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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-cpp'>#if __GLASGOW_HASKELL__ >= 707</span>
<a name="line-3"></a><span class='hs-comment'>{-# LANGUAGE DeriveDataTypeable, StandaloneDeriving, Safe, DefaultSignatures #-}</span>
<a name="line-4"></a><span class='hs-cpp'>#elif __GLASGOW_HASKELL__ >= 702</span>
<a name="line-5"></a><span class='hs-comment'>{-# LANGUAGE Trustworthy, DefaultSignatures #-}</span>
<a name="line-6"></a><span class='hs-cpp'>#endif</span>
<a name="line-7"></a> <span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-8"></a><span class='hs-comment'>-- |</span>
<a name="line-9"></a><span class='hs-comment'>-- Module : Control.Comonad</span>
<a name="line-10"></a><span class='hs-comment'>-- Copyright : (C) 2008-2015 Edward Kmett,</span>
<a name="line-11"></a><span class='hs-comment'>-- (C) 2004 Dave Menendez</span>
<a name="line-12"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-13"></a><span class='hs-comment'>--</span>
<a name="line-14"></a><span class='hs-comment'>-- Maintainer : Edward Kmett <ekmett@gmail.com></span>
<a name="line-15"></a><span class='hs-comment'>-- Stability : provisional</span>
<a name="line-16"></a><span class='hs-comment'>-- Portability : portable</span>
<a name="line-17"></a><span class='hs-comment'>--</span>
<a name="line-18"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-19"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Comonad</span> <span class='hs-layout'>(</span>
<a name="line-20"></a> <span class='hs-comment'>-- * Comonads</span>
<a name="line-21"></a> <span class='hs-conid'>Comonad</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-varid'>liftW</span> <span class='hs-comment'>-- :: Comonad w => (a -> b) -> w a -> w b</span>
<a name="line-23"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>wfix</span> <span class='hs-comment'>-- :: Comonad w => w (w a -> a) -> a</span>
<a name="line-24"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>cfix</span> <span class='hs-comment'>-- :: Comonad w => (w a -> a) -> w a</span>
<a name="line-25"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>kfix</span> <span class='hs-comment'>-- :: ComonadApply w => w (w a -> a) -> w a</span>
<a name="line-26"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>=>=</span><span class='hs-layout'>)</span>
<a name="line-27"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>=<=</span><span class='hs-layout'>)</span>
<a name="line-28"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'><<=</span><span class='hs-layout'>)</span>
<a name="line-29"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>=>></span><span class='hs-layout'>)</span>
<a name="line-30"></a> <span class='hs-comment'>-- * Combining Comonads</span>
<a name="line-31"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>ComonadApply</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-32"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'><@@></span><span class='hs-layout'>)</span> <span class='hs-comment'>-- :: ComonadApply w => w a -> w (a -> b) -> w b</span>
<a name="line-33"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>liftW2</span> <span class='hs-comment'>-- :: ComonadApply w => (a -> b -> c) -> w a -> w b -> w c</span>
<a name="line-34"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>liftW3</span> <span class='hs-comment'>-- :: ComonadApply w => (a -> b -> c -> d) -> w a -> w b -> w c -> w d</span>
<a name="line-35"></a> <span class='hs-comment'>-- * Cokleisli Arrows</span>
<a name="line-36"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Cokleisli</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-37"></a> <span class='hs-comment'>-- * Functors</span>
<a name="line-38"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Functor</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-39"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'><$></span><span class='hs-layout'>)</span> <span class='hs-comment'>-- :: Functor f => (a -> b) -> f a -> f b</span>
<a name="line-40"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>$></span><span class='hs-layout'>)</span> <span class='hs-comment'>-- :: Functor f => f a -> b -> f b</span>
<a name="line-41"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-42"></a>
<a name="line-43"></a><span class='hs-comment'>-- import _everything_</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'>Functor</span>
<a name="line-45"></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-46"></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-47"></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-48"></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'>ap</span><span class='hs-layout'>)</span>
<a name="line-49"></a><span class='hs-cpp'>#if MIN_VERSION_base(4,7,0)</span>
