14 

    15 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    16 \begin{frame}[t]

    17 \frametitle{%

    18   \begin{tabular}{@ {}c@ {}}

    19   \\[-3mm]

    20   \LARGE Compilers and \\[-2mm] 

    21   \LARGE Formal Languages\\[3mm] 

    22   \end{tabular}}

    23 

    24   \normalsize

    25   \begin{center}

    26   \begin{tabular}{ll}

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

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

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

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

    31   \end{tabular}

    32   \end{center}

    33 

    34   \begin{center}

    35     \begin{tikzpicture}

    36       \node[drop shadow,fill=white,inner sep=0pt] 

    37       {\footnotesize\rowcolors{1}{capri!10}{white}

    38         \begin{tabular}{|p{4.8cm}|p{4.8cm}|}\hline

    39           1 Introduction, Languages          & 6 While-Language \\

    40           2 Regular Expressions, Derivatives & 7 Compilation, JVM \\

    41           3 Automata, Regular Languages      & \cellcolor{blue!50} 8 Compiling Functional Languages \\

    42           4 Lexing, Tokenising               & 9 Optimisations \\

    43           5 Grammars, Parsing                & 10 LLVM \\ \hline

    44         \end{tabular}%

    45       };

    46     \end{tikzpicture}

    47   \end{center}

    48 \end{frame}

    49 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    50 

  1077 

  1078 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  1079 \begin{frame}[t, fragile]

  1080 \frametitle{Function Definitions}

  1081 

  1082 \footnotesize

  1083 \begin{lstlisting}[language=JVMIS, 

  1084                    xleftmargin=2mm, 

  1085                    numbers=none]

  1086 .method public static write(I)V 

  1087    .limit locals 1

  1088    .limit stack 2

  1089    getstatic java/lang/System/out Ljava/io/PrintStream; 

  1090    iload 0 

  1091    invokevirtual java/io/PrintStream/println(I)V 

  1092    return 

  1093 .end method

  1094 \end{lstlisting}\bigskip

  1095 

  1096 \small We will need methods for definitions like\footnotesize\medskip

  1097 

  1098 \begin{lstlisting}[language=JVMIS, 

  1099                    xleftmargin=2mm, 

  1100                    numbers=none]

  1101 def fname (x1, ... , xn) = ...                   

  1102                    

  1103 .method public static fname (I...I)I

  1104   .limit locals ??

  1105   .limit stack ?? 

  1106   ??

  1107 .end method

  1108 \end{lstlisting}

  1109 

  1110 \end{frame}

  1111 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

  1112 

  1113 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  1114 \begin{frame}[c, fragile]

  1115 \frametitle{Stack Estimation}

  1116 \small

  1117 \mbox{}\\[-15mm]

  1118 

  1119 \bl{\begin{center}

  1120 \begin{tabular}{@{\hspace{-4mm}}l@{\hspace{2mm}}c@{\hspace{2mm}}l@{}}

  1121 $\textit{estimate}(n)$ & $\dn$ & $1$\\

  1122 $\textit{estimate}(x)$ & $\dn$ & $1$\\

  1123 $\textit{estimate}(a_1\;aop\;a_2)$ & $\dn$ &

  1124 $\textit{estimate}(a_1) + \textit{estimate}(a_2)$\\

  1125 $\textit{estimate}(\pcode{if}\;b\;\pcode{then}\;e_1\;\pcode{else}\;e_2)$ & $\dn$ & 

  1126 $\textit{estimate}(b) +$\\ 

  1127 & & $\quad max(\textit{estimate}(e_1), \textit{estimate}(e_2))$\\

  1128 $\textit{estimate}(\pcode{write}(e))$ & $\dn$ & 

  1129 $\textit{estimate}(e) + 1$\\

  1130 $\textit{estimate}(e_1 ; e_2)$ & $\dn$ & 

  1131 $max(\textit{estimate}(e_1), \textit{estimate}(e_2))$\\

  1132 $\textit{estimate}(f(e_1, ..., e_n))$ & $\dn$ & 

  1133 $\sum_{i = 1..n}\;estimate(e_i)$\medskip\\

  1134 $\textit{estimate}(a_1\;bop\;a_2)$ & $\dn$ &

  1135 $\textit{estimate}(a_1) + \textit{estimate}(a_2)$\\

  1136 \end{tabular}

  1137 \end{center}}

  1138 

  1139 \end{frame}

  1140 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

  1141 

  1142