expr dsimplify_core_fn::visit_let(expr const & e) {
if (m_cfg.m_zeta) {
return visit(instantiate(let_body(e), let_value(e)));
} else {
type_context::tmp_locals locals(m_ctx);
expr b = e;
bool modified = false;
while (is_let(b)) {
expr t = instantiate_rev(let_type(b), locals.size(), locals.data());
expr v = instantiate_rev(let_value(b), locals.size(), locals.data());
expr new_t = visit(t);
expr new_v = visit(v);
if (!is_eqp(t, new_t) || !is_eqp(v, new_v)) modified = true;
locals.push_let(let_name(b), new_t, new_v);
b = let_body(b);
}
b = instantiate_rev(b, locals.size(), locals.data());
expr new_b = visit(b);
if (!is_eqp(b, new_b)) modified = true;
if (modified)
return locals.mk_lambda(new_b);
else
return e;
}
}
bool apply(expr const & a, expr const & b) {
if (is_eqp(a, b)) return true;
if (a.hash() != b.hash()) return false;
if (a.kind() != b.kind()) return false;
if (is_var(a)) return var_idx(a) == var_idx(b);
if (m_cache.check(a, b))
return true;
switch (a.kind()) {
case expr_kind::Var:
lean_unreachable(); // LCOV_EXCL_LINE
case expr_kind::Constant:
return
const_name(a) == const_name(b) &&
compare(const_levels(a), const_levels(b), [](level const & l1, level const & l2) { return l1 == l2; });
case expr_kind::Meta:
return
mlocal_name(a) == mlocal_name(b) &&
apply(mlocal_type(a), mlocal_type(b));
case expr_kind::Local:
return
mlocal_name(a) == mlocal_name(b) &&
apply(mlocal_type(a), mlocal_type(b)) &&
(!CompareBinderInfo || local_pp_name(a) == local_pp_name(b)) &&
(!CompareBinderInfo || local_info(a) == local_info(b));
case expr_kind::App:
check_system();
return
apply(app_fn(a), app_fn(b)) &&
apply(app_arg(a), app_arg(b));
case expr_kind::Lambda: case expr_kind::Pi:
check_system();
return
apply(binding_domain(a), binding_domain(b)) &&
apply(binding_body(a), binding_body(b)) &&
(!CompareBinderInfo || binding_name(a) == binding_name(b)) &&
(!CompareBinderInfo || binding_info(a) == binding_info(b));
case expr_kind::Let:
check_system();
return
apply(let_type(a), let_type(b)) &&
apply(let_value(a), let_value(b)) &&
apply(let_body(a), let_body(b)) &&
(!CompareBinderInfo || let_name(a) == let_name(b));
case expr_kind::Sort:
return sort_level(a) == sort_level(b);
case expr_kind::Macro:
check_system();
if (macro_def(a) != macro_def(b) || macro_num_args(a) != macro_num_args(b))
return false;
for (unsigned i = 0; i < macro_num_args(a); i++) {
if (!apply(macro_arg(a, i), macro_arg(b, i)))
return false;
}
return true;
}
lean_unreachable(); // LCOV_EXCL_LINE
}
bool is_lt(expr const & a, expr const & b, bool use_hash) {
if (is_eqp(a, b)) return false;
unsigned wa = get_weight(a);
unsigned wb = get_weight(b);
if (wa < wb) return true;
if (wa > wb) return false;
if (a.kind() != b.kind()) return a.kind() < b.kind();
if (use_hash) {
if (a.hash() < b.hash()) return true;
if (a.hash() > b.hash()) return false;
}
if (a == b) return false;
switch (a.kind()) {
case expr_kind::Var:
return var_idx(a) < var_idx(b);
case expr_kind::Constant:
if (const_name(a) != const_name(b))
return const_name(a) < const_name(b);
else
return is_lt(const_levels(a), const_levels(b), use_hash);
case expr_kind::App:
