cvc5/examples/api/java/BitVectors.java

/******************************************************************************
 * Top contributors (to current version):
 *   Aina Niemetz, Liana Hadarean, Makai Mann
 *
 * This file is part of the cvc5 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.
 * ****************************************************************************
 *
 * A simple demonstration of the solving capabilities of the cvc5
 * bit-vector solver.
 *
 */

import cvc5.*;
import java.util.*;

public class BitVectors
{
  public static void main(String args[]) throws CVC5ApiException
  {
    Solver slv = new Solver();
    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 cvc5 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 Kind.EQUAL to a or b
    Term x_eq_a = slv.mkTerm(Kind.EQUAL, x, a);
    Term x_eq_b = slv.mkTerm(Kind.EQUAL, x, b);
    Term assumption = slv.mkTerm(Kind.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(Kind.ITE, x_eq_a, b, a);
    Term assignment0 = slv.mkTerm(Kind.EQUAL, new_x, ite);

    // Assert the encoding of code (0)
    System.out.println("Asserting " + assignment0 + " to cvc5 ");
    slv.assertFormula(assignment0);
    System.out.println("Pushing a new context.");
    slv.push();

    // Encoding code (1)
    // new_x_ = a xor b xor x
    Term a_xor_b_xor_x = slv.mkTerm(Kind.BITVECTOR_XOR, a, b, x);
    Term assignment1 = slv.mkTerm(Kind.EQUAL, new_x_, a_xor_b_xor_x);

    // Assert encoding to cvc5 in current context;
    System.out.println("Asserting " + assignment1 + " to cvc5 ");
    slv.assertFormula(assignment1);
    Term new_x_eq_new_x_ = slv.mkTerm(Kind.EQUAL, new_x, new_x_);

    System.out.println(" Check entailment assuming: " + new_x_eq_new_x_);
    System.out.println(" Expect ENTAILED. ");
    System.out.println(" cvc5: " + slv.checkEntailed(new_x_eq_new_x_));
    System.out.println(" Popping context. ");
    slv.pop();

    // Encoding code (2)
    // new_x_ = a + b - x
    Term a_plus_b = slv.mkTerm(Kind.BITVECTOR_ADD, a, b);
    Term a_plus_b_minus_x = slv.mkTerm(Kind.BITVECTOR_SUB, a_plus_b, x);
    Term assignment2 = slv.mkTerm(Kind.EQUAL, new_x_, a_plus_b_minus_x);

    // Assert encoding to cvc5 in current context;
    System.out.println("Asserting " + assignment2 + " to cvc5 ");
    slv.assertFormula(assignment2);

    System.out.println(" Check entailment assuming: " + new_x_eq_new_x_);
    System.out.println(" Expect ENTAILED. ");
    System.out.println(" cvc5: " + slv.checkEntailed(new_x_eq_new_x_));

    Term x_neq_x = slv.mkTerm(Kind.EQUAL, x, x).notTerm();
    Term[] v = new Term[] {new_x_eq_new_x_, x_neq_x};
    System.out.println(" Check entailment assuming: " + v);
    System.out.println(" Expect NOT_ENTAILED. ");
    System.out.println(" cvc5: " + slv.checkEntailed(v));

    // Assert that a is odd
    Op extract_op = slv.mkOp(Kind.BITVECTOR_EXTRACT, 0, 0);
    Term lsb_of_a = slv.mkTerm(extract_op, a);
    System.out.println("Sort of " + lsb_of_a + " is " + lsb_of_a.getSort());
    Term a_odd = slv.mkTerm(Kind.EQUAL, lsb_of_a, slv.mkBitVector(1, 1));
    System.out.println("Assert " + a_odd);
    System.out.println("Check satisfiability.");
    slv.assertFormula(a_odd);
    System.out.println(" Expect sat. ");
    System.out.println(" cvc5: " + slv.checkSat());
  }
}