Also worth considering:

manyM :: (Alternative f, Monad f) => f a -> f [a]
manyM v = many_v
    where
        many_v = do
          ma <- optional v
          case ma of
            Nothing -> pure []
            Just a -> liftA2 (:) a many_v

someM :: (Alternative f, Monad f) => f a -> f [a]
someM v = liftA2 (:) v (manyM v)

Unlike the default definitions, these bound backtracking when (<|>) represents that.

On Sat, Aug 11, 2018, 1:19 PM David Feuer <david.feuer@gmail.com> wrote:
We currently offer liftA, liftM, liftM2, and ap to implement Functor and Applicative methods in terms of Applicative and Monad ones. But there are a couple other functions in that general vein that are missing. I propose that we should add at least replaceA, and perhaps also beforeM.

-- (<$) = replaceA
-- This may be better than the default if there is
-- an optimized definition of *> (which may be
-- based on an optimized >>).
replaceA :: Applicative f => a -> f x -> f a
replaceA a fa = fa *> pure a

-- (<*) = beforeM
-- This may be better than the default if there is
-- an optimized definition of <$, or if <$ is defined as 
-- replaceA and *> is optimized.
beforeM :: Monad f => f a -> f x -> f a
beforeM fa fx = fa >>= \a -> a <$ fx

Why a <$ fx and not fx >> pure a? Because <$ could be implemented specially, and is unlikely to be implemented by hand using <* if there isn't a custom <*.