--- a/progs/roman.scala	Wed Jan 25 01:25:17 2017 +0000
+++ b/progs/roman.scala	Wed Jan 25 14:36:39 2017 +0000
@@ -1,3 +1,7 @@
+// Part 1 about Roman Numerals
+//=============================
+
+
 abstract class RomanDigit 
 case object I extends RomanDigit 
 case object V extends RomanDigit 
@@ -6,3 +10,101 @@
 case object C extends RomanDigit 
 case object D extends RomanDigit 
 case object M extends RomanDigit 
+
+type RomanNumeral = List[RomanDigit] 
+
+// (1) First write a polymorphic function that recursively
+// transforms a list of options into an option of a list.
+// As soon as a None is inside the list, the result is None. 
+// Otherwise produce a list of all Some's appended.
+
+def optionlist[A](xs: List[Option[A]]): Option[List[A]] = 
+
+// (2) Write a function first a function that converts a character
+// into a roman digit (if possible). Then convert a string into
+// a roman numeral (if possible). If this is not possible, the functions
+// should return None.
+
+def Char2RomanDigit(c: Char): Option[RomanDigit] = 
+
+def String2RomanNumeral(s: String) : Option[RomanNumeral] = 
+
+
+// some test cases
+//String2RomanNumeral("IIII")
+//String2RomanNumeral("IV")
+//String2RomanNumeral("VI")
+//String2RomanNumeral("IX")
+//String2RomanNumeral("MCMLXXIX")
+//String2RomanNumeral("MCMXLIV") 
+//String2RomanNumeral("M C M X L I V")  // None
+
+// (3) Write a recursive function RomanNumral2Int that converts a
+// RomanNumeral into an integer.
+
+def RomanNumeral2Int(rs: RomanNumeral): Int = 
+
+
+// some test cases
+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
+
+// (4) Write a function that converts a string (containing
+// a roman numeral) into an integer (if possible). If not
+// this is not possible, the functions should return None.
+
+def String2Int(s: String): Option[Int] = 
+
+// some test cases
+String2Int("IIII")      // 4 (though invalid roman numeral)  
+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("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("MDCLXVI")	// 1666
+
+String2Int("VIV")       // 9 (but should be written as IX) 
+String2Int("IVX")       // 14 (also invalid)
+
+// error cases
+String2Int("MC?I")
+String2Int("abc")
+
+
+
+
+// (5) The file roman.txt contains a list of roman numerals. 
+// Read in these numerals, convert them into integers and then 
+// add them all up.
+
+import io.Source
+import scala.util._
+
+// function for reading files:
+// Source.fromFile("file_name")("ISO-8859-9")