如何规范化Haskell中MC类型嵌套的冗余Compose与Identity容器

要自动推导并扁平化嵌套的Compose/Identity容器结构，核心是通过自定义类型类描述容器的同构关系，实现自动规范化，同时可以从根源优化cross操作避免冗余嵌套。以下是具体实现方案：

1. 定义容器规范化类型类 #

先定义一个类型类，用来描述嵌套容器与扁平容器的同构转换，自动处理Identity消去和多层Compose扁平化：

{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, TypeFamilies, UndecidableInstances #-}

import Data.Functor.Compose
import Data.Functor.Identity

-- 类型类：将嵌套容器结构规范化为等价扁平结构
class NormalizeContainer nested where
  type Normalized nested :: * -> *
  -- 将嵌套容器转为扁平容器
  normalize :: nested a -> Normalized nested a
  -- 将扁平容器转回嵌套结构（用于反向兼容）
  denormalize :: Normalized nested a -> nested a

-- Identity实例：直接保留或消去（这里保留容器结构保证类型一致性）
instance NormalizeContainer Identity where
  type Normalized Identity = Identity
  normalize = id
  denormalize = id

-- 单层Compose默认实例
instance (Functor f, Functor g) => NormalizeContainer (Compose f g) where
  type Normalized (Compose f g) = Compose f g
  normalize = id
  denormalize = id

-- 处理Compose(Compose f Identity) g的情况：消去中间的Identity
instance (Functor f, Functor g) => NormalizeContainer (Compose (Compose f Identity) g) where
  type Normalized (Compose (Compose f Identity) g) = Compose f g
  normalize (Compose c) = Compose $ fmap (runIdentity . getCompose) c
  denormalize (Compose c) = Compose $ fmap (Compose . Identity) c

-- 递归处理更深层的嵌套Compose
instance (NormalizeContainer (Compose f g), Functor h) => NormalizeContainer (Compose (Compose f g) h) where
  type Normalized (Compose (Compose f g) h) = Compose (Normalized (Compose f g)) h
  normalize (Compose c) = Compose $ fmap normalize c
  denormalize (Compose c) = Compose $ fmap denormalize c

2. 给MC元容器添加规范化方法 #

假设你的MC元容器定义如下：

newtype MC f a = MC (f a) deriving (Functor, Applicative)

添加normalizeMC方法，自动规范化内部嵌套容器：

normalizeMC :: (NormalizeContainer f) => MC f a -> MC (Normalized f) a
normalizeMC (MC fa) = MC $ normalize fa

3. 结合hoist操作使用 #

针对你提到的justStrList :: MC (Compose (Compose [] Identity) Maybe) String，先规范化再执行hoist：

-- 假设hoist的定义如下
hoist :: (forall x. f x -> g x) => MC f a -> MC g a
hoist f (MC fa) = MC $ f fa

-- 规范化后再用catMaybes处理
processed :: MC [] String
processed = hoist (catMaybes . getCompose) $ normalizeMC justStrList

这里normalizeMC会自动将Compose (Compose [] Identity) Maybe转为Compose [] Maybe，getCompose取出[Maybe String]后即可直接用catMaybes处理。

4. 根源优化：让cross直接生成规范化容器 #

修改cross操作的实现，在生成结果时自动规范化，避免后续手动处理：

-- 原cross实现（会生成嵌套Compose）
cross :: (Applicative f, Applicative g) => MC f a -> MC g b -> MC (Compose f g) (a, b)
cross (MC fa) (MC gb) = MC $ Compose $ (\a -> fmap (\b -> (a,b)) gb) <$> fa

-- 优化后的cross：直接返回规范化后的容器
cross' :: (Applicative f, Applicative g, NormalizeContainer (Compose f g)) 
       => MC f a -> MC g b 
       -> MC (Normalized (Compose f g)) (a, b)
cross' fa gb = normalizeMC $ cross fa gb

调用cross'会直接得到扁平化后的容器类型，无需额外处理。

内容的提问来源于stack exchange，提问作者Blue Nebula