The rest of the S's.
This commit is contained in:
Simon Forman
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@ -2082,273 +2082,212 @@ a F a</code></pre>
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<p><a href="#split_at">split_at</a></p>
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<hr />
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<h2 id="sqr">sqr</h2>
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<p>Basis Function Combinator</p>
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<p>dup *</p>
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<p>Gentzen diagram.</p>
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<p>Function</p>
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<p>Square the number on the top of the stack.</p>
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<pre><code> n sqr
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------------
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n²</code></pre>
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<h3 id="definition-81">Definition</h3>
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<p>if not basis.</p>
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<h3 id="derivation-3">Derivation</h3>
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<p>if not basis.</p>
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<h3 id="source">Source</h3>
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<p>if basis</p>
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<h3 id="discussion-64">Discussion</h3>
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<p>Lorem ipsum.</p>
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<h3 id="crosslinks-98">Crosslinks</h3>
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<p>Lorem ipsum.</p>
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<blockquote>
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<p><a href="#dup">dup</a> <a href="#mul">mul</a></p>
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</blockquote>
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<hr />
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<h2 id="sqrt">sqrt</h2>
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<p>Basis Function Combinator</p>
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<p>Return the square root of the number a. Negative numbers return complex roots.</p>
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<p>Gentzen diagram.</p>
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<h3 id="definition-82">Definition</h3>
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<p>if not basis.</p>
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<h3 id="derivation-4">Derivation</h3>
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<p>if not basis.</p>
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<h3 id="source-1">Source</h3>
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<p>if basis</p>
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<h3 id="discussion-65">Discussion</h3>
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<p>Lorem ipsum.</p>
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<h3 id="crosslinks-99">Crosslinks</h3>
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<p>Lorem ipsum.</p>
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<h3 id="discussion-64">Discussion</h3>
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<p>Another “numeric tower” hatch…</p>
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<hr />
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<h2 id="stack">stack</h2>
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<p>Basis Function Combinator</p>
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<pre><code>(... -- ... [...])</code></pre>
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<p>Gentzen diagram.</p>
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<h3 id="definition-83">Definition</h3>
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<p>if not basis.</p>
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<h3 id="derivation-5">Derivation</h3>
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<p>if not basis.</p>
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<h3 id="source-2">Source</h3>
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<p>if basis</p>
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<h3 id="discussion-66">Discussion</h3>
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<p>Lorem ipsum.</p>
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<h3 id="crosslinks-100">Crosslinks</h3>
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<p>Lorem ipsum.</p>
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<p>Function</p>
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<p>Put the stack onto the stack.</p>
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<pre><code> ... c b a stack
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---------------------------
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... c b a [a b c ...]</code></pre>
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<h3 id="definition-82">Definition</h3>
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<blockquote>
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<p>[] <a href="#swaack">swaack</a> <a href="#dup">dup</a> <a href="#swaack">swaack</a> <a href="#first">first</a></p>
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</blockquote>
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<h3 id="discussion-65">Discussion</h3>
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<p>This function forms a pair with [unstack], and together they form the complement to the “destructive” pair <a href="#enstacken">enstacken</a> and <a href="#disenstacken">disenstacken</a>.</p>
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<h3 id="crosslinks-98">Crosslinks</h3>
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<p>[unstack] <a href="#enstacken">enstacken</a> <a href="#disenstacken">disenstacken</a></p>
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<hr />
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<h2 id="stackd">stackd</h2>
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<p>Basis Function Combinator</p>
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<p>[stack] dip</p>
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<p>Gentzen diagram.</p>
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<h3 id="definition-84">Definition</h3>
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<p>if not basis.</p>
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<h3 id="derivation-6">Derivation</h3>
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<p>if not basis.</p>
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<h3 id="source-3">Source</h3>
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<p>if basis</p>
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<h3 id="discussion-67">Discussion</h3>
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<p>Lorem ipsum.</p>
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<h3 id="crosslinks-101">Crosslinks</h3>
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<p>Lorem ipsum.</p>
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<p>Function</p>
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<p>Grab the stack under the top item and put it onto the stack.</p>
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<h3 id="example-26">Example</h3>
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<pre><code> ... 1 2 3 stackd
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------------------------
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... 1 2 [2 1 ...] 3</code></pre>
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<h3 id="definition-83">Definition</h3>
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<blockquote>
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<p>[<a href="#stack">stack</a>] <a href="#dip">dip</a></p>
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</blockquote>
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<hr />
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<h2 id="step">step</h2>
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<p>Basis Function Combinator</p>
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<p>Run a quoted program on each item in a sequence. :</p>
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<pre><code>... [] [Q] . step
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-----------------------
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... .
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<p>Combinator</p>
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<p>Run a quoted program on each item in a sequence.</p>
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<pre><code> ... [] [Q] step
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---------------------
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...
