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<title>src/full/Agda/TypeChecking/Rules/Builtin.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE PatternGuards, CPP #-}</span>
<a name="line-2"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>Rules</span><span class='hs-varop'>.</span><span class='hs-conid'>Builtin</span> <span class='hs-layout'>(</span><span class='hs-varid'>bindBuiltin</span><span class='hs-layout'>,</span> <span class='hs-varid'>bindPostulatedName</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-3"></a>
<a name="line-4"></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-5"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span>
<a name="line-6"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Error</span>
<a name="line-7"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Maybe</span>
<a name="line-8"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>List</span> <span class='hs-layout'>(</span><span class='hs-varid'>find</span><span class='hs-layout'>)</span>
<a name="line-9"></a>
<a name="line-10"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Syntax</span><span class='hs-varop'>.</span><span class='hs-conid'>Abstract</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>A</span>
<a name="line-11"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Syntax</span><span class='hs-varop'>.</span><span class='hs-conid'>Internal</span>
<a name="line-12"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Syntax</span><span class='hs-varop'>.</span><span class='hs-conid'>Common</span>
<a name="line-13"></a>
<a name="line-14"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>EtaContract</span>
<a name="line-15"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span>
<a name="line-16"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Builtin</span>
<a name="line-17"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>Conversion</span>
<a name="line-18"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>Substitute</span>
<a name="line-19"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>Primitive</span>
<a name="line-20"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>Constraints</span>
<a name="line-21"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>Reduce</span>
<a name="line-22"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>Pretty</span>
<a name="line-23"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>Irrelevance</span>
<a name="line-24"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>SizedTypes</span> <span class='hs-layout'>(</span> <span class='hs-varid'>builtinSizeHook</span> <span class='hs-layout'>)</span>
<a name="line-25"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>Rules</span><span class='hs-varop'>.</span><span class='hs-conid'>Term</span> <span class='hs-layout'>(</span> <span class='hs-varid'>checkExpr</span> <span class='hs-layout'>,</span> <span class='hs-varid'>inferExpr</span> <span class='hs-layout'>)</span>
<a name="line-26"></a><span class='hs-keyword'>import</span> <span class='hs-comment'>{-# SOURCE #-}</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>Rules</span><span class='hs-varop'>.</span><span class='hs-conid'>Builtin</span><span class='hs-varop'>.</span><span class='hs-conid'>Coinduction</span>
<a name="line-27"></a>
<a name="line-28"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Utils</span><span class='hs-varop'>.</span><span class='hs-conid'>Size</span>
<a name="line-29"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Utils</span><span class='hs-varop'>.</span><span class='hs-conid'>Impossible</span>
<a name="line-30"></a>
<a name="line-31"></a><span class='hs-cpp'>#include "../..//undefined.h"</span>
<a name="line-32"></a>
<a name="line-33"></a><span class='hs-comment'>---------------------------------------------------------------------------</span>
<a name="line-34"></a><span class='hs-comment'>-- * Checking builtin pragmas</span>
<a name="line-35"></a><span class='hs-comment'>---------------------------------------------------------------------------</span>
<a name="line-36"></a>
<a name="line-37"></a><a name="builtinPostulate"></a><span class='hs-definition'>builtinPostulate</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>TCM</span> <span class='hs-conid'>Type</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>BuiltinDescriptor</span>
<a name="line-38"></a><span class='hs-definition'>builtinPostulate</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>BuiltinPostulate</span> <span class='hs-conid'>Relevant</span>
<a name="line-39"></a>
<a name="line-40"></a><a name="coreBuiltins"></a><span class='hs-definition'>coreBuiltins</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>BuiltinInfo</span><span class='hs-keyglyph'>]</span>
<a name="line-41"></a><span class='hs-definition'>coreBuiltins</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>z</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>BuiltinInfo</span> <span class='hs-varid'>x</span> <span class='hs-varid'>z</span><span class='hs-layout'>)</span>
<a name="line-42"></a> <span class='hs-keyglyph'>[</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinList</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinData</span> <span class='hs-layout'>(</span><span class='hs-varid'>tset</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tset</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>builtinNil</span><span class='hs-layout'>,</span> <span class='hs-varid'>builtinCons</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-43"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinArg</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinData</span> <span class='hs-layout'>(</span><span class='hs-varid'>tset</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tset</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>builtinArgArg</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-44"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinBool</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinData</span> <span class='hs-varid'>tset</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>builtinTrue</span><span class='hs-layout'>,</span> <span class='hs-varid'>builtinFalse</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-45"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinNat</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinData</span> <span class='hs-varid'>tset</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>builtinZero</span><span class='hs-layout'>,</span> <span class='hs-varid'>builtinSuc</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-46"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinLevel</span> <span class='hs-varop'>|-></span> <span class='hs-varid'>builtinPostulate</span> <span class='hs-varid'>tset</span><span class='hs-layout'>)</span>
<a name="line-47"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinInteger</span> <span class='hs-varop'>|-></span> <span class='hs-varid'>builtinPostulate</span> <span class='hs-varid'>tset</span><span class='hs-layout'>)</span>
<a name="line-48"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinFloat</span> <span class='hs-varop'>|-></span> <span class='hs-varid'>builtinPostulate</span> <span class='hs-varid'>tset</span><span class='hs-layout'>)</span>
<a name="line-49"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinChar</span> <span class='hs-varop'>|-></span> <span class='hs-varid'>builtinPostulate</span> <span class='hs-varid'>tset</span><span class='hs-layout'>)</span>
<a name="line-50"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinString</span> <span class='hs-varop'>|-></span> <span class='hs-varid'>builtinPostulate</span> <span class='hs-varid'>tset</span><span class='hs-layout'>)</span>
<a name="line-51"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinQName</span> <span class='hs-varop'>|-></span> <span class='hs-varid'>builtinPostulate</span> <span class='hs-varid'>tset</span><span class='hs-layout'>)</span>
<a name="line-52"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinIO</span> <span class='hs-varop'>|-></span> <span class='hs-varid'>builtinPostulate</span> <span class='hs-layout'>(</span><span class='hs-varid'>tset</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tset</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-53"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaSort</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinData</span> <span class='hs-varid'>tset</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>builtinAgdaSortSet</span><span class='hs-layout'>,</span> <span class='hs-varid'>builtinAgdaSortLit</span><span class='hs-layout'>,</span> <span class='hs-varid'>builtinAgdaSortUnsupported</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-54"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaType</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinData</span> <span class='hs-varid'>tset</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>builtinAgdaTypeEl</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-55"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaTerm</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinData</span> <span class='hs-varid'>tset</span>
<a name="line-56"></a> <span class='hs-keyglyph'>[</span><span class='hs-varid'>builtinAgdaTermVar</span><span class='hs-layout'>,</span> <span class='hs-varid'>builtinAgdaTermLam</span>
<a name="line-57"></a> <span class='hs-layout'>,</span><span class='hs-varid'>builtinAgdaTermDef</span><span class='hs-layout'>,</span> <span class='hs-varid'>builtinAgdaTermCon</span>
<a name="line-58"></a> <span class='hs-layout'>,</span><span class='hs-varid'>builtinAgdaTermPi</span><span class='hs-layout'>,</span> <span class='hs-varid'>builtinAgdaTermSort</span>
<a name="line-59"></a> <span class='hs-layout'>,</span><span class='hs-varid'>builtinAgdaTermUnsupported</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-60"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinEquality</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinData</span> <span class='hs-layout'>(</span><span class='hs-varid'>hPi</span> <span class='hs-str'>"a"</span> <span class='hs-layout'>(</span><span class='hs-varid'>el</span> <span class='hs-varid'>primLevel</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span>
