Re: Functions in programming

["Fred E.J. Linton" <fejlinton@usa.net>]

Andrew asked (I snip heavily):

> Here's a question for those who know about translating between category
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