Focusing on each element individually and applying a function to the foci

AllContexts.hs

{-# LANGUAGE RecordWildCards #-}

module AllContexts where

import Data.List

data Context a = Context
  { before :: [a]
  , focus  :: a
  , after  :: [a]
  } deriving Show

inspect :: [a] -> Maybe (a, [a])
inspect []       = Nothing
inspect (x : xs) = Just (x, xs)

mkContext :: [a] -> Maybe (Context a)
mkContext = fmap (uncurry $ Context []) . inspect

moveRight :: Context a -> Maybe (Context a)
moveRight Context{..} = uncurry (Context (focus : before)) <$> inspect after

fromContext :: Context a -> [a]
fromContext Context{..} = reverse before ++ focus : after

allContexts :: [a] -> [Context a]
allContexts = unfoldr (fmap (\ s -> (s, moveRight s))) . mkContext

onFocus :: (a -> a) -> Context a -> Context a
onFocus f c = c { focus = f (focus c) }

applyMap :: (a -> a) -> [a] -> [[a]]
applyMap f = map (fromContext . onFocus f) . allContexts