TypeFamilies language extension allows the programmer to define type-level functions. What distinguishes type functions from non-GADT type constructors is that parameters of type functions can be non-parametric whereas parameters of type constructors are always parametric. This distinction is important to the correctness of the
GeneralizedNewTypeDeriving extension. To explicate this distinction, roles are introduced in Haskell.
Haskell Wiki has an example of a non-parametric parameter of a type function:
type family Inspect x type instance Inspect Age = Int type instance Inspect Int = Bool
x is non-parametric because to determine the outcome of applying
Inspect to a type argument, the type function must inspect
In this case, the role of
x is nominal. We can declare the role explicitly with the
type role Inspect nominal
An example of a parametric parameter of a type function:
data List a = Nil | Cons a (List a) type family DoNotInspect x type instance DoNotInspect x = List x
x is parametric because to determine the outcome of applying
DoNotInspect to a type argument, the type function do not need to inspect
In this case, the role of x is representational. We can declare the role explicitly with the
type role DoNotInspect representational
A phantom type parameter has a phantom role. Phantom roles cannot be declared explicitly.