||
<div class="cell border-box-sizing code_cell rendered">
|
<div class="cell border-box-sizing code_cell rendered">
|
||||||
<div class="input">
|
<div class="input">
|
||||||
<div class="prompt input_prompt">In [6]:</div>
|
<div class="prompt input_prompt">In [5]:</div>
|
||||||
<div class="inner_cell">
|
<div class="inner_cell">
|
||||||
<div class="input_area">
|
<div class="input_area">
|
||||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_P == [first - abs] dip <='</span><span class="p">)</span>
|
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_P == [first - abs] dip <='</span><span class="p">)</span>
|
||||||
|
|
@ -12028,7 +12013,7 @@ abs(a-b) ε <=
|
||||||
</div>
|
</div>
|
||||||
<div class="cell border-box-sizing code_cell rendered">
|
<div class="cell border-box-sizing code_cell rendered">
|
||||||
<div class="input">
|
<div class="input">
|
||||||
<div class="prompt input_prompt">In [7]:</div>
|
<div class="prompt input_prompt">In [6]:</div>
|
||||||
<div class="inner_cell">
|
<div class="inner_cell">
|
||||||
<div class="input_area">
|
<div class="input_area">
|
||||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_B == roll< popop first'</span><span class="p">)</span>
|
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_B == roll< popop first'</span><span class="p">)</span>
|
||||||
|
|
@ -12049,8 +12034,8 @@ abs(a-b) ε <=
|
||||||
</code></pre>
|
</code></pre>
|
||||||
<ol>
|
<ol>
|
||||||
<li>Discard a.</li>
|
<li>Discard a.</li>
|
||||||
<li>Use x combinator to generate next term from G.</li>
|
<li>Use <code>x</code> combinator to generate next term from <code>G</code>.</li>
|
||||||
<li>Run within with <code>i</code> (it is a <code>primrec</code> function.)</li>
|
<li>Run <code>within</code> with <code>i</code> (it is a <code>primrec</code> function.)</li>
|
||||||
</ol>
|
</ol>
|
||||||
<p>Pretty straightforward:</p>
|
<p>Pretty straightforward:</p>
|
||||||
|
|
||||||
|
|
@ -12068,7 +12053,7 @@ b [c G] ε within</code></pre>
|
||||||
</div>
|
</div>
|
||||||
<div class="cell border-box-sizing code_cell rendered">
|
<div class="cell border-box-sizing code_cell rendered">
|
||||||
<div class="input">
|
<div class="input">
|
||||||
<div class="prompt input_prompt">In [8]:</div>
|
<div class="prompt input_prompt">In [7]:</div>
|
||||||
<div class="inner_cell">
|
<div class="inner_cell">
|
||||||
<div class="input_area">
|
<div class="input_area">
|
||||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_R == [popd x] dip'</span><span class="p">)</span>
|
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_R == [popd x] dip'</span><span class="p">)</span>
|
||||||
|
|
@ -12093,7 +12078,7 @@ a [b G] ε ...</code></pre>
|
||||||
</div>
|
</div>
|
||||||
<div class="cell border-box-sizing code_cell rendered">
|
<div class="cell border-box-sizing code_cell rendered">
|
||||||
<div class="input">
|
<div class="input">
|
||||||
<div class="prompt input_prompt">In [9]:</div>
|
<div class="prompt input_prompt">In [8]:</div>
|
||||||
<div class="inner_cell">
|
<div class="inner_cell">
|
||||||
<div class="input_area">
|
<div class="input_area">
|
||||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec'</span><span class="p">)</span>
|
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec'</span><span class="p">)</span>
|
||||||
|
|
@ -12104,6 +12089,46 @@ a [b G] ε ...</code></pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
|
||||||
|
</div>
|
||||||
|
<div class="inner_cell">
|
||||||
|
<div class="text_cell_render border-box-sizing rendered_html">
|
||||||
|
<p>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 [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">'36 sqrt'</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>
|
||||||
<div class="cell border-box-sizing code_cell rendered">
|
<div class="cell border-box-sizing code_cell rendered">
|
||||||
<div class="input">
|
<div class="input">
|
||||||
|
|
@ -12135,6 +12160,15 @@ a [b G] ε ...</code></pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
|
||||||
|
</div>
|
||||||
|
<div class="inner_cell">
|
||||||
|
<div class="text_cell_render border-box-sizing rendered_html">
|
||||||
|
<p>Check it.</p>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
</div>
|
</div>
|
||||||
<div class="cell border-box-sizing code_cell rendered">
|
<div class="cell border-box-sizing code_cell rendered">
|
||||||
<div class="input">
