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-% !TEX program = xelatex
-\documentclass{article}
-\usepackage{../style}
-\usepackage{../langs}
-
-\begin{document}
-
-\section*{Coursework 2}
-
-\noindent This coursework is worth 8\% and is due on \cwTWO{} at
-18:00. You are asked to implement the Sulzmann \& Lu lexer for the
-WHILE language. You can do the implementation in any programming
-language you like, but you need to submit the source code with which
-you answered the questions, otherwise a mark of 0\% will be
-awarded. You can submit your answers in a txt-file or as pdf. Code
-submit as code. Please package everything in a zip-file that creates a
-directory with the name \texttt{YournameYourfamilyname} on my end. Thanks!
-
-\subsection*{Disclaimer\alert}
-
-It should be understood that the work you submit represents
-your own effort. You have not copied from anyone else. An
-exception is the Scala code from KEATS and the code I showed
-during the lectures, which you can both freely use. You can
-also use your own code from the CW~1.
-
-\subsection*{Question 1}
-
-To implement a lexer for the WHILE language, you first
-need to design the appropriate regular expressions for the
-following eleven syntactic entities:
-
-\begin{enumerate}
-\item keywords are
-
-\begin{center}
-\texttt{while}, 
-\texttt{if}, 
-\texttt{then}, 
-\texttt{else}, 
-\texttt{do}, 
-\texttt{for}, 
-\texttt{to}, 
-\texttt{true}, 
-\texttt{false}, 
-\texttt{read}, 
-\texttt{write},
-\texttt{skip}
-\end{center} 
-
-\item operators are:
-\texttt{+}, 
-\texttt{-}, 
-\texttt{*}, 
-\texttt{\%},
-\texttt{/},
-\texttt{==}, 
-\texttt{!=}, 
-\texttt{>}, 
-\texttt{<},
-\texttt{<=}, 
-\texttt{>=},
-\texttt{:=},
-\texttt{\&\&},
-\texttt{||}
-
-\item letters are uppercase and lowercase
-
-\item symbols are letters plus the characters
-  \texttt{.},
-  \texttt{\_},
-  \texttt{>},
-  \texttt{<},
-  \texttt{=},
-  \texttt{;},
-  \texttt{,} and
-  \texttt{:}
-
-\item strings are enclosed by \texttt{"\ldots"} and consisting of
-  symbols, whitespaces and digits
-\item parentheses are \texttt{(}, \texttt{\{}, \texttt{)} and \texttt{\}}
-\item there are semicolons \texttt{;}
-\item whitespaces are either \texttt{" "} (one or more) or \texttt{$\backslash$n} or
-  \texttt{$\backslash$t}
-\item identifiers are letters followed by underscores \texttt{\_\!\_}, letters
-or digits
-\item numbers are \pcode{0}, \pcode{1}, \ldots and so on; give 
-a regular expression that can recognise \pcode{0}, but not numbers 
-with leading zeroes, such as \pcode{001}
-\item comments start with \texttt{//} and contain symbols, spaces and digits until the end of the line
-\end{enumerate}
-
-\noindent
-You can use the basic regular expressions 
-
-\[
-\ZERO,\; \ONE,\; c,\; r_1 + r_2,\; r_1 \cdot r_2,\; r^*
-\]
-
-\noindent
-but also the following extended regular expressions
-
-\begin{center}
-\begin{tabular}{ll}
-$[c_1,c_2,\ldots,c_n]$ & a set of characters\\
-$r^+$ & one or more times $r$\\
-$r^?$ & optional $r$\\
-$r^{\{n\}}$ & n-times $r$\\
-\end{tabular}
-\end{center}
-
-\noindent
-Later on you will also need the record regular expression:
-
-\begin{center}
-\begin{tabular}{ll}
-$REC(x:r)$ & record regular expression\\
-\end{tabular}
-\end{center}
-
-\noindent Try to design your regular expressions to be as
-small as possible. For example you should use character sets
-for identifiers and numbers. Feel free to use the general
-character constructor \textit{CFUN} introduced in CW 1.
-
-\subsection*{Question 2}
-
-Implement the Sulzmann \& Lu lexer from the lectures. For
-this you need to implement the functions $nullable$ and $der$
-(you can use your code from CW~1), as well as $mkeps$ and
-$inj$. These functions need to be appropriately extended for
-the extended regular expressions from Q1. Write down the 
-clauses for
-
-\begin{center}
-\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
-$mkeps([c_1,c_2,\ldots,c_n])$  & $\dn$ & $?$\\
-$mkeps(r^+)$                   & $\dn$ & $?$\\
-$mkeps(r^?)$                   & $\dn$ & $?$\\
-$mkeps(r^{\{n\}})$             & $\dn$ & $?$\medskip\\
-$inj\, ([c_1,c_2,\ldots,c_n])\,c\,\ldots$  & $\dn$ & $?$\\
-$inj\, (r^+)\,c\,\ldots$                   & $\dn$ & $?$\\
-$inj\, (r^?)\,c\,\ldots$                   & $\dn$ & $?$\\
-$inj\, (r^{\{n\}})\,c\,\ldots$             & $\dn$ & $?$\\
-\end{tabular}
-\end{center}
-
-\noindent where $inj$ takes three arguments: a regular
-expression, a character and a value. Test your lexer code
-with at least the two small examples below:
-
-\begin{center}
-\begin{tabular}{ll}
-regex: & string:\smallskip\\
-$a^{\{3\}}$ & $aaa$\\
-$(a + \ONE)^{\{3\}}$ & $aa$
-\end{tabular}
-\end{center}
-
-
-\noindent Both strings should be successfully lexed by the
-respective regular expression, that means the lexer returns 
-in both examples a value.
-
-
-Also add the record regular expression from the
-lectures to your lexer and implement a function, say
-\pcode{env}, that returns all assignments from a value (such
-that you can extract easily the tokens from a value).\medskip 
-
-\noindent
-Finally give the tokens for your regular expressions from Q1 and the
-string
-
-\begin{center}
-\code{"read n;"}
-\end{center} 
-
-\noindent
-and use your \pcode{env} function to give the token sequence.
-
-
-\subsection*{Question 3}
-
-Extend your lexer from Q2 to also simplify regular expressions after
-each derivation step and rectify the computed values after each
-injection. Use this lexer to tokenize the programs in
-Figures~\ref{fib} -- \ref{collatz}. You can find the programms also on
-KEATS. Give the tokens of these programs where whitespaces are
-filtered out. Make sure you can tokenise \textbf{exactly} these
-programs.\bigskip
-
-
-\begin{figure}[h]
-\mbox{\lstinputlisting[language=While,xleftmargin=10mm]{../progs/while-tests/fib.while}}
-\caption{Fibonacci program in the WHILE language.\label{fib}}
-\end{figure}
-
-\begin{figure}[h]
-\mbox{\lstinputlisting[language=While,xleftmargin=10mm]{../progs/while-tests/loops.while}}
-\caption{The three-nested-loops program in the WHILE language. 
-(Usually used for timing measurements.)\label{loop}}
-\end{figure}
-
-\begin{figure}[h]
-\mbox{\lstinputlisting[language=While,xleftmargin=10mm]{../progs/while-tests/factors.while}}
-\caption{A program that calculates factors for numbers in the WHILE
-  language.\label{factors}}
-\end{figure}
-
-\begin{figure}[h]
-\mbox{\lstinputlisting[language=While,xleftmargin=10mm]{../progs/while-tests/collatz2.while}}
-\caption{A program that calculates the Collatz series for numbers
-  between 1 and 100.\label{collatz}}
-\end{figure}
-
-\end{document}
-
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