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 _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe