How can I write this recursive Haskell function

Question

Task:

Write a recursive Haskell function, which get 2 ordered list and the function decide that each of them element are equal or not (if one of them are same the function value is False ).

For example:

• myfunction [1..5] [6..10] == True
• myfunction [1..5] [5..10] == False

I cannot use the elem function. I can use recursion and case apart choice.

Function type:

myfunction :: Ord a => [a] -> [a] -> Bool

I tried something like this:

myfunction :: Ord a => [a] -> [a] -> Bool
myfunction [] list = True
myfunction list [] = True
myfunction (x:xs) (y:ys)
    | x == y = False
    | xs == myfunction ???????? = False

But it does not works...

Answer 1

(This answer is really just the comments you already received in answer form.) You'd implement it as follows:

myFunction [] _ = True
myFunction _ [] = True
myFunction (x : xs) (y : ys) = case compare x y of
  LT -> myFunction xs (y : ys)
  EQ -> False
  GT -> myFunction (x : xs) ys

This works because if x is smaller than y , x is also smaller (and therefore not equal, which is what we really wanted to know) than any element in ys . That means we can ignore it and check the rest of the lists. When x is greater than y , it's the other way around.