module Fibs where
import StreamProc
import Control.Arrow

test = take 10 $ runSP fibs [0..]

fibs :: SP a Integer
fibs = put 0 fibs'
  where fibs' = put 1 $ liftA2 (+) fibs fibs'

{-
runSP fibs [] = [0, 1]

runSP (Put 0 fibs') []
 => 0:runSP fibs' []
 => 0:runSP (Put 1 $ liftA2 (+) fibs fibs') []
 => 0:1:runSP (liftA2 (+) fibs fibs') []
 => 0:1:runSP ((fibs &&& fibs') >>> arr (uncurry (+))) []
 => 0:1:runSP (arr (\x -> (x, x)) >>> fibs *** fibs' >>> arr (uncurry (+))) [] ... [1]

arr (\x -> (x, x))
 => Get $ \a -> Put (a, a) (arr (\x -> (x, x))) ... [2]

arr (uncurry (+))
 => Get $ \(a, b) -> Put (a + b) (arr (uncurry (+))) ... [3]

fibs *** fibs'
 => first fibs >>> second fibs'
 => bypass [] fibs >>> second fibs'
 => bypass [] (Put 0 fibs') >>> second fibs'
 => Get (\(b, d) -> Put (0, d) (bypass [] fibs')) >>> second fibs'
 => Get (\(b ,d) -> Put (0, d) (bypass [] fibs')) >>> second (Put 1 $ liftA2 (+) fibs fibs')
 => Get (\(b ,d) -> Put (0, d) (bypass [] fibs')) >>> Get (\(d, b) -> Put (d, 1) (bypass [] (liftA2 (+) fibs fibs')))
 => Get (\(b, d) -> Put (0, d) (bypass [] fibs') >>> Get (\(d, b) -> Put (d, 1) (bypass [] (liftA2 (+) fibs fibs'))))  ... [4]

[2], [3], [4]から
arr (\x -> (x, x)) >>> fibs *** fibs' >>> arr (uncurry (+))
 => Get $ \a -> Put (a, a) (arr (\x -> (x, x)))
      >>> Get (\(b, d) -> Put (0, d) (bypass [] fibs') >>> Get (\(d, b) -> Put (d, 1) (bypass [] (liftA2 (+) fibs fibs'))))
      >>> Get $ \(a, b) -> Put (a + b) (arr (uncurry (+)))

 => Get $ \a -> Put (a, a) (arr (\x -> (x, x)))
      >>> Get (\a -> sp2 a >>> Get sp1)
      where sp2 = \(b, d) -> Put (0, d) (bypass [] fibs') >>> Get (\(d, b) -> Put (d, 1) (bypass [] (liftA2 (+) fibs fibs')))
            sp1 = \(a, b) -> Put (a + b) (arr (uncurry (+)))

 => Get $ \b -> sp2' b >>> Get sp1'
      where sp2' = \a -> Put (a, a) (arr (\x -> (x, x)))
            sp1' = \a -> sp2 a >>> Get sp1
            sp2 = \(b, d) -> Put (0, d) (bypass [] fibs') >>> Get (\(d, b) -> Put (d, 1) (bypass [] (liftA2 (+) fibs fibs')))
            sp1 = \(a, b) -> Put (a + b) (arr (uncurry (+))) ... [5]

[1], [5]から
0:1:runSP (arr (\x -> (x, x)) >>> fibs *** fibs' >>> arr (uncurry (+))) []
 => 0:1:runSP (Get $ \b -> sp2' b >>> Get sp1') []
      where sp2' = \a -> Put (a, a) (arr (\x -> (x, x)))
            sp1' = \a -> sp2 a >>> Get sp1
            sp2 = \(b, d) -> Put (0, d) (bypass [] fibs') >>> Get (\(d, b) -> Put (d, 1) (bypass [] (liftA2 (+) fibs fibs')))
            sp1 = \(a, b) -> Put (a + b) (arr (uncurry (+)))
 => 0:1:[]
 => [0, 1]
-}