Haskell and mathematics/Hierarchy
Here is a place to discuss ideas for a mathematician-attracting hierarchy of mathematics modules that incorporate a sound algebraic class structure.
Basic algebraic structures in Haskell: ftp://ftp.botik.ru/pub/local/Mechveliani/basAlgPropos/
Categorical Approach to representing mathematical structures in Haskell: ftp://ftp.botik.ru/pub/local/Mechveliani/docon/
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.
This article should be merged with Mathematical prelude discussion.