Fundeps and type equality
Carter Schonwald
carter.schonwald at gmail.com
Fri Jan 11 21:52:33 CET 2013
One thing thats unclear (or at least implicit) about the overlapping type
families from the docs is this:
does it let me write recursive type level functions? (I really really
really want that :) )
thanks
-Carter
On Thu, Jan 10, 2013 at 10:03 PM, Richard Eisenberg <eir at cis.upenn.edu>wrote:
> Yes, I finished and pushed in December. A description of the design and
> how to use the feature is here:
> http://hackage.haskell.org/trac/ghc/wiki/NewAxioms
>
> There's also a section (7.7.2.2 to be exact) in the manual, but building
> the manual from source is not for the faint of heart.
>
> Richard
>
> On Jan 10, 2013, at 3:14 PM, Carter Schonwald <carter.schonwald at gmail.com>
> wrote:
>
> so the overlapping type families are in HEAD?
>
> Awesome! I look forward to finding some time to try them out :)
>
>
> On Thu, Jan 10, 2013 at 1:56 PM, Richard Eisenberg <eir at cis.upenn.edu>wrote:
>
>> For better or worse, the new overlapping type family instances use a
>> different overlapping mechanism than functional dependencies do. Class
>> instances that overlap are chosen among by order of specificity;
>> overlapping instances can be declared in separate modules. Overlapping
>> family instances must be given an explicit order, and those that overlap
>> must all be in the same module. The decision to make these different was to
>> avoid type soundness issues that would arise with overlapping type family
>> instances declared in separate modules. (Ordering a set of family instance
>> equations by specificity, on the other hand, could easily be done within
>> GHC.)
>>
>> So, as yet, we can't fully encode functional dependencies with type
>> families, I don't think.
>>
>> Richard
>>
>> On Jan 2, 2013, at 4:01 PM, Martin Sulzmann <
>> martin.sulzmann.haskell at googlemail.com> wrote:
>>
>>
>> I agree with Iavor that it is fairly straight-forward to extend FC to
>> support FD-style type improvement. In fact, I've formalized such a proof
>> language in a PPDP'06 paper:
>> "Extracting programs from type class proofs"
>> (type improvement comes only at the end)
>>
>> Similar to FC, coercions (proof terms) are used to represent type
>> equations (improvement).
>>
>> Why extend FC?
>> Why not simply use type families to encode FDs (and thus keep FC simple
>> and small).
>>
>> It's been a while, but as far as I remember, the encoding is only
>> problematic in case of the combination of FDs and overlapping instances.
>> Shouldn't this now be fixable given
>> that type family instances can be overlapping?
>> Maybe I'm missing something, guess it's also time to dig out some old
>> notes ...
>>
>> -Martin
>>
>> On Wed, Jan 2, 2013 at 10:04 AM, Simon Peyton-Jones <
>> simonpj at microsoft.com> wrote:
>>
>>> As far as I understand, the reason that GHC does not construct such
>>> proofs is that it can't express them in its internal proof language (System
>>> FC). ****
>>>
>>> ** **
>>>
>>> Iavor is quite right****
>>>
>>> ** **
>>>
>>> It seems to me that it should be fairly straight-forward to extend FC to
>>> support this sort of proof, but I have not been able to convince folks that
>>> this is the case. I could elaborate, if there's interest.****
>>>
>>> ** **
>>>
>>> Iavor: I don’t think it’s straightforward, but I’m willing to be
>>> educated. By all means start a wiki page to explain how, if you think it
>>> is. ****
>>>
>>> ** **
>>>
>>> I do agree that injective type families would be a good thing, and would
>>> deal with the main reason that fundeps are sometimes better than type
>>> families. A good start would be to begin a wiki page to flesh out the
>>> design issues, perhaps linked from
>>> http://hackage.haskell.org/trac/ghc/wiki/TypeFunctions****
