单子内的值，嵌套在数据结构中？

Question

假设在 Haskell 程序中我有一些数据，其类型如下：

• IO [ IO (Int, String, Int) ], ， 或者
• IO [ (Int, String, IO Int) ], ， 或者
• [ (Int, String, IO Int) ]

但我有应该运行的纯函数 [ (Int, String, Int) ]. 。看来我必须笨拙地从 IO monad 中删除内部值，直到我得到类似 IO [ (Int, string, Int) ] 的东西，然后（从 IO monad 内部）应用纯函数。我想没有简单的预定义方法可以做到这一点？它将整个数据结构提升为一个单子，将所有 里面 类型转换为纯类型？（那会非常方便！）

Answer 1

你可以使用 liftM* 函数从 控制单子 模块，或 liftA* 函数为 应用词.

liftM 允许您提升纯函数以在 Monad 内工作，例如：

ghci> let s = return "Hello" :: IO String
ghci> liftM reverse s
"olleH"

这样你就不必手动编写诸如“s >>= \x -> return (reverse x)“无处不在。

虽然，这不会帮助你 [(String, Int, IO Int)] 例如，如果您的纯函数处理 [(String, Int, Int)]. 。由于元组中的第三个元素实际上不是 Int.

在这种情况下我建议先写一个函数 [(String, Int, IO Int)] -> IO [(String, Int, Int)] 并应用提升的纯函数。

---

这是我能想到的最通用的函数：

conv :: Monad m => (f (m a) -> m (f a)) -> [f (m a)] -> m [f a]
conv f = sequence . map f

你可以这样称呼它：

liftTrd :: Monad m => (a, b, m c) -> m (a, b, c)
liftTrd (x, y, mz) = mz >>= \z -> return (x, y, z)

conv liftTrd [("hi", 4, return 2)] :: IO [(String, Int, Int)]

仅当您有一个位于类型深处的单个 monad 时，此函数才会起作用。如果你有多个，我认为你真的应该考虑一下你使用的类型，看看是否不能让它变得更简单。

Answer 2

首先是下面的解决方案的一些使用示例 reduce （除非您建议更好的名称）：

> reduce [(["ab", "c"], "12")] :: [(String, String)]
[("ab","12"),("c","12")]

> reduce [(["ab", "c"], "12")] :: [(Char, Char)]
[('a','1'),('a','2'),('b','1'),('b','2'),('c','1'),('c','2')]

> reduce [("ab", "12"), ("cd", "3")] :: [(Char, Char)]
[('a','1'),('a','2'),('b','1'),('b','2'),('c','3'),('d','3')]

你的例子也用它解决了：

complexReduce :: Monad m => m (m (a, b, m [m (c, m d)])) -> m (a, b, [(c, d)])
complexReduce = reduce

并实施 reduce:

{-# LANGUAGE FlexibleContexts, FlexibleInstances, IncoherentInstances, MultiParamTypeClasses, UndecidableInstances #-}

import Control.Monad

-- reduce reduces types to simpler types,
-- when the reduction is in one of the following forms:
-- * make a Monad disappear, like join
-- * move a Monad out, like sequence
-- the whole magic of Reduce is all in its instances
class Reduce s d where
  reduce :: s -> d

-- Box is used only for DRY in Reduce instance definitions.
-- Without it we, a Reduce instance would need
-- to be tripled for each variable:
-- Once for a pure value, once for a monadic value,
-- and once for a reducable value
newtype Box a = Box { runBox :: a }
instance Monad m => Reduce (Box a) (m a) where
  reduce = return . runBox
instance Reduce a b => Reduce (Box a) b where
  reduce = reduce . runBox
redBox :: Reduce (Box a) b => a -> b
redBox = reduce . Box

-- we can join
instance (Monad m
  , Reduce (Box a) (m b)
  ) => Reduce (m a) (m b) where
  reduce = join . liftM redBox

-- we can sequence
-- * instance isnt "Reduce [a] (m [b])" so type is always reduced,
--   and thus we avoid overlapping instances.
-- * we cant make it general for any Traversable because then
--   the type system wont find the right patterns.
instance (Monad m
  , Reduce (Box a) (m b)
  ) => Reduce (m [a]) (m [b]) where
  reduce = join . liftM (sequence . fmap redBox)

instance (Monad m
  , Reduce (Box a) (m c)
  , Reduce (Box b) (m d)
  ) => Reduce (a, b) (m (c, d)) where
  reduce (a, b) = liftM2 (,) (redBox a) (redBox b)

instance (Monad m
  , Reduce (Box a) (m d)
  , Reduce (Box b) (m e)
  , Reduce (Box c) (m f)
  ) => Reduce (a, b, c) (m (d, e, f)) where
  reduce (a, b, c) =
    liftM3 (,,) (redBox a) (redBox b) (redBox c)