SOLVER_TERM mk_array_var(SOLVER_CONTEXT ctx, const char * name){
Z3_context z3ctx = (Z3_context) ctx;
// Indexes are integers
Z3_sort tind = Z3_mk_int_sort(z3ctx);
// Values are integers (for the moment)
Z3_sort tval = Z3_mk_int_sort(z3ctx);
// Declaration of array
Z3_sort ty = Z3_mk_array_sort(z3ctx, tind, tval);
return (SOLVER_TERM) mk_var(z3ctx, name, ty);
}
SOLVER_TERM mk_int(SOLVER_CONTEXT ctx, int v){
if (v > Z3_INT_LIMIT){ fprintf(stderr,"BUG: Z3 overflow of 32int.\n"); exit(1);}
Z3_context z3ctx = (Z3_context) ctx;
Z3_sort ty = Z3_mk_int_sort(z3ctx);
return (SOLVER_TERM) Z3_mk_int(z3ctx, v, ty);
//return (SOLVER_TERM) Z3_mk_int64(z3ctx, v, ty);
}
static void tst_get_implied_equalities1() {
Z3_config cfg = Z3_mk_config();
Z3_context ctx = Z3_mk_context(cfg);
Z3_del_config(cfg);
Z3_sort int_ty = Z3_mk_int_sort(ctx);
Z3_ast a = mk_int_var(ctx,"a");
Z3_ast b = mk_int_var(ctx,"b");
Z3_ast c = mk_int_var(ctx,"c");
Z3_ast d = mk_int_var(ctx,"d");
Z3_func_decl f = Z3_mk_func_decl(ctx, Z3_mk_string_symbol(ctx,"f"), 1, &int_ty, int_ty);
Z3_ast fa = Z3_mk_app(ctx, f, 1, &a);
Z3_ast fb = Z3_mk_app(ctx, f, 1, &b);
Z3_ast fc = Z3_mk_app(ctx, f, 1, &c);
unsigned const num_terms = 7;
unsigned i;
Z3_ast terms[7] = { a, b, c, d, fa, fb, fc };
unsigned class_ids[7] = { 0, 0, 0, 0, 0, 0, 0 };
Z3_solver solver = Z3_mk_simple_solver(ctx);
Z3_solver_inc_ref(ctx, solver);
Z3_solver_assert(ctx, solver, Z3_mk_eq(ctx, a, b));
Z3_solver_assert(ctx, solver, Z3_mk_eq(ctx, b, d));
Z3_solver_assert(ctx, solver, Z3_mk_le(ctx, fa, fc));
Z3_solver_assert(ctx, solver, Z3_mk_le(ctx, fc, d));
Z3_get_implied_equalities(ctx, solver, num_terms, terms, class_ids);
for (i = 0; i < num_terms; ++i) {
printf("Class %s |-> %d\n", Z3_ast_to_string(ctx, terms[i]), class_ids[i]);
}
SASSERT(class_ids[1] == class_ids[0]);
SASSERT(class_ids[2] != class_ids[0]);
SASSERT(class_ids[3] == class_ids[0]);
SASSERT(class_ids[4] != class_ids[0]);
SASSERT(class_ids[5] != class_ids[0]);
SASSERT(class_ids[6] != class_ids[0]);
SASSERT(class_ids[4] == class_ids[5]);
printf("asserting b <= f(a)\n");
Z3_solver_assert(ctx, solver, Z3_mk_le(ctx, b, fa));
Z3_get_implied_equalities(ctx, solver, num_terms, terms, class_ids);
for (i = 0; i < num_terms; ++i) {
printf("Class %s |-> %d\n", Z3_ast_to_string(ctx, terms[i]), class_ids[i]);
}
SASSERT(class_ids[1] == class_ids[0]);
SASSERT(class_ids[2] != class_ids[0]);
SASSERT(class_ids[3] == class_ids[0]);
SASSERT(class_ids[4] == class_ids[0]);