>>>
>>> ** **
>>>
>>> The main issues are, I think:****
>>>
>>> **· **How to express functional dependencies like “fixing the
>>> result type and the first argument will fix the second argument”****
>>>
>>> **· **How to express that idea in the proof language****
>>>
>>> ** **
>>>
>>> Simon****
>>>
>>> ** **
>>>
>>> *From:* glasgow-haskell-bugs-bounces at haskell.org [mailto:
>>> glasgow-haskell-bugs-bounces at haskell.org] *On Behalf Of *Iavor Diatchki
>>> *Sent:* 26 December 2012 02:48
>>> *To:* Conal Elliott
>>> *Cc:* glasgow-haskell-bugs at haskell.org; GHC Users Mailing List
>>> *Subject:* Re: Fundeps and type equality****
>>>
>>> ** **
>>>
>>> Hello Conal,****
>>>
>>> ** **
>>>
>>> GHC implementation of functional dependencies is incomplete: it will use
>>> functional dependencies during type inference (i.e., to determine the
>>> values of free type variables), but it will not use them in proofs, which
>>> is what is needed in examples like the one you posted. The reason some
>>> proving is needed is that the compiler needs to figure out that for each
>>> instantiation of the type `ta` and `tb` will be the same (which, of course,
>>> follows directly from the FD on the class).****
>>>
>>> ** **
>>>
>>> As far as I understand, the reason that GHC does not construct such
>>> proofs is that it can't express them in its internal proof language (System
>>> FC). It seems to me that it should be fairly straight-forward to extend FC
>>> to support this sort of proof, but I have not been able to convince folks
>>> that this is the case. I could elaborate, if there's interest.****
>>>
>>> ** **
>>>
>>> In the mean time, the way forward would probably be to express the
>>> dependency using type families, which I find tends to be more verbose but,
>>> at present, is better supported in GHC.****
>>>
>>> ** **
>>>
>>> Cheers,****
>>>
>>> -Iavor****
>>>
>>> PS: cc-ing the GHC users' list, as there was some talk of closing the
>>> ghc-bugs list, but I am not sure if the transition happened yet.****
>>>
>>> ** **
>>>
>>> ** **
>>>
>>> ** **
>>>
>>> ** **
>>>
>>> On Tue, Dec 25, 2012 at 6:15 PM, Conal Elliott <conal at conal.net> wrote:*
>>> ***
>>>
>>> I ran into a simple falure with functional dependencies (in GHC 7.4.1):
>>>
>>> > class Foo a ta | a -> ta
>>> >
>>> > foo :: (Foo a ta, Foo a tb, Eq ta) => ta -> tb -> Bool
>>> > foo = (==)
>>>
>>> I expected that the `a -> ta` functional dependency would suffice to
>>> prove that `ta ~ tb`, but
>>>
>>> Pixie/Bug1.hs:9:7:
>>> Could not deduce (ta ~ tb)
>>> from the context (Foo a ta, Foo a tb, Eq ta)
>>> bound by the type signature for
>>> foo :: (Foo a ta, Foo a tb, Eq ta) => ta -> tb ->
>>> Bool
>>> at Pixie/Bug1.hs:9:1-10
>>> `ta' is a rigid type variable bound by
>>> the type signature for
>>> foo :: (Foo a ta, Foo a tb, Eq ta) => ta -> tb -> Bool
>>> at Pixie/Bug1.hs:9:1
>>> `tb' is a rigid type variable bound by
>>> the type signature for
>>> foo :: (Foo a ta, Foo a tb, Eq ta) => ta -> tb -> Bool
>>> at Pixie/Bug1.hs:9:1
>>> Expected type: ta -> tb -> Bool
>>> Actual type: ta -> ta -> Bool
>>> In the expression: (==)
>>> In an equation for `foo': foo = (==)
>>> Failed, modules loaded: none.****
>>>
>>> Any insights about what's going wrong here?****
>>>
>>> -- Conal****
>>>
>>>
>>> _______________________________________________
>>> Glasgow-haskell-bugs mailing list
>>> Glasgow-haskell-bugs at haskell.org
>>> http://www.haskell.org/mailman/listinfo/glasgow-haskell-bugs****
>>>
>>> ** **
>>>
>>> _______________________________________________
>>> Glasgow-haskell-users mailing list
>>> Glasgow-haskell-users at haskell.org
>>> http://www.haskell.org/mailman/listinfo/glasgow-haskell-users
>>>
>>>
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