expr visit(expr const & e) {
switch (e.kind()) {
case expr_kind::Sort: case expr_kind::Constant:
case expr_kind::Var: case expr_kind::Meta:
case expr_kind::Local:
return e;
default:
break;
}
check_system("unfold macros");
auto it = m_cache.find(e);
if (it != m_cache.end())
return it->second;
switch (e.kind()) {
case expr_kind::Sort: case expr_kind::Constant:
case expr_kind::Var: case expr_kind::Meta:
case expr_kind::Local:
lean_unreachable();
case expr_kind::Macro:
return save_result(e, visit_macro(e));
case expr_kind::App:
return save_result(e, visit_app(e));
case expr_kind::Lambda: case expr_kind::Pi:
return save_result(e, visit_binding(e));
}
lean_unreachable();
}
bool is_lt(expr const & a, expr const & b, bool use_hash) {
if (is_eqp(a, b)) return false;
unsigned wa = get_weight(a);
unsigned wb = get_weight(b);
if (wa < wb) return true;
if (wa > wb) return false;
if (a.kind() != b.kind()) return a.kind() < b.kind();
if (use_hash) {
if (a.hash() < b.hash()) return true;
if (a.hash() > b.hash()) return false;
}
if (a == b) return false;
switch (a.kind()) {
case expr_kind::Var:
return var_idx(a) < var_idx(b);
case expr_kind::Constant:
if (const_name(a) != const_name(b))
return const_name(a) < const_name(b);
else
return is_lt(const_levels(a), const_levels(b), use_hash);
case expr_kind::App:
if (app_fn(a) != app_fn(b))
return is_lt(app_fn(a), app_fn(b), use_hash);
else
return is_lt(app_arg(a), app_arg(b), use_hash);
case expr_kind::Lambda: case expr_kind::Pi:
if (binding_domain(a) != binding_domain(b))
return is_lt(binding_domain(a), binding_domain(b), use_hash);
else
return is_lt(binding_body(a), binding_body(b), use_hash);
case expr_kind::Let:
if (let_type(a) != let_type(b))
return is_lt(let_type(a), let_type(b), use_hash);
else if (let_value(a) != let_value(b))
return is_lt(let_value(a), let_value(b), use_hash);
else
return is_lt(let_body(a), let_body(b), use_hash);
case expr_kind::Sort:
return is_lt(sort_level(a), sort_level(b), use_hash);
case expr_kind::Local: case expr_kind::Meta:
if (mlocal_name(a) != mlocal_name(b))
return mlocal_name(a) < mlocal_name(b);
else
return is_lt(mlocal_type(a), mlocal_type(b), use_hash);
case expr_kind::Macro:
if (macro_def(a) != macro_def(b))
return macro_def(a) < macro_def(b);
if (macro_num_args(a) != macro_num_args(b))
return macro_num_args(a) < macro_num_args(b);
for (unsigned i = 0; i < macro_num_args(a); i++) {
if (macro_arg(a, i) != macro_arg(b, i))
return is_lt(macro_arg(a, i), macro_arg(b, i), use_hash);
}
return false;
}
lean_unreachable(); // LCOV_EXCL_LINE
}
bool apply(expr const & a, expr const & b) {
if (is_eqp(a, b)) return true;
if (a.hash() != b.hash()) return false;
if (a.kind() != b.kind()) return false;
if (is_var(a)) return var_idx(a) == var_idx(b);
if (m_cache.check(a, b))
return true;
switch (a.kind()) {
case expr_kind::Var:
lean_unreachable(); // LCOV_EXCL_LINE
case expr_kind::Constant:
return
const_name(a) == const_name(b) &&
compare(const_levels(a), const_levels(b), [](level const & l1, level const & l2) { return l1 == l2; });
case expr_kind::Meta:
return
mlocal_name(a) == mlocal_name(b) &&
apply(mlocal_type(a), mlocal_type(b));
case expr_kind::Local:
return
mlocal_name(a) == mlocal_name(b) &&
apply(mlocal_type(a), mlocal_type(b)) &&
(!CompareBinderInfo || local_pp_name(a) == local_pp_name(b)) &&
(!CompareBinderInfo || local_info(a) == local_info(b));
case expr_kind::App:
check_system();
return
apply(app_fn(a), app_fn(b)) &&
apply(app_arg(a), app_arg(b));
case expr_kind::Lambda: case expr_kind::Pi:
check_system();
return
apply(binding_domain(a), binding_domain(b)) &&
apply(binding_body(a), binding_body(b)) &&
(!CompareBinderInfo || binding_name(a) == binding_name(b)) &&
(!CompareBinderInfo || binding_info(a) == binding_info(b));
case expr_kind::Let:
check_system();
return
apply(let_type(a), let_type(b)) &&
apply(let_value(a), let_value(b)) &&
apply(let_body(a), let_body(b)) &&
(!CompareBinderInfo || let_name(a) == let_name(b));
case expr_kind::Sort:
return sort_level(a) == sort_level(b);
case expr_kind::Macro:
check_system();
if (macro_def(a) != macro_def(b) || macro_num_args(a) != macro_num_args(b))
return false;
for (unsigned i = 0; i < macro_num_args(a); i++) {
if (!apply(macro_arg(a, i), macro_arg(b, i)))
return false;
}
return true;
}
lean_unreachable(); // LCOV_EXCL_LINE
}
bool expr_eq_fn::apply(expr const & a, expr const & b) {
if (is_eqp(a, b)) return true;
if (a.hash() != b.hash()) return false;
if (a.kind() != b.kind()) return false;
if (is_var(a)) return var_idx(a) == var_idx(b);
if (m_counter >= LEAN_EQ_CACHE_THRESHOLD && is_shared(a) && is_shared(b)) {
