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1172 lines
258 KiB
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<html><head><meta charset="utf-8"><title>Algebra.Bundles</title><link rel="stylesheet" href="Agda.css"></head><body><pre class="Agda"><a id="1" class="Comment">------------------------------------------------------------------------</a>
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<a id="74" class="Comment">-- The Agda standard library</a>
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<a id="103" class="Comment">--</a>
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<a id="106" class="Comment">-- Definitions of algebraic structures like monoids and rings</a>
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<a id="168" class="Comment">-- (packed in records together with sets, operations, etc.)</a>
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<a id="228" class="Comment">------------------------------------------------------------------------</a>
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<a id="302" class="Comment">-- The contents of this module should be accessed via `Algebra`.</a>
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<a id="368" class="Symbol">{-#</a> <a id="372" class="Keyword">OPTIONS</a> <a id="380" class="Pragma">--cubical-compatible</a> <a id="401" class="Pragma">--safe</a> <a id="408" class="Symbol">#-}</a>
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<a id="413" class="Keyword">module</a> <a id="420" href="Algebra.Bundles.html" class="Module">Algebra.Bundles</a> <a id="436" class="Keyword">where</a>
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<a id="443" class="Keyword">import</a> <a id="450" href="Algebra.Bundles.Raw.html" class="Module">Algebra.Bundles.Raw</a> <a id="470" class="Symbol">as</a> <a id="473" class="Module">Raw</a>
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<a id="477" class="Keyword">open</a> <a id="482" class="Keyword">import</a> <a id="489" href="Algebra.Core.html" class="Module">Algebra.Core</a>
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<a id="502" class="Keyword">open</a> <a id="507" class="Keyword">import</a> <a id="514" href="Algebra.Structures.html" class="Module">Algebra.Structures</a>
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<a id="533" class="Keyword">open</a> <a id="538" class="Keyword">import</a> <a id="545" href="Relation.Binary.Core.html" class="Module">Relation.Binary.Core</a> <a id="566" class="Keyword">using</a> <a id="572" class="Symbol">(</a><a id="573" href="Relation.Binary.Core.html#896" class="Function">Rel</a><a id="576" class="Symbol">)</a>
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<a id="578" class="Keyword">open</a> <a id="583" class="Keyword">import</a> <a id="590" href="Function.Base.html" class="Module">Function.Base</a>
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<a id="604" class="Keyword">import</a> <a id="611" href="Relation.Nullary.html" class="Module">Relation.Nullary</a> <a id="628" class="Symbol">as</a> <a id="631" class="Module">N</a>
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<a id="633" class="Keyword">open</a> <a id="638" class="Keyword">import</a> <a id="645" href="Level.html" class="Module">Level</a>
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<a id="652" class="Comment">------------------------------------------------------------------------</a>
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<a id="725" class="Comment">-- Re-export definitions of 'raw' bundles</a>
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<a id="768" class="Keyword">open</a> <a id="773" href="Algebra.Bundles.Raw.html" class="Module">Raw</a> <a id="777" class="Keyword">public</a>
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<a id="786" class="Keyword">using</a> <a id="792" class="Symbol">(</a><a id="793" href="Algebra.Bundles.Raw.html#644" class="Record">RawMagma</a><a id="801" class="Symbol">;</a> <a id="803" href="Algebra.Bundles.Raw.html#1105" class="Record">RawMonoid</a><a id="812" class="Symbol">;</a> <a id="814" href="Algebra.Bundles.Raw.html#1638" class="Record">RawGroup</a>
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<a id="831" class="Symbol">;</a> <a id="833" href="Algebra.Bundles.Raw.html#2222" class="Record">RawNearSemiring</a><a id="848" class="Symbol">;</a> <a id="850" href="Algebra.Bundles.Raw.html#2934" class="Record">RawSemiring</a>
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<a id="870" class="Symbol">;</a> <a id="872" href="Algebra.Bundles.Raw.html#3743" class="Record">RawRingWithoutOne</a><a id="889" class="Symbol">;</a> <a id="891" href="Algebra.Bundles.Raw.html#4595" class="Record">RawRing</a>
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<a id="907" class="Symbol">;</a> <a id="909" href="Algebra.Bundles.Raw.html#5560" class="Record">RawQuasigroup</a><a id="922" class="Symbol">;</a> <a id="924" href="Algebra.Bundles.Raw.html#6332" class="Record">RawLoop</a><a id="931" class="Symbol">;</a> <a id="933" href="Algebra.Bundles.Raw.html#6831" class="Record">RawKleeneAlgebra</a><a id="949" class="Symbol">)</a>
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<a id="952" class="Comment">------------------------------------------------------------------------</a>
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<a id="1025" class="Comment">-- Bundles with 1 binary operation</a>
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<a id="1060" class="Comment">------------------------------------------------------------------------</a>
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<a id="1134" class="Keyword">record</a> <a id="Magma"></a><a id="1141" href="Algebra.Bundles.html#1141" class="Record">Magma</a> <a id="1147" href="Algebra.Bundles.html#1147" class="Bound">c</a> <a id="1149" href="Algebra.Bundles.html#1149" class="Bound">ℓ</a> <a id="1151" class="Symbol">:</a> <a id="1153" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1157" class="Symbol">(</a><a id="1158" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="1162" class="Symbol">(</a><a id="1163" href="Algebra.Bundles.html#1147" class="Bound">c</a> <a id="1165" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1167" href="Algebra.Bundles.html#1149" class="Bound">ℓ</a><a id="1168" class="Symbol">))</a> <a id="1171" class="Keyword">where</a>
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<a id="1179" class="Keyword">infixl</a> <a id="1186" class="Number">7</a> <a id="1188" href="Algebra.Bundles.html#1267" class="Field Operator">_∙_</a>
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<a id="1194" class="Keyword">infix</a> <a id="1201" class="Number">4</a> <a id="1203" href="Algebra.Bundles.html#1239" class="Field Operator">_≈_</a>
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<a id="1209" class="Keyword">field</a>
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<a id="Magma.Carrier"></a><a id="1219" href="Algebra.Bundles.html#1219" class="Field">Carrier</a> <a id="1227" class="Symbol">:</a> <a id="1229" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1233" href="Algebra.Bundles.html#1147" class="Bound">c</a>
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<a id="Magma._≈_"></a><a id="1239" href="Algebra.Bundles.html#1239" class="Field Operator">_≈_</a> <a id="1247" class="Symbol">:</a> <a id="1249" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="1253" href="Algebra.Bundles.html#1219" class="Field">Carrier</a> <a id="1261" href="Algebra.Bundles.html#1149" class="Bound">ℓ</a>
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<a id="Magma._∙_"></a><a id="1267" href="Algebra.Bundles.html#1267" class="Field Operator">_∙_</a> <a id="1275" class="Symbol">:</a> <a id="1277" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="1281" href="Algebra.Bundles.html#1219" class="Field">Carrier</a>
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<a id="Magma.isMagma"></a><a id="1293" href="Algebra.Bundles.html#1293" class="Field">isMagma</a> <a id="1301" class="Symbol">:</a> <a id="1303" href="Algebra.Structures.html#1225" class="Record">IsMagma</a> <a id="1311" href="Algebra.Bundles.html#1239" class="Field Operator">_≈_</a> <a id="1315" href="Algebra.Bundles.html#1267" class="Field Operator">_∙_</a>
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<a id="1322" class="Keyword">open</a> <a id="1327" href="Algebra.Structures.html#1225" class="Module">IsMagma</a> <a id="1335" href="Algebra.Bundles.html#1293" class="Field">isMagma</a> <a id="1343" class="Keyword">public</a>
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<a id="Magma.rawMagma"></a><a id="1353" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a> <a id="1362" class="Symbol">:</a> <a id="1364" href="Algebra.Bundles.Raw.html#644" class="Record">RawMagma</a> <a id="1373" class="Symbol">_</a> <a id="1375" class="Symbol">_</a>
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<a id="1379" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a> <a id="1388" class="Symbol">=</a> <a id="1390" class="Keyword">record</a> <a id="1397" class="Symbol">{</a> <a id="1399" href="Algebra.Bundles.Raw.html#745" class="Field Operator">_≈_</a> <a id="1403" class="Symbol">=</a> <a id="1405" href="Algebra.Bundles.html#1239" class="Field Operator">_≈_</a><a id="1408" class="Symbol">;</a> <a id="1410" href="Algebra.Bundles.Raw.html#773" class="Field Operator">_∙_</a> <a id="1414" class="Symbol">=</a> <a id="1416" href="Algebra.Bundles.html#1267" class="Field Operator">_∙_</a> <a id="1420" class="Symbol">}</a>
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<a id="1425" class="Keyword">open</a> <a id="1430" href="Algebra.Bundles.Raw.html#644" class="Module">RawMagma</a> <a id="1439" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a> <a id="1448" class="Keyword">public</a>
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<a id="1459" class="Keyword">using</a> <a id="1465" class="Symbol">(</a><a id="1466" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="1469" class="Symbol">)</a>
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<a id="1473" class="Keyword">record</a> <a id="SelectiveMagma"></a><a id="1480" href="Algebra.Bundles.html#1480" class="Record">SelectiveMagma</a> <a id="1495" href="Algebra.Bundles.html#1495" class="Bound">c</a> <a id="1497" href="Algebra.Bundles.html#1497" class="Bound">ℓ</a> <a id="1499" class="Symbol">:</a> <a id="1501" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1505" class="Symbol">(</a><a id="1506" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="1510" class="Symbol">(</a><a id="1511" href="Algebra.Bundles.html#1495" class="Bound">c</a> <a id="1513" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1515" href="Algebra.Bundles.html#1497" class="Bound">ℓ</a><a id="1516" class="Symbol">))</a> <a id="1519" class="Keyword">where</a>
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<a id="1527" class="Keyword">infixl</a> <a id="1534" class="Number">7</a> <a id="1536" href="Algebra.Bundles.html#1633" class="Field Operator">_∙_</a>
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<a id="1542" class="Keyword">infix</a> <a id="1549" class="Number">4</a> <a id="1551" href="Algebra.Bundles.html#1596" class="Field Operator">_≈_</a>
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<a id="1557" class="Keyword">field</a>
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<a id="SelectiveMagma.Carrier"></a><a id="1567" href="Algebra.Bundles.html#1567" class="Field">Carrier</a> <a id="1584" class="Symbol">:</a> <a id="1586" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1590" href="Algebra.Bundles.html#1495" class="Bound">c</a>
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<a id="SelectiveMagma._≈_"></a><a id="1596" href="Algebra.Bundles.html#1596" class="Field Operator">_≈_</a> <a id="1613" class="Symbol">:</a> <a id="1615" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="1619" href="Algebra.Bundles.html#1567" class="Field">Carrier</a> <a id="1627" href="Algebra.Bundles.html#1497" class="Bound">ℓ</a>
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<a id="SelectiveMagma._∙_"></a><a id="1633" href="Algebra.Bundles.html#1633" class="Field Operator">_∙_</a> <a id="1650" class="Symbol">:</a> <a id="1652" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="1656" href="Algebra.Bundles.html#1567" class="Field">Carrier</a>
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<a id="SelectiveMagma.isSelectiveMagma"></a><a id="1668" href="Algebra.Bundles.html#1668" class="Field">isSelectiveMagma</a> <a id="1685" class="Symbol">:</a> <a id="1687" href="Algebra.Structures.html#2750" class="Record">IsSelectiveMagma</a> <a id="1704" href="Algebra.Bundles.html#1596" class="Field Operator">_≈_</a> <a id="1708" href="Algebra.Bundles.html#1633" class="Field Operator">_∙_</a>
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<a id="1715" class="Keyword">open</a> <a id="1720" href="Algebra.Structures.html#2750" class="Module">IsSelectiveMagma</a> <a id="1737" href="Algebra.Bundles.html#1668" class="Field">isSelectiveMagma</a> <a id="1754" class="Keyword">public</a>
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<a id="SelectiveMagma.magma"></a><a id="1764" href="Algebra.Bundles.html#1764" class="Function">magma</a> <a id="1770" class="Symbol">:</a> <a id="1772" href="Algebra.Bundles.html#1141" class="Record">Magma</a> <a id="1778" href="Algebra.Bundles.html#1495" class="Bound">c</a> <a id="1780" href="Algebra.Bundles.html#1497" class="Bound">ℓ</a>
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<a id="1784" href="Algebra.Bundles.html#1764" class="Function">magma</a> <a id="1790" class="Symbol">=</a> <a id="1792" class="Keyword">record</a> <a id="1799" class="Symbol">{</a> <a id="1801" href="Algebra.Bundles.html#1293" class="Field">isMagma</a> <a id="1809" class="Symbol">=</a> <a id="1811" href="Algebra.Structures.html#2811" class="Function">isMagma</a> <a id="1819" class="Symbol">}</a>
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<a id="1824" class="Keyword">open</a> <a id="1829" href="Algebra.Bundles.html#1141" class="Module">Magma</a> <a id="1835" href="Algebra.Bundles.html#1764" class="Function">magma</a> <a id="1841" class="Keyword">public</a> <a id="1848" class="Keyword">using</a> <a id="1854" class="Symbol">(</a><a id="1855" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="1863" class="Symbol">)</a>
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<a id="1867" class="Keyword">record</a> <a id="CommutativeMagma"></a><a id="1874" href="Algebra.Bundles.html#1874" class="Record">CommutativeMagma</a> <a id="1891" href="Algebra.Bundles.html#1891" class="Bound">c</a> <a id="1893" href="Algebra.Bundles.html#1893" class="Bound">ℓ</a> <a id="1895" class="Symbol">:</a> <a id="1897" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1901" class="Symbol">(</a><a id="1902" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="1906" class="Symbol">(</a><a id="1907" href="Algebra.Bundles.html#1891" class="Bound">c</a> <a id="1909" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1911" href="Algebra.Bundles.html#1893" class="Bound">ℓ</a><a id="1912" class="Symbol">))</a> <a id="1915" class="Keyword">where</a>
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<a id="1923" class="Keyword">infixl</a> <a id="1930" class="Number">7</a> <a id="1932" href="Algebra.Bundles.html#2033" class="Field Operator">_∙_</a>
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<a id="1938" class="Keyword">infix</a> <a id="1945" class="Number">4</a> <a id="1947" href="Algebra.Bundles.html#1994" class="Field Operator">_≈_</a>
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<a id="1953" class="Keyword">field</a>
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<a id="CommutativeMagma.Carrier"></a><a id="1963" href="Algebra.Bundles.html#1963" class="Field">Carrier</a> <a id="1982" class="Symbol">:</a> <a id="1984" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1988" href="Algebra.Bundles.html#1891" class="Bound">c</a>
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<a id="CommutativeMagma._≈_"></a><a id="1994" href="Algebra.Bundles.html#1994" class="Field Operator">_≈_</a> <a id="2013" class="Symbol">:</a> <a id="2015" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="2019" href="Algebra.Bundles.html#1963" class="Field">Carrier</a> <a id="2027" href="Algebra.Bundles.html#1893" class="Bound">ℓ</a>
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<a id="CommutativeMagma._∙_"></a><a id="2033" href="Algebra.Bundles.html#2033" class="Field Operator">_∙_</a> <a id="2052" class="Symbol">:</a> <a id="2054" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="2058" href="Algebra.Bundles.html#1963" class="Field">Carrier</a>
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<a id="CommutativeMagma.isCommutativeMagma"></a><a id="2070" href="Algebra.Bundles.html#2070" class="Field">isCommutativeMagma</a> <a id="2089" class="Symbol">:</a> <a id="2091" href="Algebra.Structures.html#1594" class="Record">IsCommutativeMagma</a> <a id="2110" href="Algebra.Bundles.html#1994" class="Field Operator">_≈_</a> <a id="2114" href="Algebra.Bundles.html#2033" class="Field Operator">_∙_</a>
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<a id="2121" class="Keyword">open</a> <a id="2126" href="Algebra.Structures.html#1594" class="Module">IsCommutativeMagma</a> <a id="2145" href="Algebra.Bundles.html#2070" class="Field">isCommutativeMagma</a> <a id="2164" class="Keyword">public</a>
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<a id="CommutativeMagma.magma"></a><a id="2174" href="Algebra.Bundles.html#2174" class="Function">magma</a> <a id="2180" class="Symbol">:</a> <a id="2182" href="Algebra.Bundles.html#1141" class="Record">Magma</a> <a id="2188" href="Algebra.Bundles.html#1891" class="Bound">c</a> <a id="2190" href="Algebra.Bundles.html#1893" class="Bound">ℓ</a>
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<a id="2194" href="Algebra.Bundles.html#2174" class="Function">magma</a> <a id="2200" class="Symbol">=</a> <a id="2202" class="Keyword">record</a> <a id="2209" class="Symbol">{</a> <a id="2211" href="Algebra.Bundles.html#1293" class="Field">isMagma</a> <a id="2219" class="Symbol">=</a> <a id="2221" href="Algebra.Structures.html#1657" class="Function">isMagma</a> <a id="2229" class="Symbol">}</a>
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<a id="2234" class="Keyword">open</a> <a id="2239" href="Algebra.Bundles.html#1141" class="Module">Magma</a> <a id="2245" href="Algebra.Bundles.html#2174" class="Function">magma</a> <a id="2251" class="Keyword">public</a> <a id="2258" class="Keyword">using</a> <a id="2264" class="Symbol">(</a><a id="2265" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="2273" class="Symbol">)</a>
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<a id="2276" class="Keyword">record</a> <a id="IdempotentMagma"></a><a id="2283" href="Algebra.Bundles.html#2283" class="Record">IdempotentMagma</a> <a id="2299" href="Algebra.Bundles.html#2299" class="Bound">c</a> <a id="2301" href="Algebra.Bundles.html#2301" class="Bound">ℓ</a> <a id="2303" class="Symbol">:</a> <a id="2305" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="2309" class="Symbol">(</a><a id="2310" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="2314" class="Symbol">(</a><a id="2315" href="Algebra.Bundles.html#2299" class="Bound">c</a> <a id="2317" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="2319" href="Algebra.Bundles.html#2301" class="Bound">ℓ</a><a id="2320" class="Symbol">))</a> <a id="2323" class="Keyword">where</a>
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<a id="2331" class="Keyword">infixl</a> <a id="2338" class="Number">7</a> <a id="2340" href="Algebra.Bundles.html#2419" class="Field Operator">_∙_</a>
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<a id="2346" class="Keyword">infix</a> <a id="2353" class="Number">4</a> <a id="2355" href="Algebra.Bundles.html#2391" class="Field Operator">_≈_</a>
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<a id="2361" class="Keyword">field</a>
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<a id="IdempotentMagma.Carrier"></a><a id="2371" href="Algebra.Bundles.html#2371" class="Field">Carrier</a> <a id="2379" class="Symbol">:</a> <a id="2381" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="2385" href="Algebra.Bundles.html#2299" class="Bound">c</a>
|
|||
|
|
<a id="IdempotentMagma._≈_"></a><a id="2391" href="Algebra.Bundles.html#2391" class="Field Operator">_≈_</a> <a id="2399" class="Symbol">:</a> <a id="2401" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="2405" href="Algebra.Bundles.html#2371" class="Field">Carrier</a> <a id="2413" href="Algebra.Bundles.html#2301" class="Bound">ℓ</a>
|
|||
|
|
<a id="IdempotentMagma._∙_"></a><a id="2419" href="Algebra.Bundles.html#2419" class="Field Operator">_∙_</a> <a id="2427" class="Symbol">:</a> <a id="2429" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="2433" href="Algebra.Bundles.html#2371" class="Field">Carrier</a>
|
|||
|
|
<a id="IdempotentMagma.isIdempotentMagma"></a><a id="2445" href="Algebra.Bundles.html#2445" class="Field">isIdempotentMagma</a> <a id="2464" class="Symbol">:</a> <a id="2466" href="Algebra.Structures.html#1744" class="Record">IsIdempotentMagma</a> <a id="2484" href="Algebra.Bundles.html#2391" class="Field Operator">_≈_</a> <a id="2488" href="Algebra.Bundles.html#2419" class="Field Operator">_∙_</a>
|
|||
|
|
|
|||
|
|
<a id="2495" class="Keyword">open</a> <a id="2500" href="Algebra.Structures.html#1744" class="Module">IsIdempotentMagma</a> <a id="2518" href="Algebra.Bundles.html#2445" class="Field">isIdempotentMagma</a> <a id="2536" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="IdempotentMagma.magma"></a><a id="2546" href="Algebra.Bundles.html#2546" class="Function">magma</a> <a id="2552" class="Symbol">:</a> <a id="2554" href="Algebra.Bundles.html#1141" class="Record">Magma</a> <a id="2560" href="Algebra.Bundles.html#2299" class="Bound">c</a> <a id="2562" href="Algebra.Bundles.html#2301" class="Bound">ℓ</a>
|
|||
|
|
<a id="2566" href="Algebra.Bundles.html#2546" class="Function">magma</a> <a id="2572" class="Symbol">=</a> <a id="2574" class="Keyword">record</a> <a id="2581" class="Symbol">{</a> <a id="2583" href="Algebra.Bundles.html#1293" class="Field">isMagma</a> <a id="2591" class="Symbol">=</a> <a id="2593" href="Algebra.Structures.html#1806" class="Function">isMagma</a> <a id="2601" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="2606" class="Keyword">open</a> <a id="2611" href="Algebra.Bundles.html#1141" class="Module">Magma</a> <a id="2617" href="Algebra.Bundles.html#2546" class="Function">magma</a> <a id="2623" class="Keyword">public</a>
|
|||
|
|
<a id="2634" class="Keyword">using</a> <a id="2640" class="Symbol">(</a><a id="2641" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="2649" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="2652" class="Keyword">record</a> <a id="AlternativeMagma"></a><a id="2659" href="Algebra.Bundles.html#2659" class="Record">AlternativeMagma</a> <a id="2676" href="Algebra.Bundles.html#2676" class="Bound">c</a> <a id="2678" href="Algebra.Bundles.html#2678" class="Bound">ℓ</a> <a id="2680" class="Symbol">:</a> <a id="2682" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="2686" class="Symbol">(</a><a id="2687" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="2691" class="Symbol">(</a><a id="2692" href="Algebra.Bundles.html#2676" class="Bound">c</a> <a id="2694" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="2696" href="Algebra.Bundles.html#2678" class="Bound">ℓ</a><a id="2697" class="Symbol">))</a> <a id="2700" class="Keyword">where</a>
|
|||
|
|
<a id="2708" class="Keyword">infixl</a> <a id="2715" class="Number">7</a> <a id="2717" href="Algebra.Bundles.html#2796" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="2723" class="Keyword">infix</a> <a id="2730" class="Number">4</a> <a id="2732" href="Algebra.Bundles.html#2768" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="2738" class="Keyword">field</a>
|
|||
|
|
<a id="AlternativeMagma.Carrier"></a><a id="2748" href="Algebra.Bundles.html#2748" class="Field">Carrier</a> <a id="2756" class="Symbol">:</a> <a id="2758" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="2762" href="Algebra.Bundles.html#2676" class="Bound">c</a>
|
|||
|
|
<a id="AlternativeMagma._≈_"></a><a id="2768" href="Algebra.Bundles.html#2768" class="Field Operator">_≈_</a> <a id="2776" class="Symbol">:</a> <a id="2778" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="2782" href="Algebra.Bundles.html#2748" class="Field">Carrier</a> <a id="2790" href="Algebra.Bundles.html#2678" class="Bound">ℓ</a>
|
|||
|
|
<a id="AlternativeMagma._∙_"></a><a id="2796" href="Algebra.Bundles.html#2796" class="Field Operator">_∙_</a> <a id="2804" class="Symbol">:</a> <a id="2806" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="2810" href="Algebra.Bundles.html#2748" class="Field">Carrier</a>
|
|||
|
|
<a id="AlternativeMagma.isAlternativeMagma"></a><a id="2822" href="Algebra.Bundles.html#2822" class="Field">isAlternativeMagma</a> <a id="2842" class="Symbol">:</a> <a id="2844" href="Algebra.Structures.html#1892" class="Record">IsAlternativeMagma</a> <a id="2863" href="Algebra.Bundles.html#2768" class="Field Operator">_≈_</a> <a id="2867" href="Algebra.Bundles.html#2796" class="Field Operator">_∙_</a>
|
|||
|
|
|
|||
|
|
<a id="2874" class="Keyword">open</a> <a id="2879" href="Algebra.Structures.html#1892" class="Module">IsAlternativeMagma</a> <a id="2898" href="Algebra.Bundles.html#2822" class="Field">isAlternativeMagma</a> <a id="2917" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="AlternativeMagma.magma"></a><a id="2927" href="Algebra.Bundles.html#2927" class="Function">magma</a> <a id="2933" class="Symbol">:</a> <a id="2935" href="Algebra.Bundles.html#1141" class="Record">Magma</a> <a id="2941" href="Algebra.Bundles.html#2676" class="Bound">c</a> <a id="2943" href="Algebra.Bundles.html#2678" class="Bound">ℓ</a>
|
|||
|
|
<a id="2947" href="Algebra.Bundles.html#2927" class="Function">magma</a> <a id="2953" class="Symbol">=</a> <a id="2955" class="Keyword">record</a> <a id="2962" class="Symbol">{</a> <a id="2964" href="Algebra.Bundles.html#1293" class="Field">isMagma</a> <a id="2972" class="Symbol">=</a> <a id="2974" href="Algebra.Structures.html#1955" class="Function">isMagma</a> <a id="2982" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="2987" class="Keyword">open</a> <a id="2992" href="Algebra.Bundles.html#1141" class="Module">Magma</a> <a id="2998" href="Algebra.Bundles.html#2927" class="Function">magma</a> <a id="3004" class="Keyword">public</a>
|
|||
|
|
<a id="3015" class="Keyword">using</a> <a id="3021" class="Symbol">(</a><a id="3022" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="3030" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="3033" class="Keyword">record</a> <a id="FlexibleMagma"></a><a id="3040" href="Algebra.Bundles.html#3040" class="Record">FlexibleMagma</a> <a id="3054" href="Algebra.Bundles.html#3054" class="Bound">c</a> <a id="3056" href="Algebra.Bundles.html#3056" class="Bound">ℓ</a> <a id="3058" class="Symbol">:</a> <a id="3060" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="3064" class="Symbol">(</a><a id="3065" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="3069" class="Symbol">(</a><a id="3070" href="Algebra.Bundles.html#3054" class="Bound">c</a> <a id="3072" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="3074" href="Algebra.Bundles.html#3056" class="Bound">ℓ</a><a id="3075" class="Symbol">))</a> <a id="3078" class="Keyword">where</a>
|
|||
|
|
<a id="3086" class="Keyword">infixl</a> <a id="3093" class="Number">7</a> <a id="3095" href="Algebra.Bundles.html#3174" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="3101" class="Keyword">infix</a> <a id="3108" class="Number">4</a> <a id="3110" href="Algebra.Bundles.html#3146" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="3116" class="Keyword">field</a>
|
|||
|
|
<a id="FlexibleMagma.Carrier"></a><a id="3126" href="Algebra.Bundles.html#3126" class="Field">Carrier</a> <a id="3134" class="Symbol">:</a> <a id="3136" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="3140" href="Algebra.Bundles.html#3054" class="Bound">c</a>
|
|||
|
|
<a id="FlexibleMagma._≈_"></a><a id="3146" href="Algebra.Bundles.html#3146" class="Field Operator">_≈_</a> <a id="3154" class="Symbol">:</a> <a id="3156" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="3160" href="Algebra.Bundles.html#3126" class="Field">Carrier</a> <a id="3168" href="Algebra.Bundles.html#3056" class="Bound">ℓ</a>
|
|||
|
|
<a id="FlexibleMagma._∙_"></a><a id="3174" href="Algebra.Bundles.html#3174" class="Field Operator">_∙_</a> <a id="3182" class="Symbol">:</a> <a id="3184" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="3188" href="Algebra.Bundles.html#3126" class="Field">Carrier</a>
|
|||
|
|
<a id="FlexibleMagma.isFlexibleMagma"></a><a id="3200" href="Algebra.Bundles.html#3200" class="Field">isFlexibleMagma</a> <a id="3217" class="Symbol">:</a> <a id="3219" href="Algebra.Structures.html#2175" class="Record">IsFlexibleMagma</a> <a id="3235" href="Algebra.Bundles.html#3146" class="Field Operator">_≈_</a> <a id="3239" href="Algebra.Bundles.html#3174" class="Field Operator">_∙_</a>
|
|||
|
|
|
|||
|
|
<a id="3246" class="Keyword">open</a> <a id="3251" href="Algebra.Structures.html#2175" class="Module">IsFlexibleMagma</a> <a id="3267" href="Algebra.Bundles.html#3200" class="Field">isFlexibleMagma</a> <a id="3283" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="FlexibleMagma.magma"></a><a id="3293" href="Algebra.Bundles.html#3293" class="Function">magma</a> <a id="3299" class="Symbol">:</a> <a id="3301" href="Algebra.Bundles.html#1141" class="Record">Magma</a> <a id="3307" href="Algebra.Bundles.html#3054" class="Bound">c</a> <a id="3309" href="Algebra.Bundles.html#3056" class="Bound">ℓ</a>
|
|||
|
|
<a id="3313" href="Algebra.Bundles.html#3293" class="Function">magma</a> <a id="3319" class="Symbol">=</a> <a id="3321" class="Keyword">record</a> <a id="3328" class="Symbol">{</a> <a id="3330" href="Algebra.Bundles.html#1293" class="Field">isMagma</a> <a id="3338" class="Symbol">=</a> <a id="3340" href="Algebra.Structures.html#2235" class="Function">isMagma</a> <a id="3348" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="3353" class="Keyword">open</a> <a id="3358" href="Algebra.Bundles.html#1141" class="Module">Magma</a> <a id="3364" href="Algebra.Bundles.html#3293" class="Function">magma</a> <a id="3370" class="Keyword">public</a>
|
|||
|
|
<a id="3381" class="Keyword">using</a> <a id="3387" class="Symbol">(</a><a id="3388" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="3396" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="3399" class="Keyword">record</a> <a id="MedialMagma"></a><a id="3406" href="Algebra.Bundles.html#3406" class="Record">MedialMagma</a> <a id="3418" href="Algebra.Bundles.html#3418" class="Bound">c</a> <a id="3420" href="Algebra.Bundles.html#3420" class="Bound">ℓ</a> <a id="3422" class="Symbol">:</a> <a id="3424" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="3428" class="Symbol">(</a><a id="3429" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="3433" class="Symbol">(</a><a id="3434" href="Algebra.Bundles.html#3418" class="Bound">c</a> <a id="3436" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="3438" href="Algebra.Bundles.html#3420" class="Bound">ℓ</a><a id="3439" class="Symbol">))</a> <a id="3442" class="Keyword">where</a>
|
|||
|
|
<a id="3450" class="Keyword">infixl</a> <a id="3457" class="Number">7</a> <a id="3459" href="Algebra.Bundles.html#3538" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="3465" class="Keyword">infix</a> <a id="3472" class="Number">4</a> <a id="3474" href="Algebra.Bundles.html#3510" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="3480" class="Keyword">field</a>
|
|||
|
|
<a id="MedialMagma.Carrier"></a><a id="3490" href="Algebra.Bundles.html#3490" class="Field">Carrier</a> <a id="3498" class="Symbol">:</a> <a id="3500" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="3504" href="Algebra.Bundles.html#3418" class="Bound">c</a>
|
|||
|
|
<a id="MedialMagma._≈_"></a><a id="3510" href="Algebra.Bundles.html#3510" class="Field Operator">_≈_</a> <a id="3518" class="Symbol">:</a> <a id="3520" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="3524" href="Algebra.Bundles.html#3490" class="Field">Carrier</a> <a id="3532" href="Algebra.Bundles.html#3420" class="Bound">ℓ</a>
|
|||
|
|
<a id="MedialMagma._∙_"></a><a id="3538" href="Algebra.Bundles.html#3538" class="Field Operator">_∙_</a> <a id="3546" class="Symbol">:</a> <a id="3548" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="3552" href="Algebra.Bundles.html#3490" class="Field">Carrier</a>
|
|||
|
|
<a id="MedialMagma.isMedialMagma"></a><a id="3564" href="Algebra.Bundles.html#3564" class="Field">isMedialMagma</a> <a id="3579" class="Symbol">:</a> <a id="3581" href="Algebra.Structures.html#2321" class="Record">IsMedialMagma</a> <a id="3595" href="Algebra.Bundles.html#3510" class="Field Operator">_≈_</a> <a id="3599" href="Algebra.Bundles.html#3538" class="Field Operator">_∙_</a>
|
|||
|
|
|
|||
|
|
