void tst_substitution()
{
memory::initialize(0);
smt_params params;
params.m_model = true;
enable_trace("subst_bug");
ast_manager m;
reg_decl_plugins(m);
var_ref v1(m.mk_var(0, m.mk_bool_sort()), m);
var_ref v2(m.mk_var(1, m.mk_bool_sort()), m);
var_ref v3(m.mk_var(2, m.mk_bool_sort()), m);
var_ref v4(m.mk_var(3, m.mk_bool_sort()), m);
substitution subst(m);
subst.reserve(1,4);
unifier unif(m);
bool ok1 = unif(v1.get(), v2.get(), subst, false);
bool ok2 = unif(v2.get(), v1.get(), subst, false);
expr_ref res(m);
TRACE("substitution", subst.display(tout););
void tst_expr_arith(unsigned num_files) {
ast_manager m;
reg_decl_plugins(m);
expr_rand er(m);
er.seed(rand_seed);
er.initialize_arith(20);
family_id fid = m.mk_family_id("arith");
sort* int_ty = m.mk_sort(fid, INT_SORT, 0, 0);
sort* real_ty = m.mk_sort(fid, REAL_SORT, 0, 0);
er.initialize_array(3, int_ty, int_ty);
er.initialize_array(3, int_ty, real_ty);
er.initialize_basic(20);
for (unsigned i = 0; i < num_files; ++i) {
expr_ref e(m);
er.get_next(m.mk_bool_sort(), e);
ast_smt_pp pp(m);
pp.set_logic(symbol("QF_AUFLIA"));
std::ostringstream buffer;
buffer << "random_arith_" << i << ".smt";
std::cout << buffer.str() << "\n";
std::ofstream file(buffer.str().c_str());
pp.display(file, e.get());
file.close();
}
}
void tst1() {
ast_manager m;
reg_decl_plugins(m);
sort_ref s( m.mk_uninterpreted_sort(symbol("S")), m);
func_decl_ref g( m.mk_func_decl(symbol("g"), s, s), m);
func_decl_ref h( m.mk_func_decl(symbol("h"), s, s), m);
sort * domain[2] = {s, s};
func_decl_ref f( m.mk_func_decl(symbol("f"), 2, domain, s), m);
app_ref a( m.mk_const(symbol("a"), s), m);
app_ref b( m.mk_const(symbol("b"), s), m);
expr_ref x( m.mk_var(0, s), m);
expr_ref y( m.mk_var(1, s), m);
app_ref gx( m.mk_app(g, x), m);
app_ref fgx_x( m.mk_app(f, gx.get(), x.get()), m);
app_ref ha( m.mk_app(h, a.get()), m);
app_ref gha( m.mk_app(g, ha.get()), m);
app_ref fgha_ha( m.mk_app(f, gha.get(), ha.get()), m);
tst_match(m, fgx_x, fgha_ha);
app_ref fgha_gha( m.mk_app(f, gha.get(), gha.get()), m);
tst_match(m, fgx_x, fgha_gha);
app_ref fxy( m.mk_app(f, x.get(), y.get()), m);
app_ref fyx( m.mk_app(f, y.get(), x.get()), m);
tst_match(m, fxy, fyx);
app_ref fygx( m.mk_app(f, y.get(), gx.get()), m);
tst_match(m, fxy, fygx);
tst_match(m, fygx, fxy);
}
void tst_theory_pb() {
fuzz_pb();
ast_manager m;
smt_params params;
params.m_model = true;
reg_decl_plugins(m);
expr_ref tmp(m);
enable_trace("pb");
for (unsigned N = 4; N < 11; ++N) {
for (unsigned i = 0; i < (1u << N); ++i) {
smt::literal_vector lits(N, smt::false_literal);
unsigned k = populate_literals(i, lits);
std::cout << "k:" << k << " " << N << "\n";
std::cout.flush();
TRACE("pb", tout << "k " << k << ": ";
for (unsigned j = 0; j < lits.size(); ++j) {
tout << lits[j] << " ";
}
tout << "\n";);
{
smt::context ctx(m, params);
ctx.push();
smt::literal l = smt::theory_pb::assert_ge(ctx, k+1, lits.size(), lits.c_ptr());
if (l != smt::false_literal) {
ctx.assign(l, 0, false);
TRACE("pb", tout << "assign: " << l << "\n";
ctx.display(tout););
VERIFY(l_false == ctx.check());
}
ctx.pop(1);
}
static void fuzz_pb()
{
ast_manager m;
reg_decl_plugins(m);
pb_fuzzer fuzzer(m);
fuzzer.fuzz();
}
void tst_check_assumptions()
{
memory::initialize(0);
front_end_params params;
ast_manager mgr;
reg_decl_plugins(mgr);