auto p = std::make_pair(a.raw(), b.raw());
if (!m_eq_visited)
m_eq_visited.reset(new expr_cell_pair_set);
if (m_eq_visited->find(p) != m_eq_visited->end())
return true;
m_eq_visited->insert(p);
}
check_system("expression equality test");
switch (a.kind()) {
case expr_kind::Var:
lean_unreachable(); // LCOV_EXCL_LINE
case expr_kind::Constant:
return
const_name(a) == const_name(b) &&
compare(const_levels(a), const_levels(b), [](level const & l1, level const & l2) { return l1 == l2; });
case expr_kind::Local: case expr_kind::Meta:
return
mlocal_name(a) == mlocal_name(b) &&
apply(mlocal_type(a), mlocal_type(b));
case expr_kind::App:
m_counter++;
return
apply(app_fn(a), app_fn(b)) &&
apply(app_arg(a), app_arg(b));
case expr_kind::Lambda: case expr_kind::Pi:
m_counter++;
return
apply(binding_domain(a), binding_domain(b)) &&
apply(binding_body(a), binding_body(b)) &&
(!m_compare_binder_info || binding_info(a) == binding_info(b));
case expr_kind::Sort:
return sort_level(a) == sort_level(b);
case expr_kind::Macro:
m_counter++;
if (macro_def(a) != macro_def(b) || macro_num_args(a) != macro_num_args(b))
return false;
for (unsigned i = 0; i < macro_num_args(a); i++) {
if (!apply(macro_arg(a, i), macro_arg(b, i)))
return false;
}
return true;
case expr_kind::Let:
m_counter++;
return
apply(let_type(a), let_type(b)) &&
apply(let_value(a), let_value(b)) &&
apply(let_body(a), let_body(b));
}
lean_unreachable(); // LCOV_EXCL_LINE
}
bool is_lt_no_level_params(expr const & a, expr const & b) {
if (is_eqp(a, b)) return false;
unsigned wa = get_weight(a);
unsigned wb = get_weight(b);
if (wa < wb) return true;
if (wa > wb) return false;
if (a.kind() != b.kind()) return a.kind() < b.kind();
switch (a.kind()) {
case expr_kind::Var:
return var_idx(a) < var_idx(b);
case expr_kind::Constant:
if (const_name(a) != const_name(b))
return const_name(a) < const_name(b);
else
return is_lt_no_level_params(const_levels(a), const_levels(b));
case expr_kind::App:
if (is_lt_no_level_params(app_fn(a), app_fn(b)))
return true;
else if (is_lt_no_level_params(app_fn(b), app_fn(a)))
return false;
else
return is_lt_no_level_params(app_arg(a), app_arg(b));
case expr_kind::Lambda: case expr_kind::Pi:
if (is_lt_no_level_params(binding_domain(a), binding_domain(b)))
return true;
else if (is_lt_no_level_params(binding_domain(b), binding_domain(a)))
return false;
else
return is_lt_no_level_params(binding_body(a), binding_body(b));
case expr_kind::Sort:
return is_lt_no_level_params(sort_level(a), sort_level(b));
case expr_kind::Local: case expr_kind::Meta:
if (mlocal_name(a) != mlocal_name(b))
return mlocal_name(a) < mlocal_name(b);
else
return is_lt_no_level_params(mlocal_type(a), mlocal_type(b));
case expr_kind::Macro:
if (macro_def(a) != macro_def(b))
return macro_def(a) < macro_def(b);
if (macro_num_args(a) != macro_num_args(b))
return macro_num_args(a) < macro_num_args(b);
for (unsigned i = 0; i < macro_num_args(a); i++) {
if (is_lt_no_level_params(macro_arg(a, i), macro_arg(b, i)))
return true;
else if (is_lt_no_level_params(macro_arg(b, i), macro_arg(a, i)))
return false;
}
return false;
}
lean_unreachable();
}
/** \brief Return true iff all recursive applications in \c e are structurally smaller than \c m_pattern. */
bool check_rhs(expr const & e) {
switch (e.kind()) {
case expr_kind::Var: case expr_kind::Meta:
case expr_kind::Local: case expr_kind::Constant:
case expr_kind::Sort:
return true;
case expr_kind::Macro:
for (unsigned i = 0; i < macro_num_args(e); i++)
if (!check_rhs(macro_arg(e, i)))
return false;
return true;
case expr_kind::App: {
buffer<expr> args;
expr const & fn = get_app_args(e, args);
if (!check_rhs(fn))
return false;
for (unsigned i = 0; i < args.size(); i++)
if (!check_rhs(args[i]))
return false;
if (is_local(fn) && mlocal_name(fn) == mlocal_name(m_fn)) {
/* recusive application */
if (m_arg_idx < args.size()) {
expr const & arg = args[m_arg_idx];
/* arg must be structurally smaller than m_pattern */
if (!is_lt(arg, m_pattern)) {
trace_struct_aux(tout() << "structural recursion on argument #" << (m_arg_idx+1)
<< " was not used "
<< "for '" << m_fn << "'\nargument #" << (m_arg_idx+1)
<< " in the application\n "
<< e << "\nis not structurally smaller than the one occurring in "
<< "the equation left-hand-side\n "
<< m_lhs << "\n";);
return false;
}
} else {
expr apply(expr const & a) {
check_system("max_sharing");
auto r = m_expr_cache.find(a);
if (r != m_expr_cache.end())
return *r;
expr res;
switch (a.kind()) {
case expr_kind::Var:
res = a;
break;
case expr_kind::Constant:
res = update_constant(a, map(const_levels(a), [&](level const & l) { return apply(l); }));
break;
case expr_kind::Sort:
