[Haskell-cafe] type families and type signatures
Manuel M T Chakravarty
chak at cse.unsw.edu.au
Tue Apr 8 22:24:46 EDT 2008
> Manuel Chakravarty wrote:
>> 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
>>>> 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
>>>> 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
>>> Can't it derive (Id a ~ Id b), though?
>> That's what it does derive as a proof obligation and finds it can't
>> The error message you are seeing is GHC's way of saying, I cannot
>> assert that
>> (Id a ~ Id b) holds.
> No, I meant can't it derive that equality when matching (Id a)
> against (Id b)?
> As you say, it can't derive (a ~ b) at that point, but (Id a ~ Id b)
> is known,
No, it is not know. Why do you think it is?
>>> Generally speaking, is there any way to give a signature to foo'?
>> Sorry, but in the heat of explaining what GHC does, I missed the
>> probably crucial point. Your function foo is useless, as is foo'.
>> Not only can't you rename foo (to foo'), but you generally can't use
>> it. It's signature is ambiguous. Try evaluating (foo (1::Int)).
>> problem is related to the infamous (show . read).
> My real code is somewhat analogous to (foo :: (Id Int -> Id Int))
> Isn't that unambiguous in the same way as (show.read) is if I give
> show or
> read a signature?
No. The problem with a functions that has an ambiguous signature is
that it contains type variables that are impossible to constrain by
applying the function. Providing a type signature at the application
site makes this no easier. Why? Consider what a type annotation
means. By writing e :: t, you express your intent to use e at type t,
but you also force the compiler to check that whatever type it derives
for e is more general than t. It is this check for type subsumption
that is the tricky bit when typing TFs (or FDs). See <http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html
> for more detail on why this is a hard problem.
The problem with an ambiguous signature is that the subsumption check
always fails, because the ambiguous signature contains some type
variables for which the type checker cannot deduce a type instance.
(You as a human reader may be able to *guess* an instance, but HM-
based inference does generally not guess. It's a deterministic
The problem is really with foo and its signature, not with any use of
foo. The function foo is (due to its type) unusable. Can't you
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