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?
最佳答案
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})}
关于haskell - 代表无限链 Action 的 Monad 转换器?,我们在Stack Overflow上找到一个类似的问题: https://stackoverflow.com/questions/67067754/