
diff -r 640e4a05cd9b -r d384fe01d0e8 slides/slides09.tex
--- a/slides/slides09.tex	Sun Nov 23 22:12:18 2014 +0000
+++ b/slides/slides09.tex	Mon Nov 24 00:11:31 2014 +0000
@@ -3,12 +3,39 @@
 \usepackage{../langs}
 \usepackage{../data}
 \usepackage{../graphics}
+\usepackage{soul}
+
+\tikzset{onslide/.code args={<#1>#2}{%
+  \only<#1>{\pgfkeysalso{#2}} % \pgfkeysalso doesn't change the path
+}}
+
+\makeatletter
+\newenvironment<>{btHighlight}[1][]
+{\begin{onlyenv}#2\begingroup\tikzset{bt@Highlight@par/.style={#1}}\begin{lrbox}{\@tempboxa}}
+{\end{lrbox}\bt@HL@box[bt@Highlight@par]{\@tempboxa}\endgroup\end{onlyenv}}
+
+\newcommand<>\btHL[1][]{%
+  \only#2{\begin{btHighlight}[#1]\bgroup\aftergroup\bt@HL@endenv}%
+}
+\def\bt@HL@endenv{%
+  \end{btHighlight}%   
+  \egroup
+}
+\newcommand{\bt@HL@box}[2][]{%
+  \tikz[#1]{%
+    \pgfpathrectangle{\pgfpoint{1pt}{0pt}}{\pgfpoint{\wd #2}{\ht #2}}%
+    \pgfusepath{use as bounding box}%
+    \node[anchor=base west, fill=orange!30,outer sep=0pt,inner xsep=1pt, inner ysep=0pt, rounded corners=3pt, minimum height=\ht\strutbox+1pt,#1]{\raisebox{1pt}{\strut}\strut\usebox{#2}};
+  }%
+}
+\makeatother
 
 
 % beamer stuff 
 \renewcommand{\slidecaption}{AFL 09, King's College London}
 \newcommand{\bl}[1]{\textcolor{blue}{#1}}       
 
