static expr expand_aux_recursors(environment const & env, expr const & e) {
auto tc = mk_type_checker(env, name_generator(), [=](name const & n) {
return !is_aux_recursor(env, n) && !is_user_defined_recursor(env, n);
});
constraint_seq cs;
return normalize(*tc, e, cs);
}
class_instance_context(environment const & env, io_state const & ios,
name const & prefix, bool relax, bool use_local_instances):
m_ios(ios),
m_ngen(prefix),
m_relax(relax),
m_use_local_instances(use_local_instances) {
m_fname = nullptr;
m_trace_instances = get_class_trace_instances(ios.get_options());
m_max_depth = get_class_instance_max_depth(ios.get_options());
m_conservative = get_class_conservative(ios.get_options());
if (m_conservative)
m_tc = mk_type_checker(env, m_ngen.mk_child(), false, UnfoldReducible);
else
m_tc = mk_type_checker(env, m_ngen.mk_child(), m_relax);
options opts = m_ios.get_options();
opts = opts.update_if_undef(get_pp_purify_metavars_name(), false);
opts = opts.update_if_undef(get_pp_implicit_name(), true);
m_ios.set_options(opts);
}
tactic change_goal_tactic(elaborate_fn const & elab, expr const & e) {
return tactic([=](environment const & env, io_state const & ios, proof_state const & s) {
proof_state new_s = s;
goals const & gs = new_s.get_goals();
if (!gs) {
throw_no_goal_if_enabled(s);
return proof_state_seq();
}
expr t = head(gs).get_type();
bool report_unassigned = true;
if (auto new_e = elaborate_with_respect_to(env, ios, elab, new_s, e, none_expr(), report_unassigned)) {
goals const & gs = new_s.get_goals();
goal const & g = head(gs);
substitution subst = new_s.get_subst();
auto tc = mk_type_checker(env);
constraint_seq cs;
if (tc->is_def_eq(t, *new_e, justification(), cs)) {
if (cs) {
unifier_config cfg(ios.get_options());
buffer<constraint> cs_buf;
cs.linearize(cs_buf);
to_buffer(new_s.get_postponed(), cs_buf);
unify_result_seq rseq = unify(env, cs_buf.size(), cs_buf.data(), subst, cfg);
return map2<proof_state>(rseq, [=](pair<substitution, constraints> const & p) -> proof_state {
substitution const & subst = p.first;
constraints const & postponed = p.second;
substitution new_subst = subst;
expr final_e = new_subst.instantiate_all(*new_e);
expr M = g.mk_meta(mk_fresh_name(), final_e);
goal new_g(M, final_e);
assign(new_subst, g, M);
return proof_state(new_s, cons(new_g, tail(gs)), new_subst, postponed);
});
}
expr M = g.mk_meta(mk_fresh_name(), *new_e);
goal new_g(M, *new_e);
assign(subst, g, M);
return proof_state_seq(proof_state(new_s, cons(new_g, tail(gs)), subst));
} else {
throw_tactic_exception_if_enabled(new_s, [=](formatter const & fmt) {
format r = format("invalid 'change' tactic, the given type");
r += pp_indent_expr(fmt, *new_e);
r += compose(line(), format("does not match the goal type"));
r += pp_indent_expr(fmt, t);
return r;
});
return proof_state_seq();
}
}
return proof_state_seq();
});
}
// Return true if \c e is convertible to a term of the form (h ...).
// If the result is true, update \c e and \c cs.
