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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, FunctionalDependencies
<a name="line-2"></a> , UndecidableInstances, ScopedTypeVariables
<a name="line-3"></a> #-}</span>
<a name="line-4"></a><span class='hs-comment'>{-# OPTIONS_GHC -Wall #-}</span>
<a name="line-5"></a><span class='hs-comment'>----------------------------------------------------------------------</span>
<a name="line-6"></a><span class='hs-comment'>-- |</span>
<a name="line-7"></a><span class='hs-comment'>-- Module : Data.Boolean</span>
<a name="line-8"></a><span class='hs-comment'>-- Copyright : (c) Conal Elliott 2009</span>
<a name="line-9"></a><span class='hs-comment'>-- License : BSD3</span>
<a name="line-10"></a><span class='hs-comment'>-- </span>
<a name="line-11"></a><span class='hs-comment'>-- Maintainer : conal@conal.net</span>
<a name="line-12"></a><span class='hs-comment'>-- Stability : experimental</span>
<a name="line-13"></a><span class='hs-comment'>-- </span>
<a name="line-14"></a><span class='hs-comment'>-- Some classes for generalized boolean operations.</span>
<a name="line-15"></a><span class='hs-comment'>-- </span>
<a name="line-16"></a><span class='hs-comment'>-- In this design, for if-then-else, equality and inequality tests, the</span>
<a name="line-17"></a><span class='hs-comment'>-- boolean type depends functionally on the value type. This dependency</span>
<a name="line-18"></a><span class='hs-comment'>-- allows the boolean type to be inferred in a conditional expression.</span>
<a name="line-19"></a><span class='hs-comment'>-- </span>
<a name="line-20"></a><span class='hs-comment'>-- I also tried using a unary type constructor class. The class doesn't work</span>
<a name="line-21"></a><span class='hs-comment'>-- for regular booleans, so generality is lost. Also, we'd probably have</span>
<a name="line-22"></a><span class='hs-comment'>-- to wire class constraints in like: @(==*) :: Eq a => f Bool -> f a -> f</span>
<a name="line-23"></a><span class='hs-comment'>-- a -> f a@, which disallows situations needing additional constraints,</span>
<a name="line-24"></a><span class='hs-comment'>-- e.g., Show.</span>
<a name="line-25"></a><span class='hs-comment'>-- </span>
<a name="line-26"></a><span class='hs-comment'>----------------------------------------------------------------------</span>
<a name="line-27"></a>
<a name="line-28"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Boolean</span>
<a name="line-29"></a> <span class='hs-layout'>(</span>
<a name="line-30"></a> <span class='hs-conid'>Boolean</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span><span class='hs-conid'>IfB</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'>boolean</span><span class='hs-layout'>,</span> <span class='hs-varid'>cond</span><span class='hs-layout'>,</span> <span class='hs-varid'>crop</span>
<a name="line-31"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>EqB</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-conid'>OrdB</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'>minB</span><span class='hs-layout'>,</span> <span class='hs-varid'>maxB</span>
<a name="line-32"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-33"></a>
<a name="line-34"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monoid</span><span class='hs-layout'>,</span><span class='hs-varid'>mempty</span><span class='hs-layout'>)</span>
<a name="line-35"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span> <span class='hs-layout'>(</span><span class='hs-conid'>Applicative</span><span class='hs-layout'>(</span><span class='hs-varid'>pure</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span><span class='hs-varid'>liftA2</span><span class='hs-layout'>,</span><span class='hs-varid'>liftA3</span><span class='hs-layout'>)</span>
<a name="line-36"></a>
<a name="line-37"></a>
<a name="line-38"></a><span class='hs-comment'>{--------------------------------------------------------------------
<a name="line-39"></a> Classes
<a name="line-40"></a>--------------------------------------------------------------------}</span>
<a name="line-41"></a>
<a name="line-42"></a><span class='hs-keyword'>infixr</span> <span class='hs-num'>3</span> <span class='hs-varop'>&&*</span>
<a name="line-43"></a><span class='hs-keyword'>infixr</span> <span class='hs-num'>2</span> <span class='hs-varop'>||*</span>
<a name="line-44"></a>
<a name="line-45"></a><a name="Boolean"></a><span class='hs-comment'>-- | Generalized boolean class</span>
<a name="line-46"></a><a name="Boolean"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Boolean</span> <span class='hs-varid'>b</span> <span class='hs-keyword'>where</span>
<a name="line-47"></a> <span class='hs-varid'>true</span><span class='hs-layout'>,</span> <span class='hs-varid'>false</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>b</span>
<a name="line-48"></a> <span class='hs-varid'>notB</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span>
