Generate Partitions

let rec generate start n =
  if start = 0 then
    match n with
    | 0 -> raise (Invalid_argument "n")
    | 1 -> [[1]]
    | k -> let result = generate 1 k in [k]::result
  else if start < n then
        (let result = ref [] in
          for i = start to n - start do
            let tmp_result = generate i (n - i) in
            let tmp_result_i = List.map (fun lst -> i :: lst) tmp_result in
            let tmp_result2 = tmp_result_i @ !result in
            result := tmp_result2
          done;
          !result ;)
  else
    [[n]];;


let generate_partitions n =
  generate 0 n ;;


generate_partitions 1 ;;
generate_partitions 2 ;;
generate_partitions 3 ;;