sort_ref b(mgr.mk_bool_sort(), mgr);
func_decl_ref pPred(mgr.mk_func_decl(symbol("p"), 0, static_cast<sort * const *>(0), b), mgr);
func_decl_ref qPred(mgr.mk_func_decl(symbol("q"), 0, static_cast<sort * const *>(0), b), mgr);
func_decl_ref rPred(mgr.mk_func_decl(symbol("r"), 0, static_cast<sort * const *>(0), b), mgr);
app_ref p(mgr.mk_app(pPred,0,static_cast<expr * const *>(0)), mgr);
app_ref q(mgr.mk_app(qPred,0,static_cast<expr * const *>(0)), mgr);
app_ref r(mgr.mk_app(rPred,0,static_cast<expr * const *>(0)), mgr);
app_ref pOqOr(mgr.mk_or(p,q,r), mgr);
app_ref np(mgr.mk_not(p), mgr);
app_ref nq(mgr.mk_not(q), mgr);
app_ref nr(mgr.mk_not(r), mgr);
smt::context ctx(mgr, params);
ctx.assert_expr(pOqOr);
expr * npE = np.get();
lbool res1 = ctx.check(1, &npE);
SASSERT(res1==l_true);
ctx.assert_expr(npE);
expr * assumpt[] = { nq.get(), nr.get() };
//here it should crash
ctx.check(2, assumpt);
}
static void test_ineqs() {
ast_manager m;
reg_decl_plugins(m);
arith_util a(m);
sort* s_int = a.mk_int();
sort* s_real = a.mk_real();
test_ineqs(m, s_int, true);
test_ineqs(m, s_real, false);
}
static void check_random_ineqs() {
random_gen r(1);
ast_manager m;
reg_decl_plugins(m);
for (unsigned i = 0; i < 100; ++i) {
check_random_ineqs(r, m, 4, 5, 5, 3, 6);
}
}
static void testI(char const *ex) {
ast_manager m;
reg_decl_plugins(m);
arith_util a(m);
expr_ref fml = parse_fml(m, ex);
symbol x_name("i");
sort_ref x_sort(a.mk_int(), m);
app_ref var(m.mk_const(x_name, x_sort), m);
test(var, fml);
}
void test2() {
ast_manager m;
reg_decl_plugins(m);
bv_util bv(m);
datatype_util dtutil(m);
params_ref p;
datatype_decl_plugin & dt = *(static_cast<datatype_decl_plugin*>(m.get_plugin(m.get_family_id("datatype"))));
sort_ref_vector new_sorts(m);
constructor_decl* R = mk_constructor_decl(symbol("R"), symbol("is-R"), 0, nullptr);
constructor_decl* G = mk_constructor_decl(symbol("G"), symbol("is-G"), 0, nullptr);
constructor_decl* B = mk_constructor_decl(symbol("B"), symbol("is-B"), 0, nullptr);
constructor_decl* constrs[3] = { R, G, B };
datatype_decl * enum_sort = mk_datatype_decl(dtutil, symbol("RGB"), 0, nullptr, 3, constrs);
VERIFY(dt.mk_datatypes(1, &enum_sort, 0, nullptr, new_sorts));
sort* rgb = new_sorts[0].get();
expr_ref x = mk_const(m, "x", rgb), y = mk_const(m, "y", rgb), z = mk_const(m, "z", rgb);
ptr_vector<func_decl> const& enums = *dtutil.get_datatype_constructors(rgb);
expr_ref r = expr_ref(m.mk_const(enums[0]), m);
expr_ref g = expr_ref(m.mk_const(enums[1]), m);
expr_ref b = expr_ref(m.mk_const(enums[2]), m);
ref<solver> fd_solver = mk_fd_solver(m, p);
fd_solver->assert_expr(m.mk_not(m.mk_eq(x, r)));
fd_solver->assert_expr(m.mk_not(m.mk_eq(x, b)));
expr_ref_vector asms(m), vars(m), conseq(m);
vars.push_back(x);
vars.push_back(y);
VERIFY(l_true == fd_solver->get_consequences(asms, vars, conseq));
std::cout << conseq << "\n";
conseq.reset();
fd_solver->push();
fd_solver->assert_expr(m.mk_not(m.mk_eq(x, g)));
VERIFY(l_false == fd_solver->check_sat(0,nullptr));
fd_solver->pop(1);
VERIFY(l_true == fd_solver->get_consequences(asms, vars, conseq));
std::cout << conseq << "\n";
conseq.reset();
model_ref mr;
fd_solver->get_model(mr);
model_smt2_pp(std::cout << "model:\n", m, *mr.get(), 0);
VERIFY(l_true == fd_solver->check_sat(0,nullptr));
fd_solver->get_model(mr);
