Jacques Carette wrote:
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? My guess is that there are a number of people "waiting in the wings", waiting for a critical mass of features to show up before really diving in. See http://www.cas.mcmaster.ca/plmms07/ for my reasons for being both interested and wary).
Probably the simplest test case is the difficulties that people are (still) encountering doing matrix/vector algebra in Haskell. One either quickly encounters efficiency issues (although PArr might help), or typing issues (though many tricks are known, but not necessarily simple). Blitz++ and the STL contributed heavily to C++ being taken seriously by people in the scientific computation community. Haskell has even more _potential_, but it is definitely unrealised potential.
I am one of those mathematicians "waiting in the wings." Haskell looked very appealing at first, and the type system seems perfect, especially for things like multilinear algebra where currying and duality is fundamental. I too was put off by the Num issues though--strange mixture of sophisticated category theory and lack of a sensible hierarchy of algebraic objects.
However, I've decided I'm more interested in helping to fix it than wait; so count me in on an effort to make Haskell more mathematical. For me that probably starts with the semigroup/group/ring setup, and good arbitrary-precision as well as approximate linear algebra support.
I've been watching this thread for quite a while now, and it seems to me that there is quite a bit of interest in at least working on a new Prelude. I've also noticed a 'The Other Prelude' page on the wiki [http://haskell.org/haskellwiki/The_Other_Prelude] and they seem to have a start on this. So it seems that we should actually start this, because people will contribute. Can somebody with good Cabal skills and maybe access to darcs.haskell.org start a new library for people to start patching? Bryan Burgers