Re: Fixing Fix

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 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 wrote:

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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 wrote:

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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-HFi...

...

On Tue, Mar 24, 2015 at 4:25 PM, David Feuer wrote:

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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"

wrote:

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On Tue, Mar 24, 2015 at 7:23 AM, M Farkas-Dyck wrote:

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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

...

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> 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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