/****************************************************************************** * Top contributors (to current version): * Mudathir Mohamed, Andres Noetzli * * This file is part of the cvc5 project. * * Copyright (c) 2009-2022 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 { Solver slv = new Solver(); { slv.setLogic("ALL"); // Produce models slv.setOption("produce-models", "true"); slv.setOption("incremental", "true"); Sort bag = slv.mkBagSort(slv.getStringSort()); Term A = slv.mkConst(bag, "A"); Term B = slv.mkConst(bag, "B"); Term C = slv.mkConst(bag, "C"); Term x = slv.mkConst(slv.getStringSort(), "x"); Term intersectionAC = slv.mkTerm(BAG_INTER_MIN, new Term[] {A, C}); Term intersectionBC = slv.mkTerm(BAG_INTER_MIN, new Term[] {B, C}); // union disjoint does not distribute over intersection { Term unionDisjointAB = slv.mkTerm(BAG_UNION_DISJOINT, new Term[] {A, B}); Term lhs = slv.mkTerm(BAG_INTER_MIN, new Term[] {unionDisjointAB, C}); Term rhs = slv.mkTerm(BAG_UNION_DISJOINT, new Term[] {intersectionAC, intersectionBC}); Term guess = slv.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 = slv.mkTerm(BAG_UNION_MAX, new Term[] {A, B}); Term lhs = slv.mkTerm(BAG_INTER_MIN, new Term[] {unionMaxAB, C}); Term rhs = slv.mkTerm(BAG_UNION_MAX, new Term[] {intersectionAC, intersectionBC}); Term theorem = slv.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 = slv.mkEmptyBag(bag); Term theorem = slv.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 = slv.mkInteger(1); Term two = slv.mkInteger(2); Term three = slv.mkInteger(3); Term four = slv.mkInteger(4); Term a = slv.mkString("a"); Term b = slv.mkString("b"); Term c = slv.mkString("c"); Term bag_a_2 = slv.mkTerm(BAG_MAKE, new Term[] {a, two}); Term bag_b_3 = slv.mkTerm(BAG_MAKE, new Term[] {b, three}); Term bag_b_1 = slv.mkTerm(BAG_MAKE, new Term[] {b, one}); Term bag_c_2 = slv.mkTerm(BAG_MAKE, new Term[] {c, two}); Term bag_a_2_b_3 = slv.mkTerm(BAG_UNION_DISJOINT, new Term[] {bag_a_2, bag_b_3}); Term bag_b_1_c_2 = slv.mkTerm(BAG_UNION_DISJOINT, new Term[] {bag_b_1, bag_c_2}); Term union_disjoint = slv.mkTerm(BAG_UNION_DISJOINT, new Term[] {bag_a_2_b_3, bag_b_1_c_2}); Term count_x = slv.mkTerm(BAG_COUNT, new Term[] {x, union_disjoint}); Term e = slv.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)); } } } } }