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/******************************************************************************
* Top contributors (to current version):
* Mudathir Mohamed, Daniel Larraz, Andres Noetzli
*
* 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 with cvc5.
*/
import static io.github.cvc5.Kind.*;
import io.github.cvc5.*;
public class Bags
{
public static void main(String args[]) throws CVC5ApiException
{
TermManager tm = new TermManager();
Solver slv = new Solver(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(BAG_INTER_MIN, new Term[] {A, C});
Term intersectionBC = tm.mkTerm(BAG_INTER_MIN, new Term[] {B, C});
// union disjoint does not distribute over intersection
{
Term unionDisjointAB = tm.mkTerm(BAG_UNION_DISJOINT, new Term[] {A, B});
Term lhs = tm.mkTerm(BAG_INTER_MIN, new Term[] {unionDisjointAB, C});
Term rhs = tm.mkTerm(BAG_UNION_DISJOINT, new Term[] {intersectionAC, intersectionBC});
Term guess = tm.mkTerm(EQUAL, new Term[] {lhs, rhs});
System.out.println("cvc5 reports: " + guess.notTerm() + " is "
+ slv.checkSatAssuming(guess.notTerm()) + ".");
System.out.println(A + ": " + slv.getValue(A));
System.out.println(B + ": " + slv.getValue(B));
System.out.println(C + ": " + slv.getValue(C));
System.out.println(lhs + ": " + slv.getValue(lhs));
System.out.println(rhs + ": " + slv.getValue(rhs));
}
// union max distributes over intersection
{
Term unionMaxAB = tm.mkTerm(BAG_UNION_MAX, new Term[] {A, B});
Term lhs = tm.mkTerm(BAG_INTER_MIN, new Term[] {unionMaxAB, C});
Term rhs = tm.mkTerm(BAG_UNION_MAX, new Term[] {intersectionAC, intersectionBC});
Term theorem = tm.mkTerm(EQUAL, new Term[] {lhs, rhs});
System.out.println("cvc5 reports: " + theorem.notTerm() + " is "
+ slv.checkSatAssuming(theorem.notTerm()) + ".");
}
// Verify emptbag is a subbag of any bag
{
Term emptybag = tm.mkEmptyBag(bag);
Term theorem = tm.mkTerm(BAG_SUBBAG, new Term[] {emptybag, A});
System.out.println("cvc5 reports: " + theorem.notTerm() + " is "
+ slv.checkSatAssuming(theorem.notTerm()) + ".");
}
// 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(BAG_MAKE, new Term[] {a, two});
Term bag_b_3 = tm.mkTerm(BAG_MAKE, new Term[] {b, three});
Term bag_b_1 = tm.mkTerm(BAG_MAKE, new Term[] {b, one});
Term bag_c_2 = tm.mkTerm(BAG_MAKE, new Term[] {c, two});
Term bag_a_2_b_3 = tm.mkTerm(BAG_UNION_DISJOINT, new Term[] {bag_a_2, bag_b_3});
Term bag_b_1_c_2 = tm.mkTerm(BAG_UNION_DISJOINT, new Term[] {bag_b_1, bag_c_2});
Term union_disjoint = tm.mkTerm(BAG_UNION_DISJOINT, new Term[] {bag_a_2_b_3, bag_b_1_c_2});
Term count_x = tm.mkTerm(BAG_COUNT, new Term[] {x, union_disjoint});
Term e = tm.mkTerm(EQUAL, new Term[] {four, count_x});
Result result = slv.checkSatAssuming(e);
System.out.println("cvc5 reports: " + e + " is " + result + ".");
if (result.isSat())
{
System.out.println(x + ": " + slv.getValue(x));
}
}
}
Context.deletePointers();
}
}
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