fun intf base next 0 = base
  | intf base next n = next (n, (intf base next (n-1)));
val iota = intf [0] (op ::);

local
      val append = foldl (op @) []
      fun repeat x = intf [] (fn (_,ls) => x::ls)
      fun rep2each x n ls = map (fn e => (repeat x n) @ e) ls
in
  fun change nil 0 = [[]]
    | change nil _ = []
    | change (c::cs) x =
         append (map (fn n => rep2each c n (change cs (x - n*c)))
                     (iota (x div c)))
end;


##</code><code>##

  datatype 'a option = Solution of 'a | Nothing;

##</code><code>##

  fun sflat ls = foldr (fn (Solution x, _) => Solution x
                         | (Nothing,v) => v) 
                       Nothing ls;
  fun smap _ Nothing = Nothing | smap f (Solution x) = Solution (f x)

##</code><code>##

local
  fun repeat x = intf [] (fn (_,ls) => x::ls)
in
  fun change1 nil 0 = Solution []
    | change1 nil _ = Nothing
    | change1 (c::cs) x =
         sflat (map (fn n => smap (fn x => (repeat c n) @ x) (change1 cs (x - n*c)))
                     (iota (x div c)))
end;

##</code><code>##

local val addup = foldr (fn (a,b) => a+b) 0
in
  fun countchange nil 0 = 1
    | countchange nil _ = 0
    | countchange (c::cs) x =
         addup (map (fn n => countchange cs (x - n*c))
                    (iota (x div c)))
end;