<a name="line-61"></a> <span class='hs-varid'>hPi</span> <span class='hs-str'>"A"</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-varop'>$</span> <span class='hs-varid'>sort</span> <span class='hs-varop'>$</span> <span class='hs-varid'>varSort</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span>
<a name="line-62"></a> <span class='hs-layout'>(</span><span class='hs-conid'>El</span> <span class='hs-layout'>(</span><span class='hs-varid'>varSort</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varop'><$></span> <span class='hs-varid'>varM</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span> <span class='hs-varop'>--></span>
<a name="line-63"></a> <span class='hs-layout'>(</span><span class='hs-conid'>El</span> <span class='hs-layout'>(</span><span class='hs-varid'>varSort</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varop'><$></span> <span class='hs-varid'>varM</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span> <span class='hs-varop'>--></span>
<a name="line-64"></a> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-varid'>sort</span> <span class='hs-varop'>$</span> <span class='hs-varid'>varSort</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-65"></a> <span class='hs-keyglyph'>[</span><span class='hs-varid'>builtinRefl</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-66"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinHiding</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinData</span> <span class='hs-varid'>tset</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>builtinHidden</span><span class='hs-layout'>,</span> <span class='hs-varid'>builtinInstance</span><span class='hs-layout'>,</span> <span class='hs-varid'>builtinVisible</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-67"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinRelevance</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinData</span> <span class='hs-varid'>tset</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>builtinRelevant</span><span class='hs-layout'>,</span> <span class='hs-varid'>builtinIrrelevant</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-68"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinRefl</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>hPi</span> <span class='hs-str'>"a"</span> <span class='hs-layout'>(</span><span class='hs-varid'>el</span> <span class='hs-varid'>primLevel</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>hPi</span> <span class='hs-str'>"A"</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-varop'>$</span> <span class='hs-varid'>sort</span> <span class='hs-varop'>$</span> <span class='hs-varid'>varSort</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span>
<a name="line-69"></a> <span class='hs-varid'>hPi</span> <span class='hs-str'>"x"</span> <span class='hs-layout'>(</span><span class='hs-conid'>El</span> <span class='hs-layout'>(</span><span class='hs-varid'>varSort</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varop'><$></span> <span class='hs-varid'>varM</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span>
<a name="line-70"></a> <span class='hs-conid'>El</span> <span class='hs-layout'>(</span><span class='hs-varid'>varSort</span> <span class='hs-num'>2</span><span class='hs-layout'>)</span> <span class='hs-varop'><$></span> <span class='hs-varid'>primEquality</span> <span class='hs-varop'><#></span> <span class='hs-varid'>varM</span> <span class='hs-num'>2</span> <span class='hs-varop'><#></span> <span class='hs-varid'>varM</span> <span class='hs-num'>1</span> <span class='hs-varop'><@></span> <span class='hs-varid'>varM</span> <span class='hs-num'>0</span> <span class='hs-varop'><@></span> <span class='hs-varid'>varM</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-71"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinNil</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>hPi</span> <span class='hs-str'>"A"</span> <span class='hs-varid'>tset</span> <span class='hs-layout'>(</span><span class='hs-varid'>el</span> <span class='hs-layout'>(</span><span class='hs-varid'>list</span> <span class='hs-varid'>v0</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-72"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinCons</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>hPi</span> <span class='hs-str'>"A"</span> <span class='hs-varid'>tset</span> <span class='hs-layout'>(</span><span class='hs-varid'>tv0</span> <span class='hs-varop'>--></span> <span class='hs-varid'>el</span> <span class='hs-layout'>(</span><span class='hs-varid'>list</span> <span class='hs-varid'>v0</span><span class='hs-layout'>)</span> <span class='hs-varop'>--></span> <span class='hs-varid'>el</span> <span class='hs-layout'>(</span><span class='hs-varid'>list</span> <span class='hs-varid'>v0</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-73"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinZero</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-varid'>tnat</span><span class='hs-layout'>)</span>
<a name="line-74"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinSuc</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>tnat</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tnat</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-75"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinTrue</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-varid'>tbool</span><span class='hs-layout'>)</span>
<a name="line-76"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinFalse</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-varid'>tbool</span><span class='hs-layout'>)</span>
<a name="line-77"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinArgArg</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>hPi</span> <span class='hs-str'>"A"</span> <span class='hs-varid'>tset</span> <span class='hs-layout'>(</span><span class='hs-varid'>thiding</span> <span class='hs-varop'>--></span> <span class='hs-varid'>trelevance</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tv0</span> <span class='hs-varop'>--></span> <span class='hs-varid'>targ</span> <span class='hs-varid'>tv0</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-78"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaTypeEl</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>tsort</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tterm</span> <span class='hs-varop'>--></span> <span class='hs-varid'>ttype</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-79"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaTermVar</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>tnat</span> <span class='hs-varop'>--></span> <span class='hs-varid'>targs</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tterm</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-80"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaTermLam</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>thiding</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tterm</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tterm</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-81"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaTermDef</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>tqname</span> <span class='hs-varop'>--></span> <span class='hs-varid'>targs</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tterm</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-82"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaTermCon</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>tqname</span> <span class='hs-varop'>--></span> <span class='hs-varid'>targs</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tterm</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-83"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaTermPi</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>targ</span> <span class='hs-varid'>ttype</span> <span class='hs-varop'>--></span> <span class='hs-varid'>ttype</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tterm</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-84"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaTermSort</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>tsort</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tterm</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-85"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaTermUnsupported</span><span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-varid'>tterm</span><span class='hs-layout'>)</span>
<a name="line-86"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinHidden</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-varid'>thiding</span><span class='hs-layout'>)</span>
<a name="line-87"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinInstance</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-varid'>thiding</span><span class='hs-layout'>)</span>
<a name="line-88"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinVisible</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-varid'>thiding</span><span class='hs-layout'>)</span>
<a name="line-89"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinRelevant</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-varid'>trelevance</span><span class='hs-layout'>)</span>
<a name="line-90"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinIrrelevant</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-varid'>trelevance</span><span class='hs-layout'>)</span>
<a name="line-91"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinSize</span> <span class='hs-varop'>|-></span> <span class='hs-varid'>builtinPostulate</span> <span class='hs-varid'>tset</span><span class='hs-layout'>)</span>
