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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE CPP #-}</span>
<a name="line-2"></a><span class='hs-comment'>{-# LANGUAGE GADTs #-}</span>
<a name="line-3"></a><span class='hs-comment'>{-# LANGUAGE RankNTypes #-}</span>
<a name="line-4"></a><span class='hs-comment'>{-# LANGUAGE TypeFamilies #-}</span>
<a name="line-5"></a><span class='hs-comment'>{-# LANGUAGE TypeOperators #-}</span>
<a name="line-6"></a><span class='hs-comment'>{-# LANGUAGE MultiParamTypeClasses #-}</span>
<a name="line-7"></a><span class='hs-comment'>{-# LANGUAGE UndecidableInstances #-}</span>
<a name="line-8"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ >= 702 && __GLASGOW_HASKELL__ <= 708</span>
<a name="line-9"></a><span class='hs-comment'>{-# LANGUAGE Trustworthy #-}</span>
<a name="line-10"></a><span class='hs-cpp'>#endif</span>
<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.Profunctor.Composition</span>
<a name="line-14"></a><span class='hs-comment'>-- Copyright : (C) 2014 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 : experimental</span>
<a name="line-19"></a><span class='hs-comment'>-- Portability : GADTs, TFs, MPTCs, RankN</span>
<a name="line-20"></a><span class='hs-comment'>--</span>
<a name="line-21"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-22"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Profunctor</span><span class='hs-varop'>.</span><span class='hs-conid'>Composition</span>
<a name="line-23"></a> <span class='hs-layout'>(</span>
<a name="line-24"></a> <span class='hs-comment'>-- * Profunctor Composition</span>
<a name="line-25"></a> <span class='hs-conid'>Procompose</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-varid'>procomposed</span>
<a name="line-27"></a> <span class='hs-comment'>-- * Unitors and Associator</span>
<a name="line-28"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>idl</span>
<a name="line-29"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>idr</span>
<a name="line-30"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>assoc</span>
<a name="line-31"></a> <span class='hs-comment'>-- * Generalized Composition</span>
<a name="line-32"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>stars</span><span class='hs-layout'>,</span> <span class='hs-varid'>kleislis</span>
<a name="line-33"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>costars</span><span class='hs-layout'>,</span> <span class='hs-varid'>cokleislis</span>
<a name="line-34"></a> <span class='hs-comment'>-- * Right Kan Lift</span>
<a name="line-35"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Rift</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-36"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>decomposeRift</span>
<a name="line-37"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-38"></a>
<a name="line-39"></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-40"></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-41"></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-42"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span> <span class='hs-layout'>(</span><span class='hs-varid'>liftM</span><span class='hs-layout'>)</span>
<a name="line-43"></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'>Compose</span>
<a name="line-44"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Profunctor</span>
<a name="line-45"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Profunctor</span><span class='hs-varop'>.</span><span class='hs-conid'>Adjunction</span>
<a name="line-46"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Profunctor</span><span class='hs-varop'>.</span><span class='hs-conid'>Closed</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'>Profunctor</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span>
<a name="line-48"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Profunctor</span><span class='hs-varop'>.</span><span class='hs-conid'>Rep</span>
<a name="line-49"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Profunctor</span><span class='hs-varop'>.</span><span class='hs-conid'>Sieve</span>
<a name="line-50"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Profunctor</span><span class='hs-varop'>.</span><span class='hs-conid'>Unsafe</span>
<a name="line-51"></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-layout'>(</span><span class='hs-varop'>.</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span><span class='hs-varid'>id</span><span class='hs-layout'>)</span>
<a name="line-52"></a>
<a name="line-53"></a><a name="Iso"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Iso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>p</span> <span class='hs-varid'>f</span><span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-conid'>Profunctor</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>p</span> <span class='hs-varid'>a</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>p</span> <span class='hs-varid'>s</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span>
<a name="line-54"></a>
<a name="line-55"></a><span class='hs-comment'>-- * Profunctor Composition</span>
<a name="line-56"></a>
<a name="line-57"></a><a name="Procompose"></a><span class='hs-comment'>-- | @'Procompose' p q@ is the 'Profunctor' composition of the</span>
<a name="line-58"></a><a name="Procompose"></a><span class='hs-comment'>-- 'Profunctor's @p@ and @q@.</span>
<a name="line-59"></a><a name="Procompose"></a><span class='hs-comment'>--</span>
<a name="line-60"></a><a name="Procompose"></a><span class='hs-comment'>-- For a good explanation of 'Profunctor' composition in Haskell</span>
<a name="line-61"></a><a name="Procompose"></a><span class='hs-comment'>-- see Dan Piponi's article:</span>
<a name="line-62"></a><a name="Procompose"></a><span class='hs-comment'>--</span>
