bool match_pattern(type_checker & tc, expr const & pattern, declaration const & d, unsigned max_steps, bool cheap) {
name_generator ngen = tc.mk_ngen();
buffer<level> ls;
unsigned num_ls = d.get_num_univ_params();
for (unsigned i = 0; i < num_ls; i++)
ls.push_back(mk_meta_univ(ngen.next()));
expr dt = instantiate_type_univ_params(d, to_list(ls.begin(), ls.end()));
unsigned num_e = get_expect_num_args(tc, pattern);
unsigned num_d = get_expect_num_args(tc, dt);
if (num_e > num_d)
return false;
for (unsigned i = 0; i < num_d - num_e; i++) {
dt = tc.whnf(dt).first;
expr local = mk_local(ngen.next(), binding_domain(dt));
dt = instantiate(binding_body(dt), local);
}
try {
unifier_config cfg;
cfg.m_max_steps = max_steps;
cfg.m_kind = cheap ? unifier_kind::Cheap : unifier_kind::Liberal;
cfg.m_ignore_context_check = true;
auto r = unify(tc.env(), pattern, dt, tc.mk_ngen(), substitution(), cfg);
return static_cast<bool>(r.pull());
} catch (exception&) {
return false;
}
}
bool is_ceqv(type_checker & tc, expr e) {
if (has_expr_metavar(e))
return false;
name_set to_find;
// Define a procedure for removing arguments from to_find.
auto visitor_fn = [&](expr const & e, unsigned) {
if (is_local(e)) {
to_find.erase(mlocal_name(e));
return false;
} else if (is_metavar(e)) {
return false;
} else {
return true;
}
};
environment const & env = tc.env();
bool is_std = is_standard(env);
buffer<expr> hypotheses; // arguments that are propositions
while (is_pi(e)) {
if (!to_find.empty()) {
// Support for dependent types.
// We may find the instantiation for the previous arguments
// by matching the type.
for_each(binding_domain(e), visitor_fn);
}
expr local = mk_local(tc.mk_fresh_name(), binding_domain(e));
if (binding_info(e).is_inst_implicit()) {
// If the argument can be instantiated by type class resolution, then
// we don't need to find it in the lhs
} else if (is_std && tc.is_prop(binding_domain(e)).first) {
// If the argument is a proposition, we store it in hypotheses.
// We check whether the lhs occurs in hypotheses or not.
hypotheses.push_back(binding_domain(e));
} else {
to_find.insert(mlocal_name(local));
}
e = instantiate(binding_body(e), local);
}
expr lhs, rhs;
if (!is_simp_relation(env, e, lhs, rhs))
return false;
// traverse lhs, and remove found variables from to_find
for_each(lhs, visitor_fn);
if (!to_find.empty())
return false;
// basic looping ceq detection: the left-hand-side should not occur in the right-hand-side,
// nor it should occur in any of the hypothesis
if (occurs(lhs, rhs))
return false;
if (std::any_of(hypotheses.begin(), hypotheses.end(), [&](expr const & h) { return occurs(lhs, h); }))
return false;
return true;
}
list<expr> get_coercions_from_to(type_checker & from_tc, type_checker & to_tc,
expr const & from_type, expr const & to_type, constraint_seq & cs, bool lift_coe) {
constraint_seq new_cs;
environment const & env = to_tc.env();
expr whnf_from_type = from_tc.whnf(from_type, new_cs);
expr whnf_to_type = to_tc.whnf(to_type, new_cs);
if (lift_coe && is_pi(whnf_from_type)) {
// Try to lift coercions.
