--- a/handouts/ho07.tex	Tue Nov 17 13:31:19 2015 +0000
+++ b/handouts/ho07.tex	Tue Nov 17 14:45:03 2015 +0000
@@ -398,7 +398,7 @@
 
 \begin{lstlisting}[mathescape,language={}]
    ldc 1
-   ldc 2
+   ldc 1
    if_icmpne L_ifelse $\quad\tikz[remember picture] \node (C) {\mbox{}};$
    ldc 2
    istore 0
@@ -414,23 +414,23 @@
   \draw[->,very thick] (C) edge [->,to path={-- ++(10mm,0mm) 
            -- ++(0mm,-17.3mm) |- (\tikztotarget)},line width=1mm] (D.east);
\end{tikzpicture}
 
-\noindent The first three lines correspond to the the boolean 
+\noindent The first three lines correspond to the the boolean
 expression $1 = 1$. The jump for when this boolean expression
-is false is in Line~3. Lines 4-6 corresponds to the if-branch; 
+is false is in Line~3. Lines 4-6 corresponds to the if-branch;
 the else-branch is in Lines 8 and 9. Note carefully how the
-environment $E$ is threaded through the calls of 
-\textit{compile}. The function receives an environment $E$, 
-but it might extend it when compiling the if-branch, yielding 
-$E'$. This happens for example in the if-statement above 
-whenever the variable \code{x} has not been used before. 
-Similarly with the environment $E''$ for the second call
-to \textit{compile}. $E''$ is also the environment that need
-to be returned.
+environment $E$ is threaded through the recursive calls of
+\textit{compile}. The function receives an environment $E$,
+but it might extend it when compiling the if-branch, yielding
+$E'$. This happens for example in the if-statement above
+whenever the variable \code{x} has not been used before.
+Similarly with the environment $E''$ for the second call to
+\textit{compile}. $E''$ is also the environment that needs to
+be returned as part of the answer.
 
 The compilation of the while-loops, say 
 \pcode{while} $b$ \pcode{do} $cs$, is very similar. In case
-the condition is true and we need to do another iteration, the 
-control-flow needs to be as follows
+the condition is true and we need to do another iteration, 
+and the control-flow needs to be as follows
 
 \begin{center}
 \begin{tikzpicture}[node distance=2mm and 4mm,
@@ -452,7 +452,7 @@
 \end{tikzpicture}
 \end{center}
 
-\noindent While if the condition is \emph{not} true we
+\noindent Whereas if the condition is \emph{not} true, we
 need to jump out of the loop, which gives the following
 control flow.
 
@@ -478,7 +478,7 @@
 
 \noindent Again we can use the \textit{compile}-function for
 boolean expressions to insert the appropriate jump to the
-end of the loop (label $L_{wend}$).
+end of the loop (label $L_{wend}$ below).
 
 \begin{center}
 \begin{tabular}{lcl}
@@ -489,18 +489,47 @@
 \multicolumn{3}{l}{$\qquad(L_{wbegin}:$}\\
 \multicolumn{3}{l}{$\qquad\phantom{(}@\;\textit{compile}(b, E, L_{wend})$}\\
 \multicolumn{3}{l}{$\qquad\phantom{(}@\;is$}\\
-\multicolumn{3}{l}{$\qquad\phantom{(}@\; \text{goto}\;l_{wbegin}$}\\
+\multicolumn{3}{l}{$\qquad\phantom{(}@\; \text{goto}\;L_{wbegin}$}\\
 \multicolumn{3}{l}{$\qquad\phantom{(}@\;L_{wend}:, E')$}\\
 \end{tabular}
 \end{center}
 
