Haskell：类型类问题

Question

I wish to define the following typeclass Mapping :

{-# LANGUAGE MultiParamTypeClasses #-}

class Mapping k v m where
  empty :: m v
  insert :: k -> v -> m v -> m v
  search :: k -> m v -> Maybe v
  delete :: k -> m v -> m v

One instance of Mapping is Data.Map.Map

{-# LANGUAGE ..., FlexibleInstances #-}

instance Ord k => Mapping k v (Map.Map k) where
  empty = Map.empty
  search = Map.lookup
  insert = Map.insert
  delete = Map.delete

And now I want to create a type Trie :: * -> * -> * -> * such as

{-# LANGUAGE ..., UndecidableInstances #-}

data Trie m k v = Trie {
  trValue :: Maybe v,
  trChildren :: m (Trie m k v)
}

instance Mapping k (Trie m k v) m => Mapping [k] v (Trie m k) where
  search [] tree = trValue tree
  search (x:xs) tree =
    search xs =<< search x (trChildren tree)

So far so good, now I also want to define Trie 's insert and empty , and that's where I get into problems.

I will discuss empty because it's simpler and insert needs it anyhow.. If I try this:

instance Mapping k (Trie m k v) m => Mapping [k] v (Trie m k) where
  empty = Trie { trValue = Nothing, trChildren = empty }
  ...

and that makes me get the following error:

Could not deduce (Mapping k (Trie m k1 v) (m k1))
  from the context (Mapping [k1] v (Trie m k1),
                    Mapping k1 (Trie m k1 v) (m k1))
  arising from a use of `empty' at test.hs:27:49-53
Possible fix:
  add (Mapping k (Trie m k1 v) (m k1)) to the context of
    the instance declaration
  or add an instance declaration for (Mapping k (Trie m k1 v) (m k1))
In the `trChildren' field of a record
In the expression: Trie {trValue = Nothing, trChildren = empty}
In the definition of `empty':
    empty = Trie {trValue = Nothing, trChildren = empty}

I've tried and tried to solve it but failed.

Does anyone know how to make it work? Is it even possible?

Answer 1

Add a functional dependency :

{-# LANGUAGE ..., FunctionalDependencies #-}

class Mapping k v m | m -> k where
   ...

The errors you got before were because the program was ambiguous about which key type to use in certain places, hence the errors about the type variable k1 . The functional dependency allows the key type to be deduced from the map type (by declaring that there is only one possible answer), which deals with this problem.

Answer 2

Code to demonstrate Ganesh's answer:

{-# LANGUAGE FlexibleInstances, FunctionalDependencies, MultiParamTypeClasses, StandaloneDeriving, UndecidableInstances #-}

import qualified Data.Map as Map
import Data.Maybe (fromMaybe)

class Mapping k m | m -> k where             
  empty :: m v
  insert :: k -> v -> m v -> m v
  search :: k -> m v -> Maybe v
  delete :: k -> m v -> m v

instance Ord k => Mapping k (Map.Map k) where
  empty = Map.empty
  search = Map.lookup
  insert = Map.insert
  delete = Map.delete

data Trie m v = Trie {
  trValue :: Maybe v,
  trChildren :: m (Trie m v)
}

deriving instance (Show v, Show (m (Trie m v))) => Show (Trie m v)

trieMod :: Mapping k m => Maybe v -> [k] -> Trie m v -> Trie m v
trieMod val [] trie = trie { trValue = val }
trieMod val (x:xs) trie =
  trie { trChildren = insert x newChild children }
  where
    children = trChildren trie
    newChild = trieMod val xs prevChild
    prevChild = fromMaybe empty . search x $ children

instance Mapping k m => Mapping [k] (Trie m) where
  empty = Trie { trValue = Nothing, trChildren = empty }
  search [] trie = trValue trie
  search (x:xs) trie =
    search xs =<< search x (trChildren trie)
  insert key val = trieMod (Just val) key
  delete = trieMod Nothing

type TernarySearchTree a = Trie (Map.Map a)

Btw: Had functional dependencies not existed, we would probably need to compromise on an annoying interface and use function tables instead of type classes.