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<h3>
Marge Bot pushed to branch master
at <a href="https://gitlab.haskell.org/ghc/ghc">Glasgow Haskell Compiler / GHC</a>
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<h4>
Commits:
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<strong><a href="https://gitlab.haskell.org/ghc/ghc/-/commit/55e35c0b7e0f4b907dc21d42827b1cea4317226e">55e35c0b</a></strong>
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<span>by Baldur Blöndal</span>
<i>at 2020-05-13T20:02:48-04:00</i>
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<pre class="commit-message" style="white-space: pre-wrap; margin: 0;">Predicate, Equivalence derive via `.. -> a -> All'
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<h4>1 changed file:</h4>
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<a href="#981c552f9985d1ad638a2a41841595e04a25e37f">
libraries/base/Data/Functor/Contravariant.hs
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<h4>Changes:</h4>
<li id="981c552f9985d1ad638a2a41841595e04a25e37f">
<a href="https://gitlab.haskell.org/ghc/ghc/-/commit/55e35c0b7e0f4b907dc21d42827b1cea4317226e#981c552f9985d1ad638a2a41841595e04a25e37f"><strong>libraries/base/Data/Functor/Contravariant.hs</strong></a>
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<pre style="margin: 0;">+<span id="LC1" class="line" lang="haskell"><span class="cp" style="color: #999; font-weight: 600;">{-# LANGUAGE DerivingStrategies #-}</span></span>
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<pre style="margin: 0;">+<span id="LC2" class="line" lang="haskell"><span class="cp" style="color: #999; font-weight: 600;">{-# LANGUAGE DerivingVia #-}</span></span>
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<pre style="margin: 0;"> <span id="LC3" class="line" lang="haskell"><span class="cp" style="color: #999; font-weight: 600;">{-# LANGUAGE EmptyCase #-}</span></span>
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4
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<pre style="margin: 0;"> <span id="LC4" class="line" lang="haskell"><span class="cp" style="color: #999; font-weight: 600;">{-# LANGUAGE GeneralizedNewtypeDeriving #-}</span></span>
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<pre style="margin: 0;">+<span id="LC5" class="line" lang="haskell"><span class="cp" style="color: #999; font-weight: 600;">{-# LANGUAGE InstanceSigs #-}</span></span>
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<pre style="margin: 0;"> <span id="LC6" class="line" lang="haskell"><span class="cp" style="color: #999; font-weight: 600;">{-# LANGUAGE StandaloneDeriving #-}</span></span>
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<pre style="margin: 0;"> <span id="LC7" class="line" lang="haskell"><span class="cp" style="color: #999; font-weight: 600;">{-# LANGUAGE Trustworthy #-}</span></span>
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<pre style="margin: 0;"> <span id="LC8" class="line" lang="haskell"><span class="cp" style="color: #999; font-weight: 600;">{-# LANGUAGE TypeOperators #-}</span></span>
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<td class="diff-line-num unfold js-unfold old_line" data-linenumber="53" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>
<td class="diff-line-num unfold js-unfold new_line" data-linenumber="56" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>
<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -53,11 +56,11 @@ import Data.Functor.Product</td>
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<pre style="margin: 0;"> <span id="LC56" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">Data.Functor.Sum</span></span>
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<pre style="margin: 0;"> <span id="LC57" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">Data.Functor.Compose</span></span>
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<pre style="margin: 0;"> <span id="LC58" class="line" lang="haskell"></span>
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<pre style="margin: 0;">-<span id="LC56" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">Data.Monoid</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Alt</span><span class="p">(</span><span class="o" style="font-weight: 600;">..</span><span class="p">))</span></span>
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<pre style="margin: 0;">+<span id="LC59" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">Data.Monoid</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Alt</span><span class="p">(</span><span class="o" style="font-weight: 600;">..</span><span class="p">)<span class="idiff left">,</span></span><span class="idiff"> </span><span class="kt" style="color: #458; font-weight: 600;"><span class="idiff">All</span></span><span class="p"><span class="idiff">(</span></span><span class="o" style="font-weight: 600;"><span class="idiff">..</span></span><span class="p"><span class="idiff right">)</span>)</span></span>
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<pre style="margin: 0;"> <span id="LC60" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">Data.Proxy</span></span>
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<pre style="margin: 0;"> <span id="LC61" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">GHC.Generics</span></span>
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<pre style="margin: 0;"> <span id="LC62" class="line" lang="haskell"></span>
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<pre style="margin: 0;">-<span id="LC60" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">Prelude</span> <span class="k" style="font-weight: 600;">hiding</span> <span class="p">((</span><span class="o" style="font-weight: 600;">.</span><span class="p">),</span><span class="nf" style="color: #900; font-weight: 600;">id</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC63" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">import</span> <span class="nn" style="color: #555;">Prelude</span> <span class="k" style="font-weight: 600;">hiding</span> <span class="p">((</span><span class="o" style="font-weight: 600;">.</span><span class="p">),</span><span class="idiff left right"> </span><span class="nf" style="color: #900; font-weight: 600;">id</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC64" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC65" class="line" lang="haskell"><span class="cd">-- | The class of contravariant functors.</span></span>
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<pre style="margin: 0;"> <span id="LC66" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -76,6 +79,7 @@ import Prelude hiding ((.),id)</td>
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<pre style="margin: 0;"> <span id="LC79" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- newtype Predicate a = Predicate { getPredicate :: a -> Bool }</span></span>
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<pre style="margin: 0;"> <span id="LC80" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;"> <span id="LC81" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- instance Contravariant Predicate where</span></span>
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<pre style="margin: 0;">+<span id="LC82" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- contramap :: (a' -> a) -> (Predicate a -> Predicate a')</span></span>
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<pre style="margin: 0;"> <span id="LC83" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- contramap f (Predicate p) = Predicate (p . f)</span></span>
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<pre style="margin: 0;"> <span id="LC84" class="line" lang="haskell"><span class="cd">-- | `- First, map the input...</span></span>
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<pre style="margin: 0;"> <span id="LC85" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- `----- then apply the predicate.</span></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -86,7 +90,7 @@ import Prelude hiding ((.),id)</td>
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<pre style="margin: 0;"> <span id="LC90" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;"> <span id="LC91" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- Any instance should be subject to the following laws:</span></span>
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<pre style="margin: 0;"> <span id="LC92" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;">-<span id="LC89" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- [Identity] @'contramap' 'id' = 'id'@</span></span>
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<pre style="margin: 0;">+<span id="LC93" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- [Identity] @'contramap' 'id' <span class="idiff left right"> </span>= 'id'@</span></span>
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<pre style="margin: 0;"> <span id="LC94" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- [Composition] @'contramap' (g . f) = 'contramap' f . 'contramap' g@</span></span>
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<pre style="margin: 0;"> <span id="LC95" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;"> <span id="LC96" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- Note, that the second law follows from the free theorem of the type of</span></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -94,7 +98,7 @@ import Prelude hiding ((.),id)</td>
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<pre style="margin: 0;"> <span id="LC98" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- condition holds.</span></span>