<a id="3606" class="Keyword">open</a> <a id="3611" href="Algebra.Structures.html#2321" class="Module">IsMedialMagma</a> <a id="3625" href="Algebra.Bundles.html#3564" class="Field">isMedialMagma</a> <a id="3639" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="MedialMagma.magma"></a><a id="3649" href="Algebra.Bundles.html#3649" class="Function">magma</a> <a id="3655" class="Symbol">:</a> <a id="3657" href="Algebra.Bundles.html#1141" class="Record">Magma</a> <a id="3663" href="Algebra.Bundles.html#3418" class="Bound">c</a> <a id="3665" href="Algebra.Bundles.html#3420" class="Bound">ℓ</a>
|
|||
|
|
<a id="3669" href="Algebra.Bundles.html#3649" class="Function">magma</a> <a id="3675" class="Symbol">=</a> <a id="3677" class="Keyword">record</a> <a id="3684" class="Symbol">{</a> <a id="3686" href="Algebra.Bundles.html#1293" class="Field">isMagma</a> <a id="3694" class="Symbol">=</a> <a id="3696" href="Algebra.Structures.html#2379" class="Function">isMagma</a> <a id="3704" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="3709" class="Keyword">open</a> <a id="3714" href="Algebra.Bundles.html#1141" class="Module">Magma</a> <a id="3720" href="Algebra.Bundles.html#3649" class="Function">magma</a> <a id="3726" class="Keyword">public</a>
|
|||
|
|
<a id="3737" class="Keyword">using</a> <a id="3743" class="Symbol">(</a><a id="3744" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="3752" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="3755" class="Keyword">record</a> <a id="SemimedialMagma"></a><a id="3762" href="Algebra.Bundles.html#3762" class="Record">SemimedialMagma</a> <a id="3778" href="Algebra.Bundles.html#3778" class="Bound">c</a> <a id="3780" href="Algebra.Bundles.html#3780" class="Bound">ℓ</a> <a id="3782" class="Symbol">:</a> <a id="3784" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="3788" class="Symbol">(</a><a id="3789" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="3793" class="Symbol">(</a><a id="3794" href="Algebra.Bundles.html#3778" class="Bound">c</a> <a id="3796" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="3798" href="Algebra.Bundles.html#3780" class="Bound">ℓ</a><a id="3799" class="Symbol">))</a> <a id="3802" class="Keyword">where</a>
|
|||
|
|
<a id="3810" class="Keyword">infixl</a> <a id="3817" class="Number">7</a> <a id="3819" href="Algebra.Bundles.html#3898" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="3825" class="Keyword">infix</a> <a id="3832" class="Number">4</a> <a id="3834" href="Algebra.Bundles.html#3870" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="3840" class="Keyword">field</a>
|
|||
|
|
<a id="SemimedialMagma.Carrier"></a><a id="3850" href="Algebra.Bundles.html#3850" class="Field">Carrier</a> <a id="3858" class="Symbol">:</a> <a id="3860" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="3864" href="Algebra.Bundles.html#3778" class="Bound">c</a>
|
|||
|
|
<a id="SemimedialMagma._≈_"></a><a id="3870" href="Algebra.Bundles.html#3870" class="Field Operator">_≈_</a> <a id="3878" class="Symbol">:</a> <a id="3880" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="3884" href="Algebra.Bundles.html#3850" class="Field">Carrier</a> <a id="3892" href="Algebra.Bundles.html#3780" class="Bound">ℓ</a>
|
|||
|
|
<a id="SemimedialMagma._∙_"></a><a id="3898" href="Algebra.Bundles.html#3898" class="Field Operator">_∙_</a> <a id="3906" class="Symbol">:</a> <a id="3908" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="3912" href="Algebra.Bundles.html#3850" class="Field">Carrier</a>
|
|||
|
|
<a id="SemimedialMagma.isSemimedialMagma"></a><a id="3924" href="Algebra.Bundles.html#3924" class="Field">isSemimedialMagma</a> <a id="3943" class="Symbol">:</a> <a id="3945" href="Algebra.Structures.html#2461" class="Record">IsSemimedialMagma</a> <a id="3963" href="Algebra.Bundles.html#3870" class="Field Operator">_≈_</a> <a id="3967" href="Algebra.Bundles.html#3898" class="Field Operator">_∙_</a>
|
|||
|
|
|
|||
|
|
<a id="3974" class="Keyword">open</a> <a id="3979" href="Algebra.Structures.html#2461" class="Module">IsSemimedialMagma</a> <a id="3997" href="Algebra.Bundles.html#3924" class="Field">isSemimedialMagma</a> <a id="4015" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="SemimedialMagma.magma"></a><a id="4025" href="Algebra.Bundles.html#4025" class="Function">magma</a> <a id="4031" class="Symbol">:</a> <a id="4033" href="Algebra.Bundles.html#1141" class="Record">Magma</a> <a id="4039" href="Algebra.Bundles.html#3778" class="Bound">c</a> <a id="4041" href="Algebra.Bundles.html#3780" class="Bound">ℓ</a>
|
|||
|
|
<a id="4045" href="Algebra.Bundles.html#4025" class="Function">magma</a> <a id="4051" class="Symbol">=</a> <a id="4053" class="Keyword">record</a> <a id="4060" class="Symbol">{</a> <a id="4062" href="Algebra.Bundles.html#1293" class="Field">isMagma</a> <a id="4070" class="Symbol">=</a> <a id="4072" href="Algebra.Structures.html#2523" class="Function">isMagma</a> <a id="4080" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="4085" class="Keyword">open</a> <a id="4090" href="Algebra.Bundles.html#1141" class="Module">Magma</a> <a id="4096" href="Algebra.Bundles.html#4025" class="Function">magma</a> <a id="4102" class="Keyword">public</a>
|
|||
|
|
<a id="4113" class="Keyword">using</a> <a id="4119" class="Symbol">(</a><a id="4120" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="4128" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="4132" class="Keyword">record</a> <a id="Semigroup"></a><a id="4139" href="Algebra.Bundles.html#4139" class="Record">Semigroup</a> <a id="4149" href="Algebra.Bundles.html#4149" class="Bound">c</a> <a id="4151" href="Algebra.Bundles.html#4151" class="Bound">ℓ</a> <a id="4153" class="Symbol">:</a> <a id="4155" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="4159" class="Symbol">(</a><a id="4160" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="4164" class="Symbol">(</a><a id="4165" href="Algebra.Bundles.html#4149" class="Bound">c</a> <a id="4167" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="4169" href="Algebra.Bundles.html#4151" class="Bound">ℓ</a><a id="4170" class="Symbol">))</a> <a id="4173" class="Keyword">where</a>
|
|||
|
|
<a id="4181" class="Keyword">infixl</a> <a id="4188" class="Number">7</a> <a id="4190" href="Algebra.Bundles.html#4277" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="4196" class="Keyword">infix</a> <a id="4203" class="Number">4</a> <a id="4205" href="Algebra.Bundles.html#4245" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="4211" class="Keyword">field</a>
|
|||
|
|
<a id="Semigroup.Carrier"></a><a id="4221" href="Algebra.Bundles.html#4221" class="Field">Carrier</a> <a id="4233" class="Symbol">:</a> <a id="4235" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="4239" href="Algebra.Bundles.html#4149" class="Bound">c</a>
|
|||
|
|
<a id="Semigroup._≈_"></a><a id="4245" href="Algebra.Bundles.html#4245" class="Field Operator">_≈_</a> <a id="4257" class="Symbol">:</a> <a id="4259" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="4263" href="Algebra.Bundles.html#4221" class="Field">Carrier</a> <a id="4271" href="Algebra.Bundles.html#4151" class="Bound">ℓ</a>
|
|||
|
|
<a id="Semigroup._∙_"></a><a id="4277" href="Algebra.Bundles.html#4277" class="Field Operator">_∙_</a> <a id="4289" class="Symbol">:</a> <a id="4291" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="4295" href="Algebra.Bundles.html#4221" class="Field">Carrier</a>
|
|||
|
|
<a id="Semigroup.isSemigroup"></a><a id="4307" href="Algebra.Bundles.html#4307" class="Field">isSemigroup</a> <a id="4319" class="Symbol">:</a> <a id="4321" href="Algebra.Structures.html#2897" class="Record">IsSemigroup</a> <a id="4333" href="Algebra.Bundles.html#4245" class="Field Operator">_≈_</a> <a id="4337" href="Algebra.Bundles.html#4277" class="Field Operator">_∙_</a>
|
|||
|
|
|
|||
|
|
<a id="4344" class="Keyword">open</a> <a id="4349" href="Algebra.Structures.html#2897" class="Module">IsSemigroup</a> <a id="4361" href="Algebra.Bundles.html#4307" class="Field">isSemigroup</a> <a id="4373" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="Semigroup.magma"></a><a id="4383" href="Algebra.Bundles.html#4383" class="Function">magma</a> <a id="4389" class="Symbol">:</a> <a id="4391" href="Algebra.Bundles.html#1141" class="Record">Magma</a> <a id="4397" href="Algebra.Bundles.html#4149" class="Bound">c</a> <a id="4399" href="Algebra.Bundles.html#4151" class="Bound">ℓ</a>
|
|||
|
|
<a id="4403" href="Algebra.Bundles.html#4383" class="Function">magma</a> <a id="4409" class="Symbol">=</a> <a id="4411" class="Keyword">record</a> <a id="4418" class="Symbol">{</a> <a id="4420" href="Algebra.Bundles.html#1293" class="Field">isMagma</a> <a id="4428" class="Symbol">=</a> <a id="4430" href="Algebra.Structures.html#2953" class="Function">isMagma</a> <a id="4438" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="4443" class="Keyword">open</a> <a id="4448" href="Algebra.Bundles.html#1141" class="Module">Magma</a> <a id="4454" href="Algebra.Bundles.html#4383" class="Function">magma</a> <a id="4460" class="Keyword">public</a>
|
|||
|
|
<a id="4471" class="Keyword">using</a> <a id="4477" class="Symbol">(</a><a id="4478" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="4481" class="Symbol">;</a> <a id="4483" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="4491" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="4495" class="Keyword">record</a> <a id="Band"></a><a id="4502" href="Algebra.Bundles.html#4502" class="Record">Band</a> <a id="4507" href="Algebra.Bundles.html#4507" class="Bound">c</a> <a id="4509" href="Algebra.Bundles.html#4509" class="Bound">ℓ</a> <a id="4511" class="Symbol">:</a> <a id="4513" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="4517" class="Symbol">(</a><a id="4518" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="4522" class="Symbol">(</a><a id="4523" href="Algebra.Bundles.html#4507" class="Bound">c</a> <a id="4525" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="4527" href="Algebra.Bundles.html#4509" class="Bound">ℓ</a><a id="4528" class="Symbol">))</a> <a id="4531" class="Keyword">where</a>
|
|||
|
|
<a id="4539" class="Keyword">infixl</a> <a id="4546" class="Number">7</a> <a id="4548" href="Algebra.Bundles.html#4627" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="4554" class="Keyword">infix</a> <a id="4561" class="Number">4</a> <a id="4563" href="Algebra.Bundles.html#4599" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="4569" class="Keyword">field</a>
|
|||
|
|
<a id="Band.Carrier"></a><a id="4579" href="Algebra.Bundles.html#4579" class="Field">Carrier</a> <a id="4587" class="Symbol">:</a> <a id="4589" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="4593" href="Algebra.Bundles.html#4507" class="Bound">c</a>
|
|||
|
|
<a id="Band._≈_"></a><a id="4599" href="Algebra.Bundles.html#4599" class="Field Operator">_≈_</a> <a id="4607" class="Symbol">:</a> <a id="4609" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="4613" href="Algebra.Bundles.html#4579" class="Field">Carrier</a> <a id="4621" href="Algebra.Bundles.html#4509" class="Bound">ℓ</a>
|
|||
|
|
<a id="Band._∙_"></a><a id="4627" href="Algebra.Bundles.html#4627" class="Field Operator">_∙_</a> <a id="4635" class="Symbol">:</a> <a id="4637" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="4641" href="Algebra.Bundles.html#4579" class="Field">Carrier</a>
|
|||
|
|
<a id="Band.isBand"></a><a id="4653" href="Algebra.Bundles.html#4653" class="Field">isBand</a> <a id="4661" class="Symbol">:</a> <a id="4663" href="Algebra.Structures.html#3041" class="Record">IsBand</a> <a id="4670" href="Algebra.Bundles.html#4599" class="Field Operator">_≈_</a> <a id="4674" href="Algebra.Bundles.html#4627" class="Field Operator">_∙_</a>
|
|||
|
|
|
|||
|
|
<a id="4681" class="Keyword">open</a> <a id="4686" href="Algebra.Structures.html#3041" class="Module">IsBand</a> <a id="4693" href="Algebra.Bundles.html#4653" class="Field">isBand</a> <a id="4700" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="Band.semigroup"></a><a id="4710" href="Algebra.Bundles.html#4710" class="Function">semigroup</a> <a id="4720" class="Symbol">:</a> <a id="4722" href="Algebra.Bundles.html#4139" class="Record">Semigroup</a> <a id="4732" href="Algebra.Bundles.html#4507" class="Bound">c</a> <a id="4734" href="Algebra.Bundles.html#4509" class="Bound">ℓ</a>
|
|||
|
|
<a id="4738" href="Algebra.Bundles.html#4710" class="Function">semigroup</a> <a id="4748" class="Symbol">=</a> <a id="4750" class="Keyword">record</a> <a id="4757" class="Symbol">{</a> <a id="4759" href="Algebra.Bundles.html#4307" class="Field">isSemigroup</a> <a id="4771" class="Symbol">=</a> <a id="4773" href="Algebra.Structures.html#3092" class="Function">isSemigroup</a> <a id="4785" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="4790" class="Keyword">open</a> <a id="4795" href="Algebra.Bundles.html#4139" class="Module">Semigroup</a> <a id="4805" href="Algebra.Bundles.html#4710" class="Function">semigroup</a> <a id="4815" class="Keyword">public</a>
|
|||
|
|
<a id="4826" class="Keyword">using</a> <a id="4832" class="Symbol">(</a><a id="4833" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="4836" class="Symbol">;</a> <a id="4838" href="Algebra.Bundles.html#4383" class="Function">magma</a><a id="4843" class="Symbol">;</a> <a id="4845" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="4853" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="4857" class="Keyword">record</a> <a id="CommutativeSemigroup"></a><a id="4864" href="Algebra.Bundles.html#4864" class="Record">CommutativeSemigroup</a> <a id="4885" href="Algebra.Bundles.html#4885" class="Bound">c</a> <a id="4887" href="Algebra.Bundles.html#4887" class="Bound">ℓ</a> <a id="4889" class="Symbol">:</a> <a id="4891" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="4895" class="Symbol">(</a><a id="4896" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="4900" class="Symbol">(</a><a id="4901" href="Algebra.Bundles.html#4885" class="Bound">c</a> <a id="4903" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="4905" href="Algebra.Bundles.html#4887" class="Bound">ℓ</a><a id="4906" class="Symbol">))</a> <a id="4909" class="Keyword">where</a>
|
|||
|
|
<a id="4917" class="Keyword">infixl</a> <a id="4924" class="Number">7</a> <a id="4926" href="Algebra.Bundles.html#5037" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="4932" class="Keyword">infix</a> <a id="4939" class="Number">4</a> <a id="4941" href="Algebra.Bundles.html#4993" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="4947" class="Keyword">field</a>
|
|||
|
|
<a id="CommutativeSemigroup.Carrier"></a><a id="4957" href="Algebra.Bundles.html#4957" class="Field">Carrier</a> <a id="4981" class="Symbol">:</a> <a id="4983" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="4987" href="Algebra.Bundles.html#4885" class="Bound">c</a>
|
|||
|
|
<a id="CommutativeSemigroup._≈_"></a><a id="4993" href="Algebra.Bundles.html#4993" class="Field Operator">_≈_</a> <a id="5017" class="Symbol">:</a> <a id="5019" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="5023" href="Algebra.Bundles.html#4957" class="Field">Carrier</a> <a id="5031" href="Algebra.Bundles.html#4887" class="Bound">ℓ</a>
|
|||
|
|
<a id="CommutativeSemigroup._∙_"></a><a id="5037" href="Algebra.Bundles.html#5037" class="Field Operator">_∙_</a> <a id="5061" class="Symbol">:</a> <a id="5063" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="5067" href="Algebra.Bundles.html#4957" class="Field">Carrier</a>
|
|||
|
|
<a id="CommutativeSemigroup.isCommutativeSemigroup"></a><a id="5079" href="Algebra.Bundles.html#5079" class="Field">isCommutativeSemigroup</a> <a id="5103" class="Symbol">:</a> <a id="5105" href="Algebra.Structures.html#3199" class="Record">IsCommutativeSemigroup</a> <a id="5128" href="Algebra.Bundles.html#4993" class="Field Operator">_≈_</a> <a id="5132" href="Algebra.Bundles.html#5037" class="Field Operator">_∙_</a>
|
|||
|
|
|
|||
|
|
<a id="5139" class="Keyword">open</a> <a id="5144" href="Algebra.Structures.html#3199" class="Module">IsCommutativeSemigroup</a> <a id="5167" href="Algebra.Bundles.html#5079" class="Field">isCommutativeSemigroup</a> <a id="5190" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="CommutativeSemigroup.semigroup"></a><a id="5200" href="Algebra.Bundles.html#5200" class="Function">semigroup</a> <a id="5210" class="Symbol">:</a> <a id="5212" href="Algebra.Bundles.html#4139" class="Record">Semigroup</a> <a id="5222" href="Algebra.Bundles.html#4885" class="Bound">c</a> <a id="5224" href="Algebra.Bundles.html#4887" class="Bound">ℓ</a>
|
|||
|
|
<a id="5228" href="Algebra.Bundles.html#5200" class="Function">semigroup</a> <a id="5238" class="Symbol">=</a> <a id="5240" class="Keyword">record</a> <a id="5247" class="Symbol">{</a> <a id="5249" href="Algebra.Bundles.html#4307" class="Field">isSemigroup</a> <a id="5261" class="Symbol">=</a> <a id="5263" href="Algebra.Structures.html#3266" class="Function">isSemigroup</a> <a id="5275" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="5280" class="Keyword">open</a> <a id="5285" href="Algebra.Bundles.html#4139" class="Module">Semigroup</a> <a id="5295" href="Algebra.Bundles.html#5200" class="Function">semigroup</a> <a id="5305" class="Keyword">public</a>
|
|||
|
|
<a id="5316" class="Keyword">using</a> <a id="5322" class="Symbol">(</a><a id="5323" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="5326" class="Symbol">;</a> <a id="5328" href="Algebra.Bundles.html#4383" class="Function">magma</a><a id="5333" class="Symbol">;</a> <a id="5335" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="5343" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="CommutativeSemigroup.commutativeMagma"></a><a id="5348" href="Algebra.Bundles.html#5348" class="Function">commutativeMagma</a> <a id="5365" class="Symbol">:</a> <a id="5367" href="Algebra.Bundles.html#1874" class="Record">CommutativeMagma</a> <a id="5384" href="Algebra.Bundles.html#4885" class="Bound">c</a> <a id="5386" href="Algebra.Bundles.html#4887" class="Bound">ℓ</a>
|
|||
|
|
<a id="5390" href="Algebra.Bundles.html#5348" class="Function">commutativeMagma</a> <a id="5407" class="Symbol">=</a> <a id="5409" class="Keyword">record</a> <a id="5416" class="Symbol">{</a> <a id="5418" href="Algebra.Bundles.html#2070" class="Field">isCommutativeMagma</a> <a id="5437" class="Symbol">=</a> <a id="5439" href="Algebra.Structures.html#3368" class="Function">isCommutativeMagma</a> <a id="5458" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="5461" class="Comment">------------------------------------------------------------------------</a>
|
|||
|
|
<a id="5534" class="Comment">-- Bundles with 1 binary operation & 1 element</a>
|
|||
|
|
<a id="5581" class="Comment">------------------------------------------------------------------------</a>
|
|||
|
|
|
|||
|
|
<a id="5655" class="Keyword">record</a> <a id="UnitalMagma"></a><a id="5662" href="Algebra.Bundles.html#5662" class="Record">UnitalMagma</a> <a id="5674" href="Algebra.Bundles.html#5674" class="Bound">c</a> <a id="5676" href="Algebra.Bundles.html#5676" class="Bound">ℓ</a> <a id="5678" class="Symbol">:</a> <a id="5680" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="5684" class="Symbol">(</a><a id="5685" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="5689" class="Symbol">(</a><a id="5690" href="Algebra.Bundles.html#5674" class="Bound">c</a> <a id="5692" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="5694" href="Algebra.Bundles.html#5676" class="Bound">ℓ</a><a id="5695" class="Symbol">))</a> <a id="5698" class="Keyword">where</a>
|
|||
|
|
<a id="5706" class="Keyword">infixl</a> <a id="5713" class="Number">7</a> <a id="5715" href="Algebra.Bundles.html#5796" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="5721" class="Keyword">infix</a> <a id="5728" class="Number">4</a> <a id="5730" href="Algebra.Bundles.html#5767" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="5736" class="Keyword">field</a>
|
|||
|
|
<a id="UnitalMagma.Carrier"></a><a id="5746" href="Algebra.Bundles.html#5746" class="Field">Carrier</a> <a id="5755" class="Symbol">:</a> <a id="5757" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="5761" href="Algebra.Bundles.html#5674" class="Bound">c</a>
|
|||
|
|
<a id="UnitalMagma._≈_"></a><a id="5767" href="Algebra.Bundles.html#5767" class="Field Operator">_≈_</a> <a id="5776" class="Symbol">:</a> <a id="5778" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="5782" href="Algebra.Bundles.html#5746" class="Field">Carrier</a> <a id="5790" href="Algebra.Bundles.html#5676" class="Bound">ℓ</a>
|
|||
|
|
<a id="UnitalMagma._∙_"></a><a id="5796" href="Algebra.Bundles.html#5796" class="Field Operator">_∙_</a> <a id="5805" class="Symbol">:</a> <a id="5807" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="5811" href="Algebra.Bundles.html#5746" class="Field">Carrier</a>
|
|||
|
|
<a id="UnitalMagma.ε"></a><a id="5823" href="Algebra.Bundles.html#5823" class="Field">ε</a> <a id="5832" class="Symbol">:</a> <a id="5834" href="Algebra.Bundles.html#5746" class="Field">Carrier</a>
|
|||
|
|
<a id="UnitalMagma.isUnitalMagma"></a><a id="5846" href="Algebra.Bundles.html#5846" class="Field">isUnitalMagma</a> <a id="5860" class="Symbol">:</a> <a id="5862" href="Algebra.Structures.html#3696" class="Record">IsUnitalMagma</a> <a id="5876" href="Algebra.Bundles.html#5767" class="Field Operator">_≈_</a> <a id="5880" href="Algebra.Bundles.html#5796" class="Field Operator">_∙_</a> <a id="5884" href="Algebra.Bundles.html#5823" class="Field">ε</a>
|
|||
|
|
|
|||
|
|
<a id="5889" class="Keyword">open</a> <a id="5894" href="Algebra.Structures.html#3696" class="Module">IsUnitalMagma</a> <a id="5908" href="Algebra.Bundles.html#5846" class="Field">isUnitalMagma</a> <a id="5922" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="UnitalMagma.magma"></a><a id="5932" href="Algebra.Bundles.html#5932" class="Function">magma</a> <a id="5938" class="Symbol">:</a> <a id="5940" href="Algebra.Bundles.html#1141" class="Record">Magma</a> <a id="5946" href="Algebra.Bundles.html#5674" class="Bound">c</a> <a id="5948" href="Algebra.Bundles.html#5676" class="Bound">ℓ</a>
|
|||
|
|
<a id="5952" href="Algebra.Bundles.html#5932" class="Function">magma</a> <a id="5958" class="Symbol">=</a> <a id="5960" class="Keyword">record</a> <a id="5967" class="Symbol">{</a> <a id="5969" href="Algebra.Bundles.html#1293" class="Field">isMagma</a> <a id="5977" class="Symbol">=</a> <a id="5979" href="Algebra.Structures.html#3762" class="Function">isMagma</a> <a id="5987" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="5992" class="Keyword">open</a> <a id="5997" href="Algebra.Bundles.html#1141" class="Module">Magma</a> <a id="6003" href="Algebra.Bundles.html#5932" class="Function">magma</a> <a id="6009" class="Keyword">public</a>
|
|||
|
|
<a id="6020" class="Keyword">using</a> <a id="6026" class="Symbol">(</a><a id="6027" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="6030" class="Symbol">;</a> <a id="6032" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="6040" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="6044" class="Keyword">record</a> <a id="Monoid"></a><a id="6051" href="Algebra.Bundles.html#6051" class="Record">Monoid</a> <a id="6058" href="Algebra.Bundles.html#6058" class="Bound">c</a> <a id="6060" href="Algebra.Bundles.html#6060" class="Bound">ℓ</a> <a id="6062" class="Symbol">:</a> <a id="6064" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="6068" class="Symbol">(</a><a id="6069" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="6073" class="Symbol">(</a><a id="6074" href="Algebra.Bundles.html#6058" class="Bound">c</a> <a id="6076" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="6078" href="Algebra.Bundles.html#6060" class="Bound">ℓ</a><a id="6079" class="Symbol">))</a> <a id="6082" class="Keyword">where</a>
|
|||
|
|
<a id="6090" class="Keyword">infixl</a> <a id="6097" class="Number">7</a> <a id="6099" href="Algebra.Bundles.html#6180" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="6105" class="Keyword">infix</a> <a id="6112" class="Number">4</a> <a id="6114" href="Algebra.Bundles.html#6151" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="6120" class="Keyword">field</a>
|
|||
|
|
<a id="Monoid.Carrier"></a><a id="6130" href="Algebra.Bundles.html#6130" class="Field">Carrier</a> <a id="6139" class="Symbol">:</a> <a id="6141" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="6145" href="Algebra.Bundles.html#6058" class="Bound">c</a>
|
|||
|
|
<a id="Monoid._≈_"></a><a id="6151" href="Algebra.Bundles.html#6151" class="Field Operator">_≈_</a> <a id="6160" class="Symbol">:</a> <a id="6162" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="6166" href="Algebra.Bundles.html#6130" class="Field">Carrier</a> <a id="6174" href="Algebra.Bundles.html#6060" class="Bound">ℓ</a>
|
|||
|
|
<a id="Monoid._∙_"></a><a id="6180" href="Algebra.Bundles.html#6180" class="Field Operator">_∙_</a> <a id="6189" class="Symbol">:</a> <a id="6191" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="6195" href="Algebra.Bundles.html#6130" class="Field">Carrier</a>
|
|||
|
|
<a id="Monoid.ε"></a><a id="6207" href="Algebra.Bundles.html#6207" class="Field">ε</a> <a id="6216" class="Symbol">:</a> <a id="6218" href="Algebra.Bundles.html#6130" class="Field">Carrier</a>
|
|||
|
|
<a id="Monoid.isMonoid"></a><a id="6230" href="Algebra.Bundles.html#6230" class="Field">isMonoid</a> <a id="6239" class="Symbol">:</a> <a id="6241" href="Algebra.Structures.html#3974" class="Record">IsMonoid</a> <a id="6250" href="Algebra.Bundles.html#6151" class="Field Operator">_≈_</a> <a id="6254" href="Algebra.Bundles.html#6180" class="Field Operator">_∙_</a> <a id="6258" href="Algebra.Bundles.html#6207" class="Field">ε</a>
|
|||
|
|
|
|||
|
|
<a id="6263" class="Keyword">open</a> <a id="6268" href="Algebra.Structures.html#3974" class="Module">IsMonoid</a> <a id="6277" href="Algebra.Bundles.html#6230" class="Field">isMonoid</a> <a id="6286" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="Monoid.semigroup"></a><a id="6296" href="Algebra.Bundles.html#6296" class="Function">semigroup</a> <a id="6306" class="Symbol">:</a> <a id="6308" href="Algebra.Bundles.html#4139" class="Record">Semigroup</a> <a id="6318" class="Symbol">_</a> <a id="6320" class="Symbol">_</a>
|
|||
|
|
<a id="6324" href="Algebra.Bundles.html#6296" class="Function">semigroup</a> <a id="6334" class="Symbol">=</a> <a id="6336" class="Keyword">record</a> <a id="6343" class="Symbol">{</a> <a id="6345" href="Algebra.Bundles.html#4307" class="Field">isSemigroup</a> <a id="6357" class="Symbol">=</a> <a id="6359" href="Algebra.Structures.html#4035" class="Function">isSemigroup</a> <a id="6371" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="6376" class="Keyword">open</a> <a id="6381" href="Algebra.Bundles.html#4139" class="Module">Semigroup</a> <a id="6391" href="Algebra.Bundles.html#6296" class="Function">semigroup</a> <a id="6401" class="Keyword">public</a>
|
|||
|
|
<a id="6412" class="Keyword">using</a> <a id="6418" class="Symbol">(</a><a id="6419" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="6422" class="Symbol">;</a> <a id="6424" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="6432" class="Symbol">;</a> <a id="6434" href="Algebra.Bundles.html#4383" class="Function">magma</a><a id="6439" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="Monoid.rawMonoid"></a><a id="6444" href="Algebra.Bundles.html#6444" class="Function">rawMonoid</a> <a id="6454" class="Symbol">:</a> <a id="6456" href="Algebra.Bundles.Raw.html#1105" class="Record">RawMonoid</a> <a id="6466" class="Symbol">_</a> <a id="6468" class="Symbol">_</a>
|
|||
|
|
<a id="6472" href="Algebra.Bundles.html#6444" class="Function">rawMonoid</a> <a id="6482" class="Symbol">=</a> <a id="6484" class="Keyword">record</a> <a id="6491" class="Symbol">{</a> <a id="6493" href="Algebra.Bundles.Raw.html#1207" class="Field Operator">_≈_</a> <a id="6497" class="Symbol">=</a> <a id="6499" href="Algebra.Bundles.html#6151" class="Field Operator">_≈_</a><a id="6502" class="Symbol">;</a> <a id="6504" href="Algebra.Bundles.Raw.html#1235" class="Field Operator">_∙_</a> <a id="6508" class="Symbol">=</a> <a id="6510" href="Algebra.Bundles.html#6180" class="Field Operator">_∙_</a><a id="6513" class="Symbol">;</a> <a id="6515" href="Algebra.Bundles.Raw.html#1261" class="Field">ε</a> <a id="6517" class="Symbol">=</a> <a id="6519" href="Algebra.Bundles.html#6207" class="Field">ε</a><a id="6520" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="Monoid.unitalMagma"></a><a id="6525" href="Algebra.Bundles.html#6525" class="Function">unitalMagma</a> <a id="6537" class="Symbol">:</a> <a id="6539" href="Algebra.Bundles.html#5662" class="Record">UnitalMagma</a> <a id="6551" class="Symbol">_</a> <a id="6553" class="Symbol">_</a>
|
|||
|
|
<a id="6557" href="Algebra.Bundles.html#6525" class="Function">unitalMagma</a> <a id="6569" class="Symbol">=</a> <a id="6571" class="Keyword">record</a> <a id="6578" class="Symbol">{</a> <a id="6580" href="Algebra.Bundles.html#5846" class="Field">isUnitalMagma</a> <a id="6594" class="Symbol">=</a> <a id="6596" href="Algebra.Structures.html#4259" class="Function">isUnitalMagma</a> <a id="6611" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="6615" class="Keyword">record</a> <a id="CommutativeMonoid"></a><a id="6622" href="Algebra.Bundles.html#6622" class="Record">CommutativeMonoid</a> <a id="6640" href="Algebra.Bundles.html#6640" class="Bound">c</a> <a id="6642" href="Algebra.Bundles.html#6642" class="Bound">ℓ</a> <a id="6644" class="Symbol">:</a> <a id="6646" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="6650" class="Symbol">(</a><a id="6651" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="6655" class="Symbol">(</a><a id="6656" href="Algebra.Bundles.html#6640" class="Bound">c</a> <a id="6658" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="6660" href="Algebra.Bundles.html#6642" class="Bound">ℓ</a><a id="6661" class="Symbol">))</a> <a id="6664" class="Keyword">where</a>
|
|||
|
|
<a id="6672" class="Keyword">infixl</a> <a id="6679" class="Number">7</a> <a id="6681" href="Algebra.Bundles.html#6784" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="6687" class="Keyword">infix</a> <a id="6694" class="Number">4</a> <a id="6696" href="Algebra.Bundles.html#6744" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="6702" class="Keyword">field</a>
|
|||
|
|
<a id="CommutativeMonoid.Carrier"></a><a id="6712" href="Algebra.Bundles.html#6712" class="Field">Carrier</a> <a id="6732" class="Symbol">:</a> <a id="6734" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="6738" href="Algebra.Bundles.html#6640" class="Bound">c</a>
|
|||
|
|
<a id="CommutativeMonoid._≈_"></a><a id="6744" href="Algebra.Bundles.html#6744" class="Field Operator">_≈_</a> <a id="6764" class="Symbol">:</a> <a id="6766" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="6770" href="Algebra.Bundles.html#6712" class="Field">Carrier</a> <a id="6778" href="Algebra.Bundles.html#6642" class="Bound">ℓ</a>
|
|||
|
|
<a id="CommutativeMonoid._∙_"></a><a id="6784" href="Algebra.Bundles.html#6784" class="Field Operator">_∙_</a> <a id="6804" class="Symbol">:</a> <a id="6806" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="6810" href="Algebra.Bundles.html#6712" class="Field">Carrier</a>
|
|||
|
|
<a id="CommutativeMonoid.ε"></a><a id="6822" href="Algebra.Bundles.html#6822" class="Field">ε</a> <a id="6842" class="Symbol">:</a> <a id="6844" href="Algebra.Bundles.html#6712" class="Field">Carrier</a>
|
|||
|
|
<a id="CommutativeMonoid.isCommutativeMonoid"></a><a id="6856" href="Algebra.Bundles.html#6856" class="Field">isCommutativeMonoid</a> <a id="6876" class="Symbol">:</a> <a id="6878" href="Algebra.Structures.html#4384" class="Record">IsCommutativeMonoid</a> <a id="6898" href="Algebra.Bundles.html#6744" class="Field Operator">_≈_</a> <a id="6902" href="Algebra.Bundles.html#6784" class="Field Operator">_∙_</a> <a id="6906" href="Algebra.Bundles.html#6822" class="Field">ε</a>
|
|||
|
|
|
|||
|
|
<a id="6911" class="Keyword">open</a> <a id="6916" href="Algebra.Structures.html#4384" class="Module">IsCommutativeMonoid</a> <a id="6936" href="Algebra.Bundles.html#6856" class="Field">isCommutativeMonoid</a> <a id="6956" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="CommutativeMonoid.monoid"></a><a id="6966" href="Algebra.Bundles.html#6966" class="Function">monoid</a> <a id="6973" class="Symbol">:</a> <a id="6975" href="Algebra.Bundles.html#6051" class="Record">Monoid</a> <a id="6982" class="Symbol">_</a> <a id="6984" class="Symbol">_</a>
|
|||
|
|
<a id="6988" href="Algebra.Bundles.html#6966" class="Function">monoid</a> <a id="6995" class="Symbol">=</a> <a id="6997" class="Keyword">record</a> <a id="7004" class="Symbol">{</a> <a id="7006" href="Algebra.Bundles.html#6230" class="Field">isMonoid</a> <a id="7015" class="Symbol">=</a> <a id="7017" href="Algebra.Structures.html#4456" class="Function">isMonoid</a> <a id="7026" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="7031" class="Keyword">open</a> <a id="7036" href="Algebra.Bundles.html#6051" class="Module">Monoid</a> <a id="7043" href="Algebra.Bundles.html#6966" class="Function">monoid</a> <a id="7050" class="Keyword">public</a>
|
|||
|
|
