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-/********************* */
-/*! \file bitvectors-new.cpp
- ** \verbatim
- ** Top contributors (to current version):
- ** Aina Niemetz, Makai Mann
- ** This file is part of the CVC4 project.
- ** Copyright (c) 2009-2019 by the authors listed in the file AUTHORS
- ** in the top-level source directory) and their institutional affiliations.
- ** All rights reserved. See the file COPYING in the top-level source
- ** directory for licensing information.\endverbatim
- **
- ** \brief A simple demonstration of the solving capabilities of the CVC4
- ** bit-vector solver.
- **
- **/
-
-#include <iostream>
-
-#include <cvc4/api/cvc4cpp.h>
-
-using namespace std;
-using namespace CVC4::api;
-
-int main()
-{
- Solver slv;
- slv.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
- Sort bitvector32 = slv.mkBitVectorSort(32);
-
- // Variables
- Term x = slv.mkConst(bitvector32, "x");
- Term a = slv.mkConst(bitvector32, "a");
- Term b = slv.mkConst(bitvector32, "b");
-
- // First encode the assumption that x must be equal to a or b
- Term x_eq_a = slv.mkTerm(EQUAL, x, a);
- Term x_eq_b = slv.mkTerm(EQUAL, x, b);
- Term assumption = slv.mkTerm(OR, x_eq_a, x_eq_b);
-
- // Assert the assumption
- slv.assertFormula(assumption);
-
- // Introduce a new variable for the new value of x after assignment.
- Term new_x = slv.mkConst(bitvector32, "new_x"); // x after executing code (0)
- Term new_x_ =
- slv.mkConst(bitvector32, "new_x_"); // x after executing code (1) or (2)
-
- // Encoding code (0)
- // new_x = x == a ? b : a;
- Term ite = slv.mkTerm(ITE, x_eq_a, b, a);
- Term assignment0 = slv.mkTerm(EQUAL, new_x, ite);
-
- // Assert the encoding of code (0)
- cout << "Asserting " << assignment0 << " to CVC4 " << endl;
- slv.assertFormula(assignment0);
- cout << "Pushing a new context." << endl;
- slv.push();
-
- // Encoding code (1)
- // new_x_ = a xor b xor x
- Term a_xor_b_xor_x = slv.mkTerm(BITVECTOR_XOR, a, b, x);
- Term assignment1 = slv.mkTerm(EQUAL, new_x_, a_xor_b_xor_x);
-
- // Assert encoding to CVC4 in current context;
- cout << "Asserting " << assignment1 << " to CVC4 " << endl;
- slv.assertFormula(assignment1);
- Term new_x_eq_new_x_ = slv.mkTerm(EQUAL, new_x, new_x_);
-
- cout << " Check entailment assuming: " << new_x_eq_new_x_ << endl;
- cout << " Expect ENTAILED. " << endl;
- cout << " CVC4: " << slv.checkEntailed(new_x_eq_new_x_) << endl;
- cout << " Popping context. " << endl;
- slv.pop();
-
- // Encoding code (2)
- // new_x_ = a + b - x
- Term a_plus_b = slv.mkTerm(BITVECTOR_PLUS, a, b);
- Term a_plus_b_minus_x = slv.mkTerm(BITVECTOR_SUB, a_plus_b, x);
- Term assignment2 = slv.mkTerm(EQUAL, new_x_, a_plus_b_minus_x);
-
- // Assert encoding to CVC4 in current context;
- cout << "Asserting " << assignment2 << " to CVC4 " << endl;
- slv.assertFormula(assignment2);
-
- cout << " Check entailment assuming: " << new_x_eq_new_x_ << endl;
- cout << " Expect ENTAILED. " << endl;
- cout << " CVC4: " << slv.checkEntailed(new_x_eq_new_x_) << endl;
-
- Term x_neq_x = slv.mkTerm(EQUAL, x, x).notTerm();
- std::vector<Term> v{new_x_eq_new_x_, x_neq_x};
- cout << " Check entailment assuming: " << v << endl;
- cout << " Expect NOT_ENTAILED. " << endl;
- cout << " CVC4: " << slv.checkEntailed(v) << endl;
-
- // Assert that a is odd
- Op extract_op = slv.mkOp(BITVECTOR_EXTRACT, 0, 0);
- Term lsb_of_a = slv.mkTerm(extract_op, a);
- cout << "Sort of " << lsb_of_a << " is " << lsb_of_a.getSort() << endl;
- Term a_odd = slv.mkTerm(EQUAL, lsb_of_a, slv.mkBitVector(1u, 1u));
- cout << "Assert " << a_odd << endl;
- cout << "Check satisfiability." << endl;
- slv.assertFormula(a_odd);
- cout << " Expect sat. " << endl;
- cout << " CVC4: " << slv.checkSat() << endl;
- return 0;
-}
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