[Haskell-beginners] How to manage typeclass hierarchies and instances?

[Michael Orlitzky]

On 02/20/2015 06:58 PM, Stuart Hungerford wrote:
> Hi,
> 
> I'm experimenting with Haskell typeclasses and could do with some
> advice on managing superclasses and instance declarations. Suppose I
> have these modules (please ignore any misunderstandings of abstract
> algebra concepts):
> 
> -- in Semigroup.hs
> 
> class Semigroup a where
>   (|.|) :: a -> a -> a
> 
> instance Semigroup Integer where
>   (|.|) = (+)
> 
> 
> -- In Monoid.hs
> 
> class (Semigroup a) => Monoid a where
>   identity :: a
> 
> instance Monoid Integer where
>   identity = 0
> 
> 
> -- In Group.hs
> 
> class (Monoid a) => Group a where
>   inverse :: a -> a
> 
> instance Group Integer where
>   (|.|)    = (+)
>   identity = 0
>   inverse  = (-)
> 
> 
> In Group.hs I'm trying to create an (additive) group instance for
> Integer values but GHC complains that (|.|) and identity are not
> "visible" typeclass methods.

You only get one instance per type, so the Semigroup/Monoid instances
for Integer are "set in stone." When you "import Semigroup" and "import
Monoid", those instances come into scope. So in Group.hs, '|.|' and
'identity' are already defined for Integer. All you need is,

  instance Group Integer where
    inverse = negate

To add different instances, you'll need a newtype wrapper around Integer.