module Bowling

type RollResult = int

type FrameType = Strike | Spare | Open

type FrameResult = FrameType * int

type List<FrameResult> with
  member this.TotalScore : GameScore = this |> List.map snd |> List.sum

type GameResult =
  | IncompleteFrame of scored:List<FrameResult> * unscored:List<RollResult>
  | IncompleteGame of scored:List<FrameResult>
  | CompleteGame of scored:List<FrameResult> * late:List<RollResult>

let bowl =
  let rec bowl' scored unscored
    match unscored with
    | 10 :: (b1 :: b2 :: _) as unscored                    -> unscored |> bowl' (Strike (10 + b1 + b2) :: scored)
    | r1 :: r2 :: (b1 :: _) as unscored when r1 + r2 = 10  -> unscored |> bowl' (Spare (10 + b1) :: scored)
    | r1 :: r2 :: unscored              when r1 + r2 < 10  -> unscored |> bowl' (Open (r1 + r2) :: scored)
    | late      when resultSoFar.Length = 10 -> CompleteGame    (List.rev resultSoFar, late)
    | unmatched when resultSoFar.Length < 10 -> IncompleteFrame (resultSoFar, unmatched)
    | []                                     -> IncompleteGame  (resultSoFar)
  bowl' []