|
<div class="input">
|
||||||
|
|
@ -12168,6 +12202,41 @@ a [b G] ε ...</code></pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
<div class="cell border-box-sizing code_cell rendered">
|
||||||
|
<div class="input">
|
||||||
|
<div class="prompt input_prompt">In [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>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
|
||||||
|
|
@ -87,17 +87,6 @@
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 2,
|
"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": {
|
"metadata": {
|
||||||
"scrolled": true
|
"scrolled": true
|
||||||
},
|
},
|
||||||
|
|
@ -108,7 +97,7 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 4,
|
"execution_count": 3,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
|
|
@ -132,7 +121,7 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 5,
|
"execution_count": 4,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
|
|
@ -153,11 +142,11 @@
|
||||||
"source": [
|
"source": [
|
||||||
"## Finding Consecutive Approximations within a Tolerance\n",
|
"## Finding Consecutive Approximations within a Tolerance\n",
|
||||||
"\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",
|
"\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",
|
"> 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",
|
"\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",
|
"(And note that by “list” he means a lazily-evaluated list.)\n",
|
||||||
"\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",
|
"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",
|
"cell_type": "code",
|
||||||
"execution_count": 6,
|
"execution_count": 5,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [],
|
"outputs": [],
|
||||||
"source": [
|
"source": [
|
||||||
|
|
@ -210,7 +199,7 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 7,
|
"execution_count": 6,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [],
|
"outputs": [],
|
||||||
"source": [
|
"source": [
|
||||||
|
|
@ -226,8 +215,8 @@
|
||||||
" a [b G] ε R0 [within] R1\n",
|
" a [b G] ε R0 [within] R1\n",
|
||||||
"\n",
|
"\n",
|
||||||
"1. Discard a.\n",
|
"1. Discard a.\n",
|
||||||
"2. Use x combinator to generate next term from G.\n",
|
"2. Use `x` combinator to generate next term from `G`.\n",
|
||||||
"3. Run within with `i` (it is a `primrec` function.)\n",
|
"3. Run `within` with `i` (it is a `primrec` function.)\n",
|
||||||
"\n",
|
"\n",
|
||||||
"Pretty straightforward:\n",
|
"Pretty straightforward:\n",
|
||||||
"\n",
|
"\n",
|
||||||
|
|
@ -243,7 +232,7 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 8,
|
"execution_count": 7,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [],
|
"outputs": [],
|
||||||
"source": [
|
"source": [
|
||||||
|
|
@ -264,7 +253,7 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 9,
|
"execution_count": 8,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [],
|
"outputs": [],
|
||||||
"source": [
|
"source": [
|
||||||
|
|
@ -272,6 +261,32 @@
|
||||||
"define('sqrt == gsra within')"
|
"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",
|
"cell_type": "code",
|
||||||
"execution_count": 10,
|
"execution_count": 10,
|
||||||
|
|
@ -291,6 +306,13 @@
|
||||||
"J('23 sqrt')"
|
"J('23 sqrt')"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "markdown",
|
||||||
|
"metadata": {},
|
||||||
|
"source": [
|
||||||
|
"Check it."
|
||||||
|
]
|
||||||
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 11,
|
"execution_count": 11,
|
||||||
|
|
@ -312,6 +334,28 @@
|
||||||
"source": [
|
"source": [
|
||||||
"4.795831523312719**2"
|
"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": {
|
"metadata": {
|
||||||
|
|
|
||||||
|
|
@ -55,13 +55,6 @@ The generator can be written as:
|
||||||
1 [dup 23 over / + 2 /] make_generator
|
1 [dup 23 over / + 2 /] make_generator
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
define('codireco == cons dip rest cons')
|
|
||||||
define('make_generator == [codireco] ccons')
|
|
||||||
define('ccons == cons cons')
|
|
||||||
```
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
```python
|
||||||
define('gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
|
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
|
## 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.
|
> 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.)
|
(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...
