int main() {
ExprManager em;
SmtEngine smt(&em);
// Prove that for integers x and y:
// x > 0 AND y > 0 => 2x + y >= 3
Type integer = em.integerType();
Expr x = em.mkVar("x", integer);
Expr y = em.mkVar("y", integer);
Expr zero = em.mkConst(Rational(0));
Expr x_positive = em.mkExpr(kind::GT, x, zero);
Expr y_positive = em.mkExpr(kind::GT, y, zero);
Expr two = em.mkConst(Rational(2));
Expr twox = em.mkExpr(kind::MULT, two, x);
Expr twox_plus_y = em.mkExpr(kind::PLUS, twox, y);
Expr three = em.mkConst(Rational(3));
Expr twox_plus_y_geq_3 = em.mkExpr(kind::GEQ, twox_plus_y, three);
Expr formula =
em.mkExpr(kind::AND, x_positive, y_positive).
impExpr(twox_plus_y_geq_3);
cout << "Checking validity of formula " << formula << " with CVC4." << endl;
cout << "CVC4 should report VALID." << endl;
cout << "Result from CVC4 is: " << smt.query(formula) << endl;
return 0;
}
int main() {
ExprManager em;
SmtEngine smt(&em);
smt.setLogic("QF_BV"); // Set the logic
Type bitvector32 = em.mkBitVectorType(32);
Expr x = em.mkVar("a", bitvector32);
Expr ext_31_1 = em.mkConst(CVC4::BitVectorExtract(31,1));
Expr x_31_1 = em.mkExpr(ext_31_1, x);
Expr ext_30_0 = em.mkConst(CVC4::BitVectorExtract(30,0));
Expr x_30_0 = em.mkExpr(ext_30_0, x);
Expr ext_31_31 = em.mkConst(CVC4::BitVectorExtract(31,31));
Expr x_31_31 = em.mkExpr(ext_31_31, x);
Expr ext_0_0 = em.mkConst(CVC4::BitVectorExtract(0,0));
Expr x_0_0 = em.mkExpr(ext_0_0, x);
Expr eq = em.mkExpr(kind::EQUAL, x_31_1, x_30_0);
cout << " Asserting: " << eq << endl;
smt.assertFormula(eq);
Expr eq2 = em.mkExpr(kind::EQUAL, x_31_31, x_0_0);
cout << " Querying: " << eq2 << endl;
cout << " Expect valid. " << endl;
cout << " CVC4: " << smt.query(eq2) << endl;
return 0;
}
void Tptp::addTheory(Theory theory) {
ExprManager * em = getExprManager();
switch(theory) {
case THEORY_CORE:
//TPTP (CNF and FOF) is unsorted so we define this common type
{
std::string d_unsorted_name = "$$unsorted";
d_unsorted = em->mkSort(d_unsorted_name);
preemptCommand( new DeclareTypeCommand(d_unsorted_name, 0, d_unsorted) );
}
// propositionnal
defineType("Bool", em->booleanType());
defineVar("$true", em->mkConst(true));
defineVar("$false", em->mkConst(false));
addOperator(kind::AND);
addOperator(kind::EQUAL);
addOperator(kind::IMPLIES);
//addOperator(kind::ITE); //only for tff thf
addOperator(kind::NOT);
addOperator(kind::OR);
addOperator(kind::XOR);
addOperator(kind::APPLY_UF);
//Add quantifiers?
