Examples with Expression kodkod.ast.Expression used on opensource projects

Example 16 with Expression

use of kodkod.ast.Expression in project org.alloytools.alloy by AlloyTools.

the class TranslateAlloyToKodkod method isInBinary.

/**
 * Helper method that translates the formula "r in (a ?->? b)" into a Kodkod
 * formula.
 */
private Formula isInBinary(Expression r, ExprBinary ab) throws Err {
    final Expression a = cset(ab.left), b = cset(ab.right);
    Decls d = null, d2 = null;
    Formula ans1, ans2;
    // "R in A ->op B" means for each tuple a in A, there are "op" tuples in
    // r that begins with a.
    Expression atuple = null, ar = r;
    for (int i = a.arity(); i > 0; i--) {
        Variable v = Variable.unary("v" + Integer.toString(cnt++));
        if (!am) {
            if (a.arity() == 1)
                d = v.oneOf(a);
            else if (d == null)
                d = v.oneOf(Expression.UNIV);
            else
                d = v.oneOf(Expression.UNIV).and(d);
        } else {
            d = am(a, d, i, v);
        }
        ar = v.join(ar);
        if (atuple == null)
            atuple = v;
        else
            atuple = atuple.product(v);
    }
    ans1 = isIn(ar, ab.right);
    switch(ab.op) {
        case ISSEQ_ARROW_LONE:
        case ANY_ARROW_LONE:
        case SOME_ARROW_LONE:
        case ONE_ARROW_LONE:
        case LONE_ARROW_LONE:
            ans1 = ar.lone().and(ans1);
            break;
        case ANY_ARROW_ONE:
        case SOME_ARROW_ONE:
        case ONE_ARROW_ONE:
        case LONE_ARROW_ONE:
            ans1 = ar.one().and(ans1);
            break;
        case ANY_ARROW_SOME:
        case SOME_ARROW_SOME:
        case ONE_ARROW_SOME:
        case LONE_ARROW_SOME:
            ans1 = ar.some().and(ans1);
            break;
    }
    if (a.arity() > 1) {
        Formula tmp = isIn(atuple, ab.left);
        if (tmp != Formula.TRUE)
            ans1 = tmp.implies(ans1);
    }
    ans1 = ans1.forAll(d);
    // "R in A op-> B" means for each tuple b in B, there are "op" tuples in
    // r that end with b.
    Expression btuple = null, rb = r;
    for (int i = b.arity(); i > 0; i--) {
        Variable v = Variable.unary("v" + Integer.toString(cnt++));
        if (!am) {
            if (b.arity() == 1)
                d2 = v.oneOf(b);
            else if (d2 == null)
                d2 = v.oneOf(Expression.UNIV);
            else
                d2 = v.oneOf(Expression.UNIV).and(d2);
        } else {
            d2 = am(b, d2, i, v);
        }
        rb = rb.join(v);
        if (btuple == null)
            btuple = v;
        else
            btuple = v.product(btuple);
    }
    ans2 = isIn(rb, ab.left);
    switch(ab.op) {
        case LONE_ARROW_ANY:
        case LONE_ARROW_SOME:
        case LONE_ARROW_ONE:
        case LONE_ARROW_LONE:
            ans2 = rb.lone().and(ans2);
            break;
        case ONE_ARROW_ANY:
        case ONE_ARROW_SOME:
        case ONE_ARROW_ONE:
        case ONE_ARROW_LONE:
            ans2 = rb.one().and(ans2);
            break;
        case SOME_ARROW_ANY:
        case SOME_ARROW_SOME:
        case SOME_ARROW_ONE:
        case SOME_ARROW_LONE:
            ans2 = rb.some().and(ans2);
            break;
    }
    if (b.arity() > 1) {
        Formula tmp = isIn(btuple, ab.right);
        if (tmp != Formula.TRUE)
            ans2 = tmp.implies(ans2);
    }
    ans2 = ans2.forAll(d2);
    // Now, put everything together
    Formula ans = r.in(a.product(b)).and(ans1).and(ans2);
    if (ab.op == ExprBinary.Op.ISSEQ_ARROW_LONE) {
        Expression rr = r;
        while (rr.arity() > 1) rr = rr.join(Expression.UNIV);
        ans = rr.difference(rr.join(A4Solution.KK_NEXT)).in(A4Solution.KK_ZERO).and(ans);
    }
    return ans;
}

Example 17 with Expression

use of kodkod.ast.Expression in project org.alloytools.alloy by AlloyTools.

the class TranslateAlloyToKodkod method visit.

// ==============================================================================================================//
/* ============================ */
/* Evaluates an ExprITE node. */
/* ============================ */
/**
 * {@inheritDoc}
 */
@Override
public Object visit(ExprITE x) throws Err {
    Formula c = cform(x.cond);
    Object l = visitThis(x.left);
    if (l instanceof Formula) {
        Formula c1 = c.implies((Formula) l);
        Formula c2 = c.not().implies(cform(x.right));
        return k2pos(c1.and(c2), x);
    }
    if (l instanceof Expression) {
        return c.thenElse((Expression) l, cset(x.right));
    }
    return c.thenElse((IntExpression) l, cint(x.right));
}

Example 18 with Expression

use of kodkod.ast.Expression in project org.alloytools.alloy by AlloyTools.

the class Skolemizer method visit.