<a name="line-49"></a> <span class='hs-layout'>(</span><span class='hs-varop'>&&*</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>||*</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span>
<a name="line-50"></a>
<a name="line-51"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Boolean</span> <span class='hs-conid'>Bool</span> <span class='hs-keyword'>where</span>
<a name="line-52"></a> <span class='hs-varid'>true</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-53"></a> <span class='hs-varid'>false</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-54"></a> <span class='hs-varid'>notB</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>not</span>
<a name="line-55"></a> <span class='hs-layout'>(</span><span class='hs-varop'>&&*</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'>&&</span><span class='hs-layout'>)</span>
<a name="line-56"></a> <span class='hs-layout'>(</span><span class='hs-varop'>||*</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'>||</span><span class='hs-layout'>)</span>
<a name="line-57"></a>
<a name="line-58"></a><a name="IfB"></a><span class='hs-comment'>-- | Types with conditionals</span>
<a name="line-59"></a><a name="IfB"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Boolean</span> <span class='hs-varid'>bool</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>bool</span> <span class='hs-keyword'>where</span>
<a name="line-60"></a> <span class='hs-varid'>ifB</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>bool</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-61"></a>
<a name="line-62"></a><a name="boolean"></a><span class='hs-comment'>-- | Expression-lifted conditional with condition last</span>
<a name="line-63"></a><span class='hs-definition'>boolean</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>bool</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-64"></a><span class='hs-definition'>boolean</span> <span class='hs-varid'>t</span> <span class='hs-varid'>e</span> <span class='hs-varid'>bool</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>ifB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>t</span> <span class='hs-varid'>e</span>
<a name="line-65"></a>
<a name="line-66"></a><a name="cond"></a><span class='hs-comment'>-- | Point-wise conditional</span>
<a name="line-67"></a><span class='hs-definition'>cond</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Applicative</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>f</span> <span class='hs-varid'>bool</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'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-68"></a><span class='hs-definition'>cond</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA3</span> <span class='hs-varid'>ifB</span>
<a name="line-69"></a>
<a name="line-70"></a><a name="crop"></a><span class='hs-comment'>-- | Crop a function, filling in 'mempty' where the test yeis false.</span>
<a name="line-71"></a><span class='hs-definition'>crop</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Applicative</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>f</span> <span class='hs-varid'>bool</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'>a</span>
<a name="line-72"></a><span class='hs-definition'>crop</span> <span class='hs-varid'>r</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>cond</span> <span class='hs-varid'>r</span> <span class='hs-varid'>f</span> <span class='hs-varid'>mempty</span>
<a name="line-73"></a>
<a name="line-74"></a>
<a name="line-75"></a><span class='hs-keyword'>infix</span> <span class='hs-num'>4</span> <span class='hs-varop'>==*</span><span class='hs-layout'>,</span> <span class='hs-varop'>/=*</span>
<a name="line-76"></a>
<a name="line-77"></a><a name="EqB"></a><span class='hs-comment'>-- | Types with equality. Minimum definition: '(==*)'.</span>
<a name="line-78"></a><a name="EqB"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Boolean</span> <span class='hs-varid'>bool</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>EqB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>bool</span> <span class='hs-keyword'>where</span>
<a name="line-79"></a> <span class='hs-layout'>(</span><span class='hs-varop'>==*</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>/=*</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>bool</span>
<a name="line-80"></a> <span class='hs-varid'>u</span> <span class='hs-varop'>/=*</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>notB</span> <span class='hs-layout'>(</span><span class='hs-varid'>u</span> <span class='hs-varop'>==*</span> <span class='hs-varid'>v</span><span class='hs-layout'>)</span>
<a name="line-81"></a>
<a name="line-82"></a><span class='hs-keyword'>infix</span> <span class='hs-num'>4</span> <span class='hs-varop'><*</span><span class='hs-layout'>,</span> <span class='hs-varop'><=*</span><span class='hs-layout'>,</span> <span class='hs-varop'>>=*</span><span class='hs-layout'>,</span> <span class='hs-varop'>>*</span>
