format pp_def_type_mismatch(formatter const & fmt, environment const & env, options const & opts, name const & n,
expr const & expected_type, expr const & given_type) {
format r("type mismatch at definition '");
r += format(n);
r += format("', expected type");
r += pp_indent_expr(fmt, env, opts, expected_type);
r += compose(line(), format("given type:"));
r += pp_indent_expr(fmt, env, opts, given_type);
return r;
}
format pp_app_type_mismatch(formatter const & fmt, environment const & env, options const & opts, expr const & app,
expr const & expected_type, expr const & given_type) {
format r;
r += format("type mismatch at application");
r += pp_indent_expr(fmt, env, opts, app);
r += compose(line(), format("expected type:"));
r += pp_indent_expr(fmt, env, opts, expected_type);
r += compose(line(), format("given type:"));
r += pp_indent_expr(fmt, env, opts, given_type);
return r;
}
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();
});
}
format pp_def_lvl_cnstrs_satisfied(formatter const & fmt, environment const & env, options const & opts, expr const & e,
level const & lhs, level const & rhs) {
format r("constand definition level constraints are not satisfied");
r += pp_indent_expr(fmt, env, opts, e);
r += format("level constraint:");
r += pp(lhs, rhs, opts);
return r;
}
format pp_function_expected(formatter const & fmt, environment const & env, options const & opts, expr const & e) {
return compose(format("function expected at"), pp_indent_expr(fmt, env, opts, e));
}
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);
});
}
constraint mk_class_instance_root_cnstr(std::shared_ptr<class_instance_context> const & C, local_context const & _ctx,
expr const & m, bool is_strict, unifier_config const & cfg, delay_factor const & factor) {
environment const & env = C->env();
justification j = mk_failed_to_synthesize_jst(env, m);
auto choice_fn = [=](expr const & meta, expr const & meta_type, substitution const & s,
name_generator const & ngen) {
environment const & env = C->env();
auto cls_name_it = is_ext_class(C->tc(), meta_type);
if (!cls_name_it) {
// do nothing, since type is not a class.
return lazy_list<constraints>(constraints());
}
local_context ctx = _ctx.instantiate(substitution(s));
pair<expr, justification> mj = update_meta(meta, s);
expr new_meta = mj.first;
justification new_j = mj.second;
unsigned depth = 0;
constraint c = mk_class_instance_cnstr(C, ctx, new_meta, depth);
unifier_config new_cfg(cfg);
new_cfg.m_discard = false;
new_cfg.m_use_exceptions = false;
new_cfg.m_pattern = true;
new_cfg.m_kind = C->m_conservative ? unifier_kind::VeryConservative : unifier_kind::Liberal;
auto to_cnstrs_fn = [=](substitution const & subst, constraints const & cnstrs) -> constraints {
substitution new_s = subst;
// some constraints may have been postponed (example: universe level constraints)
constraints postponed = map(cnstrs,
[&](constraint const & c) {
// we erase internal justifications
return update_justification(c, mk_composite1(j, new_j));
});
metavar_closure cls(new_meta);
cls.add(meta_type);
bool relax = C->m_relax;
constraints cs = cls.mk_constraints(new_s, new_j, relax);
return append(cs, postponed);
};
auto no_solution_fn = [=]() {
if (is_strict)
return lazy_list<constraints>();
else
return lazy_list<constraints>(constraints());
};
unify_result_seq seq1 = unify(env, 1, &c, ngen, substitution(), new_cfg);
unify_result_seq seq2 = filter(seq1, [=](pair<substitution, constraints> const & p) {
substitution new_s = p.first;
expr result = new_s.instantiate(new_meta);
// We only keep complete solutions (modulo universe metavariables)
return !has_expr_metavar_relaxed(result);
});
if (get_class_unique_class_instances(C->m_ios.get_options())) {
optional<expr> solution;
substitution subst;
constraints cnstrs;
for_each(seq2, [&](pair<substitution, constraints> const & p) {
subst = p.first;
cnstrs = p.second;
expr next_solution = subst.instantiate(new_meta);
if (solution) {
throw_class_exception(m, [=](formatter const & fmt) {
format r = format("ambiguous class-instance resolution, "
"there is more than one solution");
r += pp_indent_expr(fmt, *solution);
r += compose(line(), format("and"));
r += pp_indent_expr(fmt, next_solution);
return r;
});
} else {
solution = next_solution;
}
});
if (!solution) {
return no_solution_fn();
} else {
// some constraints may have been postponed (example: universe level constraints)
return lazy_list<constraints>(to_cnstrs_fn(subst, cnstrs));
}
} else {
if (try_multiple_instances(env, *cls_name_it)) {
lazy_list<constraints> seq3 = map2<constraints>(seq2, [=](pair<substitution, constraints> const & p) {
return to_cnstrs_fn(p.first, p.second);
});
if (is_strict) {
return seq3;
} else {
// make sure it does not fail by appending empty set of constraints
return append(seq3, lazy_list<constraints>(constraints()));
}
} else {
auto p = seq2.pull();
if (!p)
return no_solution_fn();
else
return lazy_list<constraints>(to_cnstrs_fn(p->first.first, p->first.second));
}
}
};
bool owner = false;
bool relax = C->m_relax;
return mk_choice_cnstr(m, choice_fn, factor, owner, j, relax);
}