Refactor (2)
This commit is contained in:
cannorin
282
packages/kripke/src/sat.ts
Normal file
282
packages/kripke/src/sat.ts
Normal file
@@ -0,0 +1,282 @@
|
||||
import { BitSet, maximal } from "@cannorin/utils";
|
||||
import {
|
||||
type Frame,
|
||||
type Model,
|
||||
type World,
|
||||
left,
|
||||
right,
|
||||
worlds,
|
||||
} from "./semantics";
|
||||
import {
|
||||
type Formula,
|
||||
type NNFFormula,
|
||||
not,
|
||||
propVars,
|
||||
simplify,
|
||||
tagNNF,
|
||||
toNNF,
|
||||
} from "./syntax";
|
||||
|
||||
const allValuations = worlds.flatMap((w) =>
|
||||
propVars.map((p) => `${w}${p}` as const),
|
||||
);
|
||||
|
||||
const valuationSet = new BitSet(allValuations);
|
||||
|
||||
export type Constraints = {
|
||||
positive: number;
|
||||
negative: number;
|
||||
};
|
||||
|
||||
const empty: Constraints = {
|
||||
positive: valuationSet.empty,
|
||||
negative: valuationSet.empty,
|
||||
};
|
||||
|
||||
export type Context = {
|
||||
notFml: NNFFormula<number>;
|
||||
next: Record<World, World[]>;
|
||||
memo: Map<`${World}:${number}`, Constraints[]>;
|
||||
constant: Map<`${World}:${number}`, boolean>;
|
||||
};
|
||||
|
||||
export function buildContext(frame: Frame, fml: Formula): Context {
|
||||
let index = 0;
|
||||
const notFml = tagNNF(toNNF(simplify(not(fml))), () => {
|
||||
index++;
|
||||
return index;
|
||||
});
|
||||
|
||||
const next: Record<World, World[]> = { a: [], b: [], c: [], d: [] };
|
||||
for (const rel of frame.relations.values()) {
|
||||
const u = left(rel);
|
||||
const v = right(rel);
|
||||
next[u].push(v);
|
||||
}
|
||||
|
||||
const constant: Map<`${World}:${number}`, boolean> = new Map();
|
||||
function addConstants(f: NNFFormula<number>) {
|
||||
switch (f.type) {
|
||||
case "top": {
|
||||
for (const w of worlds) constant.set(`${w}:${f.tag}`, true);
|
||||
return;
|
||||
}
|
||||
case "bot": {
|
||||
for (const w of worlds) constant.set(`${w}:${f.tag}`, false);
|
||||
return;
|
||||
}
|
||||
case "propvar":
|
||||
case "not":
|
||||
return;
|
||||
case "box": {
|
||||
addConstants(f.fml);
|
||||
for (const w1 of worlds) {
|
||||
const xs = next[w1].map((w2) => constant.get(`${w2}:${f.fml.tag}`));
|
||||
if (xs.some((x) => x === undefined)) continue;
|
||||
constant.set(
|
||||
`${w1}:${f.tag}`,
|
||||
xs.every((x) => x === true),
|
||||
);
|
||||
}
|
||||
return;
|
||||
}
|
||||
case "diamond": {
|
||||
addConstants(f.fml);
|
||||
for (const w1 of worlds) {
|
||||
const xs = next[w1].map((w2) => constant.get(`${w2}:${f.fml.tag}`));
|
||||
if (xs.some((x) => x === undefined)) continue;
|
||||
constant.set(
|
||||
`${w1}:${f.tag}`,
|
||||
xs.some((x) => x === true),
|
||||
);
|
||||
}
|
||||
return;
|
||||
}
|
||||
case "or": {
|
||||
addConstants(f.left);
|
||||
addConstants(f.right);
|
||||
for (const w of worlds) {
|
||||
const l = constant.get(`${w}:${f.left.tag}`);
|
||||
const r = constant.get(`${w}:${f.right.tag}`);
|
||||
if (l === undefined || r === undefined) continue;
|
||||
constant.set(`${w}:${f.tag}`, l || r);
|
||||
}
|
||||
return;
|
||||
}
|
||||
case "and": {
|
||||
addConstants(f.left);
|
||||
addConstants(f.right);
|
||||
for (const w of worlds) {
|
||||
const l = constant.get(`${w}:${f.left.tag}`);
|
||||
const r = constant.get(`${w}:${f.right.tag}`);
|
||||
if (l === undefined || r === undefined) continue;
|
||||
constant.set(`${w}:${f.tag}`, l && r);
|
||||
}
|
||||
return;
|
||||
}
|
||||
}
|
||||
}
|
||||
addConstants(notFml);
|
||||
|
||||
return { notFml, next, memo: new Map(), constant };
|
||||
}
|
||||
|
||||
const isWeaker = (c1: Constraints, c2: Constraints): boolean => {
|
||||
return (
|
||||
valuationSet.isSuperset(c1.positive, c2.positive) &&
|
||||
valuationSet.isSuperset(c1.negative, c2.negative)
|
||||
);
|
||||
};
|
||||
|
||||
const union = (c1: Constraints, c2: Constraints): Constraints => {
