Fixing Fix

[Erik Hesselink]

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