How exactly does the `(<*>) = ap` Applicative/Monad law relate the two classes?

Question

ap doesn\'t have a documented spec, and reads with a comment pointing out it could be <*>, but isn\'t for practical reasons:

Answer 1

Every Monad gives rise to an Applicative, and for that induced Applicative, <*> = ap will hold definitionally. But given two structures - Monad m and Applicative m - there is no guarantee that these structures agree without the two laws <*> = ap and pure = return. For example, take the 'regular' Monad instance for lists, and the zip-list Applicative instance. While there is nothing fundamentally 'wrong' about a Monad and Applicative instance disagreeing, it would probably be confusing to most users, and so it's prohibited by the Monad laws.

tl;dr The laws in question serve to ensure that Monad and Applicative agree in an intuitively obvious way.