打印免费的 monad

Question

可以将自由 monad 转换为任何其他 monad，但给定类型 Free f x 的值，我想打印整棵树，而不是将生成的 AST 的每个节点映射到另一个节点中的某个其他节点单子。

Gabriel Gonzales uses 直接值

showProgram :: (Show a, Show r) => Free (Toy a) r -> String
showProgram (Free (Output a x)) =
    "output " ++ show a ++ "\n" ++ showProgram x
showProgram (Free (Bell x)) =
    "bell\n" ++ showProgram x
showProgram (Free Done) =
    "done\n"
showProgram (Pure r) =
    "return " ++ show r ++ "\n"

可以抽象为

showF :: (x -> b) -> ((Free f x -> b) -> f (Free f x) -> b) ->  Free f x -> b
showF backLiftValue backLiftF  = fix (showFU backLiftValue backLiftF)
    where
      showFU :: (x -> b) -> ((Free f x -> b) -> f (Free f x) -> b) -> (Free f x -> b) -> Free f x -> b
      showFU backLiftValue backLiftF next = go . runIdentity . runFreeT where
          go (FreeF c ) = backLiftF next  c
          go (Pure x) =   backLiftValue x

如果我们有像这样的多态函数（使用 Choice x = Choice x x 作为函子）

，这很容易调用

showChoice :: forall x. (x -> String) ->  Choice x -> String
showChoice show (Choice a b) =  "Choice (" ++ show  a ++  "," ++ show b ++ ")"

但这对于一个简单的操作来说似乎相当复杂...... 从 f x -> b 到 Free f x -> b 还有哪些其他方法？

Answer 1

使用iter和fmap:

{-# LANGUAGE DeriveFunctor #-}

import Control.Monad.Free

data Choice x = Choice x x deriving (Functor)

-- iter :: Functor f => (f a -> a) -> Free f a -> a
-- iter _   (Pure a) = a
-- iter phi (Free m) = phi (iter phi <$> m)

showFreeChoice :: Show a => Free Choice a -> String
showFreeChoice =
      iter (\(Choice l r) -> "(Choice " ++ l ++ " " ++ r ++ ")")
    . fmap (\a -> "(Pure " ++ show a ++ ")")

fmap 将 Free f a 转换为 Free f b，剩下的由 iter 完成。您可以将其排除在外，并可能获得更好的性能：

iter' :: Functor f => (f b -> b) -> (a -> b) -> Free f a -> b
iter' f g = go where
  go (Pure a)  = g a
  go (Free fa) = f (go <$> fa)

打印免费的 monad

Printing the free monad

haskell

monads

traversal

free-monad