res = update_sort(a, apply(sort_level(a)));
break;
case expr_kind::App:
res = update_app(a, apply(app_fn(a)), apply(app_arg(a)));
break;
case expr_kind::Lambda: case expr_kind::Pi:
res = update_binding(a, apply(binding_domain(a)), apply(binding_body(a)));
break;
case expr_kind::Meta: case expr_kind::Local:
res = update_mlocal(a, apply(mlocal_type(a)));
break;
case expr_kind::Macro: {
buffer<expr> new_args;
for (unsigned i = 0; i < macro_num_args(a); i++)
new_args.push_back(macro_arg(a, i));
res = update_macro(a, new_args.size(), new_args.data());
break;
}}
m_expr_cache.insert(res);
return res;
}
void forward_branch_extension::index_expr(expr const & e) {
// TODO(dhs): index the target when it gets updated
if (auto head_idx = to_head_index(e)) {
m_index.insert(head_index(e), e);
}
switch (e.kind()) {
case expr_kind::Var:
lean_unreachable(); // LCOV_EXCL_LINE
case expr_kind::Local:
case expr_kind::Meta:
case expr_kind::Sort:
case expr_kind::Constant:
case expr_kind::Macro: // TODO(dhs): do I unfold macros?
break;
case expr_kind::Lambda:
case expr_kind::Pi:
// TODO(dhs): confirm that I only index quantified-free hypotheses
break;
case expr_kind::Let:
// Let-expressions must be unfolded before invoking this method
lean_unreachable();
case expr_kind::App:
index_expr(app_fn(e));
index_expr(app_arg(e));
break;
}
}
// scoped_expr_actions must occur after a Binder/Binders.
static void validate_transitions(bool nud, unsigned num, transition const * ts, expr const & a) {
unsigned nargs = 0;
if (!nud)
nargs++; // led tables have an implicit left argument
bool found_binder = false;
for (unsigned i = 0; i < num; i++) {
action const & a = ts[i].get_action();
switch (a.kind()) {
case action_kind::Binder: case action_kind::Binders:
found_binder = true;
break;
case action_kind::Expr: case action_kind::Exprs: case action_kind::Ext: case action_kind::LuaExt:
nargs++;
break;
case action_kind::ScopedExpr:
if (!found_binder)
throw exception("invalid notation declaration, a scoped expression must occur after a binder element");
nargs++;
break;
case action_kind::Skip:
break;
}
}
if (get_free_var_range(a) > nargs)
throw exception("invalid notation declaration, expression template has more free variables than arguments");
}
expr replace_visitor::visit(expr const & e) {
check_system("expression replacer");
bool shared = false;
if (is_shared(e)) {
shared = true;
auto it = m_cache.find(e);
if (it != m_cache.end())
return it->second;
}
switch (e.kind()) {
case expr_kind::Sort: return save_result(e, visit_sort(e), shared);
case expr_kind::Macro: return save_result(e, visit_macro(e), shared);
case expr_kind::Constant: return save_result(e, visit_constant(e), shared);
case expr_kind::Var: return save_result(e, visit_var(e), shared);
case expr_kind::Meta: return save_result(e, visit_meta(e), shared);
case expr_kind::Local: return save_result(e, visit_local(e), shared);
case expr_kind::App: return save_result(e, visit_app(e), shared);
case expr_kind::Lambda: return save_result(e, visit_lambda(e), shared);
case expr_kind::Pi: return save_result(e, visit_pi(e), shared);
case expr_kind::Let: return save_result(e, visit_let(e), shared);
}
lean_unreachable(); // LCOV_EXCL_LINE
}
void process(expr e)
{
if (e.num_args() > 0)
{
for (int i = 0; i < e.num_args(); i++)
process(e.arg(i));
return;
}
if (e.kind() != Z3_APP_AST) return; //not a variable
VARIBLE_VALUE vv;
func_decl def = e.decl();
vv.name = def.name().str();
if (e.is_bool()) // bool
{
if (vv.name == "false" || vv.name == "true") return;
vv.type = "bool";
vv.size = 1;
vv.value = "false";
}
else if (e.is_bv()) //bitvector
{
sort s = def.range();
vv.type = "bitvector";
vv.size = s.bv_size();
vv.value = "0";
}
else // we do not handle other sorts
{
std::cout << "we just handle bool or bitvector.\n";
exit(0);
}
defaultSolution.insert(std::make_pair(def.name().str(), vv));
}
unsigned get_weight(expr const & e) {
switch (e.kind()) {
case expr_kind::Var: case expr_kind::Constant: case expr_kind::Sort:
case expr_kind::Meta: case expr_kind::Local:
return 1;
case expr_kind::Lambda: case expr_kind::Pi: case expr_kind::Macro:
case expr_kind::App: case expr_kind::Let:
return static_cast<expr_composite*>(e.raw())->m_weight;
}
lean_unreachable(); // LCOV_EXCL_LINE
}
unsigned abstract_expr_manager::hash(expr const & e) {
unsigned h;
switch (e.kind()) {
case expr_kind::Constant:
case expr_kind::Local:
case expr_kind::Meta:
case expr_kind::Sort:
case expr_kind::Var:
case expr_kind::Macro:
return e.hash();
case expr_kind::Lambda:
case expr_kind::Pi:
h = hash(binding_domain(e));
// Remark binding_domain(e) may contain de-bruijn variables.
