--- a/progs/knight2.scala	Wed Nov 02 13:22:40 2016 +0000
+++ b/progs/knight2.scala	Wed Nov 02 13:26:26 2016 +0000
@@ -1,6 +1,8 @@
 import scala.util._
+type Pos = (Int, Int)
 
-def print_board(n: Int)(steps: List[(Int, Int)]): Unit = {
+
+def print_board(n: Int)(steps: List[Pos]): Unit = {
   for (i <- 0 until n) {
     for (j <- 0 until n) {
       print(f"${steps.indexOf((i, j))}%3.0f ")
@@ -11,26 +13,26 @@
   System.exit(0)
 }
 
-def add_pair(x: (Int, Int))(y: (Int, Int)) = 
+def add_pair(x: Pos)(y: Pos) = 
   (x._1 + y._1, x._2 + y._2)
 
-def is_legal(n: Int)(x: (Int, Int)) = 
+def is_legal(n: Int)(x: Pos) = 
   0 <= x._1 && 0 <= x._2 && x._1 < n && x._2 < n
 
-def moves(n: Int)(x: (Int, Int)): List[(Int, Int)] = {
+def moves(n: Int)(x: Pos): List[Pos] = {
   List((1, 2),(2, 1),(2, -1),(1, -2),
        (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)).filter(is_legal(n))
 }
 
-def ordered_moves(n: Int)(steps: List[(Int, Int)])(x : (Int, Int)): List[(Int, Int)] = 
-  moves(n)(x).sortBy((x: (Int, Int)) => moves(n)(x).filterNot(steps.contains(_)).length)
+def ordered_moves(n: Int)(steps: List[Pos])(x : Pos): List[Pos] = 
+  moves(n)(x).sortBy((x: Pos) => moves(n)(x).filterNot(steps.contains(_)).length)
 
 moves(8)(1,3)
 ordered_moves(8)(Nil)(1,3)
 ordered_moves(8)(List((2, 4), (2, 6)))(1,3)
 
-// non-circle tour parallel
-def tour(n: Int)(steps: List[(Int, Int)]): Unit = {
+// non-circle tour
+def tour(n: Int)(steps: List[Pos]): Unit = {
   if (steps.length ==  n * n)
     print_board(n)(steps)
   else