wiki:GhcKinds/KindsWithoutData

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

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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 kinds? 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...