Java Code Examples for kodkod.ast.Expression#eq()

/**
 * Helper method that translates the formula "a in b" into a Kodkod formula.
 */
private Formula isIn(Expression a, Expr right) throws Err {
    Expression b;
    if (right instanceof ExprBinary && right.mult != 0 && ((ExprBinary) right).op.isArrow) {
        // Handles possible "binary" or higher-arity multiplicity
        return isInBinary(a, (ExprBinary) right);
    }
    switch (right.mult()) {
        case EXACTLYOF :
            b = cset(right);
            return a.eq(b);
        case ONEOF :
            b = cset(right);
            return a.one().and(a.in(b));
        case LONEOF :
            b = cset(right);
            return a.lone().and(a.in(b));
        case SOMEOF :
            b = cset(right);
            return a.some().and(a.in(b));
        default :
            b = cset(right);
            return a.in(b);
    }
}
 

/**
 * Returns the wilkie conjecture.
 *
 * @return wilkie
 */
public final Formula wilkie() {
    // ! [C,P,Q,R,S,A,B] :
    // ( ( C = product(A,A)
    // & P = sum(n1,A)
    // & Q = sum(P,C)
    // & R = sum(n1,product(A,C))
    // & S = sum(sum(n1,C),product(C,C)) )
    // =>
    // product(exponent(sum(exponent(P,A),exponent(Q,A)),B),exponent(sum(exponent(R,B),exponent(S,B)),A))
    // =
    // product(exponent(sum(exponent(P,B),exponent(Q,B)),A),exponent(sum(exponent(R,A),exponent(S,A)),B))
    // ) )).
    final Variable c = Variable.unary("C");
    final Variable p = Variable.unary("P");
    final Variable q = Variable.unary("Q");
    final Variable r = Variable.unary("R");
    final Variable s = Variable.unary("S");
    final Variable a = Variable.unary("A");
    final Variable b = Variable.unary("B");
    final Formula f0 = c.eq(product(a, a));
    final Formula f1 = p.eq(sum(n1, a));
    final Formula f2 = q.eq(sum(p, c));
    final Formula f3 = r.eq(sum(n1, product(a, c)));
    final Formula f4 = s.eq(sum(sum(n1, c), product(c, c)));
    final Expression e0 = product(exponent(sum(exponent(p, a), exponent(q, a)), b), exponent(sum(exponent(r, b), exponent(s, b)), a));
    final Expression e1 = product(exponent(sum(exponent(p, b), exponent(q, b)), a), exponent(sum(exponent(r, a), exponent(s, a)), b));
    final Formula f5 = e0.eq(e1);
    return (f0.and(f1).and(f2).and(f3).and(f4)).implies(f5).forAll(c.oneOf(UNIV).and(p.oneOf(UNIV)).and(q.oneOf(UNIV)).and(r.oneOf(UNIV)).and(s.oneOf(UNIV)).and(a.oneOf(UNIV)).and(b.oneOf(UNIV)));
}
 

/**
 * Returns the application of the AbWorldSecureOp predicate.
 *
 * @return application of the AbWorldSecureOp predicate.
 */
public Formula AbWorldSecureOp(Expression s, Expression sprime, Expression a_in, Expression a_out) {
    final Formula f0 = AbOp(a_out);
    final Formula f1 = a_in.in(TransferDetails);

    final Expression e0 = a_in.join(from);
    final Expression e1 = a_in.join(to);
    final Expression e2 = s.join(abAuthPurse).difference(e0).difference(e1);
    final Expression e3 = sprime.join(abAuthPurse).difference(e0).difference(e1);
    final Formula f2 = e2.eq(e3);

    final Formula f3 = XiAbPurse(s, sprime, e2);

    return Formula.and(f0, f1, f2, f3);
}
 

/**
	 * Returns the wilkie conjecture.
	 * @return wilkie
	 */
	public final Formula wilkie() {
//		! [C,P,Q,R,S,A,B] : 
//		      ( ( C = product(A,A)
//		        & P = sum(n1,A)
//		        & Q = sum(P,C)
//		        & R = sum(n1,product(A,C))
//		        & S = sum(sum(n1,C),product(C,C)) )
//		     => product(exponent(sum(exponent(P,A),exponent(Q,A)),B),exponent(sum(exponent(R,B),exponent(S,B)),A)) = 
//		        product(exponent(sum(exponent(P,B),exponent(Q,B)),A),exponent(sum(exponent(R,A),exponent(S,A)),B)) ) )).
		final Variable c = Variable.unary("C");
		final Variable p = Variable.unary("P");
		final Variable q = Variable.unary("Q");
		final Variable r = Variable.unary("R");
		final Variable s = Variable.unary("S");
		final Variable a = Variable.unary("A");
		final Variable b = Variable.unary("B");
		final Formula f0 = c.eq(product(a,a));
		final Formula f1 = p.eq(sum(n1,a));
		final Formula f2 = q.eq(sum(p,c));
		final Formula f3 = r.eq(sum(n1,product(a,c)));
		final Formula f4 = s.eq(sum(sum(n1,c),product(c,c)));
		final Expression e0 = product(exponent(sum(exponent(p,a),exponent(q,a)),b),exponent(sum(exponent(r,b),exponent(s,b)),a));
		final Expression e1 = product(exponent(sum(exponent(p,b),exponent(q,b)),a),exponent(sum(exponent(r,a),exponent(s,a)),b));
		final Formula f5 = e0.eq(e1);
		return (f0.and(f1).and(f2).and(f3).and(f4)).implies(f5).
			forAll(c.oneOf(UNIV).and(p.oneOf(UNIV)).and(q.oneOf(UNIV)).
				   and(r.oneOf(UNIV)).and(s.oneOf(UNIV)).and(a.oneOf(UNIV)).and(b.oneOf(UNIV)));
	}
 

