--- a/progs/lecture3.scala	Tue Nov 21 16:31:11 2017 +0000
+++ b/progs/lecture3.scala	Thu Nov 23 10:56:47 2017 +0000
@@ -51,22 +51,41 @@
 
 
 
-// One of only two places where I conceded to mutable
-// data structures: The following function generates 
-// new labels
+// Roman Numerals
+abstract class RomanDigit 
+case object I extends RomanDigit 
+case object V extends RomanDigit 
+case object X extends RomanDigit 
+case object L extends RomanDigit 
+case object C extends RomanDigit 
+case object D extends RomanDigit 
+case object M extends RomanDigit 
+
+type RomanNumeral = List[RomanDigit] 
 
-var counter = -1
-
-def fresh(x: String) = {
-  counter += 1
-  x ++ "_" ++ counter.toString()
+def RomanNumeral2Int(rs: RomanNumeral): Int = rs match { 
+  case Nil => 0
+  case M::r    => 1000 + RomanNumeral2Int(r)  
+  case C::M::r => 900 + RomanNumeral2Int(r)
+  case D::r    => 500 + RomanNumeral2Int(r)
+  case C::D::r => 400 + RomanNumeral2Int(r)
+  case C::r    => 100 + RomanNumeral2Int(r)
+  case X::C::r => 90 + RomanNumeral2Int(r)
+  case L::r    => 50 + RomanNumeral2Int(r)
+  case X::L::r => 40 + RomanNumeral2Int(r)
+  case X::r    => 10 + RomanNumeral2Int(r)
+  case I::X::r => 9 + RomanNumeral2Int(r)
+  case V::r    => 5 + RomanNumeral2Int(r)
+  case I::V::r => 4 + RomanNumeral2Int(r)
+  case I::r    => 1 + RomanNumeral2Int(r)
 }
 
-fresh("x")
-fresh("x")
-
-// this can be avoided, but would have made my code more
-// complicated
+RomanNumeral2Int(List(I,I,I,I))         // 4 (invalid roman number)
+RomanNumeral2Int(List(I,V))             // 4
+RomanNumeral2Int(List(V,I))             // 6
+RomanNumeral2Int(List(I,X))             // 9
+RomanNumeral2Int(List(M,C,M,L,X,X,I,X)) // 1979
+RomanNumeral2Int(List(M,M,X,V,I,I))     // 2017
 
 
 // Tail recursion
@@ -301,11 +320,15 @@
   def ~ (r: String) = SEQ(s, r)
 }
 
+//example regular expressions
 val digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
 val sign = "+" | "-" | ""
 val number = sign ~ digit ~ digit.% 
 
 
+//implement print_re
+
+
 
 // Lazyness with style
 //=====================