
diff -r 3f4fc76dab2f -r 3db4970ad0aa slides/slides08.tex
--- a/slides/slides08.tex	Tue Nov 20 13:23:51 2018 +0000
+++ b/slides/slides08.tex	Tue Nov 20 13:37:40 2018 +0000
@@ -1,14 +1,28 @@
 \documentclass[dvipsnames,14pt,t]{beamer}
+\usepackage{xcolor}
 \usepackage{../slides}
 \usepackage{../langs}
 \usepackage{../data}
 \usepackage{../graphics}
 \usepackage{../grammar}
 
-% beamer stuff 
-\renewcommand{\slidecaption}{CFL 07, King's College London}
+\usepackage[most]{tcolorbox}
+
+\newtcbox{\hl}[1][]{%
+     size=fbox,
+    tcbox raise base, nobeforeafter, 
+    enhanced, colframe=gray,
+    colback=gray!30, boxrule=1pt,
+    fontupper=\ttfamily,
+    #1}
+
+\lstset{morekeywords={def,if,then,else,write,read},keywordstyle=\color{codepurple}\bfseries}
+
+% beamer stuff
+\renewcommand{\slidecaption}{CFL 09, King's College London}
 \newcommand{\bl}[1]{\textcolor{blue}{#1}}       
 
+
 \begin{document}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -17,80 +31,26 @@
   \begin{tabular}{@ {}c@ {}}
   \\[-3mm]
   \LARGE Compilers and \\[-2mm] 
-  \LARGE Formal Languages (7)\\[3mm] 
+  \LARGE Formal Languages (8)\\[3mm] 
   \end{tabular}}
 
   \normalsize
   \begin{center}
   \begin{tabular}{ll}
   Email:  & christian.urban at kcl.ac.uk\\
-  Office: & N\liningnums{7.07} (North Wing, Bush House)\\
-  Slides: & KEATS (also homework is there)\\
+  Office: & N7.07 (North Wing, Bush House)\\
+  Slides: & KEATS (also home work is there)\\
   \end{tabular}
   \end{center}
 
 \end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
-\frametitle{Bird's Eye View}
-
-\begin{center}
-\begin{tikzpicture}
-\node (rexp)  {\bl{\bf Lexer}};
-\node (nfa) [right=of rexp] {\bl{\bf Parser}};
-\node (dfa) [right=of nfa] 
- {\bl{\begin{tabular}{c}\bf Machine Code/\\\bf Java Byte Code\end{tabular}}};
-\path[->, red, line width=2mm] (rexp) edge node [above=4mm, black] {\begin{tabular}{c@{\hspace{9mm}}}token\\[-1mm]
-sequence\end{tabular}} (nfa);
-\path[->, red, line width=2mm] (nfa) edge node [above=4mm, black] {\begin{tabular}{c}parse\\[-1mm] tree\end{tabular}}(dfa);
-\end{tikzpicture}\\
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
- 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\begin{textblock}{10}(0.5,0.5)
-  \LARGE
-  \fontspec{Hoefler Text Black}
-  \textcolor{ProcessBlue}{JVM\\ Code}
-  \\[12mm]
-
-  \normalsize
-  Jasmin\\
-  Krakatau\\
-  ASM lib
-\end{textblock}
-
-
-\fontsize{8}{10}\selectfont
-%\footnotesize
-\mbox{}\\[-8mm]\mbox{}
-
-\begin{columns}
-\begin{column}{2cm} 
-\lstinputlisting[numbers=none]{../progs/appHa.j}
-\end{column}
-
-\begin{column}{2cm} 
-\lstinputlisting[numbers=none]{../progs/appHb.j}
-\end{column}
-
-\end{columns}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
- 
- 
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
 
