# HG changeset patch # User Christian Urban # Date 1448542559 0 # Node ID 8aa406adfde04774f661b2ed5f8ee3e563db3d0f # Parent 31295bb945c65db416f3d7b7f5b90e2c02e0c31b updated diff -r 31295bb945c6 -r 8aa406adfde0 slides/slides07.pdf Binary file slides/slides07.pdf has changed diff -r 31295bb945c6 -r 8aa406adfde0 slides/slides07.tex --- a/slides/slides07.tex Thu Nov 26 00:11:10 2015 +0000 +++ b/slides/slides07.tex Thu Nov 26 12:55:59 2015 +0000 @@ -1,12 +1,14 @@ \documentclass[dvipsnames,14pt,t]{beamer} \usepackage{../slides} +\usepackage{../graphics} \usepackage{../langs} \usepackage{../data} -\usepackage{../graphics} + % beamer stuff \renewcommand{\slidecaption}{AFL 07, King's College London} \newcommand{\bl}[1]{\textcolor{blue}{#1}} +%\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions \begin{document} @@ -16,7 +18,7 @@ \begin{tabular}{@ {}c@ {}} \\[-3mm] \LARGE Automata and \\[-2mm] - \LARGE Formal Languages (8)\\[3mm] + \LARGE Formal Languages (7)\\[3mm] \end{tabular}} \normalsize @@ -31,52 +33,322 @@ \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\newcommand{\qq}{\mbox{\texttt{"}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}[c] -\frametitle{Bird's Eye View} +\frametitle{CFGs} + +A \alert{context-free} grammar (CFG) \bl{$G$} consists of: +\begin{itemize} +\item a finite set of nonterminal symbols (upper case) +\item a finite terminal symbols or tokens (lower case) +\item a start symbol (which must be a nonterminal) +\item a set of rules \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}\\ +\bl{$A \rightarrow \text{rhs}_1 | \text{rhs}_2 | \ldots$} \end{center} +where \bl{rhs} are sequences involving terminals and nonterminals (can also be empty).\medskip\pause + +\end{itemize} + \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}Hierarchy of Languages\end{tabular}} + +Recall that languages are sets of strings. + +\begin{center} +\begin{tikzpicture} +[rect/.style={draw=black!50, top color=white,bottom color=black!20, rectangle, very thick, rounded corners}] + +\draw (0,0) node [rect, text depth=39mm, text width=68mm] {all languages}; +\draw (0,-0.4) node [rect, text depth=28.5mm, text width=64mm] {decidable languages}; +\draw (0,-0.85) node [rect, text depth=17mm] {context sensitive languages}; +\draw (0,-1.14) node [rect, text depth=9mm, text width=50mm] {context-free languages}; +\draw (0,-1.4) node [rect] {regular languages}; +\end{tikzpicture} + +\end{center} + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ \begin{frame}[c] -\begin{textblock}{10}(0.5,0.5) - \LARGE - \fontspec{Hoefler Text Black} - \textcolor{ProcessBlue}{JVM\\ Code} -\end{textblock} -\fontsize{8}{10}\selectfont -%\footnotesize -\mbox{}\\[-8mm]\mbox{} +\frametitle{\begin{tabular}{c}Arithmetic Expressions\end{tabular}} + +A grammar for arithmetic expressions and numbers: + +\begin{center} +\bl{\begin{tabular}{lcl} +$E$ & $\rightarrow$ & $E \cdot + \cdot E \;|\;E \cdot * \cdot E \;|\;( \cdot E \cdot ) \;|\;N$ \\ +$N$ & $\rightarrow$ & $N \cdot N \;|\; 0 \;|\; 1 \;|\: \ldots \;|\; 9$ +\end{tabular}} +\end{center} + +Unfortunately it is left-recursive (and ambiguous).\medskip\\ +A problem for \alert{recursive descent parsers} (e.g.