// We can instantiate them eagerly as we do here, or lazily.
// The lazy approach is potentially more efficient, but we would have
// to use something more sophisticated than an instantiate_rev at expr_kind::App
m_locals.push_back(instantiate_rev(m_tctx.mk_tmp_local(binding_domain(e)), m_locals.size(), m_locals.data()));
h = ::lean::hash(h, hash(binding_body(e)));
m_locals.pop_back();
return h;
case expr_kind::Let:
// Let-expressions must be unfolded before invoking this method
lean_unreachable();
case expr_kind::App:
buffer<expr> args;
expr const & f = get_app_args(e, args);
unsigned prefix_sz = m_congr_lemma_manager.get_specialization_prefix_size(instantiate_rev(f, m_locals.size(), m_locals.data()), args.size());
expr new_f = e;
unsigned rest_sz = args.size() - prefix_sz;
for (unsigned i = 0; i < rest_sz; i++)
new_f = app_fn(new_f);
new_f = instantiate_rev(new_f, m_locals.size(), m_locals.data());
optional<congr_lemma> congr = m_congr_lemma_manager.mk_congr(new_f, rest_sz);
h = hash(new_f);
if (!congr) {
for (unsigned i = prefix_sz; i < args.size(); i++) {
h = ::lean::hash(h, hash(args[i]));
}
} else {
lean_assert(length(congr->get_arg_kinds()) == rest_sz);
unsigned i = prefix_sz;
for_each(congr->get_arg_kinds(), [&](congr_arg_kind const & c_kind) {
if (c_kind != congr_arg_kind::Cast) {
h = ::lean::hash(h, hash(args[i]));
}
i++;
});
}
return h;
}
lean_unreachable();
}
static bool is_permutation(expr const & lhs, expr const & rhs, unsigned offset, buffer<optional<unsigned>> & p) {
if (lhs.kind() != rhs.kind())
return false;
switch (lhs.kind()) {
case expr_kind::Constant: case expr_kind::Sort:
case expr_kind::Meta: case expr_kind::Local:
return lhs == rhs;
case expr_kind::Var:
if (var_idx(lhs) < offset) {
return lhs == rhs; // locally bound variable
} else if (var_idx(lhs) - offset < p.size()) {
if (p[var_idx(lhs) - offset]) {
return *(p[var_idx(lhs) - offset]) == var_idx(rhs);
} else {
p[var_idx(lhs) - offset] = var_idx(rhs);
return true;
}
} else {
return lhs == rhs; // free variable
}
case expr_kind::Lambda: case expr_kind::Pi:
return
is_permutation(binding_domain(lhs), binding_domain(rhs), offset, p) &&
is_permutation(binding_body(lhs), binding_body(rhs), offset+1, p);
case expr_kind::App:
return
is_permutation(app_fn(lhs), app_fn(rhs), offset, p) &&
is_permutation(app_arg(lhs), app_arg(rhs), offset, p);
case expr_kind::Macro:
if (macro_def(lhs) != macro_def(rhs) ||
macro_num_args(lhs) != macro_num_args(rhs))
return false;
for (unsigned i = 0; i < macro_num_args(lhs); i++) {
if (!is_permutation(macro_arg(lhs, i), macro_arg(rhs, i), offset, p))
return false;
}
return true;
}
lean_unreachable();
}
expr visit_binding(expr e) {
expr_kind k = e.kind();
buffer<expr> es;
buffer<expr> ls;
while (e.kind() == k) {
expr d = visit(instantiate_rev(binding_domain(e), ls.size(), ls.data()));
expr l = mk_local(m_tc.mk_fresh_name(), binding_name(e), d, binding_info(e));
ls.push_back(l);
es.push_back(e);
e = binding_body(e);
}
e = visit(instantiate_rev(e, ls.size(), ls.data()));
expr r = abstract_locals(e, ls.size(), ls.data());
while (!ls.empty()) {
expr d = mlocal_type(ls.back());
ls.pop_back();
d = abstract_locals(d, ls.size(), ls.data());
r = update_binding(es.back(), d, r);
es.pop_back();
}
return r;
}
void visit(expr const & e) {
switch (e.kind()) {
case expr_kind::Sort: return;
case expr_kind::Macro: visit_macro(e); return;
case expr_kind::Constant: visit_constant(e); return;
case expr_kind::Var: lean_unreachable();
case expr_kind::Meta: lean_unreachable();
case expr_kind::Local: return;
case expr_kind::App: visit_app(e); return;
case expr_kind::Lambda: visit_binding(e); return;
case expr_kind::Pi: visit_binding(e); return;
case expr_kind::Let: visit_let(e); return;
}
}
expr apply(expr const & a) {
auto r = m_cache.find(a);
if (r != m_cache.end()) {
lean_assert((*r).raw()->max_shared());
return *r;
}
if (a.raw()->max_shared()) {
m_cache.insert(a);
return a;
}
switch (a.kind()) {
case expr_kind::Var: case expr_kind::Constant: case expr_kind::Type: case expr_kind::Value:
cache(a);
return a;
case expr_kind::App: {
expr r = update_app(a, [=](expr const & c){ return apply(c); });
cache(r);
return r;
}
case expr_kind::Eq : {
expr r = update_eq(a, [=](expr const & l, expr const & r){ return std::make_pair(apply(l), apply(r)); });
cache(r);
return r;
}
case expr_kind::Lambda:
case expr_kind::Pi: {
expr r = update_abst(a, [=](expr const & t, expr const & b) { return std::make_pair(apply(t), apply(b)); });
cache(r);
return r;
}
case expr_kind::Let: {
expr r = update_let(a, [=](expr const & t, expr const & v, expr const & b) {
expr new_t = t ? apply(t) : expr();
return std::make_tuple(new_t, apply(v), apply(b));
});
cache(r);
return r;
}
case expr_kind::MetaVar: {
expr r = update_metavar(a, [=](meta_entry const & e) -> meta_entry {
if (e.is_inst())
return mk_inst(e.s(), apply(e.v()));
else
return e;
});
cache(r);
return r;
}}
lean_unreachable();
}
bool is_atomic(expr const & e) {
switch (e.kind()) {
case expr_kind::Constant: case expr_kind::Sort:
case expr_kind::Var:
return true;
case expr_kind::Macro:
return to_macro(e)->get_num_args() == 0;
case expr_kind::App: case expr_kind::Meta:
case expr_kind::Local: case expr_kind::Lambda:
case expr_kind::Pi: case expr_kind::Let:
return false;
}
lean_unreachable(); // LCOV_EXCL_LINE
}
expr copy(expr const & a) {
switch (a.kind()) {
case expr_kind::Var: return mk_var(var_idx(a));
case expr_kind::Constant: return mk_constant(const_name(a));
case expr_kind::Type: return mk_type(ty_level(a));
case expr_kind::Value: return mk_value(static_cast<expr_value*>(a.raw())->m_val);
case expr_kind::App: return mk_app(num_args(a), begin_args(a));
case expr_kind::Eq: return mk_eq(eq_lhs(a), eq_rhs(a));
case expr_kind::Lambda: return mk_lambda(abst_name(a), abst_domain(a), abst_body(a));
case expr_kind::Pi: return mk_pi(abst_name(a), abst_domain(a), abst_body(a));
case expr_kind::Let: return mk_let(let_name(a), let_type(a), let_value(a), let_body(a));
case expr_kind::MetaVar: return mk_metavar(metavar_idx(a), metavar_ctx(a));
}
lean_unreachable();
}
void collect_locals(expr const & e, collected_locals & ls, bool restricted) {
if (!has_local(e))
return;
expr_set visited;
std::function<void(expr const & e)> visit = [&](expr const & e) {
if (!has_local(e))
return;
if (restricted && is_meta(e))
return;
if (visited.find(e) != visited.end())
return;
visited.insert(e);
switch (e.kind()) {
case expr_kind::Var: case expr_kind::Constant: case expr_kind::Sort:
break; // do nothing
case expr_kind::Local:
if (!restricted)
visit(mlocal_type(e));
ls.insert(e);
break;
case expr_kind::Meta:
lean_assert(!restricted);
visit(mlocal_type(e));
break;
case expr_kind::Macro:
for (unsigned i = 0; i < macro_num_args(e); i++)
visit(macro_arg(e, i));
break;
case expr_kind::App:
visit(app_fn(e));
visit(app_arg(e));
break;
case expr_kind::Lambda:
case expr_kind::Pi:
visit(binding_domain(e));
visit(binding_body(e));
break;
case expr_kind::Let:
visit(let_type(e));
visit(let_value(e));
visit(let_body(e));
break;
}
};
visit(e);
}
expr normalize(expr e) {
check_system("normalize");
if (!m_pred(e))
return e;
auto w = m_tc.whnf(e);
e = w.first;
if (m_save_cnstrs)
m_cnstrs += w.second;
switch (e.kind()) {
case expr_kind::Var: case expr_kind::Constant: case expr_kind::Sort:
case expr_kind::Meta: case expr_kind::Local: case expr_kind::Macro:
return e;
case expr_kind::Lambda: case expr_kind::Pi:
return normalize_binding(e);
case expr_kind::App:
return normalize_app(e);
}
lean_unreachable(); // LCOV_EXCL_LINE
}
unsigned light_lt_manager::get_weight_core(expr const & e) {
switch (e.kind()) {
case expr_kind::Var: case expr_kind::Constant: case expr_kind::Sort:
case expr_kind::Meta: case expr_kind::Local:
return 1;
case expr_kind::Lambda: case expr_kind::Pi:
return safe_add(1, safe_add(get_weight(binding_domain(e)), get_weight(binding_body(e))));
case expr_kind::Macro:
return safe_add(1, add_weight(macro_num_args(e), macro_args(e)));
case expr_kind::App:
buffer<expr> args;
expr fn = get_app_args(e, args);
if (is_constant(fn)) {