 \begin{center}
 \bl{\begin{tabular}{@{}lcl@{}}
-\\[-12mm]        
 \meta{Stmt} & $::=$ &  $\texttt{skip}$\\
               & $|$ & \textit{Id}\;\texttt{:=}\;\meta{AExp}\\
               & $|$ & \texttt{if}\; \meta{BExp} \;\texttt{then}\; \meta{Block} \;\texttt{else}\; \meta{Block}\\
@@ -109,141 +69,21 @@
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{\begin{tabular}{c}Fibonacci Numbers\end{tabular}}
-
-\mbox{}\\[-18mm]\mbox{}
-
-{\lstset{language=While}\fontsize{10}{12}\selectfont
-\texttt{\lstinputlisting{../progs/fib.while}}}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{Interpreter}
-
-\begin{center}
-\bl{\begin{tabular}{@{}lcl@{}}
-$\text{eval}(n, E)$ & $\dn$ & $n$\\
-$\text{eval}(x, E)$ & $\dn$ & $E(x)$ \;\;\;\textcolor{black}{lookup \bl{$x$} in \bl{$E$}}\\
-$\text{eval}(a_1 + a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) + \text{eval}(a_2, E)$\\
-$\text{eval}(a_1 - a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) - \text{eval}(a_2, E)$\\
-$\text{eval}(a_1 * a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) * \text{eval}(a_2, E)$\bigskip\\
-$\text{eval}(a_1 = a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) = \text{eval}(a_2, E)$\\
-$\text{eval}(a_1\,!\!= a_2, E)$ & $\dn$ & $\neg(\text{eval}(a_1, E) = \text{eval}(a_2, E))$\\
-$\text{eval}(a_1 < a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) < \text{eval}(a_2, E)$\
-\end{tabular}}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{Interpreter (2)}
-
-\begin{center}
-\bl{\begin{tabular}{@{}lcl@{}}
-$\text{eval}(\text{skip}, E)$ & $\dn$ & $E$\\
-$\text{eval}(x:=a, E)$ & $\dn$ & \bl{$E(x \mapsto \text{eval}(a, E))$}\\
-\multicolumn{3}{@{}l@{}}{$\text{eval}(\text{if}\;b\;\text{then}\;cs_1\;\text{else}\;cs_2 , E) \dn$}\\
-\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{if}\;\text{eval}(b,E)\;\text{then}\;
-\text{eval}(cs_1,E)$}\\
-\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\phantom{\text{if}\;\text{eval}(b,E)\;}\text{else}\;\text{eval}(cs_2,E)$}\\
-\multicolumn{3}{@{}l@{}}{$\text{eval}(\text{while}\;b\;\text{do}\;cs, E) \dn$}\\
-\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{if}\;\text{eval}(b,E)$}\\
-\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{then}\;
-\text{eval}(\text{while}\;b\;\text{do}\;cs, \text{eval}(cs,E))$}\\
-\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{else}\; E$}\\
-$\text{eval}(\text{write}\; x, E)$ & $\dn$ & $\{\;\text{println}(E(x))\; ;\;E\;\}$\\
-\end{tabular}}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{Test Program}
-
-\mbox{}\\[-18mm]\mbox{}
-
-{\lstset{language=While}\fontsize{10}{12}\selectfont
-\texttt{\lstinputlisting{../progs/loops.while}}}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\fontsize{7}{9}\selectfont
-
-
-\begin{columns}
-\begin{column}{7cm} 
-\lstinputlisting[numbers=none]{../progs/appHa.j}
-\end{column}
-
-\begin{column}{7cm} 
-\lstinputlisting[numbers=none]{../progs/appHb.j}
-\end{column}
-\end{columns}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
- 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Interpreted Code}
-
-\begin{center}
-\begin{tikzpicture}
-\begin{axis}[axis x line=bottom, axis y line=left, xlabel=n, ylabel=secs, legend style=small]
-\addplot+[smooth] file {interpreted.data};
-\end{axis}
-\end{tikzpicture}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{Java Virtual Machine}
-
-\begin{itemize}
-\item introduced in 1995
-\item is a stack-based VM (like Postscript, CLR of .Net)
-\item contains a JIT compiler
-\item many languages take advantage of JVM's infrastructure (JRE)
-\item is garbage collected $\Rightarrow$ no buffer overflows
-\item some languages compiled to the JVM: Scala, Clojure\ldots
-\end{itemize}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t,fragile]
 \frametitle{Compiling AExps}
 
-For example \liningnums{\bl{$1 + ((2 * 3) + (4 - 3))$}}:\medskip
-  
+For example \bl{$1 + ((2 * 3) + (4 - 3))$}:\medskip
+
 \begin{columns}[T]
 \begin{column}{.3\textwidth}
 \begin{center}
 \bl{\begin{tikzpicture}
 \tikzset{level distance=12mm,sibling distance=4mm}
-\tikzset{edge from parent/.style={draw,very thick}}
-\Tree [.$+$ [.$1$ ] [.$+$ [.$*$ $2$ $3$ ] [.$-$ $4$ $3$ ]]]
-\end{tikzpicture}}
+\tikzset{edge from parent/.style={draw,very thick}}
\Tree [.$+$ [.$1$ ] [.$+$ [.$*$ $2$ $3$ ] [.$-$ $4$ $3$ ]]]
\end{tikzpicture}}
 \end{center}
 \end{column}
-\begin{column}{.3\textwidth}  
+\begin{column}{.3\textwidth}
 \begin{lstlisting}[language=JVMIS,numbers=none]
 ldc 1 
 ldc 2 
@@ -263,261 +103,30 @@
 stack-machine
 
