structure Dict :> DICT = BinarySearchTree;

datatype square = Peg | Hole;
type board = square Dict.dict;

structure Dir =
struct
  datatype direction =
    East | NorthEast | NorthWest | West | SouthWest | SouthEast

  fun increment (East) = (1,0)
    | increment (NorthEast) = (0,1)
    | increment (NorthWest) = (~1,1)
    | increment (West) = (~1,0)
    | increment (SouthWest) = (0,~1)
    | increment (SouthEast) = (1,~1)

  fun exists p = p East orelse p NorthEast orelse p NorthWest
                 orelse p West orelse p SouthWest orelse p SouthEast
end;

fun initialize (i,j) b = next (i,j) (Dict.insert (b,((i,j),Peg)))
and next (0,0) b = b
  | next (i,0) b = initialize (i-1,5-i) b
  | next (i,j) b = initialize (i,j-1) b;

val initialBoard = initialize (4,0) (Dict.empty);