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/********************* */
/*! \file bitvectors.cpp
** \verbatim
** Top contributors (to current version):
** Liana Hadarean, Aina Niemetz, Morgan Deters
** This file is part of the CVC4 project.
** Copyright (c) 2009-2020 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/cvc4.h>
using namespace std;
using namespace CVC4;
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 entailed. " << endl;
cout << " CVC4: " << smt.checkEntailed(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 ENTAILED. " << endl;
cout << " CVC4: " << smt.checkEntailed(new_x_eq_new_x_) << endl;
Expr x_neq_x = em.mkExpr(kind::EQUAL, x, x).notExpr();
std::vector<Expr> v{new_x_eq_new_x_, x_neq_x};
cout << " Querying: " << v << endl;
cout << " Expect NOT_ENTAILED. " << endl;
cout << " CVC4: " << smt.checkEntailed(v) << endl;
// Assert that a is odd
Expr extract_op = em.mkConst(BitVectorExtract(0, 0));
Expr lsb_of_a = em.mkExpr(extract_op, a);
cout << "Type of " << lsb_of_a << " is " << lsb_of_a.getType() << endl;
Expr a_odd = em.mkExpr(kind::EQUAL, lsb_of_a, em.mkConst(BitVector(1u, 1u)));
cout << "Assert " << a_odd << endl;
cout << "Check satisfiability." << endl;
smt.assertFormula(a_odd);
cout << " Expect sat. " << endl;
cout << " CVC4: " << smt.checkSat() << endl;
return 0;
}
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