leonv/bsc-leon-vatthauer
1
0
Fork 0
mirror of https://git8.cs.fau.de/theses/bsc-leon-vatthauer.git synced 2024-05-31 07:28:34 +02:00
Code Issues Projects Releases Packages Wiki Activity
bsc-leon-vatthauer/agda/bsc-thesis/Data.Sum.Base.html

76 lines
26 KiB
HTML
Raw Normal View History

update index
2024-02-09 17:53:52 +01:00
<!DOCTYPE HTML>
<html><head><meta charset="utf-8"><title>Data.Sum.Base</title><link rel="stylesheet" href="Agda.css"></head><body><pre class="Agda"><a id="1" class="Comment">------------------------------------------------------------------------</a>
<a id="74" class="Comment">-- The Agda standard library</a>
<a id="103" class="Comment">--</a>
<a id="106" class="Comment">-- Sums (disjoint unions)</a>
<a id="132" class="Comment">------------------------------------------------------------------------</a>
<a id="206" class="Symbol">{-#</a> <a id="210" class="Keyword">OPTIONS</a> <a id="218" class="Pragma">--cubical-compatible</a> <a id="239" class="Pragma">--safe</a> <a id="246" class="Symbol">#-}</a>
<a id="251" class="Keyword">module</a> <a id="258" href="Data.Sum.Base.html" class="Module">Data.Sum.Base</a> <a id="272" class="Keyword">where</a>
<a id="279" class="Keyword">open</a> <a id="284" class="Keyword">import</a> <a id="291" href="Data.Bool.Base.html" class="Module">Data.Bool.Base</a> <a id="306" class="Keyword">using</a> <a id="312" class="Symbol">(</a><a id="313" href="Agda.Builtin.Bool.html#198" class="InductiveConstructor">true</a><a id="317" class="Symbol">;</a> <a id="319" href="Agda.Builtin.Bool.html#192" class="InductiveConstructor">false</a><a id="324" class="Symbol">)</a>
<a id="326" class="Keyword">open</a> <a id="331" class="Keyword">import</a> <a id="338" href="Function.Base.html" class="Module">Function.Base</a> <a id="352" class="Keyword">using</a> <a id="358" class="Symbol">(</a><a id="359" href="Function.Base.html#1115" class="Function Operator">_∘_</a><a id="362" class="Symbol">;</a> <a id="364" href="Function.Base.html#3626" class="Function Operator">_∘′_</a><a id="368" class="Symbol">;</a> <a id="370" href="Function.Base.html#5039" class="Function Operator">_-⟪_⟫-_</a> <a id="378" class="Symbol">;</a> <a id="380" href="Function.Base.html#704" class="Function">id</a><a id="382" class="Symbol">)</a>
<a id="384" class="Keyword">open</a> <a id="389" class="Keyword">import</a> <a id="396" href="Level.html" class="Module">Level</a> <a id="402" class="Keyword">using</a> <a id="408" class="Symbol">(</a><a id="409" href="Agda.Primitive.html#742" class="Postulate">Level</a><a id="414" class="Symbol">;</a> <a id="416" href="Agda.Primitive.html#961" class="Primitive Operator">_⊔_</a><a id="419" class="Symbol">)</a>
<a id="422" class="Keyword">private</a>
<a id="432" class="Keyword">variable</a>
<a id="445" href="Data.Sum.Base.html#445" class="Generalizable">a</a> <a id="447" href="Data.Sum.Base.html#447" class="Generalizable">b</a> <a id="449" href="Data.Sum.Base.html#449" class="Generalizable">c</a> <a id="451" href="Data.Sum.Base.html#451" class="Generalizable">d</a> <a id="453" class="Symbol">:</a> <a id="455" href="Agda.Primitive.html#742" class="Postulate">Level</a>
<a id="465" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="467" class="Symbol">:</a> <a id="469" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="473" href="Data.Sum.Base.html#445" class="Generalizable">a</a>
<a id="479" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="481" class="Symbol">:</a> <a id="483" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="487" href="Data.Sum.Base.html#447" class="Generalizable">b</a>
<a id="493" href="Data.Sum.Base.html#493" class="Generalizable">C</a> <a id="495" class="Symbol">:</a> <a id="497" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="501" href="Data.Sum.Base.html#449" class="Generalizable">c</a>
<a id="507" href="Data.Sum.Base.html#507" class="Generalizable">D</a> <a id="509" class="Symbol">:</a> <a id="511" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="515" href="Data.Sum.Base.html#451" class="Generalizable">d</a>
<a id="518" class="Comment">------------------------------------------------------------------------</a>
<a id="591" class="Comment">-- Definition</a>