<a name="line-83"></a>
<a name="line-84"></a><a name="OrdB"></a><span class='hs-comment'>-- | Types with inequality. Minimum definition: '(<*)'.</span>
<a name="line-85"></a><a name="OrdB"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Boolean</span> <span class='hs-varid'>bool</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>OrdB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>bool</span> <span class='hs-keyword'>where</span>
<a name="line-86"></a> <span class='hs-layout'>(</span><span class='hs-varop'><*</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'><=*</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>>*</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>>=*</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>bool</span>
<a name="line-87"></a> <span class='hs-varid'>u</span> <span class='hs-varop'>>*</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>v</span> <span class='hs-varop'><*</span> <span class='hs-varid'>u</span>
<a name="line-88"></a> <span class='hs-varid'>u</span> <span class='hs-varop'>>=*</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>notB</span> <span class='hs-layout'>(</span><span class='hs-varid'>u</span> <span class='hs-varop'><*</span> <span class='hs-varid'>v</span><span class='hs-layout'>)</span>
<a name="line-89"></a> <span class='hs-varid'>u</span> <span class='hs-varop'><=*</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>v</span> <span class='hs-varop'>>=*</span> <span class='hs-varid'>u</span>
<a name="line-90"></a>
<a name="line-91"></a><a name="minB"></a><span class='hs-comment'>-- | Variant of 'min' using 'ifB' and '(<=*)'</span>
<a name="line-92"></a><span class='hs-definition'>minB</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>OrdB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-93"></a><a name="minB"></a><span class='hs-definition'>u</span> <span class='hs-varop'>`minB`</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>ifB</span> <span class='hs-layout'>(</span><span class='hs-varid'>u</span> <span class='hs-varop'><=*</span> <span class='hs-varid'>v</span><span class='hs-layout'>)</span> <span class='hs-varid'>u</span> <span class='hs-varid'>v</span>
<a name="line-94"></a>
<a name="line-95"></a><a name="maxB"></a><span class='hs-comment'>-- | Variant of 'max' using 'ifB' and '(>=*)'</span>
<a name="line-96"></a><span class='hs-definition'>maxB</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>OrdB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-97"></a><a name="maxB"></a><span class='hs-definition'>u</span> <span class='hs-varop'>`maxB`</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>ifB</span> <span class='hs-layout'>(</span><span class='hs-varid'>u</span> <span class='hs-varop'>>=*</span> <span class='hs-varid'>v</span><span class='hs-layout'>)</span> <span class='hs-varid'>u</span> <span class='hs-varid'>v</span>
<a name="line-98"></a>
<a name="line-99"></a><span class='hs-comment'>{--------------------------------------------------------------------
<a name="line-100"></a> Some instances
<a name="line-101"></a>--------------------------------------------------------------------}</span>
<a name="line-102"></a>
<a name="line-103"></a><a name="ife"></a><span class='hs-definition'>ife</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Bool</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-104"></a><span class='hs-definition'>ife</span> <span class='hs-varid'>c</span> <span class='hs-varid'>t</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>c</span> <span class='hs-keyword'>then</span> <span class='hs-varid'>t</span> <span class='hs-keyword'>else</span> <span class='hs-varid'>e</span>
<a name="line-105"></a>
<a name="line-106"></a><span class='hs-comment'>-- I'd give the following instances:</span>
<a name="line-107"></a><span class='hs-comment'>-- </span>
<a name="line-108"></a><span class='hs-comment'>-- instance IfB Bool a where ifB = ife</span>
<a name="line-109"></a><span class='hs-comment'>-- instance EqB Bool a where { (==*) = (==) ; (/=*) = (/=) }</span>
<a name="line-110"></a><span class='hs-comment'>-- instance OrdB Bool a where { (<*) = (<) ; (<=*) = (<=)}</span>
<a name="line-111"></a><span class='hs-comment'>-- </span>
<a name="line-112"></a><span class='hs-comment'>-- Sadly, doing so would break the a->bool fundep, which is needed elsewhere</span>
<a name="line-113"></a><span class='hs-comment'>-- for disambiguation. So use the instances above as templates, filling</span>
<a name="line-114"></a><span class='hs-comment'>-- in specific types for a.</span>
<a name="line-115"></a>
<a name="line-116"></a>
<a name="line-117"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IfB</span> <span class='hs-conid'>Bool</span> <span class='hs-conid'>Float</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>ifB</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>ife</span>
