More than once I have observed this: A person describes a functional programming language (as opposed to a programming language that makes heavy use of interspersed states), that person will say it is very mathematical, so we should use the language of mathematics; then to demonstrate, begins, "Let's say we have a function f that takes input x and gives output y..." or something like this.
This bugs me because I have never heard a mathematician describe a function as taking inputs and giving outputs. Instead, I believe, a function is thought of as a map, and it could be said that the domain, the map, and the co-domain all exist at the same time.
In the world of computer processing, a certain time duration is typically associated with an operation, but it does not have to be: it could be that the language representation does not truly represent the operation directly (the function might even be completely removed by the code compiler or interpreter), or maybe the function actually takes some different input than it is thought to, is distributed over many processors, etc. In short, the machine operations are not necessarily represented in a straightforward way for human interpretation by the programming language.
Furthermore, the time for the operation might be negligible, might be run parallel with another operation, or the steps of a program might be run in a different sequence. It might even require some other later operations not obvious to the observer, so might have an influence on other points in time.
I think there is a more fundamental conflict possible, though. As expressed by Schopenhauer in 'The Four-Fold Root', there is a problem applying the concept of 'causation' in the physical sense to the metaphor of logical 'causation'.
Computer processing seems to be right in the space between 'inference as a physical model' and 'inference as a logical model'. Is this a fundamental problem as I've expressed it? Is it possible that these mixed metaphors are going to become more problematic as the field of data processing progresses?