/usr/share/doc/libghc-contravariant-doc/html/src/Data-Functor-Contravariant-Divisible.html is in libghc-contravariant-doc 1.3.3-1build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 | <?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html>
<head>
<!-- Generated by HsColour, http://code.haskell.org/~malcolm/hscolour/ -->
<title>src/Data/Functor/Contravariant/Divisible.hs</title>
<link type='text/css' rel='stylesheet' href='hscolour.css' />
</head>
<body>
<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE CPP #-}</span>
<a name="line-2"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-3"></a><span class='hs-comment'>-- |</span>
<a name="line-4"></a><span class='hs-comment'>-- Module : Data.Functor.Contravariant.Divisible</span>
<a name="line-5"></a><span class='hs-comment'>-- Copyright : (C) 2014-2015 Edward Kmett</span>
<a name="line-6"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-7"></a><span class='hs-comment'>--</span>
<a name="line-8"></a><span class='hs-comment'>-- Maintainer : Edward Kmett <ekmett@gmail.com></span>
<a name="line-9"></a><span class='hs-comment'>-- Stability : provisional</span>
<a name="line-10"></a><span class='hs-comment'>-- Portability : portable</span>
<a name="line-11"></a><span class='hs-comment'>--</span>
<a name="line-12"></a><span class='hs-comment'>-- This module supplies contravariant analogues to the 'Applicative' and 'Alternative' classes.</span>
<a name="line-13"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-14"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Functor</span><span class='hs-varop'>.</span><span class='hs-conid'>Contravariant</span><span class='hs-varop'>.</span><span class='hs-conid'>Divisible</span>
<a name="line-15"></a> <span class='hs-layout'>(</span>
<a name="line-16"></a> <span class='hs-comment'>-- * Contravariant Applicative</span>
<a name="line-17"></a> <span class='hs-conid'>Divisible</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>divided</span><span class='hs-layout'>,</span> <span class='hs-varid'>conquered</span><span class='hs-layout'>,</span> <span class='hs-varid'>liftD</span>
<a name="line-18"></a> <span class='hs-comment'>-- * Contravariant Alternative</span>
<a name="line-19"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Decidable</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>chosen</span><span class='hs-layout'>,</span> <span class='hs-varid'>lost</span>
<a name="line-20"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-21"></a>
<a name="line-22"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span>
<a name="line-23"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Functor</span><span class='hs-varop'>.</span><span class='hs-conid'>Contravariant</span>
<a name="line-24"></a>
<a name="line-25"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ < 710</span>
<a name="line-26"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Monoid</span>
<a name="line-27"></a><span class='hs-cpp'>#endif</span>
<a name="line-28"></a>
<a name="line-29"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Void</span>
<a name="line-30"></a>
<a name="line-31"></a><span class='hs-cpp'>#if MIN_VERSION_StateVar</span>
<a name="line-32"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>StateVar</span>
<a name="line-33"></a><span class='hs-cpp'>#endif</span>
<a name="line-34"></a>
<a name="line-35"></a><span class='hs-comment'>--------------------------------------------------------------------------------</span>
<a name="line-36"></a><span class='hs-comment'>-- * Contravariant Applicative</span>
<a name="line-37"></a><span class='hs-comment'>--------------------------------------------------------------------------------</span>
<a name="line-38"></a>
<a name="line-39"></a><a name="Divisible"></a><span class='hs-comment'>-- |</span>
<a name="line-40"></a><a name="Divisible"></a><span class='hs-comment'>--</span>
<a name="line-41"></a><a name="Divisible"></a><span class='hs-comment'>-- A 'Divisible' contravariant functor is the contravariant analogue of 'Applicative'.</span>
<a name="line-42"></a><a name="Divisible"></a><span class='hs-comment'>--</span>
<a name="line-43"></a><a name="Divisible"></a><span class='hs-comment'>-- In denser jargon, a 'Divisible' contravariant functor is a monoid object in the category</span>
<a name="line-44"></a><a name="Divisible"></a><span class='hs-comment'>-- of presheaves from Hask to Hask, equipped with Day convolution mapping the Cartesian</span>
<a name="line-45"></a><a name="Divisible"></a><span class='hs-comment'>-- product of the source to the Cartesian product of the target.</span>
<a name="line-46"></a><a name="Divisible"></a><span class='hs-comment'>--</span>
