http://hackage.haskell.org/package/base-4.7.0.1/docs/Control-Applicative.htm... says that The other methods have the following default definitions, which may be overridden with equivalent specialized implementations: u *> v = pure (const id) <*> u <*> v and If f is also a Monad, it should satisfy ... (<*>) = ap The (potential) trouble is that these have higher arities than is always natural. For example, it would seem reasonable to say (<*>) Just f = fmap f (<*>) Nothing = const Nothing and to replace the default definition of (*>) like so: (*>) a1 = (<*>) (id <$ a1) but these are not strictly equivalent because they have arity 1 instead of arity 2. Would such definitions be be better in some cases? If so, should we weaken the rules a bit?