Java Code Examples for kodkod.ast.Variable#product()
The following examples show how to use
kodkod.ast.Variable#product() .
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Example 1
| Source File: GEO158.java From org.alloytools.alloy with Apache License 2.0 | 6 votes |
|
/**
* 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)));
}
Example 2
| Source File: GEO158.java From kodkod with MIT License | 6 votes |
|
/**
* 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)));
}
Example 3
| Source File: GEO092.java From org.alloytools.alloy with Apache License 2.0 | 5 votes |
|
/**
* 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 4
| Source File: GEO158.java From org.alloytools.alloy with Apache License 2.0 | 5 votes |
|
/**
* 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)));
}
Example 5
| Source File: LAT258.java From org.alloytools.alloy with Apache License 2.0 | 5 votes |
|
/**
* Returns the less_than_meet_join axiom.
*
* @return the less_than_meet_join axiom.
*/
public final Formula lessThanMeetJoin() {
final Variable a = Variable.unary("A");
final Variable b = Variable.unary("B");
final Expression e0 = a.product(b);
final Formula f0 = e0.product(a).in(meet);
final Formula f1 = e0.product(b).in(join);
// all a: univ, b: a.lessThan | a->b->a in meet && a->b->b in join
return f0.and(f1).forAll(b.oneOf(a.join(lessThan))).forAll(a.oneOf(UNIV));
}
Example 6
| Source File: Toughnut.java From org.alloytools.alloy with Apache License 2.0 | 5 votes |
|
/**
* Returns the covering predicate. Note that we don't need to specify the first
* two lines of the predicate, since they can be expressed as bounds
* constraints.
*
* @return the covering predicate
*/
public Formula checkBelowTooDoublePrime() {
final Variable x = Variable.unary("x");
final Variable y = Variable.unary("y");
final Decls d = x.oneOf(Cell).and(y.oneOf(Cell));
final Expression xy = y.join(x.join(covered));
// covering relation is symmetric
Formula symm = xy.product(x.product(y)).in(covered).forAll(d);
// each pair of cells on the board should be covered
// by a domino, which also covers ONE of its neighbors
Expression xNeighbors = (prev(x).union(next(x))).product(y);
Expression yNeighbors = x.product(prev(y).union(next(y)));
Formula covering = (xy.one().and(xy.in(xNeighbors.union(yNeighbors)))).forAll(d);
return symm.and(covering);
}
Example 7
| Source File: GEO092.java From kodkod with MIT License | 5 votes |
|
/**
* 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 8
| Source File: GEO158.java From kodkod with MIT License | 5 votes |
|
/**
* 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)));
}
Example 9
| Source File: LAT258.java From kodkod with MIT License | 5 votes |
|
/**
* Returns the less_than_meet_join axiom.
* @return the less_than_meet_join axiom.
*/
public final Formula lessThanMeetJoin() {
final Variable a = Variable.unary("A");
final Variable b = Variable.unary("B");
final Expression e0 = a.product(b);
final Formula f0 = e0.product(a).in(meet);
final Formula f1 = e0.product(b).in(join);
// all a: univ, b: a.lessThan | a->b->a in meet && a->b->b in join
return f0.and(f1).forAll(b.oneOf(a.join(lessThan))).forAll(a.oneOf(UNIV));
}
Example 10
| Source File: Toughnut.java From kodkod with MIT License | 5 votes |
|
/**
* Returns the covering predicate. Note that we don't
* need to specify the first two lines of the predicate,
* since they can be expressed as bounds constraints.
