(* Carsten Schuermann *)
(* Torres *)

datatype Color
  = Green
  | Blue
  | Red
  | Orange
  | Black

datatype Tower 
  = Empty
  | Tile of Tower
  | Knight of Color

datatype Board1
  = Board1 of Tower * Tower * Tower * Tower * Tower * Tower * Tower * Tower
            * Tower * Tower * Tower * Tower * Tower * Tower * Tower * Tower 
            * Tower * Tower * Tower * Tower * Tower * Tower * Tower * Tower 
            * Tower * Tower * Tower * Tower * Tower * Tower * Tower * Tower 
            * Tower * Tower * Tower * Tower * Tower * Tower * Tower * Tower 
            * Tower * Tower * Tower * Tower * Tower * Tower * Tower * Tower 
            * Tower * Tower * Tower * Tower * Tower * Tower * Tower * Tower 
            * Tower * Tower * Tower * Tower * Tower * Tower * Tower * Tower 

datatype Board2
  = Row of Tower * Tower * Tower * Tower * Tower * Tower * Tower * Tower 
  | Board2 of Board2 * Board2
		  
		 
datatype Board
  = Tower of Tower
  | Board of Board * Board
           * Board * Board

datatype Address 
  = Here
  | UpperLeft of Address
  | UpperRight of Address
  | LowerLeft of Address
  | LowerRight of Address


(* rest A = A'
 
   Invariant:
   If A is not equal to HERE then
   A' is the rest of the path of A
*)
fun rest (UpperLeft A) = A
  | rest (UpperRight A) = A
  | rest (LowerLeft A) = A
  | rest (LowerRight A) = A



(* emptyBoard n = B'
 
   Invariant:
   If n >= 0
   then B' = board of size of (2^n * 2^n)
*)
fun EmptyBoard 0 = Tower Empty
  | EmptyBoard n = 
    let
      val B = EmptyBoard (n-1)
    in Board (B, B,
	      B, B)
    end