== Kind Parameters ==
We start by defining a ''kind'', which is useful for passing kinds as parameters.
{{{
data {-kind-} OfKind (a :: *) = KindParam
}}}
Note that we are only interested in the promoted version of this datatype,
so basically we just defined a singe type constant with a polymorphic kind:
{{{
KindParam :: OfKind k
}}}
In addition, it is also convenient to define the following type synonym:
{{{
type KindOf (a :: k) = (KindParam :: OfKind k)
}}}
This makes it easy to write kind parameters in terms of existing types.
Here are some examples:
{{{
KindOf Int ~ (KindParam :: OfKind *)
KindOf 1 ~ (KindParam :: OfKind Nat)
KindOf "Hi" ~ (KindParam :: OfKind Symbol)
}}}
== Kind-based Overloading ==
Using these types we can define functions that are overloaded based on their ''kind'' (rather than ''type'').
An example of such a function is `fromSing`, which given an element of a singleton family returns the run-time
value representing the singleton. This function uses kind overloading because it uses the same representation
for all singletons of a given kind. For example, here are two concrete instances of its type:
{{{
fromSing :: Sing (a :: Nat) -> Integer
fromSing :: Sing (a :: Symbol) -> String
}}}
Here is how we can define `fromSing` in its full generality:
{{{
class (kparam ~ KindParam) => SingE (kparam :: OfKind k) where
type DemoteRep kparam :: *
fromSing :: Sing (a :: k) -> DemoteRep kparam
}}}
Here are the different components of this declaration:
1. The class has a single parameter `kparam`, which is of kind `OfKind k`.
2. The super-class constraint makes it explicit that the value of the parameter will always be `KindParam`
(One we eliminate `Any`, GHC could probably work this out on its own, but for now we make this explicit.)
3. The associated type synonym `DemoteRep` chooses the representation for singletons of the given kind.
4. Finally, the method `fromSing` maps singletons to their representation.
This might look a bit complex, but defining instances is pretty simple. Here are some examples:
{{{
instance SingE (KindParam :: OfKind Nat) where
type DemoteRep (KindParam :: OfKind Nat) = Integer
fromSing (SNat n) = n
instance SingE (KindParam :: OfKind Symbol) where
type DemoteRep (KindParam :: OfKind Symbol) = String
fromSing (SSym s) = s
}}}
It is convenient to define another type synonym, which lets us name
the representation type for a given singleton:
{{{
type Demote a = DemoteRep (KindOf a)
}}}
Here are some examples of using this synonym:
{{{
Demote 1 ~ Integer
Demote 2 ~ Integer
Demote "hi" ~ String
}}}
Using this synonym we can write the type of `fromSing` like this:
{{{
fromSing :: SingE (KindOf a) => Sing a -> Demote a
}}}
Here is an example of using all this to provide a `Show` instance
for singleton families:
{{{
instance (SingE (KindOf a), Show (Demote a)) => Show (Sing a) where
showsPrec p = showsPrec p . fromSing
}}}