[Haskell] How to avoid both duplicate instances and extraneousinstance declarations?

[Robin Bate Boerop]

Claus,

You have given a very good analysis of the situation.  Thank you.

I mean to ensure that "an instance of A is a necessary consequence of  
having an instance for either of B1/B2", in your words.  Further, in  
my situation, no data type will be an instance of both B1 and B2.   
So, the compiler will never have to make the choice that you  
discuss.  However, I have no way (that I know) to tell the compiler  
this.  If I did, then the compiler would never need to decide between  
an instance of A by means of B1 and an instance of A by means of B2.

While the code you give may do the job (I haven't tried it), it  
doesn't help my problem because it requires that I do more typing.  I  
want to avoid the extra typing of "instance A T" when I've already  
typed "instance B1 T", say.

-- 
Robin Bate Boerop

On 22-Apr-06, at 3:51 PM, Claus Reinke wrote:

>> I have three classes, A, B1, and B2.  I want all instances of B1  
>> to  be instances of A.  I want all instances of B2 to be instances  
>> of A.
>
> if you mean to ensure that an instance of A should be a pre- 
> requisite for defining instances of B1/B2, then your second  
> approach might be more appropriate. if you mean to ensure that an  
> instance of A is a necessary consequence of having an instance for  
> either of B1/B2,
> then your first approach seems close, but runs into a technical issue:
>
> by default, an instance of A by means of an instance of B1 may  
> differ from an instance of A by means of an instance of B2.
>
>> None of the classes have methods.
>> The following does NOT work, because of a duplicate instance   
>> declaration for A:
>> class A a
>> class B1 b1
>> class B2 b2
>> instance B1 x => A x
>> instance B2 x => A x  -- duplicate instance, won't compile
>> data T = T
>> instance B1 T
>
> the question is: if both B1 x and B2 x hold, does it matter which  
> one is chosen in the proof of A x? if it does, how is the  
> implementation to choose the right one, and if it doesn't (one  
> might then ask why B1 and B2 are separate in the first place), how  
> is the implementation
> to know that?
>
> you can introduce an arbitrary distinction in the two proofs, and
> then throw that distinction away later, as shown below, but whether
> or not that works depends on your application context. for instance,
> f is accepted and can be applied in either hugs or ghc; but hugs
> would complain about the commented out A; ghci would accept
> A, and the definition of g, but would complain about any use of g.
>
> cheers,
> claus
>
> {-# OPTIONS_GHC -fglasgow-exts #-}
> {-# OPTIONS_GHC -fallow-undecidable-instances #-}
>
> class A' a x
> -- class A a
> -- instance A' a b => A a
>
> data B1T
> class B1 b1
>
> data B2T
> class B2 b2
>
> instance B1 x => A' x B1T
> instance B2 x => A' x B2T -- duplicate instance, won't compile
>
> data T = T
> instance B1 T
>
> f :: (forall b . A' x b => x) -> String
> f x = undefined
>
> -- g :: A x => x -> String
> -- g = undefined
>