<a name="line-50"></a><span class='hs-comment'>-- Control.Monad.Instances is empty</span>
<a name="line-51"></a><span class='hs-cpp'>#else</span>
<a name="line-52"></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>
<a name="line-53"></a><span class='hs-cpp'>#endif</span>
<a name="line-54"></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-55"></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-56"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>List</span><span class='hs-varop'>.</span><span class='hs-conid'>NonEmpty</span> <span class='hs-varid'>hiding</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span><span class='hs-layout'>)</span>
<a name="line-57"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Semigroup</span> <span class='hs-varid'>hiding</span> <span class='hs-layout'>(</span><span class='hs-conid'>Product</span><span class='hs-layout'>)</span>
<a name="line-58"></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-59"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Prelude</span> <span class='hs-varid'>hiding</span> <span class='hs-layout'>(</span><span class='hs-varid'>id</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>.</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-60"></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'>Fix</span>
<a name="line-61"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Typeable</span>
<a name="line-62"></a>
<a name="line-63"></a><span class='hs-cpp'>#ifdef MIN_VERSION_containers</span>
<a name="line-64"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Tree</span>
<a name="line-65"></a><span class='hs-cpp'>#endif</span>
<a name="line-66"></a>
<a name="line-67"></a><span class='hs-keyword'>infixl</span> <span class='hs-num'>4</span> <span class='hs-varop'><@</span><span class='hs-layout'>,</span> <span class='hs-varop'>@></span><span class='hs-layout'>,</span> <span class='hs-varop'><@@></span><span class='hs-layout'>,</span> <span class='hs-varop'><@></span>
<a name="line-68"></a><span class='hs-keyword'>infixl</span> <span class='hs-num'>1</span> <span class='hs-varop'>=>></span>
<a name="line-69"></a><span class='hs-keyword'>infixr</span> <span class='hs-num'>1</span> <span class='hs-varop'><<=</span><span class='hs-layout'>,</span> <span class='hs-varop'>=<=</span><span class='hs-layout'>,</span> <span class='hs-varop'>=>=</span>
<a name="line-70"></a>
<a name="line-71"></a><span class='hs-comment'>{- |
<a name="line-72"></a>
<a name="line-73"></a>There are two ways to define a comonad:
<a name="line-74"></a>
<a name="line-75"></a>I. Provide definitions for 'extract' and 'extend'
<a name="line-76"></a>satisfying these laws:
<a name="line-77"></a>
<a name="line-78"></a>@
<a name="line-79"></a>'extend' 'extract' = 'id'
<a name="line-80"></a>'extract' . 'extend' f = f
<a name="line-81"></a>'extend' f . 'extend' g = 'extend' (f . 'extend' g)
<a name="line-82"></a>@
<a name="line-83"></a>
<a name="line-84"></a>In this case, you may simply set 'fmap' = 'liftW'.
<a name="line-85"></a>
<a name="line-86"></a>These laws are directly analogous to the laws for monads
<a name="line-87"></a>and perhaps can be made clearer by viewing them as laws stating
<a name="line-88"></a>that Cokleisli composition must be associative, and has extract for
<a name="line-89"></a>a unit:
<a name="line-90"></a>
<a name="line-91"></a>@
<a name="line-92"></a>f '=>=' 'extract' = f
<a name="line-93"></a>'extract' '=>=' f = f
<a name="line-94"></a>(f '=>=' g) '=>=' h = f '=>=' (g '=>=' h)
<a name="line-95"></a>@
<a name="line-96"></a>
<a name="line-97"></a>II. Alternately, you may choose to provide definitions for 'fmap',
<a name="line-98"></a>'extract', and 'duplicate' satisfying these laws:
<a name="line-99"></a>
<a name="line-100"></a>@
<a name="line-101"></a>'extract' . 'duplicate' = 'id'
<a name="line-102"></a>'fmap' 'extract' . 'duplicate' = 'id'
<a name="line-103"></a>'duplicate' . 'duplicate' = 'fmap' 'duplicate' . 'duplicate'
<a name="line-104"></a>@
<a name="line-105"></a>
<a name="line-106"></a>In this case you may not rely on the ability to define 'fmap' in
<a name="line-107"></a>terms of 'liftW'.
<a name="line-108"></a>
<a name="line-109"></a>You may of course, choose to define both 'duplicate' /and/ 'extend'.
<a name="line-110"></a>In that case you must also satisfy these laws:
<a name="line-111"></a>
<a name="line-112"></a>@
<a name="line-113"></a>'extend' f = 'fmap' f . 'duplicate'
<a name="line-114"></a>'duplicate' = 'extend' id
<a name="line-115"></a>'fmap' f = 'extend' (f . 'extract')
<a name="line-116"></a>@
<a name="line-117"></a>
<a name="line-118"></a>These are the default definitions of 'extend' and 'duplicate' and
<a name="line-119"></a>the definition of 'liftW' respectively.
