> Then instead of asserting that f(1, 2) == 3 you need to do f(a, b) == a+b

Not really, no, it's right there in the name: you should be testing properties (you can call them "invariants" if you want to sound fancy).

In the example of testing an addition operator, you could test:

1. f(x,y) >= max(x,y) if x and y are non-negative

2. f(x,y) is even iff x and y have the same parity

3. f(x, y) = 0 iff x=-y

etc. etc.

The great thing is that these tests are very easy and fast to write, precisely because you don't have to re-model the entire domain. (Although it's also a great tool if you have 2 implementations, or are trying to match a reference implementation)