57 lines
1.9 KiB
HTML
57 lines
1.9 KiB
HTML
<!doctype html>
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<html>
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<head>
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<meta charset="utf-8">
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<title>Zip</title>
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<link rel="stylesheet" href="../css/font/fonts.css">
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<link rel="stylesheet" href="../css/site.css">
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<script src="../Joy.js"></script>
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<body>
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<div id="joy_interpreter"></div>
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<h1>Zip</h1>
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<p>Let's derive <code>zip</code>.</p>
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<pre><code> [a b c ...] [e f g ...] zip
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---------------------------------
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[[a e] [b f] [c g] ...]
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</code></pre>
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<p>It's a <code>genrec</code>:</p>
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<pre><code>zip == [null] [popop []] [R0] [R1] genrec
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</code></pre>
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<p>If the top list is empty, pop both lists and put a new empty list...</p>
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<p>Hmm...</p>
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<pre><code>zip == [null] [pop] [R0] [R1] genrec
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</code></pre>
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<p>We will assume that both lists are the same size, so if the top list is empty the second list shall be too, and we can reuse it to store our pairs.</p>
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<p>Now then, we have two non-empty lists:</p>
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<pre><code>[a b c ...] [e f g ...] R0 [zip] R1
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</code></pre>
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<p>Let's imagine a function <code>uncons-pair</code>:</p>
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<pre><code> [a ...] [e ...] uncons-pair
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--------------------------------
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[a e] [...] [...]
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</code></pre>
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<p>I'm going to defer derivation of that for now.</p>
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<pre><code>[a b c ...] [e f g ...] uncons-pair [zip] R1
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[a e] [b c ...] [f g ...] [zip] R1
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</code></pre>
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<p>And so <code>R1</code> is <code>i cons</code> (it's a list builder.)</p>
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<pre><code>zip == [null] [pop] [uncons-pair] [i cons] genrec
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</code></pre>
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<p>And now:</p>
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<pre><code>uncons-pair == uncons-two [quote-two] dipd
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</code></pre>
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<p>w/</p>
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<pre><code>uncons-two == [uncons] ii swapd
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quote-two == unit cons
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[zip [null] [pop] [uncons-pair] [i cons] genrec] inscribe
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[uncons-pair uncons-two [quote-two] dipd] inscribe
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[uncons-two [uncons] ii swapd] inscribe
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[quote-two unit cons] inscribe
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</code></pre>
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