<a name="line-120"></a>
<a name="line-121"></a>-}</span>
<a name="line-122"></a>
<a name="line-123"></a><a name="Comonad"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</span> <span class='hs-keyword'>where</span>
<a name="line-124"></a> <span class='hs-comment'>-- |</span>
<a name="line-125"></a> <span class='hs-comment'>-- @</span>
<a name="line-126"></a> <span class='hs-comment'>-- 'extract' . 'fmap' f = f . 'extract'</span>
<a name="line-127"></a> <span class='hs-comment'>-- @</span>
<a name="line-128"></a> <span class='hs-varid'>extract</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-129"></a>
<a name="line-130"></a> <span class='hs-comment'>-- |</span>
<a name="line-131"></a> <span class='hs-comment'>-- @</span>
<a name="line-132"></a> <span class='hs-comment'>-- 'duplicate' = 'extend' 'id'</span>
<a name="line-133"></a> <span class='hs-comment'>-- 'fmap' ('fmap' f) . 'duplicate' = 'duplicate' . 'fmap' f</span>
<a name="line-134"></a> <span class='hs-comment'>-- @</span>
<a name="line-135"></a> <span class='hs-varid'>duplicate</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-layout'>(</span><span class='hs-varid'>w</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-136"></a> <span class='hs-varid'>duplicate</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>extend</span> <span class='hs-varid'>id</span>
<a name="line-137"></a>
<a name="line-138"></a> <span class='hs-comment'>-- |</span>
<a name="line-139"></a> <span class='hs-comment'>-- @</span>
<a name="line-140"></a> <span class='hs-comment'>-- 'extend' f = 'fmap' f . 'duplicate'</span>
<a name="line-141"></a> <span class='hs-comment'>-- @</span>
<a name="line-142"></a> <span class='hs-varid'>extend</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>w</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'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>b</span>
<a name="line-143"></a> <span class='hs-varid'>extend</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'>duplicate</span>
<a name="line-144"></a>
<a name="line-145"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ >= 708</span>
<a name="line-146"></a> <span class='hs-comment'>{-# MINIMAL extract, (duplicate | extend) #-}</span>
<a name="line-147"></a><span class='hs-cpp'>#endif</span>
<a name="line-148"></a>
<a name="line-149"></a>
<a name="line-150"></a><a name="instance%20Comonad%20((,)e)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Comonad</span> <span class='hs-layout'>(</span><span class='hs-conid'>(,)</span><span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-151"></a> <span class='hs-varid'>duplicate</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>fst</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span>
<a name="line-152"></a> <span class='hs-comment'>{-# INLINE duplicate #-}</span>
<a name="line-153"></a> <span class='hs-varid'>extract</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>snd</span>
<a name="line-154"></a> <span class='hs-comment'>{-# INLINE extract #-}</span>
<a name="line-155"></a>
<a name="line-156"></a><span class='hs-cpp'>#if MIN_VERSION_semigroups(0,16,2)</span>
<a name="line-157"></a><a name="instance%20Comonad%20(Arg%20e)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Comonad</span> <span class='hs-layout'>(</span><span class='hs-conid'>Arg</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-158"></a> <span class='hs-varid'>duplicate</span> <span class='hs-varid'>w</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>Arg</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-conid'>Arg</span> <span class='hs-varid'>a</span> <span class='hs-varid'>w</span>
<a name="line-159"></a> <span class='hs-comment'>{-# INLINE duplicate #-}</span>
<a name="line-160"></a> <span class='hs-varid'>extend</span> <span class='hs-varid'>f</span> <span class='hs-varid'>w</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>Arg</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-conid'>Arg</span> <span class='hs-varid'>a</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span>
<a name="line-161"></a> <span class='hs-comment'>{-# INLINE extend #-}</span>
<a name="line-162"></a> <span class='hs-varid'>extract</span> <span class='hs-layout'>(</span><span class='hs-conid'>Arg</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-163"></a> <span class='hs-comment'>{-# INLINE extract #-}</span>
<a name="line-164"></a><span class='hs-cpp'>#endif</span>
<a name="line-165"></a>
<a name="line-166"></a><a name="instance%20Comonad%20((-%3e)m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Comonad</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'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-167"></a> <span class='hs-varid'>duplicate</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>mappend</span> <span class='hs-varid'>m</span>
<a name="line-168"></a> <span class='hs-comment'>{-# INLINE duplicate #-}</span>
<a name="line-169"></a> <span class='hs-varid'>extract</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>mempty</span>
<a name="line-170"></a> <span class='hs-comment'>{-# INLINE extract #-}</span>
<a name="line-171"></a>
<a name="line-172"></a><a name="instance%20Comonad%20Identity"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Comonad</span> <span class='hs-conid'>Identity</span> <span class='hs-keyword'>where</span>
<a name="line-173"></a> <span class='hs-varid'>duplicate</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Identity</span>
<a name="line-174"></a> <span class='hs-comment'>{-# INLINE duplicate #-}</span>
<a name="line-175"></a> <span class='hs-varid'>extract</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runIdentity</span>
<a name="line-176"></a> <span class='hs-comment'>{-# INLINE extract #-}</span>
<a name="line-177"></a>
<a name="line-178"></a><a name="instance%20Comonad%20(Tagged%20s)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Comonad</span> <span class='hs-layout'>(</span><span class='hs-conid'>Tagged</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-179"></a> <span class='hs-varid'>duplicate</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Tagged</span>
<a name="line-180"></a> <span class='hs-comment'>{-# INLINE duplicate #-}</span>
