[Haskell-cafe] Inheritance and Wrappers

[MattMan]

tldr: Can I make arbitrary instances of one class instantiate another without
using wrappers?

I'm new to Haskell, and am trying to implement some simple typeclasses for
doing algebra.  For example I have type class (simplified for the sake of
argument)

class AbGroup a where
    add :: a -> a -> a

I would like any type instantiating Num to also be an abelian group:

instance (Num a) => AbGroup a where
 add i j = i+j,

but this doesn't compile because a is a variable, not a type constructor(or
something).  The problem is fixed, in a sense, If I introduce a wrapper
class

data Wrapper a = Wrap a
instance (Num a) => AbGroup (Wrapper a) where
     add (Wrap i) (Wrap j) = Wrap(i+j)

However, this is clumsy.  Is there something else I can do?  Thanks!

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