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... [a] [Q] . step
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------------------------
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... a . Q
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... [a] [Q] step
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----------------------
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... a Q
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... [a b c] [Q] . step
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... [a b c] [Q] . step
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----------------------------------------
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... a . Q [b c] [Q] step</code></pre>
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<p>The step combinator executes the quotation on each member of the list on top of the stack.</p>
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<p>Gentzen diagram.</p>
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<h3 id="definition-85">Definition</h3>
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<p>if not basis.</p>
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<h3 id="derivation-7">Derivation</h3>
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<p>if not basis.</p>
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<h3 id="source-4">Source</h3>
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<p>if basis</p>
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<h3 id="discussion-68">Discussion</h3>
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<p>Lorem ipsum.</p>
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<h3 id="crosslinks-102">Crosslinks</h3>
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<p>Lorem ipsum.</p>
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... a . Q [b c] [Q] step</code></pre>
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<h3 id="discussion-66">Discussion</h3>
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<p>See the <a href="https://joypy.osdn.io/notebooks/Recursion_Combinators.html">Recursion Combinators notebook</a>.</p>
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<h3 id="crosslinks-99">Crosslinks</h3>
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<p><a href="#step_zero">step_zero</a></p>
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<hr />
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<h2 id="step_zero">step_zero</h2>
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<p>Basis Function Combinator</p>
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<p>0 roll> step</p>
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<p>Gentzen diagram.</p>
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<h3 id="definition-86">Definition</h3>
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<p>if not basis.</p>
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<h3 id="derivation-8">Derivation</h3>
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<p>if not basis.</p>
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<h3 id="source-5">Source</h3>
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<p>if basis</p>
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<h3 id="discussion-69">Discussion</h3>
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<p>Lorem ipsum.</p>
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<h3 id="crosslinks-103">Crosslinks</h3>
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<p>Lorem ipsum.</p>
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<p>Combinator</p>
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<p>Like <a href="#step">step</a> but with 0 as the initial value.</p>
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<pre><code> [...] [F] step_zero
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-------------------------
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0 [...] [F] step</code></pre>
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<h3 id="definition-84">Definition</h3>
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<blockquote>
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<p>0 <a href="#roll">roll></a> <a href="#step">step</a></p>
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</blockquote>
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<h3 id="discussion-67">Discussion</h3>
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<p><a href="#size">size</a> and <a href="#sum">sum</a> can both be defined in terms of this specialization of <a href="#step">step</a>.</p>
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<h3 id="crosslinks-100">Crosslinks</h3>
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<p><a href="#step">step</a></p>
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<hr />
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<h2 id="stuncons">stuncons</h2>
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<p>Basis Function Combinator</p>
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<pre><code>(... a1 -- ... a1 a1 [...])</code></pre>
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<p>Gentzen diagram.</p>
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<h3 id="definition-87">Definition</h3>
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<p>if not basis.</p>
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<h3 id="derivation-9">Derivation</h3>
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<p>if not basis.</p>
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<h3 id="source-6">Source</h3>
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<p>if basis</p>
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<h3 id="discussion-70">Discussion</h3>
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<p>Lorem ipsum.</p>
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<h3 id="crosslinks-104">Crosslinks</h3>
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<p>Lorem ipsum.</p>
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<p>Function</p>
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<p>Take the <a href="#stack">stack</a> and <a href="#uncons">uncons</a> the top item.</p>
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<h3 id="example-27">Example</h3>
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<pre><code> 1 2 3 stuncons
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--------------------
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1 2 3 3 [2 1]</code></pre>
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<h3 id="definition-85">Definition</h3>
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<blockquote>
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<p><a href="#stack">stack</a> <a href="#uncons">uncons</a></p>
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</blockquote>
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<hr />
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<h2 id="stununcons">stununcons</h2>
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<p>Basis Function Combinator</p>
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<pre><code>(... a2 a1 -- ... a2 a1 a1 a2 [...])</code></pre>
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<p>Gentzen diagram.</p>
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<h3 id="definition-88">Definition</h3>
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<p>if not basis.</p>
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<h3 id="derivation-10">Derivation</h3>
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<p>if not basis.</p>
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<h3 id="source-7">Source</h3>
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<p>if basis</p>
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<h3 id="discussion-71">Discussion</h3>
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<p>Lorem ipsum.</p>
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<h3 id="crosslinks-105">Crosslinks</h3>
