Question

Is there any limitations in functions declaring?

For example, this piece of code returning unsat.

from z3 import *

def one_op (op, arg1, arg2):
    if op==1:
        return arg1*arg2
    if op==2:
        return arg1-arg2
    if op==3:
        return arg1+arg2

    return arg1+arg2 # default

s=Solver()

arg1, arg2, result, unk_op=Ints ('arg1 arg2 result unk_op')

s.add (unk_op>=1, unk_op<=3)

s.add (arg1==1)
s.add (arg2==2)
s.add (result==3)
s.add (one_op(unk_op, arg1, arg2)==result)

print s.check()

How Z3Py interpret declared function? Is it just calling it some times or some hidden machinery also here?

Answer 1

In the function call one_op(unk_op, arg1, arg2), unk_op is a Z3 expression. Then, expressions such as op==1 and op==2 (in the definition of one_op) are also Z3 symbolic expressions. Since op==1 is not the Python Boolean expression False. The function one_op will always return the Z3 expression arg1*arg2. We can check that by executing print one_op(unk_op, arg1, arg2). Note that the if statements in the definition of one_op are Python statements.

I believe your true intention is to return a Z3 expression that contains conditional expressions. You can accomplish that by defining one_op as:

def one_op (op, arg1, arg2):
    return  If(op==1,
               arg1*arg2,
               If(op==2,
                  arg1-arg2,
                  If(op==3,
                     arg1+arg2,
                     arg1+arg2)))

Now, the command If builds a Z3 conditional expression. By using, this definition, we can find a satisfying solution. Here is the complete example:

from z3 import *

def one_op (op, arg1, arg2):
    return  If(op==1,
               arg1*arg2,
               If(op==2,
                  arg1-arg2,
                  If(op==3,
                     arg1+arg2,
                     arg1+arg2)))

s=Solver()

arg1, arg2, result, unk_op=Ints ('arg1 arg2 result unk_op')

s.add (unk_op>=1, unk_op<=3)
s.add (arg1==1)
s.add (arg2==2)
s.add (result==3)
s.add (one_op(unk_op, arg1, arg2)==result)

print s.check()
print s.model()

The result is:

sat
[unk_op = 3, result = 3, arg2 = 2, arg1 = 1]