{-# LANGUAGE Arrows #-}

import Control.Arrow
import qualified Control.Category as Cat

addA :: Arrow a => a b Int -> a b Int -> a b Int
addA f g = proc x -> do
                y <- f -< x
                z <- g -< x
                returnA -< y + z

newtype Circuit a b = Circuit { unCircuit :: a -> (Circuit a b, b) }

instance Cat.Category Circuit where
    id = Circuit $ \a -> (Cat.id, a)
    (.) = dot
      where
        (Circuit cir2) `dot` (Circuit cir1) = Circuit $ \a ->
            let (cir1', b) = cir1 a
                (cir2', c) = cir2 b
            in  (cir2' `dot` cir1', c)

instance Arrow Circuit where
    arr f = Circuit $ \a -> (arr f, f a)
    first (Circuit cir) = Circuit $ \(b, d) ->
        let (cir', c) = cir b
        in  (first cir', (c, d))

-- | Accumulator that outputs a value determined by the supplied function.
accum :: acc -> (a -> acc -> (b, acc)) -> Circuit a b
accum acc f = Circuit $ \input ->
    let (output, acc') = input `f` acc
    in  (accum acc' f, output)

-- | Accumulator that outputs the accumulator value.
accum' :: b -> (a -> b -> b) -> Circuit a b
accum' acc f = accum acc (\a b -> let b' = a `f` b in (b', b'))

total :: Num a => Circuit a a
total = accum' 0 (+)

mean3 :: Fractional a => Circuit a a
mean3 = proc value -> do
    (t, n) <- (| (&&&) (total -< value) (total -< 1) |)
    returnA -< t / n