bool try_normalize_to_head(environment const & env, name const & h, expr & e, constraint_seq & cs) {
type_checker_ptr tc = mk_type_checker(env, [=](name const & n) { return n == h; });
constraint_seq new_cs;
expr new_e = tc->whnf(e, new_cs);
expr const & fn = get_app_fn(new_e);
if (is_constant(fn) && const_name(fn) == h) {
e = new_e;
cs += new_cs;
return true;
} else {
return false;
}
}
tactic intros_tactic(list<name> _ns, bool relax_main_opaque) {
auto fn = [=](environment const & env, io_state const &, proof_state const & s) {
list<name> ns = _ns;
goals const & gs = s.get_goals();
if (empty(gs)) {
throw_no_goal_if_enabled(s);
return optional<proof_state>();
}
goal const & g = head(gs);
name_generator ngen = s.get_ngen();
auto tc = mk_type_checker(env, ngen.mk_child(), relax_main_opaque);
expr t = g.get_type();
expr m = g.get_meta();
bool gen_names = empty(ns);
try {
while (true) {
if (!gen_names && is_nil(ns))
break;
if (!is_pi(t)) {
if (!is_nil(ns)) {
t = tc->ensure_pi(t).first;
} else {
expr new_t = tc->whnf(t).first;
if (!is_pi(new_t))
break;
t = new_t;
}
}
name new_name;
if (!is_nil(ns)) {
new_name = head(ns);
ns = tail(ns);
} else {
new_name = get_unused_name(binding_name(t), m);
}
expr new_local = mk_local(ngen.next(), new_name, binding_domain(t), binding_info(t));
t = instantiate(binding_body(t), new_local);
m = mk_app(m, new_local);
}
goal new_g(m, t);
return some(proof_state(s, goals(new_g, tail(gs)), ngen));
} catch (exception &) {
return optional<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);
});
}
static proof_state_seq apply_tactic_core(environment const & env, io_state const & ios, proof_state const & s,
expr const & _e, buffer<constraint> & cs,
add_meta_kind add_meta, subgoals_action_kind subgoals_action,
optional<unifier_kind> const & uk = optional<unifier_kind>()) {
goals const & gs = s.get_goals();
if (empty(gs)) {
throw_no_goal_if_enabled(s);
return proof_state_seq();
}
bool class_inst = get_apply_class_instance(ios.get_options());
name_generator ngen = s.get_ngen();
std::shared_ptr<type_checker> tc(mk_type_checker(env, ngen.mk_child()));
goal g = head(gs);
goals tail_gs = tail(gs);
expr t = g.get_type();
expr e = _e;
auto e_t_cs = tc->infer(e);
e_t_cs.second.linearize(cs);
expr e_t = e_t_cs.first;
buffer<expr> metas;
local_context ctx;
bool initialized_ctx = false;
unifier_config cfg(ios.get_options());
if (uk)
cfg.m_kind = *uk;
if (add_meta != DoNotAdd) {
unsigned num_e_t = get_expect_num_args(*tc, e_t);
if (add_meta == AddDiff) {
unsigned num_t = get_expect_num_args(*tc, t);
if (num_t <= num_e_t)
num_e_t -= num_t;
else
num_e_t = 0;
} else {
lean_assert(add_meta == AddAll);
}
for (unsigned i = 0; i < num_e_t; i++) {
auto e_t_cs = tc->whnf(e_t);
e_t_cs.second.linearize(cs);
e_t = e_t_cs.first;
expr meta;
if (class_inst && binding_info(e_t).is_inst_implicit()) {
if (!initialized_ctx) {
ctx = g.to_local_context();
initialized_ctx = true;
}
bool use_local_insts = true;
bool is_strict = false;
auto mc = mk_class_instance_elaborator(
env, ios, ctx, ngen.next(), optional<name>(),
use_local_insts, is_strict,
some_expr(head_beta_reduce(binding_domain(e_t))), e.get_tag(), cfg, nullptr);
meta = mc.first;
cs.push_back(mc.second);
} else {
meta = g.mk_meta(ngen.next(), head_beta_reduce(binding_domain(e_t)));
}
e = mk_app(e, meta);
e_t = instantiate(binding_body(e_t), meta);
metas.push_back(meta);
}
}
metavar_closure cls(t);
cls.mk_constraints(s.get_subst(), justification());
pair<bool, constraint_seq> dcs = tc->is_def_eq(t, e_t);
if (!dcs.first) {
throw_tactic_exception_if_enabled(s, [=](formatter const & fmt) {