<a id="606" class="Keyword">infixr</a> <a id="613" class="Number">1</a> <a id="615" href="Data.Sum.Base.html#625" class="Datatype Operator">_⊎_</a>
<a id="620" class="Keyword">data</a> <a id="_⊎_"></a><a id="625" href="Data.Sum.Base.html#625" class="Datatype Operator">_⊎_</a> <a id="629" class="Symbol">(</a><a id="630" href="Data.Sum.Base.html#630" class="Bound">A</a> <a id="632" class="Symbol">:</a> <a id="634" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="638" href="Data.Sum.Base.html#445" class="Generalizable">a</a><a id="639" class="Symbol">)</a> <a id="641" class="Symbol">(</a><a id="642" href="Data.Sum.Base.html#642" class="Bound">B</a> <a id="644" class="Symbol">:</a> <a id="646" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="650" href="Data.Sum.Base.html#447" class="Generalizable">b</a><a id="651" class="Symbol">)</a> <a id="653" class="Symbol">:</a> <a id="655" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="659" class="Symbol">(</a><a id="660" href="Data.Sum.Base.html#638" class="Bound">a</a> <a id="662" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="664" href="Data.Sum.Base.html#650" class="Bound">b</a><a id="665" class="Symbol">)</a> <a id="667" class="Keyword">where</a>
<a id="_⊎_.inj₁"></a><a id="675" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="680" class="Symbol">:</a> <a id="682" class="Symbol">(</a><a id="683" href="Data.Sum.Base.html#683" class="Bound">x</a> <a id="685" class="Symbol">:</a> <a id="687" href="Data.Sum.Base.html#630" class="Bound">A</a><a id="688" class="Symbol">)</a> <a id="690" class="Symbol">→</a> <a id="692" href="Data.Sum.Base.html#630" class="Bound">A</a> <a id="694" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="696" href="Data.Sum.Base.html#642" class="Bound">B</a>
<a id="_⊎_.inj₂"></a><a id="700" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="705" class="Symbol">:</a> <a id="707" class="Symbol">(</a><a id="708" href="Data.Sum.Base.html#708" class="Bound">y</a> <a id="710" class="Symbol">:</a> <a id="712" href="Data.Sum.Base.html#642" class="Bound">B</a><a id="713" class="Symbol">)</a> <a id="715" class="Symbol">→</a> <a id="717" href="Data.Sum.Base.html#630" class="Bound">A</a> <a id="719" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="721" href="Data.Sum.Base.html#642" class="Bound">B</a>
<a id="724" class="Comment">------------------------------------------------------------------------</a>
<a id="797" class="Comment">-- Functions</a>
<a id="[_,_]"></a><a id="811" href="Data.Sum.Base.html#811" class="Function Operator">[_,_]</a> <a id="817" class="Symbol">:</a> <a id="819" class="Symbol">∀</a> <a id="821" class="Symbol">{</a><a id="822" href="Data.Sum.Base.html#822" class="Bound">C</a> <a id="824" class="Symbol">:</a> <a id="826" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="828" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="830" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="832" class="Symbol">→</a> <a id="834" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="838" href="Data.Sum.Base.html#449" class="Generalizable">c</a><a id="839" class="Symbol">}</a> <a id="841" class="Symbol">→</a>
<a id="851" class="Symbol">((</a><a id="853" href="Data.Sum.Base.html#853" class="Bound">x</a> <a id="855" class="Symbol">:</a> <a id="857" href="Data.Sum.Base.html#465" class="Generalizable">A</a><a id="858" class="Symbol">)</a> <a id="860" class="Symbol">→</a> <a id="862" href="Data.Sum.Base.html#822" class="Bound">C</a> <a id="864" class="Symbol">(</a><a id="865" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="870" href="Data.Sum.Base.html#853" class="Bound">x</a><a id="871" class="Symbol">))</a> <a id="874" class="Symbol">→</a> <a id="876" class="Symbol">((</a><a id="878" href="Data.Sum.Base.html#878" class="Bound">x</a> <a id="880" class="Symbol">:</a> <a id="882" href="Data.Sum.Base.html#479" class="Generalizable">B</a><a id="883" class="Symbol">)</a> <a id="885" class="Symbol">→</a> <a id="887" href="Data.Sum.Base.html#822" class="Bound">C</a> <a id="889" class="Symbol">(</a><a id="890" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="895" href="Data.Sum.Base.html#878" class="Bound">x</a><a id="896" class="Symbol">))</a> <a id="899" class="Symbol">→</a>
