I think this suffices for the empty type in OCaml, but I'm not certain.

empty.ml

module type TYPE = sig
  type t
end

module type EMPTY = functor (T : TYPE) -> sig
  val apply : T.t
end

type empty = (module EMPTY)

(* Absurdity *)
let rec (!) (e : empty) : 'a = ! e

I was going to use type abstraction along with assert false to achieve the same, but though I'd do a quick search first, and found your Gist.

I think it holds as far as OCaml goes, but a logical purist might point out that "let rec" is itself unsound. I propose the alternative:

type t = {elim_empty : 'a. 'a}
let (!) {elim_empty} = elim_empty