break;
default:
std::stringstream ss;
ss << "internal error: Tptp::addTheory(): unhandled theory " << theory;
throw ParserException(ss.str());
}
}
int main() {
ExprManager em;
Options opts;
SmtEngine smt(&em);
SmtEngine smt2(&em);
Result r = smt.query(em.mkConst(true));
Result r2 = smt2.query(em.mkConst(true));
return r == Result::VALID && r2 == Result::VALID ? 0 : 1;
}
int main() {
ExprManager em;
Options opts;
SmtEngine smt(&em);
Result r = smt.query(em.mkConst(true));
return (Result::VALID == r) ? 0 : 1;
}
int main() {
ExprManager em;
Options opts;
SmtEngine smt(&em);
smt.setOption("incremental", SExpr("true"));
Expr x = em.mkVar("x", em.integerType());
Expr y = em.mkVar("y", em.integerType());
smt.assertFormula(em.mkExpr(kind::GT, em.mkExpr(kind::PLUS, x, y), em.mkConst(Rational(5))));
Expr q = em.mkExpr(kind::GT, x, em.mkConst(Rational(0)));
Result r = smt.query(q);
if(r != Result::INVALID) {
exit(1);
}
Statistics stats = smt.getStatistics();
for(Statistics::iterator i = stats.begin(); i != stats.end(); ++i) {
cout << "stat " << (*i).first << " is " << (*i).second << endl;
}
smt.assertFormula(em.mkExpr(kind::LT, y, em.mkConst(Rational(5))));
r = smt.query(q);
Statistics stats2 = smt.getStatistics();
bool different = false;
for(Statistics::iterator i = stats2.begin(); i != stats2.end(); ++i) {
cout << "stat1 " << (*i).first << " is " << stats.getStatistic((*i).first) << endl;
cout << "stat2 " << (*i).first << " is " << (*i).second << endl;
if(smt.getStatistic((*i).first) != (*i).second) {
cout << "SMT engine reports different value for statistic "
<< (*i).first << ": " << smt.getStatistic((*i).first) << endl;
exit(1);
}
different = different || stats.getStatistic((*i).first) != (*i).second;
}
#ifdef CVC4_STATISTICS_ON
if(!different) {
cout << "stats are the same! bailing.." << endl;
exit(1);
}
#endif /* CVC4_STATISTICS_ON */
return r == Result::VALID ? 0 : 1;
}
int main() {
ExprManager em;
SmtEngine smt(&em);
smt.setOption("produce-models", true); // Produce Models
smt.setOption("output-language", "cvc4"); // Set the output-language to CVC's
smt.setOption("default-dag-thresh", 0); //Disable dagifying the output
smt.setLogic(string("QF_UFLIRA"));
// Sorts
SortType u = em.mkSort("u");
Type integer = em.integerType();
Type boolean = em.booleanType();
Type uToInt = em.mkFunctionType(u, integer);
Type intPred = em.mkFunctionType(integer, boolean);
// Variables
Expr x = em.mkVar("x", u);
Expr y = em.mkVar("y", u);
// Functions
Expr f = em.mkVar("f", uToInt);
Expr p = em.mkVar("p", intPred);
// Constants
Expr zero = em.mkConst(Rational(0));
Expr one = em.mkConst(Rational(1));
// Terms
Expr f_x = em.mkExpr(kind::APPLY_UF, f, x);
Expr f_y = em.mkExpr(kind::APPLY_UF, f, y);
Expr sum = em.mkExpr(kind::PLUS, f_x, f_y);
Expr p_0 = em.mkExpr(kind::APPLY_UF, p, zero);
Expr p_f_y = em.mkExpr(kind::APPLY_UF, p, f_y);
// Construct the assumptions
Expr assumptions =
em.mkExpr(kind::AND,
em.mkExpr(kind::LEQ, zero, f_x), // 0 <= f(x)
em.mkExpr(kind::LEQ, zero, f_y), // 0 <= f(y)
em.mkExpr(kind::LEQ, sum, one), // f(x) + f(y) <= 1
p_0.notExpr(), // not p(0)
p_f_y); // p(f(y))
smt.assertFormula(assumptions);
cout << "Given the following assumptions:" << endl
<< assumptions << endl
<< "Prove x /= y is valid. "
<< "CVC4 says: " << smt.query(em.mkExpr(kind::DISTINCT, x, y))
<< "." << endl;
cout << "Now we call checksat on a trivial query to show that" << endl
<< "the assumptions are satisfiable: "
<< smt.checkSat(em.mkConst(true)) << "."<< endl;
cout << "Finally, after a SAT call, we recursively call smt.getValue(...) on"
<< "all of the assumptions to see what the satisfying model looks like."
<< endl;
prefixPrintGetValue(smt, assumptions);
return 0;
}
int main() {
ExprManager em;
SmtEngine smt(&em);
smt.setOption("produce-models", true); // Produce Models
smt.setOption("output-language", "smtlib"); // output-language
smt.setLogic("QF_AUFBV"); // Set the logic
// Consider the following code (where size is some previously defined constant):
//
//
// Assert (current_array[0] > 0);
// for (unsigned i = 1; i < k; ++i) {
// current_array[i] = 2 * current_array[i - 1];
// Assert (current_array[i-1] < current_array[i]);
// }
//
// We want to check whether the assertion in the body of the for loop holds
// throughout the loop.
