Re: [Haskell-cafe] Thoughts about redesigning "Num" type class

On 8/09/2015, at 2:08 am, DreamApart AtHaskells wrote:

class SemiGroup a where (+) :: a -> a -> a

class Group a => Ring a where -- not sure about the name ... (*) :: a -> a -> a

class Ring a => Num a where abs :: a -> a signum :: a -> a fromInteger :: Integer -> a

sum :: (Foldable t, Monoid a) => t a -> a sum = foldl' (+) zero

Traditionally, + is used only for Abelian groups, with a non-commutative binary operation being thought of as a "product", not a sum. I am not very happy at the idea of being told to use the wrong operator for a group operation. Sounds like you want NumericPrelude. (Or possibly the AXIOM computer algebra language...)