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/******************************************************************************
* 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 io.github.cvc5.api.*;
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());
}
}
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