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;
}
int main() {
ExprManager em;
SmtEngine smt(&em);
smt.setLogic("QF_BV"); // Set the logic
// The following example has been adapted from the book A Hacker's Delight by
// Henry S. Warren.
//
// Given a variable x that can only have two values, a or b. We want to
// assign to x a value other than the current one. The straightforward code
// to do that is:
//
//(0) if (x == a ) x = b;
// else x = a;
//
// Two more efficient yet equivalent methods are:
//
//(1) x = a ⊕ b ⊕ x;
//
//(2) x = a + b - x;
//
// We will use CVC4 to prove that the three pieces of code above are all
// equivalent by encoding the problem in the bit-vector theory.
// Creating a bit-vector type of width 32
Type bitvector32 = em.mkBitVectorType(32);
// Variables
Expr x = em.mkVar("x", bitvector32);
Expr a = em.mkVar("a", bitvector32);
Expr b = em.mkVar("b", bitvector32);
// First encode the assumption that x must be equal to a or b
Expr x_eq_a = em.mkExpr(kind::EQUAL, x, a);
Expr x_eq_b = em.mkExpr(kind::EQUAL, x, b);
Expr assumption = em.mkExpr(kind::OR, x_eq_a, x_eq_b);
// Assert the assumption
smt.assertFormula(assumption);
// Introduce a new variable for the new value of x after assignment.
Expr new_x = em.mkVar("new_x", bitvector32); // x after executing code (0)
Expr new_x_ = em.mkVar("new_x_", bitvector32); // x after executing code (1) or (2)
// Encoding code (0)
// new_x = x == a ? b : a;
Expr ite = em.mkExpr(kind::ITE, x_eq_a, b, a);
Expr assignment0 = em.mkExpr(kind::EQUAL, new_x, ite);
// Assert the encoding of code (0)
cout << "Asserting " << assignment0 << " to CVC4 " << endl;
smt.assertFormula(assignment0);
cout << "Pushing a new context." << endl;
smt.push();
// Encoding code (1)
// new_x_ = a xor b xor x
Expr a_xor_b_xor_x = em.mkExpr(kind::BITVECTOR_XOR, a, b, x);
Expr assignment1 = em.mkExpr(kind::EQUAL, new_x_, a_xor_b_xor_x);
// Assert encoding to CVC4 in current context;
cout << "Asserting " << assignment1 << " to CVC4 " << endl;
smt.assertFormula(assignment1);
Expr new_x_eq_new_x_ = em.mkExpr(kind::EQUAL, new_x, new_x_);
cout << " Querying: " << new_x_eq_new_x_ << endl;
cout << " Expect valid. " << endl;
cout << " CVC4: " << smt.query(new_x_eq_new_x_) << endl;
cout << " Popping context. " << endl;
smt.pop();
// Encoding code (2)
// new_x_ = a + b - x
Expr a_plus_b = em.mkExpr(kind::BITVECTOR_PLUS, a, b);
Expr a_plus_b_minus_x = em.mkExpr(kind::BITVECTOR_SUB, a_plus_b, x);
Expr assignment2 = em.mkExpr(kind::EQUAL, new_x_, a_plus_b_minus_x);
// Assert encoding to CVC4 in current context;
cout << "Asserting " << assignment2 << " to CVC4 " << endl;
smt.assertFormula(assignment2);
cout << " Querying: " << new_x_eq_new_x_ << endl;
cout << " Expect valid. " << endl;
cout << " CVC4: " << smt.query(new_x_eq_new_x_) << endl;
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;
}