<a name="line-92"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinSizeLt</span> <span class='hs-varop'>|-></span> <span class='hs-varid'>builtinPostulate</span> <span class='hs-layout'>(</span><span class='hs-varid'>tsize</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tset</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-93"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinSizeSuc</span> <span class='hs-varop'>|-></span> <span class='hs-varid'>builtinPostulate</span> <span class='hs-layout'>(</span><span class='hs-varid'>tsize</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tsize</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-94"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinSizeInf</span> <span class='hs-varop'>|-></span> <span class='hs-varid'>builtinPostulate</span> <span class='hs-varid'>tsize</span><span class='hs-layout'>)</span>
<a name="line-95"></a> <span class='hs-comment'>-- postulate max : {i : Size} -> Size< i -> Size< i -> Size< i</span>
<a name="line-96"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinSizeMax</span> <span class='hs-varop'>|-></span> <span class='hs-varid'>builtinPostulate</span> <span class='hs-layout'>(</span><span class='hs-varid'>tsize</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tsize</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tsize</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-97"></a> <span class='hs-comment'>-- (hPi "i" tsize $ let a = el $ primSizeLt <@> v0 in (a --> a --> a)))</span>
<a name="line-98"></a> <span class='hs-comment'>-- postulate .irrelevant : {a : Level}{A : Set a} -> .A -> A</span>
<a name="line-99"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinIrrAxiom</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinPostulate</span> <span class='hs-conid'>Irrelevant</span>
<a name="line-100"></a> <span class='hs-layout'>(</span><span class='hs-varid'>hPi</span> <span class='hs-str'>"a"</span> <span class='hs-layout'>(</span><span class='hs-varid'>el</span> <span class='hs-varid'>primLevel</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>hPi</span> <span class='hs-str'>"A"</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-varop'>$</span> <span class='hs-varid'>sort</span> <span class='hs-varop'>$</span> <span class='hs-varid'>varSort</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span>
<a name="line-101"></a> <span class='hs-layout'>(</span><span class='hs-conid'>El</span> <span class='hs-layout'>(</span><span class='hs-varid'>varSort</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varop'><$></span> <span class='hs-varid'>varM</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span> <span class='hs-varop'>.--></span> <span class='hs-layout'>(</span><span class='hs-conid'>El</span> <span class='hs-layout'>(</span><span class='hs-varid'>varSort</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varop'><$></span> <span class='hs-varid'>varM</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-102"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaSortSet</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>tterm</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tsort</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-103"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaSortLit</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>tnat</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tsort</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-104"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaSortUnsupported</span><span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-varid'>tsort</span><span class='hs-layout'>)</span>
<a name="line-105"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinNatPlus</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinPrim</span> <span class='hs-str'>"primNatPlus"</span> <span class='hs-varid'>verifyPlus</span><span class='hs-layout'>)</span>
<a name="line-106"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinNatMinus</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinPrim</span> <span class='hs-str'>"primNatMinus"</span> <span class='hs-varid'>verifyMinus</span><span class='hs-layout'>)</span>
<a name="line-107"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinNatTimes</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinPrim</span> <span class='hs-str'>"primNatTimes"</span> <span class='hs-varid'>verifyTimes</span><span class='hs-layout'>)</span>
<a name="line-108"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinNatDivSucAux</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinPrim</span> <span class='hs-str'>"primNatDivSucAux"</span> <span class='hs-varid'>verifyDivSucAux</span><span class='hs-layout'>)</span>
<a name="line-109"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinNatModSucAux</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinPrim</span> <span class='hs-str'>"primNatModSucAux"</span> <span class='hs-varid'>verifyModSucAux</span><span class='hs-layout'>)</span>
<a name="line-110"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinNatEquals</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinPrim</span> <span class='hs-str'>"primNatEquality"</span> <span class='hs-varid'>verifyEquals</span><span class='hs-layout'>)</span>
<a name="line-111"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinNatLess</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinPrim</span> <span class='hs-str'>"primNatLess"</span> <span class='hs-varid'>verifyLess</span><span class='hs-layout'>)</span>
<a name="line-112"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinLevelZero</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinPrim</span> <span class='hs-str'>"primLevelZero"</span> <span class='hs-layout'>(</span><span class='hs-varid'>const</span> <span class='hs-varop'>$</span> <span class='hs-varid'>return</span> <span class='hs-conid'>()</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-113"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinLevelSuc</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinPrim</span> <span class='hs-str'>"primLevelSuc"</span> <span class='hs-layout'>(</span><span class='hs-varid'>const</span> <span class='hs-varop'>$</span> <span class='hs-varid'>return</span> <span class='hs-conid'>()</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-114"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinLevelMax</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinPrim</span> <span class='hs-str'>"primLevelMax"</span> <span class='hs-varid'>verifyMax</span><span class='hs-layout'>)</span>
<a name="line-115"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaFunDef</span> <span class='hs-varop'>|-></span> <span class='hs-varid'>builtinPostulate</span> <span class='hs-varid'>tset</span><span class='hs-layout'>)</span> <span class='hs-comment'>-- internally this is QName</span>
<a name="line-116"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaDataDef</span> <span class='hs-varop'>|-></span> <span class='hs-varid'>builtinPostulate</span> <span class='hs-varid'>tset</span><span class='hs-layout'>)</span> <span class='hs-comment'>-- internally this is QName</span>
<a name="line-117"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaRecordDef</span> <span class='hs-varop'>|-></span> <span class='hs-varid'>builtinPostulate</span> <span class='hs-varid'>tset</span><span class='hs-layout'>)</span> <span class='hs-comment'>-- internally this is QName</span>
<a name="line-118"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaDefinition</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinData</span> <span class='hs-varid'>tset</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>builtinAgdaDefinitionFunDef</span>
<a name="line-119"></a> <span class='hs-layout'>,</span><span class='hs-varid'>builtinAgdaDefinitionDataDef</span>
<a name="line-120"></a> <span class='hs-layout'>,</span><span class='hs-varid'>builtinAgdaDefinitionDataConstructor</span>
<a name="line-121"></a> <span class='hs-layout'>,</span><span class='hs-varid'>builtinAgdaDefinitionRecordDef</span>
<a name="line-122"></a> <span class='hs-layout'>,</span><span class='hs-varid'>builtinAgdaDefinitionPostulate</span>
<a name="line-123"></a> <span class='hs-layout'>,</span><span class='hs-varid'>builtinAgdaDefinitionPrimitive</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-124"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaDefinitionFunDef</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>tfun</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tdefn</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-125"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaDefinitionDataDef</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>tdtype</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tdefn</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-126"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaDefinitionDataConstructor</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-varid'>tdefn</span><span class='hs-layout'>)</span>
<a name="line-127"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaDefinitionRecordDef</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-layout'>(</span><span class='hs-varid'>trec</span> <span class='hs-varop'>--></span> <span class='hs-varid'>tdefn</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-128"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaDefinitionPostulate</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-varid'>tdefn</span><span class='hs-layout'>)</span>
<a name="line-129"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>builtinAgdaDefinitionPrimitive</span> <span class='hs-varop'>|-></span> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-varid'>tdefn</span><span class='hs-layout'>)</span>
<a name="line-130"></a> <span class='hs-keyglyph'>]</span>
<a name="line-131"></a> <span class='hs-keyword'>where</span>
<a name="line-132"></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'>(,)</span>
<a name="line-133"></a>
<a name="line-134"></a> <span class='hs-varid'>v0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>varM</span> <span class='hs-num'>0</span>
<a name="line-135"></a> <span class='hs-varid'>v1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>varM</span> <span class='hs-num'>1</span>
<a name="line-136"></a>