|
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
|
a [b G] ε R0 [within] R1
|
||||||
|
|
||||||
1. Discard a.
|
1. Discard a.
|
||||||
2. Use x combinator to generate next term from G.
|
2. Use `x` combinator to generate next term from `G`.
|
||||||
3. Run within with `i` (it is a `primrec` function.)
|
3. Run `within` with `i` (it is a `primrec` function.)
|
||||||
|
|
||||||
Pretty straightforward:
|
Pretty straightforward:
|
||||||
|
|
||||||
|
|
@ -169,6 +162,16 @@ define('within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec')
|
||||||
define('sqrt == gsra within')
|
define('sqrt == gsra within')
|
||||||
```
|
```
|
||||||
|
|
||||||
|
Try it out...
|
||||||
|
|
||||||
|
|
||||||
|
```python
|
||||||
|
J('36 sqrt')
|
||||||
|
```
|
||||||
|
|
||||||
|
6.0
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
```python
|
||||||
J('23 sqrt')
|
J('23 sqrt')
|
||||||
|
|
@ -177,6 +180,8 @@ J('23 sqrt')
|
||||||
4.795831523312719
|
4.795831523312719
|
||||||
|
|
||||||
|
|
||||||
|
Check it.
|
||||||
|
|
||||||
|
|
||||||
```python
|
```python
|
||||||
4.795831523312719**2
|
4.795831523312719**2
|
||||||
|
|
@ -188,3 +193,17 @@ J('23 sqrt')
|
||||||
22.999999999999996
|
22.999999999999996
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
```python
|
||||||
|
from math import sqrt
|
||||||
|
|
||||||
|
sqrt(23)
|
||||||
|
```
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
4.795831523312719
|
||||||
|
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -76,12 +76,6 @@ The generator can be written as:
|
||||||
1 [23 over / + 2 /] [dup] swoncat make_generator
|
1 [23 over / + 2 /] [dup] swoncat make_generator
|
||||||
1 [dup 23 over / + 2 /] 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
|
.. code:: ipython2
|
||||||
|
|
||||||
define('gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
|
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
|
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
|
The remainder of a square root finder is a function *within*, which
|
||||||
takes a tolerance and a list of approximations and looks down the
|
takes a tolerance and a list of approximations and looks down the
|
||||||
list for two successive approximations that differ by no more than
|
list for two successive approximations that differ by no more than
|
||||||
the given tolerance.
|
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.)
|
(And note that by “list” he means a lazily-evaluated list.)
|
||||||
|
|
||||||
Using the *output* ``[a G]`` of the above generator for square root
|
Using the *output* ``[a G]`` of the above generator for square root
|
||||||
|
|
@ -175,8 +169,8 @@ Recur
|
||||||
a [b G] ε R0 [within] R1
|
a [b G] ε R0 [within] R1
|
||||||
|
|
||||||
1. Discard a.
|
1. Discard a.
|
||||||
2. Use x combinator to generate next term from G.
|
2. Use ``x`` combinator to generate next term from ``G``.
|
||||||
3. Run within with ``i`` (it is a ``primrec`` function.)
|
3. Run ``within`` with ``i`` (it is a ``primrec`` function.)
|
||||||
|
|
||||||
Pretty straightforward:
|
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('within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec')
|
||||||
define('sqrt == gsra within')
|
define('sqrt == gsra within')
|
||||||
|
|
||||||
|
Try it out...
|
||||||
|
|
||||||
|
.. code:: ipython2
|
||||||
|
|
||||||
|
J('36 sqrt')
|
||||||
|
|
||||||
|
|
||||||
|
.. parsed-literal::
|
||||||
|
|
||||||
|
6.0
|
||||||
|
|
||||||
|
|
||||||
.. code:: ipython2
|
.. code:: ipython2
|
||||||
|
|
||||||
J('23 sqrt')
|
J('23 sqrt')
|
||||||
|
|
@ -221,6 +227,8 @@ The recursive function we have defined so far needs a slight preamble:
|
||||||
4.795831523312719
|
4.795831523312719
|
||||||
|
|
||||||
|
|
||||||
|
Check it.
