Ejemplo n.º 1
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;
}
Ejemplo n.º 2
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;
}
Ejemplo n.º 3
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;
}