<a name="line-137"></a> <span class='hs-varid'>tv0</span><span class='hs-layout'>,</span><span class='hs-varid'>tv1</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>TCM</span> <span class='hs-conid'>Type</span>
<a name="line-138"></a> <span class='hs-varid'>tv0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-varid'>v0</span>
<a name="line-139"></a> <span class='hs-varid'>tv1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-varid'>v1</span>
<a name="line-140"></a>
<a name="line-141"></a> <span class='hs-varid'>arg</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>TCM</span> <span class='hs-conid'>Term</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>TCM</span> <span class='hs-conid'>Term</span>
<a name="line-142"></a> <span class='hs-varid'>arg</span> <span class='hs-varid'>t</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>primArg</span> <span class='hs-varop'><@></span> <span class='hs-varid'>t</span>
<a name="line-143"></a>
<a name="line-144"></a> <span class='hs-varid'>targ</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-layout'>(</span><span class='hs-varid'>arg</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>unEl</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-145"></a> <span class='hs-varid'>targs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-layout'>(</span><span class='hs-varid'>list</span> <span class='hs-layout'>(</span><span class='hs-varid'>arg</span> <span class='hs-varid'>primAgdaTerm</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-146"></a> <span class='hs-varid'>tterm</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-varid'>primAgdaTerm</span>
<a name="line-147"></a> <span class='hs-varid'>tqname</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-varid'>primQName</span>
<a name="line-148"></a> <span class='hs-varid'>tnat</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-varid'>primNat</span>
<a name="line-149"></a> <span class='hs-varid'>tsize</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-varid'>primSize</span>
<a name="line-150"></a> <span class='hs-varid'>tbool</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-varid'>primBool</span>
<a name="line-151"></a> <span class='hs-varid'>thiding</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-varid'>primHiding</span>
<a name="line-152"></a> <span class='hs-varid'>trelevance</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-varid'>primRelevance</span>
<a name="line-153"></a> <span class='hs-varid'>ttype</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-varid'>primAgdaType</span>
<a name="line-154"></a> <span class='hs-varid'>tsort</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-varid'>primAgdaSort</span>
<a name="line-155"></a> <span class='hs-varid'>tdefn</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-varid'>primAgdaDefinition</span>
<a name="line-156"></a> <span class='hs-varid'>tfun</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-varid'>primAgdaFunDef</span>
<a name="line-157"></a> <span class='hs-varid'>tdtype</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-varid'>primAgdaDataDef</span>
<a name="line-158"></a> <span class='hs-varid'>trec</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>el</span> <span class='hs-varid'>primAgdaRecordDef</span>
<a name="line-159"></a>
<a name="line-160"></a> <span class='hs-varid'>verifyPlus</span> <span class='hs-varid'>plus</span> <span class='hs-keyglyph'>=</span>
<a name="line-161"></a> <span class='hs-varid'>verify</span> <span class='hs-keyglyph'>[</span><span class='hs-str'>"n"</span><span class='hs-layout'>,</span><span class='hs-str'>"m"</span><span class='hs-keyglyph'>]</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-varop'>@@</span><span class='hs-layout'>)</span> <span class='hs-varid'>zero</span> <span class='hs-varid'>suc</span> <span class='hs-layout'>(</span><span class='hs-varop'>==</span><span class='hs-layout'>)</span> <span class='hs-varid'>choice</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-162"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>0</span>
<a name="line-163"></a> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>1</span>
<a name="line-164"></a> <span class='hs-varid'>x</span> <span class='hs-varop'>+</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plus</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>x</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>y</span>
<a name="line-165"></a>
<a name="line-166"></a> <span class='hs-comment'>-- We allow recursion on any argument</span>
<a name="line-167"></a> <span class='hs-varid'>choice</span>
<a name="line-168"></a> <span class='hs-keyglyph'>[</span> <span class='hs-keyword'>do</span> <span class='hs-varid'>n</span> <span class='hs-varop'>+</span> <span class='hs-varid'>zero</span> <span class='hs-varop'>==</span> <span class='hs-varid'>n</span>
<a name="line-169"></a> <span class='hs-varid'>n</span> <span class='hs-varop'>+</span> <span class='hs-varid'>suc</span> <span class='hs-varid'>m</span> <span class='hs-varop'>==</span> <span class='hs-varid'>suc</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'>+</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span>
<a name="line-170"></a> <span class='hs-layout'>,</span> <span class='hs-keyword'>do</span> <span class='hs-varid'>suc</span> <span class='hs-varid'>n</span> <span class='hs-varop'>+</span> <span class='hs-varid'>m</span> <span class='hs-varop'>==</span> <span class='hs-varid'>suc</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'>+</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span>
<a name="line-171"></a> <span class='hs-varid'>zero</span> <span class='hs-varop'>+</span> <span class='hs-varid'>m</span> <span class='hs-varop'>==</span> <span class='hs-varid'>m</span>
<a name="line-172"></a> <span class='hs-keyglyph'>]</span>
<a name="line-173"></a>
<a name="line-174"></a> <span class='hs-varid'>verifyMinus</span> <span class='hs-varid'>minus</span> <span class='hs-keyglyph'>=</span>
<a name="line-175"></a> <span class='hs-varid'>verify</span> <span class='hs-keyglyph'>[</span><span class='hs-str'>"n"</span><span class='hs-layout'>,</span><span class='hs-str'>"m"</span><span class='hs-keyglyph'>]</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-varop'>@@</span><span class='hs-layout'>)</span> <span class='hs-varid'>zero</span> <span class='hs-varid'>suc</span> <span class='hs-layout'>(</span><span class='hs-varop'>==</span><span class='hs-layout'>)</span> <span class='hs-varid'>choice</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-176"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>0</span>
<a name="line-177"></a> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>1</span>
<a name="line-178"></a> <span class='hs-varid'>x</span> <span class='hs-comment'>-</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>minus</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>x</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>y</span>
<a name="line-179"></a>
<a name="line-180"></a> <span class='hs-comment'>-- We allow recursion on any argument</span>
<a name="line-181"></a> <span class='hs-varid'>zero</span> <span class='hs-comment'>-</span> <span class='hs-varid'>zero</span> <span class='hs-varop'>==</span> <span class='hs-varid'>zero</span>
<a name="line-182"></a> <span class='hs-varid'>zero</span> <span class='hs-comment'>-</span> <span class='hs-varid'>suc</span> <span class='hs-varid'>m</span> <span class='hs-varop'>==</span> <span class='hs-varid'>zero</span>
<a name="line-183"></a> <span class='hs-varid'>suc</span> <span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-varid'>zero</span> <span class='hs-varop'>==</span> <span class='hs-varid'>suc</span> <span class='hs-varid'>n</span>
<a name="line-184"></a> <span class='hs-varid'>suc</span> <span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-varid'>suc</span> <span class='hs-varid'>m</span> <span class='hs-varop'>==</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span>
<a name="line-185"></a>
<a name="line-186"></a> <span class='hs-varid'>verifyTimes</span> <span class='hs-varid'>times</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<a name="line-187"></a> <span class='hs-varid'>plus</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>primNatPlus</span>
<a name="line-188"></a> <span class='hs-varid'>verify</span> <span class='hs-keyglyph'>[</span><span class='hs-str'>"n"</span><span class='hs-layout'>,</span><span class='hs-str'>"m"</span><span class='hs-keyglyph'>]</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-varop'>@@</span><span class='hs-layout'>)</span> <span class='hs-varid'>zero</span> <span class='hs-varid'>suc</span> <span class='hs-layout'>(</span><span class='hs-varop'>==</span><span class='hs-layout'>)</span> <span class='hs-varid'>choice</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-189"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>0</span>
<a name="line-190"></a> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>1</span>
<a name="line-191"></a> <span class='hs-varid'>x</span> <span class='hs-varop'>+</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>plus</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>x</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>y</span>
<a name="line-192"></a> <span class='hs-varid'>x</span> <span class='hs-varop'>*</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>times</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>x</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>y</span>
<a name="line-193"></a>
<a name="line-194"></a> <span class='hs-varid'>choice</span>
<a name="line-195"></a> <span class='hs-keyglyph'>[</span> <span class='hs-keyword'>do</span> <span class='hs-varid'>n</span> <span class='hs-varop'>*</span> <span class='hs-varid'>zero</span> <span class='hs-varop'>==</span> <span class='hs-varid'>zero</span>
