[Haskell-cafe] type families and type signatures

[Ganesh Sittampalam]

On Mon, 7 Apr 2008, Manuel M T Chakravarty wrote:

> Ganesh Sittampalam:
>> The following program doesn't compile in latest GHC HEAD, although it does 
>> if I remove the signature on foo'. Is this expected?
>
> Yes, unfortunately, this is expected, although it is very unintuitive. 
> This is for the following reason.
>
> Let's alpha-rename the signatures and use explicit foralls for clarity:
>
> foo  :: forall a. Id a -> Id a
> foo' :: forall b. Id b -> Id b
>
> GHC will try to match (Id a) against (Id b).  As Id is a type synonym family, 
> it would *not* be valid to derive (a ~ b) from this.  After all, Id could 
> have the same result for different argument types.  (That's not the case for 
> your one instance, but maybe in another module, there are additional 
> instances for Id, where that is the case.)

Can't it derive (Id a ~ Id b), though?

> Now, as GHC cannot show that a and b are the same, it can also not show that 
> (Id a) and (Id b) are the same.  It does look odd when you use the same type 
> variable in both signatures, especially as Haskell allows you to leave out 
> the quantifiers, but the 'a' in the signature of foo and the 'a' in the 
> signatures of foo' are not the same thing; they just happen to have the same 
> name.

Sure, but forall a . Id a ~ Id a is the same thing as forall b . Id b ~ Id 
b.

Thanks for the explanation, anyway. I'll need to have another think about 
what I'm actually trying to do (which roughly speaking is to specialise a 
general function over type families using a signature which I think I need 
for other reasons).

Generally speaking, is there any way to give a signature to foo'?

> Given that this is a confusing issue, I am wondering whether we could improve 
> matters by giving a better error message, or an additional hint in the 
> message.  Do you have any suggestion regarding what sort of message might 
> have helped you?

I can't think of anything good. Perhaps printing out the (type classes + 
equalities) context would have helped me to see that it was empty and 
understand why, but probably not.

Cheers,

Ganesh