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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Data-Semigroupoid.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">semigroupoids-5.2.1: Semigroupoids: Category sans id</p></div><div id="content"><div id="module-header"><table class="info"><tr><th valign="top">Copyright</th><td>(C) 2007-2015 Edward Kmett</td></tr><tr><th>License</th><td>BSD-style (see the file LICENSE)</td></tr><tr><th>Maintainer</th><td>Edward Kmett <ekmett@gmail.com></td></tr><tr><th>Stability</th><td>provisional</td></tr><tr><th>Portability</th><td>portable</td></tr><tr><th>Safe Haskell</th><td>Safe</td></tr><tr><th>Language</th><td>Haskell98</td></tr></table><p class="caption">Data.Semigroupoid</p></div><div id="description"><p class="caption">Description</p><div class="doc"><p>A semigroupoid satisfies all of the requirements to be a Category except
for the existence of identity arrows.</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="#t:Semigroupoid">Semigroupoid</a> c <span class="keyword">where</span><ul class="subs"></ul></li><li class="src short"><span class="keyword">newtype</span> <a href="#t:WrappedCategory">WrappedCategory</a> k a b = <a href="#v:WrapCategory">WrapCategory</a> {<ul class="subs"><li><a href="#v:unwrapCategory">unwrapCategory</a> :: k a b</li></ul>}</li><li class="src short"><span class="keyword">newtype</span> <a href="#t:Semi">Semi</a> m a b = <a href="#v:Semi">Semi</a> {<ul class="subs"><li><a href="#v:getSemi">getSemi</a> :: m</li></ul>}</li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">class</span> <a id="t:Semigroupoid" class="def">Semigroupoid</a> c <span class="keyword">where</span> <a href="src/Data-Semigroupoid.html#Semigroupoid" class="link">Source</a> <a href="#t:Semigroupoid" class="selflink">#</a></p><div class="doc"><p><code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Category.html#t:Category">Category</a></code> sans <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Category.html#v:id">id</a></code></p></div><div class="subs minimal"><p class="caption">Minimal complete definition</p><p class="src"><a href="Data-Semigroupoid.html#v:o">o</a></p></div><div class="subs methods"><p class="caption">Methods</p><p class="src"><a id="v:o" class="def">o</a> :: c j k -> c i j -> c i k <a href="src/Data-Semigroupoid.html#o" class="link">Source</a> <a href="#v:o" class="selflink">#</a></p></div><div class="subs instances"><p id="control.i:Semigroupoid" class="caption collapser" onclick="toggleSection('i:Semigroupoid')">Instances</p><div id="section.i:Semigroupoid" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Semigroupoid:Semigroupoid:1" class="instance expander" onclick="toggleSection('i:ic:Semigroupoid:Semigroupoid:1')"></span> <a href="Data-Semigroupoid.html#t:Semigroupoid">Semigroupoid</a> k k1 => <a href="Data-Semigroupoid.html#t:Semigroupoid">Semigroupoid</a> k (<a href="Data-Isomorphism.html#t:Iso">Iso</a> k k1)</span> <a href="src/Data-Semigroupoid.html#line-27" class="link">Source</a> <a href="#t:Semigroupoid" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Semigroupoid:Semigroupoid:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:o">o</a> :: c j k -> c i j -> c i k <a href="src/Data-Semigroupoid.html#o" class="link">Source</a> <a href="#v:o" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Semigroupoid:Semigroupoid:2" class="instance expander" onclick="toggleSection('i:ic:Semigroupoid:Semigroupoid:2')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Semigroup.html#t:Semigroup">Semigroup</a> m => <a href="Data-Semigroupoid.html#t:Semigroupoid">Semigroupoid</a> k (<a href="Data-Semigroupoid.html#t:Semi">Semi</a> k k m)</span> <a href="src/Data-Semigroupoid.html#line-85" class="link">Source</a> <a href="#t:Semigroupoid" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Semigroupoid:Semigroupoid:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:o">o</a> :: c j k -> c i j -> c i k <a href="src/Data-Semigroupoid.html#o" class="link">Source</a> <a href="#v:o" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Semigroupoid:Semigroupoid:3" class="instance