ENSURE(mr.get());
model_smt2_pp(std::cout, m, *mr.get(), 0);
}
void tst_horn_subsume_model_converter() {
ast_manager m;
reg_decl_plugins(m);
arith_util a(m);
ptr_vector<sort> ints;
ints.push_back(a.mk_int());
ints.push_back(a.mk_int());
ints.push_back(a.mk_int());
func_decl_ref p(m), q(m), r(m);
p = m.mk_func_decl(symbol("p"), 2, ints.c_ptr(), m.mk_bool_sort());
q = m.mk_func_decl(symbol("q"), 2, ints.c_ptr(), m.mk_bool_sort());
r = m.mk_func_decl(symbol("r"), 2, ints.c_ptr(), m.mk_bool_sort());
ref<horn_subsume_model_converter> mc = alloc(horn_subsume_model_converter,m);
model_ref mr = alloc(model, m);
mc->insert(p, m.mk_app(q, a.mk_numeral(rational(1), true), a.mk_numeral(rational(2), true)));
model_converter_ref mcr = mc.get();
apply(mcr, mr, 0);
model_smt2_pp(std::cout, m, *mr.get(), 0);
mr = alloc(model, m);
mc->insert(p, m.mk_app(q, a.mk_numeral(rational(3), true), a.mk_numeral(rational(5), true)));
apply(mcr, mr, 0);
model_smt2_pp(std::cout, m, *mr.get(), 0);
mr = alloc(model, m);
mc->insert(p, m.mk_app(r, m.mk_var(0,a.mk_int()), m.mk_var(1, a.mk_int())));
apply(mcr, mr, 0);
model_smt2_pp(std::cout, m, *mr.get(), 0);
mr = alloc(model, m);
app_ref head1(m);
expr_ref body1(m), body2(m);
func_decl_ref pred(m);
head1 = m.mk_app(p, m.mk_var(0, a.mk_int()), m.mk_var(0, a.mk_int()));
body1 = m.mk_app(q, m.mk_var(1, a.mk_int()), m.mk_var(2, a.mk_int()));
VERIFY(mc->mk_horn(head1, body1, pred, body2));
mc->insert(pred, body2);
apply(mcr, mr, 0);
model_smt2_pp(std::cout, m, *mr.get(), 0);
mr = alloc(model, m);
head1 = m.mk_app(p, m.mk_var(0, a.mk_int()), m.mk_var(0, a.mk_int()));
body1 = m.mk_app(q, m.mk_var(1, a.mk_int()), m.mk_var(0, a.mk_int()));
VERIFY(mc->mk_horn(head1, body1, pred, body2));
mc->insert(pred, body2);
apply(mcr, mr, 0);
model_smt2_pp(std::cout, m, *mr.get(), 0);
}
static void test2(char const *ex) {
smt_params params;
params.m_model = true;
ast_manager m;
reg_decl_plugins(m);
arith_util a(m);
expr_ref fml = parse_fml(m, ex);
app_ref_vector vars(m);
expr_ref_vector lits(m);
vars.push_back(m.mk_const(symbol("x"), a.mk_real()));
vars.push_back(m.mk_const(symbol("y"), a.mk_real()));
vars.push_back(m.mk_const(symbol("z"), a.mk_real()));
flatten_and(fml, lits);
smt::context ctx(m, params);
ctx.push();
ctx.assert_expr(fml);
lbool result = ctx.check();
VERIFY(result == l_true);
ref<model> md;
ctx.get_model(md);
ctx.pop(1);
std::cout << mk_pp(fml, m) << "\n";
expr_ref pr1(m), pr2(m), fml2(m);
expr_ref_vector bound(m);
ptr_vector<sort> sorts;
svector<symbol> names;
for (unsigned i = 0; i < vars.size(); ++i) {
bound.push_back(vars[i].get());
names.push_back(vars[i]->get_decl()->get_name());
sorts.push_back(m.get_sort(vars[i].get()));
}
expr_abstract(m, 0, bound.size(), bound.c_ptr(), fml, fml2);
fml2 = m.mk_exists(bound.size(), sorts.c_ptr(), names.c_ptr(), fml2);
qe::expr_quant_elim qe(m, params);
for (unsigned i = 0; i < vars.size(); ++i) {
VERIFY(qe::arith_project(*md, vars[i].get(), lits));
}
pr1 = mk_and(lits);
qe(m.mk_true(), fml2, pr2);
std::cout << mk_pp(pr1, m) << "\n";
std::cout << mk_pp(pr2, m) << "\n";
expr_ref npr2(m);
npr2 = m.mk_not(pr2);
ctx.push();
ctx.assert_expr(pr1);
ctx.assert_expr(npr2);
VERIFY(l_false == ctx.check());
ctx.pop(1);
}
void test_sorting3() {
ast_manager m;
reg_decl_plugins(m);
expr_ref_vector in(m), out(m);