SASSERT(class_ids[5] == class_ids[0]);
SASSERT(class_ids[6] == class_ids[0]);
Z3_solver_dec_ref(ctx, solver);
/* delete logical context */
Z3_del_context(ctx);
}
static void tst_get_implied_equalities2() {
enable_trace("after_search");
enable_trace("get_implied_equalities");
enable_trace("implied_equalities");
Z3_config cfg = Z3_mk_config();
Z3_context ctx = Z3_mk_context(cfg);
Z3_del_config(cfg);
Z3_solver solver = Z3_mk_simple_solver(ctx);
Z3_solver_inc_ref(ctx, solver);
Z3_sort int_ty = Z3_mk_int_sort(ctx);
Z3_ast a = mk_int_var(ctx,"a");
Z3_ast b = mk_int_var(ctx,"b");
Z3_ast one = Z3_mk_numeral(ctx, "1", int_ty);
Z3_ast two = Z3_mk_numeral(ctx, "2", int_ty);
Z3_ast x = Z3_mk_const_array(ctx, int_ty, one);
Z3_ast y = Z3_mk_store(ctx, x, one, a);
Z3_ast z = Z3_mk_store(ctx, y, two , b);
Z3_ast u = Z3_mk_store(ctx, x, two , b);
Z3_ast v = Z3_mk_store(ctx, u, one , a);
unsigned const num_terms = 5;
unsigned i;
Z3_ast terms[5] = { x, y, z, u, v};
unsigned class_ids[5] = { 0, 0, 0, 0, 0};
Z3_get_implied_equalities(ctx, solver, num_terms, terms, class_ids);
for (i = 0; i < num_terms; ++i) {
printf("Class %s |-> %d\n", Z3_ast_to_string(ctx, terms[i]), class_ids[i]);
}
SASSERT(class_ids[1] != class_ids[0]);
SASSERT(class_ids[2] != class_ids[0]);
SASSERT(class_ids[3] != class_ids[0]);
SASSERT(class_ids[4] != class_ids[0]);
SASSERT(class_ids[4] == class_ids[2]);
SASSERT(class_ids[2] != class_ids[1]);
SASSERT(class_ids[3] != class_ids[1]);
SASSERT(class_ids[4] != class_ids[1]);
SASSERT(class_ids[3] != class_ids[2]);
/* delete logical context */
Z3_solver_dec_ref(ctx, solver);
Z3_del_context(ctx);
}
int test(){
int i;
/* Create a Z3 context to contain formulas */
Z3_config cfg = Z3_mk_config();
Z3_context ctx = iz3_mk_context(cfg);
int num = 2;
Z3_ast *constraints = (Z3_ast *)malloc(num * sizeof(Z3_ast));
#if 1
Z3_sort arr = Z3_mk_array_sort(ctx,Z3_mk_int_sort(ctx),Z3_mk_bool_sort(ctx));
Z3_symbol as = Z3_mk_string_symbol(ctx, "a");
Z3_symbol bs = Z3_mk_string_symbol(ctx, "b");
Z3_symbol xs = Z3_mk_string_symbol(ctx, "x");
Z3_ast a = Z3_mk_const(ctx,as,arr);
Z3_ast b = Z3_mk_const(ctx,bs,arr);
Z3_ast x = Z3_mk_const(ctx,xs,Z3_mk_int_sort(ctx));
Z3_ast c1 = Z3_mk_eq(ctx,a,Z3_mk_store(ctx,b,x,Z3_mk_true(ctx)));
Z3_ast c2 = Z3_mk_not(ctx,Z3_mk_select(ctx,a,x));
#else
Z3_symbol xs = Z3_mk_string_symbol(ctx, "x");
Z3_ast x = Z3_mk_const(ctx,xs,Z3_mk_bool_sort(ctx));
Z3_ast c1 = Z3_mk_eq(ctx,x,Z3_mk_true(ctx));
