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https://github.com/AdaCore/cvc5.git
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98 lines
3.2 KiB
Java
98 lines
3.2 KiB
Java
/******************************************************************************
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* Top contributors (to current version):
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* Mudathir Mohamed, Daniel Larraz, Andres Noetzli
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*
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* This file is part of the cvc5 project.
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*
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* Copyright (c) 2009-2025 by the authors listed in the file AUTHORS
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* in the top-level source directory and their institutional affiliations.
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* All rights reserved. See the file COPYING in the top-level source
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* directory for licensing information.
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* ****************************************************************************
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*
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* A simple demonstration of reasoning about sets with cvc5.
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*/
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import static io.github.cvc5.Kind.*;
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import io.github.cvc5.*;
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public class Sets
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{
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public static void main(String args[]) throws CVC5ApiException
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{
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TermManager tm = new TermManager();
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Solver slv = new Solver(tm);
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{
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// Optionally, set the logic. We need at least UF for equality predicate,
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// integers (LIA) and sets (FS).
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slv.setLogic("QF_UFLIAFS");
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// Produce models
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slv.setOption("produce-models", "true");
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slv.setOption("output-language", "smt2");
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Sort integer = tm.getIntegerSort();
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Sort set = tm.mkSetSort(integer);
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// Verify union distributions over intersection
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// (A union B) intersection C = (A intersection C) union (B intersection C)
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{
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Term A = tm.mkConst(set, "A");
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Term B = tm.mkConst(set, "B");
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Term C = tm.mkConst(set, "C");
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Term unionAB = tm.mkTerm(SET_UNION, A, B);
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Term lhs = tm.mkTerm(SET_INTER, unionAB, C);
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Term intersectionAC = tm.mkTerm(SET_INTER, A, C);
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Term intersectionBC = tm.mkTerm(SET_INTER, B, C);
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Term rhs = tm.mkTerm(SET_UNION, intersectionAC, intersectionBC);
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Term theorem = tm.mkTerm(EQUAL, lhs, rhs);
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System.out.println(
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"cvc5 reports: " + theorem + " is " + slv.checkSatAssuming(theorem.notTerm()) + ".");
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}
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// Verify set.empty is a subset of any set
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{
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Term A = tm.mkConst(set, "A");
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Term emptyset = tm.mkEmptySet(set);
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Term theorem = tm.mkTerm(SET_SUBSET, emptyset, A);
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System.out.println(
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"cvc5 reports: " + theorem + " is " + slv.checkSatAssuming(theorem.notTerm()) + ".");
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}
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// Find me an element in {1, 2} intersection {2, 3}, if there is one.
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{
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Term one = tm.mkInteger(1);
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Term two = tm.mkInteger(2);
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Term three = tm.mkInteger(3);
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Term singleton_one = tm.mkTerm(SET_SINGLETON, one);
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Term singleton_two = tm.mkTerm(SET_SINGLETON, two);
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Term singleton_three = tm.mkTerm(SET_SINGLETON, three);
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Term one_two = tm.mkTerm(SET_UNION, singleton_one, singleton_two);
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Term two_three = tm.mkTerm(SET_UNION, singleton_two, singleton_three);
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Term intersection = tm.mkTerm(SET_INTER, one_two, two_three);
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Term x = tm.mkConst(integer, "x");
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Term e = tm.mkTerm(SET_MEMBER, x, intersection);
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Result result = slv.checkSatAssuming(e);
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System.out.println("cvc5 reports: " + e + " is " + result + ".");
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if (result.isSat())
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{
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System.out.println("For instance, " + slv.getValue(x) + " is a member.");
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}
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}
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}
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Context.deletePointers();
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}
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}
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