fun r [] = []
    | r(x :: xs) = r xs @ [x];

fun prod(n, 0) = 0
    | prod(n, m) = prod(n, m-1) + n;

fun fastPow(b, 0) = 1
    | fastPow(b, k) =
        if k mod 2 = 0 then
            fastPow(b * b, k div 2)
        else
            fastPow(b * b, (k - 1) div 2) * b

fun prodAccum(0, n, a) = a
    | prodAccum(m, n, a) = prodAccum(m - 1, n, n + a);

fun min(NONE, NONE) = NONE
    | min(NONE, SOME b) = SOME b
    | min(SOME a, NONE) = SOME a
    | min(SOME a, SOME b) = if a < b then SOME a else SOME b;

fun optionalAdd(NONE, NONE) = NONE
    | optionalAdd(NONE, b) = NONE
    | optionalAdd(a, NONE) = NONE
    | optionalAdd(SOME a, SOME b) = SOME(a + b);

fun minChange(0, ds) = SOME 0
    | minChange(a, []) = NONE
    | minChange(a, dds as d :: ds) =
        if d > a then
            minChange(a, ds)
        else
            min(optionalAdd(SOME (1), minChange(a - d, dds)), minChange(a, ds));

fun greedyMinChange(0, ds) = SOME 0
    | greedyMinChange(a, []) = NONE
    | greedyMinChange(a, d :: ds) =
        if d > a then
            greedyMinChange(a, ds)
        else
            let
                val q = a div d
                val r = a mod d
            in
                optionalAdd(SOME (q), greedyMinChange(r, ds))
            end;

r([1, 2, 3])