
diff -r 155426396b5f -r f063a6cd5d91 slides/slides01.tex
--- a/slides/slides01.tex	Thu Jul 30 13:50:54 2020 +0100
+++ b/slides/slides01.tex	Sat Aug 15 14:18:37 2020 +0100
@@ -1,10 +1,12 @@
 % !TEX program = xelatex
-\documentclass[dvipsnames,14pt,t,xelatex]{beamer}
+\documentclass[dvipsnames,14pt,t,xelatex,aspectratio=169,xcolor={table}]{beamer}
 \usepackage{../slides}
 \usepackage{../graphics}
 \usepackage{../langs}
 \usepackage{../data}
 
+
+
 \hfuzz=220pt 
 
 \lstset{language=Scala,
@@ -24,13 +26,15 @@
 
 \begin{document}
 
+
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
 \frametitle{%  
   \begin{tabular}{@ {}c@ {}}
   \\[-3mm]
   \LARGE Compilers and \\[-1mm] 
-  \LARGE Formal Languages (1)\\[-3mm] 
+  \LARGE Formal Languages\\[-3mm] 
   \end{tabular}}
 
   \begin{center}
@@ -43,12 +47,28 @@
   \begin{center}
   \begin{tabular}{ll}
   Email:  & christian.urban at kcl.ac.uk\\
-  Office Hours: & Thursdays 12 -- 14\\
-  Location: & N7.07 (North Wing, Bush House)\\
+  %Office Hours: & Thursdays 12 -- 14\\
+  %Location: & N7.07 (North Wing, Bush House)\\
   Slides \& Progs: & KEATS\\
   \end{tabular}
   \end{center}
 
+  \begin{center}
+    \begin{tikzpicture}
+      \node[drop shadow,fill=white,inner sep=0pt] 
+      {\footnotesize\rowcolors{1}{capri!10}{white}
+        \begin{tabular}{|p{4.8cm}|p{4.8cm}|}\hline
+          \cellcolor{blue!50}
+          1 Introduction, Languages          & 6 While-Language \\
+          2 Regular Expressions, Derivatives & 7 Compilation, JVM \\
+          3 Automata, Regular Languages      & 8 Compiling Functional Languages \\
+          4 Lexing, Tokenising               & 9 Optimisations \\
+          5 Grammars, Parsing                & 10 LLVM \\ \hline
+        \end{tabular}%
+      };
+    \end{tikzpicture}
+  \end{center}
+
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
@@ -56,7 +76,10 @@
 \begin{frame}[t]
 \frametitle{Why Study Compilers?}
 
-John Regehr {\small(Univ.~Utah, LLVM compiler hacker)}\smallskip\\
+
+John Regehr {\small(Univ.~Utah, LLVM compiler hacker)}
+\here{https://blog.regehr.org/archives/1419}
+\smallskip\\
 
 \begin{bubble}[10.5cm]
   \bf ``\ldots{}It’s effectively a perpetual
@@ -104,12 +127,12 @@
   \node (1) [right=35mm] at (0) {\includegraphics[scale=0.3]{pics/cassmbl.png}}; 
   \draw [->,line width=4mm, red] (0) -- (1);   
   \node (2) [below=25mm] at (0) {\LARGE\bf``source''};
-  \node (3) [right=35mm] at (2) {\LARGE\bf``binary''};
+  \node (3) [right=40mm] at (2) {\LARGE\bf``binary''};
   \draw [->,line width=1mm] (2) -- (3);   
 \end{tikzpicture}
 \end{center}
 
-\begin{textblock}{10}(1,13.5)
+\begin{textblock}{12}(1,14.5)
 Compiler explorers, e.g.: \url{https://gcc.godbolt.org}
 \end{textblock}
 
@@ -296,7 +319,7 @@
                       node/.style={
                       rectangle,rounded corners=3mm,
                       very thick,draw=black!50,minimum height=18mm, minimum width=20mm,
-                      top color=white,bottom color=black!20}]
+                      top color=white,bottom color=black!20,drop shadow}]
 
   \node at (3.05, 1.8) {\Large\bf write a compiler};
 
