Re: Foldable.Mapped

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" 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-Co...

Shachaf

On Sun, Jan 3, 2016 at 5:11 PM, Henning Thielemann wrote:

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On Mon, 4 Jan 2016, Oliver Charles wrote:

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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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