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\section*{Coursework 3}

\noindent This coursework is worth 10\% and is due on \cwTHREE{} at

16:00. You are asked to implement a parser for the WHILE language and

also an interpreter. 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 should use the lexer from the previous coursework for the

parser.  Please submit your code to Github by the deadline.

\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 I showed during the lectures or uploaded to KEATS, which

you can both use. You can also use your own code from the CW~1 and

CW~2. But do not

be tempted to ask Github Copilot for help or do any other

shenanigans like this!

\subsection*{Question 1}

Design a grammar for the WHILE language and give the grammar

rules. The main categories of non-terminals should be:

\begin{itemize}

\item arithmetic expressions (with the operations from the

  previous coursework, that is \pcode{+}, \pcode{-}, \pcode{*},

  \pcode{/} and \pcode{\%})

\item boolean expressions (with the operations \pcode{==}, \pcode{<}, \pcode{>},

  \code{>=}, \code{<=}, 

  \code{!=}, \pcode{&&}, \pcode{||}, \pcode{true} and \pcode{false})

\item single statements (that is \pcode{skip}, assignments, \pcode{if}s,

  \pcode{while}-loops, \pcode{read} and \pcode{write})

\item compound statements separated by semicolons

\item blocks which are enclosed in curly parentheses

\end{itemize}

\noindent

Make sure the grammar is not left-recursive.

\subsection*{Question 2}

You should implement a parser for the WHILE language using parser

combinators. Be careful that the parser takes as input a stream, or

list, of \emph{tokens} generated by the tokenizer from the previous

coursework. For this you might want to filter out whitespaces and

comments. Your parser should be able to handle the WHILE programs in

Figures~\ref{fib} -- \ref{collatz}.  In addition give the

parse tree according to your grammar for the statement:

\begin{lstlisting}[language=While,numbers=none]

if (a < b) then skip else a := a * b + 1

\end{lstlisting}

\noindent

The output of the parser is an abstract syntax tree (AST).

A (possibly incomplete) datatype for ASTs of the WHILE language

is shown in Figure~\ref{trees}.

\begin{figure}[p]

\begin{lstlisting}[language=Scala]

abstract class Stmt

abstract class AExp

abstract class BExp 

type Block = List[Stmt]

case object Skip extends Stmt

case class If(a: BExp, bl1: Block, bl2: Block) extends Stmt

case class While(b: BExp, bl: Block) extends Stmt

case class Assign(s: String, a: AExp) extends Stmt

case class Read(s: String) extends Stmt

case class WriteVar(s: String) extends Stmt  

case class WriteStr(s: String) extends Stmt 

                      // for printing variables and strings

case class Var(s: String) extends AExp

case class Num(i: Int) extends AExp

case class Aop(o: String, a1: AExp, a2: AExp) extends AExp

case object True extends BExp

case object False extends BExp

case class Bop(o: String, a1: AExp, a2: AExp) extends BExp

case class Lop(o: String, b1: BExp, b2: BExp) extends BExp

                     // logical operations: and, or

\end{lstlisting}

\caption{The datatype for abstract syntax trees in Scala.\label{trees}}

\end{figure}

\subsection*{Question 3}

Implement an interpreter for the WHILE language you designed

and parsed in Question 1 and 2. This interpreter should take

as input an AST. However be careful because, programs

contain variables and variable assignments. This means

you need to maintain a kind of memory, or environment,

where you can look up a value of a variable and also

store a new value if it is assigned. Therefore an

evaluation function (interpreter) needs to look roughly as 

follows 

\begin{lstlisting}[numbers=none]

eval_stmt(stmt, env)

\end{lstlisting}

\noindent 

where \pcode{stmt} corresponds to the parse tree

of the program and \pcode{env} is an environment

acting as a store for variable values. 

Consider the Fibonacci program in Figure~\ref{fib}.

At the beginning of the program this store will be 

empty, but needs to be extended in line 3 and 4 where 

the variables \pcode{minus1} and \pcode{minus2}

are assigned values. These values need to be reassigned in

lines 7 and 8. The program should  be interpreted

according to straightforward rules: for example an

if-statement will ``run'' the if-branch if the boolean

evaluates to \pcode{true}, otherwise the else-branch.

Loops should be run as long as the boolean is \pcode{true}.

Programs you should be able to run are shown in

Give some time measurements for your interpreter

and the loop program in Figure~\ref{loop}. For example

how long does your interpreter take when \pcode{start}

is initialised with 100, 500 and so on. How far can

you scale this value if you are willing to wait, say

1 Minute?

\begin{figure}[h]

\lstinputlisting[language=while,xleftmargin=20mm]{../cwtests/cw03/fib.while}

\caption{Fibonacci program in the WHILE language.\label{fib}}

\end{figure}

\begin{figure}[h]

\lstinputlisting[language=while,xleftmargin=20mm]{../cwtests/cw03/loops.while}

\caption{The three-nested-loops program in the WHILE language. 

Usually used for timing measurements.\label{loop}}

\end{figure}

\begin{figure}[h]

\lstinputlisting[language=while,xleftmargin=0mm]{../cwtests/cw03/primes.while}

\caption{Prime number program.\label{primes}}

\end{figure}

\begin{figure}[p]

\lstinputlisting[language=while,xleftmargin=0mm]{../cwtests/cw03/collatz2.while}

\caption{Collatz series program.\label{collatz}}

\end{figure}

\clearpage

\newpage

\section*{Answers}

\noindent

\textbf{Question 1 (Grammar):}\\

\mbox{}\\[9cm]

\noindent

\mbox{}\\[8cm]

\noindent

\textbf{Question 3 (Timings):}\\

\begin{center}

  \def\arraystretch{1.5}

  \begin{tabular}{l|l}

    n & secs\\

    \hline

    100 & \\

    500 & \\

    700 & \\

    1000 & \\

    \\

    \\

    \\

    \\

   \end{tabular} 

\end{center}  

\end{document}

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