<a name="line-63"></a><a name="Procompose"></a><span class='hs-comment'>-- <<a href="http://blog.sigfpe.com/2011/07/profunctors-in-haskell.html">http://blog.sigfpe.com/2011/07/profunctors-in-haskell.html</a>></span>
<a name="line-64"></a><a name="Procompose"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span> <span class='hs-varid'>d</span> <span class='hs-varid'>c</span> <span class='hs-keyword'>where</span>
<a name="line-65"></a> <span class='hs-conid'>Procompose</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>p</span> <span class='hs-varid'>x</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>q</span> <span class='hs-varid'>d</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span> <span class='hs-varid'>d</span> <span class='hs-varid'>c</span>
<a name="line-66"></a>
<a name="line-67"></a><a name="instance%20ProfunctorFunctor%20(Procompose%20p)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>ProfunctorFunctor</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-68"></a> <span class='hs-varid'>promap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span>
<a name="line-69"></a>
<a name="line-70"></a><a name="instance%20ProfunctorMonad%20(Procompose%20p)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Category</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>ProfunctorMonad</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-71"></a> <span class='hs-varid'>proreturn</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-varid'>id</span>
<a name="line-72"></a> <span class='hs-varid'>projoin</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>q</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span> <span class='hs-varop'>.</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-varid'>r</span>
<a name="line-73"></a>
<a name="line-74"></a><a name="procomposed"></a><span class='hs-definition'>procomposed</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Category</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>p</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>p</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-75"></a><span class='hs-definition'>procomposed</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>pxc</span> <span class='hs-varid'>pdx</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pxc</span> <span class='hs-varop'>.</span> <span class='hs-varid'>pdx</span>
<a name="line-76"></a><span class='hs-comment'>{-# INLINE procomposed #-}</span>
<a name="line-77"></a>
<a name="line-78"></a><a name="instance%20Profunctor%20(Procompose%20p%20q)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Profunctor</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-conid'>Profunctor</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Profunctor</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-79"></a> <span class='hs-varid'>dimap</span> <span class='hs-varid'>l</span> <span class='hs-varid'>r</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-varid'>rmap</span> <span class='hs-varid'>r</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>lmap</span> <span class='hs-varid'>l</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span>
<a name="line-80"></a> <span class='hs-comment'>{-# INLINE dimap #-}</span>
<a name="line-81"></a> <span class='hs-varid'>lmap</span> <span class='hs-varid'>k</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>lmap</span> <span class='hs-varid'>k</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span>
<a name="line-82"></a> <span class='hs-comment'>{-# INLINE rmap #-}</span>
<a name="line-83"></a> <span class='hs-varid'>rmap</span> <span class='hs-varid'>k</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-varid'>rmap</span> <span class='hs-varid'>k</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>g</span>
<a name="line-84"></a> <span class='hs-comment'>{-# INLINE lmap #-}</span>
<a name="line-85"></a> <span class='hs-varid'>k</span> <span class='hs-cpp'>#.</span> <span class='hs-conid'>Procompose</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-varid'>k</span> <span class='hs-cpp'>#.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>g</span>
<a name="line-86"></a> <span class='hs-comment'>{-# INLINE ( #. ) #-}</span>
<a name="line-87"></a> <span class='hs-conid'>Procompose</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varop'>.#</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varop'>.#</span> <span class='hs-varid'>k</span><span class='hs-layout'>)</span>
<a name="line-88"></a> <span class='hs-comment'>{-# INLINE ( .# ) #-}</span>
<a name="line-89"></a>
<a name="line-90"></a><a name="instance%20Functor%20(Procompose%20p%20q%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Profunctor</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Functor</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-91"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>k</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-varid'>rmap</span> <span class='hs-varid'>k</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>g</span>
<a name="line-92"></a> <span class='hs-comment'>{-# INLINE fmap #-}</span>
<a name="line-93"></a>
<a name="line-94"></a><a name="instance%20Sieve%20(Procompose%20p%20q)%20(Compose%20g%20f)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sieve</span> <span class='hs-varid'>p</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Sieve</span> <span class='hs-varid'>q</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Sieve</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Compose</span> <span class='hs-varid'>g</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-95"></a> <span class='hs-varid'>sieve</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>g</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>d</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Compose</span> <span class='hs-varop'>$</span> <span class='hs-varid'>sieve</span> <span class='hs-varid'>g</span> <span class='hs-varop'><$></span> <span class='hs-varid'>sieve</span> <span class='hs-varid'>f</span> <span class='hs-varid'>d</span>
