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

[Henning Thielemann]

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