<a id="909" class="Symbol">((</a><a id="911" href="Data.Sum.Base.html#911" class="Bound">x</a> <a id="913" class="Symbol">:</a> <a id="915" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="917" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="919" href="Data.Sum.Base.html#479" class="Generalizable">B</a><a id="920" class="Symbol">)</a> <a id="922" class="Symbol">→</a> <a id="924" href="Data.Sum.Base.html#822" class="Bound">C</a> <a id="926" href="Data.Sum.Base.html#911" class="Bound">x</a><a id="927" class="Symbol">)</a>
<a id="929" href="Data.Sum.Base.html#811" class="Function Operator">[</a> <a id="931" href="Data.Sum.Base.html#931" class="Bound">f</a> <a id="933" href="Data.Sum.Base.html#811" class="Function Operator">,</a> <a id="935" href="Data.Sum.Base.html#935" class="Bound">g</a> <a id="937" href="Data.Sum.Base.html#811" class="Function Operator">]</a> <a id="939" class="Symbol">(</a><a id="940" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="945" href="Data.Sum.Base.html#945" class="Bound">x</a><a id="946" class="Symbol">)</a> <a id="948" class="Symbol">=</a> <a id="950" href="Data.Sum.Base.html#931" class="Bound">f</a> <a id="952" href="Data.Sum.Base.html#945" class="Bound">x</a>
<a id="954" href="Data.Sum.Base.html#811" class="Function Operator">[</a> <a id="956" href="Data.Sum.Base.html#956" class="Bound">f</a> <a id="958" href="Data.Sum.Base.html#811" class="Function Operator">,</a> <a id="960" href="Data.Sum.Base.html#960" class="Bound">g</a> <a id="962" href="Data.Sum.Base.html#811" class="Function Operator">]</a> <a id="964" class="Symbol">(</a><a id="965" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="970" href="Data.Sum.Base.html#970" class="Bound">y</a><a id="971" class="Symbol">)</a> <a id="973" class="Symbol">=</a> <a id="975" href="Data.Sum.Base.html#960" class="Bound">g</a> <a id="977" href="Data.Sum.Base.html#970" class="Bound">y</a>
<a id="[_,_]′"></a><a id="980" href="Data.Sum.Base.html#980" class="Function Operator">[_,_]′</a> <a id="987" class="Symbol">:</a> <a id="989" class="Symbol">(</a><a id="990" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="992" class="Symbol">→</a> <a id="994" href="Data.Sum.Base.html#493" class="Generalizable">C</a><a id="995" class="Symbol">)</a> <a id="997" class="Symbol">→</a> <a id="999" class="Symbol">(</a><a id="1000" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1002" class="Symbol">→</a> <a id="1004" href="Data.Sum.Base.html#493" class="Generalizable">C</a><a id="1005" class="Symbol">)</a> <a id="1007" class="Symbol">→</a> <a id="1009" class="Symbol">(</a><a id="1010" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1012" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1014" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1016" class="Symbol">→</a> <a id="1018" href="Data.Sum.Base.html#493" class="Generalizable">C</a><a id="1019" class="Symbol">)</a>
<a id="1021" href="Data.Sum.Base.html#980" class="Function Operator">[_,_]′</a> <a id="1028" class="Symbol">=</a> <a id="1030" href="Data.Sum.Base.html#811" class="Function Operator">[_,_]</a>
<a id="fromInj₁"></a><a id="1037" href="Data.Sum.Base.html#1037" class="Function">fromInj₁</a> <a id="1046" class="Symbol">:</a> <a id="1048" class="Symbol">(</a><a id="1049" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1051" class="Symbol">→</a> <a id="1053" href="Data.Sum.Base.html#465" class="Generalizable">A</a><a id="1054" class="Symbol">)</a> <a id="1056" class="Symbol">→</a> <a id="1058" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1060" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1062" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1064" class="Symbol">→</a> <a id="1066" href="Data.Sum.Base.html#465" class="Generalizable">A</a>
<a id="1068" href="Data.Sum.Base.html#1037" class="Function">fromInj₁</a> <a id="1077" class="Symbol">=</a> <a id="1079" href="Data.Sum.Base.html#980" class="Function Operator">[</a> <a id="1081" href="Function.Base.html#704" class="Function">id</a> <a id="1084" href="Data.Sum.Base.html#980" class="Function Operator">,_]′</a>