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<p>Lorem ipsum.</p>
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<p>Function</p>
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<p>Take the <a href="#stack">stack</a> and <a href="#uncons">uncons</a> the top two items.</p>
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<h3 id="example-28">Example</h3>
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<pre><code> 1 2 3 stununcons
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----------------------
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1 2 3 3 2 [1]</code></pre>
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<h3 id="definition-86">Definition</h3>
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<blockquote>
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<p><a href="#stack">stack</a> <a href="#uncons">uncons</a> <a href="#uncons">uncons</a></p>
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</blockquote>
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<h3 id="crosslinks-101">Crosslinks</h3>
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<p><a href="#stuncons">stuncons</a></p>
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<hr />
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<h2 id="sub">sub</h2>
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<p>Basis Function Combinator</p>
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<p>Same as a - b.</p>
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<p>Gentzen diagram.</p>
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<h3 id="definition-89">Definition</h3>
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<p>if not basis.</p>
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<h3 id="derivation-11">Derivation</h3>
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<p>if not basis.</p>
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<h3 id="source-8">Source</h3>
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<p>if basis</p>
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<h3 id="discussion-72">Discussion</h3>
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<p>Lorem ipsum.</p>
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<h3 id="crosslinks-106">Crosslinks</h3>
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<p>Lorem ipsum.</p>
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<p>Basis Function</p>
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<p>Subtract the number on the top of the stack from the number below it.</p>
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<pre><code> a b sub
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-------------
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(a-b)</code></pre>
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<h3 id="crosslinks-102">Crosslinks</h3>
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<p><a href="#add">add</a></p>
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<hr />
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<h2 id="succ">succ</h2>
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<p>Basis Function Combinator</p>
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<p>Increment TOS.</p>
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<p>Gentzen diagram.</p>
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<h3 id="definition-90">Definition</h3>
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<p>if not basis.</p>
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<h3 id="derivation-12">Derivation</h3>
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<p>if not basis.</p>
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<h3 id="source-9">Source</h3>
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<p>if basis</p>
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<h3 id="discussion-73">Discussion</h3>
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<p>Lorem ipsum.</p>
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<h3 id="crosslinks-107">Crosslinks</h3>
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<p>Lorem ipsum.</p>
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<p>Function</p>
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<p>Successor. Increment TOS.</p>
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<h3 id="definition-87">Definition</h3>
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<blockquote>
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<p>1 +</p>
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</blockquote>
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<h3 id="crosslinks-103">Crosslinks</h3>
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<p><a href="#pred">pred</a></p>
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<hr />
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<h2 id="sum">sum</h2>
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<p>Basis Function Combinator</p>
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<p>Given a quoted sequence of numbers return the sum. :</p>
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<pre><code>sum == 0 swap [+] step</code></pre>
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<p>Gentzen diagram.</p>
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<h3 id="definition-91">Definition</h3>
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<p>if not basis.</p>
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<h3 id="derivation-13">Derivation</h3>
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<p>if not basis.</p>
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<h3 id="source-10">Source</h3>
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<p>if basis</p>
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<h3 id="discussion-74">Discussion</h3>
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<p>Lorem ipsum.</p>
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<h3 id="crosslinks-108">Crosslinks</h3>
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<p>Lorem ipsum.</p>
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<p>Combinator</p>
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<p>Given a quoted sequence of numbers return the sum.</p>
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<h3 id="example-29">Example</h3>
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<pre><code> [1 2 3 4 5] sum
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---------------------
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15</code></pre>
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<h3 id="definition-88">Definition</h3>
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<blockquote>
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<p>[+] <a href="#step_zero">step_zero</a></p>
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</blockquote>
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<h3 id="crosslinks-104">Crosslinks</h3>
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<p><a href="#size">size</a></p>
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<hr />
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<h2 id="swaack">swaack</h2>
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<p>Basis Function Combinator</p>
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<pre><code>([...1] -- [...0])</code></pre>
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<p>Gentzen diagram.</p>
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<h3 id="definition-92">Definition</h3>
|
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<p>if not basis.</p>
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<h3 id="derivation-14">Derivation</h3>
|
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<p>if not basis.</p>
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<h3 id="source-11">Source</h3>
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<p>if basis</p>
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<h3 id="discussion-75">Discussion</h3>