<a id="7061" class="Keyword">using</a> <a id="7067" class="Symbol">(</a><a id="7068" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="7071" class="Symbol">;</a> <a id="7073" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="7081" class="Symbol">;</a> <a id="7083" href="Algebra.Bundles.html#4383" class="Function">magma</a><a id="7088" class="Symbol">;</a> <a id="7090" href="Algebra.Bundles.html#6296" class="Function">semigroup</a><a id="7099" class="Symbol">;</a> <a id="7101" href="Algebra.Bundles.html#6525" class="Function">unitalMagma</a><a id="7112" class="Symbol">;</a> <a id="7114" href="Algebra.Bundles.html#6444" class="Function">rawMonoid</a><a id="7123" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="CommutativeMonoid.commutativeSemigroup"></a><a id="7128" href="Algebra.Bundles.html#7128" class="Function">commutativeSemigroup</a> <a id="7149" class="Symbol">:</a> <a id="7151" href="Algebra.Bundles.html#4864" class="Record">CommutativeSemigroup</a> <a id="7172" class="Symbol">_</a> <a id="7174" class="Symbol">_</a>
|
|||
|
|
<a id="7178" href="Algebra.Bundles.html#7128" class="Function">commutativeSemigroup</a> <a id="7199" class="Symbol">=</a> <a id="7201" class="Keyword">record</a> <a id="7208" class="Symbol">{</a> <a id="7210" href="Algebra.Bundles.html#5079" class="Field">isCommutativeSemigroup</a> <a id="7233" class="Symbol">=</a> <a id="7235" href="Algebra.Structures.html#4545" class="Function">isCommutativeSemigroup</a> <a id="7258" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="7263" class="Keyword">open</a> <a id="7268" href="Algebra.Bundles.html#4864" class="Module">CommutativeSemigroup</a> <a id="7289" href="Algebra.Bundles.html#7128" class="Function">commutativeSemigroup</a> <a id="7310" class="Keyword">public</a>
|
|||
|
|
<a id="7321" class="Keyword">using</a> <a id="7327" class="Symbol">(</a><a id="7328" href="Algebra.Bundles.html#5348" class="Function">commutativeMagma</a><a id="7344" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="7348" class="Keyword">record</a> <a id="IdempotentCommutativeMonoid"></a><a id="7355" href="Algebra.Bundles.html#7355" class="Record">IdempotentCommutativeMonoid</a> <a id="7383" href="Algebra.Bundles.html#7383" class="Bound">c</a> <a id="7385" href="Algebra.Bundles.html#7385" class="Bound">ℓ</a> <a id="7387" class="Symbol">:</a> <a id="7389" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="7393" class="Symbol">(</a><a id="7394" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="7398" class="Symbol">(</a><a id="7399" href="Algebra.Bundles.html#7383" class="Bound">c</a> <a id="7401" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="7403" href="Algebra.Bundles.html#7385" class="Bound">ℓ</a><a id="7404" class="Symbol">))</a> <a id="7407" class="Keyword">where</a>
|
|||
|
|
<a id="7415" class="Keyword">infixl</a> <a id="7422" class="Number">7</a> <a id="7424" href="Algebra.Bundles.html#7547" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="7430" class="Keyword">infix</a> <a id="7437" class="Number">4</a> <a id="7439" href="Algebra.Bundles.html#7497" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="7445" class="Keyword">field</a>
|
|||
|
|
<a id="IdempotentCommutativeMonoid.Carrier"></a><a id="7455" href="Algebra.Bundles.html#7455" class="Field">Carrier</a> <a id="7485" class="Symbol">:</a> <a id="7487" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="7491" href="Algebra.Bundles.html#7383" class="Bound">c</a>
|
|||
|
|
<a id="IdempotentCommutativeMonoid._≈_"></a><a id="7497" href="Algebra.Bundles.html#7497" class="Field Operator">_≈_</a> <a id="7527" class="Symbol">:</a> <a id="7529" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="7533" href="Algebra.Bundles.html#7455" class="Field">Carrier</a> <a id="7541" href="Algebra.Bundles.html#7385" class="Bound">ℓ</a>
|
|||
|
|
<a id="IdempotentCommutativeMonoid._∙_"></a><a id="7547" href="Algebra.Bundles.html#7547" class="Field Operator">_∙_</a> <a id="7577" class="Symbol">:</a> <a id="7579" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="7583" href="Algebra.Bundles.html#7455" class="Field">Carrier</a>
|
|||
|
|
<a id="IdempotentCommutativeMonoid.ε"></a><a id="7595" href="Algebra.Bundles.html#7595" class="Field">ε</a> <a id="7625" class="Symbol">:</a> <a id="7627" href="Algebra.Bundles.html#7455" class="Field">Carrier</a>
|
|||
|
|
<a id="IdempotentCommutativeMonoid.isIdempotentCommutativeMonoid"></a><a id="7639" href="Algebra.Bundles.html#7639" class="Field">isIdempotentCommutativeMonoid</a> <a id="7669" class="Symbol">:</a> <a id="7671" href="Algebra.Structures.html#4793" class="Record">IsIdempotentCommutativeMonoid</a> <a id="7701" href="Algebra.Bundles.html#7497" class="Field Operator">_≈_</a> <a id="7705" href="Algebra.Bundles.html#7547" class="Field Operator">_∙_</a> <a id="7709" href="Algebra.Bundles.html#7595" class="Field">ε</a>
|
|||
|
|
|
|||
|
|
<a id="7714" class="Keyword">open</a> <a id="7719" href="Algebra.Structures.html#4793" class="Module">IsIdempotentCommutativeMonoid</a> <a id="7749" href="Algebra.Bundles.html#7639" class="Field">isIdempotentCommutativeMonoid</a> <a id="7779" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="IdempotentCommutativeMonoid.commutativeMonoid"></a><a id="7789" href="Algebra.Bundles.html#7789" class="Function">commutativeMonoid</a> <a id="7807" class="Symbol">:</a> <a id="7809" href="Algebra.Bundles.html#6622" class="Record">CommutativeMonoid</a> <a id="7827" class="Symbol">_</a> <a id="7829" class="Symbol">_</a>
|
|||
|
|
<a id="7833" href="Algebra.Bundles.html#7789" class="Function">commutativeMonoid</a> <a id="7851" class="Symbol">=</a> <a id="7853" class="Keyword">record</a> <a id="7860" class="Symbol">{</a> <a id="7862" href="Algebra.Bundles.html#6856" class="Field">isCommutativeMonoid</a> <a id="7882" class="Symbol">=</a> <a id="7884" href="Algebra.Structures.html#4912" class="Function">isCommutativeMonoid</a> <a id="7904" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="7909" class="Keyword">open</a> <a id="7914" href="Algebra.Bundles.html#6622" class="Module">CommutativeMonoid</a> <a id="7932" href="Algebra.Bundles.html#7789" class="Function">commutativeMonoid</a> <a id="7950" class="Keyword">public</a>
|
|||
|
|
<a id="7961" class="Keyword">using</a>
|
|||
|
|
<a id="7971" class="Symbol">(</a> <a id="7973" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="7976" class="Symbol">;</a> <a id="7978" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="7986" class="Symbol">;</a> <a id="7988" href="Algebra.Bundles.html#4383" class="Function">magma</a><a id="7993" class="Symbol">;</a> <a id="7995" href="Algebra.Bundles.html#6525" class="Function">unitalMagma</a><a id="8006" class="Symbol">;</a> <a id="8008" href="Algebra.Bundles.html#5348" class="Function">commutativeMagma</a>
|
|||
|
|
<a id="8029" class="Symbol">;</a> <a id="8031" href="Algebra.Bundles.html#6296" class="Function">semigroup</a><a id="8040" class="Symbol">;</a> <a id="8042" href="Algebra.Bundles.html#7128" class="Function">commutativeSemigroup</a>
|
|||
|
|
<a id="8067" class="Symbol">;</a> <a id="8069" href="Algebra.Bundles.html#6444" class="Function">rawMonoid</a><a id="8078" class="Symbol">;</a> <a id="8080" href="Algebra.Bundles.html#6966" class="Function">monoid</a>
|
|||
|
|
<a id="8091" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="8095" class="Comment">-- Idempotent commutative monoids are also known as bounded lattices.</a>
|
|||
|
|
<a id="8165" class="Comment">-- Note that the BoundedLattice necessarily uses the notation inherited</a>
|
|||
|
|
<a id="8237" class="Comment">-- from monoids rather than lattices.</a>
|
|||
|
|
|
|||
|
|
<a id="BoundedLattice"></a><a id="8276" href="Algebra.Bundles.html#8276" class="Function">BoundedLattice</a> <a id="8291" class="Symbol">=</a> <a id="8293" href="Algebra.Bundles.html#7355" class="Record">IdempotentCommutativeMonoid</a>
|
|||
|
|
|
|||
|
|
<a id="8322" class="Keyword">module</a> <a id="BoundedLattice"></a><a id="8329" href="Algebra.Bundles.html#8329" class="Module">BoundedLattice</a> <a id="8344" class="Symbol">{</a><a id="8345" href="Algebra.Bundles.html#8345" class="Bound">c</a> <a id="8347" href="Algebra.Bundles.html#8347" class="Bound">ℓ</a><a id="8348" class="Symbol">}</a> <a id="8350" class="Symbol">(</a><a id="8351" href="Algebra.Bundles.html#8351" class="Bound">idemCommMonoid</a> <a id="8366" class="Symbol">:</a> <a id="8368" href="Algebra.Bundles.html#7355" class="Record">IdempotentCommutativeMonoid</a> <a id="8396" href="Algebra.Bundles.html#8345" class="Bound">c</a> <a id="8398" href="Algebra.Bundles.html#8347" class="Bound">ℓ</a><a id="8399" class="Symbol">)</a> <a id="8401" class="Symbol">=</a>
|
|||
|
|
<a id="8410" href="Algebra.Bundles.html#7355" class="Module">IdempotentCommutativeMonoid</a> <a id="8438" href="Algebra.Bundles.html#8351" class="Bound">idemCommMonoid</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="8455" class="Comment">------------------------------------------------------------------------</a>
|
|||
|
|
<a id="8528" class="Comment">-- Bundles with 1 binary operation, 1 unary operation & 1 element</a>
|
|||
|
|
<a id="8594" class="Comment">------------------------------------------------------------------------</a>
|
|||
|
|
|
|||
|
|
<a id="8668" class="Keyword">record</a> <a id="InvertibleMagma"></a><a id="8675" href="Algebra.Bundles.html#8675" class="Record">InvertibleMagma</a> <a id="8691" href="Algebra.Bundles.html#8691" class="Bound">c</a> <a id="8693" href="Algebra.Bundles.html#8693" class="Bound">ℓ</a> <a id="8695" class="Symbol">:</a> <a id="8697" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="8701" class="Symbol">(</a><a id="8702" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="8706" class="Symbol">(</a><a id="8707" href="Algebra.Bundles.html#8691" class="Bound">c</a> <a id="8709" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="8711" href="Algebra.Bundles.html#8693" class="Bound">ℓ</a><a id="8712" class="Symbol">))</a> <a id="8715" class="Keyword">where</a>
|
|||
|
|
<a id="8723" class="Keyword">infix</a> <a id="8730" class="Number">8</a> <a id="8732" href="Algebra.Bundles.html#8874" class="Field Operator">_⁻¹</a>
|
|||
|
|
<a id="8738" class="Keyword">infixl</a> <a id="8745" class="Number">7</a> <a id="8747" href="Algebra.Bundles.html#8826" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="8753" class="Keyword">infix</a> <a id="8760" class="Number">4</a> <a id="8762" href="Algebra.Bundles.html#8798" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="8768" class="Keyword">field</a>
|
|||
|
|
<a id="InvertibleMagma.Carrier"></a><a id="8778" href="Algebra.Bundles.html#8778" class="Field">Carrier</a> <a id="8786" class="Symbol">:</a> <a id="8788" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="8792" href="Algebra.Bundles.html#8691" class="Bound">c</a>
|
|||
|
|
<a id="InvertibleMagma._≈_"></a><a id="8798" href="Algebra.Bundles.html#8798" class="Field Operator">_≈_</a> <a id="8806" class="Symbol">:</a> <a id="8808" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="8812" href="Algebra.Bundles.html#8778" class="Field">Carrier</a> <a id="8820" href="Algebra.Bundles.html#8693" class="Bound">ℓ</a>
|
|||
|
|
<a id="InvertibleMagma._∙_"></a><a id="8826" href="Algebra.Bundles.html#8826" class="Field Operator">_∙_</a> <a id="8834" class="Symbol">:</a> <a id="8836" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="8840" href="Algebra.Bundles.html#8778" class="Field">Carrier</a>
|
|||
|
|
<a id="InvertibleMagma.ε"></a><a id="8852" href="Algebra.Bundles.html#8852" class="Field">ε</a> <a id="8860" class="Symbol">:</a> <a id="8862" href="Algebra.Bundles.html#8778" class="Field">Carrier</a>
|
|||
|
|
<a id="InvertibleMagma._⁻¹"></a><a id="8874" href="Algebra.Bundles.html#8874" class="Field Operator">_⁻¹</a> <a id="8882" class="Symbol">:</a> <a id="8884" href="Algebra.Core.html#484" class="Function">Op₁</a> <a id="8888" href="Algebra.Bundles.html#8778" class="Field">Carrier</a>
|
|||
|
|
<a id="InvertibleMagma.isInvertibleMagma"></a><a id="8900" href="Algebra.Bundles.html#8900" class="Field">isInvertibleMagma</a> <a id="8918" class="Symbol">:</a> <a id="8920" href="Algebra.Structures.html#5360" class="Record">IsInvertibleMagma</a> <a id="8938" href="Algebra.Bundles.html#8798" class="Field Operator">_≈_</a> <a id="8942" href="Algebra.Bundles.html#8826" class="Field Operator">_∙_</a> <a id="8946" href="Algebra.Bundles.html#8852" class="Field">ε</a> <a id="8948" href="Algebra.Bundles.html#8874" class="Field Operator">_⁻¹</a>
|
|||
|
|
|
|||
|
|
<a id="8955" class="Keyword">open</a> <a id="8960" href="Algebra.Structures.html#5360" class="Module">IsInvertibleMagma</a> <a id="8978" href="Algebra.Bundles.html#8900" class="Field">isInvertibleMagma</a> <a id="8996" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="InvertibleMagma.magma"></a><a id="9006" href="Algebra.Bundles.html#9006" class="Function">magma</a> <a id="9012" class="Symbol">:</a> <a id="9014" href="Algebra.Bundles.html#1141" class="Record">Magma</a> <a id="9020" class="Symbol">_</a> <a id="9022" class="Symbol">_</a>
|
|||
|
|
<a id="9026" href="Algebra.Bundles.html#9006" class="Function">magma</a> <a id="9032" class="Symbol">=</a> <a id="9034" class="Keyword">record</a> <a id="9041" class="Symbol">{</a> <a id="9043" href="Algebra.Bundles.html#1293" class="Field">isMagma</a> <a id="9051" class="Symbol">=</a> <a id="9053" href="Algebra.Structures.html#5446" class="Function">isMagma</a> <a id="9061" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="9066" class="Keyword">open</a> <a id="9071" href="Algebra.Bundles.html#1141" class="Module">Magma</a> <a id="9077" href="Algebra.Bundles.html#9006" class="Function">magma</a> <a id="9083" class="Keyword">public</a>
|
|||
|
|
<a id="9094" class="Keyword">using</a> <a id="9100" class="Symbol">(</a><a id="9101" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="9104" class="Symbol">;</a> <a id="9106" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="9114" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="9118" class="Keyword">record</a> <a id="InvertibleUnitalMagma"></a><a id="9125" href="Algebra.Bundles.html#9125" class="Record">InvertibleUnitalMagma</a> <a id="9147" href="Algebra.Bundles.html#9147" class="Bound">c</a> <a id="9149" href="Algebra.Bundles.html#9149" class="Bound">ℓ</a> <a id="9151" class="Symbol">:</a> <a id="9153" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="9157" class="Symbol">(</a><a id="9158" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="9162" class="Symbol">(</a><a id="9163" href="Algebra.Bundles.html#9147" class="Bound">c</a> <a id="9165" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="9167" href="Algebra.Bundles.html#9149" class="Bound">ℓ</a><a id="9168" class="Symbol">))</a> <a id="9171" class="Keyword">where</a>
|
|||
|
|
<a id="9179" class="Keyword">infix</a> <a id="9186" class="Number">8</a> <a id="9188" href="Algebra.Bundles.html#9398" class="Field Operator">_⁻¹</a>
|
|||
|
|
<a id="9194" class="Keyword">infixl</a> <a id="9201" class="Number">7</a> <a id="9203" href="Algebra.Bundles.html#9316" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="9209" class="Keyword">infix</a> <a id="9216" class="Number">4</a> <a id="9218" href="Algebra.Bundles.html#9271" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="9224" class="Keyword">field</a>
|
|||
|
|
<a id="InvertibleUnitalMagma.Carrier"></a><a id="9234" href="Algebra.Bundles.html#9234" class="Field">Carrier</a> <a id="9259" class="Symbol">:</a> <a id="9261" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="9265" href="Algebra.Bundles.html#9147" class="Bound">c</a>
|
|||
|
|
<a id="InvertibleUnitalMagma._≈_"></a><a id="9271" href="Algebra.Bundles.html#9271" class="Field Operator">_≈_</a> <a id="9296" class="Symbol">:</a> <a id="9298" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="9302" href="Algebra.Bundles.html#9234" class="Field">Carrier</a> <a id="9310" href="Algebra.Bundles.html#9149" class="Bound">ℓ</a>
|
|||
|
|
<a id="InvertibleUnitalMagma._∙_"></a><a id="9316" href="Algebra.Bundles.html#9316" class="Field Operator">_∙_</a> <a id="9341" class="Symbol">:</a> <a id="9343" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="9347" href="Algebra.Bundles.html#9234" class="Field">Carrier</a>
|
|||
|
|
<a id="InvertibleUnitalMagma.ε"></a><a id="9359" href="Algebra.Bundles.html#9359" class="Field">ε</a> <a id="9384" class="Symbol">:</a> <a id="9386" href="Algebra.Bundles.html#9234" class="Field">Carrier</a>
|
|||
|
|
<a id="InvertibleUnitalMagma._⁻¹"></a><a id="9398" href="Algebra.Bundles.html#9398" class="Field Operator">_⁻¹</a> <a id="9423" class="Symbol">:</a> <a id="9425" href="Algebra.Core.html#484" class="Function">Op₁</a> <a id="9429" href="Algebra.Bundles.html#9234" class="Field">Carrier</a>
|
|||
|
|
<a id="InvertibleUnitalMagma.isInvertibleUnitalMagma"></a><a id="9441" href="Algebra.Bundles.html#9441" class="Field">isInvertibleUnitalMagma</a> <a id="9466" class="Symbol">:</a> <a id="9468" href="Algebra.Structures.html#5701" class="Record">IsInvertibleUnitalMagma</a> <a id="9492" href="Algebra.Bundles.html#9271" class="Field Operator">_≈_</a> <a id="9496" href="Algebra.Bundles.html#9316" class="Field Operator">_∙_</a> <a id="9500" href="Algebra.Bundles.html#9359" class="Field">ε</a> <a id="9502" href="Algebra.Bundles.html#9398" class="Field Operator">_⁻¹</a>
|
|||
|
|
|
|||
|
|
<a id="9509" class="Keyword">open</a> <a id="9514" href="Algebra.Structures.html#5701" class="Module">IsInvertibleUnitalMagma</a> <a id="9538" href="Algebra.Bundles.html#9441" class="Field">isInvertibleUnitalMagma</a> <a id="9562" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="InvertibleUnitalMagma.invertibleMagma"></a><a id="9572" href="Algebra.Bundles.html#9572" class="Function">invertibleMagma</a> <a id="9588" class="Symbol">:</a> <a id="9590" href="Algebra.Bundles.html#8675" class="Record">InvertibleMagma</a> <a id="9606" class="Symbol">_</a> <a id="9608" class="Symbol">_</a>
|
|||
|
|
<a id="9612" href="Algebra.Bundles.html#9572" class="Function">invertibleMagma</a> <a id="9628" class="Symbol">=</a> <a id="9630" class="Keyword">record</a> <a id="9637" class="Symbol">{</a> <a id="9639" href="Algebra.Bundles.html#8900" class="Field">isInvertibleMagma</a> <a id="9657" class="Symbol">=</a> <a id="9659" href="Algebra.Structures.html#5792" class="Function">isInvertibleMagma</a> <a id="9677" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="9682" class="Keyword">open</a> <a id="9687" href="Algebra.Bundles.html#8675" class="Module">InvertibleMagma</a> <a id="9703" href="Algebra.Bundles.html#9572" class="Function">invertibleMagma</a> <a id="9719" class="Keyword">public</a>
|
|||
|
|
<a id="9730" class="Keyword">using</a> <a id="9736" class="Symbol">(</a><a id="9737" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="9740" class="Symbol">;</a> <a id="9742" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="9750" class="Symbol">;</a> <a id="9752" href="Algebra.Bundles.html#9006" class="Function">magma</a><a id="9757" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="9760" class="Keyword">record</a> <a id="Group"></a><a id="9767" href="Algebra.Bundles.html#9767" class="Record">Group</a> <a id="9773" href="Algebra.Bundles.html#9773" class="Bound">c</a> <a id="9775" href="Algebra.Bundles.html#9775" class="Bound">ℓ</a> <a id="9777" class="Symbol">:</a> <a id="9779" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="9783" class="Symbol">(</a><a id="9784" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="9788" class="Symbol">(</a><a id="9789" href="Algebra.Bundles.html#9773" class="Bound">c</a> <a id="9791" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="9793" href="Algebra.Bundles.html#9775" class="Bound">ℓ</a><a id="9794" class="Symbol">))</a> <a id="9797" class="Keyword">where</a>
|
|||
|
|
<a id="9805" class="Keyword">infix</a> <a id="9812" class="Number">8</a> <a id="9814" href="Algebra.Bundles.html#9956" class="Field Operator">_⁻¹</a>
|
|||
|
|
<a id="9820" class="Keyword">infixl</a> <a id="9827" class="Number">7</a> <a id="9829" href="Algebra.Bundles.html#9908" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="9835" class="Keyword">infix</a> <a id="9842" class="Number">4</a> <a id="9844" href="Algebra.Bundles.html#9880" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="9850" class="Keyword">field</a>
|
|||
|
|
<a id="Group.Carrier"></a><a id="9860" href="Algebra.Bundles.html#9860" class="Field">Carrier</a> <a id="9868" class="Symbol">:</a> <a id="9870" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="9874" href="Algebra.Bundles.html#9773" class="Bound">c</a>
|
|||
|
|
<a id="Group._≈_"></a><a id="9880" href="Algebra.Bundles.html#9880" class="Field Operator">_≈_</a> <a id="9888" class="Symbol">:</a> <a id="9890" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="9894" href="Algebra.Bundles.html#9860" class="Field">Carrier</a> <a id="9902" href="Algebra.Bundles.html#9775" class="Bound">ℓ</a>
|
|||
|
|
<a id="Group._∙_"></a><a id="9908" href="Algebra.Bundles.html#9908" class="Field Operator">_∙_</a> <a id="9916" class="Symbol">:</a> <a id="9918" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="9922" href="Algebra.Bundles.html#9860" class="Field">Carrier</a>
|
|||
|
|
<a id="Group.ε"></a><a id="9934" href="Algebra.Bundles.html#9934" class="Field">ε</a> <a id="9942" class="Symbol">:</a> <a id="9944" href="Algebra.Bundles.html#9860" class="Field">Carrier</a>
|
|||
|
|
<a id="Group._⁻¹"></a><a id="9956" href="Algebra.Bundles.html#9956" class="Field Operator">_⁻¹</a> <a id="9964" class="Symbol">:</a> <a id="9966" href="Algebra.Core.html#484" class="Function">Op₁</a> <a id="9970" href="Algebra.Bundles.html#9860" class="Field">Carrier</a>
|
|||
|
|
<a id="Group.isGroup"></a><a id="9982" href="Algebra.Bundles.html#9982" class="Field">isGroup</a> <a id="9990" class="Symbol">:</a> <a id="9992" href="Algebra.Structures.html#6188" class="Record">IsGroup</a> <a id="10000" href="Algebra.Bundles.html#9880" class="Field Operator">_≈_</a> <a id="10004" href="Algebra.Bundles.html#9908" class="Field Operator">_∙_</a> <a id="10008" href="Algebra.Bundles.html#9934" class="Field">ε</a> <a id="10010" href="Algebra.Bundles.html#9956" class="Field Operator">_⁻¹</a>
|
|||
|
|
|
|||
|
|
<a id="10017" class="Keyword">open</a> <a id="10022" href="Algebra.Structures.html#6188" class="Module">IsGroup</a> <a id="10030" href="Algebra.Bundles.html#9982" class="Field">isGroup</a> <a id="10038" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="Group.rawGroup"></a><a id="10048" href="Algebra.Bundles.html#10048" class="Function">rawGroup</a> <a id="10057" class="Symbol">:</a> <a id="10059" href="Algebra.Bundles.Raw.html#1638" class="Record">RawGroup</a> <a id="10068" class="Symbol">_</a> <a id="10070" class="Symbol">_</a>
|
|||
|
|
<a id="10074" href="Algebra.Bundles.html#10048" class="Function">rawGroup</a> <a id="10083" class="Symbol">=</a> <a id="10085" class="Keyword">record</a> <a id="10092" class="Symbol">{</a> <a id="10094" href="Algebra.Bundles.Raw.html#1754" class="Field Operator">_≈_</a> <a id="10098" class="Symbol">=</a> <a id="10100" href="Algebra.Bundles.html#9880" class="Field Operator">_≈_</a><a id="10103" class="Symbol">;</a> <a id="10105" href="Algebra.Bundles.Raw.html#1782" class="Field Operator">_∙_</a> <a id="10109" class="Symbol">=</a> <a id="10111" href="Algebra.Bundles.html#9908" class="Field Operator">_∙_</a><a id="10114" class="Symbol">;</a> <a id="10116" href="Algebra.Bundles.Raw.html#1808" class="Field">ε</a> <a id="10118" class="Symbol">=</a> <a id="10120" href="Algebra.Bundles.html#9934" class="Field">ε</a><a id="10121" class="Symbol">;</a> <a id="10123" href="Algebra.Bundles.Raw.html#1830" class="Field Operator">_⁻¹</a> <a id="10127" class="Symbol">=</a> <a id="10129" href="Algebra.Bundles.html#9956" class="Field Operator">_⁻¹</a><a id="10132" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="Group.monoid"></a><a id="10137" href="Algebra.Bundles.html#10137" class="Function">monoid</a> <a id="10144" class="Symbol">:</a> <a id="10146" href="Algebra.Bundles.html#6051" class="Record">Monoid</a> <a id="10153" class="Symbol">_</a> <a id="10155" class="Symbol">_</a>
|
|||
|
|
<a id="10159" href="Algebra.Bundles.html#10137" class="Function">monoid</a> <a id="10166" class="Symbol">=</a> <a id="10168" class="Keyword">record</a> <a id="10175" class="Symbol">{</a> <a id="10177" href="Algebra.Bundles.html#6230" class="Field">isMonoid</a> <a id="10186" class="Symbol">=</a> <a id="10188" href="Algebra.Structures.html#6264" class="Function">isMonoid</a> <a id="10197" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="10202" class="Keyword">open</a> <a id="10207" href="Algebra.Bundles.html#6051" class="Module">Monoid</a> <a id="10214" href="Algebra.Bundles.html#10137" class="Function">monoid</a> <a id="10221" class="Keyword">public</a>
|
|||
|
|
<a id="10232" class="Keyword">using</a> <a id="10238" class="Symbol">(</a><a id="10239" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="10242" class="Symbol">;</a> <a id="10244" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="10252" class="Symbol">;</a> <a id="10254" href="Algebra.Bundles.html#4383" class="Function">magma</a><a id="10259" class="Symbol">;</a> <a id="10261" href="Algebra.Bundles.html#6296" class="Function">semigroup</a><a id="10270" class="Symbol">;</a> <a id="10272" href="Algebra.Bundles.html#6525" class="Function">unitalMagma</a><a id="10283" class="Symbol">;</a> <a id="10285" href="Algebra.Bundles.html#6444" class="Function">rawMonoid</a><a id="10294" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="Group.invertibleMagma"></a><a id="10299" href="Algebra.Bundles.html#10299" class="Function">invertibleMagma</a> <a id="10315" class="Symbol">:</a> <a id="10317" href="Algebra.Bundles.html#8675" class="Record">InvertibleMagma</a> <a id="10333" href="Algebra.Bundles.html#9773" class="Bound">c</a> <a id="10335" href="Algebra.Bundles.html#9775" class="Bound">ℓ</a>
|
|||
|
|
<a id="10339" href="Algebra.Bundles.html#10299" class="Function">invertibleMagma</a> <a id="10355" class="Symbol">=</a> <a id="10357" class="Keyword">record</a>
|
|||
|
|
<a id="10368" class="Symbol">{</a> <a id="10370" href="Algebra.Bundles.html#8900" class="Field">isInvertibleMagma</a> <a id="10388" class="Symbol">=</a> <a id="10390" href="Algebra.Structures.html#6884" class="Function">isInvertibleMagma</a>
|
|||
|
|
<a id="10412" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="Group.invertibleUnitalMagma"></a><a id="10417" href="Algebra.Bundles.html#10417" class="Function">invertibleUnitalMagma</a> <a id="10439" class="Symbol">:</a> <a id="10441" href="Algebra.Bundles.html#9125" class="Record">InvertibleUnitalMagma</a> <a id="10463" href="Algebra.Bundles.html#9773" class="Bound">c</a> <a id="10465" href="Algebra.Bundles.html#9775" class="Bound">ℓ</a>
|
|||
|
|
<a id="10469" href="Algebra.Bundles.html#10417" class="Function">invertibleUnitalMagma</a> <a id="10491" class="Symbol">=</a> <a id="10493" class="Keyword">record</a>
|
|||
|
|
<a id="10504" class="Symbol">{</a> <a id="10506" href="Algebra.Bundles.html#9441" class="Field">isInvertibleUnitalMagma</a> <a id="10530" class="Symbol">=</a> <a id="10532" href="Algebra.Structures.html#7042" class="Function">isInvertibleUnitalMagma</a>
|
|||
|
|
<a id="10560" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="10563" class="Keyword">record</a> <a id="AbelianGroup"></a><a id="10570" href="Algebra.Bundles.html#10570" class="Record">AbelianGroup</a> <a id="10583" href="Algebra.Bundles.html#10583" class="Bound">c</a> <a id="10585" href="Algebra.Bundles.html#10585" class="Bound">ℓ</a> <a id="10587" class="Symbol">:</a> <a id="10589" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="10593" class="Symbol">(</a><a id="10594" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="10598" class="Symbol">(</a><a id="10599" href="Algebra.Bundles.html#10583" class="Bound">c</a> <a id="10601" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="10603" href="Algebra.Bundles.html#10585" class="Bound">ℓ</a><a id="10604" class="Symbol">))</a> <a id="10607" class="Keyword">where</a>
|
|||
|
|
<a id="10615" class="Keyword">infix</a> <a id="10622" class="Number">8</a> <a id="10624" href="Algebra.Bundles.html#10794" class="Field Operator">_⁻¹</a>
|
|||
|
|
<a id="10630" class="Keyword">infixl</a> <a id="10637" class="Number">7</a> <a id="10639" href="Algebra.Bundles.html#10732" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="10645" class="Keyword">infix</a> <a id="10652" class="Number">4</a> <a id="10654" href="Algebra.Bundles.html#10697" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="10660" class="Keyword">field</a>
|
|||
|
|
<a id="AbelianGroup.Carrier"></a><a id="10670" href="Algebra.Bundles.html#10670" class="Field">Carrier</a> <a id="10685" class="Symbol">:</a> <a id="10687" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="10691" href="Algebra.Bundles.html#10583" class="Bound">c</a>
|
|||
|
|
<a id="AbelianGroup._≈_"></a><a id="10697" href="Algebra.Bundles.html#10697" class="Field Operator">_≈_</a> <a id="10712" class="Symbol">:</a> <a id="10714" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="10718" href="Algebra.Bundles.html#10670" class="Field">Carrier</a> <a id="10726" href="Algebra.Bundles.html#10585" class="Bound">ℓ</a>
|
|||
|
|
<a id="AbelianGroup._∙_"></a><a id="10732" href="Algebra.Bundles.html#10732" class="Field Operator">_∙_</a> <a id="10747" class="Symbol">:</a> <a id="10749" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="10753" href="Algebra.Bundles.html#10670" class="Field">Carrier</a>
|
|||
|
|
<a id="AbelianGroup.ε"></a><a id="10765" href="Algebra.Bundles.html#10765" class="Field">ε</a> <a id="10780" class="Symbol">:</a> <a id="10782" href="Algebra.Bundles.html#10670" class="Field">Carrier</a>
|
|||
|
|
<a id="AbelianGroup._⁻¹"></a><a id="10794" href="Algebra.Bundles.html#10794" class="Field Operator">_⁻¹</a> <a id="10809" class="Symbol">:</a> <a id="10811" href="Algebra.Core.html#484" class="Function">Op₁</a> <a id="10815" href="Algebra.Bundles.html#10670" class="Field">Carrier</a>
|
|||
|
|
<a id="AbelianGroup.isAbelianGroup"></a><a id="10827" href="Algebra.Bundles.html#10827" class="Field">isAbelianGroup</a> <a id="10842" class="Symbol">:</a> <a id="10844" href="Algebra.Structures.html#7222" class="Record">IsAbelianGroup</a> <a id="10859" href="Algebra.Bundles.html#10697" class="Field Operator">_≈_</a> <a id="10863" href="Algebra.Bundles.html#10732" class="Field Operator">_∙_</a> <a id="10867" href="Algebra.Bundles.html#10765" class="Field">ε</a> <a id="10869" href="Algebra.Bundles.html#10794" class="Field Operator">_⁻¹</a>
|
|||
|
|
|
|||
|
|
<a id="10876" class="Keyword">open</a> <a id="10881" href="Algebra.Structures.html#7222" class="Module">IsAbelianGroup</a> <a id="10896" href="Algebra.Bundles.html#10827" class="Field">isAbelianGroup</a> <a id="10911" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="AbelianGroup.group"></a><a id="10921" href="Algebra.Bundles.html#10921" class="Function">group</a> <a id="10927" class="Symbol">:</a> <a id="10929" href="Algebra.Bundles.html#9767" class="Record">Group</a> <a id="10935" class="Symbol">_</a> <a id="10937" class="Symbol">_</a>
|
|||
|
|
<a id="10941" href="Algebra.Bundles.html#10921" class="Function">group</a> <a id="10947" class="Symbol">=</a> <a id="10949" class="Keyword">record</a> <a id="10956" class="Symbol">{</a> <a id="10958" href="Algebra.Bundles.html#9982" class="Field">isGroup</a> <a id="10966" class="Symbol">=</a> <a id="10968" href="Algebra.Structures.html#7324" class="Function">isGroup</a> <a id="10976" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="10981" class="Keyword">open</a> <a id="10986" href="Algebra.Bundles.html#9767" class="Module">Group</a> <a id="10992" href="Algebra.Bundles.html#10921" class="Function">group</a> <a id="10998" class="Keyword">public</a> <a id="11005" class="Keyword">using</a>
|
|||
|
|
<a id="11015" class="Symbol">(</a><a id="11016" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="11019" class="Symbol">;</a> <a id="11021" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="11029" class="Symbol">;</a> <a id="11031" href="Algebra.Bundles.html#4383" class="Function">magma</a><a id="11036" class="Symbol">;</a> <a id="11038" href="Algebra.Bundles.html#6296" class="Function">semigroup</a>
|
|||
|
|
<a id="11052" class="Symbol">;</a> <a id="11054" href="Algebra.Bundles.html#6444" class="Function">rawMonoid</a><a id="11063" class="Symbol">;</a> <a id="11065" href="Algebra.Bundles.html#10137" class="Function">monoid</a><a id="11071" class="Symbol">;</a> <a id="11073" href="Algebra.Bundles.html#10048" class="Function">rawGroup</a><a id="11081" class="Symbol">;</a> <a id="11083" href="Algebra.Bundles.html#10299" class="Function">invertibleMagma</a><a id="11098" class="Symbol">;</a> <a id="11100" href="Algebra.Bundles.html#10417" class="Function">invertibleUnitalMagma</a>
|
|||
|
|
<a id="11126" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="AbelianGroup.commutativeMonoid"></a><a id="11131" href="Algebra.Bundles.html#11131" class="Function">commutativeMonoid</a> <a id="11149" class="Symbol">:</a> <a id="11151" href="Algebra.Bundles.html#6622" class="Record">CommutativeMonoid</a> <a id="11169" class="Symbol">_</a> <a id="11171" class="Symbol">_</a>
|
|||
|
|
<a id="11175" href="Algebra.Bundles.html#11131" class="Function">commutativeMonoid</a> <a id="11193" class="Symbol">=</a> <a id="11195" class="Keyword">record</a> <a id="11202" class="Symbol">{</a> <a id="11204" href="Algebra.Bundles.html#6856" class="Field">isCommutativeMonoid</a> <a id="11224" class="Symbol">=</a> <a id="11226" href="Algebra.Structures.html#7411" class="Function">isCommutativeMonoid</a> <a id="11246" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="11251" class="Keyword">open</a> <a id="11256" href="Algebra.Bundles.html#6622" class="Module">CommutativeMonoid</a> <a id="11274" href="Algebra.Bundles.html#11131" class="Function">commutativeMonoid</a> <a id="11292" class="Keyword">public</a>
