AutoIso.hs

data Auto1 a b = A1 { runAuto :: a -> (b, Auto1 a b) }
data Auto2 a b = forall s. A2 s ((a, s) -> (b, s))


sumFrom1 :: Int -> Auto1 Int Int
sumFrom1 n = A1 $ \x -> (x + n, sumFrom1 (x + n))

sumFrom2 :: Int -> Auto2 Int Int
sumFrom2 n0 = A2 n0 $ \(x, n) -> (x + n, x + n)

oneTwo :: Auto1 a b -> Auto2 a b
oneTwo a0 = A2 a0 $ \(x, a) -> runAuto a x

twoOne :: Auto2 a b -> Auto1 a b
twoOne (A2 s0 f) = A1 $ \x -> let (y, s1) = f (x, s0)
                              in  (y, twoOne (A s1 f))