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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

\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

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

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

\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}.

Note also that some programs contain a read-statement,

which means you need to read and integer from the commandline

and store the value in the corresponding variable.

of the \texttt{primes.while} should look as follows:

\begin{figure}[h]

{\small

\begin{lstlisting}[numbers=none]

2

3

5

7

11

13

17

19

23

29

31

37

41

43

47

53

59

61

67

71

73

79

83

89

97

Map(end -> 100, n -> 100, f -> 4, tmp -> 1)

\end{lstlisting}}

\caption{Sample output for the file \texttt{primes.while}.\label{fib}}

\end{figure}

\end{document}

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