if (app_fn(a) != app_fn(b))
return is_lt(app_fn(a), app_fn(b), use_hash);
else
return is_lt(app_arg(a), app_arg(b), use_hash);
case expr_kind::Lambda: case expr_kind::Pi:
if (binding_domain(a) != binding_domain(b))
return is_lt(binding_domain(a), binding_domain(b), use_hash);
else
return is_lt(binding_body(a), binding_body(b), use_hash);
case expr_kind::Let:
if (let_type(a) != let_type(b))
return is_lt(let_type(a), let_type(b), use_hash);
else if (let_value(a) != let_value(b))
return is_lt(let_value(a), let_value(b), use_hash);
else
return is_lt(let_body(a), let_body(b), use_hash);
case expr_kind::Sort:
return is_lt(sort_level(a), sort_level(b), use_hash);
case expr_kind::Local: case expr_kind::Meta:
if (mlocal_name(a) != mlocal_name(b))
return mlocal_name(a) < mlocal_name(b);
else
return is_lt(mlocal_type(a), mlocal_type(b), use_hash);
case expr_kind::Macro:
if (macro_def(a) != macro_def(b))
return macro_def(a) < macro_def(b);
if (macro_num_args(a) != macro_num_args(b))
return macro_num_args(a) < macro_num_args(b);
for (unsigned i = 0; i < macro_num_args(a); i++) {
if (macro_arg(a, i) != macro_arg(b, i))
return is_lt(macro_arg(a, i), macro_arg(b, i), use_hash);
}
return false;
}
lean_unreachable(); // LCOV_EXCL_LINE
}
bool expr_eq_fn::apply(expr const & a, expr const & b) {
if (is_eqp(a, b)) return true;
if (a.hash() != b.hash()) return false;
if (a.kind() != b.kind()) return false;
if (is_var(a)) return var_idx(a) == var_idx(b);
if (m_counter >= LEAN_EQ_CACHE_THRESHOLD && is_shared(a) && is_shared(b)) {
auto p = std::make_pair(a.raw(), b.raw());
if (!m_eq_visited)
m_eq_visited.reset(new expr_cell_pair_set);
if (m_eq_visited->find(p) != m_eq_visited->end())
return true;
m_eq_visited->insert(p);
}
check_system("expression equality test");
switch (a.kind()) {
case expr_kind::Var:
lean_unreachable(); // LCOV_EXCL_LINE
case expr_kind::Constant:
return
const_name(a) == const_name(b) &&
compare(const_levels(a), const_levels(b), [](level const & l1, level const & l2) { return l1 == l2; });
case expr_kind::Local: case expr_kind::Meta:
return
mlocal_name(a) == mlocal_name(b) &&
apply(mlocal_type(a), mlocal_type(b));
case expr_kind::App:
m_counter++;
return
apply(app_fn(a), app_fn(b)) &&
apply(app_arg(a), app_arg(b));
case expr_kind::Lambda: case expr_kind::Pi:
m_counter++;
return
apply(binding_domain(a), binding_domain(b)) &&
apply(binding_body(a), binding_body(b)) &&
(!m_compare_binder_info || binding_info(a) == binding_info(b));
case expr_kind::Sort:
return sort_level(a) == sort_level(b);
case expr_kind::Macro:
m_counter++;
if (macro_def(a) != macro_def(b) || macro_num_args(a) != macro_num_args(b))
return false;
for (unsigned i = 0; i < macro_num_args(a); i++) {
if (!apply(macro_arg(a, i), macro_arg(b, i)))
return false;
}
return true;
case expr_kind::Let:
m_counter++;
return
apply(let_type(a), let_type(b)) &&
apply(let_value(a), let_value(b)) &&
apply(let_body(a), let_body(b));
}
lean_unreachable(); // LCOV_EXCL_LINE
}
expr replace_visitor::visit_let(expr const & e) {
lean_assert(is_let(e));
expr new_t = visit(let_type(e));
expr new_v = visit(let_value(e));
expr new_b = visit(let_body(e));