 \end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t,fragile]
-\frametitle{Compiling AExps}
-
-\liningnums{\textbf{\Large\bl{1 + 2 + 3}}}
-
-\begin{lstlisting}[language=JVMIS,numbers=none,xleftmargin=6cm]  
-ldc 1
-ldc 2
-iadd
-ldc 3
-iadd
-\end{lstlisting}
-
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t,fragile]
-\frametitle{Compiling AExps}
-
-\liningnums{\textbf{\Large\bl{1 + (2 + 3)}}}
-
-\begin{lstlisting}[language=JVMIS,numbers=none,xleftmargin=6cm]  
-ldc 1
-ldc 2
-ldc 3
-iadd
-iadd
-\end{lstlisting}
-\bigskip\pause
-\vfill
-
-\textcolor{codepurple}{\textbf{\texttt{dadd}}},
-\textcolor{codepurple}{\textbf{\texttt{fadd}}},
-\textcolor{codepurple}{\textbf{\texttt{ladd}}}, \ldots
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling AExps}
-
-\begin{center}
-\bl{\begin{tabular}{@{}lcl@{}}
-$\text{compile}(n)$ & $\dn$ & $\text{ldc}\;n$\\
-$\text{compile}(a_1 + a_2)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\qquad\text{compile}(a_1) \;@\;\text{compile}(a_2)\;@\; \text{iadd}$}\smallskip\\
-$\text{compile}(a_1 - a_2)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\qquad\text{compile}(a_1) \;@\; \text{compile}(a_2)\;@\; \text{isub}$}\smallskip\\
-$\text{compile}(a_1 * a_2)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\qquad\text{compile}(a_1) \;@\; \text{compile}(a_2)\;@\; \text{imul}$}\smallskip\\
-\end{tabular}}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t,fragile]
-\frametitle{\begin{tabular}{c}Compiling AExps\end{tabular}}
-
-\liningnums{\textbf{\Large\bl{1 $+$ 2 $*$ 3 $+$ (4 $-$ 3)}}}
-
-\begin{lstlisting}[language=JVMIS,numbers=none,xleftmargin=6cm]         
-ldc 1
-ldc 2
-ldc 3
-imul
-ldc 4
-ldc 3
-isub
-iadd
-iadd
-\end{lstlisting}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{Variables}
-\liningnums{\textbf{\Large\bl{x $:=$ 5 $+$ y $*$ 2}}}\bigskip\pause   
-
-\begin{itemize}
-\item lookup: \bl{$\textcolor{codepurple}{\textbf{\texttt{iload}}}\; index$}
-\item store: \bl{$\textcolor{codepurple}{\textbf{\texttt{istore}}}\; index$}
-\end{itemize}\bigskip\pause
-
-while compilating we have to maintain a map between our identifiers and the
-Java bytecode indices
-
-\begin{center}
-\bl{$\text{compile}(a, E)$}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling AExps}
-
-\begin{center}
-\bl{\begin{tabular}{@{}lcl@{}}
-$\text{compile}(n, E)$ & $\dn$ & $\text{ldc}\;n$\\
-$\text{compile}(a_1 + a_2, E)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\qquad\text{compile}(a_1, E) \;@\;\text{compile}(a_2, E)\;@\; \text{iadd}$}\smallskip\\
-$\text{compile}(a_1 - a_2, E)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\qquad\text{compile}(a_1, E) \;@\; \text{compile}(a_2, E)\;@\; \text{isub}$}\smallskip\\
-$\text{compile}(a_1 * a_2, E)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\qquad\text{compile}(a_1, E) \;@\; \text{compile}(a_2, E)\;@\; \text{imul}$}\bigskip\\
-$\text{compile}(x, E)$ & $\dn$ & $\text{iload}\;E(x)$\\
-\end{tabular}}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c, fragile]
-\frametitle{Mathematical Functions}
-
-Compilation of some mathematical functions:
-
-\begin{center}
-\begin{tabular}{lcl}
-\texttt{Aop("+", a1, a2)} & $\Rightarrow$ & \texttt{...iadd}\\
-\texttt{Aop("-", a1, a2)} & $\Rightarrow$ & \texttt{...isub}\\
-\texttt{Aop("*", a1, a2)} & $\Rightarrow$ & \texttt{...imul}\\
-\texttt{Aop("/", a1, a2)} & $\Rightarrow$ & \texttt{...idiv}\\
-\texttt{Aop("\%", a1, a2)} & $\Rightarrow$ & \texttt{...irem}\\
-\end{tabular}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{Compiling Statements}
-
-We return a list of instructions and an environment for the
-variables
-
-\begin{center}
-\bl{\begin{tabular}{@{}l@{\hspace{1mm}}c@{\hspace{1mm}}l@{}}
-$\text{compile}(\text{skip}, E)$ & $\dn$ & $(\textit{Nil}, E)$\bigskip\\
-$\text{compile}(x := a, E)$ & $\dn$\\
-\multicolumn{3}{l}{$(\text{compile}(a, E) \;@\;\text{istore}\;index, E(x\mapsto index))$}\\
-\end{tabular}}
-\end{center}\medskip
-
-where \bl{$index$} is \bl{$E(x)$} if it is already defined, 
-or if it is not, then the largest index not yet seen
-
-\end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c,fragile]
-\frametitle{Compiling Assignments}
-
-\liningnums{\textbf{\Large\bl{x $:=$ x $+$ 1}}}
+\frametitle{Compiling AExps}
 
-\begin{lstlisting}[language=JVMIS,numbers=none,xleftmargin=6cm]        
-iload /*@\bl{$n_x$}@*/
-ldc 1
-iadd
-istore /*@\bl{$n_x$}@*/
-\end{lstlisting}\medskip
-
-where \bl{$n_x$} is the index corresponding to the variable~\bl{$x$}
+\bl{
+\begin{center}
+\begin{tabular}{lcl}
+$\textit{compile}(n, E)$ & $\dn$ & $\pcode{ldc}\;n$\smallskip\\
+$\textit{compile}(a_1 + a_2, E)$ & $\dn$ \\
+\multicolumn{3}{c}{$\qquad\textit{compile}(a_1, E) \;@\;\textit{compile}(a_2, E)\;@\; \pcode{iadd}$}\smallskip\\
+$\textit{compile}(a_1 - a_2, E)$ & $\dn$ \\
+\multicolumn{3}{c}{$\qquad\textit{compile}(a_1, E) \;@\; \textit{compile}(a_2, E)\;@\; \pcode{isub}$}\smallskip\\
+$\textit{compile}(a_1 * a_2, E)$ & $\dn$ \\
+\multicolumn{3}{c}{$\qquad\textit{compile}(a_1, E) \;@\; \textit{compile}(a_2, E)\;@\; \pcode{imul}$}\smallskip\\
+$\textit{compile}(a_1 \backslash a_2, E)$ & $\dn$\\ 
+\multicolumn{3}{c}{$\qquad\textit{compile}(a_1, E) \;@\; \textit{compile}(a_2, E)\;@\; \pcode{idiv}$}\smallskip\\
+$\textit{compile}(x, E)$ & $\dn$ & $\pcode{iload}\;E(x)$\\
+\end{tabular}
+\end{center}}
 