for (unsigned i = 0; i < 7; ++i) {
in.push_back(m.mk_fresh_const("a",m.mk_bool_sort()));
}
for (unsigned i = 0; i < in.size(); ++i) {
std::cout << mk_pp(in[i].get(), m) << "\n";
}
ast_ext aext(m);
sorting_network<ast_ext> sn(aext);
sn(in, out);
std::cout << "size: " << out.size() << "\n";
for (unsigned i = 0; i < out.size(); ++i) {
std::cout << mk_pp(out[i].get(), m) << "\n";
}
}
static void test_sorting_eq(unsigned n, unsigned k) {
SASSERT(k < n);
ast_manager m;
reg_decl_plugins(m);
ast_ext2 ext(m);
expr_ref_vector in(m), out(m);
for (unsigned i = 0; i < n; ++i) {
in.push_back(m.mk_fresh_const("a",m.mk_bool_sort()));
}
smt_params fp;
smt::kernel solver(m, fp);
psort_nw<ast_ext2> sn(ext);
expr_ref result(m);
// equality:
std::cout << "eq " << k << "\n";
solver.push();
result = sn.eq(true, k, in.size(), in.c_ptr());
solver.assert_expr(result);
for (unsigned i = 0; i < ext.m_clauses.size(); ++i) {
solver.assert_expr(ext.m_clauses[i].get());
}
lbool res = solver.check();
SASSERT(res == l_true);
solver.push();
for (unsigned i = 0; i < k; ++i) {
solver.assert_expr(in[i].get());
}
res = solver.check();
SASSERT(res == l_true);
solver.assert_expr(in[k].get());
res = solver.check();
if (res == l_true) {
TRACE("pb",
unsigned sz = solver.size();
for (unsigned i = 0; i < sz; ++i) {
tout << mk_pp(solver.get_formulas()[i], m) << "\n";
});
void tst_expr_substitution() {
memory::initialize(0);
ast_manager m;
reg_decl_plugins(m);
bv_util bv(m);
expr_ref a(m), b(m), c(m), d(m);
expr_ref x(m);
expr_ref new_a(m);
proof_ref pr(m);
x = m.mk_const(symbol("x"), bv.mk_sort(8));
a = mk_bv_and(bv, mk_bv_xor(bv, x,bv.mk_numeral(8,8)), mk_bv_xor(bv,x,x));
b = x;
c = bv.mk_bv_sub(x, bv.mk_numeral(4, 8));
expr_substitution subst(m);
th_rewriter rw(m);
std::cout << mk_pp(c, m) << "\n";
// normalizing c does not help.
rw(c, d, pr);
std::cout << mk_pp(d, m) << "\n";
// This portion diverges. It attempts to replace x by (bvadd #xfc x), which contains x.
// subst.insert(b, d);
// std::cout << mk_pp(a, m) << "\n";
// rw.set_substitution(&subst);
// enable_trace("th_rewriter_step");
// rw(a, new_a, pr);
// std::cout << mk_pp(new_a, m) << "\n";
}
static void test_formula(lbool expected_outcome, char const* fml) {
ast_manager m;
reg_decl_plugins(m);
scoped_ptr<smtlib::parser> parser = smtlib::parser::create(m);
parser->initialize_smtlib();
std::ostringstream buffer;
buffer << "(benchmark presburger :status unknown :logic AUFLIA :extrapreds ((p1) (p2) (p3)) "
<< ":extrafuns ((a Int) (b Int))\n"
<< ":extrapreds ((p) (q) (r))\n"
<< ":datatypes ((list (nil) (cons (hd Int) (tl list))))\n"
<< ":datatypes ((cell (cnil) (ccons (car cell) (cdr cell))))\n"
<< ":extrasorts (U)\n"
<< ":extrafuns ((f U U))\n"
<< ":formula " << fml << ")";
parser->parse_string(buffer.str().c_str());
smtlib::benchmark* b = parser->get_benchmark();
smtlib::theory::expr_iterator it = b->begin_formulas();
smtlib::theory::expr_iterator end = b->end_formulas();
for (; it != end; ++it) {
test_qe(m, expected_outcome, *it, 0);
}
}
void tst_arith_rewriter() {
ast_manager m;
reg_decl_plugins(m);
arith_rewriter ar(m);
arith_util au(m);
expr_ref t1(m), t2(m), result(m);
t1 = au.mk_numeral(rational(0),false);
t2 = au.mk_numeral(rational(-3),false);
expr* args[2] = { t1, t2 };
ar.mk_mul(2, args, result);
std::cout << mk_pp(result, m) << "\n";
