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86 lines
2.7 KiB
Python
86 lines
2.7 KiB
Python
#!/usr/bin/env python
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#####################
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## sets.py
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## Top contributors (to current version):
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## Makai Mann, Mudathir Mohamed, Aina Niemetz
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## This file is part of the CVC4 project.
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## Copyright (c) 2009-2021 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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## \brief A simple demonstration of the solving capabilities of the CVC4
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## sets solver through the Python API. This is a direct translation
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## of sets-new.cpp.
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##
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import pycvc4
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from pycvc4 import kinds
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if __name__ == "__main__":
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slv = pycvc4.Solver()
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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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integer = slv.getIntegerSort()
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set_ = slv.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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A = slv.mkConst(set_, "A")
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B = slv.mkConst(set_, "B")
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C = slv.mkConst(set_, "C")
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unionAB = slv.mkTerm(kinds.Union, A, B)
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lhs = slv.mkTerm(kinds.Intersection, unionAB, C)
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intersectionAC = slv.mkTerm(kinds.Intersection, A, C)
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intersectionBC = slv.mkTerm(kinds.Intersection, B, C)
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rhs = slv.mkTerm(kinds.Union, intersectionAC, intersectionBC)
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theorem = slv.mkTerm(kinds.Equal, lhs, rhs)
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print("CVC4 reports: {} is {}".format(theorem,
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slv.checkEntailed(theorem)))
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# Verify emptset is a subset of any set
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A = slv.mkConst(set_, "A")
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emptyset = slv.mkEmptySet(set_)
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theorem = slv.mkTerm(kinds.Subset, emptyset, A)
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print("CVC4 reports: {} is {}".format(theorem,
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slv.checkEntailed(theorem)))
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# Find me an element in 1, 2 intersection 2, 3, if there is one.
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one = slv.mkInteger(1)
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two = slv.mkInteger(2)
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three = slv.mkInteger(3)
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singleton_one = slv.mkTerm(kinds.Singleton, one)
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singleton_two = slv.mkTerm(kinds.Singleton, two)
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singleton_three = slv.mkTerm(kinds.Singleton, three)
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one_two = slv.mkTerm(kinds.Union, singleton_one, singleton_two)
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two_three = slv.mkTerm(kinds.Union, singleton_two, singleton_three)
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intersection = slv.mkTerm(kinds.Intersection, one_two, two_three)
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x = slv.mkConst(integer, "x")
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e = slv.mkTerm(kinds.Member, x, intersection)
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result = slv.checkSatAssuming(e)
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print("CVC4 reports: {} is {}".format(e, result))
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if result:
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print("For instance, {} is a member".format(slv.getValue(x)))
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