Bill Wood
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. Chad Scherrer Computational Mathematics Group Pacific Northwest National Laboratory "Time flies like an arrow; fruit flies like a banana." -- Groucho Marx