<a name="line-196"></a> <span class='hs-varid'>choice</span> <span class='hs-keyglyph'>[</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'>*</span> <span class='hs-varid'>suc</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varop'>==</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'>+</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'>*</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-197"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'>*</span> <span class='hs-varid'>suc</span> <span class='hs-varid'>m</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'>n</span> <span class='hs-varop'>*</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varop'>+</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-198"></a> <span class='hs-keyglyph'>]</span>
<a name="line-199"></a> <span class='hs-layout'>,</span> <span class='hs-keyword'>do</span> <span class='hs-varid'>zero</span> <span class='hs-varop'>*</span> <span class='hs-varid'>n</span> <span class='hs-varop'>==</span> <span class='hs-varid'>zero</span>
<a name="line-200"></a> <span class='hs-varid'>choice</span> <span class='hs-keyglyph'>[</span> <span class='hs-layout'>(</span><span class='hs-varid'>suc</span> <span class='hs-varid'>n</span> <span class='hs-varop'>*</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varop'>==</span> <span class='hs-layout'>(</span><span class='hs-varid'>m</span> <span class='hs-varop'>+</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'>*</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-201"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>suc</span> <span class='hs-varid'>n</span> <span class='hs-varop'>*</span> <span class='hs-varid'>m</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'>n</span> <span class='hs-varop'>*</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varop'>+</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span>
<a name="line-202"></a> <span class='hs-keyglyph'>]</span>
<a name="line-203"></a> <span class='hs-keyglyph'>]</span>
<a name="line-204"></a>
<a name="line-205"></a> <span class='hs-varid'>verifyDivSucAux</span> <span class='hs-varid'>dsAux</span> <span class='hs-keyglyph'>=</span>
<a name="line-206"></a> <span class='hs-varid'>verify</span> <span class='hs-keyglyph'>[</span><span class='hs-str'>"k"</span><span class='hs-layout'>,</span><span class='hs-str'>"m"</span><span class='hs-layout'>,</span><span class='hs-str'>"n"</span><span class='hs-layout'>,</span><span class='hs-str'>"j"</span><span class='hs-keyglyph'>]</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-varop'>@@</span><span class='hs-layout'>)</span> <span class='hs-varid'>zero</span> <span class='hs-varid'>suc</span> <span class='hs-layout'>(</span><span class='hs-varop'>==</span><span class='hs-layout'>)</span> <span class='hs-varid'>choice</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-207"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>aux</span> <span class='hs-varid'>k</span> <span class='hs-varid'>m</span> <span class='hs-varid'>n</span> <span class='hs-varid'>j</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>dsAux</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>k</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>m</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>n</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>j</span>
<a name="line-208"></a> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>0</span>
<a name="line-209"></a> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>1</span>
<a name="line-210"></a> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>2</span>
<a name="line-211"></a> <span class='hs-varid'>j</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>3</span>
<a name="line-212"></a>
<a name="line-213"></a> <span class='hs-varid'>aux</span> <span class='hs-varid'>k</span> <span class='hs-varid'>m</span> <span class='hs-varid'>zero</span> <span class='hs-varid'>j</span> <span class='hs-varop'>==</span> <span class='hs-varid'>k</span>
<a name="line-214"></a> <span class='hs-varid'>aux</span> <span class='hs-varid'>k</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>suc</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-varid'>zero</span> <span class='hs-varop'>==</span> <span class='hs-varid'>aux</span> <span class='hs-layout'>(</span><span class='hs-varid'>suc</span> <span class='hs-varid'>k</span><span class='hs-layout'>)</span> <span class='hs-varid'>m</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span>
<a name="line-215"></a> <span class='hs-varid'>aux</span> <span class='hs-varid'>k</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>suc</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>suc</span> <span class='hs-varid'>j</span><span class='hs-layout'>)</span> <span class='hs-varop'>==</span> <span class='hs-varid'>aux</span> <span class='hs-varid'>k</span> <span class='hs-varid'>m</span> <span class='hs-varid'>n</span> <span class='hs-varid'>j</span>
<a name="line-216"></a>
<a name="line-217"></a> <span class='hs-varid'>verifyModSucAux</span> <span class='hs-varid'>dsAux</span> <span class='hs-keyglyph'>=</span>
<a name="line-218"></a> <span class='hs-varid'>verify</span> <span class='hs-keyglyph'>[</span><span class='hs-str'>"k"</span><span class='hs-layout'>,</span><span class='hs-str'>"m"</span><span class='hs-layout'>,</span><span class='hs-str'>"n"</span><span class='hs-layout'>,</span><span class='hs-str'>"j"</span><span class='hs-keyglyph'>]</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-varop'>@@</span><span class='hs-layout'>)</span> <span class='hs-varid'>zero</span> <span class='hs-varid'>suc</span> <span class='hs-layout'>(</span><span class='hs-varop'>==</span><span class='hs-layout'>)</span> <span class='hs-varid'>choice</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-219"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>aux</span> <span class='hs-varid'>k</span> <span class='hs-varid'>m</span> <span class='hs-varid'>n</span> <span class='hs-varid'>j</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>dsAux</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>k</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>m</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>n</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>j</span>
<a name="line-220"></a> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>0</span>
<a name="line-221"></a> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>1</span>
<a name="line-222"></a> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>2</span>
<a name="line-223"></a> <span class='hs-varid'>j</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>3</span>
<a name="line-224"></a>
<a name="line-225"></a> <span class='hs-varid'>aux</span> <span class='hs-varid'>k</span> <span class='hs-varid'>m</span> <span class='hs-varid'>zero</span> <span class='hs-varid'>j</span> <span class='hs-varop'>==</span> <span class='hs-varid'>k</span>
<a name="line-226"></a> <span class='hs-varid'>aux</span> <span class='hs-varid'>k</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>suc</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-varid'>zero</span> <span class='hs-varop'>==</span> <span class='hs-varid'>aux</span> <span class='hs-varid'>zero</span> <span class='hs-varid'>m</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span>
<a name="line-227"></a> <span class='hs-varid'>aux</span> <span class='hs-varid'>k</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>suc</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>suc</span> <span class='hs-varid'>j</span><span class='hs-layout'>)</span> <span class='hs-varop'>==</span> <span class='hs-varid'>aux</span> <span class='hs-layout'>(</span><span class='hs-varid'>suc</span> <span class='hs-varid'>k</span><span class='hs-layout'>)</span> <span class='hs-varid'>m</span> <span class='hs-varid'>n</span> <span class='hs-varid'>j</span>
<a name="line-228"></a>
<a name="line-229"></a> <span class='hs-varid'>verifyEquals</span> <span class='hs-varid'>eq</span> <span class='hs-keyglyph'>=</span>
<a name="line-230"></a> <span class='hs-varid'>verify</span> <span class='hs-keyglyph'>[</span><span class='hs-str'>"n"</span><span class='hs-layout'>,</span><span class='hs-str'>"m"</span><span class='hs-keyglyph'>]</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-varop'>@@</span><span class='hs-layout'>)</span> <span class='hs-varid'>zero</span> <span class='hs-varid'>suc</span> <span class='hs-layout'>(</span><span class='hs-varop'>===</span><span class='hs-layout'>)</span> <span class='hs-varid'>choice</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-231"></a> <span class='hs-varid'>true</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>primTrue</span>
<a name="line-232"></a> <span class='hs-varid'>false</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>primFalse</span>
<a name="line-233"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>eq</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>x</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>y</span>
<a name="line-234"></a> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>0</span>
<a name="line-235"></a> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>1</span>
<a name="line-236"></a> <span class='hs-layout'>(</span><span class='hs-varid'>zero</span> <span class='hs-varop'>==</span> <span class='hs-varid'>zero</span> <span class='hs-layout'>)</span> <span class='hs-varop'>===</span> <span class='hs-varid'>true</span>
<a name="line-237"></a> <span class='hs-layout'>(</span><span class='hs-varid'>suc</span> <span class='hs-varid'>n</span> <span class='hs-varop'>==</span> <span class='hs-varid'>suc</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varop'>===</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'>==</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span>
<a name="line-238"></a> <span class='hs-layout'>(</span><span class='hs-varid'>suc</span> <span class='hs-varid'>n</span> <span class='hs-varop'>==</span> <span class='hs-varid'>zero</span> <span class='hs-layout'>)</span> <span class='hs-varop'>===</span> <span class='hs-varid'>false</span>
<a name="line-239"></a> <span class='hs-layout'>(</span><span class='hs-varid'>zero</span> <span class='hs-varop'>==</span> <span class='hs-varid'>suc</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-varop'>===</span> <span class='hs-varid'>false</span>
