All Applicatives have those two variants, not just Applicatives which are also Monads. There is a Backwards newtype in Control.Applicative.Backwards which reverses the order of effects for any Applicative:

    GHCi> import Control.Applicative.Backwards
    GHCi> :i Backwards
    newtype Backwards (f :: k -> *) (a :: k)
      = Backwards {forwards :: f a}
    GHCi> forwards $ (++) <$> Backwards ("foo" <$ print 1) <*> Backwards ("bar" <$ print 2)
    2
    1
    "foobar"

As you can see, the result is the same but the effects are reversed. The definition is simple:

    instance Applicative f => Applicative (Backwards f) where
       pure = Backwards . pure
       Backwards f <*> Backwards a = Backwards $ (flip ($)) <$> a <*> f