void scanner::next_utf_core(char c, buffer<char> & cs) {
cs.push_back(c);
while (m_uskip > 0) {
next();
cs.push_back(curr());
}
}
level collect(level const & l) {
return replace(l, [&](level const & l) {
if (is_meta(l)) {
name const & id = meta_id(l);
if (auto r = m_univ_meta_to_param.find(id)) {
return some_level(*r);
} else {
name n = m_prefix.append_after(m_next_idx);
m_next_idx++;
level new_r = mk_param_univ(n);
m_univ_meta_to_param.insert(id, new_r);
m_univ_meta_to_param_inv.insert(n, l);
m_level_params.push_back(n);
return some_level(new_r);
}
} else if (is_param(l)) {
name const & id = param_id(l);
if (!m_found_univ_params.contains(id)) {
m_found_univ_params.insert(id);
m_level_params.push_back(id);
}
}
return none_level();
});
}
expr collect(expr const & e) {
return replace(e, [&](expr const & e, unsigned) {
if (is_metavar(e)) {
name const & id = mlocal_name(e);
if (auto r = m_meta_to_param.find(id)) {
return some_expr(*r);
} else {
expr type = m_ctx.infer(e);
expr x = m_ctx.push_local("_x", type);
m_meta_to_param.insert(id, x);
m_meta_to_param_inv.insert(mlocal_name(x), e);
m_params.push_back(x);
return some_expr(x);
}
} else if (is_local(e)) {
name const & id = mlocal_name(e);
if (!m_found_local.contains(id)) {
m_found_local.insert(id);
m_params.push_back(e);
}
} else if (is_sort(e)) {
return some_expr(update_sort(e, collect(sort_level(e))));
} else if (is_constant(e)) {
return some_expr(update_constant(e, collect(const_levels(e))));
}
return none_expr();
});
}
static name parse_quoted_symbol_or_token(parser & p, buffer<token_entry> & new_tokens, bool & used_default, notation_entry_group grp) {
used_default = false;
if (p.curr_is_quoted_symbol()) {
environment const & env = p.env();
auto pp_tk = p.get_name_val();
auto tks = utf8_trim(pp_tk.to_string());
auto tkcs = tks.c_str();
check_not_forbidden(tkcs);
p.next();
if (p.curr_is_token(get_colon_tk())) {
p.next();
unsigned prec = parse_precedence(p);
new_tokens.push_back(mk_token_entry(tkcs, prec, grp));
} else if (!get_precedence(env, tkcs, grp)) {
new_tokens.push_back(mk_token_entry(tkcs, LEAN_DEFAULT_PRECEDENCE, grp));
used_default = true;
}
return pp_tk;
} else if (p.curr_is_keyword()) {
auto tk = p.get_token_info().token();
check_not_forbidden(tk.to_string().c_str());
p.next();
return tk;
} else {
throw parser_error("invalid notation declaration, symbol expected", p.pos());
}
}
unsigned list_cases_on_core(list<A> const & l, buffer<vm_obj> & data) {
if (empty(l)) {
return 0;
} else {
data.push_back(to_obj(head(l)));
data.push_back(list_to_obj(tail(l)));
return 1;
}
}
void destruct_structure_instance(expr const & e, expr & t, buffer<name> & field_names,
buffer<expr> & field_values, buffer<expr> & using_exprs) {
lean_assert(is_structure_instance(e));
t = macro_arg(e, 0);
list<name> const & fns = static_cast<structure_instance_macro_cell const*>(macro_def(e).raw())->get_field_names();
unsigned num_fileds = length(fns);
to_buffer(fns, field_names);
for (unsigned i = 1; i < num_fileds+1; i++)
field_values.push_back(macro_arg(e, i));
for (unsigned i = num_fileds+1; i < macro_num_args(e); i++)
using_exprs.push_back(macro_arg(e, i));
}
static void parse_filters(parser & p, buffer<std::string> & pos_names, buffer<std::string> & neg_names) {
name plus("+"); name minus("-");
while (p.curr_is_token(get_comma_tk())) {
p.next();
if (p.curr_is_token(plus)) {
p.next();
pos_names.push_back(p.check_id_next("invalid find_decl command, identifier expected").to_string());
} else if (p.curr_is_token(minus)) {
p.next();
neg_names.push_back(p.check_id_next("invalid find_decl command, identifier expected").to_string());
} else {
pos_names.push_back(p.check_id_next("invalid find_decl command, '+', '-', or identifier expected").to_string());