<a name="line-47"></a><a name="Divisible"></a><span class='hs-comment'>-- By way of contrast, an 'Applicative' functor can be viewed as a monoid object in the</span>
<a name="line-48"></a><a name="Divisible"></a><span class='hs-comment'>-- category of copresheaves from Hask to Hask, equipped with Day convolution mapping the</span>
<a name="line-49"></a><a name="Divisible"></a><span class='hs-comment'>-- Cartesian product of the source to the Cartesian product of the target.</span>
<a name="line-50"></a><a name="Divisible"></a><span class='hs-comment'>--</span>
<a name="line-51"></a><a name="Divisible"></a><span class='hs-comment'>-- Given the canonical diagonal morphism:</span>
<a name="line-52"></a><a name="Divisible"></a><span class='hs-comment'>--</span>
<a name="line-53"></a><a name="Divisible"></a><span class='hs-comment'>-- @</span>
<a name="line-54"></a><a name="Divisible"></a><span class='hs-comment'>-- delta a = (a,a)</span>
<a name="line-55"></a><a name="Divisible"></a><span class='hs-comment'>-- @</span>
<a name="line-56"></a><a name="Divisible"></a><span class='hs-comment'>-- </span>
<a name="line-57"></a><a name="Divisible"></a><span class='hs-comment'>-- @'divide' 'delta'@ should be associative with 'conquer' as a unit</span>
<a name="line-58"></a><a name="Divisible"></a><span class='hs-comment'>--</span>
<a name="line-59"></a><a name="Divisible"></a><span class='hs-comment'>-- @</span>
<a name="line-60"></a><a name="Divisible"></a><span class='hs-comment'>-- 'divide' 'delta' m 'conquer' = m</span>
<a name="line-61"></a><a name="Divisible"></a><span class='hs-comment'>-- 'divide' 'delta' 'conquer' m = m</span>
<a name="line-62"></a><a name="Divisible"></a><span class='hs-comment'>-- 'divide' 'delta' ('divide' 'delta' m n) o = 'divide' 'delta' m ('divide' 'delta' n o)</span>
<a name="line-63"></a><a name="Divisible"></a><span class='hs-comment'>-- @</span>
<a name="line-64"></a><a name="Divisible"></a><span class='hs-comment'>--</span>
<a name="line-65"></a><a name="Divisible"></a><span class='hs-comment'>-- With more general arguments you'll need to reassociate and project using the monoidal</span>
<a name="line-66"></a><a name="Divisible"></a><span class='hs-comment'>-- structure of the source category. (Here fst and snd are used in lieu of the more restricted</span>
<a name="line-67"></a><a name="Divisible"></a><span class='hs-comment'>-- lambda and rho, but this construction works with just a monoidal category.)</span>
<a name="line-68"></a><a name="Divisible"></a><span class='hs-comment'>--</span>
<a name="line-69"></a><a name="Divisible"></a><span class='hs-comment'>-- @</span>
<a name="line-70"></a><a name="Divisible"></a><span class='hs-comment'>-- 'divide' f m 'conquer' = 'contramap' ('fst' . f) m</span>
<a name="line-71"></a><a name="Divisible"></a><span class='hs-comment'>-- 'divide' f 'conquer' m = 'contramap' ('snd' . f) m</span>
<a name="line-72"></a><a name="Divisible"></a><span class='hs-comment'>-- 'divide' f ('divide' g m n) o = 'divide' f' m ('divide' 'id' n o) where</span>
<a name="line-73"></a><a name="Divisible"></a><span class='hs-comment'>-- f' a = case f a of (bc,d) -> case g bc of (b,c) -> (a,(b,c))</span>
<a name="line-74"></a><a name="Divisible"></a><span class='hs-comment'>-- @</span>
<a name="line-75"></a><a name="Divisible"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Divisible</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>where</span>
<a name="line-76"></a> <span class='hs-varid'>divide</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-77"></a> <span class='hs-comment'>-- | The underlying theory would suggest that this should be:</span>
<a name="line-78"></a> <span class='hs-comment'>--</span>
<a name="line-79"></a> <span class='hs-comment'>-- @</span>
<a name="line-80"></a> <span class='hs-comment'>-- conquer :: (a -> ()) -> f a</span>
<a name="line-81"></a> <span class='hs-comment'>-- @</span>
<a name="line-82"></a> <span class='hs-comment'>--</span>
<a name="line-83"></a> <span class='hs-comment'>-- However, as we are working over a Cartesian category (Hask) and the Cartesian product, such an input</span>
<a name="line-84"></a> <span class='hs-comment'>-- morphism is uniquely determined to be @'const' 'mempty'@, so we elide it.</span>
<a name="line-85"></a> <span class='hs-varid'>conquer</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-86"></a>
<a name="line-87"></a><a name="divided"></a><span class='hs-comment'>-- |</span>
<a name="line-88"></a><span class='hs-comment'>-- @</span>
<a name="line-89"></a><span class='hs-comment'>-- 'divided' = 'divide' 'id'</span>
<a name="line-90"></a><span class='hs-comment'>-- @</span>
