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import static org.junit.Assert.assertEquals;
import org.junit.Before;
import org.junit.Test;
import edu.nyu.acsys.CVC4.*;
public class BitVectors {
static {
System.loadLibrary("cvc4jni");
}
ExprManager em;
SmtEngine smt;
@Before
public void initialize() {
em = new ExprManager();
smt = new SmtEngine(em);
}
@Test
public void evaluatesExpression() {
Result.Validity expect, actual;
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)
smt.assertFormula(assignment0);
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;
smt.assertFormula(assignment1);
Expr new_x_eq_new_x_ = em.mkExpr(Kind.EQUAL, new_x, new_x_);
expect = Result.Validity.VALID;
actual = smt.query(new_x_eq_new_x_).isValid();
assertEquals(expect, actual);
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;
smt.assertFormula(assignment2);
expect = Result.Validity.VALID;
actual = smt.query(new_x_eq_new_x_).isValid();
assertEquals(expect, actual);
}
}
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