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<p>Lorem ipsum.</p>
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<h3 id="crosslinks-109">Crosslinks</h3>
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<p>Lorem ipsum.</p>
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<p>Basis Function</p>
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<p>Swap stack. Take a list from the top of the stack, replace the stack with the list, and put the old stack onto it.</p>
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<h3 id="example-30">Example</h3>
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<pre><code> 1 2 3 [4 5 6] swaack
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--------------------------
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6 5 4 [3 2 1]</code></pre>
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<h3 id="discussion-68">Discussion</h3>
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<p>This function works as a kind of “context switch”. It’s used in the definition of <a href="#infra">infra</a>.</p>
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<h3 id="crosslinks-105">Crosslinks</h3>
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<p><a href="#infra">infra</a></p>
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<hr />
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<h2 id="swap">swap</h2>
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<p>Basis Function Combinator</p>
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<pre><code>(a1 a2 -- a2 a1)</code></pre>
|
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<p>Gentzen diagram.</p>
|
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<h3 id="definition-93">Definition</h3>
|
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<p>if not basis.</p>
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<h3 id="derivation-15">Derivation</h3>
|
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<p>if not basis.</p>
|
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<h3 id="source-12">Source</h3>
|
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<p>if basis</p>
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<h3 id="discussion-76">Discussion</h3>
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<p>Lorem ipsum.</p>
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<h3 id="crosslinks-110">Crosslinks</h3>
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<p>Lorem ipsum.</p>
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<p>Basis Function</p>
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<p>Swap the top two items on the stack.</p>
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<pre><code> a b swap
|
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--------------
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b a</code></pre>
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<h3 id="crosslinks-106">Crosslinks</h3>
|
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<p><a href="#swapd">swapd</a></p>
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<hr />
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<h2 id="swapd">swapd</h2>
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<p>Basis Function Combinator</p>
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<p>[swap] dip</p>
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<p>Gentzen diagram.</p>
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<h3 id="definition-94">Definition</h3>
|
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<p>if not basis.</p>
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<h3 id="derivation-16">Derivation</h3>
|
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<p>if not basis.</p>
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<h3 id="source-13">Source</h3>
|
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<p>if basis</p>
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<h3 id="discussion-77">Discussion</h3>
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<p>Lorem ipsum.</p>
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<h3 id="crosslinks-111">Crosslinks</h3>
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<p>Lorem ipsum.</p>
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<p>Function</p>
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<p>Swap the second and third items on the stack.</p>
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<pre><code> a b c swapd
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-----------------
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b a c</code></pre>
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<h3 id="definition-89">Definition</h3>
|
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<blockquote>
|
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<p>[<a href="#swap">swap</a>] <a href="#dip">dip</a></p>
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</blockquote>
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<h3 id="crosslinks-107">Crosslinks</h3>
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<p><a href="#over">over</a> <a href="#tuck">tuck</a></p>
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<hr />
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<h2 id="swoncat">swoncat</h2>
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<p>Basis Function Combinator</p>
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<p>swap concat</p>
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<p>Gentzen diagram.</p>
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<h3 id="definition-95">Definition</h3>
|
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<p>if not basis.</p>
|
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<h3 id="derivation-17">Derivation</h3>
|
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<p>if not basis.</p>
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<h3 id="source-14">Source</h3>
|
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<p>if basis</p>
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<h3 id="discussion-78">Discussion</h3>
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<p>Lorem ipsum.</p>
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<h3 id="crosslinks-112">Crosslinks</h3>
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<p>Lorem ipsum.</p>
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<p>Function</p>
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<p><a href="#concat">concat</a> two lists, but <a href="#swap">swap</a> the lists first.</p>
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<h3 id="definition-90">Definition</h3>
|
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<blockquote>
|
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<p><a href="#swap">swap</a> <a href="#concat">concat</a></p>
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</blockquote>
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<h3 id="crosslinks-108">Crosslinks</h3>
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<p><a href="#concat">concat</a></p>
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<hr />
|
||||
<h2 id="swons">swons</h2>
|
||||
<p>Basis Function Combinator</p>
|
||||
<pre><code>([...1] a1 -- [a1 ...1])</code></pre>
|
||||
<p>Gentzen diagram.</p>
|
||||
<h3 id="definition-96">Definition</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="derivation-18">Derivation</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="source-15">Source</h3>
|
||||
<p>if basis</p>
|
||||
<h3 id="discussion-79">Discussion</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<h3 id="crosslinks-113">Crosslinks</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<p>Function</p>
|
||||
<p>Like <a href="#cons">cons</a> but <a href="#swap">swap</a> the item and list.</p>
|
||||
<pre><code> [...] a swons
|
||||
-------------------
|
||||
[a ...]</code></pre>
|
||||
<h3 id="definition-91">Definition</h3>
