## 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:

- The class has a single parameter
`kparam`

, which is of kind`OfKind k`

. - 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.) - The associated type synonym
`DemoteRep`

chooses the representation for singletons of the given kind. - 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