{- successively select elements from xs and remove one in each result list -}

import List

removeEach :: [a] -> [[a]]
removeEach xs =
   zipWith (++) (List.inits xs) (tail (List.tails xs))

alternate :: (Num a) => [a] -> [a]
alternate = zipWith id (cycle [id, negate])

det :: (Num a) => [[a]] -> a
det [] = 1
det m  = sum (alternate
                 (zipWith (*) (map head m)
                     (map det (removeEach (map tail m)))))