Type Synonyms Generalized

Type functions are the new trend. Ωmega has them with the following syntax:

tfun :: Nat ~> Nat

{tfun Z} = S Z

Haskell (that is GHC) has them in the flavor of type families.

It has just occurred to me that they can be considered as a syntactic relaxation of type synonyms! Look:

tfun :: Nat ~> Nat

type tfun Z = S Z

type tfun (S n) = Z

When conventional type synonyms are used they must be fully applied. This should be the case here too. I am not sure whether type families or Ωmega-style type functions can be partially applied, though.

Anyway, a bit more to write at the definition site but less curlies to type at the call site; it may well be worth it.