我试图实现一个表示无限动作链的 monad 转换器，如下所示：

import Control.Arrow
import Control.Monad
import Data.Functor.Classes
import Data.Functor.Identity
import Data.Monoid
import Data.Semigroup
import Text.Read

import qualified Control.Monad.Trans.Class as T

newtype WhileT m a = WhileT {uncons :: m (a, WhileT m a)}

instance T.MonadTrans WhileT where
    lift m = WhileT $ do
        x <- m
        pure (x, T.lift m)

headW :: Functor m => WhileT m a -> m a
headW (WhileT m) = fmap fst m

tailW :: Functor m => WhileT m a -> m (WhileT m a)
tailW (WhileT m) = fmap snd m

drop1 :: Monad m => WhileT m a -> WhileT m a
drop1 m = WhileT (tailW m >>= uncons)

dropN :: Monad m => Int -> WhileT m a -> WhileT m a
dropN n = appEndo (stimes n (Endo drop1))

instance Functor m => Functor (WhileT m) where
    fmap f (WhileT m) = WhileT (fmap (f *** fmap f) m)

instance Monad m => Applicative (WhileT m) where
    pure x = WhileT (pure (x, pure x))
    (<*>) = ap

instance Monad m => Monad (WhileT m) where
    WhileT m >>= f = WhileT $ do
        (x, xs) <- m
        y <- headW (f x)
        let ys = xs >>= drop1 . f
        pure (y, ys)

名称WhileT在 C 之后while。很容易看出这WhileT Identity是一个monad。

但是其他的选择m呢？特别是，从一些实验来看，WhileT Maybe似乎等价于ZipList。但已经知道没有instance Monad ZipList。这是否意味着WhileT它不是真正的 monad 转换器？

回答

-- to make these things a bit more convenient to type/read
fromListW :: [a] -> WhileT Maybe a
fromListW [] = WhileT Nothing
fromListW (x:xs) = WhileT (Just (x, fromListW xs))

xs = fromListW [1,2]

f 1 = fromListW [11]
f 2 = fromListW [21, 22]

g 11 = fromListW [111]
g 21 = fromListW []
g 22 = fromListW [221, 222]

> (xs >>= f) >>= g
WhileT {uncons = Just (111,WhileT {uncons = Just (222,WhileT {uncons = Nothing})})}
> xs >>= (x -> f x >>= g)
WhileT {uncons = Just (111,WhileT {uncons = Nothing})}