Haskell语言学习笔记（10）Writer Monad

Writer 是 Monad

旧的定义

newtype Writer w a = Writer { runWriter :: (a, w) }instance (Monoid w) => Monad (Writer w) where    return x = Writer (x, mempty)    (Writer (x,v)) >>= f = let (Writer (y, v')) = f x in Writer (y, v `mappend` v')

这里旧的定义是指API更改之前的定义，也就是Learn You a Haskell for Great Good!（中文版Haskell趣学指南）这本书中的定义。

• newtype Writer w a = Writer { runWriter :: (a, w) }
  这里 Writer 类型是个 newtype，也就是对现有类型的封装。Writer 类型有两个类型参数：表示状态的类型参数 w 以及表示结果的类型参数 a。
  这里 Writer 类型封装的是一对值：(a,w)，包括结果值 a 和状态值 w。通过 runWriter 字段可以从 Writer 类型中取出这对值。
  
• instance (Monoid w) => Monad (Writer w) where
  (Writer w) 类型是 Monad 类型类的一个实例，前提是 w 类型是 Monoid 类型类的一个实例。
  对比 Monad 类型类的定义，可知 return 函数的类型签名为：
  return :: x -> Writer w x
  而 bind 函数的类型签名为：
  (>>=) :: Writer w a -> (a -> Writer w a) -> Writer w a
• return x = Writer (x, mempty)
  return 函数将结果值设为 x, 状态值设为单位元。
  
• (Writer (x,v)) >>= f = let (Writer (y, v')) = f x in Writer (y, v `mappend` v')
  对比函数签名，可知 f 的类型为 (a -> Writer w a)。
  bind组合函数首先计算 f x，即是用原来的结果值 x 来调用 f，其结果为新的结果值 y 以及新的状态值 v'。
  然后将结果值设为新的结果值 y，状态值则设为原来的状态值 v 与新的状态值 v' 联结后的值。

新的定义

newtype WriterT w m a = WriterT { runWriterT :: m (a, w) }instance (Monoid w, Monad m) => Monad (WriterT w m) where    return a = WriterT $ return (a, mempty)    m >>= k  = WriterT $ do        ~(a, w)  <- runWriterT m        ~(b, w') <- runWriterT (k a)        return (b, w `mappend` w')type Writer w = WriterT w Identity

根据新的定义，Writer 类型只是 WriterT 类型的一个特例。

Writer Monad 函数

• writer (a,w)：将一对结果值和状态值封装进Writer Monad。
• tell w：将状态值设为 w，结果值设为空。
• listen (a,w)：将结果值设为 (a,w)，状态值设为 w。
• pass ((a,f),w)：将结果值设为 a，状态值设为 f w。

What is the point of pass and listen in Writer monad? [duplicate]

gcd

import Control.Monad.Trans.Writergcd' :: Int -> Int -> Writer [String] Intgcd' a b    | b == 0 = do        tell ["Finished with " ++ show a]        return a    | otherwise = do        tell [show a ++ " mod " ++ show b ++ " = " ++ show (a `mod` b)]        gcd' b (a `mod` b)main = mapM_ putStrLn . snd . runWriter $ gcd' 8 3{-8 mod 3 = 23 mod 2 = 12 mod 1 = 0Finished with 1=}

gcd

import Control.Monad.Trans.Writernewtype DiffList a = DiffList { getDiffList :: [a] -> [a] }toDiffList :: [a] -> DiffList atoDiffList xs = DiffList (xs++)fromDiffList :: DiffList a -> [a]fromDiffList (DiffList f) = f []instance Monoid (DiffList a) where    mempty = DiffList (\xs -> [] ++ xs)    (DiffList f) `mappend` (DiffList g) = DiffList (\xs -> f (g xs))gcd'' :: Int -> Int -> Writer (DiffList String) Intgcd'' a b    | b == 0 = do        tell (toDiffList ["Finished with " ++ show a])        return a    | otherwise = do        result <- gcd'' b (a `mod` b)        tell (toDiffList [show a ++ " mod " ++ show b ++ " = " ++ show (a `mod` b)])        return resultmain = mapM_ putStrLn . fromDiffList . snd . runWriter $ gcd'' 8 3{-Finished with 12 mod 1 = 03 mod 2 = 18 mod 3 = 2=}