115 \begin{frame}[c]

    94 \begin{frame}[t]

   116 \frametitle{Revision: Proofs}

    95 \frametitle{Last Week}

   117 

    96 

   118 \begin{center}

    97 \begin{center}

   119 %%\includegraphics[scale=0.4]{river-stones.jpg}

    98 if \bl{$\varnothing$} does not occur in \bl{$r$} \;\;then\;\;\bl{$L(r) \not= \{\}$}

   120 \end{center}

    99 \end{center}

   121 

   100 

   122 \end{frame}}

   101 \noindent

   123 

   102 holds, or equivalently

   124 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   103 

   125 \mode<presentation>{

   104 \begin{center}

   126 \begin{frame}[c]

   105 \bl{$L(r) = \{\}$} \;\;implies\;\; \bl{$\varnothing$} occurs in \bl{$r$}.\pause

   127 \frametitle{Subsets}

   106 \end{center}

   128 

   107 

   129 \Large

   108 \begin{center}

   130 \bl{$A \subseteq B$}\bigskip\bigskip\\

   109 \bl{\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}

   131 

   110 $occurs(\varnothing)$      & $\dn$ & $true$\\

   132 \bl{$\forall e.\; e \in A \Rightarrow e \in B$}

   111 $occurs(\epsilon)$           & $\dn$ &  $f\!alse$\\

   112 $occurs (c)$                    & $\dn$ &  $f\!alse$\\

   113 $occurs (r_1 + r_2)$       & $\dn$ &  $occurs(r_1) \vee occurs(r_2)$\\ 

   114 $occurs (r_1 \cdot r_2)$ & $\dn$ &  $occurs(r_1) \vee occurs(r_2)$\\

   115 $occurs (r^*)$                & $\dn$ & $occurs(r)$ \\

   116 \end{tabular}}

   117 \end{center}

   118 

   119 \end{frame}}

   120 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   121 

   122 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   123 \begin{frame}[c,fragile]

   124 \frametitle{Functional Programming}

   125 

   126 \footnotesize

   127 \begin{textblock}{13}(0.9,3)

   128 \lstset{emph={def,if,then,else},emphstyle=\color{javapurple}}

   129 \begin{lstlisting}[basicstyle=\ttfamily, numbers=none]

   130 def fib(n) = if n == 0 then 0 

   131              else if n == 1 then 1 

   132              else fib(n - 1) + fib(n - 2);

   133 

   134 def fact(n) = if n == 0 then 1 else n * fact(n - 1);

   135 

   136 def ack(m, n) = if m == 0 then n + 1

   137                 else if n == 0 then ack(m - 1, 1)

   138                 else ack(m - 1, ack(m, n - 1));

   139                 

   140 def gcd(a, b) = if b == 0 then a else gcd(b, a % b);                

   141 \end{lstlisting}

   142 \end{textblock}

   143 

   144 \end{frame}

   145 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   146 

   147 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   148 \mode<presentation>{

   149 \begin{frame}[c]

   150 

   151 \begin{center}

   152 \bl{\begin{tabular}{@{}lcl@{}}

   153 \textit{Exp} & $\rightarrow$ &  \textit{Var} $|$ \textit{Num}\\

   154               & $|$ & \textit{Exp} \texttt{+} \textit{Exp} $|$ ... $|$ ( \textit{Exp} )\\

   155               & $|$ & \texttt{if}\; \textit{BExp} \;\texttt{then}\; \textit{Exp} \;\texttt{else}\; \textit{Exp}\\

   156               & $|$ & \texttt{write}\;\textit{Exp}\\

   157               & $|$ & \textit{Exp}\;\texttt{;}\;\textit{Exp}\\

   158               & $|$ & \textit{FunName} \texttt{(}\textit{Exp},...,\textit{Exp}\texttt{)}\medskip\\

   159 \textit{BExp} & $\rightarrow$ & \ldots\medskip\\

   160 \textit{Decl} & $\rightarrow$ &  \textit{Def} \;\texttt{;}\; \textit{Decl}\\

   161               & $|$ & \textit{Exp}\medskip\\

   162 \textit{Def} & 

   163 $\rightarrow$ &  \texttt{def} \textit{FunName}\texttt{(}\textit{x}$_1$,..., \textit{x}$_n$\texttt{)} \texttt{=} \textit{Exp}\\

   164 \end{tabular}}

   165 \end{center}

   166 

   167 

   168 \end{frame}}

   169 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   170 

   171 

   172 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   173 \begin{frame}[c, fragile]

   174 \frametitle{Abstract Syntax Tree}

   175 

   176 \footnotesize

   177 \begin{textblock}{13}(0.3,2)

   178 \begin{lstlisting}[language=Scala,basicstyle=\ttfamily, numbers=none]

