allLists.hs

module Everything where

{- replicate does not support integer :/ -}
repl :: Integer -> Integer -> [Integer]
repl x times = [x | i <- [1..times]]

{- take needs Int as well -}
myTake :: Integer -> [a] -> [a]
myTake len [] = []
myTake 0   xs = []
myTake len (x:xs) = x:myTake (len - 1) xs

{- builds all permutations of lists with 'len' elements and values between 0 and 'max' -}
permutLen :: Integer -> Integer -> [[Integer]]
permutLen len max = myTake ((max+1) ^ len) $ iterate next $ repl 0 len
    where
        next :: [Integer] -> [Integer]
        next []      = []
        next (x:xs)
         | x >= max  = 0:next xs
         | otherwise = (x+1):xs

permut :: Integer -> [[Integer]]
permut max = [ l | len <- [0..max], l <- permutLen len max, len == max || elem max l] {- The last condition will prevent duplications -}

{- a list with every possibile list of positive integeres -}
allLists :: [[Integer]]
allLists = []:[ l | max <- [1..], l <- permut max]