<a name="line-96"></a> <span class='hs-comment'>{-# INLINE sieve #-}</span>
<a name="line-97"></a>
<a name="line-98"></a><a name="instance%20Representable%20(Procompose%20p%20q)"></a><span class='hs-comment'>-- | The composition of two 'Representable' 'Profunctor's is 'Representable' by</span>
<a name="line-99"></a><a name="instance%20Representable%20(Procompose%20p%20q)"></a><span class='hs-comment'>-- the composition of their representations.</span>
<a name="line-100"></a><a name="instance%20Representable%20(Procompose%20p%20q)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Representable</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-conid'>Representable</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Representable</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-101"></a> <span class='hs-keyword'>type</span> <span class='hs-conid'>Rep</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Compose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rep</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rep</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span>
<a name="line-102"></a> <span class='hs-varid'>tabulate</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-varid'>tabulate</span> <span class='hs-varid'>id</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>tabulate</span> <span class='hs-layout'>(</span><span class='hs-varid'>getCompose</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-103"></a> <span class='hs-comment'>{-# INLINE tabulate #-}</span>
<a name="line-104"></a>
<a name="line-105"></a><a name="instance%20Cosieve%20(Procompose%20p%20q)%20(Compose%20f%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cosieve</span> <span class='hs-varid'>p</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Cosieve</span> <span class='hs-varid'>q</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Cosieve</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Compose</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-106"></a> <span class='hs-varid'>cosieve</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>g</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Compose</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>cosieve</span> <span class='hs-varid'>g</span> <span class='hs-varop'>$</span> <span class='hs-varid'>cosieve</span> <span class='hs-varid'>f</span> <span class='hs-varop'><$></span> <span class='hs-varid'>d</span>
<a name="line-107"></a> <span class='hs-comment'>{-# INLINE cosieve #-}</span>
<a name="line-108"></a>
<a name="line-109"></a><a name="instance%20Corepresentable%20(Procompose%20p%20q)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Corepresentable</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-conid'>Corepresentable</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Corepresentable</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-110"></a> <span class='hs-keyword'>type</span> <span class='hs-conid'>Corep</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Compose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Corep</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Corep</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span>
<a name="line-111"></a> <span class='hs-varid'>cotabulate</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-varid'>cotabulate</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Compose</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>cotabulate</span> <span class='hs-varid'>id</span><span class='hs-layout'>)</span>
<a name="line-112"></a> <span class='hs-comment'>{-# INLINE cotabulate #-}</span>
<a name="line-113"></a>
<a name="line-114"></a><a name="instance%20Strong%20(Procompose%20p%20q)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Strong</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-conid'>Strong</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Strong</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-115"></a> <span class='hs-varid'>first'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-varid'>first'</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>first'</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-116"></a> <span class='hs-comment'>{-# INLINE first' #-}</span>
<a name="line-117"></a> <span class='hs-varid'>second'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-varid'>second'</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>second'</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-118"></a> <span class='hs-comment'>{-# INLINE second' #-}</span>
<a name="line-119"></a>
<a name="line-120"></a><a name="instance%20Choice%20(Procompose%20p%20q)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Choice</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-conid'>Choice</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Choice</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-121"></a> <span class='hs-varid'>left'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-varid'>left'</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>left'</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-122"></a> <span class='hs-comment'>{-# INLINE left' #-}</span>
<a name="line-123"></a> <span class='hs-varid'>right'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-varid'>right'</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>right'</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-124"></a> <span class='hs-comment'>{-# INLINE right' #-}</span>
<a name="line-125"></a>