|
|||
|
|
<a id="11303" class="Keyword">using</a> <a id="11309" class="Symbol">(</a><a id="11310" href="Algebra.Bundles.html#5348" class="Function">commutativeMagma</a><a id="11326" class="Symbol">;</a> <a id="11328" href="Algebra.Bundles.html#7128" class="Function">commutativeSemigroup</a><a id="11348" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="11351" class="Comment">------------------------------------------------------------------------</a>
|
|||
|
|
<a id="11424" class="Comment">-- Bundles with 2 binary operations & 1 element</a>
|
|||
|
|
<a id="11472" class="Comment">------------------------------------------------------------------------</a>
|
|||
|
|
|
|||
|
|
<a id="11546" class="Keyword">record</a> <a id="NearSemiring"></a><a id="11553" href="Algebra.Bundles.html#11553" class="Record">NearSemiring</a> <a id="11566" href="Algebra.Bundles.html#11566" class="Bound">c</a> <a id="11568" href="Algebra.Bundles.html#11568" class="Bound">ℓ</a> <a id="11570" class="Symbol">:</a> <a id="11572" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="11576" class="Symbol">(</a><a id="11577" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="11581" class="Symbol">(</a><a id="11582" href="Algebra.Bundles.html#11566" class="Bound">c</a> <a id="11584" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="11586" href="Algebra.Bundles.html#11568" class="Bound">ℓ</a><a id="11587" class="Symbol">))</a> <a id="11590" class="Keyword">where</a>
|
|||
|
|
<a id="11598" class="Keyword">infixl</a> <a id="11605" class="Number">7</a> <a id="11607" href="Algebra.Bundles.html#11748" class="Field Operator">_*_</a>
|
|||
|
|
<a id="11613" class="Keyword">infixl</a> <a id="11620" class="Number">6</a> <a id="11622" href="Algebra.Bundles.html#11715" class="Field Operator">_+_</a>
|
|||
|
|
<a id="11628" class="Keyword">infix</a> <a id="11635" class="Number">4</a> <a id="11637" href="Algebra.Bundles.html#11680" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="11643" class="Keyword">field</a>
|
|||
|
|
<a id="NearSemiring.Carrier"></a><a id="11653" href="Algebra.Bundles.html#11653" class="Field">Carrier</a> <a id="11668" class="Symbol">:</a> <a id="11670" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="11674" href="Algebra.Bundles.html#11566" class="Bound">c</a>
|
|||
|
|
<a id="NearSemiring._≈_"></a><a id="11680" href="Algebra.Bundles.html#11680" class="Field Operator">_≈_</a> <a id="11695" class="Symbol">:</a> <a id="11697" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="11701" href="Algebra.Bundles.html#11653" class="Field">Carrier</a> <a id="11709" href="Algebra.Bundles.html#11568" class="Bound">ℓ</a>
|
|||
|
|
<a id="NearSemiring._+_"></a><a id="11715" href="Algebra.Bundles.html#11715" class="Field Operator">_+_</a> <a id="11730" class="Symbol">:</a> <a id="11732" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="11736" href="Algebra.Bundles.html#11653" class="Field">Carrier</a>
|
|||
|
|
<a id="NearSemiring._*_"></a><a id="11748" href="Algebra.Bundles.html#11748" class="Field Operator">_*_</a> <a id="11763" class="Symbol">:</a> <a id="11765" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="11769" href="Algebra.Bundles.html#11653" class="Field">Carrier</a>
|
|||
|
|
<a id="NearSemiring.0#"></a><a id="11781" href="Algebra.Bundles.html#11781" class="Field">0#</a> <a id="11796" class="Symbol">:</a> <a id="11798" href="Algebra.Bundles.html#11653" class="Field">Carrier</a>
|
|||
|
|
<a id="NearSemiring.isNearSemiring"></a><a id="11810" href="Algebra.Bundles.html#11810" class="Field">isNearSemiring</a> <a id="11825" class="Symbol">:</a> <a id="11827" href="Algebra.Structures.html#7859" class="Record">IsNearSemiring</a> <a id="11842" href="Algebra.Bundles.html#11680" class="Field Operator">_≈_</a> <a id="11846" href="Algebra.Bundles.html#11715" class="Field Operator">_+_</a> <a id="11850" href="Algebra.Bundles.html#11748" class="Field Operator">_*_</a> <a id="11854" href="Algebra.Bundles.html#11781" class="Field">0#</a>
|
|||
|
|
|
|||
|
|
<a id="11860" class="Keyword">open</a> <a id="11865" href="Algebra.Structures.html#7859" class="Module">IsNearSemiring</a> <a id="11880" href="Algebra.Bundles.html#11810" class="Field">isNearSemiring</a> <a id="11895" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="NearSemiring.rawNearSemiring"></a><a id="11905" href="Algebra.Bundles.html#11905" class="Function">rawNearSemiring</a> <a id="11921" class="Symbol">:</a> <a id="11923" href="Algebra.Bundles.Raw.html#2222" class="Record">RawNearSemiring</a> <a id="11939" class="Symbol">_</a> <a id="11941" class="Symbol">_</a>
|
|||
|
|
<a id="11945" href="Algebra.Bundles.html#11905" class="Function">rawNearSemiring</a> <a id="11961" class="Symbol">=</a> <a id="11963" class="Keyword">record</a>
|
|||
|
|
<a id="11974" class="Symbol">{</a> <a id="11976" href="Algebra.Bundles.Raw.html#2345" class="Field Operator">_≈_</a> <a id="11980" class="Symbol">=</a> <a id="11982" href="Algebra.Bundles.html#11680" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="11990" class="Symbol">;</a> <a id="11992" href="Algebra.Bundles.Raw.html#2373" class="Field Operator">_+_</a> <a id="11996" class="Symbol">=</a> <a id="11998" href="Algebra.Bundles.html#11715" class="Field Operator">_+_</a>
|
|||
|
|
<a id="12006" class="Symbol">;</a> <a id="12008" href="Algebra.Bundles.Raw.html#2399" class="Field Operator">_*_</a> <a id="12012" class="Symbol">=</a> <a id="12014" href="Algebra.Bundles.html#11748" class="Field Operator">_*_</a>
|
|||
|
|
<a id="12022" class="Symbol">;</a> <a id="12024" href="Algebra.Bundles.Raw.html#2425" class="Field">0#</a> <a id="12028" class="Symbol">=</a> <a id="12030" href="Algebra.Bundles.html#11781" class="Field">0#</a>
|
|||
|
|
<a id="12037" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="NearSemiring.+-monoid"></a><a id="12042" href="Algebra.Bundles.html#12042" class="Function">+-monoid</a> <a id="12051" class="Symbol">:</a> <a id="12053" href="Algebra.Bundles.html#6051" class="Record">Monoid</a> <a id="12060" class="Symbol">_</a> <a id="12062" class="Symbol">_</a>
|
|||
|
|
<a id="12066" href="Algebra.Bundles.html#12042" class="Function">+-monoid</a> <a id="12075" class="Symbol">=</a> <a id="12077" class="Keyword">record</a> <a id="12084" class="Symbol">{</a> <a id="12086" href="Algebra.Bundles.html#6230" class="Field">isMonoid</a> <a id="12095" class="Symbol">=</a> <a id="12097" href="Algebra.Structures.html#7929" class="Function">+-isMonoid</a> <a id="12108" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="12113" class="Keyword">open</a> <a id="12118" href="Algebra.Bundles.html#6051" class="Module">Monoid</a> <a id="12125" href="Algebra.Bundles.html#12042" class="Function">+-monoid</a> <a id="12134" class="Keyword">public</a>
|
|||
|
|
<a id="12145" class="Keyword">using</a> <a id="12151" class="Symbol">(</a><a id="12152" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="12155" class="Symbol">)</a> <a id="12157" class="Keyword">renaming</a>
|
|||
|
|
<a id="12170" class="Symbol">(</a> <a id="12172" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a> <a id="12184" class="Symbol">to</a> <a id="12188" class="Function">+-rawMagma</a>
|
|||
|
|
<a id="12203" class="Symbol">;</a> <a id="12205" href="Algebra.Bundles.html#4383" class="Function">magma</a> <a id="12217" class="Symbol">to</a> <a id="12221" class="Function">+-magma</a>
|
|||
|
|
<a id="12233" class="Symbol">;</a> <a id="12235" href="Algebra.Bundles.html#6296" class="Function">semigroup</a> <a id="12247" class="Symbol">to</a> <a id="12251" class="Function">+-semigroup</a>
|
|||
|
|
<a id="12267" class="Symbol">;</a> <a id="12269" href="Algebra.Bundles.html#6525" class="Function">unitalMagma</a> <a id="12281" class="Symbol">to</a> <a id="12285" class="Function">+-unitalMagma</a>
|
|||
|
|
<a id="12303" class="Symbol">;</a> <a id="12305" href="Algebra.Bundles.html#6444" class="Function">rawMonoid</a> <a id="12317" class="Symbol">to</a> <a id="12321" class="Function">+-rawMonoid</a>
|
|||
|
|
<a id="12337" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="NearSemiring.*-semigroup"></a><a id="12342" href="Algebra.Bundles.html#12342" class="Function">*-semigroup</a> <a id="12354" class="Symbol">:</a> <a id="12356" href="Algebra.Bundles.html#4139" class="Record">Semigroup</a> <a id="12366" class="Symbol">_</a> <a id="12368" class="Symbol">_</a>
|
|||
|
|
<a id="12372" href="Algebra.Bundles.html#12342" class="Function">*-semigroup</a> <a id="12384" class="Symbol">=</a> <a id="12386" class="Keyword">record</a> <a id="12393" class="Symbol">{</a> <a id="12395" href="Algebra.Bundles.html#4307" class="Field">isSemigroup</a> <a id="12407" class="Symbol">=</a> <a id="12409" href="Algebra.Structures.html#8611" class="Function">*-isSemigroup</a> <a id="12423" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="12428" class="Keyword">open</a> <a id="12433" href="Algebra.Bundles.html#4139" class="Module">Semigroup</a> <a id="12443" href="Algebra.Bundles.html#12342" class="Function">*-semigroup</a> <a id="12455" class="Keyword">public</a>
|
|||
|
|
<a id="12466" class="Keyword">using</a> <a id="12472" class="Symbol">()</a> <a id="12475" class="Keyword">renaming</a>
|
|||
|
|
<a id="12488" class="Symbol">(</a> <a id="12490" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a> <a id="12499" class="Symbol">to</a> <a id="12502" class="Function">*-rawMagma</a>
|
|||
|
|
<a id="12517" class="Symbol">;</a> <a id="12519" href="Algebra.Bundles.html#4383" class="Function">magma</a> <a id="12528" class="Symbol">to</a> <a id="12531" class="Function">*-magma</a>
|
|||
|
|
<a id="12543" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="12547" class="Keyword">record</a> <a id="SemiringWithoutOne"></a><a id="12554" href="Algebra.Bundles.html#12554" class="Record">SemiringWithoutOne</a> <a id="12573" href="Algebra.Bundles.html#12573" class="Bound">c</a> <a id="12575" href="Algebra.Bundles.html#12575" class="Bound">ℓ</a> <a id="12577" class="Symbol">:</a> <a id="12579" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="12583" class="Symbol">(</a><a id="12584" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="12588" class="Symbol">(</a><a id="12589" href="Algebra.Bundles.html#12573" class="Bound">c</a> <a id="12591" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="12593" href="Algebra.Bundles.html#12575" class="Bound">ℓ</a><a id="12594" class="Symbol">))</a> <a id="12597" class="Keyword">where</a>
|
|||
|
|
<a id="12605" class="Keyword">infixl</a> <a id="12612" class="Number">7</a> <a id="12614" href="Algebra.Bundles.html#12773" class="Field Operator">_*_</a>
|
|||
|
|
<a id="12620" class="Keyword">infixl</a> <a id="12627" class="Number">6</a> <a id="12629" href="Algebra.Bundles.html#12734" class="Field Operator">_+_</a>
|
|||
|
|
<a id="12635" class="Keyword">infix</a> <a id="12642" class="Number">4</a> <a id="12644" href="Algebra.Bundles.html#12693" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="12650" class="Keyword">field</a>
|
|||
|
|
<a id="SemiringWithoutOne.Carrier"></a><a id="12660" href="Algebra.Bundles.html#12660" class="Field">Carrier</a> <a id="12681" class="Symbol">:</a> <a id="12683" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="12687" href="Algebra.Bundles.html#12573" class="Bound">c</a>
|
|||
|
|
<a id="SemiringWithoutOne._≈_"></a><a id="12693" href="Algebra.Bundles.html#12693" class="Field Operator">_≈_</a> <a id="12714" class="Symbol">:</a> <a id="12716" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="12720" href="Algebra.Bundles.html#12660" class="Field">Carrier</a> <a id="12728" href="Algebra.Bundles.html#12575" class="Bound">ℓ</a>
|
|||
|
|
<a id="SemiringWithoutOne._+_"></a><a id="12734" href="Algebra.Bundles.html#12734" class="Field Operator">_+_</a> <a id="12755" class="Symbol">:</a> <a id="12757" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="12761" href="Algebra.Bundles.html#12660" class="Field">Carrier</a>
|
|||
|
|
<a id="SemiringWithoutOne._*_"></a><a id="12773" href="Algebra.Bundles.html#12773" class="Field Operator">_*_</a> <a id="12794" class="Symbol">:</a> <a id="12796" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="12800" href="Algebra.Bundles.html#12660" class="Field">Carrier</a>
|
|||
|
|
<a id="SemiringWithoutOne.0#"></a><a id="12812" href="Algebra.Bundles.html#12812" class="Field">0#</a> <a id="12833" class="Symbol">:</a> <a id="12835" href="Algebra.Bundles.html#12660" class="Field">Carrier</a>
|
|||
|
|
<a id="SemiringWithoutOne.isSemiringWithoutOne"></a><a id="12847" href="Algebra.Bundles.html#12847" class="Field">isSemiringWithoutOne</a> <a id="12868" class="Symbol">:</a> <a id="12870" href="Algebra.Structures.html#8848" class="Record">IsSemiringWithoutOne</a> <a id="12891" href="Algebra.Bundles.html#12693" class="Field Operator">_≈_</a> <a id="12895" href="Algebra.Bundles.html#12734" class="Field Operator">_+_</a> <a id="12899" href="Algebra.Bundles.html#12773" class="Field Operator">_*_</a> <a id="12903" href="Algebra.Bundles.html#12812" class="Field">0#</a>
|
|||
|
|
|
|||
|
|
<a id="12909" class="Keyword">open</a> <a id="12914" href="Algebra.Structures.html#8848" class="Module">IsSemiringWithoutOne</a> <a id="12935" href="Algebra.Bundles.html#12847" class="Field">isSemiringWithoutOne</a> <a id="12956" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="SemiringWithoutOne.nearSemiring"></a><a id="12966" href="Algebra.Bundles.html#12966" class="Function">nearSemiring</a> <a id="12979" class="Symbol">:</a> <a id="12981" href="Algebra.Bundles.html#11553" class="Record">NearSemiring</a> <a id="12994" class="Symbol">_</a> <a id="12996" class="Symbol">_</a>
|
|||
|
|
<a id="13000" href="Algebra.Bundles.html#12966" class="Function">nearSemiring</a> <a id="13013" class="Symbol">=</a> <a id="13015" class="Keyword">record</a> <a id="13022" class="Symbol">{</a> <a id="13024" href="Algebra.Bundles.html#11810" class="Field">isNearSemiring</a> <a id="13039" class="Symbol">=</a> <a id="13041" href="Algebra.Structures.html#9900" class="Function">isNearSemiring</a> <a id="13056" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="13061" class="Keyword">open</a> <a id="13066" href="Algebra.Bundles.html#11553" class="Module">NearSemiring</a> <a id="13079" href="Algebra.Bundles.html#12966" class="Function">nearSemiring</a> <a id="13092" class="Keyword">public</a>
|
|||
|
|
<a id="13103" class="Keyword">using</a>
|
|||
|
|
<a id="13113" class="Symbol">(</a> <a id="13115" href="Algebra.Bundles.html#12188" class="Function">+-rawMagma</a><a id="13125" class="Symbol">;</a> <a id="13127" href="Algebra.Bundles.html#12221" class="Function">+-magma</a><a id="13134" class="Symbol">;</a> <a id="13136" href="Algebra.Bundles.html#12285" class="Function">+-unitalMagma</a><a id="13149" class="Symbol">;</a> <a id="13151" href="Algebra.Bundles.html#12251" class="Function">+-semigroup</a>
|
|||
|
|
<a id="13167" class="Symbol">;</a> <a id="13169" href="Algebra.Bundles.html#12321" class="Function">+-rawMonoid</a><a id="13180" class="Symbol">;</a> <a id="13182" href="Algebra.Bundles.html#12042" class="Function">+-monoid</a>
|
|||
|
|
<a id="13195" class="Symbol">;</a> <a id="13197" href="Algebra.Bundles.html#12502" class="Function">*-rawMagma</a><a id="13207" class="Symbol">;</a> <a id="13209" href="Algebra.Bundles.html#12531" class="Function">*-magma</a><a id="13216" class="Symbol">;</a> <a id="13218" href="Algebra.Bundles.html#12342" class="Function">*-semigroup</a>
|
|||
|
|
<a id="13234" class="Symbol">;</a> <a id="13236" href="Algebra.Bundles.html#11905" class="Function">rawNearSemiring</a>
|
|||
|
|
<a id="13256" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="SemiringWithoutOne.+-commutativeMonoid"></a><a id="13261" href="Algebra.Bundles.html#13261" class="Function">+-commutativeMonoid</a> <a id="13281" class="Symbol">:</a> <a id="13283" href="Algebra.Bundles.html#6622" class="Record">CommutativeMonoid</a> <a id="13301" class="Symbol">_</a> <a id="13303" class="Symbol">_</a>
|
|||
|
|
<a id="13307" href="Algebra.Bundles.html#13261" class="Function">+-commutativeMonoid</a> <a id="13327" class="Symbol">=</a> <a id="13329" class="Keyword">record</a> <a id="13336" class="Symbol">{</a> <a id="13338" href="Algebra.Bundles.html#6856" class="Field">isCommutativeMonoid</a> <a id="13358" class="Symbol">=</a> <a id="13360" href="Algebra.Structures.html#8924" class="Function">+-isCommutativeMonoid</a> <a id="13382" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="13387" class="Keyword">open</a> <a id="13392" href="Algebra.Bundles.html#6622" class="Module">CommutativeMonoid</a> <a id="13410" href="Algebra.Bundles.html#13261" class="Function">+-commutativeMonoid</a> <a id="13430" class="Keyword">public</a>
|
|||
|
|
<a id="13441" class="Keyword">using</a> <a id="13447" class="Symbol">()</a> <a id="13450" class="Keyword">renaming</a>
|
|||
|
|
<a id="13463" class="Symbol">(</a> <a id="13465" href="Algebra.Bundles.html#5348" class="Function">commutativeMagma</a> <a id="13486" class="Symbol">to</a> <a id="13489" class="Function">+-commutativeMagma</a>
|
|||
|
|
<a id="13512" class="Symbol">;</a> <a id="13514" href="Algebra.Bundles.html#7128" class="Function">commutativeSemigroup</a> <a id="13535" class="Symbol">to</a> <a id="13538" class="Function">+-commutativeSemigroup</a>
|
|||
|
|
<a id="13565" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="13569" class="Keyword">record</a> <a id="CommutativeSemiringWithoutOne"></a><a id="13576" href="Algebra.Bundles.html#13576" class="Record">CommutativeSemiringWithoutOne</a> <a id="13606" href="Algebra.Bundles.html#13606" class="Bound">c</a> <a id="13608" href="Algebra.Bundles.html#13608" class="Bound">ℓ</a> <a id="13610" class="Symbol">:</a> <a id="13612" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="13616" class="Symbol">(</a><a id="13617" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="13621" class="Symbol">(</a><a id="13622" href="Algebra.Bundles.html#13606" class="Bound">c</a> <a id="13624" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="13626" href="Algebra.Bundles.html#13608" class="Bound">ℓ</a><a id="13627" class="Symbol">))</a> <a id="13630" class="Keyword">where</a>
|
|||
|
|
<a id="13638" class="Keyword">infixl</a> <a id="13645" class="Number">7</a> <a id="13647" href="Algebra.Bundles.html#13839" class="Field Operator">_*_</a>
|
|||
|
|
<a id="13653" class="Keyword">infixl</a> <a id="13660" class="Number">6</a> <a id="13662" href="Algebra.Bundles.html#13789" class="Field Operator">_+_</a>
|
|||
|
|
<a id="13668" class="Keyword">infix</a> <a id="13675" class="Number">4</a> <a id="13677" href="Algebra.Bundles.html#13737" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="13683" class="Keyword">field</a>
|
|||
|
|
<a id="CommutativeSemiringWithoutOne.Carrier"></a><a id="13693" href="Algebra.Bundles.html#13693" class="Field">Carrier</a> <a id="13725" class="Symbol">:</a> <a id="13727" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="13731" href="Algebra.Bundles.html#13606" class="Bound">c</a>
|
|||
|
|
<a id="CommutativeSemiringWithoutOne._≈_"></a><a id="13737" href="Algebra.Bundles.html#13737" class="Field Operator">_≈_</a> <a id="13769" class="Symbol">:</a> <a id="13771" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="13775" href="Algebra.Bundles.html#13693" class="Field">Carrier</a> <a id="13783" href="Algebra.Bundles.html#13608" class="Bound">ℓ</a>
|
|||
|
|
<a id="CommutativeSemiringWithoutOne._+_"></a><a id="13789" href="Algebra.Bundles.html#13789" class="Field Operator">_+_</a> <a id="13821" class="Symbol">:</a> <a id="13823" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="13827" href="Algebra.Bundles.html#13693" class="Field">Carrier</a>
|
|||
|
|
<a id="CommutativeSemiringWithoutOne._*_"></a><a id="13839" href="Algebra.Bundles.html#13839" class="Field Operator">_*_</a> <a id="13871" class="Symbol">:</a> <a id="13873" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="13877" href="Algebra.Bundles.html#13693" class="Field">Carrier</a>
|
|||
|
|
<a id="CommutativeSemiringWithoutOne.0#"></a><a id="13889" href="Algebra.Bundles.html#13889" class="Field">0#</a> <a id="13921" class="Symbol">:</a> <a id="13923" href="Algebra.Bundles.html#13693" class="Field">Carrier</a>
|
|||
|
|
<a id="CommutativeSemiringWithoutOne.isCommutativeSemiringWithoutOne"></a><a id="13935" href="Algebra.Bundles.html#13935" class="Field">isCommutativeSemiringWithoutOne</a> <a id="13967" class="Symbol">:</a>
|
|||
|
|
<a id="13975" href="Algebra.Structures.html#10135" class="Record">IsCommutativeSemiringWithoutOne</a> <a id="14007" href="Algebra.Bundles.html#13737" class="Field Operator">_≈_</a> <a id="14011" href="Algebra.Bundles.html#13789" class="Field Operator">_+_</a> <a id="14015" href="Algebra.Bundles.html#13839" class="Field Operator">_*_</a> <a id="14019" href="Algebra.Bundles.html#13889" class="Field">0#</a>
|
|||
|
|
|
|||
|
|
<a id="14025" class="Keyword">open</a> <a id="14030" href="Algebra.Structures.html#10135" class="Module">IsCommutativeSemiringWithoutOne</a>
|
|||
|
|
<a id="14071" href="Algebra.Bundles.html#13935" class="Field">isCommutativeSemiringWithoutOne</a> <a id="14103" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="CommutativeSemiringWithoutOne.semiringWithoutOne"></a><a id="14113" href="Algebra.Bundles.html#14113" class="Function">semiringWithoutOne</a> <a id="14132" class="Symbol">:</a> <a id="14134" href="Algebra.Bundles.html#12554" class="Record">SemiringWithoutOne</a> <a id="14153" class="Symbol">_</a> <a id="14155" class="Symbol">_</a>
|
|||
|
|
<a id="14159" href="Algebra.Bundles.html#14113" class="Function">semiringWithoutOne</a> <a id="14178" class="Symbol">=</a>
|
|||
|
|
<a id="14184" class="Keyword">record</a> <a id="14191" class="Symbol">{</a> <a id="14193" href="Algebra.Bundles.html#12847" class="Field">isSemiringWithoutOne</a> <a id="14214" class="Symbol">=</a> <a id="14216" href="Algebra.Structures.html#10231" class="Function">isSemiringWithoutOne</a> <a id="14237" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="14242" class="Keyword">open</a> <a id="14247" href="Algebra.Bundles.html#12554" class="Module">SemiringWithoutOne</a> <a id="14266" href="Algebra.Bundles.html#14113" class="Function">semiringWithoutOne</a> <a id="14285" class="Keyword">public</a>
|
|||
|
|
<a id="14296" class="Keyword">using</a>
|
|||
|
|
<a id="14306" class="Symbol">(</a> <a id="14308" href="Algebra.Bundles.html#12188" class="Function">+-rawMagma</a><a id="14318" class="Symbol">;</a> <a id="14320" href="Algebra.Bundles.html#12221" class="Function">+-magma</a><a id="14327" class="Symbol">;</a> <a id="14329" href="Algebra.Bundles.html#12285" class="Function">+-unitalMagma</a><a id="14342" class="Symbol">;</a> <a id="14344" href="Algebra.Bundles.html#12251" class="Function">+-semigroup</a><a id="14355" class="Symbol">;</a> <a id="14357" href="Algebra.Bundles.html#13538" class="Function">+-commutativeSemigroup</a>
|
|||
|
|
<a id="14384" class="Symbol">;</a> <a id="14386" href="Algebra.Bundles.html#12502" class="Function">*-rawMagma</a><a id="14396" class="Symbol">;</a> <a id="14398" href="Algebra.Bundles.html#12531" class="Function">*-magma</a><a id="14405" class="Symbol">;</a> <a id="14407" href="Algebra.Bundles.html#12342" class="Function">*-semigroup</a>
|
|||
|
|
<a id="14423" class="Symbol">;</a> <a id="14425" href="Algebra.Bundles.html#12321" class="Function">+-rawMonoid</a><a id="14436" class="Symbol">;</a> <a id="14438" href="Algebra.Bundles.html#12042" class="Function">+-monoid</a><a id="14446" class="Symbol">;</a> <a id="14448" href="Algebra.Bundles.html#13261" class="Function">+-commutativeMonoid</a>
|
|||
|
|
<a id="14472" class="Symbol">;</a> <a id="14474" href="Algebra.Bundles.html#12966" class="Function">nearSemiring</a><a id="14486" class="Symbol">;</a> <a id="14488" href="Algebra.Bundles.html#11905" class="Function">rawNearSemiring</a>
|
|||
|
|
<a id="14508" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="14511" class="Comment">------------------------------------------------------------------------</a>
|
|||
|
|
<a id="14584" class="Comment">-- Bundles with 2 binary operations & 2 elements</a>
|
|||
|
|
<a id="14633" class="Comment">------------------------------------------------------------------------</a>
|
|||
|
|
|
|||
|
|
<a id="14707" class="Keyword">record</a> <a id="SemiringWithoutAnnihilatingZero"></a><a id="14714" href="Algebra.Bundles.html#14714" class="Record">SemiringWithoutAnnihilatingZero</a> <a id="14746" href="Algebra.Bundles.html#14746" class="Bound">c</a> <a id="14748" href="Algebra.Bundles.html#14748" class="Bound">ℓ</a> <a id="14750" class="Symbol">:</a> <a id="14752" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="14756" class="Symbol">(</a><a id="14757" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="14761" class="Symbol">(</a><a id="14762" href="Algebra.Bundles.html#14746" class="Bound">c</a> <a id="14764" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="14766" href="Algebra.Bundles.html#14748" class="Bound">ℓ</a><a id="14767" class="Symbol">))</a> <a id="14770" class="Keyword">where</a>
|
|||
|
|
<a id="14778" class="Keyword">infixl</a> <a id="14785" class="Number">7</a> <a id="14787" href="Algebra.Bundles.html#14985" class="Field Operator">_*_</a>
|
|||
|
|
<a id="14793" class="Keyword">infixl</a> <a id="14800" class="Number">6</a> <a id="14802" href="Algebra.Bundles.html#14933" class="Field Operator">_+_</a>
|
|||
|
|
<a id="14808" class="Keyword">infix</a> <a id="14815" class="Number">4</a> <a id="14817" href="Algebra.Bundles.html#14879" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="14823" class="Keyword">field</a>
|
|||
|
|
<a id="SemiringWithoutAnnihilatingZero.Carrier"></a><a id="14833" href="Algebra.Bundles.html#14833" class="Field">Carrier</a> <a id="14867" class="Symbol">:</a> <a id="14869" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="14873" href="Algebra.Bundles.html#14746" class="Bound">c</a>
|
|||
|
|
<a id="SemiringWithoutAnnihilatingZero._≈_"></a><a id="14879" href="Algebra.Bundles.html#14879" class="Field Operator">_≈_</a> <a id="14913" class="Symbol">:</a> <a id="14915" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="14919" href="Algebra.Bundles.html#14833" class="Field">Carrier</a> <a id="14927" href="Algebra.Bundles.html#14748" class="Bound">ℓ</a>
|
|||
|
|
<a id="SemiringWithoutAnnihilatingZero._+_"></a><a id="14933" href="Algebra.Bundles.html#14933" class="Field Operator">_+_</a> <a id="14967" class="Symbol">:</a> <a id="14969" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="14973" href="Algebra.Bundles.html#14833" class="Field">Carrier</a>
|
|||
|
|
<a id="SemiringWithoutAnnihilatingZero._*_"></a><a id="14985" href="Algebra.Bundles.html#14985" class="Field Operator">_*_</a> <a id="15019" class="Symbol">:</a> <a id="15021" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="15025" href="Algebra.Bundles.html#14833" class="Field">Carrier</a>
|
|||
|
|
<a id="SemiringWithoutAnnihilatingZero.0#"></a><a id="15037" href="Algebra.Bundles.html#15037" class="Field">0#</a> <a id="15071" class="Symbol">:</a> <a id="15073" href="Algebra.Bundles.html#14833" class="Field">Carrier</a>
|
|||
|
|
<a id="SemiringWithoutAnnihilatingZero.1#"></a><a id="15085" href="Algebra.Bundles.html#15085" class="Field">1#</a> <a id="15119" class="Symbol">:</a> <a id="15121" href="Algebra.Bundles.html#14833" class="Field">Carrier</a>
|
|||
|
|
<a id="SemiringWithoutAnnihilatingZero.isSemiringWithoutAnnihilatingZero"></a><a id="15133" href="Algebra.Bundles.html#15133" class="Field">isSemiringWithoutAnnihilatingZero</a> <a id="15167" class="Symbol">:</a>
|
|||
|
|
<a id="15175" href="Algebra.Structures.html#10875" class="Record">IsSemiringWithoutAnnihilatingZero</a> <a id="15209" href="Algebra.Bundles.html#14879" class="Field Operator">_≈_</a> <a id="15213" href="Algebra.Bundles.html#14933" class="Field Operator">_+_</a> <a id="15217" href="Algebra.Bundles.html#14985" class="Field Operator">_*_</a> <a id="15221" href="Algebra.Bundles.html#15037" class="Field">0#</a> <a id="15224" href="Algebra.Bundles.html#15085" class="Field">1#</a>
|
|||
|
|
|
|||
|
|
<a id="15230" class="Keyword">open</a> <a id="15235" href="Algebra.Structures.html#10875" class="Module">IsSemiringWithoutAnnihilatingZero</a>
|
|||
|
|
<a id="15278" href="Algebra.Bundles.html#15133" class="Field">isSemiringWithoutAnnihilatingZero</a> <a id="15312" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="SemiringWithoutAnnihilatingZero.rawSemiring"></a><a id="15322" href="Algebra.Bundles.html#15322" class="Function">rawSemiring</a> <a id="15334" class="Symbol">:</a> <a id="15336" href="Algebra.Bundles.Raw.html#2934" class="Record">RawSemiring</a> <a id="15348" href="Algebra.Bundles.html#14746" class="Bound">c</a> <a id="15350" href="Algebra.Bundles.html#14748" class="Bound">ℓ</a>
|
|||
|
|
<a id="15354" href="Algebra.Bundles.html#15322" class="Function">rawSemiring</a> <a id="15366" class="Symbol">=</a> <a id="15368" class="Keyword">record</a>
|
|||
|
|
<a id="15379" class="Symbol">{</a> <a id="15381" href="Algebra.Bundles.Raw.html#3053" class="Field Operator">_≈_</a> <a id="15385" class="Symbol">=</a> <a id="15387" href="Algebra.Bundles.html#14879" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="15395" class="Symbol">;</a> <a id="15397" href="Algebra.Bundles.Raw.html#3081" class="Field Operator">_+_</a> <a id="15401" class="Symbol">=</a> <a id="15403" href="Algebra.Bundles.html#14933" class="Field Operator">_+_</a>
|
|||
|
|
<a id="15411" class="Symbol">;</a> <a id="15413" href="Algebra.Bundles.Raw.html#3107" class="Field Operator">_*_</a> <a id="15417" class="Symbol">=</a> <a id="15419" href="Algebra.Bundles.html#14985" class="Field Operator">_*_</a>
|
|||
|
|
<a id="15427" class="Symbol">;</a> <a id="15429" href="Algebra.Bundles.Raw.html#3133" class="Field">0#</a> <a id="15433" class="Symbol">=</a> <a id="15435" href="Algebra.Bundles.html#15037" class="Field">0#</a>
|
|||
|
|
<a id="15442" class="Symbol">;</a> <a id="15444" href="Algebra.Bundles.Raw.html#3155" class="Field">1#</a> <a id="15448" class="Symbol">=</a> <a id="15450" href="Algebra.Bundles.html#15085" class="Field">1#</a>
|
|||
|
|
<a id="15457" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="15462" class="Keyword">open</a> <a id="15467" href="Algebra.Bundles.Raw.html#2934" class="Module">RawSemiring</a> <a id="15479" href="Algebra.Bundles.html#15322" class="Function">rawSemiring</a> <a id="15491" class="Keyword">public</a>
|
|||
|
|
<a id="15502" class="Keyword">using</a> <a id="15508" class="Symbol">(</a><a id="15509" href="Algebra.Bundles.Raw.html#3176" class="Function">rawNearSemiring</a><a id="15524" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="SemiringWithoutAnnihilatingZero.+-commutativeMonoid"></a><a id="15529" href="Algebra.Bundles.html#15529" class="Function">+-commutativeMonoid</a> <a id="15549" class="Symbol">:</a> <a id="15551" href="Algebra.Bundles.html#6622" class="Record">CommutativeMonoid</a> <a id="15569" class="Symbol">_</a> <a id="15571" class="Symbol">_</a>
|
|||
|
|
<a id="15575" href="Algebra.Bundles.html#15529" class="Function">+-commutativeMonoid</a> <a id="15595" class="Symbol">=</a>
|
|||
|
|
<a id="15601" class="Keyword">record</a> <a id="15608" class="Symbol">{</a> <a id="15610" href="Algebra.Bundles.html#6856" class="Field">isCommutativeMonoid</a> <a id="15630" class="Symbol">=</a> <a id="15632" href="Algebra.Structures.html#11137" class="Function">+-isCommutativeMonoid</a> <a id="15654" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="15659" class="Keyword">open</a> <a id="15664" href="Algebra.Bundles.html#6622" class="Module">CommutativeMonoid</a> <a id="15682" href="Algebra.Bundles.html#15529" class="Function">+-commutativeMonoid</a> <a id="15702" class="Keyword">public</a>
|
|||
|
|
<a id="15713" class="Keyword">using</a> <a id="15719" class="Symbol">(</a><a id="15720" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="15723" class="Symbol">)</a> <a id="15725" class="Keyword">renaming</a>
|
|||
|
|
<a id="15738" class="Symbol">(</a> <a id="15740" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a> <a id="15761" class="Symbol">to</a> <a id="15764" class="Function">+-rawMagma</a>
|
|||
|
|
<a id="15779" class="Symbol">;</a> <a id="15781" href="Algebra.Bundles.html#4383" class="Function">magma</a> <a id="15802" class="Symbol">to</a> <a id="15805" class="Function">+-magma</a>
|
|||
|
|
<a id="15817" class="Symbol">;</a> <a id="15819" href="Algebra.Bundles.html#6525" class="Function">unitalMagma</a> <a id="15840" class="Symbol">to</a> <a id="15843" class="Function">+-unitalMagma</a>
|
|||
|
|
<a id="15861" class="Symbol">;</a> <a id="15863" href="Algebra.Bundles.html#5348" class="Function">commutativeMagma</a> <a id="15884" class="Symbol">to</a> <a id="15887" class="Function">+-commutativeMagma</a>
|
|||
|
|
<a id="15910" class="Symbol">;</a> <a id="15912" href="Algebra.Bundles.html#6296" class="Function">semigroup</a> <a id="15933" class="Symbol">to</a> <a id="15936" class="Function">+-semigroup</a>
|
|||
|
|
<a id="15952" class="Symbol">;</a> <a id="15954" href="Algebra.Bundles.html#7128" class="Function">commutativeSemigroup</a> <a id="15975" class="Symbol">to</a> <a id="15978" class="Function">+-commutativeSemigroup</a>
|
|||
|
|
