Refactor (2)
This commit is contained in:
cannorin
374
packages/kripke/src/syntax.ts
Normal file
374
packages/kripke/src/syntax.ts
Normal file
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export type PropVar = "p" | "q" | "r" | "s";
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export const propVars = ["p", "q", "r", "s"] as const satisfies PropVar[];
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export type Formula =
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| { type: "top" | "bot" }
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| { type: "propvar"; name: PropVar }
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| { type: "not" | "box" | "diamond"; fml: Formula }
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| {
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type: "to" | "or" | "and" | "eq";
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left: Formula;
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right: Formula;
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};
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export function vars(fml: Formula): Set<PropVar> {
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switch (fml.type) {
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case "top":
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case "bot":
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return new Set();
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case "box":
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case "diamond":
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case "not":
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return vars(fml.fml);
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case "to":
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case "or":
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case "and":
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case "eq":
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return new Set([...vars(fml.left), ...vars(fml.right)]);
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case "propvar":
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return new Set([fml.name]);
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}
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}
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export const propvar = (name: PropVar) => ({ type: "propvar", name }) as const;
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export const top = { type: "top" } as const satisfies Formula;
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export const bot = { type: "bot" } as const satisfies Formula;
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export const box = (fml: Formula) =>
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({ type: "box", fml }) as const satisfies Formula;
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export const diamond = (fml: Formula) =>
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({ type: "diamond", fml }) as const satisfies Formula;
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export const not = (fml: Formula) =>
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({ type: "not", fml }) as const satisfies Formula;
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export const to = (left: Formula, right: Formula) =>
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({ type: "to", left, right }) as const satisfies Formula;
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export const and = (left: Formula, right: Formula) =>
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({ type: "and", left, right }) as const satisfies Formula;
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export const or = (left: Formula, right: Formula) =>
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({ type: "or", left, right }) as const satisfies Formula;
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export const eq = (left: Formula, right: Formula) =>
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({ type: "eq", left, right }) as const satisfies Formula;
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export type Symbols = Record<Exclude<Formula["type"], "propvar">, string>;
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export const asciiSymbols: Symbols = {
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top: "T",
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bot: "F",
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box: "[]",
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diamond: "<>",
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not: "~",
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and: "^",
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or: "v",
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to: "->",
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eq: "<->",
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};
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export const unicodeSymbols: Symbols = {
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top: "⊤",
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bot: "⊥",
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box: "□",
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diamond: "◇",
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not: "¬",
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and: "∧",
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or: "∨",
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to: "→",
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eq: "↔",
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};
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export const latexSymbols: Symbols = {
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top: "\\top ",
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bot: "\\bot ",
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box: "\\Box ",
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diamond: "\\Diamond ",
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not: "\\neg ",
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and: "\\land",
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or: "\\lor",
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to: "\\to",
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eq: "\\leftrightarrow",
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};
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export function prettyPrint(
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fml: Formula,
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config?: { paren?: boolean | ((fml: Formula) => boolean); symbols?: Symbols },
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): string {
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const { paren = false, symbols = unicodeSymbols } = config ?? {};
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const withParen = (s: string) =>
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(typeof paren === "boolean" ? paren : paren(fml)) ? `(${s})` : s;
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switch (fml.type) {
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case "top":
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return symbols.top;
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case "bot":
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return symbols.bot;
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case "propvar":
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return fml.name;
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case "not":
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return `${symbols.not}${prettyPrint(fml.fml, { paren: true, symbols })}`;
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case "box":
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return `${symbols.box}${prettyPrint(fml.fml, { paren: true, symbols })}`;
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case "diamond":
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return `${symbols.diamond}${prettyPrint(fml.fml, { paren: true, symbols })}`;
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case "and": {
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const newConfig: typeof config = {
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symbols,
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paren: (f) => f.type !== "and",
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};
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return withParen(
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`${prettyPrint(fml.left, newConfig)} ${symbols.and} ${prettyPrint(fml.right, newConfig)}`,
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);
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}
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case "or": {
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const newConfig: typeof config = {
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symbols,
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paren: (f) => f.type !== "or",
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};
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return withParen(
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`${prettyPrint(fml.left, newConfig)} ${symbols.or} ${prettyPrint(fml.right, newConfig)}`,
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);
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}
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case "to": {
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const newConfig: typeof config = {
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symbols,
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paren: (f) => f.type !== "to",
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};
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return withParen(
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`${prettyPrint(fml.left, { symbols, paren: true })} ${symbols.to} ${prettyPrint(fml.right, newConfig)}`,
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);
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}
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case "eq": {
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const newConfig: typeof config = {
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symbols,
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paren: (f) => f.type !== "eq",
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};
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return withParen(
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`${prettyPrint(fml.left, newConfig)} ${symbols.eq} ${prettyPrint(fml.right, newConfig)}`,
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);
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}
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}
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}
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export function simplify(fml: Formula): Formula {
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switch (fml.type) {
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case "top":
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case "bot":
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case "propvar":
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return fml;
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case "not":
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case "box":
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case "diamond": {
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const inner = simplify(fml.fml);
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if (fml.type === "not" && inner.type === "not") return inner.fml;
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if (fml.type === "not" && inner.type === "top") return bot;
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if (fml.type === "not" && inner.type === "bot") return top;
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if (fml.type === "box" && inner.type === "top") return top;
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if (fml.type === "diamond" && inner.type === "bot") return bot;
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return {
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type: fml.type,
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fml: inner,
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};
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}
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case "or":
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case "and":
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case "to":
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case "eq": {
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const innerLeft = simplify(fml.left);
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const innerRight = simplify(fml.right);
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if (fml.type === "and" && innerLeft.type === "top") return innerRight;
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if (fml.type === "and" && innerRight.type === "top") return innerLeft;
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if (
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fml.type === "and" &&
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(innerLeft.type === "bot" || innerRight.type === "bot")
