How do I create additional constraints from a model obtained by a solver in z3 Python API?

Question

Once I have a constraint problem, I would like to see if it is satisfiable. Based on the returned model (when it is sat) I would like to add assertions and then run the solver again. However, it seems like I am misunderstanding some of the types/values contained in the returned model. Consider the following example:

solv = z3.Solver()
n = z3.Int("n")
solv.add(n >= 42)
solv.check()  # This is satisfiable
model = solv.model()
for var in model:
    # do something
    solv.add(var == model[var])
solv.check() # This is unsat

I would expect that after the loop i essentially have the two constraints n >= 42 and n == 42, assuming of course that z3 produces the model n=42 in the first call. Despite this, in the second call check() returns unsat. What am I missing?

Sidenote: when replacing solv.add(var == model[var]) with solv.add(var >= model[var]) I get a z3.z3types.Z3Exception: Python value cannot be used as a Z3 integer. Why is that?

Answer 1

When you loop over a model, you do not get a variable that you can directly query. What you get is an internal representation, which can correspond to a constant, or it can correspond to something more complicated like a function or an array. Typically, you should query the model with the variables you have, i.e., with n. (As in model[n].)

You can fix your immediate problem like this:

for var in model:
  solve.add(var() == model[var()])

but this'll only work assuming you have simple variables in the model, i.e., no uninterpreted-functions, arrays, or other objects. See this question for a detailed discussion: https://stackoverflow.com/a/11869410/936310

Similarly, your second expression throws an exception because while == is defined over arbitrary objects (though doing the wrong thing here), >= isn't. So, in a sense it's the "right" thing to do to throw an exception here. (That is, == should've thrown an exception as well.) Alas, the Python bindings are loosely typed, meaning it'll try to make sense of what you wrote, not necessarily always doing what you intended along the way.