void context::display_subexprs_info(std::ostream & out, expr * n) const {
ptr_buffer<expr> todo;
todo.push_back(n);
while (!todo.empty()) {
expr * n = todo.back();
todo.pop_back();
out << "#";
out.width(6);
out << std::left << n->get_id();
out << ", relevant: " << is_relevant(n);
if (m_manager.is_bool(n)) {
out << ", val: ";
out.width(7);
out << std::right;
if (lit_internalized(n))
out << get_assignment(n);
else
out << "l_undef";
}
if (e_internalized(n)) {
enode * e = get_enode(n);
out << ", root: #" << e->get_root()->get_owner_id();
}
out << "\n";
if (is_app(n)) {
for (unsigned i = 0; i < to_app(n)->get_num_args(); i++)
todo.push_back(to_app(n)->get_arg(i));
}
}
}
bool quasi_macros::depends_on(expr * e, func_decl * f) const {
ptr_vector<expr> todo;
expr_mark visited;
todo.push_back(e);
while(!todo.empty()) {
expr * cur = todo.back();
todo.pop_back();
if (visited.is_marked(cur))
continue;
if (is_app(cur)) {
app * a = to_app(cur);
if (a->get_decl() == f)
return true;
unsigned j = a->get_num_args();
while (j>0)
todo.push_back(a->get_arg(--j));
}
visited.mark(cur, true);
}
return false;
}
void save_candidate(expr * t, bool form_ctx) {
if (!form_ctx)
return;
if (!m.is_bool(t))
return;
if (!m_has_term_ite.is_marked(t))
return;
if (!is_app(t))
return;
if (to_app(t)->get_family_id() == m.get_basic_family_id()) {
switch (to_app(t)->get_decl_kind()) {
case OP_OR:
case OP_AND:
case OP_NOT:
case OP_XOR:
case OP_IMPLIES:
case OP_TRUE:
case OP_FALSE:
case OP_ITE:
return;
case OP_EQ:
case OP_DISTINCT:
if (m.is_bool(to_app(t)->get_arg(0)))
return;
break;
default:
break;
}
}
// it is an atom in a formula context (i.e., it is not nested inside a term),
// and it contains a term if-then-else.
m_candidates.insert(t);
}
void mk_interp_tail_simplifier::rule_substitution::apply(app * a, app_ref& res) {
SASSERT(m_rule);
expr_ref res_e(m);
m_subst.apply(a, res_e);
SASSERT(is_app(res_e.get()));
res = to_app(res_e.get());
}
void process(expr * f) {
if (fvisited.is_marked(f))
return;
fvisited.mark(f);
todo.push_back(f);
while (!todo.empty()) {
expr * t = todo.back();
todo.pop_back();
if (is_uninterp_const(t))
continue;
if (is_app(t) && to_app(t)->get_family_id() == m.get_basic_family_id() && to_app(t)->get_num_args() > 0) {
decl_kind k = to_app(t)->get_decl_kind();
if (k == OP_OR || k == OP_NOT || k == OP_IFF || ((k == OP_EQ || k == OP_ITE) && m.is_bool(to_app(t)->get_arg(1)))) {
unsigned num = to_app(t)->get_num_args();
for (unsigned i = 0; i < num; i++) {
expr * arg = to_app(t)->get_arg(i);
if (fvisited.is_marked(arg))
continue;
fvisited.mark(arg);
todo.push_back(arg);
}
}
}
else {
quick_for_each_expr(proc, tvisited, t);
}
}
}
void variable_intersection::populate_self(const app * a)
{
SASSERT(is_uninterp(a));
//TODO: optimize quadratic complexity
//TODO: optimize number of checks when variable occurs multiple times
unsigned arity = a->get_num_args();
for(unsigned i1=0; i1<arity; i1++) {
expr * e1=a->get_arg(i1);
if(is_var(e1)) {
var* v1=to_var(e1);
for(unsigned i2=i1+1; i2<arity; i2++) {
expr * e2=a->get_arg(i2);
if(!is_var(e2)) {
continue;
}
var* v2=to_var(e2);
if(v1->get_idx()==v2->get_idx()) {
