.. _promotion:

Datatype promotion
==================

.. extension:: DataKinds
    :shortdesc: Enable datatype promotion.

    :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
:extension:`DataKinds`, and described in more detail in the paper `Giving
Haskell a Promotion <https://dreixel.net/research/pdf/ghp.pdf>`__, which
appeared at TLDI 2012.

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 (:ref:`type-families`) or GADTs
(:ref:`gadt`), 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 :extension:`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.

Overview
--------

With :extension:`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 = MkPair a b

    data Sum a b = L a | R b

give rise to the following kinds and type constructors: ::

    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
    MkPair :: 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.

.. _promotion-syntax:

Distinguishing between types and constructors
---------------------------------------------

Consider ::

    data P = MkP    -- 1

    data Prom = P   -- 2

The name ``P`` on the type level will refer to the type ``P`` (which has
a constructor ``MkP``) rather than the promoted data constructor
``P`` of kind ``Prom``. To refer to the latter, prefix it with a
single quote mark: ``'P``.

This syntax can be used even if there is no ambiguity (i.e.
there's no type ``P`` in scope).

GHC supports :ghc-flag:`-Wunticked-promoted-constructors` that warns
whenever a promoted data constructor is written without a quote mark.
As of GHC 9.4, this warning is no longer enabled by :ghc-flag:`-Wall`;
we no longer recommend quote marks as a preferred default
(see :ghc-ticket:`20531`).

Just as in the case of Template Haskell (:ref:`th-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'`

Type-level literals
-------------------

:extension:`DataKinds` enables the use of numeric and string literals at the
type level. For more information, see :ref:`type-level-literals`.

.. _promoted-lists-and-tuples:

Promoted list and tuple types
-----------------------------

With :extension:`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 :extension:`TypeOperators`
    because of infix type operator ``(':)``


.. _promotion-existentials:

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.

See also :ghc-ticket:`7347`.

.. _constraints_in_kinds:

Constraints in kinds
--------------------

Kinds can (with :extension:`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 :ref:`complete-kind-signatures`).
