Version 4 (modified by dreixel, 22 months ago) (diff) |
---|

# 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`...