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<pre style="margin: 0;"> <span id="LC99" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC100" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">class</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">f</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">-<span id="LC97" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="n" style="color: #333;">a</span><span class="idiff left"> </span><span class="o" style="font-weight: 600;"><span class="idiff">-></span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">b</span></span><span class="p"><span class="idiff">)</span></span><span class="idiff"> </span><span class="o" style="font-weight: 600;"><span class="idiff">-></span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">f</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">b</span></span><span class="idiff"> </span><span class="o" style="font-weight: 600;"><span class="idiff">-></span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">f</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff right">a</span></span></span>
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<pre style="margin: 0;">+<span id="LC101" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="n" style="color: #333;">a<span class="idiff left">'</span></span><span class="idiff"> </span><span class="o" style="font-weight: 600;"><span class="idiff">-></span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">a</span></span><span class="p"><span class="idiff">)</span></span><span class="idiff"> </span><span class="o" style="font-weight: 600;"><span class="idiff">-></span></span><span class="idiff"> </span><span class="p"><span class="idiff">(</span></span><span class="n" style="color: #333;"><span class="idiff">f</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">a</span></span><span class="idiff"> </span><span class="o" style="font-weight: 600;"><span class="idiff">-></span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">f</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">a'</span></span><span class="p"><span class="idiff right">)</span></span></span>
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<pre style="margin: 0;"> <span id="LC102" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC103" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- | Replace all locations in the output with the same value.</span></span>
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<pre style="margin: 0;"> <span id="LC104" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- The default definition is @'contramap' . 'const'@, but this may be</span></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -110,7 +114,7 @@ class Contravariant f where</td>
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<pre style="margin: 0;"> <span id="LC114" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- lawful we have the following laws:</span></span>
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<pre style="margin: 0;"> <span id="LC115" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;"> <span id="LC116" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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<pre style="margin: 0;">-<span id="LC113" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- 'fmap' f ≡ 'phantom'</span></span>
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<pre style="margin: 0;">+<span id="LC117" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- 'fmap' <span class="idiff left right"> </span>f ≡ 'phantom'</span></span>
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<pre style="margin: 0;"> <span id="LC118" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- 'contramap' f ≡ 'phantom'</span></span>
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<pre style="margin: 0;"> <span id="LC119" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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<pre style="margin: 0;"> <span id="LC120" class="line" lang="haskell"><span class="n" style="color: #333;">phantom</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Functor</span> <span class="n" style="color: #333;">f</span><span class="p">,</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">f</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=></span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">b</span></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -123,79 +127,134 @@ infixl 4 >$, $<, >$<, >$$<</td>
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<pre style="margin: 0;"> <span id="LC127" class="line" lang="haskell"><span class="p">(</span><span class="o" style="font-weight: 600;">$<</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">flip</span> <span class="p">(</span><span class="o" style="font-weight: 600;">>$</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC128" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC129" class="line" lang="haskell"><span class="cd">-- | This is an infix alias for 'contramap'.</span></span>
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<pre style="margin: 0;">-<span id="LC126" class="line" lang="haskell"><span class="p">(</span><span class="o" style="font-weight: 600;">>$<</span><span class="p">)</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">=></span> <span class="p">(</span><span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;"><span class="idiff left">f</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">b</span></span><span class="idiff"> </span><span class="o" style="font-weight: 600;"><span class="idiff">-></span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">f</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff right">a</span></span></span>
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<pre style="margin: 0;">+<span id="LC130" class="line" lang="haskell"><span class="p">(</span><span class="o" style="font-weight: 600;">>$<</span><span class="p">)</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">=></span> <span class="p">(</span><span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p"><span class="idiff left">(</span></span><span class="n" style="color: #333;"><span class="idiff">f</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">b</span></span><span class="idiff"> </span><span class="o" style="font-weight: 600;"><span class="idiff">-></span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">f</span></span><span class="idiff"> </span><span class="n" style="color: #333;"><span class="idiff">a</span></span><span class="p"><span class="idiff right">)</span></span></span>
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<pre style="margin: 0;"> <span id="LC131" class="line" lang="haskell"><span class="p">(</span><span class="o" style="font-weight: 600;">>$<</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">contramap</span></span>
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<pre style="margin: 0;"> <span id="LC132" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC133" class="line" lang="haskell"><span class="cd">-- | This is an infix version of 'contramap' with the arguments flipped.</span></span>
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<pre style="margin: 0;"> <span id="LC134" class="line" lang="haskell"><span class="p">(</span><span class="o" style="font-weight: 600;">>$$<</span><span class="p">)</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">=></span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">b</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">a</span></span>
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<pre style="margin: 0;"> <span id="LC135" class="line" lang="haskell"><span class="p">(</span><span class="o" style="font-weight: 600;">>$$<</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">flip</span> <span class="n" style="color: #333;">contramap</span></span>
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<pre style="margin: 0;"> <span id="LC136" class="line" lang="haskell"></span>
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<pre style="margin: 0;">-<span id="LC133" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">deriving</span> <span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Alt</span> <span class="n" style="color: #333;">f</span><span class="p">)</span></span>
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<pre style="margin: 0;">-<span id="LC134" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">deriving</span> <span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Rec1</span> <span class="n" style="color: #333;">f</span><span class="p">)</span></span>
