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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. The parser needs to use parser combinators.  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. If you use Scala
in your code, a good place to start is the file \texttt{comb1.sc} and
\texttt{comb2.sc} uploaded to KEATS. Feel free to use the ``hack''
explained during the lectures. This might make your grammar
simpler. However, make sure you understand the code involved in the
``hack'' because if you just do ``mix-and-match'' you will receive
strange errors.  The main function that will be tested is called
\texttt{eval} and \texttt{Stmts.parse\_all}. The latter expects a list
of tokens as input and generates an AST. The former expects an AST and
``runs'' the program. The marks will be distributed such that 6 marks
are given for the correct grammar (and parsers); 4 marks for the correct
\texttt{eval} function.  You should use the lexer from CW2 for the
parser - you potentially need to make additions for CW2.  

\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*{Syntax Error in Template File cw03.sc\alert}

Apologies, there is a small syntax error in the template file where a variable
needs to be called \texttt{tks} instead of \texttt{tk}. The code
in question is at the end of \texttt{cw03.sc} and should be like
this (see lines 5, 6 and 8):

\begin{lstlisting}[language=Scala,numbers=left]
@main
def test(file: String) = {
  val contents = os.read(os.pwd / "examples" / file)
  println(s"Lex $file: ")
  val tks = tokenise(contents)
  println(tks.mkString(","))
  println(s"Parse $file: ")
  val ast = Stmts.parse_all(tks).head
  println(ast)
  println(s"Eval $file: ")
  println(eval(ast))
}
\end{lstlisting}  



\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 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
the \texttt{examples} directory.  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}.
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.
Programs you should be able to run are given in  the
\texttt{examples} directory. The output
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}


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