import Data.Ratio
 
main :: IO ()
main = do
  print $ dicePosteriors [6] [6]
  print $ dicePosteriors [4, 6, 8] [6]
  mapM_ (print . map fromRational . dicePosteriors [4,6,8,12,20])
        [[6], [6,4,8,7,7,2,6], [4,8,7,7,2,6], [6,8,7,7,5,4]]
 
dicePosteriors :: [Integer] -> [Integer] -> [Ratio Integer]
dicePosteriors suite xxs = f xxs
  where
    f (x:xs) = g (p x [1,1..]) xs
      where
        g ys []     = ys
        g ys (h:t) = g (p h ys) t
    f _      = []
    p x priors = map (/ n) zs
      where
        n  = sum zs
        zs = zipWith (*) priors ls
        ls = map (likelihood x) suite
 
    likelihood :: Integer -> Integer -> Ratio Integer
    likelihood x hypo
      | hypo < x  = 0
      | otherwise = 1 % hypo
 

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