Ocaml can do this

  let do_something (thing : Thing.t) (logging : [`With_logging | `No_logging])  =
  ...

Even better, it can even infer the type based on you using it (for example matching on it):

  let do_something thing logging =
    let logging_as_bool = 
      match logging with
      | `With_logging -> true
      | `No_logging -> false
    in
    ....