expander" onclick="toggleSection('i:ic:Semigroupoid:Semigroupoid:3')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Category.html#t:Category">Category</a> k k1 => <a href="Data-Semigroupoid.html#t:Semigroupoid">Semigroupoid</a> k (<a href="Data-Semigroupoid.html#t:WrappedCategory">WrappedCategory</a> k k k1)</span> <a href="src/Data-Semigroupoid.html#line-76" class="link">Source</a> <a href="#t:Semigroupoid" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Semigroupoid:Semigroupoid:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:o">o</a> :: c j k -> c i j -> c i k <a href="src/Data-Semigroupoid.html#o" class="link">Source</a> <a href="#v:o" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Semigroupoid:Semigroupoid:4" class="instance expander" onclick="toggleSection('i:ic:Semigroupoid:Semigroupoid:4')"></span> <a href="Data-Semigroupoid.html#t:Semigroupoid">Semigroupoid</a> k k1 => <a href="Data-Semigroupoid.html#t:Semigroupoid">Semigroupoid</a> k (<a href="Data-Semigroupoid-Dual.html#t:Dual">Dual</a> k k k1)</span> <a href="src/Data-Semigroupoid.html#line-25" class="link">Source</a> <a href="#t:Semigroupoid" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Semigroupoid:Semigroupoid:4" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:o">o</a> :: c j k -> c i j -> c i k <a href="src/Data-Semigroupoid.html#o" class="link">Source</a> <a href="#v:o" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Semigroupoid:Semigroupoid:5" class="instance expander" onclick="toggleSection('i:ic:Semigroupoid:Semigroupoid:5')"></span> <a href="Data-Semigroupoid.html#t:Semigroupoid">Semigroupoid</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a> (->)</span> <a href="src/Data-Semigroupoid.html#line-54" class="link">Source</a> <a href="#t:Semigroupoid" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Semigroupoid:Semigroupoid:5" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:o">o</a> :: c j k -> c i j -> c i k <a href="src/Data-Semigroupoid.html#o" class="link">Source</a> <a href="#v:o" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Semigroupoid:Semigroupoid:6" class="instance expander" onclick="toggleSection('i:ic:Semigroupoid:Semigroupoid:6')"></span> <a href="Data-Semigroupoid.html#t:Semigroupoid">Semigroupoid</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.5.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a></span> <a href="src/Data-Semigroupoid.html#line-58" class="link">Source</a> <a href="#t:Semigroupoid" class="selflink">#</a></td><td class="doc"><p><a href="http://en.wikipedia.org/wiki/Band_(mathematics)#Rectangular_bands">http://en.wikipedia.org/wiki/Band_(mathematics)#Rectangular_bands</a></p></td></tr><tr><td colspan="2"><div id="section.i:ic:Semigroupoid:Semigroupoid:6" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:o">o</a> :: c j k -> c i j -> c i k <a href="src/Data-Semigroupoid.html#o" class="link">Source</a> <a href="#v:o" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Semigroupoid:Semigroupoid:7" class="instance expander" onclick="toggleSection('i:ic:Semigroupoid:Semigroupoid:7')"></span> <a href="Data-Semigroupoid.html#t:Semigroupoid">Semigroupoid</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a> <a href="file:///usr/share/doc/libghc-contravariant-doc/html/Data-Functor-Contravariant.html#t:Op">Op</a></span> <a href="src/Data-Semigroupoid.html#line-70" class="link">Source</a> <a href="#t:Semigroupoid" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Semigroupoid:Semigroupoid:7" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:o">o</a> :: c j k -> c i j -> c i k <a href="src/Data-Semigroupoid.html#o" class="link">Source</a> <a href="#v:o" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Semigroupoid:Semigroupoid:8" class="instance expander" onclick="toggleSection('i:ic:Semigroupoid:Semigroupoid:8')"></span> <a href="Data-Functor-Bind.html#t:Bind">Bind</a> m => <a href="Data-Semigroupoid.html#t:Semigroupoid">Semigroupoid</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Arrow.html#t:Kleisli">Kleisli</a> m)</span> <a href="src/Data-Semigroupoid.html#line-61" class="link">Source</a> <a