<a name="line-181"></a> <span class='hs-varid'>extract</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unTagged</span>
<a name="line-182"></a> <span class='hs-comment'>{-# INLINE extract #-}</span>
<a name="line-183"></a>
<a name="line-184"></a><a name="instance%20Comonad%20(IdentityT%20w)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Comonad</span> <span class='hs-layout'>(</span><span class='hs-conid'>IdentityT</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-185"></a> <span class='hs-varid'>extend</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>IdentityT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>IdentityT</span> <span class='hs-layout'>(</span><span class='hs-varid'>extend</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-conid'>IdentityT</span><span class='hs-layout'>)</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span>
<a name="line-186"></a> <span class='hs-varid'>extract</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>extract</span> <span class='hs-varop'>.</span> <span class='hs-varid'>runIdentityT</span>
<a name="line-187"></a> <span class='hs-comment'>{-# INLINE extract #-}</span>
<a name="line-188"></a>
<a name="line-189"></a><span class='hs-cpp'>#ifdef MIN_VERSION_containers</span>
<a name="line-190"></a><a name="instance%20Comonad%20Tree"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Comonad</span> <span class='hs-conid'>Tree</span> <span class='hs-keyword'>where</span>
<a name="line-191"></a> <span class='hs-varid'>duplicate</span> <span class='hs-varid'>w</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>Node</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>as</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Node</span> <span class='hs-varid'>w</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-varid'>duplicate</span> <span class='hs-keyword'>as</span><span class='hs-layout'>)</span>
<a name="line-192"></a> <span class='hs-varid'>extract</span> <span class='hs-layout'>(</span><span class='hs-conid'>Node</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-193"></a> <span class='hs-comment'>{-# INLINE extract #-}</span>
<a name="line-194"></a><span class='hs-cpp'>#endif</span>
<a name="line-195"></a>
<a name="line-196"></a><a name="instance%20Comonad%20NonEmpty"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Comonad</span> <span class='hs-conid'>NonEmpty</span> <span class='hs-keyword'>where</span>
<a name="line-197"></a> <span class='hs-varid'>extend</span> <span class='hs-varid'>f</span> <span class='hs-varid'>w</span><span class='hs-keyglyph'>@</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-keyword'>_</span> <span class='hs-conop'>:|</span> <span class='hs-varid'>aas</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>w</span> <span class='hs-conop'>:|</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>aas</span> <span class='hs-keyword'>of</span>
<a name="line-198"></a> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>[]</span>
<a name="line-199"></a> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-conop'>:</span><span class='hs-keyword'>as</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>toList</span> <span class='hs-layout'>(</span><span class='hs-varid'>extend</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-conop'>:|</span> <span class='hs-keyword'>as</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-200"></a> <span class='hs-varid'>extract</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-conop'>:|</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-201"></a> <span class='hs-comment'>{-# INLINE extract #-}</span>
<a name="line-202"></a>
<a name="line-203"></a><span class='hs-comment'>-- | @ComonadApply@ is to @Comonad@ like @Applicative@ is to @Monad@.</span>
<a name="line-204"></a><span class='hs-comment'>--</span>
<a name="line-205"></a><span class='hs-comment'>-- Mathematically, it is a strong lax symmetric semi-monoidal comonad on the</span>
<a name="line-206"></a><span class='hs-comment'>-- category @Hask@ of Haskell types. That it to say that @w@ is a strong lax</span>
<a name="line-207"></a><span class='hs-comment'>-- symmetric semi-monoidal functor on Hask, where both 'extract' and 'duplicate' are</span>
<a name="line-208"></a><span class='hs-comment'>-- symmetric monoidal natural transformations.</span>
<a name="line-209"></a><span class='hs-comment'>--</span>
<a name="line-210"></a><span class='hs-comment'>-- Laws:</span>
<a name="line-211"></a><span class='hs-comment'>--</span>
<a name="line-212"></a><span class='hs-comment'>-- @</span>
<a name="line-213"></a><span class='hs-comment'>-- ('.') '<$>' u '<@>' v '<@>' w = u '<@>' (v '<@>' w)</span>
<a name="line-214"></a><span class='hs-comment'>-- 'extract' (p '<@>' q) = 'extract' p ('extract' q)</span>
<a name="line-215"></a><span class='hs-comment'>-- 'duplicate' (p '<@>' q) = ('<@>') '<$>' 'duplicate' p '<@>' 'duplicate' q</span>
<a name="line-216"></a><span class='hs-comment'>-- @</span>
<a name="line-217"></a><span class='hs-comment'>--</span>
<a name="line-218"></a><span class='hs-comment'>-- If our type is both a 'ComonadApply' and 'Applicative' we further require</span>
<a name="line-219"></a><span class='hs-comment'>--</span>
<a name="line-220"></a><span class='hs-comment'>-- @</span>
<a name="line-221"></a><span class='hs-comment'>-- ('<*>') = ('<@>')</span>
<a name="line-222"></a><span class='hs-comment'>-- @</span>
<a name="line-223"></a><span class='hs-comment'>--</span>
<a name="line-224"></a><span class='hs-comment'>-- Finally, if you choose to define ('<@') and ('@>'), the results of your</span>
<a name="line-225"></a><span class='hs-comment'>-- definitions should match the following laws:</span>
<a name="line-226"></a><span class='hs-comment'>--</span>
<a name="line-227"></a><span class='hs-comment'>-- @</span>
<a name="line-228"></a><span class='hs-comment'>-- a '@>' b = 'const' 'id' '<$>' a '<@>' b</span>
<a name="line-229"></a><span class='hs-comment'>-- a '<@' b = 'const' '<$>' a '<@>' b</span>
<a name="line-230"></a><span class='hs-comment'>-- @</span>
<a name="line-231"></a>
<a name="line-232"></a><a name="ComonadApply"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>ComonadApply</span> <span class='hs-varid'>w</span> <span class='hs-keyword'>where</span>
