<!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>Agda.Utils.SemiRing</title><link href="ocean.css" rel="stylesheet" type="text/css" title="Ocean" /><script src="haddock-util.js" 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/Agda-Utils-SemiRing.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">Agda-2.3.2.1: A dependently typed functional programming language and proof assistant</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Safe Haskell</th><td>Safe-Infered</td></tr></table><p class="caption">Agda.Utils.SemiRing</p></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">class</span> <a name="t:SemiRing" class="def">SemiRing</a> a <span class="keyword">where</span><a href="src/Agda-Utils-SemiRing.html#SemiRing" class="link">Source</a></p><div class="subs methods"><p class="caption">Methods</p><p class="src"><a name="v:oplus" class="def">oplus</a> :: a -> a -> a<a href="src/Agda-Utils-SemiRing.html#oplus" class="link">Source</a></p><p class="src"><a name="v:otimes" class="def">otimes</a> :: a -> a -> a<a href="src/Agda-Utils-SemiRing.html#otimes" class="link">Source</a></p></div><div class="subs instances"><p id="control.i:SemiRing" class="caption collapser" onclick="toggleSection('i:SemiRing')">Instances</p><div id="section.i:SemiRing" class="show"><table><tr><td class="src"><a href="Agda-Utils-SemiRing.html#t:SemiRing">SemiRing</a> E</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Agda-Utils-SemiRing.html#t:SemiRing">SemiRing</a> <a href="Agda-Utils-Warshall.html#t:Distance">Distance</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Agda-Utils-SemiRing.html#t:SemiRing">SemiRing</a> <a href="Agda-Utils-Warshall.html#t:Weight">Weight</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Agda-Utils-SemiRing.html#t:SemiRing">SemiRing</a> <a href="Agda-TypeChecking-Monad-Base.html#t:Occurrence">Occurrence</a></td><td class="doc"><p><code><a href="Agda-TypeChecking-Monad-Base.html#t:Occurrence">Occurrence</a></code> is a complete lattice with least element <code><a href="Agda-TypeChecking-Monad-Base.html#v:Mixed">Mixed</a></code>
and greatest element <code><a href="Agda-TypeChecking-Monad-Base.html#v:Unused">Unused</a></code>.
</p><p>It forms a commutative semiring where <code><a href="Agda-Utils-SemiRing.html#v:oplus">oplus</a></code> is meet (glb)
and <code><a href="Agda-Utils-SemiRing.html#v:otimes">otimes</a></code> is composition. Both operations are idempotent.
</p><p>For <code><a href="Agda-Utils-SemiRing.html#v:oplus">oplus</a></code>, <code><a href="Agda-TypeChecking-Monad-Base.html#v:Unused">Unused</a></code> is neutral (zero) and <code><a href="Agda-TypeChecking-Monad-Base.html#v:Mixed">Mixed</a></code> is dominant.
For <code><a href="Agda-Utils-SemiRing.html#v:otimes">otimes</a></code>, <code><a href="Agda-TypeChecking-Monad-Base.html#v:StrictPos">StrictPos</a></code> is neutral (one) and <code><a href="Agda-TypeChecking-Monad-Base.html#v:Unused">Unused</a></code> is dominant.
</p></td></tr><tr><td class="src"><a href="Agda-Utils-SemiRing.html#t:SemiRing">SemiRing</a> <a href="Agda-TypeChecking-Positivity.html#t:Edge">Edge</a></td><td class="doc"><p>These operations form a semiring if we quotient by the relation
"the <code><a href="Agda-TypeChecking-Monad-Base.html#t:Occurrence">Occurrence</a></code> components are equal".
</p></td></tr><tr><td class="src"><a href="Agda-Utils-SemiRing.html#t:SemiRing">SemiRing</a> a => <a href="Agda-Utils-SemiRing.html#t:SemiRing">SemiRing</a> (<a href="/usr/share/doc/ghc/html/libraries/base-4.5.1.0/Data-Maybe.html#t:Maybe">Maybe</a> a)</td><td class="doc empty"> </td></tr></table></div></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.11.0</p></div></body></html>
