how to convert from an ('a -> bot) to 'a cont in sml/nj

cc.sml

(* how to convert from an ('a -> bot) to 'a cont *)
structure CCC =
struct
    structure CC = SMLofNJ.Cont

    datatype bot = Bot of bot
    fun abort (Bot x) = abort x
    type 'a cont = 'a -> bot

    (* convert using an exception - unsatisfying *)
    fun conv_exc (k: 'a cont) =
        let
            exception E of 'a CC.cont
        in
            abort (k (CC.callcc (fn k' => raise E k')))
            handle E k' => k'
        end

    (* convert using two callccs *)
    fun conv (k: 'a cont) =
        CC.callcc (
            fn k' : 'a CC.cont CC.cont =>
               abort (k (CC.callcc (fn k'' : 'a CC.cont => CC.throw k' k'')))
        )

end