<a name="line-233"></a> <span class='hs-layout'>(</span><span class='hs-varop'><@></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>w</span> <span class='hs-layout'>(</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'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>b</span>
<a name="line-234"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ >= 702</span>
<a name="line-235"></a> <span class='hs-keyword'>default</span> <span class='hs-layout'>(</span><span class='hs-varop'><@></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Applicative</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>w</span> <span class='hs-layout'>(</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'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>b</span>
<a name="line-236"></a> <span class='hs-layout'>(</span><span class='hs-varop'><@></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'><*></span><span class='hs-layout'>)</span>
<a name="line-237"></a><span class='hs-cpp'>#endif</span>
<a name="line-238"></a>
<a name="line-239"></a> <span class='hs-layout'>(</span><span class='hs-varop'>@></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>b</span>
<a name="line-240"></a> <span class='hs-varid'>a</span> <span class='hs-varop'>@></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>const</span> <span class='hs-varid'>id</span> <span class='hs-varop'><$></span> <span class='hs-varid'>a</span> <span class='hs-varop'><@></span> <span class='hs-varid'>b</span>
<a name="line-241"></a>
<a name="line-242"></a> <span class='hs-layout'>(</span><span class='hs-varop'><@</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span>
<a name="line-243"></a> <span class='hs-varid'>a</span> <span class='hs-varop'><@</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>const</span> <span class='hs-varop'><$></span> <span class='hs-varid'>a</span> <span class='hs-varop'><@></span> <span class='hs-varid'>b</span>
<a name="line-244"></a>
<a name="line-245"></a><a name="instance%20ComonadApply%20((,)m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>ComonadApply</span> <span class='hs-layout'>(</span><span class='hs-conid'>(,)</span><span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-246"></a> <span class='hs-layout'>(</span><span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varop'><@></span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span><span class='hs-layout'>,</span> <span class='hs-varid'>a</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-varop'><></span> <span class='hs-varid'>n</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-247"></a> <span class='hs-layout'>(</span><span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-varop'><@</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span><span class='hs-layout'>,</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>m</span> <span class='hs-varop'><></span> <span class='hs-varid'>n</span><span class='hs-layout'>,</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-248"></a> <span class='hs-layout'>(</span><span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-varop'>@></span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</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-varop'><></span> <span class='hs-varid'>n</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-249"></a>
<a name="line-250"></a><a name="instance%20ComonadApply%20NonEmpty"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>ComonadApply</span> <span class='hs-conid'>NonEmpty</span> <span class='hs-keyword'>where</span>
<a name="line-251"></a> <span class='hs-layout'>(</span><span class='hs-varop'><@></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>ap</span>
<a name="line-252"></a>
<a name="line-253"></a><a name="instance%20ComonadApply%20((-%3e)m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>ComonadApply</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'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-254"></a> <span class='hs-layout'>(</span><span class='hs-varop'><@></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'><*></span><span class='hs-layout'>)</span>
<a name="line-255"></a> <span class='hs-layout'>(</span><span class='hs-varop'><@</span> <span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'><*</span> <span class='hs-layout'>)</span>
<a name="line-256"></a> <span class='hs-layout'>(</span> <span class='hs-varop'>@></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span> <span class='hs-varop'>*></span><span class='hs-layout'>)</span>
<a name="line-257"></a>
<a name="line-258"></a><a name="instance%20ComonadApply%20Identity"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>ComonadApply</span> <span class='hs-conid'>Identity</span> <span class='hs-keyword'>where</span>
<a name="line-259"></a> <span class='hs-layout'>(</span><span class='hs-varop'><@></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'><*></span><span class='hs-layout'>)</span>
<a name="line-260"></a> <span class='hs-layout'>(</span><span class='hs-varop'><@</span> <span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'><*</span> <span class='hs-layout'>)</span>
<a name="line-261"></a> <span class='hs-layout'>(</span> <span class='hs-varop'>@></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span> <span class='hs-varop'>*></span><span class='hs-layout'>)</span>
<a name="line-262"></a>
<a name="line-263"></a><a name="instance%20ComonadApply%20(IdentityT%20w)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>ComonadApply</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>ComonadApply</span> <span class='hs-layout'>(</span><span class='hs-conid'>IdentityT</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-264"></a> <span class='hs-conid'>IdentityT</span> <span class='hs-varid'>wa</span> <span class='hs-varop'><@></span> <span class='hs-conid'>IdentityT</span> <span class='hs-varid'>wb</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>IdentityT</span> <span class='hs-layout'>(</span><span class='hs-varid'>wa</span> <span class='hs-varop'><@></span> <span class='hs-varid'>wb</span><span class='hs-layout'>)</span>
<a name="line-265"></a>
<a name="line-266"></a><span class='hs-cpp'>#ifdef MIN_VERSION_containers</span>
