--<PRE>

import Memo

data Stream a = a :^ Stream a

twoz = 2 : twoz

ex1 = head twos

ignore a b = b

fibA 0 = 1
fibA 1 = 1
fibA n = fibA(n-1) + fibA(n-2)

fibs = 1 : 1 : (zipWith (+) fibs (tail fibs))

--- Stream Diagram example:

counter :: [ Bool ] -> [ Integer ]
counter inp = out
    where
        out = ifx inp Then (lift 0) Else next
        next = [0] `followedBy` map (+ 1) out

data Then = Then
data Else = Else

ifx :: [Bool] -> Then -> [a] -> Else -> [a] -> [a]
ifx (b:bs) Then (x:xs) Else (y:ys) =
  (if b then x else y) : (ifx bs Then xs Else ys)
  
followedBy = (++)
lift n = n : (lift n)

--- Client Server Example ------

type Response = Integer
type Request = Integer

client :: [Response] -> [Request]
client ys = 1 : ys

server :: [Request] -> [Response]
server xs = map (+1) xs

reqs = client resps
resps = server reqs

clientB (y : ys) = 
   if ok y 
      then 1 :(y:ys) 
      else error "faulty server"
   where ok x = True
   
clientC ys = 
   1 : (if ok (head ys) then ys else error "faulty server")
 where ok x = True

clientD ~(y:ys) = 
   1 : (if ok y then ys else error "faulty server")
 where ok x = True

---- Memoization ----

fibsFn :: () -> [ Integer ]
fibsFn () = 1 : 1 : (zipWith (+) (fibsFn ()) (tail (fibsFn ())))

mfibsFn x = let mfibs = memo1 mfibsFn
            in 1:1:zipWith(+)(mfibs()) (tail (mfibs()))

--</PRE>