The following module does not compile, and I can't figure out why:

{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE KindSignatures #-}

module Foo where

import Control.Monad
import Data.Maybe

class Key k where
type Map k :: * -> *
empty :: Map k v

look :: k -> Map k v -> Maybe v
update :: k -> (Maybe v -> Maybe v) -> Map k v -> Map k v

instance (Key k1, Key k2) => Key (k1, k2) where
type Map (k1, k2) v = Map k1 (Map k2 v)

The arity of the instance has to be exactly the same as is declared. So the v is one too many parameters. That does make your life a little more difficult (but points to an abstraction you may not have seen :-).

I would resolve this as:

type Map (k1,k2) = Map k1 `O` Map k2

Where O is functor composition from TypeCompose on hackage.

empty = empty

update (k1, k2) f = update k1 (update k2 f . fromMaybe empty)
look (k1, k2) = look k1 >=> look k2

The compile fails with
Foo.hs:16:1:
   Number of parameters must match family declaration; expected 1
   In the type synonym instance declaration for `Map'

   In the instance declaration for `Key (k1, k2)'

Is this a bug with type synonym families? Is there something silly I'm missing?

Louis Wasserman
wasserman.louis@gmail.com

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