unsigned const * light_arg = m_lrs.find(const_name(fn));
if (light_arg && args.size() > *light_arg) return get_weight(args[*light_arg]);
}
return safe_add(1, safe_add(get_weight(app_fn(e)), get_weight(app_arg(e))));
}
lean_unreachable(); // LCOV_EXCL_LINE
}
expr dsimplify_core_fn::visit_binding(expr const & e) {
expr_kind k = e.kind();
type_context::tmp_locals locals(m_ctx);
expr b = e;
bool modified = false;
while (b.kind() == k) {
expr d = instantiate_rev(binding_domain(b), locals.size(), locals.data());
expr new_d = visit(d);
if (!is_eqp(d, new_d)) modified = true;
locals.push_local(binding_name(b), new_d, binding_info(b));
b = binding_body(b);
}
b = instantiate_rev(b, locals.size(), locals.data());
expr new_b = visit(b);
if (!is_eqp(b, new_b)) modified = true;
if (modified)
return k == expr_kind::Pi ? locals.mk_pi(new_b) : locals.mk_lambda(new_b);
else
return e;
}
expr apply(expr const & e, unsigned offset) {
bool shared = false;
if (m_use_cache && is_shared(e)) {
if (auto r = m_cache->find(e, offset))
return *r;
shared = true;
}
check_interrupted();
check_memory("replace");
if (optional<expr> r = m_f(e, offset)) {
return save_result(e, offset, *r, shared);
} else {
switch (e.kind()) {
case expr_kind::Constant: case expr_kind::Sort: case expr_kind::Var:
return save_result(e, offset, e, shared);
case expr_kind::Meta: case expr_kind::Local: {
expr new_t = apply(mlocal_type(e), offset);
return save_result(e, offset, update_mlocal(e, new_t), shared);
}
case expr_kind::App: {
expr new_f = apply(app_fn(e), offset);
expr new_a = apply(app_arg(e), offset);
return save_result(e, offset, update_app(e, new_f, new_a), shared);
}
case expr_kind::Pi: case expr_kind::Lambda: {
expr new_d = apply(binding_domain(e), offset);
expr new_b = apply(binding_body(e), offset+1);
return save_result(e, offset, update_binding(e, new_d, new_b), shared);
}
case expr_kind::Macro: {
buffer<expr> new_args;
unsigned nargs = macro_num_args(e);
for (unsigned i = 0; i < nargs; i++)
new_args.push_back(apply(macro_arg(e, i), offset));
return save_result(e, offset, update_macro(e, new_args.size(), new_args.data()), shared);
}}
lean_unreachable();
}
}
expr apply(expr const & a) {
bool sh = false;
if (is_shared(a)) {
auto r = m_cache.find(a.raw());
if (r != m_cache.end())
return r->second;
sh = true;
}
switch (a.kind()) {
case expr_kind::Var: case expr_kind::Constant: case expr_kind::Type: case expr_kind::Value:
return save_result(a, copy(a), sh);
case expr_kind::App: {
buffer<expr> new_args;
for (expr const & old_arg : args(a))
new_args.push_back(apply(old_arg));
return save_result(a, mk_app(new_args), sh);
}
case expr_kind::HEq: return save_result(a, mk_heq(apply(heq_lhs(a)), apply(heq_rhs(a))), sh);
case expr_kind::Pair: return save_result(a, mk_pair(apply(pair_first(a)), apply(pair_second(a)), apply(pair_type(a))), sh);
case expr_kind::Proj: return save_result(a, mk_proj(proj_first(a), apply(proj_arg(a))), sh);
case expr_kind::Lambda: return save_result(a, mk_lambda(abst_name(a), apply(abst_domain(a)), apply(abst_body(a))), sh);
case expr_kind::Pi: return save_result(a, mk_pi(abst_name(a), apply(abst_domain(a)), apply(abst_body(a))), sh);
case expr_kind::Sigma: return save_result(a, mk_sigma(abst_name(a), apply(abst_domain(a)), apply(abst_body(a))), sh);
case expr_kind::Let: return save_result(a, mk_let(let_name(a), apply(let_type(a)), apply(let_value(a)), apply(let_body(a))), sh);
case expr_kind::MetaVar:
return save_result(a,
update_metavar(a, [&](local_entry const & e) -> local_entry {
if (e.is_inst())
return mk_inst(e.s(), apply(e.v()));
else
return e;
}),
sh);
}
lean_unreachable(); // LCOV_EXCL_LINE
}
bool light_lt_manager::is_lt(expr const & a, expr const & b) {
if (is_eqp(a, b)) return false;
unsigned wa = get_weight(a);
unsigned wb = get_weight(b);
if (wa < wb) return true;
if (wa > wb) return false;
if (is_constant(get_app_fn(a))) {
unsigned const * light_arg = m_lrs.find(const_name(get_app_fn(a)));
if (light_arg) {
buffer<expr> args;
get_app_args(a, args);
