Haskell 使用类型族时简化类型签名？

我正在重写一些库，以使用类型族而不是函数依赖项。然而，为了使函数能够编译，我必须添加到函数中的一些约束似乎是不必要的。这让我怀疑我没有以最好的方式做事

在下面的示例中，是否有方法改进

Grid

和

GridMap

的定义，以便

diff

和

classify

的签名更简单？特别是，

BaseGrid（Container gm k）~BaseGrid gm

、

Container（Container gm k）~Container gm

和

GridMap（Container gm k）

对

classify

的约束似乎不雅观

{-# LANGUAGE TypeFamilies, FlexibleContexts #-}

import Prelude hiding (map)
import Data.List (minimumBy)
import qualified Data.Map as M
import Data.Ord (comparing)

class Grid g where
  type Index g
  indices :: g -> [Index g]
  -- plus other functions

class (Grid (BaseGrid gm)) => GridMap gm where
  type BaseGrid gm
  type Value gm
  type Container gm :: * -> *

  toMap :: gm -> M.Map (Index (BaseGrid gm)) (Value gm)
  toList :: gm -> [(Index (BaseGrid gm), Value gm)]
  toList = M.toList . toMap

  map
    :: (GridMap gm2, gm2 ~ Container gm (Value gm2)) => 
      (Value gm -> Value gm2) -> gm -> gm2

  mapWithKey 
    :: (GridMap gm2, gm2 ~ Container gm (Value gm2)) => 
      (Index gm -> Value gm -> Value gm2) -> gm -> gm2
  -- plus other functions

class Pattern p where
  type Metric p
  difference :: p -> p -> Metric p
  makeSimilar :: p -> Metric p -> p -> p

diff 
  :: (GridMap gm1, p ~ Value gm1, GridMap gm2, Pattern p, 
      Metric p ~ Value gm2, Container gm1 ~ Container gm2, 
      BaseGrid gm1 ~ BaseGrid gm2,
      gm2 ~ Container gm2 (Value gm2)) => 
    gm1 -> p -> gm2
diff c pattern = map (pattern `difference`) c

classify
  :: (GridMap gm, p ~ Value gm, Pattern p, Ord k, k ~ Metric p, 
      k ~ Index (BaseGrid gm), k ~ Value (Container gm k),
      BaseGrid (Container gm k) ~ BaseGrid gm,
      Container (Container gm k) ~ Container gm,
      GridMap (Container gm k)) =>
    gm -> p -> k
classify c pattern = 
  fst $ minimumBy (comparing snd) $ toList $ diff c pattern

---

编辑：我喜欢leventov的解决方案，但当我尝试实现它时，我得到了一个我不理解的编译错误

{-# LANGUAGE TypeFamilies, FlexibleContexts #-}

import Prelude hiding (map)
import Data.List (minimumBy)
import qualified Data.Map as M
import Data.Ord (comparing)

class Grid g where
  type Index g
  indices :: g -> [Index g]
  -- plus other functions

class (Grid (BaseGrid gm a)) => GridMap gm a where
  type BaseGrid gm a

  toMap :: gm -> M.Map (Index (BaseGrid gm a)) a
  toList :: gm -> [(Index (BaseGrid gm a), a)]
  toList = M.toList . toMap

  map :: GridMap gm b => (a -> b) -> gm a -> gm b -- <<<<<LINE 20>>>>>

  mapWithKey 
    :: GridMap gm b => 
      (Index (BaseGrid gm a) -> a -> b) -> gm a -> gm b
  -- plus other functions

class Pattern p where
  type Metric p
  difference :: p -> p -> Metric p
  makeSimilar :: p -> Metric p -> p -> p

diff 
  :: (GridMap gm p, Pattern p, GridMap gm m,
      Metric p ~ m, BaseGrid gm p ~ BaseGrid gm m) => 
    gm p -> p -> gm m
diff c pattern = map (pattern `difference`) c

classify
  :: (GridMap gm p, Pattern p, Ord k, k ~ Metric p, 
      k ~ Index (BaseGrid gm p),
      BaseGrid gm k ~ BaseGrid gm p) =>
    gm p -> p -> k
classify c pattern = 
  fst $ minimumBy (comparing snd) $ toList $ diff c pattern