Z3_ast c2 = Z3_mk_eq(ctx,x,Z3_mk_false(ctx));
#endif
constraints[0] = c1;
constraints[1] = c2;
/* print out the result for grins. */
// Z3_string smtout = Z3_benchmark_to_smtlib_string (ctx, "foo", "QFLIA", "sat", "", num, constraints, Z3_mk_true(ctx));
// Z3_string smtout = Z3_ast_to_string(ctx,constraints[0]);
// Z3_string smtout = Z3_context_to_string(ctx);
// puts(smtout);
iz3_print(ctx,num,constraints,"iZ3temp.smt");
/* Make room for interpolants. */
Z3_ast *interpolants = (Z3_ast *)malloc((num-1) * sizeof(Z3_ast));
/* Make room for the model. */
Z3_model model = 0;
/* Call the prover */
Z3_lbool result = iz3_interpolate(ctx, num, constraints, interpolants, &model);
switch (result) {
/* If UNSAT, print the interpolants */
case Z3_L_FALSE:
printf("unsat, interpolants:\n");
for(i = 0; i < num-1; i++)
printf("%s\n", Z3_ast_to_string(ctx, interpolants[i]));
break;
case Z3_L_UNDEF:
printf("fail\n");
break;
case Z3_L_TRUE:
printf("sat\n");
printf("model:\n%s\n", Z3_model_to_string(ctx, model));
break;
}
/* Delete the model if there is one */
if (model)
Z3_del_model(ctx, model);
/* Delete logical context (note, we call iz3_del_context, not
Z3_del_context */
iz3_del_context(ctx);
return 1;
}
static Z3_ast mk_int_var(Z3_context ctx, char const* name) {
return mk_var(ctx, name, Z3_mk_int_sort(ctx));
}
SOLVER_TERM mk_int_var(SOLVER_CONTEXT ctx, const char * name){
Z3_context z3ctx = (Z3_context) ctx;
Z3_sort ty = Z3_mk_int_sort(z3ctx);
return (SOLVER_TERM) mk_var(z3ctx, name, ty);
}
void test_smt_relation_api() {
enable_trace("smt_relation");
enable_trace("smt_relation2");
enable_trace("quant_elim");
Z3_config cfg = Z3_mk_config();
Z3_set_param_value(cfg, "DL_DEFAULT_RELATION", "smt_relation2");
Z3_context ctx = Z3_mk_context(cfg);
Z3_fixedpoint dl = Z3_mk_fixedpoint(ctx);
Z3_fixedpoint_inc_ref(ctx,dl);
Z3_del_config(cfg);
Z3_sort int_sort = Z3_mk_int_sort(ctx);
Z3_sort bool_sort = Z3_mk_bool_sort(ctx);
Z3_func_decl nil_decl, is_nil_decl;
Z3_func_decl cons_decl, is_cons_decl, head_decl, tail_decl;
Z3_sort list = Z3_mk_list_sort(
ctx,
Z3_mk_string_symbol(ctx, "list"),
int_sort,
&nil_decl,
&is_nil_decl,
&cons_decl,
&is_cons_decl,
&head_decl,
&tail_decl);
Z3_sort listint[2] = { list, int_sort };
Z3_symbol p_sym = Z3_mk_string_symbol(ctx, "p");
Z3_symbol q_sym = Z3_mk_string_symbol(ctx, "q");
Z3_func_decl p = Z3_mk_func_decl(ctx, p_sym, 2, listint, bool_sort);
Z3_func_decl q = Z3_mk_func_decl(ctx, q_sym, 2, listint, bool_sort);
