On 2 Apr 2008, at 11:22, Henning Thielemann wrote:
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.
When I take a quick look into Hörmander's book on distributions, then he writes (D f)(phi), and not D f(phi). So there might be a difference between math that is drawn towards pure or applied math.
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 think that in RTL, one do that as well: x tau, instead of (x)tau.
...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.)
Math usage is probably in minority these days. As I noted, looking into books on axiomatic set theory, one construct tuplets it so that (x) = x. So it seems possible, although for function application f(z) seems the normal notation. But one should also be able to write (f+g)(x). - This does not work in Haskell, because Num requires an instance of Eq and Show. Hans