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/********************* */
/*! \file LinearArith.java
** \verbatim
** Top contributors (to current version):
** Morgan Deters, Tim King, Aina Niemetz
** 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 linear arithmetic capabilities of CVC4
**
** A simple demonstration of the linear arithmetic solving capabilities and
** the push pop of CVC4. This also gives an example option.
**/
import edu.stanford.CVC4.*;
public class LinearArith {
public static void main(String[] args) {
System.loadLibrary("cvc4jni");
ExprManager em = new ExprManager();
SmtEngine smt = new SmtEngine(em);
smt.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
// Types
Type real = em.realType();
Type integer = em.integerType();
// Variables
Expr x = em.mkVar("x", integer);
Expr y = em.mkVar("y", real);
// Constants
Expr three = em.mkConst(new Rational(3));
Expr neg2 = em.mkConst(new Rational(-2));
Expr two_thirds = em.mkConst(new Rational(2,3));
// Terms
Expr three_y = em.mkExpr(Kind.MULT, three, y);
Expr diff = em.mkExpr(Kind.MINUS, y, x);
// Formulas
Expr x_geq_3y = em.mkExpr(Kind.GEQ, x, three_y);
Expr x_leq_y = em.mkExpr(Kind.LEQ, x, y);
Expr neg2_lt_x = em.mkExpr(Kind.LT, neg2, x);
Expr assumptions =
em.mkExpr(Kind.AND, x_geq_3y, x_leq_y, neg2_lt_x);
System.out.println("Given the assumptions " + assumptions);
smt.assertFormula(assumptions);
smt.push();
Expr diff_leq_two_thirds = em.mkExpr(Kind.LEQ, diff, two_thirds);
System.out.println("Prove that " + diff_leq_two_thirds + " with CVC4.");
System.out.println("CVC4 should report ENTAILED.");
System.out.println(
"Result from CVC4 is: " + smt.checkEntailed(diff_leq_two_thirds));
smt.pop();
System.out.println();
smt.push();
Expr diff_is_two_thirds = em.mkExpr(Kind.EQUAL, diff, two_thirds);
smt.assertFormula(diff_is_two_thirds);
System.out.println("Show that the asserts are consistent with ");
System.out.println(diff_is_two_thirds + " with CVC4.");
System.out.println("CVC4 should report SAT.");
System.out.println("Result from CVC4 is: " + smt.checkSat(em.mkConst(true)));
smt.pop();
System.out.println("Thus the maximum value of (y - x) is 2/3.");
}
}
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