[Haskell-cafe] Strange type error with associated type synonyms

[Manuel M T Chakravarty]

Peter Berry:
>> {-# LANGUAGE TypeFamilies, TypeSynonymInstances,  
>> ScopedTypeVariables #-}
>
> The following is a class of memo tries indexed by d:
>
>> class Fun d where
>>    type Memo d :: * -> *
>>    abst :: (d -> a) -> Memo d a
>>    appl :: Memo d a -> (d -> a)
>>    -- Law: abst . appl = id
>>    -- Law: appl . abst = id (denotationally)
>
> Any such type Memo d is naturally a functor:
>
>> memo_fmap f x = abst (f . appl x)
>
> The type of memo_fmap (as given by ghci) is (Fun d) => (a -> c) ->
> Memo d a -> Memo d c. (Obviously this would also be the type of fmap
> for Memo d, so we could declare a Functor instance in principle.) If
> we add this signature:
>
>> memo_fmap' :: Fun d => (a -> b) -> Memo d a -> Memo d b
>> memo_fmap' f x = abst (f . appl x)
>
> it doesn't type check:
>
> TypeSynonymTest.hs:14:17:
>    Couldn't match expected type `Memo d1 b'
>           against inferred type `Memo d b'
>    In the expression: abst (f . appl x)
>    In the definition of `memo_fmap'':
>        memo_fmap' f x = abst (f . appl x)
>
> TypeSynonymTest.hs:14:32:
>    Couldn't match expected type `Memo d a'
>           against inferred type `Memo d1 a'
>    In the first argument of `appl', namely `x'
>    In the second argument of `(.)', namely `appl x'
>    In the first argument of `abst', namely `(f . appl x)'
> Failed, modules loaded: none.
>
> As I understand it, the type checker's thought process should be along
> these lines:
>
> 1) the type signature dictates that x has type Memo d a.
> 2) appl has type Memo d1 a -> d1 -> a for some d1.
> 3) we apply appl to x, so Memo d1 a = Memo d a. unify d = d1
>
> But for some reason, step 3 fails.

Step 3 is invalid - cf, <http://www.haskell.org/pipermail/haskell-cafe/2009-April/059196.html 
 >.

More generally, the signature of memo_fmap is ambiguous, and hence,  
correctly rejected.  We need to improve the error message, though.   
Here is a previous discussion of the subject:

   http://www.mail-archive.com/haskell-cafe@haskell.org/msg39673.html

Manuel