<a name="line-267"></a><a name="instance%20ComonadApply%20Tree"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>ComonadApply</span> <span class='hs-conid'>Tree</span> <span class='hs-keyword'>where</span>
<a name="line-268"></a> <span class='hs-layout'>(</span><span class='hs-varop'><@></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'><*></span><span class='hs-layout'>)</span>
<a name="line-269"></a> <span class='hs-layout'>(</span><span class='hs-varop'><@</span> <span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'><*</span> <span class='hs-layout'>)</span>
<a name="line-270"></a> <span class='hs-layout'>(</span> <span class='hs-varop'>@></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span> <span class='hs-varop'>*></span><span class='hs-layout'>)</span>
<a name="line-271"></a><span class='hs-cpp'>#endif</span>
<a name="line-272"></a>
<a name="line-273"></a><a name="liftW"></a><span class='hs-comment'>-- | A suitable default definition for 'fmap' for a 'Comonad'.</span>
<a name="line-274"></a><span class='hs-comment'>-- Promotes a function to a comonad.</span>
<a name="line-275"></a><span class='hs-comment'>--</span>
<a name="line-276"></a><span class='hs-comment'>-- You can only safely use to define 'fmap' if your 'Comonad'</span>
<a name="line-277"></a><span class='hs-comment'>-- defined 'extend', not just 'duplicate', since defining</span>
<a name="line-278"></a><span class='hs-comment'>-- 'extend' in terms of duplicate uses 'fmap'!</span>
<a name="line-279"></a><span class='hs-comment'>--</span>
<a name="line-280"></a><span class='hs-comment'>-- @</span>
<a name="line-281"></a><span class='hs-comment'>-- 'fmap' f = 'liftW' f = 'extend' (f . 'extract')</span>
<a name="line-282"></a><span class='hs-comment'>-- @</span>
<a name="line-283"></a><span class='hs-definition'>liftW</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</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'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>b</span>
<a name="line-284"></a><span class='hs-definition'>liftW</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>extend</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>extract</span><span class='hs-layout'>)</span>
<a name="line-285"></a><span class='hs-comment'>{-# INLINE liftW #-}</span>
<a name="line-286"></a>
<a name="line-287"></a><a name="wfix"></a><span class='hs-comment'>-- | Comonadic fixed point à la David Menendez</span>
<a name="line-288"></a><span class='hs-definition'>wfix</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>w</span> <span class='hs-layout'>(</span><span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-289"></a><span class='hs-definition'>wfix</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>extract</span> <span class='hs-varid'>w</span> <span class='hs-layout'>(</span><span class='hs-varid'>extend</span> <span class='hs-varid'>wfix</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span>
<a name="line-290"></a>
<a name="line-291"></a><a name="cfix"></a><span class='hs-comment'>-- | Comonadic fixed point à la Dominic Orchard</span>
<a name="line-292"></a><span class='hs-definition'>cfix</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span>
<a name="line-293"></a><span class='hs-definition'>cfix</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fix</span> <span class='hs-layout'>(</span><span class='hs-varid'>extend</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-294"></a><span class='hs-comment'>{-# INLINE cfix #-}</span>
<a name="line-295"></a>
<a name="line-296"></a><a name="kfix"></a><span class='hs-comment'>-- | Comonadic fixed point à la Kenneth Foner:</span>
<a name="line-297"></a><span class='hs-comment'>--</span>
<a name="line-298"></a><span class='hs-comment'>-- This is the @evaluate@ function from his <https://www.youtube.com/watch?v=F7F-BzOB670 "Getting a Quick Fix on Comonads"> talk.</span>
<a name="line-299"></a><span class='hs-definition'>kfix</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>ComonadApply</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>w</span> <span class='hs-layout'>(</span><span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span>
<a name="line-300"></a><span class='hs-definition'>kfix</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fix</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>u</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varop'><@></span> <span class='hs-varid'>duplicate</span> <span class='hs-varid'>u</span>
<a name="line-301"></a><span class='hs-comment'>{-# INLINE kfix #-}</span>
<a name="line-302"></a>
<a name="line-303"></a><a name="=%3e%3e"></a><span class='hs-comment'>-- | 'extend' with the arguments swapped. Dual to '>>=' for a 'Monad'.</span>
<a name="line-304"></a><span class='hs-layout'>(</span><span class='hs-varop'>=>></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>w</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'>w</span> <span class='hs-varid'>b</span>
<a name="line-305"></a><span class='hs-layout'>(</span><span class='hs-varop'>=>></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>flip</span> <span class='hs-varid'>extend</span>
<a name="line-306"></a><span class='hs-comment'>{-# INLINE (=>>) #-}</span>
<a name="line-307"></a>
<a name="line-308"></a><a name="%3c%3c="></a><span class='hs-comment'>-- | 'extend' in operator form</span>
<a name="line-309"></a><span class='hs-layout'>(</span><span class='hs-varop'><<=</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>w</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'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>b</span>
<a name="line-310"></a><span class='hs-layout'>(</span><span class='hs-varop'><<=</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>extend</span>
<a name="line-311"></a><span class='hs-comment'>{-# INLINE (<<=) #-}</span>
<a name="line-312"></a>
<a name="line-313"></a><a name="=%3c="></a><span class='hs-comment'>-- | Right-to-left 'Cokleisli' composition</span>
<a name="line-314"></a><span class='hs-layout'>(</span><span class='hs-varop'>=<=</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>w</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>w</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'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>c</span>
