[Haskell-cafe] Applicative/Monad for Either

[Tony Morris]

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In the code below, the Applicative instance accumulates on the Left
constructor using Monoid/mappend.
Is it possible to write an equivalent Monad such that ap = (<*>) ? I'm
finding difficulty in proving to myself either way.




import Control.Monad.Instances
import Control.Applicative
import Data.Monoid

newtype Z e a = Z {
  either :: Either e a
}

instance Functor (Z e) where
  fmap f (Z e) = Z (f `fmap` e)

instance (Monoid e) => Applicative (Z e) where
  pure = Z . Right
  (Z (Left e1)) <*> (Z (Left e2)) = Z (Left (e1 `mappend` e2))
  (Z (Left e1)) <*> (Z (Right _)) = Z (Left e1)
  (Z (Right _)) <*> (Z (Left e2)) = Z (Left e2)
  (Z (Right f)) <*> (Z (Right a)) = Z (Right (f a))

instance (Monoid e) => Monad (Z e) where
  return = pure
  (Z e) >>= f = error "todo" -- ?

- --
Tony Morris
http://tmorris.net/

S, K and I ought to be enough for anybody.

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