Here's a question for those who know about translating between category
Andrew asked (I snip heavily): theory
for mathematicians and category theory for computer programmers.
In class today I was discussing functions with domain the empty set. ... ... [One student reported] that a function that takes no input is known as a "constant function" and so wasn't sure how to fit the two notions together.
I think "constant function" should be reserved for functions that *do* take input, but care not a whit what that input is, always providing the same output regardless what the input. A function with empty domain, on the other hand, never even has a chance of getting called (as you so correctly observe below), hence has *no* output whatsoever (and is certainly not a constant function).
The best that I could think of was that program functions have a 'hidden' input: the fact that they have been called. So a function defined on the empty set corresponds to a function that can never be called.
Think your student would be able to digest that? If suitably premasticated, perhaps? Cheers, -- Fred