Input is an obvious example, as it's impossible to predict the value of an input.
Output is less obvious, but there is uncertainty like whether the filesystem is full.
The original Haskell style was to have a World object that was an input to every non-pure function.
Do you mean this more abstractly or literally? In the example of PacMan, for every frame, the only possible input is nothing, left, right, up, or down. So you are be able to predict it is going to be one of those five, though not which one.
If you model the controller input as a function parameter, that's just a state argument, and FP can handle it declaratively just fine without having side effects.
>> Input is an obvious example, as it's impossible to predict the value of an input.
> though not which one
Literally.
So because the possible input is not just a single value, it is not predictable. It doesn’t matter if the input was limited to a set of two values, or infinite, it is literally not predictable so therefore we don’t know the future state of the program?