// Monotonic total order on universe level terms.
bool is_lt(level const & a, level const & b, bool use_hash) {
if (is_eqp(a, b)) return false;
unsigned da = get_depth(a);
unsigned db = get_depth(b);
if (da < db) return true;
if (da > db) return false;
if (kind(a) != kind(b)) return kind(a) < kind(b);
if (use_hash) {
if (hash(a) < hash(b)) return true;
if (hash(a) > hash(b)) return false;
}
if (a == b) return false;
switch (kind(a)) {
case level_kind::Zero:
lean_unreachable(); // LCOV_EXCL_LINE
case level_kind::Param: case level_kind::Global: case level_kind::Meta:
return to_param_core(a).m_id < to_param_core(b).m_id;
case level_kind::Max: case level_kind::IMax:
if (to_max_core(a).m_lhs != to_max_core(b).m_lhs)
return is_lt(to_max_core(a).m_lhs, to_max_core(b).m_lhs, use_hash);
else
return is_lt(to_max_core(a).m_rhs, to_max_core(b).m_rhs, use_hash);
case level_kind::Succ:
return is_lt(succ_of(a), succ_of(b), use_hash);
}
lean_unreachable(); // LCOV_EXCL_LINE
}
bool is_lt_no_level_params(level const & a, level const & b) {
if (is_eqp(a, b)) return false;
if (kind(a) != kind(b)) {
if (kind(a) == level_kind::Param || kind(b) == level_kind::Param)
return false;
return kind(a) < kind(b);
}
switch (kind(a)) {
case level_kind::Zero:
lean_unreachable(); // LCOV_EXCL_LINE
case level_kind::Param:
return false;
case level_kind::Global:
return global_id(a) < global_id(b);
case level_kind::Meta:
return meta_id(a) < meta_id(b);
case level_kind::Max:
if (is_lt_no_level_params(max_lhs(a), max_lhs(b)))
return true;
else if (is_lt_no_level_params(max_lhs(b), max_lhs(a)))
return false;
else
return is_lt_no_level_params(max_rhs(a), max_rhs(b));
case level_kind::IMax:
if (is_lt_no_level_params(imax_lhs(a), imax_lhs(b)))
return true;
else if (is_lt_no_level_params(imax_lhs(b), imax_lhs(a)))
return false;
else
return is_lt_no_level_params(imax_rhs(a), imax_rhs(b));
case level_kind::Succ:
return is_lt_no_level_params(succ_of(a), succ_of(b));
}
lean_unreachable();
}
bool operator==(level const & l1, level const & l2) {
if (kind(l1) != kind(l2)) return false;
if (hash(l1) != hash(l2)) return false;
if (is_eqp(l1, l2)) return true;
switch (kind(l1)) {
case level_kind::Zero:
return true;
case level_kind::Param: case level_kind::Global: case level_kind::Meta:
return to_param_core(l1).m_id == to_param_core(l2).m_id;
case level_kind::Max: case level_kind::IMax: case level_kind::Succ:
if (to_composite(l1).m_depth != to_composite(l2).m_depth)
return false;
break;
}
switch (kind(l1)) {
case level_kind::Zero: case level_kind::Param: case level_kind::Global: case level_kind::Meta:
lean_unreachable(); // LCOV_EXCL_LINE
case level_kind::Max: case level_kind::IMax:
return
to_max_core(l1).m_lhs == to_max_core(l2).m_lhs &&
to_max_core(l1).m_rhs == to_max_core(l2).m_rhs;
case level_kind::Succ:
if (is_explicit(l1) != is_explicit(l2)) {
return false;
} else if (is_explicit(l1)) {
lean_assert(get_depth(l1) == get_depth(l2));
// the depths are equal, then l1 and l2 must be the same universe
return true;
} else {
return succ_of(l1) == succ_of(l2);
}
}
lean_unreachable(); // LCOV_EXCL_LINE
}