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<pre style="margin: 0;">-<span id="LC135" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">deriving</span> <span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">M1</span> <span class="n" style="color: #333;">i</span> <span class="n" style="color: #333;">c</span> <span class="n" style="color: #333;">f</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC137" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">deriving</span> <span class="kr" style="font-weight: 600;"><span class="idiff left">newtype</span></span><span class="idiff right"> </span><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Alt</span> <span class="n" style="color: #333;">f</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC138" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">deriving</span> <span class="kr" style="font-weight: 600;"><span class="idiff left">newtype</span></span><span class="idiff right"> </span><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Rec1</span> <span class="n" style="color: #333;">f</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC139" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">deriving</span> <span class="kr" style="font-weight: 600;"><span class="idiff left">newtype</span></span><span class="idiff right"> </span><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">M1</span> <span class="n" style="color: #333;">i</span> <span class="n" style="color: #333;">c</span> <span class="n" style="color: #333;">f</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC140" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC141" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="kt" style="color: #458; font-weight: 600;">V1</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">+<span id="LC142" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="n" style="color: #333;">a'</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">V1</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">V1</span> <span class="n" style="color: #333;">a'</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC143" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="kr" style="font-weight: 600;">_</span> <span class="n" style="color: #333;">x</span> <span class="o" style="font-weight: 600;">=</span> <span class="kr" style="font-weight: 600;">case</span> <span class="n" style="color: #333;">x</span> <span class="kr" style="font-weight: 600;">of</span></span>
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<pre style="margin: 0;"> <span id="LC144" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC145" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="kt" style="color: #458; font-weight: 600;">U1</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">+<span id="LC146" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="n" style="color: #333;">a'</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">U1</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">U1</span> <span class="n" style="color: #333;">a'</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC147" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="kr" style="font-weight: 600;">_</span> <span class="kr" style="font-weight: 600;">_</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">U1</span></span>
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<pre style="margin: 0;"> <span id="LC148" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC149" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">K1</span> <span class="n" style="color: #333;">i</span> <span class="n" style="color: #333;">c</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">+<span id="LC150" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="n" style="color: #333;">a'</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">K1</span> <span class="n" style="color: #333;">i</span> <span class="n" style="color: #333;">c</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">K1</span> <span class="n" style="color: #333;">i</span> <span class="n" style="color: #333;">c</span> <span class="n" style="color: #333;">a'</span><span class="p">)</span></span>
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144
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151
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<pre style="margin: 0;"> <span id="LC151" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="kr" style="font-weight: 600;">_</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">K1</span> <span class="n" style="color: #333;">c</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">K1</span> <span class="n" style="color: #333;">c</span></span>
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145
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152
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<pre style="margin: 0;"> <span id="LC152" class="line" lang="haskell"></span>
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146
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153
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<pre style="margin: 0;"> <span id="LC153" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">f</span><span class="p">,</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="p">(</span><span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">:*:</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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154
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<pre style="margin: 0;">+<span id="LC154" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="n" style="color: #333;">a'</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">((</span><span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">:*:</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">:*:</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="n" style="color: #333;">a'</span><span class="p">)</span></span>
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147
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155
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<pre style="margin: 0;"> <span id="LC155" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="p">(</span><span class="n" style="color: #333;">xs</span> <span class="o" style="font-weight: 600;">:*:</span> <span class="n" style="color: #333;">ys</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">xs</span> <span class="o" style="font-weight: 600;">:*:</span> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">ys</span></span>
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148
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156
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<pre style="margin: 0;"> <span id="LC156" class="line" lang="haskell"></span>
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149
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157
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<pre style="margin: 0;"> <span id="LC157" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Functor</span> <span class="n" style="color: #333;">f</span><span class="p">,</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="p">(</span><span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">:.:</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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158
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<pre style="margin: 0;">+<span id="LC158" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="n" style="color: #333;">a'</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">((</span><span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">:.:</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">:.:</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="n" style="color: #333;">a'</span><span class="p">)</span></span>
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150
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159
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<pre style="margin: 0;"> <span id="LC159" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Comp1</span> <span class="n" style="color: #333;">fg</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Comp1</span> <span class="p">(</span><span class="n" style="color: #333;">fmap</span> <span class="p">(</span><span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span><span class="p">)</span> <span class="n" style="color: #333;">fg</span><span class="p">)</span></span>
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160
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<pre style="margin: 0;"> <span id="LC160" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC161" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">f</span><span class="p">,</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="p">(</span><span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">:+:</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">+<span id="LC162" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="n" style="color: #333;">a'</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">((</span><span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">:+:</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">:+:</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="n" style="color: #333;">a'</span><span class="p">)</span></span>
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163
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<pre style="margin: 0;"> <span id="LC163" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">L1</span> <span class="n" style="color: #333;">xs</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">L1</span> <span class="p">(</span><span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">xs</span><span class="p">)</span></span>
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164
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<pre style="margin: 0;"> <span id="LC164" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">R1</span> <span class="n" style="color: #333;">ys</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">R1</span> <span class="p">(</span><span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">ys</span><span class="p">)</span></span>
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165
