haskell - Combining lenses

Question

Using a lens library I can apply a modification function to individual targets, like so:

Prelude Control.Lens> (1, 'a', 2) & _1 %~ (*3)
(3,'a',2)
Prelude Control.Lens> (1, 'a', 2) & _3 %~ (*3)
(1,'a',6)

How can I combine those individual lenses (_1 and _3) to be able to perform this update to both of the targets at once? I expect something in the spirit of the following:

Prelude Control.Lens> (1, 'a', 2) & ??? %~ (*3)
(3,'a',6)

Answer 1

Using untainted from the Settable type class in Control.Lens.Internal.Setter, it is possible to combine two setters, but the result will also only be a setter and not a getter.

import Control.Lens.Internal.Setter

-- (&&&) is already taken by Control.Arrow
(~&~) :: (Settable f) => (c -> d -> f a) -> (c -> a -> t) -> c -> d -> t
(~&~) a b f = b f . untainted . a f

You can test this:

>>> import Control.Lens
>>> (1, 'a', 2) & (_1 ~&~ _3) %~ (*3)
(3,'a',6)

EDIT

You don't actually need to use internal functions. You can use the fact that Mutator is a monad:

{-# LANGUAGE NoMonomorphismRestriction #-}

import Control.Monad
import Control.Applicative

(~&~) = liftA2 (>=>)

-- This works too, and is maybe easier to understand: 
(~&~) a b f x = a f x >>= b f