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<title>Data/Generics/Uniplate/Typeable.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, UndecidableInstances #-}</span>
<a name="line-2"></a>
<a name="line-3"></a><span class='hs-comment'>{- |
<a name="line-4"></a> /RECOMMENDATION:/ Use "Data.Generics.Uniplate.Data" instead - it usually performs
<a name="line-5"></a> faster (sometimes significantly so) and requires no special instance declarations.
<a name="line-6"></a>
<a name="line-7"></a> This module supplies a method for writing 'Uniplate' / 'Biplate' instances. One
<a name="line-8"></a> instance declaration is required for each data type you wish to work with. The
<a name="line-9"></a> instances can be generated using Derive: <<a href="http://community.haskell.org/~ndm/derive/">http://community.haskell.org/~ndm/derive/</a>>.
<a name="line-10"></a>
<a name="line-11"></a> To take an example:
<a name="line-12"></a>
<a name="line-13"></a> > data Expr = Var Int | Neg Expr | Add Expr Expr
<a name="line-14"></a> > deriving Typeable
<a name="line-15"></a> >
<a name="line-16"></a> > instance (Typeable a, Uniplate a) => PlateAll Expr a where
<a name="line-17"></a> > plateAll (Var x ) = plate Var |+ x
<a name="line-18"></a> > plateAll (Neg x ) = plate Neg |+ x
<a name="line-19"></a> > plateAll (Add x y) = plate Add |+ x |+ y
<a name="line-20"></a>-}</span>
<a name="line-21"></a>
<a name="line-22"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Generics</span><span class='hs-varop'>.</span><span class='hs-conid'>Uniplate</span><span class='hs-varop'>.</span><span class='hs-conid'>Typeable</span><span class='hs-layout'>(</span>
<a name="line-23"></a> <span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Generics</span><span class='hs-varop'>.</span><span class='hs-conid'>Uniplate</span><span class='hs-varop'>.</span><span class='hs-conid'>Operations</span><span class='hs-layout'>,</span>
<a name="line-24"></a> <span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Typeable</span><span class='hs-layout'>,</span>
<a name="line-25"></a> <span class='hs-comment'>-- * The Class</span>
<a name="line-26"></a> <span class='hs-conid'>PlateAll</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span>
<a name="line-27"></a> <span class='hs-comment'>-- * The Combinators</span>
<a name="line-28"></a> <span class='hs-varid'>plate</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-varid'>plateProject</span>
<a name="line-29"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-30"></a>
<a name="line-31"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Arrow</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'>Generics</span><span class='hs-varop'>.</span><span class='hs-conid'>Uniplate</span><span class='hs-varop'>.</span><span class='hs-conid'>Operations</span>
<a name="line-33"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Generics</span><span class='hs-varop'>.</span><span class='hs-conid'>Uniplate</span><span class='hs-varop'>.</span><span class='hs-conid'>Internal</span><span class='hs-varop'>.</span><span class='hs-conid'>Utils</span>
<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'>Generics</span><span class='hs-varop'>.</span><span class='hs-conid'>Str</span>
<a name="line-35"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Typeable</span>
<a name="line-36"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Ratio</span>
<a name="line-37"></a>
<a name="line-38"></a>
<a name="line-39"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Typeable</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Uniplate</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>PlateAll</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Biplate</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyword'>where</span>
<a name="line-40"></a> <span class='hs-varid'>biplate</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plateMore</span>
<a name="line-41"></a>
<a name="line-42"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>PlateAll</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Uniplate</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>where</span>
<a name="line-43"></a> <span class='hs-varid'>uniplate</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plateAll</span>
<a name="line-44"></a>
<a name="line-45"></a>
<a name="line-46"></a><a name="Type"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Type</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>Str</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Str</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>from</span><span class='hs-layout'>)</span>
<a name="line-47"></a>
<a name="line-48"></a>
<a name="line-49"></a><a name="plateMore"></a><span class='hs-definition'>plateMore</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Typeable</span> <span class='hs-varid'>from</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>PlateAll</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>from</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Type</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span>
<a name="line-50"></a><span class='hs-definition'>plateMore</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>res</span>
<a name="line-51"></a> <span class='hs-keyword'>where</span>
<a name="line-52"></a> <span class='hs-varid'>res</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>asTypeOf</span> <span class='hs-layout'>(</span><span class='hs-varid'>cast</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varop'>$</span> <span class='hs-varid'>strType</span> <span class='hs-varop'>$</span> <span class='hs-varid'>fst</span> <span class='hs-varid'>res</span><span class='hs-layout'>)</span> <span class='hs-keyword'>of</span>
<a name="line-53"></a> <span class='hs-conid'>Nothing</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>plateAll</span> <span class='hs-varid'>x</span>
<a name="line-54"></a> <span class='hs-conid'>Just</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-conid'>One</span> <span class='hs-varid'>y</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-conid'>One</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>unsafeCoerce</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-55"></a>
