366 \multicolumn{3}{l}{$\qquad l_\textit{ifelse}\;$ (fresh label)}\\

   366 \multicolumn{3}{l}{$\qquad L_\textit{ifelse}\;$ (fresh label)}\\

   367 \multicolumn{3}{l}{$\qquad l_\textit{ifend}\;$ (fresh label)}\\

   367 \multicolumn{3}{l}{$\qquad L_\textit{ifend}\;$ (fresh label)}\\

   370 \multicolumn{3}{l}{$\qquad(\textit{compile}(b, E, l_\textit{ifelse})$}\\

   370 \multicolumn{3}{l}{$\qquad(\textit{compile}(b, E, L_\textit{ifelse})$}\\

   372 \multicolumn{3}{l}{$\qquad\phantom{(}@\; \pcode{goto}\;l_\textit{ifend}$}\\

   372 \multicolumn{3}{l}{$\qquad\phantom{(}@\; \pcode{goto}\;L_\textit{ifend}$}\\

   373 \multicolumn{3}{l}{$\qquad\phantom{(}@\;l_\textit{ifelse}:$}\\

   373 \multicolumn{3}{l}{$\qquad\phantom{(}@\;L_\textit{ifelse}:$}\\

   375 \multicolumn{3}{l}{$\qquad\phantom{(}@\;l_\textit{ifend}:, E'')$}\\

   375 \multicolumn{3}{l}{$\qquad\phantom{(}@\;L_\textit{ifend}:, E'')$}\\

   376 \end{tabular}

   376 \end{tabular}

   377 \end{center}

   377 \end{center}

   378 

   379 \noindent In the first two lines we generate two fresh labels

   380 for the jump addresses (just before the else-branch and just

   381 after). In the next two lines we generate the instructions for

   382 the two branches, $is_1$ and $is_2$. The final code will

   383 be first the code for $b$ (including the label 

   384 just-before-the-else-branch), then the \pcode{goto} for after

   385 the else-branch, the label $L_\textit{ifesle}$, followed by

   386 the instructions for the else-branch, followed by the 

   387 after-the-else-branch label. Consider for example the 

   388 if-statement:

   389 

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

   391 if 1 = 1 then x := 2 else y := 3

   392 \end{lstlisting}

   393 

   394 \noindent 

   395 The generated code is as follows:

   396 

   397 \begin{lstlisting}[mathescape,language={}]

   398    ldc 1

   399    ldc 2

   400    if_icmpne L_ifelse $\quad\tikz[remember picture] \node (C) {\mbox{}};$

   401    ldc 2

   402    istore 0

   403    goto L_ifend $\quad\tikz[remember picture] \node (A) {\mbox{}};$

   404 L_ifelse: $\quad\tikz[remember picture] \node[] (D) {\mbox{}};$

   405    ldc 3

   406    istore 1

   407 L_ifend: $\quad\tikz[remember picture] \node[] (B) {\mbox{}};$

   408 \end{lstlisting}

   409 

   410 \begin{tikzpicture}[remember picture,overlay]

   411   \draw[->,very thick] (A) edge [->,to path={-- ++(10mm,0mm) 

   412            -- ++(0mm,-17.3mm) |- (\tikztotarget)},line width=1mm] (B.east);

   413   \draw[->,very thick] (C) edge [->,to path={-- ++(10mm,0mm) 

   414            -- ++(0mm,-17.3mm) |- (\tikztotarget)},line width=1mm] (D.east);

   415 \end{tikzpicture}

   416 

   417 \noindent The first three lines correspond to the the boolean 

   418 expression $1 = 1$. The jump for when this boolean expression

   419 is false is in Line~3. Lines 4-6 corresponds to the if-branch; 

   420 the else-branch is in Lines 8 and 9. Note carefully how the

   421 environment $E$ is threaded through the calls of 

   422 \textit{compile}. The function receives an environment $E$, 

   423 but it might extend it when compiling the if-branch, yielding 

   424 $E'$. This happens for example in the if-statement above 

   425 whenever the variable \code{x} has not been used before. 

   426 Similarly with the environment $E''$ for the second call

   427 to \textit{compile}. $E''$ is also the environment that need

   428 to be returned.

