Trying to find all solutions to a boolean formula using Z3 in python

Question

I'm new to Z3, and trying to make a solver which returns every satisfiable solution to a boolean formula. Taking notes from other SO-posts, I've coded what I hoped would work, but isn't. The problem seems to that by adding the previous solutions, I remove some of the variables, but then they return in later solutions?

Currently I am just trying to solve a or b or c.

If I explained poorly, let me know and I will try to explain further.

Thanks in advance for the response :)

My code:

from z3 import *

a, b, c = Bools('a b c')
s = Solver()
s.add(Or([a, b, c]))

while (s.check() == sat):
        print(s.check())
        print(s)
        print(s.model())
        print(s.model().decls())
        print("\n")
        s.add(Or([ f() != s.model()[f] for f in s.model().decls() if f.arity() == 0])) 

My output:

sat
[Or(a, b, c)]
[c = False, b = False, a = True]
[c, b, a]


sat
[Or(a, b, c), Or(c != False, b != False, a != True)]
[b = True, a = False]
[b, a]


sat
[Or(a, b, c),
 Or(c != False, b != False, a != True),
 Or(b != True, a != False)]
[b = True, a = True]
[b, a]


sat
[Or(a, b, c),
 Or(c != False, b != False, a != True),
 Or(b != True, a != False),
 Or(b != True, a != True)]
[b = False, c = True]
[b, c]

Answer 1

The typical way to code such problems is as follows:

from z3 import *

a, b, c = Bools('a b c')
s = Solver()
s.add(Or([a, b, c]))

res = s.check()
while (res == sat):
  m = s.model()
  print(m)
  block = []
  for var in m:
      block.append(var() != m[var])
  s.add(Or(block))
  res = s.check()

This prints:

[b = True, a = False, c = False]
[a = True]
[c = True, a = False]

You'll notice that not all models are "complete." This is because z3 will typically "stop" assigning variables once it decides the problem is sat, as the other variables are irrelevant.

I suppose your confusion is that there should be 7 models to your problem: Aside from the all-False assignment, you should have a model. If you want to get the values of all your variables in this way, then you should explicitly query for them, like this:

from z3 import *

a, b, c = Bools('a b c')
s = Solver()
s.add(Or([a, b, c]))

myvars = [a, b, c]

res = s.check()
while (res == sat):
  m = s.model()
  block = []
  for var in myvars:
      v = m.evaluate(var, model_completion=True)
      print("%s = %s " % (var, v)),
      block.append(var != v)
  s.add(Or(block))
  print("\n")
  res = s.check()

This prints:

a = False  b = True  c = False

a = True  b = False  c = False

a = True  b = True  c = False

a = True  b = True  c = True

a = True  b = False  c = True

a = False  b = False  c = True

a = False  b = True  c = True

And there are exactly 7 models as you would've expected.

Note the model_completion parameter. This is a common pitfall for newcomers as there isn't a "out-of-the-box" method in z3 for getting all possible assignments, so you have to be careful coding it yourself like above. The reason why there isn't such a function is that it's really hard to implement it in general: Think about how it should work if your variables were functions, arrays, user-defined data-types, etc. as opposed to simple booleans. It can get really tricky to implement a generic all-sat function with all these possibilities handled correctly and efficiently. So, it's left to the user, as most of the time you only care about a specific notion of all-sat that's typically not hard to code once you learn the basic idioms.