Re: [Haskell-cafe] mapFst and mapSnd

class BinaryFunctor f where bimap :: (a -> c) -> (b -> d) -> f a b -> f c d mapFst = (`bimap id`) mapSnd = bimap id On 31/05/2013 12:16 PM, "Shachaf Ben-Kiki" wrote:

On Thu, May 30, 2013 at 7:12 PM, Shachaf Ben-Kiki wrote:

...

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.

I spoke too quickly -- your mapPair is something different. Indeed bimap (or (***), if you prefer base) is the place to find it -- lenses don't really fit here. My "both" is for mapping one function over both elements.

Shachaf

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