GADTs and functional dependencies

[Jason Dagit]

On Tue, Sep 23, 2008 at 9:36 AM, Wolfgang Jeltsch
<g9ks157k at acme.softbase.org> wrote:
> Am Dienstag, 23. September 2008 18:19 schrieben Sie:
>> On Tue, Sep 23, 2008 at 6:07 PM, Wolfgang Jeltsch
>>
>> <g9ks157k at acme.softbase.org> wrote:
>> > Hello,
>> >
>> > please consider the following code:
>> >> {-# LANGUAGE GADTs, MultiParamTypeClasses, FunctionalDependencies #-}
>> >>
>> >> data GADT a where
>> >>
>> >>     GADT :: GADT ()
>> >>
>> >> class Class a b | a -> b
>> >>
>> >> instance Class () ()
>> >>
>> >> fun :: (Class a b) => GADT a -> b
>> >> fun GADT = ()
>> >
>> > I'd expect this to work but unfortunately, using GHC 6.8.2, it fails with
>> > the following message:
>>
>> bear in mind that the only instance you defined is
>>
>> instance Class () ()
>>
>> which doesn't involve your GADT at all.
>
> This is correct.  (It's only a trimmed-down example, after all.)
>
>> Maybe you meant something like:
>>
>> instance Class (GADT a) ()
>
> No, I didn't.
>
>> Moreover, your fun cannot typecheck, regardless of using MPTC or
>> GADTs. The unit constructor, (), has type () and not b.
>
> Pattern matching against the data constructor GADT specializes a to ().  Since
> Class uses a functional dependency, it is clear that b has to be ().  So it
> should typecheck.  At least, I want it to.  ;-)

I'm re-reading what you said after my first reply.  I'm inserting
types in places that may not be valid in Haskell...

You're saying that the types should be like this:

fun :: (Class a b) => GADT a -> b
fun (GADT :: GADT ()) = ()

So, now I'm more inclined to agree with you than before.  And suppose
we added this:

data GADT a where
     GADT :: GADT ()
     GADT2 :: GADT String

Now I would expect this:
fun :: (Class a b) => GADT a -> b
fun (GADT :: GADT ()) = ()
fun (GADT2 :: GADT String) = -- I can't put anything here till I add
more instances of Class

Now, I'm too confused about how this should work.

Jason