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();
}
bool is_arrow(expr const & t) {
return is_pi(t) && !has_free_var(abst_body(t), 0);
}
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
}
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
}
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);
}