Re: Functions in programming

[Vaughan Pratt <pratt@cs.stanford.edu>]

> I, on the other hand, am at the level of "Ooo, look!  Mathematicians and
> computer programmers both use the word 'function'.  So do biologists and event
> organisers.  Maybe we should organise a function whose function would be to
> investigate all these different uses.'

Even a perfunctory analysis should indicate that the attendees would be
likely to come away disfunctional.  :)

> 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.
>
> Can anyone help me straighten this out?

That's easy: just have them visualize a function as a list of its values
at the points in its domain enumerated in some fixed order.  Programmers
can easily see how many lists of length n there are for any given size
of codomain of the function (e.g. lists of bits as functions to {0,1}).
  The empty list should hold no terrors for programmers: in particular
they should know it exists, and they should know why there aren't two
empty lists.

Vaughan Pratt