Alternative van Laarhoven lenses are non-deterministic lenses.

AlternativeLens.hs

{-# LANGUAGE RankNTypes #-}

import Control.Applicative
import Data.Monoid

type AltLens a b = forall m. Alternative m => (b -> m b) -> a -> m a

-- This instance is a bit odd, but it works.
instance Monoid m => Alternative (Const m) where
  empty = Const mempty
  Const m1 <|> Const m2 = Const (m1 `mappend` m2)

get :: AltLens a b -> a -> [b]
get l = getConst . l (Const . pure)

modify :: AltLens a b -> (b -> b) -> a -> [a]
modify l f = l (pure . f)

set :: AltLens a b -> b -> a -> [a]
set l = modify l . const


list :: AltLens [a] a
list _ [] = empty
list f (x:xs) = (:) <$> f x <*> pure xs <|> (:) <$> pure x <*> list f xs

powerlist :: AltLens [a] a
powerlist _ [] = pure []
powerlist f (x:xs) = (:) <$> (pure x <|> f x) <*> powerlist f xs