A (failed) attempt at generating Hamming numbers (aka regular numbers) for Code Dojo

hamming-numbers.hs

hamming :: (Int, Int, Int) -> Int
hamming (two, three, five) = 2^two * 3^three * 5^five

nextHammingCoefficient (x, y, z)
  | minimum [nextX, nextY, nextZ] == nextX = (x + 1, y, z)
  | minimum [nextX, nextY, nextZ] == nextY = (x, y + 1, z)
  | minimum [nextX, nextY, nextZ] == nextZ = (x, y, z + 1)
  where nextX = hamming (x + 1, y, z)
        nextY = hamming (x, y + 1, z)
        nextZ = hamming (x, y, z + 1)

hammingCoefficients = iterate nextHammingCoefficient (0, 0, 0)
hammingNumbers = take 10 hammingCoefficients

Here is a working implementation based on the solution at rosettacode -- the recursion going on here is pretty trippy!

hamming :: [Int]
hamming = 1:(minMerge (map (*2) hamming) (minMerge (map (*3) hamming) (map (*5) hamming)))

minMerge :: Ord a => [a] -> [a] -> [a]
minMerge (x:xs) (y:ys)
  | x < y     = x:(minMerge xs (y:ys))
  | y < x     = y:(minMerge (x:xs) ys)
  | otherwise = x:(minMerge xs ys)