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

Example 16 with Formula

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

the class Lists method facts.

/**
 * Returns all facts in the model.
 *
 * @return the facts.
 */
public final Formula facts() {
    // fact NoStrayThings {Thing in List.car}
    final Formula f0 = Thing.in(List.join(car));
    // fact finite {all L: List | isFinite(L)}
    final Variable L = Variable.unary("L");
    final Formula f1 = isFinite(L).forAll(L.oneOf(List));
    // fact Equivalence {
    // all a,b: List | (a in b.equivTo) <=> (a.car = b.car and b.cdr in
    // a.cdr.equivTo)
    // }
    final Variable a = Variable.unary("a");
    final Variable b = Variable.unary("b");
    final Formula f2 = a.in(b.join(equivTo));
    final Formula f3 = a.join(car).eq(b.join(car));
    final Formula f4 = b.join(cdr).in(a.join(cdr).join(equivTo));
    final Formula f6 = f2.iff(f3.and(f4)).forAll(a.oneOf(List).and(b.oneOf(List)));
    // fact prefix { //a is a prefix of b
    // List->EmptyList in prefixes
    // all a,b: NonEmptyList | (a in b.prefixes) <=> (a.car = b.car
    // and a.cdr in b.cdr.prefixes)
    // }
    final Formula f7 = List.product(EmptyList).in(prefixes);
    final Formula f8 = a.in(b.join(prefixes));
    final Formula f9 = a.join(cdr).in(b.join(cdr).join(prefixes));
    final Formula f11 = f8.iff(f3.and(f9)).forAll(a.oneOf(NonEmptyList).and(b.oneOf(NonEmptyList)));
    return f0.and(f1).and(f6).and(f7).and(f11);
}

Example 17 with Formula

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

the class RingElection method defineElected.

/**
 * Return DefineElected fact.
 *
 * @return
 *
 *         <pre>
 * fact DefineElected {
 *  no elected.TO/first()
 *  all t: Time - TO/first()|
 *   elected.t = {p: Process | p in p.toSend.t - p.toSend.(TO/prev(t))} }
 *         </pre>
 */
public Formula defineElected() {
    final Variable t = Variable.unary("t");
    final Formula f1 = elected.join(tfirst).no();
    final Variable p = Variable.unary("p");
    final Formula c = p.in(p.join(toSend).join(t).difference(p.join(toSend).join(t.join(tord.transpose()))));
    final Expression comprehension = c.comprehension(p.oneOf(Process));
    final Formula f2 = elected.join(t).eq(comprehension).forAll(t.oneOf(Time.difference(tfirst)));
    return f1.and(f2);
}

Example 18 with Formula

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

the class RingElection method step.

/**
 * Returns the step predicate.
 *
 * @return
 *
 *         <pre>
 * pred step (t, t': Time, p: Process) {
 *  let from = p.toSend, to = p.succ.toSend |
 *   some id: from.t {
 *    from.t' = from.t - id
 *    to.t' = to.t + (id - PO/prevs(p.succ)) } }
 *         </pre>
 */
public Formula step(Expression t1, Expression t2, Expression p) {
    final Expression from = p.join(toSend);
    final Expression to = p.join(succ).join(toSend);
    final Variable id = Variable.unary("id");
    final Expression prevs = (p.join(succ)).join((pord.transpose()).closure());
    final Formula f1 = from.join(t2).eq(from.join(t1).difference(id));
    final Formula f2 = to.join(t2).eq(to.join(t1).union(id.difference(prevs)));
    return f1.and(f2).forSome(id.oneOf(from.join(t1)));
}

Example 19 with Formula

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

the class RingElection method progress.

/**
 * Returns the progress predicate.
 *
 * @return
 *
 *         <pre>
 * pred progress () {
 *  all t: Time - TO/last() | let t' = TO/next (t) |
 *   some Process.toSend.t => some p: Process | not skip (t, t', p) }
 *         </pre>
 */
public Formula progress() {
    final Variable t1 = Variable.unary("t");
    final Expression t2 = t1.join(tord);
    final Variable p = Variable.unary("p");
    final Formula f1 = Process.join(toSend).join(t1).some().implies(skip(t1, t2, p).not().forSome(p.oneOf(Process)));
    return f1.forAll(t1.oneOf(Time.difference(tlast)));
}

Example 20 with Formula

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

the class RingElection method declarations.

/**
 * Returns the declaration constraints.
 *
 * @return
 *
 *         <pre>
 * sig Time {}
 * sig Process {
 *  succ: Process,
 *  toSend: Process -> Time,
 *  elected: set Time }
 *         </pre>
 */
public Formula declarations() {
    final Formula ordTime = tord.totalOrder(Time, tfirst, tlast);
    final Formula ordProcess = pord.totalOrder(Process, pfirst, plast);
    final Formula succFunction = succ.function(Process, Process);
    final Formula electedDomRange = elected.in(Process.product(Time));
    return succFunction.and(ordTime).and(ordProcess).and(electedDomRange);
}