(*  9 *) fun x -> x
(* 10 *) fun x y f -> f x = f y
(* 11 *) compose
(* 12 *) fun p x -> if p x then 0. else 1.
(* 13 *) fun c1 c2-> fst c1 = snd c2 && snd c1 = fst c2

(* 14 *) type time = Time of int * int
(* 15 *)
let hour time =
  let Time(hour, _) = time in hour

let minute time =
  let Time(_, minute) = time in minute

(* 16 *)
let noon = Time(12,0)
let midnight = Time(0,0)

(* 17 *)
let time_inf time1 time2 =
  let h1, h2, m1, m2 =
    hour time1, hour time2, minute time1, minute time2
  in h1 < h2 || h1 = h2 && m1 < m2

(* 18 *)   
let pm_p time =
  time_inf noon time && time_inf time midnight

(* 19 *)
let rec syracuse m n =
  if n = 0 then m
  else let u = syracuse m (n - 1) in
       if u mod 2 = 0 then
         u / 2
       else 3 * u + 1
       
(* 20 *)       
let _ = syracuse 5

(* 21 *)      
let m_full multiplicity =  fun e -> multiplicity

(* 22 *)
let m_adjoin e mset count = fun x ->
  let c = m_multiplicity x mset in
  if x = e then c + count
    else c

(* 23 *)                                      
let m_union mset1 mset2 = 
  fun x ->
    (m_multiplicity x mset1) +  (m_multiplicity x mset2)
  
(* 24 *)
let m_count n mset =
  let rec aux n mset cpt =
    if n < 0 then cpt
    else aux (pred n) mset (m_multiplicity n mset + cpt) in
  aux n mset 0