return update_let(e, new_t, new_v, new_b);
}
expr copy(expr const & a) {
switch (a.kind()) {
case expr_kind::Var: return mk_var(var_idx(a));
case expr_kind::Constant: return mk_constant(const_name(a));
case expr_kind::Type: return mk_type(ty_level(a));
case expr_kind::Value: return mk_value(static_cast<expr_value*>(a.raw())->m_val);
case expr_kind::App: return mk_app(num_args(a), begin_args(a));
case expr_kind::Eq: return mk_eq(eq_lhs(a), eq_rhs(a));
case expr_kind::Lambda: return mk_lambda(abst_name(a), abst_domain(a), abst_body(a));
case expr_kind::Pi: return mk_pi(abst_name(a), abst_domain(a), abst_body(a));
case expr_kind::Let: return mk_let(let_name(a), let_type(a), let_value(a), let_body(a));
case expr_kind::MetaVar: return mk_metavar(metavar_idx(a), metavar_ctx(a));
}
lean_unreachable();
}
expr apply(expr const & a) {
check_system("max_sharing");
auto r = m_expr_cache.find(a);
if (r != m_expr_cache.end())
return *r;
expr res;
switch (a.kind()) {
case expr_kind::Var:
res = a;
break;
case expr_kind::Constant:
res = update_constant(a, map(const_levels(a), [&](level const & l) { return apply(l); }));
break;
case expr_kind::Sort:
res = update_sort(a, apply(sort_level(a)));
break;
case expr_kind::App: {
expr new_f = apply(app_fn(a));
expr new_a = apply(app_arg(a));
res = update_app(a, new_f, new_a);
break;
}
case expr_kind::Lambda: case expr_kind::Pi: {
expr new_d = apply(binding_domain(a));
expr new_b = apply(binding_body(a));
res = update_binding(a, new_d, new_b);
break;
}
case expr_kind::Let: {
expr new_t = apply(let_type(a));
expr new_v = apply(let_value(a));
expr new_b = apply(let_body(a));
res = update_let(a, new_t, new_v, new_b);
break;
}
case expr_kind::Meta: case expr_kind::Local:
res = update_mlocal(a, apply(mlocal_type(a)));
break;
case expr_kind::Macro: {
buffer<expr> new_args;
for (unsigned i = 0; i < macro_num_args(a); i++)
new_args.push_back(macro_arg(a, i));
res = update_macro(a, new_args.size(), new_args.data());
break;
}}
m_expr_cache.insert(res);
return res;
}
void collect_locals(expr const & e, collected_locals & ls, bool restricted) {
if (!has_local(e))
return;
expr_set visited;
std::function<void(expr const & e)> visit = [&](expr const & e) {
if (!has_local(e))
return;
if (restricted && is_meta(e))
return;
if (visited.find(e) != visited.end())
return;
visited.insert(e);
switch (e.kind()) {
case expr_kind::Var: case expr_kind::Constant: case expr_kind::Sort:
break; // do nothing
case expr_kind::Local:
if (!restricted)
visit(mlocal_type(e));
ls.insert(e);
break;
case expr_kind::Meta:
lean_assert(!restricted);
visit(mlocal_type(e));
break;
case expr_kind::Macro:
for (unsigned i = 0; i < macro_num_args(e); i++)
visit(macro_arg(e, i));
break;
case expr_kind::App:
visit(app_fn(e));
visit(app_arg(e));
break;
case expr_kind::Lambda:
case expr_kind::Pi:
visit(binding_domain(e));
visit(binding_body(e));
break;
case expr_kind::Let:
visit(let_type(e));
visit(let_value(e));
visit(let_body(e));
break;
}
};
visit(e);
}
expr compiler_step_visitor::visit_lambda_let(expr const & e) {
type_context::tmp_locals locals(m_ctx);
expr t = e;
while (true) {