<a id="16005" class="Symbol">;</a> <a id="16007" href="Algebra.Bundles.html#6444" class="Function">rawMonoid</a> <a id="16028" class="Symbol">to</a> <a id="16031" class="Function">+-rawMonoid</a>
|
|||
|
|
<a id="16047" class="Symbol">;</a> <a id="16049" href="Algebra.Bundles.html#6966" class="Function">monoid</a> <a id="16070" class="Symbol">to</a> <a id="16073" class="Function">+-monoid</a>
|
|||
|
|
<a id="16086" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="SemiringWithoutAnnihilatingZero.*-monoid"></a><a id="16091" href="Algebra.Bundles.html#16091" class="Function">*-monoid</a> <a id="16100" class="Symbol">:</a> <a id="16102" href="Algebra.Bundles.html#6051" class="Record">Monoid</a> <a id="16109" class="Symbol">_</a> <a id="16111" class="Symbol">_</a>
|
|||
|
|
<a id="16115" href="Algebra.Bundles.html#16091" class="Function">*-monoid</a> <a id="16124" class="Symbol">=</a> <a id="16126" class="Keyword">record</a> <a id="16133" class="Symbol">{</a> <a id="16135" href="Algebra.Bundles.html#6230" class="Field">isMonoid</a> <a id="16144" class="Symbol">=</a> <a id="16146" href="Algebra.Structures.html#12411" class="Function">*-isMonoid</a> <a id="16157" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="16162" class="Keyword">open</a> <a id="16167" href="Algebra.Bundles.html#6051" class="Module">Monoid</a> <a id="16174" href="Algebra.Bundles.html#16091" class="Function">*-monoid</a> <a id="16183" class="Keyword">public</a>
|
|||
|
|
<a id="16194" class="Keyword">using</a> <a id="16200" class="Symbol">()</a> <a id="16203" class="Keyword">renaming</a>
|
|||
|
|
<a id="16216" class="Symbol">(</a> <a id="16218" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a> <a id="16228" class="Symbol">to</a> <a id="16231" class="Function">*-rawMagma</a>
|
|||
|
|
<a id="16246" class="Symbol">;</a> <a id="16248" href="Algebra.Bundles.html#4383" class="Function">magma</a> <a id="16258" class="Symbol">to</a> <a id="16261" class="Function">*-magma</a>
|
|||
|
|
<a id="16273" class="Symbol">;</a> <a id="16275" href="Algebra.Bundles.html#6296" class="Function">semigroup</a> <a id="16285" class="Symbol">to</a> <a id="16288" class="Function">*-semigroup</a>
|
|||
|
|
<a id="16304" class="Symbol">;</a> <a id="16306" href="Algebra.Bundles.html#6444" class="Function">rawMonoid</a> <a id="16316" class="Symbol">to</a> <a id="16319" class="Function">*-rawMonoid</a>
|
|||
|
|
<a id="16335" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="16339" class="Keyword">record</a> <a id="Semiring"></a><a id="16346" href="Algebra.Bundles.html#16346" class="Record">Semiring</a> <a id="16355" href="Algebra.Bundles.html#16355" class="Bound">c</a> <a id="16357" href="Algebra.Bundles.html#16357" class="Bound">ℓ</a> <a id="16359" class="Symbol">:</a> <a id="16361" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="16365" class="Symbol">(</a><a id="16366" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="16370" class="Symbol">(</a><a id="16371" href="Algebra.Bundles.html#16355" class="Bound">c</a> <a id="16373" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="16375" href="Algebra.Bundles.html#16357" class="Bound">ℓ</a><a id="16376" class="Symbol">))</a> <a id="16379" class="Keyword">where</a>
|
|||
|
|
<a id="16387" class="Keyword">infixl</a> <a id="16394" class="Number">7</a> <a id="16396" href="Algebra.Bundles.html#16525" class="Field Operator">_*_</a>
|
|||
|
|
<a id="16402" class="Keyword">infixl</a> <a id="16409" class="Number">6</a> <a id="16411" href="Algebra.Bundles.html#16496" class="Field Operator">_+_</a>
|
|||
|
|
<a id="16417" class="Keyword">infix</a> <a id="16424" class="Number">4</a> <a id="16426" href="Algebra.Bundles.html#16465" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="16432" class="Keyword">field</a>
|
|||
|
|
<a id="Semiring.Carrier"></a><a id="16442" href="Algebra.Bundles.html#16442" class="Field">Carrier</a> <a id="16453" class="Symbol">:</a> <a id="16455" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="16459" href="Algebra.Bundles.html#16355" class="Bound">c</a>
|
|||
|
|
<a id="Semiring._≈_"></a><a id="16465" href="Algebra.Bundles.html#16465" class="Field Operator">_≈_</a> <a id="16476" class="Symbol">:</a> <a id="16478" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="16482" href="Algebra.Bundles.html#16442" class="Field">Carrier</a> <a id="16490" href="Algebra.Bundles.html#16357" class="Bound">ℓ</a>
|
|||
|
|
<a id="Semiring._+_"></a><a id="16496" href="Algebra.Bundles.html#16496" class="Field Operator">_+_</a> <a id="16507" class="Symbol">:</a> <a id="16509" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="16513" href="Algebra.Bundles.html#16442" class="Field">Carrier</a>
|
|||
|
|
<a id="Semiring._*_"></a><a id="16525" href="Algebra.Bundles.html#16525" class="Field Operator">_*_</a> <a id="16536" class="Symbol">:</a> <a id="16538" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="16542" href="Algebra.Bundles.html#16442" class="Field">Carrier</a>
|
|||
|
|
<a id="Semiring.0#"></a><a id="16554" href="Algebra.Bundles.html#16554" class="Field">0#</a> <a id="16565" class="Symbol">:</a> <a id="16567" href="Algebra.Bundles.html#16442" class="Field">Carrier</a>
|
|||
|
|
<a id="Semiring.1#"></a><a id="16579" href="Algebra.Bundles.html#16579" class="Field">1#</a> <a id="16590" class="Symbol">:</a> <a id="16592" href="Algebra.Bundles.html#16442" class="Field">Carrier</a>
|
|||
|
|
<a id="Semiring.isSemiring"></a><a id="16604" href="Algebra.Bundles.html#16604" class="Field">isSemiring</a> <a id="16615" class="Symbol">:</a> <a id="16617" href="Algebra.Structures.html#12731" class="Record">IsSemiring</a> <a id="16628" href="Algebra.Bundles.html#16465" class="Field Operator">_≈_</a> <a id="16632" href="Algebra.Bundles.html#16496" class="Field Operator">_+_</a> <a id="16636" href="Algebra.Bundles.html#16525" class="Field Operator">_*_</a> <a id="16640" href="Algebra.Bundles.html#16554" class="Field">0#</a> <a id="16643" href="Algebra.Bundles.html#16579" class="Field">1#</a>
|
|||
|
|
|
|||
|
|
<a id="16649" class="Keyword">open</a> <a id="16654" href="Algebra.Structures.html#12731" class="Module">IsSemiring</a> <a id="16665" href="Algebra.Bundles.html#16604" class="Field">isSemiring</a> <a id="16676" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="Semiring.semiringWithoutAnnihilatingZero"></a><a id="16686" href="Algebra.Bundles.html#16686" class="Function">semiringWithoutAnnihilatingZero</a> <a id="16718" class="Symbol">:</a> <a id="16720" href="Algebra.Bundles.html#14714" class="Record">SemiringWithoutAnnihilatingZero</a> <a id="16752" class="Symbol">_</a> <a id="16754" class="Symbol">_</a>
|
|||
|
|
<a id="16758" href="Algebra.Bundles.html#16686" class="Function">semiringWithoutAnnihilatingZero</a> <a id="16790" class="Symbol">=</a> <a id="16792" class="Keyword">record</a>
|
|||
|
|
<a id="16803" class="Symbol">{</a> <a id="16805" href="Algebra.Bundles.html#15133" class="Field">isSemiringWithoutAnnihilatingZero</a> <a id="16839" class="Symbol">=</a>
|
|||
|
|
<a id="16849" href="Algebra.Structures.html#12800" class="Function">isSemiringWithoutAnnihilatingZero</a>
|
|||
|
|
<a id="16887" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="16892" class="Keyword">open</a> <a id="16897" href="Algebra.Bundles.html#14714" class="Module">SemiringWithoutAnnihilatingZero</a>
|
|||
|
|
<a id="16938" href="Algebra.Bundles.html#16686" class="Function">semiringWithoutAnnihilatingZero</a> <a id="16970" class="Keyword">public</a>
|
|||
|
|
<a id="16981" class="Keyword">using</a>
|
|||
|
|
<a id="16991" class="Symbol">(</a> <a id="16993" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="16996" class="Symbol">;</a> <a id="16998" href="Algebra.Bundles.html#15764" class="Function">+-rawMagma</a><a id="17008" class="Symbol">;</a> <a id="17010" href="Algebra.Bundles.html#15805" class="Function">+-magma</a><a id="17017" class="Symbol">;</a> <a id="17019" href="Algebra.Bundles.html#15843" class="Function">+-unitalMagma</a><a id="17032" class="Symbol">;</a> <a id="17034" href="Algebra.Bundles.html#15887" class="Function">+-commutativeMagma</a>
|
|||
|
|
<a id="17057" class="Symbol">;</a> <a id="17059" href="Algebra.Bundles.html#15936" class="Function">+-semigroup</a><a id="17070" class="Symbol">;</a> <a id="17072" href="Algebra.Bundles.html#15978" class="Function">+-commutativeSemigroup</a>
|
|||
|
|
<a id="17099" class="Symbol">;</a> <a id="17101" href="Algebra.Bundles.html#16231" class="Function">*-rawMagma</a><a id="17111" class="Symbol">;</a> <a id="17114" href="Algebra.Bundles.html#16261" class="Function">*-magma</a><a id="17121" class="Symbol">;</a> <a id="17124" href="Algebra.Bundles.html#16288" class="Function">*-semigroup</a>
|
|||
|
|
<a id="17140" class="Symbol">;</a> <a id="17142" href="Algebra.Bundles.html#16031" class="Function">+-rawMonoid</a><a id="17153" class="Symbol">;</a> <a id="17155" href="Algebra.Bundles.html#16073" class="Function">+-monoid</a><a id="17163" class="Symbol">;</a> <a id="17165" href="Algebra.Bundles.html#15529" class="Function">+-commutativeMonoid</a>
|
|||
|
|
<a id="17189" class="Symbol">;</a> <a id="17191" href="Algebra.Bundles.html#16319" class="Function">*-rawMonoid</a><a id="17202" class="Symbol">;</a> <a id="17204" href="Algebra.Bundles.html#16091" class="Function">*-monoid</a>
|
|||
|
|
<a id="17217" class="Symbol">;</a> <a id="17219" href="Algebra.Bundles.Raw.html#3176" class="Function">rawNearSemiring</a> <a id="17235" class="Symbol">;</a> <a id="17237" href="Algebra.Bundles.html#15322" class="Function">rawSemiring</a>
|
|||
|
|
<a id="17253" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="Semiring.semiringWithoutOne"></a><a id="17258" href="Algebra.Bundles.html#17258" class="Function">semiringWithoutOne</a> <a id="17277" class="Symbol">:</a> <a id="17279" href="Algebra.Bundles.html#12554" class="Record">SemiringWithoutOne</a> <a id="17298" class="Symbol">_</a> <a id="17300" class="Symbol">_</a>
|
|||
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|
<a id="17304" href="Algebra.Bundles.html#17258" class="Function">semiringWithoutOne</a> <a id="17323" class="Symbol">=</a>
|
|||
|
|
<a id="17329" class="Keyword">record</a> <a id="17336" class="Symbol">{</a> <a id="17338" href="Algebra.Bundles.html#12847" class="Field">isSemiringWithoutOne</a> <a id="17359" class="Symbol">=</a> <a id="17361" href="Algebra.Structures.html#13002" class="Function">isSemiringWithoutOne</a> <a id="17382" class="Symbol">}</a>
|
|||
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|
|||
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<a id="17387" class="Keyword">open</a> <a id="17392" href="Algebra.Bundles.html#12554" class="Module">SemiringWithoutOne</a> <a id="17411" href="Algebra.Bundles.html#17258" class="Function">semiringWithoutOne</a> <a id="17430" class="Keyword">public</a>
|
|||
|
|
<a id="17441" class="Keyword">using</a> <a id="17447" class="Symbol">(</a><a id="17448" href="Algebra.Bundles.html#12966" class="Function">nearSemiring</a><a id="17460" class="Symbol">)</a>
|
|||
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|||
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|||
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<a id="17464" class="Keyword">record</a> <a id="CommutativeSemiring"></a><a id="17471" href="Algebra.Bundles.html#17471" class="Record">CommutativeSemiring</a> <a id="17491" href="Algebra.Bundles.html#17491" class="Bound">c</a> <a id="17493" href="Algebra.Bundles.html#17493" class="Bound">ℓ</a> <a id="17495" class="Symbol">:</a> <a id="17497" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="17501" class="Symbol">(</a><a id="17502" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="17506" class="Symbol">(</a><a id="17507" href="Algebra.Bundles.html#17491" class="Bound">c</a> <a id="17509" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="17511" href="Algebra.Bundles.html#17493" class="Bound">ℓ</a><a id="17512" class="Symbol">))</a> <a id="17515" class="Keyword">where</a>
|
|||
|
|
<a id="17523" class="Keyword">infixl</a> <a id="17530" class="Number">7</a> <a id="17532" href="Algebra.Bundles.html#17694" class="Field Operator">_*_</a>
|
|||
|
|
<a id="17538" class="Keyword">infixl</a> <a id="17545" class="Number">6</a> <a id="17547" href="Algebra.Bundles.html#17654" class="Field Operator">_+_</a>
|
|||
|
|
<a id="17553" class="Keyword">infix</a> <a id="17560" class="Number">4</a> <a id="17562" href="Algebra.Bundles.html#17612" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="17568" class="Keyword">field</a>
|
|||
|
|
<a id="CommutativeSemiring.Carrier"></a><a id="17578" href="Algebra.Bundles.html#17578" class="Field">Carrier</a> <a id="17600" class="Symbol">:</a> <a id="17602" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="17606" href="Algebra.Bundles.html#17491" class="Bound">c</a>
|
|||
|
|
<a id="CommutativeSemiring._≈_"></a><a id="17612" href="Algebra.Bundles.html#17612" class="Field Operator">_≈_</a> <a id="17634" class="Symbol">:</a> <a id="17636" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="17640" href="Algebra.Bundles.html#17578" class="Field">Carrier</a> <a id="17648" href="Algebra.Bundles.html#17493" class="Bound">ℓ</a>
|
|||
|
|
<a id="CommutativeSemiring._+_"></a><a id="17654" href="Algebra.Bundles.html#17654" class="Field Operator">_+_</a> <a id="17676" class="Symbol">:</a> <a id="17678" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="17682" href="Algebra.Bundles.html#17578" class="Field">Carrier</a>
|
|||
|
|
<a id="CommutativeSemiring._*_"></a><a id="17694" href="Algebra.Bundles.html#17694" class="Field Operator">_*_</a> <a id="17716" class="Symbol">:</a> <a id="17718" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="17722" href="Algebra.Bundles.html#17578" class="Field">Carrier</a>
|
|||
|
|
<a id="CommutativeSemiring.0#"></a><a id="17734" href="Algebra.Bundles.html#17734" class="Field">0#</a> <a id="17756" class="Symbol">:</a> <a id="17758" href="Algebra.Bundles.html#17578" class="Field">Carrier</a>
|
|||
|
|
<a id="CommutativeSemiring.1#"></a><a id="17770" href="Algebra.Bundles.html#17770" class="Field">1#</a> <a id="17792" class="Symbol">:</a> <a id="17794" href="Algebra.Bundles.html#17578" class="Field">Carrier</a>
|
|||
|
|
<a id="CommutativeSemiring.isCommutativeSemiring"></a><a id="17806" href="Algebra.Bundles.html#17806" class="Field">isCommutativeSemiring</a> <a id="17828" class="Symbol">:</a> <a id="17830" href="Algebra.Structures.html#13418" class="Record">IsCommutativeSemiring</a> <a id="17852" href="Algebra.Bundles.html#17612" class="Field Operator">_≈_</a> <a id="17856" href="Algebra.Bundles.html#17654" class="Field Operator">_+_</a> <a id="17860" href="Algebra.Bundles.html#17694" class="Field Operator">_*_</a> <a id="17864" href="Algebra.Bundles.html#17734" class="Field">0#</a> <a id="17867" href="Algebra.Bundles.html#17770" class="Field">1#</a>
|
|||
|
|
|
|||
|
|
<a id="17873" class="Keyword">open</a> <a id="17878" href="Algebra.Structures.html#13418" class="Module">IsCommutativeSemiring</a> <a id="17900" href="Algebra.Bundles.html#17806" class="Field">isCommutativeSemiring</a> <a id="17922" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="CommutativeSemiring.semiring"></a><a id="17932" href="Algebra.Bundles.html#17932" class="Function">semiring</a> <a id="17941" class="Symbol">:</a> <a id="17943" href="Algebra.Bundles.html#16346" class="Record">Semiring</a> <a id="17952" class="Symbol">_</a> <a id="17954" class="Symbol">_</a>
|
|||
|
|
<a id="17958" href="Algebra.Bundles.html#17932" class="Function">semiring</a> <a id="17967" class="Symbol">=</a> <a id="17969" class="Keyword">record</a> <a id="17976" class="Symbol">{</a> <a id="17978" href="Algebra.Bundles.html#16604" class="Field">isSemiring</a> <a id="17989" class="Symbol">=</a> <a id="17991" href="Algebra.Structures.html#13498" class="Function">isSemiring</a> <a id="18002" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="18007" class="Keyword">open</a> <a id="18012" href="Algebra.Bundles.html#16346" class="Module">Semiring</a> <a id="18021" href="Algebra.Bundles.html#17932" class="Function">semiring</a> <a id="18030" class="Keyword">public</a>
|
|||
|
|
<a id="18041" class="Keyword">using</a>
|
|||
|
|
<a id="18051" class="Symbol">(</a> <a id="18053" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="18056" class="Symbol">;</a> <a id="18058" href="Algebra.Bundles.html#15764" class="Function">+-rawMagma</a><a id="18068" class="Symbol">;</a> <a id="18070" href="Algebra.Bundles.html#15805" class="Function">+-magma</a><a id="18077" class="Symbol">;</a> <a id="18079" href="Algebra.Bundles.html#15843" class="Function">+-unitalMagma</a><a id="18092" class="Symbol">;</a> <a id="18094" href="Algebra.Bundles.html#15887" class="Function">+-commutativeMagma</a>
|
|||
|
|
<a id="18117" class="Symbol">;</a> <a id="18119" href="Algebra.Bundles.html#15936" class="Function">+-semigroup</a><a id="18130" class="Symbol">;</a> <a id="18132" href="Algebra.Bundles.html#15978" class="Function">+-commutativeSemigroup</a>
|
|||
|
|
<a id="18159" class="Symbol">;</a> <a id="18161" href="Algebra.Bundles.html#16231" class="Function">*-rawMagma</a><a id="18171" class="Symbol">;</a> <a id="18173" href="Algebra.Bundles.html#16261" class="Function">*-magma</a><a id="18180" class="Symbol">;</a> <a id="18182" href="Algebra.Bundles.html#16288" class="Function">*-semigroup</a>
|
|||
|
|
<a id="18198" class="Symbol">;</a> <a id="18200" href="Algebra.Bundles.html#16031" class="Function">+-rawMonoid</a><a id="18211" class="Symbol">;</a> <a id="18213" href="Algebra.Bundles.html#16073" class="Function">+-monoid</a><a id="18221" class="Symbol">;</a> <a id="18223" href="Algebra.Bundles.html#15529" class="Function">+-commutativeMonoid</a>
|
|||
|
|
<a id="18247" class="Symbol">;</a> <a id="18249" href="Algebra.Bundles.html#16319" class="Function">*-rawMonoid</a><a id="18260" class="Symbol">;</a> <a id="18262" href="Algebra.Bundles.html#16091" class="Function">*-monoid</a>
|
|||
|
|
<a id="18275" class="Symbol">;</a> <a id="18277" href="Algebra.Bundles.html#12966" class="Function">nearSemiring</a><a id="18289" class="Symbol">;</a> <a id="18291" href="Algebra.Bundles.html#17258" class="Function">semiringWithoutOne</a>
|
|||
|
|
<a id="18314" class="Symbol">;</a> <a id="18316" href="Algebra.Bundles.html#16686" class="Function">semiringWithoutAnnihilatingZero</a>
|
|||
|
|
<a id="18352" class="Symbol">;</a> <a id="18354" href="Algebra.Bundles.html#15322" class="Function">rawSemiring</a>
|
|||
|
|
<a id="18370" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="CommutativeSemiring.*-commutativeMonoid"></a><a id="18375" href="Algebra.Bundles.html#18375" class="Function">*-commutativeMonoid</a> <a id="18395" class="Symbol">:</a> <a id="18397" href="Algebra.Bundles.html#6622" class="Record">CommutativeMonoid</a> <a id="18415" class="Symbol">_</a> <a id="18417" class="Symbol">_</a>
|
|||
|
|
<a id="18421" href="Algebra.Bundles.html#18375" class="Function">*-commutativeMonoid</a> <a id="18441" class="Symbol">=</a> <a id="18443" class="Keyword">record</a>
|
|||
|
|
<a id="18454" class="Symbol">{</a> <a id="18456" href="Algebra.Bundles.html#6856" class="Field">isCommutativeMonoid</a> <a id="18476" class="Symbol">=</a> <a id="18478" href="Algebra.Structures.html#13957" class="Function">*-isCommutativeMonoid</a>
|
|||
|
|
<a id="18504" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="18509" class="Keyword">open</a> <a id="18514" href="Algebra.Bundles.html#6622" class="Module">CommutativeMonoid</a> <a id="18532" href="Algebra.Bundles.html#18375" class="Function">*-commutativeMonoid</a> <a id="18552" class="Keyword">public</a>
|
|||
|
|
<a id="18563" class="Keyword">using</a> <a id="18569" class="Symbol">()</a> <a id="18572" class="Keyword">renaming</a>
|
|||
|
|
<a id="18585" class="Symbol">(</a> <a id="18587" href="Algebra.Bundles.html#5348" class="Function">commutativeMagma</a> <a id="18608" class="Symbol">to</a> <a id="18611" class="Function">*-commutativeMagma</a>
|
|||
|
|
<a id="18634" class="Symbol">;</a> <a id="18636" href="Algebra.Bundles.html#7128" class="Function">commutativeSemigroup</a> <a id="18657" class="Symbol">to</a> <a id="18660" class="Function">*-commutativeSemigroup</a>
|
|||
|
|
<a id="18687" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="CommutativeSemiring.commutativeSemiringWithoutOne"></a><a id="18692" href="Algebra.Bundles.html#18692" class="Function">commutativeSemiringWithoutOne</a> <a id="18722" class="Symbol">:</a> <a id="18724" href="Algebra.Bundles.html#13576" class="Record">CommutativeSemiringWithoutOne</a> <a id="18754" class="Symbol">_</a> <a id="18756" class="Symbol">_</a>
|
|||
|
|
<a id="18760" href="Algebra.Bundles.html#18692" class="Function">commutativeSemiringWithoutOne</a> <a id="18790" class="Symbol">=</a> <a id="18792" class="Keyword">record</a>
|
|||
|
|
<a id="18803" class="Symbol">{</a> <a id="18805" href="Algebra.Bundles.html#13935" class="Field">isCommutativeSemiringWithoutOne</a> <a id="18837" class="Symbol">=</a> <a id="18839" href="Algebra.Structures.html#13603" class="Function">isCommutativeSemiringWithoutOne</a>
|
|||
|
|
<a id="18875" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="18879" class="Keyword">record</a> <a id="CancellativeCommutativeSemiring"></a><a id="18886" href="Algebra.Bundles.html#18886" class="Record">CancellativeCommutativeSemiring</a> <a id="18918" href="Algebra.Bundles.html#18918" class="Bound">c</a> <a id="18920" href="Algebra.Bundles.html#18920" class="Bound">ℓ</a> <a id="18922" class="Symbol">:</a> <a id="18924" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="18928" class="Symbol">(</a><a id="18929" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="18933" class="Symbol">(</a><a id="18934" href="Algebra.Bundles.html#18918" class="Bound">c</a> <a id="18936" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="18938" href="Algebra.Bundles.html#18920" class="Bound">ℓ</a><a id="18939" class="Symbol">))</a> <a id="18942" class="Keyword">where</a>
|
|||
|
|
<a id="18950" class="Keyword">infixl</a> <a id="18957" class="Number">7</a> <a id="18959" href="Algebra.Bundles.html#19157" class="Field Operator">_*_</a>
|
|||
|
|
<a id="18965" class="Keyword">infixl</a> <a id="18972" class="Number">6</a> <a id="18974" href="Algebra.Bundles.html#19105" class="Field Operator">_+_</a>
|
|||
|
|
<a id="18980" class="Keyword">infix</a> <a id="18987" class="Number">4</a> <a id="18989" href="Algebra.Bundles.html#19051" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="18995" class="Keyword">field</a>
|
|||
|
|
<a id="CancellativeCommutativeSemiring.Carrier"></a><a id="19005" href="Algebra.Bundles.html#19005" class="Field">Carrier</a> <a id="19039" class="Symbol">:</a> <a id="19041" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="19045" href="Algebra.Bundles.html#18918" class="Bound">c</a>
|
|||
|
|
<a id="CancellativeCommutativeSemiring._≈_"></a><a id="19051" href="Algebra.Bundles.html#19051" class="Field Operator">_≈_</a> <a id="19085" class="Symbol">:</a> <a id="19087" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="19091" href="Algebra.Bundles.html#19005" class="Field">Carrier</a> <a id="19099" href="Algebra.Bundles.html#18920" class="Bound">ℓ</a>
|
|||
|
|
<a id="CancellativeCommutativeSemiring._+_"></a><a id="19105" href="Algebra.Bundles.html#19105" class="Field Operator">_+_</a> <a id="19139" class="Symbol">:</a> <a id="19141" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="19145" href="Algebra.Bundles.html#19005" class="Field">Carrier</a>
|
|||
|
|
<a id="CancellativeCommutativeSemiring._*_"></a><a id="19157" href="Algebra.Bundles.html#19157" class="Field Operator">_*_</a> <a id="19191" class="Symbol">:</a> <a id="19193" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="19197" href="Algebra.Bundles.html#19005" class="Field">Carrier</a>
|
|||
|
|
<a id="CancellativeCommutativeSemiring.0#"></a><a id="19209" href="Algebra.Bundles.html#19209" class="Field">0#</a> <a id="19243" class="Symbol">:</a> <a id="19245" href="Algebra.Bundles.html#19005" class="Field">Carrier</a>
|
|||
|
|
<a id="CancellativeCommutativeSemiring.1#"></a><a id="19257" href="Algebra.Bundles.html#19257" class="Field">1#</a> <a id="19291" class="Symbol">:</a> <a id="19293" href="Algebra.Bundles.html#19005" class="Field">Carrier</a>
|
|||
|
|
<a id="CancellativeCommutativeSemiring.isCancellativeCommutativeSemiring"></a><a id="19305" href="Algebra.Bundles.html#19305" class="Field">isCancellativeCommutativeSemiring</a> <a id="19339" class="Symbol">:</a> <a id="19341" href="Algebra.Structures.html#14106" class="Record">IsCancellativeCommutativeSemiring</a> <a id="19375" href="Algebra.Bundles.html#19051" class="Field Operator">_≈_</a> <a id="19379" href="Algebra.Bundles.html#19105" class="Field Operator">_+_</a> <a id="19383" href="Algebra.Bundles.html#19157" class="Field Operator">_*_</a> <a id="19387" href="Algebra.Bundles.html#19209" class="Field">0#</a> <a id="19390" href="Algebra.Bundles.html#19257" class="Field">1#</a>
|
|||
|
|
|
|||
|
|
<a id="19396" class="Keyword">open</a> <a id="19401" href="Algebra.Structures.html#14106" class="Module">IsCancellativeCommutativeSemiring</a> <a id="19435" href="Algebra.Bundles.html#19305" class="Field">isCancellativeCommutativeSemiring</a> <a id="19469" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="CancellativeCommutativeSemiring.commutativeSemiring"></a><a id="19479" href="Algebra.Bundles.html#19479" class="Function">commutativeSemiring</a> <a id="19499" class="Symbol">:</a> <a id="19501" href="Algebra.Bundles.html#17471" class="Record">CommutativeSemiring</a> <a id="19521" href="Algebra.Bundles.html#18918" class="Bound">c</a> <a id="19523" href="Algebra.Bundles.html#18920" class="Bound">ℓ</a>
|
|||
|
|
<a id="19527" href="Algebra.Bundles.html#19479" class="Function">commutativeSemiring</a> <a id="19547" class="Symbol">=</a> <a id="19549" class="Keyword">record</a>
|
|||
|
|
<a id="19560" class="Symbol">{</a> <a id="19562" href="Algebra.Bundles.html#17806" class="Field">isCommutativeSemiring</a> <a id="19584" class="Symbol">=</a> <a id="19586" href="Algebra.Structures.html#14198" class="Function">isCommutativeSemiring</a>
|
|||
|
|
<a id="19612" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="19617" class="Keyword">open</a> <a id="19622" href="Algebra.Bundles.html#17471" class="Module">CommutativeSemiring</a> <a id="19642" href="Algebra.Bundles.html#19479" class="Function">commutativeSemiring</a> <a id="19662" class="Keyword">public</a>
|
|||
|
|
<a id="19673" class="Keyword">using</a>
|
|||
|
|
<a id="19683" class="Symbol">(</a> <a id="19685" href="Algebra.Bundles.html#15764" class="Function">+-rawMagma</a><a id="19695" class="Symbol">;</a> <a id="19697" href="Algebra.Bundles.html#15805" class="Function">+-magma</a><a id="19704" class="Symbol">;</a> <a id="19706" href="Algebra.Bundles.html#15843" class="Function">+-unitalMagma</a><a id="19719" class="Symbol">;</a> <a id="19721" href="Algebra.Bundles.html#15887" class="Function">+-commutativeMagma</a>
|
|||
|
|
<a id="19744" class="Symbol">;</a> <a id="19746" href="Algebra.Bundles.html#15936" class="Function">+-semigroup</a><a id="19757" class="Symbol">;</a> <a id="19759" href="Algebra.Bundles.html#15978" class="Function">+-commutativeSemigroup</a>
|
|||
|
|
<a id="19786" class="Symbol">;</a> <a id="19788" href="Algebra.Bundles.html#16231" class="Function">*-rawMagma</a><a id="19798" class="Symbol">;</a> <a id="19800" href="Algebra.Bundles.html#16261" class="Function">*-magma</a><a id="19807" class="Symbol">;</a> <a id="19809" href="Algebra.Bundles.html#18611" class="Function">*-commutativeMagma</a><a id="19827" class="Symbol">;</a> <a id="19829" href="Algebra.Bundles.html#16288" class="Function">*-semigroup</a><a id="19840" class="Symbol">;</a> <a id="19842" href="Algebra.Bundles.html#18660" class="Function">*-commutativeSemigroup</a>
|
|||
|
|
<a id="19869" class="Symbol">;</a> <a id="19871" href="Algebra.Bundles.html#16031" class="Function">+-rawMonoid</a><a id="19882" class="Symbol">;</a> <a id="19884" href="Algebra.Bundles.html#16073" class="Function">+-monoid</a><a id="19892" class="Symbol">;</a> <a id="19894" href="Algebra.Bundles.html#15529" class="Function">+-commutativeMonoid</a>
|
|||
|
|
<a id="19918" class="Symbol">;</a> <a id="19920" href="Algebra.Bundles.html#16319" class="Function">*-rawMonoid</a><a id="19931" class="Symbol">;</a> <a id="19933" href="Algebra.Bundles.html#16091" class="Function">*-monoid</a><a id="19941" class="Symbol">;</a> <a id="19943" href="Algebra.Bundles.html#18375" class="Function">*-commutativeMonoid</a>
|
|||
|
|
<a id="19967" class="Symbol">;</a> <a id="19969" href="Algebra.Bundles.html#12966" class="Function">nearSemiring</a><a id="19981" class="Symbol">;</a> <a id="19983" href="Algebra.Bundles.html#17258" class="Function">semiringWithoutOne</a>
|
|||
|
|
<a id="20006" class="Symbol">;</a> <a id="20008" href="Algebra.Bundles.html#16686" class="Function">semiringWithoutAnnihilatingZero</a>
|
|||
|
|
<a id="20044" class="Symbol">;</a> <a id="20046" href="Algebra.Bundles.html#15322" class="Function">rawSemiring</a>
|
|||
|
|
<a id="20062" class="Symbol">;</a> <a id="20064" href="Algebra.Bundles.html#17932" class="Function">semiring</a>
|
|||
|
|
<a id="20077" class="Symbol">;</a> <a id="20079" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a>
|
|||
|
|
<a id="20087" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="20090" class="Keyword">record</a> <a id="IdempotentSemiring"></a><a id="20097" href="Algebra.Bundles.html#20097" class="Record">IdempotentSemiring</a> <a id="20116" href="Algebra.Bundles.html#20116" class="Bound">c</a> <a id="20118" href="Algebra.Bundles.html#20118" class="Bound">ℓ</a> <a id="20120" class="Symbol">:</a> <a id="20122" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="20126" class="Symbol">(</a><a id="20127" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="20131" class="Symbol">(</a><a id="20132" href="Algebra.Bundles.html#20116" class="Bound">c</a> <a id="20134" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="20136" href="Algebra.Bundles.html#20118" class="Bound">ℓ</a><a id="20137" class="Symbol">))</a> <a id="20140" class="Keyword">where</a>
|
|||
|
|
<a id="20148" class="Keyword">infixl</a> <a id="20155" class="Number">7</a> <a id="20157" href="Algebra.Bundles.html#20322" class="Field Operator">_*_</a>
|
|||
|
|
<a id="20163" class="Keyword">infixl</a> <a id="20170" class="Number">6</a> <a id="20172" href="Algebra.Bundles.html#20281" class="Field Operator">_+_</a>
|
|||
|
|
<a id="20178" class="Keyword">infix</a> <a id="20185" class="Number">4</a> <a id="20187" href="Algebra.Bundles.html#20238" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="20193" class="Keyword">field</a>
|
|||
|
|
<a id="IdempotentSemiring.Carrier"></a><a id="20203" href="Algebra.Bundles.html#20203" class="Field">Carrier</a> <a id="20226" class="Symbol">:</a> <a id="20228" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="20232" href="Algebra.Bundles.html#20116" class="Bound">c</a>
|
|||
|
|
<a id="IdempotentSemiring._≈_"></a><a id="20238" href="Algebra.Bundles.html#20238" class="Field Operator">_≈_</a> <a id="20261" class="Symbol">:</a> <a id="20263" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="20267" href="Algebra.Bundles.html#20203" class="Field">Carrier</a> <a id="20275" href="Algebra.Bundles.html#20118" class="Bound">ℓ</a>
|
|||
|
|
<a id="IdempotentSemiring._+_"></a><a id="20281" href="Algebra.Bundles.html#20281" class="Field Operator">_+_</a> <a id="20304" class="Symbol">:</a> <a id="20306" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="20310" href="Algebra.Bundles.html#20203" class="Field">Carrier</a>
|
|||
|
|
<a id="IdempotentSemiring._*_"></a><a id="20322" href="Algebra.Bundles.html#20322" class="Field Operator">_*_</a> <a id="20345" class="Symbol">:</a> <a id="20347" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="20351" href="Algebra.Bundles.html#20203" class="Field">Carrier</a>
|
|||
|
|
<a id="IdempotentSemiring.0#"></a><a id="20363" href="Algebra.Bundles.html#20363" class="Field">0#</a> <a id="20386" class="Symbol">:</a> <a id="20388" href="Algebra.Bundles.html#20203" class="Field">Carrier</a>
|
|||
|
|
<a id="IdempotentSemiring.1#"></a><a id="20400" href="Algebra.Bundles.html#20400" class="Field">1#</a> <a id="20423" class="Symbol">:</a> <a id="20425" href="Algebra.Bundles.html#20203" class="Field">Carrier</a>
|
|||
|
|
<a id="IdempotentSemiring.isIdempotentSemiring"></a><a id="20437" href="Algebra.Bundles.html#20437" class="Field">isIdempotentSemiring</a> <a id="20460" class="Symbol">:</a> <a id="20462" href="Algebra.Structures.html#14377" class="Record">IsIdempotentSemiring</a> <a id="20483" href="Algebra.Bundles.html#20238" class="Field Operator">_≈_</a> <a id="20487" href="Algebra.Bundles.html#20281" class="Field Operator">_+_</a> <a id="20491" href="Algebra.Bundles.html#20322" class="Field Operator">_*_</a> <a id="20495" href="Algebra.Bundles.html#20363" class="Field">0#</a> <a id="20498" href="Algebra.Bundles.html#20400" class="Field">1#</a>
|
|||
|
|
|
|||
|
|
<a id="20504" class="Keyword">open</a> <a id="20509" href="Algebra.Structures.html#14377" class="Module">IsIdempotentSemiring</a> <a id="20530" href="Algebra.Bundles.html#20437" class="Field">isIdempotentSemiring</a> <a id="20551" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="IdempotentSemiring.semiring"></a><a id="20561" href="Algebra.Bundles.html#20561" class="Function">semiring</a> <a id="20570" class="Symbol">:</a> <a id="20572" href="Algebra.Bundles.html#16346" class="Record">Semiring</a> <a id="20581" class="Symbol">_</a> <a id="20583" class="Symbol">_</a>
