2b:null 2c:["$","title",null,{"children":"Quarternary Functions | Nat Alison | Observable"}] 31:Tf9e,intersections = { let Bins = [Impl, If, Eq, Or]; let binFns = Bins.map((Bin) => Bin(Var, Var)); let items = {}; let Terns = [ Or, Eq, Neq, Odd, // Even, CountEq(1), CountNeq(1), CountLeq(1), // CountGeq(2), Mux, EquivImpl, NEquivImpl ]; let ternFns = Terns.map((Tern) => Tern(Var, Var, Var)).concat([ // andOr, // orAnd, andEq, // orEq, // eqAnd, eqOr // xorAnd, // xorOr ]); function check(Fn, label) { let fn = Fn(Var, Var, Var, Var); let idx = codeToClassMap[getCode(4, fn)]; if (!fnNamesList[idx].repr) { if (!items[idx]) { items[idx] = []; items[idx].label = label; } items[idx].push(fn.format(..."abcd")); } } for (let ternFn of ternFns) { for (let i of [0, 1, 2]) { for (let binFn of binFns) { let Fn = makeCombinationFunction( (args) => ternFn(...args.slice(0, 3)) && binFn(args[i], args[3]), (args) => `${ternFn.format(...args.slice(0, 3))} && ${binFn.format( args[i], args[3] )}` ); check(Fn); } } for (let [i, j] of [ [0, 1], [0, 2], [1, 2] ]) { for (let binFn1 of binFns) { for (let binFn2 of binFns) { let Fn = makeCombinationFunction( (args) => ternFn(...args.slice(0, 3)) && binFn1(args[i], args[3]) && binFn2(args[j], args[3]), (args) => `${ternFn.format(...args.slice(0, 3))} && ${binFn1.format( args[i], args[3] )} && ${binFn2.format(args[j], args[3])}` ); check(Fn); } } } let [i, j, k] = [0, 1, 2]; for (let binFn1 of binFns) { for (let binFn2 of binFns) { for (let binFn3 of binFns) { let Fn = makeCombinationFunction( (args) => ternFn(...args.slice(0, 3)) && binFn1(args[i], args[3]) && binFn2(args[j], args[3]) && binFn3(args[k], args[3]), (args) => `${ternFn.format(...args.slice(0, 3))} && ${binFn1.format( args[i], args[3] )} && ${binFn2.format(args[j], args[3])} && ${binFn3.format( args[k], args[3] )}` ); check(Fn); } } } } let fullTerns = ternFns .concat([andOr, orAnd, orEq, eqAnd, xorAnd, xorOr]) .concat([Even, CountGeq(2)].map((F) => F(Var, Var, Var))); for (let ternFn of fullTerns) { for (let ternFn2 of fullTerns) { for (let i = 0; i < 2 ** 4; i++) { let Fn = makeCombinationFunction( ([a, b, c, d]) => ternFn(a, b, c) && applyNegations(ternFn2, i)(a, b, d), ([a, b, c, d]) => `${ternFn.format(a, b, c)} && ${ternFn2.format(a, b, d)}` ); check(Fn, "terns"); } for (let ternFn3 of fullTerns) { let Fn = makeCombinationFunction( ([a, b, c, d]) => ternFn(a, b, c) && ternFn2(a, b, d) && ternFn3(a, c, d), ([a, b, c, d]) => `${ternFn.format(a, b, c)} && ${ternFn2.format( a, b, d )} && ${ternFn3.format(a, c, d)}` ); check(Fn, "terns"); for (let ternFn4 of fullTerns) { let Fn = makeCombinationFunction( ([a, b, c, d]) => ternFn(a, b, c) && ternFn2(a, b, d) && ternFn3(a, c, d) && ternFn4(b, c, d), ([a, b, c, d]) => `${ternFn.format(a, b, c)} && ${ternFn2.format( a, b, d )} && ${ternFn3.format(a, c, d)} && ${ternFn4.format(b, c, d)}` ); check(Fn, "terns"); } } } } return items; }32:T883,function setRepsQuartenary(setAsRepr) { for (let fn of [ // withFormat( // (a, b, c, d) => a == b && b == c && (!c || d), // (a, b, c, d) => `${a} == ${b} == ${c} => ${d}` // ), // withFormat( // (a, b, c, d) => a == b && (!b || c) && (!c || d), // (a, b, c, d) => `${a} == ${b} => ${c} => ${d}` // ), // withFormat( // (a, b, c, d) => (!a || b) && (!b || c) && (!c || d), // (a, b, c, d) => `${a} => ${b} => ${c} => ${d}` // ), // withFormat( // (a, b, c, d) => (!a || b) && b == c && (!c || d), // (a, b, c, d) => `${a} => ${b} == ${c} => ${d}` // ), // withFormat( // (a, b, c, d) => a == b && (!b || c) && c == d, // (a, b, c, d) => `${a} == ${b} => ${c} == ${d}` // ), // withFormat( // (a, b, c, d) => (a || !b) && (!b || c) && (!c || d), // (a, b, c, d) => `${a} <= ${b} => ${c} => ${d}` // ), // withFormat( // (a, b, c, d) => (a || !b) && (!b || c) && (c || !d), // (a, b, c, d) => `${a} <= ${b} => ${c} <= ${d}` // ), // withFormat( // (a, b, c, d) => (a || !b) && (!b || c) && c == d, // (a, b, c, d) => `${a} <= ${b} => ${c} == ${d}` // ), // withFormat( // (a, b, c, d) => (!a || b) && (!b || d) && (!a || c) && (!c || d), // (a, b, c, d) => `${a} => {${b}, ${c}} => ${d}` // ), andFn, oddFn, eqFn, countEq1, countEq2, countLeq1, countEq02, countEq03, countEq12, orOfAnds, andOrAnd, eqOfAnds, andOfEqs, orOfAndEq, eqOrAnd, andEqAnd, andOrEq, eqAndEq, orAnd3, eqAnd3, andOdd3, andEq3, xorEq3, andCountEq1, orCountEq1, eqCountEq1, andCountLeq1, eqCountLeq1, and3Or, and3Eq, odd3And, eq3And, eq3Or, eq3Xor, countEq1And, countEq1Or, countEq1Eq, countLeq1And, countLeq1Eq, andMux, andCMux, eqMux, eqCMux, muxAnd, muxEq, andEquivImpl, andCEquivImpl, orEquivImpl, orCEquivImpl, eqEquivImpl, eqCEquivImpl, equivImplAnd, equivImplOr, equivImplEq ]) { setAsRepr(fn); } }33:T12ec,function fillQuartenary(setList) { // commutative functions setList(oddFn); setList(evenFn); for (let i = 0; i < 2 ** 4; i++) { for (let fn of [ andFn, orFn, countEq1, countNeq1, countLeq1, countLeq2, countEq02, countNeq02, countEq03, countNeq03, countEq12, countNeq12 ]) { setList(applyNegations(fn, i)); } } for (let i = 0; i < 2 ** 4; i++) { let bitCount = countBits(i); if (bitCount < 2 || (bitCount === 2 && i % 2 === 0)) { for (let fn of [eqFn, neqFn, countEq2, countNeq2]) { setList(applyNegations(fn, i)); } } } for (let order of permutations(_.range(4))) { for (let i = 0; i < 2 ** 3; i++) { for (let fn of [muxAnd, muxOr]) { setList(permuteFn(applyNegations(fn, i << 1), order)); } } for (let i = 0; i < 2 ** 2; i++) { for (let fn of [muxEq]) { setList(permuteFn(applyNegations(fn, i << 1), order)); } } if (order[0] < order[1]) { for (let i = 0; i < 2 ** 4; i++) { for (let fn of [ andOrAnd, orAndOr, andOrEq, andEqAnd, andEqOr, andEquivImpl, andNEquivImpl, orEquivImpl, orNEquivImpl, equivImplAnd, equivImplOr, nEquivImplAnd, nEquivImplOr, equivImplEq ]) { setList(permuteFn(applyNegations(fn, i), order)); } } for (let i = 0; i < 2 ** 4; i += 2) { for (let fn of [eqAndOr, eqOrAnd, eqAndEq, eqEquivImpl, eqNEquivImpl]) { setList(permuteFn(applyNegations(fn, i), order)); } } } if (order[2] < order[3]) { for (let i = 0; i < 2 ** 4; i++) { for (let fn of [andCMux, orCMux]) { setList(permuteFn(applyNegations(fn, i), order)); } } for (let i = 0; i < 2 ** 3; i++) { setList(permuteFn(applyNegations(eqCMux, i), order)); } } if (order[0] < order[1] && order[2] < order[3]) { for (let i = 0; i < 2 ** 3; i++) { for (let fn of [orOfAndEq, andOfOrEq, eqCEquivImpl, eqCNEquivImpl]) { setList(permuteFn(applyNegations(fn, i), order)); } } for (let i = 0; i < 2 ** 4; i++) { for (let fn of [ orAnd3, andOr3, andEq3, andNeq3, andCountEq1, andCountNeq1, orCountEq1, orCountNeq1, andCountLeq1, andCountGeq2, andMux, orMux, andCEquivImpl, andCNEquivImpl, orCEquivImpl, orCNEquivImpl ]) { setList(permuteFn(applyNegations(fn, i), order)); } } for (let i = 0; i < 2 ** 4; i += 2) { setList(permuteFn(applyNegations(eqAnd3, i), order)); setList(permuteFn(applyNegations(eqOr3, i), order)); setList(permuteFn(applyNegations(eqCountEq1, i), order)); setList(permuteFn(applyNegations(eqCountNeq1, i), order)); setList(permuteFn(applyNegations(eqCountLeq1, i), order)); setList(permuteFn(applyNegations(eqMux, i), order)); } for (let i = 0; i < 2 ** 2; i++) { setList(permuteFn(applyNegations(andOdd3, i), order)); setList(permuteFn(applyNegations(andEven3, i), order)); setList(permuteFn(applyNegations(xorEq3, i << 2), order)); setList(permuteFn(applyNegations(xorNeq3, i << 2), order)); } } } // A is fixed, all others permute for (let order of cycle([1, 2, 3])) { order = [0, ...order]; for (let i = 0; i < 2 ** 4; i++) { for (let fn of [andOfOrs, orOfAnds, eqOfAnds, neqOfAnds]) { setList(permuteFn(applyNegations(fn, i), order)); } } for (let i of [0, 0b0010, 0b1000, 