/** Allocate relations for SubsetSig top-down. */
private Expression allocateSubsetSig(SubsetSig sig) throws Err {
// We must not visit the same SubsetSig more than once, so if we've been here already, then
// return the old value right away
Expression sum = sol.a2k(sig);
if (sum != null && sum != Expression.NONE) return sum;
// Recursively form the union of all parent expressions
TupleSet ts = factory.noneOf(1);
for (Sig parent : sig.parents) {
Expression p =
(parent instanceof PrimSig) ? sol.a2k(parent) : allocateSubsetSig((SubsetSig) parent);
ts.addAll(sol.query(true, p, false));
if (sum == null) sum = p;
else sum = sum.union(p);
}
// If subset is exact, then just use the "sum" as is
if (sig.exact) {
sol.addSig(sig, sum);
return sum;
}
// Allocate a relation for this subset sig, then bound it
rep.bound("Sig " + sig + " in " + ts + "\n");
Relation r = sol.addRel(sig.label, null, ts);
sol.addSig(sig, r);
// Add a constraint that it is INDEED a subset of the union of its parents
sol.addFormula(r.in(sum), sig.isSubset);
return r;
}
/**
* Computes the lowerbound from bottom-up; it will also set a suitable initial value for each
* sig's upperbound. Precondition: sig is not a builtin sig
*/
private TupleSet computeLowerBound(List<Tuple> atoms, final PrimSig sig) throws Err {
int n = sc.sig2scope(sig);
TupleSet lower = factory.noneOf(1);
for (PrimSig c : sig.children()) lower.addAll(computeLowerBound(atoms, c));
TupleSet upper = lower.clone();
boolean isExact = sc.isExact(sig);
if (isExact || sig.isTopLevel())
for (n = n - upper.size(); n > 0; n--) {
Tuple atom = atoms.remove(atoms.size() - 1);
// If MUST<SCOPE and s is exact, then add fresh atoms to both LOWERBOUND and UPPERBOUND.
// If MUST<SCOPE and s is inexact but toplevel, then add fresh atoms to the UPPERBOUND.
if (isExact) lower.add(atom);
upper.add(atom);
}
lb.put(sig, lower);
ub.put(sig, upper);
return lower;
}
/**
* Computes the bounds for sigs/fields, then construct a BoundsComputer object that you can query.
*/
private BoundsComputer(A4Reporter rep, A4Solution sol, ScopeComputer sc, Iterable<Sig> sigs)
throws Err {
this.sc = sc;
this.factory = sol.getFactory();
this.rep = rep;
this.sol = sol;
// Figure out the sig bounds
final Universe universe = factory.universe();
final int atomN = universe.size();
final List<Tuple> atoms = new ArrayList<Tuple>(atomN);
for (int i = atomN - 1; i >= 0; i--) atoms.add(factory.tuple(universe.atom(i)));
for (Sig s : sigs) if (!s.builtin && s.isTopLevel()) computeLowerBound(atoms, (PrimSig) s);
for (Sig s : sigs) if (!s.builtin && s.isTopLevel()) computeUpperBound((PrimSig) s);
// Bound the sigs
for (Sig s : sigs) if (!s.builtin && s.isTopLevel()) allocatePrimSig((PrimSig) s);
for (Sig s : sigs) if (s instanceof SubsetSig) allocateSubsetSig((SubsetSig) s);
// Bound the fields
again:
for (Sig s : sigs) {
while (s.isOne != null
&& s.getFieldDecls().size() == 2
&& s.getFields().size() == 2
&& s.getFacts().size() == 1) {
// Let's check whether this is a total ordering on an enum...
