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<html xmlns="http://www.w3.org/1999/xhtml"><head><title>WeakTopologicalOrder (infer.IR.WeakTopologicalOrder)</title><link rel="stylesheet" href="../../../odoc.css"/><meta charset="utf-8"/><meta name="generator" content="odoc 1.5.1"/><meta name="viewport" content="width=device-width,initial-scale=1.0"/><script src="../../../highlight.pack.js"></script><script>hljs.initHighlightingOnLoad();</script></head><body><div class="content"><header><nav><a href="../index.html">Up</a> – <a href="../../index.html">infer</a> » <a href="../index.html">IR</a> » WeakTopologicalOrder</nav><h1>Module <code>IR.WeakTopologicalOrder</code></h1></header><div class="spec module" id="module-F"><a href="#module-F" class="anchor"></a><code><span class="keyword">module</span> F = Stdlib.Format</code></div><aside><p>A hierarchical ordering of a set is a well-parenthesized permutation of its elements without two consecutive "(". I defines a total order <= over its elements. The elements between two matching parentheses are called a Component. The first element of a Component is called the head. Let denote by H(v) the set of head of the nested components containing v.</p></aside><div class="spec module" id="module-Partition"><a href="#module-Partition" class="anchor"></a><code><span class="keyword">module</span> <a href="Partition/index.html">Partition</a> : <span class="keyword">sig</span> ... <span class="keyword">end</span></code></div><div class="spec module-type" id="module-type-PreProcCfg"><a href="#module-type-PreProcCfg" class="anchor"></a><code><span class="keyword">module</span> <span class="keyword">type</span> <a href="module-type-PreProcCfg/index.html">PreProcCfg</a> = <span class="keyword">sig</span> ... <span class="keyword">end</span></code></div><aside><p>A weak topological ordering (WTO) of a directed graph is a hierarchical ordering of its vertices such that for every edge u -> v,</p><p>u < v and v is not in H(u) (forward edge)</p><p>or</p><p>v <= u and v is in H(u) (feedback edge)</p><p>where H(u) is the set of heads of the nested components containing u.</p><p>A WTO of a directed graph is such that the head v of every feedback edge u -> v is the head of a component containing its tail u.</p></aside><div class="spec module-type" id="module-type-S"><a href="#module-type-S" class="anchor"></a><code><span class="keyword">module</span> <span class="keyword">type</span> <a href="module-type-S/index.html">S</a> = <span class="keyword">sig</span> ... <span class="keyword">end</span></code></div><div class="spec module-type" id="module-type-Make"><a href="#module-type-Make" class="anchor"></a><code><span class="keyword">module</span> <span class="keyword">type</span> <a href="module-type-Make/index.html">Make</a> = <span class="keyword">functor</span> (<a href="module-type-Make/argument-1-CFG/index.html">CFG</a> : <a href="index.html#module-type-PreProcCfg">PreProcCfg</a>) <span>-></span> <a href="index.html#module-type-S">S</a> <span class="keyword">with</span> <span class="keyword">module</span> <a href="module-type-Make/CFG/index.html">CFG</a> = <a href="module-type-Make/index.html#argument-1-CFG">CFG</a></code></div><dl><dt class="spec module" id="module-Bourdoncle_SCC"><a href="#module-Bourdoncle_SCC" class="anchor"></a><code><span class="keyword">module</span> <a href="Bourdoncle_SCC/index.html">Bourdoncle_SCC</a> : <a href="index.html#module-type-Make">Make</a></code></dt><dd><p>Implementation of Bourdoncle's "Hierarchical decomposition of a directed graph into strongly connected components and subcomponents". See <code>Bou</code> Figure 4, page 10.</p></dd></dl></div></body></html>
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