我必须实现Applicative和Functor来实现Monad

Question

I'm trying to implement a Monad instance. As a simpler example, assume the following:

data Maybee a = Notheeng | Juust a 

instance Monad Maybee where
   return x = Juust x
   Notheeng >>= f = Notheeng
   Juust x >>= f = f x
   fail _ = Notheeng 

This should be the standard implementation of Maybe as far as I know. However, this doesn't compile, because the compiler complains:

No instance for (Applicative Maybee)

and similarly he wants a Functor instance once the Applicative is given.

So: Simple question: Must I always implement Functor and Applicative before I can implement a Monad?

Answer 1

是的，事实并非如此，这是ghc7.10中以Functor-Applicative-Monad Proposal名义引入的变化。

Answer 2

It is compulsory to define instances for Functor and Applicative (the second one is a new requirement in newer versions of Haskell), but it's actually no big deal because if you don't want to hand-write your own instances you can just use these ones:

import Control.Applicative (Applicative(..))
import Control.Monad       (liftM, ap)

-- Monad m

instance Functor m where
    fmap = liftM

instance Applicative m where
    pure  = return
    (<*>) = ap

Answer 3

With GHC 7.10 and above, you must implement Functor and Applicative . The class definitions for Monad mandate the superclass instances:

class Functor f => Applicative f where ...
class Applicative m => Monad m where ...

Note that once you have a Monad instance, the Functor and Applicative instances can be defined generically with no additional effort:

import Control.Monad

-- suppose we defined a Monad instance:
instance Monad m where ...

instance Functor m where
    fmap = liftM

instance Applicative m where
    pure = return
    (<*>) = ap