|
||||
<blockquote>
|
||||
<p><a href="#swap">swap</a> <a href="#cons">cons</a></p>
|
||||
</blockquote>
|
||||
<hr />
|
||||
<h2 id="tailrec">tailrec</h2>
|
||||
<p>Basis Function Combinator</p>
|
||||
<p>[i] genrec</p>
|
||||
<p>Gentzen diagram.</p>
|
||||
<h3 id="definition-97">Definition</h3>
|
||||
<h3 id="definition-92">Definition</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="derivation-19">Derivation</h3>
|
||||
<h3 id="derivation-3">Derivation</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="source-16">Source</h3>
|
||||
<h3 id="source">Source</h3>
|
||||
<p>if basis</p>
|
||||
<h3 id="discussion-80">Discussion</h3>
|
||||
<h3 id="discussion-69">Discussion</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<h3 id="crosslinks-114">Crosslinks</h3>
|
||||
<h3 id="crosslinks-109">Crosslinks</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<hr />
|
||||
<h2 id="take">take</h2>
|
||||
|
|
@ -2358,15 +2297,15 @@ a F a</code></pre>
|
|||
----------------------
|
||||
[b a]</code></pre>
|
||||
<p>Gentzen diagram.</p>
|
||||
<h3 id="definition-98">Definition</h3>
|
||||
<h3 id="definition-93">Definition</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="derivation-20">Derivation</h3>
|
||||
<h3 id="derivation-4">Derivation</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="source-17">Source</h3>
|
||||
<h3 id="source-1">Source</h3>
|
||||
<p>if basis</p>
|
||||
<h3 id="discussion-81">Discussion</h3>
|
||||
<h3 id="discussion-70">Discussion</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<h3 id="crosslinks-115">Crosslinks</h3>
|
||||
<h3 id="crosslinks-110">Crosslinks</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<hr />
|
||||
<h2 id="ternary">ternary</h2>
|
||||
|
|
@ -2375,26 +2314,26 @@ a F a</code></pre>
|
|||
<pre><code> ... z y x [P] unary
|
||||
-------------------------
|
||||
... A</code></pre>
|
||||
<h3 id="definition-99">Definition</h3>
|
||||
<h3 id="definition-94">Definition</h3>
|
||||
<pre><code>binary popd</code></pre>
|
||||
<h3 id="discussion-82">Discussion</h3>
|
||||
<h3 id="discussion-71">Discussion</h3>
|
||||
<p>Runs any other quoted function and returns its first result while consuming exactly three items from the stack.</p>
|
||||
<h3 id="crosslinks-116">Crosslinks</h3>
|
||||
<h3 id="crosslinks-111">Crosslinks</h3>
|
||||
<p><a href="#binary">binary</a> <a href="#nullary">nullary</a> <a href="#unary">unary</a></p>
|
||||
<hr />
|
||||
<h2 id="third">third</h2>
|
||||
<p>Basis Function Combinator</p>
|
||||
<pre><code>([a1 a2 a3 ...1] -- a3)</code></pre>
|
||||
<p>Gentzen diagram.</p>
|
||||
<h3 id="definition-100">Definition</h3>
|
||||
<h3 id="definition-95">Definition</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="derivation-21">Derivation</h3>
|
||||
<h3 id="derivation-5">Derivation</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="source-18">Source</h3>
|
||||
<h3 id="source-2">Source</h3>
|
||||
<p>if basis</p>
|
||||
<h3 id="discussion-83">Discussion</h3>
|
||||
<h3 id="discussion-72">Discussion</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<h3 id="crosslinks-117">Crosslinks</h3>
|
||||
<h3 id="crosslinks-112">Crosslinks</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<hr />
|
||||
<h2 id="times">times</h2>
|
||||
|
|
@ -2414,15 +2353,15 @@ a F a</code></pre>
|
|||
------------------------------------- w/ n > 1
|
||||
... . Q (n - 1) [Q] times</code></pre>
|
||||
<p>Gentzen diagram.</p>
|
||||
<h3 id="definition-101">Definition</h3>
|
||||
<h3 id="definition-96">Definition</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="derivation-22">Derivation</h3>
|
||||
<h3 id="derivation-6">Derivation</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="source-19">Source</h3>
|
||||
<h3 id="source-3">Source</h3>
|
||||
<p>if basis</p>
|
||||
<h3 id="discussion-84">Discussion</h3>
|
||||
<h3 id="discussion-73">Discussion</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<h3 id="crosslinks-118">Crosslinks</h3>
|
||||
<h3 id="crosslinks-113">Crosslinks</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<hr />
|
||||
<h2 id="truthy">truthy</h2>
|
||||
|
|
@ -2432,15 +2371,15 @@ a F a</code></pre>
|
|||
<p>Basis Function Combinator</p>
|
||||
<pre><code>(a2 a1 -- a1 a2 a1)</code></pre>
|
||||
<p>Gentzen diagram.</p>
|
||||
<h3 id="definition-102">Definition</h3>
|
||||
<h3 id="definition-97">Definition</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="derivation-23">Derivation</h3>
|
||||
<h3 id="derivation-7">Derivation</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="source-20">Source</h3>
|
||||
<h3 id="source-4">Source</h3>
|
||||
<p>if basis</p>
|
||||
<h3 id="discussion-85">Discussion</h3>
|
||||
<h3 id="discussion-74">Discussion</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<h3 id="crosslinks-119">Crosslinks</h3>
|
||||
<h3 id="crosslinks-114">Crosslinks</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<hr />
|
||||
<h2 id="unary">unary</h2>
|
||||
|
|
@ -2449,11 +2388,11 @@ a F a</code></pre>
|
|||
<pre><code> ... x [P] unary
|
||||
---------------------
|
||||
... A</code></pre>
|
||||
<h3 id="definition-103">Definition</h3>
|
||||
<h3 id="definition-98">Definition</h3>
|
||||
<pre><code>nullary popd</code></pre>
|
||||
<h3 id="discussion-86">Discussion</h3>
|
||||
<h3 id="discussion-75">Discussion</h3>
|
||||
<p>Runs any other quoted function and returns its first result while consuming exactly one item from the stack.</p>
|
||||
<h3 id="crosslinks-120">Crosslinks</h3>
|
||||
<h3 id="crosslinks-115">Crosslinks</h3>
|
||||
<p><a href="#binary">binary</a> <a href="#nullary">nullary</a> <a href="#ternary">ternary</a></p>
|
||||
<hr />
|
||||
<h2 id="uncons">uncons</h2>
|
||||
|
|
@ -2462,131 +2401,131 @@ a F a</code></pre>
|
|||
<pre><code> [A ...] uncons
|
||||
--------------------
|
||||
A [...]</code></pre>
|
||||
<h3 id="source-21">Source</h3>
|
||||
<h3 id="source-5">Source</h3>
|
||||
<pre><code>func(uncons, Si, So) :- func(cons, So, Si).</code></pre>
|
||||
<h3 id="discussion-87">Discussion</h3>
|
||||
<h3 id="discussion-76">Discussion</h3>
|
||||
<p>This is the inverse of <code>cons</code>.</p>
|
||||
<h3 id="crosslinks-121">Crosslinks</h3>
|
||||
<h3 id="crosslinks-116">Crosslinks</h3>
|
||||
<p><a href="#cons">cons</a></p>
|
||||
<hr />
|
||||
<h2 id="unique">unique</h2>
|
||||
<p>Basis Function Combinator</p>
|
||||
<p>Given a list remove duplicate items.</p>
|
||||
<p>Gentzen diagram.</p>
|
||||
<h3 id="definition-104">Definition</h3>
|
||||
<h3 id="definition-99">Definition</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="derivation-24">Derivation</h3>
|
||||
<h3 id="derivation-8">Derivation</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="source-22">Source</h3>
|
||||
<h3 id="source-6">Source</h3>
|
||||
<p>if basis</p>
|
||||
<h3 id="discussion-88">Discussion</h3>
|
||||
<h3 id="discussion-77">Discussion</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<h3 id="crosslinks-122">Crosslinks</h3>
|
||||
<h3 id="crosslinks-117">Crosslinks</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<hr />
|
||||
<h2 id="unit">unit</h2>
|
||||
<p>Basis Function Combinator</p>
|
||||
<pre><code>(a1 -- [a1 ])</code></pre>
|
||||
<p>Gentzen diagram.</p>
|
||||
<h3 id="definition-105">Definition</h3>
|
||||
<h3 id="definition-100">Definition</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="derivation-25">Derivation</h3>
|
||||
<h3 id="derivation-9">Derivation</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="source-23">Source</h3>
|
||||
<h3 id="source-7">Source</h3>
|
||||
<p>if basis</p>
|
||||
<h3 id="discussion-89">Discussion</h3>
|
||||
<h3 id="discussion-78">Discussion</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<h3 id="crosslinks-123">Crosslinks</h3>
|
||||
<h3 id="crosslinks-118">Crosslinks</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<hr />
|
||||
<h2 id="unquoted">unquoted</h2>
|
||||
<p>Basis Function Combinator</p>
|
||||
<p>[i] dip</p>
|
||||
<p>Gentzen diagram.</p>
|
||||
