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<title>src/Data/Semigroupoid.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE CPP #-}</span>
<a name="line-2"></a>
<a name="line-3"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ >= 706</span>
<a name="line-4"></a><span class='hs-comment'>{-# LANGUAGE PolyKinds #-}</span>
<a name="line-5"></a><span class='hs-cpp'>#endif</span>
<a name="line-6"></a>
<a name="line-7"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ >= 702 && __GLASGOW_HASKELL <= 706 && defined(MIN_VERSION_comonad) && !(MIN_VERSION_comonad(3,0,3))</span>
<a name="line-8"></a><span class='hs-comment'>{-# LANGUAGE Trustworthy #-}</span>
<a name="line-9"></a><span class='hs-cpp'>#endif</span>
<a name="line-10"></a>
<a name="line-11"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-12"></a><span class='hs-comment'>-- |</span>
<a name="line-13"></a><span class='hs-comment'>-- Module : Data.Semigroupoid</span>
<a name="line-14"></a><span class='hs-comment'>-- Copyright : (C) 2007-2015 Edward Kmett</span>
<a name="line-15"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-16"></a><span class='hs-comment'>--</span>
<a name="line-17"></a><span class='hs-comment'>-- Maintainer : Edward Kmett <ekmett@gmail.com></span>
<a name="line-18"></a><span class='hs-comment'>-- Stability : provisional</span>
<a name="line-19"></a><span class='hs-comment'>-- Portability : portable</span>
<a name="line-20"></a><span class='hs-comment'>--</span>
<a name="line-21"></a><span class='hs-comment'>-- A semigroupoid satisfies all of the requirements to be a Category except</span>
<a name="line-22"></a><span class='hs-comment'>-- for the existence of identity arrows.</span>
<a name="line-23"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-24"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Semigroupoid</span>
<a name="line-25"></a> <span class='hs-layout'>(</span> <span class='hs-conid'>Semigroupoid</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-26"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>WrappedCategory</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-27"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Semi</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-28"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-29"></a>
<a name="line-30"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span>
<a name="line-31"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Arrow</span>
<a name="line-32"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Functor</span><span class='hs-varop'>.</span><span class='hs-conid'>Bind</span>
<a name="line-33"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Semigroup</span>
<a name="line-34"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Category</span>
<a name="line-35"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Prelude</span> <span class='hs-varid'>hiding</span> <span class='hs-layout'>(</span><span class='hs-varid'>id</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>.</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-36"></a>
<a name="line-37"></a><span class='hs-cpp'>#ifdef MIN_VERSION_contravariant</span>
<a name="line-38"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Functor</span><span class='hs-varop'>.</span><span class='hs-conid'>Contravariant</span>
<a name="line-39"></a><span class='hs-cpp'>#endif</span>
<a name="line-40"></a>
<a name="line-41"></a><span class='hs-cpp'>#ifdef MIN_VERSION_comonad</span>
<a name="line-42"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Functor</span><span class='hs-varop'>.</span><span class='hs-conid'>Extend</span>
<a name="line-43"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Comonad</span>
<a name="line-44"></a><span class='hs-cpp'>#endif</span>
<a name="line-45"></a>
<a name="line-46"></a><span class='hs-cpp'>#ifdef MIN_VERSION_tagged</span>
<a name="line-47"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Tagged</span> <span class='hs-layout'>(</span><span class='hs-conid'>Tagged</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-48"></a><span class='hs-cpp'>#endif</span>
<a name="line-49"></a>
<a name="line-50"></a><a name="Semigroupoid"></a><span class='hs-comment'>-- | 'Control.Category.Category' sans 'Control.Category.id'</span>
<a name="line-51"></a><a name="Semigroupoid"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Semigroupoid</span> <span class='hs-varid'>c</span> <span class='hs-keyword'>where</span>
<a name="line-52"></a> <span class='hs-varid'>o</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>c</span> <span class='hs-varid'>j</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>c</span> <span class='hs-varid'>i</span> <span class='hs-varid'>j</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>c</span> <span class='hs-varid'>i</span> <span class='hs-varid'>k</span>
<a name="line-53"></a>
<a name="line-54"></a><a name="instance%20Semigroupoid%20(-%3e)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroupoid</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>-></span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-55"></a> <span class='hs-varid'>o</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'>.</span><span class='hs-layout'>)</span>
<a name="line-56"></a>
<a name="line-57"></a><a name="instance%20Semigroupoid%20(,)"></a><span class='hs-comment'>-- | <<a href="http://en.wikipedia.org/wiki/Band_(mathematics)#Rectangular_bands">http://en.wikipedia.org/wiki/Band_(mathematics)#Rectangular_bands</a>></span>
<a name="line-58"></a><a name="instance%20Semigroupoid%20(,)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroupoid</span> <span class='hs-conid'>(,)</span> <span class='hs-keyword'>where</span>
<a name="line-59"></a> <span class='hs-varid'>o</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span><span class='hs-varid'>k</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>i</span><span class='hs-layout'>,</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>i</span><span class='hs-layout'>,</span><span class='hs-varid'>k</span><span class='hs-layout'>)</span>
<a name="line-60"></a>
