--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/roman_sol.scala	Wed Jan 25 14:36:39 2017 +0000
@@ -0,0 +1,136 @@
+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] 
+
+def optionlist[A](xs: List[Option[A]]): Option[List[A]] = xs match {
+  case Nil => Some(Nil)
+  case x::xs => (x, optionlist(xs)) match {
+    case (None, _) => None
+    case (_, None) => None
+    case (Some(y), Some(ys)) => Some(y::ys)  
+  }
+}
+
+def char2romandigit(c: Char): Option[RomanDigit] = c match {
+  case 'I' => Some(I)
+  case 'V' => Some(V)
+  case 'X' => Some(X)
+  case 'L' => Some(L)
+  case 'C' => Some(C)
+  case 'D' => Some(D)
+  case 'M' => Some(M)
+  case _ => None
+}
+
+def String2RomanNumeral(s: String) : Option[RomanNumeral] = 
+  optionlist(s.toList.map(char2romandigit))
+
+String2RomanNumeral("IIII")
+String2RomanNumeral("IV")
+String2RomanNumeral("VI")
+String2RomanNumeral("IX")
+String2RomanNumeral("MCMLXXIX")
+String2RomanNumeral("MCMXLIV") 
+String2RomanNumeral("M C M X L I V")  // None
+
+////////////////
+
+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)
+}
+
+RomanNumeral2Int(List(I,I,I,I))         // 4
+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,C,M,X,L,I,V))   // 1944
+
+
+def String2Int(s: String): Option[Int] = 
+  String2RomanNumeral(s).map(RomanNumeral2Int(_))
+
+
+String2Int("IIII")      // 4 invalid 
+String2Int("IV")        // 4
+String2Int("VI")        // 6
+String2Int("IX")        // 9
+String2Int("MCMLXXIX")  // 1979
+String2Int("MCMXLIV")   // 1944
+String2Int("")          // 0
+String2Int("MDCLXI")    // 1661
+String2Int("MMMCMXCIX") // 3999
+String2Int("XLVIII")    // 48
+String2Int("MMVIII")    // 2008
+
+String2Int("MMXI")      // 2011 
+String2Int("MIM")       // 1999
+String2Int("MCMLVI")    // 1956 
+String2Int("XXCIII")    // ?? 103 / 83
+String2Int("LXXIIX")    // ?? 80 / 78
+String2Int("IIIIX")     // ?? 12 invalid  
+String2Int("IIXX")      // ?? 20 / 18 invalid
+
+String2Int("III") 	// 3
+String2Int("XXX") 	// 30
+String2Int("CCC") 	// 300
+String2Int("MMM") 	// 3000
+String2Int("VII") 	// 7
+String2Int("LXVI") 	// 66
+String2Int("CL") 	// 150
+String2Int("MCC") 	// 1200
+String2Int("IV") 	// 4
+String2Int("IX") 	// 9
+String2Int("XC") 	// 90
+String2Int("ICM") 	// ?? 901
+String2Int("CIM") 	// ?? 899
+String2Int("MDCLXVI")	// 1666
+
+String2Int("VIV")       //9, but should be written as IX 
+String2Int("IVX")       // 14 invalid
+
+// error cases
+String2Int("MC?I")
+String2Int("abc")
+
+
+def runsAllowed(r: RomanDigit) = r match {
+  case I | X | C | M => true
+  case V | L | D => false
+}
+
+def norunsAllowed(r: RomanDigit) = !runsAllowed(r)
+
+
+def isValidNumeral(digitList: RomanNumeral): Bool = digitList match {
+
+    // empty list is valid
+  case Nil => true
+
+    // a following digit that is equal or larger is an error
+  case d1::d2::_ if (d1 <= d2)  => false 
+
+    // A single digit is always allowed
+  case _::ds => isValidNumeral(ds) 
+
+}