<a name="line-240"></a>
<a name="line-241"></a> <span class='hs-varid'>verifyLess</span> <span class='hs-varid'>leq</span> <span class='hs-keyglyph'>=</span>
<a name="line-242"></a> <span class='hs-varid'>verify</span> <span class='hs-keyglyph'>[</span><span class='hs-str'>"n"</span><span class='hs-layout'>,</span><span class='hs-str'>"m"</span><span class='hs-keyglyph'>]</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-varop'>@@</span><span class='hs-layout'>)</span> <span class='hs-varid'>zero</span> <span class='hs-varid'>suc</span> <span class='hs-layout'>(</span><span class='hs-varop'>===</span><span class='hs-layout'>)</span> <span class='hs-varid'>choice</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-243"></a> <span class='hs-varid'>true</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>primTrue</span>
<a name="line-244"></a> <span class='hs-varid'>false</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>primFalse</span>
<a name="line-245"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>x</span> <span class='hs-varop'><</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>leq</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>x</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>y</span>
<a name="line-246"></a> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>0</span>
<a name="line-247"></a> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-num'>1</span>
<a name="line-248"></a> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'><</span> <span class='hs-varid'>zero</span><span class='hs-layout'>)</span> <span class='hs-varop'>===</span> <span class='hs-varid'>false</span>
<a name="line-249"></a> <span class='hs-layout'>(</span><span class='hs-varid'>suc</span> <span class='hs-varid'>n</span> <span class='hs-varop'><</span> <span class='hs-varid'>suc</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varop'>===</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'><</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span>
<a name="line-250"></a> <span class='hs-layout'>(</span><span class='hs-varid'>zero</span> <span class='hs-varop'><</span> <span class='hs-varid'>suc</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varop'>===</span> <span class='hs-varid'>true</span>
<a name="line-251"></a>
<a name="line-252"></a> <span class='hs-varid'>verifyMax</span> <span class='hs-varid'>maxV</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>return</span> <span class='hs-conid'>()</span> <span class='hs-comment'>-- TODO: make max a postulate</span>
<a name="line-253"></a>
<a name="line-254"></a> <span class='hs-varid'>verify</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>verify'</span> <span class='hs-varid'>primNat</span> <span class='hs-varid'>primZero</span> <span class='hs-varid'>primSuc</span> <span class='hs-varid'>xs</span>
<a name="line-255"></a>
<a name="line-256"></a> <span class='hs-varid'>verify'</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>TCM</span> <span class='hs-conid'>Term</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>TCM</span> <span class='hs-conid'>Term</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>TCM</span> <span class='hs-conid'>Term</span> <span class='hs-keyglyph'>-></span>
<a name="line-257"></a> <span class='hs-keyglyph'>[</span><span class='hs-conid'>String</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span> <span class='hs-layout'>(</span><span class='hs-conid'>Term</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Term</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Term</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Term</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-conid'>Term</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Term</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span>
<a name="line-258"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Term</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Term</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>TCM</span> <span class='hs-conid'>()</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span>
<a name="line-259"></a> <span class='hs-layout'>(</span><span class='hs-keyglyph'>[</span><span class='hs-conid'>TCM</span> <span class='hs-conid'>()</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>TCM</span> <span class='hs-conid'>()</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>TCM</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>TCM</span> <span class='hs-varid'>a</span>
<a name="line-260"></a> <span class='hs-varid'>verify'</span> <span class='hs-varid'>pNat</span> <span class='hs-varid'>pZero</span> <span class='hs-varid'>pSuc</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<a name="line-261"></a> <span class='hs-varid'>nat</span> <span class='hs-keyglyph'><-</span> <span class='hs-conid'>El</span> <span class='hs-layout'>(</span><span class='hs-varid'>mkType</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span> <span class='hs-varop'><$></span> <span class='hs-varid'>pNat</span>
<a name="line-262"></a> <span class='hs-varid'>zero</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>pZero</span>
<a name="line-263"></a> <span class='hs-varid'>s</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>pSuc</span>
<a name="line-264"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>x</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <span class='hs-varop'>`apply`</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>defaultArg</span> <span class='hs-varid'>y</span><span class='hs-keyglyph'>]</span>
<a name="line-265"></a> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>noConstraints</span> <span class='hs-varop'>$</span> <span class='hs-varid'>equalTerm</span> <span class='hs-varid'>nat</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span>
<a name="line-266"></a> <span class='hs-varid'>suc</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>s</span> <span class='hs-varop'>@@</span> <span class='hs-varid'>n</span>
<a name="line-267"></a> <span class='hs-varid'>choice</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldr1</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>x</span> <span class='hs-varop'>`catchError`</span> <span class='hs-keyglyph'>\</span><span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-268"></a> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>mapM</span> <span class='hs-varid'>freshName_</span> <span class='hs-varid'>xs</span>
<a name="line-269"></a> <span class='hs-varid'>addCtxs</span> <span class='hs-varid'>xs</span> <span class='hs-layout'>(</span><span class='hs-varid'>domFromArg</span> <span class='hs-varop'>$</span> <span class='hs-varid'>defaultArg</span> <span class='hs-varid'>nat</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varop'>@@</span><span class='hs-layout'>)</span> <span class='hs-varid'>zero</span> <span class='hs-varid'>suc</span> <span class='hs-layout'>(</span><span class='hs-varop'>==</span><span class='hs-layout'>)</span> <span class='hs-varid'>choice</span>
<a name="line-270"></a>
<a name="line-271"></a>
<a name="line-272"></a><a name="inductiveCheck"></a><span class='hs-definition'>inductiveCheck</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>String</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Term</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>TCM</span> <span class='hs-conid'>()</span>
<a name="line-273"></a><span class='hs-definition'>inductiveCheck</span> <span class='hs-varid'>b</span> <span class='hs-varid'>n</span> <span class='hs-varid'>t</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<a name="line-274"></a> <span class='hs-varid'>t</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>etaContract</span> <span class='hs-varop'>=<<</span> <span class='hs-varid'>normalise</span> <span class='hs-varid'>t</span>
<a name="line-275"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>err</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>typeError</span> <span class='hs-layout'>(</span><span class='hs-conid'>NotInductive</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span>
<a name="line-276"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>ignoreSharing</span> <span class='hs-varid'>t</span> <span class='hs-keyword'>of</span>
<a name="line-277"></a> <span class='hs-conid'>Def</span> <span class='hs-varid'>t</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-278"></a> <span class='hs-varid'>t</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>theDef</span> <span class='hs-varop'><$></span> <span class='hs-varid'>getConstInfo</span> <span class='hs-varid'>t</span>
<a name="line-279"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>t</span> <span class='hs-keyword'>of</span>
<a name="line-280"></a> <span class='hs-conid'>Datatype</span> <span class='hs-layout'>{</span> <span class='hs-varid'>dataInduction</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Inductive</span>
<a name="line-281"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>dataCons</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>cs</span>
<a name="line-282"></a> <span class='hs-layout'>}</span>
<a name="line-283"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>length</span> <span class='hs-varid'>cs</span> <span class='hs-varop'>==</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>return</span> <span class='hs-conid'>()</span>
<a name="line-284"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>-></span>
<a name="line-285"></a> <span class='hs-varid'>typeError</span> <span class='hs-varop'>$</span> <span class='hs-conid'>GenericError</span> <span class='hs-varop'>$</span> <span class='hs-varid'>unwords</span>
<a name="line-286"></a> <span class='hs-keyglyph'>[</span> <span class='hs-str'>"The builtin"</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span>
<a name="line-287"></a> <span class='hs-layout'>,</span> <span class='hs-str'>"must be a datatype with"</span><span class='hs-layout'>,</span> <span class='hs-varid'>show</span> <span class='hs-varid'>n</span>
<a name="line-288"></a> <span class='hs-layout'>,</span> <span class='hs-str'>"constructors"</span> <span class='hs-keyglyph'>]</span>
