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<html xmlns="http://www.w3.org/1999/xhtml"><head><title>Free (kado.Kado.Syntax.Free)</title><link rel="stylesheet" href="../../../../odoc.support/odoc.css"/><meta charset="utf-8"/><meta name="generator" content="odoc 2.2.1"/><meta name="viewport" content="width=device-width,initial-scale=1.0"/><script src="../../../../odoc.support/highlight.pack.js"></script><script>hljs.initHighlightingOnLoad();</script></head><body class="odoc"><nav class="odoc-nav"><a href="../index.html">Up</a> – <a href="../../../index.html">kado</a> &#x00BB; <a href="../../index.html">Kado</a> &#x00BB; <a href="../index.html">Syntax</a> &#x00BB; Free</nav><header class="odoc-preamble"><h1>Module <code><span>Syntax.Free</span></code></h1><p>Stupid constructors for <a href="../index.html#type-free"><code>free</code></a>.</p></header><div class="odoc-content"><div class="odoc-spec"><div class="spec type anchored" id="type-endo"><a href="#type-endo" class="anchor"></a><code><span><span class="keyword">type</span> <span class="keyword">nonrec</span> <span>('r, 'a) endo</span></span><span> = <span><span>(<span class="type-var">'r</span>, <span class="type-var">'a</span>)</span> <a href="../index.html#type-endo">endo</a></span></span><span> = </span></code><ol><li id="type-endo.Le" class="def variant constructor anchored"><a href="#type-endo.Le" class="anchor"></a><code><span>| </span><span><span class="constructor">Le</span> <span class="keyword">of</span> <span class="type-var">'r</span> * <span class="type-var">'r</span></span></code></li><li id="type-endo.Join" class="def variant constructor anchored"><a href="#type-endo.Join" class="anchor"></a><code><span>| </span><span><span class="constructor">Join</span> <span class="keyword">of</span> <span><span class="type-var">'a</span> list</span></span></code></li><li id="type-endo.Meet" class="def variant constructor anchored"><a href="#type-endo.Meet" class="anchor"></a><code><span>| </span><span><span class="constructor">Meet</span> <span class="keyword">of</span> <span><span class="type-var">'a</span> list</span></span></code></li></ol></div><div class="spec-doc"><p>A family of polynomial endofunctors <code>('r, -) t</code> indexed in an interpretation of the interval algebra <code>'r</code>. This is for multiple types (for example, abstract syntax) to <em>embed</em> the langauge of cofibrations.</p></div></div><div class="odoc-spec"><div class="spec type anchored" id="type-t"><a href="#type-t" class="anchor"></a><code><span><span class="keyword">type</span> <span>('r, 'v) t</span></span><span> = <span><span>(<span class="type-var">'r</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span></span><span> = </span></code><ol><li id="type-t.Cof" class="def variant constructor anchored"><a href="#type-t.Cof" class="anchor"></a><code><span>| </span><span><span class="constructor">Cof</span> <span class="keyword">of</span> <span><span>(<span class="type-var">'r</span>, <span><span>(<span class="type-var">'r</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span>)</span> <a href="../index.html#type-endo">endo</a></span></span></code></li><li id="type-t.Var" class="def variant constructor anchored"><a href="#type-t.Var" class="anchor"></a><code><span>| </span><span><span class="constructor">Var</span> <span class="keyword">of</span> <span class="type-var">'v</span></span></code></li></ol></div><div class="spec-doc"><p>For each interval algebra <code>'r</code>, we define the <em>free monad</em> <code>('r, -) t</code> on the polynomial endofunctor <code>('r, -) endo</code>: each <code>('r, 'v) t</code> is the language of cofibrations over an interval algebra <code>'r</code>, with indeterminates drawn from <code>'v</code>.</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-var"><a href="#val-var" class="anchor"></a><code><span><span class="keyword">val</span> var : <span><span class="type-var">'v</span> <span class="arrow">&#45;&gt;</span></span> <span><span>(<span class="type-var">'a</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span></span></code></div><div class="spec-doc"><p><code>var v</code> is <code>Var v</code></p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-cof"><a href="#val-cof" class="anchor"></a><code><span><span class="keyword">val</span> cof : <span><span><span>(<span class="type-var">'r</span>, <span><span>(<span class="type-var">'r</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span>)</span> <a href="../index.html#type-endo">endo</a></span> <span class="arrow">&#45;&gt;</span></span> <span><span>(<span class="type-var">'r</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span></span></code></div><div class="spec-doc"><p><code>cof phi</code> is <code>Cof phi</code></p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-le"><a href="#val-le" class="anchor"></a><code><span><span class="keyword">val</span> le : <span><span class="type-var">'a</span> <span class="arrow">&#45;&gt;</span></span> <span><span