   429 

   430 The compilation of the while-loops, say 

   431 \pcode{while} $b$ \pcode{do} $cs$, is very similar. In case

   432 the condition is true and we need to do another iteration, the 

   433 control-flow needs to be as follows

   434 

   435 \begin{center}

   436 \begin{tikzpicture}[node distance=2mm and 4mm,

   437  block/.style={rectangle, minimum size=1cm, draw=black, line width=1mm},

   438  point/.style={rectangle, inner sep=0mm, minimum size=0mm, fill=red},

   439  skip loop/.style={black, line width=1mm, to path={-- ++(0,-10mm) -| (\tikztotarget)}}]

   440 \node (A0) [point, left=of A1] {};

   441 \node (A1) [point] {};

   442 \node (b) [block, right=of A1] {code of $b$};

   443 \node (A2) [point, right=of b] {};

   444 \node (cs1) [block, right=of A2] {code of $cs$};

   445 \node (A3) [point, right=of cs1] {};

   446 \node (A4) [point, right=of A3] {};

   447 

   448 \draw (A0) edge [->, black, line width=1mm] (b);

   449 \draw (b) edge [->, black, line width=1mm] (cs1);

   450 \draw (cs1) edge [->, black, line width=1mm] (A3);

   451 \draw (A3) edge [->,skip loop] (A1);

   452 \end{tikzpicture}

   453 \end{center}

   454 

   455 \noindent While if the condition is \emph{not} true we

   456 need to jump out of the loop, which gives the following

   457 control flow.

   458 

   459 \begin{center}

   460 \begin{tikzpicture}[node distance=2mm and 4mm,

   461  block/.style={rectangle, minimum size=1cm, draw=black, line width=1mm},

   462  point/.style={rectangle, inner sep=0mm, minimum size=0mm, fill=red},

   463  skip loop/.style={black, line width=1mm, to path={-- ++(0,-10mm) -| (\tikztotarget)}}]

   464 \node (A0) [point, left=of A1] {};

   465 \node (A1) [point] {};

   466 \node (b) [block, right=of A1] {code of $b$};

   467 \node (A2) [point, right=of b] {};

   468 \node (cs1) [block, right=of A2] {code of $cs$};

   469 \node (A3) [point, right=of cs1] {};

   470 \node (A4) [point, right=of A3] {};

   471 

   472 \draw (A0) edge [->, black, line width=1mm] (b);

   473 \draw (b) edge [->, black, line width=1mm] (A2);

   474 \draw (A2) edge [skip loop] (A3);

   475 \draw (A3) edge [->, black, line width=1mm] (A4);

   476 \end{tikzpicture}

   477 \end{center}

   478 

   479 \noindent Again we can use the \textit{compile}-function for

   480 boolean expressions to insert the appropriate jump to the

   481 end of the loop (label $L_{wend}$).

   482 

   483 \begin{center}

   484 \begin{tabular}{lcl}

   485 $\textit{compile}(\pcode{while}\; b\; \pcode{do} \;cs, E)$ & $\dn$\\ 

   486 \multicolumn{3}{l}{$\qquad L_{wbegin}\;$ (fresh label)}\\

   487 \multicolumn{3}{l}{$\qquad L_{wend}\;$ (fresh label)}\\

   488 \multicolumn{3}{l}{$\qquad (is, E') = \textit{compile}(cs_1, E)$}\\

   489 \multicolumn{3}{l}{$\qquad(L_{wbegin}:$}\\

   490 \multicolumn{3}{l}{$\qquad\phantom{(}@\;\textit{compile}(b, E, L_{wend})$}\\

   491 \multicolumn{3}{l}{$\qquad\phantom{(}@\;is$}\\

   492 \multicolumn{3}{l}{$\qquad\phantom{(}@\; \text{goto}\;l_{wbegin}$}\\

   493 \multicolumn{3}{l}{$\qquad\phantom{(}@\;L_{wend}:, E')$}\\

   494 \end{tabular}

   495 \end{center}

   496 

   497 Next we need to consider the statement \pcode{write x}, which 

   498 can be used to write out the content of a variable. For this 

   499 we need to use a Java library function. In order to avoid

   500 having to generate a lot of code for each 

   501 \pcode{write}-command, we use a separate method and just call

   502 this method with an appropriate stack.

   503 

   504 \begin{lstlisting}[language=JVMIS]

   505 .method public static write(I)V 

   506     .limit locals 5 

   507     .limit stack 5  

   508     getstatic java/lang/System/out Ljava/io/PrintStream; 

   509     iload 0

   510     invokevirtual java/io/PrintStream/println(I)V 

   511     return 

   512 .end method

   513 \end{lstlisting}