-- | The Misc module contains helper functions that seem out of place
--   anywhere else.
module Misc
where


-- | The standard factorial function. See
--   <http://www.willamette.edu/~fruehr/haskell/evolution.html> for
--   possible improvements.
--
--   Examples:
--
--   >>> factorial 0
--   1
--
--   >>> factorial 4
--   24
--
factorial :: Int -> Int
factorial n
    | n <= 1 = 1
    | n > 20 = error "integer overflow in factorial function"
    | otherwise = product [1..n]


-- | Takes a three-dimensional list, and flattens it into a
--   one-dimensional one.
flatten :: [[[a]]] -> [a]
flatten xs = concat $ concat xs


-- | Takes a list, and returns True if its elements are pairwise
--   equal. Returns False otherwise.
all_equal :: (Eq a) => [a] -> Bool
all_equal xs =
    all (== first_element) other_elements
    where
      first_element  = head xs
      other_elements = tail xs