<a name="line-91"></a><span class='hs-definition'>divided</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Divisible</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-92"></a><span class='hs-definition'>divided</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>divide</span> <span class='hs-varid'>id</span>
<a name="line-93"></a>
<a name="line-94"></a><a name="conquered"></a><span class='hs-comment'>-- | Redundant, but provided for symmetry.</span>
<a name="line-95"></a><span class='hs-comment'>--</span>
<a name="line-96"></a><span class='hs-comment'>-- @</span>
<a name="line-97"></a><span class='hs-comment'>-- 'conquered' = 'conquer</span>
<a name="line-98"></a><span class='hs-comment'>-- @</span>
<a name="line-99"></a><span class='hs-definition'>conquered</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Divisible</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>f</span> <span class='hs-conid'>()</span>
<a name="line-100"></a><span class='hs-definition'>conquered</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>conquer</span>
<a name="line-101"></a>
<a name="line-102"></a><a name="liftD"></a><span class='hs-comment'>-- |</span>
<a name="line-103"></a><span class='hs-comment'>-- This is the divisible analogue of 'liftA'. It gives a viable default definition for 'contramap' in terms</span>
<a name="line-104"></a><span class='hs-comment'>-- of the members of 'Divisible'.</span>
<a name="line-105"></a><span class='hs-comment'>--</span>
<a name="line-106"></a><span class='hs-comment'>-- @</span>
<a name="line-107"></a><span class='hs-comment'>-- 'liftD' f = 'divide' ((,) () . f) 'conquer'</span>
<a name="line-108"></a><span class='hs-comment'>-- @</span>
<a name="line-109"></a><span class='hs-definition'>liftD</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Divisible</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-110"></a><span class='hs-definition'>liftD</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>divide</span> <span class='hs-layout'>(</span><span class='hs-conid'>(,)</span> <span class='hs-conid'>()</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>conquer</span>
<a name="line-111"></a>
<a name="line-112"></a><a name="instance%20Divisible%20(Op%20r)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Divisible</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-113"></a> <span class='hs-varid'>divide</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>of</span>
<a name="line-114"></a> <span class='hs-layout'>(</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>h</span> <span class='hs-varid'>c</span>
<a name="line-115"></a> <span class='hs-varid'>conquer</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>const</span> <span class='hs-varid'>mempty</span>
<a name="line-116"></a>
<a name="line-117"></a><a name="instance%20Divisible%20Comparison"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Divisible</span> <span class='hs-conid'>Comparison</span> <span class='hs-keyword'>where</span>
<a name="line-118"></a> <span class='hs-varid'>divide</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Comparison</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Comparison</span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Comparison</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>of</span>
<a name="line-119"></a> <span class='hs-layout'>(</span><span class='hs-varid'>a'</span><span class='hs-layout'>,</span><span class='hs-varid'>a''</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyword'>of</span>
<a name="line-120"></a> <span class='hs-layout'>(</span><span class='hs-varid'>b'</span><span class='hs-layout'>,</span><span class='hs-varid'>b''</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-varid'>a'</span> <span class='hs-varid'>b'</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>h</span> <span class='hs-varid'>a''</span> <span class='hs-varid'>b''</span>
<a name="line-121"></a> <span class='hs-varid'>conquer</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Comparison</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>EQ</span>
<a name="line-122"></a>
<a name="line-123"></a><a name="instance%20Divisible%20Equivalence"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Divisible</span> <span class='hs-conid'>Equivalence</span> <span class='hs-keyword'>where</span>
<a name="line-124"></a> <span class='hs-varid'>divide</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Equivalence</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Equivalence</span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Equivalence</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>of</span>
<a name="line-125"></a> <span class='hs-layout'>(</span><span class='hs-varid'>a'</span><span class='hs-layout'>,</span><span class='hs-varid'>a''</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyword'>of</span>