if (args.size() > *light_arg) return is_lt(args[*light_arg], b);
}
}
if (is_constant(get_app_fn(b))) {
unsigned const * light_arg = m_lrs.find(const_name(get_app_fn(b)));
if (light_arg) {
buffer<expr> args;
get_app_args(b, args);
if (args.size() > *light_arg) return !is_lt(args[*light_arg], a);
}
}
if (a.kind() != b.kind()) return a.kind() < b.kind();
if (a == b) return false;
switch (a.kind()) {
case expr_kind::Var:
return var_idx(a) < var_idx(b);
case expr_kind::Constant:
if (const_name(a) != const_name(b))
return const_name(a) < const_name(b);
else
return ::lean::is_lt(const_levels(a), const_levels(b), false);
case expr_kind::App:
if (app_fn(a) != app_fn(b))
return is_lt(app_fn(a), app_fn(b));
else
return is_lt(app_arg(a), app_arg(b));
case expr_kind::Lambda: case expr_kind::Pi:
if (binding_domain(a) != binding_domain(b))
return is_lt(binding_domain(a), binding_domain(b));
else
return is_lt(binding_body(a), binding_body(b));
case expr_kind::Sort:
return ::lean::is_lt(sort_level(a), sort_level(b), false);
case expr_kind::Local: case expr_kind::Meta:
if (mlocal_name(a) != mlocal_name(b))
return mlocal_name(a) < mlocal_name(b);
else
return is_lt(mlocal_type(a), mlocal_type(b));
case expr_kind::Macro:
if (macro_def(a) != macro_def(b))
return macro_def(a) < macro_def(b);
if (macro_num_args(a) != macro_num_args(b))
return macro_num_args(a) < macro_num_args(b);
for (unsigned i = 0; i < macro_num_args(a); i++) {
if (macro_arg(a, i) != macro_arg(b, i))
return is_lt(macro_arg(a, i), macro_arg(b, i));
}
return false;
}
lean_unreachable(); // LCOV_EXCL_LINE
}
optional<substitution> fo_unify(expr e1, expr e2) {
substitution s;
unsigned i1, i2;
buffer<expr_pair> todo;
todo.emplace_back(e1, e2);
while (!todo.empty()) {
auto p = todo.back();
todo.pop_back();
e1 = find(s, p.first);
e2 = find(s, p.second);
if (e1 != e2) {
if (is_metavar_wo_local_context(e1)) {
assign(s, e1, e2);
} else if (is_metavar_wo_local_context(e2)) {
assign(s, e2, e1);
} else if (is_equality(e1) && is_equality(e2)) {
expr_pair p1 = get_equality_args(e1);
expr_pair p2 = get_equality_args(e2);
todo.emplace_back(p1.second, p2.second);
todo.emplace_back(p1.first, p2.first);
} else {
if (e1.kind() != e2.kind())
return optional<substitution>();
switch (e1.kind()) {
case expr_kind::Var: case expr_kind::Constant: case expr_kind::Type: case expr_kind::Value: case expr_kind::MetaVar:
return optional<substitution>();
case expr_kind::App:
i1 = num_args(e1);
i2 = num_args(e2);
while (i1 > 0 && i2 > 0) {
--i1;
--i2;
if (i1 == 0 && i2 > 0) {
todo.emplace_back(arg(e1, i1), mk_app(i2+1, begin_args(e2)));
} else if (i2 == 0 && i1 > 0) {
todo.emplace_back(mk_app(i1+1, begin_args(e1)), arg(e2, i2));
} else {
todo.emplace_back(arg(e1, i1), arg(e2, i2));
}
}
break;
case expr_kind::Lambda: case expr_kind::Pi:
todo.emplace_back(abst_body(e1), abst_body(e2));
todo.emplace_back(abst_domain(e1), abst_domain(e2));
break;
case expr_kind::Let:
todo.emplace_back(let_body(e1), let_body(e2));
todo.emplace_back(let_value(e1), let_value(e2));
if (static_cast<bool>(let_type(e1)) != static_cast<bool>(let_type(e2)))
return optional<substitution>();
if (let_type(e1)) {
lean_assert(let_type(e2));
todo.emplace_back(*let_type(e1), *let_type(e2));
}
break;
}
}
}
}
return optional<substitution>(s);
}
bool is_lt(expr const & a, expr const & b, bool use_hash) {
if (is_eqp(a, b)) return false;
unsigned da = get_depth(a);
unsigned db = get_depth(b);
if (da < db) return true;
if (da > db) return false;
if (a.kind() != b.kind()) return a.kind() < b.kind();
if (use_hash) {
if (a.hash() < b.hash()) return true;
if (a.hash() > b.hash()) return false;
}
if (a == b) return false;
if (is_var(a)) return var_idx(a) < var_idx(b);
switch (a.kind()) {
case expr_kind::Var:
lean_unreachable(); // LCOV_EXCL_LINE
case expr_kind::Constant:
return const_name(a) < const_name(b);
case expr_kind::App:
if (num_args(a) != num_args(b))
return num_args(a) < num_args(b);
for (unsigned i = 0; i < num_args(a); i++) {
if (arg(a, i) != arg(b, i))
return is_lt(arg(a, i), arg(b, i), use_hash);
