Could I has one question? What is the purpose of the "stream" function in the ArrowLoop instance? Is it just to catch an unexpected [] at runtime?

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module Main where

import Control.Arrow
import Control.Arrow.Operations
import Control.Arrow.Transformer.Reader

--
-- Standard list/stream arrow.
--

newtype SF b c = SF { runSF :: [b] -> [c] }

instance Arrow SF where
   arr f = SF (map f)
   SF f >>> SF g = SF (g . f)
   first  (SF f) = SF (uncurry zip . (f *** id) . unzip)
   second (SF f) = SF (uncurry zip . (id *** f) . unzip)

instance ArrowLoop SF where
   loop (SF f) = SF $ \as ->
       let (bs,cs) = unzip (f (zip as (stream cs))) in bs
     where stream ~(x:xs) = x:stream xs

It looks like stream is (almost) an identity which would crash at runtime if it encountered a []. In particular it is equivalent to

>      where stream xs = head xs:stream (tail xs)


instance ArrowCircuit SF where
   delay x = SF (init . (x:))


--
-- Some state we want to pass around without manual plumbing.
--

data AudioState = AudioState { sampleRate :: Double }

runAudio state graph = proc p -> (| runReader (graph -< p) |) state


--
-- Some unit generators for audio.
--

wrap x = x - fromIntegral (floor x)

-- phasor needs the sample rate
phasor phase0 = proc hz -> do
   sr <- pure sampleRate <<< readState -< ()
   rec accum <- delay (wrap phase0) -< wrap (accum + hz / sr)
   returnA -< accum

-- osc doesn't need to know about sample rate
osc phase0 = proc hz -> do
   phase <- phasor phase0 -< hz
   returnA -< cos (2 * pi * phase)


--
-- Test it out.
--

main = print (runSF (runAudio (AudioState{sampleRate=1000}) (osc 0)) (replicate 10 100))

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