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/********************* */
/*! \file sets.cpp
** \verbatim
** Top contributors (to current version):
** Aina Niemetz, Kshitij Bansal, Mudathir Mohamed
** This file is part of the CVC4 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.\endverbatim
**
** \brief Reasoning about sets with CVC4.
**
** A simple demonstration of reasoning about sets with CVC4.
**/
#include <iostream>
#include <cvc4/api/cvc4cpp.h>
using namespace std;
using namespace CVC5::api;
int main()
{
Solver slv;
// Optionally, set the logic. We need at least UF for equality predicate,
// integers (LIA) and sets (FS).
slv.setLogic("QF_UFLIAFS");
// Produce models
slv.setOption("produce-models", "true");
slv.setOption("output-language", "smt2");
Sort integer = slv.getIntegerSort();
Sort set = slv.mkSetSort(integer);
// Verify union distributions over intersection
// (A union B) intersection C = (A intersection C) union (B intersection C)
{
Term A = slv.mkConst(set, "A");
Term B = slv.mkConst(set, "B");
Term C = slv.mkConst(set, "C");
Term unionAB = slv.mkTerm(UNION, A, B);
Term lhs = slv.mkTerm(INTERSECTION, unionAB, C);
Term intersectionAC = slv.mkTerm(INTERSECTION, A, C);
Term intersectionBC = slv.mkTerm(INTERSECTION, B, C);
Term rhs = slv.mkTerm(UNION, intersectionAC, intersectionBC);
Term theorem = slv.mkTerm(EQUAL, lhs, rhs);
cout << "CVC4 reports: " << theorem << " is " << slv.checkEntailed(theorem)
<< "." << endl;
}
// Verify emptset is a subset of any set
{
Term A = slv.mkConst(set, "A");
Term emptyset = slv.mkEmptySet(set);
Term theorem = slv.mkTerm(SUBSET, emptyset, A);
cout << "CVC4 reports: " << theorem << " is " << slv.checkEntailed(theorem)
<< "." << endl;
}
// Find me an element in {1, 2} intersection {2, 3}, if there is one.
{
Term one = slv.mkInteger(1);
Term two = slv.mkInteger(2);
Term three = slv.mkInteger(3);
Term singleton_one = slv.mkTerm(SINGLETON, one);
Term singleton_two = slv.mkTerm(SINGLETON, two);
Term singleton_three = slv.mkTerm(SINGLETON, three);
Term one_two = slv.mkTerm(UNION, singleton_one, singleton_two);
Term two_three = slv.mkTerm(UNION, singleton_two, singleton_three);
Term intersection = slv.mkTerm(INTERSECTION, one_two, two_three);
Term x = slv.mkConst(integer, "x");
Term e = slv.mkTerm(MEMBER, x, intersection);
Result result = slv.checkSatAssuming(e);
cout << "CVC4 reports: " << e << " is " << result << "." << endl;
if (result.isSat())
{
cout << "For instance, " << slv.getValue(x) << " is a member." << endl;
}
}
}
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