Version 3 (modified by ross@…, 12 years ago) (diff)

Existential Quantification

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Brief Explanation

Local existential quantification of type variables in a data constructor, introduced with forall before the data constructor, e.g.

data Accum a = forall s. MkAccum s (a -> s -> s) (s -> a)

The forall is justified by the type of the data constructor:

MkAccum :: s -> (a -> s -> s) -> (s -> a) -> Accum a

but some have suggested using exists instead to avoid confusion with PolymorphicComponents.



  • Hugs allows existential quantification for newtype declarations, as long as there are no class constraints.
    newtype T = forall a. C a
    GHC and Nhc98 do not.
  • Hugs and Nhc98 allow matching on an existentially quantified constructor in a pattern binding declaration, except at the top level.
    data T = forall a. C (a -> Int) a
    foo t = let C f x = t in f x
    GHC does not allow such matching.
  • None of the implementations can derive instances for existentially quantified types, but this could be relaxed, e.g
    data T = forall a. Show a => C [a]
            deriving Show
  • GHC 6.5 allows fields with existentially quantified types, though selectors may only be used if their type does not include the quantified variable.
    data T = forall a. C { f1 :: a, f2 :: Int }


  • quite handy for representations that delay composition or application, e.g. objects, various parser combinator libraries from Utrecht.