Haskell 用我的 state monad 标记二叉树的节点不起作用

Question

到目前为止，我编写了以下代码，我测试了所有功能，并且它们运行良好，但是测试 indexNodesM function，它不起作用，我认为 put 方法无法正常工作。

给定的测试用例是：

execState (indexNodesM exTree1) 0 == 6
evalState (indexNodesM exTree1) 0 == Node (5,3) (Node (3,1) Leaf (Node (2,11) (Node (0,7) Leaf Leaf) (Node (1,5) Leaf Leaf))) (Node (4,13) Leaf Leaf)

例如，执行execState (indexNodesM exTree1) 0会给出 0 作为结果。

我的代码：

{-# LANGUAGE InstanceSigs #-}


import Control.Monad (ap)


newtype State s a = S { runState :: s -> (a,s) }

evalState :: State s a -> s -> a
evalState (S f) s = fst (f s)

execState :: State s a -> s -> s
execState (S f) s = snd (f s)

instance Functor (State s) where
 fmap :: (a -> b) -> (State s a) -> (State s b)
 fmap f (S g) = S (\n -> (f (fst (g (n))), n))

instance Applicative (State s) where
  pure  = return
  (<*>) = ap 

instance Monad (State s) where
 return :: a -> (State s a)
 return a = S (\n -> (a, n))
 (>>=) :: (State s a) -> (a -> State s b) -> (State s b)
 (>>=) (S f) g   = S (\n -> runState (g (fst (f n))) (n))

get :: State s s
get = S (\n -> (n, n))

put :: s -> State s ()
put x = S (\n -> ((),x))

modify :: (a -> a) -> State a ()
modify f = S (\n -> ((),  f n))

data Tree a = Leaf | Node a (Tree a) (Tree a)
  deriving (Eq, Ord, Show)

exTree1 :: Tree Int
exTree1 =
  Node 3
    (Node 1
      Leaf
      (Node 11
        (Node 7
          Leaf
          Leaf)
        (Node 5
          Leaf
          Leaf)))
    (Node 13
      Leaf
      Leaf)

indexNodesM :: Tree a -> State Int (Tree (Int, a))
indexNodesM Leaf = return Leaf
indexNodesM (Node x tree1 tree2) = do
 i <- get
 put (i + 1)
 t1 <- indexNodesM tree1
 t2 <- indexNodesM tree2
 return (Node (i, x) t1 t2)

可能是什么问题呢？ 提前致谢。

Answer 1

欢迎来到堆栈溢出。 如果您修复了 State monad 的定义，那么它将按您的预期工作。 您当前实现的问题在于， >>=和fmap都没有真正更新 state，因为您总是使用fst将 state 扔掉，然后使用旧的 state。 这是更正后的实现：

import Control.Monad (ap, liftM)

...

instance Functor (State s) where
 fmap = liftM

instance Applicative (State s) where
  pure  = return
  (<*>) = ap

instance Monad (State s) where
 return :: a -> (State s a)
 return a = S (\n -> (a, n))
 (>>=) :: (State s a) -> (a -> State s b) -> (State s b)
 (>>=) (S f) g   = S (\n -> let (a, n') = f n in runState (g a) n')

现在您的测试用例几乎可以按预期工作，除了indexNodesM标记节点：

*Main> execState (indexNodesM exTree1) 0 == 6
True

*Main> evalState (indexNodesM exTree1) 0
Node (0,3) (Node (1,1) Leaf (Node (2,11) (Node (3,7) Leaf Leaf) (Node (4,5) Leaf Leaf))) (Node (5,13) Leaf Leaf)