Haskell's Either v. Error

Question

Learn You a Haskell presents Error:

instance (Error e) => Monad (Either e) where  
    return x = Right x   
    Right x >>= f = f x  
    Left err >>= f = Left err  
    fail msg = Left (strMsg msg) 

Hackage presents Either:

data Either a b = Left a | Right b

If I understand correctly, then Error is a Monad with Either as it's a type. Also, it looks like there's a fail to handle exceptions.

But, I also see that there's a Control.Monad.Either too - http://hackage.haskell.org/package/category-extras-0.53.4/docs/Control-Monad-Either.html.

Why would Control.Monad.Error be chosen over Control.Monad.Either, and vice-versa?

Answer 1

No, Error is not a monad. Either e is a monad, and Error e was a typeclass prerequisite for the Monad instance for Either e to exist. Basically Error e means that e is a type which you can convert error messages into with strMsg, which was used for Either e's fail method.

However, people found this requirement to have an Error e instance just to be able to use Either e as a monad annoying, so after LYAH was written it was actually removed. Now the instance is just

instance Monad (Either e) where
    return = Right
    Left  l >>= _ = Left l
    Right r >>= k = k r

and fail instead uses the default from the Monad class definition:

fail s      = error s

However, the Error e requirement is still (as of newest Haskell Platform at least) required for the monads and transformers defined in Control.Monad.Error, while Control.Monad.Either leaves out that requirement.