where is the homological algebra library in haskell ? what is the name of it?
Neither precisely fits the bill, but...
DoCon: A functoral approach to computer algebra (and commutative algebra in particular): http://botik.ru/pub/local/Mechveliani/docon/2.11/announce.txt
Also see HaskellForMaths, which provides code for combinatorics, group theory, commutative algebra, and non-commutative algebra: http://hackage.haskell.org/package/HaskellForMaths