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97 lines
3.0 KiB
C++
97 lines
3.0 KiB
C++
/******************************************************************************
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* Top contributors (to current version):
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* Aina Niemetz, Kshitij Bansal, Andrew Reynolds
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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) 2009-2024 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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#include <cvc5/cvc5.h>
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#include <iostream>
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using namespace std;
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using namespace cvc5;
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int main()
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{
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TermManager tm;
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Solver slv(tm);
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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(Kind::SET_UNION, {A, B});
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Term lhs = tm.mkTerm(Kind::SET_INTER, {unionAB, C});
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Term intersectionAC = tm.mkTerm(Kind::SET_INTER, {A, C});
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Term intersectionBC = tm.mkTerm(Kind::SET_INTER, {B, C});
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Term rhs = tm.mkTerm(Kind::SET_UNION, {intersectionAC, intersectionBC});
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Term theorem = tm.mkTerm(Kind::EQUAL, {lhs, rhs});
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cout << "cvc5 reports: " << theorem << " is "
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<< slv.checkSatAssuming(theorem.notTerm()) << "." << endl;
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}
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// Verify emptset 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(Kind::SET_SUBSET, {emptyset, A});
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cout << "cvc5 reports: " << theorem << " is "
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<< slv.checkSatAssuming(theorem.notTerm()) << "." << endl;
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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(Kind::SET_SINGLETON, {one});
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Term singleton_two = tm.mkTerm(Kind::SET_SINGLETON, {two});
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Term singleton_three = tm.mkTerm(Kind::SET_SINGLETON, {three});
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Term one_two = tm.mkTerm(Kind::SET_UNION, {singleton_one, singleton_two});
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Term two_three =
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tm.mkTerm(Kind::SET_UNION, {singleton_two, singleton_three});
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Term intersection = tm.mkTerm(Kind::SET_INTER, {one_two, two_three});
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Term x = tm.mkConst(integer, "x");
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Term e = tm.mkTerm(Kind::SET_MEMBER, {x, intersection});
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Result result = slv.checkSatAssuming(e);
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cout << "cvc5 reports: " << e << " is " << result << "." << endl;
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if (result.isSat())
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{
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cout << "For instance, " << slv.getValue(x) << " is a member." << endl;
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}
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}
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}
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