Cartesian product of two Lwt_stream

What is the preferred way to write a lwt_stream which is the cartesian product of two other lwt_streams?

I figured out an answer though it doesn’t look very pretty to me. The code uses async and iter_p.

open Lwt.Infix

let product_stream s1 s2 =
  let s, f = Lwt_stream.create () in
  Lwt.async (fun () ->
        (fun v2 ->
            (fun v1 ->
              f (Some (v1, v2)) ;
            (Lwt_stream.clone s1))
        (Lwt_stream.clone s2)
      >|= fun () -> f None) ;

I prepared a few test cases here which cover situations where streams are closed and not closed; stream values are in one shot and interleaved.