href="#t:Semigroupoid" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Semigroupoid:Semigroupoid:8" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:o">o</a> :: c j k -> c i j -> c i k <a href="src/Data-Semigroupoid.html#o" class="link">Source</a> <a href="#v:o" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Semigroupoid:Semigroupoid:9" class="instance expander" onclick="toggleSection('i:ic:Semigroupoid:Semigroupoid:9')"></span> <a href="Data-Semigroupoid.html#t:Semigroupoid">Semigroupoid</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Functor-Const.html#t:Const">Const</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a>)</span> <a href="src/Data-Semigroupoid.html#line-92" class="link">Source</a> <a href="#t:Semigroupoid" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Semigroupoid:Semigroupoid:9" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:o">o</a> :: c j k -> c i j -> c i k <a href="src/Data-Semigroupoid.html#o" class="link">Source</a> <a href="#v:o" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Semigroupoid:Semigroupoid:10" class="instance expander" onclick="toggleSection('i:ic:Semigroupoid:Semigroupoid:10')"></span> <a href="Data-Functor-Extend.html#t:Extend">Extend</a> w => <a href="Data-Semigroupoid.html#t:Semigroupoid">Semigroupoid</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a> (<a href="file:///usr/share/doc/libghc-comonad-doc/html/Control-Comonad.html#t:Cokleisli">Cokleisli</a> w)</span> <a href="src/Data-Semigroupoid.html#line-65" class="link">Source</a> <a href="#t:Semigroupoid" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Semigroupoid:Semigroupoid:10" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:o">o</a> :: c j k -> c i j -> c i k <a href="src/Data-Semigroupoid.html#o" class="link">Source</a> <a href="#v:o" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Semigroupoid:Semigroupoid:11" class="instance expander" onclick="toggleSection('i:ic:Semigroupoid:Semigroupoid:11')"></span> <a href="Data-Semigroupoid.html#t:Semigroupoid">Semigroupoid</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a> (<a href="file:///usr/share/doc/libghc-tagged-doc/html/Data-Tagged.html#t:Tagged">Tagged</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a>)</span> <a href="src/Data-Semigroupoid.html#line-96" class="link">Source</a> <a href="#t:Semigroupoid" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Semigroupoid:Semigroupoid:11" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:o">o</a> :: c j k -> c i j -> c i k <a href="src/Data-Semigroupoid.html#o" class="link">Source</a> <a href="#v:o" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Semigroupoid:Semigroupoid:12" class="instance expander" onclick="toggleSection('i:ic:Semigroupoid:Semigroupoid:12')"></span> <a href="Data-Functor-Apply.html#t:Apply">Apply</a> f => <a href="Data-Semigroupoid.html#t:Semigroupoid">Semigroupoid</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a> (<a href="Data-Semigroupoid-Static.html#t:Static">Static</a> f)</span> <a href="src/Data-Semigroupoid.html#line-72" class="link">Source</a> <a href="#t:Semigroupoid" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Semigroupoid:Semigroupoid:12" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:o">o</a> :: c j k -> c i j -> c i k <a href="src/Data-Semigroupoid.html#o" class="link">Source</a> <a href="#v:o" class="selflink">#</a></p></div></div></td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">newtype</span> <a id="t:WrappedCategory" class="def">WrappedCategory</a> k a b <a href="src/Data-Semigroupoid.html#WrappedCategory" class="link">Source</a> <a href="#t:WrappedCategory" class="selflink">#</a></p><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a id="v:WrapCategory" class="def">WrapCategory</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div class="subs fields"><p class="caption">Fields</p><ul><li><dfn class="src"><a id="v:unwrapCategory" class="def">unwrapCategory</a> :: k a b</dfn><div class="doc empty"> </div></li></ul></div></td></tr></table></div><div class="subs instances"><p