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问题描述

我正在尝试使用免费monad基于一些我在网上阅读的有用文献构建AST。



我有一些关于使用这些工具的问题在实践中使用了几种AST,我将它们归结为以下示例。



假设我的语言允许使用以下命令:

  { - #LANGUAGE DeriveFunctor# - } 

data下一个
= DisplayChar Char下一个
| DisplayString String next
|重复Int(Free Command())next
|完成
派生(Eq,Show,Functor)

我定义了Free monad样板:

  displayChar :: Char  - > Free Command()
displayChar ch = liftF(DisplayChar ch())

displayString :: String - > Free Command()
displayString str = liftF(DisplayString str())

repeat :: Int - > Free Command() - > Free Command()
重复次数block = liftF(重复次数块())

完成:: Free命令r
完成= liftF完成

$ p
$ b

允许我指定如下程序:

  prog :: Free命令r 
prog =
做displayChar'A'
displayStringabc

重复5 $
displayChar 'Z'

displayChar'\\\
'
完成

现在,我想执行我的程序,这似乎很简单。

  execute :: Free命令r  - > IO()
execute(Free(DisplayChar ch next))= putChar ch>>执行next
execute(Free(DisplayString str next))= putStr str>>执行next
execute(Free(Repeat n block next))= forM_ [1..n](\ - >执行块)>>执行next
execute(Free Done)= return()
execute(Pure r)= return()



 λ>执执行
AabcZZZZZ

好的。这很好,但现在我想了解我的AST的一些事情,并对其执行转换。

以下是一个简单的例子:如果 Repeat 块只包含 DisplayChar 命令,那么我想用适当的 DisplayString 替换整个事物。换句话说,
我想用重复2(displayChar'A'>>> displayChar'B') displayStringABAB



这是我的尝试:

  optimize c @(Free(Repeat n block next))= 
如果全部是jrs charsToDisplay then
let chars = catMaybes charsToDisplay
in
displayString(concat $ replicate n个字符)>>优化next
else
c>>优化next
where
charsToDisplay = project getDisplayChar block
optimize(Free(DisplayChar ch next))= displayChar ch>>优化next
optimize(Free(DisplayString str next))= displayString str>>优化下一个
优化(免费完成)=完成
优化c @(Pure r)= c

getDisplayChar(Free(DisplayChar ch _))=只需ch
getDisplayChar _ = Nothing

项目::(免费命令a - >也许u) - >免费命令a - > [也许你]
project f = maybes
其中
maybes(Pure a)= []
maybes c @(Free cmd)=
let build next = fc :maybes next
in
case cmd of
DisplayChar _ next - >构建下一个
DisplayString _ next - >构建下一个
重复_ _ next - >构建下一个
完成 - > []

观察GHCI中的AST显示,这个工作正确,实际上是

 λ>优化$ repeat 3(displayChar'A'>> displayChar'B')
Free(DisplayStringABABAB(Pure()))


λ>执行 。优化$ prog
AabcZZZZZ
λ>执执行
AabcZZZZZ

但我不高兴。在我看来,这个代码是重复的。我必须定义每次我想要检查AST时如何遍历AST,或者定义像我的项目这样的函数,以便我查看它。



所以,我的问题:这是我唯一的选择吗?我可以在AST上进行模式匹配而不需要处理大量的嵌套?我可以用一致和通用的方式遍历树吗(也许拉链,或者可穿越或其他)?





$ p $ c> { - #LANGUAGE DeriveFunctor# - }

模块Main其中

导入前导隐藏(重复)

导入Control.Monad.Free

导入Control.Monad(forM_)
导入Data.Maybe(catMaybes,isJust)
$ b $ main :: IO()
main = execute prog

prog :: Free命令r
prog =
做displayChar'A'
displayStringabc

重复5 $
displayChar'Z'

displayChar'\''
完成

优化c @(免费(下一个重复n块))=
if所有是charsToDisplay then
let chars = catMaybes charsToDisplay
in
displayString(concat $ replicate n chars)>>优化next
else
c>>优化next
where
charsToDisplay = project getDisplayChar block
optimize(Free(DisplayChar ch next))= displayChar ch>>优化next
optimize(Free(DisplayString str next))= displayString str>>优化下一个
优化(免费完成)=完成
优化c @(Pure r)= c

getDisplayChar(Free(DisplayChar ch _))=只需ch
getDisplayChar _ = Nothing

项目::(免费命令a - >也许u) - >免费命令a - > [也许你]
project f = maybes
其中
maybes(Pure a)= []
maybes c @(Free cmd)=
let build next = fc :maybes next
in
case cmd of
DisplayChar _ next - >构建下一个
DisplayString _ next - >构建下一个
重复_ _ next - >构建下一个
完成 - > []