<a name="line-315"></a><a name="f"></a><span class='hs-definition'>f</span> <span class='hs-varop'>=<=</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>extend</span> <span class='hs-varid'>g</span>
<a name="line-316"></a><span class='hs-comment'>{-# INLINE (=<=) #-}</span>
<a name="line-317"></a>
<a name="line-318"></a><a name="=%3e="></a><span class='hs-comment'>-- | Left-to-right 'Cokleisli' composition</span>
<a name="line-319"></a><span class='hs-layout'>(</span><span class='hs-varop'>=>=</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>w</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-layout'>(</span><span class='hs-varid'>w</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>c</span>
<a name="line-320"></a><span class='hs-definition'>f</span> <span class='hs-varop'>=>=</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>g</span> <span class='hs-varop'>.</span> <span class='hs-varid'>extend</span> <span class='hs-varid'>f</span>
<a name="line-321"></a><span class='hs-comment'>{-# INLINE (=>=) #-}</span>
<a name="line-322"></a>
<a name="line-323"></a><a name="%3c@@%3e"></a><span class='hs-comment'>-- | A variant of '<@>' with the arguments reversed.</span>
<a name="line-324"></a><span class='hs-layout'>(</span><span class='hs-varop'><@@></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>ComonadApply</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-layout'>(</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'>w</span> <span class='hs-varid'>b</span>
<a name="line-325"></a><span class='hs-layout'>(</span><span class='hs-varop'><@@></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftW2</span> <span class='hs-layout'>(</span><span class='hs-varid'>flip</span> <span class='hs-varid'>id</span><span class='hs-layout'>)</span>
<a name="line-326"></a><span class='hs-comment'>{-# INLINE (<@@>) #-}</span>
<a name="line-327"></a>
<a name="line-328"></a><a name="liftW2"></a><span class='hs-comment'>-- | Lift a binary function into a 'Comonad' with zipping</span>
<a name="line-329"></a><span class='hs-definition'>liftW2</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>ComonadApply</span> <span class='hs-varid'>w</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'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>c</span>
<a name="line-330"></a><span class='hs-definition'>liftW2</span> <span class='hs-varid'>f</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-varop'><$></span> <span class='hs-varid'>a</span> <span class='hs-varop'><@></span> <span class='hs-varid'>b</span>
<a name="line-331"></a><span class='hs-comment'>{-# INLINE liftW2 #-}</span>
<a name="line-332"></a>
<a name="line-333"></a><a name="liftW3"></a><span class='hs-comment'>-- | Lift a ternary function into a 'Comonad' with zipping</span>
<a name="line-334"></a><span class='hs-definition'>liftW3</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>ComonadApply</span> <span class='hs-varid'>w</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'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>d</span>
<a name="line-335"></a><span class='hs-definition'>liftW3</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varop'><$></span> <span class='hs-varid'>a</span> <span class='hs-varop'><@></span> <span class='hs-varid'>b</span> <span class='hs-varop'><@></span> <span class='hs-varid'>c</span>
<a name="line-336"></a><span class='hs-comment'>{-# INLINE liftW3 #-}</span>
<a name="line-337"></a>
<a name="line-338"></a><a name="Cokleisli"></a><span class='hs-comment'>-- | The 'Cokleisli' 'Arrow's of a given 'Comonad'</span>
<a name="line-339"></a><a name="Cokleisli"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-layout'>{</span> <span class='hs-varid'>runCokleisli</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-layout'>}</span>
<a name="line-340"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ >= 707</span>
<a name="line-341"></a> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-342"></a><span class='hs-cpp'>#else</span>
<a name="line-343"></a><span class='hs-cpp'>#ifdef __GLASGOW_HASKELL__</span>
<a name="line-344"></a><a name="instance%20Typeable2%20(Cokleisli%20w)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Typeable1</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Typeable2</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-345"></a> <span class='hs-varid'>typeOf2</span> <span class='hs-varid'>twab</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mkTyConApp</span> <span class='hs-varid'>cokleisliTyCon</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>typeOf1</span> <span class='hs-layout'>(</span><span class='hs-varid'>wa</span> <span class='hs-varid'>twab</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span>
<a name="line-346"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>wa</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span>
<a name="line-347"></a> <span class='hs-varid'>wa</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>undefined</span>
<a name="line-348"></a><span class='hs-cpp'>#endif</span>
<a name="line-349"></a>
<a name="line-350"></a><a name="cokleisliTyCon"></a><span class='hs-definition'>cokleisliTyCon</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>TyCon</span>
<a name="line-351"></a><span class='hs-cpp'>#if MIN_VERSION_base(4,4,0)</span>
<a name="line-352"></a><span class='hs-definition'>cokleisliTyCon</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mkTyCon3</span> <span class='hs-str'>"comonad"</span> <span class='hs-str'>"Control.Comonad"</span> <span class='hs-str'>"Cokleisli"</span>
<a name="line-353"></a><span class='hs-cpp'>#else</span>
<a name="line-354"></a><span class='hs-definition'>cokleisliTyCon</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mkTyCon</span> <span class='hs-str'>"Control.Comonad.Cokleisli"</span>
<a name="line-355"></a><span class='hs-cpp'>#endif</span>
<a name="line-356"></a><span class='hs-comment'>{-# NOINLINE cokleisliTyCon #-}</span>
<a name="line-357"></a><span class='hs-cpp'>#endif</span>
<a name="line-358"></a>
<a name="line-359"></a><a name="instance%20Category%20(Cokleisli%20w)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Category</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-360"></a> <span class='hs-varid'>id</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>extract</span>
