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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html>
<head>
<!-- Generated by HsColour, http://code.haskell.org/~malcolm/hscolour/ -->
<title>src/Data/Functor/Contravariant.hs</title>
<link type='text/css' rel='stylesheet' href='hscolour.css' />
</head>
<body>
<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE CPP #-}</span>
<a name="line-2"></a><span class='hs-comment'>{-# LANGUAGE TypeOperators #-}</span>
<a name="line-3"></a>
<a name="line-4"></a><span class='hs-cpp'>#ifdef __GLASGOW_HASKELL__</span>
<a name="line-5"></a><span class='hs-cpp'>#define LANGUAGE_DeriveDataTypeable</span>
<a name="line-6"></a><span class='hs-comment'>{-# LANGUAGE DeriveDataTypeable #-}</span>
<a name="line-7"></a><span class='hs-cpp'>#endif</span>
<a name="line-8"></a>
<a name="line-9"></a><span class='hs-cpp'>#ifndef MIN_VERSION_tagged</span>
<a name="line-10"></a><span class='hs-cpp'>#define MIN_VERSION_tagged(x,y,z) 1</span>
<a name="line-11"></a><span class='hs-cpp'>#endif</span>
<a name="line-12"></a>
<a name="line-13"></a><span class='hs-cpp'>#ifndef MIN_VERSION_base</span>
<a name="line-14"></a><span class='hs-cpp'>#define MIN_VERSION_base(x,y,z) 1</span>
<a name="line-15"></a><span class='hs-cpp'>#endif</span>
<a name="line-16"></a>
<a name="line-17"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ &gt;= 704</span>
<a name="line-18"></a><span class='hs-cpp'>#if MIN_VERSION_transformers(0,3,0) &amp;&amp; MIN_VERSION_tagged(0,6,1)</span>
<a name="line-19"></a><span class='hs-comment'>{-# LANGUAGE Safe #-}</span>
<a name="line-20"></a><span class='hs-cpp'>#else</span>
<a name="line-21"></a><span class='hs-comment'>{-# LANGUAGE Trustworthy #-}</span>
<a name="line-22"></a><span class='hs-cpp'>#endif</span>
<a name="line-23"></a><span class='hs-cpp'>#endif</span>
<a name="line-24"></a>
<a name="line-25"></a><span class='hs-comment'>{-# OPTIONS_GHC -fno-warn-deprecations #-}</span>
<a name="line-26"></a>
<a name="line-27"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-28"></a><span class='hs-comment'>-- |</span>
<a name="line-29"></a><span class='hs-comment'>-- Module      :  Data.Functor.Contravariant</span>
<a name="line-30"></a><span class='hs-comment'>-- Copyright   :  (C) 2007-2015 Edward Kmett</span>
<a name="line-31"></a><span class='hs-comment'>-- License     :  BSD-style (see the file LICENSE)</span>
<a name="line-32"></a><span class='hs-comment'>--</span>
<a name="line-33"></a><span class='hs-comment'>-- Maintainer  :  Edward Kmett &lt;ekmett@gmail.com&gt;</span>
<a name="line-34"></a><span class='hs-comment'>-- Stability   :  provisional</span>
<a name="line-35"></a><span class='hs-comment'>-- Portability :  portable</span>
<a name="line-36"></a><span class='hs-comment'>--</span>
<a name="line-37"></a><span class='hs-comment'>-- 'Contravariant' functors, sometimes referred to colloquially as @Cofunctor@,</span>
<a name="line-38"></a><span class='hs-comment'>-- even though the dual of a 'Functor' is just a 'Functor'. As with 'Functor'</span>
<a name="line-39"></a><span class='hs-comment'>-- the definition of 'Contravariant' for a given ADT is unambiguous.</span>
<a name="line-40"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-41"></a>
<a name="line-42"></a><span class='hs-keyword'>module</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'>Contravariant</span> <span class='hs-layout'>(</span>
<a name="line-43"></a>  <span class='hs-comment'>-- * Contravariant Functors</span>
<a name="line-44"></a>    <span class='hs-conid'>Contravariant</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-45"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>phantom</span>
<a name="line-46"></a>
<a name="line-47"></a>  <span class='hs-comment'>-- * Operators</span>
<a name="line-48"></a>  <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>&gt;$&lt;</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>&gt;$$&lt;</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>$&lt;</span><span class='hs-layout'>)</span>
<a name="line-49"></a>
<a name="line-50"></a>  <span class='hs-comment'>-- * Predicates</span>
<a name="line-51"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>Predicate</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-52"></a>
<a name="line-53"></a>  <span class='hs-comment'>-- * Comparisons</span>
<a name="line-54"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>Comparison</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-55"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>defaultComparison</span>
<a name="line-56"></a>
<a name="line-57"></a>  <span class='hs-comment'>-- * Equivalence Relations</span>
<a name="line-58"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>Equivalence</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-59"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>defaultEquivalence</span>
<a name="line-60"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>comparisonEquivalence</span>
<a name="line-61"></a>
<a name="line-62"></a>  <span class='hs-comment'>-- * Dual arrows</span>
<a name="line-63"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>Op</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-64"></a>  <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-65"></a>
<a name="line-66"></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-67"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span><span class='hs-varop'>.</span><span class='hs-conid'>Backwards</span>
<a name="line-68"></a>
<a name="line-69"></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-70"></a>
<a name="line-71"></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'>Error</span>
<a name="line-72"></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'>Except</span>
<a name="line-73"></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-74"></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'>List</span>
<a name="line-75"></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'>Maybe</span>
<a name="line-76"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</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'>RWS</span><span class='hs-varop'>.</span><span class='hs-conid'>Lazy</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Lazy</span>
<a name="line-77"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</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'>RWS</span><span class='hs-varop'>.</span><span class='hs-conid'>Strict</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Strict</span>
<a name="line-78"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Trans</span><span class='hs-varop'>.</span><span class='hs-conid'>Reader</span>