<h3 id="definition-106">Definition</h3>
|
||||
<h3 id="definition-101">Definition</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="derivation-26">Derivation</h3>
|
||||
<h3 id="derivation-10">Derivation</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="source-24">Source</h3>
|
||||
<h3 id="source-8">Source</h3>
|
||||
<p>if basis</p>
|
||||
<h3 id="discussion-90">Discussion</h3>
|
||||
<h3 id="discussion-79">Discussion</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<h3 id="crosslinks-124">Crosslinks</h3>
|
||||
<h3 id="crosslinks-119">Crosslinks</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<hr />
|
||||
<h2 id="unswons">unswons</h2>
|
||||
<p>Basis Function Combinator</p>
|
||||
<pre><code>([a1 ...1] -- [...1] a1)</code></pre>
|
||||
<p>Gentzen diagram.</p>
|
||||
<h3 id="definition-107">Definition</h3>
|
||||
<h3 id="definition-102">Definition</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="derivation-27">Derivation</h3>
|
||||
<h3 id="derivation-11">Derivation</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="source-25">Source</h3>
|
||||
<h3 id="source-9">Source</h3>
|
||||
<p>if basis</p>
|
||||
<h3 id="discussion-91">Discussion</h3>
|
||||
<h3 id="discussion-80">Discussion</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<h3 id="crosslinks-125">Crosslinks</h3>
|
||||
<h3 id="crosslinks-120">Crosslinks</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<hr />
|
||||
<h2 id="void">void</h2>
|
||||
<p>Basis Function Combinator</p>
|
||||
<p>True if the form on TOS is void otherwise False.</p>
|
||||
<p>Gentzen diagram.</p>
|
||||
<h3 id="definition-108">Definition</h3>
|
||||
<h3 id="definition-103">Definition</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="derivation-28">Derivation</h3>
|
||||
<h3 id="derivation-12">Derivation</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="source-26">Source</h3>
|
||||
<h3 id="source-10">Source</h3>
|
||||
<p>if basis</p>
|
||||
<h3 id="discussion-92">Discussion</h3>
|
||||
<h3 id="discussion-81">Discussion</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<h3 id="crosslinks-126">Crosslinks</h3>
|
||||
<h3 id="crosslinks-121">Crosslinks</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<hr />
|
||||
<h2 id="warranty">warranty</h2>
|
||||
<p>Basis Function Combinator</p>
|
||||
<p>Print warranty information.</p>
|
||||
<p>Gentzen diagram.</p>
|
||||
<h3 id="definition-109">Definition</h3>
|
||||
<h3 id="definition-104">Definition</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="derivation-29">Derivation</h3>
|
||||
<h3 id="derivation-13">Derivation</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="source-27">Source</h3>
|
||||
<h3 id="source-11">Source</h3>
|
||||
<p>if basis</p>
|
||||
<h3 id="discussion-93">Discussion</h3>
|
||||
<h3 id="discussion-82">Discussion</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<h3 id="crosslinks-127">Crosslinks</h3>
|
||||
<h3 id="crosslinks-122">Crosslinks</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<hr />
|
||||
<h2 id="while">while</h2>
|
||||
<p>Basis Function Combinator</p>
|
||||
<p>swap nulco dupdipd concat loop</p>
|
||||
<p>Gentzen diagram.</p>
|
||||
<h3 id="definition-110">Definition</h3>
|
||||
<h3 id="definition-105">Definition</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="derivation-30">Derivation</h3>
|
||||
<h3 id="derivation-14">Derivation</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="source-28">Source</h3>
|
||||
<h3 id="source-12">Source</h3>
|
||||
<p>if basis</p>
|
||||
<h3 id="discussion-94">Discussion</h3>
|
||||
<h3 id="discussion-83">Discussion</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<h3 id="crosslinks-128">Crosslinks</h3>
|
||||
<h3 id="crosslinks-123">Crosslinks</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<hr />
|
||||
<h2 id="words">words</h2>
|
||||
<p>Basis Function Combinator</p>
|
||||
<p>Print all the words in alphabetical order.</p>
|
||||
<p>Gentzen diagram.</p>
|
||||
<h3 id="definition-111">Definition</h3>
|
||||
<h3 id="definition-106">Definition</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="derivation-31">Derivation</h3>
|
||||
<h3 id="derivation-15">Derivation</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="source-29">Source</h3>
|
||||
<h3 id="source-13">Source</h3>
|
||||
<p>if basis</p>
|
||||
<h3 id="discussion-95">Discussion</h3>
|
||||
<h3 id="discussion-84">Discussion</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<h3 id="crosslinks-129">Crosslinks</h3>
|
||||
<h3 id="crosslinks-124">Crosslinks</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<hr />
|
||||
<h2 id="x">x</h2>
|
||||
|
|
@ -2594,39 +2533,39 @@ a F a</code></pre>
|
|||
<pre><code> [F] x
|
||||
-----------
|
||||
[F] F</code></pre>
|
||||
<h3 id="definition-112">Definition</h3>
|
||||
<h3 id="definition-107">Definition</h3>
|
||||
<pre><code>dup i</code></pre>
|
||||
<h3 id="discussion-96">Discussion</h3>
|
||||
<h3 id="discussion-85">Discussion</h3>
|
||||
<p>The <code>x</code> combinator …</p>
|
||||
<hr />
|
||||
<h2 id="xor">xor</h2>
|
||||
<p>Basis Function Combinator</p>
|
||||
<p>Same as a ^ b.</p>
|
||||
<p>Gentzen diagram.</p>
|
||||
<h3 id="definition-113">Definition</h3>
|
||||
<h3 id="definition-108">Definition</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="derivation-32">Derivation</h3>
|
||||
<h3 id="derivation-16">Derivation</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="source-30">Source</h3>
|
||||
<h3 id="source-14">Source</h3>
|
||||
<p>if basis</p>
|
||||
<h3 id="discussion-97">Discussion</h3>
|
||||
<h3 id="discussion-86">Discussion</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<h3 id="crosslinks-130">Crosslinks</h3>
|
||||
<h3 id="crosslinks-125">Crosslinks</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<hr />
|
||||
<h2 id="zip">zip</h2>
|
||||
<p>Basis Function Combinator</p>
|
||||
<p>Replace the two lists on the top of the stack with a list of the pairs from each list. The smallest list sets the length of the result list.</p>
|
||||
<p>Gentzen diagram.</p>
|
||||
<h3 id="definition-114">Definition</h3>
|
||||
<h3 id="definition-109">Definition</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="derivation-33">Derivation</h3>
|
||||
<h3 id="derivation-17">Derivation</h3>
|
||||
<p>if not basis.</p>
|
||||
<h3 id="source-31">Source</h3>
|
||||
<h3 id="source-15">Source</h3>
|
||||
<p>if basis</p>
|
||||
<h3 id="discussion-98">Discussion</h3>
|
||||
<h3 id="discussion-87">Discussion</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
<h3 id="crosslinks-131">Crosslinks</h3>
|
||||
<h3 id="crosslinks-126">Crosslinks</h3>
|
||||
<p>Lorem ipsum.</p>
|
||||
</body>
|
||||
</html>
|
||||
|
|
|
|||
|
|
@ -3324,31 +3324,18 @@ Compare with [split_at]. This function does extra work to ensure that
|
|||
|
||||
## sqr
|
||||
|
||||
Basis Function Combinator
|
||||
Function
|
||||
|
||||
dup \*
|
||||
Square the number on the top of the stack.
|
||||
|
||||
Gentzen diagram.
|
||||
n sqr
|
||||
------------
|
||||
n²
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
> [dup] [mul]
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
|
|
@ -3359,466 +3346,311 @@ Basis Function Combinator
|
|||
Return the square root of the number a. Negative numbers return complex
|
||||
roots.
|
||||
|
||||
Gentzen diagram.
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
Another "numeric tower" hatch...
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
## stack
|
||||
|
||||
Basis Function Combinator
|
||||
Function
|
||||
|
||||
(... -- ... [...])
|
||||
Put the stack onto the stack.
|
||||
|
||||
Gentzen diagram.
|
||||
... c b a stack
|
||||
---------------------------
|
||||
... c b a [a b c ...]
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
> \[\] [swaack] [dup] [swaack] [first]
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
This function forms a pair with [unstack], and together they form the
|
||||
complement to the "destructive" pair [enstacken] and [disenstacken].
