let add_3 b1 b2 b3 = match b1, b2, b3 with
  | true, true, true -> true, true
  | true, true, false
  | true, false, true
  | false, true, true -> true, false
  | true, false, false
  | false, true, false
  | false, false, true -> false, true
  | false, false, false -> false, false;;

let rec add_bin n1 n2 carry = match n1, n2 with
  | [], [] -> [carry]
  | [], n2 -> add_bin [false] n2 carry
  | n1, [] -> add_bin n1 [false] carry
  | d1 :: d1s, d2 :: d2s ->
    let (carry, d) = add_3 d1 d2 carry in
    d :: (add_bin d1s d2s carry);;

let rec add_bin_list' xss = match xss with
|[]    -> []
|[h]   -> h
|h1 :: h2 :: t  -> add_bin_list' (([add_bin h1 h2 false]) @ t);;

let rec cut xs = match xs with
|[] -> []
|x::xs -> if x = false then cut xs else List.rev (x::xs) ;;

let add_bin_list xss = add_bin_list' xss |> List.rev |> cut ;;