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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Data-Group.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">groups-0.4.0.0: Haskell 98 groups</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Safe Haskell</th><td>Safe-Inferred</td></tr></table><p class="caption">Data.Group</p></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="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Monoid.html#t:Monoid">Monoid</a> m => <a href="#t:Group">Group</a> m <span class="keyword">where</span><ul class="subs"><li><a href="#v:invert">invert</a> :: m -> m</li><li><a href="#v:pow">pow</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integral">Integral</a> x => m -> x -> m</li></ul></li><li class="src short"><span class="keyword">class</span> <a href="Data-Group.html#t:Group">Group</a> g => <a href="#t:Abelian">Abelian</a> g </li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">class</span> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Monoid.html#t:Monoid">Monoid</a> m => <a name="t:Group" class="def">Group</a> m <span class="keyword">where</span><a href="src/Data-Group.html#Group" class="link">Source</a></p><div class="doc"><p>A <code><a href="Data-Group.html#t:Group">Group</a></code> is a <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Monoid.html#t:Monoid">Monoid</a></code> plus a function, <code><a href="Data-Group.html#v:invert">invert</a></code>, such that:
</p><pre>a <> invert a == mempty</pre><pre>invert a <> a == mempty</pre></div><div class="subs methods"><p class="caption">Methods</p><p class="src"><a name="v:invert" class="def">invert</a> :: m -> m<a href="src/Data-Group.html#invert" class="link">Source</a></p><p class="src"><a name="v:pow" class="def">pow</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integral">Integral</a> x => m -> x -> m<a href="src/Data-Group.html#pow" class="link">Source</a></p><div class="doc"><pre><code><a href="Data-Group.html#v:pow">pow</a></code> a n == a <> a <> ... <> a</pre><pre> (n lots of a)</pre><p>If n is negative, the result is inverted.
</p></div></div><div class="subs instances"><p id="control.i:Group" class="caption collapser" onclick="toggleSection('i:Group')">Instances</p><div id="section.i:Group" class="show"><table><tr><td class="src"><a href="Data-Group.html#t:Group">Group</a> ()</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-Group.html#t:Group">Group</a> a => <a href="Data-Group.html#t:Group">Group</a> (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Monoid.html#t:Dual">Dual</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Num">Num</a> a => <a href="Data-Group.html#t:Group">Group</a> (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Monoid.html#t:Sum">Sum</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Fractional">Fractional</a> a => <a href="Data-Group.html#t:Group">Group</a> (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Monoid.html#t:Product">Product</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-Group.html#t:Group">Group</a> b => <a href="Data-Group.html#t:Group">Group</a> (a -> b)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-Group.html#t:Group">Group</a> a, <a href="Data-Group.html#t:Group">Group</a> b) => <a href="Data-Group.html#t:Group">Group</a> (a, b)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-Group.html#t:Group">Group</a> a, <a href="Data-Group.html#t:Group">Group</a> b, <a href="Data-Group.html#t:Group">Group</a> c) => <a href="Data-Group.html#t:Group">Group</a> (a, b, c)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-Group.html#t:Group">Group</a> a, <a href="Data-Group.html#t:Group">Group</a> b, <a href="Data-Group.html#t:Group">Group</a> c, <a href="Data-Group.html#t:Group">Group</a> d) => <a href="Data-Group.html#t:Group">Group</a> (a, b, c, d)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-Group.html#t:Group">Group</a> a, <a href="Data-Group.html#t:Group">Group</a> b, <a href="Data-Group.html#t:Group">Group</a> c, <a href="Data-Group.html#t:Group">Group</a> d, <a href="Data-Group.html#t:Group">Group</a> e) => <a href="Data-Group.html#t:Group">Group</a> (a, b, c, d, e)</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">class</span> <a href="Data-Group.html#t:Group">Group</a> g => <a name="t:Abelian" class="def">Abelian</a> g <a href="src/Data-Group.html#Abelian" class="link">Source</a></p><div class="doc"><p>An <code><a href="Data-Group.html#t:Abelian">Abelian</a></code> group is a <code><a href="Data-Group.html#t:Group">Group</a></code> that follows the rule:
</p><pre>a <> b == b <> a</pre></div><div class="subs instances"><p id="control.i:Abelian" class="caption collapser" onclick="toggleSection('i:Abelian')">Instances</p><div id="section.i:Abelian" class="show"><table><tr><td class="src"><a href="Data-Group.html#t:Abelian">Abelian</a> ()</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-Group.html#t:Abelian">Abelian</a> a => <a href="Data-Group.html#t:Abelian">Abelian</a> (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Monoid.html#t:Dual">Dual</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Num">Num</a> a => <a href="Data-Group.html#t:Abelian">Abelian</a> (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Monoid.html#t:Sum">Sum</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Fractional">Fractional</a> a => <a href="Data-Group.html#t:Abelian">Abelian</a> (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Monoid.html#t:Product">Product</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-Group.html#t:Abelian">Abelian</a> b => <a href="Data-Group.html#t:Abelian">Abelian</a> (a -> b)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-Group.html#t:Abelian">Abelian</a> a, <a href="Data-Group.html#t:Abelian">Abelian</a> b) => <a href="Data-Group.html#t:Abelian">Abelian</a> (a, b)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-Group.html#t:Abelian">Abelian</a> a, <a href="Data-Group.html#t:Abelian">Abelian</a> b, <a href="Data-Group.html#t:Abelian">Abelian</a> c) => <a href="Data-Group.html#t:Abelian">Abelian</a> (a, b, c)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-Group.html#t:Abelian">Abelian</a> a, <a href="Data-Group.html#t:Abelian">Abelian</a> b, <a href="Data-Group.html#t:Abelian">Abelian</a> c, <a href="Data-Group.html#t:Abelian">Abelian</a> d) => <a href="Data-Group.html#t:Abelian">Abelian</a> (a, b, c, d)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-Group.html#t:Abelian">Abelian</a> a, <a href="Data-Group.html#t:Abelian">Abelian</a> b, <a href="Data-Group.html#t:Abelian">Abelian</a> c, <a href="Data-Group.html#t:Abelian">Abelian</a> d, <a href="Data-Group.html#t:Abelian">Abelian</a> e) => <a href="Data-Group.html#t:Abelian">Abelian</a> (a, b, c, d, e)</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 2.13.2</p></div></body></html>
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