Don't make the mistake of thinking that translating a type signature into written English gives a canonical description of the function. The first definition sa

Don't make the mistake of thinking that translating a type signature into written English gives a canonical description of the function. The first definition says "(a -> b) -> f a -> f b" - that is it. You can translate one into the other easily map' :: (a -> b) -> f a -> f b map' i j = map'' j i map'' :: f a -> (a -> b) -> f b map'' m n = map' n m