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/********************* */
/*! \file bitvectors.cpp
** \verbatim
** Top contributors (to current version):
** Aina Niemetz, Liana Hadarean, Makai Mann
** This file is part of the CVC4 project.
** Copyright (c) 2009-2021 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 cvc5::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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