<a name="line-126"></a><a name="instance%20Closed%20(Procompose%20p%20q)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Closed</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-conid'>Closed</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Closed</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-127"></a> <span class='hs-varid'>closed</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-varid'>closed</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>closed</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-128"></a> <span class='hs-comment'>{-# INLINE closed #-}</span>
<a name="line-129"></a>
<a name="line-130"></a><a name="instance%20Costrong%20(Procompose%20p%20q)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Corepresentable</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-conid'>Corepresentable</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Costrong</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-131"></a> <span class='hs-varid'>unfirst</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unfirstCorep</span>
<a name="line-132"></a> <span class='hs-varid'>unsecond</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unsecondCorep</span>
<a name="line-133"></a>
<a name="line-134"></a><span class='hs-comment'>-- * Lax identity</span>
<a name="line-135"></a>
<a name="line-136"></a><a name="idl"></a><span class='hs-comment'>-- | @(->)@ functions as a lax identity for 'Profunctor' composition.</span>
<a name="line-137"></a><span class='hs-comment'>--</span>
<a name="line-138"></a><span class='hs-comment'>-- This provides an 'Iso' for the @lens@ package that witnesses the</span>
<a name="line-139"></a><span class='hs-comment'>-- isomorphism between @'Procompose' (->) q d c@ and @q d c@, which</span>
<a name="line-140"></a><span class='hs-comment'>-- is the left identity law.</span>
<a name="line-141"></a><span class='hs-comment'>--</span>
<a name="line-142"></a><span class='hs-comment'>-- @</span>
<a name="line-143"></a><span class='hs-comment'>-- 'idl' :: 'Profunctor' q => Iso' ('Procompose' (->) q d c) (q d c)</span>
<a name="line-144"></a><span class='hs-comment'>-- @</span>
<a name="line-145"></a><span class='hs-definition'>idl</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Profunctor</span> <span class='hs-varid'>q</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>-></span><span class='hs-layout'>)</span> <span class='hs-varid'>q</span> <span class='hs-varid'>d</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>-></span><span class='hs-layout'>)</span> <span class='hs-varid'>r</span> <span class='hs-varid'>d'</span> <span class='hs-varid'>c'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>q</span> <span class='hs-varid'>d</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>r</span> <span class='hs-varid'>d'</span> <span class='hs-varid'>c'</span><span class='hs-layout'>)</span>
<a name="line-146"></a><span class='hs-definition'>idl</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>dimap</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>g</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>rmap</span> <span class='hs-varid'>g</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>id</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-147"></a>
<a name="line-148"></a><a name="idr"></a><span class='hs-comment'>-- | @(->)@ functions as a lax identity for 'Profunctor' composition.</span>
<a name="line-149"></a><span class='hs-comment'>--</span>
<a name="line-150"></a><span class='hs-comment'>-- This provides an 'Iso' for the @lens@ package that witnesses the</span>
<a name="line-151"></a><span class='hs-comment'>-- isomorphism between @'Procompose' q (->) d c@ and @q d c@, which</span>
<a name="line-152"></a><span class='hs-comment'>-- is the right identity law.</span>
<a name="line-153"></a><span class='hs-comment'>--</span>
<a name="line-154"></a><span class='hs-comment'>-- @</span>
<a name="line-155"></a><span class='hs-comment'>-- 'idr' :: 'Profunctor' q => Iso' ('Procompose' q (->) d c) (q d c)</span>
<a name="line-156"></a><span class='hs-comment'>-- @</span>
<a name="line-157"></a><span class='hs-definition'>idr</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Profunctor</span> <span class='hs-varid'>q</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>q</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>-></span><span class='hs-layout'>)</span> <span class='hs-varid'>d</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>r</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>-></span><span class='hs-layout'>)</span> <span class='hs-varid'>d'</span> <span class='hs-varid'>c'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>q</span> <span class='hs-varid'>d</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>r</span> <span class='hs-varid'>d'</span> <span class='hs-varid'>c'</span><span class='hs-layout'>)</span>
<a name="line-158"></a><span class='hs-definition'>idr</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>dimap</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>g</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>lmap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varop'>`Procompose`</span> <span class='hs-varid'>id</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-159"></a>
<a name="line-160"></a>
<a name="line-161"></a><a name="assoc"></a><span class='hs-comment'>-- | The associator for 'Profunctor' composition.</span>
<a name="line-162"></a><span class='hs-comment'>--</span>
<a name="line-163"></a><span class='hs-comment'>-- This provides an 'Iso' for the @lens@ package that witnesses the</span>
<a name="line-164"></a><span class='hs-comment'>-- isomorphism between @'Procompose' p ('Procompose' q r) a b@ and</span>
<a name="line-165"></a><span class='hs-comment'>-- @'Procompose' ('Procompose' p q) r a b@, which arises because</span>
<a name="line-166"></a><span class='hs-comment'>-- @Prof@ is only a bicategory, rather than a strict 2-category.</span>
