data family List a

data instance List Char = Empty | Cons Char (List Char)

data instance List ()   = Count Int

Instead why not define it as:

data List :: * -> *

data List Char = Empty | Cons Char (List Char)

data List ()   = Count Int

The latter form looks more intuitive and easy to remember to me since it is very similar to the way value level functions are defined (signature & pattern matching defs). Here we are just defining a type level function instead.

-harendra