~parser combinators). +\bigskip\pause + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[t] +\frametitle{\begin{tabular}{c}Numbers\end{tabular}} + + + +\begin{center} +\bl{\begin{tabular}{lcl} +$N$ & $\rightarrow$ & $N \cdot N \;|\; 0 \;|\; 1 \;|\; \ldots \;|\; 9$\\ +\end{tabular}} +\end{center} + +A non-left-recursive, non-ambiguous grammar for numbers: + +\begin{center} +\bl{\begin{tabular}{lcl} +$N$ & $\rightarrow$ & $0 \cdot N \;|\;1 \cdot N \;|\;\ldots\;|\; 0 \;|\; 1 \;|\; \ldots \;|\; 9$\\ +\end{tabular}} +\end{center} + + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}Operator Precedences\end{tabular}} + + +To disambiguate + +\begin{center} +\bl{\begin{tabular}{lcl} +$E$ & $\rightarrow$ & $E \cdot + \cdot E \;|\;E \cdot * \cdot E \;|\;( \cdot E \cdot ) \;|\;N$ \\ +\end{tabular}} +\end{center} + +Decide on how many precedence levels, say\medskip\\ +\hspace{5mm}highest for \bl{$()$}, medium for \bl{*}, lowest for \bl{+} + +\begin{center} +\bl{\begin{tabular}{lcl} +$E_{low}$ & $\rightarrow$ & $E_{med} \cdot + \cdot E_{low} \;|\; E_{med}$ \\ +$E_{med}$ & $\rightarrow$ & $E_{hi} \cdot * \cdot E_{med} \;|\; E_{hi}$\\ +$E_{hi}$ & $\rightarrow$ & $( \cdot E_{low} \cdot ) \;|\;N$ \\ +\end{tabular}} +\end{center}\pause + +\small What happens with \bl{$1 + 3 + 4$}? +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}Removing Left-Recursion\end{tabular}} + +The rule for numbers is directly left-recursive: + +\begin{center} +\bl{\begin{tabular}{lcl} +$N$ & $\rightarrow$ & $N \cdot N \;|\; 0 \;|\; 1\;\;\;\;(\ldots)$ +\end{tabular}} +\end{center} + +Translate + +\begin{center} +\begin{tabular}{ccc} +\bl{\begin{tabular}{lcl} +$N$ & $\rightarrow$ & $N \cdot \alpha$\\ + & $\;|\;$ & $\beta$\\ + \\ +\end{tabular}} +& {\Large$\Rightarrow$} & +\bl{\begin{tabular}{lcl} +$N$ & $\rightarrow$ & $\beta \cdot N'$\\ +$N'$ & $\rightarrow$ & $\alpha \cdot N'$\\ + & $\;|\;$ & $\epsilon$ +\end{tabular}} +\end{tabular} +\end{center}\pause + +Which means + +\begin{center} +\bl{\begin{tabular}{lcl} +$N$ & $\rightarrow$ & $0 \cdot N' \;|\; 1 \cdot N'$\\ +$N'$ & $\rightarrow$ & $N \cdot N' \;|\; \epsilon$\\ +\end{tabular}} +\end{center} + + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{columns} -\begin{column}{2cm} -\lstinputlisting[numbers=none]{../progs/appHa.j} -\end{column} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}Chomsky Normal Form\end{tabular}} + +All rules must be of the form + +\begin{center} +\bl{$A \rightarrow a$} +\end{center} + +or + +\begin{center} +\bl{$A \rightarrow B\cdot C$} +\end{center} + +No rule can contain \bl{$\epsilon$}. + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}$\epsilon$-Removal\end{tabular}} + +\begin{enumerate} +\item If \bl{$A\rightarrow \alpha \cdot B \cdot \beta$} and \bl{$B \rightarrow \epsilon$} are in the grammar, +then add \bl{$A\rightarrow \alpha \cdot \beta$} (iterate if necessary). +\item Throw out all \bl{$B \rightarrow \epsilon$}. +\end{enumerate} + +\small +\begin{center} +\begin{tabular}{ccc} +\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l} +$N$ & $\rightarrow$ & $0 \cdot N' \;|\; 1\cdot N'$\\ +$N'$ & $\rightarrow$ & $N \cdot N'\;|\;\epsilon$\\ +\\ +\\ +\\ +\\ +\\ +\end{tabular}} & +\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l} +\\ +$N$ & $\rightarrow$ & $0 \cdot N' \;|\; 1\cdot N'\;|\;0\;|\;1$\\ +$N'$ & $\rightarrow$ & $N \cdot N'\;|\;N\;|\;\epsilon$\\ +\\ +$N$ & $\rightarrow$ & $0 \cdot N' \;|\; 1\cdot N'\;|\;0\;|\;1$\\ +$N'$ & $\rightarrow$ & $N \cdot N'\;|\;N$\\ +\end{tabular}} +\end{tabular} +\end{center} + +\pause\normalsize +\begin{center} +\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l} +$N$ & $\rightarrow$ & $0 \cdot N\;|\; 1\cdot N\;|\;0\;|\;1$\\ +\end{tabular}} + +\end{center} +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}CYK Algorithm\end{tabular}} + +If grammar is in Chomsky normalform \ldots -\begin{column}{2cm} -\lstinputlisting[numbers=none]{../progs/appHb.j} -\end{column} +\begin{center} +\bl{\begin{tabular}{@ {}lcl@ {}} +$S$ & $\rightarrow$ & $N\cdot P$ \\ +$P$ & $\rightarrow$ & $V\cdot N$ \\ +$N$ & $\rightarrow$ & $N\cdot N$ \\ +$N$ & $\rightarrow$ & $\texttt{students} \;|\; \texttt{Jeff} \;|\; \texttt{geometry} \;|\; \texttt{trains} $ \\ +$V$ & $\rightarrow$ & $\texttt{trains}$ +\end{tabular}} +\end{center} + +\bl{\texttt{Jeff trains geometry students}} -\end{columns} +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}CYK Algorithm\end{tabular}} + + +\begin{itemize} +\item fastest possible algorithm for recognition problem +\item runtime is \bl{$O(n^3)$}\bigskip +\item grammars need to be transferred into CNF +\end{itemize} + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}Hierarchy of Languages\end{tabular}} + +Recall that languages are sets of strings. -\end{frame} +\begin{center} +\begin{tikzpicture} +[rect/.style={draw=black!50, top color=white,bottom color=black!20, rectangle, very thick, rounded corners}] + +\draw (0,0) node [rect, text depth=39mm, text width=68mm] {all languages}; +\draw (0,-0.4) node [rect, text depth=28.5mm, text width=64mm] {decidable languages}; +\draw (0,-0.85) node [rect, text depth=17mm] {context sensitive languages}; +\draw (0,-1.14) node [rect, text depth=9mm, text width=50mm] {context-free languages}; +\draw (0,-1.4) node [rect] {regular languages}; +\end{tikzpicture} + +\end{center} + +\end{frame}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - - + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}Context Sensitive Grms\end{tabular}} + + +\begin{center} +\bl{\begin{tabular}{lcl} +$S$ & $\Rightarrow$ & $bSAA\;|\; \epsilon$\\ +$A$ & $\Rightarrow$ & $a$\\ +$bA$ & $\Rightarrow$ & $Ab$\\ +\end{tabular}} +\end{center}\pause + +\begin{center} +\bl{$S \Rightarrow\ldots\Rightarrow^? "ababaa"$} +\end{center} + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \mode{ \begin{frame}[c] @@ -98,26 +370,48 @@ \textit{BExp} & $\rightarrow$ & \ldots\\ \end{tabular}} \end{center} - - \end{frame}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ \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}}} +\mbox{\lstinputlisting[language=while]{../progs/fib.while}} -\end{frame} +\end{frame}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ \begin{frame}[c] -\frametitle{Interpreter} +\frametitle{\begin{tabular}{c}An Interpreter\end{tabular}} + +\begin{center} +\bl{\begin{tabular}{l} +$\{$\\ +\;\;$x := 5 \text{;}$\\ +\;\;$y := x * 3\text{;}$\\ +\;\;$y := x * 4\text{;}$\\ +\;\;$x := u * 3$\\ +$\}$ +\end{tabular}} +\end{center} + +\begin{itemize} +\item the interpreter has to record the value of \bl{$x$} before assigning a value to \bl{$y$}\pause +\item \bl{\text{eval}(stmt, env)} +\end{itemize} + + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}Interpreter\end{tabular}} \begin{center} \bl{\begin{tabular}{@{}lcl@{}} @@ -132,12 +426,12 @@ \end{tabular}} \end{center} -\end{frame} +\end{frame}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ \begin{frame}[c] -\frametitle{Interpreter (2)} +\frametitle{\begin{tabular}{c}Interpreter (2)\end{tabular}} \begin{center} \bl{\begin{tabular}{@{}lcl@{}} @@ -156,42 +450,27 @@ \end{tabular}} \end{center} -\end{frame} +\end{frame}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ \begin{frame}[c] -\frametitle{Test Program} +\frametitle{\begin{tabular}{c}Test Program\end{tabular}} \mbox{}\\[-18mm]\mbox{} -{\lstset{language=While}\fontsize{10}{12}\selectfont +{\lstset{language=While}%%\fontsize{10}{12}\selectfont \texttt{\lstinputlisting{../progs/loops.while}}} -\end{frame} +\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} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ \begin{frame}[t] -\frametitle{Interpreted Code} +\frametitle{\begin{tabular}{c}Interpreted Code\end{tabular}} \begin{center} \begin{tikzpicture} @@ -201,12 +480,13 @@ \end{tikzpicture} \end{center} -\end{frame} +\end{frame}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ \begin{frame}[c] -\frametitle{Java Virtual Machine} +\frametitle{\begin{tabular}{c}Java Virtual Machine\end{tabular}} \begin{itemize} \item introduced in 1995 @@ -214,583 +494,12 @@ \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 +\item some languages compile to the JVM: Scala, Clojure\ldots \end{itemize} -\end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}[t] -\frametitle{Compiling AExps} - -{\Large\bl{1 + 2}} - -\begin{center} -\bl{\begin{tabular}{l} -ldc 1\\ -ldc 2\\ -iadd\\ -\end{tabular}} -\end{center} -\end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ -\begin{frame}[t] -\frametitle{\begin{tabular}{c}Compiling AExps\end{tabular}} - -{\Large\bl{1 + 2 + 3}} - -\begin{center} -\bl{\begin{tabular}{l} -ldc 1\\ -ldc 2\\ -iadd\\ -ldc 3\\ -iadd\\ -\end{tabular}} -\end{center} - -\end{frame}} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ -\begin{frame}[t] -\frametitle{\begin{tabular}{c}Compiling AExps\end{tabular}} - -{\Large\bl{1 + (2 + 3)}} - -\begin{center} -\bl{\begin{tabular}{l} -ldc 1\\ -ldc 2\\ -ldc 3\\ -iadd\\ -iadd\\ -\end{tabular}} -\end{center}\bigskip\pause -\vfill - -\bl{dadd, fadd, 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} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ -\begin{frame}[t] -\frametitle{\begin{tabular}{c}Compiling AExps\end{tabular}} - -{\Large\bl{1 + 2 * 3 + (4 - 3)}} - -\begin{center} -\bl{\begin{tabular}{l} -ldc 1\\ -ldc 2\\ -ldc 3\\ -imul\\ -ldc 4\\ -ldc 3\\ -isub\\ -iadd\\ -iadd\\ -\end{tabular}} -\end{center} - \end{frame}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}[t] -\frametitle{Variables} - -{\Large\bl{$x := 5 + y * 2$}}\bigskip\pause - -\begin{itemize} -\item lookup: \bl{$\text{iload}\; index$} -\item store: \bl{$\text{istore}\; index$} -\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}[t] -\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] -\frametitle{Compiling Assignments} - -{\Large\bl{$x := x + 1$}} - -\begin{center} -\bl{\begin{tabular}{l} -iload $n_x$\\ -ldc 1\\ -iadd\\ -istore $n_x$\\ -\end{tabular}} -\end{center} - -where \bl{$n_x$} is the index corresponding to the variable~\bl{$x$} - -\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] -\frametitle{Conditional Jumps} - -\begin{minipage}{1.1\textwidth} -\begin{itemize} -\item \bl{if\_icmpeq $label$} if two ints are equal, then jump\medskip -\item \bl{if\_icmpne $label$} if two ints aren't equal, then jump\medskip -\item \bl{if\_icmpge $label$} if one int is greater or equal then another, then jump -\item[]\ldots -\end{itemize} -\end{minipage}\pause - - -\begin{center} -\bl{\begin{tabular}{l} -$L_1$:\\ -\hspace{5mm}if\_icmpeq\;$L_2$\\ -\hspace{5mm}iload 1\\ -\hspace{5mm}ldc 1\\ -\hspace{5mm}iadd\\ -\hspace{5mm}if\_icmpeq\;$L_1$\\ -$L_2$: -\end{tabular}} -\end{center} - -\begin{textblock}{3.5}(11,12) -\only<3>{labels must be unique} -\end{textblock} -\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} - -\end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}[t] -\frametitle{Compiling Writes} - -{\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} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}[c] - -\begin{center} -\small\bl{\begin{tabular}{l} -.class public XXX.XXX\\ -.super java/lang/Object\\ -\\ -.method public ()V\\ -\;\; aload\_0\\ -\;\; invokenonvirtual java/lang/Object/()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} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ -\begin{frame}[c] -\frametitle{\begin{tabular}{c}Next Compiler Phases\end{tabular}} - -\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} - -\end{frame}} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ -\begin{frame}[t] -\frametitle{\begin{tabular}{c}Compiled Code\end{tabular}} - -\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} - -\end{frame}} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ -\begin{frame}[t] -\frametitle{\begin{tabular}{c}Compiler vs.~Interpreter\end{tabular}} - -\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}} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ -\begin{frame}[c] -\frametitle{Backend} - -\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} - -\end{frame}} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ -\begin{frame}[t] -\frametitle{\begin{tabular}{c}What Next\end{tabular}} - -\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 -\end{itemize} - -\end{frame}} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \end{document} diff -r 31295bb945c6 -r 8aa406adfde0 slides/slides08.pdf Binary file slides/slides08.pdf has changed diff -r 31295bb945c6 -r 8aa406adfde0 slides/slides08.tex --- a/slides/slides08.tex Thu Nov 26 00:11:10 2015 +0000 +++ b/slides/slides08.tex Thu Nov 26 12:55:59 2015 +0000 @@ -5,7 +5,7 @@ \usepackage{../graphics} % beamer stuff -\renewcommand{\slidecaption}{AFL 09, King's College London} +\renewcommand{\slidecaption}{AFL 07, King's College London} \newcommand{\bl}[1]{\textcolor{blue}{#1}} \begin{document} @@ -39,7 +39,8 @@ \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 Byte Code\end{tabular}}}; +\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); @@ -51,16 +52,21 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}[c] -\frametitle{JVM Code} -\footnotesize -\mbox{}\\[-20mm]\mbox{} +\begin{textblock}{10}(0.5,0.5) + \LARGE + \fontspec{Hoefler Text Black} + \textcolor{ProcessBlue}{JVM\\ Code} +\end{textblock} +\fontsize{8}{10}\selectfont +%\footnotesize +\mbox{}\\[-8mm]\mbox{} \begin{columns} -\begin{column}{7cm} +\begin{column}{2cm} \lstinputlisting[numbers=none]{../progs/appHa.j} \end{column} -\begin{column}{7cm} +\begin{column}{2cm} \lstinputlisting[numbers=none]{../progs/appHb.j} \end{column} @@ -98,7 +104,6 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ \begin{frame}[c] \frametitle{\begin{tabular}{c}Fibonacci