// Setting up the problem parameters
unsigned k = 4; // number of unrollings (should be a power of 2)
unsigned index_size = log2(k); // size of the index
// Types
Type elementType = em.mkBitVectorType(32);
Type indexType = em.mkBitVectorType(index_size);
Type arrayType = em.mkArrayType(indexType, elementType);
// Variables
Expr current_array = em.mkVar("current_array", arrayType);
// Making a bit-vector constant
Expr zero = em.mkConst(BitVector(index_size, 0u));
// Asserting that current_array[0] > 0
Expr current_array0 = em.mkExpr(kind::SELECT, current_array, zero);
Expr current_array0_gt_0 = em.mkExpr(kind::BITVECTOR_SGT, current_array0, em.mkConst(BitVector(32, 0u)));
smt.assertFormula(current_array0_gt_0);
// Building the assertions in the loop unrolling
Expr index = em.mkConst(BitVector(index_size, 0u));
Expr old_current = em.mkExpr(kind::SELECT, current_array, index);
Expr two = em.mkConst(BitVector(32, 2u));
std::vector<Expr> assertions;
for (unsigned i = 1; i < k; ++i) {
index = em.mkConst(BitVector(index_size, Integer(i)));
Expr new_current = em.mkExpr(kind::BITVECTOR_MULT, two, old_current);
// current[i] = 2 * current[i-1]
current_array = em.mkExpr(kind::STORE, current_array, index, new_current);
// current[i-1] < current [i]
Expr current_slt_new_current = em.mkExpr(kind::BITVECTOR_SLT, old_current, new_current);
assertions.push_back(current_slt_new_current);
old_current = em.mkExpr(kind::SELECT, current_array, index);
}
Expr query = em.mkExpr(kind::NOT, em.mkExpr(kind::AND, assertions));
cout << "Asserting " << query << " to CVC4 " << endl;
smt.assertFormula(query);
cout << "Expect sat. " << endl;
cout << "CVC4: " << smt.checkSat(em.mkConst(true)) << endl;
// Getting the model
cout << "The satisfying model is: " << endl;
cout << " current_array = " << smt.getValue(current_array) << endl;
cout << " current_array[0] = " << smt.getValue(current_array0) << endl;
return 0;
}
int main() {
ExprManager em;
SmtEngine smt(&em);
// Set the logic
smt.setLogic("S");
// Produce models
smt.setOption("produce-models", true);
// The option strings-exp is needed
smt.setOption("strings-exp", true);
// Set output language to SMTLIB2
std::cout << language::SetLanguage(language::output::LANG_SMTLIB_V2);
// String type
Type string = em.stringType();
// std::string
std::string std_str_ab("ab");
// CVC4::String
CVC4::String cvc4_str_ab(std_str_ab);
CVC4::String cvc4_str_abc("abc");
// String constants
Expr ab = em.mkConst(cvc4_str_ab);
Expr abc = em.mkConst(CVC4::String("abc"));
// String variables
Expr x = em.mkVar("x", string);
Expr y = em.mkVar("y", string);
Expr z = em.mkVar("z", string);
// String concatenation: x.ab.y
Expr lhs = em.mkExpr(kind::STRING_CONCAT, x, ab, y);
// String concatenation: abc.z
Expr rhs = em.mkExpr(kind::STRING_CONCAT, abc, z);
// x.ab.y = abc.z
Expr formula1 = em.mkExpr(kind::EQUAL, lhs, rhs);
// Length of y: |y|
Expr leny = em.mkExpr(kind::STRING_LENGTH, y);
// |y| >= 0
Expr formula2 = em.mkExpr(kind::GEQ, leny, em.mkConst(Rational(0)));
// Regular expression: (ab[c-e]*f)|g|h
Expr r = em.mkExpr(kind::REGEXP_UNION,
em.mkExpr(kind::REGEXP_CONCAT,
em.mkExpr(kind::STRING_TO_REGEXP, em.mkConst(String("ab"))),
em.mkExpr(kind::REGEXP_STAR,
em.mkExpr(kind::REGEXP_RANGE, em.mkConst(String("c")), em.mkConst(String("e")))),
em.mkExpr(kind::STRING_TO_REGEXP, em.mkConst(String("f")))),
em.mkExpr(kind::STRING_TO_REGEXP, em.mkConst(String("g"))),
em.mkExpr(kind::STRING_TO_REGEXP, em.mkConst(String("h"))));
// String variables
Expr s1 = em.mkVar("s1", string);
Expr s2 = em.mkVar("s2", string);
// String concatenation: s1.s2
Expr s = em.mkExpr(kind::STRING_CONCAT, s1, s2);
// s1.s2 in (ab[c-e]*f)|g|h
Expr formula3 = em.mkExpr(kind::STRING_IN_REGEXP, s, r);
// Make a query
Expr q = em.mkExpr(kind::AND,
formula1,
formula2,
formula3);
// check sat
Result result = smt.checkSat(q);
std::cout << "CVC4 reports: " << q << " is " << result << "." << std::endl;
if(result == Result::SAT) {
std::cout << " x = " << smt.getValue(x) << std::endl;
std::cout << " s1.s2 = " << smt.getValue(s) << std::endl;
}
}