Re: [Haskell-cafe] Num is such a fat and greedy class

On Fri, 8 Dec 2006, Dan Weston wrote:

1) Groups may only want to define addition. Why can't they use + (instead of <+>, >++++?&**+>, or other such perversion)?

http://darcs.haskell.org/numericprelude/src/Algebra/Monoid.hs

2) Affine spaces have a (-) but no (+). Worse, the signature might be (-) :: Point -> Point -> Vector, which doesn't unify with (a -> a -> a).

yet to come

3) Quaternions have no signum, unit quaternions have (*), (/) but no (+) or (-), abs would have a different signatures (Quaternion -> Double) which doesn't unify with (a -> a), and fields cannot be scaled with (*) as in (*) :: (Field f) => Double -> f -> f

http://darcs.haskell.org/numericprelude/src/Number/Quaternion.hs -> norm