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#!/usr/bin/env python
#####################
#! \file sets.py
## \verbatim
## Top contributors (to current version):
## Makai Mann, Aina Niemetz
## This file is part of the CVC4 project.
## Copyright (c) 2009-2018 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.\endverbatim
##
## \brief A simple demonstration of the solving capabilities of the CVC4
## sets solver through the Python API. This is a direct translation
## of sets-new.cpp.
import pycvc4
from pycvc4 import kinds
if __name__ == "__main__":
slv = pycvc4.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")
integer = slv.getIntegerSort()
set_ = slv.mkSetSort(integer)
# Verify union distributions over intersection
# (A union B) intersection C = (A intersection C) union (B intersection C)
A = slv.mkConst(set_, "A")
B = slv.mkConst(set_, "B")
C = slv.mkConst(set_, "C")
unionAB = slv.mkTerm(kinds.Union, A, B)
lhs = slv.mkTerm(kinds.Intersection, unionAB, C)
intersectionAC = slv.mkTerm(kinds.Intersection, A, C)
intersectionBC = slv.mkTerm(kinds.Intersection, B, C)
rhs = slv.mkTerm(kinds.Union, intersectionAC, intersectionBC)
theorem = slv.mkTerm(kinds.Equal, lhs, rhs)
print("CVC4 reports: {} is {}".format(theorem,
slv.checkEntailed(theorem)))
# Verify emptset is a subset of any set
A = slv.mkConst(set_, "A")
emptyset = slv.mkEmptySet(set_)
theorem = slv.mkTerm(kinds.Subset, emptyset, A)
print("CVC4 reports: {} is {}".format(theorem,
slv.checkEntailed(theorem)))
# Find me an element in 1, 2 intersection 2, 3, if there is one.
one = slv.mkReal(1)
two = slv.mkReal(2)
three = slv.mkReal(3)
singleton_one = slv.mkTerm(kinds.Singleton, one)
singleton_two = slv.mkTerm(kinds.Singleton, two)
singleton_three = slv.mkTerm(kinds.Singleton, three)
one_two = slv.mkTerm(kinds.Union, singleton_one, singleton_two)
two_three = slv.mkTerm(kinds.Union, singleton_two, singleton_three)
intersection = slv.mkTerm(kinds.Intersection, one_two, two_three)
x = slv.mkConst(integer, "x")
e = slv.mkTerm(kinds.Member, x, intersection)
result = slv.checkSatAssuming(e)
print("CVC4 reports: {} is {}".format(e, result))
if result:
print("For instance, {} is a member".format(slv.getValue(x)))
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