Haskell: type classes question

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.