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fol.js
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fol.js
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// For reference purposes only
nodeTypes = [
"VARIABLE",
"FUNCTION",
"RELATION",
"QUANTIFIER",
"BINARY-CONNECTIVE",
"UNARY-CONNECTIVE"
]
function untilValid(ls, f) {
for (let i = 0; i < ls.length; i++) {
let res = f(ls.at(i));
if (res != undefined) {
return res
}
}
return undefined
}
class FirstOrderNode {
constructor(token, children) {
this.token = token;
this.children = children;
}
}
class FirstOrderParser {
constructor(varTokens, fxnTokens, relTokens, cstTokens) {
this.varTokens = varTokens;
this.fxnTokens = fxnTokens;
this.relTokens = relTokens;
this.cstTokens = cstTokens;
this.qfrTokens = ['A', 'E'];
this.binConTokens = ['&', '|'];
this.unConTokens = ['~'];
this.unconsumed = "";
}
tryParseToken(tok) {
while (this.unconsumed.startsWith(' ')) {
this.unconsumed = this.unconsumed.slice(1);
}
if (this.unconsumed.startsWith(tok)) {
this.unconsumed = this.unconsumed.slice(tok.length)
return new FirstOrderNode(tok, [])
}
return undefined
}
tryParseAnyToken(toks) {
for (let i = 0; i < toks.length; i++) {
let res = this.tryParseToken(toks.at(i));
if (res != undefined) return res
}
return undefined
}
tryParseVar() {
return this.tryParseAnyToken(this.varTokens)
}
tryParseCst() {
return this.tryParseAnyToken(this.cstTokens)
}
mustParseFxn() {
let fxn = this.tryParseAnyToken(this.fxnTokens);
if (fxn == undefined) return undefined
if (this.tryParseToken('(') == undefined)
throw new SyntaxError("Expected open paren following function name " + fxn.token)
let args = []
args.push(this.mustParseExpr())
while (this.tryParseToken(',') != undefined) {
args.push(this.mustParseExpr())
}
if (this.tryParseToken(')') == undefined)
throw new SyntaxError("Expected close paren following args of function " + fxn.token)
fxn.children = args
return fxn
}
mustParseExpr() {
// An expression can be a constant...
let res = this.tryParseCst();
if (res != undefined) return res;
// ... or a variable...
res = this.tryParseVar();
if (res != undefined) return res;
// ... or a function evaluation.
res = this.mustParseFxn()
if (res != undefined) return res;
throw new SyntaxError("Expected expression, but instead found " + this.unconsumed)
}
mustParseFormula(withBinop = true) {
// A formula can be a parenthesized formula...
let fNode = undefined;
let res = this.tryParseToken("(");
if (res != undefined) {
fNode = this.mustParseFormula();
if (this.tryParseToken(")") == undefined)
throw new SyntaxError("Expected close paren closing parenthesized formula");
}
// ... or it can start with a unary connective...
if (fNode == undefined) {
res = this.tryParseAnyToken(this.unConTokens);
if (res != undefined) {
fNode = res;
fNode.children.push(this.mustParseFormula(false));
if (withBinop) {
res = this.tryParseAnyToken(this.binConTokens);
if (res != undefined) {
let fNode2 = res;
fNode2.children = [fNode, this.mustParseFormula()];
fNode = fNode2;
}
}
}
}
// ... or it can start with a quantifier...
if (fNode == undefined) {
res = this.tryParseAnyToken(this.qfrTokens);
if (res != undefined) {
fNode = res;
res = this.tryParseAnyToken(this.varTokens);
if (res == undefined)
throw new SyntaxError("Expected variable name after quantifier " + fNode.token);
fNode.children = [res, this.mustParseFormula(false)];
}
}
// ... or it can consist of a relation evaluation.
if (fNode == undefined) {
res = this.tryParseAnyToken(this.relTokens);
if (res != undefined) {
fNode = res;
if (this.tryParseToken('(') == undefined)
throw new SyntaxError("Expected open paren for call to relation " + fNode.token);
fNode.children.push(this.mustParseExpr());
while (this.tryParseToken(',') != undefined) {
fNode.children.push(this.mustParseExpr());
}
if (this.tryParseToken(')') == undefined)
throw new SyntaxError("Expected close paren for call to relation " + fNode.token);
}
}
if (fNode == undefined)
throw new SyntaxError("Expected string starting with formula, but found " + this.unconsumed);
// Optionally, the formula can be conjoined with others using binary connectives.