// The idea is to convert a coercion from A to B, into a coercion from D->A to D->B
if (!is_pi(whnf_to_type))
return list<expr>(); // failed
if (!from_tc.is_def_eq(binding_domain(whnf_from_type), binding_domain(whnf_to_type), justification(), new_cs))
return list<expr>(); // failed, the domains must be definitionally equal
expr x = mk_local(mk_fresh_name(), "x", binding_domain(whnf_from_type), binder_info());
expr A = instantiate(binding_body(whnf_from_type), x);
expr B = instantiate(binding_body(whnf_to_type), x);
list<expr> coe = get_coercions_from_to(from_tc, to_tc, A, B, new_cs, lift_coe);
if (coe) {
cs += new_cs;
// Remark: each coercion c in coe is a function from A to B
// We create a new list: (fun (f : D -> A) (x : D), c (f x))
expr f = mk_local(mk_fresh_name(), "f", whnf_from_type, binder_info());
expr fx = mk_app(f, x);
return map(coe, [&](expr const & c) { return Fun(f, Fun(x, mk_app(c, fx))); });
} else {
return list<expr>();
}
} else {
expr const & fn = get_app_fn(whnf_to_type);
list<expr> r;
if (is_constant(fn)) {
r = get_coercions(env, whnf_from_type, const_name(fn));
} else if (is_pi(whnf_to_type)) {
r = get_coercions_to_fun(env, whnf_from_type);
} else if (is_sort(whnf_to_type)) {
r = get_coercions_to_sort(env, whnf_from_type);
}
if (r)
cs += new_cs;
return r;
}
}
optional<expr> projection_converter::is_stuck(expr const & e, type_checker & c) {
projection_info const * info = is_projection(e);
if (!info)
return default_converter::is_stuck(e, c);
buffer<expr> args;
get_app_args(e, args);
if (args.size() <= info->m_nparams)
return none_expr();
expr mk = whnf(args[info->m_nparams], c).first;
return c.is_stuck(mk);
}
static simp_rule_sets add_core(type_checker & tc, simp_rule_sets const & s, name const & cname) {
declaration const & d = tc.env().get(cname);
buffer<level> us;
unsigned num_univs = d.get_num_univ_params();
for (unsigned i = 0; i < num_univs; i++) {
us.push_back(mk_meta_univ(name(*g_prefix, i)));
}
levels ls = to_list(us);
expr e = instantiate_type_univ_params(d, ls);
expr h = mk_constant(cname, ls);
return add_core(tc, s, cname, ls, e, h);
}
expr visit_macro(expr const & e) {
buffer<expr> new_args;
for (unsigned i = 0; i < macro_num_args(e); i++)
new_args.push_back(visit(macro_arg(e, i)));
auto def = macro_def(e);
expr r = update_macro(e, new_args.size(), new_args.data());
if (def.trust_level() >= m_trust_lvl) {
if (optional<expr> new_r = m_tc.expand_macro(r)) {
return *new_r;
} else {
throw_generic_exception("failed to expand macro", e);
}
} else {
return r;
}
}
expr extract(expr const & e) {
lean_assert(is_nested_declaration(e));
expr const & d = visit(get_nested_declaration_arg(e));
name new_name = mk_name_for(e);
name new_real_name = get_namespace(m_env) + new_name;
collected_locals locals;
collect_locals(d, locals);
buffer<name> uparams;
collect_univ_params(d).to_buffer(uparams);
expr new_value = Fun(locals.get_collected(), d);
expr new_type = m_tc.infer(new_value).first;
level_param_names new_ps = to_list(uparams);
levels ls = param_names_to_levels(new_ps);
m_env = module::add(m_env, check(m_env, mk_definition(m_env, new_real_name, new_ps,
new_type, new_value)));
if (new_name != new_real_name)
m_env = add_expr_alias_rec(m_env, new_name, new_real_name);
decl_attributes const & attrs = get_nested_declaration_attributes(e);
m_env = attrs.apply(m_env, m_ios, new_real_name, get_namespace(m_env));
return mk_app(mk_constant(new_real_name, ls), locals.get_collected());
}
expr visit_binding(expr e) {
expr_kind k = e.kind();
buffer<expr> es;
buffer<expr> ls;
while (e.kind() == k) {
expr d = visit(instantiate_rev(binding_domain(e), ls.size(), ls.data()));
expr l = mk_local(m_tc.mk_fresh_name(), binding_name(e), d, binding_info(e));
ls.push_back(l);
es.push_back(e);
e = binding_body(e);
}
e = visit(instantiate_rev(e, ls.size(), ls.data()));
expr r = abstract_locals(e, ls.size(), ls.data());