|
||||
return {
|
||||
positive: valuationSet.union(c1.positive, c2.positive),
|
||||
negative: valuationSet.union(c1.negative, c2.negative),
|
||||
};
|
||||
};
|
||||
|
||||
const consistent = (c: Constraints) => {
|
||||
return valuationSet.isDisjoint(c.positive, c.negative);
|
||||
};
|
||||
|
||||
function sat(
|
||||
frame: Frame,
|
||||
fml: NNFFormula<number>,
|
||||
world: World,
|
||||
ctx: Context = buildContext(frame, fml),
|
||||
): Constraints[] {
|
||||
const key = `${world}:${fml.tag}` as const;
|
||||
const c = ctx.constant.get(key);
|
||||
if (c === true) return [empty];
|
||||
if (c === false) return [];
|
||||
|
||||
let result = ctx.memo.get(key);
|
||||
if (result) return result;
|
||||
|
||||
switch (fml.type) {
|
||||
case "top":
|
||||
result = [empty];
|
||||
break;
|
||||
case "bot":
|
||||
result = [];
|
||||
break;
|
||||
case "propvar":
|
||||
result = [
|
||||
{
|
||||
positive: valuationSet.create(`${world}${fml.name}`),
|
||||
negative: valuationSet.empty,
|
||||
},
|
||||
];
|
||||
break;
|
||||
case "not":
|
||||
result = [
|
||||
{
|
||||
positive: valuationSet.empty,
|
||||
negative: valuationSet.create(`${world}${fml.fml.name}`),
|
||||
},
|
||||
];
|
||||
break;
|
||||
case "box": {
|
||||
result = ctx.next[world]
|
||||
.map((w) => sat(frame, fml.fml, w, ctx))
|
||||
.reduce(
|
||||
(prev, current) =>
|
||||
maximal(
|
||||
current.flatMap((c1) =>
|
||||
prev.map((c2) => union(c1, c2)).filter(consistent),
|
||||
),
|
||||
isWeaker,
|
||||
),
|
||||
[empty],
|
||||
);
|
||||
break;
|
||||
}
|
||||
case "diamond": {
|
||||
result = maximal(
|
||||
ctx.next[world].flatMap((w) => sat(frame, fml.fml, w, ctx)),
|
||||
isWeaker,
|
||||
);
|
||||
break;
|
||||
}
|
||||
case "and": {
|
||||
result = [
|
||||
sat(frame, fml.left, world, ctx),
|
||||
sat(frame, fml.right, world, ctx),
|
||||
].reduce(
|
||||
(prev, current) =>
|
||||
maximal(
|
||||
current.flatMap((c1) =>
|
||||
prev.map((c2) => union(c1, c2)).filter(consistent),
|
||||
),
|
||||
isWeaker,
|
||||
),
|
||||
[empty],
|
||||
);
|
||||
break;
|
||||
}
|
||||
case "or": {
|
||||
result = maximal(
|
||||
[
|
||||
sat(frame, fml.left, world, ctx),
|
||||
sat(frame, fml.right, world, ctx),
|
||||
].flat(),
|
||||
isWeaker,
|
||||
);
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
ctx.memo.set(key, result);
|
||||
return result;
|
||||
}
|
||||
|
||||
export function findCountermodelsAt(
|
||||
frame: Frame,
|
||||
fml: Formula,
|
||||
world: World,
|
||||
ctx = buildContext(frame, fml),
|
||||
): Model[] {
|
||||
return sat(frame, ctx.notFml, world, ctx).map(({ positive }) => ({
|
||||
...frame,
|
||||
valuations: valuationSet.decode(positive),
|
||||
}));
|
||||
}
|
||||
|
||||
export function findCountermodels(
|
||||
frame: Frame,
|
||||
fml: Formula,
|
||||
ctx = buildContext(frame, fml),
|
||||
): Model[] {
|
||||
return maximal(
|
||||
worlds.flatMap((world) => sat(frame, ctx.notFml, world, ctx)),
|
||||
isWeaker,
|
||||
).map(({ positive }) => ({
|
||||
...frame,
|
||||
valuations: valuationSet.decode(positive),
|
||||
}));
|
||||
}
|
||||
|
||||
export function validInWorld(
|
||||
frame: Frame,
|
||||
fml: Formula,
|
||||
world: World,
|
||||
ctx = buildContext(frame, fml),
|
||||
) {
|
||||
return sat(frame, ctx.notFml, world, ctx).length === 0;
|
||||
}
|
||||
|
||||
export function validWorlds(
|
||||
frame: Frame,
|
||||
fml: Formula,
|
||||
ctx = buildContext(frame, fml),
|
||||
) {
|
||||
return worlds.filter((world) => validInWorld(frame, ctx.notFml, world, ctx));
|
||||
}
|
||||
|
||||
export function validInFrame(
|
||||
frame: Frame,
|
||||
fml: Formula,
|
||||
ctx = buildContext(frame, fml),
|
||||
) {
|
||||
return worlds.every((world) => validInWorld(frame, ctx.notFml, world, ctx));
|
||||
}
|
||||
Reference in New Issue
Block a user