type ('s, 'a) state =
  { mutable state : 's;
    mutable input : 'a option;
    mutable time : Ztypes.time;
    mutable jump : bool; }

let lift_hsim_full (n : unit Ztypes.hsimu)
  : (unit, unit, unit, Ztypes.cvec, Ztypes.dvec, Ztypes.zoutvec, Ztypes.zinvec option) Full.hnode * int
= let Hsim { alloc; step; reset; derivative; crossings; maxsize; _ } = n in
  let state = { state = alloc (); input = None; time = 0.0; jump = false } in
  let csize, zsize = maxsize state.state in
  let no_zin, no_zout = Zls.zmake zsize, Zls.cmake zsize in
  let no_der, pos = Zls.cmake csize, Zls.cmake csize in
  let no_time = -1.0 in reset state.state;
  let fder { state; time; _ } offset () y =
    derivative state y no_der no_zin no_zout (time +. offset);
    no_der in
  let fzer { state; time; _ } offset () y =
    crossings state y no_zin no_zout (time +. offset); no_zout in
  let fout _ _ () _ = () in
  let step { state; time; _ } offset () =
    { state; time=time +. offset; input=Some (); jump = false },
    step state pos no_der no_zin (time +. offset) in
  let reset ({ state; _ } as st) () = reset state; st in
  let jump s = s.jump in
  let cset ({ state; _ } as st) _ =
    derivative state pos no_der no_zin no_zout no_time; st in
  let zset ({ state; _ } as st) = function None -> st | Some zinvec ->
    derivative state pos no_der zinvec no_zout no_time; { st with jump = true } in
  let cget { state; _ } =
    derivative state pos no_der no_zin no_zout no_time; pos in
  HNode { state; fder; fzer; fout; step; reset; jump; cget; cset; zset }, zsize

let lift_hsim (n : unit Ztypes.hsimu)
  : (unit, unit, unit, Ztypes.cvec, Ztypes.dvec, Ztypes.zoutvec, Ztypes.zinvec option) Fill.hnode * int
= let Hsim { alloc; step; reset; derivative; crossings; maxsize; _ } = n in
  let state = { state = alloc (); input = None; time = 0.0; jump = false } in
  let csize, zsize = maxsize state.state in
  let no_zin, no_zout = Zls.zmake zsize, Zls.cmake zsize in
  let no_der, pos = Zls.cmake csize, Zls.cmake csize in
  let no_time = -1.0 in reset state.state;
  let fder { state; time; _ } offset () y =
    derivative state y no_der no_zin no_zout (time +. offset);
    no_der in
  let fzer { state; time; _ } offset () y =
    crossings state y no_zin no_zout (time +. offset); no_zout in
  let fout _ _ () _ = () in
  let step { state; time; _ } offset () =
    { state; time=time +. offset; input=Some (); jump = false },
    step state pos no_der no_zin (time +. offset) in
  let reset ({ state; _ } as st) () = reset state; st in
  let jump s = s.jump in
  let cset ({ state; _ } as st) _ =
    derivative state pos no_der no_zin no_zout no_time; st in
  let zset ({ state; _ } as st) = function None -> st | Some zinvec ->
    derivative state pos no_der zinvec no_zout no_time; { st with jump = true } in
  let cget { state; _ } =
    derivative state pos no_der no_zin no_zout no_time; pos in
  HNode { state; fder; fzer; fout; step; reset; jump; cget; cset; zset }, zsize