cvc5/examples/api/java/LinearArith.java

/******************************************************************************
 * Top contributors (to current version):
 *   Aina Niemetz, Tim King, Mudathir Mohamed
 *
 * 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 linear arithmetic solving capabilities and
 * the push pop of cvc5. This also gives an example option.
 */

import cvc5.*;
public class LinearArith
{
  public static void main(String args[]) throws CVC5ApiException
  {
    Solver slv = new Solver();
    slv.setLogic("QF_LIRA"); // Set the logic

    // Prove that if given x (Integer) and y (Real) then
    // the maximum value of y - x is 2/3

    // Sorts
    Sort real = slv.getRealSort();
    Sort integer = slv.getIntegerSort();

    // Variables
    Term x = slv.mkConst(integer, "x");
    Term y = slv.mkConst(real, "y");

    // Constants
    Term three = slv.mkInteger(3);
    Term neg2 = slv.mkInteger(-2);
    Term two_thirds = slv.mkReal(2, 3);

    // Terms
    Term three_y = slv.mkTerm(Kind.MULT, three, y);
    Term diff = slv.mkTerm(Kind.MINUS, y, x);

    // Formulas
    Term x_geq_3y = slv.mkTerm(Kind.GEQ, x, three_y);
    Term x_leq_y = slv.mkTerm(Kind.LEQ, x, y);
    Term neg2_lt_x = slv.mkTerm(Kind.LT, neg2, x);

    Term assertions = slv.mkTerm(Kind.AND, x_geq_3y, x_leq_y, neg2_lt_x);

    System.out.println("Given the assertions " + assertions);
    slv.assertFormula(assertions);

    slv.push();
    Term diff_leq_two_thirds = slv.mkTerm(Kind.LEQ, diff, two_thirds);
    System.out.println("Prove that " + diff_leq_two_thirds + " with cvc5.");
    System.out.println("cvc5 should report ENTAILED.");
    System.out.println("Result from cvc5 is: " + slv.checkEntailed(diff_leq_two_thirds));
    slv.pop();

    System.out.println();

    slv.push();
    Term diff_is_two_thirds = slv.mkTerm(Kind.EQUAL, diff, two_thirds);
    slv.assertFormula(diff_is_two_thirds);
    System.out.println("Show that the assertions are consistent with ");
    System.out.println(diff_is_two_thirds + " with cvc5.");
    System.out.println("cvc5 should report SAT.");
    System.out.println("Result from cvc5 is: " + slv.checkSat());
    slv.pop();

    System.out.println("Thus the maximum value of (y - x) is 2/3.");
  }
}