Role

Introduction#

The 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.

Remarks#

Nominal Role

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

Here x is non-parametric because to determine the outcome of applying Inspect to a type argument, the type function must inspect x.

In this case, the role of x is nominal. We can declare the role explicitly with the RoleAnnotations extension:

type role Inspect nominal

Representational Role

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

Here x is parametric because to determine the outcome of applying DoNotInspect to a type argument, the type function do not need to inspect x.

In this case, the role of x is representational. We can declare the role explicitly with the RoleAnnotations extension:

type role DoNotInspect representational

Phantom Role

A phantom type parameter has a phantom role. Phantom roles cannot be declared explicitly.