Your definition of order is not the standard one!

Usually one would have:

    zerothOrderFunction :: a
    firstOrderFunction :: a -> b
    firstOrderFunction' :: a -> (b -> c)
    SecondOrderFunction :: (a -> b) -> c

After all, the functions firstOrderFunction and firstOrderFunction' are the same up to currying.

The standard definition of order is given here (at the end of the section):

https://en.wikipedia.org/wiki/Simply_typed_lambda_calculus#T...