   179 abstract class Exp

   180 abstract class BExp 

   181 abstract class Decl

   182 

   183 case class 

   184   Def(name: String, args: List[String], body: Exp) 

   185                                           extends Decl

   186 case class Main(e: Exp) extends Decl

   187 

   188 case class Call(name: String, args: List[Exp]) extends Exp

   189 case class If(a: BExp, e1: Exp, e2: Exp) extends Exp

   190 case class Write(e: Exp) extends Exp

   191 case class Var(s: String) extends Exp

   192 case class Num(i: Int) extends Exp

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

   194 case class Sequ(e1: Exp, e2: Exp) extends Exp

   195 

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

   197 \end{lstlisting}

   198 \end{textblock}

   199 

   200 \end{frame}

   201 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

   202 

   203 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   204 \begin{frame}[c, fragile]

   205 \frametitle{Mathematical Functions}

   206 

   207 Compilation of some mathematical functions:

   208 

   209 \begin{center}

   210 \begin{tabular}{lcl}

   211 \texttt{Aop("+", a1, a2)} & $\Rightarrow$ & \texttt{...iadd}\\

   212 \texttt{Aop("-", a1, a2)} & $\Rightarrow$ & \texttt{...isub}\\

   213 \texttt{Aop("*", a1, a2)} & $\Rightarrow$ & \texttt{...imul}\\

   214 \texttt{Aop("/", a1, a2)} & $\Rightarrow$ & \texttt{...idiv}\\

   215 \texttt{Aop("\%", a1, a2)} & $\Rightarrow$ & \texttt{...irem}\\

   216 \end{tabular}

   217 \end{center}

   218 

   219 \end{frame}

   220 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

   221 

   222 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   223 \begin{frame}[c, fragile]

   224 \frametitle{Boolean Expressions}

   225 

   226 Compilation of boolean expressions:

   227 

   228 \begin{center}

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

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

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

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

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

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

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

   236 \node (cs1) [block, right=of A2] {code of \bl{$cs_1$}};

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

   238 \node (cs2) [block, right=of A3] {code of \bl{$cs_2$}};

   239 \node (A4) [point, right=of cs2] {};

   240 

   241 \only<1>{

   242 \draw (A1) edge [->, red, line width=1mm] (b);

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

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

   245 \draw (A3) edge [->, red, line width=1mm] (cs2);

   246 \draw (cs2) edge [->,red, line width=1mm] (A4);

   247 \node [below=of cs1] {\raisebox{-5mm}{\small{}conditional jump}};}

   248 \end{tikzpicture}

   249 \end{center}

   250 

   251 \begin{center}

   252 \begin{tabular}{lcl}

   253 \texttt{Bop("==", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpne...}\\

   254 \texttt{Bop("!=", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpeq...}\\

   255 \texttt{Bop("<", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpge...}\\

   256 \texttt{Bop("<=", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpgt...}\\

   257 \end{tabular}

   258 \end{center}

   259 

   260 \end{frame}

   261 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

   262 

   263 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   264 \begin{frame}[t, fragile]

   265 \frametitle{Sequences}

   266 

   267 Compiling \texttt{arg1 ; arg2}:

   268 

   269 

   270 \begin{textblock}{7}(2,5)\footnotesize

   271 \begin{minipage}{6cm}

   272 \begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]

   273 ...arg1...

   274 pop

   275 ...arg1...

   276 \end{lstlisting}

   277 \end{minipage}

   278 \end{textblock}

   279 

   280   

   281 \end{frame}

   282 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

   283 

   284 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   285 \begin{frame}[t, fragile]

   286 \frametitle{Write}

   287 

   288 Compiling \texttt{write(arg)}:

   289 

   290 

   291 \begin{textblock}{7}(2,4)\footnotesize

   292 \begin{minipage}{6cm}

   293 \begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]

   294 ...arg...

   295 dup

   296 invokestatic XXX/XXX/write(I)V

   297 \end{lstlisting}

   298 \end{minipage}

   299 \end{textblock}

   300 

   301 

   302 

   303 \begin{textblock}{7}(2,8)\footnotesize

   304 \begin{minipage}{6cm}

   305 \begin{lstlisting}[language=Scala,basicstyle=\ttfamily, numbers=none]

   306 case Write(a1) => {

   307     compile_exp(a1, env) ++

   308     List("dup\n",

   309          "invokestatic XXX/XXX/write(I)V\n")

   310   }

   311 \end{lstlisting}

   312 \end{minipage}

   313 \end{textblock}

   314   

   315 \end{frame}

   316 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

   317 

   318 

   319 

   320 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   321 \begin{frame}[c, fragile]

   322 \frametitle{Functions}

   323 

   324 \begin{textblock}{7}(1,2)\footnotesize

   325 \begin{minipage}{6cm}

   326 \begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]

   327 .method public static write(I)V 

   328    .limit locals 5 

   329    .limit stack 5 

   330    iload 0 

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

   332    swap 

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

   334    return 

   335 .end method

   336 \end{lstlisting}

   337 \end{minipage}

   338 \end{textblock}

   339 

   340 

   341 \begin{textblock}{10}(1,9.8)

   342 \small We will need for definitions\\[-8mm]\mbox{}\footnotesize

   343 \begin{center}

   344 \begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]

   345 .method public static f (I...I)I

   346   .limit locals ??

