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<pre><a name="line-1"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-2"></a><span class='hs-comment'>-- |</span>
<a name="line-3"></a><span class='hs-comment'>-- Module : Data.Bifunctor</span>
<a name="line-4"></a><span class='hs-comment'>-- Copyright : (C) 2008-2013 Edward Kmett,</span>
<a name="line-5"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-6"></a><span class='hs-comment'>--</span>
<a name="line-7"></a><span class='hs-comment'>-- Maintainer : Edward Kmett <ekmett@gmail.com></span>
<a name="line-8"></a><span class='hs-comment'>-- Stability : provisional</span>
<a name="line-9"></a><span class='hs-comment'>-- Portability : portable</span>
<a name="line-10"></a><span class='hs-comment'>--</span>
<a name="line-11"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-12"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Bifunctor</span>
<a name="line-13"></a> <span class='hs-layout'>(</span> <span class='hs-conid'>Bifunctor</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-14"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-15"></a>
<a name="line-16"></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-17"></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-18"></a>
<a name="line-19"></a><span class='hs-comment'>-- | Minimal definition either 'bimap' or 'first' and 'second'</span>
<a name="line-20"></a>
<a name="line-21"></a><a name="Bifunctor"></a><span class='hs-comment'>-- | Formally, the class 'Bifunctor' represents a bifunctor</span>
<a name="line-22"></a><a name="Bifunctor"></a><span class='hs-comment'>-- from @Hask@ -> @Hask@.</span>
<a name="line-23"></a><a name="Bifunctor"></a><span class='hs-comment'>--</span>
<a name="line-24"></a><a name="Bifunctor"></a><span class='hs-comment'>-- Intuitively it is a bifunctor where both the first and second arguments are covariant.</span>
<a name="line-25"></a><a name="Bifunctor"></a><span class='hs-comment'>--</span>
<a name="line-26"></a><a name="Bifunctor"></a><span class='hs-comment'>-- You can define a 'Bifunctor' by either defining 'bimap' or by defining both</span>
<a name="line-27"></a><a name="Bifunctor"></a><span class='hs-comment'>-- 'first' and 'second'.</span>
<a name="line-28"></a><a name="Bifunctor"></a><span class='hs-comment'>--</span>
<a name="line-29"></a><a name="Bifunctor"></a><span class='hs-comment'>-- If you supply 'bimap', you should ensure that:</span>
<a name="line-30"></a><a name="Bifunctor"></a><span class='hs-comment'>--</span>
<a name="line-31"></a><a name="Bifunctor"></a><span class='hs-comment'>-- @'bimap' 'id' 'id' ≡ 'id'@</span>
<a name="line-32"></a><a name="Bifunctor"></a><span class='hs-comment'>--</span>
<a name="line-33"></a><a name="Bifunctor"></a><span class='hs-comment'>-- If you supply 'first' and 'second', ensure:</span>
<a name="line-34"></a><a name="Bifunctor"></a><span class='hs-comment'>--</span>
<a name="line-35"></a><a name="Bifunctor"></a><span class='hs-comment'>-- @</span>
<a name="line-36"></a><a name="Bifunctor"></a><span class='hs-comment'>-- 'first' 'id' ≡ 'id'</span>
<a name="line-37"></a><a name="Bifunctor"></a><span class='hs-comment'>-- 'second' 'id' ≡ 'id'</span>
<a name="line-38"></a><a name="Bifunctor"></a><span class='hs-comment'>-- @</span>
<a name="line-39"></a><a name="Bifunctor"></a><span class='hs-comment'>--</span>
<a name="line-40"></a><a name="Bifunctor"></a><span class='hs-comment'>-- If you supply both, you should also ensure:</span>
<a name="line-41"></a><a name="Bifunctor"></a><span class='hs-comment'>--</span>
<a name="line-42"></a><a name="Bifunctor"></a><span class='hs-comment'>-- @'bimap' f g ≡ 'first' f '.' 'second' g@</span>
<a name="line-43"></a><a name="Bifunctor"></a><span class='hs-comment'>--</span>
<a name="line-44"></a><a name="Bifunctor"></a><span class='hs-comment'>-- These ensure by parametricity:</span>
<a name="line-45"></a><a name="Bifunctor"></a><span class='hs-comment'>--</span>
<a name="line-46"></a><a name="Bifunctor"></a><span class='hs-comment'>-- @</span>
<a name="line-47"></a><a name="Bifunctor"></a><span class='hs-comment'>-- 'bimap' (f '.' g) (h '.' i) ≡ 'bimap' f h '.' 'bimap' g i</span>
<a name="line-48"></a><a name="Bifunctor"></a><span class='hs-comment'>-- 'first' (f '.' g) ≡ 'first' f '.' 'first' g</span>
<a name="line-49"></a><a name="Bifunctor"></a><span class='hs-comment'>-- 'second' (f '.' g) ≡ 'second' f '.' 'second' g</span>
<a name="line-50"></a><a name="Bifunctor"></a><span class='hs-comment'>-- @</span>
<a name="line-51"></a><a name="Bifunctor"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Bifunctor</span> <span class='hs-varid'>p</span> <span class='hs-keyword'>where</span>
<a name="line-52"></a> <span class='hs-comment'>-- | Map over both arguments at the same time.</span>
<a name="line-53"></a> <span class='hs-comment'>--</span>
<a name="line-54"></a> <span class='hs-comment'>-- @'bimap' f g ≡ 'first' f '.' 'second' g@</span>
<a name="line-55"></a> <span class='hs-varid'>bimap</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-layout'>(</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'>p</span> <span class='hs-varid'>a</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>p</span> <span class='hs-varid'>b</span> <span class='hs-varid'>d</span>
<a name="line-56"></a> <span class='hs-varid'>bimap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>first</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>second</span> <span class='hs-varid'>g</span>
<a name="line-57"></a> <span class='hs-comment'>{-# INLINE bimap #-}</span>
<a name="line-58"></a>
<a name="line-59"></a> <span class='hs-comment'>-- | Map covariantly over the first argument.</span>
<a name="line-60"></a> <span class='hs-comment'>--</span>
<a name="line-61"></a> <span class='hs-comment'>-- @'first' f ≡ 'bimap' f 'id'@</span>