<a name="line-79"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</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'>State</span><span class='hs-varop'>.</span><span class='hs-conid'>Lazy</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Lazy</span>
<a name="line-80"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</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'>State</span><span class='hs-varop'>.</span><span class='hs-conid'>Strict</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Strict</span>
<a name="line-81"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</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'>Writer</span><span class='hs-varop'>.</span><span class='hs-conid'>Lazy</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Lazy</span>
<a name="line-82"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</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'>Writer</span><span class='hs-varop'>.</span><span class='hs-conid'>Strict</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Strict</span>
<a name="line-83"></a>
<a name="line-84"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Function</span> <span class='hs-layout'>(</span><span class='hs-varid'>on</span><span class='hs-layout'>)</span>
<a name="line-85"></a>
<a name="line-86"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Functor</span><span class='hs-varop'>.</span><span class='hs-conid'>Product</span>
<a name="line-87"></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'>Sum</span>
<a name="line-88"></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'>Constant</span>
<a name="line-89"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Functor</span><span class='hs-varop'>.</span><span class='hs-conid'>Compose</span>
<a name="line-90"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Functor</span><span class='hs-varop'>.</span><span class='hs-conid'>Reverse</span>
<a name="line-91"></a>
<a name="line-92"></a><span class='hs-cpp'>#if MIN_VERSION_base(4,8,0)</span>
<a name="line-93"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Alt</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-94"></a><span class='hs-cpp'>#else</span>
<a name="line-95"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monoid</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-96"></a><span class='hs-cpp'>#endif</span>
<a name="line-97"></a>
<a name="line-98"></a><span class='hs-cpp'>#ifdef MIN_VERSION_semigroups</span>
<a name="line-99"></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-layout'>(</span><span class='hs-conid'>Semigroup</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-100"></a><span class='hs-cpp'>#endif</span>
<a name="line-101"></a>
<a name="line-102"></a><span class='hs-cpp'>#ifdef LANGUAGE_DeriveDataTypeable</span>
<a name="line-103"></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-104"></a><span class='hs-cpp'>#endif</span>
<a name="line-105"></a>
<a name="line-106"></a><span class='hs-cpp'>#if defined(__GLASGOW_HASKELL__) &amp;&amp; __GLASGOW_HASKELL__ &lt; 707 &amp;&amp; defined(VERSION_tagged)</span>
<a name="line-107"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Proxy</span>
<a name="line-108"></a><span class='hs-cpp'>#endif</span>
<a name="line-109"></a>
<a name="line-110"></a><span class='hs-cpp'>#ifdef MIN_VERSION_StateVar</span>
<a name="line-111"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>StateVar</span>
<a name="line-112"></a><span class='hs-cpp'>#endif</span>
<a name="line-113"></a>
<a name="line-114"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ &gt;= 702</span>
<a name="line-115"></a><span class='hs-cpp'>#define GHC_GENERICS</span>
<a name="line-116"></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-117"></a><span class='hs-cpp'>#endif</span>
<a name="line-118"></a>
<a name="line-119"></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-layout'>(</span><span class='hs-varop'>.</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span><span class='hs-varid'>id</span><span class='hs-layout'>)</span>
<a name="line-120"></a>
<a name="line-121"></a><span class='hs-comment'>-- | Any instance should be subject to the following laws:</span>
<a name="line-122"></a><span class='hs-comment'>--</span>
<a name="line-123"></a><span class='hs-comment'>-- &gt; contramap id = id</span>
<a name="line-124"></a><span class='hs-comment'>-- &gt; contramap f . contramap g = contramap (g . f)</span>
<a name="line-125"></a><span class='hs-comment'>--</span>
<a name="line-126"></a><span class='hs-comment'>-- Note, that the second law follows from the free theorem of the type of</span>
<a name="line-127"></a><span class='hs-comment'>-- 'contramap' and the first law, so you need only check that the former</span>
<a name="line-128"></a><span class='hs-comment'>-- condition holds.</span>
<a name="line-129"></a>
<a name="line-130"></a><a name="Contravariant"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>where</span>
<a name="line-131"></a>  <span class='hs-varid'>contramap</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-132"></a>
<a name="line-133"></a>  <span class='hs-comment'>-- | Replace all locations in the output with the same value.</span>
<a name="line-134"></a>  <span class='hs-comment'>-- The default definition is @'contramap' . 'const'@, but this may be</span>
<a name="line-135"></a>  <span class='hs-comment'>-- overridden with a more efficient version.</span>
<a name="line-136"></a>  <span class='hs-layout'>(</span><span class='hs-varop'>&gt;$</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-137"></a>  <span class='hs-layout'>(</span><span class='hs-varop'>&gt;$</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>contramap</span> <span class='hs-varop'>.</span> <span class='hs-varid'>const</span>
<a name="line-138"></a>
<a name="line-139"></a><a name="phantom"></a><span class='hs-comment'>-- | If 'f' is both 'Functor' and 'Contravariant' then by the time you factor in the laws</span>
<a name="line-140"></a><span class='hs-comment'>-- of each of those classes, it can't actually use it's argument in any meaningful capacity.</span>
<a name="line-141"></a><span class='hs-comment'>--</span>
<a name="line-142"></a><span class='hs-comment'>-- This method is surprisingly useful. Where both instances exist and are lawful we have</span>
<a name="line-143"></a><span class='hs-comment'>-- the following laws:</span>
<a name="line-144"></a><span class='hs-comment'>--</span>
<a name="line-145"></a><span class='hs-comment'>-- @</span>
<a name="line-146"></a><span class='hs-comment'>-- 'fmap' f ≡ 'phantom'</span>
