void ConstraintManager::addConstraint(expr constraint) {
cid idx = id2Constraint.size();
expr pi = Utils::get_ctx().bool_const(string("pmuc"+to_string(idx)).c_str());
id2Constraint.push_back(constraint);
if (isHLC)
constraint = Utils::convert_to_cnf_simplified(constraint);
vector<clid> clauses;
if (constraint.decl().decl_kind() == Z3_OP_AND) {
for (unsigned i = 0; i < constraint.num_args(); ++i) {
clauses.push_back(clid2Clause.size());
clid2Clause.push_back(constraint.arg(i));
clid2Cid.push_back(idx);
}
}
else {
clauses.push_back(clid2Clause.size());
clid2Clause.push_back(constraint);
clid2Cid.push_back(idx);
}
cid2clauses.push_back(clauses);
id2CnfConstraint.push_back(constraint);
id2AssumptionP.push_back(pi);
p2Id[pi] = idx;
}
expr_let::expr_let(name const & n, expr const & t, expr const & v, expr const & b):
expr_cell(expr_kind::Let, ::lean::hash(v.hash(), b.hash()), v.has_metavar() || b.has_metavar() || (t && t.has_metavar())),
m_name(n),
m_type(t),
m_value(v),
m_body(b) {
}
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();
}
virtual stecoll *used_stes() const {
stecoll *l = left ? left->used_stes() : new stecoll;
stecoll *r = right ? right->used_stes() : new stecoll;
l->append(r);
return l;
}
expr update_mlocal(expr const & e, expr const & new_type) {
if (is_eqp(mlocal_type(e), new_type))
return e;
else if (is_metavar(e))
return mk_metavar(mlocal_name(e), new_type, e.get_tag());
else
return mk_local(mlocal_name(e), local_pp_name(e), new_type, local_info(e), e.get_tag());
}
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
}
/*!\brief Expand an expression of the form scale * addition
*
* Provided \c scale is not a sum, expand the expression
* <tt>scale * (+ c a1 ...)</tt> into <tt>scale * c + scale * a1 + ...</tt>.
*/
ptr<const sum>
expand_prod_sum( const expr &scale, const sum &addition )
{
ASSERT( addition.is_expanded() && ! scale.is_a< sum >() );
if( scale.is_numerical() )
{ // easy case -> sum::sca does the work
const number &ns = scale.as_a< numerical >()->get();
ptr< const sum > ret
= ns.unit()
? &addition
: sum::sca( ns, addition );
ret->basic::expand();
return ret;
}
// hard case : distribute term by term
number coef = 0;
ptr< const prod > scale_prod = scale.get()->as_prod();
// addition.size() for nsp * addition
// + 1 for scale_prod * addition.coef()
container::ptr_unsafe_vector< const prod > seq ( addition.size() + 1 );
{ // coefficient handling
const prod* ph = scale_prod.get();
// cannot be numerical since [scale_prod] isn't
seq.push_back( prod::handle::sca( ph, addition.coef() ) );
}
for(const prod* p : addition)
{
ASSERT( p );
const expr ex = prod::mul( *p, *scale_prod );
// seams reasonable here
ASSERT( ! ex.is_a< sum >() );
if( ex.is_numerical() )
coef += ex.as_a< numerical >()->get();
else
seq.push_back( ex.get()->as_prod() );
}
expand_detail::sort( seq.begin(), seq.end() );
ptr< const sum > ret = sum::from_sorted_prod_range( coef, seq.begin(), seq.end() );
ret->basic::expand(); // mark expanded
return ret;
}
bool basic::match(const expr &e, match_state &mm) const
{
if( e.is_a< wildcard_ >() )
return match_wild( *this, *e.as_a< wildcard_ >(), mm );
if( RTTI_ID( this ) != RTTI_ID( e.get() ) )
return false;
return match_same_type( *e.get(), mm );
}
bool is_arrow(expr const & t) {
optional<bool> r = t.raw()->is_arrow();
if (r) {
return *r;
} else {
bool res = is_pi(t) && !has_free_var(binding_body(t), 0);
t.raw()->set_is_arrow(res);
return res;
}
}
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
}
virtual stecoll *used_stes() const {
stecoll *t = test ? test->used_stes() : new stecoll;
stecoll *l = left ? left->used_stes() : new stecoll;
stecoll *r = right ? right->used_stes() : new stecoll;
t->append(l);
t->append(r);
return t;
}
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();
}
expr_app::expr_app(expr const & fn, expr const & arg, tag g):
expr_composite(expr_kind::App, ::lean::hash(fn.hash(), arg.hash()),
fn.has_expr_metavar() || arg.has_expr_metavar(),
fn.has_univ_metavar() || arg.has_univ_metavar(),
fn.has_local() || arg.has_local(),
fn.has_param_univ() || arg.has_param_univ(),
inc_weight(add_weight(get_weight(fn), get_weight(arg))),
std::max(get_free_var_range(fn), get_free_var_range(arg)),
g),
m_fn(fn), m_arg(arg) {
m_hash = ::lean::hash(m_hash, m_weight);
}
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();
}
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();
}
expr_binding::expr_binding(expr_kind k, name const & n, expr const & t, expr const & b, binder_info const & i, tag g):
expr_composite(k, ::lean::hash(t.hash(), b.hash()),
t.has_expr_metavar() || b.has_expr_metavar(),
t.has_univ_metavar() || b.has_univ_metavar(),
t.has_local() || b.has_local(),
t.has_param_univ() || b.has_param_univ(),
inc_weight(add_weight(get_weight(t), get_weight(b))),
std::max(get_free_var_range(t), dec(get_free_var_range(b))),
g),
m_binder(n, t, i),
m_body(b) {
m_hash = ::lean::hash(m_hash, m_weight);
lean_assert(k == expr_kind::Lambda || k == expr_kind::Pi);
}
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();
}
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();
}
}
// 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");
}
value expr_copy(const expr &e)
{
value res = expr_allocate();
Field( res, 1 ) = RTTI_ID( e.get() );
expr_construct( res ) expr( e );
return res;
}
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;
}
}
/** \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 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
}
virtual stecoll *used_stes() const {
stecoll *x = e ? e->used_stes() : new stecoll;
stecoll *n = next ? next->used_stes() : new stecoll;
x->append(n);
return x;
}
CoreParser::CoreParser(expr& _ast, ArgParser& _parser): formula(_ast), core(_ast){
stats.isInitCoreUsed = true;
vector<expr> initialCore;
stats.originalProblemSize = _ast.num_args();
extractInitialCore(_ast, _parser, initialCore);
stats.coreSize = initialCore.size();
core = Utils::convert_to_cnf_simplified(Utils::m_and(initialCore));
}
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 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));
}
optional<pos_info> parser_pos_provider::get_pos_info(expr const & e) const {
tag t = e.get_tag();
if (t == nulltag)
return optional<pos_info>();
if (auto it = m_pos_table.find(t))
return optional<pos_info>(*it);
else
return optional<pos_info>();
}
bool expr_binop::operator==(expr const& o) const {
bool is_equal = false;
expr_visitor v;
v._([&](expr_binop const* o) {
is_equal =
this->op == o->op && *this->lhs == *o->lhs && *this->rhs == *o->rhs;
});
o.accept(v);
return is_equal;
}