<a id="fromInj₂"></a><a id="1090" href="Data.Sum.Base.html#1090" class="Function">fromInj₂</a> <a id="1099" class="Symbol">:</a> <a id="1101" class="Symbol">(</a><a id="1102" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1104" class="Symbol">→</a> <a id="1106" href="Data.Sum.Base.html#479" class="Generalizable">B</a><a id="1107" class="Symbol">)</a> <a id="1109" class="Symbol">→</a> <a id="1111" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1113" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1115" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1117" class="Symbol">→</a> <a id="1119" href="Data.Sum.Base.html#479" class="Generalizable">B</a>
<a id="1121" href="Data.Sum.Base.html#1090" class="Function">fromInj₂</a> <a id="1130" class="Symbol">=</a> <a id="1132" href="Data.Sum.Base.html#980" class="Function Operator">[_,</a> <a id="1136" href="Function.Base.html#704" class="Function">id</a> <a id="1139" href="Data.Sum.Base.html#980" class="Function Operator">]′</a>
<a id="reduce"></a><a id="1143" href="Data.Sum.Base.html#1143" class="Function">reduce</a> <a id="1150" class="Symbol">:</a> <a id="1152" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1154" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1156" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1158" class="Symbol">→</a> <a id="1160" href="Data.Sum.Base.html#465" class="Generalizable">A</a>
<a id="1162" href="Data.Sum.Base.html#1143" class="Function">reduce</a> <a id="1169" class="Symbol">=</a> <a id="1171" href="Data.Sum.Base.html#980" class="Function Operator">[</a> <a id="1173" href="Function.Base.html#704" class="Function">id</a> <a id="1176" href="Data.Sum.Base.html#980" class="Function Operator">,</a> <a id="1178" href="Function.Base.html#704" class="Function">id</a> <a id="1181" href="Data.Sum.Base.html#980" class="Function Operator">]′</a>
<a id="swap"></a><a id="1185" href="Data.Sum.Base.html#1185" class="Function">swap</a> <a id="1190" class="Symbol">:</a> <a id="1192" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1194" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1196" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1198" class="Symbol">→</a> <a id="1200" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1202" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1204" href="Data.Sum.Base.html#465" class="Generalizable">A</a>
<a id="1206" href="Data.Sum.Base.html#1185" class="Function">swap</a> <a id="1211" class="Symbol">(</a><a id="1212" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="1217" href="Data.Sum.Base.html#1217" class="Bound">x</a><a id="1218" class="Symbol">)</a> <a id="1220" class="Symbol">=</a> <a id="1222" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="1227" href="Data.Sum.Base.html#1217" class="Bound">x</a>
<a id="1229" href="Data.Sum.Base.html#1185" class="Function">swap</a> <a id="1234" class="Symbol">(</a><a id="1235" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="1240" href="Data.Sum.Base.html#1240" class="Bound">x</a><a id="1241" class="Symbol">)</a> <a id="1243" class="Symbol">=</a> <a id="1245" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="1250" href="Data.Sum.Base.html#1240" class="Bound">x</a>
<a id="map"></a><a id="1253" href="Data.Sum.Base.html#1253" class="Function">map</a> <a id="1257" class="Symbol">:</a> <a id="1259" class="Symbol">(</a><a id="1260" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1262" class="Symbol">→</a> <a id="1264" href="Data.Sum.Base.html#493" class="Generalizable">C</a><a id="1265" class="Symbol">)</a> <a id="1267" class="Symbol">→</a> <a id="1269" class="Symbol">(</a><a id="1270" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1272" class="Symbol">→</a> <a id="1274" href="Data.Sum.Base.html#507" class="Generalizable">D</a><a id="1275" class="Symbol">)</a> <a id="1277" class="Symbol">→</a> <a id="1279" class="Symbol">(</a><a id="1280" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1282" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1284" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1286" class="Symbol">→</a> <a id="1288" href="Data.Sum.Base.html#493" class="Generalizable">C</a> <a id="1290" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1292" href="Data.Sum.Base.html#507" class="Generalizable">D</a><a id="1293" class="Symbol">)</a>
