Kind polymorphism and datatype promotion
This page gives additional implementation details for the -XPolyKinds flag. The grand design is described in the paper Giving Haskell a Promotion. Most of the work has been done and merged into GHC 7.4.1. The relevant user documentation is in [the user's guide (add link when it's up)] and on the Haskell wiki page. What still doesn't work, or doesn't work correctly, is described here.
- GhcKinds/PolyTypeable A kind-polymorphic version of the Typeable class.
- ExplicitTypeApplication proposes a syntax for explicit kind application
Promoting data families
data family T a data instance T Int = MkT data Proxy (a :: k) data S = MkS (Proxy 'MkT)
Is it ok to use the promoted data family instance constructor MkT in the data declaration for S? No, we don't allow this. It might make sense, but at least it would mean that we'd have to interleave typechecking instances and data types, whereas at present we do data types then instances.
A couple of people have asked about this
#5682 (proper handling of infix promoted constructors)
Bug report #5682 shows a problem in parsing promoted infix datatypes.
Future work: handle kind operators properly in the parser.
Kind synonyms (from type synonym promotion)
At the moment we are not promoting type synonyms, i.e. the following is invalid:
data Nat = Ze | Su Nat type Nat2 = Nat type family Add (m :: Nat2) (n :: Nat2) :: Nat2
We propose to change this, and make GHC promote type synonyms to kind synonyms by default with -XDataKinds. For instance, type String = [Char] should give rise to a kind String.
Question: are there dangerous interactions with -XLiberalTypeSynonyms? E.g. what's the kind of type K a = forall b. b -> a`?
By extension, we might want to have kind synonyms that do not arise from promotion: type kind K .... And perhaps even type synonyms that never give rise to a promoted kind: type type T ....
Generalized Algebraic Data Kinds (GADKs)
Future work: this section deals with a proposal to collapse kinds and sorts into a single system so as to allow Generalised Algebraic DataKinds (GADKs). The sort BOX should become a kind, whose kind is again BOX. Kinds would no longer be classified by sorts; they would be classified by kinds.
(As an aside, sets containing themselves result in an inconsistent system; see, for instance, this example. This is not of practical concern for Haskell.)
Collapsing kinds and sorts would allow some form of indexing on kinds. Consider the following two types, currently not promotable in FC-pro:
data Proxy a = Proxy data Ind (n :: Nat) :: * where ...
In Proxy, a has kind forall k. k. This type is not promotable because a does not have kind *. This is unfortunate, since a new feature (kind polymorphism) is getting on the way of another new feature (promoting datatypes). As for Ind, it takes an argument of kind (promoted) Nat, which renders it non-promotable. Why is this? Well, promoted Proxy and Ind would have sorts:
Proxy :: forall s. s -> BOX Ind :: 'Nat -> BOX
But s is a sort variable, and 'Nat is the sort arising from promoting the kind Nat (which itself arose from promoting a datatype). FC-pro has neither sort variables nor promoted sorts. However, if there are no sorts, and BOX is the kind of all kinds, the "sorts" ("kinds", now) of promoted Proxy and Ind become:
Proxy :: forall k. k -> BOX Ind :: Nat -> BOX
Now instead of sort variables we have kind variables, and we do not need to promote Nat again.
Kind indexing alone should not require kind equality constraints; we always require type/kind signatures for kind polymorphic stuff, so then wobbly types can be used to type check generalised algebraic kinds, avoiding the need for coercions. While this would still require some implementation effort, it should be "doable".