<a name="line-147"></a><span class='hs-comment'>-- 'contramap' f ≡ 'phantom'</span>
<a name="line-148"></a><span class='hs-comment'>-- @</span>
<a name="line-149"></a><span class='hs-definition'>phantom</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Functor</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span>
<a name="line-150"></a><span class='hs-definition'>phantom</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>()</span> <span class='hs-varop'>&lt;$</span> <span class='hs-varid'>x</span> <span class='hs-varop'>$&lt;</span> <span class='hs-conid'>()</span>
<a name="line-151"></a>
<a name="line-152"></a><span class='hs-keyword'>infixl</span> <span class='hs-num'>4</span> <span class='hs-varop'>&gt;$</span><span class='hs-layout'>,</span> <span class='hs-varop'>$&lt;</span><span class='hs-layout'>,</span> <span class='hs-varop'>&gt;$&lt;</span><span class='hs-layout'>,</span> <span class='hs-varop'>&gt;$$&lt;</span>
<a name="line-153"></a>
<a name="line-154"></a><a name="$%3c"></a><span class='hs-comment'>-- | This is '&gt;$' with its arguments flipped.</span>
<a name="line-155"></a><span class='hs-layout'>(</span><span class='hs-varop'>$&lt;</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-156"></a><span class='hs-layout'>(</span><span class='hs-varop'>$&lt;</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'>&gt;$</span><span class='hs-layout'>)</span>
<a name="line-157"></a><span class='hs-comment'>{-# INLINE ($&lt;) #-}</span>
<a name="line-158"></a>
<a name="line-159"></a><a name="%3e$%3c"></a><span class='hs-comment'>-- | This is an infix alias for 'contramap'</span>
<a name="line-160"></a><span class='hs-layout'>(</span><span class='hs-varop'>&gt;$&lt;</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-161"></a><span class='hs-layout'>(</span><span class='hs-varop'>&gt;$&lt;</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>contramap</span>
<a name="line-162"></a><span class='hs-comment'>{-# INLINE (&gt;$&lt;) #-}</span>
<a name="line-163"></a>
<a name="line-164"></a><a name="%3e$$%3c"></a><span class='hs-comment'>-- | This is an infix version of 'contramap' with the arguments flipped.</span>
<a name="line-165"></a><span class='hs-layout'>(</span><span class='hs-varop'>&gt;$$&lt;</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-166"></a><span class='hs-layout'>(</span><span class='hs-varop'>&gt;$$&lt;</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>flip</span> <span class='hs-varid'>contramap</span>
<a name="line-167"></a><span class='hs-comment'>{-# INLINE (&gt;$$&lt;) #-}</span>
<a name="line-168"></a>
<a name="line-169"></a><span class='hs-cpp'>#if MIN_VERSION_base(4,8,0)</span>
<a name="line-170"></a><a name="instance%20Contravariant%20(Alt%20f)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>Alt</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-171"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Alt</span> <span class='hs-varop'>.</span> <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>getAlt</span>
<a name="line-172"></a><span class='hs-cpp'>#endif</span>
<a name="line-173"></a>
<a name="line-174"></a><span class='hs-cpp'>#ifdef GHC_GENERICS</span>
<a name="line-175"></a><a name="instance%20Contravariant%20V1"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-conid'>V1</span> <span class='hs-keyword'>where</span>
<a name="line-176"></a>  <span class='hs-varid'>contramap</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <span class='hs-varop'>`seq`</span> <span class='hs-varid'>undefined</span>
<a name="line-177"></a>
<a name="line-178"></a><a name="instance%20Contravariant%20U1"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-conid'>U1</span> <span class='hs-keyword'>where</span>
<a name="line-179"></a>  <span class='hs-varid'>contramap</span> <span class='hs-keyword'>_</span> <span class='hs-conid'>U1</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>U1</span>
<a name="line-180"></a>
<a name="line-181"></a><a name="instance%20Contravariant%20(Rec1%20f)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rec1</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-182"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rec1</span> <span class='hs-varid'>fp</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>=</span> <span class='hs-conid'>Rec1</span> <span class='hs-layout'>(</span><span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>fp</span><span class='hs-layout'>)</span>
<a name="line-183"></a>
<a name="line-184"></a><a name="instance%20Contravariant%20(M1%20i%20c%20f)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</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-185"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>M1</span> <span class='hs-varid'>fp</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'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>fp</span><span class='hs-layout'>)</span>
<a name="line-186"></a>
<a name="line-187"></a><a name="instance%20Contravariant%20(K1%20i%20c)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>K1</span> <span class='hs-varid'>i</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-188"></a>  <span class='hs-varid'>contramap</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>(</span><span class='hs-conid'>K1</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>K1</span> <span class='hs-varid'>c</span>
<a name="line-189"></a>
<a name="line-190"></a><a name="instance%20Contravariant%20(f%20:*:%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</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-191"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>xs</span> <span class='hs-conop'>:*:</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span> <span class='hs-conop'>:*:</span> <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>ys</span>
<a name="line-192"></a>
<a name="line-193"></a><a name="instance%20Contravariant%20(f%20:.:%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Functor</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</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-194"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Comp1</span> <span class='hs-varid'>fg</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Comp1</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>fg</span><span class='hs-layout'>)</span>
<a name="line-195"></a>  <span class='hs-comment'>{-# INLINE contramap #-}</span>
<a name="line-196"></a>