执行:: Free命令r - > IO()
execute(Free(DisplayChar ch next))= putChar ch>>执行next
execute(Free(DisplayString str next))= putStr str>>执行next
execute(Free(Repeat n block next))= forM_ [1..n](\ - >执行块)>>执行next
execute(Free Done)= return()
execute(Pure r)= return()

data命令next
= DisplayChar Char next
| DisplayString String next
|重复Int(Free Command())next
|完成
导出(Eq,Show,Functor)

displayChar :: Char - > Free Command()
displayChar ch = liftF(DisplayChar ch())

displayString :: String - > Free Command()
displayString str = liftF(DisplayString str())

repeat :: Int - > Free Command() - > Free Command()
重复次数block = liftF(重复次数块())

完成:: Free命令r
完成= liftF完成


解决方案

这是我使用 syb

  { - #LANGUAGE LambdaCase# - } 
{ - #LANGUAGE DeriveFunctor# - }
{ - # #LANGUAGE TemplateHaskell# - }
{ - #LANGUAGE FlexibleContexts# - }
{ - #LANGUAGE DeriveDataTypeable# - }

模块Main其中

导入Prelude隐藏(重复)

导入Data.Data

导入Control.Monad(forM_)

导入Control.Monad.Free
import Control.Monad.Free.TH

import Data.Generics(everywhere,mkT)

data CommandF next = DisplayChar Char next
| DisplayString String next
|重复Int(自由CommandF())next
|完成
导出(Eq,Show,Functor,Data,Typeable)

makeFree''CommandF

类型Command = Free CommandF

execute :: Command() - > IO()
execute = iterM句柄
其中
句柄= \ case
DisplayChar ch next - > putChar ch>> next
DisplayString str next - > putStr str>>下一个
下一个重复n块 - > forM_ [1..n](\ _→>执行块)>>下一个
完成 - > return()

optimize :: Command() - > Command()
optimize = optimize'。优化'
where
optimize'=无处不在(mkT inner)

inner :: Command() - > Command()
- char + char变成字符串
inner(Free(DisplayChar c1(Free(DisplayChar c2 next))))= do
displayString [c1,c2]
下一个

- char +字符串变成字符串
inner(Free(DisplayChar c(Free(DisplayString s next))))= do
displayString $ c:s
下一个

- 字符串+字符串变为字符串
内部(Free(DisplayString s1(Free(DisplayString s2 next))))= do
displayString $ s1 ++ s2
next

- 循环展开
内部f @(Free(重复n个下一个块))| n< 5 = forM_ [1..n](\→→block)>>下一个
|否则= f

内部a = a

编程:: Command()
编程=执行
displayChar'a'
displayChar' b'
重复1 $ displayChar'c'>> displayStringdef
displayChar'g'
displayChar'h'
repeat 10 $ do
displayChar'i'
displayChar'j'
displayString klm
repeat 3 $ displayChar'n'

main :: IO()
main = do
putStrLn原始程序:
print prog
putStrLn评估原始程序:
执行prog
putStrLn\\\


let opt =优化编程
putStrLn优化程序:
打印opt
putStrLn优化程序评估:
执行opt
putStrLn

输出:

  $ cabal exec runhaskell ast.hs 
原始程序:
Free(DisplayChar'a'(Free(DisplayChar'b'(Free(Repeat 1)(Free(DisplayChar'c'(Free(DisplayStringdef(Pure())))))(Free(DisplayChar 'g'(Free(DisplayChar'h'(Free)(Repeat 10(Free(DisplayChar'i'(Fre e(DisplayChar'j'(Free(DisplayStringklm(Pure())))))))(Free(Repeat3(Free(DisplayChar'n'(Pure())))(Pure()))) )))))))))))))))))))
原始程序的评估:
abcdefghijklmijklmijklmijklmijklmijklmijklmijklmijklmijklmijklmijklmijklmijklmijklmnnn

优化程序:
Free(DisplayStringabcdefgh(Free 10(自由(DisplayStringijklm(Pure())))(Free(DisplayStringnnn(Pure()))))))
优化程序的评估:
abcdefghijklmijklmijklmijklmijklmijklmijklmijklmijklmijklmijklmnnn

使用GHC 7.8 模式同义词可以消除* Free * ,但出于某种原因,上述代码仅适用于GHC 7.6, Data 实例似乎缺失。应该看看......


I'm attempting to structure an AST using the Free monad based on some helpful literature that I've read online.

I have some questions about working with these kinds of ASTs in practice, which I've boiled down to the following example.

