/**
* Returns the declaration constraints.
*
* @return declaration constraints
*/
public final Formula decls() {
// File and Dir partition object
final Formula f0 = Obj.eq(File.union(Dir)).and(File.intersection(Dir).no());
// Root and Cur are in Dir and do not intersect
final Formula f1 = Root.in(Dir).and(Cur.in(Dir)).and(Root.intersection(Cur).no());
// don't need to specify that Dir, Name, and DirEntry are disjoint; implied by bounds
final Formula f2 = entries.in(Dir.product(DirEntry));
final Formula f3 = parent.partialFunction(Dir, Dir);
final Formula f4 = name.function(DirEntry, Name);
final Formula f5 = contents.function(DirEntry, Obj);
return f0.and(f1).and(f2).and(f3).and(f4).and(f5);
}
/**
* 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);
}