<a name="line-126"></a> <span class='hs-layout'>(</span><span class='hs-varid'>b'</span><span class='hs-layout'>,</span><span class='hs-varid'>b''</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-varid'>a'</span> <span class='hs-varid'>b'</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>h</span> <span class='hs-varid'>a''</span> <span class='hs-varid'>b''</span>
<a name="line-127"></a> <span class='hs-varid'>conquer</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Equivalence</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>True</span>
<a name="line-128"></a>
<a name="line-129"></a><a name="instance%20Divisible%20Predicate"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Divisible</span> <span class='hs-conid'>Predicate</span> <span class='hs-keyword'>where</span>
<a name="line-130"></a> <span class='hs-varid'>divide</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Predicate</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Predicate</span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Predicate</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>of</span>
<a name="line-131"></a> <span class='hs-layout'>(</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>h</span> <span class='hs-varid'>c</span>
<a name="line-132"></a> <span class='hs-varid'>conquer</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Predicate</span> <span class='hs-varop'>$</span> <span class='hs-varid'>const</span> <span class='hs-conid'>True</span>
<a name="line-133"></a>
<a name="line-134"></a><a name="instance%20Divisible%20(Const%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Divisible</span> <span class='hs-layout'>(</span><span class='hs-conid'>Const</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-135"></a> <span class='hs-varid'>divide</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>(</span><span class='hs-conid'>Const</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Const</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Const</span> <span class='hs-layout'>(</span><span class='hs-varid'>mappend</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-136"></a> <span class='hs-varid'>conquer</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Const</span> <span class='hs-varid'>mempty</span>
<a name="line-137"></a>
<a name="line-138"></a><span class='hs-cpp'>#if MIN_VERSION_StateVar</span>
<a name="line-139"></a><a name="instance%20Divisible%20SettableStateVar"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Divisible</span> <span class='hs-conid'>SettableStateVar</span> <span class='hs-keyword'>where</span>
<a name="line-140"></a> <span class='hs-varid'>divide</span> <span class='hs-varid'>k</span> <span class='hs-layout'>(</span><span class='hs-conid'>SettableStateVar</span> <span class='hs-varid'>l</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>SettableStateVar</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>SettableStateVar</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>k</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>of</span>
<a name="line-141"></a> <span class='hs-layout'>(</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>l</span> <span class='hs-varid'>b</span> <span class='hs-varop'>>></span> <span class='hs-varid'>r</span> <span class='hs-varid'>c</span>
<a name="line-142"></a> <span class='hs-varid'>conquer</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>SettableStateVar</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>return</span> <span class='hs-conid'>()</span>
<a name="line-143"></a><span class='hs-cpp'>#endif</span>
<a name="line-144"></a>
<a name="line-145"></a><span class='hs-comment'>--------------------------------------------------------------------------------</span>
<a name="line-146"></a><span class='hs-comment'>-- * Contravariant Alternative</span>
<a name="line-147"></a><span class='hs-comment'>--------------------------------------------------------------------------------</span>
<a name="line-148"></a>
<a name="line-149"></a><span class='hs-comment'>-- |</span>
<a name="line-150"></a><span class='hs-comment'>--</span>
<a name="line-151"></a><span class='hs-comment'>-- A 'Divisible' contravariant functor is a monoid object in the category of presheaves </span>
<a name="line-152"></a><span class='hs-comment'>-- from Hask to Hask, equipped with Day convolution mapping the cartesian product of the</span>
<a name="line-153"></a><span class='hs-comment'>-- source to the Cartesian product of the target.</span>
<a name="line-154"></a><span class='hs-comment'>--</span>
<a name="line-155"></a><span class='hs-comment'>-- @</span>
<a name="line-156"></a><span class='hs-comment'>-- 'choose' 'Left' m ('lose' f) = m</span>
