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<title>src/Data/Profunctor/Sieve.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE UndecidableInstances #-}</span>
<a name="line-2"></a><span class='hs-comment'>{-# LANGUAGE FlexibleInstances #-}</span>
<a name="line-3"></a><span class='hs-comment'>{-# LANGUAGE FlexibleContexts #-}</span>
<a name="line-4"></a><span class='hs-comment'>{-# LANGUAGE MultiParamTypeClasses #-}</span>
<a name="line-5"></a><span class='hs-comment'>{-# LANGUAGE FunctionalDependencies #-}</span>
<a name="line-6"></a><span class='hs-comment'>{-# LANGUAGE CPP #-}</span>
<a name="line-7"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ >= 702 && __GLASGOW_HASKELL__ <= 708</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><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-11"></a><span class='hs-comment'>-- |</span>
<a name="line-12"></a><span class='hs-comment'>-- Copyright : (C) 2015 Edward Kmett</span>
<a name="line-13"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-14"></a><span class='hs-comment'>--</span>
<a name="line-15"></a><span class='hs-comment'>-- Maintainer : Edward Kmett <ekmett@gmail.com></span>
<a name="line-16"></a><span class='hs-comment'>-- Stability : provisional</span>
<a name="line-17"></a><span class='hs-comment'>-- Portability : MPTCs, fundeps</span>
<a name="line-18"></a><span class='hs-comment'>--</span>
<a name="line-19"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-20"></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'>Sieve</span>
<a name="line-21"></a> <span class='hs-layout'>(</span> <span class='hs-conid'>Sieve</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-22"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Cosieve</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-23"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-24"></a>
<a name="line-25"></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-26"></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-27"></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-28"></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'>Identity</span>
<a name="line-29"></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-30"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Proxy</span>
<a name="line-31"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Tagged</span>
<a name="line-32"></a>
<a name="line-33"></a><a name="Sieve"></a><span class='hs-comment'>-- | A 'Profunctor' @p@ is a 'Sieve' __on__ @f@ if it is a subprofunctor of @'Star' f@.</span>
<a name="line-34"></a><a name="Sieve"></a><span class='hs-comment'>--</span>
<a name="line-35"></a><a name="Sieve"></a><span class='hs-comment'>-- That is to say it is a subset of @Hom(-,f=)@ closed under 'lmap' and 'rmap'.</span>
<a name="line-36"></a><a name="Sieve"></a><span class='hs-comment'>--</span>
<a name="line-37"></a><a name="Sieve"></a><span class='hs-comment'>-- Alternately, you can view it as a sieve __in__ the comma category @Hask/f@.</span>
<a name="line-38"></a><a name="Sieve"></a><span class='hs-keyword'>class</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-conid'>Sieve</span> <span class='hs-varid'>p</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-keyword'>where</span>
<a name="line-39"></a> <span class='hs-varid'>sieve</span> <span class='hs-keyglyph'>::</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'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span>
<a name="line-40"></a>
<a name="line-41"></a><a name="instance%20Sieve%20(-%3e)%20Identity"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Sieve</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>-></span><span class='hs-layout'>)</span> <span class='hs-conid'>Identity</span> <span class='hs-keyword'>where</span>
<a name="line-42"></a> <span class='hs-varid'>sieve</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Identity</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-43"></a> <span class='hs-comment'>{-# INLINE sieve #-}</span>
<a name="line-44"></a>
<a name="line-45"></a><a name="instance%20Sieve%20(Kleisli%20m)%20m"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>m</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'>Kleisli</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varid'>m</span> <span class='hs-keyword'>where</span>
<a name="line-46"></a> <span class='hs-varid'>sieve</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runKleisli</span>
<a name="line-47"></a> <span class='hs-comment'>{-# INLINE sieve #-}</span>
<a name="line-48"></a>
<a name="line-49"></a><a name="instance%20Sieve%20(Star%20f)%20f"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Sieve</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-varid'>f</span> <span class='hs-keyword'>where</span>
<a name="line-50"></a> <span class='hs-varid'>sieve</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runStar</span>
<a name="line-51"></a> <span class='hs-comment'>{-# INLINE sieve #-}</span>
<a name="line-52"></a>
<a name="line-53"></a><a name="instance%20Sieve%20(Forget%20r)%20(Const%20r)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Sieve</span> <span class='hs-layout'>(</span><span class='hs-conid'>Forget</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Const</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-54"></a> <span class='hs-varid'>sieve</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>Const</span> <span class='hs-varop'>.</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>runForget</span>
<a name="line-55"></a> <span class='hs-comment'>{-# INLINE sieve #-}</span>
<a name="line-56"></a>
<a name="line-57"></a><a name="Cosieve"></a><span class='hs-comment'>-- | A 'Profunctor' @p@ is a 'Cosieve' __on__ @f@ if it is a subprofunctor of @'Costar' f@.</span>
<a name="line-58"></a><a name="Cosieve"></a><span class='hs-comment'>--</span>
<a name="line-59"></a><a name="Cosieve"></a><span class='hs-comment'>-- That is to say it is a subset of @Hom(f-,=)@ closed under 'lmap' and 'rmap'.</span>
<a name="line-60"></a><a name="Cosieve"></a><span class='hs-comment'>--</span>
<a name="line-61"></a><a name="Cosieve"></a><span class='hs-comment'>-- Alternately, you can view it as a cosieve __in__ the comma category @f/Hask@.</span>
<a name="line-62"></a><a name="Cosieve"></a><span class='hs-keyword'>class</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-conid'>Cosieve</span> <span class='hs-varid'>p</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-keyword'>where</span>
<a name="line-63"></a> <span class='hs-varid'>cosieve</span> <span class='hs-keyglyph'>::</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'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span>
<a name="line-64"></a>
<a name="line-65"></a><a name="instance%20Cosieve%20(-%3e)%20Identity"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Cosieve</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>-></span><span class='hs-layout'>)</span> <span class='hs-conid'>Identity</span> <span class='hs-keyword'>where</span>
<a name="line-66"></a> <span class='hs-varid'>cosieve</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Identity</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>d</span>
<a name="line-67"></a> <span class='hs-comment'>{-# INLINE cosieve #-}</span>
<a name="line-68"></a>
<a name="line-69"></a><a name="instance%20Cosieve%20(Cokleisli%20w)%20w"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Cosieve</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-varid'>w</span> <span class='hs-keyword'>where</span>
<a name="line-70"></a> <span class='hs-varid'>cosieve</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runCokleisli</span>
<a name="line-71"></a> <span class='hs-comment'>{-# INLINE cosieve #-}</span>
<a name="line-72"></a>
<a name="line-73"></a><a name="instance%20Cosieve%20Tagged%20Proxy"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Cosieve</span> <span class='hs-conid'>Tagged</span> <span class='hs-conid'>Proxy</span> <span class='hs-keyword'>where</span>
<a name="line-74"></a> <span class='hs-varid'>cosieve</span> <span class='hs-layout'>(</span><span class='hs-conid'>Tagged</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-75"></a> <span class='hs-comment'>{-# INLINE cosieve #-}</span>
<a name="line-76"></a>
<a name="line-77"></a><a name="instance%20Cosieve%20(Costar%20f)%20f"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Cosieve</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-varid'>f</span> <span class='hs-keyword'>where</span>
<a name="line-78"></a> <span class='hs-varid'>cosieve</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runCostar</span>
<a name="line-79"></a> <span class='hs-comment'>{-# INLINE cosieve #-}</span>
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