th_rewriter rw(m);
expr_ref fml = parse_fml(m, example1);
rw(fml);
std::cout << mk_pp(fml, m) << "\n";
fml = parse_fml(m, example2);
rw(fml);
std::cout << mk_pp(fml, m) << "\n";
}
static unsigned parse_opt(std::istream& in, bool is_wcnf) {
ast_manager m;
reg_decl_plugins(m);
opt::context opt(m);
g_opt = &opt;
params_ref p = gparams::get_module("opt");
opt.updt_params(p);
if (is_wcnf) {
parse_wcnf(opt, in, g_handles);
}
else {
parse_opb(opt, in, g_handles);
}
try {
lbool r = opt.optimize();
switch (r) {
case l_true: std::cout << "sat\n"; break;
case l_false: std::cout << "unsat\n"; break;
case l_undef: std::cout << "unknown\n"; break;
}
DEBUG_CODE(
if (false && r == l_true) {
model_ref mdl;
opt.get_model(mdl);
expr_ref_vector hard(m);
opt.get_hard_constraints(hard);
for (unsigned i = 0; i < hard.size(); ++i) {
std::cout << "validate: " << i << "\n";
expr_ref tmp(m);
VERIFY(mdl->eval(hard[i].get(), tmp));
if (!m.is_true(tmp)) {
std::cout << tmp << "\n";
}
}
});
}
static void test1() {
ast_manager m;
reg_decl_plugins(m);
bv_util bv(m);
params_ref p;
ref<solver> solver = mk_inc_sat_solver(m, p);
expr_ref a = mk_bool(m, "a"), b = mk_bool(m, "b"), c = mk_bool(m, "c");
expr_ref ba = mk_bv(m, "ba", 3), bb = mk_bv(m, "bb", 3), bc = mk_bv(m, "bc", 3);
solver->assert_expr(m.mk_implies(a, b));
solver->assert_expr(m.mk_implies(b, c));
expr_ref_vector asms(m), vars(m), conseq(m);
asms.push_back(a);
vars.push_back(b);
vars.push_back(c);
vars.push_back(bb);
vars.push_back(bc);
solver->assert_expr(m.mk_eq(ba, bc));
solver->assert_expr(m.mk_eq(bv.mk_numeral(2, 3), ba));
solver->get_consequences(asms, vars, conseq);
std::cout << conseq << "\n";
}
static void test(char const *ex) {
smt_params params;
params.m_model = true;
ast_manager m;
reg_decl_plugins(m);
arith_util a(m);
expr_ref fml = parse_fml(m, ex);
app_ref_vector vars(m);
expr_ref_vector lits(m);
vars.push_back(m.mk_const(symbol("x"), a.mk_real()));
flatten_and(fml, lits);
smt::context ctx(m, params);
ctx.assert_expr(fml);
lbool result = ctx.check();
SASSERT(result == l_true);
ref<model> md;
ctx.get_model(md);
expr_ref pr = qe::arith_project(*md, vars, lits);
std::cout << mk_pp(fml, m) << "\n";
std::cout << mk_pp(pr, m) << "\n";
}
void test_smt_relation_unit() {
ast_manager m;
reg_decl_plugins(m);
arith_util a(m);
sort* int_sort = a.mk_int();
sort* real_sort = a.mk_real();
front_end_params params;
context ctx(m, params);
relation_manager & rm = ctx.get_rmanager();
relation_signature sig1;
sig1.push_back(int_sort);
sig1.push_back(int_sort);
sig1.push_back(real_sort);
smt_relation_plugin plugin(rm);
scoped_rel<relation_base> r1 = plugin.mk_empty(sig1);
// add_fact
relation_fact fact1(m);
fact1.push_back(a.mk_numeral(rational(1), true));
fact1.push_back(a.mk_numeral(rational(2), true));
fact1.push_back(a.mk_numeral(rational(3), false));
relation_fact fact2(m);
fact2.push_back(a.mk_numeral(rational(2), true));
fact2.push_back(a.mk_numeral(rational(2), true));
fact2.push_back(a.mk_numeral(rational(3), false));
r1->add_fact(fact1);
r1->display(std::cout << "r1: ");
// contains_fact
SASSERT(r1->contains_fact(fact1));
SASSERT(!r1->contains_fact(fact2));
// empty
scoped_rel<relation_base> r2 = plugin.mk_empty(sig1);
SASSERT(!r1->empty());
SASSERT(r2->empty());
// clone
scoped_rel<relation_base> r3 = r1->clone();
// complement?
