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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 FlexibleContexts #-}</span>
<a name="line-3"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-4"></a><span class='hs-comment'>-- |</span>
<a name="line-5"></a><span class='hs-comment'>-- Module : Data.Distributive</span>
<a name="line-6"></a><span class='hs-comment'>-- Copyright : (C) 2011-2014 Edward Kmett</span>
<a name="line-7"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-8"></a><span class='hs-comment'>--</span>
<a name="line-9"></a><span class='hs-comment'>-- Maintainer : Edward Kmett <ekmett@gmail.com></span>
<a name="line-10"></a><span class='hs-comment'>-- Stability : provisional</span>
<a name="line-11"></a><span class='hs-comment'>-- Portability : portable</span>
<a name="line-12"></a><span class='hs-comment'>--</span>
<a name="line-13"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-14"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Distributive</span>
<a name="line-15"></a> <span class='hs-layout'>(</span> <span class='hs-conid'>Distributive</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-16"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>cotraverse</span>
<a name="line-17"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>comapM</span>
<a name="line-18"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-19"></a>
<a name="line-20"></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-21"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span><span class='hs-varop'>.</span><span class='hs-conid'>Backwards</span>
<a name="line-22"></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-23"></a><span class='hs-cpp'>#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ < 707</span>
<a name="line-24"></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-varop'>.</span><span class='hs-conid'>Instances</span> <span class='hs-conid'>()</span>
<a name="line-25"></a><span class='hs-cpp'>#endif</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'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Trans</span><span class='hs-varop'>.</span><span class='hs-conid'>Identity</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'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Trans</span><span class='hs-varop'>.</span><span class='hs-conid'>Reader</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'>Compose</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'>Functor</span><span class='hs-varop'>.</span><span class='hs-conid'>Identity</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'>Functor</span><span class='hs-varop'>.</span><span class='hs-conid'>Product</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'>Functor</span><span class='hs-varop'>.</span><span class='hs-conid'>Reverse</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'>Proxy</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'>Tagged</span>
<a name="line-34"></a>
<a name="line-35"></a><span class='hs-cpp'>#ifdef HLINT</span>
<a name="line-36"></a><span class='hs-comment'>{-# ANN module "hlint: ignore Use section" #-}</span>
<a name="line-37"></a><span class='hs-cpp'>#endif</span>
<a name="line-38"></a>
<a name="line-39"></a><a name="Distributive"></a><span class='hs-comment'>-- | This is the categorical dual of 'Traversable'.</span>
<a name="line-40"></a><a name="Distributive"></a><span class='hs-comment'>--</span>
<a name="line-41"></a><a name="Distributive"></a><span class='hs-comment'>-- Due to the lack of non-trivial comonoids in Haskell, we can restrict</span>
<a name="line-42"></a><a name="Distributive"></a><span class='hs-comment'>-- ourselves to requiring a 'Functor' rather than</span>
<a name="line-43"></a><a name="Distributive"></a><span class='hs-comment'>-- some Coapplicative class. Categorically every 'Distributive'</span>
<a name="line-44"></a><a name="Distributive"></a><span class='hs-comment'>-- functor is actually a right adjoint, and so it must be 'Representable'</span>
<a name="line-45"></a><a name="Distributive"></a><span class='hs-comment'>-- endofunctor and preserve all limits. This is a fancy way of saying it</span>
<a name="line-46"></a><a name="Distributive"></a><span class='hs-comment'>-- isomorphic to `(->) x` for some x.</span>
<a name="line-47"></a><a name="Distributive"></a><span class='hs-comment'>--</span>
<a name="line-48"></a><a name="Distributive"></a><span class='hs-comment'>-- Minimal complete definition: 'distribute' or 'collect'</span>
<a name="line-49"></a><a name="Distributive"></a><span class='hs-comment'>--</span>
<a name="line-50"></a><a name="Distributive"></a><span class='hs-comment'>-- To be distributable a container will need to have a way to consistently</span>
<a name="line-51"></a><a name="Distributive"></a><span class='hs-comment'>-- zip a potentially infinite number of copies of itself. This effectively</span>
<a name="line-52"></a><a name="Distributive"></a><span class='hs-comment'>-- means that the holes in all values of that type, must have the same</span>
<a name="line-53"></a><a name="Distributive"></a><span class='hs-comment'>-- cardinality, fixed sized vectors, infinite streams, functions, etc.</span>
<a name="line-54"></a><a name="Distributive"></a><span class='hs-comment'>-- and no extra information to try to merge together.</span>
<a name="line-55"></a><a name="Distributive"></a><span class='hs-comment'>--</span>
