What's the highest order function used in practice?

Question

For instance, mask in Haskell is of type (((forall a . IO a -> IO a) -> IO b) -> IO b). What is the purpose of such a function? Any language with a notion of a higher-order function is welcome.

For purposes of exactness, include only functions which are defined in public libraries or in use in live code.

Answer 1

Okasaki exhibits a 6th order function: Even Higher-Order Functions for Parsing or Why Would Anyone Ever Want To Use a Sixth-Order Function?