--q103x.hs
--http://ideone.com/vfdapF
 
--infinite_product_process :: 
infinite_product_process values [] = [(values, [])]
infinite_product_process values (x:xs) = [(values ++ [e], xs) | e <- x]
 
infinite_product [] = []
infinite_product xs = 
    let q = [infinite_product_process [] xs]
        fn [] = []
        fn (((vals,[]):[]):ys) = vals : (fn ys)
        fn (((vals,[]):vs):ys) = vals : (fn (ys ++ [vs]))
        fn (((vals,itrs):[]):ys) = fn (ys ++ [infinite_product_process vals itrs])
        fn (((vals,itrs):vs):ys) = fn (ys ++ [infinite_product_process vals itrs] ++ [vs])
    in  fn q
 
primes = 
    let minus [] _  = []
        minus xs [] = xs
        minus (x:xs) (y:ys)
            | x < y     = x : minus xs (y:ys)
            | x > y     = minus (x:xs) ys
            | otherwise = minus xs ys
        eratos (p:xs) = p : eratos (xs `minus` [p*p, (p+2)*p..])
    in  2 : eratos [3, 5..]
 
nats = [1, 2..]
 
fibs = fib_gen 1 1 where
    fib_gen a b = a : (fib_gen b (a+b))
 
join sep [] = ""
join sep (x:[]) = show x
join sep (x:xs) = (show x) ++ sep ++ (join sep xs)
 
product_fibs_only = infinite_product [fibs]
product_nats_fibs = infinite_product [nats, fibs]
product_primes_nats_fibs = infinite_product [primes, nats, fibs]
product_nats_1_3 = infinite_product [nats, [1, 2, 3]]
product_1_3_nats = infinite_product [[1, 2, 3], nats]
 
main = do
    putStrLn $ join "," (take 10 product_fibs_only)
    putStrLn $ join "," (take 21 product_nats_fibs)
    putStrLn $ join "," (take 35 product_primes_nats_fibs)
    putStrLn $ join "," (take 15 product_nats_1_3)
    putStrLn $ join "," (take 15 product_1_3_nats)
    putStrLn $ join "," (infinite_product [[1, 2], [1, 2], [1, 2]])
    putStrLn $ join "," (infinite_product [[1, 2], [1, 2], [1, 2], [1, 2]])