+
 \begin{document}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -33,6 +60,500 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c,fragile]
+\frametitle{Functional Programming}
+
+\footnotesize
+\begin{textblock}{13}(0.9,3)
+\lstset{emph={def,if,then,else},emphstyle=\color{codepurple}}
+\begin{lstlisting}[basicstyle=\ttfamily, 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}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+\begin{center}
+\bl{\begin{tabular}{@{}lcl@{}}
+\textit{Exp} & $\rightarrow$ &  \textit{Var} $|$ \textit{Num}\\
+              & $|$ & \textit{Exp} \texttt{+} \textit{Exp} $|$ ... $|$ ( \textit{Exp} )\\
+              & $|$ & \texttt{if}\; \textit{BExp} \;\texttt{then}\; \textit{Exp} \;\texttt{else}\; \textit{Exp}\\
+              & $|$ & \texttt{write}\;\textit{Exp}\\
+              & $|$ & \textit{Exp}\;\texttt{;}\;\textit{Exp}\\
+              & $|$ & \textit{FunName} \texttt{(}\textit{Exp},...,\textit{Exp}\texttt{)}\medskip\\
+\textit{BExp} & $\rightarrow$ & \ldots\medskip\\
+\textit{Decl} & $\rightarrow$ &  \textit{Def} \;\texttt{;}\; \textit{Decl}\\
+              & $|$ & \textit{Exp}\medskip\\
+\textit{Def} & 
+$\rightarrow$ &  \texttt{def} \textit{FunName}\texttt{(}\textit{x}$_1$,..., \textit{x}$_n$\texttt{)} \texttt{=} \textit{Exp}\\
+\end{tabular}}
+\end{center}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c, fragile]
+\frametitle{Abstract Syntax Tree}
+
+\footnotesize
+\begin{textblock}{13}(0.3,2)
+\begin{lstlisting}[language=Scala,basicstyle=\ttfamily, numbers=none]
+abstract class Exp
+abstract class BExp 
+abstract class Decl
+
+case class 
+  Def(name: String, args: List[String], body: Exp) 
+                                          extends Decl
+case class Main(e: Exp) extends Decl
+
+case class Call(name: String, args: List[Exp]) extends Exp
+case class If(a: BExp, e1: Exp, e2: Exp) extends Exp
+case class Write(e: Exp) extends Exp
+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 Sequ(e1: Exp, e2: Exp) extends Exp
+case class Bop(o: String, a1: Exp, a2: Exp) extends BExp
+\end{lstlisting}
+\end{textblock}
+
+\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, 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, fragile]
+\frametitle{Sequences}
+
+Compiling \texttt{arg1 ; arg2}:
+
+
+\begin{textblock}{7}(2,5)\footnotesize
+\begin{minipage}{6cm}
+\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
+...arg1...
+pop
+...arg1...
+\end{lstlisting}
+\end{minipage}
+\end{textblock}
+
+  
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[t, fragile]
+\frametitle{Write}
+
+Compiling \texttt{write(arg)}:
+
+
+\begin{textblock}{7}(2,4)\footnotesize
+\begin{minipage}{6cm}
+\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
+...arg...
+dup
+invokestatic XXX/XXX/write(I)V
+\end{lstlisting}
+\end{minipage}
+\end{textblock}
+
+
+
+\begin{textblock}{7}(2,8)\footnotesize
+\begin{minipage}{6cm}
+\begin{lstlisting}[language=Scala,basicstyle=\ttfamily, numbers=none]
+case Write(a1) => {
+    compile_exp(a1, env) ++
+    List("dup\n",
+         "invokestatic XXX/XXX/write(I)V\n")
+  }
+\end{lstlisting}
+\end{minipage}
+\end{textblock}
+  
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c, fragile]
+\frametitle{Functions}
+
+\begin{textblock}{7}(1,2)\footnotesize
+\begin{minipage}{6cm}
+\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
+.method public static write(I)V 
+   .limit locals 5 
+   .limit stack 5 
+   iload 0 
+   getstatic java/lang/System/out Ljava/io/PrintStream; 
+   swap 
+   invokevirtual java/io/PrintStream/println(I)V 
+   return 
+.end method
+\end{lstlisting}
+\end{minipage}
+\end{textblock}
+
+
+\begin{textblock}{10}(1,9.8)
+\small We will need for definitions\\[-8mm]\mbox{}\footnotesize
+\begin{center}
+\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
+.method public static f (I...I)I
+  .limit locals ??
+  .limit stack ?? 
+  ??
+.end method
+\end{lstlisting}
+\end{center}
+\end{textblock}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c, fragile]
+\frametitle{Stack Estimation}
+\footnotesize
+\begin{center}
+\begin{lstlisting}[language=Scala,basicstyle=\ttfamily, numbers=none]
+def max_stack_exp(e: Exp): Int = e match {
+  case Call(_, args) => args.map(max_stack_exp).sum
+  case If(a, e1, e2) => max_stack_bexp(a) + 
+  	(List(max_stack_exp(e1), max_stack_exp(e1)).max)
+  case Write(e) => max_stack_exp(e) + 1
+  case Var(_) => 1
+  case Num(_) => 1
+  case Aop(_, a1, a2) => 
+  	max_stack_exp(a1) + max_stack_exp(a2)
+  case Sequ(e1, e2) => 
+  	List(max_stack_exp(e1), max_stack_exp(e2)).max
+}
+
+def max_stack_bexp(e: BExp): Int = e match {
+  case Bop(_, a1, a2) => 
+  	max_stack_exp(a1) + max_stack_exp(a2)
+}
+\end{lstlisting}
+\end{center}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[fragile]
+\frametitle{Successor}
+
+\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
+  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]
+def suc(x) = x + 1;
+\end{lstlisting}
+\end{bubble}
+\end{textblock}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[fragile]
+\frametitle{Addition}
+
+\begin{textblock}{7}(1,1.5)\footnotesize
+\begin{minipage}{6cm}
+\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
+.method public static add(II)I 
+.limit locals 2
+.limit stack 4
+  iload 0
+  ldc 0
+  if_icmpne If_else_2
+  iload 1
+  goto If_end_3
+If_else_2:
+  iload 0
+  ldc 1
+  isub
+  iload 1
+  invokestatic defs/defs/add(II)I
+  invokestatic defs/defs/suc(I)I
+If_end_3:
+  ireturn
+.end method
+\end{lstlisting}
+\end{minipage}
+\end{textblock}
+
+\begin{textblock}{7}(6,6.2)
+\begin{bubble}[7cm]\small
+\begin{lstlisting}[language=Lisp,
+                   basicstyle=\ttfamily, 
+                   numbers=none,
+                   xleftmargin=1mm]
+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}[fragile]
+\frametitle{Factorial}
+
+\begin{textblock}{7}(1,1.5)\footnotesize
+\begin{minipage}{6cm}
+\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
+.method public static facT(II)I 
+.limit locals 2
+.limit stack 4
+  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]
+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}[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 4
+(*@\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]
+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}[c, 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}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
 \begin{frame}[c]
 
