(* times : int -> int -> int *)
let times n = function m -> n * m

(* sum : (int -> int) -> (int * int) -> int *)
(* sum f (lower,upper) = (f lower) + (f (lower+1)) + .... + (f upper) *)
let rec sum f = function
    (lower,upper) -> if lower > upper then 0
                     else f lower + sum f (lower +1,upper)
(* or *)
let rec sum f (lower,upper) =
  if lower > upper then 0
  else f lower + sum f (lower +1,upper)

(* sumbetween : int * int -> int *)
(* sumbetween (n,m) = n + (n+1) + ... + m *)
let rec sumbetween (n,m) =
  if n>m then 0 else n + sumbetween (n+1,m)

(* sumbetw : int -> int -> int *)
(* sumbetw n m =  sumbetween (n,m) *)
let rec sumbetw n m =
  if n>m then 0 else n + sumbetw (n+1) m

(* comp : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b *)
let comp f g = function x -> f (g x)
(* or *)
let comp f g x = f (g x)