Add packages/kripke

2025-02-17 23:21:53 +09:00
parent 1465acdf24
commit 2e36390a5d
11 changed files with 505 additions and 0 deletions
--- a/packages/kripke/syntax.ts
+++ b/packages/kripke/syntax.ts
@@ -0,0 +1,53 @@
+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" | "iff";
+      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 "iff":
+      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 iff = (left: Formula, right: Formula) =>
+  ({ type: "iff", left, right }) as const satisfies Formula;