while (!ls.empty()) {
expr d = mlocal_type(ls.back());
ls.pop_back();
d = abstract_locals(d, ls.size(), ls.data());
r = update_binding(es.back(), d, r);
es.pop_back();
}
return r;
}
simp_rule_sets add_core(type_checker & tc, simp_rule_sets const & s,
name const & id, levels const & univ_metas, expr const & e, expr const & h) {
list<expr_pair> ceqvs = to_ceqvs(tc, e, h);
environment const & env = tc.env();
simp_rule_sets new_s = s;
for (expr_pair const & p : ceqvs) {
expr new_e = p.first;
expr new_h = p.second;
bool is_perm = is_permutation_ceqv(env, new_e);
buffer<expr> metas;
unsigned idx = 0;
while (is_pi(new_e)) {
expr mvar = mk_metavar(name(*g_prefix, idx), binding_domain(new_e));
idx++;
metas.push_back(mvar);
new_e = instantiate(binding_body(new_e), mvar);
}
expr rel, lhs, rhs;
if (is_simp_relation(env, new_e, rel, lhs, rhs) && is_constant(rel)) {
new_s.insert(const_name(rel), simp_rule(id, univ_metas, to_list(metas), lhs, rhs, new_h, is_perm));
}
}
return new_s;
}
optional<expr> mk_hset_instance(type_checker & tc, io_state const & ios, list<expr> const & ctx, expr const & type) {
expr trunc_index = mk_app(mk_constant(get_is_trunc_trunc_index_of_nat_name()), mk_constant(get_nat_zero_name()));
level lvl = sort_level(tc.ensure_type(type).first);
expr is_hset = mk_app(mk_constant(get_is_trunc_name(), {lvl}), trunc_index, type);
return mk_class_instance(tc.env(), ios, ctx, tc.mk_fresh_name(), is_hset);
}
/** \brief Given a term <tt>a : a_type</tt>, and a metavariable \c m, creates a constraint
that considers coercions from a_type to the type assigned to \c m. */
constraint mk_coercion_cnstr(type_checker & from_tc, type_checker & to_tc, coercion_info_manager & infom,
expr const & m, expr const & a, expr const & a_type,
justification const & j, unsigned delay_factor, bool lift_coe) {
auto choice_fn = [=, &from_tc, &to_tc, &infom](expr const & meta, expr const & d_type, substitution const & s) {
expr new_a_type;
justification new_a_type_jst;
if (is_meta(a_type)) {
auto p = substitution(s).instantiate_metavars(a_type);
new_a_type = p.first;
new_a_type_jst = p.second;
} else {
new_a_type = a_type;
}
if (is_meta(new_a_type)) {
if (delay_factor < to_delay_factor(cnstr_group::DelayedChoice)) {
// postpone...
return lazy_list<constraints>(constraints(mk_coercion_cnstr(from_tc, to_tc, infom, m, a, a_type, justification(),
delay_factor+1, lift_coe)));
} else {
// giveup...
return lazy_list<constraints>(constraints(mk_eq_cnstr(meta, a, justification())));
}
}
constraint_seq cs;
new_a_type = from_tc.whnf(new_a_type, cs);
if ((lift_coe && is_pi_meta(d_type)) || (!lift_coe && is_meta(d_type))) {
// case-split
buffer<expr> locals;
expr it_from = new_a_type;
expr it_to = d_type;
while (is_pi(it_from) && is_pi(it_to)) {
expr dom_from = binding_domain(it_from);
expr dom_to = binding_domain(it_to);
if (!from_tc.is_def_eq(dom_from, dom_to, justification(), cs))
return lazy_list<constraints>();
expr local = mk_local(mk_fresh_name(), binding_name(it_from), dom_from, binder_info());
locals.push_back(local);
it_from = instantiate(binding_body(it_from), local);
it_to = instantiate(binding_body(it_to), local);
}
buffer<expr> alts;
get_coercions_from(from_tc.env(), it_from, alts);
expr fn_a;
if (!locals.empty())
fn_a = mk_local(mk_fresh_name(), "f", new_a_type, binder_info());
buffer<constraints> choices;
buffer<expr> coes;
// first alternative: no coercion
constraint_seq cs1 = cs + mk_eq_cnstr(meta, a, justification());
choices.push_back(cs1.to_list());
unsigned i = alts.size();
while (i > 0) {
--i;
expr coe = alts[i];
if (!locals.empty())
coe = Fun(fn_a, Fun(locals, mk_app(coe, mk_app(fn_a, locals))));
expr new_a = copy_tag(a, mk_app(coe, a));
coes.push_back(coe);
constraint_seq csi = cs + mk_eq_cnstr(meta, new_a, new_a_type_jst);
choices.push_back(csi.to_list());
}
return choose(std::make_shared<coercion_elaborator>(infom, meta,