<a name="line-361"></a> <span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-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-362"></a>
<a name="line-363"></a><a name="instance%20Arrow%20(Cokleisli%20w)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Arrow</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-364"></a> <span class='hs-varid'>arr</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>extract</span><span class='hs-layout'>)</span>
<a name="line-365"></a> <span class='hs-varid'>first</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varop'>***</span> <span class='hs-varid'>id</span>
<a name="line-366"></a> <span class='hs-varid'>second</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>id</span> <span class='hs-varop'>***</span> <span class='hs-varid'>f</span>
<a name="line-367"></a> <span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>f</span> <span class='hs-varop'>***</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>fst</span> <span class='hs-varop'>&&&</span> <span class='hs-varid'>g</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>snd</span><span class='hs-layout'>)</span>
<a name="line-368"></a> <span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>f</span> <span class='hs-varop'>&&&</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-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-369"></a>
<a name="line-370"></a><a name="instance%20ArrowApply%20(Cokleisli%20w)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>ArrowApply</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-371"></a> <span class='hs-varid'>app</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>w</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>runCokleisli</span> <span class='hs-layout'>(</span><span class='hs-varid'>fst</span> <span class='hs-layout'>(</span><span class='hs-varid'>extract</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>snd</span> <span class='hs-varop'><$></span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span>
<a name="line-372"></a>
<a name="line-373"></a><a name="instance%20ArrowChoice%20(Cokleisli%20w)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>ArrowChoice</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-374"></a> <span class='hs-varid'>left</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>leftApp</span>
<a name="line-375"></a>
<a name="line-376"></a><a name="instance%20ArrowLoop%20(Cokleisli%20w)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>ComonadApply</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>ArrowLoop</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-377"></a> <span class='hs-varid'>loop</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-layout'>(</span><span class='hs-varid'>fst</span> <span class='hs-varop'>.</span> <span class='hs-varid'>wfix</span> <span class='hs-varop'>.</span> <span class='hs-varid'>extend</span> <span class='hs-varid'>f'</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-378"></a> <span class='hs-varid'>f'</span> <span class='hs-varid'>wa</span> <span class='hs-varid'>wb</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>(,)</span> <span class='hs-varop'><$></span> <span class='hs-varid'>wa</span> <span class='hs-varop'><@></span> <span class='hs-layout'>(</span><span class='hs-varid'>snd</span> <span class='hs-varop'><$></span> <span class='hs-varid'>wb</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-379"></a>
<a name="line-380"></a><a name="instance%20Functor%20(Cokleisli%20w%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-381"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</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-keyglyph'>=</span> <span class='hs-conid'>Cokleisli</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-382"></a>
<a name="line-383"></a><a name="instance%20Applicative%20(Cokleisli%20w%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Applicative</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-384"></a> <span class='hs-varid'>pure</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-varop'>.</span> <span class='hs-varid'>const</span>
<a name="line-385"></a> <span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>f</span> <span class='hs-varop'><*></span> <span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>w</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>w</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-386"></a>
<a name="line-387"></a><a name="instance%20Monad%20(Cokleisli%20w%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monad</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-388"></a> <span class='hs-varid'>return</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-varop'>.</span> <span class='hs-varid'>const</span>
<a name="line-389"></a> <span class='hs-conid'>Cokleisli</span> <span class='hs-varid'>k</span> <span class='hs-varop'>>>=</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cokleisli</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>w</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>runCokleisli</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>k</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varid'>w</span>
<a name="line-390"></a>
<a name="line-391"></a><span class='hs-cpp'>#if !(MIN_VERSION_base(4,7,0))</span>
<a name="line-392"></a>
<a name="line-393"></a><span class='hs-keyword'>infixl</span> <span class='hs-num'>4</span> <span class='hs-varop'>$></span>
<a name="line-394"></a>
<a name="line-395"></a><a name="$%3e"></a><span class='hs-comment'>-- | Replace the contents of a functor uniformly with a constant value.</span>
<a name="line-396"></a><span class='hs-layout'>(</span><span class='hs-varop'>$></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span>
<a name="line-397"></a><span class='hs-layout'>(</span><span class='hs-varop'>$></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>flip</span> <span class='hs-layout'>(</span><span class='hs-varop'><$</span><span class='hs-layout'>)</span>
<a name="line-398"></a>
<a name="line-399"></a><span class='hs-cpp'>#endif</span>
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