OCaml stable multi-key sort with nulls last

type person = { name : string; age : int option; city : string }

let compare_option compare a b =
  match (a, b) with
  | None, None -> 0
  | Some x, Some y -> compare x y
  | None, Some _ -> 1 (* missing values sort last *)
  | Some _, None -> -1

let compare_people a b =
  match String.compare a.city b.city with
  | 0 -> (
      match compare_option Int.compare a.age b.age with
      | 0 -> String.compare a.name b.name
      | other -> other)
  | other -> other

let sort_people people = List.stable_sort compare_people people