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<pre style="margin: 0;"> <span id="LC165" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC166" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">f</span><span class="p">,</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Sum</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">+<span id="LC167" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="n" style="color: #333;">a'</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Sum</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">g</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Sum</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">g</span> <span class="n" style="color: #333;">a'</span><span class="p">)</span></span>
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157
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168
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<pre style="margin: 0;"> <span id="LC168" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">InL</span> <span class="n" style="color: #333;">xs</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">InL</span> <span class="p">(</span><span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">xs</span><span class="p">)</span></span>
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158
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169
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<pre style="margin: 0;"> <span id="LC169" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">InR</span> <span class="n" style="color: #333;">ys</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">InR</span> <span class="p">(</span><span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">ys</span><span class="p">)</span></span>
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159
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170
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<pre style="margin: 0;"> <span id="LC170" class="line" lang="haskell"></span>
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160
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171
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<pre style="margin: 0;"> <span id="LC171" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">f</span><span class="p">,</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">g</span><span class="p">)</span></span>
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161
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<pre style="margin: 0;">-<span id="LC161" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Product</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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162
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<pre style="margin: 0;">-<span id="LC162" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Pair</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Pair</span> <span class="p">(</span><span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="p">(</span><span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">b</span><span class="p">)</span></span>
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172
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<pre style="margin: 0;">+<span id="LC172" class="line" lang="haskell"> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Product</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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173
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<pre style="margin: 0;">+<span id="LC173" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="n" style="color: #333;">a'</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Product</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">g</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Product</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">g</span> <span class="n" style="color: #333;">a'</span><span class="p">)</span></span>
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174
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<pre style="margin: 0;">+<span id="LC174" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Pair</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Pair</span> <span class="p">(</span><span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="p">(</span><span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">b</span><span class="p">)</span></span>
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163
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175
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<pre style="margin: 0;"> <span id="LC175" class="line" lang="haskell"></span>
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164
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176
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<pre style="margin: 0;"> <span id="LC176" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Const</span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">+<span id="LC177" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="n" style="color: #333;">b'</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Const</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">b</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Const</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">b'</span><span class="p">)</span></span>
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165
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178
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<pre style="margin: 0;"> <span id="LC178" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="kr" style="font-weight: 600;">_</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Const</span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Const</span> <span class="n" style="color: #333;">a</span></span>
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166
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179
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<pre style="margin: 0;"> <span id="LC179" class="line" lang="haskell"></span>
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167
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180
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<pre style="margin: 0;"> <span id="LC180" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Functor</span> <span class="n" style="color: #333;">f</span><span class="p">,</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Compose</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">+<span id="LC181" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="n" style="color: #333;">a'</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Compose</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">g</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Compose</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">g</span> <span class="n" style="color: #333;">a'</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC182" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Compose</span> <span class="n" style="color: #333;">fga</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Compose</span> <span class="p">(</span><span class="n" style="color: #333;">fmap</span> <span class="p">(</span><span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span><span class="p">)</span> <span class="n" style="color: #333;">fga</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC183" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC184" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="kt" style="color: #458; font-weight: 600;">Proxy</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">+<span id="LC185" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="n" style="color: #333;">a'</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Proxy</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Proxy</span> <span class="n" style="color: #333;">a'</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC186" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="kr" style="font-weight: 600;">_</span> <span class="kr" style="font-weight: 600;">_</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Proxy</span></span>
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<pre style="margin: 0;"> <span id="LC187" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC188" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">newtype</span> <span class="kt" style="color: #458; font-weight: 600;">Predicate</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Predicate</span> <span class="p">{</span> <span class="n" style="color: #333;">getPredicate</span> <span class="o" style="font-weight: 600;">::</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Bool</span> <span class="p">}</span></span>
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<pre style="margin: 0;">-<span id="LC174" class="line" lang="haskell"></span>
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<pre style="margin: 0;">-<span id="LC175" class="line" lang="haskell"><span class="cd">-- | A 'Predicate' is a 'Contravariant' 'Functor', because 'contramap' can</span></span>
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<pre style="margin: 0;">-<span id="LC176" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- apply its function argument to the input of the predicate.</span></span>
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<pre style="margin: 0;">-<span id="LC177" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="kt" style="color: #458; font-weight: 600;">Predicate</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">-<span id="LC178" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">g</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Predicate</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">getPredicate</span> <span class="n" style="color: #333;">g</span> <span class="o" style="font-weight: 600;">.</span> <span class="n" style="color: #333;">f</span></span>
