vm_obj tactic_to_expr_core(vm_obj const & relaxed, vm_obj const & qe, vm_obj const & _s) {
tactic_state const & s = to_tactic_state(_s);
optional<metavar_decl> g = s.get_main_goal_decl();
if (!g) return mk_no_goals_exception(s);
if (!g_elaborate) {
return mk_tactic_exception("elaborator is not available", s);
}
metavar_context mctx = s.mctx();
try {
environment env = s.env();
expr r = (*g_elaborate)(env, s.get_options(), mctx, g->get_context(), to_expr(qe), to_bool(relaxed));
r = mctx.instantiate_mvars(r);
if (relaxed && has_expr_metavar(r)) {
buffer<expr> new_goals;
name_set found;
for_each(r, [&](expr const & e, unsigned) {
if (!has_expr_metavar(e)) return false;
if (is_metavar_decl_ref(e) && !found.contains(mlocal_name(e))) {
mctx.instantiate_mvars_at_type_of(e);
new_goals.push_back(e);
found.insert(mlocal_name(e));
}
return true;
});
list<expr> new_gs = cons(head(s.goals()), to_list(new_goals.begin(), new_goals.end(), tail(s.goals())));
return mk_tactic_success(to_obj(r), set_env_mctx_goals(s, env, mctx, new_gs));
} else {
return mk_tactic_success(to_obj(r), set_env_mctx(s, env, mctx));
}
} catch (exception & ex) {
return mk_tactic_exception(ex, s);
}
}
optional<expr> has_expr_metavar_strict(expr const & e) {
if (!has_expr_metavar(e))
return none_expr();
optional<expr> r;
for_each(e, [&](expr const & e, unsigned) {
if (r || !has_expr_metavar(e)) return false;
if (is_meta(e)) { r = e; return false; }
if (is_local(e)) return false; // do not visit type
return true;
});
return r;
}
bool projection_converter::postpone_is_def_eq(expr const & t, expr const & s) {
if (has_expr_metavar(t) || has_expr_metavar(s)) {
auto it1 = is_projection(t);
auto it2 = is_projection(s);
if (it1 && it2) {
return true;
}
if (it1 && is_stuck(t, *m_tc))
return true;
if (it2 && is_stuck(s, *m_tc))
return true;
}
return default_converter::postpone_is_def_eq(t, s);
}
action_result assert_cc_action(hypothesis_idx hidx) {
if (!get_config().m_cc)
return action_result::failed();
congruence_closure & cc = get_cc();
if (has_expr_metavar(curr_state().get_hypothesis_decl(hidx).get_type()))
return action_result::failed();
cc.add(hidx);
// cc.display();
if (cc.is_inconsistent()) {
try {
app_builder & b = get_app_builder();
expr false_proof = *cc.get_inconsistency_proof();
trace_action("contradiction by congruence closure");
return action_result(b.mk_false_rec(curr_state().get_target(), false_proof));
} catch (app_builder_exception &) {
return action_result::failed();
}
} else {
expr const & target = curr_state().get_target();
name R; expr lhs, rhs;
if (is_relation_app(target, R, lhs, rhs) && cc.is_eqv(R, lhs, rhs)) {
expr proof = *cc.get_eqv_proof(R, lhs, rhs);
trace_action("equivalence by congruence closure");
return action_result(proof);
} else if (is_prop(target) && !is_false(target) && cc.proved(target)) {
expr proof = *cc.get_proof(target);
trace_action("equivalent to true by congruence closure");
return action_result(proof);
} else {
return action_result::new_branch();
}
}
}
bool has_idx_metavar(expr const & e) {
if (!has_univ_metavar(e) && !has_expr_metavar(e))
return false;
bool found = false;
for_each(e, [&](expr const & e, unsigned) {
if (found) return false;
if (!has_univ_metavar(e) && !has_expr_metavar(e)) return false;
if (is_idx_metavar(e))
found = true;
else if (is_constant(e) && std::any_of(const_levels(e).begin(), const_levels(e).end(), has_idx_metauniv))
found = true;
else if (is_sort(e) && has_idx_metauniv(sort_level(e)))
found = true;
return true;
});
return found;
}
bool is_ceqv(tmp_type_context & tctx, 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 = tctx.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 = tctx.mk_tmp_local(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 && tctx.is_prop(binding_domain(e))) {
// 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;
}
bool substitution::occurs_expr_core(name const & m, expr const & e, name_set & visited) const {
bool found = false;
for_each(e, [&](expr const & e, unsigned) {
if (found || !has_expr_metavar(e)) return false;
if (is_metavar(e)) {
name const & n = mlocal_name(e);
if (n == m)
found = true;
auto s = get_expr(e);
if (!s || visited.contains(n))
return false; // do not visit type
visited.insert(n);
if (s && occurs_expr_core(m, *s, visited))
found = true;
return false; // do not visit type
}
if (is_local(e)) return false; // do not visit type
return true;
});
return found;
}
bool substitution::occurs_expr(name const & m, expr const & e) const {
if (!has_expr_metavar(e))
return false;
name_set visited;
return occurs_expr_core(m, e, visited);
}