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)
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return bot;
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if (fml.type === "or" && innerLeft.type === "bot") return innerRight;
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if (fml.type === "or" && innerRight.type === "bot") return innerLeft;
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if (
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fml.type === "or" &&
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(innerLeft.type === "top" || innerRight.type === "top")
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)
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return top;
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if (fml.type === "to" && innerLeft.type === "top") return innerRight;
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if (fml.type === "to" && innerLeft.type === "bot") return top;
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if (fml.type === "to" && innerRight.type === "top") return top;
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if (fml.type === "to" && innerRight.type === "bot")
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return simplify(not(innerLeft));
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if (fml.type === "eq" && innerLeft.type === "top") return innerRight;
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if (fml.type === "eq" && innerRight.type === "top") return innerLeft;
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if (fml.type === "eq" && innerRight.type === "bot")
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return simplify(not(innerLeft));
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if (fml.type === "eq" && innerLeft.type === "bot")
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return simplify(not(innerRight));
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return {
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type: fml.type,
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left: innerLeft,
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right: innerRight,
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};
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}
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}
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}
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export type NNFFormula<T = undefined> =
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| { type: "top" | "bot"; tag: T }
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| { type: "propvar"; name: PropVar; tag: T }
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| { type: "not"; fml: { type: "propvar"; name: PropVar; tag: T }; tag: T }
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| { type: "box" | "diamond"; fml: NNFFormula<T>; tag: T }
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| {
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type: "and" | "or";
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left: NNFFormula<T>;
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right: NNFFormula<T>;
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tag: T;
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};
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export function toNNF(fml: Formula): NNFFormula {
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switch (fml.type) {
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case "top":
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return { ...fml, tag: undefined };
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case "bot":
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return { ...fml, tag: undefined };
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case "propvar":
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return { ...fml, tag: undefined };
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case "box": {
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return {
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type: "box",
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fml: toNNF(fml.fml),
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tag: undefined,
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};
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}
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case "diamond": {
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return {
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type: "diamond",
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fml: toNNF(fml.fml),
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tag: undefined,
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};
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}
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case "to": {
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return toNNF(or(not(fml.left), fml.right));
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}
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case "eq": {
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return toNNF(
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and(or(not(fml.left), fml.right), or(not(fml.right), fml.left)),
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);
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}
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case "or": {
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return {
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type: "or",
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left: toNNF(fml.left),
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right: toNNF(fml.right),
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tag: undefined,
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};
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}
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case "and": {
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return {
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type: "and",
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left: toNNF(fml.left),
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right: toNNF(fml.right),
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tag: undefined,
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};
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}
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case "not": {
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switch (fml.fml.type) {
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case "top":
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return { ...bot, tag: undefined };
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case "bot":
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return { ...top, tag: undefined };
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case "propvar":
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return {
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type: "not",
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fml: { ...fml.fml, tag: undefined },
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tag: undefined,
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};
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case "not":
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return toNNF(fml.fml.fml);
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case "box":
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return {
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type: "diamond",
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fml: toNNF(not(fml.fml.fml)),
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tag: undefined,
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};
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case "diamond":
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return { type: "box", fml: toNNF(not(fml.fml.fml)), tag: undefined };
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case "or":
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return {
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type: "and",
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left: toNNF(not(fml.fml.left)),
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right: toNNF(not(fml.fml.right)),
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tag: undefined,
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};
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case "and":
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return {
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type: "or",
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left: toNNF(not(fml.fml.left)),
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right: toNNF(not(fml.fml.right)),
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tag: undefined,
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};
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case "to":
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return {
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type: "and",
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left: toNNF(fml.fml.left),
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right: toNNF(not(fml.fml.right)),
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tag: undefined,
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};
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case "eq":
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return {
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type: "or",
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left: {
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type: "and",
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left: toNNF(fml.fml.left),
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right: toNNF(not(fml.fml.right)),
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tag: undefined,
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},
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right: {
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type: "and",
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left: toNNF(not(fml.fml.left)),
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right: toNNF(fml.fml.right),
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tag: undefined,
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},
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tag: undefined,
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};
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}
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}
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}
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}
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export function tagNNF<T, U>(
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fml: NNFFormula<T>,
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tagger: (fml: Omit<NNFFormula<T>, "tag">, tag: T) => U,
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): NNFFormula<U> {
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switch (fml.type) {
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case "top":
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case "bot":
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case "propvar":
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return { ...fml, tag: tagger(fml, fml.tag) };
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case "not":
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return {
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type: "not",
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fml: {
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type: "propvar",
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name: fml.fml.name,
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tag: tagger(fml.fml, fml.fml.tag),
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},
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tag: tagger(fml, fml.tag),
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};
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case "box":
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case "diamond":
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return {
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type: fml.type,
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fml: tagNNF(fml.fml, tagger),
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tag: tagger(fml, fml.tag),
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};
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case "and":
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case "or":
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return {
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type: fml.type,
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left: tagNNF(fml.left, tagger),
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right: tagNNF(fml.right, tagger),
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tag: tagger(fml, fml.tag),
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};
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}
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}
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