/**
* Helper method that returns the constraint that the sig has exactly "n" elements, or at most "n"
* elements
*/
private Formula size(Sig sig, int n, boolean exact) {
Expression a = sol.a2k(sig);
if (n <= 0) return a.no();
if (n == 1) return exact ? a.one() : a.lone();
Formula f = exact ? Formula.TRUE : null;
Decls d = null;
Expression sum = null;
while (n > 0) {
n--;
Variable v = Variable.unary("");
kodkod.ast.Decl dd = v.oneOf(a);
if (d == null) d = dd;
else d = dd.and(d);
if (sum == null) sum = v;
else {
if (f != null) f = v.intersection(sum).no().and(f);
sum = v.union(sum);
}
}
if (f != null) return sum.eq(a).and(f).forSome(d);
else return a.no().or(sum.eq(a).forSome(d));
}
/**
* Returns the conjecture theorem_3_8_5.
*
* @return theorem_3_8_5
*/
public final Formula theorem385() {
// all c: curve, p, q, r: point |
// c->p->q->r in between =>
// incident.c - q in q.(p.(c.between)) + ((c.between).r).q
final Variable c = Variable.unary("C");
final Variable p = Variable.unary("P");
final Variable q = Variable.unary("Q");
final Variable r = Variable.unary("R");
final Formula f0 = c.product(p).product(q).product(r).in(between);
final Expression e0 = q.join(p.join(c.join(between)));
final Expression e1 = c.join(between).join(r).join(q);
final Formula f1 = incident.join(c).difference(q).in(e0.union(e1));
return f0.implies(f1)
.forAll(p.oneOf(point).and(q.oneOf(point)).and(r.oneOf(point)).and(c.oneOf(curve)));
}
/**
* 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)));
}
/**
* Returns a relational encoding of the problem.
*
* @return a relational encoding of the problem.
*/
public Formula rules() {
final List<Formula> rules = new ArrayList<Formula>();
rules.add(x.function(queen, num));
rules.add(y.function(queen, num));
final Variable i = Variable.unary("n");
final Variable q1 = Variable.unary("q1"), q2 = Variable.unary("q2");
// at most one queen in each row: all i: num | lone x.i
rules.add(x.join(i).lone().forAll(i.oneOf(num)));
// at most one queen in each column: all i: num | lone y.i
rules.add(y.join(i).lone().forAll(i.oneOf(num)));
// no queen in a blocked position: all q: Queen | q.x->q.y !in blocked
rules.add(q1.join(x).product(q1.join(y)).intersection(blocked).no().forAll(q1.oneOf(queen)));
// at most one queen on each diagonal
// all q1: Queen, q2: Queen - q1 |
// let xu = prevs[q2.x] + prevs[q1.x],
// xi = prevs[q2.x] & prevs[q1.x],
// yu = prevs[q2.y] + prevs[q1.y],
// yi = prevs[q2.y] & prevs[q1.y] |
// #(xu - xi) != #(yu - yi)
final Expression ordClosure = ord.closure();
final Expression q2xPrevs = ordClosure.join(q2.join(x)), q1xPrevs = ordClosure.join(q1.join(x));
final Expression q2yPrevs = ordClosure.join(q2.join(y)), q1yPrevs = ordClosure.join(q1.join(y));
final IntExpression xDiff =
(q2xPrevs.union(q1xPrevs)).difference(q2xPrevs.intersection(q1xPrevs)).count();
final IntExpression yDiff =
(q2yPrevs.union(q1yPrevs)).difference(q2yPrevs.intersection(q1yPrevs)).count();
rules.add(xDiff.eq(yDiff).not().forAll(q1.oneOf(queen).and(q2.oneOf(queen.difference(q1)))));
return Formula.and(rules);
}
public static void main(String[] args) throws Exception {
Relation x0 = Relation.unary("Int/min");
Relation x1 = Relation.unary("Int/zero");
Relation x2 = Relation.unary("Int/max");
Relation x3 = Relation.nary("Int/next", 2);
Relation x4 = Relation.unary("seq/Int");
Relation x5 = Relation.unary("String");
Relation x6 = Relation.unary("this/A");
Relation x7 = Relation.unary("this/Relation");
Relation x8 = Relation.nary("this/Relation.r", 4);
List<String> atomlist =
Arrays.asList(
"-1",
"-2",
"-3",
"-4",
"-5",
"-6",
"-7",
"-8",
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"A$0",
"A$1",
"A$2",
"Relation$0",
"unused0",
"unused1");
Universe universe = new Universe(atomlist);
TupleFactory factory = universe.factory();
Bounds bounds = new Bounds(universe);
TupleSet x0_upper = factory.noneOf(1);
x0_upper.add(factory.tuple("-8"));
bounds.boundExactly(x0, x0_upper);
TupleSet x1_upper = factory.noneOf(1);
x1_upper.add(factory.tuple("0"));
bounds.boundExactly(x1, x1_upper);
TupleSet x2_upper = factory.noneOf(1);
x2_upper.add(factory.tuple("7"));
bounds.boundExactly(x2, x2_upper);
TupleSet x3_upper = factory.noneOf(2);
x3_upper.add(factory.tuple("-8").product(factory.tuple("-7")));
x3_upper.add(factory.tuple("-7").product(factory.tuple("-6")));
x3_upper.add(factory.tuple("-6").product(factory.tuple("-5")));