<a id="1295" href="Data.Sum.Base.html#1253" class="Function">map</a> <a id="1299" href="Data.Sum.Base.html#1299" class="Bound">f</a> <a id="1301" href="Data.Sum.Base.html#1301" class="Bound">g</a> <a id="1303" class="Symbol">=</a> <a id="1305" href="Data.Sum.Base.html#980" class="Function Operator">[</a> <a id="1307" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="1312" href="Function.Base.html#1115" class="Function Operator">∘</a> <a id="1314" href="Data.Sum.Base.html#1299" class="Bound">f</a> <a id="1316" href="Data.Sum.Base.html#980" class="Function Operator">,</a> <a id="1318" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="1323" href="Function.Base.html#1115" class="Function Operator">∘</a> <a id="1325" href="Data.Sum.Base.html#1301" class="Bound">g</a> <a id="1327" href="Data.Sum.Base.html#980" class="Function Operator">]′</a>
<a id="map₁"></a><a id="1331" href="Data.Sum.Base.html#1331" class="Function">map₁</a> <a id="1336" class="Symbol">:</a> <a id="1338" class="Symbol">(</a><a id="1339" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1341" class="Symbol">→</a> <a id="1343" href="Data.Sum.Base.html#493" class="Generalizable">C</a><a id="1344" class="Symbol">)</a> <a id="1346" class="Symbol">→</a> <a id="1348" class="Symbol">(</a><a id="1349" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1351" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1353" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1355" class="Symbol">→</a> <a id="1357" href="Data.Sum.Base.html#493" class="Generalizable">C</a> <a id="1359" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1361" href="Data.Sum.Base.html#479" class="Generalizable">B</a><a id="1362" class="Symbol">)</a>
<a id="1364" href="Data.Sum.Base.html#1331" class="Function">map₁</a> <a id="1369" href="Data.Sum.Base.html#1369" class="Bound">f</a> <a id="1371" class="Symbol">=</a> <a id="1373" href="Data.Sum.Base.html#1253" class="Function">map</a> <a id="1377" href="Data.Sum.Base.html#1369" class="Bound">f</a> <a id="1379" href="Function.Base.html#704" class="Function">id</a>
<a id="map₂"></a><a id="1383" href="Data.Sum.Base.html#1383" class="Function">map₂</a> <a id="1388" class="Symbol">:</a> <a id="1390" class="Symbol">(</a><a id="1391" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1393" class="Symbol">→</a> <a id="1395" href="Data.Sum.Base.html#507" class="Generalizable">D</a><a id="1396" class="Symbol">)</a> <a id="1398" class="Symbol">→</a> <a id="1400" class="Symbol">(</a><a id="1401" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1403" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1405" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1407" class="Symbol">→</a> <a id="1409" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1411" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1413" href="Data.Sum.Base.html#507" class="Generalizable">D</a><a id="1414" class="Symbol">)</a>
<a id="1416" href="Data.Sum.Base.html#1383" class="Function">map₂</a> <a id="1421" class="Symbol">=</a> <a id="1423" href="Data.Sum.Base.html#1253" class="Function">map</a> <a id="1427" href="Function.Base.html#704" class="Function">id</a>
<a id="assocʳ"></a><a id="1431" href="Data.Sum.Base.html#1431" class="Function">assocʳ</a> <a id="1438" class="Symbol">:</a> <a id="1440" class="Symbol">(</a><a id="1441" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1443" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1445" href="Data.Sum.Base.html#479" class="Generalizable">B</a><a id="1446" class="Symbol">)</a> <a id="1448" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1450" href="Data.Sum.Base.html#493" class="Generalizable">C</a> <a id="1452" class="Symbol">→</a> <a id="1454" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1456" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1458" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1460" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1462" href="Data.Sum.Base.html#493" class="Generalizable">C</a>
