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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE TypeOperators #-}</span>
<a name="line-2"></a><span class='hs-comment'>{-# LANGUAGE FlexibleContexts #-}</span>
<a name="line-3"></a><span class='hs-comment'>{-# LANGUAGE Safe #-}</span>
<a name="line-4"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-5"></a><span class='hs-comment'>-- |</span>
<a name="line-6"></a><span class='hs-comment'>-- Module : Data.Semigroup.Generic</span>
<a name="line-7"></a><span class='hs-comment'>-- Copyright : (C) 2014-2015 Edward Kmett, Eric Mertens</span>
<a name="line-8"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-9"></a><span class='hs-comment'>--</span>
<a name="line-10"></a><span class='hs-comment'>-- Maintainer : Edward Kmett <ekmett@gmail.com></span>
<a name="line-11"></a><span class='hs-comment'>-- Stability : provisional</span>
<a name="line-12"></a><span class='hs-comment'>-- Portability : portable</span>
<a name="line-13"></a><span class='hs-comment'>--</span>
<a name="line-14"></a><span class='hs-comment'>-- This module provides generic deriving tools for monoids and semigroups for</span>
<a name="line-15"></a><span class='hs-comment'>-- product-like structures.</span>
<a name="line-16"></a><span class='hs-comment'>--</span>
<a name="line-17"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-18"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Semigroup</span><span class='hs-varop'>.</span><span class='hs-conid'>Generic</span>
<a name="line-19"></a> <span class='hs-layout'>(</span> <span class='hs-conid'>GSemigroup</span>
<a name="line-20"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>gmappend</span>
<a name="line-21"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>GMonoid</span>
<a name="line-22"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>gmempty</span>
<a name="line-23"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-24"></a>
<a name="line-25"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Semigroup</span>
<a name="line-26"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>GHC</span><span class='hs-varop'>.</span><span class='hs-conid'>Generics</span>
<a name="line-27"></a>
<a name="line-28"></a><a name="gmappend"></a><span class='hs-comment'>-- | Generically generate a 'Semigroup' ('<>') operation for any type</span>
<a name="line-29"></a><span class='hs-comment'>-- implementing 'Generic'. This operation will append two values</span>
<a name="line-30"></a><span class='hs-comment'>-- by point-wise appending their component fields. It is only defined</span>
<a name="line-31"></a><span class='hs-comment'>-- for product types.</span>
<a name="line-32"></a><span class='hs-comment'>--</span>
<a name="line-33"></a><span class='hs-comment'>-- @</span>
<a name="line-34"></a><span class='hs-comment'>-- 'gmappend' a ('gmappend' b c) = 'gmappend' ('gmappend' a b) c</span>
<a name="line-35"></a><span class='hs-comment'>-- @</span>
<a name="line-36"></a><span class='hs-definition'>gmappend</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Generic</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>GSemigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rep</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-37"></a><span class='hs-definition'>gmappend</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>to</span> <span class='hs-layout'>(</span><span class='hs-varid'>gmappend'</span> <span class='hs-layout'>(</span><span class='hs-varid'>from</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>from</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-38"></a>
<a name="line-39"></a><a name="GSemigroup"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>GSemigroup</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>where</span>
<a name="line-40"></a> <span class='hs-varid'>gmappend'</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>f</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>p</span>
<a name="line-41"></a>
<a name="line-42"></a><a name="instance%20GSemigroup%20U1"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>GSemigroup</span> <span class='hs-conid'>U1</span> <span class='hs-keyword'>where</span>
<a name="line-43"></a> <span class='hs-varid'>gmappend'</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>U1</span>
<a name="line-44"></a>
<a name="line-45"></a><a name="instance%20GSemigroup%20V1"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>GSemigroup</span> <span class='hs-conid'>V1</span> <span class='hs-keyword'>where</span>
<a name="line-46"></a> <span class='hs-varid'>gmappend'</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <span class='hs-varop'>`seq`</span> <span class='hs-varid'>y</span> <span class='hs-varop'>`seq`</span> <span class='hs-varid'>error</span> <span class='hs-str'>"GSemigroup.V1: gmappend'"</span>
<a name="line-47"></a>
<a name="line-48"></a><a name="instance%20GSemigroup%20(K1%20i%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>GSemigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>K1</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-49"></a> <span class='hs-varid'>gmappend'</span> <span class='hs-layout'>(</span><span class='hs-conid'>K1</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>K1</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>K1</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'><></span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-50"></a>