format r = format("invalid 'apply' tactic, failed to unify");
r += pp_indent_expr(fmt, t);
r += compose(line(), format("with"));
r += pp_indent_expr(fmt, e_t);
return r;
});
return proof_state_seq();
}
dcs.second.linearize(cs);
unify_result_seq rseq = unify(env, cs.size(), cs.data(), ngen.mk_child(), s.get_subst(), cfg);
list<expr> meta_lst = to_list(metas.begin(), metas.end());
return map2<proof_state>(rseq, [=](pair<substitution, constraints> const & p) -> proof_state {
substitution const & subst = p.first;
constraints const & postponed = p.second;
name_generator new_ngen(ngen);
substitution new_subst = subst;
expr new_e = new_subst.instantiate_all(e);
assign(new_subst, g, new_e);
goals new_gs = tail_gs;
if (subgoals_action != IgnoreSubgoals) {
buffer<expr> metas;
for (auto m : meta_lst) {
if (!new_subst.is_assigned(get_app_fn(m)))
metas.push_back(m);
}
if (subgoals_action == AddRevSubgoals) {
for (unsigned i = 0; i < metas.size(); i++)
new_gs = cons(goal(metas[i], new_subst.instantiate_all(tc->infer(metas[i]).first)), new_gs);
} else {
lean_assert(subgoals_action == AddSubgoals || subgoals_action == AddAllSubgoals);
if (subgoals_action == AddSubgoals)
remove_redundant_metas(metas);
unsigned i = metas.size();
while (i > 0) {
--i;
new_gs = cons(goal(metas[i], new_subst.instantiate_all(tc->infer(metas[i]).first)), new_gs);
}
}
}
return proof_state(s, new_gs, new_subst, new_ngen, postponed);
});
}
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);
}
expr normalize(environment const & env, level_param_names const & ls, expr const & e) {
auto tc = mk_type_checker(env, true);
bool save_cnstrs = false;
return normalize_fn(*tc, save_cnstrs)(ls, e);
}
expr normalize(environment const & env, expr const & e) {
auto tc = mk_type_checker(env, true);
bool save_cnstrs = false;
return normalize_fn(*tc, save_cnstrs)(e);
}
/** \brief Create a "choice" constraint that postpones the resolution of a calc proof step.
By delaying it, we can perform quick fixes such as:
- adding symmetry
- adding !
- adding subst
*/
constraint mk_calc_proof_cnstr(environment const & env, options const & opts,
old_local_context const & _ctx, expr const & m, expr const & _e,
constraint_seq const & cs, unifier_config const & cfg,
info_manager * im, update_type_info_fn const & fn) {
justification j = mk_failed_to_synthesize_jst(env, m);
auto choice_fn = [=](expr const & meta, expr const & _meta_type, substitution const & _s) {
old_local_context ctx = _ctx;
expr e = _e;
substitution s = _s;
expr meta_type = _meta_type;
type_checker_ptr tc = mk_type_checker(env);
constraint_seq new_cs = cs;
expr e_type = tc->infer(e, new_cs);
e_type = s.instantiate(e_type);
tag g = e.get_tag();
bool calc_assistant = get_elaborator_calc_assistant(opts);
if (calc_assistant) {
// add '!' is needed
while (is_norm_pi(*tc, e_type, new_cs)) {
binder_info bi = binding_info(e_type);
if (!bi.is_implicit() && !bi.is_inst_implicit()) {
if (!has_free_var(binding_body(e_type), 0)) {
// if the rest of the type does not reference argument,
// then we also stop consuming arguments
break;
}
}
expr imp_arg = ctx.mk_meta(some_expr(binding_domain(e_type)), g);
e = mk_app(e, imp_arg, g);
e_type = instantiate(binding_body(e_type), imp_arg);
}
if (im)
fn(e);
}
e_type = head_beta_reduce(e_type);
expr const & meta_type_fn = get_app_fn(meta_type);
expr const & e_type_fn = get_app_fn(e_type);
if (is_constant(meta_type_fn) && (!is_constant(e_type_fn) || const_name(e_type_fn) != const_name(meta_type_fn))) {
// try to make sure meta_type and e_type have the same head symbol