<a name="line-118"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>EqB</span> <span class='hs-conid'>Bool</span> <span class='hs-conid'>Float</span> <span class='hs-keyword'>where</span> <span class='hs-layout'>{</span> <span class='hs-layout'>(</span><span class='hs-varop'>==*</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'>==</span><span class='hs-layout'>)</span> <span class='hs-layout'>;</span> <span class='hs-layout'>(</span><span class='hs-varop'>/=*</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'>/=</span><span class='hs-layout'>)</span> <span class='hs-layout'>}</span>
<a name="line-119"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>OrdB</span> <span class='hs-conid'>Bool</span> <span class='hs-conid'>Float</span> <span class='hs-keyword'>where</span> <span class='hs-layout'>{</span> <span class='hs-layout'>(</span><span class='hs-varop'><*</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'><</span><span class='hs-layout'>)</span> <span class='hs-layout'>;</span> <span class='hs-layout'>(</span><span class='hs-varop'><=*</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'><=</span><span class='hs-layout'>)</span> <span class='hs-layout'>}</span>
<a name="line-120"></a>
<a name="line-121"></a><span class='hs-comment'>-- Similarly for other types. </span>
<a name="line-122"></a>
<a name="line-123"></a>
<a name="line-124"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span><span class='hs-layout'>,</span><span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-125"></a> <span class='hs-varid'>ifB</span> <span class='hs-varid'>w</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span><span class='hs-layout'>,</span><span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>p'</span><span class='hs-layout'>,</span><span class='hs-varid'>q'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>ifB</span> <span class='hs-varid'>w</span> <span class='hs-varid'>p</span> <span class='hs-varid'>p'</span><span class='hs-layout'>,</span> <span class='hs-varid'>ifB</span> <span class='hs-varid'>w</span> <span class='hs-varid'>q</span> <span class='hs-varid'>q'</span><span class='hs-layout'>)</span>
<a name="line-126"></a>
<a name="line-127"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>q</span><span class='hs-layout'>,</span> <span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span><span class='hs-layout'>,</span><span class='hs-varid'>q</span><span class='hs-layout'>,</span><span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-128"></a> <span class='hs-varid'>ifB</span> <span class='hs-varid'>w</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span><span class='hs-layout'>,</span><span class='hs-varid'>q</span><span class='hs-layout'>,</span><span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>p'</span><span class='hs-layout'>,</span><span class='hs-varid'>q'</span><span class='hs-layout'>,</span><span class='hs-varid'>r'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>ifB</span> <span class='hs-varid'>w</span> <span class='hs-varid'>p</span> <span class='hs-varid'>p'</span><span class='hs-layout'>,</span> <span class='hs-varid'>ifB</span> <span class='hs-varid'>w</span> <span class='hs-varid'>q</span> <span class='hs-varid'>q'</span><span class='hs-layout'>,</span> <span class='hs-varid'>ifB</span> <span class='hs-varid'>w</span> <span class='hs-varid'>r</span> <span class='hs-varid'>r'</span><span class='hs-layout'>)</span>
<a name="line-129"></a>
<a name="line-130"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>q</span><span class='hs-layout'>,</span> <span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>r</span><span class='hs-layout'>,</span> <span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span><span class='hs-layout'>,</span><span class='hs-varid'>q</span><span class='hs-layout'>,</span><span class='hs-varid'>r</span><span class='hs-layout'>,</span><span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-131"></a> <span class='hs-varid'>ifB</span> <span class='hs-varid'>w</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span><span class='hs-layout'>,</span><span class='hs-varid'>q</span><span class='hs-layout'>,</span><span class='hs-varid'>r</span><span class='hs-layout'>,</span><span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>p'</span><span class='hs-layout'>,</span><span class='hs-varid'>q'</span><span class='hs-layout'>,</span><span class='hs-varid'>r'</span><span class='hs-layout'>,</span><span class='hs-varid'>s'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-132"></a> <span class='hs-layout'>(</span><span class='hs-varid'>ifB</span> <span class='hs-varid'>w</span> <span class='hs-varid'>p</span> <span class='hs-varid'>p'</span><span class='hs-layout'>,</span> <span class='hs-varid'>ifB</span> <span class='hs-varid'>w</span> <span class='hs-varid'>q</span> <span class='hs-varid'>q'</span><span class='hs-layout'>,</span> <span class='hs-varid'>ifB</span> <span class='hs-varid'>w</span> <span class='hs-varid'>r</span> <span class='hs-varid'>r'</span><span class='hs-layout'>,</span> <span class='hs-varid'>ifB</span> <span class='hs-varid'>w</span> <span class='hs-varid'>s</span> <span class='hs-varid'>s'</span><span class='hs-layout'>)</span>