unsigned level_cases_on(vm_obj const & o, buffer<vm_obj> & data) {
level const & l = to_level(o);
switch (l.kind()) {
case level_kind::Zero:
break;
case level_kind::Succ:
data.push_back(to_obj(succ_of(l)));
break;
case level_kind::Max:
data.push_back(to_obj(max_lhs(l)));
data.push_back(to_obj(max_rhs(l)));
break;
case level_kind::IMax:
data.push_back(to_obj(imax_lhs(l)));
data.push_back(to_obj(imax_rhs(l)));
break;
case level_kind::Param:
data.push_back(to_obj(param_id(l)));
break;
case level_kind::Global:
data.push_back(to_obj(global_id(l)));
break;
case level_kind::Meta:
data.push_back(to_obj(meta_id(l)));
break;
}
return static_cast<unsigned>(l.kind());
}
static void print(std::ostream & out, level l) {
if (is_explicit(l)) {
lean_assert(get_depth(l) > 0);
out << get_depth(l) - 1;
} else {
switch (kind(l)) {
case level_kind::Zero:
lean_unreachable(); // LCOV_EXCL_LINE
case level_kind::Param: case level_kind::Global:
out << to_param_core(l).m_id; break;
case level_kind::Meta:
out << "?" << meta_id(l); break;
case level_kind::Succ:
out << "succ "; print_child(out, succ_of(l)); break;
case level_kind::Max: case level_kind::IMax:
if (is_max(l))
out << "max ";
else
out << "imax ";
print_child(out, to_max_core(l).m_lhs);
// max and imax are right associative
while (kind(to_max_core(l).m_rhs) == kind(l)) {
l = to_max_core(l).m_rhs;
out << " ";
print_child(out, to_max_core(l).m_lhs);
}
out << " ";
print_child(out, to_max_core(l).m_rhs);
break;
}
}
}
/** \brief Convert (succ^k l) into (l, k). If l is not a succ, then return (l, 0) */
pair<level, unsigned> to_offset(level l) {
unsigned k = 0;
while (is_succ(l)) {
l = succ_of(l);
k++;
}
return mk_pair(l, k);
}
void for_each_level_fn::apply(level const & l) {
if (!m_f(l))
return;
switch (l.kind()) {
case level_kind::Succ: apply(succ_of(l)); break;
case level_kind::Max: case level_kind::IMax: apply(to_max_core(l).m_lhs); apply(to_max_core(l).m_rhs); break;
case level_kind::Zero: case level_kind::Param:
case level_kind::Meta: case level_kind::Global: break;
}
}
level replace_level_fn::apply(level const & l) {
optional<level> r = m_f(l);
if (r)
return *r;
switch (l.kind()) {
case level_kind::Succ:
return update_succ(l, apply(succ_of(l)));
case level_kind::Max: case level_kind::IMax:
return update_max(l, apply(to_max_core(l).m_lhs), apply(to_max_core(l).m_rhs));
case level_kind::Zero: case level_kind::Param: case level_kind::Meta: case level_kind::Global:
return l;
}
lean_unreachable(); // LCOV_EXCL_LINE
}
level apply(level const & l) {
auto r = m_lvl_cache.find(l);
if (r != m_lvl_cache.end())
return *r;
level res;
switch (l.kind()) {
case level_kind::Zero: case level_kind::Param:
case level_kind::Global: case level_kind::Meta:
res = l;
break;
case level_kind::Succ:
res = update_succ(l, apply(succ_of(l)));
break;
case level_kind::Max:
res = update_max(l, apply(max_lhs(l)), apply(max_rhs(l)));
break;
case level_kind::IMax:
res = update_max(l, apply(imax_lhs(l)), apply(imax_rhs(l)));
break;
}
m_lvl_cache.insert(res);
return res;
}
level update_succ(level const & l, level const & new_arg) {
if (is_eqp(succ_of(l), new_arg))
return l;
else
return mk_succ(new_arg);
}