|
|||
|
|
<a id="20587" href="Algebra.Bundles.html#20561" class="Function">semiring</a> <a id="20596" class="Symbol">=</a> <a id="20598" class="Keyword">record</a> <a id="20605" class="Symbol">{</a> <a id="20607" href="Algebra.Bundles.html#16604" class="Field">isSemiring</a> <a id="20618" class="Symbol">=</a> <a id="20620" href="Algebra.Structures.html#14456" class="Function">isSemiring</a> <a id="20631" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="20636" class="Keyword">open</a> <a id="20641" href="Algebra.Bundles.html#16346" class="Module">Semiring</a> <a id="20650" href="Algebra.Bundles.html#20561" class="Function">semiring</a> <a id="20659" class="Keyword">public</a>
|
|||
|
|
<a id="20670" class="Keyword">using</a>
|
|||
|
|
<a id="20680" class="Symbol">(</a> <a id="20682" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="20685" class="Symbol">;</a> <a id="20687" href="Algebra.Bundles.html#15764" class="Function">+-rawMagma</a><a id="20697" class="Symbol">;</a> <a id="20699" href="Algebra.Bundles.html#15805" class="Function">+-magma</a><a id="20706" class="Symbol">;</a> <a id="20708" href="Algebra.Bundles.html#15843" class="Function">+-unitalMagma</a><a id="20721" class="Symbol">;</a> <a id="20723" href="Algebra.Bundles.html#15887" class="Function">+-commutativeMagma</a>
|
|||
|
|
<a id="20746" class="Symbol">;</a> <a id="20748" href="Algebra.Bundles.html#15936" class="Function">+-semigroup</a><a id="20759" class="Symbol">;</a> <a id="20761" href="Algebra.Bundles.html#15978" class="Function">+-commutativeSemigroup</a>
|
|||
|
|
<a id="20788" class="Symbol">;</a> <a id="20790" href="Algebra.Bundles.html#16231" class="Function">*-rawMagma</a><a id="20800" class="Symbol">;</a> <a id="20802" href="Algebra.Bundles.html#16261" class="Function">*-magma</a><a id="20809" class="Symbol">;</a> <a id="20811" href="Algebra.Bundles.html#16288" class="Function">*-semigroup</a>
|
|||
|
|
<a id="20827" class="Symbol">;</a> <a id="20829" href="Algebra.Bundles.html#16031" class="Function">+-rawMonoid</a><a id="20840" class="Symbol">;</a> <a id="20842" href="Algebra.Bundles.html#16073" class="Function">+-monoid</a><a id="20850" class="Symbol">;</a> <a id="20852" href="Algebra.Bundles.html#15529" class="Function">+-commutativeMonoid</a>
|
|||
|
|
<a id="20876" class="Symbol">;</a> <a id="20878" href="Algebra.Bundles.html#16319" class="Function">*-rawMonoid</a><a id="20889" class="Symbol">;</a> <a id="20891" href="Algebra.Bundles.html#16091" class="Function">*-monoid</a>
|
|||
|
|
<a id="20904" class="Symbol">;</a> <a id="20906" href="Algebra.Bundles.html#12966" class="Function">nearSemiring</a><a id="20918" class="Symbol">;</a> <a id="20920" href="Algebra.Bundles.html#17258" class="Function">semiringWithoutOne</a>
|
|||
|
|
<a id="20943" class="Symbol">;</a> <a id="20945" href="Algebra.Bundles.html#16686" class="Function">semiringWithoutAnnihilatingZero</a>
|
|||
|
|
<a id="20981" class="Symbol">;</a> <a id="20983" href="Algebra.Bundles.html#15322" class="Function">rawSemiring</a>
|
|||
|
|
<a id="20999" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="21002" class="Keyword">record</a> <a id="KleeneAlgebra"></a><a id="21009" href="Algebra.Bundles.html#21009" class="Record">KleeneAlgebra</a> <a id="21023" href="Algebra.Bundles.html#21023" class="Bound">c</a> <a id="21025" href="Algebra.Bundles.html#21025" class="Bound">ℓ</a> <a id="21027" class="Symbol">:</a> <a id="21029" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="21033" class="Symbol">(</a><a id="21034" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="21038" class="Symbol">(</a><a id="21039" href="Algebra.Bundles.html#21023" class="Bound">c</a> <a id="21041" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="21043" href="Algebra.Bundles.html#21025" class="Bound">ℓ</a><a id="21044" class="Symbol">))</a> <a id="21047" class="Keyword">where</a>
|
|||
|
|
<a id="21055" class="Keyword">infix</a> <a id="21062" class="Number">8</a> <a id="21064" href="Algebra.Bundles.html#21280" class="Field Operator">_⋆</a>
|
|||
|
|
<a id="21069" class="Keyword">infixl</a> <a id="21076" class="Number">7</a> <a id="21078" href="Algebra.Bundles.html#21240" class="Field Operator">_*_</a>
|
|||
|
|
<a id="21084" class="Keyword">infixl</a> <a id="21091" class="Number">6</a> <a id="21093" href="Algebra.Bundles.html#21200" class="Field Operator">_+_</a>
|
|||
|
|
<a id="21099" class="Keyword">infix</a> <a id="21106" class="Number">4</a> <a id="21108" href="Algebra.Bundles.html#21158" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="21114" class="Keyword">field</a>
|
|||
|
|
<a id="KleeneAlgebra.Carrier"></a><a id="21124" href="Algebra.Bundles.html#21124" class="Field">Carrier</a> <a id="21146" class="Symbol">:</a> <a id="21148" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="21152" href="Algebra.Bundles.html#21023" class="Bound">c</a>
|
|||
|
|
<a id="KleeneAlgebra._≈_"></a><a id="21158" href="Algebra.Bundles.html#21158" class="Field Operator">_≈_</a> <a id="21180" class="Symbol">:</a> <a id="21182" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="21186" href="Algebra.Bundles.html#21124" class="Field">Carrier</a> <a id="21194" href="Algebra.Bundles.html#21025" class="Bound">ℓ</a>
|
|||
|
|
<a id="KleeneAlgebra._+_"></a><a id="21200" href="Algebra.Bundles.html#21200" class="Field Operator">_+_</a> <a id="21222" class="Symbol">:</a> <a id="21224" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="21228" href="Algebra.Bundles.html#21124" class="Field">Carrier</a>
|
|||
|
|
<a id="KleeneAlgebra._*_"></a><a id="21240" href="Algebra.Bundles.html#21240" class="Field Operator">_*_</a> <a id="21262" class="Symbol">:</a> <a id="21264" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="21268" href="Algebra.Bundles.html#21124" class="Field">Carrier</a>
|
|||
|
|
<a id="KleeneAlgebra._⋆"></a><a id="21280" href="Algebra.Bundles.html#21280" class="Field Operator">_⋆</a> <a id="21302" class="Symbol">:</a> <a id="21304" href="Algebra.Core.html#484" class="Function">Op₁</a> <a id="21308" href="Algebra.Bundles.html#21124" class="Field">Carrier</a>
|
|||
|
|
<a id="KleeneAlgebra.0#"></a><a id="21320" href="Algebra.Bundles.html#21320" class="Field">0#</a> <a id="21342" class="Symbol">:</a> <a id="21344" href="Algebra.Bundles.html#21124" class="Field">Carrier</a>
|
|||
|
|
<a id="KleeneAlgebra.1#"></a><a id="21356" href="Algebra.Bundles.html#21356" class="Field">1#</a> <a id="21378" class="Symbol">:</a> <a id="21380" href="Algebra.Bundles.html#21124" class="Field">Carrier</a>
|
|||
|
|
<a id="KleeneAlgebra.isKleeneAlgebra"></a><a id="21392" href="Algebra.Bundles.html#21392" class="Field">isKleeneAlgebra</a> <a id="21414" class="Symbol">:</a> <a id="21416" href="Algebra.Structures.html#14573" class="Record">IsKleeneAlgebra</a> <a id="21432" href="Algebra.Bundles.html#21158" class="Field Operator">_≈_</a> <a id="21436" href="Algebra.Bundles.html#21200" class="Field Operator">_+_</a> <a id="21440" href="Algebra.Bundles.html#21240" class="Field Operator">_*_</a> <a id="21444" href="Algebra.Bundles.html#21280" class="Field Operator">_⋆</a> <a id="21447" href="Algebra.Bundles.html#21320" class="Field">0#</a> <a id="21450" href="Algebra.Bundles.html#21356" class="Field">1#</a>
|
|||
|
|
|
|||
|
|
<a id="21456" class="Keyword">open</a> <a id="21461" href="Algebra.Structures.html#14573" class="Module">IsKleeneAlgebra</a> <a id="21477" href="Algebra.Bundles.html#21392" class="Field">isKleeneAlgebra</a> <a id="21493" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="KleeneAlgebra.idempotentSemiring"></a><a id="21503" href="Algebra.Bundles.html#21503" class="Function">idempotentSemiring</a> <a id="21522" class="Symbol">:</a> <a id="21524" href="Algebra.Bundles.html#20097" class="Record">IdempotentSemiring</a> <a id="21543" class="Symbol">_</a> <a id="21545" class="Symbol">_</a>
|
|||
|
|
<a id="21549" href="Algebra.Bundles.html#21503" class="Function">idempotentSemiring</a> <a id="21568" class="Symbol">=</a> <a id="21570" class="Keyword">record</a> <a id="21577" class="Symbol">{</a> <a id="21579" href="Algebra.Bundles.html#20437" class="Field">isIdempotentSemiring</a> <a id="21600" class="Symbol">=</a> <a id="21602" href="Algebra.Structures.html#14659" class="Function">isIdempotentSemiring</a> <a id="21623" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="21628" class="Keyword">open</a> <a id="21633" href="Algebra.Bundles.html#20097" class="Module">IdempotentSemiring</a> <a id="21652" href="Algebra.Bundles.html#21503" class="Function">idempotentSemiring</a> <a id="21671" class="Keyword">public</a>
|
|||
|
|
<a id="21682" class="Keyword">using</a>
|
|||
|
|
<a id="21692" class="Symbol">(</a> <a id="21694" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="21697" class="Symbol">;</a> <a id="21699" href="Algebra.Bundles.html#15764" class="Function">+-rawMagma</a><a id="21709" class="Symbol">;</a> <a id="21711" href="Algebra.Bundles.html#15805" class="Function">+-magma</a><a id="21718" class="Symbol">;</a> <a id="21720" href="Algebra.Bundles.html#15843" class="Function">+-unitalMagma</a><a id="21733" class="Symbol">;</a> <a id="21735" href="Algebra.Bundles.html#15887" class="Function">+-commutativeMagma</a>
|
|||
|
|
<a id="21758" class="Symbol">;</a> <a id="21760" href="Algebra.Bundles.html#15936" class="Function">+-semigroup</a><a id="21771" class="Symbol">;</a> <a id="21773" href="Algebra.Bundles.html#15978" class="Function">+-commutativeSemigroup</a>
|
|||
|
|
<a id="21800" class="Symbol">;</a> <a id="21802" href="Algebra.Bundles.html#16231" class="Function">*-rawMagma</a><a id="21812" class="Symbol">;</a> <a id="21814" href="Algebra.Bundles.html#16261" class="Function">*-magma</a><a id="21821" class="Symbol">;</a> <a id="21823" href="Algebra.Bundles.html#16288" class="Function">*-semigroup</a>
|
|||
|
|
<a id="21839" class="Symbol">;</a> <a id="21841" href="Algebra.Bundles.html#16031" class="Function">+-rawMonoid</a><a id="21852" class="Symbol">;</a> <a id="21854" href="Algebra.Bundles.html#16073" class="Function">+-monoid</a><a id="21862" class="Symbol">;</a> <a id="21864" href="Algebra.Bundles.html#15529" class="Function">+-commutativeMonoid</a>
|
|||
|
|
<a id="21888" class="Symbol">;</a> <a id="21890" href="Algebra.Bundles.html#16319" class="Function">*-rawMonoid</a><a id="21901" class="Symbol">;</a> <a id="21903" href="Algebra.Bundles.html#16091" class="Function">*-monoid</a>
|
|||
|
|
<a id="21916" class="Symbol">;</a> <a id="21918" href="Algebra.Bundles.html#12966" class="Function">nearSemiring</a><a id="21930" class="Symbol">;</a> <a id="21932" href="Algebra.Bundles.html#17258" class="Function">semiringWithoutOne</a>
|
|||
|
|
<a id="21955" class="Symbol">;</a> <a id="21957" href="Algebra.Bundles.html#16686" class="Function">semiringWithoutAnnihilatingZero</a>
|
|||
|
|
<a id="21993" class="Symbol">;</a> <a id="21995" href="Algebra.Bundles.html#15322" class="Function">rawSemiring</a><a id="22006" class="Symbol">;</a> <a id="22008" href="Algebra.Bundles.html#20561" class="Function">semiring</a>
|
|||
|
|
<a id="22021" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="22024" class="Keyword">record</a> <a id="Quasiring"></a><a id="22031" href="Algebra.Bundles.html#22031" class="Record">Quasiring</a> <a id="22041" href="Algebra.Bundles.html#22041" class="Bound">c</a> <a id="22043" href="Algebra.Bundles.html#22043" class="Bound">ℓ</a> <a id="22045" class="Symbol">:</a> <a id="22047" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="22051" class="Symbol">(</a><a id="22052" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="22056" class="Symbol">(</a><a id="22057" href="Algebra.Bundles.html#22041" class="Bound">c</a> <a id="22059" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="22061" href="Algebra.Bundles.html#22043" class="Bound">ℓ</a><a id="22062" class="Symbol">))</a> <a id="22065" class="Keyword">where</a>
|
|||
|
|
<a id="22073" class="Keyword">infixl</a> <a id="22080" class="Number">7</a> <a id="22082" href="Algebra.Bundles.html#22220" class="Field Operator">_*_</a>
|
|||
|
|
<a id="22088" class="Keyword">infixl</a> <a id="22095" class="Number">6</a> <a id="22097" href="Algebra.Bundles.html#22188" class="Field Operator">_+_</a>
|
|||
|
|
<a id="22103" class="Keyword">infix</a> <a id="22110" class="Number">4</a> <a id="22112" href="Algebra.Bundles.html#22154" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="22118" class="Keyword">field</a>
|
|||
|
|
<a id="Quasiring.Carrier"></a><a id="22128" href="Algebra.Bundles.html#22128" class="Field">Carrier</a> <a id="22142" class="Symbol">:</a> <a id="22144" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="22148" href="Algebra.Bundles.html#22041" class="Bound">c</a>
|
|||
|
|
<a id="Quasiring._≈_"></a><a id="22154" href="Algebra.Bundles.html#22154" class="Field Operator">_≈_</a> <a id="22168" class="Symbol">:</a> <a id="22170" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="22174" href="Algebra.Bundles.html#22128" class="Field">Carrier</a> <a id="22182" href="Algebra.Bundles.html#22043" class="Bound">ℓ</a>
|
|||
|
|
<a id="Quasiring._+_"></a><a id="22188" href="Algebra.Bundles.html#22188" class="Field Operator">_+_</a> <a id="22202" class="Symbol">:</a> <a id="22204" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="22208" href="Algebra.Bundles.html#22128" class="Field">Carrier</a>
|
|||
|
|
<a id="Quasiring._*_"></a><a id="22220" href="Algebra.Bundles.html#22220" class="Field Operator">_*_</a> <a id="22234" class="Symbol">:</a> <a id="22236" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="22240" href="Algebra.Bundles.html#22128" class="Field">Carrier</a>
|
|||
|
|
<a id="Quasiring.0#"></a><a id="22252" href="Algebra.Bundles.html#22252" class="Field">0#</a> <a id="22266" class="Symbol">:</a> <a id="22268" href="Algebra.Bundles.html#22128" class="Field">Carrier</a>
|
|||
|
|
<a id="Quasiring.1#"></a><a id="22280" href="Algebra.Bundles.html#22280" class="Field">1#</a> <a id="22294" class="Symbol">:</a> <a id="22296" href="Algebra.Bundles.html#22128" class="Field">Carrier</a>
|
|||
|
|
<a id="Quasiring.isQuasiring"></a><a id="22308" href="Algebra.Bundles.html#22308" class="Field">isQuasiring</a> <a id="22322" class="Symbol">:</a> <a id="22324" href="Algebra.Structures.html#15236" class="Record">IsQuasiring</a> <a id="22336" href="Algebra.Bundles.html#22154" class="Field Operator">_≈_</a> <a id="22340" href="Algebra.Bundles.html#22188" class="Field Operator">_+_</a> <a id="22344" href="Algebra.Bundles.html#22220" class="Field Operator">_*_</a> <a id="22348" href="Algebra.Bundles.html#22252" class="Field">0#</a> <a id="22351" href="Algebra.Bundles.html#22280" class="Field">1#</a>
|
|||
|
|
|
|||
|
|
<a id="22357" class="Keyword">open</a> <a id="22362" href="Algebra.Structures.html#15236" class="Module">IsQuasiring</a> <a id="22374" href="Algebra.Bundles.html#22308" class="Field">isQuasiring</a> <a id="22386" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="Quasiring.+-monoid"></a><a id="22396" href="Algebra.Bundles.html#22396" class="Function">+-monoid</a> <a id="22405" class="Symbol">:</a> <a id="22407" href="Algebra.Bundles.html#6051" class="Record">Monoid</a> <a id="22414" class="Symbol">_</a> <a id="22416" class="Symbol">_</a>
|
|||
|
|
<a id="22420" href="Algebra.Bundles.html#22396" class="Function">+-monoid</a> <a id="22429" class="Symbol">=</a> <a id="22431" class="Keyword">record</a> <a id="22438" class="Symbol">{</a> <a id="22440" href="Algebra.Bundles.html#6230" class="Field">isMonoid</a> <a id="22449" class="Symbol">=</a> <a id="22451" href="Algebra.Structures.html#15306" class="Function">+-isMonoid</a> <a id="22462" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="22467" class="Keyword">open</a> <a id="22472" href="Algebra.Bundles.html#6051" class="Module">Monoid</a> <a id="22479" href="Algebra.Bundles.html#22396" class="Function">+-monoid</a> <a id="22488" class="Keyword">public</a>
|
|||
|
|
<a id="22499" class="Keyword">using</a> <a id="22505" class="Symbol">(</a><a id="22506" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="22509" class="Symbol">)</a> <a id="22511" class="Keyword">renaming</a>
|
|||
|
|
<a id="22524" class="Symbol">(</a> <a id="22526" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a> <a id="22538" class="Symbol">to</a> <a id="22542" class="Function">+-rawMagma</a>
|
|||
|
|
<a id="22557" class="Symbol">;</a> <a id="22559" href="Algebra.Bundles.html#4383" class="Function">magma</a> <a id="22571" class="Symbol">to</a> <a id="22575" class="Function">+-magma</a>
|
|||
|
|
<a id="22587" class="Symbol">;</a> <a id="22589" href="Algebra.Bundles.html#6296" class="Function">semigroup</a> <a id="22601" class="Symbol">to</a> <a id="22605" class="Function">+-semigroup</a>
|
|||
|
|
<a id="22621" class="Symbol">;</a> <a id="22623" href="Algebra.Bundles.html#6525" class="Function">unitalMagma</a> <a id="22635" class="Symbol">to</a> <a id="22639" class="Function">+-unitalMagma</a>
|
|||
|
|
<a id="22657" class="Symbol">;</a> <a id="22659" href="Algebra.Bundles.html#6444" class="Function">rawMonoid</a> <a id="22671" class="Symbol">to</a> <a id="22675" class="Function">+-rawMonoid</a>
|
|||
|
|
<a id="22691" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="Quasiring.*-monoid"></a><a id="22696" href="Algebra.Bundles.html#22696" class="Function">*-monoid</a> <a id="22705" class="Symbol">:</a> <a id="22707" href="Algebra.Bundles.html#6051" class="Record">Monoid</a> <a id="22714" class="Symbol">_</a> <a id="22716" class="Symbol">_</a>
|
|||
|
|
<a id="22720" href="Algebra.Bundles.html#22696" class="Function">*-monoid</a> <a id="22729" class="Symbol">=</a> <a id="22731" class="Keyword">record</a> <a id="22738" class="Symbol">{</a> <a id="22740" href="Algebra.Bundles.html#6230" class="Field">isMonoid</a> <a id="22749" class="Symbol">=</a> <a id="22751" href="Algebra.Structures.html#16477" class="Function">*-isMonoid</a> <a id="22762" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="22767" class="Keyword">open</a> <a id="22772" href="Algebra.Bundles.html#6051" class="Module">Monoid</a> <a id="22779" href="Algebra.Bundles.html#22696" class="Function">*-monoid</a> <a id="22788" class="Keyword">public</a>
|
|||
|
|
<a id="22799" class="Keyword">using</a> <a id="22805" class="Symbol">()</a> <a id="22808" class="Keyword">renaming</a>
|
|||
|
|
<a id="22821" class="Symbol">(</a> <a id="22823" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a> <a id="22833" class="Symbol">to</a> <a id="22836" class="Function">*-rawMagma</a>
|
|||
|
|
<a id="22851" class="Symbol">;</a> <a id="22853" href="Algebra.Bundles.html#4383" class="Function">magma</a> <a id="22863" class="Symbol">to</a> <a id="22866" class="Function">*-magma</a>
|
|||
|
|
<a id="22878" class="Symbol">;</a> <a id="22880" href="Algebra.Bundles.html#6296" class="Function">semigroup</a> <a id="22890" class="Symbol">to</a> <a id="22893" class="Function">*-semigroup</a>
|
|||
|
|
<a id="22909" class="Symbol">;</a> <a id="22911" href="Algebra.Bundles.html#6444" class="Function">rawMonoid</a> <a id="22921" class="Symbol">to</a> <a id="22924" class="Function">*-rawMonoid</a>
|
|||
|
|
<a id="22940" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="22943" class="Comment">------------------------------------------------------------------------</a>
|
|||
|
|
<a id="23016" class="Comment">-- Bundles with 2 binary operations, 1 unary operation & 1 element</a>
|
|||
|
|
<a id="23083" class="Comment">------------------------------------------------------------------------</a>
|
|||
|
|
|
|||
|
|
<a id="23157" class="Keyword">record</a> <a id="RingWithoutOne"></a><a id="23164" href="Algebra.Bundles.html#23164" class="Record">RingWithoutOne</a> <a id="23179" href="Algebra.Bundles.html#23179" class="Bound">c</a> <a id="23181" href="Algebra.Bundles.html#23181" class="Bound">ℓ</a> <a id="23183" class="Symbol">:</a> <a id="23185" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="23189" class="Symbol">(</a><a id="23190" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="23194" class="Symbol">(</a><a id="23195" href="Algebra.Bundles.html#23179" class="Bound">c</a> <a id="23197" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="23199" href="Algebra.Bundles.html#23181" class="Bound">ℓ</a><a id="23200" class="Symbol">))</a> <a id="23203" class="Keyword">where</a>
|
|||
|
|
<a id="23211" class="Keyword">infix</a> <a id="23218" class="Number">8</a> <a id="23220" href="Algebra.Bundles.html#23420" class="Field Operator">-_</a>
|
|||
|
|
<a id="23225" class="Keyword">infixl</a> <a id="23232" class="Number">7</a> <a id="23234" href="Algebra.Bundles.html#23384" class="Field Operator">_*_</a>
|
|||
|
|
<a id="23240" class="Keyword">infixl</a> <a id="23247" class="Number">6</a> <a id="23249" href="Algebra.Bundles.html#23348" class="Field Operator">_+_</a>
|
|||
|
|
<a id="23255" class="Keyword">infix</a> <a id="23262" class="Number">4</a> <a id="23264" href="Algebra.Bundles.html#23310" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="23270" class="Keyword">field</a>
|
|||
|
|
<a id="RingWithoutOne.Carrier"></a><a id="23280" href="Algebra.Bundles.html#23280" class="Field">Carrier</a> <a id="23298" class="Symbol">:</a> <a id="23300" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="23304" href="Algebra.Bundles.html#23179" class="Bound">c</a>
|
|||
|
|
<a id="RingWithoutOne._≈_"></a><a id="23310" href="Algebra.Bundles.html#23310" class="Field Operator">_≈_</a> <a id="23328" class="Symbol">:</a> <a id="23330" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="23334" href="Algebra.Bundles.html#23280" class="Field">Carrier</a> <a id="23342" href="Algebra.Bundles.html#23181" class="Bound">ℓ</a>
|
|||
|
|
<a id="RingWithoutOne._+_"></a><a id="23348" href="Algebra.Bundles.html#23348" class="Field Operator">_+_</a> <a id="23366" class="Symbol">:</a> <a id="23368" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="23372" href="Algebra.Bundles.html#23280" class="Field">Carrier</a>
|
|||
|
|
<a id="RingWithoutOne._*_"></a><a id="23384" href="Algebra.Bundles.html#23384" class="Field Operator">_*_</a> <a id="23402" class="Symbol">:</a> <a id="23404" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="23408" href="Algebra.Bundles.html#23280" class="Field">Carrier</a>
|
|||
|
|
<a id="RingWithoutOne.-_"></a><a id="23420" href="Algebra.Bundles.html#23420" class="Field Operator">-_</a> <a id="23438" class="Symbol">:</a> <a id="23440" href="Algebra.Core.html#484" class="Function">Op₁</a> <a id="23444" href="Algebra.Bundles.html#23280" class="Field">Carrier</a>
|
|||
|
|
<a id="RingWithoutOne.0#"></a><a id="23456" href="Algebra.Bundles.html#23456" class="Field">0#</a> <a id="23474" class="Symbol">:</a> <a id="23476" href="Algebra.Bundles.html#23280" class="Field">Carrier</a>
|
|||
|
|
<a id="RingWithoutOne.isRingWithoutOne"></a><a id="23488" href="Algebra.Bundles.html#23488" class="Field">isRingWithoutOne</a> <a id="23506" class="Symbol">:</a> <a id="23508" href="Algebra.Structures.html#17013" class="Record">IsRingWithoutOne</a> <a id="23525" href="Algebra.Bundles.html#23310" class="Field Operator">_≈_</a> <a id="23529" href="Algebra.Bundles.html#23348" class="Field Operator">_+_</a> <a id="23533" href="Algebra.Bundles.html#23384" class="Field Operator">_*_</a> <a id="23537" href="Algebra.Bundles.html#23420" class="Field Operator">-_</a> <a id="23540" href="Algebra.Bundles.html#23456" class="Field">0#</a>
|
|||
|
|
|
|||
|
|
<a id="23546" class="Keyword">open</a> <a id="23551" href="Algebra.Structures.html#17013" class="Module">IsRingWithoutOne</a> <a id="23568" href="Algebra.Bundles.html#23488" class="Field">isRingWithoutOne</a> <a id="23585" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="RingWithoutOne.+-abelianGroup"></a><a id="23595" href="Algebra.Bundles.html#23595" class="Function">+-abelianGroup</a> <a id="23610" class="Symbol">:</a> <a id="23612" href="Algebra.Bundles.html#10570" class="Record">AbelianGroup</a> <a id="23625" class="Symbol">_</a> <a id="23627" class="Symbol">_</a>
|
|||
|
|
<a id="23631" href="Algebra.Bundles.html#23595" class="Function">+-abelianGroup</a> <a id="23646" class="Symbol">=</a> <a id="23648" class="Keyword">record</a> <a id="23655" class="Symbol">{</a> <a id="23657" href="Algebra.Bundles.html#10827" class="Field">isAbelianGroup</a> <a id="23672" class="Symbol">=</a> <a id="23674" href="Algebra.Structures.html#17098" class="Function">+-isAbelianGroup</a> <a id="23691" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="RingWithoutOne.*-semigroup"></a><a id="23696" href="Algebra.Bundles.html#23696" class="Function">*-semigroup</a> <a id="23708" class="Symbol">:</a> <a id="23710" href="Algebra.Bundles.html#4139" class="Record">Semigroup</a> <a id="23720" class="Symbol">_</a> <a id="23722" class="Symbol">_</a>
|
|||
|
|
<a id="23726" href="Algebra.Bundles.html#23696" class="Function">*-semigroup</a> <a id="23738" class="Symbol">=</a> <a id="23740" class="Keyword">record</a> <a id="23747" class="Symbol">{</a> <a id="23749" href="Algebra.Bundles.html#4307" class="Field">isSemigroup</a> <a id="23761" class="Symbol">=</a> <a id="23763" href="Algebra.Structures.html#18905" class="Function">*-isSemigroup</a> <a id="23777" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="23782" class="Keyword">open</a> <a id="23787" href="Algebra.Bundles.html#10570" class="Module">AbelianGroup</a> <a id="23800" href="Algebra.Bundles.html#23595" class="Function">+-abelianGroup</a> <a id="23815" class="Keyword">public</a>
|
|||
|
|
<a id="23826" class="Keyword">using</a> <a id="23832" class="Symbol">()</a> <a id="23835" class="Keyword">renaming</a> <a id="23844" class="Symbol">(</a><a id="23845" href="Algebra.Bundles.html#10921" class="Function">group</a> <a id="23851" class="Symbol">to</a> <a id="23854" class="Function">+-group</a><a id="23861" class="Symbol">;</a> <a id="23863" href="Algebra.Bundles.html#10299" class="Function">invertibleMagma</a> <a id="23879" class="Symbol">to</a> <a id="23882" class="Function">+-invertibleMagma</a><a id="23899" class="Symbol">;</a> <a id="23901" href="Algebra.Bundles.html#10417" class="Function">invertibleUnitalMagma</a> <a id="23923" class="Symbol">to</a> <a id="23926" class="Function">+-invertibleUnitalMagma</a><a id="23949" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="23954" class="Keyword">open</a> <a id="23959" href="Algebra.Bundles.html#4139" class="Module">Semigroup</a> <a id="23969" href="Algebra.Bundles.html#23696" class="Function">*-semigroup</a> <a id="23981" class="Keyword">public</a>
|
|||
|
|
<a id="23992" class="Keyword">using</a> <a id="23998" class="Symbol">()</a> <a id="24001" class="Keyword">renaming</a>
|
|||
|
|
<a id="24014" class="Symbol">(</a> <a id="24016" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a> <a id="24025" class="Symbol">to</a> <a id="24028" class="Function">*-rawMagma</a>
|
|||
|
|
<a id="24043" class="Symbol">;</a> <a id="24045" href="Algebra.Bundles.html#4383" class="Function">magma</a> <a id="24054" class="Symbol">to</a> <a id="24057" class="Function">*-magma</a>
|
|||
|
|
<a id="24069" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="24072" class="Comment">------------------------------------------------------------------------</a>
|
|||
|
|
<a id="24145" class="Comment">-- Bundles with 2 binary operations, 1 unary operation & 2 elements</a>
|
|||
|
|
<a id="24213" class="Comment">------------------------------------------------------------------------</a>
|
|||
|
|
|
|||
|
|
<a id="24287" class="Keyword">record</a> <a id="NonAssociativeRing"></a><a id="24294" href="Algebra.Bundles.html#24294" class="Record">NonAssociativeRing</a> <a id="24313" href="Algebra.Bundles.html#24313" class="Bound">c</a> <a id="24315" href="Algebra.Bundles.html#24315" class="Bound">ℓ</a> <a id="24317" class="Symbol">:</a> <a id="24319" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="24323" class="Symbol">(</a><a id="24324" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="24328" class="Symbol">(</a><a id="24329" href="Algebra.Bundles.html#24313" class="Bound">c</a> <a id="24331" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="24333" href="Algebra.Bundles.html#24315" class="Bound">ℓ</a><a id="24334" class="Symbol">))</a> <a id="24337" class="Keyword">where</a>
|
|||
|
|
<a id="24345" class="Keyword">infix</a> <a id="24352" class="Number">8</a> <a id="24354" href="Algebra.Bundles.html#24570" class="Field Operator">-_</a>
|
|||
|
|
<a id="24359" class="Keyword">infixl</a> <a id="24366" class="Number">7</a> <a id="24368" href="Algebra.Bundles.html#24530" class="Field Operator">_*_</a>
|
|||
|
|
<a id="24374" class="Keyword">infixl</a> <a id="24381" class="Number">6</a> <a id="24383" href="Algebra.Bundles.html#24490" class="Field Operator">_+_</a>
|
|||
|
|
<a id="24389" class="Keyword">infix</a> <a id="24396" class="Number">4</a> <a id="24398" href="Algebra.Bundles.html#24448" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="24404" class="Keyword">field</a>
|
|||
|
|
<a id="NonAssociativeRing.Carrier"></a><a id="24414" href="Algebra.Bundles.html#24414" class="Field">Carrier</a> <a id="24436" class="Symbol">:</a> <a id="24438" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="24442" href="Algebra.Bundles.html#24313" class="Bound">c</a>
|
|||
|
|
<a id="NonAssociativeRing._≈_"></a><a id="24448" href="Algebra.Bundles.html#24448" class="Field Operator">_≈_</a> <a id="24470" class="Symbol">:</a> <a id="24472" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="24476" href="Algebra.Bundles.html#24414" class="Field">Carrier</a> <a id="24484" href="Algebra.Bundles.html#24315" class="Bound">ℓ</a>
|
|||
|
|
<a id="NonAssociativeRing._+_"></a><a id="24490" href="Algebra.Bundles.html#24490" class="Field Operator">_+_</a> <a id="24512" class="Symbol">:</a> <a id="24514" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="24518" href="Algebra.Bundles.html#24414" class="Field">Carrier</a>
|
|||
|
|
<a id="NonAssociativeRing._*_"></a><a id="24530" href="Algebra.Bundles.html#24530" class="Field Operator">_*_</a> <a id="24552" class="Symbol">:</a> <a id="24554" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="24558" href="Algebra.Bundles.html#24414" class="Field">Carrier</a>
|
|||
|
|
<a id="NonAssociativeRing.-_"></a><a id="24570" href="Algebra.Bundles.html#24570" class="Field Operator">-_</a> <a id="24592" class="Symbol">:</a> <a id="24594" href="Algebra.Core.html#484" class="Function">Op₁</a> <a id="24598" href="Algebra.Bundles.html#24414" class="Field">Carrier</a>
|
|||
|
|
<a id="NonAssociativeRing.0#"></a><a id="24610" href="Algebra.Bundles.html#24610" class="Field">0#</a> <a id="24632" class="Symbol">:</a> <a id="24634" href="Algebra.Bundles.html#24414" class="Field">Carrier</a>
|
|||
|
|
<a id="NonAssociativeRing.1#"></a><a id="24646" href="Algebra.Bundles.html#24646" class="Field">1#</a> <a id="24668" class="Symbol">:</a> <a id="24670" href="Algebra.Bundles.html#24414" class="Field">Carrier</a>
|
|||
|
|
<a id="NonAssociativeRing.isNonAssociativeRing"></a><a id="24682" href="Algebra.Bundles.html#24682" class="Field">isNonAssociativeRing</a> <a id="24704" class="Symbol">:</a> <a id="24706" href="Algebra.Structures.html#19369" class="Record">IsNonAssociativeRing</a> <a id="24727" href="Algebra.Bundles.html#24448" class="Field Operator">_≈_</a> <a id="24731" href="Algebra.Bundles.html#24490" class="Field Operator">_+_</a> <a id="24735" href="Algebra.Bundles.html#24530" class="Field Operator">_*_</a> <a id="24739" href="Algebra.Bundles.html#24570" class="Field Operator">-_</a> <a id="24742" href="Algebra.Bundles.html#24610" class="Field">0#</a> <a id="24745" href="Algebra.Bundles.html#24646" class="Field">1#</a>
|
|||
|
|
|
|||
|
|
<a id="24751" class="Keyword">open</a> <a id="24756" href="Algebra.Structures.html#19369" class="Module">IsNonAssociativeRing</a> <a id="24777" href="Algebra.Bundles.html#24682" class="Field">isNonAssociativeRing</a> <a id="24798" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="NonAssociativeRing.+-abelianGroup"></a><a id="24808" href="Algebra.Bundles.html#24808" class="Function">+-abelianGroup</a> <a id="24823" class="Symbol">:</a> <a id="24825" href="Algebra.Bundles.html#10570" class="Record">AbelianGroup</a> <a id="24838" class="Symbol">_</a> <a id="24840" class="Symbol">_</a>
|
|||
|
|
<a id="24844" href="Algebra.Bundles.html#24808" class="Function">+-abelianGroup</a> <a id="24859" class="Symbol">=</a> <a id="24861" class="Keyword">record</a> <a id="24868" class="Symbol">{</a> <a id="24870" href="Algebra.Bundles.html#10827" class="Field">isAbelianGroup</a> <a id="24885" class="Symbol">=</a> <a id="24887" href="Algebra.Structures.html#19461" class="Function">+-isAbelianGroup</a> <a id="24904" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="24909" class="Keyword">open</a> <a id="24914" href="Algebra.Bundles.html#10570" class="Module">AbelianGroup</a> <a id="24927" href="Algebra.Bundles.html#24808" class="Function">+-abelianGroup</a> <a id="24942" class="Keyword">public</a>
|
|||
|
|