<a name="line-133"></a>
<a name="line-134"></a>
<a name="line-135"></a>
<a name="line-136"></a><span class='hs-comment'>-- Standard pattern for applicative functors:</span>
<a name="line-137"></a>
<a name="line-138"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Boolean</span> <span class='hs-varid'>bool</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Boolean</span> <span class='hs-layout'>(</span><span class='hs-varid'>z</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>bool</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-139"></a> <span class='hs-varid'>true</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pure</span> <span class='hs-varid'>true</span>
<a name="line-140"></a> <span class='hs-varid'>false</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pure</span> <span class='hs-varid'>false</span>
<a name="line-141"></a> <span class='hs-varid'>notB</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>notB</span>
<a name="line-142"></a> <span class='hs-layout'>(</span><span class='hs-varop'>&&*</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA2</span> <span class='hs-layout'>(</span><span class='hs-varop'>&&*</span><span class='hs-layout'>)</span>
<a name="line-143"></a> <span class='hs-layout'>(</span><span class='hs-varop'>||*</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA2</span> <span class='hs-layout'>(</span><span class='hs-varop'>||*</span><span class='hs-layout'>)</span>
<a name="line-144"></a>
<a name="line-145"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IfB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>IfB</span> <span class='hs-layout'>(</span><span class='hs-varid'>z</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>bool</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>z</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-146"></a> <span class='hs-varid'>ifB</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>cond</span>
<a name="line-147"></a>
<a name="line-148"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>EqB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>EqB</span> <span class='hs-layout'>(</span><span class='hs-varid'>z</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>bool</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>z</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-149"></a> <span class='hs-layout'>{</span> <span class='hs-layout'>(</span><span class='hs-varop'>==*</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA2</span> <span class='hs-layout'>(</span><span class='hs-varop'>==*</span><span class='hs-layout'>)</span> <span class='hs-layout'>;</span> <span class='hs-layout'>(</span><span class='hs-varop'>/=*</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA2</span> <span class='hs-layout'>(</span><span class='hs-varop'>/=*</span><span class='hs-layout'>)</span> <span class='hs-layout'>}</span>
<a name="line-150"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>OrdB</span> <span class='hs-varid'>bool</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>OrdB</span> <span class='hs-layout'>(</span><span class='hs-varid'>z</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>bool</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>z</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-151"></a> <span class='hs-layout'>{</span> <span class='hs-layout'>(</span><span class='hs-varop'><*</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA2</span><span class='hs-layout'>(</span><span class='hs-varop'><*</span><span class='hs-layout'>)</span> <span class='hs-layout'>;</span> <span class='hs-layout'>(</span><span class='hs-varop'><=*</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA2</span><span class='hs-layout'>(</span><span class='hs-varop'><=*</span><span class='hs-layout'>)</span> <span class='hs-layout'>}</span>
<a name="line-152"></a>
<a name="line-153"></a>
<a name="line-154"></a><span class='hs-comment'>{-
<a name="line-155"></a>
<a name="line-156"></a>{--------------------------------------------------------------------
<a name="line-157"></a> Tests
<a name="line-158"></a>--------------------------------------------------------------------}
<a name="line-159"></a>
<a name="line-160"></a>t1 :: String
<a name="line-161"></a>t1 = ifB True "foo" "bar"
<a name="line-162"></a>
<a name="line-163"></a>t2 :: Float -> Float
<a name="line-164"></a>t2 = ifB (< 0) negate id
<a name="line-165"></a>
<a name="line-166"></a>-- No instance for (IfB (a -> Bool) (a1 -> a1))
<a name="line-167"></a>-- arising from a use of `ifB'
<a name="line-168"></a>--
<a name="line-169"></a>-- t2 = ifB (< 0) negate id -- abs
<a name="line-170"></a>
<a name="line-171"></a>-}</span>
</pre></body>
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