Numbers\end{tabular}} @@ -107,13 +112,12 @@ {\lstset{language=While}\fontsize{10}{12}\selectfont \texttt{\lstinputlisting{../progs/fib.while}}} -\end{frame}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ \begin{frame}[c] -\frametitle{\begin{tabular}{c}Interpreter\end{tabular}} +\frametitle{Interpreter} \begin{center} \bl{\begin{tabular}{@{}lcl@{}} @@ -128,13 +132,12 @@ \end{tabular}} \end{center} -\end{frame}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ \begin{frame}[c] -\frametitle{\begin{tabular}{c}Interpreter (2)\end{tabular}} +\frametitle{Interpreter (2)} \begin{center} \bl{\begin{tabular}{@{}lcl@{}} @@ -153,25 +156,25 @@ \end{tabular}} \end{center} -\end{frame}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ \begin{frame}[c] -\frametitle{\begin{tabular}{c}Test Program\end{tabular}} +\frametitle{Test Program} \mbox{}\\[-18mm]\mbox{} {\lstset{language=While}\fontsize{10}{12}\selectfont \texttt{\lstinputlisting{../progs/loops.while}}} -\end{frame}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}[c] -\tiny +\fontsize{7}{9}\selectfont + \begin{columns} \begin{column}{7cm} @@ -181,19 +184,14 @@ \begin{column}{7cm} \lstinputlisting[numbers=none]{../progs/appHb.j} \end{column} - \end{columns} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ \begin{frame}[t] -\frametitle{\begin{tabular}{c}Interpreted Code\end{tabular}} +\frametitle{Interpreted Code} \begin{center} \begin{tikzpicture} @@ -203,13 +201,12 @@ \end{tikzpicture} \end{center} -\end{frame}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ \begin{frame}[c] -\frametitle{\begin{tabular}{c}Java Virtual Machine\end{tabular}} +\frametitle{Java Virtual Machine} \begin{itemize} \item introduced in 1995 @@ -220,13 +217,12 @@ \item some languages compiled to the JVM: Scala, Clojure\ldots \end{itemize} -\end{frame}} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ \begin{frame}[t] -\frametitle{\begin{tabular}{c}Compiling AExps\end{tabular}} +\frametitle{Compiling AExps} {\Large\bl{1 + 2}} @@ -236,7 +232,8 @@ ldc 2\\ iadd\\ \end{tabular}} -\end{center}\end{frame}} +\end{center} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -284,9 +281,8 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ \begin{frame}[t] -\frametitle{\begin{tabular}{c}Compiling AExps\end{tabular}} +\frametitle{Compiling AExps} \begin{center} \bl{\begin{tabular}{@{}lcl@{}} @@ -298,9 +294,9 @@ $\text{compile}(a_1 * a_2)$ & $\dn$\\ \multicolumn{3}{l}{$\qquad\text{compile}(a_1) \;@\; \text{compile}(a_2)\;@\; \text{imul}$}\smallskip\\ \end{tabular}} -\end{center}\pause +\end{center} -\end{frame}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -328,9 +324,8 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ \begin{frame}[t] -\frametitle{\begin{tabular}{c}Variables\end{tabular}} +\frametitle{Variables} {\Large\bl{$x := 5 + y * 2$}}\bigskip\pause @@ -346,54 +341,72 @@ \bl{$\text{compile}(a, E)$} \end{center} -\end{frame}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ \begin{frame}[t] -\frametitle{\begin{tabular}{c}Compiling AExps\end{tabular}} +\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\\ +\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}\pause +\end{center} -\end{frame}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ +\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}[t] -\frametitle{\begin{tabular}{c}Compiling Statements\end{tabular}} +\frametitle{Compiling