if (withBinop) {
res = this.tryParseAnyToken(this.binConTokens);
if (res != undefined) {
let fNode2 = res;
fNode2.children = [fNode, this.mustParseFormula()];
fNode = fNode2;
}
}
return fNode
}
mustParseEntireFormula() {
let fNode = this.mustParseFormula();
if (this.unconsumed.replace(/\s/g, "").length > 0) {
throw new SyntaxError("Unexpected tokens at end of string: " + this.unconsumed);
}
return fNode;
}
}
class FirstOrderModel {
constructor(universe, cmap, fmap, rmap) {
this.universe = universe;
this.cmap = cmap;
this.fmap = fmap;
this.rmap = rmap;
let vars = [...Array(99).keys()].map((n)=>{ return "x"+n });
this.parser = new FirstOrderParser(vars, Object.keys(fmap), Object.keys(rmap), Object.keys(cmap));
}
evaluateExprNodeInContext(eNode, table) {
// Function evaluation
if (Object.keys(this.fmap).indexOf(eNode.token) > -1) {
let f = this.fmap[eNode.token];
if (eNode.children.length != f.length)
throw new Error("Function " + eNode.token + " expected " + f.length + " arguments, got " + eNode.children.length);
return f(...(eNode.children.map((en) => { return this.evaluateExprNodeInContext(en, table) })));
}
// Constant symbol evaluation
if (Object.keys(this.cmap).indexOf(eNode.token) > -1) {
return this.cmap[eNode.token];
}
// Variable evaluation, in context
if (Object.keys(table).indexOf(eNode.token) > -1) {
return table[eNode.token];
}
throw new Error("Literal '" + eNode.token + "' unrecognized");
}
evaluateExpr(strin) {
this.parser.unconsumed = strin;
let eNode = this.parser.mustParseExpr();
return this.evaluateNodeInContext(eNode, {});
}
evaluateFormulaNodeInContext(fNode, table) {
if (this.parser.unConTokens.indexOf(fNode.token) > -1) {
if (fNode.token == "~") {
return !(this.evaluateFormulaNodeInContext(fNode.children[0], table));
}
}
if (this.parser.binConTokens.indexOf(fNode.token) > -1) {
if (fNode.token === "&") {
return this.evaluateFormulaNodeInContext(fNode.children[0], table)
&& this.evaluateFormulaNodeInContext(fNode.children[1], table)
} else if (fNode.token === "|") {
return this.evaluateFormulaNodeInContext(fNode.children[0], table)
|| this.evaluateFormulaNodeInContext(fNode.children[1], table)
}
}
if (this.parser.relTokens.indexOf(fNode.token) > -1) {
let rel = this.rmap[fNode.token];
let args = fNode.children.map((eNode) => { return this.evaluateExprNodeInContext(eNode, table) });
return rel(...args)
}
if (this.parser.qfrTokens.indexOf(fNode.token) > -1) {
if (fNode.token === "A") {
for (let i = 0; i < this.universe.length; i++) {
let augTable = {...table};
augTable[fNode.children[0].token] = this.universe[i];
let truthVal = this.evaluateFormulaNodeInContext(fNode.children[1], augTable);
if (!truthVal) return false;
}
return true;
} else if (fNode.token === "E") {
for (let i = 0; i < this.universe.length; i++) {
let augTable = {...table};
augTable[fNode.children[0].token] = this.universe[i];
let truthVal = this.evaluateFormulaNodeInContext(fNode.children[1], augTable);
if (truthVal) return true;
}
return false;
}
}
throw new SyntaxError("Unrecognized token " + fNode.token);
}
evaluateFormulaInContext(strin, table) {
this.parser.unconsumed = strin;
let fNode = this.parser.mustParseEntireFormula();
return this.evaluateFormulaNodeInContext(fNode, table);
}
}
varnames = ["y"].concat(Array.from(Array(99).keys()).map((n) => `x${n}`))
fop = new FirstOrderParser(varnames, [], ['eq', 'R'], [])