<a name="line-289"></a> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>err</span>
<a name="line-290"></a> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>err</span>
<a name="line-291"></a>
<a name="line-292"></a><span class='hs-comment'>-- | @bindPostulatedName builtin e m@ checks that @e@ is a postulated</span>
<a name="line-293"></a><span class='hs-comment'>-- name @q@, and binds the builtin @builtin@ to the term @m q def@,</span>
<a name="line-294"></a><span class='hs-comment'>-- where @def@ is the current 'Definition' of @q@.</span>
<a name="line-295"></a>
<a name="line-296"></a><a name="bindPostulatedName"></a><span class='hs-definition'>bindPostulatedName</span> <span class='hs-keyglyph'>::</span>
<a name="line-297"></a> <span class='hs-conid'>String</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>A</span><span class='hs-varop'>.</span><span class='hs-conid'>Expr</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-conid'>QName</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Definition</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>TCM</span> <span class='hs-conid'>Term</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>TCM</span> <span class='hs-conid'>()</span>
<a name="line-298"></a><span class='hs-definition'>bindPostulatedName</span> <span class='hs-varid'>builtin</span> <span class='hs-varid'>e</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<a name="line-299"></a> <span class='hs-varid'>q</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>getName</span> <span class='hs-varid'>e</span>
<a name="line-300"></a> <span class='hs-varid'>def</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>ignoreAbstractMode</span> <span class='hs-varop'>$</span> <span class='hs-varid'>getConstInfo</span> <span class='hs-varid'>q</span>
<a name="line-301"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>theDef</span> <span class='hs-varid'>def</span> <span class='hs-keyword'>of</span>
<a name="line-302"></a> <span class='hs-conid'>Axiom</span> <span class='hs-layout'>{</span><span class='hs-layout'>}</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>bindBuiltinName</span> <span class='hs-varid'>builtin</span> <span class='hs-varop'>=<<</span> <span class='hs-varid'>m</span> <span class='hs-varid'>q</span> <span class='hs-varid'>def</span>
<a name="line-303"></a> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>err</span>
<a name="line-304"></a> <span class='hs-keyword'>where</span>
<a name="line-305"></a> <span class='hs-varid'>err</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>typeError</span> <span class='hs-varop'>$</span> <span class='hs-conid'>GenericError</span> <span class='hs-varop'>$</span>
<a name="line-306"></a> <span class='hs-str'>"The argument to BUILTIN "</span> <span class='hs-varop'>++</span> <span class='hs-varid'>builtin</span> <span class='hs-varop'>++</span>
<a name="line-307"></a> <span class='hs-str'>" must be a postulated name"</span>
<a name="line-308"></a>
<a name="line-309"></a> <span class='hs-varid'>getName</span> <span class='hs-layout'>(</span><span class='hs-conid'>A</span><span class='hs-varop'>.</span><span class='hs-conid'>Def</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>return</span> <span class='hs-varid'>q</span>
<a name="line-310"></a> <span class='hs-varid'>getName</span> <span class='hs-layout'>(</span><span class='hs-conid'>A</span><span class='hs-varop'>.</span><span class='hs-conid'>ScopedExpr</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>getName</span> <span class='hs-varid'>e</span>
<a name="line-311"></a> <span class='hs-varid'>getName</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>err</span>
<a name="line-312"></a>
<a name="line-313"></a><a name="bindBuiltinInfo"></a><span class='hs-definition'>bindBuiltinInfo</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>BuiltinInfo</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>A</span><span class='hs-varop'>.</span><span class='hs-conid'>Expr</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>TCM</span> <span class='hs-conid'>()</span>
<a name="line-314"></a><span class='hs-definition'>bindBuiltinInfo</span> <span class='hs-varid'>i</span> <span class='hs-layout'>(</span><span class='hs-conid'>A</span><span class='hs-varop'>.</span><span class='hs-conid'>ScopedExpr</span> <span class='hs-varid'>scope</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>setScope</span> <span class='hs-varid'>scope</span> <span class='hs-varop'>>></span> <span class='hs-varid'>bindBuiltinInfo</span> <span class='hs-varid'>i</span> <span class='hs-varid'>e</span>
<a name="line-315"></a><span class='hs-definition'>bindBuiltinInfo</span> <span class='hs-layout'>(</span><span class='hs-conid'>BuiltinInfo</span> <span class='hs-varid'>s</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<a name="line-316"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>d</span> <span class='hs-keyword'>of</span>
<a name="line-317"></a> <span class='hs-conid'>BuiltinData</span> <span class='hs-varid'>t</span> <span class='hs-varid'>cs</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-318"></a> <span class='hs-varid'>e'</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>checkExpr</span> <span class='hs-varid'>e</span> <span class='hs-varop'>=<<</span> <span class='hs-varid'>t</span>
<a name="line-319"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>length</span> <span class='hs-varid'>cs</span>
<a name="line-320"></a> <span class='hs-varid'>inductiveCheck</span> <span class='hs-varid'>s</span> <span class='hs-varid'>n</span> <span class='hs-varid'>e'</span>
<a name="line-321"></a> <span class='hs-varid'>bindBuiltinName</span> <span class='hs-varid'>s</span> <span class='hs-varid'>e'</span>
<a name="line-322"></a> <span class='hs-comment'>-- NAT and LEVEL must be different. (Why?)</span>
<a name="line-323"></a> <span class='hs-varid'>when</span> <span class='hs-layout'>(</span><span class='hs-varid'>s</span> <span class='hs-varop'>`elem`</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>builtinNat</span><span class='hs-layout'>,</span> <span class='hs-varid'>builtinLevel</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-keyword'>do</span>
<a name="line-324"></a> <span class='hs-varid'>nat</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>getBuiltin'</span> <span class='hs-varid'>builtinNat</span>
<a name="line-325"></a> <span class='hs-varid'>level</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>getBuiltin'</span> <span class='hs-varid'>builtinLevel</span>
<a name="line-326"></a> <span class='hs-keyword'>case</span> <span class='hs-layout'>(</span><span class='hs-varid'>nat</span><span class='hs-layout'>,</span> <span class='hs-varid'>level</span><span class='hs-layout'>)</span> <span class='hs-keyword'>of</span>
<a name="line-327"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varid'>nat</span><span class='hs-layout'>,</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>level</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-328"></a> <span class='hs-conid'>Def</span> <span class='hs-varid'>nat</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>ignoreSharing</span> <span class='hs-varop'><$></span> <span class='hs-varid'>normalise</span> <span class='hs-varid'>nat</span>
<a name="line-329"></a> <span class='hs-conid'>Def</span> <span class='hs-varid'>level</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>ignoreSharing</span> <span class='hs-varop'><$></span> <span class='hs-varid'>normalise</span> <span class='hs-varid'>level</span>
<a name="line-330"></a> <span class='hs-varid'>when</span> <span class='hs-layout'>(</span><span class='hs-varid'>nat</span> <span class='hs-varop'>==</span> <span class='hs-varid'>level</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>typeError</span> <span class='hs-varop'>$</span> <span class='hs-conid'>GenericError</span> <span class='hs-varop'>$</span>
<a name="line-331"></a> <span class='hs-varid'>builtinNat</span> <span class='hs-varop'>++</span> <span class='hs-str'>" and "</span> <span class='hs-varop'>++</span> <span class='hs-varid'>builtinLevel</span> <span class='hs-varop'>++</span>
<a name="line-332"></a> <span class='hs-str'>" have to be different types."</span>
<a name="line-333"></a> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>return</span> <span class='hs-conid'>()</span>
<a name="line-334"></a>
<a name="line-335"></a>
<a name="line-336"></a> <span class='hs-conid'>BuiltinDataCons</span> <span class='hs-varid'>t</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-337"></a>
<a name="line-338"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>name</span> <span class='hs-layout'>(</span><span class='hs-conid'>Lam</span> <span class='hs-varid'>h</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>name</span> <span class='hs-layout'>(</span><span class='hs-varid'>absBody</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-339"></a> <span class='hs-varid'>name</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>c</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Con</span> <span class='hs-varid'>c</span> <span class='hs-conid'>[]</span>
<a name="line-340"></a> <span class='hs-varid'>name</span> <span class='hs-layout'>(</span><span class='hs-conid'>Shared</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>name</span> <span class='hs-varop'>$</span> <span class='hs-varid'>ignoreSharing</span> <span class='hs-layout'>(</span><span class='hs-varid'>derefPtr</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span>
<a name="line-341"></a> <span class='hs-varid'>name</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-sel'>__IMPOSSIBLE__</span>
<a name="line-342"></a>
<a name="line-343"></a> <span class='hs-varid'>e'</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>checkExpr</span> <span class='hs-varid'>e</span> <span class='hs-varop'>=<<</span> <span class='hs-varid'>t</span>
<a name="line-344"></a>
<a name="line-345"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>e</span> <span class='hs-keyword'>of</span>
