What is the DataKinds extension of Haskell?

Question

I am trying to find an explanation of the DataKinds extension that will make sense to me having come from only having read Learn You a Haskell. Is there a standard source that will make sense to me with what little I've learned?

Edit: For example the documentation says

With -XDataKinds, GHC automatically promotes every suitable datatype to be a kind, and its (value) constructors to be type constructors. The following types

and gives the example

data Nat = Ze | Su Nat

give rise to the following kinds and type constructors:

Nat :: BOX
Ze :: Nat
Su :: Nat -> Nat

I am not getting the point. Although I don't understand what BOX means, the statements Ze :: Nat and Su :: Nat -> Nat seem to state what is already normally the case that Ze and Su are normal data constructors exactly as you would expect to see with ghci

Prelude> :t Su
Su :: Nat -> Nat

Answer 1

Here is my take:

Consider a length indexed Vector of type:

data Vec n a where
  Vnil  :: Vec Zero a
  Vcons :: a -> Vec n a -> Vec (Succ n) a

data Zero
data Succ a

Here we have a Kind Vec :: * -> * -> *. Since you can represent a zero length Vector of Int by:

Vect Zero Int

You can also declare meaningless types say:

Vect Bool Int

This means we can have untyped functional programming at the type level. Hence we get rid of such ambiguity by introducing data kinds and can have such a kind:

Vec :: Nat -> * -> *

So now our Vec gets a DataKind named Nat which we can declare as:

datakind Nat = Zero | Succ Nat

By introducing a new data kind, no one can declare a meaningless type since Vec now has a more constrained kind signature.