0b1010]) { setList(permuteFn(applyNegations(andOfEqs, i), order)); setList(permuteFn(applyNegations(orOfEqs, i), order)); } } for (let order of cycle(_.range(4))) { for (let i = 0; i < 2 ** 4; i++) { for (let fn of [ and3Or, or3And, and3Eq, countEq1And, countNeq1Or, countEq1Or, countNeq1And, countEq1Eq, countLeq1And, countLeq1Or ]) { setList(permuteFn(applyNegations(fn, i), order)); } if (countBits(i % 2 ** 3) <= 1) { for (let fn of [eq3And, neq3Or, eq3Or, neq3And, eq3Xor]) { setList(permuteFn(applyNegations(fn, i), order)); } } } for (let i = 0; i < 2 ** 3; i++) { setList(permuteFn(applyNegations(countLeq1Eq, i), order)); } for (let i = 0; i < 2 ** 2; i++) { for (let fn of [odd3And, odd3Or]) { setList(permuteFn(applyNegations(fn, i << 2), order)); } } } }34:[] 2f:{"id":"a8d3c14a4a9c8e5a","slug":null,"title":"Quarternary Functions","thumbnail":"15a9a43ba5684e7393e714b30954be3444b6b7b811e357f798a1a11b95abb74f","access_level":"public","create_time":"$D2024-01-14T06:35:01.717Z","update_time":"$D2024-01-20T07:45:07.608Z","view_time":null,"first_public_time":"$D2024-01-14T06:35:01.717Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"b2691018f1bbc657","login":"tesseralis","name":"Nat 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Alison"}},"type":"notebook","body":{"title":"Quarternary Functions","cells":[{"id":0,"value":"# Quarternary Functions","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":81,"value":"numFilled = fnNamesList.filter((x) => x.repr).length","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":481,"value":"missingClasses = {\n let result = [];\n return result;\n function checkFunction(Fn) {\n let cls = codeToClassMap[getCode(4, Fn)];\n if (!fnNamesList[cls].repr) {\n result.push(Fn.format(...\"abcd\"));\n }\n }\n\n for (let Tern of [Mux, EquivImpl]) {\n for (let Bin of [And, Or, Xor, Eq]) {\n checkFunction(Tern(Bin(Var, Var), Var, Var));\n checkFunction(Tern(Var, Bin(Var, Var), Var));\n checkFunction(Tern(Var, Var, Bin(Var, Var)));\n checkFunction(Bin(Tern(Var, Var, Var), Var));\n }\n }\n // for (let Fn1 of [And, Or, Xor]) {\n // for (let Fn2 of [And, Or, Xor]) {\n // for (let Fn3 of [And, Or, Xor]) {\n // let Fn = Fn3(Fn2(Fn1(Var, Var), Var), Var);\n // checkFunction(Fn);\n // }\n // }\n // }\n\n // for (let Tern of [And, Or, Odd, Even, Eq, Neq, CountEq(1), CountLeq(1)]) {\n // for (let Bin of [And, Or, Xor]) {\n // checkFunction(Tern(Bin(Var, Var), Var, Var));\n // checkFunction(Bin(Tern(Var, Var, Var), Var));\n // }\n // }\n\n return result;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1110,"value":"Object.values(intersections).filter((arr) => arr.label === \"terns\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":934,"value":"Object.entries(intersections).length","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":901,"value":"$31","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":906,"value":"Impl = makeCombinationFunction(\n ([p, q]) => !p || q,\n ([p, q]) => `${p} => ${q}`\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":911,"value":"If = makeCombinationFunction(\n ([p, q]) => p || !q,\n ([p, q]) => `${p} <= ${q}`\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":669,"value":"{\n let idx =\n codeToClassMap[getCode(4, (a, b, c, d) => (a || b || c) && (a && b) == d)];\n return [idx, fnNamesList[idx].repr || intersections[idx][0]];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1019,"value":"incompleteClasses = foundClasses.filter((x) =>\n Object.values(x.fnNames).some((list) => list.length !