[Haskell-cafe] Examples of useful functions of order >= 3?

[Ben Lippmeier]

Hi all,

I'm working on a type-based side effect analysis for a Haskell-like
language, and need to test it against some more higher order functions.
The situation is a bit icky because it uses bounded quantification
and various related issues (ie covariance vs contravariance) only
come into play when dealing with functions of order >= 3.

Trouble is, the vast majority of useful higher order functions
that I can think of are of order 2. Oh, I can certainly invent toys
like:

order3 f   = f succ
order4 b f = if b then f else order3

.. and so on, but I'm left feeling unsatisfied.

I vaguely remember a paper called something like "Is there any use
for a seventh order function?", but I forget why they were used, and
I can't find it on Google, or ACM or any of the other likely places.

Does anyone have any examples of code (in whatever language) which
usefully uses functions of order >= 3?? Preferably up to 5?

Thanks,
Ben.