/**
 * Skolemizes the given formula, if possible, otherwise returns the result of
 * replacing its free variables according to the current replacement
 * environment.
 *
 * @see kodkod.ast.visitor.AbstractReplacer#visit(kodkod.ast.QuantifiedFormula)
 */
@Override
public final Formula visit(QuantifiedFormula qf) {
    Formula ret = lookup(qf);
    if (ret != null)
        return ret;
    final Environment<Expression, Expression> oldRepEnv = repEnv;
    final Quantifier quant = qf.quantifier();
    final Decls decls = qf.decls();
    if (skolemDepth >= 0 && (negated && quant == ALL || !negated && quant == SOME)) {
        // skolemizable
        // formula
        final List<Formula> rangeConstraints = new LinkedList<Formula>();
        final List<Formula> domConstraints = new LinkedList<Formula>();
        for (Decl decl : decls) {
            final Decl skolemDecl = visit(decl);
            Variable skVar = skolemDecl.variable();
            final Relation skolem = Relation.skolem("$" + skVar.name(), nonSkolems.size() + skVar.arity(), skVar, skolemDecl, quant);
            reporter.skolemizing(decl, skolem, nonSkolemsView);
            final Expression skolemExpr = skolemExpr(skolemDecl, skolem);
            final Multiplicity mult = decl.multiplicity();
            rangeConstraints.add(source(skolemExpr.in(skolemDecl.expression()), decl));
            if (mult != Multiplicity.SET) {
                rangeConstraints.add(source(skolemExpr.apply(mult), decl));
            }
            if (!nonSkolems.isEmpty())
                domConstraints.add(source(domainConstraint(skolemDecl, skolem), decl));
            repEnv = repEnv.extend(decl.variable(), decl.expression(), skolemExpr);
        }
        ret = source(Formula.and(rangeConstraints), decls).compose(negated ? IMPLIES : AND, qf.formula().accept(this));
        if (!domConstraints.isEmpty())
            topSkolemConstraints.add(source(Formula.and(domConstraints), decls));
    } else {
        // non-skolemizable formula
        final Decls newDecls = visit(qf.decls());
        if (skolemDepth >= nonSkolems.size() + newDecls.size()) {
            // below
            for (Decl d : newDecls) {
                nonSkolems.add(new DeclInfo(d));
            }
            final Formula domain = qf.domain().accept(this);
            final Formula body = qf.body().accept(this);
            ret = ((newDecls == decls && domain == qf.domain() && body == qf.body()) ? qf : body.quantify(quant, newDecls, domain));
            for (int i = newDecls.size(); i > 0; i--) {
                nonSkolems.remove(nonSkolems.size() - 1);
            }
        } else {
            // can't skolemize below
            final int oldDepth = skolemDepth;
            skolemDepth = -1;
            final Formula domain = qf.domain().accept(this);
            final Formula body = qf.body().accept(this);
            ret = ((newDecls == decls && domain == qf.domain() && body == qf.body()) ? qf : body.quantify(quant, newDecls, domain));
            skolemDepth = oldDepth;
        }
    }
    repEnv = oldRepEnv;
    if (repEnv.isEmpty() && !topSkolemConstraints.isEmpty()) {
        ret = source(Formula.and(topSkolemConstraints), qf).compose(negated ? IMPLIES : AND, ret);
    }
    return source(cache(qf, ret), qf);
}

Example 19 with Expression

use of kodkod.ast.Expression in project org.alloytools.alloy by AlloyTools.

the class Skolemizer method visit.

/*-------declarations---------*/
/**
 * Visits the given decl's expression. Note that we must not visit variables in
 * case they are re-used. For example, consider the formula some x: X | all x: Y
 * | F(x). Since x bound by the existential quantifier is going to be
 * skolemized, if we visited the variable in the enclosed declaration, we would
 * get the skolem constant as a return value and a ClassCastException would be
 * thrown.
 *
 * @return { d: Declaration | d.variable = decl.variable && d.multiplicity =
 *         decl.multiplicity && d.expression = decl.expression.accept(this) }
 */
@Override
public final Decl visit(Decl decl) {
    Decl ret = lookup(decl);
    if (ret != null)
        return ret;
    final int oldDepth = skolemDepth;
    // can't skolemize inside a decl
    skolemDepth = -1;
    final Expression expression = decl.expression().accept(this);
    skolemDepth = oldDepth;
    ret = (expression == decl.expression()) ? decl : decl.variable().declare(decl.multiplicity(), expression);
    return cache(decl, ret);
}

Example 20 with Expression

use of kodkod.ast.Expression in project org.alloytools.alloy by AlloyTools.

the class Skolemizer method skolemExpr.

/**
 * Adds a bound for the given skolem relation to this.bounds, and returns the
 * expression that should replace skolemDecl.variable in the final formula.
 *
 * @requires skolem !in this.bounds.relations
 * @requires skolem.arity = nonSkolems.size() + skolemDecl.variable().arity()
 * @ensures adds a sound upper bound for the given skolem relation to
 *          this.bounds
 * @return the expression that should replace skolemDecl.variable in the final
 *         formula
 */
private Expression skolemExpr(Decl skolemDecl, Relation skolem) {
    final int depth = nonSkolems.size();
    final int arity = depth + skolemDecl.variable().arity();
    Expression skolemExpr = skolem;
    Environment<BooleanMatrix, Expression> skolemEnv = Environment.empty();
    for (DeclInfo info : nonSkolems) {
        if (info.upperBound == null) {
            info.upperBound = upperBound(info.decl.expression(), skolemEnv);
        }
        skolemEnv = skolemEnv.extend(info.decl.variable(), info.decl.expression(), info.upperBound);
        skolemExpr = info.decl.variable().join(skolemExpr);
    }
    BooleanMatrix matrixBound = upperBound(skolemDecl.expression(), skolemEnv);
    for (int i = depth - 1; i >= 0; i--) {
        matrixBound = nonSkolems.get(i).upperBound.cross(matrixBound);
    }
    final TupleSet skolemBound = bounds.universe().factory().setOf(arity, matrixBound.denseIndices());
    bounds.bound(skolem, skolemBound);
    return skolemExpr;
}