add_pair(i1, i2);
}
}
}
else {
SASSERT(is_app(e1));
app * c1 = to_app(e1);
SASSERT(c1->get_num_args()==0); //c1 must be a constant
m_const_indexes.push_back(i1);
m_consts.push_back(c1);
SASSERT(m_const_indexes.size()==m_consts.size());
}
}
}
void mk_array_instantiation::retrieve_selects(expr* e)
{
//If the expression is not a function application, we ignore it
if (!is_app(e)) {
return;
}
app*f=to_app(e);
//Call the function recursively on all arguments
unsigned nbargs = f->get_num_args();
for(unsigned i=0;i<nbargs;i++)
{
retrieve_selects(f->get_arg(i));
}
//If it is a select, then add it to selects
if(m_a.is_select(f))
{
SASSERT(!m_a.is_array(get_sort(e)));
selects.insert_if_not_there(f->get_arg(0), ptr_vector<expr>());
selects[f->get_arg(0)].push_back(e);
}
//If it is a condition between arrays, for example the result of a store, then add it to the equiv_classes
if(m_a.is_store(f))
{
eq_classes.merge(e, f->get_arg(0));
}
else if(m.is_eq(f) && m_a.is_array(get_sort(f->get_arg(0))))
{
eq_classes.merge(f->get_arg(0), f->get_arg(1));
}
}
bool expr_delta::delta_dfs(unsigned& n, expr* e, expr_ref& result) {
ast_manager& m = m_manager;
if (m.is_true(e) || m.is_false(e)) {
return false;
}
if (n == 0 && m.is_bool(e)) {
result = m.mk_true();
return true;
}
else if (n == 1 && m.is_bool(e)) {
result = m.mk_false();
return true;
}
else if (is_app(e)) {
if (m.is_bool(e)) {
SASSERT(n >= 2);
n -= 2;
}
return delta_dfs(n, to_app(e), result);
}
else if (is_quantifier(e)) {
SASSERT(n >= 2);
n -= 2;
quantifier* q = to_quantifier(e);
if (delta_dfs(n, q->get_expr(), result)) {
result = m.update_quantifier(q, result.get());
return true;
}
else {
return false;
}
}
return false;
}
void expr_context_simplifier::reduce_rec(expr * m, expr_ref & result) {
//
// reduce expr in context evaluation.
//
bool polarity;
if (m_context.find(m, polarity)) {
result = polarity ? m_manager.mk_true() : m_manager.mk_false();
}
else if (m_mark.is_marked(m) && !m_manager.is_not(m)) {
result = m;
}
else if (is_quantifier(m)) {
reduce_rec(to_quantifier(m), result);
m_mark.mark(m, true);
}
else if (is_app(m)) {
reduce_rec(to_app(m), result);
m_mark.mark(m, true);
}
else if (is_var(m)) {
result = m;
m_mark.mark(m, true);
}
else {
UNREACHABLE();
result = m;
}
}
expr const & get_app_rev_args(expr const & e, buffer<expr> & args) {
expr const * it = &e;
while (is_app(*it)) {
args.push_back(app_arg(*it));
it = &(app_fn(*it));
}
return *it;
}
void visit_args(expr * t, expr_fast_mark1 & visited) {
if (is_app(t)) {
for (expr * arg : *to_app(t)) {
save_degree(arg, m_one);
visit(arg, visited);
}
}
}
unsigned get_app_num_args(expr const & e) {
expr const * it = &e;
unsigned n = 0;
while (is_app(*it)) {
it = &(app_fn(*it));
n++;
}
return n;
}
static bool to_apps(unsigned n, Z3_app const es[], app_ref_vector& result) {
for (unsigned i = 0; i < n; ++i) {
if (!is_app(to_app(es[i]))) {
return false;
}
result.push_back (to_app (es [i]));
}
return true;
}
br_status pull_ite(expr_ref & result) {
expr * t = result.get();
if (is_app(t)) {
br_status st = pull_ite(to_app(t)->get_decl(), to_app(t)->get_num_args(), to_app(t)->get_args(), result);