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[unstack]
|
||||
[enstacken]
|
||||
[disenstacken]
|
||||
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
## stackd
|
||||
|
||||
Basis Function Combinator
|
||||
Function
|
||||
|
||||
\[stack\] dip
|
||||
Grab the stack under the top item and put it onto the stack.
|
||||
|
||||
Gentzen diagram.
|
||||
### Example
|
||||
|
||||
... 1 2 3 stackd
|
||||
------------------------
|
||||
... 1 2 [2 1 ...] 3
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
> \[[stack]\] [dip]
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
## step
|
||||
|
||||
Basis Function Combinator
|
||||
Combinator
|
||||
|
||||
Run a quoted program on each item in a sequence. :
|
||||
Run a quoted program on each item in a sequence.
|
||||
|
||||
... [] [Q] . step
|
||||
-----------------------
|
||||
... .
|
||||
... [] [Q] step
|
||||
---------------------
|
||||
...
|
||||
|
||||
|
||||
... [a] [Q] . step
|
||||
------------------------
|
||||
... a . Q
|
||||
... [a] [Q] step
|
||||
----------------------
|
||||
... a Q
|
||||
|
||||
|
||||
... [a b c] [Q] . step
|
||||
... [a b c] [Q] . step
|
||||
----------------------------------------
|
||||
... a . Q [b c] [Q] step
|
||||
|
||||
The step combinator executes the quotation on each member of the list on
|
||||
top of the stack.
|
||||
|
||||
Gentzen diagram.
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
... a . Q [b c] [Q] step
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
See the [Recursion Combinators notebook](https://joypy.osdn.io/notebooks/Recursion_Combinators.html).
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[step_zero]
|
||||
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
## step_zero
|
||||
|
||||
Basis Function Combinator
|
||||
Combinator
|
||||
|
||||
0 roll> step
|
||||
Like [step] but with 0 as the initial value.
|
||||
|
||||
Gentzen diagram.
|
||||
[...] [F] step_zero
|
||||
-------------------------
|
||||
0 [...] [F] step
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
> 0 [roll>] [step]
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
[size] and [sum] can both be defined in terms of this specialization of
|
||||
[step].
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[step]
|
||||
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
## stuncons
|
||||
|
||||
Basis Function Combinator
|
||||
Function
|
||||
|
||||
(... a1 -- ... a1 a1 [...])
|
||||
Take the [stack] and [uncons] the top item.
|
||||
|
||||
Gentzen diagram.
|
||||
### Example
|
||||
|
||||
1 2 3 stuncons
|
||||
--------------------
|
||||
1 2 3 3 [2 1]
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
> [stack] [uncons]
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
## stununcons
|
||||
|
||||
Basis Function Combinator
|
||||
Function
|
||||
|
||||
(... a2 a1 -- ... a2 a1 a1 a2 [...])
|
||||
Take the [stack] and [uncons] the top two items.
|
||||
|
||||
Gentzen diagram.
|
||||
### Example
|
||||
|
||||
1 2 3 stununcons
|
||||
----------------------
|
||||
1 2 3 3 2 [1]
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
> [stack] [uncons] [uncons]
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[stuncons]
|
||||
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
## sub
|
||||
|
||||
Basis Function Combinator
|
||||
Basis Function
|
||||
|
||||
Same as a - b.
|
||||
Subtract the number on the top of the stack from the number below it.
|
||||
|
||||
Gentzen diagram.
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
a b sub
|
||||
-------------
|
||||
(a-b)
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[add]
|
||||
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
## succ
|
||||
|
||||
Basis Function Combinator
|
||||
Function
|
||||
|
||||
Increment TOS.
|
||||
|
||||
Gentzen diagram.
|
||||
Successor. Increment TOS.
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
> 1 +
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[pred]
|
||||
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
## sum
|
||||
|
||||
Basis Function Combinator
|
||||
Combinator
|
||||
|
||||
Given a quoted sequence of numbers return the sum. :
|
||||
Given a quoted sequence of numbers return the sum.
|
||||
|
||||
sum == 0 swap [+] step
|
||||
### Example
|
||||
|
||||
Gentzen diagram.
|
||||
[1 2 3 4 5] sum
|
||||
---------------------
|
||||
15
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
> \[+\] [step_zero]
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[size]
|
||||
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
## swaack
|
||||
|
||||
Basis Function Combinator
|
||||
Basis Function
|
||||
|
||||
([...1] -- [...0])
|
||||
Swap stack. Take a list from the top of the stack, replace the stack
|
||||
with the list, and put the old stack onto it.
|
||||
|
||||
Gentzen diagram.
|
||||
### Example
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
1 2 3 [4 5 6] swaack
|
||||
--------------------------
|
||||
6 5 4 [3 2 1]
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
This function works as a kind of "context switch". It's used in the
|
||||
definition of [infra].
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[infra]
|
||||
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
## swap
|
||||
|
||||
Basis Function Combinator
|
||||
Basis Function
|
||||
|
||||
(a1 a2 -- a2 a1)
|
||||
Swap the top two items on the stack.
|
||||
|
||||
Gentzen diagram.
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
a b swap
|
||||
--------------
|
||||
b a
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[swapd]
|
||||
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
## swapd
|
||||
|
||||
Basis Function Combinator
|
||||
Function
|
||||
|
||||
\[swap\] dip
|
||||
Swap the second and third items on the stack.
|
||||
|
||||
Gentzen diagram.
|
||||
a b c swapd
|
||||
-----------------
|
||||
b a c
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
> \[[swap]\] [dip]
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[over]
|
||||
[tuck]
|
||||
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
## swoncat
|
||||
|
||||
Basis Function Combinator
|
||||
Function
|
||||
|
||||
swap concat
|
||||
|
||||
Gentzen diagram.
|
||||
[concat] two lists, but [swap] the lists first.
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
> [swap] [concat]
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[concat]
|
||||
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
## swons
|
||||
|
||||
Basis Function Combinator
|
||||
Function
|
||||
|
||||
([...1] a1 -- [a1 ...1])
|
||||
Like [cons] but [swap] the item and list.
|
||||
|
||||
Gentzen diagram.
|
||||
[...] a swons
|
||||
-------------------
|
||||
[a ...]
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
> [swap] [cons]
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
|
|
|
|||
|
|
@ -4,26 +4,22 @@
|
|||
|
||||
Combinator
|
||||
|
||||
0 roll> step
|
||||
Like [step] but with 0 as the initial value.
|
||||
|
||||
Gentzen diagram.
|
||||
[...] [F] step_zero
|
||||
-------------------------
|
||||
0 [...] [F] step
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
> 0 [roll>] [step]
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
[size] and [sum] can both be defined in terms of this specialization of
|
||||
[step].