<a name="line-56"></a>
<a name="line-57"></a><a name="PlateAll"></a><span class='hs-comment'>-- | This class should be defined for each data type of interest.</span>
<a name="line-58"></a><a name="PlateAll"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>PlateAll</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span> <span class='hs-keyword'>where</span>
<a name="line-59"></a> <span class='hs-comment'>-- | This method should be defined using 'plate' and '|+', '|-'.</span>
<a name="line-60"></a> <span class='hs-varid'>plateAll</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>from</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Type</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span>
<a name="line-61"></a>
<a name="line-62"></a>
<a name="line-63"></a><a name="plate"></a><span class='hs-comment'>-- | The main combinator used to start the chain.</span>
<a name="line-64"></a><span class='hs-definition'>plate</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>from</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Type</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span>
<a name="line-65"></a><span class='hs-definition'>plate</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zero</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>\</span><span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-66"></a>
<a name="line-67"></a>
<a name="line-68"></a><a name="|+"></a><span class='hs-comment'>-- | The field to the right may contain the target.</span>
<a name="line-69"></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-conid'>Typeable</span> <span class='hs-varid'>item</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>PlateAll</span> <span class='hs-varid'>item</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Type</span> <span class='hs-layout'>(</span><span class='hs-varid'>item</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>from</span><span class='hs-layout'>)</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>item</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Type</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span>
<a name="line-70"></a><span class='hs-layout'>(</span><span class='hs-varop'>|+</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>xs</span><span class='hs-layout'>,</span><span class='hs-varid'>x_</span><span class='hs-layout'>)</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>plateMore</span> <span class='hs-varid'>y</span> <span class='hs-keyword'>of</span>
<a name="line-71"></a> <span class='hs-layout'>(</span><span class='hs-varid'>ys</span><span class='hs-layout'>,</span><span class='hs-varid'>y_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-conid'>Two</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>ys</span><span class='hs-layout'>,</span><span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-conid'>Two</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>x_</span> <span class='hs-varid'>xs</span> <span class='hs-layout'>(</span><span class='hs-varid'>y_</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-72"></a>
<a name="line-73"></a><a name="|-"></a><span class='hs-comment'>-- | The field to the right /does not/ contain the target.</span>
<a name="line-74"></a><span class='hs-comment'>-- This can be used as either an optimisation, or more commonly for excluding</span>
<a name="line-75"></a><span class='hs-comment'>-- primitives such as Int.</span>
<a name="line-76"></a><span class='hs-layout'>(</span><span class='hs-varop'>|-</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Type</span> <span class='hs-layout'>(</span><span class='hs-varid'>item</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>from</span><span class='hs-layout'>)</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>item</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Type</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span>
<a name="line-77"></a><span class='hs-layout'>(</span><span class='hs-varop'>|-</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>xs</span><span class='hs-layout'>,</span><span class='hs-varid'>x_</span><span class='hs-layout'>)</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>xs</span><span class='hs-layout'>,</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>xs</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>x_</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-78"></a>
<a name="line-79"></a>
<a name="line-80"></a><a name="plateProject"></a><span class='hs-comment'>-- | Write an instance in terms of a projection/injection pair. Usually used to define instances</span>
<a name="line-81"></a><span class='hs-comment'>-- for abstract containers such as Map:</span>
<a name="line-82"></a><span class='hs-comment'>--</span>
<a name="line-83"></a><span class='hs-comment'>-- > instance (Ord a, Typeable a, PlateAll a c, Typeable b, PlateAll b c,</span>
<a name="line-84"></a><span class='hs-comment'>-- > Typeable c, PlateAll c c) => PlateAll (Map.Map a b) c where</span>
<a name="line-85"></a><span class='hs-comment'>-- > plateAll = plateProject Map.toList Map.fromList</span>
<a name="line-86"></a><span class='hs-definition'>plateProject</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Typeable</span> <span class='hs-varid'>item</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>PlateAll</span> <span class='hs-varid'>item</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>from</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>item</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>item</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>from</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>from</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Type</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span>
<a name="line-87"></a><span class='hs-definition'>plateProject</span> <span class='hs-varid'>into</span> <span class='hs-varid'>outof</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>second</span> <span class='hs-layout'>(</span><span class='hs-varid'>outof</span> <span class='hs-varop'>.</span> <span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>plateAll</span> <span class='hs-varop'>.</span> <span class='hs-varid'>into</span>
<a name="line-88"></a>
