如何解决代表无限动作链的 Monad 转换器?
我尝试实现一个表示无限动作链的单子转换器,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 的 while
之后。很容易看出 WhileT Identity
是一个 monad。
但是 m
的其他选择呢?特别是,从一些实验来看,WhileT Maybe
似乎等价于ZipList
。但是已经知道没有instance Monad ZipList
。这是否意味着 WhileT
不是真正的 monad 转换器?
解决方法
this link 的反例也适用于您的 WhileT Maybe
。
-- 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})}
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