6.4.10. Datatype promotion¶

DataKinds
¶ Since: 7.4.1 Allow promotion of data types to kind level.
This section describes data type promotion, an extension to the kind
system that complements kind polymorphism. It is enabled by
DataKinds
, and described in more detail in the paper Giving
Haskell a Promotion, which
appeared at TLDI 2012.
6.4.10.1. Motivation¶
Standard Haskell has a rich type language. Types classify terms and
serve to avoid many common programming mistakes. The kind language,
however, is relatively simple, distinguishing only regular types (kind
Type
) and type constructors (e.g. kind Type > Type > Type
).
In particular when using advanced type
system features, such as type families (Type families) or GADTs
(Generalised Algebraic Data Types (GADTs)), this simple kind system is insufficient, and fails to
prevent simple errors. Consider the example of typelevel natural
numbers, and lengthindexed vectors:
data Ze
data Su n
data Vec :: Type > Type > Type where
Nil :: Vec a Ze
Cons :: a > Vec a n > Vec a (Su n)
The kind of Vec
is Type > Type > Type
. This means that, e.g.,
Vec Int Char
is a wellkinded type, even though this is not what we
intend when defining lengthindexed vectors.
With DataKinds
, the example above can then be rewritten to:
data Nat = Ze  Su Nat
data Vec :: Type > Nat > Type where
Nil :: Vec a 'Ze
Cons :: a > Vec a n > Vec a ('Su n)
With the improved kind of Vec
, things like Vec Int Char
are now
illkinded, and GHC will report an error.
6.4.10.2. Overview¶
With DataKinds
, GHC automatically promotes every datatype
to be a kind and its (value) constructors to be type constructors. The
following types
data Nat = Zero  Succ Nat
data List a = Nil  Cons a (List a)
data Pair a b = Pair a b
data Sum a b = L a  R b
give rise to the following kinds and type constructors (where promoted
constructors are prefixed by a tick '
):
Nat :: Type
'Zero :: Nat
'Succ :: Nat > Nat
List :: Type > Type
'Nil :: forall k. List k
'Cons :: forall k. k > List k > List k
Pair :: Type > Type > Type
'Pair :: forall k1 k2. k1 > k2 > Pair k1 k2
Sum :: Type > Type > Type
'L :: k1 > Sum k1 k2
'R :: k2 > Sum k1 k2
Virtually all data constructors, even those with rich kinds, can be promoted. There are only a couple of exceptions to this rule:
Data family instance constructors cannot be promoted at the moment. GHC’s type theory just isn’t up to the task of promoting data families, which requires full dependent types.
Data constructors with contexts that contain nonequality constraints cannot be promoted. For example:
data Foo :: Type > Type where MkFoo1 :: a ~ Int => Foo a  promotable MkFoo2 :: a ~~ Int => Foo a  promotable MkFoo3 :: Show a => Foo a  not promotable
MkFoo1
andMkFoo2
can be promoted, since their contexts only involve equalityoriented constraints. However,MkFoo3
‘s context contains a nonequality constraintShow a
, and thus cannot be promoted.
6.4.10.3. Distinguishing between types and constructors¶
In the examples above, all promoted constructors are prefixed with a single
quote mark '
. This mark tells GHC to look in the data constructor namespace
for a name, not the type (constructor) namespace. Consider
data P = MkP  1
data Prom = P  2
We can thus distinguish the type P
(which has a constructor MkP
)
from the promoted data constructor 'P
(of kind Prom
).
As a convenience, GHC allows you to omit the quote mark when the name is
unambiguous. However, our experience has shown that the quote mark helps
to make code more readable and less errorprone. GHC thus supports
Wuntickedpromotedconstructors
that will warn you if you
use a promoted data constructor without a preceding quote mark.
Just as in the case of Template Haskell (Syntax), GHC gets confused if you put a quote mark before a data constructor whose second character is a quote mark. In this case, just put a space between the promotion quote and the data constructor:
data T = A'
type S = 'A'  ERROR: looks like a character
type R = ' A'  OK: promoted `A'`
6.4.10.4. Typelevel literals¶
DataKinds
enables the use of numeric and string literals at the
type level. For more information, see TypeLevel Literals.
6.4.10.5. Promoted list and tuple types¶
With DataKinds
, Haskell’s list and tuple types are natively
promoted to kinds, and enjoy the same convenient syntax at the type
level, albeit prefixed with a quote:
data HList :: [Type] > Type where
HNil :: HList '[]
HCons :: a > HList t > HList (a ': t)
data Tuple :: (Type,Type) > Type where
Tuple :: a > b > Tuple '(a,b)
foo0 :: HList '[]
foo0 = HNil
foo1 :: HList '[Int]
foo1 = HCons (3::Int) HNil
foo2 :: HList [Int, Bool]
foo2 = ...
For typelevel lists of two or more elements, such as the signature of
foo2
above, the quote may be omitted because the meaning is unambiguous. But
for lists of one or zero elements (as in foo0
and foo1
), the quote is
required, because the types []
and [Int]
have existing meanings in
Haskell.
Note
The declaration for HCons
also requires TypeOperators
because of infix type operator (':)
6.4.10.6. Promoting existential data constructors¶
Note that we do promote existential data constructors that are otherwise suitable. For example, consider the following:
data Ex :: Type where
MkEx :: forall a. a > Ex
Both the type Ex
and the data constructor MkEx
get promoted,
with the polymorphic kind 'MkEx :: forall k. k > Ex
. Somewhat
surprisingly, you can write a type family to extract the member of a
typelevel existential:
type family UnEx (ex :: Ex) :: k
type instance UnEx (MkEx x) = x
At first blush, UnEx
seems poorlykinded. The return kind k
is
not mentioned in the arguments, and thus it would seem that an instance
would have to return a member of k
for any k
. However, this is
not the case. The type family UnEx
is a kindindexed type family.
The return kind k
is an implicit parameter to UnEx
. The
elaborated definitions are as follows (where implicit parameters are
denoted by braces):
type family UnEx {k :: Type} (ex :: Ex) :: k
type instance UnEx {k} (MkEx @k x) = x
Thus, the instance triggers only when the implicit parameter to UnEx
matches the implicit parameter to MkEx
. Because k
is actually a
parameter to UnEx
, the kind is not escaping the existential, and the
above code is valid.
See also #7347.
6.4.10.7. Constraints in kinds¶
Kinds can (with DataKinds
) contain type constraints. However,
only equality constraints are supported.
Here is an example of a constrained kind:
type family IsTypeLit a where
IsTypeLit Nat = 'True
IsTypeLit Symbol = 'True
IsTypeLit a = 'False
data T :: forall a. (IsTypeLit a ~ 'True) => a > Type where
MkNat :: T 42
MkSymbol :: T "Don't panic!"
The declarations above are accepted. However, if we add MkOther :: T Int
,
we get an error that the equality constraint is not satisfied; Int
is
not a type literal. Note that explicitly quantifying with forall a
is
necessary in order for T
to typecheck
(see Complete usersupplied kind signatures and polymorphic recursion).