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/********************* */
/*! \file linear_arith.cpp
** \verbatim
** Top contributors (to current version):
** Tim King, Aina Niemetz
** This file is part of the CVC4 project.
** Copyright (c) 2009-2018 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.
**/
#include <iostream>
//#include <cvc4/cvc4.h> // use this after CVC4 is properly installed
#include "api/cvc4cpp.h"
using namespace std;
using namespace CVC4::api;
int main()
{
Solver slv;
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.mkVar(integer, "x");
Term y = slv.mkVar(real, "y");
// Constants
Term three = slv.mkReal(3);
Term neg2 = slv.mkReal(-2);
Term two_thirds = slv.mkReal(2, 3);
// Terms
Term three_y = slv.mkTerm(MULT, three, y);
Term diff = slv.mkTerm(MINUS, y, x);
// Formulas
Term x_geq_3y = slv.mkTerm(GEQ, x, three_y);
Term x_leq_y = slv.mkTerm(LEQ, x, y);
Term neg2_lt_x = slv.mkTerm(LT, neg2, x);
Term assertions =
slv.mkTerm(AND, x_geq_3y, x_leq_y, neg2_lt_x);
cout << "Given the assertions " << assertions << endl;
slv.assertFormula(assertions);
slv.push();
Term diff_leq_two_thirds = slv.mkTerm(LEQ, diff, two_thirds);
cout << "Prove that " << diff_leq_two_thirds << " with CVC4." << endl;
cout << "CVC4 should report VALID." << endl;
cout << "Result from CVC4 is: "
<< slv.checkValidAssuming(diff_leq_two_thirds) << endl;
slv.pop();
cout << endl;
slv.push();
Term diff_is_two_thirds = slv.mkTerm(EQUAL, diff, two_thirds);
slv.assertFormula(diff_is_two_thirds);
cout << "Show that the assertions are consistent with " << endl;
cout << diff_is_two_thirds << " with CVC4." << endl;
cout << "CVC4 should report SAT." << endl;
cout << "Result from CVC4 is: " << slv.checkSat() << endl;
slv.pop();
cout << "Thus the maximum value of (y - x) is 2/3."<< endl;
return 0;
}
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