+\noindent I let you go through how this clause works. As an example
+you can consider the while-loop
+
+\begin{lstlisting}[mathescape,numbers=none,language={}]
+while x <= 10 do x := x + 1
+\end{lstlisting}
+
+\noindent yielding the following code
+
+\begin{lstlisting}[mathescape,language={}]
+L_wbegin: $\quad\tikz[remember picture] \node[] (LB) {\mbox{}};$
+   iload 0
+   ldc 10
+   if_icmpgt L_wend $\quad\tikz[remember picture] \node (LC) {\mbox{}};$
+   iload 0
+   ldc 1
+   iadd
+   istore 0
+   goto L_wbegin $\quad\tikz[remember picture] \node (LA) {\mbox{}};$
+L_wend: $\quad\tikz[remember picture] \node[] (LD) {\mbox{}};$
+\end{lstlisting}
+ 
+\begin{tikzpicture}[remember picture,overlay]
  \draw[->,very thick] (LA) edge [->,to path={-- ++(10mm,0mm) 
+           -- ++(0mm,17.3mm) |- (\tikztotarget)},line width=1mm] (LB.east);
+  \draw[->,very thick] (LC) edge [->,to path={-- ++(10mm,0mm) 
+           -- ++(0mm,-17.3mm) |- (\tikztotarget)},line width=1mm] (LD.east);
\end{tikzpicture}
+
+
 Next we need to consider the statement \pcode{write x}, which
-can be used to write out the content of a variable. For this
+can be used to print out the content of a variable. For this
 we need to use a Java library function. In order to avoid
 having to generate a lot of code for each
-\pcode{write}-command, we use a separate method and just call
-this method with an argument (which needs to be placed on the
-stack). The code is as follows.
+\pcode{write}-command, we use a separate helper-method and
+just call this method with an argument (which needs to be
+placed onto the stack). The code of the helper-method is as
+follows.
 
 
 \begin{lstlisting}[language=JVMIS]
@@ -527,12 +556,12 @@
 print out onto the stack. In the next line we call the method
 \pcode{println} (from the class \pcode{java/io/PrintStream}).
 We want to print out an integer and do not expect anything
-back (that is why the type annotation \pcode{(I)V}). The
+back (that is why the type annotation is \pcode{(I)V}). The
 \pcode{return}-instruction in the next line changes the
 control-flow back to the place from where \pcode{write} was
 called. This method needs to be part of a header that is
-included in any code we generate. The method \pcode{write} can
-be invoked with the two instructions
+included in any code we generate. The helper-method
+\pcode{write} can be invoked with the two instructions
 
 \begin{lstlisting}[mathescape,language=JVMIS]
 iload $E(x)$ 
@@ -540,9 +569,9 @@
 \end{lstlisting}
 
 \noindent where we first place the variable to be printed on
-the stack and then call \pcode{write}. The \pcode{XXX} need to
-be replaced by appropriate class name (this will be explained
-shortly).
+top of the stack and then call \pcode{write}. The \pcode{XXX}
+need to be replaced by an appropriate class name (this will be
+explained shortly).
 
 
 \begin{figure}[t]
@@ -572,17 +601,19 @@
 By generating code for a While-program, we end up with a list
 of (JVM assembly) instructions. Unfortunately, there is a bit
 more boilerplate code needed before these instructions can be
-run. The code is shown in Figure~\ref{boiler}. This
-boilerplate code is very specific to the JVM. Lines 4 to 8 
-contains a method for object creation in the JVM and is called 
-\emph{before} the \pcode{main}-method in Lines 10 to 17. 
-Interesting are the Lines 11 and 12 where we hardwire that the 
-stack of our program will never be larger than 200 and that 
-the maximum number of variables is also 200. This seem 
-conservative default values that allow is to run some simple
-While-programs. In a real compiler, we would of course need to
-work harder and find out appropriate values for the stack and 
-local variables.
+run. The complete code is shown in Figure~\ref{boiler}. This
+boilerplate code is very specific to the JVM. If we target any
+other virtual machine or a machine language, then we would
+need to change this code. Lines 4 to 8 in Figure~\ref{boiler}
+contain a method for object creation in the JVM; this method
+is called \emph{before} the \pcode{main}-method in Lines 10 to
+17. Interesting are the Lines 11 and 12 where we hardwire that
+the stack of our programs will never be larger than 200 and
+that the maximum number of variables is also 200. This seem to
+be conservative default values that allow is to run some
+simple While-programs. In a real compiler, we would of course
+need to work harder and find out appropriate values for the
+stack and local variables.
 
 To sum up, in Figure~\ref{test} is the complete code generated
 for the slightly non-sensical program
@@ -593,13 +624,16 @@
 \end{lstlisting}
 
 \noindent Having this code at our disposal, we need the
-assembler to translate the generated code into bytecode (a
-class file) that can be understood by the JVM.
+assembler to translate the generated code into JVM bytecode (a
+class file). This bytecode is understood by the JVM and can be
+run by just invoking the \pcode{java}-program.
 
 
 \begin{figure}[p]
 \lstinputlisting{../progs/test-small.j}
-\caption{Generated code for a test program.\label{test}}
+\caption{Generated code for a test program. This code can be 
+processed by an Java assembler producing a class-file, which
+can be run by the \pcode{java}-program.\label{test}}
 \end{figure}
 
 \end{document}