Mathematical prelude discussion
There have been many ideas for improving the prelude's support for mathematics. Including the addition of algebraic classes. But the discussion is spread over years of list archives and a half dozen websites. And the discussion has never gelled.
This page is intended to collect links to past discussion, and to provide a focal point for advancing the discussion.
- Flesh out list of proposals. First from Libraries_and_tools/Mathematics.
- Add links to discussions in list archive, and elsewhere.
Libraries and proposals
Working set of common type classes and instances.
Basic Algebra Library (BAL)
- Is not in community report 2006-06.
- 0.04/announce.txt (2006-02)
- Formerly refered to as "basic algebra proposal".
Categorical Approach to representing mathematical structures in Haskell: 
Numeric classes on the Haskell' wiki
For me that probably starts with the semigroup/group/ring setup, and good arbitrary-precision as well as approximate linear algebra support.
I agree: semigoups like lattices are everywhere. Then there could be a uniform treatment of linear algebra, polynomial equations, operator algebra, etc.
- Discussion 2010-04 in Haskell-Cafe on Google-Summer-of-Code proposal for richer numerical type classes and supporting algorithms
- Aldor/Axiom may be a place to look for a good type class hierarchy
- Elements of Programming, Chapter 5