Z3_fixedpoint_register_relation(ctx, dl, p);
Z3_fixedpoint_register_relation(ctx, dl, q);
Z3_ast zero = Z3_mk_numeral(ctx, "0", int_sort);
Z3_ast one = Z3_mk_numeral(ctx, "1", int_sort);
Z3_ast two = Z3_mk_numeral(ctx, "2", int_sort);
Z3_ast x = Z3_mk_bound(ctx, 0, list);
Z3_ast y = Z3_mk_bound(ctx, 1, int_sort);
Z3_ast z = Z3_mk_bound(ctx, 2, list);
Z3_ast zero_x[2] = { zero, x };
Z3_ast fx = Z3_mk_app(ctx, cons_decl, 2, zero_x);
Z3_ast zero_fx[2] = { zero, fx };
Z3_ast ffx = Z3_mk_app(ctx, cons_decl, 2, zero_fx);
Z3_ast xy[2] = { x, y };
Z3_ast zy[2] = { z, y };
// Z3_ast ffxy[2] = { ffx, y };
// Z3_ast fxy[2] = { fx, y };
Z3_ast zero_nil[2] = { zero, Z3_mk_app(ctx, nil_decl, 0, 0) };
Z3_ast f0 = Z3_mk_app(ctx, cons_decl, 2, zero_nil);
Z3_ast zero_f0[2] = { zero, f0 };
Z3_ast f1 = Z3_mk_app(ctx, cons_decl, 2, zero_f0);
Z3_ast zero_f1[2] = { zero, f1 };
Z3_ast f2 = Z3_mk_app(ctx, cons_decl, 2, zero_f1);
Z3_ast zero_f2[2] = { zero, f2 };
Z3_ast f3 = Z3_mk_app(ctx, cons_decl, 2, zero_f2);
Z3_ast zero_f3[2] = { zero, f3 };
Z3_ast f4 = Z3_mk_app(ctx, cons_decl, 2, zero_f3);
Z3_ast zero_f4[2] = { zero, f4 };
Z3_ast f5 = Z3_mk_app(ctx, cons_decl, 2, zero_f4);
Z3_ast zero_z[2] = { zero, z };
Z3_ast fz = Z3_mk_app(ctx, cons_decl, 2, zero_z);
Z3_ast pxy = Z3_mk_app(ctx, p, 2, xy);
Z3_ast pzy = Z3_mk_app(ctx, p, 2, zy);
Z3_ast qxy = Z3_mk_app(ctx, q, 2, xy);
Z3_ast qzy = Z3_mk_app(ctx, q, 2, zy);
Z3_ast even_y = Z3_mk_eq(ctx, zero, Z3_mk_mod(ctx, y, two));
Z3_ast odd_y = Z3_mk_eq(ctx, one, Z3_mk_mod(ctx, y, two));
// p(x, y) :- odd(y), p(z,y), f(z) = x . // dead rule.
// q(x, y) :- p(f(f(x)), y).
// p(x, y) :- q(f(x), y) // x decreases
// p(x, y) :- even y, x = f^5(0) // initial condition.
Z3_ast body1[3] = { pzy, Z3_mk_eq(ctx, fz, x), odd_y };
Z3_ast body2[2] = { pzy, Z3_mk_eq(ctx, ffx, z) };
Z3_ast body3[2] = { qzy, Z3_mk_eq(ctx, fx, z) };
Z3_ast body4[2] = { even_y, Z3_mk_eq(ctx, x, f5) };
Z3_fixedpoint_add_rule(ctx, dl, Z3_mk_implies(ctx, Z3_mk_and(ctx, 3, body1), pxy), 0);
Z3_fixedpoint_add_rule(ctx, dl, Z3_mk_implies(ctx, Z3_mk_and(ctx, 2, body2), qxy), 0);
Z3_fixedpoint_add_rule(ctx, dl, Z3_mk_implies(ctx, Z3_mk_and(ctx, 2, body3), pxy), 0);
Z3_fixedpoint_add_rule(ctx, dl, Z3_mk_implies(ctx, Z3_mk_and(ctx, 2, body4), pxy), 0);
Z3_lbool r = Z3_fixedpoint_query(ctx, dl, pxy);
if (r != Z3_L_UNDEF) {
std::cout << Z3_ast_to_string(ctx, Z3_fixedpoint_get_answer(ctx, dl)) << "\n";
}
Z3_del_context(ctx);
}
