Vivian McPhail wrote:
What I want to push is a 'mathematically sound' numeric prelude. A proper numerical prelude should have bona fide mathematical obects like groups, rings, and fields underlying common numerical classes. .. Some classes would become even more important: monoid, groupoid, semi-group, loop (semi-group with identity), etc. But all of those are, to the average programmer (and many a mathematician), just as scary as Monad.
as long as those concepts, like monads, are clearly defined, consistent, and have practical uses that directly correspond to those concepts and fulfill the laws associated with them, that should not be a hindrance.. ;) ok, tongue out of cheek again, someone would need to investigate the particular shape in which such abstract concepts would be most useful (which may or may not be the same shape best known in maths, see Monad, Monoid, Applicative, Arrow,..), and how those shapes are best expressed within the programming language abilities. and then, of course, someone would need to write code and tutorials. i know there has been a lot more than just talk wrt numeric preludes for haskell, but just now, it took me a while to find the main incumbents, and i could easily have been put off track by other mathematical libraries. when i found that mathematical prelude discussion page at haskell.org, it was disappointingly brief, so i might not have followed through to the sources, which seem rather better developed. when i did go to the darcs site for the sources, there were haddocks, but for introduction and overview, there is only a brief entry for the haskell communities report, in .tex format. perhaps i was mistaken in thinking that there is a group of math-interested haskellers out there discussing, developing, and documenting the area? or perhaps that group needs introductory tutorials presenting its work? long ago, there was a start in Jeroen Fokker's Explaining Algebraic Theory with Functional Programs. FPLE 1995 http://www.cs.uu.nl/people/jeroen/article/algebra/ but what would be today's updated equivalent? claus monad -- one of the secret commands of haskellbot; when uttered on one of the channels haskellbot is lurking on (mailing lists, news groups, irc, blogs, feeds,..), it will generally result in yet another monad tutorial (YAMT) to be written and published; although, if haskellbot is bored, it might simply point randomly to one of its earlier works; documentation on haskellbot commands is sketchy, possibly to discourage trolls, but it has been known to react to "oop in haskell", "killer application", "mainstream", "static vs dynamic typing", and "category theory"