Implementing MyStateT

MyStateT.hs

data MyStateT s m a = MyStateT (s -> m (a, s))

runStateT :: MyStateT s m a -> s -> m (a, s)
runStateT = \ (MyStateT f) s -> f s

get :: Monad m => MyStateT s m s
get = MyStateT $ \ s -> return (s, s)

put :: Monad m => s -> MyStateT s m ()
put = \ s -> MyStateT $ \ s' -> return ((), s)

modify :: Monad m => (s -> s) -> MyStateT s m ()
modify = \ f -> MyStateT $ \ s -> return ((), f s)

instance Functor m => Functor (MyStateT s m) where
  -- fmap :: (a -> b) -> (MyStateT s m) a -> (MyStateT s m) b
  fmap = \ f g -> MyStateT $ \ s -> let x = runStateT g s
                                        f' = \ (a, s) -> (f a, s)
                                    in fmap f' x

instance (Functor m, Monad m) => Applicative (MyStateT s m) where
  -- pure :: a -> (MyStateT s m) a
  pure = return
  -- (<*>) :: (MyStateT s m) (a -> b) -> (MyStateT s m) a -> (MyStateT s m) b
  (<*>) = \ f g -> MyStateT $ \ s -> do (f', s') <- runStateT f s
                                        (a', s'') <- runStateT g s'
                                        return (f' a', s'')

instance Monad m => Monad (MyStateT s m) where
  -- return :: a -> (MyStateT s m) a
  return = \ a -> MyStateT $ \ s -> return (a, s)
  -- (>>=) :: (MyStateT s m) a -> (a -> (MyStateT s m) b) -> (MyStateT s m) b
  (>>=) = \ m f -> MyStateT $ \ s -> do (a, s') <- runStateT m s
                                        let k = f a
                                        runStateT k s'

type MyState s = MyStateT s Identity

runState :: MyState s a -> s -> (a, s)
runState = \ m s -> runIdentity (runStateT m s)