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;
}
}
static optional<pair<expr, expr>> mk_op(environment const & env, old_local_context & ctx, type_checker_ptr & tc,
name const & op, unsigned nunivs, unsigned nargs, std::initializer_list<expr> const & explicit_args,
constraint_seq & cs, tag g) {
levels lvls;
for (unsigned i = 0; i < nunivs; i++)
lvls = levels(mk_meta_univ(mk_fresh_name()), lvls);
expr c = mk_constant(op, lvls);
expr op_type = instantiate_type_univ_params(env.get(op), lvls);
buffer<expr> args;
for (unsigned i = 0; i < nargs; i++) {
if (!is_pi(op_type))
return optional<pair<expr, expr>>();
expr arg = ctx.mk_meta(some_expr(binding_domain(op_type)), g);
args.push_back(arg);
op_type = instantiate(binding_body(op_type), arg);
}
expr r = mk_app(c, args, g);
for (expr const & explicit_arg : explicit_args) {
if (!is_pi(op_type))
return optional<pair<expr, expr>>();
r = mk_app(r, explicit_arg);
expr type = tc->infer(explicit_arg, cs);
justification j = mk_app_justification(r, op_type, explicit_arg, type);
if (!tc->is_def_eq(binding_domain(op_type), type, j, cs))
return optional<pair<expr, expr>>();
op_type = instantiate(binding_body(op_type), explicit_arg);
}
return some(mk_pair(r, op_type));
}
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);
}
optional<constraints> try_instance(name const & inst) {
environment const & env = m_C->env();
if (auto decl = env.find(inst)) {
name_generator & ngen = m_C->m_ngen;
buffer<level> ls_buffer;
unsigned num_univ_ps = decl->get_num_univ_params();
for (unsigned i = 0; i < num_univ_ps; i++)
ls_buffer.push_back(mk_meta_univ(ngen.next()));
levels ls = to_list(ls_buffer.begin(), ls_buffer.end());
expr inst_cnst = copy_tag(m_meta, mk_constant(inst, ls));
expr inst_type = instantiate_type_univ_params(*decl, ls);
return try_instance(inst_cnst, inst_type);
} else {
return optional<constraints>();
}
}
level mk_idx_metauniv(unsigned i) {
return mk_meta_univ(name(*g_tmp_prefix, i));
}
vm_obj level_meta(vm_obj const & n) {
return to_obj(mk_meta_univ(to_name(n)));
}
void add_congr_core(environment const & env, simp_rule_sets & s, name const & n) {
declaration const & d = env.get(n);
type_checker tc(env);
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 pr = mk_constant(n, ls);
expr e = instantiate_type_univ_params(d, ls);
buffer<bool> explicit_args;
buffer<expr> metas;
unsigned idx = 0;
while (is_pi(e)) {
expr mvar = mk_metavar(name(*g_prefix, idx), binding_domain(e));
idx++;
explicit_args.push_back(is_explicit(binding_info(e)));
metas.push_back(mvar);
e = instantiate(binding_body(e), mvar);
pr = mk_app(pr, mvar);
}
expr rel, lhs, rhs;
if (!is_simp_relation(env, e, rel, lhs, rhs) || !is_constant(rel)) {
throw exception(sstream() << "invalid congruence rule, '" << n
<< "' resulting type is not of the form t ~ s, where '~' is a transitive and reflexive relation");
}
name_set found_mvars;
buffer<expr> lhs_args, rhs_args;
expr const & lhs_fn = get_app_args(lhs, lhs_args);
expr const & rhs_fn = get_app_args(rhs, rhs_args);
if (is_constant(lhs_fn)) {
if (!is_constant(rhs_fn) || const_name(lhs_fn) != const_name(rhs_fn) || lhs_args.size() != rhs_args.size()) {
throw exception(sstream() << "invalid congruence rule, '" << n
<< "' resulting type is not of the form (" << const_name(lhs_fn) << " ...) "
<< "~ (" << const_name(lhs_fn) << " ...), where ~ is '" << const_name(rel) << "'");
}
for (expr const & lhs_arg : lhs_args) {
if (is_sort(lhs_arg))
continue;
if (!is_metavar(lhs_arg) || found_mvars.contains(mlocal_name(lhs_arg))) {
throw exception(sstream() << "invalid congruence rule, '" << n
<< "' the left-hand-side of the congruence resulting type must be of the form ("
<< const_name(lhs_fn) << " x_1 ... x_n), where each x_i is a distinct variable or a sort");
}
found_mvars.insert(mlocal_name(lhs_arg));
}
} else if (is_binding(lhs)) {
if (lhs.kind() != rhs.kind()) {
throw exception(sstream() << "invalid congruence rule, '" << n
<< "' kinds of the left-hand-side and right-hand-side of "
<< "the congruence resulting type do not match");
}
if (!is_valid_congr_rule_binding_lhs(lhs, found_mvars)) {
throw exception(sstream() << "invalid congruence rule, '" << n
<< "' left-hand-side of the congruence resulting type must "
<< "be of the form (fun/Pi (x : A), B x)");
}
} else {
throw exception(sstream() << "invalid congruence rule, '" << n
<< "' left-hand-side is not an application nor a binding");
}
buffer<expr> congr_hyps;
lean_assert(metas.size() == explicit_args.size());
for (unsigned i = 0; i < metas.size(); i++) {
expr const & mvar = metas[i];
if (explicit_args[i] && !found_mvars.contains(mlocal_name(mvar))) {
buffer<expr> locals;
expr type = mlocal_type(mvar);
while (is_pi(type)) {
expr local = mk_local(tc.mk_fresh_name(), binding_domain(type));
locals.push_back(local);
type = instantiate(binding_body(type), local);
}
expr h_rel, h_lhs, h_rhs;
if (!is_simp_relation(env, type, h_rel, h_lhs, h_rhs) || !is_constant(h_rel))
continue;
unsigned j = 0;
for (expr const & local : locals) {
j++;
if (!only_found_mvars(mlocal_type(local), found_mvars)) {
throw exception(sstream() << "invalid congruence rule, '" << n
<< "' argument #" << j << " of parameter #" << (i+1) << " contains "
<< "unresolved parameters");
}
}
if (!only_found_mvars(h_lhs, found_mvars)) {
throw exception(sstream() << "invalid congruence rule, '" << n
<< "' argument #" << (i+1) << " is not a valid hypothesis, the left-hand-side contains "
<< "unresolved parameters");
}
if (!is_valid_congr_hyp_rhs(h_rhs, found_mvars)) {
throw exception(sstream() << "invalid congruence rule, '" << n
<< "' argument #" << (i+1) << " is not a valid hypothesis, the right-hand-side must be "
<< "of the form (m l_1 ... l_n) where m is parameter that was not "
<< "'assigned/resolved' yet and l_i's are locals");
}
found_mvars.insert(mlocal_name(mvar));
congr_hyps.push_back(mvar);
}
}
congr_rule rule(n, ls, to_list(metas), lhs, rhs, pr, to_list(congr_hyps));
s.insert(const_name(rel), rule);
}
