Files
cannorin.net/packages/kripke/syntax.ts
2025-02-22 11:19:58 +09:00

152 lines
4.0 KiB
TypeScript
Raw Permalink Blame History

This file contains ambiguous Unicode characters
This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.
export type PropVar = "p" | "q" | "r" | "s";
export const propVars: PropVar[] = ["p", "q", "r", "s"];
export type Formula =
| { type: "top" | "bot" }
| { type: "propvar"; name: PropVar }
| { type: "not" | "box" | "diamond"; fml: Formula }
| {
type: "to" | "or" | "and" | "eq";
left: Formula;
right: Formula;
};
export function vars(fml: Formula): Set<PropVar> {
switch (fml.type) {
case "top":
case "bot":
return new Set();
case "box":
case "diamond":
case "not":
return vars(fml.fml);
case "to":
case "or":
case "and":
case "eq":
return new Set([...vars(fml.left), ...vars(fml.right)]);
case "propvar":
return new Set([fml.name]);
}
}
export const propvar = (name: PropVar) => ({ type: "propvar", name }) as const;
export const top = { type: "top" } as const satisfies Formula;
export const bot = { type: "bot" } as const satisfies Formula;
export const box = (fml: Formula) =>
({ type: "box", fml }) as const satisfies Formula;
export const diamond = (fml: Formula) =>
({ type: "diamond", fml }) as const satisfies Formula;
export const not = (fml: Formula) =>
({ type: "not", fml }) as const satisfies Formula;
export const to = (left: Formula, right: Formula) =>
({ type: "to", left, right }) as const satisfies Formula;
export const and = (left: Formula, right: Formula) =>
({ type: "and", left, right }) as const satisfies Formula;
export const or = (left: Formula, right: Formula) =>
({ type: "or", left, right }) as const satisfies Formula;
export const eq = (left: Formula, right: Formula) =>
({ type: "eq", left, right }) as const satisfies Formula;
export type Symbols = Record<Exclude<Formula["type"], "propvar">, string>;
export const asciiSymbols: Symbols = {
top: "T",
bot: "F",
box: "[]",
diamond: "<>",
not: "~",
and: "^",
or: "v",
to: "->",
eq: "<->",
};
export const unicodeSymbols: Symbols = {
top: "",
bot: "⊥",
box: "□",
diamond: "◇",
not: "¬",
and: "∧",
or: "",
to: "→",
eq: "↔",
};
export const latexSymbols: Symbols = {
top: "\\top ",
bot: "\\bot ",
box: "\\Box ",
diamond: "\\Diamond ",
not: "\\neg ",
and: "\\land",
or: "\\lor",
to: "\\to",
eq: "\\leftrightarrow",
};
export function prettyPrint(
fml: Formula,
config?: { paren?: boolean | ((fml: Formula) => boolean); symbols?: Symbols },
): string {
const { paren = false, symbols = unicodeSymbols } = config ?? {};
const withParen = (s: string) =>
(typeof paren === "boolean" ? paren : paren(fml)) ? `(${s})` : s;
switch (fml.type) {
case "top":
return symbols.top;
case "bot":
return symbols.bot;
case "propvar":
return fml.name;
case "not":
return `${symbols.not}${prettyPrint(fml.fml, { paren: true, symbols })}`;
case "box":
return `${symbols.box}${prettyPrint(fml.fml, { paren: true, symbols })}`;
case "diamond":
return `${symbols.diamond}${prettyPrint(fml.fml, { paren: true, symbols })}`;
case "and": {
const newConfig: typeof config = {
symbols,
paren: (f) => f.type !== "and",
};
return withParen(
`${prettyPrint(fml.left, newConfig)} ${symbols.and} ${prettyPrint(fml.right, newConfig)}`,
);
}
case "or": {
const newConfig: typeof config = {
symbols,
paren: (f) => f.type !== "or",
};
return withParen(
`${prettyPrint(fml.left, newConfig)} ${symbols.or} ${prettyPrint(fml.right, newConfig)}`,
);
}
case "to": {
const newConfig: typeof config = {
symbols,
paren: (f) => f.type !== "to",
};
return withParen(
`${prettyPrint(fml.left, { symbols, paren: true })} ${symbols.to} ${prettyPrint(fml.right, newConfig)}`,
);
}
case "eq": {
const newConfig: typeof config = {
symbols,
paren: (f) => f.type !== "eq",
};
return withParen(
`${prettyPrint(fml.left, newConfig)} ${symbols.eq} ${prettyPrint(fml.right, newConfig)}`,
);
}
}
}