 \end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling Ifs}
-
-{\Large\bl{$\text{if}\;b\;\text{then}\;cs_1\;\text{else}\;cs_2$}}\bigskip\bigskip
-
-\onslide<2->{Case }\only<2>{{\bf True}:}\only<3>{{\bf False}:}
-
-\begin{center}
-\begin{tikzpicture}[node distance=2mm and 4mm,
- block/.style={rectangle, minimum size=1cm, draw=black, line width=1mm},
- point/.style={rectangle, inner sep=0mm, minimum size=0mm, fill=red},
- skip loop/.style={red, line width=1mm, to path={-- ++(0,-10mm) -| (\tikztotarget)}}]
-\node (A1) [point] {};
-\node (b) [block, right=of A1] {code of \bl{$b$}};
-\node (A2) [point, right=of b] {};
-\node (cs1) [block, right=of A2] {code of \bl{$cs_1$}};
-\node (A3) [point, right=of cs1] {};
-\node (cs2) [block, right=of A3] {code of \bl{$cs_2$}};
-\node (A4) [point, right=of cs2] {};
-
-\only<2>{
-\draw (A1) edge [->, red, line width=1mm] (b);
-\draw (b) edge [->, red, line width=1mm] (cs1);
-\draw (cs1) edge [->, red, line width=1mm] (A3);
-\draw (A3) edge [->,skip loop] (A4);
-\node [below=of cs2] {\raisebox{-5mm}{\small{}jump}};}
-\only<3>{
-\draw (A1) edge [->, red, line width=1mm] (b);
-\draw (b) edge [->, red, line width=1mm] (A2);
-\draw (A2) edge [skip loop] (A3);
-\draw (A3) edge [->, red, line width=1mm] (cs2);
-\draw (cs2) edge [->,red, line width=1mm] (A4);
-\node [below=of cs1] {\raisebox{-5mm}{\small{}conditional jump}};}
-\end{tikzpicture}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t,fragile]
-\frametitle{Conditional Jumps}
-
-\begin{minipage}{1.1\textwidth}
-\begin{itemize}
-\item \textcolor{codepurple}{\textbf{\texttt{if\_icmpeq}}} \bl{$label$}
-  if two ints are equal, then jump\medskip
-\item \textcolor{codepurple}{\textbf{\texttt{if\_icmpne}}} \bl{$label$}
-  if two ints aren't equal, then jump\medskip
-\item \textcolor{codepurple}{\textbf{\texttt{if\_icmpge}}} \bl{$label$}
-  if one int is greater or equal then another, then jump
-\item[]\ldots
-\end{itemize}
-\end{minipage}\pause
-
-\begin{lstlisting}[language=JVMIS,numbers=none,xleftmargin=2cm]
-/*@\bl{$L_1$:}@*/
-  if_icmpeq /*@\bl{$L_2$}@*/
-  iload 1
-  ldc 1
-  iadd
-  if_icmpeq /*@\bl{$L_1$}@*/
-/*@\bl{$L_2$:}@*/
-\end{lstlisting}
-
-
-\begin{textblock}{3.5}(11,12)
-\only<3>{labels must be unique}
-\end{textblock}
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c,fragile]
@@ -545,156 +154,10 @@
 \end{lstlisting}
 \end{center}
 
