我试图实现一种方法来延迟构造非确定性有限自动机（NFA），我在F#中完成了years ago，现在想在利用Monoid类型类的同时用Haskell尝试一下。

{-# LANGUAGE TypeSynonymInstances, FlexibleInstances #-}

module NFA where

data State = State Match State | Split State State | Final deriving (Show)
data Match = Any | Char Char | ... deriving (Show)

type StateF = State -> State

complete :: StateF -> State -> State
complete statef exit = statef exit

connect :: StateF -> StateF -> StateF
connect fst snd = complete fst . complete snd

empty :: StateF
empty = id

instance Semigroup StateF where
  (<>) = connect

instance Monoid StateF where
  mempty = empty

这段代码无法编译，因为我的Semigroup和Monoid示例与GHC.Base中的instance Semigroup b => Semigroup (a -> b)和instance Monoid b => Monoid (a -> b)重叠，但我不明白为什么。
我看到函数a -> b上有一个Monoid示例，其中b本身就是Monoid，但是State没有Monoid示例，那么StateF（State -> State）怎么会重叠呢？
是因为有人 * 可能 * 在其他地方为State实现Monoid吗？
还有，我该怎么解决这个问题？
我知道a可以将StateF定义为...

data StateF = StateF (State -> State)

......但这也会在模式匹配和构造StateF时增加语法噪声。
编译器错误：

src\NFA.hs:10:10: error:
    * Overlapping instances for Semigroup StateF
        arising from a use of `GHC.Base.$dmsconcat'
      Matching instances:
        instance Semigroup b => Semigroup (a -> b) -- Defined in `GHC.Base'
        instance Semigroup StateF -- Defined at src\NFA.hs:10:10
    * In the expression: GHC.Base.$dmsconcat @(StateF)
      In an equation for `GHC.Base.sconcat':
          GHC.Base.sconcat = GHC.Base.$dmsconcat @(StateF)
      In the instance declaration for `Semigroup StateF'
   |
10 | instance Semigroup StateF where
   |          ^^^^^^^^^^^^^^^^

src\NFA.hs:10:10: error:
    * Overlapping instances for Semigroup StateF
        arising from a use of `GHC.Base.$dmstimes'
      Matching instances:
        instance Semigroup b => Semigroup (a -> b) -- Defined in `GHC.Base'
        instance Semigroup StateF -- Defined at src\NFA.hs:10:10
    * In the expression: GHC.Base.$dmstimes @(StateF)
      In an equation for `GHC.Base.stimes':
          GHC.Base.stimes = GHC.Base.$dmstimes @(StateF)
      In the instance declaration for `Semigroup StateF'
   |
10 | instance Semigroup StateF where
   |          ^^^^^^^^^^^^^^^^

src\NFA.hs:13:10: error:
    * Overlapping instances for Semigroup StateF
        arising from the superclasses of an instance declaration
      Matching instances:
        instance Semigroup b => Semigroup (a -> b) -- Defined in `GHC.Base'
        instance Semigroup StateF -- Defined at src\NFA.hs:10:10
    * In the instance declaration for `Monoid StateF'
   |
13 | instance Monoid StateF where
   |          ^^^^^^^^^^^^^

src\NFA.hs:13:10: error:
    * Overlapping instances for Monoid StateF
        arising from a use of `GHC.Base.$dmmappend'
      Matching instances:
        instance Monoid b => Monoid (a -> b) -- Defined in `GHC.Base'
        instance Monoid StateF -- Defined at src\NFA.hs:13:10
    * In the expression: GHC.Base.$dmmappend @(StateF)
      In an equation for `mappend':
          mappend = GHC.Base.$dmmappend @(StateF)
      In the instance declaration for `Monoid StateF'
   |
13 | instance Monoid StateF where
   |          ^^^^^^^^^^^^^

src\NFA.hs:13:10: error:
    * Overlapping instances for Monoid StateF
        arising from a use of `GHC.Base.$dmmconcat'
      Matching instances:
        instance Monoid b => Monoid (a -> b) -- Defined in `GHC.Base'
        instance Monoid StateF -- Defined at src\NFA.hs:13:10
    * In the expression: GHC.Base.$dmmconcat @(StateF)
      In an equation for `mconcat':
          mconcat = GHC.Base.$dmmconcat @(StateF)
      In the instance declaration for `Monoid StateF'
   |
13 | instance Monoid StateF where
   |          ^^^^^^^^^^^^^