Re: Functions in programming

[Luis Barbosa <lsb@di.uminho.pt>]

On 2009/03/13, at 11:29, Andrew Stacey wrote:

>
> Afterwards, one student asked about how this related to functions
> as used in
> computer programming.  It seemed from what he said that he had some
> understanding of the formal relationship between functions in
> mathematics and
> functions in computer programs - beyond them having the same name.
> He said
> 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.

A constant function in Haskell, as in Maths, has 1 as a domain. The
(isomorphism class of the)
singleton set is written as (); so, for example, the function always
returning integer 5 is declared as

five :: () -> Int

and defined by five () = 5 (notice notation () is used to denote both
set 1 and its (unique) element)

Your student is probably confusing notation () with the empty set.
The notation may be a bit unfortunate
as () may suggest "no input" ... but, of course functions, in
functional programming are just
functions.

Luis
---------------------------------------
Luis S. Barbosa
www.di.uminho.pt/~lsb