-\begin{tikzpicture}[remember picture,overlay]
-  \draw[->,very thick] (A) edge [->,to path={-- ++(10mm,0mm) 
+\begin{tikzpicture}[remember picture,overlay]
  \draw[->,very thick] (A) edge [->,to path={-- ++(10mm,0mm) 
            -- ++(0mm,-17.3mm) |- (\tikztotarget)},line width=1mm] (B.east);
   \draw[->,very thick] (C) edge [->,to path={-- ++(10mm,0mm) 
-           -- ++(0mm,-17.3mm) |- (\tikztotarget)},line width=1mm] (D.east);
-\end{tikzpicture}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling BExps}
-
-{\Large\bl{$a_1 = a_2$}}
-
-\begin{center}
-\bl{\begin{tabular}{lcl}
-$\text{compile}(a_1 = a_2, E, lab)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\quad\text{compile}(a_1, E) \;@\;\text{compile}(a_2, E)\;@\; \text{if\_icmpne}\;lab$}
-\end{tabular}}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c, fragile]
-\frametitle{Boolean Expressions}
-
-Compilation of boolean expressions:
-
-\begin{center}
-\begin{tikzpicture}[node distance=2mm and 4mm,
- block/.style={rectangle, minimum size=1cm, draw=black, line width=1mm},
- point/.style={rectangle, inner sep=0mm, minimum size=0mm, fill=red},
- skip loop/.style={red, line width=1mm, to path={-- ++(0,-10mm) -| (\tikztotarget)}}]
-\node (A1) [point] {};
-\node (b) [block, right=of A1] {code of \bl{$b$}};
-\node (A2) [point, right=of b] {};
-\node (cs1) [block, right=of A2] {code of \bl{$cs_1$}};
-\node (A3) [point, right=of cs1] {};
-\node (cs2) [block, right=of A3] {code of \bl{$cs_2$}};
-\node (A4) [point, right=of cs2] {};
-
-\only<1>{
-\draw (A1) edge [->, red, line width=1mm] (b);
-\draw (b) edge [->, red, line width=1mm] (A2);
-\draw (A2) edge [skip loop] (A3);
-\draw (A3) edge [->, red, line width=1mm] (cs2);
-\draw (cs2) edge [->,red, line width=1mm] (A4);
-\node [below=of cs1] {\raisebox{-5mm}{\small{}conditional jump}};}
-\end{tikzpicture}
-\end{center}
-
-\begin{center}
-\begin{tabular}{lcl}
-\texttt{Bop("==", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpne...}\\
-\texttt{Bop("!=", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpeq...}\\
-\texttt{Bop("<", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpge...}\\
-\texttt{Bop("<=", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpgt...}\\
-\end{tabular}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling Ifs}
-
-{\Large\bl{if $b$ then $cs_1$ else $cs_2$}}
-
-\begin{center}
-\bl{\begin{tabular}{lcl}
-$\text{compile}(\text{if}\;b\;\text{then}\; cs_1\;\text{else}\; cs_2, E)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\quad l_{ifelse}\;$ \textcolor{black}{(fresh label)}}\\
-\multicolumn{3}{l}{$\quad l_{ifend}\;$ \textcolor{black}{(fresh label)}}\\
-\multicolumn{3}{l}{$\quad (is_1, E') = \text{compile}(cs_1, E)$}\\
-\multicolumn{3}{l}{$\quad (is_2, E'') = \text{compile}(cs_2, E')$}\\
-\multicolumn{3}{l}{$\quad(\text{compile}(b, E, l_{ifelse})$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\;is_1$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\; \text{goto}\;l_{ifend}$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\;l_{ifelse}:$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\;is_2$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\;l_{ifend}:, E'')$}\\
-\end{tabular}}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling Whiles}
-
-{\Large\bl{$\text{while}\;b\;\text{do}\;cs$}}\bigskip\bigskip
-
-\onslide<2->{Case }\only<2>{{\bf True}:}\only<3>{{\bf False}:}
-
-\begin{center}
-\begin{tikzpicture}[node distance=2mm and 4mm,
- block/.style={rectangle, minimum size=1cm, draw=black, line width=1mm},
- point/.style={rectangle, inner sep=0mm, minimum size=0mm, fill=red},
- skip loop/.style={red, line width=1mm, to path={-- ++(0,-10mm) -| (\tikztotarget)}}]
-\node (A0) [point, left=of A1] {};
-\node (A1) [point] {};
-\node (b) [block, right=of A1] {code of \bl{$b$}};
-\node (A2) [point, right=of b] {};
-\node (cs1) [block, right=of A2] {code of \bl{$cs$}};
-\node (A3) [point, right=of cs1] {};
-\node (A4) [point, right=of A3] {};
-
-\only<2>{
-\draw (A0) edge [->, red, line width=1mm] (b);
-\draw (b) edge [->, red, line width=1mm] (cs1);
-\draw (cs1) edge [->, red, line width=1mm] (A3);
-\draw (A3) edge [->,skip loop] (A1);}
-\only<3>{
-\draw (A0) edge [->, red, line width=1mm] (b);
-\draw (b) edge [->, red, line width=1mm] (A2);
-\draw (A2) edge [skip loop] (A3);
-\draw (A3) edge [->, red, line width=1mm] (A4);}
-\end{tikzpicture}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling Whiles}
-
-{\Large\bl{while $b$ do $cs$}}
-
-\begin{center}
-\bl{\begin{tabular}{lcl}
-$\text{compile}(\text{while}\; b\; \text{do} \;cs, E)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\quad l_{wbegin}\;$ \textcolor{black}{(fresh label)}}\\
-\multicolumn{3}{l}{$\quad l_{wend}\;$ \textcolor{black}{(fresh label)}}\\
-\multicolumn{3}{l}{$\quad (is, E') = \text{compile}(cs_1, E)$}\\
-\multicolumn{3}{l}{$\quad(l_{wbegin}:$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\;\text{compile}(b, E, l_{wend})$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\;is$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\; \text{goto}\;l_{wbegin}$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\;l_{wend}:, E')$}\\
-\end{tabular}}
-\end{center}
+           -- ++(0mm,-17.3mm) |- (\tikztotarget)},line width=1mm] (D.east);
\end{tikzpicture}
 
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
@@ -729,13 +192,11 @@
   \draw[->,very thick] (LA) edge [->,to path={-- ++(12mm,0mm) 
            -- ++(0mm,17.3mm) |- (\tikztotarget)},line width=1mm] (LB.east);
   \draw[->,very thick] (LC) edge [->,to path={-- ++(12mm,0mm) 
-           -- ++(0mm,-17.3mm) |- (\tikztotarget)},line width=1mm] (LD.east);
-\end{tikzpicture}
+           -- ++(0mm,-17.3mm) |- (\tikztotarget)},line width=1mm] (LD.east);
\end{tikzpicture}
 
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c,fragile]
 \frametitle{Compiling Writes}
@@ -760,9 +221,9 @@
 \end{lstlisting}
 
 \end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c,fragile]
 \frametitle{Compiling Main}
 
@@ -793,101 +254,532 @@
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{\begin{tabular}{c}Next Compiler Phases\end{tabular}}
+\begin{frame}[c,fragile]
+\frametitle{Functional Programming}
+
+\footnotesize
+\begin{textblock}{13}(0.9,3)
+\begin{lstlisting}[]numbers=none]
+def fib(n) = if n == 0 then 0 
+             else if n == 1 then 1 
+             else fib(n - 1) + fib(n - 2);
+
+def fact(n) = if n == 0 then 1 else n * fact(n - 1);
+
+def ack(m, n) = if m == 0 then n + 1
+                else if n == 0 then ack(m - 1, 1)
+                else ack(m - 1, ack(m, n - 1));
+                
+def gcd(a, b) = if b == 0 then a else gcd(b, a % b);                
+\end{lstlisting}
+\end{textblock}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
-\begin{itemize}
-\item assembly $\Rightarrow$ byte code (class file)
-\item labels $\Rightarrow$ absolute or relative jumps\bigskip\bigskip
-\item \texttt{javap} is a disassembler for class files
-\end{itemize}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c]
+\frametitle{Fun Grammar}
+\bl{
+\begin{plstx}[rhs style=]
+: \meta{Exp} ::= \meta{Var} | \meta{Num}{\hspace{3cm}}
+             |   \meta{Exp} + \meta{Exp} | ... | (\meta{Exp})
+             |   \code{if} \meta{BExp} \code{then} \meta{Exp} \code{else} \meta{Exp}
+             |   \code{write} \meta{Exp} {\hspace{3cm}}
+             |   \meta{Exp} ; \meta{Exp}
+             |   \textit{FunName} (\meta{Exp}, ... , \meta{Exp})\\
+: \meta{BExp} ::= ...\\
+: \meta{Def} ::= \code{def} \textit{FunName} ($\hspace{0.4mm}x_1$, ... , $x_n$) = \meta{Exp}\\               
+: \meta{Prog} ::= \meta{Def} ; \meta{Prog}
+               | \meta{Exp} ; \meta{Prog}
+               | \meta{Exp}\\
+\end{plstx}}
 
