--- a/cws/cw04.tex	Thu Jan 26 01:43:31 2017 +0000
+++ b/cws/cw04.tex	Fri Jan 27 14:55:56 2017 +0000
@@ -36,14 +36,14 @@
 Roman numerals are strings consisting of the letters $I$, $V$, $X$,
 $L$, $C$, $D$, and $M$. Such strings should be transformed into an
 internal representation using the datatypes \texttt{RomanDigit} and
-\texttt{RomanNumeral}, and then from this internal representation
-converted into an Integer.
+\texttt{RomanNumeral} (defined in \texttt{roman.scala}), and then from
+this internal representation converted into Integers.
 
 \begin{itemize}
 \item[(1)] First write a polymorphic function that recursively
   transforms a list of options into an option of a list. For example,
-  if you have the lists on the left, they should be transformed into
-  the option on the right:
+  if you have the lists on the left-hand side, they should be transformed into
+  the option on the right-hand side:
 
   \begin{center}
   \begin{tabular}{lcl}  
@@ -61,28 +61,29 @@
   produces \texttt{Some} of the empty list. \hfill[1 Mark]
 
  
-\item[(2)] Write a function first a function that converts a character
-  $I$, $V$, $X$, $L$, $C$, $D$, or $M$ into an option of a \texttt{RomanDigit}.
+\item[(2)] Write first a function that converts the characters $I$, $V$,
+  $X$, $L$, $C$, $D$, and $M$ into an option of a \texttt{RomanDigit}.
   If it is one of the roman digits, it should produce \texttt{Some};
   otherwise \texttt{None}.
   
-  Next write a function that converts a string into a \texttt{RomanNumeral}.
-  Again, this function should return an \texttt{Option}:
-  If the string consists of $I$, $V$, $X$, $L$, $C$, $D$, and $M$ only, then
-  it produces \texttt{Some}; otherwise if there is any other character in
-  the string, it should produce \texttt{None}. The empty string is just
-  the empty \texttt{RomanNumeral}, that is empty list of \texttt{RomanDigit}'s.
-  You should use the function under Task (1) to produce the result.
-  \hfill[2 Marks]
+  Next write a function that converts a string into a
+  \texttt{RomanNumeral}.  Again, this function should return an
+  \texttt{Option}: If the string consists of $I$, $V$, $X$, $L$, $C$,
+  $D$, and $M$ only, then it produces \texttt{Some}; otherwise if
+  there is any other character in the string, it should produce
+  \texttt{None}. The empty string is just the empty
+  \texttt{RomanNumeral}, that is the empty list of
+  \texttt{RomanDigit}'s.  You should use the function under Task (1)
+  to produce the result.  \hfill[2 Marks]
 
-\item[(3)] Write a recursive function RomanNumral2Int that converts a
-  \texttt{RomanNumeral} into an integer. You can assume the generated
-  integer will be between 0 and 3999.  The argument of the function is
-  a list of roman digits. It should look how this list starts and then
-  calculate what the corresponding integer is for this ``start'' and
-  add it with the integer for the rest of the list. That means if the
-  argument is of the form shown on the left-hand side, it should do
-  the calculation on the right-hand side.
+\item[(3)] Write a recursive function \texttt{RomanNumral2Int} that
+  converts a \texttt{RomanNumeral} into an integer. You can assume the
+  generated integer will be between 0 and 3999.  The argument of the
+  function is a list of roman digits. It should look how this list
+  starts and then calculate what the corresponding integer is for this
+  ``start'' and add it with the integer for the rest of the list. That
+  means if the argument is of the form shown on the left-hand side, it
+  should do the calculation on the right-hand side.
 
   \begin{center}
   \begin{tabular}{lcl}
@@ -102,30 +103,82 @@
   \end{tabular}  
   \end{center}    
 
-  The empty list will be converted into integer $0$.\hfill[1 Mark]
+  The empty list will be converted to integer $0$.\hfill[1 Mark]
   
 \item[(4)] Write a function that takes a string and if possible
-  converts it into the internal representation. If successful, then
-  calculate the integer (an option of an integer) according to the
+  converts it into the internal representation. If successful, it then
+  calculates the integer (an option of an integer) according to the
   function in (3).  If this is not possible, then return
   \texttt{None}.\hfill[1 Mark]
 
 
 \item[(5)] The file \texttt{roman.txt} contains a list of roman numerals.
   Read in these numerals, convert them into integers and then add them all
-  up. The function for reading a file is
+  up. The Scala function for reading a file is
 
   \begin{center}
   \texttt{Source.fromFile("filename")("ISO-8859-9")}
   \end{center}
 
   Make sure you process the strings correctly by ignoring whitespaces
-  where neded.\\ \mbox{}\hfill[1 Mark]
+  where needed.\\ \mbox{}\hfill[1 Mark]
 \end{itemize}
 
 
 \subsection*{Part 2 (Validation)}
 
+As you can see the function under Task (3) can produce some unexpected
+results. For example for $XXCIII$ it produces 103. The reason for this
+unexpected result is that $XXCIII$ is actually not a valid roman
+number, neither is $IIII$ for 4 nor $MIM$ for 1999. Although actual
+Romans were not so fussy about this,\footnote{They happily used
+  numbers like $XIIX$ or $IIXX$ for 18.} but modern times declared
+that there are precise rules for what a valid roman number is, namely:
+
+\begin{itemize}
+\item Repeatable roman digits are $I$, $X$, $C$ and $M$. The other ones
+  are non-repeatable. Repeatable digits can be repeated upto 3 times in a
+  number (for example $MMM$ is OK); non-repeatable digits cannot be
+  repeated at all (for example $VV$ is excluded).
+  
+\item If a smaller digits precedes a bigger digit, then $I$ can precede $V$ and $C$; $X$ can preced
+  $L$ and $C$; and $C$ can preced $D$ and $M$. No other combination is permitted in this case.
+
+\item If a smaller digit precedes a bigger digit (for example $IV$), then the smaller number   
+  must be either the first digit in the number, or follow a digit which is at least 10 times its value.
+  So $VIV$ is excluded, because $I$ follows $V$ and $I * 10$ is bigger than $V$; but $XIV$ is
+  allowed, because $I$ follows $X$ and $I * 10$ is equal to $X$.
+
+\item Let us say two digits are called a \emph{compound} roman digit
+  when a smaller digit precedes a bigger digit (so $IV$, $XL$, $CM$
+  for example). If a compound digit is followed by another digit, then
+  this digit must be smaller than the first digit in the compound
+  digit. For example $IXI$ is excluded, but $XLI$ is not.
+
+\item The empty roman numeral is valid.  
+\end{itemize}
+
+\noindent
+The tasks in this part are as follows:
+
+\begin{itemize}
+\item[(6)] Implement a recursive function \texttt{isValidNumeral} that
+  takes a \texttt{RomanNumeral} as argument and produces true if \textbf{all}
+  the rules above are satisfied, and otherwise false.
+
+  Hint: It might be more convenient to test when the rules fail and then return false;
+  return true in all other cases.
+  \mbox{}\hfill[2 Marks]
+
+\item[(7)] Write a recursive function that converts an Integer into a \texttt{RomanNumeral}.
+  You can assume the function will only be called for integers between 0 and 3999.\mbox{}\hfill[1 Mark]
+  
+\item[(8)] Write a function that reads a text file (for example \texttt{roman2.txt})
+  containing valid and invalid roman numerals. Convert all valid roman numerals into
+  integers, add them up and produce the result as a \texttt{RomanNumeral} (using the function
+  from (7)). \hfill[1 Mark]
+\end{itemize}
+  
 
 \end{document}