<a name="line-56"></a><a name="Distributive"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Distributive</span> <span class='hs-varid'>g</span> <span class='hs-keyword'>where</span>
<a name="line-57"></a> <span class='hs-comment'>-- | The dual of 'Data.Traversable.sequenceA'</span>
<a name="line-58"></a> <span class='hs-comment'>--</span>
<a name="line-59"></a> <span class='hs-comment'>-- >>> distribute [(+1),(+2)] 1</span>
<a name="line-60"></a> <span class='hs-comment'>-- [2,3]</span>
<a name="line-61"></a> <span class='hs-comment'>--</span>
<a name="line-62"></a> <span class='hs-comment'>-- @'distribute' = 'collect' 'id'@</span>
<a name="line-63"></a> <span class='hs-varid'>distribute</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-64"></a> <span class='hs-varid'>distribute</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>collect</span> <span class='hs-varid'>id</span>
<a name="line-65"></a>
<a name="line-66"></a> <span class='hs-comment'>-- |</span>
<a name="line-67"></a> <span class='hs-comment'>-- @'collect' f = 'distribute' . 'fmap' f@</span>
<a name="line-68"></a> <span class='hs-varid'>collect</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</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'>g</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-69"></a> <span class='hs-varid'>collect</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>distribute</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span>
<a name="line-70"></a>
<a name="line-71"></a> <span class='hs-comment'>-- | The dual of 'Data.Traversable.sequence'</span>
<a name="line-72"></a> <span class='hs-comment'>--</span>
<a name="line-73"></a> <span class='hs-comment'>-- @'distributeM' = 'fmap' 'unwrapMonad' . 'distribute' . 'WrapMonad'@</span>
<a name="line-74"></a> <span class='hs-varid'>distributeM</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-75"></a> <span class='hs-varid'>distributeM</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>unwrapMonad</span> <span class='hs-varop'>.</span> <span class='hs-varid'>distribute</span> <span class='hs-varop'>.</span> <span class='hs-conid'>WrapMonad</span>
<a name="line-76"></a>
<a name="line-77"></a> <span class='hs-comment'>-- |</span>
<a name="line-78"></a> <span class='hs-comment'>-- @'collectM' = 'distributeM' . 'liftM' f@</span>
<a name="line-79"></a> <span class='hs-varid'>collectM</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-varid'>m</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-80"></a> <span class='hs-varid'>collectM</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>distributeM</span> <span class='hs-varop'>.</span> <span class='hs-varid'>liftM</span> <span class='hs-varid'>f</span>
<a name="line-81"></a>
<a name="line-82"></a><a name="cotraverse"></a><span class='hs-comment'>-- | The dual of 'Data.Traversable.traverse'</span>
<a name="line-83"></a><span class='hs-comment'>--</span>
<a name="line-84"></a><span class='hs-comment'>-- @'cotraverse' f = 'fmap' f . 'distribute'@</span>
<a name="line-85"></a><span class='hs-definition'>cotraverse</span> <span class='hs-keyglyph'>::</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-conid'>Distributive</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span>
<a name="line-86"></a><span class='hs-definition'>cotraverse</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>distribute</span>
<a name="line-87"></a>
<a name="line-88"></a><a name="comapM"></a><span class='hs-comment'>-- | The dual of 'Data.Traversable.mapM'</span>
<a name="line-89"></a><span class='hs-comment'>--</span>
<a name="line-90"></a><span class='hs-comment'>-- @'comapM' f = 'fmap' f . 'distributeM'@</span>
<a name="line-91"></a><span class='hs-definition'>comapM</span> <span class='hs-keyglyph'>::</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'>Distributive</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>m</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span>
<a name="line-92"></a><span class='hs-definition'>comapM</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>distributeM</span>
<a name="line-93"></a>
<a name="line-94"></a><a name="instance%20Distributive%20Identity"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Distributive</span> <span class='hs-conid'>Identity</span> <span class='hs-keyword'>where</span>
<a name="line-95"></a> <span class='hs-varid'>collect</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'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varid'>runIdentity</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-96"></a> <span class='hs-varid'>distribute</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Identity</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>runIdentity</span>
<a name="line-97"></a>
<a name="line-98"></a><a name="instance%20Distributive%20Proxy"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Distributive</span> <span class='hs-conid'>Proxy</span> <span class='hs-keyword'>where</span>
<a name="line-99"></a> <span class='hs-varid'>collect</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Proxy</span>
<a name="line-100"></a> <span class='hs-varid'>distribute</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Proxy</span>
<a name="line-101"></a>
