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<html><head><meta charset="utf-8"><title>Function.Construct.Setoid</title><link rel="stylesheet" href="Agda.css"></head><body><pre class="Agda"><a id="1" class="Symbol">{-#</a> <a id="5" class="Keyword">OPTIONS</a> <a id="13" class="Pragma">--without-K</a> <a id="25" class="Pragma">--safe</a> <a id="32" class="Symbol">#-}</a>
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<a id="37" class="Comment">-- was not ported from old function hierarchy</a>
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<a id="84" class="Keyword">module</a> <a id="91" href="Function.Construct.Setoid.html" class="Module">Function.Construct.Setoid</a> <a id="117" class="Keyword">where</a>
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<a id="126" class="Keyword">open</a> <a id="131" class="Keyword">import</a> <a id="138" href="Function.Bundles.html" class="Module">Function.Bundles</a> <a id="155" class="Keyword">using</a> <a id="161" class="Symbol">(</a><a id="162" href="Function.Bundles.html#2043" class="Record">Func</a><a id="166" class="Symbol">;</a> <a id="168" href="Function.Bundles.html#15133" class="Function Operator">_⟨$⟩_</a><a id="173" class="Symbol">)</a>
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<a id="177" class="Keyword">import</a> <a id="184" href="Function.Construct.Composition.html" class="Module">Function.Construct.Composition</a> <a id="215" class="Symbol">as</a> <a id="218" class="Module">Comp</a>
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<a id="225" class="Keyword">open</a> <a id="230" class="Keyword">import</a> <a id="237" href="Level.html" class="Module">Level</a> <a id="243" class="Keyword">using</a> <a id="249" class="Symbol">(</a><a id="250" href="Agda.Primitive.html#742" class="Postulate">Level</a><a id="255" class="Symbol">)</a>
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<a id="259" class="Keyword">open</a> <a id="264" class="Keyword">import</a> <a id="271" href="Relation.Binary.Bundles.html" class="Module">Relation.Binary.Bundles</a> <a id="295" class="Keyword">using</a> <a id="301" class="Symbol">(</a><a id="302" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a><a id="308" class="Symbol">)</a>
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<a id="314" class="Keyword">private</a>
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<a id="326" class="Keyword">variable</a>
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<a id="341" href="Function.Construct.Setoid.html#341" class="Generalizable">a₁</a> <a id="344" href="Function.Construct.Setoid.html#344" class="Generalizable">a₂</a> <a id="347" href="Function.Construct.Setoid.html#347" class="Generalizable">b₁</a> <a id="350" href="Function.Construct.Setoid.html#350" class="Generalizable">b₂</a> <a id="353" href="Function.Construct.Setoid.html#353" class="Generalizable">c₁</a> <a id="356" href="Function.Construct.Setoid.html#356" class="Generalizable">c₂</a> <a id="359" class="Symbol">:</a> <a id="361" href="Agda.Primitive.html#742" class="Postulate">Level</a>
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<a id="setoid"></a><a id="376" href="Function.Construct.Setoid.html#376" class="Function">setoid</a> <a id="383" class="Symbol">:</a> <a id="385" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="392" href="Function.Construct.Setoid.html#341" class="Generalizable">a₁</a> <a id="395" href="Function.Construct.Setoid.html#344" class="Generalizable">a₂</a> <a id="398" class="Symbol">→</a> <a id="400" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="407" href="Function.Construct.Setoid.html#347" class="Generalizable">b₁</a> <a id="410" href="Function.Construct.Setoid.html#350" class="Generalizable">b₂</a> <a id="413" class="Symbol">→</a> <a id="415" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="422" class="Symbol">_</a> <a id="424" class="Symbol">_</a>
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<a id="428" href="Function.Construct.Setoid.html#376" class="Function">setoid</a> <a id="435" href="Function.Construct.Setoid.html#435" class="Bound">From</a> <a id="440" href="Function.Construct.Setoid.html#440" class="Bound">To</a> <a id="443" class="Symbol">=</a> <a id="445" class="Keyword">record</a>
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<a id="456" class="Symbol">{</a> <a id="458" href="Relation.Binary.Bundles.html#1143" class="Field">Carrier</a> <a id="466" class="Symbol">=</a> <a id="468" href="Function.Bundles.html#2043" class="Record">Func</a> <a id="473" href="Function.Construct.Setoid.html#435" class="Bound">From</a> <a id="478" href="Function.Construct.Setoid.html#440" class="Bound">To</a>
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<a id="485" class="Symbol">;</a> <a id="487" href="Relation.Binary.Bundles.html#1169" class="Field Operator">_≈_</a> <a id="491" class="Symbol">=</a> <a id="493" class="Symbol">λ</a> <a id="495" href="Function.Construct.Setoid.html#495" class="Bound">f</a> <a id="497" href="Function.Construct.Setoid.html#497" class="Bound">g</a> <a id="499" class="Symbol">→</a> <a id="501" class="Symbol">∀</a> <a id="503" class="Symbol">{</a><a id="504" href="Function.Construct.Setoid.html#504" class="Bound">x</a><a id="505" class="Symbol">}</a> <a id="507" class="Symbol">→</a> <a id="509" href="Function.Construct.Setoid.html#495" class="Bound">f</a> <a id="511" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="515" href="Function.Construct.Setoid.html#504" class="Bound">x</a> <a id="517" href="Relation.Binary.Bundles.html#1169" class="Field Operator">To.≈</a> <a id="522" href="Function.Construct.Setoid.html#497" class="Bound">g</a> <a id="524" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="528" href="Function.Construct.Setoid.html#504" class="Bound">x</a>
