-- Factorial function:
fac :: Int -> Int
fac n = if n == 0 then 1
                  else n * fac (n-1)

(++) :: [a] -> [a] -> [a]
[]     ++ ys = ys
(x:xs) ++ ys = x : (xs ++ ys)

test1234 = [1,2] ++ [3,4]

-- Computing the last element of a list: the logic programming way
last :: Eq a => [a] -> a
last xs | _ ++ [x] == xs
        = x
 where x free

-- Functional pattern:
last' (_ ++ [x]) = x

-- Computation permutations via functional patterns
perm []                = []
perm (xs ++ [x] ++ ys) = x : perm (xs ++ ys)