if (st != BR_FAILED)
return st;
}
return BR_DONE;
}
void visit_args(expr * t, expr_fast_mark1 & visited) {
if (is_app(t)) {
unsigned num_args = to_app(t)->get_num_args();
for (unsigned i = 0; i < num_args; i++) {
expr * arg = to_app(t)->get_arg(i);
save_degree(arg, m_one);
visit(arg, visited);
}
}
}
expr const & get_app_args(expr const & e, buffer<expr> & args) {
unsigned sz = args.size();
expr const * it = &e;
while (is_app(*it)) {
args.push_back(app_arg(*it));
it = &(app_fn(*it));
}
std::reverse(args.begin() + sz, args.end());
return *it;
}
br_status datatype_rewriter::mk_eq_core(expr * lhs, expr * rhs, expr_ref & result) {
if (!is_app(lhs) || !is_app(rhs) || !m_util.is_constructor(to_app(lhs)) || !m_util.is_constructor(to_app(rhs)))
return BR_FAILED;
if (to_app(lhs)->get_decl() != to_app(rhs)->get_decl()) {
result = m().mk_false();
return BR_DONE;
}
// Remark: In datatype_simplifier_plugin, we used
// m_basic_simplifier to create '=' and 'and' applications in the
// following code. This trick not guarantee that the final expression
// will be fully simplified.
//
// Example:
// The assertion
// (assert (= (cons a1 (cons a2 (cons a3 (cons (+ a4 1) (cons (+ a5 c5) (cons a6 nil))))))
// (cons b1 (cons b2 (cons b3 (cons b4 (cons b5 (cons b6 nil))))))))
//
// After applying asserted_formulas::reduce(), the following formula was generated.
//
// (= a1 b1)
// (= a2 b2)
// (= a3 b3)
// (= (+ a4 (* (- 1) b4)) (- 1))
// (= (+ c5 a5) b5) <<< NOT SIMPLIFIED WITH RESPECT TO ARITHMETIC
// (= (cons a6 nil) (cons b6 nil))) <<< NOT SIMPLIFIED WITH RESPECT TO DATATYPE theory
//
// Note that asserted_formulas::reduce() applied the simplier many times.
// After the first simplification step we had:
// (= a1 b1)
// (= (cons a2 (cons a3 (cons (+ a4 1) (cons (+ a5 c5) (cons a6 nil))))))
// (cons b2 (cons b3 (cons b4 (cons b5 (cons b6 nil))))))
ptr_buffer<expr> eqs;
unsigned num = to_app(lhs)->get_num_args();
SASSERT(num == to_app(rhs)->get_num_args());
for (unsigned i = 0; i < num; ++i) {
eqs.push_back(m().mk_eq(to_app(lhs)->get_arg(i), to_app(rhs)->get_arg(i)));
}
result = m().mk_and(eqs.size(), eqs.c_ptr());
return BR_REWRITE2;
}
/**
\brief Return true if s >_{lpo} t_i forall children t_i of t.
*/
bool lpo::dominates_args(expr_offset s, expr_offset t, unsigned depth) {
SASSERT(is_app(t.get_expr()));
unsigned num_args = to_app(t.get_expr())->get_num_args();
unsigned off = t.get_offset();
for (unsigned i = 0; i < num_args; i++) {
expr * t_i = to_app(t.get_expr())->get_arg(i);
if (!greater(s, expr_offset(t_i, off), depth+1))
return false;
}
return true;
}
expr* apply_accessor(
ptr_vector<func_decl> const& acc,
unsigned j,
func_decl* f,
expr* c) {
if (is_app(c) && to_app(c)->get_decl() == f) {
return to_app(c)->get_arg(j);
}
else {
return m.mk_app(acc[j], c);
}
}
bool is_atom(ast_manager & m, expr * n) {
if (is_quantifier(n) || !m.is_bool(n))
return false;
if (is_var(n))
return true;
SASSERT(is_app(n));
if (to_app(n)->get_family_id() != m.get_basic_family_id()) {
return true;
}
// the other operators of the basic family are not considered atomic: distinct, ite, and, or, iff, xor, not, implies.
