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

/**
 * Returns the end_point_defn axiom.
 *
 * @return end_point_defn
 */
public final Formula endPointDefn() {
    /*
     * all P: Point, C: Curve | P->C in endPoint iff (P->C in incident && all C1,
     * C2: partOf.C & P.incident | C1->C2 in partOf || C2->C1 in partOf)
     */
    final Variable c = Variable.unary("C");
    final Variable p = Variable.unary("P");

    final Expression e0 = p.product(c);
    final Formula f0 = e0.in(endPoint);
    final Formula f1 = e0.in(incident);

    final Variable c1 = Variable.unary("C1"), c2 = Variable.unary("C2");
    final Formula f2 = c1.product(c2).in(partOf).or(c2.product(c1).in(partOf));
    final Expression e1 = partOf.join(c).intersection(p.join(incident));
    final Formula f3 = f2.forAll(c1.oneOf(e1).and(c2.oneOf(e1)));

    return f0.iff(f1.and(f3)).forAll(p.oneOf(point).and(c.oneOf(curve)));
}
 

/**
 * Returns the meet_defn axiom.
 *
 * @return meet_defn
 */
public final Formula meetDefn() {
    // all P: Point, C, C1: Curve | P->C->C1 in meet iff
    // (P->C in incident && P->C1 in incident &&
    // incident.C & incident.C1 in endPoint.C & endPoint.C1)
    final Variable c = Variable.unary("C");
    final Variable c1 = Variable.unary("C1");
    final Variable p = Variable.unary("P");

    final Formula f0 = p.product(c).product(c1).in(meet);
    final Formula f1 = p.product(c).in(incident).and(p.product(c1).in(incident));
    final Expression e0 = incident.join(c).intersection(incident.join(c1));
    final Expression e1 = endPoint.join(c).intersection(endPoint.join(c1));
    final Formula f2 = e0.in(e1);

    final Formula f3 = f0.iff(f1.and(f2));

    return f3.forAll(p.oneOf(point).and(c.oneOf(curve)).and(c1.oneOf(curve)));
}
 

/**
 * Returns the end_point_defn axiom.
 * @return end_point_defn 
 */
public final Formula endPointDefn() {
	/* all P: Point, C: Curve | P->C in endPoint iff
  		 *	(P->C in incident && 
   	 *	 all C1, C2: partOf.C & P.incident | 
     	 *	  C1->C2 in partOf || C2->C1 in partOf)
	 */
	final Variable c = Variable.unary("C");
	final Variable p = Variable.unary("P");
	
	final Expression e0 = p.product(c);
	final Formula f0 = e0.in(endPoint);
	final Formula f1 = e0.in(incident);
	
	final Variable c1 = Variable.unary("C1"), c2 = Variable.unary("C2");
	final Formula f2 = c1.product(c2).in(partOf).or(c2.product(c1).in(partOf));
	final Expression e1 = partOf.join(c).intersection(p.join(incident));
	final Formula f3 = f2.forAll(c1.oneOf(e1).and(c2.oneOf(e1)));
	
	return f0.iff(f1.and(f3)).forAll(p.oneOf(point).and(c.oneOf(curve)));
}
 

/**
 * 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 a formula that properly constrains the given skolem's domain.
 *
 * @requires !nonSkolems.isEmpty()
 * @return a formula that properly constrains the given skolem's domain.
 */
private Formula domainConstraint(Decl skolemDecl, Relation skolem) {
    final Iterator<DeclInfo> itr = nonSkolems.iterator();
    Decls rangeDecls = null;
    while (itr.hasNext()) {
        Decl d = itr.next().decl;
        Decl dd = d.variable().oneOf(d.expression());
        rangeDecls = rangeDecls != null ? rangeDecls.and(dd) : dd;
    }
    // System.out.println(skolemDecl.expression());
    Expression skolemDomain = skolem;
    for (int i = 0, max = skolemDecl.variable().arity(); i < max; i++) {
        skolemDomain = skolemDomain.join(Expression.UNIV);
    }
    return skolemDomain.in(Formula.TRUE.comprehension(rangeDecls));
}
 

