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/********************* */
/*! \file linear_arith.cpp
** \verbatim
** Top contributors (to current version):
** Tim King
** 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 "smt/smt_engine.h"
using namespace std;
using namespace CVC4;
int main() {
ExprManager em;
SmtEngine smt(&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(Rational(3));
Expr neg2 = em.mkConst(Rational(-2));
Expr two_thirds = em.mkConst(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);
cout << "Given the assumptions " << assumptions << endl;
smt.assertFormula(assumptions);
smt.push();
Expr diff_leq_two_thirds = em.mkExpr(kind::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: " << smt.query(diff_leq_two_thirds) << endl;
smt.pop();
cout << endl;
smt.push();
Expr diff_is_two_thirds = em.mkExpr(kind::EQUAL, diff, two_thirds);
smt.assertFormula(diff_is_two_thirds);
cout << "Show that the asserts are consistent with " << endl;
cout << diff_is_two_thirds << " with CVC4." << endl;
cout << "CVC4 should report SAT." << endl;
cout << "Result from CVC4 is: " << smt.checkSat(em.mkConst(true)) << endl;
smt.pop();
cout << "Thus the maximum value of (y - x) is 2/3."<< endl;
return 0;
}
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