Theorem TheoryArith::canonRec(const Expr& e)
{
if (isLeaf(e)) return reflexivityRule(e);
int ar = e.arity();
if (ar > 0) {
vector<Theorem> newChildrenThm;
vector<unsigned> changed;
for(int k = 0; k < ar; ++k) {
// Recursively canonize the kids
Theorem thm = canonRec(e[k]);
if (thm.getLHS() != thm.getRHS()) {
newChildrenThm.push_back(thm);
changed.push_back(k);
}
}
if(changed.size() > 0) {
return canonThm(substitutivityRule(e, changed, newChildrenThm));
}
}
return canon(e);
}
Theorem TheoryArith::canonSimp(const Expr& e)
{
DebugAssert(canonRec(e).getRHS() == e, "canonSimp expects input to be canonized");
int ar = e.arity();
if (isLeaf(e)) return find(e);
if (ar > 0) {
vector<Theorem> newChildrenThm;
vector<unsigned> changed;
Theorem thm;
for (int k = 0; k < ar; ++k) {
thm = canonSimp(e[k]);
if (thm.getLHS() != thm.getRHS()) {
newChildrenThm.push_back(thm);
changed.push_back(k);
}
}
if(changed.size() > 0) {
thm = canonThm(substitutivityRule(e, changed, newChildrenThm));
return transitivityRule(thm, find(thm.getRHS()));
}
else return find(e);
}
return find(e);
}