<a name="line-197"></a><a name="instance%20Contravariant%20(f%20:+:%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</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-198"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>L1</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>L1</span> <span class='hs-layout'>(</span><span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span>
<a name="line-199"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>R1</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>R1</span> <span class='hs-layout'>(</span><span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span>
<a name="line-200"></a><span class='hs-cpp'>#endif</span>
<a name="line-201"></a>
<a name="line-202"></a><a name="instance%20Contravariant%20(ErrorT%20e%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>ErrorT</span> <span class='hs-varid'>e</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-203"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ErrorT</span> <span class='hs-varop'>.</span> <span class='hs-varid'>contramap</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>runErrorT</span>
<a name="line-204"></a>
<a name="line-205"></a><a name="instance%20Contravariant%20(ExceptT%20e%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>ExceptT</span> <span class='hs-varid'>e</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-206"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ExceptT</span> <span class='hs-varop'>.</span> <span class='hs-varid'>contramap</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>runExceptT</span>
<a name="line-207"></a>
<a name="line-208"></a><a name="instance%20Contravariant%20(IdentityT%20f)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>IdentityT</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-209"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>IdentityT</span> <span class='hs-varop'>.</span> <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>runIdentityT</span>
<a name="line-210"></a>
<a name="line-211"></a><a name="instance%20Contravariant%20(ListT%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>ListT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-212"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ListT</span> <span class='hs-varop'>.</span> <span class='hs-varid'>contramap</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>runListT</span>
<a name="line-213"></a>
<a name="line-214"></a><a name="instance%20Contravariant%20(MaybeT%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>MaybeT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-215"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>MaybeT</span> <span class='hs-varop'>.</span> <span class='hs-varid'>contramap</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>runMaybeT</span>
<a name="line-216"></a>
<a name="line-217"></a><a name="instance%20Contravariant%20(Lazy.RWST%20r%20w%20s%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-conid'>RWST</span> <span class='hs-varid'>r</span> <span class='hs-varid'>w</span> <span class='hs-varid'>s</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-218"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-conid'>RWST</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>r</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span>
<a name="line-219"></a>    <span class='hs-varid'>contramap</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>s'</span><span class='hs-layout'>,</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>s'</span><span class='hs-layout'>,</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-varid'>runRWST</span> <span class='hs-varid'>m</span> <span class='hs-varid'>r</span> <span class='hs-varid'>s</span>
<a name="line-220"></a>
<a name="line-221"></a><a name="instance%20Contravariant%20(Strict.RWST%20r%20w%20s%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-conid'>RWST</span> <span class='hs-varid'>r</span> <span class='hs-varid'>w</span> <span class='hs-varid'>s</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-222"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-conid'>RWST</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>r</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span>
<a name="line-223"></a>    <span class='hs-varid'>contramap</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>s'</span><span class='hs-layout'>,</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>s'</span><span class='hs-layout'>,</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-varid'>runRWST</span> <span class='hs-varid'>m</span> <span class='hs-varid'>r</span> <span class='hs-varid'>s</span>
<a name="line-224"></a>
<a name="line-225"></a><a name="instance%20Contravariant%20(ReaderT%20r%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>ReaderT</span> <span class='hs-varid'>r</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-226"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ReaderT</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>runReaderT</span>
<a name="line-227"></a>
<a name="line-228"></a><a name="instance%20Contravariant%20(Lazy.StateT%20s%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-conid'>StateT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-229"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-conid'>StateT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span>
<a name="line-230"></a>    <span class='hs-varid'>contramap</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>s'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>s'</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-varid'>runStateT</span> <span class='hs-varid'>m</span> <span class='hs-varid'>s</span>
<a name="line-231"></a>
<a name="line-232"></a><a name="instance%20Contravariant%20(Strict.StateT%20s%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-conid'>StateT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-233"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-conid'>StateT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span>
<a name="line-234"></a>    <span class='hs-varid'>contramap</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>s'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>s'</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-varid'>runStateT</span> <span class='hs-varid'>m</span> <span class='hs-varid'>s</span>
<a name="line-235"></a>
<a name="line-236"></a><a name="instance%20Contravariant%20(Lazy.WriterT%20w%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-conid'>WriterT</span> <span class='hs-varid'>w</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-237"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-varid'>mapWriterT</span> <span class='hs-varop'>$</span> <span class='hs-varid'>contramap</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</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'>w</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</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'>w</span><span class='hs-layout'>)</span>
