tactic clear_tactic(name const & n) {
auto fn = [=](environment const &, io_state const &, proof_state const & _s) -> optional<proof_state> {
if (!_s.get_goals()) {
throw_no_goal_if_enabled(_s);
return none_proof_state();
}
proof_state s = apply_substitution(_s);
goals const & gs = s.get_goals();
goal g = head(gs);
goals tail_gs = tail(gs);
if (auto p = g.find_hyp(n)) {
expr const & h = p->first;
unsigned i = p->second;
buffer<expr> hyps;
g.get_hyps(hyps);
hyps.erase(hyps.size() - i - 1);
if (depends_on(g.get_type(), h)) {
throw_tactic_exception_if_enabled(s, sstream() << "invalid 'clear' tactic, conclusion depends on '"
<< n << "'");
return none_proof_state();
}
if (auto h2 = depends_on(i, hyps.end() - i, h)) {
throw_tactic_exception_if_enabled(s, sstream() << "invalid 'clear' tactic, hypothesis '" << *h2
<< "' depends on '" << n << "'");
return none_proof_state();
}
name_generator ngen = s.get_ngen();
expr new_type = g.get_type();
expr new_meta = mk_app(mk_metavar(ngen.next(), Pi(hyps, new_type)), hyps);
goal new_g(new_meta, new_type);
substitution new_subst = s.get_subst();
assign(new_subst, g, new_meta);
proof_state new_s(s, goals(new_g, tail_gs), new_subst, ngen);
return some_proof_state(new_s);
} else {
throw_tactic_exception_if_enabled(s, sstream() << "invalid 'clear' tactic, goal does not have a hypothesis "
<< " named '" << n << "'");
return none_proof_state();
}
};
return tactic01(fn);
}
tactic revert_tactic(name const & n) {
auto fn = [=](environment const &, io_state const &, proof_state const & s) -> optional<proof_state> {
goals const & gs = s.get_goals();
if (empty(gs)) {
throw_no_goal_if_enabled(s);
return none_proof_state();
}
goal g = head(gs);
goals tail_gs = tail(gs);
if (auto p = g.find_hyp(n)) {
expr const & h = p->first;
unsigned i = p->second;
buffer<expr> hyps;
g.get_hyps(hyps);
hyps.erase(hyps.size() - i - 1);
if (optional<expr> other_h = depends_on(i, hyps.end() - i, h)) {
throw_tactic_exception_if_enabled(s, sstream() << "invalid 'revert' tactic, hypothesis '" << local_pp_name(*other_h)
<< "' depends on '" << local_pp_name(h) << "'");
return none_proof_state(); // other hypotheses depend on h
}
name_generator ngen = s.get_ngen();
expr new_type = Pi(h, g.get_type());
expr new_meta = mk_app(mk_metavar(ngen.next(), Pi(hyps, new_type)), hyps);
goal new_g(new_meta, new_type);
substitution new_subst = s.get_subst();
assign(new_subst, g, mk_app(new_meta, h));
proof_state new_s(s, goals(new_g, tail_gs), new_subst, ngen);
return some_proof_state(new_s);
} else {
throw_tactic_exception_if_enabled(s, sstream() << "invalid 'revert' tactic, unknown hypothesis '" << n << "'");
return none_proof_state();
}
};
return tactic01(fn);
}
tactic whnf_tactic(bool relax_main_opaque) {
return tactic01([=](environment const & env, io_state const & ios, proof_state const & ps) {
goals const & gs = ps.get_goals();
if (empty(gs))
return none_proof_state();
name_generator ngen = ps.get_ngen();
auto tc = mk_type_checker(env, ngen.mk_child(), relax_main_opaque);
goal g = head(gs);
goals tail_gs = tail(gs);
expr type = g.get_type();
auto t_cs = tc->whnf(type);
goals new_gs(goal(g.get_meta(), t_cs.first), tail_gs);
proof_state new_ps(ps, new_gs, ngen);
if (solve_constraints(env, ios, new_ps, t_cs.second)) {
return some_proof_state(new_ps);
} else {
return none_proof_state();
}
});
}
tactic check_expr_tactic(elaborate_fn const & elab, expr const & e,
std::string const & fname, pair<unsigned, unsigned> const & pos) {
return tactic01([=](environment const & env, io_state const & ios, proof_state const & s) {
goals const & gs = s.get_goals();
if (empty(gs)) {
throw_no_goal_if_enabled(s);
return none_proof_state();
}
goal const & g = head(gs);
name_generator ngen = s.get_ngen();
expr new_e = std::get<0>(elab(g, ios.get_options(), ngen.mk_child(), e, none_expr(), s.get_subst(), false));
auto tc = mk_type_checker(env, ngen.mk_child());
expr new_t = tc->infer(new_e).first;
auto out = regular(env, ios);
flycheck_information info(out);
if (info.enabled()) {
out << fname << ":" << pos.first << ":" << pos.second << ": information: ";
out << "check result:\n";
}
out << new_e << " : " << new_t << endl;
return some_proof_state(s);
});
}
tactic contradiction_tactic() {
auto fn = [=](environment const & env, io_state const & ios, proof_state const & s) {
goals const & gs = s.get_goals();
if (empty(gs)) {
throw_no_goal_if_enabled(s);
return optional<proof_state>();
}
goal const & g = head(gs);
expr const & t = g.get_type();
substitution subst = s.get_subst();
auto tc = mk_type_checker(env);
auto conserv_tc = mk_type_checker(env, UnfoldReducible);
buffer<expr> hyps;
g.get_hyps(hyps);
for (expr const & h : hyps) {
expr h_type = mlocal_type(h);
h_type = tc->whnf(h_type).first;
expr lhs, rhs, arg;
if (is_false(env, h_type)) {
assign(subst, g, mk_false_rec(*tc, h, t));
return some_proof_state(proof_state(s, tail(gs), subst));
} else if (is_not(env, h_type, arg)) {
optional<expr> h_pos;
for (expr const & h_prime : hyps) {
constraint_seq cs;
if (conserv_tc->is_def_eq(arg, mlocal_type(h_prime), justification(), cs) && !cs) {
h_pos = h_prime;
break;
}
}
if (h_pos) {
assign(subst, g, mk_absurd(*tc, t, *h_pos, h));
return some_proof_state(proof_state(s, tail(gs), subst));
}
} else if (is_eq(h_type, lhs, rhs)) {
lhs = tc->whnf(lhs).first;
rhs = tc->whnf(rhs).first;
optional<name> lhs_c = is_constructor_app(env, lhs);
optional<name> rhs_c = is_constructor_app(env, rhs);
if (lhs_c && rhs_c && *lhs_c != *rhs_c) {
if (optional<name> I_name = inductive::is_intro_rule(env, *lhs_c)) {
name no_confusion(*I_name, "no_confusion");
try {
expr I = tc->whnf(tc->infer(lhs).first).first;
buffer<expr> args;
expr I_fn = get_app_args(I, args);
if (is_constant(I_fn)) {
level t_lvl = sort_level(tc->ensure_type(t).first);
expr V = mk_app(mk_app(mk_constant(no_confusion, cons(t_lvl, const_levels(I_fn))), args),
t, lhs, rhs, h);
if (auto r = lift_down_if_hott(*tc, V)) {
check_term(*tc, *r);
assign(subst, g, *r);
return some_proof_state(proof_state(s, tail(gs), subst));
}
}
} catch (kernel_exception & ex) {
regular(env, ios) << ex << "\n";
}
}
}
}
}
return none_proof_state();
};
return tactic01(fn);
}
