You saw this, right? https://wiki.haskell.org/Nitpicks#Base-related_nitpicks (Just in case, maybe it was you who included this topic.) Alexey. On Monday, September 7, 2015 at 4:08:54 PM UTC+2, DreamApart AtHaskells wrote:
The class Num defines the method functions like (+), (-), (*), negate, ... But they are actually different concepts.
We often meet situations that we want an addition for some type, but not a multiplication. For example:
*data* Vec3 = Vec3 Float Float Float
The additive (and subtractive) operation is obvious, but not for a multiplication.
* Note*
(*) :: a -> a -> a -- not avaliable for a Vec3
scale :: Float -> Vec3 -> Vec3 dot :: Vec3 -> Vec3 -> Float
We cannot define a (+) alone for a type, so we got many different functions from different libs, like mappend, mplus, plus, (<+>), (.+.), (+.), which all reads "plus".
My opinion is that the methods of Num should be seperated into different type classes, so we don't need to invent a new symbol for a new lib.
A feasible design is:
*import* Prelude *hiding* ( Num (..), Monoid (..), sum )
*class* SemiGroup a *where* (+) :: a -> a -> a
*class* SemiGroup a => Monoid a *where* zero :: a
*class* Monoid a => Group a *where* negate :: a -> a (-) :: a -> a -> a
x - y = x + negate y negate x = zero - x
*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
-- for compatibility mempty = zero mappend = (+) mconcat = sum