def to_constraint(self):
if isinstance(self.args[1],Some):
if self.args[1].if_value() != None:
return And(Implies(self.args[1].args[1],
lg.Exists([self.args[1].args[0]],
And(self.args[1].args[1],Equals(self.args[0],self.args[1].if_value())))),
Or(lg.Exists([self.args[1].args[0]],self.args[1].args[1]),
Equals(self.args[0],self.args[1].else_value())))
return lg.ForAll([self.args[1].args[0]],
Implies(self.args[1].args[1],
lu.substitute(self.args[1].args[1],{self.args[1].args[0]:self.args[0]})))
if is_individual(self.args[0]):
return Equals(*self.args)
return Iff(*self.args)
if __name__ == '__main__':
S = UninterpretedSort('S')
X, Y, Z = (Var(n, S) for n in ['X', 'Y', 'Z'])
BinRel = FunctionSort(S, S, Boolean)
leq = Const('leq', BinRel)
transitive1 = ForAll((X, Y, Z),
Implies(And(leq(X, Y), leq(Y, Z)), leq(X, Z)))
transitive2 = ForAll((X, Y, Z),
Or(Not(leq(X, Y)), Not(leq(Y, Z)), leq(X, Z)))
transitive3 = Not(
Exists((X, Y, Z), And(leq(X, Y), leq(Y, Z), Not(leq(X, Z)))))
antisymmetric = ForAll((X, Y),
Implies(And(leq(X, Y), leq(Y, X), true), Eq(Y, X)))
print z3_implies(transitive1, transitive2)
print z3_implies(transitive2, transitive3)
print z3_implies(transitive3, transitive1)
print z3_implies(transitive3, antisymmetric)
print
print z3_implies(true, Iff(transitive1, transitive2))
print
x, y = (Const(n, S) for n in ['x', 'y'])
b = Const('b', Boolean)
print z3_implies(b, Eq(Ite(b, x, y), x))
print z3_implies(Not(b), Eq(Ite(b, x, y), y))
print z3_implies(Not(Eq(x, y)), Iff(Eq(Ite(b, x, y), x), b))
def to_constraint(self):
if is_individual(self.args[0]):
return Equals(*self.args)
return Iff(*self.args)
assert f1 == cf1
print
f2 = And(ps(XT), pt(xs))
cf2 = concretize_sorts(f2)
print repr(f2)
print repr(cf2)
print
f3 = Exists([TT], And(ps(XT), TT(xs)))
cf3 = concretize_sorts(f3)
print repr(f3)
print repr(cf3)
print
f4 = Iff(xt, Ite(yt, xt, XT))
cf4 = concretize_sorts(f4)
print repr(f4)
print repr(cf4)
print
# TODO: add more tests, specifically a test that checks
# unification across different quantified bodies
"""
c10 = Concept('c10',[X], And(p(X), Not(q(X))))
c01 = Concept('c01',[X], And(Not(p(X)), q(X)))
c00 = Concept('c00',[X], And(Not(p(X)), Not(q(X))))
crn = Concept([X, Y], Or(r(X,Y), n(X,Y)))
X, Y, _ = (Var(n, T) for n in ['X', 'Y', 'Z'])