<a name="line-346"></a> <span class='hs-conid'>A</span><span class='hs-varop'>.</span><span class='hs-conid'>Con</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-347"></a> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>typeError</span> <span class='hs-varop'>$</span> <span class='hs-conid'>BuiltinMustBeConstructor</span> <span class='hs-varid'>s</span> <span class='hs-varid'>e</span>
<a name="line-348"></a>
<a name="line-349"></a> <span class='hs-varid'>bindBuiltinName</span> <span class='hs-varid'>s</span> <span class='hs-layout'>(</span><span class='hs-varid'>name</span> <span class='hs-varid'>e'</span><span class='hs-layout'>)</span>
<a name="line-350"></a>
<a name="line-351"></a> <span class='hs-conid'>BuiltinPrim</span> <span class='hs-varid'>pfname</span> <span class='hs-varid'>axioms</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-352"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>e</span> <span class='hs-keyword'>of</span>
<a name="line-353"></a> <span class='hs-conid'>A</span><span class='hs-varop'>.</span><span class='hs-conid'>Def</span> <span class='hs-varid'>qx</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-354"></a>
<a name="line-355"></a> <span class='hs-conid'>PrimImpl</span> <span class='hs-varid'>t</span> <span class='hs-varid'>pf</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>lookupPrimitiveFunction</span> <span class='hs-varid'>pfname</span>
<a name="line-356"></a> <span class='hs-varid'>v</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>checkExpr</span> <span class='hs-varid'>e</span> <span class='hs-varid'>t</span>
<a name="line-357"></a>
<a name="line-358"></a> <span class='hs-varid'>axioms</span> <span class='hs-varid'>v</span>
<a name="line-359"></a>
<a name="line-360"></a> <span class='hs-varid'>info</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>getConstInfo</span> <span class='hs-varid'>qx</span>
<a name="line-361"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>cls</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>defClauses</span> <span class='hs-varid'>info</span>
<a name="line-362"></a> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>defAbstract</span> <span class='hs-varid'>info</span>
<a name="line-363"></a> <span class='hs-varid'>mcc</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>defCompiled</span> <span class='hs-varid'>info</span>
<a name="line-364"></a> <span class='hs-varid'>bindPrimitive</span> <span class='hs-varid'>pfname</span> <span class='hs-varop'>$</span> <span class='hs-varid'>pf</span> <span class='hs-layout'>{</span> <span class='hs-varid'>primFunName</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>qx</span> <span class='hs-layout'>}</span>
<a name="line-365"></a> <span class='hs-varid'>addConstant</span> <span class='hs-varid'>qx</span> <span class='hs-varop'>$</span> <span class='hs-varid'>info</span> <span class='hs-layout'>{</span> <span class='hs-varid'>theDef</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Primitive</span> <span class='hs-varid'>a</span> <span class='hs-varid'>pfname</span> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varid'>cls</span><span class='hs-layout'>)</span> <span class='hs-varid'>mcc</span> <span class='hs-layout'>}</span>
<a name="line-366"></a>
<a name="line-367"></a> <span class='hs-comment'>-- needed? yes, for checking equations for mul</span>
<a name="line-368"></a> <span class='hs-varid'>bindBuiltinName</span> <span class='hs-varid'>s</span> <span class='hs-varid'>v</span>
<a name="line-369"></a>
<a name="line-370"></a> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>typeError</span> <span class='hs-varop'>$</span> <span class='hs-conid'>GenericError</span> <span class='hs-varop'>$</span> <span class='hs-str'>"Builtin "</span> <span class='hs-varop'>++</span> <span class='hs-varid'>s</span> <span class='hs-varop'>++</span> <span class='hs-str'>" must be bound to a function"</span>
<a name="line-371"></a>
<a name="line-372"></a> <span class='hs-conid'>BuiltinPostulate</span> <span class='hs-varid'>rel</span> <span class='hs-varid'>t</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-373"></a> <span class='hs-varid'>t'</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>t</span>
<a name="line-374"></a> <span class='hs-varid'>e'</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>applyRelevanceToContext</span> <span class='hs-varid'>rel</span> <span class='hs-varop'>$</span> <span class='hs-varid'>checkExpr</span> <span class='hs-varid'>e</span> <span class='hs-varid'>t'</span>
<a name="line-375"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>err</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>typeError</span> <span class='hs-varop'>$</span> <span class='hs-conid'>GenericError</span> <span class='hs-varop'>$</span>
<a name="line-376"></a> <span class='hs-str'>"The argument to BUILTIN "</span> <span class='hs-varop'>++</span> <span class='hs-varid'>s</span> <span class='hs-varop'>++</span> <span class='hs-str'>" must be a postulated name"</span>
<a name="line-377"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>e</span> <span class='hs-keyword'>of</span>
<a name="line-378"></a> <span class='hs-conid'>A</span><span class='hs-varop'>.</span><span class='hs-conid'>Def</span> <span class='hs-varid'>q</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-379"></a> <span class='hs-varid'>def</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>ignoreAbstractMode</span> <span class='hs-varop'>$</span> <span class='hs-varid'>getConstInfo</span> <span class='hs-varid'>q</span>
<a name="line-380"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>theDef</span> <span class='hs-varid'>def</span> <span class='hs-keyword'>of</span>
<a name="line-381"></a> <span class='hs-conid'>Axiom</span> <span class='hs-layout'>{</span><span class='hs-layout'>}</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-382"></a> <span class='hs-varid'>builtinSizeHook</span> <span class='hs-varid'>s</span> <span class='hs-varid'>q</span> <span class='hs-varid'>e'</span> <span class='hs-varid'>t'</span>
<a name="line-383"></a> <span class='hs-varid'>bindBuiltinName</span> <span class='hs-varid'>s</span> <span class='hs-varid'>e'</span>
<a name="line-384"></a> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>err</span>
<a name="line-385"></a> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>err</span>
<a name="line-386"></a>
<a name="line-387"></a> <span class='hs-conid'>BuiltinUnknown</span> <span class='hs-varid'>mt</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-388"></a> <span class='hs-varid'>e'</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>maybe</span> <span class='hs-layout'>(</span><span class='hs-varid'>fst</span> <span class='hs-varop'><$></span> <span class='hs-varid'>inferExpr</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>checkExpr</span> <span class='hs-varid'>e</span> <span class='hs-varop'>=<<</span><span class='hs-layout'>)</span> <span class='hs-varid'>mt</span>
<a name="line-389"></a> <span class='hs-varid'>f</span> <span class='hs-varid'>e'</span>
<a name="line-390"></a> <span class='hs-varid'>bindBuiltinName</span> <span class='hs-varid'>s</span> <span class='hs-varid'>e'</span>
<a name="line-391"></a>
<a name="line-392"></a><a name="bindBuiltin"></a><span class='hs-comment'>-- | Bind a builtin thing to an expression.</span>
<a name="line-393"></a><span class='hs-definition'>bindBuiltin</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>String</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>A</span><span class='hs-varop'>.</span><span class='hs-conid'>Expr</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>TCM</span> <span class='hs-conid'>()</span>
<a name="line-394"></a><span class='hs-definition'>bindBuiltin</span> <span class='hs-varid'>b</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<a name="line-395"></a> <span class='hs-varid'>top</span> <span class='hs-keyglyph'><-</span> <span class='hs-layout'>(</span><span class='hs-varop'>==</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>size</span> <span class='hs-varop'><$></span> <span class='hs-varid'>getContextTelescope</span>
<a name="line-396"></a> <span class='hs-varid'>unless</span> <span class='hs-varid'>top</span> <span class='hs-varop'>$</span> <span class='hs-varid'>typeError</span> <span class='hs-varop'>$</span> <span class='hs-conid'>BuiltinInParameterisedModule</span> <span class='hs-varid'>b</span>
<a name="line-397"></a> <span class='hs-varid'>bind</span> <span class='hs-varid'>b</span> <span class='hs-varid'>e</span>
<a name="line-398"></a> <span class='hs-keyword'>where</span>
<a name="line-399"></a> <span class='hs-varid'>bind</span> <span class='hs-varid'>b</span> <span class='hs-varid'>e</span>
<a name="line-400"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>b</span> <span class='hs-varop'>==</span> <span class='hs-varid'>builtinInf</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bindBuiltinInf</span> <span class='hs-varid'>e</span>
<a name="line-401"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>b</span> <span class='hs-varop'>==</span> <span class='hs-varid'>builtinSharp</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bindBuiltinSharp</span> <span class='hs-varid'>e</span>
<a name="line-402"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>b</span> <span class='hs-varop'>==</span> <span class='hs-varid'>builtinFlat</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bindBuiltinFlat</span> <span class='hs-varid'>e</span>
<a name="line-403"></a> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>find</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varop'>==</span><span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>builtinName</span><span class='hs-layout'>)</span> <span class='hs-varid'>coreBuiltins</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bindBuiltinInfo</span> <span class='hs-varid'>i</span> <span class='hs-varid'>e</span>
<a name="line-404"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>typeError</span> <span class='hs-varop'>$</span> <span class='hs-conid'>NoSuchBuiltinName</span> <span class='hs-varid'>b</span>
</pre></body>
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