return (m.is_eq(n) && !m.is_bool(to_app(n)->get_arg(0))) || m.is_true(n) || m.is_false(n);
}
static optional<pair<expr, unsigned>> find_hyp_core(expr const & meta, F && pred) {
expr const * it = &meta;
unsigned i = 0;
while (is_app(*it)) {
expr const & h = app_arg(*it);
if (pred(h))
return some(mk_pair(h, i));
i++;
it = &app_fn(*it);
}
return optional<pair<expr, unsigned>>();
}
/**
\brief Return true if s_i >=_{lpo} t for some arg s_i of s.
*/
bool lpo::arg_dominates_expr(expr_offset s, expr_offset t, unsigned depth) {
SASSERT(is_app(s.get_expr()));
unsigned num_args = to_app(s.get_expr())->get_num_args();
unsigned off = s.get_offset();
for (unsigned i = 0; i < num_args; i++) {
expr * s_i = to_app(s.get_expr())->get_arg(i);
result r = compare(expr_offset(s_i, off), t, depth+1);
if (r == EQUAL || r == GREATER)
return true;
}
return false;
}
bool reduce_arg(expr* a, expr_ref& result) {
sort* s = get_sort(a);
if (!m_imp.is_fd(s)) {
return false;
}
unsigned bv_size = get_bv_size(s);
if (is_var(a)) {
result = m.mk_var(to_var(a)->get_idx(), m_bv.mk_sort(bv_size));
return true;
}
SASSERT(is_app(a));
func_decl* f = to_app(a)->get_decl();
if (m_dt.is_constructor(f)) {
unsigned idx = m_dt.get_constructor_idx(f);
result = m_bv.mk_numeral(idx, bv_size);
}
else if (is_uninterp_const(a)) {
func_decl* f_fresh;
if (m_imp.m_enum2bv.find(f, f_fresh)) {
result = m.mk_const(f_fresh);
return true;
}
// create a fresh variable, add bounds constraints for it.
unsigned nc = m_dt.get_datatype_num_constructors(s);
result = m.mk_fresh_const(f->get_name().str().c_str(), m_bv.mk_sort(bv_size));
f_fresh = to_app(result)->get_decl();
if (!is_power_of_two(nc) || nc == 1) {
m_imp.m_bounds.push_back(m_bv.mk_ule(result, m_bv.mk_numeral(nc-1, bv_size)));
}
expr_ref f_def(m);
ptr_vector<func_decl> const& cs = *m_dt.get_datatype_constructors(s);
f_def = m.mk_const(cs[nc-1]);
for (unsigned i = nc - 1; i > 0; ) {
--i;
f_def = m.mk_ite(m.mk_eq(result, m_bv.mk_numeral(i,bv_size)), m.mk_const(cs[i]), f_def);
}
m_imp.m_enum2def.insert(f, f_def);
m_imp.m_enum2bv.insert(f, f_fresh);
m_imp.m_bv2enum.insert(f_fresh, f);
m_imp.m_enum_consts.push_back(f);
m_imp.m_enum_bvs.push_back(f_fresh);
m_imp.m_enum_defs.push_back(f_def);
}
else {
throw_non_fd(a);
}
++m_imp.m_num_translated;
return true;
}
void operator()(expr * t) {
SASSERT(m.is_bool(t));
push_frame(t, true);
SASSERT(!m_frame_stack.empty());
