On Tue, 1 Apr 2008, Hans Aberg wrote:
On 1 Apr 2008, at 12:40, PR Stanley wrote:
Why can't we have function application implemented outwardly (inside-out). So f g x would be applied with gx first followed by its return value passed to f instead of putting g x in brackets.
It seems me it may come from an alteration of math conventions: Normally (x) = x, and function application is written as f(x), except for a few traditional names, like for example sin x. So if one reasons that f(x) can be simplified to f x, then f g x becomes short for f(g)(x) = (f(g))(x).
In functional analysis you write e.g. D f(x) meaning (D f)(x) not D(f(x)), so I wouldn't say there is any convention of precedence of function application in mathematics. Even more, in functional analysis it is common to omit the parentheses around operator arguments, and since there are a lot of standard functions like 'sin', I wouldn't say that using argument parentheses is more common than omitting them. (Btw. in good old ZX Spectrum BASIC it was also allowed to omit argument parentheses.)