let rec proc l =
    match l with
      | Dir(x,y)::[] -> Dir(x,y)
      | x::Dir(name,n)::xs -> proc (Dir(name, x::n)::xs)
            | _ -> raise Invalid_path;;

let rec addl z1 p z2 it = match p, z1, it with
| [], Dir(name, y), _ -> (Dir(name, z2::y)) @ (proc (List.rev it))
| x::xs, Dir(name, y::ys), z -> if x = getName y then addl xs y z2 (Dir(name, y::ys))::z else addl (Dir(name, ys)) p z2 z
| _, _, _ -> raise Invalid_path;;

let add z1 p z2 = addl z1 p z2 [];;