A monad transformer for Identity

IdentityT.hs

import Control.Applicative
import Control.Monad
import Control.Monad.Trans.Class
import Data.Functor.Identity

newtype IdentityT m a = IdentityT { runIdentityT :: m (Identity a) }

instance Functor f => Functor (IdentityT f) where
  fmap f = IdentityT . fmap (fmap f) . runIdentityT

instance Applicative a => Applicative (IdentityT a) where
  pure = IdentityT . pure . pure
  f <*> a = IdentityT $ liftA2 (<*>) (runIdentityT f) (runIdentityT a)

instance Monad m => Monad (IdentityT m) where
  return = IdentityT . return . Identity
  x >>= f = IdentityT $ runIdentityT x >>= (runIdentityT . f . runIdentity)

instance MonadTrans IdentityT where
  lift m = IdentityT (liftM Identity m)
  
testT :: IdentityT IO String
testT = lift getLine

main :: IO ()
main = do
  a <- runIdentityT testT
  putStrLn $ runIdentity a