main :: [sys_message]
main = [Stdout (lay
         ["First 15: " ++ show first15,
          "Indices of first 1..10: " ++ show idx10,
          "Index of first 100: " ++ show idx100,
          "The GCDs of the first 1000 pairs are all 1: " ++ show allgcd])]

first15 :: [num]
first15 = take 15 stern

idx10 :: [num]
idx10 = [find num stern | num<-[1..10]]

idx100 :: num
idx100 = find 100 stern

allgcd :: bool
allgcd = and [gcd a b = 1 | (a, b) <- take 1000 (zip2 stern (tl stern))]


|| Stern-Brocot sequence
stern :: [num]
stern = 1 : 1 : concat (map consider (zip2 stern (tl stern)))
        where consider (prev,item) = [prev + item, item]

|| Supporting functions
gcd :: num->num->num
gcd a 0 = a
gcd a b = gcd b (a mod b)

find :: *->[*]->num
find item = find' 1
            where find' idx []     = 0
                  find' idx (a:as) = idx, if a = item
                                   = find' (idx + 1) as, otherwise