[Haskell-cafe] non-uniform recursive Trie

[Kazu Yamamoto ( 山本和彦 )]

Hello cafe,

I'm now studying Trie in Okasaki's "Purely Functional Data Structure".
Attached is the program in its appendix. I cannot understand how to
use "empty", "look" and "bind". For instance, if I type 'look "" empty',
I got an error:

> look "" empty
<interactive>:2:1:
    No instance for (FiniteMap m0 [Char])
      arising from a use of `look'
    Possible fix: add an instance declaration for (FiniteMap m0 [Char])
    In the expression: look "" empty
    In an equation for `it': it = look "" empty

I have no idea how to determine the parameter 'm'. Suggestions would
be appreciated.

--Kazu

{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances #-}

class FiniteMap m k where
    empty :: m k v
    look :: k -> m k v -> Maybe v
    bind :: k -> v -> m k v -> m k v

data Trie m ks v = Trie (Maybe v) (m (Trie m ks v))

instance FiniteMap m k => FiniteMap (Trie (m k)) [k] where
    empty = Trie Nothing empty

    look [] (Trie b _) = b
    look (k:ks) (Trie _ m) = look k m >>= look ks

    bind [] x (Trie _ m) = Trie (Just x) m
    bind (k:ks) x (Trie b m) = Trie b (bind k t' m)
      where
        t = case look k m of
            Just a  -> a
            Nothing -> empty
        t' = bind ks x t