[Haskell-cafe] mapFst and mapSnd

[Shachaf Ben-Kiki]

On Tue, May 28, 2013 at 1:54 AM, Dominique Devriese
<dominique.devriese at cs.kuleuven.be> wrote:
> Hi all,
>
> I often find myself needing the following definitions:
>
>   mapPair :: (a -> b) -> (c -> d) -> (a,c) -> (b,d)
>   mapPair f g (x,y) = (f x, g y)
>
>   mapFst :: (a -> b) -> (a,c) -> (b,c)
>   mapFst f = mapPair f id
>
>   mapSnd :: (b -> c) -> (a,b) -> (a,c)
>   mapSnd = mapPair id
>
> But they seem missing from the prelude and Hoogle or Hayoo only turn
> up versions of them in packages like scion or fgl.  Has anyone else
> felt the need for these functions?  Am I missing some generalisation
> of them perhaps?
>

One generalization of them is to lenses. For example `lens` has
"both", "_1", "_2", such that "mapPair = over both", "mapFst = over
_1", etc., but you can also get "fst = view _1", "set _2 = \y' (x,_)
-> (x,y')", and so on. (Since "both" refers to two elements, you end
up with "view both = \(x,y) -> mappend x y".) The types you end up
with are simple generalizations of mapFoo, with just an extra Functor
or Applicative (think mapMFoo):

both :: Applicative f => (a -> f b) -> (a,a) -> f (b,b)
both f (x,y) = (,) <$> f x <*> g y

_2 :: Functor f => (a -> f b) -> (e,a) -> f (e,b)
_2 f (x,y) = (,) x <$> f y

With an appropriate choice of f you can get many useful functions.

    Shachaf