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+% Almost what is implemented - Exp ; Exp is left-recursive
+%
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[t]
-\frametitle{\begin{tabular}{c}Compiled Code\end{tabular}}
+\begin{frame}[c, fragile]
+\frametitle{Abstract Syntax Trees}
+
+\footnotesize
+\begin{lstlisting}[language=Scala, numbers=none, xleftmargin=-1mm]
+abstract class Exp
+abstract class BExp 
+abstract class Decl
+
+case class Var(s: String) extends Exp
+case class Num(i: Int) extends Exp
+case class Aop(o: String, a1: Exp, a2: Exp) extends Exp
+case class If(a: BExp, e1: Exp, e2: Exp) extends Exp
+case class Write(e: Exp) extends Exp
+case class Sequ(e1: Exp, e2: Exp) extends Exp
+case class Call(name: String, args: List[Exp]) extends Exp
+
+case class Bop(o: String, a1: Exp, a2: Exp) extends BExp
+
+case class Def(name: String, 
+               args: List[String], 
+               body: Exp) extends Decl
+case class Main(e: Exp) extends Decl
+\end{lstlisting}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c, fragile]
+\frametitle{Idea}
+
+Compile \texttt{exp} such that the result of the expression
+is on top of the stack.\bigskip
+
+\begin{itemize}
+\item \texttt{\color{codepurple}{write}}\texttt{(1 + 2)}
+\item \texttt{1 + 2; 3 + 4} 
+\end{itemize}
+  
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
-\begin{center}
-\begin{tikzpicture}
-\begin{axis}[axis x line=bottom, axis y line=left, xlabel=n, ylabel=secs, legend style=small]
-\addplot+[smooth] file {compiled.data};
-\end{axis}
-\end{tikzpicture}
-\end{center}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c, fragile]
+\frametitle{Sequences}
+
+Compiling \texttt{exp1 ; exp2}:\bigskip
+
+
+\begin{lstlisting}[mathescape,language=JVMIS, numbers=none]
+$\textit{compile}$(exp1)
+pop
+$\textit{compile}$(exp2)
+\end{lstlisting}
+  
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[t, fragile]
+\frametitle{Write}
+
+Compiling call to \texttt{write(1+2)}:\bigskip
+
 
-\end{frame}}
+\begin{lstlisting}[mathescape,language=JVMIS, numbers=none]
+$\textit{compile}$(1+2)
+dup
+invokestatic XXX/XXX/write(I)V
+\end{lstlisting}\bigskip
+
+\small
+needs the helper method
+
+\footnotesize
+\begin{lstlisting}[language=JVMIS, 
+                   xleftmargin=2mm, 
+                   numbers=none]
+.method public static write(I)V 
+   .limit locals 1
+   .limit stack 2
+   getstatic java/lang/System/out Ljava/io/PrintStream; 
+   iload 0 
+   invokevirtual java/io/PrintStream/println(I)V 
+   return 
+.end method
+\end{lstlisting}
+\end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[t]
-\frametitle{\begin{tabular}{c}Compiler vs.~Interpreter\end{tabular}}
+\begin{frame}[t, fragile]
+\frametitle{Function Definitions}
+
+\footnotesize
+\begin{lstlisting}[language=JVMIS, 
+                   xleftmargin=2mm, 
+                   numbers=none]
+.method public static write(I)V 
+   .limit locals 1
+   .limit stack 2
+   getstatic java/lang/System/out Ljava/io/PrintStream; 
+   iload 0 
+   invokevirtual java/io/PrintStream/println(I)V 
+   return 
+.end method
+\end{lstlisting}\bigskip
+
+\small We will need for definitions, like\footnotesize\medskip
+
+\begin{lstlisting}[language=JVMIS, 
+                   xleftmargin=2mm, 
+                   numbers=none]
+def fname (x1, ... , xn) = ...                   
+                   
+.method public static fname (I...I)I
+  .limit locals ??
+  .limit stack ?? 
+  ??
+.end method
+\end{lstlisting}
 
-\begin{center}
-\begin{tikzpicture}
-\begin{axis}[axis x line=bottom, axis y line=left, ylabel=secs,
-    xlabel=n,
-    enlargelimits=0.05,
-    ybar interval=0.7, legend style=small]
-\addplot file {interpreted2.data};
-\addplot file {compiled2.data};
-%\legend{interpreted, compiled}
-\end{axis}
-\end{tikzpicture}
-\end{center}
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c, fragile]
+\frametitle{Stack Estimation}
+\small
+\mbox{}\\[-15mm]
 