}
lean_unreachable(); // LCOV_EXCL_LINE
case expr_kind::Lambda: // Remark: we ignore get_abs_name because we want alpha-equivalence
case expr_kind::Pi:
if (abst_domain(a) != abst_domain(b))
return is_lt(abst_domain(a), abst_domain(b), use_hash);
else
return is_lt(abst_body(a), abst_body(b), use_hash);
case expr_kind::Type:
return ty_level(a) < ty_level(b);
case expr_kind::Value:
return to_value(a) < to_value(b);
case expr_kind::Let:
if (let_type(a) != let_type(b)) {
return is_lt(let_type(a), let_type(b), use_hash);
} else if (let_value(a) != let_value(b)){
return is_lt(let_value(a), let_value(b), use_hash);
} else {
return is_lt(let_body(a), let_body(b), use_hash);
}
case expr_kind::MetaVar:
if (metavar_name(a) != metavar_name(b)) {
return metavar_name(a) < metavar_name(b);
} else {
auto it1 = metavar_lctx(a).begin();
auto it2 = metavar_lctx(b).begin();
auto end1 = metavar_lctx(a).end();
auto end2 = metavar_lctx(b).end();
for (; it1 != end1 && it2 != end2; ++it1, ++it2) {
if (it1->kind() != it2->kind()) {
return it1->kind() < it2->kind();
} else if (it1->s() != it2->s()) {
return it1->s() < it2->s();
} else if (it1->is_inst()) {
if (it1->v() != it2->v())
return is_lt(it1->v(), it2->v(), use_hash);
} else {
if (it1->n() != it2->n())
return it1->n() < it2->n();
}
}
return it1 == end1 && it2 != end2;
}
}
lean_unreachable(); // LCOV_EXCL_LINE
}
expr update_binding(expr const & e, expr const & new_domain, expr const & new_body, binder_info const & bi) {
if (!is_eqp(binding_domain(e), new_domain) || !is_eqp(binding_body(e), new_body) || bi != binding_info(e))
return mk_binding(e.kind(), binding_name(e), new_domain, new_body, bi, e.get_tag());
else
return e;
}
bool abstract_expr_manager::is_equal(expr const & a, expr const & b) {
if (is_eqp(a, b)) return true;
if (a.kind() != b.kind()) return false;
if (is_var(a)) return var_idx(a) == var_idx(b);
bool is_eq;
switch (a.kind()) {
case expr_kind::Var:
lean_unreachable(); // LCOV_EXCL_LINE
case expr_kind::Constant: case expr_kind::Sort:
return a == b;
case expr_kind::Meta: case expr_kind::Local:
return mlocal_name(a) == mlocal_name(b) && is_equal(mlocal_type(a), mlocal_type(b));
case expr_kind::Lambda: case expr_kind::Pi:
if (!is_equal(binding_domain(a), binding_domain(b))) return false;
// see comment at abstract_expr_manager::hash
m_locals.push_back(instantiate_rev(m_tctx.mk_tmp_local(binding_domain(a)), m_locals.size(), m_locals.data()));
is_eq = is_equal(binding_body(a), binding_body(b));
m_locals.pop_back();
return is_eq;
case expr_kind::Macro:
if (macro_def(a) != macro_def(b) || macro_num_args(a) != macro_num_args(b))
return false;
for (unsigned i = 0; i < macro_num_args(a); i++) {
if (!is_equal(macro_arg(a, i), macro_arg(b, i)))
return false;
}
return true;
case expr_kind::App:
buffer<expr> a_args, b_args;
expr const & f_a = get_app_args(a, a_args);
expr const & f_b = get_app_args(b, b_args);
if (!is_equal(f_a, f_b))
return false;
if (a_args.size() != b_args.size())
return false;
unsigned prefix_sz = m_congr_lemma_manager.get_specialization_prefix_size(instantiate_rev(f_a, m_locals.size(), m_locals.data()), a_args.size());
for (unsigned i = 0; i < prefix_sz; i++) {
if (!is_equal(a_args[i], b_args[i]))
return false;
}
expr new_f_a = a;
unsigned rest_sz = a_args.size() - prefix_sz;
for (unsigned i = 0; i < rest_sz; i++) {
new_f_a = app_fn(new_f_a);
}
new_f_a = instantiate_rev(new_f_a, m_locals.size(), m_locals.data());
optional<congr_lemma> congr = m_congr_lemma_manager.mk_congr(new_f_a, rest_sz);
bool not_equal = false;
if (!congr) {
for (unsigned i = prefix_sz; i < a_args.size(); ++i) {
if (!is_equal(a_args[i], b_args[i])) {
not_equal = true;
break;
}
}
} else {
lean_assert(length(congr->get_arg_kinds()) == rest_sz);
unsigned i = prefix_sz;
for_each(congr->get_arg_kinds(), [&](congr_arg_kind const & c_kind) {
if (not_equal)
return;
if (c_kind != congr_arg_kind::Cast && !is_equal(a_args[i], b_args[i])) {
not_equal = true;
}
i++;
});
}
return !not_equal;
}
lean_unreachable(); // LCOV_EXCL_LINE
}