/* Types are ignored in compilation steps. So, we do not invoke visit for d. */
if (is_lambda(t)) {
expr d = instantiate_rev(binding_domain(t), locals.size(), locals.data());
locals.push_local(binding_name(t), d, binding_info(t));
t = binding_body(t);
} else if (is_let(t)) {
expr d = instantiate_rev(let_type(t), locals.size(), locals.data());
expr v = visit(instantiate_rev(let_value(t), locals.size(), locals.data()));
locals.push_let(let_name(t), d, v);
t = let_body(t);
} else {
break;
}
}
t = instantiate_rev(t, locals.size(), locals.data());
t = visit(t);
return copy_tag(e, locals.mk_lambda(t));
}
expr visit_let(expr const & e) {
// TODO(Leo): improve
return visit(instantiate(let_body(e), let_value(e)));
}
expr update_let(expr const & e, expr const & new_type, expr const & new_value, expr const & new_body) {
if (!is_eqp(let_type(e), new_type) || !is_eqp(let_value(e), new_value) || !is_eqp(let_body(e), new_body))
return mk_let(let_name(e), new_type, new_value, new_body);
else
return e;
}
void visit_let(expr const & e) {
if (should_visit(e)) {
visit(instantiate(let_body(e), let_value(e)));
}
}
bool is_lt(expr const & a, expr 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 (a.kind() != b.kind()) return a.kind() < b.kind();
if (use_hash) {
if (a.hash() < b.hash()) return true;
if (a.hash() > b.hash()) return false;
}
if (a == b) return false;
if (is_var(a)) return var_idx(a) < var_idx(b);
switch (a.kind()) {
case expr_kind::Var:
lean_unreachable(); // LCOV_EXCL_LINE
case expr_kind::Constant:
return const_name(a) < const_name(b);
case expr_kind::App:
if (num_args(a) != num_args(b))
return num_args(a) < num_args(b);
for (unsigned i = 0; i < num_args(a); i++) {
if (arg(a, i) != arg(b, i))
return is_lt(arg(a, i), arg(b, i), use_hash);
}
lean_unreachable(); // LCOV_EXCL_LINE
case expr_kind::Lambda: // Remark: we ignore get_abs_name because we want alpha-equivalence
case expr_kind::Pi:
if (abst_domain(a) != abst_domain(b))
return is_lt(abst_domain(a), abst_domain(b), use_hash);
else
return is_lt(abst_body(a), abst_body(b), use_hash);
case expr_kind::Type:
return ty_level(a) < ty_level(b);
case expr_kind::Value:
return to_value(a) < to_value(b);
case expr_kind::Let:
if (let_type(a) != let_type(b)) {
return is_lt(let_type(a), let_type(b), use_hash);
} else if (let_value(a) != let_value(b)){
return is_lt(let_value(a), let_value(b), use_hash);
} else {
return is_lt(let_body(a), let_body(b), use_hash);
}
case expr_kind::MetaVar:
if (metavar_name(a) != metavar_name(b)) {
return metavar_name(a) < metavar_name(b);
} else {
auto it1 = metavar_lctx(a).begin();
auto it2 = metavar_lctx(b).begin();
auto end1 = metavar_lctx(a).end();
auto end2 = metavar_lctx(b).end();
for (; it1 != end1 && it2 != end2; ++it1, ++it2) {
if (it1->kind() != it2->kind()) {
return it1->kind() < it2->kind();
} else if (it1->s() != it2->s()) {
return it1->s() < it2->s();
} else if (it1->is_inst()) {
if (it1->v() != it2->v())
return is_lt(it1->v(), it2->v(), use_hash);
} else {
if (it1->n() != it2->n())
return it1->n() < it2->n();
}
}
return it1 == end1 && it2 != end2;
}
}
lean_unreachable(); // LCOV_EXCL_LINE
}
expr apply(expr const & a) {
bool sh = false;
