I would like to assert that the most significant digit of a number is a particular value, but I don't actually know the length of the number. If it was the least significant digit, I know I could use the python mod (%) to check for it. But with an unknown number of digits, I'm unsure of how I could check this in z3.
For example, I may know that the left most digit is a 9, such as 9x, or 9xx, or 9xxx etc.
Thanks so much in advance
The generic way to do this would be to convert to a string and check that the first character matches:
from z3 import *
s = Solver()
n = Int('n')
s.add(SubString(IntToStr(n), 0, 1) == "9")
r = s.check()
if r == sat:
m = s.model()
print("n =", m[n])
else:
print("Solver said:", r)
This prints:
n = 9
Note that IntToStr
expects its argument to be non-negative, so if you need to support negative numbers, you'll have to write extra code to accommodate for that. See https://smtlib.cs.uiowa.edu/theories-UnicodeStrings.shtml for details.
Aside While this will accomplish what you want in its generality, it may not be the most efficient way to encode this constraint. Since it goes through strings, the constraints generated might cause performance issues. If you have an upper limit on your number, it might be more efficient to code it explicitly. For instance, if you know your number is less than a 1000, I'd code it as (pseudocode):
n == 9 || n >= 90 && n <= 99 || n >= 900 && n <= 999
etc. until you have the range you needed covered. This would lead to much simpler constraints and perform a lot better in general. Note that this'll work even if you don't know the exact length, but have an upper bound on it. But of course, it all depends on what you are trying to achieve and what else you know about the number itself.