propositional/lib/cnf/dpll.js

Propositional logic symbolic computation library

"use strict";
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var __importStar = (this && this.__importStar) || function (mod) {
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Object.defineProperty(exports, "__esModule", { value: true });
exports.dpll = void 0;
const __1 = require("..");
const AST = __importStar(require("../syntax/ast"));
const equivalence_1 = require("../syntax/equivalence");
const generate_1 = require("../syntax/generate");
const token_1 = require("../syntax/token");
function dpll(formula) {
    let clauses = clauseSet(formula.ast);
    let failed = false;
    let assumptions = {};
    while (clauses.length) {
        if (failed) {
            // If the previous set of assumptions led to failure and all the assumptions were natural,
            // the formula is unsatisfiable
            if (Object.keys(assumptions).every(variable => !assumptions[variable].forced)) {
                return null;
            }
            // Otherwise, all assumptions following from the first forced one are invalid
            let corrected = false;
            for (let variable in assumptions) {
                if (corrected) {
                    delete assumptions[variable];
                    continue;
                }
                if (assumptions[variable].forced) {
                    // The first forced assumption is now necessarily incorrect
                    assumptions[variable].value = !assumptions[variable].value;
                    assumptions[variable].forced = false;
                    corrected = true;
                }
            }
            // Reset clauses and simplify from previous natural assumptions
            clauses = clauseSet(formula.ast);
            for (let [variable, { value }] of Object.entries(assumptions)) {
                clauses = clauses.map(clause => new __1.Formula(clause).substitute(variable, value).simplify().ast).filter(clause => !(0, equivalence_1.syntacticallyEquivalent)(clause, generate_1.TRUE));
            }
        }
        // Find the first unit clause
        let forcedAssumption = false;
        let unitClause = null;
        for (let clause of clauses) {
            if (clause instanceof AST.BinaryExpression)
                continue;
            unitClause = clause;
            break;
        }
        // If there are none, force an assumption by the first variable of the first clause
        if (!unitClause) {
            forcedAssumption = true;
            unitClause = clauses[0];
            while (unitClause instanceof AST.BinaryExpression) {
                unitClause = unitClause.left;
            }
        }
        // Assume and simplify
        let assumedVariable = (unitClause instanceof AST.UnaryExpression ? unitClause.inner : unitClause).value.lexeme;
        let assumedValue = unitClause instanceof AST.Literal;
        assumptions[assumedVariable] = { value: assumedValue, forced: forcedAssumption };
        // Substitute the assumption, simplify and remove true clauses
        clauses = clauses.map(clause => new __1.Formula(clause).substitute(assumedVariable, assumedValue).simplify().ast)
            .filter(clause => !(0, equivalence_1.syntacticallyEquivalent)(clause, generate_1.TRUE));
        // If any of the clauses are 0, the assumptions have failed
        if (clauses.some(clause => (0, equivalence_1.syntacticallyEquivalent)(clause, generate_1.FALSE))) {
            failed = true;
        }
    }
    // A solution has been found, return
    let solution = {};
    for (let variable in assumptions) {
        solution[variable] = assumptions[variable].value;
    }
    return solution;
}
exports.dpll = dpll;
function clauseSet(expression) {
    switch (true) {
        case expression instanceof AST.BinaryExpression:
            switch (expression.operator.type) {
                case token_1.TokenType.AND:
                    return [...clauseSet(expression.left), ...clauseSet(expression.right)];
                case token_1.TokenType.OR:
                    return [expression];
            }
        case expression instanceof AST.UnaryExpression:
        case expression instanceof AST.Literal:
            return [expression];
    }
}