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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Abstract.Cocomplete</title><link href="ocean.css" rel="stylesheet" type="text/css" title="Ocean" /><script src="haddock-util.js" type="text/javascript"></script><script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script><script type="text/javascript">//<![CDATA[
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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Abstract.Cocomplete.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">verigraph-1.1.1: Software specification and verification tool based on graph rewriting.</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Safe Haskell</th><td>Safe</td></tr><tr><th>Language</th><td>Haskell2010</td></tr></table><p class="caption">Abstract.Cocomplete</p></div><div id="description"><p class="caption">Description</p><div class="doc"><p>A Cocomplete category is one which has all small colimits. This module provides a signature for
such colimits and a default implementation of pushouts based on coequalizers and coproducts.</p></div></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><span class="keyword">class</span> <a href="Abstract-Morphism.html#t:Morphism">Morphism</a> m => <a href="#t:Cocomplete">Cocomplete</a> m <span class="keyword">where</span><ul class="subs"></ul></li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">class</span> <a href="Abstract-Morphism.html#t:Morphism">Morphism</a> m => <a id="t:Cocomplete" class="def">Cocomplete</a> m <span class="keyword">where</span> <a href="src/Abstract.Cocomplete.html#Cocomplete" class="link">Source</a> <a href="#t:Cocomplete" class="selflink">#</a></p><div class="doc"><p>Type class for morphisms whose category is Cocomplete.</p><p>Mainly provides categorical operations that Cocomplete categories
are guaranteed to have.</p><p>Note that for performance reasons, verigraph assumes that the parameters
are valid for all functions in this module.</p></div><div class="subs minimal"><p class="caption">Minimal complete definition</p><p class="src"><a href="Abstract-Cocomplete.html#v:calculateCoequalizer">calculateCoequalizer</a>, <a href="Abstract-Cocomplete.html#v:calculateNCoequalizer">calculateNCoequalizer</a>, <a href="Abstract-Cocomplete.html#v:calculateCoproduct">calculateCoproduct</a>, <a href="Abstract-Cocomplete.html#v:calculateNCoproduct">calculateNCoproduct</a>, <a href="Abstract-Cocomplete.html#v:initialObject">initialObject</a></p></div><div class="subs methods"><p class="caption">Methods</p><p class="src"><a id="v:calculateCoequalizer" class="def">calculateCoequalizer</a> :: m -> m -> m <a href="src/Abstract.Cocomplete.html#calculateCoequalizer" class="link">Source</a> <a href="#v:calculateCoequalizer" class="selflink">#</a></p><div class="doc"><p>Given two morphisms <code><em>f : A -> B</em></code> and <code><em>g : A -> B</em></code> retuns the coequalizer morphism
<code><em>h : B -> X</em></code></p></div><p class="src"><a id="v:calculateNCoequalizer" class="def">calculateNCoequalizer</a> :: <a href="../base-4.9.1.0/Data-List-NonEmpty.html#t:NonEmpty">NonEmpty</a> m -> m <a href="src/Abstract.Cocomplete.html#calculateNCoequalizer" class="link">Source</a> <a href="#v:calculateNCoequalizer" class="selflink">#</a></p><div class="doc"><p>Given a non-empty list of morphisms of the form <code><em>f : A -> B</em></code> returns the coequalizer Morphism
<code><em>h : B -> X</em></code></p></div><p class="src"><a id="v:calculateCoproduct" class="def">calculateCoproduct</a> :: <a href="Abstract-Morphism.html#t:Obj">Obj</a> m -> <a href="Abstract-Morphism.html#t:Obj">Obj</a> m -> (m, m) <a href="src/Abstract.Cocomplete.html#calculateCoproduct" class="link">Source</a> <a href="#v:calculateCoproduct" class="selflink">#</a></p><div class="doc"><p>Given two objects <code>A</code> and <code>B</code> it returns the coproduct <code>(A+B, f: A -> A+B, g: B -> A+B)</code></p></div><p class="src"><a id="v:calculateNCoproduct" class="def">calculateNCoproduct</a> :: <a href="../base-4.9.1.0/Data-List-NonEmpty.html#t:NonEmpty">NonEmpty</a> (<a href="Abstract-Morphism.html#t:Obj">Obj</a> m) -> [m] <a href="src/Abstract.Cocomplete.html#calculateNCoproduct" class="link">Source</a> <a href="#v:calculateNCoproduct" class="selflink">#</a></p><div class="doc"><p>Given a non-empty list of objects <code>Bi</code> it returns the coproduct <code>fi : Bi -> SUM(Bi)</code></p></div><p class="src"><a id="v:initialObject" class="def">initialObject</a> :: m -> <a href="Abstract-Morphism.html#t:Obj">Obj</a> m <a href="src/Abstract.Cocomplete.html#initialObject" class="link">Source</a> <a href="#v:initialObject" class="selflink">#</a></p><p class="src"><a id="v:calculatePushout" class="def">calculatePushout</a> :: m -> m -> (m, m) <a href="src/Abstract.Cocomplete.html#calculatePushout" class="link">Source</a> <a href="#v:calculatePushout" class="selflink">#</a></p></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.17.3</p></div></body></html>