r2->add_fact(fact2);
scoped_rel<relation_base> r4 = dynamic_cast<smt_relation&>(*r2).complement(0);
r4->display(std::cout << "complement r4: " );
// join
unsigned col_cnt = 2;
unsigned cols1[2] = {1, 2};
unsigned cols2[2] = {0, 2};
scoped_ptr<relation_join_fn> joinfn = plugin.mk_join_fn(*r1, *r4, col_cnt, cols1, cols2);
scoped_rel<relation_base> r5 = (*joinfn)(*r1, *r4);
r5->display(std::cout<< "join r5: ");
relation_fact fact3(m);
fact3.push_back(a.mk_numeral(rational(1), true));
fact3.push_back(a.mk_numeral(rational(2), true));
fact3.push_back(a.mk_numeral(rational(3), false));
fact3.push_back(a.mk_numeral(rational(2), true));
fact3.push_back(a.mk_numeral(rational(2), true));
fact3.push_back(a.mk_numeral(rational(3), false));
SASSERT(!r5->contains_fact(fact3));
fact3[5] = a.mk_numeral(rational(4), false);
SASSERT(!r5->contains_fact(fact3));
fact3[5] = a.mk_numeral(rational(3), false);
fact3[4] = a.mk_numeral(rational(3), true);
SASSERT(r5->contains_fact(fact3));
// project
unsigned removed_cols[2] = { 1, 4 };
scoped_ptr<relation_transformer_fn> projfn = plugin.mk_project_fn(*r5, col_cnt, removed_cols);
scoped_rel<relation_base> r6 = (*projfn)(*r5);
r6->display(std::cout<< "project r6: ");
// rename
unsigned cycle[3] = { 0, 2, 4 };
unsigned cycle_len = 3;
scoped_rel<relation_transformer_fn> renamefn = plugin.mk_rename_fn(*r5, cycle_len, cycle);
scoped_rel<relation_base> r7 = (*renamefn)(*r5);
r7->display(std::cout << "rename r7: ");
// union
// widen
relation_base* delta = 0;
scoped_ptr<relation_union_fn> widenfn = plugin.mk_widen_fn(*r1, *r2, delta);
scoped_ptr<relation_union_fn> unionfn = plugin.mk_union_fn(*r1, *r2, delta);
scoped_rel<relation_base> r8 = r1->clone();
(*unionfn)(*r8,*r2,0);
r8->display(std::cout << "union r8: ");
// filter_identical
unsigned identical_cols[2] = { 1, 3 };
scoped_ptr<relation_mutator_fn> filti = plugin.mk_filter_identical_fn(*r5, col_cnt, identical_cols);
scoped_rel<relation_base> r9 = r1->clone();
(*filti)(*r9);
r9->display(std::cout << "filter identical r9: ");
// filter_equal
app_ref value(m);
value = m.mk_const(symbol("x"), int_sort);
scoped_rel<relation_mutator_fn> eqn = plugin.mk_filter_equal_fn(*r5, value.get(), 3);
scoped_rel<relation_base> r10 = r1->clone();
(*eqn)(*r10);
r10->display(std::cout << "filter equal r10: ");
// filter_interpreted
app_ref cond(m);
cond = a.mk_lt(m.mk_var(3, int_sort), m.mk_var(4, int_sort));
scoped_rel<relation_mutator_fn> filtint = plugin.mk_filter_interpreted_fn(*r5, cond);
scoped_rel<relation_base> r11 = r5->clone();
(*filtint)(*r11);
r11->display(std::cout << "filter interpreted r11: ");
}
static void test_quant_solve1() {
ast_manager m;
arith_util ar(m);
reg_decl_plugins(m);
sort* i = ar.mk_int();
app_ref xr(m.mk_const(symbol("x"),i), m);
app_ref yr(m.mk_const(symbol("y"),i), m);
app* x = xr.get();
app* y = yr.get();
app* xy[2] = { x, y };
test_quant_solver(m, x, "(and (<= x y) (= (mod x 2) 0))");
test_quant_solver(m, x, "(and (<= (* 2 x) y) (= (mod x 2) 0))");
test_quant_solver(m, x, "(and (>= x y) (= (mod x 2) 0))");
test_quant_solver(m, x, "(and (>= (* 2 x) y) (= (mod x 2) 0))");
test_quant_solver(m, x, "(and (<= (* 2 x) y) (>= x z) (= (mod x 2) 0))");
test_quant_solver(m, x, "(and (<= (* 2 x) y) (>= (* 3 x) z) (= (mod x 2) 0))");
test_quant_solver(m, x, "(>= (* 2 x) a)");
test_quant_solver(m, x, "(<= (* 2 x) a)");
test_quant_solver(m, x, "(< (* 2 x) a)");
test_quant_solver(m, x, "(= (* 2 x) a)");