<a id="24953" class="Keyword">using</a> <a id="24959" class="Symbol">()</a> <a id="24962" class="Keyword">renaming</a> <a id="24971" class="Symbol">(</a><a id="24972" href="Algebra.Bundles.html#10921" class="Function">group</a> <a id="24978" class="Symbol">to</a> <a id="24981" class="Function">+-group</a><a id="24988" class="Symbol">;</a> <a id="24990" href="Algebra.Bundles.html#10299" class="Function">invertibleMagma</a> <a id="25006" class="Symbol">to</a> <a id="25009" class="Function">+-invertibleMagma</a><a id="25026" class="Symbol">;</a> <a id="25028" href="Algebra.Bundles.html#10417" class="Function">invertibleUnitalMagma</a> <a id="25050" class="Symbol">to</a> <a id="25053" class="Function">+-invertibleUnitalMagma</a><a id="25076" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="NonAssociativeRing.*-unitalMagma"></a><a id="25081" href="Algebra.Bundles.html#25081" class="Function">*-unitalMagma</a> <a id="25095" class="Symbol">:</a> <a id="25097" href="Algebra.Bundles.html#5662" class="Record">UnitalMagma</a> <a id="25109" class="Symbol">_</a> <a id="25111" class="Symbol">_</a>
|
|||
|
|
<a id="25115" href="Algebra.Bundles.html#25081" class="Function">*-unitalMagma</a> <a id="25129" class="Symbol">=</a> <a id="25131" class="Keyword">record</a> <a id="25138" class="Symbol">{</a> <a id="25140" href="Algebra.Bundles.html#5846" class="Field">isUnitalMagma</a> <a id="25154" class="Symbol">=</a> <a id="25156" href="Algebra.Structures.html#21205" class="Function">*-isUnitalMagma</a><a id="25171" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="25176" class="Keyword">open</a> <a id="25181" href="Algebra.Bundles.html#5662" class="Module">UnitalMagma</a> <a id="25193" href="Algebra.Bundles.html#25081" class="Function">*-unitalMagma</a> <a id="25207" class="Keyword">public</a>
|
|||
|
|
<a id="25218" class="Keyword">using</a> <a id="25224" class="Symbol">()</a> <a id="25227" class="Keyword">renaming</a> <a id="25236" class="Symbol">(</a><a id="25237" href="Algebra.Bundles.html#5932" class="Function">magma</a> <a id="25243" class="Symbol">to</a> <a id="25246" class="Function">*-magma</a><a id="25253" class="Symbol">;</a> <a id="25255" href="Algebra.Structures.html#3787" class="Function">identity</a> <a id="25264" class="Symbol">to</a> <a id="25267" class="Function">*-identity</a><a id="25277" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="25280" class="Keyword">record</a> <a id="Nearring"></a><a id="25287" href="Algebra.Bundles.html#25287" class="Record">Nearring</a> <a id="25296" href="Algebra.Bundles.html#25296" class="Bound">c</a> <a id="25298" href="Algebra.Bundles.html#25298" class="Bound">ℓ</a> <a id="25300" class="Symbol">:</a> <a id="25302" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="25306" class="Symbol">(</a><a id="25307" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="25311" class="Symbol">(</a><a id="25312" href="Algebra.Bundles.html#25296" class="Bound">c</a> <a id="25314" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="25316" href="Algebra.Bundles.html#25298" class="Bound">ℓ</a><a id="25317" class="Symbol">))</a> <a id="25320" class="Keyword">where</a>
|
|||
|
|
<a id="25328" class="Keyword">infixl</a> <a id="25335" class="Number">7</a> <a id="25337" href="Algebra.Bundles.html#25475" class="Field Operator">_*_</a>
|
|||
|
|
<a id="25343" class="Keyword">infixl</a> <a id="25350" class="Number">6</a> <a id="25352" href="Algebra.Bundles.html#25443" class="Field Operator">_+_</a>
|
|||
|
|
<a id="25358" class="Keyword">infix</a> <a id="25365" class="Number">4</a> <a id="25367" href="Algebra.Bundles.html#25409" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="25373" class="Keyword">field</a>
|
|||
|
|
<a id="Nearring.Carrier"></a><a id="25383" href="Algebra.Bundles.html#25383" class="Field">Carrier</a> <a id="25397" class="Symbol">:</a> <a id="25399" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="25403" href="Algebra.Bundles.html#25296" class="Bound">c</a>
|
|||
|
|
<a id="Nearring._≈_"></a><a id="25409" href="Algebra.Bundles.html#25409" class="Field Operator">_≈_</a> <a id="25423" class="Symbol">:</a> <a id="25425" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="25429" href="Algebra.Bundles.html#25383" class="Field">Carrier</a> <a id="25437" href="Algebra.Bundles.html#25298" class="Bound">ℓ</a>
|
|||
|
|
<a id="Nearring._+_"></a><a id="25443" href="Algebra.Bundles.html#25443" class="Field Operator">_+_</a> <a id="25457" class="Symbol">:</a> <a id="25459" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="25463" href="Algebra.Bundles.html#25383" class="Field">Carrier</a>
|
|||
|
|
<a id="Nearring._*_"></a><a id="25475" href="Algebra.Bundles.html#25475" class="Field Operator">_*_</a> <a id="25489" class="Symbol">:</a> <a id="25491" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="25495" href="Algebra.Bundles.html#25383" class="Field">Carrier</a>
|
|||
|
|
<a id="Nearring.-_"></a><a id="25507" href="Algebra.Bundles.html#25507" class="Field Operator">-_</a> <a id="25521" class="Symbol">:</a> <a id="25523" href="Algebra.Core.html#484" class="Function">Op₁</a> <a id="25527" href="Algebra.Bundles.html#25383" class="Field">Carrier</a>
|
|||
|
|
<a id="Nearring.0#"></a><a id="25539" href="Algebra.Bundles.html#25539" class="Field">0#</a> <a id="25553" class="Symbol">:</a> <a id="25555" href="Algebra.Bundles.html#25383" class="Field">Carrier</a>
|
|||
|
|
<a id="Nearring.1#"></a><a id="25567" href="Algebra.Bundles.html#25567" class="Field">1#</a> <a id="25581" class="Symbol">:</a> <a id="25583" href="Algebra.Bundles.html#25383" class="Field">Carrier</a>
|
|||
|
|
<a id="Nearring.isNearring"></a><a id="25595" href="Algebra.Bundles.html#25595" class="Field">isNearring</a> <a id="25609" class="Symbol">:</a> <a id="25611" href="Algebra.Structures.html#21468" class="Record">IsNearring</a> <a id="25622" href="Algebra.Bundles.html#25409" class="Field Operator">_≈_</a> <a id="25626" href="Algebra.Bundles.html#25443" class="Field Operator">_+_</a> <a id="25630" href="Algebra.Bundles.html#25475" class="Field Operator">_*_</a> <a id="25634" href="Algebra.Bundles.html#25539" class="Field">0#</a> <a id="25637" href="Algebra.Bundles.html#25567" class="Field">1#</a> <a id="25640" href="Algebra.Bundles.html#25507" class="Field Operator">-_</a>
|
|||
|
|
|
|||
|
|
<a id="25646" class="Keyword">open</a> <a id="25651" href="Algebra.Structures.html#21468" class="Module">IsNearring</a> <a id="25662" href="Algebra.Bundles.html#25595" class="Field">isNearring</a> <a id="25673" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="Nearring.quasiring"></a><a id="25683" href="Algebra.Bundles.html#25683" class="Function">quasiring</a> <a id="25693" class="Symbol">:</a> <a id="25695" href="Algebra.Bundles.html#22031" class="Record">Quasiring</a> <a id="25705" class="Symbol">_</a> <a id="25707" class="Symbol">_</a>
|
|||
|
|
<a id="25711" href="Algebra.Bundles.html#25683" class="Function">quasiring</a> <a id="25721" class="Symbol">=</a> <a id="25723" class="Keyword">record</a> <a id="25730" class="Symbol">{</a> <a id="25732" href="Algebra.Bundles.html#22308" class="Field">isQuasiring</a> <a id="25744" class="Symbol">=</a> <a id="25746" href="Algebra.Structures.html#21551" class="Function">isQuasiring</a> <a id="25758" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="25763" class="Keyword">open</a> <a id="25768" href="Algebra.Bundles.html#22031" class="Module">Quasiring</a> <a id="25778" href="Algebra.Bundles.html#25683" class="Function">quasiring</a> <a id="25788" class="Keyword">public</a>
|
|||
|
|
<a id="25799" class="Keyword">using</a>
|
|||
|
|
<a id="25809" class="Symbol">(</a><a id="25810" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="25813" class="Symbol">;</a> <a id="25815" href="Algebra.Bundles.html#22542" class="Function">+-rawMagma</a><a id="25825" class="Symbol">;</a> <a id="25827" href="Algebra.Bundles.html#22575" class="Function">+-magma</a><a id="25834" class="Symbol">;</a> <a id="25836" href="Algebra.Bundles.html#22639" class="Function">+-unitalMagma</a><a id="25849" class="Symbol">;</a> <a id="25851" href="Algebra.Bundles.html#22605" class="Function">+-semigroup</a><a id="25862" class="Symbol">;</a> <a id="25864" href="Algebra.Bundles.html#22396" class="Function">+-monoid</a><a id="25872" class="Symbol">;</a> <a id="25874" href="Algebra.Bundles.html#22675" class="Function">+-rawMonoid</a>
|
|||
|
|
<a id="25890" class="Symbol">;</a><a id="25891" href="Algebra.Bundles.html#22836" class="Function">*-rawMagma</a><a id="25901" class="Symbol">;</a> <a id="25903" href="Algebra.Bundles.html#22866" class="Function">*-magma</a><a id="25910" class="Symbol">;</a> <a id="25912" href="Algebra.Bundles.html#22893" class="Function">*-semigroup</a><a id="25923" class="Symbol">;</a> <a id="25925" href="Algebra.Bundles.html#22696" class="Function">*-monoid</a>
|
|||
|
|
<a id="25938" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="25942" class="Keyword">record</a> <a id="Ring"></a><a id="25949" href="Algebra.Bundles.html#25949" class="Record">Ring</a> <a id="25954" href="Algebra.Bundles.html#25954" class="Bound">c</a> <a id="25956" href="Algebra.Bundles.html#25956" class="Bound">ℓ</a> <a id="25958" class="Symbol">:</a> <a id="25960" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="25964" class="Symbol">(</a><a id="25965" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="25969" class="Symbol">(</a><a id="25970" href="Algebra.Bundles.html#25954" class="Bound">c</a> <a id="25972" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="25974" href="Algebra.Bundles.html#25956" class="Bound">ℓ</a><a id="25975" class="Symbol">))</a> <a id="25978" class="Keyword">where</a>
|
|||
|
|
<a id="25986" class="Keyword">infix</a> <a id="25993" class="Number">8</a> <a id="25995" href="Algebra.Bundles.html#26155" class="Field Operator">-_</a>
|
|||
|
|
<a id="26000" class="Keyword">infixl</a> <a id="26007" class="Number">7</a> <a id="26009" href="Algebra.Bundles.html#26129" class="Field Operator">_*_</a>
|
|||
|
|
<a id="26015" class="Keyword">infixl</a> <a id="26022" class="Number">6</a> <a id="26024" href="Algebra.Bundles.html#26103" class="Field Operator">_+_</a>
|
|||
|
|
<a id="26030" class="Keyword">infix</a> <a id="26037" class="Number">4</a> <a id="26039" href="Algebra.Bundles.html#26075" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="26045" class="Keyword">field</a>
|
|||
|
|
<a id="Ring.Carrier"></a><a id="26055" href="Algebra.Bundles.html#26055" class="Field">Carrier</a> <a id="26063" class="Symbol">:</a> <a id="26065" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="26069" href="Algebra.Bundles.html#25954" class="Bound">c</a>
|
|||
|
|
<a id="Ring._≈_"></a><a id="26075" href="Algebra.Bundles.html#26075" class="Field Operator">_≈_</a> <a id="26083" class="Symbol">:</a> <a id="26085" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="26089" href="Algebra.Bundles.html#26055" class="Field">Carrier</a> <a id="26097" href="Algebra.Bundles.html#25956" class="Bound">ℓ</a>
|
|||
|
|
<a id="Ring._+_"></a><a id="26103" href="Algebra.Bundles.html#26103" class="Field Operator">_+_</a> <a id="26111" class="Symbol">:</a> <a id="26113" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="26117" href="Algebra.Bundles.html#26055" class="Field">Carrier</a>
|
|||
|
|
<a id="Ring._*_"></a><a id="26129" href="Algebra.Bundles.html#26129" class="Field Operator">_*_</a> <a id="26137" class="Symbol">:</a> <a id="26139" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="26143" href="Algebra.Bundles.html#26055" class="Field">Carrier</a>
|
|||
|
|
<a id="Ring.-_"></a><a id="26155" href="Algebra.Bundles.html#26155" class="Field Operator">-_</a> <a id="26163" class="Symbol">:</a> <a id="26165" href="Algebra.Core.html#484" class="Function">Op₁</a> <a id="26169" href="Algebra.Bundles.html#26055" class="Field">Carrier</a>
|
|||
|
|
<a id="Ring.0#"></a><a id="26181" href="Algebra.Bundles.html#26181" class="Field">0#</a> <a id="26189" class="Symbol">:</a> <a id="26191" href="Algebra.Bundles.html#26055" class="Field">Carrier</a>
|
|||
|
|
<a id="Ring.1#"></a><a id="26203" href="Algebra.Bundles.html#26203" class="Field">1#</a> <a id="26211" class="Symbol">:</a> <a id="26213" href="Algebra.Bundles.html#26055" class="Field">Carrier</a>
|
|||
|
|
<a id="Ring.isRing"></a><a id="26225" href="Algebra.Bundles.html#26225" class="Field">isRing</a> <a id="26233" class="Symbol">:</a> <a id="26235" href="Algebra.Structures.html#21839" class="Record">IsRing</a> <a id="26242" href="Algebra.Bundles.html#26075" class="Field Operator">_≈_</a> <a id="26246" href="Algebra.Bundles.html#26103" class="Field Operator">_+_</a> <a id="26250" href="Algebra.Bundles.html#26129" class="Field Operator">_*_</a> <a id="26254" href="Algebra.Bundles.html#26155" class="Field Operator">-_</a> <a id="26257" href="Algebra.Bundles.html#26181" class="Field">0#</a> <a id="26260" href="Algebra.Bundles.html#26203" class="Field">1#</a>
|
|||
|
|
|
|||
|
|
<a id="26266" class="Keyword">open</a> <a id="26271" href="Algebra.Structures.html#21839" class="Module">IsRing</a> <a id="26278" href="Algebra.Bundles.html#26225" class="Field">isRing</a> <a id="26285" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="Ring.+-abelianGroup"></a><a id="26295" href="Algebra.Bundles.html#26295" class="Function">+-abelianGroup</a> <a id="26310" class="Symbol">:</a> <a id="26312" href="Algebra.Bundles.html#10570" class="Record">AbelianGroup</a> <a id="26325" class="Symbol">_</a> <a id="26327" class="Symbol">_</a>
|
|||
|
|
<a id="26331" href="Algebra.Bundles.html#26295" class="Function">+-abelianGroup</a> <a id="26346" class="Symbol">=</a> <a id="26348" class="Keyword">record</a> <a id="26355" class="Symbol">{</a> <a id="26357" href="Algebra.Bundles.html#10827" class="Field">isAbelianGroup</a> <a id="26372" class="Symbol">=</a> <a id="26374" href="Algebra.Structures.html#21917" class="Function">+-isAbelianGroup</a> <a id="26391" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="Ring.ringWithoutOne"></a><a id="26396" href="Algebra.Bundles.html#26396" class="Function">ringWithoutOne</a> <a id="26411" class="Symbol">:</a> <a id="26413" href="Algebra.Bundles.html#23164" class="Record">RingWithoutOne</a> <a id="26428" class="Symbol">_</a> <a id="26430" class="Symbol">_</a>
|
|||
|
|
<a id="26434" href="Algebra.Bundles.html#26396" class="Function">ringWithoutOne</a> <a id="26449" class="Symbol">=</a> <a id="26451" class="Keyword">record</a> <a id="26458" class="Symbol">{</a> <a id="26460" href="Algebra.Bundles.html#23488" class="Field">isRingWithoutOne</a> <a id="26477" class="Symbol">=</a> <a id="26479" href="Algebra.Structures.html#22115" class="Function">isRingWithoutOne</a> <a id="26496" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="Ring.semiring"></a><a id="26501" href="Algebra.Bundles.html#26501" class="Function">semiring</a> <a id="26510" class="Symbol">:</a> <a id="26512" href="Algebra.Bundles.html#16346" class="Record">Semiring</a> <a id="26521" class="Symbol">_</a> <a id="26523" class="Symbol">_</a>
|
|||
|
|
<a id="26527" href="Algebra.Bundles.html#26501" class="Function">semiring</a> <a id="26536" class="Symbol">=</a> <a id="26538" class="Keyword">record</a> <a id="26545" class="Symbol">{</a> <a id="26547" href="Algebra.Bundles.html#16604" class="Field">isSemiring</a> <a id="26558" class="Symbol">=</a> <a id="26560" href="Algebra.Structures.html#23016" class="Function">isSemiring</a> <a id="26571" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="26576" class="Keyword">open</a> <a id="26581" href="Algebra.Bundles.html#16346" class="Module">Semiring</a> <a id="26590" href="Algebra.Bundles.html#26501" class="Function">semiring</a> <a id="26599" class="Keyword">public</a>
|
|||
|
|
<a id="26610" class="Keyword">using</a>
|
|||
|
|
<a id="26620" class="Symbol">(</a> <a id="26622" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="26625" class="Symbol">;</a> <a id="26627" href="Algebra.Bundles.html#15764" class="Function">+-rawMagma</a><a id="26637" class="Symbol">;</a> <a id="26639" href="Algebra.Bundles.html#15805" class="Function">+-magma</a><a id="26646" class="Symbol">;</a> <a id="26648" href="Algebra.Bundles.html#15843" class="Function">+-unitalMagma</a><a id="26661" class="Symbol">;</a> <a id="26663" href="Algebra.Bundles.html#15887" class="Function">+-commutativeMagma</a>
|
|||
|
|
<a id="26686" class="Symbol">;</a> <a id="26688" href="Algebra.Bundles.html#15936" class="Function">+-semigroup</a><a id="26699" class="Symbol">;</a> <a id="26701" href="Algebra.Bundles.html#15978" class="Function">+-commutativeSemigroup</a>
|
|||
|
|
<a id="26728" class="Symbol">;</a> <a id="26730" href="Algebra.Bundles.html#16231" class="Function">*-rawMagma</a><a id="26740" class="Symbol">;</a> <a id="26742" href="Algebra.Bundles.html#16261" class="Function">*-magma</a><a id="26749" class="Symbol">;</a> <a id="26751" href="Algebra.Bundles.html#16288" class="Function">*-semigroup</a>
|
|||
|
|
<a id="26767" class="Symbol">;</a> <a id="26769" href="Algebra.Bundles.html#16031" class="Function">+-rawMonoid</a><a id="26780" class="Symbol">;</a> <a id="26782" href="Algebra.Bundles.html#16073" class="Function">+-monoid</a> <a id="26791" class="Symbol">;</a> <a id="26793" href="Algebra.Bundles.html#15529" class="Function">+-commutativeMonoid</a>
|
|||
|
|
<a id="26817" class="Symbol">;</a> <a id="26819" href="Algebra.Bundles.html#16319" class="Function">*-rawMonoid</a><a id="26830" class="Symbol">;</a> <a id="26832" href="Algebra.Bundles.html#16091" class="Function">*-monoid</a>
|
|||
|
|
<a id="26845" class="Symbol">;</a> <a id="26847" href="Algebra.Bundles.html#12966" class="Function">nearSemiring</a><a id="26859" class="Symbol">;</a> <a id="26861" href="Algebra.Bundles.html#17258" class="Function">semiringWithoutOne</a>
|
|||
|
|
<a id="26884" class="Symbol">;</a> <a id="26886" href="Algebra.Bundles.html#16686" class="Function">semiringWithoutAnnihilatingZero</a>
|
|||
|
|
<a id="26922" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="26927" class="Keyword">open</a> <a id="26932" href="Algebra.Bundles.html#10570" class="Module">AbelianGroup</a> <a id="26945" href="Algebra.Bundles.html#26295" class="Function">+-abelianGroup</a> <a id="26960" class="Keyword">public</a>
|
|||
|
|
<a id="26971" class="Keyword">using</a> <a id="26977" class="Symbol">()</a> <a id="26980" class="Keyword">renaming</a> <a id="26989" class="Symbol">(</a><a id="26990" href="Algebra.Bundles.html#10921" class="Function">group</a> <a id="26996" class="Symbol">to</a> <a id="26999" class="Function">+-group</a><a id="27006" class="Symbol">;</a> <a id="27008" href="Algebra.Bundles.html#10299" class="Function">invertibleMagma</a> <a id="27024" class="Symbol">to</a> <a id="27027" class="Function">+-invertibleMagma</a><a id="27044" class="Symbol">;</a> <a id="27046" href="Algebra.Bundles.html#10417" class="Function">invertibleUnitalMagma</a> <a id="27068" class="Symbol">to</a> <a id="27071" class="Function">+-invertibleUnitalMagma</a><a id="27094" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="Ring.rawRing"></a><a id="27099" href="Algebra.Bundles.html#27099" class="Function">rawRing</a> <a id="27107" class="Symbol">:</a> <a id="27109" href="Algebra.Bundles.Raw.html#4595" class="Record">RawRing</a> <a id="27117" class="Symbol">_</a> <a id="27119" class="Symbol">_</a>
|
|||
|
|
<a id="27123" href="Algebra.Bundles.html#27099" class="Function">rawRing</a> <a id="27131" class="Symbol">=</a> <a id="27133" class="Keyword">record</a>
|
|||
|
|
<a id="27144" class="Symbol">{</a> <a id="27146" href="Algebra.Bundles.Raw.html#4724" class="Field Operator">_≈_</a> <a id="27150" class="Symbol">=</a> <a id="27152" href="Algebra.Bundles.html#26075" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="27160" class="Symbol">;</a> <a id="27162" href="Algebra.Bundles.Raw.html#4752" class="Field Operator">_+_</a> <a id="27166" class="Symbol">=</a> <a id="27168" href="Algebra.Bundles.html#26103" class="Field Operator">_+_</a>
|
|||
|
|
<a id="27176" class="Symbol">;</a> <a id="27178" href="Algebra.Bundles.Raw.html#4778" class="Field Operator">_*_</a> <a id="27182" class="Symbol">=</a> <a id="27184" href="Algebra.Bundles.html#26129" class="Field Operator">_*_</a>
|
|||
|
|
<a id="27192" class="Symbol">;</a> <a id="27194" href="Algebra.Bundles.Raw.html#4804" class="Field Operator">-_</a> <a id="27198" class="Symbol">=</a> <a id="27200" href="Algebra.Bundles.html#26155" class="Field Operator">-_</a>
|
|||
|
|
<a id="27207" class="Symbol">;</a> <a id="27209" href="Algebra.Bundles.Raw.html#4830" class="Field">0#</a> <a id="27213" class="Symbol">=</a> <a id="27215" href="Algebra.Bundles.html#26181" class="Field">0#</a>
|
|||
|
|
<a id="27222" class="Symbol">;</a> <a id="27224" href="Algebra.Bundles.Raw.html#4852" class="Field">1#</a> <a id="27228" class="Symbol">=</a> <a id="27230" href="Algebra.Bundles.html#26203" class="Field">1#</a>
|
|||
|
|
<a id="27237" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="27241" class="Keyword">record</a> <a id="CommutativeRing"></a><a id="27248" href="Algebra.Bundles.html#27248" class="Record">CommutativeRing</a> <a id="27264" href="Algebra.Bundles.html#27264" class="Bound">c</a> <a id="27266" href="Algebra.Bundles.html#27266" class="Bound">ℓ</a> <a id="27268" class="Symbol">:</a> <a id="27270" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="27274" class="Symbol">(</a><a id="27275" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="27279" class="Symbol">(</a><a id="27280" href="Algebra.Bundles.html#27264" class="Bound">c</a> <a id="27282" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="27284" href="Algebra.Bundles.html#27266" class="Bound">ℓ</a><a id="27285" class="Symbol">))</a> <a id="27288" class="Keyword">where</a>
|
|||
|
|
<a id="27296" class="Keyword">infix</a> <a id="27303" class="Number">8</a> <a id="27305" href="Algebra.Bundles.html#27505" class="Field Operator">-_</a>
|
|||
|
|
<a id="27310" class="Keyword">infixl</a> <a id="27317" class="Number">7</a> <a id="27319" href="Algebra.Bundles.html#27469" class="Field Operator">_*_</a>
|
|||
|
|
<a id="27325" class="Keyword">infixl</a> <a id="27332" class="Number">6</a> <a id="27334" href="Algebra.Bundles.html#27433" class="Field Operator">_+_</a>
|
|||
|
|
<a id="27340" class="Keyword">infix</a> <a id="27347" class="Number">4</a> <a id="27349" href="Algebra.Bundles.html#27395" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="27355" class="Keyword">field</a>
|
|||
|
|
<a id="CommutativeRing.Carrier"></a><a id="27365" href="Algebra.Bundles.html#27365" class="Field">Carrier</a> <a id="27383" class="Symbol">:</a> <a id="27385" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="27389" href="Algebra.Bundles.html#27264" class="Bound">c</a>
|
|||
|
|
<a id="CommutativeRing._≈_"></a><a id="27395" href="Algebra.Bundles.html#27395" class="Field Operator">_≈_</a> <a id="27413" class="Symbol">:</a> <a id="27415" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="27419" href="Algebra.Bundles.html#27365" class="Field">Carrier</a> <a id="27427" href="Algebra.Bundles.html#27266" class="Bound">ℓ</a>
|
|||
|
|
<a id="CommutativeRing._+_"></a><a id="27433" href="Algebra.Bundles.html#27433" class="Field Operator">_+_</a> <a id="27451" class="Symbol">:</a> <a id="27453" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="27457" href="Algebra.Bundles.html#27365" class="Field">Carrier</a>
|
|||
|
|
<a id="CommutativeRing._*_"></a><a id="27469" href="Algebra.Bundles.html#27469" class="Field Operator">_*_</a> <a id="27487" class="Symbol">:</a> <a id="27489" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="27493" href="Algebra.Bundles.html#27365" class="Field">Carrier</a>
|
|||
|
|
<a id="CommutativeRing.-_"></a><a id="27505" href="Algebra.Bundles.html#27505" class="Field Operator">-_</a> <a id="27523" class="Symbol">:</a> <a id="27525" href="Algebra.Core.html#484" class="Function">Op₁</a> <a id="27529" href="Algebra.Bundles.html#27365" class="Field">Carrier</a>
|
|||
|
|
<a id="CommutativeRing.0#"></a><a id="27541" href="Algebra.Bundles.html#27541" class="Field">0#</a> <a id="27559" class="Symbol">:</a> <a id="27561" href="Algebra.Bundles.html#27365" class="Field">Carrier</a>
|
|||
|
|
<a id="CommutativeRing.1#"></a><a id="27573" href="Algebra.Bundles.html#27573" class="Field">1#</a> <a id="27591" class="Symbol">:</a> <a id="27593" href="Algebra.Bundles.html#27365" class="Field">Carrier</a>
|
|||
|
|
<a id="CommutativeRing.isCommutativeRing"></a><a id="27605" href="Algebra.Bundles.html#27605" class="Field">isCommutativeRing</a> <a id="27623" class="Symbol">:</a> <a id="27625" href="Algebra.Structures.html#23275" class="Record">IsCommutativeRing</a> <a id="27643" href="Algebra.Bundles.html#27395" class="Field Operator">_≈_</a> <a id="27647" href="Algebra.Bundles.html#27433" class="Field Operator">_+_</a> <a id="27651" href="Algebra.Bundles.html#27469" class="Field Operator">_*_</a> <a id="27655" href="Algebra.Bundles.html#27505" class="Field Operator">-_</a> <a id="27658" href="Algebra.Bundles.html#27541" class="Field">0#</a> <a id="27661" href="Algebra.Bundles.html#27573" class="Field">1#</a>
|
|||
|
|
|
|||
|
|
<a id="27667" class="Keyword">open</a> <a id="27672" href="Algebra.Structures.html#23275" class="Module">IsCommutativeRing</a> <a id="27690" href="Algebra.Bundles.html#27605" class="Field">isCommutativeRing</a> <a id="27708" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="CommutativeRing.ring"></a><a id="27718" href="Algebra.Bundles.html#27718" class="Function">ring</a> <a id="27723" class="Symbol">:</a> <a id="27725" href="Algebra.Bundles.html#25949" class="Record">Ring</a> <a id="27730" class="Symbol">_</a> <a id="27732" class="Symbol">_</a>
|
|||
|
|
<a id="27736" href="Algebra.Bundles.html#27718" class="Function">ring</a> <a id="27741" class="Symbol">=</a> <a id="27743" class="Keyword">record</a> <a id="27750" class="Symbol">{</a> <a id="27752" href="Algebra.Bundles.html#26225" class="Field">isRing</a> <a id="27759" class="Symbol">=</a> <a id="27761" href="Algebra.Structures.html#23372" class="Function">isRing</a> <a id="27768" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="27773" class="Keyword">open</a> <a id="27778" href="Algebra.Bundles.html#25949" class="Module">Ring</a> <a id="27783" href="Algebra.Bundles.html#27718" class="Function">ring</a> <a id="27788" class="Keyword">public</a> <a id="27795" class="Keyword">using</a> <a id="27801" class="Symbol">(</a><a id="27802" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="27805" class="Symbol">;</a> <a id="27807" href="Algebra.Bundles.html#27099" class="Function">rawRing</a><a id="27814" class="Symbol">;</a> <a id="27816" href="Algebra.Bundles.html#27027" class="Function">+-invertibleMagma</a><a id="27833" class="Symbol">;</a> <a id="27835" href="Algebra.Bundles.html#27071" class="Function">+-invertibleUnitalMagma</a><a id="27858" class="Symbol">;</a> <a id="27860" href="Algebra.Bundles.html#26999" class="Function">+-group</a><a id="27867" class="Symbol">;</a> <a id="27869" href="Algebra.Bundles.html#26295" class="Function">+-abelianGroup</a><a id="27883" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="CommutativeRing.commutativeSemiring"></a><a id="27888" href="Algebra.Bundles.html#27888" class="Function">commutativeSemiring</a> <a id="27908" class="Symbol">:</a> <a id="27910" href="Algebra.Bundles.html#17471" class="Record">CommutativeSemiring</a> <a id="27930" class="Symbol">_</a> <a id="27932" class="Symbol">_</a>
|
|||
|
|
<a id="27936" href="Algebra.Bundles.html#27888" class="Function">commutativeSemiring</a> <a id="27956" class="Symbol">=</a>
|
|||
|
|
<a id="27962" class="Keyword">record</a> <a id="27969" class="Symbol">{</a> <a id="27971" href="Algebra.Bundles.html#17806" class="Field">isCommutativeSemiring</a> <a id="27993" class="Symbol">=</a> <a id="27995" href="Algebra.Structures.html#23459" class="Function">isCommutativeSemiring</a> <a id="28017" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="28022" class="Keyword">open</a> <a id="28027" href="Algebra.Bundles.html#17471" class="Module">CommutativeSemiring</a> <a id="28047" href="Algebra.Bundles.html#27888" class="Function">commutativeSemiring</a> <a id="28067" class="Keyword">public</a>
|
|||
|
|
<a id="28078" class="Keyword">using</a>
|
|||
|
|
<a id="28088" class="Symbol">(</a> <a id="28090" href="Algebra.Bundles.html#15764" class="Function">+-rawMagma</a><a id="28100" class="Symbol">;</a> <a id="28102" href="Algebra.Bundles.html#15805" class="Function">+-magma</a><a id="28109" class="Symbol">;</a> <a id="28111" href="Algebra.Bundles.html#15843" class="Function">+-unitalMagma</a><a id="28124" class="Symbol">;</a> <a id="28126" href="Algebra.Bundles.html#15887" class="Function">+-commutativeMagma</a>
|
|||
|
|
<a id="28149" class="Symbol">;</a> <a id="28151" href="Algebra.Bundles.html#15936" class="Function">+-semigroup</a><a id="28162" class="Symbol">;</a> <a id="28164" href="Algebra.Bundles.html#15978" class="Function">+-commutativeSemigroup</a>
|
|||
|
|
<a id="28191" class="Symbol">;</a> <a id="28193" href="Algebra.Bundles.html#16231" class="Function">*-rawMagma</a><a id="28203" class="Symbol">;</a> <a id="28205" href="Algebra.Bundles.html#16261" class="Function">*-magma</a><a id="28212" class="Symbol">;</a> <a id="28214" href="Algebra.Bundles.html#18611" class="Function">*-commutativeMagma</a><a id="28232" class="Symbol">;</a> <a id="28234" href="Algebra.Bundles.html#16288" class="Function">*-semigroup</a><a id="28245" class="Symbol">;</a> <a id="28247" href="Algebra.Bundles.html#18660" class="Function">*-commutativeSemigroup</a>
|
|||
|
|
<a id="28274" class="Symbol">;</a> <a id="28276" href="Algebra.Bundles.html#16031" class="Function">+-rawMonoid</a><a id="28287" class="Symbol">;</a> <a id="28289" href="Algebra.Bundles.html#16073" class="Function">+-monoid</a><a id="28297" class="Symbol">;</a> <a id="28299" href="Algebra.Bundles.html#15529" class="Function">+-commutativeMonoid</a>
|
|||
|
|
<a id="28323" class="Symbol">;</a> <a id="28325" href="Algebra.Bundles.html#16319" class="Function">*-rawMonoid</a><a id="28336" class="Symbol">;</a> <a id="28338" href="Algebra.Bundles.html#16091" class="Function">*-monoid</a><a id="28346" class="Symbol">;</a> <a id="28348" href="Algebra.Bundles.html#18375" class="Function">*-commutativeMonoid</a>
|
|||
|
|
<a id="28372" class="Symbol">;</a> <a id="28374" href="Algebra.Bundles.html#12966" class="Function">nearSemiring</a><a id="28386" class="Symbol">;</a> <a id="28388" href="Algebra.Bundles.html#17258" class="Function">semiringWithoutOne</a>
|
|||
|
|
<a id="28411" class="Symbol">;</a> <a id="28413" href="Algebra.Bundles.html#16686" class="Function">semiringWithoutAnnihilatingZero</a><a id="28444" class="Symbol">;</a> <a id="28446" href="Algebra.Bundles.html#17932" class="Function">semiring</a>
|
|||
|
|
<a id="28459" class="Symbol">;</a> <a id="28461" href="Algebra.Bundles.html#18692" class="Function">commutativeSemiringWithoutOne</a>
|
|||
|
|
<a id="28495" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="28498" class="Comment">------------------------------------------------------------------------</a>
|
|||
|
|
<a id="28571" class="Comment">-- Bundles with 3 binary operations</a>
|
|||
|
|
<a id="28607" class="Comment">------------------------------------------------------------------------</a>
|
|||
|
|
|
|||
|
|
<a id="28681" class="Keyword">record</a> <a id="Quasigroup"></a><a id="28688" href="Algebra.Bundles.html#28688" class="Record">Quasigroup</a> <a id="28699" href="Algebra.Bundles.html#28699" class="Bound">c</a> <a id="28701" href="Algebra.Bundles.html#28701" class="Bound">ℓ</a> <a id="28703" class="Symbol">:</a> <a id="28705" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="28709" class="Symbol">(</a><a id="28710" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="28714" class="Symbol">(</a><a id="28715" href="Algebra.Bundles.html#28699" class="Bound">c</a> <a id="28717" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="28719" href="Algebra.Bundles.html#28701" class="Bound">ℓ</a><a id="28720" class="Symbol">))</a> <a id="28723" class="Keyword">where</a>
|
|||
|
|
<a id="28731" class="Keyword">infixl</a> <a id="28738" class="Number">7</a> <a id="28740" href="Algebra.Bundles.html#28861" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="28746" class="Keyword">infixl</a> <a id="28753" class="Number">7</a> <a id="28755" href="Algebra.Bundles.html#28892" class="Field Operator">_\\_</a>
|
|||
|
|
<a id="28762" class="Keyword">infixl</a> <a id="28769" class="Number">7</a> <a id="28771" href="Algebra.Bundles.html#28923" class="Field Operator">_//_</a>
|
|||
|
|
<a id="28778" class="Keyword">infix</a> <a id="28785" class="Number">4</a> <a id="28787" href="Algebra.Bundles.html#28828" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="28793" class="Keyword">field</a>
|
|||
|
|
<a id="Quasigroup.Carrier"></a><a id="28803" href="Algebra.Bundles.html#28803" class="Field">Carrier</a> <a id="28816" class="Symbol">:</a> <a id="28818" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="28822" href="Algebra.Bundles.html#28699" class="Bound">c</a>
|
|||
|
|
<a id="Quasigroup._≈_"></a><a id="28828" href="Algebra.Bundles.html#28828" class="Field Operator">_≈_</a> <a id="28841" class="Symbol">:</a> <a id="28843" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="28847" href="Algebra.Bundles.html#28803" class="Field">Carrier</a> <a id="28855" href="Algebra.Bundles.html#28701" class="Bound">ℓ</a>
|
|||
|
|
<a id="Quasigroup._∙_"></a><a id="28861" href="Algebra.Bundles.html#28861" class="Field Operator">_∙_</a> <a id="28874" class="Symbol">:</a> <a id="28876" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="28880" href="Algebra.Bundles.html#28803" class="Field">Carrier</a>
|
|||
|
|
