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 type-level natural numbers, and length-indexed 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 well-kinded type, even though this is not what we intend when defining length-indexed 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 ill-kinded, 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 non-equality 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 and MkFoo2 can be promoted, since their contexts only involve equality-oriented constraints. However, MkFoo3‘s context contains a non-equality constraint Show 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 error-prone. GHC thus supports -Wunticked-promoted-constructors 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. Type-level literals¶

DataKinds enables the use of numeric and string literals at the type level. For more information, see Type-Level 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 type-level 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 type-level existential:

type family UnEx (ex :: Ex) :: k
type instance UnEx (MkEx x) = x

At first blush, UnEx seems poorly-kinded. 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 kind-indexed 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.

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 user-supplied kind signatures and polymorphic recursion).