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<title>TypeLevel/Boolean.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE TypeFamilies #-}</span>
<a name="line-2"></a><span class='hs-comment'>{-# LANGUAGE EmptyDataDecls #-}</span>
<a name="line-3"></a><span class='hs-comment'>{-# LANGUAGE MultiParamTypeClasses #-}</span>
<a name="line-4"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>TypeLevel</span><span class='hs-varop'>.</span><span class='hs-conid'>Boolean</span> <span class='hs-layout'>(</span> <span class='hs-conid'>True</span>
<a name="line-5"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>False</span>
<a name="line-6"></a> <span class='hs-comment'>-- * Boolean operations</span>
<a name="line-7"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Not</span>
<a name="line-8"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>notT</span>
<a name="line-9"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>And</span>
<a name="line-10"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>andT</span>
<a name="line-11"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Or</span>
<a name="line-12"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>orT</span>
<a name="line-13"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Xor</span>
<a name="line-14"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>xorT</span>
<a name="line-15"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-16"></a>
<a name="line-17"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>TypeLevel</span><span class='hs-varop'>.</span><span class='hs-conid'>Reify</span>
<a name="line-18"></a>
<a name="line-19"></a><a name="True"></a><span class='hs-comment'>-- | Data type for truth</span>
<a name="line-20"></a><a name="True"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>True</span>
<a name="line-21"></a><a name="False"></a><span class='hs-comment'>-- | Data type for false.</span>
<a name="line-22"></a><a name="False"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>False</span>
<a name="line-23"></a>
<a name="line-24"></a><a name="instance%20Show%20False"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-conid'>False</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>show</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-str'>"False"</span>
<a name="line-25"></a><a name="instance%20Show%20True"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-conid'>True</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>show</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-str'>"True"</span>
<a name="line-26"></a>
<a name="line-27"></a><a name="instance%20Reify%20True%20Bool"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Reify</span> <span class='hs-conid'>True</span> <span class='hs-conid'>Bool</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>witness</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Witness</span> <span class='hs-conid'>True</span>
<a name="line-28"></a><a name="instance%20Reify%20False%20Bool"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Reify</span> <span class='hs-conid'>False</span> <span class='hs-conid'>Bool</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>witness</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Witness</span> <span class='hs-conid'>False</span>
<a name="line-29"></a>
<a name="line-30"></a><span class='hs-comment'>----------------------------------------------------------------</span>
<a name="line-31"></a><span class='hs-comment'>-- | Negation</span>
<a name="line-32"></a>
<a name="line-33"></a><a name="Not"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>family</span> <span class='hs-conid'>Not</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>::</span> <span class='hs-varop'>*</span>
<a name="line-34"></a>
<a name="line-35"></a><a name="notT"></a><span class='hs-definition'>notT</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Not</span> <span class='hs-varid'>a</span>
<a name="line-36"></a><span class='hs-definition'>notT</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>undefined</span>
<a name="line-37"></a>
<a name="line-38"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Not</span> <span class='hs-conid'>False</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-39"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Not</span> <span class='hs-conid'>True</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-40"></a>
<a name="line-41"></a><a name="And"></a><span class='hs-comment'>----------------------------------------------------------------</span>
<a name="line-42"></a><a name="And"></a><span class='hs-comment'>-- | And for boolean types</span>
<a name="line-43"></a><a name="And"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>family</span> <span class='hs-conid'>And</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>::</span> <span class='hs-varop'>*</span>
<a name="line-44"></a>
<a name="line-45"></a><a name="andT"></a><span class='hs-definition'>andT</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>And</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-46"></a><span class='hs-definition'>andT</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>undefined</span>
<a name="line-47"></a>
<a name="line-48"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>And</span> <span class='hs-conid'>False</span> <span class='hs-conid'>False</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-49"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>And</span> <span class='hs-conid'>False</span> <span class='hs-conid'>True</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-50"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>And</span> <span class='hs-conid'>True</span> <span class='hs-conid'>False</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-51"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>And</span> <span class='hs-conid'>True</span> <span class='hs-conid'>True</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-52"></a>
<a name="line-53"></a><a name="Or"></a><span class='hs-comment'>----------------------------------------------------------------</span>
<a name="line-54"></a><a name="Or"></a><span class='hs-comment'>-- | Or for boolean types</span>
<a name="line-55"></a><a name="Or"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>family</span> <span class='hs-conid'>Or</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>::</span> <span class='hs-varop'>*</span>
<a name="line-56"></a>
<a name="line-57"></a><a name="orT"></a><span class='hs-definition'>orT</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Or</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-58"></a><span class='hs-definition'>orT</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>undefined</span>
<a name="line-59"></a>
<a name="line-60"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Or</span> <span class='hs-conid'>False</span> <span class='hs-conid'>False</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-61"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Or</span> <span class='hs-conid'>False</span> <span class='hs-conid'>True</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-62"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Or</span> <span class='hs-conid'>True</span> <span class='hs-conid'>False</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-63"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Or</span> <span class='hs-conid'>True</span> <span class='hs-conid'>True</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-64"></a>
<a name="line-65"></a><a name="Xor"></a><span class='hs-comment'>----------------------------------------------------------------</span>
<a name="line-66"></a><a name="Xor"></a><span class='hs-comment'>-- | Exlusive or for boolean types</span>
<a name="line-67"></a><a name="Xor"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>family</span> <span class='hs-conid'>Xor</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>::</span> <span class='hs-varop'>*</span>
<a name="line-68"></a>
<a name="line-69"></a><a name="xorT"></a><span class='hs-definition'>xorT</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Xor</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-70"></a><span class='hs-definition'>xorT</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>undefined</span>
<a name="line-71"></a>
<a name="line-72"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Xor</span> <span class='hs-conid'>False</span> <span class='hs-conid'>False</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-73"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Xor</span> <span class='hs-conid'>False</span> <span class='hs-conid'>True</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-74"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Xor</span> <span class='hs-conid'>True</span> <span class='hs-conid'>False</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-75"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Xor</span> <span class='hs-conid'>True</span> <span class='hs-conid'>True</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
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