while (!m_frame_stack.empty()) {
frame & fr = m_frame_stack.back();
expr * t = fr.m_t;
bool form_ctx = fr.m_form_ctx;
TRACE("cofactor", tout << "processing, form_ctx: " << form_ctx << "\n" << mk_bounded_pp(t, m) << "\n";);
m_owner.checkpoint();
if (m_processed.is_marked(t)) {
save_candidate(t, form_ctx);
m_frame_stack.pop_back();
continue;
}
if (m.is_term_ite(t)) {
m_has_term_ite.mark(t);
m_processed.mark(t);
m_frame_stack.pop_back();
continue;
}
if (fr.m_first) {
fr.m_first = false;
bool visited = true;
if (is_app(t)) {
unsigned num_args = to_app(t)->get_num_args();
for (unsigned i = 0; i < num_args; i++)
visit(to_app(t)->get_arg(i), form_ctx, visited);
}
// ignoring quantifiers
if (!visited)
continue;
}
if (is_app(t)) {
unsigned num_args = to_app(t)->get_num_args();
unsigned i;
for (i = 0; i < num_args; i++) {
if (m_has_term_ite.is_marked(to_app(t)->get_arg(i)))
break;
}
if (i < num_args) {
m_has_term_ite.mark(t);
TRACE("cofactor", tout << "saving candidate: " << form_ctx << "\n" << mk_bounded_pp(t, m) << "\n";);
save_candidate(t, form_ctx);
}
expr const & get_app_args_at_most(expr const & e, unsigned num, buffer<expr> & args) {
unsigned sz = args.size();
expr const * it = &e;
unsigned i = 0;
while (is_app(*it)) {
if (i == num)
break;
args.push_back(app_arg(*it));
it = &(app_fn(*it));
i++;
}
std::reverse(args.begin() + sz, args.end());
return *it;
}
void fixedpoint_context::simplify_rules(
unsigned num_rules, expr* const* rules,
unsigned num_outputs, func_decl* const* outputs, expr_ref_vector& result) {
ast_manager& m = m_context.get_manager();
datalog::context ctx(m, m_context.get_fparams());
datalog::rule_manager& rm = ctx.get_rule_manager();
for (unsigned i = 0; i < num_rules; ++i) {
expr* rule = rules[i], *body, *head;
while (true) {
if (is_quantifier(rule)) {
rule = to_quantifier(rule)->get_expr();
}
else if (m.is_implies(rule, body, head)) {
rule = head;
}
else {
break;
}
}
if (is_app(rule)) {
func_decl* r = to_app(rule)->get_decl();
if (!ctx.is_predicate(r)) {
ctx.register_predicate(r);
if (num_outputs == 0) {
ctx.set_output_predicate(r);
}
}
}
}
for (unsigned i = 0; i < num_outputs; ++i) {
ctx.set_output_predicate(outputs[i]);
}
for (unsigned i = 0; i < num_rules; ++i) {
expr* rule = rules[i];
ctx.add_rule(rule, symbol::null);
}
model_converter_ref mc; // not exposed.
proof_converter_ref pc; // not exposed.
