Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Functional programming, design and analysis of algorithms / 1 / d

Application binds more tightly than function composition, and (.) associates to the right. Let

g :: a -> b -> c

Then y :: a and g y :: b -> c. To compose to its left, h x must have type c -> a, so x :: d and h :: d -> c -> a. The outer occurrence of g receives that a, producing a function of type b -> c. Consequently g . h x . g y has type b -> b -> c, and the principal type is f :: (a -> b -> c) -> (d -> c -> a) -> d -> a -> b -> b -> c. No Haskell type class constraint is introduced.