Ocaml: Recursion: intersection

Question

function name: intersection: takes 2 lists and returns list of all elements that appear in both

ie: [1; 2; 2; 3; 4; 4; 3] [2; 3] -> [2; 2; 3; 3]

let rec intersection (l1: int list) (l2: int list) : int list = 
    begin match l1, l2 with
      | hd :: tl, hd2 :: tl2 -> if hd = hd2 then hd :: intersection tl l2
                                            else intersection tl l2
      | _ -> []
    end

There is a problem with this code, but I'm not sure how to fix it - The code will run through and get [2; 2] because it keeps comparing to 2, the first element in l2, but I want l1 to also compare with tl2, does anyone have any suggestions?

 Should I add another match [], [] -> to clarify base case at the beginning?

Answer 1

how do you refer to the first element in the other list?

Use another match statement:

let rec intersection (l1: int list) (l2: int list) : int list = 
    begin match l2 with
      | []         -> []
      | hd2 :: tl2 -> begin match l1 with
                        | []         -> …
                        | hd1 :: tl1 -> …
                      end
    end

You can also simplify this by omitting the begin / end parenthesis that are unnecessary in this case, and by matching upon a tuple right away:

let rec intersection (l1: int list) (l2: int list) : int list = match l1, l2 with
  | [],       _        -> []
  | hd1::tl1, []       -> …
  | hd1::tl1, hd2::tl2 -> …

_{(Disclaimer: I ignored the question whether looking at the two first elements in the same function is useful for implementing intersection at all)}