/**
 * Returns the application of the AbWorldSecureOp predicate.
 * @return application of the AbWorldSecureOp predicate.
 */
public Formula AbWorldSecureOp(Expression s, Expression sprime, Expression a_in, Expression a_out) {
	final Formula f0 = AbOp(a_out);
	final Formula f1 = a_in.in(TransferDetails);

	final Expression e0 = a_in.join(from);
	final Expression e1 = a_in.join(to);
	final Expression e2 = s.join(abAuthPurse).difference(e0).difference(e1);
	final Expression e3 = sprime.join(abAuthPurse).difference(e0).difference(e1);
	final Formula f2 = e2.eq(e3);
	
	final Formula f3 = XiAbPurse(s, sprime, e2);
	
	return Formula.and(f0, f1, f2, f3);
}
 

public final void testFelix_06192008() {
    Relation x5 = Relation.unary("R");

    List<String> atomlist = Arrays.asList("X");

    Universe universe = new Universe(atomlist);
    TupleFactory factory = universe.factory();
    Bounds bounds = new Bounds(universe);

    TupleSet x5_upper = factory.noneOf(1);
    x5_upper.add(factory.tuple("X"));
    bounds.bound(x5, x5_upper);

    Variable x10 = Variable.unary("a");
    Expression x11 = x5.difference(x5);
    Decls x9 = x10.oneOf(x11);
    Variable x14 = Variable.nary("b", 2);
    Expression x15 = x5.product(x5);
    Decls x13 = x14.setOf(x15);
    Expression x19 = x5.product(x5);
    Formula x17 = x14.in(x19);
    Expression x22 = x10.product(x10);
    Formula x21 = x22.eq(x14);
    Formula x16 = x17.and(x21);
    Formula x12 = x16.forSome(x13);
    Formula x7 = x12.forAll(x9);

    // System.out.println(x7);

    Solver solver = new Solver();
    solver.options().setSolver(SATFactory.DefaultSAT4J);
    solver.options().setBitwidth(4);
    // solver.options().setFlatten(false);
    solver.options().setIntEncoding(Options.IntEncoding.TWOSCOMPLEMENT);
    solver.options().setSymmetryBreaking(20);

    // System.out.println("Depth=0..."); System.out.flush();
    solver.options().setSkolemDepth(0);
    assertEquals(Solution.Outcome.TRIVIALLY_SATISFIABLE, solver.solve(x7, bounds).outcome());

    // System.out.println("Depth=1..."); System.out.flush();
    solver.options().setSkolemDepth(1);
    final Solution sol = solver.solve(x7, bounds);
    assertEquals(Solution.Outcome.SATISFIABLE, sol.outcome());
    assertEquals(2, sol.instance().relations().size());
    for (Relation r : sol.instance().relations()) {
        assertTrue(sol.instance().tuples(r).isEmpty());
    }
}
 

@Test
public final void testFelix_06192008() {
	Relation x5 = Relation.unary("R");

	List<String> atomlist = Arrays.asList("X");

	Universe universe = new Universe(atomlist);
	TupleFactory factory = universe.factory();
	Bounds bounds = new Bounds(universe);

	TupleSet x5_upper = factory.noneOf(1);
	x5_upper.add(factory.tuple("X"));
	bounds.bound(x5, x5_upper);

	Variable x10=Variable.unary("a");
	Expression x11=x5.difference(x5);
	Decls x9=x10.oneOf(x11);
	Variable x14=Variable.nary("b",2);
	Expression x15=x5.product(x5);
	Decls x13=x14.setOf(x15);
	Expression x19=x5.product(x5);
	Formula x17=x14.in(x19);
	Expression x22=x10.product(x10);
	Formula x21=x22.eq(x14);
	Formula x16=x17.and(x21);
	Formula x12=x16.forSome(x13);
	Formula x7= x12.forAll(x9);

	//		System.out.println(x7);

	Solver solver = new Solver();
	solver.options().setSolver(SATFactory.DefaultSAT4J);
	solver.options().setBitwidth(4);
	solver.options().setIntEncoding(Options.IntEncoding.TWOSCOMPLEMENT);
	solver.options().setSymmetryBreaking(20);

	//		System.out.println("Depth=0..."); System.out.flush();
	solver.options().setSkolemDepth(0);
	assertEquals(Solution.Outcome.TRIVIALLY_SATISFIABLE, solver.solve(x7, bounds).outcome());

	//		System.out.println("Depth=1..."); System.out.flush();
	solver.options().setSkolemDepth(1);
	final Solution sol = solver.solve(x7, bounds);
	assertEquals(Solution.Outcome.SATISFIABLE, sol.outcome());
	assertEquals(2, sol.instance().relations().size());
	for(Relation r : sol.instance().relations()) { 
		assertTrue(sol.instance().tuples(r).isEmpty());
	}
}
 

private Formula isType(Expression type, String typeName) {
	// return type.intersection(typeRelation(typeName)).one();
	return type.eq(typeRelation(typeName));
}
 

/**
 * Returns the application of the AbOp predicate.
 *
 * @return application of the AbOp predicate.
 */
public Formula AbOp(Expression a_out) {
    return a_out.eq(aNullOut);
}
 

/**
 * Returns the application of the AbOp predicate.
 * @return application of the AbOp predicate.
 */
public Formula AbOp(Expression a_out) {
	return a_out.eq(aNullOut);
}