Empty model in z3

Question

z3py snippet:

x = Int('x')

s = Solver()
s.add(x <= x)
print s.check()
print s.model()
print s.model().sexpr()

http://rise4fun.com/Z3Py/mfPU

Output:

sat
[]

Any value of x would do but z3 returns empty model. Does a missing free variable x in the model indicates that any integer value is a valid model?

Answer 1

Yes, in Z3, if a constant (such as x) does not appear in the model, then it is a "don't care". That is, any value of x will satisfy the formula. When evaluating the value of a constant, we can enable "model completion". That is, Z3 will use an arbitrary interpretation for "don't care" symbols. Here is an example http://rise4fun.com/Z3Py/bvVO

x = Int('x')
s = Solver()
s.add(x <= x)
print s.check()
m = s.model()
print m.evaluate(x)
print m.evaluate(x, model_completion=True)
print m