Bind Lwt functions in ocaml-lua

Learning
,
1

Hello,
I am embeding the Lua interpreter ocaml-lua into my application. I want to bind an ocaml function returning a Lwt promise f : unit -> int Lwt.t. The execution of the lua script will be made by Lwt_main.run. My attempt was to bind the function

function () -> Lwt_main.run @@ f ()

as follows

val f : unit -> int Lwt.t

let g (lua : Lua.state) = 
  let n = Lwt_main.run (f ()) in
  let () = Lua.pushinteger lua n in
  1

let open_api (lua : Lua.state) =
  let () = Lua.pushocamlfunction lua g in
  let () = Lua.setglobal lua "f" in
  ()

let script = {eos|
  x = f()
  print(x)
|eos}

let run_script () =
  let lua = LuaL.newstate () in
  let () = LuaL.openlibs lua in
  let () = open_api lua in
  let _status = LuaL.loadbuffer lua script "my_script" in
  match Lua.pcall lua 0 0 0 with
  | Lua.LUA_OK -> ()
  | _ -> let () = Lua.pop lua 1 in
         failwith "ERROR"

But run_script will be called in Lwt_main.run and we will have nested calls to Lwt_main.run, which is not allowed.

Any idea on how to bind the function f? In the lua script, the expected behavior is that f() waits until the promise is resolved.

Thank you!