[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

Sittampalam, Ganesh:
> 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
>>>> 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?
>> That's what it does derive as a proof obligation and finds it can't  
>> prove.
>> 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,
> surely?

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)).   
>> The
>> problem is related to the infamous (show . read).
> My real code is somewhat analogous to (foo :: (Id Int -> Id Int))  
> (1::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  
change foo?


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