<a name="line-167"></a><span class='hs-definition'>assoc</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>q</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>x</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>y</span> <span class='hs-varid'>z</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-168"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-varid'>z</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-169"></a><span class='hs-definition'>assoc</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>dimap</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>g</span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span>
<a name="line-170"></a> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Procompose</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>g</span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-171"></a>
<a name="line-172"></a><a name="stars"></a><span class='hs-comment'>-- | 'Profunctor' composition generalizes 'Functor' composition in two ways.</span>
<a name="line-173"></a><span class='hs-comment'>--</span>
<a name="line-174"></a><span class='hs-comment'>-- This is the first, which shows that @exists b. (a -> f b, b -> g c)@ is</span>
<a name="line-175"></a><span class='hs-comment'>-- isomorphic to @a -> f (g c)@.</span>
<a name="line-176"></a><span class='hs-comment'>--</span>
<a name="line-177"></a><span class='hs-comment'>-- @'stars' :: 'Functor' f => Iso' ('Procompose' ('Star' f) ('Star' g) d c) ('Star' ('Compose' f g) d c)@</span>
<a name="line-178"></a><span class='hs-definition'>stars</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>g</span>
<a name="line-179"></a> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Star</span> <span class='hs-varid'>f</span> <span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Star</span> <span class='hs-varid'>g</span> <span class='hs-layout'>)</span> <span class='hs-varid'>d</span> <span class='hs-varid'>c</span> <span class='hs-layout'>)</span>
<a name="line-180"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Star</span> <span class='hs-varid'>f'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Star</span> <span class='hs-varid'>g'</span><span class='hs-layout'>)</span> <span class='hs-varid'>d'</span> <span class='hs-varid'>c'</span><span class='hs-layout'>)</span>
<a name="line-181"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Star</span> <span class='hs-layout'>(</span><span class='hs-conid'>Compose</span> <span class='hs-varid'>g</span> <span class='hs-varid'>f</span> <span class='hs-layout'>)</span> <span class='hs-varid'>d</span> <span class='hs-varid'>c</span> <span class='hs-layout'>)</span>
<a name="line-182"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Star</span> <span class='hs-layout'>(</span><span class='hs-conid'>Compose</span> <span class='hs-varid'>g'</span> <span class='hs-varid'>f'</span><span class='hs-layout'>)</span> <span class='hs-varid'>d'</span> <span class='hs-varid'>c'</span><span class='hs-layout'>)</span>
<a name="line-183"></a><span class='hs-definition'>stars</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>dimap</span> <span class='hs-varid'>hither</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>yon</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-184"></a> <span class='hs-varid'>hither</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Star</span> <span class='hs-varid'>xgc</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Star</span> <span class='hs-varid'>dfx</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Star</span> <span class='hs-layout'>(</span><span class='hs-conid'>Compose</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>xgc</span> <span class='hs-varop'>.</span> <span class='hs-varid'>dfx</span><span class='hs-layout'>)</span>
<a name="line-185"></a> <span class='hs-varid'>yon</span> <span class='hs-layout'>(</span><span class='hs-conid'>Star</span> <span class='hs-varid'>dfgc</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Star</span> <span class='hs-varid'>id</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Star</span> <span class='hs-layout'>(</span><span class='hs-varid'>getCompose</span> <span class='hs-varop'>.</span> <span class='hs-varid'>dfgc</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-186"></a>
<a name="line-187"></a><a name="costars"></a><span class='hs-comment'>-- | 'Profunctor' composition generalizes 'Functor' composition in two ways.</span>
<a name="line-188"></a><span class='hs-comment'>--</span>
<a name="line-189"></a><span class='hs-comment'>-- This is the second, which shows that @exists b. (f a -> b, g b -> c)@ is</span>
<a name="line-190"></a><span class='hs-comment'>-- isomorphic to @g (f a) -> c@.</span>
<a name="line-191"></a><span class='hs-comment'>--</span>
<a name="line-192"></a><span class='hs-comment'>-- @'costars' :: 'Functor' f => Iso' ('Procompose' ('Costar' f) ('Costar' g) d c) ('Costar' ('Compose' g f) d c)@</span>
<a name="line-193"></a><span class='hs-definition'>costars</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>f</span>
<a name="line-194"></a> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Costar</span> <span class='hs-varid'>f</span> <span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Costar</span> <span class='hs-varid'>g</span> <span class='hs-layout'>)</span> <span class='hs-varid'>d</span> <span class='hs-varid'>c</span> <span class='hs-layout'>)</span>
<a name="line-195"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Costar</span> <span class='hs-varid'>f'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Costar</span> <span class='hs-varid'>g'</span><span class='hs-layout'>)</span> <span class='hs-varid'>d'</span> <span class='hs-varid'>c'</span><span class='hs-layout'>)</span>
