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

Example 51 with Expression

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

the class ALG195_1 method ax16_22.

/**
 * Parametrization of axioms 16-22.
 *
 * @requires e is unary, h is binary
 */
Formula ax16_22(Relation e, Relation h) {
    // op2(e,...)
    final Expression expr0 = e.join(op2);
    // op2(e,e)
    final Expression expr1 = e.join(expr0);
    // op2(e,op2(e,e))
    final Expression expr2 = expr1.join(expr0);
    // op2(op2(e,op2(e,e)),op2(e,op2(e,e)))
    final Expression expr3 = expr2.join(expr2.join(op2));
    // op2(op2(op2(e,op2(e,e)),op2(e,op2(e,e))),...)
    final Expression expr3a = expr3.join(op2);
    // op2(op2(op2(e,op2(e,e)),op2(e,op2(e,e))),e)
    final Expression expr4 = e.join(expr3a);
    // h(e10) = op2(op2(op2(e,op2(e,e)),op2(e,op2(e,e))),op2(e,op2(e,e)))
    final Formula f0 = e1[0].join(h).eq(expr2.join(expr3a));
    // h(e11) = op2(e,e)
    final Formula f1 = e1[1].join(h).eq(expr1);
    // h(e12) = op2(op2(e,op2(e,e)),op2(e,op2(e,e)))
    final Formula f2 = e1[2].join(h).eq(expr3);
    // h(e13) = op2(op2(op2(e,op2(e,e)),op2(e,op2(e,e))),e)
    final Formula f3 = e1[3].join(h).eq(expr4);
    // h(e14) = op2(e,op2(e,e))
    final Formula f4 = e1[4].join(h).eq(expr2);
    // h1(e15) = e
    final Formula f5 = e1[5].join(h).eq(e);
    // h(e16) =
    // op2(op2(op2(op2(e,op2(e,e)),op2(e,op2(e,e))),e),op2(e,op2(e,e)))
    final Formula f6 = e1[6].join(h).eq(expr2.join(expr4.join(op2)));
    return f0.and(f1).and(f2).and(f3).and(f4).and(f5).and(f6);
}

Example 52 with Expression

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

the class ALG212 method distLong.

/**
 * Returns the dist_long conjecture.
 *
 * @return dist_long
 */
public final Formula distLong() {
    // all u, w, x, y, z: A | f[f[x][y][z]][u][w] =
    // f[f[x][u][w]][f[y][u][w]][f[z][u][w]]
    final Variable u = Variable.unary("u");
    final Variable w = Variable.unary("w");
    final Variable x = Variable.unary("x");
    final Variable y = Variable.unary("y");
    final Variable z = Variable.unary("z");
    final Expression e0 = z.join(y.join(x.join(f)));
    final Expression e1 = w.join(u.join(e0.join(f)));
    final Expression e2 = w.join(u.join(x.join(f)));
    final Expression e3 = w.join(u.join(y.join(f)));
    final Expression e4 = w.join(u.join(z.join(f)));
    final Expression e5 = e4.join(e3.join(e2.join(f)));
    return e1.eq(e5).forAll(u.oneOf(UNIV).and(w.oneOf(UNIV)).and(x.oneOf(UNIV)).and(y.oneOf(UNIV)).and(z.oneOf(UNIV)));
}

Example 53 with Expression

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

the class ALG195 method ax16_22.

/**
 * Parametrization of axioms 16-22.
 *
 * @requires e is unary, h is binary
 */
@Override
Formula ax16_22(Relation e, Relation h) {
    // op2(e,...)
    final Expression expr0 = e.join(op2);
    // op2(e,e)
    final Expression expr1 = e.join(expr0);
    // op2(e,op2(e,e))
    final Expression expr2 = expr1.join(expr0);
    // op2(op2(e,op2(e,e)),op2(e,op2(e,e)))
    final Expression expr3 = expr2.join(expr2.join(op2));
    // op2(op2(op2(e,op2(e,e)),op2(e,op2(e,e))),...)
    final Expression expr3a = expr3.join(op2);
    // op2(op2(op2(e,op2(e,e)),op2(e,op2(e,e))),e)
    final Expression expr4 = e.join(expr3a);
    // h(e10) = op2(op2(op2(e,op2(e,e)),op2(e,op2(e,e))),op2(e,op2(e,e)))
    final Formula f0 = e1[0].join(h).eq(expr2.join(expr3a));
    // h(e11) = op2(e,e)
    final Formula f1 = e1[1].join(h).eq(expr1);
    // h(e12) = op2(op2(e,op2(e,e)),op2(e,op2(e,e)))
    final Formula f2 = e1[2].join(h).eq(expr3);
    // h(e13) = op2(op2(op2(e,op2(e,e)),op2(e,op2(e,e))),e)
    final Formula f3 = e1[3].join(h).eq(expr4);
    // h(e14) = op2(e,op2(e,e))
    final Formula f4 = e1[4].join(h).eq(expr2);
    // h(e16) =
    // op2(op2(op2(op2(e,op2(e,e)),op2(e,op2(e,e))),e),op2(e,op2(e,e)))
    final Formula f6 = e1[6].join(h).eq(expr2.join(expr4.join(op2)));
    return and(f0, f1, f2, f3, f4, f6);
}

Example 54 with Expression

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

the class GEO092 method proposition2141.

/*
     * fof(proposition_2_14_1,conjecture, ( ! [C1,C2,P] : ( ( meet(P,C1,C2) &
     * open(sum(C1,C2)) ) => ! [Q] : ( Q != P => ~ ( incident_c(Q,C1) &
     * incident_c(Q,C2) ) ) ) )).
     */
/**
 * Returns the conjecture proposition_2_14_1.
 *
 * @return proposition_2_14_1
 */
public final Formula proposition2141() {
    // all c1, c2: curve, p: point |
    // p->c1->c2 in meet && c1->c2 in sum.open =>
    // all q: point - p | c1 + c2 !in q.incident
    final Variable c1 = Variable.unary("C1");
    final Variable c2 = Variable.unary("C2");
    final Variable p = Variable.unary("P");
    final Variable q = Variable.unary("Q");
    final Expression e0 = c1.product(c2);
    final Formula f0 = p.product(e0).in(meet).and(e0.in(sum.join(open)));
    final Formula f1 = c1.union(c2).in(q.join(incident)).not().forAll(q.oneOf(point.difference(p)));
    return f0.implies(f1).forAll(c1.oneOf(curve).and(c2.oneOf(curve)).and(p.oneOf(point)));
}

Example 55 with Expression

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

the class GEO158 method endPointDefn.

/**
 * 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)));
}