Foldable.Mapped

[David Feuer]

That's what I was thinking too. While that's not Haskell 98, I believe it
can be justified on Haskell 98 grounds by approximate equivalence with the
representation of a foldable container by a binary tree. I'm no expert, but
I think the hypothetical alternative formulation might look like this:

--Free magma
data Tree a = Leaf a | Bin (Tree a) (Tree a) deriving (Functor, Foldable)

--Adjoin an identity and a phantom.
--The phantom isn't Haskell 98, but
--it would be possible to accomplish the
--same purpose in Haskell 98
data R (f :: * -> *) a = Empty | FM (Tree a) deriving (Functor, Foldable)

--Improper, but probably sane for the purpose
instance Monoid (R f a) where
  mempty = Empty
  mappend Empty ys = ys
  mappend xs Empty = xs
  mappend (FM xs) (FM ys) = FM (Bin xs ys)

rep :: Foldable f => f a -> R f a
rep = foldMap (FM . Leaf)

We can apply rep to a foldable container to get a reusable representation
of that container for folding purposes that is also a Functor.
On Jan 3, 2016 8:21 PM, "Shachaf Ben-Kiki" <shachaf at gmail.com> wrote:

> It sounds like Coyoneda -- i.e. Mapped with the "a" existential --
> might be what you're looking for:
>
> http://hackage.haskell.org/package/kan-extensions-4.2.3/docs/Data-Functor-Coyoneda.html
>
>      Shachaf
>
> On Sun, Jan 3, 2016 at 5:11 PM, Henning Thielemann
> <lemming at henning-thielemann.de> wrote:
> >
> > On Mon, 4 Jan 2016, Oliver Charles wrote:
> >
> >> Could you provide some examples where you have found it useful?
> >
> >
> > E.g. Set has Foldable instance, but not Functor. Using Mapped I can
> > implement argmax in a generic way, such that it also works on Set.
> >
> > argmax :: (Ord b, Foldable f) => (a -> b) -> f a -> a
> > argmax f = snd . Fold.maximumBy (comparing fst) . Mapped (\a -> (f a, a))
> >
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