store.hs

data Store s a = Store (s -> a) s

instance Comonad (Store s) where
  extract :: Store s a -> a
  extract (Store f s) = f s

  -- "replacing all values with containers, and then consuming those containers again"
  extend :: Store s a -> (Store s a -> b) -> Store s b
  extend s f = fmap f $ duplicate s
   -- verbose: Store (\x -> f' $ Store f x) s

duplicate :: Store s a -> Store s (Store s a)
duplicate (Store f s) = Store (\x -> Store f x) s

-- Read out the store at some specific position
peek :: s -> Store s a -> a
peek s (Store f _) = f s

-- Modify the current focus, and read the store using the new focus.
peeks :: (s -> s) -> Store s a -> a
peeks f (Store f' s) = f' (f s)

-- Set the current focus
seek :: s -> Store s a -> Store s a
seek s (Store f _) = Store f s

-- Modify the current focus
seeks :: (s -> s) -> Store s a -> Store s a
seeks f (Store f' s) = Store f' (f s)

-- Run an experiment in the store.
experiment :: Functor f => (s -> f s) -> Store s a -> f a
experiment f (Store s a) = fmap s (f a)