x3_upper.add(factory.tuple("-5").product(factory.tuple("-4")));
x3_upper.add(factory.tuple("-4").product(factory.tuple("-3")));
x3_upper.add(factory.tuple("-3").product(factory.tuple("-2")));
x3_upper.add(factory.tuple("-2").product(factory.tuple("-1")));
x3_upper.add(factory.tuple("-1").product(factory.tuple("0")));
x3_upper.add(factory.tuple("0").product(factory.tuple("1")));
x3_upper.add(factory.tuple("1").product(factory.tuple("2")));
x3_upper.add(factory.tuple("2").product(factory.tuple("3")));
x3_upper.add(factory.tuple("3").product(factory.tuple("4")));
x3_upper.add(factory.tuple("4").product(factory.tuple("5")));
x3_upper.add(factory.tuple("5").product(factory.tuple("6")));
x3_upper.add(factory.tuple("6").product(factory.tuple("7")));
bounds.boundExactly(x3, x3_upper);
TupleSet x4_upper = factory.noneOf(1);
x4_upper.add(factory.tuple("0"));
x4_upper.add(factory.tuple("1"));
x4_upper.add(factory.tuple("2"));
bounds.boundExactly(x4, x4_upper);
TupleSet x5_upper = factory.noneOf(1);
bounds.boundExactly(x5, x5_upper);
TupleSet x6_upper = factory.noneOf(1);
x6_upper.add(factory.tuple("A$0"));
x6_upper.add(factory.tuple("A$1"));
x6_upper.add(factory.tuple("A$2"));
bounds.boundExactly(x6, x6_upper);
TupleSet x7_upper = factory.noneOf(1);
x7_upper.add(factory.tuple("unused0"));
x7_upper.add(factory.tuple("unused1"));
x7_upper.add(factory.tuple("Relation$0"));
bounds.bound(x7, x7_upper);
TupleSet x8_upper = factory.noneOf(4);
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
bounds.bound(x8, x8_upper);
bounds.boundExactly(-8, factory.range(factory.tuple("-8"), factory.tuple("-8")));
bounds.boundExactly(-7, factory.range(factory.tuple("-7"), factory.tuple("-7")));
bounds.boundExactly(-6, factory.range(factory.tuple("-6"), factory.tuple("-6")));
bounds.boundExactly(-5, factory.range(factory.tuple("-5"), factory.tuple("-5")));
bounds.boundExactly(-4, factory.range(factory.tuple("-4"), factory.tuple("-4")));
bounds.boundExactly(-3, factory.range(factory.tuple("-3"), factory.tuple("-3")));
bounds.boundExactly(-2, factory.range(factory.tuple("-2"), factory.tuple("-2")));
bounds.boundExactly(-1, factory.range(factory.tuple("-1"), factory.tuple("-1")));
bounds.boundExactly(0, factory.range(factory.tuple("0"), factory.tuple("0")));
bounds.boundExactly(1, factory.range(factory.tuple("1"), factory.tuple("1")));
bounds.boundExactly(2, factory.range(factory.tuple("2"), factory.tuple("2")));
bounds.boundExactly(3, factory.range(factory.tuple("3"), factory.tuple("3")));
bounds.boundExactly(4, factory.range(factory.tuple("4"), factory.tuple("4")));
bounds.boundExactly(5, factory.range(factory.tuple("5"), factory.tuple("5")));
bounds.boundExactly(6, factory.range(factory.tuple("6"), factory.tuple("6")));
bounds.boundExactly(7, factory.range(factory.tuple("7"), factory.tuple("7")));
Variable x12 = Variable.unary("this");
Decls x11 = x12.oneOf(x7);
Expression x16 = x12.join(x8);
Expression x18 = x6.product(x6);
Expression x17 = x6.product(x18);
Formula x15 = x16.in(x17);
Variable x21 = Variable.unary("x21");
Decls x20 = x21.oneOf(x6);
Expression x25 = x21.join(x16);
Expression x26 = x6.product(x6);
Formula x24 = x25.in(x26);
Variable x29 = Variable.unary("x29");
Decls x28 = x29.oneOf(x6);
Expression x32 = x29.join(x25);
Formula x31 = x32.one();
Formula x33 = x32.in(x6);
Formula x30 = x31.and(x33);
Formula x27 = x30.forAll(x28);
Formula x23 = x24.and(x27);
Variable x36 = Variable.unary("x36");
Decls x35 = x36.oneOf(x6);
Expression x38 = x25.join(x36);
Formula x37 = x38.in(x6);
Formula x34 = x37.forAll(x35);
Formula x22 = x23.and(x34);
Formula x19 = x22.forAll(x20);
Formula x14 = x15.and(x19);
Variable x42 = Variable.unary("x42");
Decls x41 = x42.oneOf(Expression.UNIV);
Variable x45 = Variable.unary("x45");
Decls x44 = x45.oneOf(Expression.UNIV);
Decls x40 = x41.and(x44);
Expression x50 = x42.product(x45);
Expression x51 = x6.product(x6);
Formula x49 = x50.in(x51);
Variable x54 = Variable.unary("x54");
Decls x53 = x54.oneOf(x6);
Expression x57 = x54.join(x50);
Formula x56 = x57.one();
Formula x58 = x57.in(x6);
Formula x55 = x56.and(x58);
Formula x52 = x55.forAll(x53);
Formula x48 = x49.and(x52);
Variable x61 = Variable.unary("x61");
Decls x60 = x61.oneOf(x6);
Expression x63 = x50.join(x61);
Formula x62 = x63.in(x6);
Formula x59 = x62.forAll(x60);
Formula x47 = x48.and(x59);
Expression x66 = x16.join(x45);
Expression x65 = x66.join(x42);
Formula x64 = x65.in(x6);
Formula x46 = x47.implies(x64);
