Classes of arbitrary kind

The type class system in the Haskell Programming language provides a useful abstraction for a wide range of types, such as those that support comparison, serialization, ordering, between others. This system can be extended by the programmer by providing custom instances to one’s custom types. Yet, this is often a monotonous task. Some notions, such as equality, are very regular regardless if it is being encoded for a ground type or a type constructor. In this paper we present a technique that unifies the treatment of ground types and type constructors whenever possible. This reduces code duplication and improves consistency. We discuss the encoding of several classes in this form, including the generic programming facility in GHC