> @Matthew -- re:
> while `Maybe a` is not necessarily a monoid, `Maybe [a]` *is*
> This seems to be a special case of a more general result, namely that if `Moo` is a monoid, then we can define a canonical monoid structure on `Maybe Moo`.
> The unit is `Nothing`, and we define `(Just x) <> (Just y)` to be `Just (x <> y)`.
You are absolutely right!
Haskell's defines the instance `Semigroup a => Semigroup (Maybe a)` in the [Prelude](https://hackage.haskell.org/package/base-188.8.131.52/docs/src/GHC.Base.html#line-406), following your specification:
instance Semigroup a => Semigroup (Maybe a) where
Nothing <> b = b
a <> Nothing = a
Just a <> Just b = Just (a <> b)
And the *unit* for this monoid is defined in [Data.Monoid](https://hackage.haskell.org/package/base-184.108.40.206/docs/src/GHC.Base.html#line-422), again exactly as you suggest:
instance Semigroup a => Monoid (Maybe a) where
mempty = Nothing