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();
}
}
}
virtual action_result resolve(expr const & pr) const override {
try {
expr it = pr;
bool skip = true;
for (unsigned i = 0; i < m_num_new_eqs; i++) {
if (!is_lambda(it)) {
break;
skip = false;
}
it = binding_body(it);
}
if (skip && closed(it)) {
// new eq hypotheses were not used
return action_result::solved(it);
}
state & s = curr_state();
app_builder & b = get_app_builder();
hypothesis const & h = s.get_hypothesis_decl(href_index(m_eq_href));
expr type = h.get_type();
expr lhs, rhs;
lean_verify(is_eq(type, lhs, rhs));
name nc_name(m_I_name, "no_confusion");
expr new_pr = mk_app(b.mk_app(nc_name, {m_target, lhs, rhs, m_eq_href}), pr);
return action_result::solved(new_pr);
} catch (app_builder_exception &) {
return action_result::failed();
}
}
action_result no_confusion_action(hypothesis_idx hidx) {
try {
state & s = curr_state();
app_builder & b = get_app_builder();
hypothesis const & h = s.get_hypothesis_decl(hidx);
expr type = h.get_type();
expr lhs, rhs;
if (!is_eq(type, lhs, rhs))
return action_result::failed();
lhs = whnf(lhs);
rhs = whnf(rhs);
optional<name> c1 = is_constructor_app(env(), lhs);
optional<name> c2 = is_constructor_app(env(), rhs);
if (!c1 || !c2)
return action_result::failed();
expr A = whnf(infer_type(lhs));
expr I = get_app_fn(A);
if (!is_constant(I) || !inductive::is_inductive_decl(env(), const_name(I)))
return action_result::failed();
name nct_name(const_name(I), "no_confusion_type");
if (!env().find(nct_name))
return action_result::failed();
expr target = s.get_target();
expr nct = whnf(b.mk_app(nct_name, target, lhs, rhs));
if (c1 == c2) {
if (!is_pi(nct))
return action_result::failed();
if (s.has_target_forward_deps(hidx)) {
// TODO(Leo): we currently do not handle this case.
// To avoid non-termination we remove the given hypothesis, if there
// forward dependencies, we would also have to remove them.
// Remark: this is a low priority refinement since it will not happen
// very often in practice.
return action_result::failed();
}
unsigned num_params = *inductive::get_num_params(env(), const_name(I));
unsigned cnstr_arity = get_arity(env().get(*c1).get_type());
lean_assert(cnstr_arity >= num_params);
unsigned num_new_eqs = cnstr_arity - num_params;
s.push_proof_step(new no_confusion_proof_step_cell(const_name(I), target, h.get_self(), num_new_eqs));
s.set_target(binding_domain(nct));
s.del_hypothesis(hidx);
trace_action("no_confusion");
return action_result::new_branch();
} else {
name nc_name(const_name(I), "no_confusion");
expr pr = b.mk_app(nc_name, {target, lhs, rhs, h.get_self()});
trace_action("no_confusion");
return action_result::solved(pr);
}
} catch (app_builder_exception &) {
return action_result::failed();
}
}
action_result by_contradiction_action() {
state & s = curr_state();
expr target = whnf(s.get_target());
if (!is_prop(target)) return action_result::failed();
if (blast::is_false(target)) return action_result::failed();
expr not_target;
if (is_not(target, not_target)) {
s.set_target(mk_arrow(not_target, mk_constant(get_false_name())));
return intros_action(1);
}
blast_tmp_type_context tmp_tctx;
optional<expr> target_decidable = tmp_tctx->mk_class_instance(mk_app(mk_constant(get_decidable_name()), target));
if (!target_decidable) return action_result::failed();
expr href = s.mk_hypothesis(get_app_builder().mk_not(target));
auto pcell = new by_contradiction_proof_step_cell(href);
s.push_proof_step(pcell);
s.set_target(mk_constant(get_false_name()));
trace_action("by_contradiction");
return action_result::new_branch();
}
result simplifier::finalize(result const & r) {
if (r.has_proof()) return r;
expr pf = get_app_builder().mk_refl(m_rel, r.get_new());
return result(r.get_new(), pf);
}