}
}
}
static transition parse_transition(parser & p, optional<parse_table> const & pt, name const & tk,
buffer<expr> & locals, buffer<token_entry> & new_tokens, notation_entry_group grp,
name const & pp_tk) {
if (p.curr_is_token_or_id(get_binder_tk())) {
p.next();
unsigned rbp = parse_binders_rbp(p);
return transition(tk, mk_binder_action(rbp), pp_tk);
} else if (p.curr_is_token_or_id(get_binders_tk())) {
p.next();
unsigned rbp = parse_binders_rbp(p);
return transition(tk, mk_binders_action(rbp), pp_tk);
} else if (p.curr_is_identifier()) {
unsigned default_prec = get_default_prec(pt, tk);
name n = p.get_name_val();
p.next();
action a = parse_action(p, tk, default_prec, locals, new_tokens, grp);
expr local_type = mk_Prop(); // type used in notation local declarations, it is irrelevant
expr l = mk_local(n, local_type);
p.add_local(l);
locals.push_back(l);
return transition(tk, a, pp_tk);
} else if (p.curr_is_quoted_symbol() || p.curr_is_keyword() ||
p.curr_is_token(get_assign_tk()) || p.curr_is_command() || p.curr_is_eof()) {
return transition(tk, mk_skip_action(), pp_tk);
} else {
throw parser_error("invalid notation declaration, quoted-symbol, identifier, "
"'binder', 'binders' expected", p.pos());
}
}
static notation_entry parse_mixfix_notation(parser & p, mixfix_kind k, bool overload, notation_entry_group grp,
buffer<token_entry> & new_tokens, bool parse_only, unsigned priority) {
auto nt = parse_mixfix_notation(p, k, overload, grp, parse_only, priority);
if (nt.second)
new_tokens.push_back(*nt.second);
return nt.first;
}
void get_rec_args(environment const & env, name const & n, buffer<buffer<bool>> & r) {
lean_assert(inductive::is_inductive_decl(env, n));
type_checker tc(env);
name_generator ngen;
declaration ind_decl = env.get(n);
declaration rec_decl = env.get(inductive::get_elim_name(n));
unsigned nparams = *inductive::get_num_params(env, n);
unsigned nminors = *inductive::get_num_minor_premises(env, n);
unsigned ntypeformers = *inductive::get_num_type_formers(env, n);
buffer<expr> rec_args;
to_telescope(ngen, rec_decl.get_type(), rec_args);
buffer<name> typeformer_names;
for (unsigned i = nparams; i < nparams + ntypeformers; i++) {
typeformer_names.push_back(mlocal_name(rec_args[i]));
}
lean_assert(typeformer_names.size() == ntypeformers);
r.clear();
// add minor premises
for (unsigned i = nparams + ntypeformers; i < nparams + ntypeformers + nminors; i++) {
r.push_back(buffer<bool>());
buffer<bool> & bv = r.back();
expr minor_type = mlocal_type(rec_args[i]);
buffer<expr> minor_args;
to_telescope(ngen, minor_type, minor_args);
for (expr & minor_arg : minor_args) {
buffer<expr> minor_arg_args;
expr minor_arg_type = to_telescope(tc, mlocal_type(minor_arg), minor_arg_args);
bv.push_back(is_typeformer_app(typeformer_names, minor_arg_type));
}
}
}
void expr_cell::dec_ref(expr & e, buffer<expr_cell*> & todelete) {
if (e.m_ptr) {
expr_cell * c = e.steal_ptr();
lean_assert(!(e.m_ptr));
if (c->dec_ref_core())
todelete.push_back(c);
}
}
void push_max_args(level const & l, buffer<level> & r) {
if (is_max(l)) {
push_max_args(max_lhs(l), r);
push_max_args(max_rhs(l), r);
} else {
r.push_back(l);
}
}
friend void copy_limbs(imp * p, buffer<name::imp *> & limbs) {
limbs.clear();
while (p != nullptr) {
limbs.push_back(p);
p = p->m_prefix;
}
std::reverse(limbs.begin(), limbs.end());
}
static pair<expr, unsigned> extract_arg_types_core(environment const & env, name const & f, buffer<expr> & arg_types) {
declaration d = env.get(f);
expr f_type = d.get_type();
while (is_pi(f_type)) {
arg_types.push_back(binding_domain(f_type));
f_type = binding_body(f_type);
}
return mk_pair(f_type, length(d.get_univ_params()));
}