   347   .limit stack ?? 

   348   ??

   349 .end method

   350 \end{lstlisting}

   351 \end{center}

   352 \end{textblock}

   353 

   354 \end{frame}

   355 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   356 

   357 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   358 \begin{frame}[c, fragile]

   359 \frametitle{Stack Estimation}

   360 \footnotesize

   361 \begin{center}

   362 \begin{lstlisting}[language=Scala,basicstyle=\ttfamily, numbers=none]

   363 def max_stack_exp(e: Exp): Int = e match {

   364   case Call(_, args) => args.map(max_stack_exp).sum

   365   case If(a, e1, e2) => max_stack_bexp(a) + 

   366   	(List(max_stack_exp(e1), max_stack_exp(e1)).max)

   367   case Write(e) => max_stack_exp(e) + 1

   368   case Var(_) => 1

   369   case Num(_) => 1

   370   case Aop(_, a1, a2) => 

   371   	max_stack_exp(a1) + max_stack_exp(a2)

   372   case Sequ(e1, e2) => 

   373   	List(max_stack_exp(e1), max_stack_exp(e2)).max

   374 }

   375 

   376 def max_stack_bexp(e: BExp): Int = e match {

   377   case Bop(_, a1, a2) => 

   378   	max_stack_exp(a1) + max_stack_exp(a2)

   379 }

   380 \end{lstlisting}

   381 \end{center}

   382 

   383 \end{frame}

   384 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

   385 

   386 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   387 \begin{frame}[fragile]

   388 \frametitle{Successor}

   389 

   390 \begin{textblock}{7}(1,2.5)\footnotesize

   391 \begin{minipage}{6cm}

   392 \begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]

   393 .method public static suc(I)I 

   394 .limit locals 1

   395 .limit stack

   396   iload 0

   397   ldc 1

   398   iadd

   399   ireturn

   400 .end method 

   401 \end{lstlisting}

   402 \end{minipage}

   403 \end{textblock}

   404 

   405 \begin{textblock}{7}(6,8)

   406 \begin{tikzpicture}\small

   407 \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 

   408 {\begin{minipage}{5cm}

   409 \begin{lstlisting}[language=Lisp,basicstyle=\ttfamily, numbers=none]

   410 def suc(x) = x + 1;

   411 \end{lstlisting}

   412 \end{minipage}};

   413 \end{tikzpicture}

   414 \end{textblock}

   415 \end{frame}

   416 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   417 

   418 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   419 \begin{frame}[fragile]

   420 \frametitle{Addition}

   421 

   422 \begin{textblock}{7}(1,1.5)\footnotesize

   423 \begin{minipage}{6cm}

   424 \begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]

   425 .method public static add(II)I 

   426 .limit locals 2

   427 .limit stack 4

   428   iload 0

   429   ldc 0

   430   if_icmpne If_else_2

   431   iload 1

   432   goto If_end_3

   433 If_else_2:

   434   iload 0

   435   ldc 1

   436   isub

   437   iload 1

   438   invokestatic defs/defs/add(II)I

   439   invokestatic defs/defs/suc(I)I

   440 If_end_3:

   441   ireturn

   442 .end method

   443 \end{lstlisting}

   444 \end{minipage}

   445 \end{textblock}

   446 

   447 \begin{textblock}{7}(6,6.2)

   448 \begin{tikzpicture}\small

   449 \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 

   450 {\begin{minipage}{7cm}

   451 \begin{lstlisting}[language=Lisp,basicstyle=\ttfamily, numbers=none]

   452 def add(x, y) = 

   453     if x == 0 then y 

   454     else suc(add(x - 1, y));

   455 \end{lstlisting}

   456 \end{minipage}};

   457 \end{tikzpicture}

   458 \end{textblock}

   459 \end{frame}

   460 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   461 

   462 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   463 \begin{frame}[fragile]

   464 \frametitle{Factorial}

   465 

   466 \begin{textblock}{7}(1,1.5)\footnotesize

   467 \begin{minipage}{6cm}

   468 \begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]

