25   \LARGE Formal Languages\\[3mm] 

    25   \LARGE Formal Languages\\[-3mm] 

    31     Email:  & christian.urban at kcl.ac.uk\\

    31   Email:  & christian.urban at kcl.ac.uk\\

    32     %Office Hours: & Thursdays 12 -- 14\\

    32   Office Hour: & Fridays 11 -- 12\\

    33     %Location: & N7.07 (North Wing, Bush House)\\

    33   Location: & N7.07 (North Wing, Bush House)\\

    34     Slides \& Progs: & KEATS (also homework is there)\\  

    34   Slides \& Progs: & KEATS\\

    35   Pollev: & \texttt{\alert{https://pollev.com/cfltutoratki576}}\\  

    78 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    79 

    80 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    81 \begin{frame}[c, fragile]

    82 \frametitle{Stack Estimation}

    83 \small

    84 \mbox{}\\[-15mm]

    85 

    86 \bl{\begin{center}

    87 \begin{tabular}{@{\hspace{-4mm}}l@{\hspace{2mm}}c@{\hspace{2mm}}l@{}}

    88 $\textit{estimate}(n)$ & $\dn$ & $1$\\

    89 $\textit{estimate}(x)$ & $\dn$ & $1$\\

    90 $\textit{estimate}(a_1\;aop\;a_2)$ & $\dn$ &

    91 $\textit{estimate}(a_1) + \textit{estimate}(a_2)$\\

    92 $\textit{estimate}(\pcode{if}\;b\;\pcode{then}\;e_1\;\pcode{else}\;e_2)$ & $\dn$ & 

    93 $\textit{estimate}(b) +$\\ 

    94 & & $\quad max(\textit{estimate}(e_1), \textit{estimate}(e_2))$\\

    95 $\textit{estimate}(\pcode{write}(e))$ & $\dn$ & 

    96 $\textit{estimate}(e) + 1$\\

    97 $\textit{estimate}(e_1 ; e_2)$ & $\dn$ & 

    98 $max(\textit{estimate}(e_1), \textit{estimate}(e_2))$\\

    99 $\textit{estimate}(f(e_1, ..., e_n))$ & $\dn$ & 

   100 $\sum_{i = 1..n}\;estimate(e_i)$\medskip\\

   101 $\textit{estimate}(a_1\;bop\;a_2)$ & $\dn$ &

   102 $\textit{estimate}(a_1) + \textit{estimate}(a_2)$\\

   103 \end{tabular}

   104 \end{center}}

   105 

   106 \end{frame}

   107 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

   108 

   109 

   110 

   111 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   112 

   113 

   232 \frametitle{Factorial Funct.~on the JVM}

   267 \frametitle{Peephole Optimisations}

   233 

   268 

   234 \begin{textblock}{7}(1,1.8)\footnotesize

   269 \begin{center}

   235 \begin{minipage}{6cm}

   270 \begin{tabular}{ll}

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

   271   \texttt{ldc}:  & \texttt{iconst\_0} \ldots \texttt{iconst\_5}\\

   237 .method public static facT(II)I 

   272                  & \texttt{bipush} $n$ where $-128 < n <= 128$\bigskip\\  

   238 .limit locals 2

   273   \texttt{iload}: &  \texttt{iload\_0} \ldots \texttt{iload\_3}\bigskip\\

   239 .limit stack 6

   274   \texttt{istore}: &  \texttt{istore\_0} \ldots \texttt{istore\_3}\\

   240   iload 0

   275 \end{tabular}

   241   ldc 0

   276 \end{center}  

   242   if_icmpne If_else_2

   277 

   243   iload 1

   278 \end{frame}

   244   goto If_end_3

   279 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   245 If_else_2:

   280 

   246   iload 0

   281 

   247   ldc 1

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

   248   isub

   283 %\begin{frame}[c,fragile]

   249   iload 0

   284 %\frametitle{Factorial Funct.~on the JVM}

   250   iload 1

   285 %

   251   imul

   286 %\begin{textblock}{7}(1,1.8)\footnotesize

   252   invokestatic fact/fact/facT(II)I

   287 %\begin{minipage}{6cm}

   253 If_end_3:

   288 %\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]

   254   ireturn

   289 %.method public static facT(II)I 

   255 .end method 

   290 %.limit locals 2

   256 \end{lstlisting}

   291 %.limit stack 6

   257 \end{minipage}

   292 %  iload 0

   258 \end{textblock}

   293 %  ldc 0

   259 

   294 %  if_icmpne If_else_2

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

   295 %  iload 1

   261 \begin{bubble}[7cm]\small

   296 %  goto If_end_3

   262 \begin{lstlisting}[language=Lisp,

   297 %If_else_2:

   263                    basicstyle=\ttfamily, 

   298 %  iload 0

   264                    numbers=none,

   299 %  ldc 1

   265                    xleftmargin=1mm,linebackgroundcolor=\color{cream}]

   300 %  isub

   266 def facT(n, acc) = 

   301 %  iload 0

   267   if n == 0 then acc 

   302 %  iload 1

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

   303 %  imul

   269 \end{lstlisting}

   304 %  invokestatic fact/fact/facT(II)I

   270 \end{bubble}

   305 %If_end_3:

   271 \end{textblock}

   306 %  ireturn

   272 

   307 %.end method 

   273 \end{frame}

   308 %\end{lstlisting}

   309 %\end{minipage}

   310 %\end{textblock}

   311 %

   312 %\begin{textblock}{7}(6,7)

   313 %\begin{bubble}[7cm]\small

   314 %\begin{lstlisting}[language=Lisp,

   315 %                   basicstyle=\ttfamily, 

   316 %                   numbers=none,

   317 %                   xleftmargin=1mm,linebackgroundcolor=\color{cream}]

   318 %def facT(n, acc) = 

   319 %  if n == 0 then acc 

   320 %  else facT(n - 1, n * acc);

   321 %\end{lstlisting}

   322 %\end{bubble}

   323 %\end{textblock}

   324 %

   325 %\end{frame}