Statements} -We return a list of instructions and an environment for the variables +We return a list of instructions and an environment for the +variables \begin{center} \bl{\begin{tabular}{@{}l@{\hspace{1mm}}c@{\hspace{1mm}}l@{}} -$\text{compile}(\text{skip}, E)$ & $\dn$ & $(N\!il, E)$\bigskip\\ +$\text{compile}(\text{skip}, E)$ & $\dn$ & $(\textit{Nil}, E)$\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 +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}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ -\begin{frame}[t] -\frametitle{\begin{tabular}{c}Compiling AExps\end{tabular}} +\begin{frame}[c] +\frametitle{Compiling Assignments} {\Large\bl{$x := x + 1$}} @@ -406,15 +419,15 @@ \end{tabular}} \end{center} -where \bl{$n_x$} is the index corresponding to the variable \bl{$x$} +where \bl{$n_x$} is the index corresponding to the variable~\bl{$x$} -\end{frame}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ \begin{frame}[t] -\frametitle{\begin{tabular}{c}Compiling Ifs\end{tabular}} +\frametitle{Compiling Ifs} {\Large\bl{$\text{if}\;b\;\text{then}\;cs_1\;\text{else}\;cs_2$}}\bigskip\bigskip @@ -449,14 +462,12 @@ \end{tikzpicture} \end{center} - -\end{frame}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ -\begin{frame}[c] -\frametitle{\begin{tabular}{c}Conditional Jumps\end{tabular}} +\begin{frame}[t] +\frametitle{Conditional Jumps} \begin{minipage}{1.1\textwidth} \begin{itemize} @@ -483,13 +494,12 @@ \begin{textblock}{3.5}(11,12) \only<3>{labels must be unique} \end{textblock} -\end{frame}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ \begin{frame}[t] -\frametitle{\begin{tabular}{c}Compiling BExps\end{tabular}} +\frametitle{Compiling BExps} {\Large\bl{$a_1 = a_2$}} @@ -500,13 +510,54 @@ \end{tabular}} \end{center} -\end{frame}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ +\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{\begin{tabular}{c}Compiling Ifs\end{tabular}} +\frametitle{Compiling Ifs} {\Large\bl{if $b$ then $cs_1$ else $cs_2$}} @@ -526,13 +577,12 @@ \end{tabular}} \end{center} -\end{frame}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ \begin{frame}[t] -\frametitle{\begin{tabular}{c}Compiling Whiles\end{tabular}} +\frametitle{Compiling Whiles} {\Large\bl{$\text{while}\;b\;\text{do}\;cs$}}\bigskip\bigskip @@ -564,14 +614,12 @@ \end{tikzpicture} \end{center} - -\end{frame}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ \begin{frame}[t] -\frametitle{\begin{tabular}{c}Compiling Whiles\end{tabular}} +\frametitle{Compiling Whiles} {\Large\bl{while $b$ do $cs$}} @@ -589,13 +637,12 @@ \end{tabular}} \end{center} -\end{frame}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ \begin{frame}[t] -\frametitle{\begin{tabular}{c}Compiling Writes\end{tabular}} +\frametitle{Compiling Writes} {\Large\bl{write $x$}} @@ -617,41 +664,12 @@ \end{tabular}} \end{center} -\end{frame}} +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \mode{ \begin{frame}[c] - -\begin{center} -\small\bl{\begin{tabular}{l} -.class public XXX.XXX\\ -.super java/lang/Object\\ -\\ -.method public ()V\\ -\;\; aload\_0\\ -\;\; invokenonvirtual java/lang/Object/()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}} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\mode{ -\begin{frame}[c] \frametitle{\begin{tabular}{c}Next Compiler Phases\end{tabular}} \begin{itemize}