Formula x39 = x46.forAll(x40);
Formula x13 = x14.and(x39);
Formula x10 = x13.forAll(x11);
Expression x70 = x8.join(Expression.UNIV);
Expression x69 = x70.join(Expression.UNIV);
Expression x68 = x69.join(Expression.UNIV);
Formula x67 = x68.in(x7);
Formula x71 = x0.eq(x0);
Formula x72 = x1.eq(x1);
Formula x73 = x2.eq(x2);
Formula x74 = x3.eq(x3);
Formula x75 = x4.eq(x4);
Formula x76 = x5.eq(x5);
Formula x77 = x6.eq(x6);
Formula x78 = x7.eq(x7);
Formula x79 = x8.eq(x8);
Formula x9 =
Formula.compose(FormulaOperator.AND, x10, x67, x71, x72, x73, x74, x75, x76, x77, x78, x79);
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);
solver.options().setSkolemDepth(0);
System.out.println(PrettyPrinter.print(x9, 0));
System.out.println(bounds);
System.out.println("Solving...");
System.out.flush();
Solution sol = solver.solve(x9, bounds);
System.out.println(sol.toString());
Instance inst = sol.instance();
Evaluator ev = new Evaluator(inst);
System.out.println("Universe: " + ev.evaluate(Expression.UNIV));
Formula xx = x46.forAll(x40).forAll(x11);
System.out.println(PrettyPrinter.print(xx, 2));
System.out.println(ev.evaluate(xx));
System.out.println(PrettyPrinter.print(x46, 4));
// Variable r = Variable.unary("this");
// Variable u1 = Variable.unary("u1");
// Variable u2 = Variable.unary("u2");
//
// Formula ff =
// u1.product(u2).in(x6.product(x6)).forAll(u1.oneOf(Expression.UNIV).and(u2.oneOf(Expression.UNIV))).forAll(r.oneOf(x7));
// System.out.println(PrettyPrinter.print(ff, 0));
// System.out.println(ev.evaluate(ff));
}
public static void main(String[] args) throws Exception {
Relation x0 = Relation.unary("Int/min");
Relation x1 = Relation.unary("Int/zero");
Relation x2 = Relation.unary("Int/max");
Relation x3 = Relation.nary("Int/next", 2);
Relation x4 = Relation.unary("seq/Int");
Relation x5 = Relation.unary("String");
Relation x6 = Relation.unary("this/Test");
Relation x7 = Relation.nary("this/Test.weight", 2);
Relation x8 = Relation.nary("this/Test.x", 2);
Relation x9 = Relation.nary("this/Test.y", 2);
List<String> atomlist =
Arrays.asList(
"-1", "-2", "-3", "-4", "-5", "-6", "-7", "-8", "0", "1", "2", "3", "4", "5", "6", "7",
"Test$0", "Test$1", "Test$2");
Universe universe = new Universe(atomlist);
TupleFactory factory = universe.factory();
Bounds bounds = new Bounds(universe);
TupleSet x0_upper = factory.noneOf(1);
x0_upper.add(factory.tuple("-8"));
bounds.boundExactly(x0, x0_upper);
TupleSet x1_upper = factory.noneOf(1);
x1_upper.add(factory.tuple("0"));
bounds.boundExactly(x1, x1_upper);
TupleSet x2_upper = factory.noneOf(1);
x2_upper.add(factory.tuple("7"));
bounds.boundExactly(x2, x2_upper);
TupleSet x3_upper = factory.noneOf(2);
x3_upper.add(factory.tuple("-8").product(factory.tuple("-7")));
x3_upper.add(factory.tuple("-7").product(factory.tuple("-6")));
x3_upper.add(factory.tuple("-6").product(factory.tuple("-5")));
x3_upper.add(factory.tuple("-5").product(factory.tuple("-4")));
x3_upper.add(factory.tuple("-4").product(factory.tuple("-3")));
x3_upper.add(factory.tuple("-3").product(factory.tuple("-2")));
x3_upper.add(factory.tuple("-2").product(factory.tuple("-1")));
x3_upper.add(factory.tuple("-1").product(factory.tuple("0")));
x3_upper.add(factory.tuple("0").product(factory.tuple("1")));
x3_upper.add(factory.tuple("1").product(factory.tuple("2")));
x3_upper.add(factory.tuple("2").product(factory.tuple("3")));
x3_upper.add(factory.tuple("3").product(factory.tuple("4")));
x3_upper.add(factory.tuple("4").product(factory.tuple("5")));
x3_upper.add(factory.tuple("5").product(factory.tuple("6")));
x3_upper.add(factory.tuple("6").product(factory.tuple("7")));
bounds.boundExactly(x3, x3_upper);
TupleSet x4_upper = factory.noneOf(1);
x4_upper.add(factory.tuple("0"));
x4_upper.add(factory.tuple("1"));
x4_upper.add(factory.tuple("2"));
x4_upper.add(factory.tuple("3"));
bounds.boundExactly(x4, x4_upper);
TupleSet x5_upper = factory.noneOf(1);
bounds.boundExactly(x5, x5_upper);
TupleSet x6_upper = factory.noneOf(1);
x6_upper.add(factory.tuple("Test$0"));
x6_upper.add(factory.tuple("Test$1"));
x6_upper.add(factory.tuple("Test$2"));
bounds.boundExactly(x6, x6_upper);
TupleSet x7_upper = factory.noneOf(2);
