Haskell LanguageRole

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.