<a id="1464" href="Data.Sum.Base.html#1431" class="Function">assocʳ</a> <a id="1471" class="Symbol">=</a> <a id="1473" href="Data.Sum.Base.html#980" class="Function Operator">[</a> <a id="1475" href="Data.Sum.Base.html#1383" class="Function">map₂</a> <a id="1480" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="1485" href="Data.Sum.Base.html#980" class="Function Operator">,</a> <a id="1487" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="1492" href="Function.Base.html#3626" class="Function Operator">∘′</a> <a id="1495" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="1500" href="Data.Sum.Base.html#980" class="Function Operator">]′</a>
<a id="assocˡ"></a><a id="1504" href="Data.Sum.Base.html#1504" class="Function">assocˡ</a> <a id="1511" class="Symbol">:</a> <a id="1513" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1515" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1517" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1519" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1521" href="Data.Sum.Base.html#493" class="Generalizable">C</a> <a id="1523" class="Symbol">→</a> <a id="1525" class="Symbol">(</a><a id="1526" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1528" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1530" href="Data.Sum.Base.html#479" class="Generalizable">B</a><a id="1531" class="Symbol">)</a> <a id="1533" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="1535" href="Data.Sum.Base.html#493" class="Generalizable">C</a>
<a id="1537" href="Data.Sum.Base.html#1504" class="Function">assocˡ</a> <a id="1544" class="Symbol">=</a> <a id="1546" href="Data.Sum.Base.html#980" class="Function Operator">[</a> <a id="1548" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="1553" href="Function.Base.html#3626" class="Function Operator">∘′</a> <a id="1556" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="1561" href="Data.Sum.Base.html#980" class="Function Operator">,</a> <a id="1563" href="Data.Sum.Base.html#1331" class="Function">map₁</a> <a id="1568" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="1573" href="Data.Sum.Base.html#980" class="Function Operator">]′</a>
<a id="1577" class="Keyword">infixr</a> <a id="1584" class="Number">1</a> <a id="1586" href="Data.Sum.Base.html#1592" class="Function Operator">_-⊎-_</a>
<a id="_-⊎-_"></a><a id="1592" href="Data.Sum.Base.html#1592" class="Function Operator">_-⊎-_</a> <a id="1598" class="Symbol">:</a> <a id="1600" class="Symbol">(</a><a id="1601" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1603" class="Symbol">→</a> <a id="1605" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1607" class="Symbol">→</a> <a id="1609" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1613" href="Data.Sum.Base.html#449" class="Generalizable">c</a><a id="1614" class="Symbol">)</a> <a id="1616" class="Symbol">→</a> <a id="1618" class="Symbol">(</a><a id="1619" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1621" class="Symbol">→</a> <a id="1623" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1625" class="Symbol">→</a> <a id="1627" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1631" href="Data.Sum.Base.html#451" class="Generalizable">d</a><a id="1632" class="Symbol">)</a> <a id="1634" class="Symbol">→</a> <a id="1636" class="Symbol">(</a><a id="1637" href="Data.Sum.Base.html#465" class="Generalizable">A</a> <a id="1639" class="Symbol">→</a> <a id="1641" href="Data.Sum.Base.html#479" class="Generalizable">B</a> <a id="1643" class="Symbol">→</a> <a id="1645" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1649" class="Symbol">(</a><a id="1650" href="Data.Sum.Base.html#449" class="Generalizable">c</a> <a id="1652" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1654" href="Data.Sum.Base.html#451" class="Generalizable">d</a><a id="1655" class="Symbol">))</a>
<a id="1658" href="Data.Sum.Base.html#1658" class="Bound">f</a> <a id="1660" href="Data.Sum.Base.html#1592" class="Function Operator">-⊎-</a> <a id="1664" href="Data.Sum.Base.html#1664" class="Bound">g</a> <a id="1666" class="Symbol">=</a> <a id="1668" href="Data.Sum.Base.html#1658" class="Bound">f</a> <a id="1670" href="Function.Base.html#5039" class="Function Operator">-⟪</a> <a id="1673" href="Data.Sum.Base.html#625" class="Datatype Operator">_⊎_</a> <a id="1677" href="Function.Base.html#5039" class="Function Operator">⟫-</a> <a id="1680" href="Data.Sum.Base.html#1664" class="Bound">g</a>
</pre></body></html>
Reference in a new issue Copy permalink