if (is_shared(a)) {
auto r = m_cache.find(a.raw());
if (r != m_cache.end())
return r->second;
sh = true;
}
switch (a.kind()) {
case expr_kind::Var: case expr_kind::Constant: case expr_kind::Type: case expr_kind::Value:
return save_result(a, copy(a), sh);
case expr_kind::App: {
buffer<expr> new_args;
for (expr const & old_arg : args(a))
new_args.push_back(apply(old_arg));
return save_result(a, mk_app(new_args), sh);
}
case expr_kind::HEq: return save_result(a, mk_heq(apply(heq_lhs(a)), apply(heq_rhs(a))), sh);
case expr_kind::Pair: return save_result(a, mk_pair(apply(pair_first(a)), apply(pair_second(a)), apply(pair_type(a))), sh);
case expr_kind::Proj: return save_result(a, mk_proj(proj_first(a), apply(proj_arg(a))), sh);
case expr_kind::Lambda: return save_result(a, mk_lambda(abst_name(a), apply(abst_domain(a)), apply(abst_body(a))), sh);
case expr_kind::Pi: return save_result(a, mk_pi(abst_name(a), apply(abst_domain(a)), apply(abst_body(a))), sh);
case expr_kind::Sigma: return save_result(a, mk_sigma(abst_name(a), apply(abst_domain(a)), apply(abst_body(a))), sh);
case expr_kind::Let: return save_result(a, mk_let(let_name(a), apply(let_type(a)), apply(let_value(a)), apply(let_body(a))), sh);
case expr_kind::MetaVar:
return save_result(a,
update_metavar(a, [&](local_entry const & e) -> local_entry {
if (e.is_inst())
return mk_inst(e.s(), apply(e.v()));
else
return e;
}),
sh);
}
lean_unreachable(); // LCOV_EXCL_LINE
}
optional<substitution> fo_unify(expr e1, expr e2) {
substitution s;
unsigned i1, i2;
buffer<expr_pair> todo;
todo.emplace_back(e1, e2);
while (!todo.empty()) {
auto p = todo.back();
todo.pop_back();
e1 = find(s, p.first);
e2 = find(s, p.second);
if (e1 != e2) {
if (is_metavar_wo_local_context(e1)) {
assign(s, e1, e2);
} else if (is_metavar_wo_local_context(e2)) {
assign(s, e2, e1);
} else if (is_equality(e1) && is_equality(e2)) {
expr_pair p1 = get_equality_args(e1);
expr_pair p2 = get_equality_args(e2);
todo.emplace_back(p1.second, p2.second);
todo.emplace_back(p1.first, p2.first);
} else {
if (e1.kind() != e2.kind())
return optional<substitution>();
switch (e1.kind()) {
case expr_kind::Var: case expr_kind::Constant: case expr_kind::Type: case expr_kind::Value: case expr_kind::MetaVar:
return optional<substitution>();
case expr_kind::App:
i1 = num_args(e1);
i2 = num_args(e2);
while (i1 > 0 && i2 > 0) {
--i1;
--i2;
if (i1 == 0 && i2 > 0) {
todo.emplace_back(arg(e1, i1), mk_app(i2+1, begin_args(e2)));
} else if (i2 == 0 && i1 > 0) {
todo.emplace_back(mk_app(i1+1, begin_args(e1)), arg(e2, i2));
} else {
todo.emplace_back(arg(e1, i1), arg(e2, i2));
}
}
break;
case expr_kind::Lambda: case expr_kind::Pi:
todo.emplace_back(abst_body(e1), abst_body(e2));
todo.emplace_back(abst_domain(e1), abst_domain(e2));
break;
case expr_kind::Let:
todo.emplace_back(let_body(e1), let_body(e2));
todo.emplace_back(let_value(e1), let_value(e2));
if (static_cast<bool>(let_type(e1)) != static_cast<bool>(let_type(e2)))
return optional<substitution>();
if (let_type(e1)) {
lean_assert(let_type(e2));
todo.emplace_back(*let_type(e1), *let_type(e2));
}
break;
}
}
}
}
return optional<substitution>(s);
}