if (!try_normalize_to_head(env, const_name(meta_type_fn), e_type, new_cs) &&
is_constant(e_type_fn)) {
try_normalize_to_head(env, const_name(e_type_fn), meta_type, new_cs);
}
}
auto try_alternative = [&](expr const & e, expr const & e_type, constraint_seq fcs, bool conservative) {
justification new_j = mk_type_mismatch_jst(e, e_type, meta_type);
if (!tc->is_def_eq(e_type, meta_type, new_j, fcs))
throw unifier_exception(new_j, s);
buffer<constraint> cs_buffer;
fcs.linearize(cs_buffer);
metavar_closure cls(meta);
cls.add(meta_type);
cls.mk_constraints(s, j, cs_buffer);
unifier_config new_cfg(cfg);
new_cfg.m_discard = false;
new_cfg.m_kind = conservative ? unifier_kind::Conservative : unifier_kind::Liberal;
unify_result_seq seq = unify(env, cs_buffer.size(), cs_buffer.data(), substitution(), new_cfg);
auto p = seq.pull();
lean_assert(p);
substitution new_s = p->first.first;
constraints postponed = map(p->first.second,
[&](constraint const & c) {
// we erase internal justifications
return update_justification(c, j);
});
expr new_e = new_s.instantiate(e);
if (conservative && has_expr_metavar_relaxed(new_s.instantiate_all(e)))
throw_elaborator_exception("solution contains metavariables", e);
if (im)
im->instantiate(new_s);
constraints r = cls.mk_constraints(new_s, j);
buffer<expr> locals;
expr mvar = get_app_args(meta, locals);
expr val = Fun(locals, new_e);
r = cons(mk_eq_cnstr(mvar, val, j), r);
return append(r, postponed);
};
if (!get_elaborator_calc_assistant(opts)) {
bool conservative = false;
return try_alternative(e, e_type, new_cs, conservative);
} else {
// TODO(Leo): after we have the simplifier and rewriter tactic, we should revise
// this code. It is "abusing" the higher-order unifier.
{
// Try the following possible intrepretations using a "conservative" unification procedure.
// That is, we only unfold definitions marked as reducible.
// Assume pr is the proof provided.
// 1. pr
bool conservative = true;
try { return try_alternative(e, e_type, new_cs, conservative); } catch (exception & ex) {}
// 2. eq.symm pr
constraint_seq symm_cs = new_cs;
auto symm = apply_symmetry(env, ctx, tc, e, e_type, symm_cs, g);
if (symm) {
try { return try_alternative(symm->first, symm->second, symm_cs, conservative); } catch (exception &) {}
}
// 3. subst pr (eq.refl lhs)
constraint_seq subst_cs = new_cs;
if (auto subst = apply_subst(env, ctx, tc, e, e_type, meta_type, subst_cs, g)) {
try { return try_alternative(subst->first, subst->second, subst_cs, conservative); } catch (exception&) {}
}
// 4. subst (eq.symm pr) (eq.refl lhs)
if (symm) {
constraint_seq subst_cs = symm_cs;
if (auto subst = apply_subst(env, ctx, tc, symm->first, symm->second,
meta_type, subst_cs, g)) {
try { return try_alternative(subst->first, subst->second, subst_cs, conservative); }
catch (exception&) {}
}
}
}
{
// Try the following possible insterpretations using the default unification procedure.
// 1. pr
bool conservative = false;
std::unique_ptr<throwable> saved_ex;
try {
return try_alternative(e, e_type, new_cs, conservative);
} catch (exception & ex) {
saved_ex.reset(ex.clone());
}
// 2. eq.symm pr
constraint_seq symm_cs = new_cs;
auto symm = apply_symmetry(env, ctx, tc, e, e_type, symm_cs, g);
if (symm) {
try { return try_alternative(symm->first, symm->second, symm_cs, conservative); }
catch (exception &) {}
}
// We use the exception for the first alternative as the error message
saved_ex->rethrow();
lean_unreachable();
}
}
};
bool owner = false;
return mk_choice_cnstr(m, choice_fn, to_delay_factor(cnstr_group::Epilogue), owner, j);
}