<a name="line-196"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Costar</span> <span class='hs-layout'>(</span><span class='hs-conid'>Compose</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-layout'>)</span> <span class='hs-varid'>d</span> <span class='hs-varid'>c</span> <span class='hs-layout'>)</span>
<a name="line-197"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Costar</span> <span class='hs-layout'>(</span><span class='hs-conid'>Compose</span> <span class='hs-varid'>f'</span> <span class='hs-varid'>g'</span><span class='hs-layout'>)</span> <span class='hs-varid'>d'</span> <span class='hs-varid'>c'</span><span class='hs-layout'>)</span>
<a name="line-198"></a><span class='hs-definition'>costars</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>dimap</span> <span class='hs-varid'>hither</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>yon</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-199"></a> <span class='hs-varid'>hither</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Costar</span> <span class='hs-varid'>gxc</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Costar</span> <span class='hs-varid'>fdx</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Costar</span> <span class='hs-layout'>(</span><span class='hs-varid'>gxc</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>fdx</span> <span class='hs-varop'>.</span> <span class='hs-varid'>getCompose</span><span class='hs-layout'>)</span>
<a name="line-200"></a> <span class='hs-varid'>yon</span> <span class='hs-layout'>(</span><span class='hs-conid'>Costar</span> <span class='hs-varid'>dgfc</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Costar</span> <span class='hs-layout'>(</span><span class='hs-varid'>dgfc</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Compose</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Costar</span> <span class='hs-varid'>id</span><span class='hs-layout'>)</span>
<a name="line-201"></a>
<a name="line-202"></a><a name="kleislis"></a><span class='hs-comment'>-- | This is a variant on 'stars' that uses 'Kleisli' instead of 'Star'.</span>
<a name="line-203"></a><span class='hs-comment'>--</span>
<a name="line-204"></a><span class='hs-comment'>-- @'kleislis' :: 'Monad' f => Iso' ('Procompose' ('Kleisli' f) ('Kleisli' g) d c) ('Kleisli' ('Compose' f g) d c)@</span>
<a name="line-205"></a><span class='hs-definition'>kleislis</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>g</span>
<a name="line-206"></a> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Kleisli</span> <span class='hs-varid'>f</span> <span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Kleisli</span> <span class='hs-varid'>g</span> <span class='hs-layout'>)</span> <span class='hs-varid'>d</span> <span class='hs-varid'>c</span> <span class='hs-layout'>)</span>
<a name="line-207"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Kleisli</span> <span class='hs-varid'>f'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Kleisli</span> <span class='hs-varid'>g'</span><span class='hs-layout'>)</span> <span class='hs-varid'>d'</span> <span class='hs-varid'>c'</span><span class='hs-layout'>)</span>
<a name="line-208"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Kleisli</span> <span class='hs-layout'>(</span><span class='hs-conid'>Compose</span> <span class='hs-varid'>g</span> <span class='hs-varid'>f</span> <span class='hs-layout'>)</span> <span class='hs-varid'>d</span> <span class='hs-varid'>c</span> <span class='hs-layout'>)</span>
<a name="line-209"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Kleisli</span> <span class='hs-layout'>(</span><span class='hs-conid'>Compose</span> <span class='hs-varid'>g'</span> <span class='hs-varid'>f'</span><span class='hs-layout'>)</span> <span class='hs-varid'>d'</span> <span class='hs-varid'>c'</span><span class='hs-layout'>)</span>
<a name="line-210"></a><span class='hs-definition'>kleislis</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>dimap</span> <span class='hs-varid'>hither</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>yon</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-211"></a> <span class='hs-varid'>hither</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Kleisli</span> <span class='hs-varid'>xgc</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Kleisli</span> <span class='hs-varid'>dfx</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Kleisli</span> <span class='hs-layout'>(</span><span class='hs-conid'>Compose</span> <span class='hs-varop'>.</span> <span class='hs-varid'>liftM</span> <span class='hs-varid'>xgc</span> <span class='hs-varop'>.</span> <span class='hs-varid'>dfx</span><span class='hs-layout'>)</span>
<a name="line-212"></a> <span class='hs-varid'>yon</span> <span class='hs-layout'>(</span><span class='hs-conid'>Kleisli</span> <span class='hs-varid'>dfgc</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Kleisli</span> <span class='hs-varid'>id</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Kleisli</span> <span class='hs-layout'>(</span><span class='hs-varid'>getCompose</span> <span class='hs-varop'>.</span> <span class='hs-varid'>dfgc</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-213"></a>
<a name="line-214"></a><a name="cokleislis"></a><span class='hs-comment'>-- | This is a variant on 'costars' that uses 'Cokleisli' instead</span>
<a name="line-215"></a><span class='hs-comment'>-- of 'Costar'.</span>
<a name="line-216"></a><span class='hs-comment'>--</span>
<a name="line-217"></a><span class='hs-comment'>-- @'cokleislis' :: 'Functor' f => Iso' ('Procompose' ('Cokleisli' f) ('Cokleisli' g) d c) ('Cokleisli' ('Compose' g f) d c)@</span>
<a name="line-218"></a><span class='hs-definition'>cokleislis</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>f</span>