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-8")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-7")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-6")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-5")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-4")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-3")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-2")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-1")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("0")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("1")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("2")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("3")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("4")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("5")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("6")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("7")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-8")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-7")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-6")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-5")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-4")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-3")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-2")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-1")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("0")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("1")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("2")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("3")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("4")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("5")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("6")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("7")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-8")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-7")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-6")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-5")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-4")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-3")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-2")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-1")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("0")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("1")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("2")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("3")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("4")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("5")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("6")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("7")));
bounds.bound(x7, x7_upper);
TupleSet x8_upper = factory.noneOf(2);
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-8")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-7")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-6")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-5")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-4")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-3")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-2")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-1")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("0")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("1")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("2")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("3")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("4")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("5")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("6")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("7")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-8")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-7")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-6")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-5")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-4")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-3")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-2")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-1")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("0")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("1")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("2")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("3")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("4")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("5")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("6")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("7")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-8")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-7")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-6")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-5")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-4")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-3")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-2")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-1")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("0")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("1")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("2")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("3")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("4")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("5")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("6")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("7")));
bounds.bound(x8, x8_upper);
TupleSet x9_upper = factory.noneOf(2);
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-8")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-7")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-6")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-5")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-4")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-3")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-2")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-1")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("0")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("1")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("2")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("3")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("4")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("5")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("6")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("7")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-8")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-7")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-6")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-5")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-4")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-3")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-2")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-1")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("0")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("1")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("2")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("3")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("4")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("5")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("6")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("7")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-8")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-7")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-6")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-5")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-4")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-3")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-2")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-1")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("0")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("1")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("2")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("3")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("4")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("5")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("6")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("7")));
bounds.bound(x9, x9_upper);
bounds.boundExactly(-8, factory.range(factory.tuple("-8"), factory.tuple("-8")));
bounds.boundExactly(-7, factory.range(factory.tuple("-7"), factory.tuple("-7")));
bounds.boundExactly(-6, factory.range(factory.tuple("-6"), factory.tuple("-6")));
bounds.boundExactly(-5, factory.range(factory.tuple("-5"), factory.tuple("-5")));
bounds.boundExactly(-4, factory.range(factory.tuple("-4"), factory.tuple("-4")));
bounds.boundExactly(-3, factory.range(factory.tuple("-3"), factory.tuple("-3")));
bounds.boundExactly(-2, factory.range(factory.tuple("-2"), factory.tuple("-2")));
bounds.boundExactly(-1, factory.range(factory.tuple("-1"), factory.tuple("-1")));