<a id="Quasigroup._\\_"></a><a id="28892" href="Algebra.Bundles.html#28892" class="Field Operator">_\\_</a> <a id="28905" class="Symbol">:</a> <a id="28907" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="28911" href="Algebra.Bundles.html#28803" class="Field">Carrier</a>
|
|||
|
|
<a id="Quasigroup._//_"></a><a id="28923" href="Algebra.Bundles.html#28923" class="Field Operator">_//_</a> <a id="28936" class="Symbol">:</a> <a id="28938" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="28942" href="Algebra.Bundles.html#28803" class="Field">Carrier</a>
|
|||
|
|
<a id="Quasigroup.isQuasigroup"></a><a id="28954" href="Algebra.Bundles.html#28954" class="Field">isQuasigroup</a> <a id="28967" class="Symbol">:</a> <a id="28969" href="Algebra.Structures.html#23999" class="Record">IsQuasigroup</a> <a id="28983" href="Algebra.Bundles.html#28828" class="Field Operator">_≈_</a> <a id="28987" href="Algebra.Bundles.html#28861" class="Field Operator">_∙_</a> <a id="28991" href="Algebra.Bundles.html#28892" class="Field Operator">_\\_</a> <a id="28996" href="Algebra.Bundles.html#28923" class="Field Operator">_//_</a>
|
|||
|
|
|
|||
|
|
<a id="29004" class="Keyword">open</a> <a id="29009" href="Algebra.Structures.html#23999" class="Module">IsQuasigroup</a> <a id="29022" href="Algebra.Bundles.html#28954" class="Field">isQuasigroup</a> <a id="29035" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="Quasigroup.magma"></a><a id="29045" href="Algebra.Bundles.html#29045" class="Function">magma</a> <a id="29051" class="Symbol">:</a> <a id="29053" href="Algebra.Bundles.html#1141" class="Record">Magma</a> <a id="29059" href="Algebra.Bundles.html#28699" class="Bound">c</a> <a id="29061" href="Algebra.Bundles.html#28701" class="Bound">ℓ</a>
|
|||
|
|
<a id="29065" href="Algebra.Bundles.html#29045" class="Function">magma</a> <a id="29071" class="Symbol">=</a> <a id="29073" class="Keyword">record</a> <a id="29080" class="Symbol">{</a> <a id="29082" href="Algebra.Bundles.html#1293" class="Field">isMagma</a> <a id="29090" class="Symbol">=</a> <a id="29092" href="Algebra.Structures.html#24062" class="Function">isMagma</a> <a id="29100" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="29105" class="Keyword">open</a> <a id="29110" href="Algebra.Bundles.html#1141" class="Module">Magma</a> <a id="29116" href="Algebra.Bundles.html#29045" class="Function">magma</a> <a id="29122" class="Keyword">public</a>
|
|||
|
|
<a id="29133" class="Keyword">using</a> <a id="29139" class="Symbol">(</a><a id="29140" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="29143" class="Symbol">;</a> <a id="29145" href="Algebra.Bundles.html#1353" class="Function">rawMagma</a><a id="29153" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="Quasigroup.rawQuasigroup"></a><a id="29158" href="Algebra.Bundles.html#29158" class="Function">rawQuasigroup</a> <a id="29172" class="Symbol">:</a> <a id="29174" href="Algebra.Bundles.Raw.html#5560" class="Record">RawQuasigroup</a> <a id="29188" href="Algebra.Bundles.html#28699" class="Bound">c</a> <a id="29190" href="Algebra.Bundles.html#28701" class="Bound">ℓ</a>
|
|||
|
|
<a id="29194" href="Algebra.Bundles.html#29158" class="Function">rawQuasigroup</a> <a id="29208" class="Symbol">=</a> <a id="29210" class="Keyword">record</a>
|
|||
|
|
<a id="29221" class="Symbol">{</a> <a id="29223" href="Algebra.Bundles.Raw.html#5698" class="Field Operator">_≈_</a> <a id="29228" class="Symbol">=</a> <a id="29230" href="Algebra.Bundles.html#28828" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="29238" class="Symbol">;</a> <a id="29240" href="Algebra.Bundles.Raw.html#5726" class="Field Operator">_∙_</a> <a id="29245" class="Symbol">=</a> <a id="29247" href="Algebra.Bundles.html#28861" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="29255" class="Symbol">;</a> <a id="29257" href="Algebra.Bundles.Raw.html#5752" class="Field Operator">_\\_</a> <a id="29263" class="Symbol">=</a> <a id="29265" href="Algebra.Bundles.html#28892" class="Field Operator">_\\_</a>
|
|||
|
|
<a id="29274" class="Symbol">;</a> <a id="29276" href="Algebra.Bundles.Raw.html#5778" class="Field Operator">_//_</a> <a id="29282" class="Symbol">=</a> <a id="29284" href="Algebra.Bundles.html#28923" class="Field Operator">_//_</a>
|
|||
|
|
<a id="29293" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="29298" class="Keyword">open</a> <a id="29303" href="Algebra.Bundles.Raw.html#5560" class="Module">RawQuasigroup</a> <a id="29317" href="Algebra.Bundles.html#29158" class="Function">rawQuasigroup</a> <a id="29331" class="Keyword">public</a>
|
|||
|
|
<a id="29342" class="Keyword">using</a> <a id="29348" class="Symbol">(</a><a id="29349" href="Algebra.Bundles.Raw.html#5984" class="Function">//-rawMagma</a><a id="29360" class="Symbol">;</a> <a id="29362" href="Algebra.Bundles.Raw.html#5892" class="Function">\\-rawMagma</a><a id="29373" class="Symbol">;</a> <a id="29375" href="Algebra.Bundles.Raw.html#5803" class="Function">∙-rawMagma</a><a id="29385" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="29388" class="Keyword">record</a> <a id="Loop"></a><a id="29395" href="Algebra.Bundles.html#29395" class="Record">Loop</a> <a id="29401" href="Algebra.Bundles.html#29401" class="Bound">c</a> <a id="29403" href="Algebra.Bundles.html#29403" class="Bound">ℓ</a> <a id="29405" class="Symbol">:</a> <a id="29407" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="29411" class="Symbol">(</a><a id="29412" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="29416" class="Symbol">(</a><a id="29417" href="Algebra.Bundles.html#29401" class="Bound">c</a> <a id="29419" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="29421" href="Algebra.Bundles.html#29403" class="Bound">ℓ</a><a id="29422" class="Symbol">))</a> <a id="29425" class="Keyword">where</a>
|
|||
|
|
<a id="29433" class="Keyword">infixl</a> <a id="29440" class="Number">7</a> <a id="29442" href="Algebra.Bundles.html#29553" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="29448" class="Keyword">infixl</a> <a id="29455" class="Number">7</a> <a id="29457" href="Algebra.Bundles.html#29579" class="Field Operator">_\\_</a>
|
|||
|
|
<a id="29464" class="Keyword">infixl</a> <a id="29471" class="Number">7</a> <a id="29473" href="Algebra.Bundles.html#29605" class="Field Operator">_//_</a>
|
|||
|
|
<a id="29480" class="Keyword">infix</a> <a id="29487" class="Number">4</a> <a id="29489" href="Algebra.Bundles.html#29525" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="29495" class="Keyword">field</a>
|
|||
|
|
<a id="Loop.Carrier"></a><a id="29505" href="Algebra.Bundles.html#29505" class="Field">Carrier</a> <a id="29513" class="Symbol">:</a> <a id="29515" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="29519" href="Algebra.Bundles.html#29401" class="Bound">c</a>
|
|||
|
|
<a id="Loop._≈_"></a><a id="29525" href="Algebra.Bundles.html#29525" class="Field Operator">_≈_</a> <a id="29533" class="Symbol">:</a> <a id="29535" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="29539" href="Algebra.Bundles.html#29505" class="Field">Carrier</a> <a id="29547" href="Algebra.Bundles.html#29403" class="Bound">ℓ</a>
|
|||
|
|
<a id="Loop._∙_"></a><a id="29553" href="Algebra.Bundles.html#29553" class="Field Operator">_∙_</a> <a id="29561" class="Symbol">:</a> <a id="29563" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="29567" href="Algebra.Bundles.html#29505" class="Field">Carrier</a>
|
|||
|
|
<a id="Loop._\\_"></a><a id="29579" href="Algebra.Bundles.html#29579" class="Field Operator">_\\_</a> <a id="29587" class="Symbol">:</a> <a id="29589" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="29593" href="Algebra.Bundles.html#29505" class="Field">Carrier</a>
|
|||
|
|
<a id="Loop._//_"></a><a id="29605" href="Algebra.Bundles.html#29605" class="Field Operator">_//_</a> <a id="29613" class="Symbol">:</a> <a id="29615" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="29619" href="Algebra.Bundles.html#29505" class="Field">Carrier</a>
|
|||
|
|
<a id="Loop.ε"></a><a id="29631" href="Algebra.Bundles.html#29631" class="Field">ε</a> <a id="29639" class="Symbol">:</a> <a id="29641" href="Algebra.Bundles.html#29505" class="Field">Carrier</a>
|
|||
|
|
<a id="Loop.isLoop"></a><a id="29653" href="Algebra.Bundles.html#29653" class="Field">isLoop</a> <a id="29661" class="Symbol">:</a> <a id="29663" href="Algebra.Structures.html#24825" class="Record">IsLoop</a> <a id="29671" href="Algebra.Bundles.html#29525" class="Field Operator">_≈_</a> <a id="29675" href="Algebra.Bundles.html#29553" class="Field Operator">_∙_</a> <a id="29679" href="Algebra.Bundles.html#29579" class="Field Operator">_\\_</a> <a id="29684" href="Algebra.Bundles.html#29605" class="Field Operator">_//_</a> <a id="29689" href="Algebra.Bundles.html#29631" class="Field">ε</a>
|
|||
|
|
|
|||
|
|
<a id="29694" class="Keyword">open</a> <a id="29699" href="Algebra.Structures.html#24825" class="Module">IsLoop</a> <a id="29706" href="Algebra.Bundles.html#29653" class="Field">isLoop</a> <a id="29713" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="Loop.rawLoop"></a><a id="29723" href="Algebra.Bundles.html#29723" class="Function">rawLoop</a> <a id="29731" class="Symbol">:</a> <a id="29733" href="Algebra.Bundles.Raw.html#6332" class="Record">RawLoop</a> <a id="29741" href="Algebra.Bundles.html#29401" class="Bound">c</a> <a id="29743" href="Algebra.Bundles.html#29403" class="Bound">ℓ</a>
|
|||
|
|
<a id="29747" href="Algebra.Bundles.html#29723" class="Function">rawLoop</a> <a id="29755" class="Symbol">=</a> <a id="29757" class="Keyword">record</a>
|
|||
|
|
<a id="29768" class="Symbol">{</a> <a id="29770" href="Algebra.Bundles.Raw.html#6465" class="Field Operator">_≈_</a> <a id="29774" class="Symbol">=</a> <a id="29776" href="Algebra.Bundles.html#29525" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="29784" class="Symbol">;</a> <a id="29786" href="Algebra.Bundles.Raw.html#6493" class="Field Operator">_∙_</a> <a id="29790" class="Symbol">=</a> <a id="29792" href="Algebra.Bundles.html#29553" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="29800" class="Symbol">;</a> <a id="29802" href="Algebra.Bundles.Raw.html#6519" class="Field Operator">_\\_</a> <a id="29807" class="Symbol">=</a> <a id="29809" href="Algebra.Bundles.html#29579" class="Field Operator">_\\_</a>
|
|||
|
|
<a id="29818" class="Symbol">;</a> <a id="29820" href="Algebra.Bundles.Raw.html#6545" class="Field Operator">_//_</a> <a id="29825" class="Symbol">=</a> <a id="29827" href="Algebra.Bundles.html#29605" class="Field Operator">_//_</a>
|
|||
|
|
<a id="29836" class="Symbol">;</a> <a id="29838" href="Algebra.Bundles.Raw.html#6571" class="Field">ε</a> <a id="29840" class="Symbol">=</a> <a id="29842" href="Algebra.Bundles.html#29631" class="Field">ε</a>
|
|||
|
|
<a id="29848" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="Loop.quasigroup"></a><a id="29853" href="Algebra.Bundles.html#29853" class="Function">quasigroup</a> <a id="29864" class="Symbol">:</a> <a id="29866" href="Algebra.Bundles.html#28688" class="Record">Quasigroup</a> <a id="29877" class="Symbol">_</a> <a id="29879" class="Symbol">_</a>
|
|||
|
|
<a id="29883" href="Algebra.Bundles.html#29853" class="Function">quasigroup</a> <a id="29894" class="Symbol">=</a> <a id="29896" class="Keyword">record</a> <a id="29903" class="Symbol">{</a> <a id="29905" href="Algebra.Bundles.html#28954" class="Field">isQuasigroup</a> <a id="29918" class="Symbol">=</a> <a id="29920" href="Algebra.Structures.html#24890" class="Function">isQuasigroup</a> <a id="29933" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="29938" class="Keyword">open</a> <a id="29943" href="Algebra.Bundles.html#28688" class="Module">Quasigroup</a> <a id="29954" href="Algebra.Bundles.html#29853" class="Function">quasigroup</a> <a id="29965" class="Keyword">public</a>
|
|||
|
|
<a id="29976" class="Keyword">using</a> <a id="29982" class="Symbol">(</a><a id="29983" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="29986" class="Symbol">;</a> <a id="29988" href="Algebra.Bundles.Raw.html#5803" class="Function">∙-rawMagma</a><a id="29998" class="Symbol">;</a> <a id="30000" href="Algebra.Bundles.Raw.html#5892" class="Function">\\-rawMagma</a><a id="30011" class="Symbol">;</a> <a id="30013" href="Algebra.Bundles.Raw.html#5984" class="Function">//-rawMagma</a><a id="30024" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="30027" class="Keyword">record</a> <a id="LeftBolLoop"></a><a id="30034" href="Algebra.Bundles.html#30034" class="Record">LeftBolLoop</a> <a id="30046" href="Algebra.Bundles.html#30046" class="Bound">c</a> <a id="30048" href="Algebra.Bundles.html#30048" class="Bound">ℓ</a> <a id="30050" class="Symbol">:</a> <a id="30052" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="30056" class="Symbol">(</a><a id="30057" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="30061" class="Symbol">(</a><a id="30062" href="Algebra.Bundles.html#30046" class="Bound">c</a> <a id="30064" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="30066" href="Algebra.Bundles.html#30048" class="Bound">ℓ</a><a id="30067" class="Symbol">))</a> <a id="30070" class="Keyword">where</a>
|
|||
|
|
<a id="30078" class="Keyword">infixl</a> <a id="30085" class="Number">7</a> <a id="30087" href="Algebra.Bundles.html#30198" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="30093" class="Keyword">infixl</a> <a id="30100" class="Number">7</a> <a id="30102" href="Algebra.Bundles.html#30224" class="Field Operator">_\\_</a>
|
|||
|
|
<a id="30109" class="Keyword">infixl</a> <a id="30116" class="Number">7</a> <a id="30118" href="Algebra.Bundles.html#30250" class="Field Operator">_//_</a>
|
|||
|
|
<a id="30125" class="Keyword">infix</a> <a id="30132" class="Number">4</a> <a id="30134" href="Algebra.Bundles.html#30170" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="30140" class="Keyword">field</a>
|
|||
|
|
<a id="LeftBolLoop.Carrier"></a><a id="30150" href="Algebra.Bundles.html#30150" class="Field">Carrier</a> <a id="30158" class="Symbol">:</a> <a id="30160" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="30164" href="Algebra.Bundles.html#30046" class="Bound">c</a>
|
|||
|
|
<a id="LeftBolLoop._≈_"></a><a id="30170" href="Algebra.Bundles.html#30170" class="Field Operator">_≈_</a> <a id="30178" class="Symbol">:</a> <a id="30180" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="30184" href="Algebra.Bundles.html#30150" class="Field">Carrier</a> <a id="30192" href="Algebra.Bundles.html#30048" class="Bound">ℓ</a>
|
|||
|
|
<a id="LeftBolLoop._∙_"></a><a id="30198" href="Algebra.Bundles.html#30198" class="Field Operator">_∙_</a> <a id="30206" class="Symbol">:</a> <a id="30208" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="30212" href="Algebra.Bundles.html#30150" class="Field">Carrier</a>
|
|||
|
|
<a id="LeftBolLoop._\\_"></a><a id="30224" href="Algebra.Bundles.html#30224" class="Field Operator">_\\_</a> <a id="30232" class="Symbol">:</a> <a id="30234" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="30238" href="Algebra.Bundles.html#30150" class="Field">Carrier</a>
|
|||
|
|
<a id="LeftBolLoop._//_"></a><a id="30250" href="Algebra.Bundles.html#30250" class="Field Operator">_//_</a> <a id="30258" class="Symbol">:</a> <a id="30260" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="30264" href="Algebra.Bundles.html#30150" class="Field">Carrier</a>
|
|||
|
|
<a id="LeftBolLoop.ε"></a><a id="30276" href="Algebra.Bundles.html#30276" class="Field">ε</a> <a id="30284" class="Symbol">:</a> <a id="30286" href="Algebra.Bundles.html#30150" class="Field">Carrier</a>
|
|||
|
|
<a id="LeftBolLoop.isLeftBolLoop"></a><a id="30298" href="Algebra.Bundles.html#30298" class="Field">isLeftBolLoop</a> <a id="30312" class="Symbol">:</a> <a id="30314" href="Algebra.Structures.html#25130" class="Record">IsLeftBolLoop</a> <a id="30329" href="Algebra.Bundles.html#30170" class="Field Operator">_≈_</a> <a id="30333" href="Algebra.Bundles.html#30198" class="Field Operator">_∙_</a> <a id="30337" href="Algebra.Bundles.html#30224" class="Field Operator">_\\_</a> <a id="30342" href="Algebra.Bundles.html#30250" class="Field Operator">_//_</a> <a id="30347" href="Algebra.Bundles.html#30276" class="Field">ε</a>
|
|||
|
|
|
|||
|
|
<a id="30352" class="Keyword">open</a> <a id="30357" href="Algebra.Structures.html#25130" class="Module">IsLeftBolLoop</a> <a id="30371" href="Algebra.Bundles.html#30298" class="Field">isLeftBolLoop</a> <a id="30385" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="LeftBolLoop.loop"></a><a id="30395" href="Algebra.Bundles.html#30395" class="Function">loop</a> <a id="30400" class="Symbol">:</a> <a id="30402" href="Algebra.Bundles.html#29395" class="Record">Loop</a> <a id="30407" class="Symbol">_</a> <a id="30409" class="Symbol">_</a>
|
|||
|
|
<a id="30413" href="Algebra.Bundles.html#30395" class="Function">loop</a> <a id="30418" class="Symbol">=</a> <a id="30420" class="Keyword">record</a> <a id="30427" class="Symbol">{</a> <a id="30429" href="Algebra.Bundles.html#29653" class="Field">isLoop</a> <a id="30436" class="Symbol">=</a> <a id="30438" href="Algebra.Structures.html#25202" class="Function">isLoop</a> <a id="30445" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="30450" class="Keyword">open</a> <a id="30455" href="Algebra.Bundles.html#29395" class="Module">Loop</a> <a id="30460" href="Algebra.Bundles.html#30395" class="Function">loop</a> <a id="30465" class="Keyword">public</a>
|
|||
|
|
<a id="30476" class="Keyword">using</a> <a id="30482" class="Symbol">(</a><a id="30483" href="Algebra.Bundles.html#29853" class="Function">quasigroup</a><a id="30493" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="30496" class="Keyword">record</a> <a id="RightBolLoop"></a><a id="30503" href="Algebra.Bundles.html#30503" class="Record">RightBolLoop</a> <a id="30516" href="Algebra.Bundles.html#30516" class="Bound">c</a> <a id="30518" href="Algebra.Bundles.html#30518" class="Bound">ℓ</a> <a id="30520" class="Symbol">:</a> <a id="30522" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="30526" class="Symbol">(</a><a id="30527" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="30531" class="Symbol">(</a><a id="30532" href="Algebra.Bundles.html#30516" class="Bound">c</a> <a id="30534" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="30536" href="Algebra.Bundles.html#30518" class="Bound">ℓ</a><a id="30537" class="Symbol">))</a> <a id="30540" class="Keyword">where</a>
|
|||
|
|
<a id="30548" class="Keyword">infixl</a> <a id="30555" class="Number">7</a> <a id="30557" href="Algebra.Bundles.html#30668" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="30563" class="Keyword">infixl</a> <a id="30570" class="Number">7</a> <a id="30572" href="Algebra.Bundles.html#30694" class="Field Operator">_\\_</a>
|
|||
|
|
<a id="30579" class="Keyword">infixl</a> <a id="30586" class="Number">7</a> <a id="30588" href="Algebra.Bundles.html#30720" class="Field Operator">_//_</a>
|
|||
|
|
<a id="30595" class="Keyword">infix</a> <a id="30602" class="Number">4</a> <a id="30604" href="Algebra.Bundles.html#30640" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="30610" class="Keyword">field</a>
|
|||
|
|
<a id="RightBolLoop.Carrier"></a><a id="30620" href="Algebra.Bundles.html#30620" class="Field">Carrier</a> <a id="30628" class="Symbol">:</a> <a id="30630" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="30634" href="Algebra.Bundles.html#30516" class="Bound">c</a>
|
|||
|
|
<a id="RightBolLoop._≈_"></a><a id="30640" href="Algebra.Bundles.html#30640" class="Field Operator">_≈_</a> <a id="30648" class="Symbol">:</a> <a id="30650" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="30654" href="Algebra.Bundles.html#30620" class="Field">Carrier</a> <a id="30662" href="Algebra.Bundles.html#30518" class="Bound">ℓ</a>
|
|||
|
|
<a id="RightBolLoop._∙_"></a><a id="30668" href="Algebra.Bundles.html#30668" class="Field Operator">_∙_</a> <a id="30676" class="Symbol">:</a> <a id="30678" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="30682" href="Algebra.Bundles.html#30620" class="Field">Carrier</a>
|
|||
|
|
<a id="RightBolLoop._\\_"></a><a id="30694" href="Algebra.Bundles.html#30694" class="Field Operator">_\\_</a> <a id="30702" class="Symbol">:</a> <a id="30704" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="30708" href="Algebra.Bundles.html#30620" class="Field">Carrier</a>
|
|||
|
|
<a id="RightBolLoop._//_"></a><a id="30720" href="Algebra.Bundles.html#30720" class="Field Operator">_//_</a> <a id="30728" class="Symbol">:</a> <a id="30730" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="30734" href="Algebra.Bundles.html#30620" class="Field">Carrier</a>
|
|||
|
|
<a id="RightBolLoop.ε"></a><a id="30746" href="Algebra.Bundles.html#30746" class="Field">ε</a> <a id="30754" class="Symbol">:</a> <a id="30756" href="Algebra.Bundles.html#30620" class="Field">Carrier</a>
|
|||
|
|
<a id="RightBolLoop.isRightBolLoop"></a><a id="30768" href="Algebra.Bundles.html#30768" class="Field">isRightBolLoop</a> <a id="30783" class="Symbol">:</a> <a id="30785" href="Algebra.Structures.html#25291" class="Record">IsRightBolLoop</a> <a id="30801" href="Algebra.Bundles.html#30640" class="Field Operator">_≈_</a> <a id="30805" href="Algebra.Bundles.html#30668" class="Field Operator">_∙_</a> <a id="30809" href="Algebra.Bundles.html#30694" class="Field Operator">_\\_</a> <a id="30814" href="Algebra.Bundles.html#30720" class="Field Operator">_//_</a> <a id="30819" href="Algebra.Bundles.html#30746" class="Field">ε</a>
|
|||
|
|
|
|||
|
|
<a id="30824" class="Keyword">open</a> <a id="30829" href="Algebra.Structures.html#25291" class="Module">IsRightBolLoop</a> <a id="30844" href="Algebra.Bundles.html#30768" class="Field">isRightBolLoop</a> <a id="30859" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="RightBolLoop.loop"></a><a id="30869" href="Algebra.Bundles.html#30869" class="Function">loop</a> <a id="30874" class="Symbol">:</a> <a id="30876" href="Algebra.Bundles.html#29395" class="Record">Loop</a> <a id="30881" class="Symbol">_</a> <a id="30883" class="Symbol">_</a>
|
|||
|
|
<a id="30887" href="Algebra.Bundles.html#30869" class="Function">loop</a> <a id="30892" class="Symbol">=</a> <a id="30894" class="Keyword">record</a> <a id="30901" class="Symbol">{</a> <a id="30903" href="Algebra.Bundles.html#29653" class="Field">isLoop</a> <a id="30910" class="Symbol">=</a> <a id="30912" href="Algebra.Structures.html#25364" class="Function">isLoop</a> <a id="30919" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="30924" class="Keyword">open</a> <a id="30929" href="Algebra.Bundles.html#29395" class="Module">Loop</a> <a id="30934" href="Algebra.Bundles.html#30869" class="Function">loop</a> <a id="30939" class="Keyword">public</a>
|
|||
|
|
<a id="30950" class="Keyword">using</a> <a id="30956" class="Symbol">(</a><a id="30957" href="Algebra.Bundles.html#29853" class="Function">quasigroup</a><a id="30967" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="30970" class="Keyword">record</a> <a id="MoufangLoop"></a><a id="30977" href="Algebra.Bundles.html#30977" class="Record">MoufangLoop</a> <a id="30989" href="Algebra.Bundles.html#30989" class="Bound">c</a> <a id="30991" href="Algebra.Bundles.html#30991" class="Bound">ℓ</a> <a id="30993" class="Symbol">:</a> <a id="30995" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="30999" class="Symbol">(</a><a id="31000" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="31004" class="Symbol">(</a><a id="31005" href="Algebra.Bundles.html#30989" class="Bound">c</a> <a id="31007" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="31009" href="Algebra.Bundles.html#30991" class="Bound">ℓ</a><a id="31010" class="Symbol">))</a> <a id="31013" class="Keyword">where</a>
|
|||
|
|
<a id="31021" class="Keyword">infixl</a> <a id="31028" class="Number">7</a> <a id="31030" href="Algebra.Bundles.html#31141" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="31036" class="Keyword">infixl</a> <a id="31043" class="Number">7</a> <a id="31045" href="Algebra.Bundles.html#31167" class="Field Operator">_\\_</a>
|
|||
|
|
<a id="31052" class="Keyword">infixl</a> <a id="31059" class="Number">7</a> <a id="31061" href="Algebra.Bundles.html#31193" class="Field Operator">_//_</a>
|
|||
|
|
<a id="31068" class="Keyword">infix</a> <a id="31075" class="Number">4</a> <a id="31077" href="Algebra.Bundles.html#31113" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="31083" class="Keyword">field</a>
|
|||
|
|
<a id="MoufangLoop.Carrier"></a><a id="31093" href="Algebra.Bundles.html#31093" class="Field">Carrier</a> <a id="31101" class="Symbol">:</a> <a id="31103" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="31107" href="Algebra.Bundles.html#30989" class="Bound">c</a>
|
|||
|
|
<a id="MoufangLoop._≈_"></a><a id="31113" href="Algebra.Bundles.html#31113" class="Field Operator">_≈_</a> <a id="31121" class="Symbol">:</a> <a id="31123" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="31127" href="Algebra.Bundles.html#31093" class="Field">Carrier</a> <a id="31135" href="Algebra.Bundles.html#30991" class="Bound">ℓ</a>
|
|||
|
|
<a id="MoufangLoop._∙_"></a><a id="31141" href="Algebra.Bundles.html#31141" class="Field Operator">_∙_</a> <a id="31149" class="Symbol">:</a> <a id="31151" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="31155" href="Algebra.Bundles.html#31093" class="Field">Carrier</a>
|
|||
|
|
<a id="MoufangLoop._\\_"></a><a id="31167" href="Algebra.Bundles.html#31167" class="Field Operator">_\\_</a> <a id="31175" class="Symbol">:</a> <a id="31177" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="31181" href="Algebra.Bundles.html#31093" class="Field">Carrier</a>
|
|||
|
|
<a id="MoufangLoop._//_"></a><a id="31193" href="Algebra.Bundles.html#31193" class="Field Operator">_//_</a> <a id="31201" class="Symbol">:</a> <a id="31203" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="31207" href="Algebra.Bundles.html#31093" class="Field">Carrier</a>
|
|||
|
|
<a id="MoufangLoop.ε"></a><a id="31219" href="Algebra.Bundles.html#31219" class="Field">ε</a> <a id="31227" class="Symbol">:</a> <a id="31229" href="Algebra.Bundles.html#31093" class="Field">Carrier</a>
|
|||
|
|
<a id="MoufangLoop.isMoufangLoop"></a><a id="31241" href="Algebra.Bundles.html#31241" class="Field">isMoufangLoop</a> <a id="31255" class="Symbol">:</a> <a id="31257" href="Algebra.Structures.html#25456" class="Record">IsMoufangLoop</a> <a id="31272" href="Algebra.Bundles.html#31113" class="Field Operator">_≈_</a> <a id="31276" href="Algebra.Bundles.html#31141" class="Field Operator">_∙_</a> <a id="31280" href="Algebra.Bundles.html#31167" class="Field Operator">_\\_</a> <a id="31285" href="Algebra.Bundles.html#31193" class="Field Operator">_//_</a> <a id="31290" href="Algebra.Bundles.html#31219" class="Field">ε</a>
|
|||
|
|
|
|||
|
|
<a id="31295" class="Keyword">open</a> <a id="31300" href="Algebra.Structures.html#25456" class="Module">IsMoufangLoop</a> <a id="31314" href="Algebra.Bundles.html#31241" class="Field">isMoufangLoop</a> <a id="31328" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="MoufangLoop.leftBolLoop"></a><a id="31338" href="Algebra.Bundles.html#31338" class="Function">leftBolLoop</a> <a id="31350" class="Symbol">:</a> <a id="31352" href="Algebra.Bundles.html#30034" class="Record">LeftBolLoop</a> <a id="31364" class="Symbol">_</a> <a id="31366" class="Symbol">_</a>
|
|||
|
|
<a id="31370" href="Algebra.Bundles.html#31338" class="Function">leftBolLoop</a> <a id="31382" class="Symbol">=</a> <a id="31384" class="Keyword">record</a> <a id="31391" class="Symbol">{</a> <a id="31393" href="Algebra.Bundles.html#30298" class="Field">isLeftBolLoop</a> <a id="31407" class="Symbol">=</a> <a id="31409" href="Algebra.Structures.html#25528" class="Function">isLeftBolLoop</a> <a id="31423" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="31428" class="Keyword">open</a> <a id="31433" href="Algebra.Bundles.html#30034" class="Module">LeftBolLoop</a> <a id="31445" href="Algebra.Bundles.html#31338" class="Function">leftBolLoop</a> <a id="31457" class="Keyword">public</a>
|
|||
|
|
<a id="31468" class="Keyword">using</a> <a id="31474" class="Symbol">(</a><a id="31475" href="Algebra.Bundles.html#30395" class="Function">loop</a><a id="31479" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="31482" class="Keyword">record</a> <a id="MiddleBolLoop"></a><a id="31489" href="Algebra.Bundles.html#31489" class="Record">MiddleBolLoop</a> <a id="31503" href="Algebra.Bundles.html#31503" class="Bound">c</a> <a id="31505" href="Algebra.Bundles.html#31505" class="Bound">ℓ</a> <a id="31507" class="Symbol">:</a> <a id="31509" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="31513" class="Symbol">(</a><a id="31514" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="31518" class="Symbol">(</a><a id="31519" href="Algebra.Bundles.html#31503" class="Bound">c</a> <a id="31521" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="31523" href="Algebra.Bundles.html#31505" class="Bound">ℓ</a><a id="31524" class="Symbol">))</a> <a id="31527" class="Keyword">where</a>
|
|||
|
|
<a id="31535" class="Keyword">infixl</a> <a id="31542" class="Number">7</a> <a id="31544" href="Algebra.Bundles.html#31671" class="Field Operator">_∙_</a>
|
|||
|
|
<a id="31550" class="Keyword">infixl</a> <a id="31557" class="Number">7</a> <a id="31559" href="Algebra.Bundles.html#31705" class="Field Operator">_\\_</a>
|
|||
|
|
<a id="31566" class="Keyword">infixl</a> <a id="31573" class="Number">7</a> <a id="31575" href="Algebra.Bundles.html#31739" class="Field Operator">_//_</a>
|
|||
|
|
<a id="31582" class="Keyword">infix</a> <a id="31589" class="Number">4</a> <a id="31591" href="Algebra.Bundles.html#31635" class="Field Operator">_≈_</a>
|
|||
|
|
<a id="31597" class="Keyword">field</a>
|
|||
|
|
<a id="MiddleBolLoop.Carrier"></a><a id="31607" href="Algebra.Bundles.html#31607" class="Field">Carrier</a> <a id="31623" class="Symbol">:</a> <a id="31625" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="31629" href="Algebra.Bundles.html#31503" class="Bound">c</a>
|
|||
|
|
<a id="MiddleBolLoop._≈_"></a><a id="31635" href="Algebra.Bundles.html#31635" class="Field Operator">_≈_</a> <a id="31651" class="Symbol">:</a> <a id="31653" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="31657" href="Algebra.Bundles.html#31607" class="Field">Carrier</a> <a id="31665" href="Algebra.Bundles.html#31505" class="Bound">ℓ</a>
|
|||
|
|
<a id="MiddleBolLoop._∙_"></a><a id="31671" href="Algebra.Bundles.html#31671" class="Field Operator">_∙_</a> <a id="31687" class="Symbol">:</a> <a id="31689" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="31693" href="Algebra.Bundles.html#31607" class="Field">Carrier</a>
|
|||
|
|
<a id="MiddleBolLoop._\\_"></a><a id="31705" href="Algebra.Bundles.html#31705" class="Field Operator">_\\_</a> <a id="31721" class="Symbol">:</a> <a id="31723" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="31727" href="Algebra.Bundles.html#31607" class="Field">Carrier</a>
|
|||
|
|
<a id="MiddleBolLoop._//_"></a><a id="31739" href="Algebra.Bundles.html#31739" class="Field Operator">_//_</a> <a id="31755" class="Symbol">:</a> <a id="31757" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="31761" href="Algebra.Bundles.html#31607" class="Field">Carrier</a>
|
|||
|
|
<a id="MiddleBolLoop.ε"></a><a id="31773" href="Algebra.Bundles.html#31773" class="Field">ε</a> <a id="31789" class="Symbol">:</a> <a id="31791" href="Algebra.Bundles.html#31607" class="Field">Carrier</a>
|
|||
|
|
<a id="MiddleBolLoop.isMiddleBolLoop"></a><a id="31803" href="Algebra.Bundles.html#31803" class="Field">isMiddleBolLoop</a> <a id="31819" class="Symbol">:</a> <a id="31821" href="Algebra.Structures.html#25686" class="Record">IsMiddleBolLoop</a> <a id="31838" href="Algebra.Bundles.html#31635" class="Field Operator">_≈_</a> <a id="31842" href="Algebra.Bundles.html#31671" class="Field Operator">_∙_</a> <a id="31846" href="Algebra.Bundles.html#31705" class="Field Operator">_\\_</a> <a id="31851" href="Algebra.Bundles.html#31739" class="Field Operator">_//_</a> <a id="31856" href="Algebra.Bundles.html#31773" class="Field">ε</a>
|
|||
|
|
|
|||
|
|
<a id="31861" class="Keyword">open</a> <a id="31866" href="Algebra.Structures.html#25686" class="Module">IsMiddleBolLoop</a> <a id="31882" href="Algebra.Bundles.html#31803" class="Field">isMiddleBolLoop</a> <a id="31898" class="Keyword">public</a>
|
|||
|
|
|
|||
|
|
<a id="MiddleBolLoop.loop"></a><a id="31908" href="Algebra.Bundles.html#31908" class="Function">loop</a> <a id="31913" class="Symbol">:</a> <a id="31915" href="Algebra.Bundles.html#29395" class="Record">Loop</a> <a id="31920" class="Symbol">_</a> <a id="31922" class="Symbol">_</a>
|
|||
|
|
<a id="31926" href="Algebra.Bundles.html#31908" class="Function">loop</a> <a id="31931" class="Symbol">=</a> <a id="31933" class="Keyword">record</a> <a id="31940" class="Symbol">{</a> <a id="31942" href="Algebra.Bundles.html#29653" class="Field">isLoop</a> <a id="31949" class="Symbol">=</a> <a id="31951" href="Algebra.Structures.html#25760" class="Function">isLoop</a> <a id="31958" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="31963" class="Keyword">open</a> <a id="31968" href="Algebra.Bundles.html#29395" class="Module">Loop</a> <a id="31973" href="Algebra.Bundles.html#31908" class="Function">loop</a> <a id="31978" class="Keyword">public</a>
|
|||
|
|
<a id="31989" class="Keyword">using</a> <a id="31995" class="Symbol">(</a><a id="31996" href="Algebra.Bundles.html#29853" class="Function">quasigroup</a><a id="32006" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
</pre></body></html>
|