to_list(choices.begin(), choices.end()),
to_list(coes.begin(), coes.end())));
} else {
list<expr> coes = get_coercions_from_to(from_tc, to_tc, new_a_type, d_type, cs, lift_coe);
if (is_nil(coes)) {
expr new_a = a;
infom.erase_coercion_info(a);
cs += mk_eq_cnstr(meta, new_a, new_a_type_jst);
return lazy_list<constraints>(cs.to_list());
} else if (is_nil(tail(coes))) {
expr new_a = copy_tag(a, mk_app(head(coes), a));
infom.save_coercion_info(a, new_a);
cs += mk_eq_cnstr(meta, new_a, new_a_type_jst);
return lazy_list<constraints>(cs.to_list());
} else {
list<constraints> choices = map2<constraints>(coes, [&](expr const & coe) {
expr new_a = copy_tag(a, mk_app(coe, a));
constraint c = mk_eq_cnstr(meta, new_a, new_a_type_jst);
return (cs + c).to_list();
});
return choose(std::make_shared<coercion_elaborator>(infom, meta, choices, coes, false));
}
}
};
return mk_choice_cnstr(m, choice_fn, delay_factor, true, j);
}
std::cout << "expected error: " << ex.pp(mk_formatter(ex.get_environment())) << "\n";
}
try {
auto env7 = add_decl(env2, mk_definition("foo", level_param_names(), mk_Type() >> mk_Type(), mk_Prop()));
lean_unreachable();
} catch (kernel_exception & ex) {
std::cout << "expected error: " << ex.pp(mk_formatter(ex.get_environment())) << "\n";
}
expr A = Local("A", Type);
expr x = Local("x", A);
auto env3 = add_decl(env2, mk_definition("id", level_param_names(),
Pi(A, A >> A),
Fun({A, x}, x)));
expr c = mk_local("c", Prop);
expr id = Const("id");
type_checker checker(env3, name_generator("tmp"));
lean_assert(checker.check(id(Prop)) == Prop >> Prop);
lean_assert(checker.whnf(id(Prop, c)) == c);
lean_assert(checker.whnf(id(Prop, id(Prop, id(Prop, c)))) == c);
type_checker checker2(env2, name_generator("tmp"));
lean_assert(checker2.whnf(id(Prop, id(Prop, id(Prop, c)))) == id(Prop, id(Prop, id(Prop, c))));
}
static void tst2() {
environment env;
name base("base");
env = add_decl(env, mk_var_decl(name(base, 0u), level_param_names(), Prop >> (Prop >> Prop)));
expr x = Local("x", Prop);
expr y = Local("y", Prop);
for (unsigned i = 1; i <= 100; i++) {
expr visit_binding(expr const & b) {
expr new_domain = visit(binding_domain(b));
expr l = mk_local(m_tc.mk_fresh_name(), new_domain);
expr new_body = abstract(visit(instantiate(binding_body(b), l)), l);
return update_binding(b, new_domain, new_body);
}
to_ceqvs_fn(type_checker & tc):m_env(tc.env()), m_tc(tc) {}
get_noncomputable_reason_fn(type_checker & tc):
m_tc(tc), m_ext(get_extension(tc.env())) {
}
try {
auto env7 = add_decl(env2, mk_definition("foo", level_param_names(), mk_Type() >> mk_Type(), mk_Prop()));
lean_unreachable();
} catch (kernel_exception & ex) {
std::cout << "expected error: " << ex.pp(mk_formatter(ex.get_environment())) << "\n";
}
expr Type = mk_Type();
expr A = Local("A", Type);
expr x = Local("x", A);
auto env3 = add_decl(env2, mk_definition("id", level_param_names(),
Pi(A, A >> A),
Fun({A, x}, x)));
expr Prop = mk_Prop();
expr c = mk_local("c", Prop);
expr id = Const("id");
type_checker checker(env3, name_generator("tmp"));
lean_assert(checker.check(mk_app(id, Prop)).first == Prop >> Prop);
lean_assert(checker.whnf(mk_app(id, Prop, c)).first == c);
lean_assert(checker.whnf(mk_app(id, Prop, mk_app(id, Prop, mk_app(id, Prop, c)))).first == c);
type_checker checker2(env2, name_generator("tmp"));
lean_assert(checker2.whnf(mk_app(id, Prop, mk_app(id, Prop, mk_app(id, Prop, c)))).first == mk_app(id, Prop, mk_app(id, Prop, mk_app(id, Prop, c))));
}
static void tst2() {
environment env;
name base("base");
expr Prop = mk_Prop();
env = add_decl(env, mk_constant_assumption(name(base, 0u), level_param_names(), Prop >> (Prop >> Prop)));
expr x = Local("x", Prop);
expr y = Local("y", Prop);
name converter::mk_fresh_name(type_checker & tc) { return tc.mk_fresh_name(); }
pair<expr, constraint_seq> converter::infer_type(type_checker & tc, expr const & e) { return tc.infer_type(e); }
