Editing GHC/Type families (section)

=== The class declaration ===

We define a type class whose instances are the types that we can use as keys in our generic maps:
<haskell>
class GMapKey k where
  data GMap k :: * -> *
  empty       :: GMap k v
  lookup      :: k -> GMap k v -> Maybe v
  insert      :: k -> v -> GMap k v -> GMap k v
</haskell>
The interesting part is the ''associated data family'' declaration of the class.  It gives a [https://downloads.haskell.org/ghc/8.10.3/docs/html/users_guide/glasgow_exts.html#data-families ''kind signature''] (here <hask>* -> *</hask>) for the associated data type <hask>GMap k</hask> - analogous to how methods receive a type signature in a class declaration.

What it is important to notice is that the first parameter of the associated type <hask>GMap</hask> coincides with the class parameter of <hask>GMapKey</hask>.  This indicates that also in all instances of the class, the instances of the associated data type need to have their first argument match up with the instance type.  In general, the type arguments of an associated type can be a subset of the class parameters (in a multi-parameter type class) and they can appear in any order, possibly in an order other than in the class head.  The latter can be useful if the associated data type is partially applied in some contexts.

The second important point is that as <hask>GMap k</hask> has kind <hask>* -> *</hask> and <hask>k</hask> (implicitly) has kind <hask>*</hask>, the type constructor <hask>GMap</hask> (without an argument) has kind <hask>* -> * -> *</hask>.  Consequently, we see that <hask>GMap</hask> is applied to two arguments in the signatures of the methods <hask>empty</hask>, <hask>lookup</hask>, and <hask>insert</hask>.