MonadFix :+: instance for GHC Generics

Motivation

I was reading Control.Monad.Fix in base and noticed that there was no instance for :+:. But there are instances for several concrete sum types like Maybe, Either, and [], so there doesn't seem to be a reason to omit it.

Proposal

As noted in Erkok's thesis, Remark 2.6.4, for any monad based on a sum type, f of bottom determines the top level structure of mfix f. Erkok in fact provides an alternative MonadFix Maybe instance based on pattern-matching f undefined (eqn 4.3). My proposed instance for :+: is thus along the same lines:

instance (MonadFix f, MonadFix g) => MonadFix (f :+: g) where 
  mfix f = case f undefined of
   L1 _ -> L1 $ mfix (\x -> case f x of L1 y -> y)
   R1 _ -> R1 $ mfix (\x -> case f x of R1 y -> y)

There doesn't seem to be a testsuite for MonadFix but a few examples show that my instance works similarly to the existing instances:

f, f2, f3 :: [Integer] -> Maybe [Integer]
f = const Nothing
f2 = \x -> Just (take 100 (1:x))
f3 = Just
test f = mfix f == to1 (mfix (from1 . f))
main = print [test f, test f2, test f3] -- [True,True,<infinite loop>]

It was a little tricky to test it due to the Monad constraint on MonadFix. Perhaps the difficulty arises from deciding how to implement pure for :+:? I think most people would be happy with an instance that was right-biased like Either, pure = R1 pure. Or the instance could have a constraint instance (MonadFix f, MonadFix g, Monad (f :+: g)) => MonadFix (f :+: g) with UndecidableInstances and leave it to the user to write an instance.