[Haskell-cafe] monoids and monads

[John Lato]

Hello,

I was wondering today, is this generally true?

instance (Monad m, Monoid a) => Monoid (m a) where
  mempty = return mempty
  mappend = liftM2 mappend

I know it isn't a good idea to use this instance, but assuming that
the instance head does what I mean, is it valid?  Or more generally is
it true for applicative functors as well?  I think it works for a few
tricky monads, but that's not any sort of proof.  I don't even know
how to express what would need to be proven here.

Any resources for how I could develop a means to reason about this
sort of property?

Thanks,
John