void get_simp_extensions_for(environment const & env, name const & head, buffer<unsigned> & ext_ids) {
simp_ext_state s = simp_ext_ext::get_state(env);
if (auto q = s.find(head)) {
buffer<simp_ext_record> records;
q->for_each([&](simp_ext_record const & r) {
ext_ids.push_back(r.m_ext_id);
});
}
}
void ast_translation::copy_params(decl * d, unsigned rpos, buffer<parameter> & ps) {
unsigned num = d->get_num_parameters();
unsigned j = rpos;
for (unsigned i = 0; i < num; i++) {
parameter const & p = d->get_parameter(i);
if (p.is_ast()) {
ps.push_back(parameter(m_result_stack[j]));
j++;
}
else if (p.is_external()) {
SASSERT(d->get_family_id() != null_family_id);
decl_plugin & from_plugin = *(m_from_manager.get_plugin(d->get_family_id()));
decl_plugin & to_plugin = *(m_to_manager.get_plugin(d->get_family_id()));
ps.push_back(from_plugin.translate(p, to_plugin));
}
else {
ps.push_back(p);
}
}
}
static void parse_notation_local(parser & p, buffer<expr> & locals) {
if (p.curr_is_identifier()) {
name n = p.get_name_val();
p.next();
expr local_type = mk_Prop(); // type used in notation local declarations, it is irrelevant
expr l = mk_local(n, local_type); // remark: the type doesn't matter
p.add_local(l);
locals.push_back(l);
} else {
throw parser_error("invalid notation declaration, identifier expected", p.pos());
}
}
unsigned level_cases_on(vm_obj const & o, buffer<vm_obj> & data) {
level const & l = to_level(o);
switch (l.kind()) {
case level_kind::Zero:
break;
case level_kind::Succ:
data.push_back(to_obj(succ_of(l)));
break;
case level_kind::Max:
data.push_back(to_obj(max_lhs(l)));
data.push_back(to_obj(max_rhs(l)));
break;
case level_kind::IMax:
data.push_back(to_obj(imax_lhs(l)));
data.push_back(to_obj(imax_rhs(l)));
break;
case level_kind::Param:
data.push_back(to_obj(param_id(l)));
break;
case level_kind::Global:
data.push_back(to_obj(global_id(l)));
break;
case level_kind::Meta:
data.push_back(to_obj(meta_id(l)));
break;
}
return static_cast<unsigned>(l.kind());
}
void parse_table::for_each(buffer<transition> & ts,
std::function<void(unsigned, transition const *,
list<accepting> const &)> const & fn) const {
if (!is_nil(m_ptr->m_accept))
fn(ts.size(), ts.data(), m_ptr->m_accept);
m_ptr->m_children.for_each([&](name const & k, list<pair<action, parse_table>> const & lst) {
for (auto const & p : lst) {
ts.push_back(transition(k, p.first));
p.second.for_each(ts, fn);
ts.pop_back();
}
});
}
void get_structure_instance_info(expr const & e,
name & struct_name,
optional<expr> & source,
buffer<name> & field_names,
buffer<expr> & field_values) {
lean_assert(is_structure_instance(e));
struct_name = static_cast<structure_instance_macro_cell const*>(macro_def(e).raw())->get_struct();
list<name> const & fns = static_cast<structure_instance_macro_cell const*>(macro_def(e).raw())->get_field_names();
to_buffer(fns, field_names);
unsigned num_fields = field_names.size();
lean_assert(macro_num_args(e) == num_fields || macro_num_args(e) == num_fields+1);
if (num_fields < macro_num_args(e))
source = macro_arg(e, num_fields);
for (unsigned i = 0; i < num_fields; i++)
field_values.push_back(macro_arg(e, i));
}
parse_table parse_table::add_core(unsigned num, transition const * ts, expr const & a,
unsigned priority, bool overload, buffer<action> & post_buffer) const {
parse_table r(new cell(*m_ptr));
if (num == 0) {
list<action> postponed = to_list(post_buffer);
if (!overload) {
r.m_ptr->m_accept = to_list(accepting(priority, postponed, a));
} else {
auto new_accept = filter(r.m_ptr->m_accept, [&](accepting const & p) {
return p.get_expr() != a || p.get_postponed() != postponed;
});
r.m_ptr->m_accept = insert(new_accept, priority, postponed, a);
}
} else {
