[Haskell-cafe] Function application like a Unix pipe

[Cale Gibbard]

On 23/11/05, Scherrer, Chad <Chad.Scherrer at pnl.gov> wrote:
> Bill Wood <william.wood3 at comcast.net> 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