-- board piece
type P = X | O | E

type Board = Board P P P P P P P P P

use Board Board
use P O X E
use Optional Some None

orElse a b =
  case a of
    None -> b
    a -> a

namespace P where
  (/=) : P -> P -> Boolean
  a /= b = not (a == b)
  (==) : P -> P -> Boolean
  a == b = case (a,b) of
    (X,X) -> true
    (O,O) -> true
    _ -> false

isWin : Board -> Optional P
isWin board =
  same : P -> P -> P -> Optional P
  same a b c = if and (and (a P.== b) (a P.== c)) (a P./= E)
               then Some a
               else None
  case board of
    -- vertical top/center/bottom
    -- horizontal left/center/right
    -- diagonal rising/falling
    Board a b c
          d e f
          g h i ->
      (same a b c `orElse` same d e f `orElse` same g h i `orElse`
       same a d g `orElse` same b e h `orElse` same c f i `orElse`
       same a e i `orElse` same g e c)

isWin (Board X O X
             O X X
             O E X)