Past exam of the computer science course of the University of Oxford / 2015 / Principles of programming languages / 2 / a / Solution

The continuation receives both the computed value and the current computer memory. Therefore return invokes it with unchanged computer memory, while sequencing installs a continuation that passes the produced value and updated computer memory to the next computation:

result :: a -> M a
result x k s = k x s

bind :: M a -> (a -> M b) -> M b
bind p f k s = p (\x s' -> f x k s') s

For left identity, expand the two definitions:For right identity,For associativity, both groupings reduce to the same expression:By function extensionality, these establish all three monad laws: