cvc5/examples/api/java/Sets.java

/******************************************************************************
 * Top contributors (to current version):
 *   Aina Niemetz, Kshitij Bansal, Mudathir Mohamed
 *
 * This file is part of the cvc5 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.
 * ****************************************************************************
 *
 * A simple demonstration of reasoning about sets with cvc5.
 */

import static io.github.cvc5.api.Kind.*;

import io.github.cvc5.api.*;

public class Sets
{
  public static void main(String args[]) throws CVC5ApiException
  {
    Solver slv = new Solver();

    // 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);

      System.out.println("cvc5 reports: " + theorem + " is " + slv.checkEntailed(theorem) + ".");
    }

    // 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);

      System.out.println("cvc5 reports: " + theorem + " is " + slv.checkEntailed(theorem) + ".");
    }

    // 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);
      System.out.println("cvc5 reports: " + e + " is " + result + ".");

      if (result.isSat())
      {
        System.out.println("For instance, " + slv.getValue(x) + " is a member.");
      }
    }
  }
}