Marcin Kowalczyk continues:
On Mon, 12 Feb 2001, Jerzy Karczmarczuk wrote:
I want to be *able* to define mathematical operations upon objects which by their intrinsic nature permit so!
You can't do it in Haskell as it stands now, no matter what the Prelude would be.
For example I would say that with the definition abs x = if x >= 0 then x else -x it's obvious how to obtain abs :: ([Int]->Int) -> ([Int]->Int): apply the definition pointwise.
But it will never work in Haskell, unless we changed the type rules for if and the tyoe of the result of (>=).
You are asking for letting abs x = max x (-x) work on functions. OK, in this particular case it can be made to work ....
Why don't you try from time to time to attempt to understand what other people want? And wait, say 2 hours, before responding? I DON'T WANT max TO WORK ON FUNCTIONS. I never did. I will soon (because I am writing a graphical package where max serves to intersect implicit graphical objects) need that, but for very specific functions which represent textures, but NOT in general. I repeat for the last time, that I want to have those operations which are *implied* by the mathematical properties. And anyway, if you replace x>=0 by x>=zero with an appropriate zero, this should work as well. I want only that Prelude avoids spurious dependencies. This is the way I program in Clean, where there is no Num, and (+), (*), zero, abs, etc. constitute classes by themselves. So, when you say:
You are asking for an impossible thing.
My impression is what is impossible, is your way of interpreting/ understanding the statements (and/or desiderata) of other people.
I defined hundred times some special functions to add lists or records, to multiply a tree by a scalar (btw.: Jón Fairbarn proposes (.*), I have in principle nothing against, but these operators is used elsewhere, in other languages, CAML and Matlab; I use (*>) ).
Please show a concrete proposal how Prelude classes could be improved.
(Why do you precede your query by this citation? What do you have to say here about the syntax proposed by Jón Fairbarn, or whatever??) I am Haskell USER. I have no ambition to save the world. The "proposal" has been presented in 1995 in Nijmegen (FP in education). Actually, it hasn't, I concentrated on lazy power series etc., and the math oriented prelude has been mentioned casually. Jeroen Fokker presented similar ideas, implemented differently. If you have nothing else to do (but only in this case!) you may find the modified prelude called math.hs for Hugs (which needs a modified prelude.hs exporting primitives) in http://users.info.unicaen.fr/~karczma/humat/ This is NOT a "public proposal" and I *don't want* your public comments on it. If you want to be nice, show me some of *your* Haskell programs. Jerzy Karczmarczuk Caen, France