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# Defining kinds without an associated datatype

When using `-XDataKinds`

GHC automatically promotes every datatype to a kind, and its constructors to
types. This forces us to declare a datatype for every kind. However, sometimes we are not interested
in the datatype at all, only on the kind. Consider the following data kind that defines a small
universe for generic programming:

data Universe star = Sum Universe Universe | Prod Universe Universe | K star

This universe comes with an associated interpretation:

data Interpretation :: Universe * -> * where L :: Interpretation a -> Interpretation (Sum a b) R :: Interpretation b -> Interpretation (Sum a b) Prod :: Interpretation a -> Interpretation b -> Interpretation (Prod a b) K :: a -> Interpretation (K a)

In this case, having to declare a datatype for `Universe`

has two disadvantages:

- We lose constructor name space, because the datatype constructor names will be taken, even though
we will never use them. So
`Prod`

and`K`

cannot be used as constructors of`Interpretation`

as above, because those are also constructors of`Universe`

.

- We cannot use kinds (such as
`*`

) while defining a datatype, so we are forced to make`Universe`

a parametrised datatype, and later always instantiate this parameter to`*`

(like in the kind of`Interpretation`

).

**Proposal:** allow defining kinds directly, as in the following example:

data kind Universe = Sum Universe Universe | Prod Universe Universe | K *

By using `data kind`

, we tell GHC that we are only interested in the `Universe`

kind, and not the datatype.
Consequently, `Sum`

, `Prod`

, and `K`

will be types only, and not constructors. Note however that this would
imply being able to parse kinds (`*`

, at the very least) on the right-hand side of data kind declarations.
To avoid this, we propose instead using a kind `Type`

(or `Star`

), defined in `GHC.Exts`

, that acts as a
synonym of `*`

.

# Notes

`data kind K ...`

- Allow
`*`

on`data kind`

s? Or maybe`Type`

, or`Star`

.

- Perhaps also
`data type D ...`

- Promote type synonyms by default

- What about
`type kind K1 = K2`

?

- Even worse:
`type type T1 = T2`

...