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+\bl{\begin{center}
+\begin{tabular}{@{\hspace{-4mm}}l@{\hspace{2mm}}c@{\hspace{2mm}}l@{}}
+$\textit{estimate}(n)$ & $\dn$ & $1$\\
+$\textit{estimate}(x)$ & $\dn$ & $1$\\
+$\textit{estimate}(a_1\;aop\;a_2)$ & $\dn$ &
+$\textit{estimate}(a_1) + \textit{estimate}(a_2)$\\
+$\textit{estimate}(\pcode{if}\;b\;\pcode{then}\;e_1\;\pcode{else}\;e_2)$ & $\dn$ & 
+$\textit{estimate}(b) +$\\ 
+& & $\quad max(\textit{estimate}(e_1), \textit{estimate}(e_2))$\\
+$\textit{estimate}(\pcode{write}(e))$ & $\dn$ & 
+$\textit{estimate}(e) + 1$\\
+$\textit{estimate}(e_1 ; e_2)$ & $\dn$ & 
+$max(\textit{estimate}(e_1), \textit{estimate}(e_2))$\\
+$\textit{estimate}(f(e_1, ..., e_n))$ & $\dn$ & 
+$\sum_{i = 1..n}\;estimate(e_i)$\medskip\\
+$\textit{estimate}(a_1\;bop\;a_2)$ & $\dn$ &
+$\textit{estimate}(a_1) + \textit{estimate}(a_2)$\\
+\end{tabular}
+\end{center}}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{Backend}
+\begin{frame}[fragile]
+\frametitle{Successor Function}
+
+\begin{textblock}{7}(1,2.5)\footnotesize
+\begin{minipage}{6cm}
+\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
+.method public static suc(I)I 
+.limit locals 1
+.limit stack 2
+  iload 0
+  ldc 1
+  iadd
+  ireturn
+.end method 
+\end{lstlisting}
+\end{minipage}
+\end{textblock}
+
+\begin{textblock}{7}(6,8)
+\begin{bubble}[5cm]\small
+\begin{lstlisting}[language=Lisp,
+                   basicstyle=\ttfamily, 
+                   numbers=none,
+                   xleftmargin=1mm,linebackgroundcolor=\color{cream}]
+def suc(x) = x + 1;
+\end{lstlisting}
+\end{bubble}
+\end{textblock}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[fragile]
+\frametitle{Addition Function}
+
+\begin{textblock}{7}(1,1.9)\footnotesize
+\begin{minipage}{6cm}
+\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
+.method public static add(II)I 
+.limit locals 2
+.limit stack 5
+  iload 0
+  ldc 0
+  if_icmpne If_else
+  iload 1
+  goto If_end
+If_else:
+  iload 0
+  ldc 1
+  isub
+  iload 1
+  invokestatic XXX/XXX/add(II)I
+  invokestatic XXX/XXX/suc(I)I
+If_end:
+  ireturn
+.end method
+\end{lstlisting}
+\end{minipage}
+\end{textblock}
 
-\begin{center}
-\begin{tikzpicture}
-\node (rexp)  {\bl{\bf Lexer}};
-\node (nfa) [right=of rexp] {\bl{\bf Parser}};
-\node (dfa) [right=of nfa] {\bl{\begin{tabular}{c}\bf Optimizations\end{tabular}}};
-\path[->, red, line width=2mm] (rexp) edge node [above=4mm, black] {\begin{tabular}{c@{\hspace{9mm}}}token\\[-1mm]
-sequence\end{tabular}} (nfa);
-\node (final) [below=of dfa] {\bl{\begin{tabular}{c}\bf Machine Code/\\\bf Byte Code\end{tabular}}};
-\path[->, red, line width=2mm] (nfa) edge node [above=4mm, black] {\begin{tabular}{c}parse\\[-1mm] tree
-\end{tabular}}(dfa);
-\path[->, red, line width=2mm] (dfa) edge (final);
-\end{tikzpicture}\\
-\end{center}
+\begin{textblock}{7}(6,6.6)
+\begin{bubble}[7cm]\small
+\begin{lstlisting}[language=Lisp,
+                   basicstyle=\ttfamily, 
+                   numbers=none,
+                   xleftmargin=1mm,linebackgroundcolor=\color{cream}]
+def add(x, y) = 
+    if x == 0 then y 
+    else suc(add(x - 1, y));
+\end{lstlisting}
+\end{bubble}
+\end{textblock}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c,fragile]
+\frametitle{Factorial}
 