test_quant_solver(m, x, "(< (* 2 x) a)");
test_quant_solver(m, x, "(> (* 2 x) a)");
test_quant_solver(m, x, "(and (<= a x) (<= (* 2 x) b))");
test_quant_solver(m, x, "(and (<= a x) (<= x b))");
test_quant_solver(m, x, "(and (<= (* 2 a) x) (<= x b))");
test_quant_solver(m, x, "(and (<= (* 2 a) x) (<= (* 2 x) b))");
test_quant_solver(m, x, "(and (<= a x) (<= (* 3 x) b))");
test_quant_solver(m, x, "(and (<= (* 3 a) x) (<= x b))");
test_quant_solver(m, x, "(and (<= (* 3 a) x) (<= (* 3 x) b))");
test_quant_solver(m, x, "(and (< a (* 3 x)) (< (* 3 x) b))");
test_quant_solver(m, x, "(< (* 3 x) a)");
test_quant_solver(m, x, "(= (* 3 x) a)");
test_quant_solver(m, x, "(< (* 3 x) a)");
test_quant_solver(m, x, "(> (* 3 x) a)");
test_quant_solver(m, x, "(<= (* 3 x) a)");
test_quant_solver(m, x, "(>= (* 3 x) a)");
test_quant_solver(m, x, "(<= (* 2 x) a)");
test_quant_solver(m, x, "(or (= (* 2 x) y) (= (+ (* 2 x) 1) y))");
test_quant_solver(m, x, "(= x a)");
test_quant_solver(m, x, "(< x a)");
test_quant_solver(m, x, "(> x a)");
test_quant_solver(m, x, "(and (> x a) (< x b))");
test_quant_solver(m, x, "(and (> x a) (< x b))");
test_quant_solver(m, x, "(<= x a)");
test_quant_solver(m, x, "(>= x a)");
test_quant_solver(m, x, "(and (<= (* 2 x) y) (= (mod x 2) 0))");
test_quant_solver(m, x, "(= (* 2 x) y)");
test_quant_solver(m, x, "(or (< x 0) (> x 1))");
test_quant_solver(m, x, "(or (< x y) (> x y))");
test_quant_solver(m, x, "(= x y)");
test_quant_solver(m, x, "(<= x y)");
test_quant_solver(m, x, "(>= x y)");
test_quant_solver(m, x, "(and (<= (+ x y) 0) (<= (+ x z) 0))");
test_quant_solver(m, x, "(and (<= (+ x y) 0) (<= (+ (* 2 x) z) 0))");
test_quant_solver(m, x, "(and (<= (+ (* 3 x) y) 0) (<= (+ (* 2 x) z) 0))");
test_quant_solver(m, x, "(and (>= x y) (>= x z))");
test_quant_solver(m, x, "(< x y)");
test_quant_solver(m, x, "(> x y)");
test_quant_solver(m, 2, xy, "(and (<= (- (* 2 y) b) (+ (* 3 x) a)) (<= (- (* 2 x) a) (+ (* 4 y) b)))");
test_quant_solver(m, "(exists ((c Cell)) (= c null))");
test_quant_solver(m, "(exists ((c Cell)) (= c (cell null c1)))");
test_quant_solver(m, "(exists ((c Cell)) (not (= c null)))", false);
test_quant_solver(m, "(exists ((c Cell)) (= (cell c c) c1))", false);
test_quant_solver(m, "(exists ((c Cell)) (= (cell c (cdr c1)) c1))", false);
test_quant_solver(m, "(exists ((t Tuple)) (= (tuple a P r1) t))");
test_quant_solver(m, "(exists ((t Tuple)) (= a (first t)))");
test_quant_solver(m, "(exists ((t Tuple)) (= P (second t)))");
test_quant_solver(m, "(exists ((t Tuple)) (= r2 (third t)))");
test_quant_solver(m, "(exists ((t Tuple)) (not (= a (first t))))");
test_quant_solver(m, "(exists ((t Tuple)) (not (= P (second t))))");
test_quant_solver(m, "(exists ((t Tuple)) (not (= r2 (third t))))");
}
static void test_project() {
ast_manager m;
reg_decl_plugins(m);
qe::arith_project_plugin plugin(m);
arith_util a(m);
app_ref_vector vars(m);
expr_ref_vector lits(m), ds(m);
model mdl(m);
app_ref x(m), y(m), z(m), u(m);
x = m.mk_const(symbol("x"), a.mk_int());
y = m.mk_const(symbol("y"), a.mk_int());
z = m.mk_const(symbol("z"), a.mk_int());
u = m.mk_const(symbol("u"), a.mk_int());
func_decl_ref f(m);
sort* int_sort = a.mk_int();
f = m.mk_func_decl(symbol("f"), 1, &int_sort, int_sort);
// test non-projection
mdl.register_decl(x->get_decl(), a.mk_int(0));
mdl.register_decl(y->get_decl(), a.mk_int(1));
mdl.register_decl(z->get_decl(), a.mk_int(2));
mdl.register_decl(u->get_decl(), a.mk_int(3));