|
||||||
|
|
||||||
.. code:: ipython2
|
.. code:: ipython2
|
||||||
|
|
||||||
4.795831523312719**2
|
4.795831523312719**2
|
||||||
|
|
@ -233,3 +241,18 @@ The recursive function we have defined so far needs a slight preamble:
|
||||||
22.999999999999996
|
22.999999999999996
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
.. code:: ipython2
|
||||||
|
|
||||||
|
from math import sqrt
|
||||||
|
|
||||||
|
sqrt(23)
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
.. parsed-literal::
|
||||||
|
|
||||||
|
4.795831523312719
|
||||||
|
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -157,6 +157,9 @@
|
||||||
<span class="s1">dudipd == dup dipd</span>
|
<span class="s1">dudipd == dup dipd</span>
|
||||||
<span class="s1">primrec == [i] genrec</span>
|
<span class="s1">primrec == [i] genrec</span>
|
||||||
<span class="s1">step_zero == 0 roll> step</span>
|
<span class="s1">step_zero == 0 roll> 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">'''</span>
|
<span class="s1">'''</span>
|
||||||
|
|
||||||
<span class="c1">##Zipper</span>
|
<span class="c1">##Zipper</span>
|
||||||
|
|
|
||||||
|
|
@ -17,7 +17,7 @@
|
||||||
<link rel="index" title="Index" href="../genindex.html" />
|
<link rel="index" title="Index" href="../genindex.html" />
|
||||||
<link rel="search" title="Search" href="../search.html" />
|
<link rel="search" title="Search" href="../search.html" />
|
||||||
<link rel="next" title="Quadratic formula" href="Quadratic.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" />
|
<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
|
||||||
|
|
||||||
|
|
@ -34,16 +34,18 @@
|
||||||
|
|
||||||
<div class="section" id="newton-s-method">
|
<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>
|
<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>
|
<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>
|
</pre></div>
|
||||||
</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">
|
<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>
|
<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
|
||||||
<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>
|
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>
|
<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="o">---------</span>
|
||||||
<span class="n">a</span><span class="s1">'</span>
|
<span class="n">a</span><span class="s1">'</span>
|
||||||
|
|
@ -51,7 +53,8 @@ Hughes</a></p>
|
||||||
</div>
|
</div>
|
||||||
<div class="section" id="a-function-to-compute-the-next-approximation">
|
<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>
|
<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>
|
<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>
|
<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>
|
<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>
|
<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>
|
</pre></div>
|
||||||
</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>
|
<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">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>
|
<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>
|
</pre></div>
|
||||||
</div>
|
</div>
|
||||||
<p>The generator can be written as:</p>
|
<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>
|
<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="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="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="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>
|
</pre></div>
|
||||||
</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">'gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
</div>
|
</div>
|
||||||
<div class="section" id="a-generator-of-square-root-approximations">
|
<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">'23 gsra'</span><span class="p">)</span>
|
||||||
<h3>A Generator of Square Root Approximations<a class="headerlink" href="#a-generator-of-square-root-approximations" title="Permalink to this headline">¶</a></h3>
|
</pre></div>
|
||||||
<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>
|
||||||
|
<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">'23 gsra 6 [x popd] times first sqr'</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>
|
</pre></div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
<div class="section" id="finding-consecutive-approximations-within-a-tolerance">
|
<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>
|
<h2>Finding Consecutive Approximations within 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>
|
|
||||||
<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
|
<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>(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>
|
<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"><=</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"><=</span>
|
||||||
<span class="n">b</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">></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">></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>
|
<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>
|
</pre></div>
|
||||||
</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"><=</span><span class="n">ε</span><span class="p">)</span>
|
<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"><=</span><span class="n">ε</span><span class="p">)</span>
|
||||||
</pre></div>
|
</pre></div>
|
||||||
</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"><=</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">'_within_P == [first - abs] dip <='</span><span class="p">)</span>
|
||||||
</pre></div>
|
</pre></div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
@ -147,7 +154,7 @@ Hughes</a></p>
|
||||||
<span class="n">b</span>
|
<span class="n">b</span>
|
||||||
</pre></div>
|
</pre></div>
|
||||||
</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"><</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">'_within_B == roll< popop first'</span><span class="p">)</span>
|
||||||
</pre></div>
|
</pre></div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
@ -157,10 +164,11 @@ Hughes</a></p>
|
||||||
</pre></div>
|
</pre></div>
|
||||||
</div>
|
</div>
|
||||||
<ol class="arabic simple">
|
<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>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>
|
<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>
|
</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>
|
<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">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>
|
<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>
|
<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>
