[Haskell-beginners] EitherT

[mike h]

Hi,
I’m trying to write EitherT from first principles and I’m stuck at the first hurdle - Functor.  I’m looking for a hint rather than a complete answer :) 


This is what I have

newtype EitherT m a b = EitherT {runEitherT :: m (Either a b)}
instance Monad m => Functor (EitherT m a) where
    ---- fmap :: (a -> b) -> f a -> f b
    fmap f m = EitherT $ do
        mv <- runEitherT m
        case mv of
            Left _   -> return mv
            Right rv -> return $ Right (f rv)



and here is the compilers view
Phrase.hs:31:25: error:
    • Couldn't match type ‘b’ with ‘a1’
      ‘b’ is a rigid type variable bound by
        the type signature for:
          fmap :: forall a1 b. (a1 -> b) -> EitherT m a a1 -> EitherT m a b
        at Phrase.hs:27:5-8
      ‘a1’ is a rigid type variable bound by
        the type signature for:
          fmap :: forall a1 b. (a1 -> b) -> EitherT m a a1 -> EitherT m a b
        at Phrase.hs:27:5-8
      Expected type: m (Either a a1)
        Actual type: m (Either a b)
    • In the expression: return $ Right (f rv)
      In a case alternative: Right rv -> return $ Right (f rv)
      In a stmt of a 'do' block:
        case mv of
          Left _ -> return mv
          Right rv -> return $ Right (f rv)
    • Relevant bindings include
        rv :: a1 (bound at Phrase.hs:31:19)
        mv :: Either a a1 (bound at Phrase.hs:28:9)
        m :: EitherT m a a1 (bound at Phrase.hs:27:12)
        f :: a1 -> b (bound at Phrase.hs:27:10)
        fmap :: (a1 -> b) -> EitherT m a a1 -> EitherT m a b
          (bound at Phrase.hs:27:5)
   

what I think I need to do is fmap over the right value after pulling if out of the monad m by doing   mv <- runEitherT m

these lines from the compiler are particularly confusing 
      Expected type: m (Either a a1)
        Actual type: m (Either a b)

as I believe f is    f:: a1->b 

So just hints please and I expect I’ll have another duh moment. 

Thanks

Mike