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
- 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
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
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
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 ...
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)
which renders it non-promotable. Why is this? Well, promoted
would have sorts:
Proxy :: forall s. s -> BOX Ind :: 'Nat -> BOX
s is a sort variable, and
'Nat is the sort arising from promoting
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 :: forall k. k -> BOX Ind :: Nat -> BOX
Now instead of sort variables we have kind variables, and we do not need to promote
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".