Fixing Fix

[Edward Kmett]

History of indexed:

The version of indexed on hackage was split out of my old category-extras
package by Reiner Pope. I asked a couple of years back if I could replace
it with a new version, and he said yes.

The version on my github is my exploration of that design space. It was
stalled because of issues with GHC circa 7.6. Notably: Any inhabiting every
kind meant that it wasn't sound to assume that the only inhabitants of the
product kind (i,j) are of the form '(a, b) for a :: i, and b :: j. We've
fixed most of those issues in GHC 7.10, so in theory i could pick up my
indexed package and finish it. There are other issues still outstanding,
but that was the big one.

I think there are enough points in this design space that I'm much much
happier to have this sort of thing in libraries that are removed from base
than having it in base itself. As an example: Making useful instances for
it requires either UndecidableInstances or switching to something like
Data.Functor.Classes or the machinery prelude-extras. I'm not terribly
comfortable with base making a bet on one such horse at the expense of the
others, and I'm even less comfortable moving the data type up where any
such instances would perforce be orphans if we didn't supply them.

*tl;dr* -1

-Edward


On Tue, Mar 24, 2015 at 1:00 PM, Oliver Charles <ollie at ocharles.org.uk>
wrote:

> Oh, I see your confusion - you're looking at `indexed` on Hackage, but I
> meant the unreleased library on Github. That uses the slice category
> presentation of higher-order monads/functors, which is what you're talking
> about:
>
> https://github.com/ekmett/indexed/blob/master/src/Indexed/Functor.hs#L53
>
> Though HFix isn't there, but I feel it would be a suitable addition to the
> library.
>
> It is unfortunate that there is a name conflict.
>
> On Tue, Mar 24, 2015 at 4:28 PM, Erik Hesselink <hesselink at gmail.com>
> wrote:
>
>> That seems slightly different, more related to indexed monads with
>> pre- and postconditions. They have many more type variables...
>>
>> Erik
>>
>> On Tue, Mar 24, 2015 at 5:20 PM, Oliver Charles <ollie at ocharles.org.uk>
>> wrote:
>> > Higher order stuff is very useful, but I don't think it needs to belong
>> in
>> > the same place as Data.Functor.Fix. Edward Kmett's 'indexed' library
>> will
>> > probably deal with this, when we have a GHC that's smart enough to
>> > understand it ;)
>> >
>> > - Ollie
>> >
>> > On Tue, Mar 24, 2015 at 3:40 PM, Erik Hesselink <hesselink at gmail.com>
>> wrote:
>> >>
>> >> Ugh, you're right, I renamed the variables and made a mistake. The
>> >> outer variable should stay the same of course, your signature is
>> >> correct.
>> >>
>> >> For a use site of HFix, see the multirec package [0], although that
>> >> might not really clarify things :) We also have a use internally, but
>> >> I just realized we can probably simplify that away.
>> >>
>> >> Regards,
>> >>
>> >> Erik
>> >>
>> >> [0]
>> >>
>> http://hackage.haskell.org/package/multirec-0.7.5/docs/Generics-MultiRec-HFix.html
>> >>
>> >> On Tue, Mar 24, 2015 at 4:25 PM, David Feuer <david.feuer at gmail.com>
>> >> wrote:
>> >> > I have no comment on your higher-order version (because I don't
>> >> > understand
>> >> > it yet), but the type you give for hmap looks unlikely. Did you mean
>> >> >
>> >> > hmap :: (g :-> h) -> f g :-> f h ?
>> >> >
>> >> > On Mar 24, 2015 10:58 AM, "Erik Hesselink" <hesselink at gmail.com>
>> wrote:
>> >> >>
>> >> >> On Tue, Mar 24, 2015 at 7:23 AM, M Farkas-Dyck <strake888 at gmail.com
>> >
>> >> >> wrote:
>> >> >> > On 22/03/2015 at 23:01:47 -0400, David Feuer wrote:
>> >> >> >> There are a good number of different packages that define either
>> >> >> >>
>> >> >> >> newtype Fix f = Fix (f (Fix f))
>> >> >> >>
>> >> >> >> or something equivalent except for naming. Most of the name
>> >> >> >> variation
>> >> >> >> is in the name of the data constructor and/or record selector.
>> This
>> >> >> >> does not look like an ideal situation to me. Most
>> problematically,
>> >> >> >> the
>> >> >> >> only way to convert one to another is with unsafeCoerce.
>> >> >> >>
>> >> >> >> I think it would be rather nice to choose one canonical place for
>> >> >> >> this
>> >> >> >> definition, and let everyone else use it.
>> >> >> >
>> >> >> > +1
>> >> >> >
>> >> >> > I propose
>> >> >> >
>> >> >> > module Data.Fix where
>> >> >> >
>> >> >> > newtype Fix f = Fix { unFix :: f (Fix f) }
>> >> >>
>> >> >> I'm used to
>> >> >>
>> >> >>     newtype Fix f = In { out : f (Fix f) }
>> >> >>
>> >> >> But all the other suggestions look fine to me, too.
>> >> >>
>> >> >> I've also often used this variation:
>> >> >>
>> >> >>     newtype HFix f a = In { out :: f (HFix f) a }
>> >> >>
>> >> >> This allows you to take the fixed point of e.g. monad stacks and
>> >> >> indexed types. The function you propose below can then be a type
>> class
>> >> >> function of an indexed Functor class:
>> >> >>
>> >> >>     type f :-> g = forall a. f a -> g a
>> >> >>
>> >> >>     class HFunctor f where
>> >> >>       hmap :: (a :-> b) -> f a :-> g a
>> >> >>
>> >> >> Does this deserve a place somewhere as well? Or is it too
>> specialized?
>> >> >>
>> >> >> > Perhaps too we ought to name and define _ :: (∀ a . f a -> g a) ->
>> >> >> > Fix f
>> >> >> > -> Fix g there.
>> >> >>
>> >> >> Some variation of 'map' seems sensible, like 'hmap' (but see above)
>> or
>> >> >> 'mapFix'.
>> >> >>
>> >> >> Erik
>> >> _______________________________________________
>> >> Libraries mailing list
>> >> Libraries at haskell.org
>> >> http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries
>> >
>> >
>>
>
>
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