id="control.i:WrappedCategory" class="caption collapser" onclick="toggleSection('i:WrappedCategory')">Instances</p><div id="section.i:WrappedCategory" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:WrappedCategory:Category:1" class="instance expander" onclick="toggleSection('i:id:WrappedCategory:Category:1')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Category.html#t:Category">Category</a> k k1 => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Category.html#t:Category">Category</a> k (<a href="Data-Semigroupoid.html#t:WrappedCategory">WrappedCategory</a> k k k1)</span> <a href="src/Data-Semigroupoid.html#line-79" class="link">Source</a> <a href="#t:WrappedCategory" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:WrappedCategory:Category:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:id">id</a> :: cat a a <a href="#v:id" class="selflink">#</a></p><p class="src"><a href="#v:.">(.)</a> :: cat b c -> cat a b -> cat a c <a href="#v:." class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:WrappedCategory:Semigroupoid:2" class="instance expander" onclick="toggleSection('i:id:WrappedCategory:Semigroupoid:2')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Category.html#t:Category">Category</a> k k1 => <a href="Data-Semigroupoid.html#t:Semigroupoid">Semigroupoid</a> k (<a href="Data-Semigroupoid.html#t:WrappedCategory">WrappedCategory</a> k k k1)</span> <a href="src/Data-Semigroupoid.html#line-76" class="link">Source</a> <a href="#t:WrappedCategory" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:WrappedCategory:Semigroupoid:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:o">o</a> :: c j k -> c i j -> c i k <a href="src/Data-Semigroupoid.html#o" class="link">Source</a> <a href="#v:o" class="selflink">#</a></p></div></div></td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">newtype</span> <a id="t:Semi" class="def">Semi</a> m a b <a href="src/Data-Semigroupoid.html#Semi" class="link">Source</a> <a href="#t:Semi" class="selflink">#</a></p><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a id="v:Semi" class="def">Semi</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div class="subs fields"><p class="caption">Fields</p><ul><li><dfn class="src"><a id="v:getSemi" class="def">getSemi</a> :: m</dfn><div class="doc empty"> </div></li></ul></div></td></tr></table></div><div class="subs instances"><p id="control.i:Semi" class="caption collapser" onclick="toggleSection('i:Semi')">Instances</p><div id="section.i:Semi" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Semi:Category:1" class="instance expander" onclick="toggleSection('i:id:Semi:Category:1')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Monoid.html#t:Monoid">Monoid</a> m => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Category.html#t:Category">Category</a> k (<a href="Data-Semigroupoid.html#t:Semi">Semi</a> k k m)</span> <a href="src/Data-Semigroupoid.html#line-88" class="link">Source</a> <a href="#t:Semi" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Semi:Category:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:id">id</a> :: cat a a <a href="#v:id" class="selflink">#</a></p><p class="src"><a href="#v:.">(.)</a> :: cat b c -> cat a b -> cat a c <a href="#v:." class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Semi:Semigroupoid:2" class="instance expander" onclick="toggleSection('i:id:Semi:Semigroupoid:2')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Semigroup.html#t:Semigroup">Semigroup</a> m => <a href="Data-Semigroupoid.html#t:Semigroupoid">Semigroupoid</a> k (<a href="Data-Semigroupoid.html#t:Semi">Semi</a> k k m)</span> <a href="src/Data-Semigroupoid.html#line-85" class="link">Source</a> <a href="#t:Semi" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Semi:Semigroupoid:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:o">o</a> :: c j k -> c i j -> c i k <a href="src/Data-Semigroupoid.html#o" class="link">Source</a> <a href="#v:o" class="selflink">#</a></p></div></div></td></tr></table></div></div></div></div></div><div id="footer"><p>Produced by <a 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