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

Example 86 with Expression

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

the class ALG195_1 method ax3and6.

/**
 * Parametrization of axioms 3 and 6.
 *
 * @requires s is unary, op is ternary
 */
private static Formula ax3and6(Relation[] e, Relation op) {
    Formula f = Formula.TRUE;
    for (Relation x : e) {
        for (Relation y : e) {
            // op(y,x)
            Expression expr0 = x.join(y.join(op));
            // op(op(y,x),y)
            Expression expr1 = y.join(expr0.join(op));
            // op(op(op(y,x),y),y)
            Expression expr2 = y.join(expr1.join(op));
            f = f.and(expr2.eq(x));
        }
    }
    return f;
}

Example 87 with Expression

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

the class ALG212 method associativity.

/**
 * Returns the associativity axiom.
 *
 * @return associativity
 */
public final Formula associativity() {
    // all w, x, y, z: A | f[f[x][w][y]][w][z] = f[x][w][f[y][w][z]]
    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 = y.join(w.join(x.join(f)));
    final Expression e1 = z.join(w.join(e0.join(f)));
    final Expression e2 = z.join(w.join(y.join(f)));
    final Expression e3 = e2.join(w.join(x.join(f)));
    return e1.eq(e3).forAll(w.oneOf(UNIV).and(x.oneOf(UNIV)).and(y.oneOf(UNIV)).and(z.oneOf(UNIV)));
}

Example 88 with Expression

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

the class ALG195 method ax14and15.

/**
 * Parametrization of axioms 14 and 15.
 *
 * @requires e's are unary, op is ternary
 */
@Override
Formula ax14and15(Relation[] e, Relation op) {
    // op(e5,...)
    final Expression expr0 = e[5].join(op);
    // op(e5,e5)
    final Expression expr1 = e[5].join(expr0);
    // op(e5,op(e5,e5))
    final Expression expr2 = expr1.join(expr0);
    // op(op(e5,op(e5,e5)),op(e5,op(e5,e5)))
    final Expression expr3 = expr2.join(expr2.join(op));
    // op(op(op(e5,op(e5,e5)),op(e5,op(e5,e5))),...)
    final Expression expr3a = expr3.join(op);
    // op(op(op(e5,op(e5,e5)),op(e5,op(e5,e5))),e5)
    final Expression expr4 = e[5].join(expr3a);
    // e0 = op(op(op(e5,op(e5,e5)),op(e5,op(e5,e5))),op(e5,op(e5,e5)))
    final Formula f0 = e[0].eq(expr2.join(expr3a));
    // e2 = op(op(e5,op(e5,e5)),op(e5,op(e5,e5)))
    final Formula f2 = e[2].eq(expr3);
    // e3 = op(op(op(e5,op(e5,e5)),op(e5,op(e5,e5))),e5)
    final Formula f3 = e[3].eq(expr4);
    // e4 = op(e5,op(e5,e5))
    final Formula f4 = e[4].eq(expr2);
    // e6 =
    // op(op(op(op(e5,op(e5,e5)),op(e5,op(e5,e5))),e5),op(e5,op(e5,e5)))
    final Formula f6 = e[6].eq(expr2.join(expr4.join(op)));
    return and(f0, f2, f3, f4, f6);
}

Example 89 with Expression

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

the class ALG197 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(op2(e,e),op2(e,e))
    final Expression expr2 = expr1.join(expr1.join(op2));
    // op2(e,op2(op2(e,e),op2(e,e)))
    final Expression expr3 = expr2.join(expr0);
    // h(e10) = op2(e,op2(e,e))
    final Formula f0 = e1[0].join(h).eq(expr1.join(expr0));
    // h(e11) = op2(op2(e,e),op2(e,e))
    final Formula f1 = e1[1].join(h).eq(expr2);
    // h(e12) = op2(op2(op2(e,e),op2(e,e)),op2(e,e))
    final Formula f2 = e1[2].join(h).eq(expr1.join(expr2.join(op2)));
    // h(e13) = op2(e,op2(op2(e,e),op2(e,e)))
    final Formula f3 = e1[3].join(h).eq(expr3);
    // h(e14) = op2(e,op2(e,op2(op2(e,e),op2(e,e))))
    final Formula f4 = e1[4].join(h).eq(expr3.join(expr0));
    // h(e15) = op2(e,e)
    final Formula f5 = e1[5].join(h).eq(expr1);
    return Formula.and(f0, f1, f2, f3, f4, f5);
}

Example 90 with Expression

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

the class ALG197 method ax14and15.

/**
 * Parametrization of axioms 14 and 15.
 *
 * @requires e's are unary, op is ternary
 */
@Override
Formula ax14and15(Relation[] e, Relation op) {
    // op(e6,...)
    final Expression expr0 = e[6].join(op);
    // op(e6,e6)
    final Expression expr1 = e[6].join(expr0);
    // op(op(e6,e6),op(e6,e6))
    final Expression expr2 = expr1.join(expr1.join(op));
    // op(e6,op(op(e6,e6),op(e6,e6)))
    final Expression expr3 = expr2.join(expr0);
    // e0 = op(e6,op(e6,e6))
    final Formula f0 = e[0].eq(expr1.join(expr0));
    // e1 = op(op(e6,e6),op(e6,e6))
    final Formula f1 = e[1].eq(expr2);
    // e2 = op(op(op(e6,e6),op(e6,e6)),op(e6,e6))
    final Formula f2 = e[2].eq(expr1.join(expr2.join(op)));
    // e3 = op(e6,op(op(e6,e6),op(e6,e6)))
    final Formula f3 = e[3].eq(expr3);
    // e4 = op(e6,op(e6,op(op(e6,e6),op(e6,e6))))
    final Formula f4 = e[4].eq(expr3.join(expr0));
    return Formula.and(f0, f1, f2, f3, f4);
}