@@ -473,7 +496,7 @@
   \end{tabular}  
   \end{center}\bigskip  
   
-  \texttt{char field[30000]\\ char *ptr = &field[15000]}
+  \texttt{char field[30000]\\ char *ptr = \&field[15000]}
   
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
@@ -956,6 +979,110 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
+\frametitle{Languages (Sets of Strings)}
+
+\begin{itemize}
+
+\item A \alert{\bf Language} is a set of strings, for example\medskip
+\begin{center}
+\bl{$\{[], hello, foobar, a, abc\}$}
+\end{center}\bigskip
+
+\item \alert{\bf Concatenation} for strings and languages
+
+\begin{center}
+\begin{tabular}{rcl}
+\bl{$foo\;@\;bar$} & \bl{$=$} & \bl{$foobar$}\medskip\\
+\bl{$A\;@\;B$}     & \bl{$\dn$} & \bl{$\{ s_1\,@\,s_2 \;\mid\; s_1 \in A \wedge s_2 \in B\}$}
+\end{tabular}
+\end{center}
+\bigskip
+
+\small
+\item [] For example \bl{$A = \{foo, bar\}$}, \bl{$B = \{a, b\}$}
+
+\[
+\bl{A \,@\, B = \{fooa, foob, bara, barb\}}
+\]
+
+\end{itemize}  
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c]
+  \frametitle{Two Corner Cases}
+   
+  \Large
+  \begin{center}
+  \bl{$A \,@\, \{[]\} = \;?$}\bigskip\bigskip\pause\\
+  \bl{$A \,@\, \{\} = \;?$}
+  \end{center}  
+    
+  \end{frame}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+  
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c]
+\frametitle{
+    The Meaning of a\\[-2mm] 
+    Regular Expression}
+
+ ...all the strings a regular expression can match.   
+
+\begin{center}
+ \begin{tabular}{rcl}
+ \bl{$L(\ZERO)$}  & \bl{$\dn$} & \bl{$\{\}$}\\
+ \bl{$L(\ONE)$}     & \bl{$\dn$} & \bl{$\{[]\}$}\\
+ \bl{$L(c)$}            & \bl{$\dn$} & \bl{$\{[c]\}$}\\
+ \bl{$L(r_1 + r_2)$}    & \bl{$\dn$} & \bl{$L(r_1) \cup L(r_2)$}\\
+ \bl{$L(r_1 \cdot r_2)$} & \bl{$\dn$} & \bl{$L(r_1) \,@\, L(r_2)$}\\
+ \bl{$L(r^*)$}           & \bl{$\dn$} & \\
+  \end{tabular}
+\end{center}
+
+\begin{textblock}{14}(1.5,13.5)\small
+\bl{$L$} is a function from regular expressions to 
+sets of strings (languages):\smallskip\\
+\bl{\quad$L$ : Rexp $\Rightarrow$ Set$[$String$]$}
+\end{textblock}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c]
+\frametitle{The Power Operation}
+
+\begin{itemize}
+\item The \alert{\textbf{\boldmath$n$th Power}} of a language:
+
+\begin{center}
+\begin{tabular}{lcl}
+\bl{$A^0$}    & \bl{$\dn$} & \bl{$\{[]\}$}\\
+\bl{$A^{n+1}$} & \bl{$\dn$} & \bl{$A \,@\, A^n$}
+\end{tabular}
+\end{center}\bigskip
+
+\item[] For example
+
+\begin{center}
+\begin{tabular}{lcl@{\hspace{10mm}}l}
+\bl{$A^4$} & \bl{$=$} & \bl{$A \,@\, A \,@\, A \,@\, A$} & \bl{$(@\,\{[]\})$}\\
+\bl{$A^1$} & \bl{$=$} & \bl{$A$} & \bl{$(@\,\{[]\})$}\\
+\bl{$A^0$} & \bl{$=$} & \bl{$\{[]\}$}\\
+\end{tabular}
+\end{center}
+
+\end{itemize}  
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c]
   \frametitle{The Star Operation}
   
   \begin{itemize}