<a name="line-61"></a><a name="instance%20Semigroupoid%20(Kleisli%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Bind</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroupoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Kleisli</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-62"></a> <span class='hs-conid'>Kleisli</span> <span class='hs-varid'>g</span> <span class='hs-varop'>`o`</span> <span class='hs-conid'>Kleisli</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Kleisli</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-varop'>>>-</span> <span class='hs-varid'>g</span>
<a name="line-63"></a>
<a name="line-64"></a><span class='hs-cpp'>#ifdef MIN_VERSION_comonad</span>
<a name="line-65"></a><a name="instance%20Semigroupoid%20(Cokleisli%20w)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Extend</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroupoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-66"></a> <span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>f</span> <span class='hs-varop'>`o`</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-varop'>$</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>extended</span> <span class='hs-varid'>g</span>
<a name="line-67"></a><span class='hs-cpp'>#endif</span>
<a name="line-68"></a>
<a name="line-69"></a><span class='hs-cpp'>#ifdef MIN_VERSION_contravariant</span>
<a name="line-70"></a><a name="instance%20Semigroupoid%20Op"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroupoid</span> <span class='hs-conid'>Op</span> <span class='hs-keyword'>where</span>
<a name="line-71"></a> <span class='hs-conid'>Op</span> <span class='hs-varid'>f</span> <span class='hs-varop'>`o`</span> <span class='hs-conid'>Op</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varop'>`o`</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-72"></a><span class='hs-cpp'>#endif</span>
<a name="line-73"></a>
<a name="line-74"></a><a name="WrappedCategory"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>WrappedCategory</span> <span class='hs-varid'>k</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>WrapCategory</span> <span class='hs-layout'>{</span> <span class='hs-varid'>unwrapCategory</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>k</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-layout'>}</span>
<a name="line-75"></a>
<a name="line-76"></a><a name="instance%20Semigroupoid%20(WrappedCategory%20k)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Category</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroupoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>WrappedCategory</span> <span class='hs-varid'>k</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-77"></a> <span class='hs-conid'>WrapCategory</span> <span class='hs-varid'>f</span> <span class='hs-varop'>`o`</span> <span class='hs-conid'>WrapCategory</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>WrapCategory</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span>
<a name="line-78"></a>
<a name="line-79"></a><a name="instance%20Category%20(WrappedCategory%20k)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Category</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Category</span> <span class='hs-layout'>(</span><span class='hs-conid'>WrappedCategory</span> <span class='hs-varid'>k</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-80"></a> <span class='hs-varid'>id</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>WrapCategory</span> <span class='hs-varid'>id</span>
<a name="line-81"></a> <span class='hs-conid'>WrapCategory</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-conid'>WrapCategory</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>WrapCategory</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span>
<a name="line-82"></a>
<a name="line-83"></a><a name="Semi"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Semi</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Semi</span> <span class='hs-layout'>{</span> <span class='hs-varid'>getSemi</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>m</span> <span class='hs-layout'>}</span>
<a name="line-84"></a>
<a name="line-85"></a><a name="instance%20Semigroupoid%20(Semi%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroupoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Semi</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-86"></a> <span class='hs-conid'>Semi</span> <span class='hs-varid'>m</span> <span class='hs-varop'>`o`</span> <span class='hs-conid'>Semi</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Semi</span> <span class='hs-layout'>(</span><span class='hs-varid'>m</span> <span class='hs-varop'><></span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-87"></a>
<a name="line-88"></a><a name="instance%20Category%20(Semi%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Category</span> <span class='hs-layout'>(</span><span class='hs-conid'>Semi</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-89"></a> <span class='hs-varid'>id</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Semi</span> <span class='hs-varid'>mempty</span>
<a name="line-90"></a> <span class='hs-conid'>Semi</span> <span class='hs-varid'>m</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Semi</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Semi</span> <span class='hs-layout'>(</span><span class='hs-varid'>m</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-91"></a>
<a name="line-92"></a><a name="instance%20Semigroupoid%20Const"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroupoid</span> <span class='hs-conid'>Const</span> <span class='hs-keyword'>where</span>
<a name="line-93"></a> <span class='hs-keyword'>_</span> <span class='hs-varop'>`o`</span> <span class='hs-conid'>Const</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Const</span> <span class='hs-varid'>a</span>
<a name="line-94"></a>
<a name="line-95"></a><span class='hs-cpp'>#ifdef MIN_VERSION_tagged</span>
<a name="line-96"></a><a name="instance%20Semigroupoid%20Tagged"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroupoid</span> <span class='hs-conid'>Tagged</span> <span class='hs-keyword'>where</span>
<a name="line-97"></a> <span class='hs-conid'>Tagged</span> <span class='hs-varid'>b</span> <span class='hs-varop'>`o`</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Tagged</span> <span class='hs-varid'>b</span>
<a name="line-98"></a><span class='hs-cpp'>#endif</span>
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