<a name="line-219"></a> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>f</span> <span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>g</span> <span class='hs-layout'>)</span> <span class='hs-varid'>d</span> <span class='hs-varid'>c</span> <span class='hs-layout'>)</span>
<a name="line-220"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>f'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>g'</span><span class='hs-layout'>)</span> <span class='hs-varid'>d'</span> <span class='hs-varid'>c'</span><span class='hs-layout'>)</span>
<a name="line-221"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-layout'>(</span><span class='hs-conid'>Compose</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-layout'>)</span> <span class='hs-varid'>d</span> <span class='hs-varid'>c</span> <span class='hs-layout'>)</span>
<a name="line-222"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-layout'>(</span><span class='hs-conid'>Compose</span> <span class='hs-varid'>f'</span> <span class='hs-varid'>g'</span><span class='hs-layout'>)</span> <span class='hs-varid'>d'</span> <span class='hs-varid'>c'</span><span class='hs-layout'>)</span>
<a name="line-223"></a><span class='hs-definition'>cokleislis</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>dimap</span> <span class='hs-varid'>hither</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>yon</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-224"></a> <span class='hs-varid'>hither</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>gxc</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>fdx</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-layout'>(</span><span class='hs-varid'>gxc</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>fdx</span> <span class='hs-varop'>.</span> <span class='hs-varid'>getCompose</span><span class='hs-layout'>)</span>
<a name="line-225"></a> <span class='hs-varid'>yon</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>dgfc</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Procompose</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-layout'>(</span><span class='hs-varid'>dgfc</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Compose</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>id</span><span class='hs-layout'>)</span>
<a name="line-226"></a>
<a name="line-227"></a><a name="Rift"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-228"></a><a name="Rift"></a><span class='hs-comment'>-- * Rift</span>
<a name="line-229"></a><a name="Rift"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-230"></a><a name="Rift"></a><span class='hs-comment'>-- | This represents the right Kan lift of a 'Profunctor' @q@ along a 'Profunctor' @p@ in a limited version of the 2-category of Profunctors where the only object is the category Hask, 1-morphisms are profunctors composed and compose with Profunctor composition, and 2-morphisms are just natural transformations.</span>
<a name="line-231"></a><a name="Rift"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Rift</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Rift</span> <span class='hs-layout'>{</span> <span class='hs-varid'>runRift</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>x</span><span class='hs-varop'>.</span> <span class='hs-varid'>p</span> <span class='hs-varid'>b</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>q</span> <span class='hs-varid'>a</span> <span class='hs-varid'>x</span> <span class='hs-layout'>}</span>
<a name="line-232"></a>
<a name="line-233"></a><a name="instance%20ProfunctorFunctor%20(Rift%20p)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>ProfunctorFunctor</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rift</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-234"></a> <span class='hs-varid'>promap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rift</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Rift</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-235"></a>
<a name="line-236"></a><a name="instance%20ProfunctorComonad%20(Rift%20p)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Category</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>ProfunctorComonad</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rift</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-237"></a> <span class='hs-varid'>proextract</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rift</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>id</span>
<a name="line-238"></a> <span class='hs-varid'>produplicate</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rift</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Rift</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>p</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Rift</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>q</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>q</span> <span class='hs-varop'>.</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span>
<a name="line-239"></a>
<a name="line-240"></a><a name="instance%20Profunctor%20(Rift%20p%20q)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Profunctor</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-conid'>Profunctor</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Profunctor</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rift</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-241"></a> <span class='hs-varid'>dimap</span> <span class='hs-varid'>ca</span> <span class='hs-varid'>bd</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Rift</span> <span class='hs-layout'>(</span><span class='hs-varid'>lmap</span> <span class='hs-varid'>ca</span> <span class='hs-varop'>.</span> <span class='hs-varid'>runRift</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>lmap</span> <span class='hs-varid'>bd</span><span class='hs-layout'>)</span>
<a name="line-242"></a> <span class='hs-comment'>{-# INLINE dimap #-}</span>
