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.. _impredicative-polymorphism:
Impredicative polymorphism
==========================
.. extension:: ImpredicativeTypes
:shortdesc: Enable impredicative types.
Implies :extension:`RankNTypes`.
:implies: :extension:`RankNTypes`
:since: 6.10.1
Allow impredicative polymorphic types.
In general, GHC will only instantiate a polymorphic function at a
monomorphic type (one with no foralls). For example, ::
runST :: (forall s. ST s a) -> a
id :: forall b. b -> b
foo = id runST -- Rejected
The definition of ``foo`` is rejected because one would have to
instantiate ``id``\'s type with ``b := (forall s. ST s a) -> a``, and
that is not allowed. Instantiating polymorphic type variables with
polymorphic types is called *impredicative polymorphism*.
GHC has extremely flaky support for *impredicative polymorphism*,
enabled with :extension:`ImpredicativeTypes`. If it worked, this would mean
that you *could* call a polymorphic function at a polymorphic type, and
parameterise data structures over polymorphic types. For example: ::
f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
f (Just g) = Just (g [3], g "hello")
f Nothing = Nothing
Notice here that the ``Maybe`` type is parameterised by the
*polymorphic* type ``(forall a. [a] -> [a])``. However *the extension
should be considered highly experimental, and certainly un-supported*.
You are welcome to try it, but please don't rely on it working
consistently, or working the same in subsequent releases. See
:ghc-wiki:`this wiki page <impredicative-polymorphism>` for more details.
If you want impredicative polymorphism, the main workaround is to use a
newtype wrapper. The ``id runST`` example can be written using this
workaround like this: ::
runST :: (forall s. ST s a) -> a
id :: forall b. b -> b
newtype Wrap a = Wrap { unWrap :: (forall s. ST s a) -> a }
foo :: (forall s. ST s a) -> a
foo = unWrap (id (Wrap runST))
-- Here id is called at monomorphic type (Wrap a)
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