list<pair<action, parse_table>> const * it = r.m_ptr->m_children.find(ts->get_token());
action const & ts_act = ts->get_action();
action_kind k = ts_act.kind();
if (k == action_kind::Exprs || k == action_kind::ScopedExpr)
post_buffer.push_back(ts_act);
list<pair<action, parse_table>> new_lst;
if (it) {
if (contains_equivalent_action(*it, ts_act)) {
buffer<pair<action, parse_table>> tmp;
to_buffer(*it, tmp);
for (pair<action, parse_table> & p : tmp) {
if (p.first.is_equivalent(ts_act)) {
p.second = p.second.add_core(num-1, ts+1, a, priority, overload, post_buffer);
break;
}
}
new_lst = to_list(tmp);
} else {
// remove incompatible actions
new_lst = filter(*it, [&](pair<action, parse_table> const & p) {
return p.first.is_compatible(ts_act);
});
parse_table new_child = parse_table().add_core(num-1, ts+1, a, priority, overload, post_buffer);
new_lst = cons(mk_pair(ts_act, new_child), new_lst);
}
} else {
parse_table new_child = parse_table().add_core(num-1, ts+1, a, priority, overload, post_buffer);
new_lst = to_list(mk_pair(ts_act, new_child));
}
r.m_ptr->m_children.insert(ts->get_token(), new_lst);
}
return r;
}
bool collect(expr cls, expr const & l, buffer<expr> & R, extension_context & ctx) const {
check_system("resolve macro");
expr lhs, rhs;
if (is_or(cls, lhs, rhs)) {
return collect(lhs, rhs, l, R, ctx);
} else {
cls = whnf(cls, ctx);
if (is_or(cls, lhs, rhs)) {
return collect(lhs, rhs, l, R, ctx);
} else if (is_def_eq(cls, l, ctx)) {
return true; // found literal l
} else {
if (!already_contains(cls, R, ctx))
R.push_back(cls);
return false;
}
}
}
/* Collect (and sort) dependencies of collected parameters */
void collect_and_normalize_dependencies(buffer<expr> & norm_params) {
name_map<expr> new_types;
for (unsigned i = 0; i < m_params.size(); i++) {
expr x = m_params[i];
expr new_type = collect(m_ctx.instantiate_mvars(m_ctx.infer(x)));
new_types.insert(mlocal_name(x), new_type);
}
local_context const & lctx = m_ctx.lctx();
std::sort(m_params.begin(), m_params.end(), [&](expr const & l1, expr const & l2) {
return lctx.get_local_decl(l1)->get_idx() < lctx.get_local_decl(l2)->get_idx();
});
for (unsigned i = 0; i < m_params.size(); i++) {
expr x = m_params[i];
expr type = *new_types.find(mlocal_name(x));
expr new_type = replace_locals(type, i, m_params.data(), norm_params.data());
expr new_param = m_ctx.push_local(local_pp_name(x), new_type, local_info(x));
norm_params.push_back(new_param);
}
}
void lar_solver::get_infeasibility_evidence_for_inf_sign(buffer<std::pair<mpq, constraint_index>> & evidence,
const std::vector<std::pair<mpq, unsigned>> & inf_row,
int inf_sign) {
for (auto & it : inf_row) {
mpq coeff = it.first;
unsigned j = it.second;
auto it1 = m_map_from_column_indices_to_var_index.find(j);
lean_assert(it1 != m_map_from_column_indices_to_var_index.end());
unsigned var_j = it1->second;
auto it2 = m_map_from_var_index_to_column_info_with_cls.find(var_j);
lean_assert(it2 != m_map_from_var_index_to_column_info_with_cls.end());
canonic_left_side * ls = it2->second.m_canonic_left_side;
int adj_sign = coeff.is_pos() ? inf_sign : -inf_sign;
lar_normalized_constraint * bound_constr = adj_sign < 0? ls->m_upper_bound_witness : ls->m_low_bound_witness;
lean_assert(bound_constr != nullptr);
evidence.push_back(std::make_pair(coeff / bound_constr->m_ratio_to_original, bound_constr->m_index));
}
}
void simp_rule_sets::get_relations(buffer<name> & rs) const {
m_sets.for_each([&](name const & r, simp_rule_set const &) {
rs.push_back(r);
});
}
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);
});
}
unsigned array_cases_on(vm_obj const & o, buffer<vm_obj> & data) {
vm_obj d[3] = {o, mk_vm_unit(), mk_vm_unit()};
vm_obj fn = mk_vm_closure(g_array_read_idx, 3, d);
data.push_back(fn);
return 0;
}