/**
* 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;
}