Suppose my language allows for the following commands:

{-# LANGUAGE DeriveFunctor #-}

data Command next
  = DisplayChar Char next
  | DisplayString String next
  | Repeat Int (Free Command ()) next
  | Done
  deriving (Eq, Show, Functor)

and I define the Free monad boilerplate manually:

displayChar :: Char -> Free Command ()
displayChar ch = liftF (DisplayChar ch ())

displayString :: String -> Free Command ()
displayString str = liftF (DisplayString str ())

repeat :: Int -> Free Command () -> Free Command ()
repeat times block = liftF (Repeat times block ())

done :: Free Command r
done = liftF Done

which allows me to specify programs like the following:

prog :: Free Command r
prog =
  do displayChar 'A'
     displayString "abc"

     repeat 5 $
       displayChar 'Z'

     displayChar '\n'
     done

Now, I'd like to execute my program, which seems simple enough.

execute :: Free Command r -> IO ()
execute (Free (DisplayChar ch next)) = putChar ch >> execute next
execute (Free (DisplayString str next)) = putStr str >> execute next
execute (Free (Repeat n block next)) = forM_ [1 .. n] (\_ -> execute block) >> execute next
execute (Free Done) = return ()
execute (Pure r) = return ()

and

λ> execute prog
AabcZZZZZ

Okay. That's all nice, but now I want to learn things about my AST, and execute transformations on it. Think like optimizations in a compiler.

Here's a simple one: If a Repeat block only contains DisplayChar commands, then I'd like to replace the whole thing with an appropriate DisplayString. In other words,I'd like to transform repeat 2 (displayChar 'A' >> displayChar 'B') with displayString "ABAB".

Here's my attempt:

optimize c@(Free (Repeat n block next)) =
  if all isJust charsToDisplay then
    let chars = catMaybes charsToDisplay
    in
      displayString (concat $ replicate n chars) >> optimize next
  else
    c >> optimize next
  where
    charsToDisplay = project getDisplayChar block
optimize (Free (DisplayChar ch next)) = displayChar ch >> optimize next
optimize (Free (DisplayString str next)) = displayString str >> optimize next
optimize (Free Done) = done
optimize c@(Pure r) = c

getDisplayChar (Free (DisplayChar ch _)) = Just ch
getDisplayChar _ = Nothing

project :: (Free Command a -> Maybe u) -> Free Command a -> [Maybe u]
project f = maybes
  where
    maybes (Pure a) = []
    maybes c@(Free cmd) =
      let build next = f c : maybes next
      in
        case cmd of
          DisplayChar _ next -> build next
          DisplayString _ next -> build next
          Repeat _ _ next -> build next
          Done -> []

Observing the AST in GHCI shows that this work correctly, and indeed

λ> optimize $ repeat 3 (displayChar 'A' >> displayChar 'B')
Free (DisplayString "ABABAB" (Pure ()))


λ> execute . optimize $ prog
AabcZZZZZ
λ> execute prog
AabcZZZZZ 

But I'm not happy. In my opinion, this code is repetitive. I have to define how to traverse through my AST every time I want to examine it, or define functions like my project that give me a view into it. I have to do this same thing when I want to modify the tree.

So, my question: is this approach my only option? Can I pattern-match on my AST without dealing with tonnes of nesting? Can I traverse the tree in a consistent and generic way (maybe Zippers, or Traversable, or something else)? What approaches are commonly taken here?

The whole file is below:

{-# LANGUAGE DeriveFunctor #-}

module Main where

import Prelude hiding (repeat)

import Control.Monad.Free

import Control.Monad (forM_)
import Data.Maybe (catMaybes, isJust)

main :: IO ()
main = execute prog

prog :: Free Command r
prog =
  do displayChar 'A'
     displayString "abc"

     repeat 5 $
       displayChar 'Z'

     displayChar '\n'
     done

optimize c@(Free (Repeat n block next)) =
  if all isJust charsToDisplay then
    let chars = catMaybes charsToDisplay
    in
      displayString (concat $ replicate n chars) >> optimize next
  else
    c >> optimize next
  where
    charsToDisplay = project getDisplayChar block
optimize (Free (DisplayChar ch next)) = displayChar ch >> optimize next
optimize (Free (DisplayString str next)) = displayString str >> optimize next
optimize (Free Done) = done
optimize c@(Pure r) = c

getDisplayChar (Free (DisplayChar ch _)) = Just ch
getDisplayChar _ = Nothing

project :: (Free Command a -> Maybe u) -> Free Command a -> [Maybe u]
project f = maybes
  where
    maybes (Pure a) = []
    maybes c@(Free cmd) =
      let build next = f c : maybes next
      in
        case cmd of
          DisplayChar _ next -> build next
          DisplayString _ next -> build next
          Repeat _ _ next -> build next
          Done -> []