bounds.boundExactly(0, factory.range(factory.tuple("0"), factory.tuple("0")));
bounds.boundExactly(1, factory.range(factory.tuple("1"), factory.tuple("1")));
bounds.boundExactly(2, factory.range(factory.tuple("2"), factory.tuple("2")));
bounds.boundExactly(3, factory.range(factory.tuple("3"), factory.tuple("3")));
bounds.boundExactly(4, factory.range(factory.tuple("4"), factory.tuple("4")));
bounds.boundExactly(5, factory.range(factory.tuple("5"), factory.tuple("5")));
bounds.boundExactly(6, factory.range(factory.tuple("6"), factory.tuple("6")));
bounds.boundExactly(7, factory.range(factory.tuple("7"), factory.tuple("7")));
Variable x13 = Variable.unary("this");
Decls x12 = x13.oneOf(x6);
Expression x16 = x13.join(x7);
Formula x15 = x16.one();
Formula x17 = x16.in(Expression.INTS);
Formula x14 = x15.and(x17);
Formula x11 = x14.forAll(x12);
Expression x20 = x7.join(Expression.UNIV);
Formula x19 = x20.in(x6);
Variable x24 = Variable.unary("this");
Decls x23 = x24.oneOf(x6);
Expression x27 = x24.join(x8);
Formula x26 = x27.lone();
Formula x28 = x27.in(Expression.INTS);
Formula x25 = x26.and(x28);
Formula x22 = x25.forAll(x23);
Expression x30 = x8.join(Expression.UNIV);
Formula x29 = x30.in(x6);
Variable x33 = Variable.unary("this");
Decls x32 = x33.oneOf(x6);
Expression x36 = x33.join(x9);
Formula x35 = x36.one();
Formula x37 = x36.in(Expression.INTS);
Formula x34 = x35.and(x37);
Formula x31 = x34.forAll(x32);
Expression x39 = x9.join(Expression.UNIV);
Formula x38 = x39.in(x6);
Variable x42 = Variable.unary("this");
Decls x41 = x42.oneOf(x6);
Expression x44 = x42.join(x7);
Expression x48 = x42.join(x8);
IntExpression x47 = x48.sum();
Expression x50 = x42.join(x9);
IntExpression x49 = x50.sum();
IntExpression x46 = x47.plus(x49);
Expression x45 = x46.toExpression();
Formula x43 = x44.eq(x45);
Formula x40 = x43.forAll(x41);
Formula x51 = x0.eq(x0);
Formula x52 = x1.eq(x1);
Formula x53 = x2.eq(x2);
Formula x54 = x3.eq(x3);
Formula x55 = x4.eq(x4);
Formula x56 = x5.eq(x5);
Formula x57 = x6.eq(x6);
Formula x58 = x7.eq(x7);
Formula x59 = x8.eq(x8);
Formula x60 = x9.eq(x9);
IntExprReduction ier = new IntExprReduction();
Formula[] formulas =
ier.reduceIntExpressions(
x11, x19, x22, x29, x31, x38, x40, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60);
Formula newFormula = Formula.compose(FormulaOperator.AND, formulas);
ier.solve(newFormula, bounds, factory, universe, 32);
}
/**
* Returns all facts in the model.
*
* @return the facts.
*/
public final Formula facts() {
// sig File extends Object {} { some d: Dir | this in d.entries.contents }
final Variable file = Variable.unary("this");
final Variable d = Variable.unary("d");
final Formula f0 =
file.in(d.join(entries).join(contents)).forSome(d.oneOf(Dir)).forAll(file.oneOf(File));
// sig Dir extends Object {
// entries: set DirEntry,
// parent: lone Dir
// } {
// parent = this.~@contents.~@entries
// all e1, e2 : entries | e1.name = e2.name => e1 = e2
// this !in this.^@parent
// this != Root => Root in this.^@parent
// }
final Variable dir = Variable.unary("this");
final Variable e1 = Variable.unary("e1"), e2 = Variable.unary("e2");
final Formula f1 =
(dir.join(parent)).eq(dir.join(contents.transpose()).join(entries.transpose()));
final Expression e0 = dir.join(entries);
final Formula f2 =
e1.join(name).eq(e2.join(name)).implies(e1.eq(e2)).forAll(e1.oneOf(e0).and(e2.oneOf(e0)));
final Formula f3 = dir.in(dir.join(parent.closure())).not();
final Formula f4 = dir.eq(Root).not().implies(Root.in(dir.join(parent.closure())));
final Formula f5 = f1.and(f2).and(f3).and(f4).forAll(dir.oneOf(Dir));
// one sig Root extends Dir {} { no parent }
final Formula f6 = Root.join(parent).no();
// sig DirEntry {
// name: Name,
// contents: Object
// } { one this.~entries }
final Variable entry = Variable.unary("this");
final Formula f7 = entry.join(entries.transpose()).one().forAll(entry.oneOf(DirEntry));
// fact OneParent {
// // all directories besides root xhave one parent
// all d: Dir - Root | one d.parent
// }
final Formula f8 = d.join(parent).one().forAll(d.oneOf(Dir.difference(Root)));
return f0.and(f5).and(f6).and(f7).and(f8);
}
/**
* Returns the no aliases assertion.
*
* @return the no aliases assertion.
*/
public final Formula noDirAliases() {
// all o: Dir | lone o.~contents
final Variable o = Variable.unary("o");
return o.join(contents.transpose()).lone().forAll(o.oneOf(Dir));
}