<a name="line-102"></a><a name="instance%20Distributive%20(Tagged%20t)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Distributive</span> <span class='hs-layout'>(</span><span class='hs-conid'>Tagged</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-103"></a> <span class='hs-varid'>collect</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Tagged</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varid'>unTagged</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-104"></a> <span class='hs-varid'>distribute</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Tagged</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>unTagged</span>
<a name="line-105"></a>
<a name="line-106"></a><a name="instance%20Distributive%20((-%3e)e)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Distributive</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>-></span><span class='hs-layout'>)</span><span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-107"></a> <span class='hs-varid'>distribute</span> <span class='hs-varid'>a</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varop'>$</span><span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span>
<a name="line-108"></a>
<a name="line-109"></a><a name="instance%20Distributive%20(ReaderT%20e%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Distributive</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Distributive</span> <span class='hs-layout'>(</span><span class='hs-conid'>ReaderT</span> <span class='hs-varid'>e</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-110"></a> <span class='hs-varid'>distribute</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ReaderT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>e</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>collect</span> <span class='hs-layout'>(</span><span class='hs-varid'>flip</span> <span class='hs-varid'>runReaderT</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span>
<a name="line-111"></a>
<a name="line-112"></a><a name="instance%20Distributive%20(IdentityT%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Distributive</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Distributive</span> <span class='hs-layout'>(</span><span class='hs-conid'>IdentityT</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-113"></a> <span class='hs-varid'>collect</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>IdentityT</span> <span class='hs-varop'>.</span> <span class='hs-varid'>collect</span> <span class='hs-layout'>(</span><span class='hs-varid'>runIdentityT</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-114"></a>
<a name="line-115"></a><a name="instance%20Distributive%20(Compose%20f%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Distributive</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Distributive</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Distributive</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-116"></a> <span class='hs-varid'>distribute</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Compose</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>distribute</span> <span class='hs-varop'>.</span> <span class='hs-varid'>collect</span> <span class='hs-varid'>getCompose</span>
<a name="line-117"></a>
<a name="line-118"></a><a name="instance%20Distributive%20(Product%20f%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Distributive</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Distributive</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Distributive</span> <span class='hs-layout'>(</span><span class='hs-conid'>Product</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-119"></a> <span class='hs-varid'>distribute</span> <span class='hs-varid'>wp</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Pair</span> <span class='hs-layout'>(</span><span class='hs-varid'>collect</span> <span class='hs-varid'>fstP</span> <span class='hs-varid'>wp</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>collect</span> <span class='hs-varid'>sndP</span> <span class='hs-varid'>wp</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-120"></a> <span class='hs-varid'>fstP</span> <span class='hs-layout'>(</span><span class='hs-conid'>Pair</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-121"></a> <span class='hs-varid'>sndP</span> <span class='hs-layout'>(</span><span class='hs-conid'>Pair</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>b</span>
<a name="line-122"></a>
<a name="line-123"></a><a name="instance%20Distributive%20(Backwards%20f)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Distributive</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Distributive</span> <span class='hs-layout'>(</span><span class='hs-conid'>Backwards</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-124"></a> <span class='hs-varid'>distribute</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Backwards</span> <span class='hs-varop'>.</span> <span class='hs-varid'>collect</span> <span class='hs-varid'>forwards</span>
<a name="line-125"></a>
<a name="line-126"></a><a name="instance%20Distributive%20(Reverse%20f)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Distributive</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Distributive</span> <span class='hs-layout'>(</span><span class='hs-conid'>Reverse</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-127"></a> <span class='hs-varid'>distribute</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Reverse</span> <span class='hs-varop'>.</span> <span class='hs-varid'>collect</span> <span class='hs-varid'>getReverse</span>
</pre></body>
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