import Control.Applicative


-- Applicative functor with nothing but threaded state.

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

runThread (Thread inc a) = (a, inc 0)

appThread :: Thread s (a -> b) -> Thread s a -> Thread s b
appThread (Thread cf f) (Thread ca a) = Thread cb b where
  b = f a
  cb = ca . cf
    
instance Applicative (Thread s) where    
  (<*>) = appThread
  pure a = Thread (\n -> n) a

instance Functor (Thread s) where
  fmap f = (pure f <*>)
          


makeCount x = Thread (\n -> n + 1) x




-- Probably makes more sense to start with the pure combination
-- approach to Applicatives (Monoidal)
--    unit :: f ()
--    <,>  :: f a -> f b -> f (a,b)