<a name="line-238"></a>
<a name="line-239"></a><a name="instance%20Contravariant%20(Strict.WriterT%20w%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-conid'>WriterT</span> <span class='hs-varid'>w</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-240"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-varid'>mapWriterT</span> <span class='hs-varop'>$</span> <span class='hs-varid'>contramap</span> <span class='hs-varop'>$</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'>w</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</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'>w</span><span class='hs-layout'>)</span>
<a name="line-241"></a>
<a name="line-242"></a><a name="instance%20Contravariant%20(Sum%20f%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sum</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-243"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>InL</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>InL</span> <span class='hs-layout'>(</span><span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span>
<a name="line-244"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>InR</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>InR</span> <span class='hs-layout'>(</span><span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span>
<a name="line-245"></a>
<a name="line-246"></a><a name="instance%20Contravariant%20(Product%20f%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>Product</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-247"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Pair</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Pair</span> <span class='hs-layout'>(</span><span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-248"></a>
<a name="line-249"></a><a name="instance%20Contravariant%20(Constant%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>Constant</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-250"></a>  <span class='hs-varid'>contramap</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>(</span><span class='hs-conid'>Constant</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Constant</span> <span class='hs-varid'>a</span>
<a name="line-251"></a>
<a name="line-252"></a><a name="instance%20Contravariant%20(Const%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</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-keyword'>where</span>
<a name="line-253"></a>  <span class='hs-varid'>contramap</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-varid'>a</span>
<a name="line-254"></a>
<a name="line-255"></a><a name="instance%20Contravariant%20(Compose%20f%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Functor</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>Compose</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-256"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Compose</span> <span class='hs-varid'>fga</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Compose</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>fga</span><span class='hs-layout'>)</span>
<a name="line-257"></a>  <span class='hs-comment'>{-# INLINE contramap #-}</span>
<a name="line-258"></a>
<a name="line-259"></a><a name="instance%20Contravariant%20(Backwards%20f)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>Backwards</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-260"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Backwards</span> <span class='hs-varop'>.</span> <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>forwards</span>
<a name="line-261"></a>  <span class='hs-comment'>{-# INLINE contramap #-}</span>
<a name="line-262"></a>
<a name="line-263"></a><a name="instance%20Contravariant%20(Reverse%20f)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>Reverse</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-264"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Reverse</span> <span class='hs-varop'>.</span> <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>getReverse</span>
<a name="line-265"></a>  <span class='hs-comment'>{-# INLINE contramap #-}</span>
<a name="line-266"></a>
<a name="line-267"></a><span class='hs-cpp'>#ifdef MIN_VERSION_StateVar</span>
<a name="line-268"></a><a name="instance%20Contravariant%20SettableStateVar"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-conid'>SettableStateVar</span> <span class='hs-keyword'>where</span>
<a name="line-269"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>SettableStateVar</span> <span class='hs-varid'>k</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>SettableStateVar</span> <span class='hs-layout'>(</span><span class='hs-varid'>k</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-270"></a>  <span class='hs-comment'>{-# INLINE contramap #-}</span>
<a name="line-271"></a><span class='hs-cpp'>#endif</span>
<a name="line-272"></a>
<a name="line-273"></a><span class='hs-cpp'>#if (__GLASGOW_HASKELL__ &gt;= 707) || defined(VERSION_tagged)</span>
<a name="line-274"></a><a name="instance%20Contravariant%20Proxy"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-conid'>Proxy</span> <span class='hs-keyword'>where</span>
<a name="line-275"></a>  <span class='hs-varid'>contramap</span> <span class='hs-keyword'>_</span> <span class='hs-conid'>Proxy</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Proxy</span>
<a name="line-276"></a><span class='hs-cpp'>#endif</span>
<a name="line-277"></a>
<a name="line-278"></a><a name="Predicate"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Predicate</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Predicate</span> <span class='hs-layout'>{</span> <span class='hs-varid'>getPredicate</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Bool</span> <span class='hs-layout'>}</span>
<a name="line-279"></a><span class='hs-cpp'>#ifdef LANGUAGE_DeriveDataTypeable</span>
<a name="line-280"></a>  <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-281"></a><span class='hs-cpp'>#endif</span>
<a name="line-282"></a>
<a name="line-283"></a><a name="instance%20Contravariant%20Predicate"></a><span class='hs-comment'>-- | A 'Predicate' is a 'Contravariant' 'Functor', because 'contramap' can</span>
<a name="line-284"></a><a name="instance%20Contravariant%20Predicate"></a><span class='hs-comment'>-- apply its function argument to the input of the predicate.</span>