class="type-var">'a</span> <span class="arrow">&#45;&gt;</span></span> <span><span>(<span class="type-var">'a</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span></span></code></div><div class="spec-doc"><p><code>le x y</code> is <code>Le (x, y)</code></p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-join"><a href="#val-join" class="anchor"></a><code><span><span class="keyword">val</span> join : <span><span><span><span>(<span class="type-var">'a</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span> list</span> <span class="arrow">&#45;&gt;</span></span> <span><span>(<span class="type-var">'a</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span></span></code></div><div class="spec-doc"><p><code>join phis</code> is <code>Cof (Join phis)</code></p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-meet"><a href="#val-meet" class="anchor"></a><code><span><span class="keyword">val</span> meet : <span><span><span><span>(<span class="type-var">'a</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span> list</span> <span class="arrow">&#45;&gt;</span></span> <span><span>(<span class="type-var">'a</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span></span></code></div><div class="spec-doc"><p><code>meet phis</code> is <code>Cof (Meet phis)</code></p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-bot"><a href="#val-bot" class="anchor"></a><code><span><span class="keyword">val</span> bot : <span><span>(<span class="type-var">'a</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span></span></code></div><div class="spec-doc"><p><code>bot</code> is <code>Cof (Join [])</code></p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-top"><a href="#val-top" class="anchor"></a><code><span><span class="keyword">val</span> top : <span><span>(<span class="type-var">'a</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span></span></code></div><div class="spec-doc"><p><code>top</code> is <code>Cof (Meet [])</code></p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-dump"><a href="#val-dump" class="anchor"></a><code><span><span class="keyword">val</span> dump :
<html xmlns="http://www.w3.org/1999/xhtml"><head><title>Free (kado.Kado.Syntax.Free)</title><link rel="stylesheet" href="../../../../odoc.support/odoc.css"/><meta charset="utf-8"/><meta name="generator" content="odoc 2.2.1"/><meta name="viewport" content="width=device-width,initial-scale=1.0"/><script src="../../../../odoc.support/highlight.pack.js"></script><script>hljs.initHighlightingOnLoad();</script></head><body class="odoc"><nav class="odoc-nav"><a href="../index.html">Up</a> – <a href="../../../index.html">kado</a> &#x00BB; <a href="../../index.html">Kado</a> &#x00BB; <a href="../index.html">Syntax</a> &#x00BB; Free</nav><header class="odoc-preamble"><h1>Module <code><span>Syntax.Free</span></code></h1><p>Stupid constructors for <a href="../index.html#type-free"><code>free</code></a>.</p></header><div class="odoc-content"><div class="odoc-spec"><div class="spec type anchored" id="type-endo"><a href="#type-endo" class="anchor"></a><code><span><span class="keyword">type</span> <span class="keyword">nonrec</span> <span>('r, 'a) endo</span></span><span> = <span><span>(<span class="type-var">'r</span>, <span class="type-var">'a</span>)</span> <a href="../index.html#type-endo">endo</a></span></span><span> = </span></code><ol><li id="type-endo.Le" class="def variant constructor anchored"><a href="#type-endo.Le" class="anchor"></a><code><span>| </span><span><span class="constructor">Le</span> <span class="keyword">of</span> <span class="type-var">'r</span> * <span class="type-var">'r</span></span></code></li><li id="type-endo.Join" class="def variant constructor anchored"><a href="#type-endo.Join" class="anchor"></a><code><span>| </span><span><span class="constructor">Join</span> <span class="keyword">of</span> <span><span class="type-var">'a</span> list</span></span></code></li><li id="type-endo.Meet" class="def variant constructor anchored"><a href="#type-endo.Meet" class="anchor"></a><code><span>| </span><span><span class="constructor">Meet</span> <span class="keyword">of</span> <span><span class="type-var">'a</span> list</span></span></code></li></ol></div><div class="spec-doc"><p>A family of polynomial endofunctors <code>('r, -) t</code> indexed in an interpretation of the interval algebra <code>'r</code>. This is for multiple types (for example, abstract syntax) to <em>embed</em> the langauge of cofibrations.