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/******************************************************************************
* Top contributors (to current version):
* Mudathir Mohamed, Aina Niemetz
*
* This file is part of the cvc5 project.
*
* Copyright (c) 2009-2025 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.
* ****************************************************************************
*
* A simple demonstration of reasoning about bags.
*/
#include <cvc5/cvc5.h>
#include <iostream>
using namespace std;
using namespace cvc5;
int main()
{
TermManager tm;
Solver slv(tm);
slv.setLogic("ALL");
// Produce models
slv.setOption("produce-models", "true");
slv.setOption("incremental", "true");
Sort bag = tm.mkBagSort(tm.getStringSort());
Term A = tm.mkConst(bag, "A");
Term B = tm.mkConst(bag, "B");
Term C = tm.mkConst(bag, "C");
Term x = tm.mkConst(tm.getStringSort(), "x");
Term intersectionAC = tm.mkTerm(Kind::BAG_INTER_MIN, {A, C});
Term intersectionBC = tm.mkTerm(Kind::BAG_INTER_MIN, {B, C});
// union disjoint does not distribute over intersection
{
Term unionDisjointAB = tm.mkTerm(Kind::BAG_UNION_DISJOINT, {A, B});
Term lhs = tm.mkTerm(Kind::BAG_INTER_MIN, {unionDisjointAB, C});
Term rhs =
tm.mkTerm(Kind::BAG_UNION_DISJOINT, {intersectionAC, intersectionBC});
Term guess = tm.mkTerm(Kind::EQUAL, {lhs, rhs});
cout << "cvc5 reports: " << guess.notTerm() << " is "
<< slv.checkSatAssuming(guess.notTerm()) << "." << endl;
cout << A << ": " << slv.getValue(A) << endl;
cout << B << ": " << slv.getValue(B) << endl;
cout << C << ": " << slv.getValue(C) << endl;
cout << lhs << ": " << slv.getValue(lhs) << endl;
cout << rhs << ": " << slv.getValue(rhs) << endl;
}
// union max distributes over intersection
{
Term unionMaxAB = tm.mkTerm(Kind::BAG_UNION_MAX, {A, B});
Term lhs = tm.mkTerm(Kind::BAG_INTER_MIN, {unionMaxAB, C});
Term rhs = tm.mkTerm(Kind::BAG_UNION_MAX, {intersectionAC, intersectionBC});
Term theorem = tm.mkTerm(Kind::EQUAL, {lhs, rhs});
cout << "cvc5 reports: " << theorem.notTerm() << " is "
<< slv.checkSatAssuming(theorem.notTerm()) << "." << endl;
}
// Verify emptbag is a subbag of any bag
{
Term emptybag = tm.mkEmptyBag(bag);
Term theorem = tm.mkTerm(Kind::BAG_SUBBAG, {emptybag, A});
cout << "cvc5 reports: " << theorem.notTerm() << " is "
<< slv.checkSatAssuming(theorem.notTerm()) << "." << endl;
}
// find an element with multiplicity 4 in the disjoint union of
// ; {|"a", "a", "b", "b", "b"|} and {|"b", "c", "c"|}
{
Term one = tm.mkInteger(1);
Term two = tm.mkInteger(2);
Term three = tm.mkInteger(3);
Term four = tm.mkInteger(4);
Term a = tm.mkString("a");
Term b = tm.mkString("b");
Term c = tm.mkString("c");
Term bag_a_2 = tm.mkTerm(Kind::BAG_MAKE, {a, two});
Term bag_b_3 = tm.mkTerm(Kind::BAG_MAKE, {b, three});
Term bag_b_1 = tm.mkTerm(Kind::BAG_MAKE, {b, one});
Term bag_c_2 = tm.mkTerm(Kind::BAG_MAKE, {c, two});
Term bag_a_2_b_3 = tm.mkTerm(Kind::BAG_UNION_DISJOINT, {bag_a_2, bag_b_3});
Term bag_b_1_c_2 = tm.mkTerm(Kind::BAG_UNION_DISJOINT, {bag_b_1, bag_c_2});
Term union_disjoint =
tm.mkTerm(Kind::BAG_UNION_DISJOINT, {bag_a_2_b_3, bag_b_1_c_2});
Term count_x = tm.mkTerm(Kind::BAG_COUNT, {x, union_disjoint});
Term e = tm.mkTerm(Kind::EQUAL, {four, count_x});
Result result = slv.checkSatAssuming(e);
cout << "cvc5 reports: " << e << " is " << result << "." << endl;
if (result.isSat())
{
cout << x << ": " << slv.getValue(x) << endl;
}
}
}
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