Fixing Fix

[David Feuer]

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
>
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