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<pre style="margin: 0;">-<span id="LC179" class="line" lang="haskell"></span>
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<pre style="margin: 0;">-<span id="LC180" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Semigroup</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Predicate</span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">-<span id="LC181" class="line" lang="haskell"> <span class="kt" style="color: #458; font-weight: 600;">Predicate</span> <span class="n" style="color: #333;">p</span> <span class="o" style="font-weight: 600;"><></span> <span class="kt" style="color: #458; font-weight: 600;">Predicate</span> <span class="n" style="color: #333;">q</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Predicate</span> <span class="o" style="font-weight: 600;">$</span> <span class="nf" style="color: #900; font-weight: 600;">\</span><span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">p</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">&&</span> <span class="n" style="color: #333;">q</span> <span class="n" style="color: #333;">a</span></span>
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<pre style="margin: 0;">-<span id="LC182" class="line" lang="haskell"></span>
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<pre style="margin: 0;">-<span id="LC183" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Monoid</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Predicate</span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">-<span id="LC184" class="line" lang="haskell"> <span class="n" style="color: #333;">mempty</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Predicate</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">const</span> <span class="kt" style="color: #458; font-weight: 600;">True</span></span>
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<pre style="margin: 0;">+<span id="LC189" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">deriving</span></span>
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190
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<pre style="margin: 0;">+<span id="LC190" class="line" lang="haskell"> <span class="p">(</span> <span class="c1" style="color: #998; font-style: italic;">-- | @('<>')@ on predicates uses logical conjunction @('&&')@ on</span></span>
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191
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<pre style="margin: 0;">+<span id="LC191" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- the results. Without newtypes this equals @'liftA2' (&&)@.</span></span>
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192
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<pre style="margin: 0;">+<span id="LC192" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">--</span></span>
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193
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<pre style="margin: 0;">+<span id="LC193" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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194
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<pre style="margin: 0;">+<span id="LC194" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- (<>) :: Predicate a -> Predicate a -> Predicate a</span></span>
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195
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<pre style="margin: 0;">+<span id="LC195" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- Predicate pred <> Predicate pred' = Predicate \a -></span></span>
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196
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<pre style="margin: 0;">+<span id="LC196" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- pred a && pred' a</span></span>
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197
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<pre style="margin: 0;">+<span id="LC197" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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198
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<pre style="margin: 0;">+<span id="LC198" class="line" lang="haskell"> <span class="kt" style="color: #458; font-weight: 600;">Semigroup</span></span>
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199
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<pre style="margin: 0;">+<span id="LC199" class="line" lang="haskell"> <span class="p">,</span> <span class="c1" style="color: #998; font-style: italic;">-- | @'mempty'@ on predicates always returns @True@. Without</span></span>
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200
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<pre style="margin: 0;">+<span id="LC200" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- newtypes this equals @'pure' True@.</span></span>
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201
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<pre style="margin: 0;">+<span id="LC201" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">--</span></span>
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202
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<pre style="margin: 0;">+<span id="LC202" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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203
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<pre style="margin: 0;">+<span id="LC203" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- mempty :: Predicate a</span></span>
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204
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<pre style="margin: 0;">+<span id="LC204" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- mempty = \_ -> True</span></span>
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205
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<pre style="margin: 0;">+<span id="LC205" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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206
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<pre style="margin: 0;">+<span id="LC206" class="line" lang="haskell"> <span class="kt" style="color: #458; font-weight: 600;">Monoid</span></span>
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207
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<pre style="margin: 0;">+<span id="LC207" class="line" lang="haskell"> <span class="p">)</span></span>
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208
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<pre style="margin: 0;">+<span id="LC208" class="line" lang="haskell"> <span class="n" style="color: #333;">via</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">All</span></span>
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209
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<pre style="margin: 0;">+<span id="LC209" class="line" lang="haskell"></span>
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210
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<pre style="margin: 0;">+<span id="LC210" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">deriving</span></span>
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211
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<pre style="margin: 0;">+<span id="LC211" class="line" lang="haskell"> <span class="p">(</span> <span class="c1" style="color: #998; font-style: italic;">-- | A 'Predicate' is a 'Contravariant' 'Functor', because</span></span>
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212
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<pre style="margin: 0;">+<span id="LC212" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- 'contramap' can apply its function argument to the input of</span></span>
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213
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<pre style="margin: 0;">+<span id="LC213" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- the predicate.</span></span>
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<pre style="margin: 0;">+<span id="LC214" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;">+<span id="LC215" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- Without newtypes @'contramap' f@ equals precomposing with @f@</span></span>
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216
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<pre style="margin: 0;">+<span id="LC216" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- (= @(. f)@).</span></span>
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<pre style="margin: 0;">+<span id="LC217" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">--</span></span>
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218
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<pre style="margin: 0;">+<span id="LC218" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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<pre style="margin: 0;">+<span id="LC219" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- contramap :: (a' -> a) -> (Predicate a -> Predicate a')</span></span>
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220
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<pre style="margin: 0;">+<span id="LC220" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- contramap f (Predicate g) = Predicate (g . f)</span></span>
