Holes.hs

module Holes where
import Control.Applicative

newtype Holes t a = Holes { runHoles :: t (a, a -> Holes t a) }

evalHoles :: Functor t => Holes t a -> t a
evalHoles = fmap fst . runHoles

holes :: Traversable t => t a -> Holes t a
holes ta = Holes $ traverse ctx ta `runKA` Holes

ctx :: a -> KA r (a, a -> r)
ctx a = KA $ \k ->
  let f a' = k (a', f) in (a, f)

newtype KA r a = KA { runKA :: (a -> r) -> a }

instance Functor (KA r) where fmap f a = pure f <*> a
instance Applicative (KA r) where
  pure a = KA (\_ -> a)
  liftA2 f (KA ka) (KA kb) = KA $ \cr ->
    let a = ka $ \a' -> cr $ f a' b
        b = kb $ \b' -> cr $ f a b'
    in f a b

There's also \ta -> traverse ctx ta `runKA` fmap fst, which has type Traversable f => f a -> f (a, a -> f a) and may also be worth considering.

KA is Search isn't it https://hackage.haskell.org/package/search-0.2/docs/Data-Search.html I love code like this