John Hughes: > > Look at Rex Page's Beseme project > > http://www.cs.ou.edu/research/beseme.shtml > > (which uses the Hall and O'Donnell book to do some interesting educational > research).
Just two useless words, on that project and *many* others. Rex Page focuses on *discrete math*. I believe that most of other people interested in dancing on a bridge between math and functional programming are interested in discrete math. structures. Not too much about analysis, topological problems... About differential equations. About the manipulation of "continuous objects": functions :: Real -> Real and generalizations thereof. Convergence of numerical algorithms. Algorithms for the asymptotic behaviour of some functions (and concrete asymptotic expansions: see the book by Knuth/ Graham/Patashnik...) etc. etc. Well, this is my personal field of interest, so I cannot be objective, but I assure you that all enormous niche of mathematical programming is still open. Maths, especially applied maths are often taught with the aid of computer algebra programs. Teachers, students, implementors, use Maple or Mathematica, or you name it, in order to transform *formulae*, to crunch, munch, and digest the external representation of mathematical entities not because this is something very profound, but because "standard" programming languages do not offer any reasonable facilities to manipulate objects with some mathematical contents. Named symbols, the "indeterminates" replace those entities: algebra generators, differential forms, fields, operators, etc. Good, polymorphic functional languages offer those missing tools. On this very mailing list we had at least 100 postings about math structures and their implementation in Haskell. Everybody agrees that the situation is far from ideal. Classes are not categories. Types are not domains. We don't know how to specify operationally such properties as commutativity for arbitrary binary functions, etc. We need an "object-oriented" type system adapted to math hierarchies, and this is far from trivial, people from Axiom, Magma and MuPAD zones worked for years on that. Jerzy Karczmarczuk Caen, France _______________________________________________ Haskell mailing list [EMAIL PROTECTED] http://www.haskell.org/mailman/listinfo/haskell