<a name="line-157"></a><span class='hs-comment'>-- 'choose' 'Right' ('lose' f) m = m</span>
<a name="line-158"></a><span class='hs-comment'>-- 'choose' f ('choose' g m n) o = 'divide' f' m ('divide' 'id' n o) where</span>
<a name="line-159"></a><span class='hs-comment'>-- f' bcd = 'either' ('either' 'id' ('Right' . 'Left') . g) ('Right' . 'Right') . f</span>
<a name="line-160"></a><span class='hs-comment'>-- @</span>
<a name="line-161"></a><span class='hs-comment'>--</span>
<a name="line-162"></a><span class='hs-comment'>-- In addition, we expect the same kind of distributive law as is satisfied by the usual</span>
<a name="line-163"></a><span class='hs-comment'>-- covariant 'Alternative', w.r.t 'Applicative', which should be fully formulated and</span>
<a name="line-164"></a><span class='hs-comment'>-- added here at some point!</span>
<a name="line-165"></a>
<a name="line-166"></a><a name="Decidable"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Divisible</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Decidable</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>where</span>
<a name="line-167"></a> <span class='hs-comment'>-- | The only way to win is not to play.</span>
<a name="line-168"></a> <span class='hs-varid'>lose</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Void</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-169"></a> <span class='hs-varid'>choose</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Either</span> <span class='hs-varid'>b</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-170"></a>
<a name="line-171"></a><a name="lost"></a><span class='hs-comment'>-- |</span>
<a name="line-172"></a><span class='hs-comment'>-- @</span>
<a name="line-173"></a><span class='hs-comment'>-- 'lost' = 'lose' 'id'</span>
<a name="line-174"></a><span class='hs-comment'>-- @</span>
<a name="line-175"></a><span class='hs-definition'>lost</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Decidable</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>f</span> <span class='hs-conid'>Void</span>
<a name="line-176"></a><span class='hs-definition'>lost</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lose</span> <span class='hs-varid'>id</span>
<a name="line-177"></a>
<a name="line-178"></a><a name="chosen"></a><span class='hs-comment'>-- |</span>
<a name="line-179"></a><span class='hs-comment'>-- @</span>
<a name="line-180"></a><span class='hs-comment'>-- 'chosen' = 'choose' 'id'</span>
<a name="line-181"></a><span class='hs-comment'>-- @</span>
<a name="line-182"></a><span class='hs-definition'>chosen</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Decidable</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Either</span> <span class='hs-varid'>b</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span>
<a name="line-183"></a><span class='hs-definition'>chosen</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>choose</span> <span class='hs-varid'>id</span>
<a name="line-184"></a>
<a name="line-185"></a><a name="instance%20Decidable%20Comparison"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Decidable</span> <span class='hs-conid'>Comparison</span> <span class='hs-keyword'>where</span>
<a name="line-186"></a> <span class='hs-varid'>lose</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Comparison</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>absurd</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-187"></a> <span class='hs-varid'>choose</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Comparison</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Comparison</span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Comparison</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>of</span>
<a name="line-188"></a> <span class='hs-conid'>Left</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyword'>of</span>
<a name="line-189"></a> <span class='hs-conid'>Left</span> <span class='hs-varid'>d</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-varid'>c</span> <span class='hs-varid'>d</span>
<a name="line-190"></a> <span class='hs-conid'>Right</span><span class='hs-layout'>{</span><span class='hs-layout'>}</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>LT</span>
<a name="line-191"></a> <span class='hs-conid'>Right</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyword'>of</span>
<a name="line-192"></a> <span class='hs-conid'>Left</span><span class='hs-layout'>{</span><span class='hs-layout'>}</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>GT</span>
<a name="line-193"></a> <span class='hs-conid'>Right</span> <span class='hs-varid'>d</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>h</span> <span class='hs-varid'>c</span> <span class='hs-varid'>d</span>
<a name="line-194"></a>