-\end{frame}}
+\begin{textblock}{7}(1,1.8)\footnotesize
+\begin{minipage}{6cm}
+\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
+.method public static facT(II)I 
+.limit locals 2
+.limit stack 6
+  iload 0
+  ldc 0	
+  if_icmpne If_else_2
+  iload 1
+  goto If_end_3
+If_else_2:
+  iload 0
+  ldc 1
+  isub
+  iload 0
+  iload 1
+  imul
+  invokestatic fact/fact/facT(II)I
+If_end_3:
+  ireturn
+.end method 
+\end{lstlisting}
+\end{minipage}
+\end{textblock}
+
+\begin{textblock}{7}(6,7)
+\begin{bubble}[7cm]\small
+\begin{lstlisting}[language=Lisp,
+                   basicstyle=\ttfamily, 
+                   numbers=none,
+                   xleftmargin=1mm,linebackgroundcolor=\color{cream}]
+def facT(n, acc) = 
+  if n == 0 then acc 
+  else facT(n - 1, n * acc);
+\end{lstlisting}
+\end{bubble}
+\end{textblock}
+
+\end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[t]
-\frametitle{\begin{tabular}{c}What is Next\end{tabular}}
+\begin{frame}[fragile]
+
+\begin{textblock}{7}(1,-0.2)\footnotesize
+\begin{minipage}{6cm}
+\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none, escapeinside={(*@}{@*)}]
+.method public static facT(II)I 
+.limit locals 2
+.limit stack 6
+(*@\hl{facT\_Start:} @*)
+  iload 0
+  ldc 0
+  if_icmpne If_else_2
+  iload 1
+  goto If_end_3
+If_else_2:
+  iload 0
+  ldc 1
+  isub
+  iload 0
+  iload 1
+  imul
+  (*@\hl{istore 1} @*)
+  (*@\hl{istore 0} @*)
+  (*@\hl{goto facT\_Start} @*)
+If_end_3:
+  ireturn
+.end method 
+\end{lstlisting}
+\end{minipage}
+\end{textblock}
+
+\begin{textblock}{7}(6,7)
+\begin{bubble}[7cm]\small
+\begin{lstlisting}[language=Lisp,
+                   basicstyle=\ttfamily, 
+                   numbers=none,
+                   xleftmargin=1mm,linebackgroundcolor=\color{cream}]
+def facT(n, acc) = 
+  if n == 0 then acc 
+  else facT(n - 1, n * acc);
+\end{lstlisting}
+\end{bubble}
+\end{textblock}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[t, fragile]
+\frametitle{Tail Recursion}
+
+A call to \texttt{f(args)} is usually compiled as\medskip
+
+{\small\begin{lstlisting}[basicstyle=\ttfamily, numbers=none]
+  args onto stack
+  invokestatic  .../f 
+\end{lstlisting}}\pause
+
+
+A call is in tail position provided:\medskip
+
+{\small\begin{itemize}
+\item \texttt{if Bexp then \hl{Exp} else \hl{Exp}}
+\item \texttt{Exp ; \hl{Exp}}
+\item \texttt{Exp  op Exp}
+\end{itemize}}\medskip
+
+then a call \texttt{f(args)} can be compiled as\medskip\small
+
+\begin{lstlisting}[basicstyle=\ttfamily, numbers=none]
+  prepare environment
+  jump to start of function
+\end{lstlisting}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c, fragile]
+\frametitle{Tail Recursive Call}
+\footnotesize
+
+\begin{textblock}{13}(-0.3,2)
+\begin{lstlisting}[language=Scala,basicstyle=\ttfamily, numbers=none]
+def compile_expT(a: Exp, env: Mem, name: String): Instrs = 
+  ...
+  case Call(n, args) => if (name == n) 
+  { 
+    val stores = args.zipWithIndex.map 
+       { case (x, y) => "istore " + y.toString + "\n" } 
+    args.flatMap(a => compile_expT(a, env, "")) ++
+    stores.reverse ++ 
+    List ("goto " + n + "_Start\n") 
+  } 
+  else 
+  {
+    val is = "I" * args.length
+    args.flatMap(a => compile_expT(a, env, "")) ++
+    List ("invokestatic XXX/XXX/" + n + "(" + is + ")I\n")
+  }
+\end{lstlisting}
+\end{textblock}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \begin{frame}[c]
+  \frametitle{Dijkstra on Testing}
+  
+  \begin{bubble}[10cm]
+  ``Program testing can be a very effective way to show the
+  presence of bugs, but it is hopelessly inadequate for showing
+  their absence.''
+  \end{bubble}\bigskip
+  
+  \small
+  What is good about compilers: the either seem to work,
+  or go horribly wrong (most of the time).
+  
+  \end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c]
+\frametitle{\Large Proving Programs to be Correct}
+
+\begin{bubble}[10cm]
+\small
+{\bf Theorem:} There are infinitely many prime 
+numbers.\medskip\\
+
+{\bf Proof} \ldots\\
+\end{bubble}\bigskip
+
+
+similarly\bigskip
+
+\begin{bubble}[10cm]
+\small
+{\bf Theorem:} The program is doing what 
+it is supposed to be doing.\medskip
+
+{\bf Long, long proof} \ldots\\
+\end{bubble}\bigskip\medskip
+
+\small This can be a gigantic proof. The only hope is to have
+help from the computer. `Program' is here to be understood to be
+quite general (compiler, OS, \ldots).
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+
+\begin{frame}[c]
+\frametitle{Can This Be Done?}
 
 \begin{itemize}
-\item register spilling
-\item dead code removal
-\item loop optimisations
-\item instruction selection
-\item type checking
-\item concurrency
-\item fuzzy testing
-\item verification\bigskip\\
-
-\item GCC, LLVM, tracing JITs
+\item in 2008, verification of a small C-compiler
+\begin{itemize}
+\item ``if my input program has a certain behaviour, then the compiled machine code has the same behaviour''
+\item is as good as \texttt{gcc -O1}, but much, much less buggy 
+\end{itemize}
 \end{itemize}
 
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+\begin{center}
+  \includegraphics[scale=0.12]{../pics/compcert.png}
+\end{center}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+\begin{frame}[c]
+\frametitle{Fuzzy Testing C-Compilers}
 
+\begin{itemize}
+\item tested GCC, LLVM and others by randomly generating 
+C-programs
+\item found more than 300 bugs in GCC and also
+many in LLVM (some of them highest-level critical)\bigskip
+\item about CompCert:
+
+\begin{bubble}[10cm]\small ``The striking thing about our CompCert
+results is that the middle-end bugs we found in all other
+compilers are absent. As of early 2011, the under-development
+version of CompCert is the only compiler we have tested for
+which Csmith cannot find wrong-code errors. This is not for
+lack of trying: we have devoted about six CPU-years to the
+task.'' 
+\end{bubble} 
+\end{itemize}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
 
 \end{document}
 




