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sforman
2023-10-09 11:50:37 -07:00
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docs/html/notebooks/DeriveZip.html
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<p>Now then, we have two non-empty lists:</p>
<pre><code>[a b c ...] [e f g ...] R0 [zip] R1
</code></pre>
<p>Let's imagine a function <code>shift-pair</code>:</p>
<pre><code> [a ...] [e ...] shift-pair
<p>Let's imagine a function <code>uncons-pair</code>:</p>
<pre><code> [a ...] [e ...] uncons-pair
--------------------------------
[a e] [...] [...]
</code></pre>
<p>I'm going to defer derivation of that for now.</p>
<pre><code>[a b c ...] [e f g ...] shift-pair [zip] R1
<pre><code>[a b c ...] [e f g ...] uncons-pair [zip] R1
[a e] [b c ...] [f g ...] [zip] R1
</code></pre>
<p>And so <code>R1</code> is <code>i cons</code> (it's a list builder.)</p>
<pre><code>zip == [null] [pop] [shift-pair] [i cons] genrec
<pre><code>zip == [null] [pop] [uncons-pair] [i cons] genrec
</code></pre>
<p>And now:</p>
<pre><code>shift-pair == uncons-two [quote-two] dipd
<pre><code>uncons-pair == uncons-two [quote-two] dipd
</code></pre>
<p>w/</p>
<pre><code>uncons-two == [uncons] ii swapd
quote-two == unit cons
[zip [null] [pop] [shift-pair] [i cons] genrec] inscribe
[shift-pair uncons-two [quote-two] dipd] inscribe
[zip [null] [pop] [uncons-pair] [i cons] genrec] inscribe
[uncons-pair uncons-two [quote-two] dipd] inscribe
[uncons-two [uncons] ii swapd] inscribe
[quote-two unit cons] inscribe
</code></pre>