On 23/11/05, Scherrer, Chad <[EMAIL PROTECTED]> wrote:
> Bill Wood <[EMAIL PROTECTED]> writes:
>
> > Interesting note: in Richard Bird and Oege de Moor, _Algebra
> > of Programming_, pp. 2-3, the authors write
> >
> > As a departure from tradition, we write "f : A <- B" rather than
> > "f : B -> A" to indicate the source and target types associated
> > with a function "f". ... The reason for this choice has to do with
> > functional composition, whose definition now takes the smooth
> > form: if f : A <- B and g : B <- C, then f . g : A <- C is defined
> > by (f . g) x = f(g x).
> >
> > Further along the same paragraph they write:
> >
> > In the alternative, so-called diagrammatic forms, one writes
> > "x f" for application and "f ; g" for composition, where
> > x (f ; g) = (x f) g.
> >
> > I know I've read about the latter notation as one used by
> > some algebraists, but I can't put my hands on a source right now.
> >
> > I guess it's not even entirely clear what constitutes
> > "mathematical notation". :-)
> >
> > -- Bill Wood
>
> Good point. One of my undergrad algebra books ("Contemporary Abstract
> Algebra", by Gallian) actually used notation like this. Function
> application was written (x f). Some people even write the function as an
> exponential. But (f x) is still far more common.
Hmm, which edition? My copy (5th ed.) uses the ordinary notation: f(x).
x f does perhaps make more sense, especially with the current
categorical view of functions, but there would have to be a really
hugely good reason to change notation, as almost all current work puts
things the other way around.
- Cale
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