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<a id="534" class="Symbol">;</a> <a id="536" href="Relation.Binary.Bundles.html#1203" class="Field">isEquivalence</a> <a id="550" class="Symbol">=</a> <a id="552" class="Keyword">record</a>
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<a id="565" class="Symbol">{</a> <a id="567" href="Relation.Binary.Structures.html#1596" class="Field">refl</a> <a id="572" class="Symbol">=</a> <a id="574" href="Relation.Binary.Structures.html#1596" class="Function">To.refl</a>
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<a id="588" class="Symbol">;</a> <a id="590" href="Relation.Binary.Structures.html#1622" class="Field">sym</a> <a id="594" class="Symbol">=</a> <a id="596" class="Symbol">λ</a> <a id="598" href="Function.Construct.Setoid.html#598" class="Bound">f≈g</a> <a id="602" class="Symbol">→</a> <a id="604" href="Relation.Binary.Structures.html#1200" class="Function">To.sym</a> <a id="611" href="Function.Construct.Setoid.html#598" class="Bound">f≈g</a>
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<a id="621" class="Symbol">;</a> <a id="623" href="Relation.Binary.Structures.html#1648" class="Field">trans</a> <a id="629" class="Symbol">=</a> <a id="631" class="Symbol">λ</a> <a id="633" href="Function.Construct.Setoid.html#633" class="Bound">f≈g</a> <a id="637" href="Function.Construct.Setoid.html#637" class="Bound">g≈h</a> <a id="641" class="Symbol">→</a> <a id="643" href="Relation.Binary.Structures.html#1226" class="Function">To.trans</a> <a id="652" href="Function.Construct.Setoid.html#633" class="Bound">f≈g</a> <a id="656" href="Function.Construct.Setoid.html#637" class="Bound">g≈h</a>
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<a id="666" class="Symbol">}</a>
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<a id="672" class="Symbol">}</a>
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<a id="678" class="Keyword">where</a>
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<a id="690" class="Keyword">module</a> <a id="697" href="Function.Construct.Setoid.html#697" class="Module">To</a> <a id="700" class="Symbol">=</a> <a id="702" href="Relation.Binary.Bundles.html#1080" class="Module">Setoid</a> <a id="709" href="Function.Construct.Setoid.html#440" class="Bound">To</a>
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<a id="715" class="Comment">-- This doesn't really belong here, it should be in Function.Construct.Composition but that's in stdlib</a>
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<a id="821" class="Comment">-- so will need to be contributed to there first.</a>
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<a id="873" class="Keyword">infixr</a> <a id="880" class="Number">9</a> <a id="882" href="Function.Construct.Setoid.html#888" class="Function Operator">_∙_</a>
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<a id="_∙_"></a><a id="888" href="Function.Construct.Setoid.html#888" class="Function Operator">_∙_</a> <a id="892" class="Symbol">:</a> <a id="894" class="Symbol">{</a><a id="895" href="Function.Construct.Setoid.html#895" class="Bound">A</a> <a id="897" class="Symbol">:</a> <a id="899" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="906" href="Function.Construct.Setoid.html#341" class="Generalizable">a₁</a> <a id="909" href="Function.Construct.Setoid.html#344" class="Generalizable">a₂</a><a id="911" class="Symbol">}</a> <a id="913" class="Symbol">{</a><a id="914" href="Function.Construct.Setoid.html#914" class="Bound">B</a> <a id="916" class="Symbol">:</a> <a id="918" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="925" href="Function.Construct.Setoid.html#347" class="Generalizable">b₁</a> <a id="928" href="Function.Construct.Setoid.html#350" class="Generalizable">b₂</a><a id="930" class="Symbol">}</a> <a id="932" class="Symbol">{</a><a id="933" href="Function.Construct.Setoid.html#933" class="Bound">C</a> <a id="935" class="Symbol">:</a> <a id="937" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="944" href="Function.Construct.Setoid.html#353" class="Generalizable">c₁</a> <a id="947" href="Function.Construct.Setoid.html#356" class="Generalizable">c₂</a><a id="949" class="Symbol">}</a> <a id="951" class="Symbol">→</a> <a id="953" href="Function.Bundles.html#2043" class="Record">Func</a> <a id="958" href="Function.Construct.Setoid.html#914" class="Bound">B</a> <a id="960" href="Function.Construct.Setoid.html#933" class="Bound">C</a> <a id="962" class="Symbol">→</a> <a id="964" href="Function.Bundles.html#2043" class="Record">Func</a> <a id="969" href="Function.Construct.Setoid.html#895" class="Bound">A</a> <a id="971" href="Function.Construct.Setoid.html#914" class="Bound">B</a> <a id="973" class="Symbol">→</a> <a id="975" href="Function.Bundles.html#2043" class="Record">Func</a> <a id="980" href="Function.Construct.Setoid.html#895" class="Bound">A</a> <a id="982" href="Function.Construct.Setoid.html#933" class="Bound">C</a>
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<a id="986" href="Function.Construct.Setoid.html#986" class="Bound">f</a> <a id="988" href="Function.Construct.Setoid.html#888" class="Function Operator">∙</a> <a id="990" href="Function.Construct.Setoid.html#990" class="Bound">g</a> <a id="992" class="Symbol">=</a> <a id="994" href="Function.Construct.Composition.html#5240" class="Function">Comp.function</a> <a id="1008" href="Function.Construct.Setoid.html#990" class="Bound">g</a> <a id="1010" href="Function.Construct.Setoid.html#986" class="Bound">f</a>
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</pre></body></html> |