Impredicative types

Impredicative types are an advanced form of polymorphism, 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.

See also

• The GHC User's Guide on impredicative polymorphism.
• A Pythonesque EDSL that makes use of impredicative polymorphism