Backwards and Reverse

[dcastro]

I was wondering what the maintainers think about adding something like Haskell's Control.Applicative.Backwards and Data.Functor.Reverse to cats.
Or maybe something like this already exists in cats and I missed it.

Backwards

Backwards is a newtype wrapper around any f a.
If that f has an instance for Applicative, then so does Backwards f.

With good ol' applicative composition, this code will print "1" and "2", in that order.

data Test = Test Int String
  deriving Show

let x = do putStrLn "1"; pure 1 :: IO Int
let y = do putStrLn "2"; pure "2" :: IO String

Test <$> x <*> y

But by wrapping the effects in Backwards, "2" is printed before "1":

forwards $ Test <$> Backwards x <*> Backwards y

Reverse

Reverse is a newtype wrapper around any f a.
If that f has an instance for Foldable, then so does Reverse f.
If that f has an instance for Traversable, then so does Reverse f.

Good ol' traversal will apply the effects to each element of a list, going left to right:

λ> traverse print [1,2,3]
1
2
3

But by wrapping the f a in Reverse, the effects of the traversal are observed in right to left fashion.

traverse print (Reverse [1,2,3])
3
2
1

If this is deemed a good fit for cats, I wouldn't mind giving it a go.

[chuwy]

Regardless of whether this should belong to cats core or not, I would like to have it in Scala.

[LukaJCB]

We have newts for these kinds of things. But maybe with #1800 and opaque types on the horizon, it might make sense to rethink the separation and consider moving them into the cats repo. :)

[dcastro]

@LukaJCB So, should this go in newts for now, and maybe be moved into cats later?