== 1)\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":25,"value":"foundClasses = fnNamesList.filter((x) => x.repr)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"fnNamesList = {\n let list = quartClasses.map((classList) => {\n return {\n fnNames: Object.fromEntries([...classList].map((code) => [code, []]))\n };\n });\n function setList(fn) {\n let code = getCode(4, fn);\n let index = codeToClassMap[code];\n list[index].fnNames[code].push(fn.format(\"a\", \"b\", \"c\", \"d\"));\n }\n function setAsRepr(fn) {\n let code = getCode(4, fn);\n let index = codeToClassMap[code];\n list[index].repr = fn.format(\"a\", \"b\", \"c\", \"d\");\n }\n\n populateNullary(setAsRepr, setList);\n populateUnary(setAsRepr, setList, 4);\n populateBinary(setAsRepr, setList, 4);\n populateTernary(setAsRepr, setList, 4);\n\n setRepsQuartenary(setAsRepr);\n fillQuartenary(setList);\n return list;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":35,"value":"$32","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":37,"value":"$33","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":118,"value":"## (A ? B) ? (C ? D)","pinned":true,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":109,"value":"orOfAnds = Or(And(Var, Var), And(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":130,"value":"andOfOrs = And(Or(Var, Var), Or(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":142,"value":"eqOfAnds = Eq(And(Var, Var), And(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":144,"value":"neqOfAnds = Xor(And(Var, Var), And(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":156,"value":"andOfEqs = And(Eq(Var, Var), Eq(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":158,"value":"orOfEqs = Or(Eq(Var, Var), Eq(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":165,"value":"orOfAndEq = Or(And(Var, Var), Eq(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":167,"value":"andOfOrEq = And(Or(Var, Var), Eq(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":274,"value":"## (A ? B) ? C ? D","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":504,"value":"### Commutative","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":276,"value":"orAnd3 = And(Or(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":286,"value":"andOr3 = Or(And(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":279,"value":"eqAnd3 = And(Eq(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":289,"value":"eqOr3 = Or(Eq(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":293,"value":"andOdd3 = Odd(And(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":301,"value":"andEven3 = Even(And(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":304,"value":"andEq3 = Eq(And(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":310,"value":"andNeq3 = Neq(And(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":314,"value":"xorEq3 = Eq(Xor(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":320,"value":"xorNeq3 = Neq(Xor(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":325,"value":"andCountEq1 = CountEq(1)(And(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":327,"value":"andCountNeq1 = CountNeq(1)(And(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":495,"value":"orCountEq1 = CountEq(1)(Or(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":497,"value":"orCountNeq1 = CountNeq(1)(Or(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":332,"value":"eqCountEq1 = CountEq(1)(Eq(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":334,"value":"eqCountNeq1 = CountNeq(1)(Eq(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":340,"value":"andCountLeq1 = CountLeq(1)(And(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":342,"value":"andCountGeq2 = CountGeq(2)(And(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":349,"value":"eqCountLeq1 = CountLeq(1)(Eq(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":508,"value":"### Non-commutative","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":511,"value":"andMux = Mux(And(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":516,"value":"orMux = Mux(Or(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":519,"value":"andCMux = Mux(Var, Var, And(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":528,"value":"orCMux = Mux(Var, Var, Or(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":532,"value":"eqMux = Mux(Eq(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":538,"value":"eqCMux = Mux(Var, Var, Eq(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":562,"value":"andEquivImpl = EquivImpl(And(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":567,"value":"andNEquivImpl = NEquivImpl(And(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":603,"value":"andCEquivImpl = EquivImpl(Var, Var, And(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":606,"value":"andCNEquivImpl = NEquivImpl(Var, Var, And(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":576,"value":"orEquivImpl = EquivImpl(Or(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":578,"value":"orNEquivImpl = NEquivImpl(Or(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":608,"value":"orCEquivImpl = EquivImpl(Var, Var, Or(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":610,"value":"orCNEquivImpl = NEquivImpl(Var, Var, Or(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":582,"value":"eqEquivImpl = EquivImpl(Eq(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":584,"value":"eqNEquivImpl = NEquivImpl(Eq(Var, Var), Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":615,"value":"eqCEquivImpl = EquivImpl(Var, Var, Eq(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":617,"value":"eqCNEquivImpl = NEquivImpl(Var, Var, Eq(Var, Var))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":359,"value":"## (A ? B ? C) ? D","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":543,"value":"### Commutative","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":361,"value":"and3Or = Or(And(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":363,"value":"or3And = And(Or(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":377,"value":"and3Eq = Eq(And(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":381,"value":"odd3And = And(Odd(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":383,"value":"odd3Or = Or(Odd(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":395,"value":"eq3And = And(Eq(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":397,"value":"neq3Or = Or(Neq(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":412,"value":"eq3Or = Or(Eq(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":414,"value":"neq3And = And(Neq(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":420,"value":"eq3Xor = Xor(Eq(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":428,"value":"countEq1And = And(CountEq(1)(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":430,"value":"countNeq1Or = Or(CountNeq(1)(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":440,"value":"countEq1Or = Or(CountEq(1)(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":467,"value":"countEq1Eq = Eq(CountEq(1)(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":443,"value":"countNeq1And = And(CountNeq(1)(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":447,"value":"countLeq1And = And(CountLeq(1)(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":453,"value":"countLeq1Or = Or(CountLeq(1)(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":475,"value":"countLeq1Eq = Eq(CountLeq(1)(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":545,"value":"### Noncommutative","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":547,"value":"muxAnd = And(Mux(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":554,"value":"muxOr = Or(Mux(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":549,"value":"muxEq = Eq(Mux(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":628,"value":"equivImplAnd = And(EquivImpl(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":630,"value":"nEquivImplOr = Or(NEquivImpl(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":633,"value":"equivImplOr = Or(EquivImpl(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":635,"value":"nEquivImplAnd = And(NEquivImpl(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":642,"value":"equivImplEq = Eq(EquivImpl(Var, Var, Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":239,"value":"## ((A ? B) ? C) ? D","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":112,"value":"andOrAnd = And(Or(And(Var, Var), Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":124,"value":"orAndOr = Or(And(Or(Var, Var), Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":176,"value":"eqOrAnd = And(Or(Eq(Var, Var), Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":180,"value":"eqAndOr = Or(And(Eq(Var, Var), Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":187,"value":"andEqAnd = And(Eq(And(Var, Var), Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":232,"value":"andEqOr = Or(Eq(And(Var, Var), Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":190,"value":"andOrEq = Eq(Or(And(Var, Var), Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":223,"value":"eqAndEq = Eq(And(Eq(Var, Var), Var), Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":54,"value":"## 4-ary Commutative","pinned":true,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":57,"value":"countEq1 = CountEq(1)(Var, Var, Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":59,"value":"countNeq1 = CountNeq(1)(Var, Var, Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":66,"value":"countEq2 = CountEq(2)(Var, Var, Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":68,"value":"countNeq2 = CountNeq(2)(Var, Var, Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":84,"value":"countLeq1 = CountLeq(1)(Var, Var, Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":86,"value":"countLeq2 = CountLeq(2)(Var, Var, Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":93,"value":"countEq02 = CountEq(0, 2)(Var, Var, Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":100,"value":"countNeq02 = CountNeq(0, 2)(Var, Var, Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":650,"value":"countEq03 = CountEq(0, 3)(Var, Var, Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":652,"value":"countNeq03 = CountNeq(0, 3)(Var, Var, Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":103,"value":"countEq12 = CountEq(1, 2)(Var, Var, Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":105,"value":"countNeq12 = CountNeq(1, 2)(Var, Var, Var, Var)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"codeToClassMap = getClassIndexMap(quartClasses)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"quartClasses = getConjugacyClasses(4)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"function getClassIndexMap(equivClasses) {\n let map = [];\n for (let [idx, cls] of equivClasses.entries()) {\n for (let item of cls) {\n map[item] = idx;\n }\n }\n return map;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"import {\n populateTernary,\n Mux,\n EquivImpl,\n NEquivImpl,\n // tern functions\n andOr,\n orAnd,\n andEq,\n orEq,\n eqAnd,\n eqOr,\n xorAnd,\n xorOr\n} from \"@tesseralis/ternary-functions\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"import {\n permutations,\n getConjugacyClasses,\n combinationsWithRepeats,\n makeCombinationFunction,\n getIndex,\n getCode,\n widen,\n countBits,\n applyNegations,\n compose,\n permuteFn,\n negateFn,\n withFormat,\n cycle,\n populateNullary,\n populateUnary,\n populateBinary,\n trueFn,\n falseFn,\n idFn,\n notFn,\n andFn,\n orFn,\n evenFn,\n oddFn,\n eqFn,\n neqFn,\n CountEq,\n CountNeq,\n CountGeq,\n CountLeq,\n xor2,\n eq2,\n Var,\n And,\n Or,\n Xor,\n Odd,\n Even,\n Eq,\n Neq\n} from \"@tesseralis/boolean-functions\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W34","stdlib":"1","titling":"auto"}} 30:"$2f:body"