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[step]
|
||||
|
||||
|
|
|
|||
|
|
@ -2,28 +2,17 @@
|
|||
|
||||
## stuncons
|
||||
|
||||
Basis Function Combinator
|
||||
Function
|
||||
|
||||
(... a1 -- ... a1 a1 [...])
|
||||
Take the [stack] and [uncons] the top item.
|
||||
|
||||
Gentzen diagram.
|
||||
### Example
|
||||
|
||||
1 2 3 stuncons
|
||||
--------------------
|
||||
1 2 3 3 [2 1]
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
> [stack] [uncons]
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
|
|
|
|||
|
|
@ -2,28 +2,21 @@
|
|||
|
||||
## stununcons
|
||||
|
||||
Basis Function Combinator
|
||||
Function
|
||||
|
||||
(... a2 a1 -- ... a2 a1 a1 a2 [...])
|
||||
Take the [stack] and [uncons] the top two items.
|
||||
|
||||
Gentzen diagram.
|
||||
### Example
|
||||
|
||||
1 2 3 stununcons
|
||||
----------------------
|
||||
1 2 3 3 2 [1]
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
> [stack] [uncons] [uncons]
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[stuncons]
|
||||
|
||||
|
|
|
|||
|
|
@ -2,28 +2,15 @@
|
|||
|
||||
## sub
|
||||
|
||||
Basis Function Combinator
|
||||
Basis Function
|
||||
|
||||
Same as a - b.
|
||||
Subtract the number on the top of the stack from the number below it.
|
||||
|
||||
Gentzen diagram.
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
a b sub
|
||||
-------------
|
||||
(a-b)
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[add]
|
||||
|
||||
|
|
|
|||
|
|
@ -2,28 +2,15 @@
|
|||
|
||||
## succ
|
||||
|
||||
Basis Function Combinator
|
||||
Function
|
||||
|
||||
Increment TOS.
|
||||
|
||||
Gentzen diagram.
|
||||
Successor. Increment TOS.
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
> 1 +
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[pred]
|
||||
|
||||
|
|
|
|||
|
|
@ -2,30 +2,21 @@
|
|||
|
||||
## sum
|
||||
|
||||
Basis Function Combinator
|
||||
Combinator
|
||||
|
||||
Given a quoted sequence of numbers return the sum. :
|
||||
Given a quoted sequence of numbers return the sum.
|
||||
|
||||
sum == 0 swap [+] step
|
||||
### Example
|
||||
|
||||
Gentzen diagram.
|
||||
[1 2 3 4 5] sum
|
||||
---------------------
|
||||
15
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
> \[+\] [step_zero]
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[size]
|
||||
|
||||
|
|
|
|||
|
|
@ -2,28 +2,23 @@
|
|||
|
||||
## swaack
|
||||
|
||||
Basis Function Combinator
|
||||
Basis Function
|
||||
|
||||
([...1] -- [...0])
|
||||
Swap stack. Take a list from the top of the stack, replace the stack
|
||||
with the list, and put the old stack onto it.
|
||||
|
||||
Gentzen diagram.
|
||||
### Example
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
1 2 3 [4 5 6] swaack
|
||||
--------------------------
|
||||
6 5 4 [3 2 1]
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
This function works as a kind of "context switch". It's used in the
|
||||
definition of [infra].
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[infra]
|
||||
|
||||
|
|
|
|||
|
|
@ -2,28 +2,15 @@
|
|||
|
||||
## swap
|
||||
|
||||
Basis Function Combinator
|
||||
Basis Function
|
||||
|
||||
(a1 a2 -- a2 a1)
|
||||
Swap the top two items on the stack.
|
||||
|
||||
Gentzen diagram.
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
a b swap
|
||||
--------------
|
||||
b a
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[swapd]
|
||||
|
||||
|
|
|
|||
|
|
@ -2,28 +2,20 @@
|
|||
|
||||
## swapd
|
||||
|
||||
Basis Function Combinator
|
||||
Function
|
||||
|
||||
\[swap\] dip
|
||||
Swap the second and third items on the stack.
|
||||
|
||||
Gentzen diagram.
|
||||
a b c swapd
|
||||
-----------------
|
||||
b a c
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
> \[[swap]\] [dip]
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[over]
|
||||
[tuck]
|
||||
|
||||
|
|
|
|||
|
|
@ -2,28 +2,15 @@
|
|||
|
||||
## swoncat
|
||||
|
||||
Basis Function Combinator
|
||||
Function
|
||||
|
||||
swap concat
|
||||
|
||||
Gentzen diagram.
|
||||
[concat] two lists, but [swap] the lists first.
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
> [swap] [concat]
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
[concat]
|
||||
|
||||
|
|
|
|||
|
|
@ -2,28 +2,15 @@
|
|||
|
||||
## swons
|
||||
|
||||
Basis Function Combinator
|
||||
Function
|
||||
|
||||
([...1] a1 -- [a1 ...1])
|
||||
Like [cons] but [swap] the item and list.
|
||||
|
||||
Gentzen diagram.
|
||||
[...] a swons
|
||||
-------------------
|
||||
[a ...]
|
||||
|
||||
### Definition
|
||||
|
||||
if not basis.
|
||||
> [swap] [cons]
|
||||
|
||||
### Derivation
|
||||
|
||||
if not basis.
|
||||
|
||||
### Source
|
||||
|
||||
if basis
|
||||
|
||||
### Discussion
|
||||
|
||||
Lorem ipsum.
|
||||
|
||||
### Crosslinks
|
||||
|
||||
Lorem ipsum.
|
||||
|
|
|
|||
|
|
@ -83,6 +83,7 @@ split_list [take reverse] [drop] clop
|
|||
sqr dup *
|
||||
stackd [stack] dip
|
||||
step_zero 0 roll> step
|
||||
stuncons stack uncons
|
||||
sum [+] step_zero
|
||||
swapd [swap] dip
|
||||
swons swap cons
|
||||
|
|
|
|||
Loading…
Reference in New Issue