/**
 * 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 inner_point_defn axiom.
 *
 * @return inner_point_defn
 */
public final Formula innerPointDefn() {
    // all P: Point, C: Curve | P->C in innerPoint iff
    // (P->C in incident && no P->C & endPoint)
    final Variable c = Variable.unary("C");
    final Variable p = Variable.unary("P");
    final Expression e0 = p.product(c);
    final Formula f0 = e0.in(innerPoint);
    final Formula f1 = e0.in(incident).and(e0.intersection(endPoint).no());
    return f0.iff(f1).forAll(p.oneOf(point).and(c.oneOf(curve)));
}
 

/**
 * Returns the application of the Abstract predicate.
 * @return application of the Abstract predicate.
 */
public Formula Abstract(Expression s) {
	final Expression e0 = s.join(abAuthPurse).join(abBalance).join(s).intersection(s.join(abAuthPurse).join(abLost).join(s));
	final Formula f0 = e0.no();
	
	final Expression e1 = s.join(abAuthPurse).product(Expression.UNIV);
	final Expression e2 = e1.intersection((abBalance.union(abLost)).join(s));
	final Formula f1 = e2.in(AbPurse.product(Coin));
	final Variable c = Variable.unary("c");
	final Formula f2 = e2.join(c).lone().forAll(c.oneOf(Coin));
	
	return Formula.and(f0, f1, f2);
}
 

/**
 * Returns the insulin_completion axiom.
 *
 * @return insulin_completion
 */
public final Formula insulin_completion() {
    final Variable x0 = Variable.unary("X0");
    final Expression x1 = UNIV.difference(x0.join(gt));
    final Formula f0 = x1.in(uptakelg.union(uptakepg));
    return f0.implies(x1.in(drugi)).forAll(x0.oneOf(UNIV));
}
 

/**
 * Returns the su_completion axiom.
 *
 * @return su_completion
 */
public final Formula su_completion() {
    final Variable x0 = Variable.unary("X0");
    final Expression x1 = UNIV.difference(x0.join(gt));
    final Formula f0 = x1.in(bsecretioni);
    return f0.implies(x1.in(drugsu).and(x0.in(bcapacityex).not())).forAll(x0.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);
}
 

private Formula prefix(Expression a, Expression b) {
    return a.in(prefixes(b));
}
 

private Formula equiv(Expression a, Expression b) {
    return a.in(equivTo(b));
}
 

/**
 * Returns the inCycle predicate.
 * @return 
 * <pre>
 * pred InCycle(v: V, c: V -> V) {
 * v in v.c or 
 * some v': v.c | v' in v.^(c - v->v' - v'->v)
 * }
 * </pre>
 */
public final Formula inCycle(Expression/*V*/ v, Expression/*V->V*/ c) {
	final Formula f0 = v.in(v.join(c));
	final Variable vp = Variable.unary("v'");
	final Formula f1 = vp.in(v.join((c.difference(v.product(vp)).difference(vp.product(v))).closure()));
	return f0.or(f1.forSome(vp.oneOf(v.join(c))));
}
 

/**
 * Returns the inCycle predicate.
 *
 * @return
 *
 *         <pre>
 * pred InCycle(v: V, c: V -> V) {
 * v in v.c or
 * some v': v.c | v' in v.^(c - v->v' - v'->v)
 * }
 *         </pre>
 */
public final Formula inCycle(Expression/* V */ v, Expression/* V->V */ c) {
    final Formula f0 = v.in(v.join(c));
    final Variable vp = Variable.unary("v'");
    final Formula f1 = vp.in(v.join((c.difference(v.product(vp)).difference(vp.product(v))).closure()));
    return f0.or(f1.forSome(vp.oneOf(v.join(c))));
}
 

/**
 * Returns the application of the Authentic predicate.
 *
 * @return application of the Authentic predicate.
 */
public Formula Authentic(Expression s, Expression p) {
    return p.in(s.join(abAuthPurse));
}
 

/**
 * Returns a in empty
 * @return a in empty
 */
final Formula empty(Expression a) {
	return a.in(empty);
}
 

/**
 * Returns a in empty
 *
 * @return a in empty
 */
final Formula empty(Expression a) {
    return a.in(empty);
}
 

private Formula equiv(Expression a, Expression b) { return a.in(equivTo(b)); } 

private Formula prefix(Expression a, Expression b) { return a.in(prefixes(b)); }