Break `abs` into two aspects

[Andrew Lelechenko]

On Tue, 28 Jan 2020, Dannyu NDos wrote:

> Second, I suggest to move `abs` and `signum` from `Num` to `Floating`

I can fully relate your frustration with `abs` and `signum` (and numeric type classes in Haskell altogether). But IMO breaking both in `Num` and in `Floating` at once is not a promising way to make things proper. 

I would rather follow the beaten track of Applicative Monad and Semigroup Monoid proposals and - as a first step - introduce a superclass (probably, borrowing the design from `semirings` package): 

class Semiring a where 
  zero  :: a
  plus  :: a -> a -> a 
  one   :: a
  times :: a -> a -> a 
  fromNatural :: Natural -> a 
class Semiring a => Num a where ...

Tangible benefits in `base` include:
a) instance Semiring Bool, 
b) a total instance Semiring Natural (in contrast to a partial instance Num Natural),
c) instance Num a => Semiring (Complex a) (in contrast to instance RealFloat a => Num (Complex a)),
d) newtypes Sum and Product would require only Semiring constraint instead of Num.

Best regards,
Andrew