<a name="line-89"></a>
<a name="line-90"></a><span class='hs-comment'>-- * Instances</span>
<a name="line-91"></a>
<a name="line-92"></a><span class='hs-comment'>-- ** Primitive Types</span>
<a name="line-93"></a>
<a name="line-94"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>PlateAll</span> <span class='hs-conid'>Int</span> <span class='hs-varid'>to</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>plateAll</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-varid'>x</span>
<a name="line-95"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>PlateAll</span> <span class='hs-conid'>Bool</span> <span class='hs-varid'>to</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>plateAll</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-varid'>x</span>
<a name="line-96"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>PlateAll</span> <span class='hs-conid'>Char</span> <span class='hs-varid'>to</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>plateAll</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-varid'>x</span>
<a name="line-97"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>PlateAll</span> <span class='hs-conid'>Integer</span> <span class='hs-varid'>to</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>plateAll</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-varid'>x</span>
<a name="line-98"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>PlateAll</span> <span class='hs-conid'>Double</span> <span class='hs-varid'>to</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>plateAll</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-varid'>x</span>
<a name="line-99"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>PlateAll</span> <span class='hs-conid'>Float</span> <span class='hs-varid'>to</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>plateAll</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-varid'>x</span>
<a name="line-100"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>PlateAll</span> <span class='hs-conid'>()</span> <span class='hs-varid'>to</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>plateAll</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-varid'>x</span>
<a name="line-101"></a>
<a name="line-102"></a><span class='hs-comment'>-- ** Container Types</span>
<a name="line-103"></a>
<a name="line-104"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>PlateAll</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>from</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Uniplate</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>PlateAll</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>from</span><span class='hs-keyglyph'>]</span> <span class='hs-varid'>to</span> <span class='hs-keyword'>where</span>
<a name="line-105"></a> <span class='hs-varid'>plateAll</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-conid'>[]</span>
<a name="line-106"></a> <span class='hs-varid'>plateAll</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-conop'>:</span><span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-layout'>(</span><span class='hs-conop'>:</span><span class='hs-layout'>)</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>x</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>xs</span>
<a name="line-107"></a>
<a name="line-108"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>PlateAll</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>from</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Uniplate</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>PlateAll</span> <span class='hs-layout'>(</span><span class='hs-conid'>Maybe</span> <span class='hs-varid'>from</span><span class='hs-layout'>)</span> <span class='hs-varid'>to</span> <span class='hs-keyword'>where</span>
<a name="line-109"></a> <span class='hs-varid'>plateAll</span> <span class='hs-conid'>Nothing</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-conid'>Nothing</span>
<a name="line-110"></a> <span class='hs-varid'>plateAll</span> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-conid'>Just</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>x</span>
<a name="line-111"></a>
<a name="line-112"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>PlateAll</span> <span class='hs-varid'>a</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>PlateAll</span> <span class='hs-varid'>b</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Uniplate</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span>
<a name="line-113"></a> <span class='hs-conid'>PlateAll</span> <span class='hs-layout'>(</span><span class='hs-conid'>Either</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-varid'>to</span> <span class='hs-keyword'>where</span>
<a name="line-114"></a> <span class='hs-varid'>plateAll</span> <span class='hs-layout'>(</span><span class='hs-conid'>Left</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-conid'>Left</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>x</span>
<a name="line-115"></a> <span class='hs-varid'>plateAll</span> <span class='hs-layout'>(</span><span class='hs-conid'>Right</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-conid'>Right</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>x</span>
<a name="line-116"></a>
<a name="line-117"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>PlateAll</span> <span class='hs-varid'>a</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>a</span>
<a name="line-118"></a> <span class='hs-layout'>,</span><span class='hs-conid'>PlateAll</span> <span class='hs-varid'>b</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>b</span>
<a name="line-119"></a> <span class='hs-layout'>,</span><span class='hs-conid'>Typeable</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Uniplate</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span>
<a name="line-120"></a> <span class='hs-conid'>PlateAll</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> <span class='hs-varid'>to</span> <span class='hs-keyword'>where</span>
<a name="line-121"></a> <span class='hs-varid'>plateAll</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> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-conid'>(,)</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>a</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>b</span>