<a name="line-62"></a> <span class='hs-varid'>first</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'>p</span> <span class='hs-varid'>a</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>p</span> <span class='hs-varid'>b</span> <span class='hs-varid'>c</span>
<a name="line-63"></a> <span class='hs-varid'>first</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bimap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>id</span>
<a name="line-64"></a> <span class='hs-comment'>{-# INLINE first #-}</span>
<a name="line-65"></a>
<a name="line-66"></a> <span class='hs-comment'>-- | Map covariantly over the second argument.</span>
<a name="line-67"></a> <span class='hs-comment'>--</span>
<a name="line-68"></a> <span class='hs-comment'>-- @'second' ≡ 'bimap' 'id'@</span>
<a name="line-69"></a> <span class='hs-varid'>second</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</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'>p</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>p</span> <span class='hs-varid'>a</span> <span class='hs-varid'>c</span>
<a name="line-70"></a> <span class='hs-varid'>second</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bimap</span> <span class='hs-varid'>id</span>
<a name="line-71"></a> <span class='hs-comment'>{-# INLINE second #-}</span>
<a name="line-72"></a>
<a name="line-73"></a><a name="instance%20Bifunctor%20(,)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Bifunctor</span> <span class='hs-conid'>(,)</span> <span class='hs-keyword'>where</span>
<a name="line-74"></a> <span class='hs-varid'>bimap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-varid'>a</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'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-75"></a> <span class='hs-comment'>{-# INLINE bimap #-}</span>
<a name="line-76"></a>
<a name="line-77"></a><a name="instance%20Bifunctor%20((,,)%20x)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Bifunctor</span> <span class='hs-layout'>(</span><span class='hs-conid'>(,,)</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-78"></a> <span class='hs-varid'>bimap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span> <span class='hs-varid'>a</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'>x</span><span class='hs-layout'>,</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-79"></a> <span class='hs-comment'>{-# INLINE bimap #-}</span>
<a name="line-80"></a>
<a name="line-81"></a><a name="instance%20Bifunctor%20((,,,)%20x%20y)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Bifunctor</span> <span class='hs-layout'>(</span><span class='hs-conid'>(,,,)</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-82"></a> <span class='hs-varid'>bimap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span> <span class='hs-varid'>y</span><span class='hs-layout'>,</span> <span class='hs-varid'>a</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'>x</span><span class='hs-layout'>,</span> <span class='hs-varid'>y</span><span class='hs-layout'>,</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-83"></a> <span class='hs-comment'>{-# INLINE bimap #-}</span>
<a name="line-84"></a>
<a name="line-85"></a><a name="instance%20Bifunctor%20((,,,,)%20x%20y%20z)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Bifunctor</span> <span class='hs-layout'>(</span><span class='hs-conid'>(,,,,)</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-varid'>z</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-86"></a> <span class='hs-varid'>bimap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span> <span class='hs-varid'>y</span><span class='hs-layout'>,</span> <span class='hs-varid'>z</span><span class='hs-layout'>,</span> <span class='hs-varid'>a</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'>x</span><span class='hs-layout'>,</span> <span class='hs-varid'>y</span><span class='hs-layout'>,</span> <span class='hs-varid'>z</span><span class='hs-layout'>,</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-87"></a> <span class='hs-comment'>{-# INLINE bimap #-}</span>
<a name="line-88"></a>
<a name="line-89"></a><a name="instance%20Bifunctor%20Either"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Bifunctor</span> <span class='hs-conid'>Either</span> <span class='hs-keyword'>where</span>
<a name="line-90"></a> <span class='hs-varid'>bimap</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>(</span><span class='hs-conid'>Left</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Left</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-91"></a> <span class='hs-varid'>bimap</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-conid'>Right</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Right</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-92"></a> <span class='hs-comment'>{-# INLINE bimap #-}</span>
<a name="line-93"></a>
<a name="line-94"></a><a name="instance%20Bifunctor%20Const"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Bifunctor</span> <span class='hs-conid'>Const</span> <span class='hs-keyword'>where</span>
<a name="line-95"></a> <span class='hs-varid'>bimap</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>(</span><span class='hs-conid'>Const</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Const</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-96"></a> <span class='hs-comment'>{-# INLINE bimap #-}</span>
<a name="line-97"></a>
<a name="line-98"></a><a name="instance%20Bifunctor%20Tagged"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Bifunctor</span> <span class='hs-conid'>Tagged</span> <span class='hs-keyword'>where</span>
<a name="line-99"></a> <span class='hs-varid'>bimap</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-conid'>Tagged</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Tagged</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-100"></a> <span class='hs-comment'>{-# INLINE bimap #-}</span>
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