optional<expr> mk_class_instance(environment const & env, io_state const & ios, local_context const & ctx,
name const & prefix, expr const & type, bool relax_opaque, bool use_local_instances,
unifier_config const & cfg) {
auto C = std::make_shared<class_instance_context>(env, ios, prefix, relax_opaque, use_local_instances);
if (!is_ext_class(C->tc(), type))
return none_expr();
expr meta = ctx.mk_meta(C->m_ngen, some_expr(type), type.get_tag());
unsigned depth = 0;
constraint c = mk_class_instance_cnstr(C, ctx, meta, depth);
unifier_config new_cfg(cfg);
new_cfg.m_discard = true;
new_cfg.m_use_exceptions = true;
new_cfg.m_pattern = true;
new_cfg.m_kind = C->m_conservative ? unifier_kind::VeryConservative : unifier_kind::Liberal;
try {
auto seq = unify(env, 1, &c, C->m_ngen.mk_child(), substitution(), new_cfg);
while (true) {
auto p = seq.pull();
lean_assert(p);
substitution s = p->first.first;
expr r = s.instantiate_all(meta);
if (!has_expr_metavar_relaxed(r))
return some_expr(r);
seq = p->second;
}
} catch (exception &) {
return none_expr();
}
}
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);
}
/** \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);
}