<a name="line-285"></a><a name="instance%20Contravariant%20Predicate"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-conid'>Predicate</span> <span class='hs-keyword'>where</span>
<a name="line-286"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Predicate</span> <span class='hs-varop'>$</span> <span class='hs-varid'>getPredicate</span> <span class='hs-varid'>g</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-287"></a>
<a name="line-288"></a><a name="Comparison"></a><span class='hs-comment'>-- | Defines a total ordering on a type as per 'compare'</span>
<a name="line-289"></a><a name="Comparison"></a><span class='hs-comment'>--</span>
<a name="line-290"></a><a name="Comparison"></a><span class='hs-comment'>-- This condition is not checked by the types. You must ensure that the supplied</span>
<a name="line-291"></a><a name="Comparison"></a><span class='hs-comment'>-- values are valid total orderings yourself.</span>
<a name="line-292"></a><a name="Comparison"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Comparison</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Comparison</span> <span class='hs-layout'>{</span> <span class='hs-varid'>getComparison</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Ordering</span> <span class='hs-layout'>}</span>
<a name="line-293"></a><span class='hs-cpp'>#ifdef LANGUAGE_DeriveDataTypeable</span>
<a name="line-294"></a>  <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-295"></a><span class='hs-cpp'>#endif</span>
<a name="line-296"></a>
<a name="line-297"></a><a name="instance%20Contravariant%20Comparison"></a><span class='hs-comment'>-- | A 'Comparison' is a 'Contravariant' 'Functor', because 'contramap' can</span>
<a name="line-298"></a><a name="instance%20Contravariant%20Comparison"></a><span class='hs-comment'>-- apply its function argument to each input of the comparison function.</span>
<a name="line-299"></a><a name="instance%20Contravariant%20Comparison"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-conid'>Comparison</span> <span class='hs-keyword'>where</span>
<a name="line-300"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Comparison</span> <span class='hs-varop'>$</span> <span class='hs-varid'>on</span> <span class='hs-layout'>(</span><span class='hs-varid'>getComparison</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-varid'>f</span>
<a name="line-301"></a>
<a name="line-302"></a><span class='hs-cpp'>#ifdef MIN_VERSION_semigroups</span>
<a name="line-303"></a><a name="instance%20Semigroup%20(Comparison%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Comparison</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-304"></a>  <span class='hs-conid'>Comparison</span> <span class='hs-varid'>p</span> <span class='hs-varop'>&lt;&gt;</span> <span class='hs-conid'>Comparison</span> <span class='hs-varid'>q</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Comparison</span> <span class='hs-varop'>$</span> <span class='hs-varid'>mappend</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span>
<a name="line-305"></a><span class='hs-cpp'>#endif</span>
<a name="line-306"></a>
<a name="line-307"></a><a name="instance%20Monoid%20(Comparison%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Comparison</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-308"></a>  <span class='hs-varid'>mempty</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Comparison</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>EQ</span><span class='hs-layout'>)</span>
<a name="line-309"></a>  <span class='hs-varid'>mappend</span> <span class='hs-layout'>(</span><span class='hs-conid'>Comparison</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Comparison</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Comparison</span> <span class='hs-varop'>$</span> <span class='hs-varid'>mappend</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span>
<a name="line-310"></a>
<a name="line-311"></a><a name="defaultComparison"></a><span class='hs-comment'>-- | Compare using 'compare'</span>
<a name="line-312"></a><span class='hs-definition'>defaultComparison</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Comparison</span> <span class='hs-varid'>a</span>
<a name="line-313"></a><span class='hs-definition'>defaultComparison</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Comparison</span> <span class='hs-varid'>compare</span>
<a name="line-314"></a>
<a name="line-315"></a><a name="Equivalence"></a><span class='hs-comment'>-- | This data type represents an equivalence relation.</span>
<a name="line-316"></a><a name="Equivalence"></a><span class='hs-comment'>--</span>
<a name="line-317"></a><a name="Equivalence"></a><span class='hs-comment'>-- Equivalence relations are expected to satisfy three laws:</span>
<a name="line-318"></a><a name="Equivalence"></a><span class='hs-comment'>--</span>
<a name="line-319"></a><a name="Equivalence"></a><span class='hs-comment'>-- __Reflexivity__:</span>
<a name="line-320"></a><a name="Equivalence"></a><span class='hs-comment'>--</span>
<a name="line-321"></a><a name="Equivalence"></a><span class='hs-comment'>-- @</span>
<a name="line-322"></a><a name="Equivalence"></a><span class='hs-comment'>-- 'getEquivalence' f a a = True</span>
<a name="line-323"></a><a name="Equivalence"></a><span class='hs-comment'>-- @</span>
<a name="line-324"></a><a name="Equivalence"></a><span class='hs-comment'>--</span>
<a name="line-325"></a><a name="Equivalence"></a><span class='hs-comment'>-- __Symmetry__:</span>
<a name="line-326"></a><a name="Equivalence"></a><span class='hs-comment'>--</span>
<a name="line-327"></a><a name="Equivalence"></a><span class='hs-comment'>-- @</span>
<a name="line-328"></a><a name="Equivalence"></a><span class='hs-comment'>-- 'getEquivalence' f a b = 'getEquivalence' f b a</span>
<a name="line-329"></a><a name="Equivalence"></a><span class='hs-comment'>-- @</span>
<a name="line-330"></a><a name="Equivalence"></a><span class='hs-comment'>--</span>
<a name="line-331"></a><a name="Equivalence"></a><span class='hs-comment'>-- __Transitivity__:</span>
<a name="line-332"></a><a name="Equivalence"></a><span class='hs-comment'>--</span>
<a name="line-333"></a><a name="Equivalence"></a><span class='hs-comment'>-- If @'getEquivalence' f a b@ and @'getEquivalence' f b c@ are both 'True' then so is @'getEquivalence' f a c@</span>
<a name="line-334"></a><a name="Equivalence"></a><span class='hs-comment'>--</span>
<a name="line-335"></a><a name="Equivalence"></a><span class='hs-comment'>-- The types alone do not enforce these laws, so you'll have to check them yourself.</span>