execute :: Free Command r -> IO ()
execute (Free (DisplayChar ch next)) = putChar ch >> execute next
execute (Free (DisplayString str next)) = putStr str >> execute next
execute (Free (Repeat n block next)) = forM_ [1 .. n] (\_ -> execute block) >> execute next
execute (Free Done) = return ()
execute (Pure r) = return ()

data Command next
  = DisplayChar Char next
  | DisplayString String next
  | Repeat Int (Free Command ()) next
  | Done
  deriving (Eq, Show, Functor)

displayChar :: Char -> Free Command ()
displayChar ch = liftF (DisplayChar ch ())

displayString :: String -> Free Command ()
displayString str = liftF (DisplayString str ())

repeat :: Int -> Free Command () -> Free Command ()
repeat times block = liftF (Repeat times block ())

done :: Free Command r
done = liftF Done
解决方案

Here's my take using syb (as mentioned on Reddit):

{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE DeriveDataTypeable #-}

module Main where

import Prelude hiding (repeat)

import Data.Data

import Control.Monad (forM_)

import Control.Monad.Free
import Control.Monad.Free.TH

import Data.Generics (everywhere, mkT)

data CommandF next = DisplayChar Char next
                   | DisplayString String next
                   | Repeat Int (Free CommandF ()) next
                   | Done
  deriving (Eq, Show, Functor, Data, Typeable)

makeFree ''CommandF

type Command = Free CommandF

execute :: Command () -> IO ()
execute = iterM handle
  where
    handle = \case
        DisplayChar ch next -> putChar ch >> next
        DisplayString str next -> putStr str >> next
        Repeat n block next -> forM_ [1 .. n] (\_ -> execute block) >> next
        Done -> return ()

optimize :: Command () -> Command ()
optimize = optimize' . optimize'
  where
    optimize' = everywhere (mkT inner)

    inner :: Command () -> Command ()
    -- char + char becomes string
    inner (Free (DisplayChar c1 (Free (DisplayChar c2 next)))) = do
        displayString [c1, c2]
        next

    -- char + string becomes string
    inner (Free (DisplayChar c (Free (DisplayString s next)))) = do
        displayString $ c : s
        next

    -- string + string becomes string
    inner (Free (DisplayString s1 (Free (DisplayString s2 next)))) = do
        displayString $ s1 ++ s2
        next

    -- Loop unrolling
    inner f@(Free (Repeat n block next)) | n < 5 = forM_ [1 .. n] (\_ -> block) >> next
                                         | otherwise = f

    inner a = a

prog :: Command ()
prog = do
    displayChar 'a'
    displayChar 'b'
    repeat 1 $ displayChar 'c' >> displayString "def"
    displayChar 'g'
    displayChar 'h'
    repeat 10 $ do
        displayChar 'i'
        displayChar 'j'
        displayString "klm"
    repeat 3 $ displayChar 'n'

main :: IO ()
main = do
    putStrLn "Original program:"
    print prog
    putStrLn "Evaluation of original program:"
    execute prog
    putStrLn "\n"

    let opt = optimize prog
    putStrLn "Optimized program:"
    print opt
    putStrLn "Evaluation of optimized program:"
    execute opt
    putStrLn ""

Output:

$ cabal exec runhaskell ast.hs
Original program:
Free (DisplayChar 'a' (Free (DisplayChar 'b' (Free (Repeat 1 (Free (DisplayChar 'c' (Free (DisplayString "def" (Pure ()))))) (Free (DisplayChar 'g' (Free (DisplayChar 'h' (Free (Repeat 10 (Free (DisplayChar 'i' (Free (DisplayChar 'j' (Free (DisplayString "klm" (Pure ()))))))) (Free (Repeat 3 (Free (DisplayChar 'n' (Pure ()))) (Pure ()))))))))))))))
Evaluation of original program:
abcdefghijklmijklmijklmijklmijklmijklmijklmijklmijklmijklmnnn

Optimized program:
Free (DisplayString "abcdefgh" (Free (Repeat 10 (Free (DisplayString "ijklm" (Pure ()))) (Free (DisplayString "nnn" (Pure ()))))))
Evaluation of optimized program:
abcdefghijklmijklmijklmijklmijklmijklmijklmijklmijklmijklmnnn

It might be possible to get rid of the *Free*s using GHC 7.8 Pattern Synonyms, but for some reason the above code only works using GHC 7.6, the Data instance of Free seems to be missing. Should look into that...

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10-27 04:05