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/********************* */
/*! \file sets.cpp
** \verbatim
** Top contributors (to current version):
** Kshitij Bansal, Tim King
** This file is part of the CVC4 project.
** Copyright (c) 2009-2019 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 Reasoning about sets with CVC4.
**
** A simple demonstration of reasoning about sets with CVC4.
**/
#include <iostream>
#include <cvc4/cvc4.h>
#include <cvc4/options/set_language.h>
using namespace std;
using namespace CVC4;
int main() {
ExprManager em;
SmtEngine smt(&em);
// Optionally, set the logic. We need at least UF for equality predicate,
// integers (LIA) and sets (FS).
smt.setLogic("QF_UFLIAFS");
// Produce models
smt.setOption("produce-models", true);
// Set output language to SMTLIB2
cout << language::SetLanguage(language::output::LANG_SMTLIB_V2);
Type integer = em.integerType();
Type set = em.mkSetType(integer);
// Verify union distributions over intersection
// (A union B) intersection C = (A intersection C) union (B intersection C)
{
Expr A = em.mkVar("A", set);
Expr B = em.mkVar("B", set);
Expr C = em.mkVar("C", set);
Expr unionAB = em.mkExpr(kind::UNION, A, B);
Expr lhs = em.mkExpr(kind::INTERSECTION, unionAB, C);
Expr intersectionAC = em.mkExpr(kind::INTERSECTION, A, C);
Expr intersectionBC = em.mkExpr(kind::INTERSECTION, B, C);
Expr rhs = em.mkExpr(kind::UNION, intersectionAC, intersectionBC);
Expr theorem = em.mkExpr(kind::EQUAL, lhs, rhs);
cout << "CVC4 reports: " << theorem << " is " << smt.checkEntailed(theorem)
<< "." << endl;
}
// Verify emptset is a subset of any set
{
Expr A = em.mkVar("A", set);
Expr emptyset = em.mkConst(EmptySet(set));
Expr theorem = em.mkExpr(kind::SUBSET, emptyset, A);
cout << "CVC4 reports: " << theorem << " is " << smt.checkEntailed(theorem)
<< "." << endl;
}
// Find me an element in {1, 2} intersection {2, 3}, if there is one.
{
Expr one = em.mkConst(Rational(1));
Expr two = em.mkConst(Rational(2));
Expr three = em.mkConst(Rational(3));
Expr singleton_one = em.mkExpr(kind::SINGLETON, one);
Expr singleton_two = em.mkExpr(kind::SINGLETON, two);
Expr singleton_three = em.mkExpr(kind::SINGLETON, three);
Expr one_two = em.mkExpr(kind::UNION, singleton_one, singleton_two);
Expr two_three = em.mkExpr(kind::UNION, singleton_two, singleton_three);
Expr intersection = em.mkExpr(kind::INTERSECTION, one_two, two_three);
Expr x = em.mkVar("x", integer);
Expr e = em.mkExpr(kind::MEMBER, x, intersection);
Result result = smt.checkSat(e);
cout << "CVC4 reports: " << e << " is " << result << "." << endl;
if(result == Result::SAT) {
cout << "For instance, " << smt.getValue(x) << " is a member." << endl;
}
}
}
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