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<pre style="margin: 0;">+<span id="LC221" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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<pre style="margin: 0;">+<span id="LC222" class="line" lang="haskell"> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span></span>
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<pre style="margin: 0;">+<span id="LC223" class="line" lang="haskell"> <span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC224" class="line" lang="haskell"> <span class="n" style="color: #333;">via</span> <span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="kt" style="color: #458; font-weight: 600;">Bool</span></span>
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185
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<pre style="margin: 0;"> <span id="LC225" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC226" class="line" lang="haskell"><span class="cd">-- | Defines a total ordering on a type as per 'compare'.</span></span>
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<pre style="margin: 0;"> <span id="LC227" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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188
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<pre style="margin: 0;"> <span id="LC228" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- This condition is not checked by the types. You must ensure that the</span></span>
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189
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<pre style="margin: 0;"> <span id="LC229" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- supplied values are valid total orderings yourself.</span></span>
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<pre style="margin: 0;"> <span id="LC230" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">newtype</span> <span class="kt" style="color: #458; font-weight: 600;">Comparison</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Comparison</span> <span class="p">{</span> <span class="n" style="color: #333;">getComparison</span> <span class="o" style="font-weight: 600;">::</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Ordering</span> <span class="p">}</span></span>
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<pre style="margin: 0;">-<span id="LC191" class="line" lang="haskell"></span>
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192
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<pre style="margin: 0;">-<span id="LC192" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">deriving</span> <span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Semigroup</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Comparison</span> <span class="n" style="color: #333;">a</span><span class="p">)</span></span>
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193
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<pre style="margin: 0;">-<span id="LC193" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">deriving</span> <span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Monoid</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Comparison</span> <span class="n" style="color: #333;">a</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC231" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">deriving</span></span>
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<pre style="margin: 0;">+<span id="LC232" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">newtype</span></span>
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<pre style="margin: 0;">+<span id="LC233" class="line" lang="haskell"> <span class="p">(</span> <span class="c1" style="color: #998; font-style: italic;">-- | @('<>')@ on comparisons combines results with @('<>')</span></span>
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<pre style="margin: 0;">+<span id="LC234" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- \@Ordering@. Without newtypes this equals @'liftA2' ('liftA2'</span></span>
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<pre style="margin: 0;">+<span id="LC235" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- ('<>'))@.</span></span>
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<pre style="margin: 0;">+<span id="LC236" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;">+<span id="LC237" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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<pre style="margin: 0;">+<span id="LC238" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- (<>) :: Comparison a -> Comparison a -> Comparison a</span></span>
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<pre style="margin: 0;">+<span id="LC239" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- Comparison cmp <> Comparison cmp' = Comparison \a a' -></span></span>
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<pre style="margin: 0;">+<span id="LC240" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- cmp a a' <> cmp a a'</span></span>
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<pre style="margin: 0;">+<span id="LC241" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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<pre style="margin: 0;">+<span id="LC242" class="line" lang="haskell"> <span class="kt" style="color: #458; font-weight: 600;">Semigroup</span></span>
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<pre style="margin: 0;">+<span id="LC243" class="line" lang="haskell"> <span class="p">,</span> <span class="c1" style="color: #998; font-style: italic;">-- | @'mempty'@ on comparisons always returns @EQ@. Without</span></span>
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<pre style="margin: 0;">+<span id="LC244" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- newtypes this equals @'pure' ('pure' EQ)@.</span></span>
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<pre style="margin: 0;">+<span id="LC245" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;">+<span id="LC246" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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<pre style="margin: 0;">+<span id="LC247" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- mempty :: Comparison a</span></span>
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<pre style="margin: 0;">+<span id="LC248" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- mempty = Comparison \_ _ -> EQ</span></span>
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<pre style="margin: 0;">+<span id="LC249" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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<pre style="margin: 0;">+<span id="LC250" class="line" lang="haskell"> <span class="kt" style="color: #458; font-weight: 600;">Monoid</span></span>
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<pre style="margin: 0;">+<span id="LC251" class="line" lang="haskell"> <span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC252" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC253" class="line" lang="haskell"><span class="cd">-- | A 'Comparison' is a 'Contravariant' 'Functor', because 'contramap' can</span></span>
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<pre style="margin: 0;"> <span id="LC254" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- apply its function argument to each input of the comparison function.</span></span>
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<pre style="margin: 0;"> <span id="LC255" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="kt" style="color: #458; font-weight: 600;">Comparison</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">-<span id="LC198" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">g</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Comparison</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">on</span> <span class="p">(</span><span class="n" style="color: #333;">getComparison</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="n" style="color: #333;">f</span></span>
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<pre style="margin: 0;">+<span id="LC256" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="n" style="color: #333;">a'</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Comparison</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Comparison</span> <span class="n" style="color: #333;">a'</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC257" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Comparison</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Comparison</span> <span class="p">(</span><span class="n" style="color: #333;">on</span> <span class="n" style="color: #333;">g</span> <span class="n" style="color: #333;">f</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC258" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC259" class="line" lang="haskell"><span class="cd">-- | Compare using 'compare'.</span></span>
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<pre style="margin: 0;"> <span id="LC260" class="line" lang="haskell"><span class="n" style="color: #333;">defaultComparison</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Ord</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Comparison</span> <span class="n" style="color: #333;">a</span></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -214,18 +273,34 @@ defaultComparison = Comparison compare</td>
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<pre style="margin: 0;"> <span id="LC273" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- The types alone do not enforce these laws, so you'll have to check them</span></span>