@@ -199,202 +720,6 @@
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
 
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{Our Compiler}
-
-  \begin{center}
-  \begin{tikzpicture}[scale=1]
-
-  \node (0) at (-2.3,0) {}; 
-  
-  \node (A) at (0,0)  [draw=black, rectangle, very thick, minimum height=18mm, minimum width=20mm] {};
-  \node [below right] at (A.north west) {lexer};
-
-  \node (B) at (3,0)  [draw=black, rectangle, very thick, minimum height=18mm, minimum width=20mm] {};
-  \node [below right=1mm] at (B.north west) {\mbox{}\hspace{-1mm}parser};
-
-  \node (C) at (6,0)  [draw=black, rectangle, very thick, minimum height=18mm, minimum width=20mm] {};
-  \node [below right] at (C.north west) {\mbox{}\hspace{-1mm}code gen};
-
-  \node (1) at (8.4,0) {}; 
-
-  \draw [->,line width=4mm] (0) -- (A); 
-  \draw [->,line width=4mm] (A) -- (B); 
-  \draw [->,line width=4mm] (B) -- (C); 
-  \draw [->,line width=4mm] (C) -- (1); 
-  \end{tikzpicture}
-  \end{center}
-
-lexer input: string\medskip\\
-lexer output: sequence of tokens\\ 
-\mbox{}\hfill(white space and comments filtered out)\medskip\\
-parser output: abstract syntax tree\medskip\\ 
-code gen output: assembler byte code / \\
-\mbox{}\hfill assembler machine code
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{\begin{tabular}{c}For-Loops\end{tabular}}
-
-
-\begin{center}\Large
-\texttt{for} \;\textit{Id} \texttt{:=} \textit{AExp}\; \texttt{upto} \;\textit{AExp}\; \texttt{do} \textit{Block}
-\end{center}\bigskip
-
-\begin{center}
-\begin{minipage}{8cm}
-\begin{tabular}{l}
-\texttt{for i := 2 upto 4 do \{}\\
-\hspace{5mm}\texttt{write i}\\	
-\texttt{\}}\
-\end{tabular}
-\end{minipage}
-\end{center}
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{\begin{tabular}{c}While-Language\end{tabular}}
-
-
-\begin{center}
-\bl{\begin{tabular}{@{}lcl@{}}
-$Stmt$ & $\rightarrow$ &  $\text{skip}$\\
-              & $|$ & $Id := AExp$\\
-              & $|$ & $\text{if}\; B\!Exp \;\text{then}\; Block \;\text{else}\; Block$\\
-              & $|$ & $\text{while}\; B\!Exp \;\text{do}\; Block$\\
-               & $|$ & $\alert{\text{write}\; Id}$\\
-                & $|$ & $\alert{\text{read}\; Id}$\medskip\\
-$Stmts$ & $\rightarrow$ &  $Stmt \;\text{;}\; Stmts$\\
-              & $|$ & $Stmt$\medskip\\
-$Block$ & $\rightarrow$ &  $\{ Stmts \}$\\
-                & $|$ & $Stmt$\medskip\\
-$AExp$ & $\rightarrow$ & \ldots\\
-$BExp$ & $\rightarrow$ & \ldots\\
-\end{tabular}}
-\end{center}
-
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{\begin{tabular}{c}Interpreter\end{tabular}}
-
-\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}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{\begin{tabular}{c}Interpreter (2)\end{tabular}}
-
-\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}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
- 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[t]
-\frametitle{\begin{tabular}{c}Compiling Writes\end{tabular}}
-
-{\Large\bl{write $x$}}
-
-\begin{center}
-\small\bl{\begin{tabular}{l}
-.method public static write(I)V\hspace{1cm}\textcolor{black}{(library function)}\\ 
-\;\;    .limit locals 5 \\
-\;\;    .limit stack 5 \\
-\;\;    iload 0 \\
-\;\;    getstatic java/lang/System/out Ljava/io/PrintStream;\\ 
-\;\;    swap \\
-\;\;    invokevirtual java/io/PrintStream/println(I)V \\
-\;\;    return \\
-.end method\bigskip\bigskip\\
-%
-\normalsize
-iload $E(x)$\\
-invokestatic write(I)V\\
-\end{tabular}}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-
-\begin{center}
-\small\bl{\begin{tabular}{l}
-.class public XXX.XXX\\
-.super java/lang/Object\\
-\\
-.method public <init>()V\\
-\;\;     aload\_0\\
-\;\;     invokenonvirtual java/lang/Object/<init>()V\\
- \;\;    return\\
-.end method\\
-\\
-.method public static main([Ljava/lang/String;)V\\
-\;\;   .limit locals 200\\
-\;\;     .limit stack 200\\
-\\
-   \textcolor{black}{(here comes the compiled code)}\\
-\\
-\;\;     return\\
-.end method\\
-\end{tabular}}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
 
 \end{document}
 




