[Haskell-cafe] Type Family Relations

[Thomas DuBuisson]

Thank you all for the responses.  I find the solution that omits type
families [Diatchki] to be too limiting while the solution 'class (Dual
(Dual s) ~ s) =>' [Ingram] isn't globally enforced.  I've yet to
closely study your first solution, Ryan, but it appears to be what I
was looking for - I'll give it a try in the coming week.

Tom

On Sat, Jan 3, 2009 at 8:18 PM, Iavor Diatchki <iavor.diatchki at gmail.com> wrote:
> Hello,
> Usually, you can program such things by using super-classes.  Here is
> how you could encode your example:
>
> {-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies,
> FlexibleInstances #-}
>
> class HeaderOf addr hdr | addr -> hdr
> class HeaderOf addr hdr => AddressOf hdr addr | addr -> hdr
>
> data IPv4Header = C1
> data IPv4       = C2
> data AppAddress = C3
> data AppHeader  = C4
>
> instance AddressOf IPv4Header IPv4
> instance HeaderOf IPv4 IPv4Header
>
> {- results in error:
> instance AddressOf AppHeader AppAddress
> instance HeaderOf AppAddress [AppHeader]
> -}
>
> Hope that this helps,
> Iavor
>
>
>
> On Sat, Jan 3, 2009 at 7:22 AM, Thomas DuBuisson
> <thomas.dubuisson at gmail.com> wrote:
>> Cafe,
>> I am wondering if there is a way to enforce compile time checking of
>> an axiom relating two separate type families.
>>
>> Mandatory contrived example:
>>
>>> type family AddressOf h
>>> type family HeaderOf a
>>>
>>> -- I'm looking for something to the effect of:
>>> type axiom HeaderOf (AddressOf x) ~ x
>>>
>>> -- Valid:
>>> type instance AddressOf IPv4Header = IPv4
>>> type instance HeaderOf IPv4 = IPv4Header
>>>
>>> -- Invalid
>>> type instance AddressOf AppHeader = AppAddress
>>> type instance HeaderOf AppAddress = [AppHeader]
>>
>> So this is  a universally enforced type equivalence.  The stipulation
>> could be arbitrarily complex, checked at compile time, and must hold
>> for all instances of either type family.
>>
>> Am I making this too hard?  Is there already a solution I'm missing?
>>
>> Cheers,
>> Tom
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>