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Impredicative types

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Impredicative types are to be contrasted with rank-N types.

A standard Haskell type is universally quantified by default, and quantifiers can only appear at the top level of a type or to the right of function arrows.

A higher-rank polymorphic type allows universal quantifiers to appear to the left of function arrows as well, so that function arguments can be functions that are themselves polymorphic.

An impredicative type, on the other hand, allows universal quantifiers anywhere: in particular, may contain ordinary datatypes with polymorphic components. The GHC User's Guide gives the following example:

f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
f (Just g) = Just (g [3], g "hello")
f Nothing  = Nothing
Impredicative types are enabled in GHC with the
{-# LANGUAGE ImpredicativeTypes #-}
pragma. They are among the less well-used and well-tested language extensions, and so some caution is advised in their use. They are rarely needed in practice.

See also

* The GHC User's Guide on impredicative polymorphism.