On 23/11/05, Scherrer, Chad wrote:

Bill Wood 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