--- a/progs/lecture3.scala	Tue Nov 19 00:40:27 2019 +0000
+++ b/progs/lecture3.scala	Tue Nov 19 06:38:10 2019 +0000
@@ -47,7 +47,8 @@
   if (n == 0) ()
   else {
     println(s"  Visiting: $n $url")
-    for (u <- get_all_URLs(get_page(url))) crawl(u, n - 1)
+    val page = get_page(url)
+    for (u <- get_all_URLs(page)) crawl(u, n - 1)
   }
 }
 
@@ -121,8 +122,9 @@
 
 def search(xs: List[Int]) : Boolean = xs match {
   case Nil => true
-  case (x::xs) =>
-    if (xs.length < x) true else moves(xs, x).exists(search(_))
+  case x::xs =>
+    if (xs.length < x) true 
+    else moves(xs, x).exists(search(_))
 }
 
 
@@ -138,7 +140,7 @@
 search(List(3,5,1,0,0,0,0,0,0,0,0,1))
 
 // generates *all* jump tours
-//    if we are only interested in the shortes one, we could
+//    if we are only interested in the shortest one, we could
 //    shortcircut the calculation and only return List(x) in
 //    case where xs.length < x, because no tour can be shorter
 //    than 1
@@ -146,7 +148,7 @@
 
 def jumps(xs: List[Int]) : List[List[Int]] = xs match {
   case Nil => Nil
-  case (x::xs) => {
+  case x::xs => {
     val children = moves(xs, x)
     val results = children.map(cs => jumps(cs).map(x :: _)).flatten
     if (xs.length < x) List(x)::results else results
@@ -180,7 +182,7 @@
 //========================
 
 
-abstract class Colour
+sealed abstract class Colour
 case object Red extends Colour 
 case object Green extends Colour 
 case object Blue extends Colour
@@ -196,7 +198,7 @@
 
 // ... a tiny bit more useful: Roman Numerals
 
-abstract class RomanDigit 
+sealed abstract class RomanDigit 
 case object I extends RomanDigit 
 case object V extends RomanDigit 
 case object X extends RomanDigit 
@@ -269,7 +271,7 @@
 
 // trees
 
-abstract class Exp
+sealed abstract class Exp
 case class N(n: Int) extends Exp                  // for numbers
 case class Plus(e1: Exp, e2: Exp) extends Exp
 case class Times(e1: Exp, e2: Exp) extends Exp
@@ -314,7 +316,7 @@
 
 
 // Tokens and Reverse Polish Notation
-abstract class Token
+sealed abstract class Token
 case class T(n: Int) extends Token
 case object PL extends Token
 case object TI extends Token