|
</pre></div>
|
||||||
</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">'_within_R == [popd x] dip'</span><span class="p">)</span>
|
||||||
</pre></div>
|
</pre></div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
<div class="section" id="setting-up">
|
<div class="section" id="setting-up">
|
||||||
<h3>Setting up<a class="headerlink" href="#setting-up" title="Permalink to this headline">¶</a></h3>
|
<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>
|
<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>
|
<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>
|
</pre></div>
|
||||||
</div>
|
</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">'within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec'</span><span class="p">)</span>
|
||||||
<div class="section" id="within">
|
<span class="n">define</span><span class="p">(</span><span class="s1">'sqrt == gsra within'</span><span class="p">)</span>
|
||||||
<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"><=</span>
|
|
||||||
<span class="n">_within_B</span> <span class="o">==</span> <span class="n">roll</span><span class="o"><</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>
|
|
||||||
</pre></div>
|
</pre></div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
<p>Try it out…</p>
|
||||||
</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">'36 sqrt'</span><span class="p">)</span>
|
||||||
<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>
|
|
||||||
</pre></div>
|
</pre></div>
|
||||||
</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">'23 sqrt'</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>
|
||||||
</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-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="#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="#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>
|
</ul>
|
||||||
</li>
|
</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="#predicate">Predicate</a></li>
|
||||||
<li><a class="reference internal" href="#base-case">Base-Case</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="#recur">Recur</a></li>
|
||||||
<li><a class="reference internal" href="#setting-up">Setting up</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>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a class="reference internal" href="#finding-square-roots">Finding Square Roots</a></li>
|
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -234,7 +256,7 @@ Hughes</a></p>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="../index.html">Documentation overview</a><ul>
|
<li><a href="../index.html">Documentation overview</a><ul>
|
||||||
<li><a href="index.html">Essays about Programming in Joy</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>
|
<li>Next: <a href="Quadratic.html" title="next chapter">Quadratic formula</a></li>
|
||||||
</ul></li>
|
</ul></li>
|
||||||
</ul></li>
|
</ul></li>
|
||||||
|
|
|
||||||
|
|
@ -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>
|
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
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||||||
<link rel="index" title="Index" href="../genindex.html" />
|
<link rel="index" title="Index" href="../genindex.html" />
|
||||||
<link rel="search" title="Search" href="../search.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="prev" title="Newton’s method" href="Newton-Raphson.html" />
|
||||||
|
|
||||||
<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
|
<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">Documentation overview</a><ul>
|
||||||
<li><a href="index.html">Essays about Programming in Joy</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>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></li>
|
</ul></li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
|
||||||
|
|
@ -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>
|
<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="index" title="Index" href="../genindex.html" />
|
||||||
<link rel="search" title="Search" href="../search.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" />
|
<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>
|
<h3>Related Topics</h3>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="../index.html">Documentation overview</a><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></li>
|
||||||
</ul>
|
</ul>
|
||||||
</div>
|
</div>
|
||||||
|
|
|
||||||
|
|
@ -86,8 +86,7 @@
|
||||||
</li>
|
</li>
|
||||||
<li class="toctree-l1"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a><ul>
|
<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#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-consecutive-approximations-within-a-tolerance">Finding Consecutive Approximations within a Tolerance</a></li>
|
||||||
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html#finding-square-roots">Finding Square Roots</a></li>
|
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li class="toctree-l1"><a class="reference internal" href="Quadratic.html">Quadratic formula</a><ul>
|
<li class="toctree-l1"><a class="reference internal" href="Quadratic.html">Quadratic formula</a><ul>
|
||||||
|
|
|
||||||
Binary file not shown.
File diff suppressed because one or more lines are too long
|
|
@ -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
|
.. code:: ipython2
|
||||||
|
|
||||||
from notebook_preamble import J, V, define
|
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
|
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 F
|
||||||
---------
|
---------
|
||||||
a'
|
a'
|
||||||
|
|
||||||
|
|
||||||
A Function to Compute the Next Approximation
|
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}`
|
: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 /
|
||||||
(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 /
|
F == n over / + 2 /
|
||||||
|
|
||||||
|
|
||||||
Make it into a Generator
|
Make it into a Generator
|
||||||
^^^^^^^^^^^^^^^^^^^^^^^^
|
~~~~~~~~~~~~~~~~~~~~~~~~
|
||||||
|
|
||||||
Our generator would be created by::
|
Our generator would be created by:
|
||||||
|
|
||||||
|
::
|
||||||
|
|
||||||
a [dup F] make_generator
|
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 /
|
||||||
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 /
|
||||||
(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
|
23 1 swap [over / + 2 /] cons [dup] swoncat make_generator
|
||||||
1 23 [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 [23 over / + 2 /] [dup] swoncat make_generator
|
||||||
1 [dup 23 over / + 2 /] make_generator
|
1 [dup 23 over / + 2 /] make_generator
|
||||||
.