   469 .method public static facT(II)I 

   470 .limit locals 2

   471 .limit stack 4

   472   iload 0

   473   ldc 0	

   474   if_icmpne If_else_2

   475   iload 1

   476   goto If_end_3

   477 If_else_2:

   478   iload 0

   479   ldc 1

   480   isub

   481   iload 0

   482   iload 1

   483   imul

   484   invokestatic fact/fact/facT(II)I

   485 If_end_3:

   486   ireturn

   487 .end method 

   488 \end{lstlisting}

   489 \end{minipage}

   490 \end{textblock}

   491 

   492 \begin{textblock}{7}(6,7)

   493 \begin{tikzpicture}\small

   494 \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 

   495 {\begin{minipage}{7cm}

   496 \begin{lstlisting}[language=Lisp,basicstyle=\ttfamily, numbers=none]

   497 def facT(n, acc) = 

   498   if n == 0 then acc 

   499   else facT(n - 1, n * acc);

   500 \end{lstlisting}

   501 \end{minipage}};

   502 \end{tikzpicture}

   503 \end{textblock}

   504 \end{frame}

   505 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   506 

   507 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   508 \begin{frame}[fragile]

   509 %\frametitle{Factorial}

   510 

   511 \begin{textblock}{7}(1,-0.2)\footnotesize

   512 \begin{minipage}{6cm}

   513 \begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none, escapeinside={(*@}{@*)}]

   514 .method public static facT(II)I 

   515 .limit locals 2

   516 .limit stack 4

   517 (*@\hl{facT\_Start:} @*)

   518   iload 0

   519   ldc 0

   520   if_icmpne If_else_2

   521   iload 1

   522   goto If_end_3

   523 If_else_2:

   524   iload 0

   525   ldc 1

   526   isub

   527   iload 0

   528   iload 1

   529   imul

   530   (*@\hl{istore 1} @*)

   531   (*@\hl{istore 0} @*)

   532   (*@\hl{goto facT\_Start} @*)

   533 If_end_3:

   534   ireturn

   535 .end method 

   536 \end{lstlisting}

   537 \end{minipage}

   538 \end{textblock}

   539 

   540 \begin{textblock}{7}(6,7)

   541 \begin{tikzpicture}\small

   542 \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 

   543 {\begin{minipage}{7cm}

   544 \begin{lstlisting}[language=Lisp,basicstyle=\ttfamily, numbers=none]

   545 def facT(n, acc) = 

   546   if n == 0 then acc 

   547   else facT(n - 1, n * acc);

   548 \end{lstlisting}

   549 \end{minipage}};

   550 \end{tikzpicture}

   551 \end{textblock}

   552 \end{frame}

   553 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   554 

   555 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   556 \begin{frame}[c, fragile]

   557 \frametitle{Tail Recursion}

   558 

   559 A call to \texttt{f(args)} is usually compiled as\medskip

   560 

   561 {\small\begin{lstlisting}[basicstyle=\ttfamily, numbers=none]

   562   args onto stack

   563   invokestatic  .../f 

   564 \end{lstlisting}}\pause

   565 

   566 

   567 A call is in tail position provided:\medskip

   568 

   569 {\small\begin{itemize}

   570 \item \texttt{if Bexp then \hl{Exp} else \hl{Exp}}

   571 \item \texttt{Exp ; \hl{Exp}}

   572 \item \texttt{Exp  op Exp}

   573 \end{itemize}}\medskip

   574 

   575 then a call \texttt{f(args)} can be compiled as\medskip\small

   576 

   577 \begin{lstlisting}[basicstyle=\ttfamily, numbers=none]

   578   prepare environment

   579   jump to start of function

   580 \end{lstlisting}

   581 

   582 \end{frame}

   583 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

   584 

   585 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   586 \begin{frame}[c, fragile]

   587 \frametitle{Tail Recursive Call}

   588 \footnotesize

   589 \begin{textblock}{13}(0.3,2)

   590 \begin{lstlisting}[language=Scala,basicstyle=\ttfamily, numbers=none]

   591 def compile_expT(a: Exp, env: Mem, name: String): Instrs = 

   592   ...

   593   case Call(n, args) => if (name == n) 

   594   { 

   595     val stores = args.zipWithIndex.map 

   596        { case (x, y) => "istore " + y.toString + "\n" } 

   597     args.flatMap(a => compile_expT(a, env, "")) ++

   598     stores.reverse ++ 

   599     List ("goto " + n + "_Start\n") 

   600   } 

   601   else 

   602   {

   603     val is = "I" * args.length

   604     args.flatMap(a => compile_expT(a, env, "")) ++

   605     List ("invokestatic XXX/XXX/" + n + "(" + is + ")I\n")

   606   }

   607 \end{lstlisting}

   608 \end{textblock}

   609 

   610 \end{frame}

   611 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

   612 

   613 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   614 \mode<presentation>{

   615 \begin{frame}[c]

   616 

   617 \Large\bf

   618 There are more problems, than there are programs.\bigskip\bigskip\pause\\

   619 

   620 There must be a problem for which there is no program.