Your definition of order is not the standard one! Usually one would have: zerothOrderFunction :: a firstOrderFunction :: a -> b firstOrderFunction

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