Monad for Const?

Question

Why is there no monad instance for Control.Applicative.Const? Is following definition correct, or violates it the monad laws?

instance Monoid a => Monad (Const a) where
  return _ = Const mempty
  (Const x) >>= _ = Const x

And can you think of any useful application?

Answer 1

It violates the left identity law: return x >>= f must be the same as f x, but consider f x = Const (x + 1).