haskell - 代表无限链 Action 的 Monad 转换器？

Question

我试图实现一个代表无限链 Action 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)

姓名 WhileT在 C 的 while 之后.很容易看出 WhileT Identity是一个单子(monad)。
但是 m 的其他选择呢？ ?特别是，通过一些实验判断， WhileT Maybe似乎相当于 ZipList .但是已经知道没有 instance Monad ZipList .这是否意味着 WhileT真的不是单子(monad)变压器吗？
编辑
看来这是正确的实现方式 instance Monad (WhileT m) :

import Control.Applicative

instance MonadPlus m => Applicative (WhileT m) where
    pure x = WhileT (pure (x, empty))
    liftA2 = liftM2
    (<*>) = ap

instance MonadPlus m => Alternative (WhileT m) where
    empty = WhileT empty
    WhileT xs <|> WhileT ys = WhileT (xs <|> ys)

instance MonadPlus m => Monad (WhileT m) where
    WhileT xs >>= f = WhileT $ do
        (y, ys) <- xs
        uncons (f y) <|> uncons (ys >>= f)

instance MonadPlus m => MonadPlus (WhileT m)

现在 WhileT Identity甚至不是一个单子(monad)，但是嘿，它只是 (->) Natural .
现在 WhileT Maybe相当于 [] .现在呢？ m 任意选择在哪里 WhileT m违反单子(monad)定律？

Answer 1

this link 的反例为您的 WhileT Maybe 工作， 也。

-- 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]

然后，在 ghci 中:

> (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})}