---

如果我取消约束

GridMap gm b=>

我也会得到这个错误，我将使用两个参数制作

GridMap

：容器本身和值类型

差不多

{-# LANGUAGE TypeFamilies, FlexibleContexts, MultiParamTypeClasses #-}

import Prelude hiding (map)
import Data.List (minimumBy)
import qualified Data.Map as M
import Data.Ord (comparing)

class Grid g where
  type Index g
  indices :: g -> [Index g]
  -- plus other functions

class (Grid (BaseGrid gm a)) => GridMap (gm :: * -> *) a where
  type BaseGrid gm a

  toMap :: gm a -> M.Map (Index (BaseGrid gm a)) a
  toList :: gm a -> [(Index (BaseGrid gm a), a)]
  toList = M.toList . toMap

  map :: GridMap gm b => (a -> b) -> gm a -> gm b -- <<<<<LINE 20>>>>>

  mapWithKey 
    :: GridMap gm b => 
      (Index (BaseGrid gm a) -> a -> b) -> gm a -> gm b
  -- plus other functions

class Pattern p where
  type Metric p
  difference :: p -> p -> Metric p
  makeSimilar :: p -> Metric p -> p -> p

diff 
  :: (GridMap gm p, Pattern p, GridMap gm m,
      Metric p ~ m, BaseGrid gm p ~ BaseGrid gm m) => 
    gm p -> p -> gm m
diff c pattern = map (pattern `difference`) c

classify
  :: (GridMap gm p, Pattern p, Ord k, k ~ Metric p, 
      k ~ Index (BaseGrid gm p),
      GridMap gm k,
      BaseGrid gm k ~ BaseGrid gm p) =>
    gm p -> p -> k
classify c pattern = 
  fst $ minimumBy (comparing snd) $ toList $ diff c pattern

{-#语言类型族、灵活上下文、多段类型类#-}
导入前奏隐藏（地图）
导入数据列表（最小值）
导入符合条件的数据。映射为M
导入数据。Ord（比较）
g类网格，其中
类型索引g
索引：：g->[索引g]
--加上其他功能
类（Grid（BaseGrid gm a））=>GridMap（gm:：*->*）a其中
基本网格类型gm a
toMap:：gm a->M.Map（索引（基本网格gm a））a
toList:：gm a->[（索引（基本网格gm a），a）]
托利斯特=M.托利斯特。托马普
地图：：网格地图gm b=>（a->b）->gm a->gm b--
mapWithKey
：：GridMap gm b=>
（索引（基本网格gm a）->a->b）->gm a->gm b
--加上其他功能
类模式p在哪里
类型度量p
差异：：p->p->度量值p
makesimular:：p->Metric p->p->p
差异
：：（GridMap gm p，模式p，GridMap gm m，
度量p~m，BaseGrid gm p~BaseGrid gm m）=>
总经理p->p->m总经理
diff c pattern=map（pattern`difference`）c
分类
：（网格图gm p，模式p，Ord k，k~度量p，
k~指数（基本网格gm p），
GridMap gm k，
BaseGrid gm k~ BaseGrid gm p）=>
总经理p->p->k
分类c模式=
fst$minimumBy（比较snd）$toList$diff c模式

这不是完全等效的转换。您的变体解除了

gm

上

a

的隐式函数依赖关系，而在原始版本中，此依赖关系是通过关联类型建模的。@Vladimir Matveev为什么

gm

与原始容器类似，属于

*->*

？对不起，我确信它只是

*

。是我的错。你完全正确。我喜欢这个解决方案，但我在编译时遇到了麻烦。我已经编辑了上面的问题。@mhwombat我已经编辑了答案，为

gm

添加了明确的数据类型签名。现在它正在为我编译。

{-# LANGUAGE TypeFamilies, FlexibleContexts, MultiParamTypeClasses #-}

import Prelude hiding (map)
import Data.List (minimumBy)
import qualified Data.Map as M
import Data.Ord (comparing)

class Grid g where
  type Index g
  indices :: g -> [Index g]
  -- plus other functions

class (Grid (BaseGrid gm a)) => GridMap (gm :: * -> *) a where
  type BaseGrid gm a

  toMap :: gm a -> M.Map (Index (BaseGrid gm a)) a
  toList :: gm a -> [(Index (BaseGrid gm a), a)]
  toList = M.toList . toMap

  map :: GridMap gm b => (a -> b) -> gm a -> gm b -- <<<<<LINE 20>>>>>

  mapWithKey 
    :: GridMap gm b => 
      (Index (BaseGrid gm a) -> a -> b) -> gm a -> gm b
  -- plus other functions

class Pattern p where
  type Metric p
  difference :: p -> p -> Metric p
  makeSimilar :: p -> Metric p -> p -> p

diff 
  :: (GridMap gm p, Pattern p, GridMap gm m,
      Metric p ~ m, BaseGrid gm p ~ BaseGrid gm m) => 
    gm p -> p -> gm m
diff c pattern = map (pattern `difference`) c

classify
  :: (GridMap gm p, Pattern p, Ord k, k ~ Metric p, 
      k ~ Index (BaseGrid gm p),
      GridMap gm k,
      BaseGrid gm k ~ BaseGrid gm p) =>
    gm p -> p -> k
classify c pattern = 
  fst $ minimumBy (comparing snd) $ toList $ diff c pattern