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<pre style="margin: 0;"> <span id="LC274" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- yourself.</span></span>
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<pre style="margin: 0;"> <span id="LC275" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">newtype</span> <span class="kt" style="color: #458; font-weight: 600;">Equivalence</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Equivalence</span> <span class="p">{</span> <span class="n" style="color: #333;">getEquivalence</span> <span class="o" style="font-weight: 600;">::</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Bool</span> <span class="p">}</span></span>
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<pre style="margin: 0;">+<span id="LC276" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">deriving</span></span>
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<pre style="margin: 0;">+<span id="LC277" class="line" lang="haskell"> <span class="p">(</span> <span class="c1" style="color: #998; font-style: italic;">-- | @('<>')@ on equivalences uses logical conjunction @('&&')@</span></span>
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<pre style="margin: 0;">+<span id="LC278" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- on the results. Without newtypes this equals @'liftA2'</span></span>
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<pre style="margin: 0;">+<span id="LC279" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- ('liftA2' (&&))@.</span></span>
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<pre style="margin: 0;">+<span id="LC280" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;">+<span id="LC281" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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<pre style="margin: 0;">+<span id="LC282" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- (<>) :: Equivalence a -> Equivalence a -> Equivalence a</span></span>
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<pre style="margin: 0;">+<span id="LC283" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- Equivalence equiv <> Equivalence equiv' = Equivalence \a b -></span></span>
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<pre style="margin: 0;">+<span id="LC284" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- equiv a b && equiv a b</span></span>
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<pre style="margin: 0;">+<span id="LC285" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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<pre style="margin: 0;">+<span id="LC286" class="line" lang="haskell"> <span class="kt" style="color: #458; font-weight: 600;">Semigroup</span></span>
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<pre style="margin: 0;">+<span id="LC287" class="line" lang="haskell"> <span class="p">,</span> <span class="c1" style="color: #998; font-style: italic;">-- | @'mempty'@ on equivalences always returns @True@. Without</span></span>
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<pre style="margin: 0;">+<span id="LC288" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- newtypes this equals @'pure' ('pure' True)@.</span></span>
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<pre style="margin: 0;">+<span id="LC289" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;">+<span id="LC290" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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<pre style="margin: 0;">+<span id="LC291" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- mempty :: Equivalence a</span></span>
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<pre style="margin: 0;">+<span id="LC292" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- mempty = Equivalence \_ _ -> True</span></span>
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<pre style="margin: 0;">+<span id="LC293" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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<pre style="margin: 0;">+<span id="LC294" class="line" lang="haskell"> <span class="kt" style="color: #458; font-weight: 600;">Monoid</span></span>
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<pre style="margin: 0;">+<span id="LC295" class="line" lang="haskell"> <span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC296" class="line" lang="haskell"> <span class="n" style="color: #333;">via</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">All</span></span>
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<pre style="margin: 0;"> <span id="LC297" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC298" class="line" lang="haskell"><span class="cd">-- | Equivalence relations are 'Contravariant', because you can</span></span>
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<pre style="margin: 0;"> <span id="LC299" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- apply the contramapped function to each input to the equivalence</span></span>
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<pre style="margin: 0;"> <span id="LC300" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">-- relation.</span></span>
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<pre style="margin: 0;"> <span id="LC301" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="kt" style="color: #458; font-weight: 600;">Equivalence</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">-<span id="LC222" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">g</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Equivalence</span> <span class="o" style="font-weight: 600;">$</span> <span class="n" style="color: #333;">on</span> <span class="p">(</span><span class="n" style="color: #333;">getEquivalence</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="n" style="color: #333;">f</span></span>
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<pre style="margin: 0;">-<span id="LC223" class="line" lang="haskell"></span>
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<pre style="margin: 0;">-<span id="LC224" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Semigroup</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Equivalence</span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">-<span id="LC225" class="line" lang="haskell"> <span class="kt" style="color: #458; font-weight: 600;">Equivalence</span> <span class="n" style="color: #333;">p</span> <span class="o" style="font-weight: 600;"><></span> <span class="kt" style="color: #458; font-weight: 600;">Equivalence</span> <span class="n" style="color: #333;">q</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Equivalence</span> <span class="o" style="font-weight: 600;">$</span> <span class="nf" style="color: #900; font-weight: 600;">\</span><span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">b</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">p</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">b</span> <span class="o" style="font-weight: 600;">&&</span> <span class="n" style="color: #333;">q</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">b</span></span>
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<pre style="margin: 0;">-<span id="LC226" class="line" lang="haskell"></span>
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<pre style="margin: 0;">-<span id="LC227" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Monoid</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Equivalence</span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">-<span id="LC228" class="line" lang="haskell"> <span class="n" style="color: #333;">mempty</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Equivalence</span> <span class="p">(</span><span class="nf" style="color: #900; font-weight: 600;">\</span><span class="kr" style="font-weight: 600;">_</span> <span class="kr" style="font-weight: 600;">_</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">True</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC302" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="n" style="color: #333;">a'</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Equivalence</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Equivalence</span> <span class="n" style="color: #333;">a'</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC303" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Equivalence</span> <span class="n" style="color: #333;">g</span><span class="p">)</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Equivalence</span> <span class="p">(</span><span class="n" style="color: #333;">on</span> <span class="n" style="color: #333;">g</span> <span class="n" style="color: #333;">f</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC304" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC305" class="line" lang="haskell"><span class="cd">-- | Check for equivalence with '=='.</span></span>
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<pre style="margin: 0;"> <span id="LC306" class="line" lang="haskell"><span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -238,15 +313,36 @@ comparisonEquivalence (Comparison p) = Equivalence $ \a b -> p a b == EQ</td>
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<pre style="margin: 0;"> <span id="LC313" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC314" class="line" lang="haskell"><span class="cd">-- | Dual function arrows.</span></span>