<a name="line-122"></a>
<a name="line-123"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>PlateAll</span> <span class='hs-varid'>a</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>a</span>
<a name="line-124"></a> <span class='hs-layout'>,</span><span class='hs-conid'>PlateAll</span> <span class='hs-varid'>b</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>b</span>
<a name="line-125"></a> <span class='hs-layout'>,</span><span class='hs-conid'>PlateAll</span> <span class='hs-varid'>c</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>c</span>
<a name="line-126"></a> <span class='hs-layout'>,</span><span class='hs-conid'>Typeable</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Uniplate</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span>
<a name="line-127"></a> <span class='hs-conid'>PlateAll</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><span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-varid'>to</span> <span class='hs-keyword'>where</span>
<a name="line-128"></a> <span class='hs-varid'>plateAll</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><span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-conid'>(,,)</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>a</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>b</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>c</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'>PlateAll</span> <span class='hs-varid'>a</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>a</span>
<a name="line-131"></a> <span class='hs-layout'>,</span><span class='hs-conid'>PlateAll</span> <span class='hs-varid'>b</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>b</span>
<a name="line-132"></a> <span class='hs-layout'>,</span><span class='hs-conid'>PlateAll</span> <span class='hs-varid'>c</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>c</span>
<a name="line-133"></a> <span class='hs-layout'>,</span><span class='hs-conid'>PlateAll</span> <span class='hs-varid'>d</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>d</span>
<a name="line-134"></a> <span class='hs-layout'>,</span><span class='hs-conid'>Typeable</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Uniplate</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span>
<a name="line-135"></a> <span class='hs-conid'>PlateAll</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><span class='hs-varid'>c</span><span class='hs-layout'>,</span><span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-varid'>to</span> <span class='hs-keyword'>where</span>
<a name="line-136"></a> <span class='hs-varid'>plateAll</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><span class='hs-varid'>c</span><span class='hs-layout'>,</span><span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-conid'>(,,,)</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>a</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>b</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>c</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>d</span>
<a name="line-137"></a>
<a name="line-138"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>PlateAll</span> <span class='hs-varid'>a</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>a</span>
<a name="line-139"></a> <span class='hs-layout'>,</span><span class='hs-conid'>PlateAll</span> <span class='hs-varid'>b</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>b</span>
<a name="line-140"></a> <span class='hs-layout'>,</span><span class='hs-conid'>PlateAll</span> <span class='hs-varid'>c</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>c</span>
<a name="line-141"></a> <span class='hs-layout'>,</span><span class='hs-conid'>PlateAll</span> <span class='hs-varid'>d</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>d</span>
<a name="line-142"></a> <span class='hs-layout'>,</span><span class='hs-conid'>PlateAll</span> <span class='hs-varid'>e</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>e</span>
<a name="line-143"></a> <span class='hs-layout'>,</span><span class='hs-conid'>Typeable</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Uniplate</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span>
<a name="line-144"></a> <span class='hs-conid'>PlateAll</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><span class='hs-varid'>c</span><span class='hs-layout'>,</span><span class='hs-varid'>d</span><span class='hs-layout'>,</span><span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-varid'>to</span> <span class='hs-keyword'>where</span>
<a name="line-145"></a> <span class='hs-varid'>plateAll</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><span class='hs-varid'>c</span><span class='hs-layout'>,</span><span class='hs-varid'>d</span><span class='hs-layout'>,</span><span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plate</span> <span class='hs-conid'>(,,,,)</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>a</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>b</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>c</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>d</span> <span class='hs-varop'>|+</span> <span class='hs-varid'>e</span>
<a name="line-146"></a>
<a name="line-147"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Integral</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>PlateAll</span> <span class='hs-varid'>a</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Uniplate</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>PlateAll</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ratio</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-varid'>to</span> <span class='hs-keyword'>where</span>
<a name="line-148"></a> <span class='hs-varid'>plateAll</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plateProject</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>numerator</span> <span class='hs-varid'>x</span><span class='hs-layout'>,</span> <span class='hs-varid'>denominator</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>uncurry</span> <span class='hs-layout'>(</span><span class='hs-varop'>%</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
</pre></body>
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