func_interp* fi = alloc(func_interp, m, 1);
expr_ref_vector nums(m);
nums.push_back(a.mk_int(0));
nums.push_back(a.mk_int(1));
nums.push_back(a.mk_int(2));
fi->insert_new_entry(nums.c_ptr(), a.mk_int(1));
fi->insert_new_entry(nums.c_ptr()+1, a.mk_int(2));
fi->insert_new_entry(nums.c_ptr()+2, a.mk_int(3));
fi->set_else(a.mk_int(10));
mdl.register_decl(f, fi);
vars.reset();
lits.reset();
vars.push_back(x);
lits.push_back(x <= app_ref(m.mk_app(f, (expr*)x), m));
lits.push_back(x < y);
plugin(mdl, vars, lits);
std::cout << lits << "\n";
// test not-equals
vars.reset();
lits.reset();
vars.push_back(x);
lits.push_back(m.mk_not(m.mk_eq(x, y)));
plugin(mdl, vars, lits);
std::cout << lits << "\n";
// test negation of distinct using bound variables
mdl.register_decl(x->get_decl(), a.mk_int(0));
mdl.register_decl(y->get_decl(), a.mk_int(1));
mdl.register_decl(z->get_decl(), a.mk_int(0));
mdl.register_decl(u->get_decl(), a.mk_int(6));
vars.reset();
lits.reset();
ds.reset();
vars.push_back(x);
vars.push_back(y);
ds.push_back(x);
ds.push_back(y);
ds.push_back(z + 2);
ds.push_back(u);
ds.push_back(z);
lits.push_back(m.mk_not(m.mk_distinct(ds.size(), ds.c_ptr())));
plugin(mdl, vars, lits);
std::cout << lits << "\n";
// test negation of distinct, not using bound variables
mdl.register_decl(x->get_decl(), a.mk_int(0));
mdl.register_decl(y->get_decl(), a.mk_int(1));
mdl.register_decl(z->get_decl(), a.mk_int(0));
mdl.register_decl(u->get_decl(), a.mk_int(6));
vars.reset();
lits.reset();
ds.reset();
vars.push_back(x);
vars.push_back(y);
ds.push_back(x);
ds.push_back(y);
ds.push_back(z + 2);
ds.push_back(u);
ds.push_back(z + 10);
ds.push_back(u + 4);
lits.push_back(m.mk_not(m.mk_distinct(ds.size(), ds.c_ptr())));
plugin(mdl, vars, lits);
std::cout << lits << "\n";
// test distinct
mdl.register_decl(x->get_decl(), a.mk_int(0));
mdl.register_decl(y->get_decl(), a.mk_int(1));
mdl.register_decl(z->get_decl(), a.mk_int(0));
mdl.register_decl(u->get_decl(), a.mk_int(6));
vars.reset();
lits.reset();
ds.reset();
vars.push_back(x);
vars.push_back(y);
ds.push_back(x);
ds.push_back(y);
ds.push_back(z + 2);
ds.push_back(u);
lits.push_back(m.mk_distinct(ds.size(), ds.c_ptr()));
plugin(mdl, vars, lits);
std::cout << lits << "\n";
// equality over modulus
mdl.register_decl(y->get_decl(), a.mk_int(4));
mdl.register_decl(z->get_decl(), a.mk_int(8));
lits.reset();
vars.reset();
vars.push_back(y);
lits.push_back(m.mk_eq(a.mk_mod(y, a.mk_int(3)), a.mk_int(1)));
lits.push_back(m.mk_eq(2*y, z));
plugin(mdl, vars, lits);
std::cout << lits << "\n";
// inequality test
mdl.register_decl(x->get_decl(), a.mk_int(0));
mdl.register_decl(y->get_decl(), a.mk_int(1));
mdl.register_decl(z->get_decl(), a.mk_int(0));
mdl.register_decl(u->get_decl(), a.mk_int(6));
vars.reset();
lits.reset();
vars.push_back(x);
vars.push_back(y);
lits.push_back(z <= (x + (2*y)));
lits.push_back(2*x < u + 3);
lits.push_back(2*y <= u);
plugin(mdl, vars, lits);
std::cout << lits << "\n";
// non-unit equalities
mdl.register_decl(x->get_decl(), a.mk_int(1));
mdl.register_decl(z->get_decl(), a.mk_int(2));
mdl.register_decl(u->get_decl(), a.mk_int(3));
mdl.register_decl(y->get_decl(), a.mk_int(4));
lits.reset();
vars.reset();
vars.push_back(x);
lits.push_back(m.mk_eq(2*x, z));
lits.push_back(m.mk_eq(3*x, u));
plugin(mdl, vars, lits);
std::cout << lits << "\n";
}
context::add_plugins::add_plugins(ast_manager & m) {
reg_decl_plugins(m);
}