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<pre style="margin: 0;"> <span id="LC315" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">newtype</span> <span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">b</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="p">{</span> <span class="n" style="color: #333;">getOp</span> <span class="o" style="font-weight: 600;">::</span> <span class="n" style="color: #333;">b</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">a</span> <span class="p">}</span></span>
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<pre style="margin: 0;">-<span id="LC241" class="line" lang="haskell"></span>
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<pre style="margin: 0;">-<span id="LC242" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">deriving</span> <span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Semigroup</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Semigroup</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">b</span><span class="p">)</span></span>
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<pre style="margin: 0;">-<span id="LC243" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">deriving</span> <span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Monoid</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Monoid</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">b</span><span class="p">)</span></span>
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<pre style="margin: 0;">+<span id="LC316" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">deriving</span></span>
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<pre style="margin: 0;">+<span id="LC317" class="line" lang="haskell"> <span class="kr" style="font-weight: 600;">newtype</span></span>
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<pre style="margin: 0;">+<span id="LC318" class="line" lang="haskell"> <span class="p">(</span> <span class="c1" style="color: #998; font-style: italic;">-- | @('<>') \@(Op a b)@ without newtypes is @('<>') \@(b->a)@ =</span></span>
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<pre style="margin: 0;">+<span id="LC319" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @liftA2 ('<>')@. This lifts the 'Semigroup' operation</span></span>
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<pre style="margin: 0;">+<span id="LC320" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @('<>')@ over the output of @a@.</span></span>
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<pre style="margin: 0;">+<span id="LC321" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;">+<span id="LC322" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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<pre style="margin: 0;">+<span id="LC323" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- (<>) :: Op a b -> Op a b -> Op a b</span></span>
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<pre style="margin: 0;">+<span id="LC324" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- Op f <> Op g = Op \a -> f a <> g a</span></span>
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<pre style="margin: 0;">+<span id="LC325" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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<pre style="margin: 0;">+<span id="LC326" class="line" lang="haskell"> <span class="kt" style="color: #458; font-weight: 600;">Semigroup</span></span>
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<pre style="margin: 0;">+<span id="LC327" class="line" lang="haskell"> <span class="p">,</span> <span class="c1" style="color: #998; font-style: italic;">-- | @'mempty' \@(Op a b)@ without newtypes is @mempty \@(b->a)@</span></span>
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<pre style="margin: 0;">+<span id="LC328" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- = @\_ -> mempty@.</span></span>
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<pre style="margin: 0;">+<span id="LC329" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">--</span></span>
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<pre style="margin: 0;">+<span id="LC330" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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<pre style="margin: 0;">+<span id="LC331" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- mempty :: Op a b</span></span>
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<pre style="margin: 0;">+<span id="LC332" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- mempty = Op \_ -> mempty</span></span>
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<pre style="margin: 0;">+<span id="LC333" class="line" lang="haskell"> <span class="c1" style="color: #998; font-style: italic;">-- @</span></span>
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<pre style="margin: 0;">+<span id="LC334" class="line" lang="haskell"> <span class="kt" style="color: #458; font-weight: 600;">Monoid</span></span>
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<pre style="margin: 0;">+<span id="LC335" class="line" lang="haskell"> <span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC336" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC337" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Category</span> <span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">+<span id="LC338" class="line" lang="haskell"> <span class="n" style="color: #333;">id</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">a</span></span>
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<pre style="margin: 0;"> <span id="LC339" class="line" lang="haskell"> <span class="n" style="color: #333;">id</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="n" style="color: #333;">id</span></span>
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<pre style="margin: 0;">+<span id="LC340" class="line" lang="haskell"></span>
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<pre style="margin: 0;">+<span id="LC341" class="line" lang="haskell"> <span class="p">(</span><span class="o" style="font-weight: 600;">.</span><span class="p">)</span> <span class="o" style="font-weight: 600;">::</span> <span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="n" style="color: #333;">b</span> <span class="n" style="color: #333;">c</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">b</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">c</span></span>
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<pre style="margin: 0;"> <span id="LC342" class="line" lang="haskell"> <span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="n" style="color: #333;">f</span> <span class="o" style="font-weight: 600;">.</span> <span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="n" style="color: #333;">g</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="p">(</span><span class="n" style="color: #333;">g</span> <span class="o" style="font-weight: 600;">.</span> <span class="n" style="color: #333;">f</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC343" class="line" lang="haskell"></span>
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<pre style="margin: 0;"> <span id="LC344" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Contravariant</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="n" style="color: #333;">a</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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<pre style="margin: 0;">+<span id="LC345" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="o" style="font-weight: 600;">::</span> <span class="p">(</span><span class="n" style="color: #333;">b'</span> <span class="o" style="font-weight: 600;">-></span> <span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="o" style="font-weight: 600;">-></span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">b</span> <span class="o" style="font-weight: 600;">-></span> <span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">b'</span><span class="p">)</span></span>
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250
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<pre style="margin: 0;"> <span id="LC346" class="line" lang="haskell"> <span class="n" style="color: #333;">contramap</span> <span class="n" style="color: #333;">f</span> <span class="n" style="color: #333;">g</span> <span class="o" style="font-weight: 600;">=</span> <span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="p">(</span><span class="n" style="color: #333;">getOp</span> <span class="n" style="color: #333;">g</span> <span class="o" style="font-weight: 600;">.</span> <span class="n" style="color: #333;">f</span><span class="p">)</span></span>
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251
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347
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<pre style="margin: 0;"> <span id="LC347" class="line" lang="haskell"></span>
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252
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<td class="diff-line-num new_line" data-linenumber="348" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
348
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<pre style="margin: 0;"> <span id="LC348" class="line" lang="haskell"><span class="kr" style="font-weight: 600;">instance</span> <span class="kt" style="color: #458; font-weight: 600;">Num</span> <span class="n" style="color: #333;">a</span> <span class="o" style="font-weight: 600;">=></span> <span class="kt" style="color: #458; font-weight: 600;">Num</span> <span class="p">(</span><span class="kt" style="color: #458; font-weight: 600;">Op</span> <span class="n" style="color: #333;">a</span> <span class="n" style="color: #333;">b</span><span class="p">)</span> <span class="kr" style="font-weight: 600;">where</span></span>
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