<a name="line-51"></a><a name="instance%20GSemigroup%20(M1%20i%20c%20f)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>GSemigroup</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>GSemigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>M1</span> <span class='hs-varid'>i</span> <span class='hs-varid'>c</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-52"></a> <span class='hs-varid'>gmappend'</span> <span class='hs-layout'>(</span><span class='hs-conid'>M1</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>M1</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>M1</span> <span class='hs-layout'>(</span><span class='hs-varid'>gmappend'</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-53"></a>
<a name="line-54"></a><a name="instance%20GSemigroup%20(f%20:*:%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>GSemigroup</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>GSemigroup</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>GSemigroup</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-conop'>:*:</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-55"></a> <span class='hs-varid'>gmappend'</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span> <span class='hs-conop'>:*:</span> <span class='hs-varid'>x2</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y1</span> <span class='hs-conop'>:*:</span> <span class='hs-varid'>y2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>gmappend'</span> <span class='hs-varid'>x1</span> <span class='hs-varid'>y1</span> <span class='hs-conop'>:*:</span> <span class='hs-varid'>gmappend'</span> <span class='hs-varid'>x2</span> <span class='hs-varid'>y2</span>
<a name="line-56"></a>
<a name="line-57"></a><span class='hs-comment'>-- | Generically generate a 'Monoid' 'mempty' for any product-like type</span>
<a name="line-58"></a><span class='hs-comment'>-- implementing 'Generic'.</span>
<a name="line-59"></a><span class='hs-comment'>--</span>
<a name="line-60"></a><span class='hs-comment'>-- It is only defined for product types.</span>
<a name="line-61"></a><span class='hs-comment'>--</span>
<a name="line-62"></a><span class='hs-comment'>-- @</span>
<a name="line-63"></a><span class='hs-comment'>-- 'gmappend' 'gmempty' a = a = 'gmappend' a 'gmempty'</span>
<a name="line-64"></a><span class='hs-comment'>-- @</span>
<a name="line-65"></a>
<a name="line-66"></a><a name="gmempty"></a><span class='hs-definition'>gmempty</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Generic</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>GMonoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rep</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span>
<a name="line-67"></a><span class='hs-definition'>gmempty</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>to</span> <span class='hs-varid'>gmempty'</span>
<a name="line-68"></a>
<a name="line-69"></a><a name="GMonoid"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>GSemigroup</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>GMonoid</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>where</span>
<a name="line-70"></a> <span class='hs-varid'>gmempty'</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>f</span> <span class='hs-varid'>p</span>
<a name="line-71"></a>
<a name="line-72"></a><a name="instance%20GMonoid%20U1"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>GMonoid</span> <span class='hs-conid'>U1</span> <span class='hs-keyword'>where</span>
<a name="line-73"></a> <span class='hs-varid'>gmempty'</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>U1</span>
<a name="line-74"></a>
<a name="line-75"></a><a name="instance%20GMonoid%20(K1%20i%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Semigroup</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Monoid</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>GMonoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>K1</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-76"></a> <span class='hs-varid'>gmempty'</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>K1</span> <span class='hs-varid'>mempty</span>
<a name="line-77"></a>
<a name="line-78"></a><a name="instance%20GMonoid%20(M1%20i%20c%20f)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>GMonoid</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>GMonoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>M1</span> <span class='hs-varid'>i</span> <span class='hs-varid'>c</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-79"></a> <span class='hs-varid'>gmempty'</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>M1</span> <span class='hs-varid'>gmempty'</span>
<a name="line-80"></a>
<a name="line-81"></a><a name="instance%20GMonoid%20(f%20:*:%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>GMonoid</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>GMonoid</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>GMonoid</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-conop'>:*:</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-82"></a> <span class='hs-varid'>gmempty'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>gmempty'</span> <span class='hs-conop'>:*:</span> <span class='hs-varid'>gmempty'</span>
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