Types of Types

Recall a couple of type classes we have seen:

class Eq t where
  (==) :: t -> t -> Bool
  (/=) :: t -> t -> Bool

class Foldable t where
  foldr :: (a -> b -> b) -> b -> t a -> b

Notice that the types t in the Foldable class are applied to other types (i.e. t a).

The types t in Eq are different types of types than those in Foldable.

Kinds

The "type of a type" is called a kind in Haskell.

Proper types, or ground types or monotypes, are described with kind * (pronounced "star").

> :kind Int
> :k Int
> :k (Int, Int)

> :k Int -> Int
> :k Int -> Int -> Int

Type constructors, or type functions or type operators, are described with arrow kinds.

> :k Maybe
> :k []
> :k (,)
> :k (,,)
> :k (->)

A "fully applied" type is a proper type or a type constructor applied to enough arguments to produce a proper type. Only proper types are "inhabited" by Haskell values.

Kinds are not written in type class definitions, but it's helpful to think about them explicitly (like forall quantifiers in polymorphic types). The KindSignatures flag allows them to be written.

{-# LANGUAGE KindSignatures #-}

class Eq (t :: *) where
  ...

class Foldable (t :: * -> *) where
  ...

Source Files

• Kinds.hs