constraint mk_class_instance_cnstr(std::shared_ptr<class_instance_context> const & C, local_context const & ctx, expr const & m, unsigned depth) {
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 &, name_generator const &) {
if (auto cls_name_it = is_ext_class(C->tc(), meta_type)) {
name cls_name = *cls_name_it;
list<expr> const & ctx_lst = ctx.get_data();
list<expr> local_insts;
if (C->use_local_instances())
local_insts = get_local_instances(C->tc(), ctx_lst, cls_name);
list<name> insts = get_class_instances(env, cls_name);
if (empty(local_insts) && empty(insts))
return lazy_list<constraints>(); // nothing to be done
// we are always strict with placeholders associated with classes
return choose(std::make_shared<class_instance_elaborator>(C, ctx, meta, meta_type, local_insts, insts, j, depth));
} else {
// do nothing, type is not a class...
return lazy_list<constraints>(constraints());
}
};
bool owner = false;
bool relax = C->m_relax;
return mk_choice_cnstr(m, choice_fn, to_delay_factor(cnstr_group::Basic),
owner, j, relax);
}
/** \brief Given a term <tt>a : a_type</tt>, and a metavariable \c m, creates a constraint
that considers coercions from a_type to the type assigned to \c m. */
constraint mk_coercion_cnstr(type_checker & from_tc, type_checker & to_tc, coercion_info_manager & infom,
expr const & m, expr const & a, expr const & a_type,
justification const & j, unsigned delay_factor, bool lift_coe) {
auto choice_fn = [=, &from_tc, &to_tc, &infom](expr const & meta, expr const & d_type, substitution const & s) {
expr new_a_type;
justification new_a_type_jst;
if (is_meta(a_type)) {
auto p = substitution(s).instantiate_metavars(a_type);
new_a_type = p.first;
new_a_type_jst = p.second;
} else {
new_a_type = a_type;
}
if (is_meta(new_a_type)) {
if (delay_factor < to_delay_factor(cnstr_group::DelayedChoice)) {
// postpone...
return lazy_list<constraints>(constraints(mk_coercion_cnstr(from_tc, to_tc, infom, m, a, a_type, justification(),
delay_factor+1, lift_coe)));
} else {
// giveup...
return lazy_list<constraints>(constraints(mk_eq_cnstr(meta, a, justification())));
}
}
constraint_seq cs;
new_a_type = from_tc.whnf(new_a_type, cs);
if ((lift_coe && is_pi_meta(d_type)) || (!lift_coe && is_meta(d_type))) {
// case-split
buffer<expr> locals;
expr it_from = new_a_type;
expr it_to = d_type;
while (is_pi(it_from) && is_pi(it_to)) {
expr dom_from = binding_domain(it_from);
expr dom_to = binding_domain(it_to);
if (!from_tc.is_def_eq(dom_from, dom_to, justification(), cs))
return lazy_list<constraints>();
expr local = mk_local(mk_fresh_name(), binding_name(it_from), dom_from, binder_info());
locals.push_back(local);
it_from = instantiate(binding_body(it_from), local);
it_to = instantiate(binding_body(it_to), local);
}
buffer<expr> alts;
get_coercions_from(from_tc.env(), it_from, alts);
expr fn_a;
if (!locals.empty())
fn_a = mk_local(mk_fresh_name(), "f", new_a_type, binder_info());
buffer<constraints> choices;
buffer<expr> coes;
// first alternative: no coercion
constraint_seq cs1 = cs + mk_eq_cnstr(meta, a, justification());
choices.push_back(cs1.to_list());
unsigned i = alts.size();
while (i > 0) {
--i;
expr coe = alts[i];
if (!locals.empty())
coe = Fun(fn_a, Fun(locals, mk_app(coe, mk_app(fn_a, locals))));
expr new_a = copy_tag(a, mk_app(coe, a));
coes.push_back(coe);
constraint_seq csi = cs + mk_eq_cnstr(meta, new_a, new_a_type_jst);
choices.push_back(csi.to_list());
}
return choose(std::make_shared<coercion_elaborator>(infom, meta,
to_list(choices.begin(), choices.end()),
to_list(coes.begin(), coes.end())));
} else {
list<expr> coes = get_coercions_from_to(from_tc, to_tc, new_a_type, d_type, cs, lift_coe);
if (is_nil(coes)) {
expr new_a = a;
infom.erase_coercion_info(a);
cs += mk_eq_cnstr(meta, new_a, new_a_type_jst);
return lazy_list<constraints>(cs.to_list());
} else if (is_nil(tail(coes))) {
expr new_a = copy_tag(a, mk_app(head(coes), a));
infom.save_coercion_info(a, new_a);
cs += mk_eq_cnstr(meta, new_a, new_a_type_jst);
return lazy_list<constraints>(cs.to_list());
} else {
list<constraints> choices = map2<constraints>(coes, [&](expr const & coe) {
expr new_a = copy_tag(a, mk_app(coe, a));
constraint c = mk_eq_cnstr(meta, new_a, new_a_type_jst);
return (cs + c).to_list();
});
return choose(std::make_shared<coercion_elaborator>(infom, meta, choices, coes, false));
}
}
};
return mk_choice_cnstr(m, choice_fn, delay_factor, true, j);
}
/** \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);
}