Question

This simple example generates UNKNOWN for me, I suppose there is something that I don’t understand about def’s.

from z3 import *
s = Solver()
def Min(b, r): 
    return If(b, r, 1)
a = Real('a')
b = Bool('b')

s.add(a==0.9)
s.add(a<=Min(b,0.9))

s.check()   
print "Presenting result "
m = s.model()
print "traversing model..."
for d in m.decls():
    print "%s = %s" % (d.name(), m[d])

Answer 1

You did not make any mistake. This is a problem in one of Z3 solvers. Your problem is in a fragment of arithmetic called “difference-logic”. A problem in in this fragment, if the arithmetic atoms can be written as x - y <= k, where k is a numeral. When a problem is in this fragment, Z3 will use a specialized solver for it. However, this solver may fail (returns unknown) when the input problem also contains if-then-else terms (the If in your Min).
The bug has been fixed, and will be available in the next release. In the meantime, you can try one of the following workarounds:

• Force Z3 to eliminate if-then-else terms before invoking the solver. You just have to replace s = Solver() with s = Then('elim-term-ite', 'smt').solver(). Here is the modified script at rise4fun.

• We can add a redundant assertion that is not in the different logic fragment. Example: z + w > 2. Here is the modified script at rise4fun.