<a name="line-243"></a> <span class='hs-varid'>lmap</span> <span class='hs-varid'>ca</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Rift</span> <span class='hs-layout'>(</span><span class='hs-varid'>lmap</span> <span class='hs-varid'>ca</span> <span class='hs-varop'>.</span> <span class='hs-varid'>runRift</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-244"></a> <span class='hs-comment'>{-# INLINE lmap #-}</span>
<a name="line-245"></a> <span class='hs-varid'>rmap</span> <span class='hs-varid'>bd</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Rift</span> <span class='hs-layout'>(</span><span class='hs-varid'>runRift</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>lmap</span> <span class='hs-varid'>bd</span><span class='hs-layout'>)</span>
<a name="line-246"></a> <span class='hs-comment'>{-# INLINE rmap #-}</span>
<a name="line-247"></a> <span class='hs-varid'>bd</span> <span class='hs-cpp'>#.</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Rift</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>p</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>runRift</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span> <span class='hs-varop'>.#</span> <span class='hs-varid'>bd</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-248"></a> <span class='hs-comment'>{-# INLINE ( #. ) #-}</span>
<a name="line-249"></a> <span class='hs-varid'>f</span> <span class='hs-varop'>.#</span> <span class='hs-varid'>ca</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Rift</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>p</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>runRift</span> <span class='hs-varid'>f</span> <span class='hs-varid'>p</span> <span class='hs-varop'>.#</span> <span class='hs-varid'>ca</span><span class='hs-layout'>)</span>
<a name="line-250"></a> <span class='hs-comment'>{-# INLINE (.#) #-}</span>
<a name="line-251"></a>
<a name="line-252"></a><a name="instance%20Functor%20(Rift%20p%20q%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Profunctor</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Functor</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rift</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-253"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>bd</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Rift</span> <span class='hs-layout'>(</span><span class='hs-varid'>runRift</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>lmap</span> <span class='hs-varid'>bd</span><span class='hs-layout'>)</span>
<a name="line-254"></a> <span class='hs-comment'>{-# INLINE fmap #-}</span>
<a name="line-255"></a>
<a name="line-256"></a><a name="instance%20Category%20(Rift%20p%20q)"></a><span class='hs-comment'>-- | @'Rift' p p@ forms a 'Monad' in the 'Profunctor' 2-category, which is isomorphic to a Haskell 'Category' instance.</span>
<a name="line-257"></a><a name="instance%20Category%20(Rift%20p%20q)"></a><span class='hs-keyword'>instance</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>~</span> <span class='hs-varid'>q</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Category</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rift</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-258"></a> <span class='hs-varid'>id</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Rift</span> <span class='hs-varid'>id</span>
<a name="line-259"></a> <span class='hs-comment'>{-# INLINE id #-}</span>
<a name="line-260"></a> <span class='hs-conid'>Rift</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Rift</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Rift</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-261"></a> <span class='hs-comment'>{-# INLINE (.) #-}</span>
<a name="line-262"></a>
<a name="line-263"></a><a name="decomposeRift"></a><span class='hs-comment'>-- | The 2-morphism that defines a left Kan lift.</span>
<a name="line-264"></a><span class='hs-comment'>--</span>
<a name="line-265"></a><span class='hs-comment'>-- Note: When @p@ is right adjoint to @'Rift' p (->)@ then 'decomposeRift' is the 'counit' of the adjunction.</span>
<a name="line-266"></a><span class='hs-definition'>decomposeRift</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rift</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-conop'>:-></span> <span class='hs-varid'>q</span>
<a name="line-267"></a><span class='hs-definition'>decomposeRift</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rift</span> <span class='hs-varid'>pq</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pq</span> <span class='hs-varid'>p</span>
<a name="line-268"></a><span class='hs-comment'>{-# INLINE decomposeRift #-}</span>
<a name="line-269"></a>
<a name="line-270"></a><a name="instance%20ProfunctorAdjunction%20(Procompose%20p)%20(Rift%20p)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>ProfunctorAdjunction</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rift</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-271"></a> <span class='hs-varid'>counit</span> <span class='hs-layout'>(</span><span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rift</span> <span class='hs-varid'>pq</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pq</span> <span class='hs-varid'>p</span>
<a name="line-272"></a> <span class='hs-varid'>unit</span> <span class='hs-varid'>q</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Rift</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>p</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Procompose</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span>
<a name="line-273"></a>
<a name="line-274"></a><span class='hs-comment'>--instance (ProfunctorAdjunction f g, ProfunctorAdjunction f' g') => ProfunctorAdjunction (ProfunctorCompose f' f) (ProfunctorCompose g g') where</span>
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