Expr fact = s.getFacts().get(0).deNOP(),
b1 = s.getFieldDecls().get(0).expr.deNOP(),
b2 = s.getFieldDecls().get(1).expr.deNOP(),
b3;
if (!(fact instanceof ExprList)
|| !(b1 instanceof ExprUnary)
|| !(b2 instanceof ExprBinary)) break;
ExprList list = (ExprList) fact;
if (list.op != ExprList.Op.TOTALORDER || list.args.size() != 3) break;
if (((ExprUnary) b1).op != ExprUnary.Op.SETOF) break;
else b1 = ((ExprUnary) b1).sub.deNOP();
if (((ExprBinary) b2).op != ExprBinary.Op.ARROW) break;
else {
b3 = ((ExprBinary) b2).right.deNOP();
b2 = ((ExprBinary) b2).left.deNOP();
}
if (!(b1 instanceof PrimSig) || b1 != b2 || b1 != b3) break;
PrimSig sub = (PrimSig) b1;
Field f1 = s.getFields().get(0), f2 = s.getFields().get(1);
if (sub.isEnum == null
|| !list.args.get(0).isSame(sub)
|| !list.args.get(1).isSame(s.join(f1))
|| !list.args.get(2).isSame(s.join(f2))) break;
// Now, we've confirmed it is a total ordering on an enum. Let's pre-bind the relations
TupleSet me = sol.query(true, sol.a2k(s), false),
firstTS = factory.noneOf(2),
lastTS = null,
nextTS = factory.noneOf(3);
if (me.size() != 1 || me.arity() != 1) break;
int n = sub.children().size();
for (PrimSig c : sub.children()) {
TupleSet TS = sol.query(true, sol.a2k(c), false);
if (TS.size() != 1 || TS.arity() != 1) {
firstTS = factory.noneOf(2);
nextTS = factory.noneOf(3);
break;
}
if (lastTS == null) {
firstTS = me.product(TS);
lastTS = TS;
continue;
}
nextTS.addAll(me.product(lastTS).product(TS));
lastTS = TS;
}
if (firstTS.size() != (n > 0 ? 1 : 0) || nextTS.size() != n - 1) break;
sol.addField(f1, sol.addRel(s.label + "." + f1.label, firstTS, firstTS));
sol.addField(f2, sol.addRel(s.label + "." + f2.label, nextTS, nextTS));
rep.bound("Field " + s.label + "." + f1.label + " == " + firstTS + "\n");
rep.bound("Field " + s.label + "." + f2.label + " == " + nextTS + "\n");
continue again;
}
for (Field f : s.getFields()) {
boolean isOne = s.isOne != null;
if (isOne && f.decl().expr.mult() == ExprUnary.Op.EXACTLYOF) {
Expression sim = sim(f.decl().expr);
if (sim != null) {
rep.bound("Field " + s.label + "." + f.label + " defined to be " + sim + "\n");
sol.addField(f, sol.a2k(s).product(sim));
continue;
}
}
Type t = isOne ? Sig.UNIV.type().join(f.type()) : f.type();
TupleSet ub = factory.noneOf(t.arity());
for (List<PrimSig> p : t.fold()) {
TupleSet upper = null;
for (PrimSig b : p) {
TupleSet tmp = sol.query(true, sol.a2k(b), false);
if (upper == null) upper = tmp;
else upper = upper.product(tmp);
}
ub.addAll(upper);
}
Relation r = sol.addRel(s.label + "." + f.label, null, ub);
sol.addField(f, isOne ? sol.a2k(s).product(r) : r);
}
}
// Add any additional SIZE constraints
for (Sig s : sigs)
if (!s.builtin) {
Expression exp = sol.a2k(s);
TupleSet upper = sol.query(true, exp, false), lower = sol.query(false, exp, false);
final int n = sc.sig2scope(s);
if (s.isOne != null && (lower.size() != 1 || upper.size() != 1)) {
rep.bound("Sig " + s + " in " + upper + " with size==1\n");
sol.addFormula(exp.one(), s.isOne);
continue;
}
if (s.isSome != null && lower.size() < 1) sol.addFormula(exp.some(), s.isSome);
if (s.isLone != null && upper.size() > 1) sol.addFormula(exp.lone(), s.isLone);
if (n < 0) continue; // This means no scope was specified
if (lower.size() == n && upper.size() == n && sc.isExact(s)) {
rep.bound("Sig " + s + " == " + upper + "\n");
} else if (sc.isExact(s)) {
rep.bound("Sig " + s + " in " + upper + " with size==" + n + "\n");
sol.addFormula(size(s, n, true), Pos.UNKNOWN);
} else if (upper.size() <= n) {
rep.bound("Sig " + s + " in " + upper + "\n");
} else {
rep.bound("Sig " + s + " in " + upper + " with size<=" + n + "\n");
sol.addFormula(size(s, n, false), Pos.UNKNOWN);
}
}
}