<a name="line-336"></a><a name="Equivalence"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Equivalence</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Equivalence</span> <span class='hs-layout'>{</span> <span class='hs-varid'>getEquivalence</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Bool</span> <span class='hs-layout'>}</span>
<a name="line-337"></a><span class='hs-cpp'>#ifdef LANGUAGE_DeriveDataTypeable</span>
<a name="line-338"></a>  <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-339"></a><span class='hs-cpp'>#endif</span>
<a name="line-340"></a>
<a name="line-341"></a><a name="instance%20Contravariant%20Equivalence"></a><span class='hs-comment'>-- | Equivalence relations are 'Contravariant', because you can</span>
<a name="line-342"></a><a name="instance%20Contravariant%20Equivalence"></a><span class='hs-comment'>-- apply the contramapped function to each input to the equivalence</span>
<a name="line-343"></a><a name="instance%20Contravariant%20Equivalence"></a><span class='hs-comment'>-- relation.</span>
<a name="line-344"></a><a name="instance%20Contravariant%20Equivalence"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-conid'>Equivalence</span> <span class='hs-keyword'>where</span>
<a name="line-345"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Equivalence</span> <span class='hs-varop'>$</span> <span class='hs-varid'>on</span> <span class='hs-layout'>(</span><span class='hs-varid'>getEquivalence</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-varid'>f</span>
<a name="line-346"></a>
<a name="line-347"></a><span class='hs-cpp'>#ifdef MIN_VERSION_semigroups</span>
<a name="line-348"></a><a name="instance%20Semigroup%20(Equivalence%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Equivalence</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-349"></a>  <span class='hs-conid'>Equivalence</span> <span class='hs-varid'>p</span> <span class='hs-varop'>&lt;&gt;</span> <span class='hs-conid'>Equivalence</span> <span class='hs-varid'>q</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Equivalence</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>p</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-varop'>&amp;&amp;</span> <span class='hs-varid'>q</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-350"></a><span class='hs-cpp'>#endif</span>
<a name="line-351"></a>
<a name="line-352"></a><a name="instance%20Monoid%20(Equivalence%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Equivalence</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-353"></a>  <span class='hs-varid'>mempty</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Equivalence</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>True</span><span class='hs-layout'>)</span>
<a name="line-354"></a>  <span class='hs-varid'>mappend</span> <span class='hs-layout'>(</span><span class='hs-conid'>Equivalence</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Equivalence</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Equivalence</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>p</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-varop'>&amp;&amp;</span> <span class='hs-varid'>q</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-355"></a>
<a name="line-356"></a><a name="defaultEquivalence"></a><span class='hs-comment'>-- | Check for equivalence with '=='</span>
<a name="line-357"></a><span class='hs-comment'>--</span>
<a name="line-358"></a><span class='hs-comment'>-- Note: The instances for 'Double' and 'Float' violate reflexivity for @NaN@.</span>
<a name="line-359"></a><span class='hs-definition'>defaultEquivalence</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Equivalence</span> <span class='hs-varid'>a</span>
<a name="line-360"></a><span class='hs-definition'>defaultEquivalence</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Equivalence</span> <span class='hs-layout'>(</span><span class='hs-varop'>==</span><span class='hs-layout'>)</span>
<a name="line-361"></a>
<a name="line-362"></a><a name="comparisonEquivalence"></a><span class='hs-definition'>comparisonEquivalence</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Comparison</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Equivalence</span> <span class='hs-varid'>a</span>
<a name="line-363"></a><span class='hs-definition'>comparisonEquivalence</span> <span class='hs-layout'>(</span><span class='hs-conid'>Comparison</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Equivalence</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>p</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-varop'>==</span> <span class='hs-conid'>EQ</span>
<a name="line-364"></a>
<a name="line-365"></a><a name="Op"></a><span class='hs-comment'>-- | Dual function arrows.</span>
<a name="line-366"></a><a name="Op"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Op</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-layout'>{</span> <span class='hs-varid'>getOp</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-layout'>}</span>
<a name="line-367"></a><span class='hs-cpp'>#ifdef LANGUAGE_DeriveDataTypeable</span>
<a name="line-368"></a>  <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-369"></a><span class='hs-cpp'>#endif</span>
<a name="line-370"></a>
<a name="line-371"></a><a name="instance%20Category%20Op"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Category</span> <span class='hs-conid'>Op</span> <span class='hs-keyword'>where</span>
<a name="line-372"></a>  <span class='hs-varid'>id</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varid'>id</span>
<a name="line-373"></a>  <span class='hs-conid'>Op</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Op</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-374"></a>
<a name="line-375"></a><a name="instance%20Contravariant%20(Op%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Contravariant</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-376"></a>  <span class='hs-varid'>contramap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-layout'>(</span><span class='hs-varid'>getOp</span> <span class='hs-varid'>g</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-377"></a>
<a name="line-378"></a><span class='hs-cpp'>#ifdef MIN_VERSION_semigroups</span>
<a name="line-379"></a><a name="instance%20Semigroup%20(Op%20a%20b)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-380"></a>  <span class='hs-conid'>Op</span> <span class='hs-varid'>p</span> <span class='hs-varop'>&lt;&gt;</span> <span class='hs-conid'>Op</span> <span class='hs-varid'>q</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>p</span> <span class='hs-varid'>a</span> <span class='hs-varop'>&lt;&gt;</span> <span class='hs-varid'>q</span> <span class='hs-varid'>a</span>
