On Mon, 17 Jul 2006 10:58:48 +1200, Vivian McPhail wrote:
Haskell is often cited as an elegant and 'mathematical' language in which to program. This post is to voice my support for a modified Numeric Prelude that would be consistent with [1] and/or [2]. It would be an improvement if the numeric classes were more structured along the lines of algebraic properties (similar to the monad laws) of various entities.
I remember griping about this when I first learned Haskell.
While the typical user may not need to know about the underlying mathematical structure of the objects that they are working with, it would be good if the system were consistent for those that do.
[1] http://haskell.org/docon/ [2] http://cvs.haskell.org/darcs/numericprelude/
The numeric prelude package (though the documentation is hard to follow with all the classes called C and types called T) seems to consist of two layers: - a bunch of unary classes refactoring the Haskell 98 numeric class hierarchy, and - multi-parameter classes, building on the former classes, for vector spaces and related concepts. A refactoring like the former would be useful on its own, and would provide a base for adding the other classes later. Of course the algebraic properties won't be satisfied by floating point arithmetic.