</p></div></div><div class="odoc-spec"><div class="spec type anchored" id="type-t"><a href="#type-t" class="anchor"></a><code><span><span class="keyword">type</span> <span>('r, 'v) t</span></span><span> = <span><span>(<span class="type-var">'r</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span></span><span> = </span></code><ol><li id="type-t.Cof" class="def variant constructor anchored"><a href="#type-t.Cof" class="anchor"></a><code><span>| </span><span><span class="constructor">Cof</span> <span class="keyword">of</span> <span><span>(<span class="type-var">'r</span>, <span><span>(<span class="type-var">'r</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span>)</span> <a href="../index.html#type-endo">endo</a></span></span></code></li><li id="type-t.Var" class="def variant constructor anchored"><a href="#type-t.Var" class="anchor"></a><code><span>| </span><span><span class="constructor">Var</span> <span class="keyword">of</span> <span class="type-var">'v</span></span></code></li></ol></div><div class="spec-doc"><p>For each interval algebra <code>'r</code>, we define the <em>free monad</em> <code>('r, -) t</code> on the polynomial endofunctor <code>('r, -) endo</code>: each <code>('r, 'v) t</code> is the language of cofibrations over an interval algebra <code>'r</code>, with indeterminates drawn from <code>'v</code>.</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-var"><a href="#val-var" class="anchor"></a><code><span><span class="keyword">val</span> var : <span><span class="type-var">'v</span> <span class="arrow">&#45;&gt;</span></span> <span><span>(<span class="type-var">'r</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span></span></code></div><div class="spec-doc"><p><code>var v</code> is <code>Var v</code></p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-cof"><a href="#val-cof" class="anchor"></a><code><span><span class="keyword">val</span> cof : <span><span><span>(<span class="type-var">'r</span>, <span><span>(<span class="type-var">'r</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span>)</span> <a href="../index.html#type-endo">endo</a></span> <span class="arrow">&#45;&gt;</span></span> <span><span>(<span class="type-var">'r</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span></span></code></div><div class="spec-doc"><p><code>cof phi</code> is <code>Cof phi</code></p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-le"><a href="#val-le" class="anchor"></a><code><span><span class="keyword">val</span> le : <span><span class="type-var">'r</span> <span class="arrow">&#45;&gt;</span></span> <span><span class="type-var">'r</span> <span class="arrow">&#45;&gt;</span></span> <span><span>(<span class="type-var">'r</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span></span></code></div><div class="spec-doc"><p><code>le x y</code> is <code>Cof (Le (x, y))</code></p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-join"><a href="#val-join" class="anchor"></a><code><span><span class="keyword">val</span> join : <span><span><span><span>(<span class="type-var">'r</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span> list</span> <span class="arrow">&#45;&gt;</span></span> <span><span>(<span class="type-var">'r</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span></span></code></div><div class="spec-doc"><p><code>join phis</code> is <code>Cof (Join phis)</code></p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-meet"><a href="#val-meet" class="anchor"></a><code><span><span class="keyword">val</span> meet : <span><span><span><span>(<span class="type-var">'r</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span> list</span> <span class="arrow">&#45;&gt;</span></span> <span><span>(<span class="type-var">'r</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span></span></code></div><div class="spec-doc"><p><code>meet phis</code> is <code>Cof (Meet phis)</code></p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-bot"><a href="#val-bot" class="anchor"></a><code><span><span class="keyword">val</span> bot : <span><span>(<span class="type-var">'r</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span></span></code></div><div class="spec-doc"><p><code>bot</code> is <code>Cof (Join [])</code></p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-top"><a href="#val-top" class="anchor"></a><code><span><span class="keyword">val</span> top : <span><span>(<span class="type-var">'r</span>, <span class="type-var">'v</span>)</span> <a href="../index.html#type-free">free</a></span></span></code></div><div class="spec-doc"><p><code>top</code> is <code>Cof (Meet [])</code></p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-dump"><a href="#val-dump" class="anchor"></a><code><span><span class="keyword">val</span> dump :
<span><span>(<span><span class="xref-unresolved">Stdlib</span>.Format.formatter <span class="arrow">&#45;&gt;</span></span> <span><span class="type-var">'r</span> <span class="arrow">&#45;&gt;</span></span> unit)</span> <span class="arrow">&#45;&gt;</span></span>
<span><span>(<span><span class="xref-unresolved">Stdlib</span>.Format.formatter <span class="arrow">&#45;&gt;</span></span> <span><span class="type-var">'v</span> <span class="arrow">&#45;&gt;</span></span> unit)</span> <span class="arrow">&#45;&gt;</span></span>
<span><span class="xref-unresolved">Stdlib</span>.Format.formatter <span class="arrow">&#45;&gt;</span></span>
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