<a name="line-381"></a><span class='hs-cpp'>#endif</span>
<a name="line-382"></a>
<a name="line-383"></a><a name="instance%20Monoid%20(Op%20a%20b)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-384"></a>  <span class='hs-varid'>mempty</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-layout'>(</span><span class='hs-varid'>const</span> <span class='hs-varid'>mempty</span><span class='hs-layout'>)</span>
<a name="line-385"></a>  <span class='hs-varid'>mappend</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>mappend</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>q</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-386"></a>
<a name="line-387"></a><span class='hs-cpp'>#if MIN_VERSION_base(4,5,0)</span>
<a name="line-388"></a><a name="instance%20Num%20(Op%20a%20b)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Num</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Num</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-389"></a>  <span class='hs-conid'>Op</span> <span class='hs-varid'>f</span> <span class='hs-varop'>+</span> <span class='hs-conid'>Op</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-varop'>+</span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span>
<a name="line-390"></a>  <span class='hs-conid'>Op</span> <span class='hs-varid'>f</span> <span class='hs-varop'>*</span> <span class='hs-conid'>Op</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-varop'>*</span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span>
<a name="line-391"></a>  <span class='hs-conid'>Op</span> <span class='hs-varid'>f</span> <span class='hs-comment'>-</span> <span class='hs-conid'>Op</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-comment'>-</span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span>
<a name="line-392"></a>  <span class='hs-varid'>abs</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>abs</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-393"></a>  <span class='hs-varid'>signum</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>signum</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-394"></a>  <span class='hs-varid'>fromInteger</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>.</span> <span class='hs-varid'>const</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fromInteger</span>
<a name="line-395"></a>
<a name="line-396"></a><a name="instance%20Fractional%20(Op%20a%20b)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Fractional</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Fractional</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-397"></a>  <span class='hs-conid'>Op</span> <span class='hs-varid'>f</span> <span class='hs-varop'>/</span> <span class='hs-conid'>Op</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-varop'>/</span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span>
<a name="line-398"></a>  <span class='hs-varid'>recip</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>recip</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-399"></a>  <span class='hs-varid'>fromRational</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>.</span> <span class='hs-varid'>const</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fromRational</span>
<a name="line-400"></a>
<a name="line-401"></a><a name="instance%20Floating%20(Op%20a%20b)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Floating</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Floating</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-402"></a>  <span class='hs-varid'>pi</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>const</span> <span class='hs-varid'>pi</span>
<a name="line-403"></a>  <span class='hs-varid'>exp</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>exp</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-404"></a>  <span class='hs-varid'>sqrt</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>sqrt</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-405"></a>  <span class='hs-varid'>log</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>log</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-406"></a>  <span class='hs-varid'>sin</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>sin</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-407"></a>  <span class='hs-varid'>tan</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>tan</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-408"></a>  <span class='hs-varid'>cos</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>cos</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-409"></a>  <span class='hs-varid'>asin</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>asin</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-410"></a>  <span class='hs-varid'>atan</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>atan</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-411"></a>  <span class='hs-varid'>acos</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>acos</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-412"></a>  <span class='hs-varid'>sinh</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>sinh</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-413"></a>  <span class='hs-varid'>tanh</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>tanh</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-414"></a>  <span class='hs-varid'>cosh</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>cosh</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-415"></a>  <span class='hs-varid'>asinh</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>asinh</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-416"></a>  <span class='hs-varid'>atanh</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>atanh</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-417"></a>  <span class='hs-varid'>acosh</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>acosh</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-418"></a>  <span class='hs-conid'>Op</span> <span class='hs-varid'>f</span> <span class='hs-varop'>**</span> <span class='hs-conid'>Op</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-varop'>**</span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span>
<a name="line-419"></a>  <span class='hs-varid'>logBase</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>logBase</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-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-420"></a><span class='hs-cpp'>#endif</span>
</pre></body>
</html>

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