Haskell and mathematics/Hierarchy

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Mathematical 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.