CPS style state in F#

module state =
  type StateM<'s,'a> = abstract Apply : 's  -> ('s -> 'a -> 'r) -> 'r

  let mkStateM (f : 's -> 's * 'a) : StateM<'s,'a> = 
     { new StateM< 's , 'a > with member __.Apply s k =  match f s with (s,a) -> k s a }

  let runStateM (m : StateM<'s,'a>) : 's -> 's * 'a = fun s ->
      m.Apply s (fun s a -> (s,a))

  // defined directly to avoid the value restriction.
  let get
    = { new StateM< 's , 's > with member __.Apply s k = k s s }

  let put s = mkStateM (fun _ -> s , ()) 

  let (>>=) (m : StateM<'s,'a>) (f : 'a -> StateM<'s,'b>) = 
    { new StateM<'s , 'b> with 
        member __.Apply s k = 
          m.Apply s (fun s a -> let n = f a in n.Apply s k )}

  let Return a : StateM<'s,'a> = mkStateM (fun s -> (s,a))