ctx.apply_default_transformation(mc, pc);
datalog::rule_set const& new_rules = ctx.get_rules();
datalog::rule_set::iterator it = new_rules.begin(), end = new_rules.end();
for (; it != end; ++it) {
datalog::rule* r = *it;
expr_ref fml(m);
r->to_formula(fml);
result.push_back(fml);
}
}
void mk_coalesce::merge_rules(rule_ref& tgt, rule const& src) {
SASSERT(same_body(*tgt.get(), src));
m_sub1.reset();
m_sub2.reset();
m_idx = 0;
app_ref pred(m), head(m);
expr_ref fml1(m), fml2(m), fml(m);
app_ref_vector tail(m);
ptr_vector<sort> sorts1, sorts2;
expr_ref_vector conjs1(m), conjs(m);
rule_ref res(rm);
bool_rewriter bwr(m);
svector<bool> is_neg;
tgt->get_vars(sorts1);
src.get_vars(sorts2);
mk_pred(head, src.get_head(), tgt->get_head());
for (unsigned i = 0; i < src.get_uninterpreted_tail_size(); ++i) {
mk_pred(pred, src.get_tail(i), tgt->get_tail(i));
tail.push_back(pred);
is_neg.push_back(src.is_neg_tail(i));
}
extract_conjs(m_sub1, src, fml1);
extract_conjs(m_sub2, *tgt.get(), fml2);
bwr.mk_or(fml1, fml2, fml);
SASSERT(is_app(fml));
tail.push_back(to_app(fml));
is_neg.push_back(false);
res = rm.mk(head, tail.size(), tail.c_ptr(), is_neg.c_ptr(), tgt->name());
if (m_ctx.generate_proof_trace()) {
src.to_formula(fml1);
tgt->to_formula(fml2);
res->to_formula(fml);
#if 0
sort* ps = m.mk_proof_sort();
sort* domain[3] = { ps, ps, m.mk_bool_sort() };
func_decl* merge = m.mk_func_decl(symbol("merge-clauses"), 3, domain, ps); // TBD: ad-hoc proof rule
expr* args[3] = { m.mk_asserted(fml1), m.mk_asserted(fml2), fml };
// ...m_pc->insert(m.mk_app(merge, 3, args));
#else
svector<std::pair<unsigned, unsigned> > pos;
vector<expr_ref_vector> substs;
proof* p = src.get_proof();
p = m.mk_hyper_resolve(1, &p, fml, pos, substs);
res->set_proof(m, p);
#endif
}
tgt = res;
}
order::result lpo::lex_compare(expr_offset s, expr_offset t, unsigned depth) {
SASSERT(is_app(s.get_expr()));
SASSERT(is_app(t.get_expr()));
app * _s = to_app(s.get_expr());
app * _t = to_app(t.get_expr());
unsigned num_args1 = _s->get_num_args();
unsigned num_args2 = _t->get_num_args();
unsigned num_args = std::min(num_args1, num_args2);
unsigned off1 = s.get_offset();
unsigned off2 = t.get_offset();
result r = EQUAL;
for (unsigned i = 0; i < num_args; i++) {
r = compare(expr_offset(_s->get_arg(i), off1), expr_offset(_t->get_arg(i), off2), depth+1);
if (r != EQUAL)
break;
}
if (r == EQUAL) {
if (num_args1 > num_args2)
return GREATER;
if (num_args1 < num_args2)
return NOT_GTEQ;
}
return r;
}
void superposition::insert_r(clause * cls, expr * n, unsigned i, bool lhs) {
if (is_app(n)) {
unsigned idx = (i << 1) | static_cast<unsigned>(lhs);
clause_pos_pair new_pair(cls, idx);
SASSERT(m_todo.empty());
m_todo.push_back(to_app(n));
while (!m_todo.empty()) {
app * n = m_todo.back();
m_todo.pop_back();
clause_pos_set * s = m_r2clause_set.get_parents(n);
if (s == 0 || !s->contains(new_pair)) {
m_r.insert(n);
m_r2clause_set.insert(new_pair, n);
unsigned num_args = n->get_num_args();
for (unsigned i = 0; i < num_args; i++) {
expr * c = n->get_arg(i);
if (is_app(c))
m_todo.push_back(to_app(c));
}
}
}
}
}
Z3_pattern Z3_API Z3_mk_pattern(Z3_context c, unsigned num_patterns, Z3_ast const terms[]) {
Z3_TRY;
LOG_Z3_mk_pattern(c, num_patterns, terms);
RESET_ERROR_CODE();
for (unsigned i = 0; i < num_patterns; ++i) {
if (!is_app(to_expr(terms[i]))) {
SET_ERROR_CODE(Z3_INVALID_ARG);
RETURN_Z3(0);
}
}
app* a = mk_c(c)->m().mk_pattern(num_patterns, reinterpret_cast<app*const*>(to_exprs(terms)));
mk_c(c)->save_ast_trail(a);
RETURN_Z3(of_pattern(a));
Z3_CATCH_RETURN(0);
}