Integral using causal commutative arrows

Integral.hs

import Control.Arrow
import Control.Arrow.Operations
import Control.Arrow.Transformer.All
import Data.Stream

frequency :: Int
frequency = 1024

exp :: StreamArrow (->) () Double
exp = fixA (integral >>> arr (+1))

fixA :: ArrowLoop a => a b b -> a () b
fixA f = loop (second f >>> arr (\((), y) -> (y, y)))

integral :: ArrowCircuit a => a Double Double
integral = loop (arr (\(v, i) -> i + dt * v) >>> delay 0 >>> arr diag)

diag :: a -> (a, a)
diag x = (x, x)

units = Cons () units

dt :: Double
dt = recip $ fromIntegral frequency

main :: IO ()
main = print $ case (fixA (integral >>> arr (+1))) of StreamArrow x -> x units Data.Stream.!! frequency