<a name="line-195"></a><a name="instance%20Decidable%20Equivalence"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Decidable</span> <span class='hs-conid'>Equivalence</span> <span class='hs-keyword'>where</span>
<a name="line-196"></a> <span class='hs-varid'>lose</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Equivalence</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>absurd</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-197"></a> <span class='hs-varid'>choose</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Equivalence</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Equivalence</span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Equivalence</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>of</span>
<a name="line-198"></a> <span class='hs-conid'>Left</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyword'>of</span>
<a name="line-199"></a> <span class='hs-conid'>Left</span> <span class='hs-varid'>d</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-varid'>c</span> <span class='hs-varid'>d</span>
<a name="line-200"></a> <span class='hs-conid'>Right</span><span class='hs-layout'>{</span><span class='hs-layout'>}</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>False</span>
<a name="line-201"></a> <span class='hs-conid'>Right</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyword'>of</span>
<a name="line-202"></a> <span class='hs-conid'>Left</span><span class='hs-layout'>{</span><span class='hs-layout'>}</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>False</span>
<a name="line-203"></a> <span class='hs-conid'>Right</span> <span class='hs-varid'>d</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>h</span> <span class='hs-varid'>c</span> <span class='hs-varid'>d</span>
<a name="line-204"></a>
<a name="line-205"></a><a name="instance%20Decidable%20Predicate"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Decidable</span> <span class='hs-conid'>Predicate</span> <span class='hs-keyword'>where</span>
<a name="line-206"></a> <span class='hs-varid'>lose</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Predicate</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>absurd</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-207"></a> <span class='hs-varid'>choose</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Predicate</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Predicate</span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Predicate</span> <span class='hs-varop'>$</span> <span class='hs-varid'>either</span> <span class='hs-varid'>g</span> <span class='hs-varid'>h</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-208"></a>
<a name="line-209"></a><a name="instance%20Decidable%20(Op%20r)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Decidable</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-210"></a> <span class='hs-varid'>lose</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>absurd</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-211"></a> <span class='hs-varid'>choose</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Op</span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Op</span> <span class='hs-varop'>$</span> <span class='hs-varid'>either</span> <span class='hs-varid'>g</span> <span class='hs-varid'>h</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-212"></a>
<a name="line-213"></a><span class='hs-cpp'>#if MIN_VERSION_StateVar</span>
<a name="line-214"></a><a name="instance%20Decidable%20SettableVar"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Decidable</span> <span class='hs-conid'>SettableVar</span> <span class='hs-keyword'>where</span>
<a name="line-215"></a> <span class='hs-varid'>lose</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>SettableStateVar</span> <span class='hs-layout'>(</span><span class='hs-varid'>absurd</span> <span class='hs-varop'>.</span> <span class='hs-varid'>k</span><span class='hs-layout'>)</span>
<a name="line-216"></a> <span class='hs-varid'>choose</span> <span class='hs-varid'>k</span> <span class='hs-layout'>(</span><span class='hs-conid'>SettableStateVar</span> <span class='hs-varid'>l</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>SettableStateVar</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>SettableStateVar</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>k</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>of</span>
<a name="line-217"></a> <span class='hs-conid'>Left</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>l</span> <span class='hs-varid'>b</span>
<a name="line-218"></a> <span class='hs-conid'>Right</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span> <span class='hs-varid'>c</span>
<a name="line-219"></a><span class='hs-cpp'>#endif</span>
</pre></body>
</html>
|