* @return the covering predicate
*/
public Formula checkBelowTooDoublePrime() {
final Variable x = Variable.unary("x");
final Variable y = Variable.unary("y");
final Decls d = x.oneOf(Cell).and(y.oneOf(Cell));
final Expression xy = y.join(x.join(covered));
// covering relation is symmetric
Formula symm = xy.product(x.product(y)).in(covered).forAll(d);
// each pair of cells on the board should be covered
// by a domino, which also covers ONE of its neighbors
Expression xNeighbors = (prev(x).union(next(x))).product(y);
Expression yNeighbors = x.product(prev(y).union(next(y)));
Formula covering = (xy.one().and(xy.in(xNeighbors.union(yNeighbors)))).forAll(d);
return symm.and(covering);
}
Example 11
| Source File: BugTests.java From org.alloytools.alloy with Apache License 2.0 | 4 votes |
|
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());
}
}
Example 12
| Source File: BugTests.java From org.alloytools.alloy with Apache License 2.0 | 4 votes |
|
public final void testFelix_03062008_2() {
Relation x5 = Relation.unary("Role");
Relation x6 = Relation.unary("Session");
List<String> atomlist = Arrays.asList("Role$0", "Session$0", "Session$1");
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("Role$0"));
bounds.bound(x5, x5_upper);
TupleSet x6_upper = factory.noneOf(1);
x6_upper.add(factory.tuple("Session$0"));
x6_upper.add(factory.tuple("Session$1"));
bounds.bound(x6, x6_upper);
Variable x11 = Variable.unary("x_a");
Decls x10 = x11.oneOf(x6);
Variable x15 = Variable.unary("x_b");
Decls x14 = x15.oneOf(x5);
Variable x17 = Variable.unary("x_c");
Decls x16 = x17.oneOf(x5);
Decls x13 = x14.and(x16);
Expression x20 = x15.product(x17);
Expression x19 = x11.product(x20);
Formula x18 = x19.some();
Formula x12 = x18.forSome(x13);
Formula x9 = x12.forAll(x10);
Formula x24 = x5.some();
Formula x23 = x24.not();
Formula x28 = x5.eq(x5);
Formula x29 = x6.eq(x6);
Formula x25 = x28.and(x29);
Formula x22 = x23.and(x25);
Formula x8 = x9.and(x22).and(x5.no()).and(x6.no());
Solver solver = new Solver();
solver.options().setSolver(SATFactory.DefaultSAT4J);
solver.options().setBitwidth(2);
// solver.options().setFlatten(false);
solver.options().setIntEncoding(Options.IntEncoding.TWOSCOMPLEMENT);
solver.options().setSymmetryBreaking(20);
solver.options().setSkolemDepth(2);
System.out.flush();
Solution sol = solver.solve(x8, bounds);
Instance inst = sol.instance();
assertNotNull(inst);
for (Relation rel : inst.relations()) {
if (rel != x5 && rel != x6) {
final TupleSet range = inst.tuples(x6).product(inst.tuples(x5));
assertTrue(range.containsAll(inst.tuples(rel)));
}
}
}
Example 13
| Source File: RegressionTests.java From kodkod with MIT License | 4 votes |
|
@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());
}
}
Example 14
| Source File: RegressionTests.java From kodkod with MIT License | 4 votes |
|
@Test
public final void testFelix_03062008_2() {
Relation x5 = Relation.unary("Role");
Relation x6 = Relation.unary("Session");
List<String> atomlist = Arrays.asList("Role$0", "Session$0", "Session$1");
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("Role$0"));
bounds.bound(x5, x5_upper);
TupleSet x6_upper = factory.noneOf(1);
x6_upper.add(factory.tuple("Session$0"));
x6_upper.add(factory.tuple("Session$1"));
bounds.bound(x6, x6_upper);
Variable x11=Variable.unary("x_a");
Decls x10=x11.oneOf(x6);
Variable x15=Variable.unary("x_b");
Decls x14=x15.oneOf(x5);
Variable x17=Variable.unary("x_c");
Decls x16=x17.oneOf(x5);
Decls x13=x14.and(x16);
Expression x20=x15.product(x17);
Expression x19=x11.product(x20);
Formula x18=x19.some();
Formula x12=x18.forSome(x13);
Formula x9=x12.forAll(x10);
Formula x24=x5.some();
Formula x23=x24.not();
Formula x28=x5.eq(x5);
Formula x29=x6.eq(x6);
Formula x25=x28.and(x29);
Formula x22=x23.and(x25);
Formula x8=x9.and(x22).and(x5.no()).and(x6.no());
Solver solver = new Solver();
solver.options().setSolver(SATFactory.DefaultSAT4J);
solver.options().setBitwidth(2);
solver.options().setIntEncoding(Options.IntEncoding.TWOSCOMPLEMENT);
solver.options().setSymmetryBreaking(20);
solver.options().setSkolemDepth(2);
System.out.flush();
Solution sol = solver.solve(x8, bounds);
Instance inst = sol.instance();
assertNotNull(inst);
for(Relation rel : inst.relations()) {
if (rel!=x5 && rel!=x6) {
final TupleSet range = inst.tuples(x6).product(inst.tuples(x5));
assertTrue(range.containsAll(inst.tuples(rel)));
}
}
}
