What is the DataKinds extension of Haskell?

Well let’s start with the basics

Kinds

Kinds are the types of types*, for example

Int :: *
Bool :: *
Maybe :: * -> *

Notice that -> is overloaded to mean “function” at the kind level too. So * is the kind of a normal Haskell type.

We can ask GHCi to print the kind of something with :k.

Data Kinds

Now this is not very useful, since we have no way to make our own kinds! With DataKinds, when we write

 data Nat = S Nat | Z

GHC will promote this to create the corresponding kind Nat and

 Prelude> :k S
 S :: Nat -> Nat
 Prelude> :k Z
 Z :: Nat

So DataKinds makes the kind system extensible.

Uses

Let’s do the prototypical kinds example using GADTs

 data Vec :: Nat -> * where
    Nil  :: Vec Z
    Cons :: Int -> Vec n -> Vec (S n)

Now we see that our Vec type is indexed by length.

That’s the basic, 10k foot overview.

* This actually continues, Values : Types : Kinds : Sorts ... Some languages (Coq, Agda ..) support this infinite stack of universes, but Haskell lumps everything into one sort.