|
|
||||||
.
|
.. code:: ipython2
|
||||||
.
|
|
||||||
[1 swap [dup 23 over / + 2 /] direco]
|
define('gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
|
||||||
|
|
||||||
|
.. code:: ipython2
|
||||||
|
|
||||||
|
J('23 gsra')
|
||||||
|
|
||||||
|
|
||||||
A Generator of Square Root Approximations
|
.. parsed-literal::
|
||||||
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
|
||||||
|
|
||||||
::
|
[1 [dup 23 over / + 2 /] codireco]
|
||||||
|
|
||||||
gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator
|
|
||||||
|
|
||||||
|
|
||||||
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
|
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 <=
|
---------------------- a b - abs ε <=
|
||||||
b
|
b
|
||||||
|
|
||||||
::
|
|
||||||
|
|
||||||
a [b G] ε within
|
a [b G] ε within
|
||||||
---------------------- a b - abs ε >
|
---------------------- a b - abs ε >
|
||||||
.
|
|
||||||
[b G] x ε ...
|
|
||||||
b [c G] ε ...
|
|
||||||
.
|
|
||||||
----------------------
|
|
||||||
b [c G] ε within
|
b [c G] ε within
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
Predicate
|
Predicate
|
||||||
^^^^^^^^^^^^^
|
~~~~~~~~~
|
||||||
|
|
||||||
::
|
::
|
||||||
|
|
||||||
|
|
@ -126,14 +143,12 @@ Predicate
|
||||||
abs(a-b) ε <=
|
abs(a-b) ε <=
|
||||||
(abs(a-b)<=ε)
|
(abs(a-b)<=ε)
|
||||||
|
|
||||||
|
.. code:: ipython2
|
||||||
|
|
||||||
::
|
define('_within_P == [first - abs] dip <=')
|
||||||
|
|
||||||
P == [first - abs] dip <=
|
|
||||||
|
|
||||||
|
|
||||||
Base-Case
|
Base-Case
|
||||||
^^^^^^^^^^^^^
|
~~~~~~~~~
|
||||||
|
|
||||||
::
|
::
|
||||||
|
|
||||||
|
|
@ -142,23 +157,23 @@ Base-Case
|
||||||
[b G] first
|
[b G] first
|
||||||
b
|
b
|
||||||
|
|
||||||
::
|
.. code:: ipython2
|
||||||
|
|
||||||
B == roll< popop first
|
|
||||||
|
|
||||||
|
define('_within_B == roll< popop first')
|
||||||
|
|
||||||
Recur
|
Recur
|
||||||
^^^^^^^^^^^^^
|
~~~~~
|
||||||
|
|
||||||
::
|
::
|
||||||
|
|
||||||
a [b G] ε R0 [within] R1
|
a [b G] ε R0 [within] R1
|
||||||
|
|
||||||
|
1. Discard a.
|
||||||
1. Discard ``a``.
|
|
||||||
2. Use ``x`` combinator to generate next term from ``G``.
|
2. Use ``x`` combinator to generate next term from ``G``.
|
||||||
3. Run ``within`` with ``i`` (it is a ``primrec`` function.)
|
3. Run ``within`` with ``i`` (it is a ``primrec`` function.)
|
||||||
|
|
||||||
|
Pretty straightforward:
|
||||||
|
|
||||||
::
|
::
|
||||||
|
|
||||||
a [b G] ε R0 [within] R1
|
a [b G] ε R0 [within] R1
|
||||||
|
|
@ -170,35 +185,74 @@ Recur
|
||||||
|
|
||||||
b [c G] ε within
|
b [c G] ε within
|
||||||
|
|
||||||
::
|
.. code:: ipython2
|
||||||
|
|
||||||
R0 == [popd x] dip
|
|
||||||
|
|
||||||
|
define('_within_R == [popd x] dip')
|
||||||
|
|
||||||
Setting up
|
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 G] x ε ...
|
||||||
a [b G] 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 <=
|
.. code:: ipython2
|
||||||
_within_B == roll< popop first
|
|
||||||
_within_R == [popd x] dip
|
J('36 sqrt')
|
||||||
within == x ε [_within_P] [_within_B] [_within_R] primrec
|
|
||||||
|
|
||||||
|
|
||||||
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
|
|
||||||
|
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue