666
|
1 |
% !TEX program = xelatex
|
49
|
2 |
\documentclass[dvipsnames,14pt,t]{beamer}
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
3 |
\usepackage{../slides}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
4 |
\usepackage{../graphics}
|
215
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
5 |
\usepackage{../langs}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
6 |
\usepackage{../data}
|
597
|
7 |
\usepackage{../grammar}
|
49
|
8 |
|
|
9 |
% beamer stuff
|
445
|
10 |
\renewcommand{\slidecaption}{CFL 06, King's College London}
|
|
11 |
|
|
12 |
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
13 |
\newcommand{\bl}[1]{\textcolor{blue}{#1}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
14 |
%\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
|
366
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
15 |
\newcommand{\qq}{\mbox{\texttt{"}}}
|
49
|
16 |
|
|
17 |
\begin{document}
|
|
18 |
|
|
19 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
20 |
\begin{frame}[t]
|
49
|
21 |
\frametitle{%
|
|
22 |
\begin{tabular}{@ {}c@ {}}
|
|
23 |
\\[-3mm]
|
445
|
24 |
\LARGE Compilers and \\[-2mm]
|
49
|
25 |
\LARGE Formal Languages (6)\\[3mm]
|
|
26 |
\end{tabular}}
|
|
27 |
|
|
28 |
\normalsize
|
|
29 |
\begin{center}
|
|
30 |
\begin{tabular}{ll}
|
683
|
31 |
Email: & christian.urban at kcl.ac.uk\\
|
|
32 |
Office Hours: & Thursdays 12 -- 14\\
|
|
33 |
Location: & N7.07 (North Wing, Bush House)\\
|
|
34 |
Slides \& Progs: & KEATS (also homework is there)\\
|
49
|
35 |
\end{tabular}
|
|
36 |
\end{center}
|
|
37 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
38 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
39 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
49
|
40 |
|
|
41 |
|
|
42 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
531
|
43 |
% \begin{frame}[c]
|
|
44 |
% \small
|
|
45 |
% \mbox{}\\[5mm]
|
|
46 |
% %\begin{textblock}{10}(3,5)
|
|
47 |
% \begin{tikzpicture}[scale=1.5,
|
|
48 |
% node distance=1cm,
|
|
49 |
% every node/.style={minimum size=7mm}]
|
|
50 |
% \node (r1) {\bl{$r_1$}};
|
|
51 |
% \node (r2) [right=of r1] {\bl{$r_2$}};
|
|
52 |
% \draw[->,line width=1mm] (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};
|
|
53 |
% \node (r3) [right=of r2] {\bl{$r_3$}};
|
|
54 |
% \draw[->,line width=1mm] (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};
|
|
55 |
% \node (r4) [right=of r3] {\bl{$r_4$}};
|
|
56 |
% \draw[->,line width=1mm] (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};
|
|
57 |
% \draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};
|
|
58 |
% \node (v4) [below=of r4] {\bl{$v_4$}};
|
|
59 |
% \draw[->,line width=1mm] (r4) -- (v4);
|
|
60 |
% \node (v3) [left=of v4] {\bl{$v_3$}};
|
|
61 |
% \draw[->,line width=1mm] (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};
|
|
62 |
% \node (v2) [left=of v3] {\bl{$v_2$}};
|
|
63 |
% \draw[->,line width=1mm] (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};
|
|
64 |
% \node (v1) [left=of v2] {\bl{$v_1$}};
|
|
65 |
% \draw[->,line width=1mm] (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};
|
|
66 |
% \draw[->,line width=0.5mm] (r3) -- (v3);
|
|
67 |
% \draw[->,line width=0.5mm] (r2) -- (v2);
|
|
68 |
% \draw[->,line width=0.5mm] (r1) -- (v1);
|
|
69 |
% \draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};
|
|
70 |
% \end{tikzpicture}
|
|
71 |
% %\end{textblock}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
72 |
|
531
|
73 |
% \begin{center}
|
|
74 |
% \begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
|
75 |
% \\[-10mm]
|
|
76 |
% \bl{$inj\,(c)\,c\,Empty$} & \bl{$\dn$} & \bl{$Char\,c$}\\
|
|
77 |
% \bl{$inj\,(r_1 + r_2)\,c\,Left(v)$} & \bl{$\dn$} & \bl{$Left(inj\,r_1\,c\,v)$}\\
|
|
78 |
% \bl{$inj\,(r_1 + r_2)\,c\,Right(v)$} & \bl{$\dn$} & \bl{$Right(inj\,r_2\,c\,v)$}\\
|
|
79 |
% \bl{$inj\,(r_1 \cdot r_2)\,c\,Seq(v_1,v_2)$} & \bl{$\dn$} & \bl{$Seq(inj\,r_1\,c\,v_1,v_2)$}\\
|
|
80 |
% \bl{$inj\,(r_1 \cdot r_2)\,c\,Left(Seq(v_1,v_2))$} & \bl{$\dn$} & \bl{$Seq(inj\,r_1\,c\,v_1,v_2)$}\\
|
|
81 |
% \bl{$inj\,(r_1 \cdot r_2)\,c\,Right(v)$} & \bl{$\dn$} & \bl{$Seq(mkeps(r_1),inj\,r_2\,c\,v)$}\\
|
|
82 |
% \bl{$inj\,(r^*)\,c\,Seq(v,vs)$} & \bl{$\dn$} & \bl{$inj\,r\,c\,v\,::\,vs$}\\
|
|
83 |
% \end{tabular}
|
|
84 |
% \end{center}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
85 |
|
531
|
86 |
% \end{frame}
|
|
87 |
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
88 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
89 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
683
|
90 |
\begin{frame}[t]
|
|
91 |
\frametitle{Starting Symbol}
|
|
92 |
|
|
93 |
\bl{\begin{plstx}[margin=1cm]
|
|
94 |
: \meta{S} ::= \meta{A}\cdot\meta{S}\cdot\meta{B} |
|
|
95 |
\meta{B}\cdot\meta{S}\cdot\meta{A} | \epsilon\\
|
|
96 |
: \meta{A} ::= a | \epsilon\\
|
|
97 |
: \meta{B} ::= b\\
|
|
98 |
\end{plstx}}
|
|
99 |
|
|
100 |
\end{frame}
|
|
101 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
102 |
|
|
103 |
|
|
104 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
105 |
\begin{frame}[c]
|
683
|
106 |
\frametitle{Hierarchy of Languages}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
107 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
108 |
Recall that languages are sets of strings.
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
109 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
110 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
111 |
\begin{tikzpicture}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
112 |
[rect/.style={draw=black!50, top color=white,bottom color=black!20, rectangle, very thick, rounded corners}]
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
113 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
114 |
\draw (0,0) node [rect, text depth=39mm, text width=68mm] {all languages};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
115 |
\draw (0,-0.4) node [rect, text depth=28.5mm, text width=64mm] {decidable languages};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
116 |
\draw (0,-0.85) node [rect, text depth=17mm] {context sensitive languages};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
117 |
\draw (0,-1.14) node [rect, text depth=9mm, text width=50mm] {context-free languages};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
118 |
\draw (0,-1.4) node [rect] {regular languages};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
119 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
120 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
121 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
122 |
|
366
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
123 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
124 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
125 |
|
531
|
126 |
|
366
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
127 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
128 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
129 |
\begin{frame}[c]
|
598
|
130 |
\frametitle{Parser Combinators}
|
|
131 |
|
366
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
132 |
Atomic parsers, for example
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
133 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
134 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
135 |
\bl{$1::rest \;\Rightarrow\; \{(1, rest)\}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
136 |
\end{center}\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
137 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
138 |
\begin{itemize}
|
597
|
139 |
\item you consume one or more tokens from the\\
|
366
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
140 |
input (stream)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
141 |
\item also works for characters and strings
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
142 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
143 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
144 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
145 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
146 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
147 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
148 |
|
686
|
149 |
Alternative parser (code \bl{$p\;|\;q$})\bigskip
|
366
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
150 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
151 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
152 |
\item apply \bl{$p$} and also \bl{$q$}; then combine
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
153 |
the outputs
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
154 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
155 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
156 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
157 |
\large \bl{$p(\text{input}) \cup q(\text{input})$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
158 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
159 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
160 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
161 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
162 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
163 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
164 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
165 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
166 |
Sequence parser (code \bl{$p\sim q$})\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
167 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
168 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
169 |
\item apply first \bl{$p$} producing a set of pairs
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
170 |
\item then apply \bl{$q$} to the unparsed parts
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
171 |
\item then combine the results:\medskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
172 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
173 |
((output$_1$, output$_2$), unparsed part)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
174 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
175 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
176 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
177 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
178 |
\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
179 |
\large \bl{$\{((o_1, o_2), u_2) \;|\;$}\\[2mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
180 |
\large\mbox{}\hspace{15mm} \bl{$(o_1, u_1) \in p(\text{input}) \wedge$}\\[2mm]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
181 |
\large\mbox{}\hspace{15mm} \bl{$(o_2, u_2) \in q(u_1)\}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
182 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
183 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
184 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
185 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
186 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
187 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
188 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
189 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
190 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
191 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
192 |
Function parser (code \bl{$p \Rightarrow f\;$})\bigskip
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
193 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
194 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
195 |
\item apply \bl{$p$} producing a set of pairs
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
196 |
\item then apply the function \bl{$f$} to each first component
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
197 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
198 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
199 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
200 |
\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
201 |
\large \bl{$\{(f(o_1), u_1) \;|\; (o_1, u_1) \in p(\text{input})\}$}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
202 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
203 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
204 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
205 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
206 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
207 |
|
531
|
208 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
209 |
\begin{frame}[c]
|
|
210 |
\frametitle{Types of Parsers}
|
|
211 |
|
|
212 |
\begin{itemize}
|
|
213 |
\item {\bf Sequencing}: if \bl{$p$} returns results of type \bl{$T$}, and \bl{$q$} results of type \bl{$S$},
|
|
214 |
then \bl{$p \sim q$} returns results of type
|
|
215 |
|
|
216 |
\begin{center}
|
|
217 |
\bl{$T \times S$}
|
|
218 |
\end{center}\pause
|
|
219 |
|
|
220 |
\item {\bf Alternative}: if \bl{$p$} returns results of type \bl{$T$} then \bl{$q$} \alert{must} also have results of type \bl{$T$},
|
686
|
221 |
and \bl{$p \;|\; q$} returns results of type
|
531
|
222 |
|
|
223 |
\begin{center}
|
|
224 |
\bl{$T$}
|
|
225 |
\end{center}\pause
|
|
226 |
|
|
227 |
\item {\bf Semantic Action}: if \bl{$p$} returns results of type \bl{$T$} and \bl{$f$} is a function from
|
|
228 |
\bl{$T$} to \bl{$S$}, then
|
|
229 |
\bl{$p \Rightarrow f$} returns results of type
|
|
230 |
|
|
231 |
\begin{center}
|
|
232 |
\bl{$S$}
|
|
233 |
\end{center}
|
|
234 |
|
|
235 |
\end{itemize}
|
|
236 |
|
|
237 |
\end{frame}
|
|
238 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
239 |
|
|
240 |
|
|
241 |
|
|
242 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
243 |
\begin{frame}[c]
|
|
244 |
\frametitle{Two Grammars}
|
|
245 |
|
|
246 |
Which languages are recognised by the following two grammars?
|
|
247 |
|
597
|
248 |
\bl{\begin{plstx}[margin=3cm]
|
|
249 |
: \meta{S} ::= \liningnums{1}\cdot\meta{S}\cdot \meta{S} | \epsilon\\
|
|
250 |
\end{plstx}}
|
531
|
251 |
|
597
|
252 |
\bl{\begin{plstx}[margin=3cm]
|
|
253 |
: \meta{U} ::= \liningnums{1}\cdot\meta{U} | \epsilon\\
|
|
254 |
\end{plstx}}
|
531
|
255 |
|
|
256 |
\end{frame}
|
|
257 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
366
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
258 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
259 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
260 |
\begin{frame}[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
261 |
\frametitle{Ambiguous Grammars}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
262 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
263 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
264 |
\begin{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
265 |
\begin{axis}[xlabel={\pcode{1}s},ylabel={time in secs},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
266 |
enlargelimits=false,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
267 |
xtick={0,100,...,1000},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
268 |
xmax=1050,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
269 |
ymax=33,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
270 |
ytick={0,5,...,30},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
271 |
scaled ticks=false,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
272 |
axis lines=left,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
273 |
width=11cm,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
274 |
height=7cm,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
275 |
legend entries={unambiguous,ambiguous},
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
276 |
legend pos=north east,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
277 |
legend cell align=left,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
278 |
x tick label style={font=\small,/pgf/number format/1000 sep={}}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
279 |
\addplot[blue,mark=*, mark options={fill=white}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
280 |
table {s-grammar1.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
281 |
\only<2>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
282 |
\addplot[red,mark=triangle*, mark options={fill=white}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
283 |
table {s-grammar2.data};}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
284 |
\end{axis}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
285 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
286 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
287 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
288 |
\end{frame}
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
289 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
290 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
291 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
292 |
\begin{frame}[c]
|
597
|
293 |
\frametitle{Arithmetic Expressions}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
294 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
295 |
A grammar for arithmetic expressions and numbers:
|
50
|
296 |
|
597
|
297 |
\bl{\begin{plstx}[margin=1cm]
|
|
298 |
: \meta{E} ::= \meta{E} \cdot + \cdot \meta{E}
|
|
299 |
| \meta{E} \cdot * \cdot \meta{E}
|
|
300 |
| ( \cdot \meta{E} \cdot ) | \meta{N}\\
|
|
301 |
: \meta{N} ::= \meta{N} \cdot \meta{N} |
|
|
302 |
0 | 1 | \ldots | 9\\
|
|
303 |
\end{plstx}}
|
49
|
304 |
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
305 |
Unfortunately it is left-recursive (and ambiguous).\medskip\\
|
597
|
306 |
A problem for \alert{recursive descent parsers} (e.g.~parser
|
|
307 |
combinators). \bigskip\pause
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
308 |
|
597
|
309 |
\end{frame}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
310 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
311 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
312 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
313 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
314 |
\begin{frame}[t]
|
597
|
315 |
\frametitle{Numbers}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
316 |
|
597
|
317 |
\bl{\begin{plstx}[margin=1cm]
|
|
318 |
: \meta{N} ::= \meta{N} \cdot \meta{N} |
|
|
319 |
0 | 1 | \ldots | 9\\
|
|
320 |
\end{plstx}}
|
49
|
321 |
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
322 |
A non-left-recursive, non-ambiguous grammar for numbers:
|
49
|
323 |
|
597
|
324 |
\bl{\begin{plstx}[margin=1cm]
|
|
325 |
: \meta{N} ::= 0 \cdot \meta{N} | 1 \cdot \meta{N} | \ldots |
|
|
326 |
0 | 1 | \ldots | 9\\
|
|
327 |
\end{plstx}}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
328 |
|
597
|
329 |
\end{frame}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
330 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
331 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
332 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
333 |
\begin{frame}[c]
|
597
|
334 |
\frametitle{Removing Left-Recursion}
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
335 |
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
336 |
The rule for numbers is directly left-recursive:
|
49
|
337 |
|
|
338 |
\begin{center}
|
50
|
339 |
\bl{\begin{tabular}{lcl}
|
597
|
340 |
$\meta{N}$ & $::=$ & $\meta{N} \cdot \meta{N} \;|\; 0 \;|\; 1\;\;\;\;(\ldots)$
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
341 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
342 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
343 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
344 |
Translate
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
345 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
346 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
347 |
\begin{tabular}{ccc}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
348 |
\bl{\begin{tabular}{lcl}
|
597
|
349 |
$\meta{N}$ & $::=$ & $\meta{N} \cdot \alpha$\\
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
350 |
& $\;|\;$ & $\beta$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
351 |
\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
352 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
353 |
& {\Large$\Rightarrow$} &
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
354 |
\bl{\begin{tabular}{lcl}
|
597
|
355 |
$\meta{N}$ & $::=$ & $\beta \cdot \meta{N}'$\\
|
|
356 |
$\meta{N}'$ & $::=$ & $\alpha \cdot \meta{N}'$\\
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
357 |
& $\;|\;$ & $\epsilon$
|
50
|
358 |
\end{tabular}}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
359 |
\end{tabular}
|
50
|
360 |
\end{center}\pause
|
|
361 |
|
597
|
362 |
Which means in this case:
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
363 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
364 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
365 |
\bl{\begin{tabular}{lcl}
|
597
|
366 |
$\meta{N}$ & $\rightarrow$ & $0 \cdot \meta{N}' \;|\; 1 \cdot \meta{N}'$\\
|
|
367 |
$\meta{N}'$ & $\rightarrow$ & $\meta{N} \cdot \meta{N}' \;|\; \epsilon$\\
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
368 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
369 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
370 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
371 |
|
597
|
372 |
\end{frame}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
373 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
374 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
375 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
685
|
376 |
%\begin{frame}[c]
|
|
377 |
%\frametitle{Operator Precedences}
|
|
378 |
%
|
|
379 |
%
|
|
380 |
%To disambiguate
|
|
381 |
%
|
|
382 |
%\begin{center}
|
|
383 |
%\bl{\begin{tabular}{lcl}
|
|
384 |
%$\meta{E}$ & $::=$ & $\meta{E} \cdot + \cdot \meta{E} \;|\;\meta{E} \cdot * \cdot \meta{E} \;|\;( \cdot \meta{E} \cdot ) \;|\;\meta{N}$ \\
|
|
385 |
%\end{tabular}}
|
|
386 |
%\end{center}
|
|
387 |
%
|
|
388 |
%Decide on how many precedence levels, say\medskip\\
|
|
389 |
%highest for \bl{$()$}, medium for \bl{*}, lowest for \bl{+}
|
|
390 |
%
|
|
391 |
%\begin{center}
|
|
392 |
%\bl{\begin{tabular}{lcl}
|
|
393 |
%$\meta{E}_{low}$ & $::=$ & $\meta{E}_{med} \cdot + \cdot \meta{E}_{low} \;|\; \meta{E}_{med}$ \\
|
|
394 |
%$\meta{E}_{med}$ & $::=$ & $\meta{E}_{hi} \cdot * \cdot \meta{E}_{med} \;|\; \meta{E}_{hi}$\\
|
|
395 |
%$\meta{E}_{hi}$ & $::=$ & $( \cdot \meta{E}_{low} \cdot ) \;|\;\meta{N}$ \\
|
|
396 |
%\end{tabular}}
|
|
397 |
%\end{center}\pause
|
|
398 |
%
|
|
399 |
%\small What happens with \bl{$1 + 3 + 4$}?
|
|
400 |
%\end{frame}
|
366
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
401 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
402 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
403 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
404 |
\begin{frame}[c]
|
597
|
405 |
\frametitle{Chomsky Normal Form}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
406 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
407 |
All rules must be of the form
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
408 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
409 |
\begin{center}
|
597
|
410 |
\bl{$\meta{A} ::= a$}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
411 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
412 |
|
50
|
413 |
or
|
|
414 |
|
|
415 |
\begin{center}
|
597
|
416 |
\bl{$\meta{A} ::= \meta{B}\cdot \meta{C}$}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
417 |
\end{center}
|
49
|
418 |
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
419 |
No rule can contain \bl{$\epsilon$}.
|
49
|
420 |
|
597
|
421 |
\end{frame}
|
49
|
422 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
423 |
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
424 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
425 |
\begin{frame}[c]
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
426 |
\frametitle{\begin{tabular}{c}$\epsilon$-Removal\end{tabular}}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
427 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
428 |
\begin{enumerate}
|
597
|
429 |
\item If \bl{$A::= \alpha \cdot B \cdot \beta$} and \bl{$B ::= \epsilon$} are in the grammar,
|
|
430 |
then add \bl{$A::= \alpha \cdot \beta$} (iterate if necessary).
|
|
431 |
\item Throw out all \bl{$B ::= \epsilon$}.
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
432 |
\end{enumerate}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
433 |
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
434 |
\small
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
435 |
\begin{center}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
436 |
\begin{tabular}{ccc}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
437 |
\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
597
|
438 |
$N$ & $::=$ & $0 \cdot N' \;|\; 1\cdot N'$\\
|
|
439 |
$N'$ & $::=$ & $N \cdot N'\;|\;\epsilon$\\
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
440 |
\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
441 |
\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
442 |
\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
443 |
\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
444 |
\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
445 |
\end{tabular}} &
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
446 |
\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
447 |
\\
|
597
|
448 |
$N$ & $::=$ & $0 \cdot N' \;|\; 1\cdot N'\;|\;0\;|\;1$\\
|
|
449 |
$N'$ & $::=$ & $N \cdot N'\;|\;N\;|\;\epsilon$\\
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
450 |
\\
|
597
|
451 |
$N$ & $::=$ & $0 \cdot N' \;|\; 1\cdot N'\;|\;0\;|\;1$\\
|
|
452 |
$N'$ & $::=$ & $N \cdot N'\;|\;N$\\
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
453 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
454 |
\end{tabular}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
455 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
456 |
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
457 |
\pause\normalsize
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
458 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
459 |
\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
597
|
460 |
$N$ & $::=$ & $0 \cdot N\;|\; 1\cdot N\;|\;0\;|\;1$\\
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
461 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
462 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
463 |
\end{center}
|
368
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
464 |
\end{frame}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
465 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
466 |
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
467 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
468 |
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
469 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
470 |
\begin{frame}[c]
|
597
|
471 |
\frametitle{CYK Algorithm}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
472 |
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
473 |
If grammar is in Chomsky normalform \ldots
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
474 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
475 |
\begin{center}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
476 |
\bl{\begin{tabular}{@ {}lcl@ {}}
|
597
|
477 |
$\meta{S}$ & $::=$ & $\meta{N}\cdot \meta{P}$ \\
|
|
478 |
$\meta{P}$ & $::=$ & $\meta{V}\cdot \meta{N}$ \\
|
|
479 |
$\meta{N}$ & $::=$ & $\meta{N}\cdot \meta{N}$ \\
|
|
480 |
$\meta{N}$ & $::=$ & $\texttt{students} \;|\; \texttt{Jeff} \;|\; \texttt{geometry} \;|\; \texttt{trains} $ \\
|
|
481 |
$\meta{V}$ & $::=$ & $\texttt{trains}$
|
49
|
482 |
\end{tabular}}
|
|
483 |
\end{center}
|
|
484 |
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
485 |
\bl{\texttt{Jeff trains geometry students}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
486 |
|
597
|
487 |
\end{frame}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
488 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
597
|
489 |
|
|
490 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
491 |
\begin{frame}[c]
|
597
|
492 |
\frametitle{CYK Algorithm}
|
49
|
493 |
|
|
494 |
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
495 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
496 |
\item fastest possible algorithm for recognition problem
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
497 |
\item runtime is \bl{$O(n^3)$}\bigskip
|
597
|
498 |
\item grammars need to be transformed into CNF
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
499 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
500 |
|
597
|
501 |
\end{frame}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
502 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
503 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
504 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
366
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
505 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
506 |
\frametitle{The Goal of this Course}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
507 |
\mbox{}\\[-26mm]\mbox{}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
508 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
509 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
510 |
\begin{tikzpicture}[scale=1,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
511 |
node/.style={
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
512 |
rectangle,rounded corners=3mm,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
513 |
very thick,draw=black!50,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
514 |
minimum height=18mm, minimum width=20mm,
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
515 |
top color=white,bottom color=black!20}]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
516 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
517 |
\node at (3.05, 1.8) {\Large\bf Write a Compiler};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
518 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
519 |
\node (0) at (-2.3,0) {};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
520 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
521 |
\node (A) at (0,0) [node] {};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
522 |
\node [below right] at (A.north west) {lexer};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
523 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
524 |
\node (B) at (3,0) [node] {};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
525 |
\node [below right=1mm] at (B.north west)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
526 |
{\mbox{}\hspace{-1mm}parser};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
527 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
528 |
\node (C) at (6,0) [node] {};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
529 |
\node [below right] at (C.north west)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
530 |
{\mbox{}\hspace{-1mm}code gen};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
531 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
532 |
\node (1) at (8.4,0) {};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
533 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
534 |
\draw [->,line width=4mm] (0) -- (A);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
535 |
\draw [->,line width=4mm] (A) -- (B);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
536 |
\draw [->,line width=4mm] (B) -- (C);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
537 |
\draw [->,line width=4mm] (C) -- (1);
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
538 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
539 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
540 |
|
598
|
541 |
We have a lexer and a parser\ldots
|
366
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
542 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
543 |
\end{frame}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
544 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
545 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
546 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
547 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
548 |
\begin{center}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
549 |
\bl{\begin{tabular}{@{}lcl@{}}
|
598
|
550 |
\meta{Stmt} & $::=$ & $\texttt{skip}$\\
|
|
551 |
& $|$ & \textit{Id}\;\texttt{:=}\;\meta{AExp}\\
|
|
552 |
& $|$ & \texttt{if}\; \meta{BExp} \;\texttt{then}\; \meta{Block} \;\texttt{else}\; \meta{Block}\\
|
|
553 |
& $|$ & \texttt{while}\; \meta{BExp} \;\texttt{do}\; \meta{Block}\\
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
554 |
& $|$ & \texttt{read}\;\textit{Id}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
555 |
& $|$ & \texttt{write}\;\textit{Id}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
556 |
& $|$ & \texttt{write}\;\textit{String}\medskip\\
|
598
|
557 |
\meta{Stmts} & $::=$ & \meta{Stmt} \;\texttt{;}\; \meta{Stmts}\\
|
|
558 |
& $|$ & \meta{Stmt}\medskip\\
|
|
559 |
\meta{Block} & $::=$ & \texttt{\{}\,\meta{Stmts}\,\texttt{\}}\\
|
|
560 |
& $|$ & \meta{Stmt}\medskip\\
|
|
561 |
\meta{AExp} & $::=$ & \ldots\\
|
|
562 |
\meta{BExp} & $::=$ & \ldots\\
|
50
|
563 |
\end{tabular}}
|
|
564 |
\end{center}
|
366
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
565 |
\end{frame}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
566 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
567 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
568 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
569 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
570 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
571 |
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
572 |
\mbox{\lstinputlisting[language=while]{../progs/fib.while}}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
573 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
574 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
575 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
576 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
577 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
578 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
579 |
\begin{frame}[c]
|
598
|
580 |
\frametitle{An Interpreter}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
581 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
582 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
583 |
\bl{\begin{tabular}{l}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
584 |
$\{$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
585 |
\;\;$x := 5 \text{;}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
586 |
\;\;$y := x * 3\text{;}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
587 |
\;\;$y := x * 4\text{;}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
588 |
\;\;$x := u * 3$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
589 |
$\}$
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
590 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
591 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
592 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
593 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
594 |
\item the interpreter has to record the value of \bl{$x$} before assigning a value to \bl{$y$}\pause
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
595 |
\item \bl{\text{eval}(stmt, env)}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
596 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
597 |
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
598 |
|
598
|
599 |
\end{frame}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
600 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
601 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
602 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
603 |
\begin{frame}[c]
|
598
|
604 |
\frametitle{An Interpreter}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
605 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
606 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
607 |
\bl{\begin{tabular}{@{}lcl@{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
608 |
$\text{eval}(n, E)$ & $\dn$ & $n$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
609 |
$\text{eval}(x, E)$ & $\dn$ & $E(x)$ \;\;\;\textcolor{black}{lookup \bl{$x$} in \bl{$E$}}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
610 |
$\text{eval}(a_1 + a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) + \text{eval}(a_2, E)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
611 |
$\text{eval}(a_1 - a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) - \text{eval}(a_2, E)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
612 |
$\text{eval}(a_1 * a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) * \text{eval}(a_2, E)$\bigskip\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
613 |
$\text{eval}(a_1 = a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) = \text{eval}(a_2, E)$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
614 |
$\text{eval}(a_1\,!\!= a_2, E)$ & $\dn$ & $\neg(\text{eval}(a_1, E) = \text{eval}(a_2, E))$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
615 |
$\text{eval}(a_1 < a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) < \text{eval}(a_2, E)$\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
616 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
617 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
618 |
|
598
|
619 |
\end{frame}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
620 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
598
|
621 |
|
|
622 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
623 |
\begin{frame}[c]
|
598
|
624 |
\frametitle{An Interpreter (2)}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
625 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
626 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
627 |
\bl{\begin{tabular}{@{}lcl@{}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
628 |
$\text{eval}(\text{skip}, E)$ & $\dn$ & $E$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
629 |
$\text{eval}(x:=a, E)$ & $\dn$ & \bl{$E(x \mapsto \text{eval}(a, E))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
630 |
\multicolumn{3}{@{}l@{}}{$\text{eval}(\text{if}\;b\;\text{then}\;cs_1\;\text{else}\;cs_2 , E) \dn$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
631 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{if}\;\text{eval}(b,E)\;\text{then}\;
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
632 |
\text{eval}(cs_1,E)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
633 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\phantom{\text{if}\;\text{eval}(b,E)\;}\text{else}\;\text{eval}(cs_2,E)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
634 |
\multicolumn{3}{@{}l@{}}{$\text{eval}(\text{while}\;b\;\text{do}\;cs, E) \dn$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
635 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{if}\;\text{eval}(b,E)$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
636 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{then}\;
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
637 |
\text{eval}(\text{while}\;b\;\text{do}\;cs, \text{eval}(cs,E))$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
638 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{else}\; E$}\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
639 |
$\text{eval}(\text{write}\; x, E)$ & $\dn$ & $\{\;\text{println}(E(x))\; ;\;E\;\}$\\
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
640 |
\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
641 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
642 |
|
598
|
643 |
\end{frame}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
644 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
645 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
646 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
647 |
\begin{frame}[c]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
648 |
\frametitle{\begin{tabular}{c}Test Program\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
649 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
650 |
\mbox{}\\[-18mm]\mbox{}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
651 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
652 |
{\lstset{language=While}%%\fontsize{10}{12}\selectfont
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
653 |
\texttt{\lstinputlisting{../progs/loops.while}}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
654 |
|
295
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
655 |
\end{frame}
|
169
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
656 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
657 |
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
658 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
659 |
\mode<presentation>{
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
660 |
\begin{frame}[t]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
661 |
\frametitle{\begin{tabular}{c}Interpreted Code\end{tabular}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
662 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
663 |
\begin{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
664 |
\begin{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
665 |
\begin{axis}[axis x line=bottom, axis y line=left, xlabel=n, ylabel=secs, legend style=small]
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
666 |
\addplot+[smooth] file {interpreted.data};
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
667 |
\end{axis}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
668 |
\end{tikzpicture}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
669 |
\end{center}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
670 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
671 |
\end{frame}}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
672 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
673 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
674 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
675 |
\begin{frame}[c]
|
685
|
676 |
\frametitle{Java Virtual Machine}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
677 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
678 |
\begin{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
679 |
\item introduced in 1995
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
680 |
\item is a stack-based VM (like Postscript, CLR of .Net)
|
685
|
681 |
\item contains a JIT compiler\\
|
|
682 |
\begin{itemize}
|
|
683 |
\item From the Cradle to the Holy Graal - the JDK Story
|
|
684 |
\item \url{https://www.youtube.com/watch?v=h419kfbLhUI}
|
|
685 |
\end{itemize}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
686 |
\item is garbage collected $\Rightarrow$ no buffer overflows
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
687 |
\item some languages compile to the JVM: Scala, Clojure\ldots
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
688 |
\end{itemize}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
689 |
|
685
|
690 |
\end{frame}
|
365
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
691 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
692 |
|
685
|
693 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
694 |
\begin{frame}[c]
|
|
695 |
\frametitle{LLVM}
|
|
696 |
|
|
697 |
\begin{itemize}
|
|
698 |
\item LLVM started by academics in 2000 (University of Illinois in
|
|
699 |
Urbana-Champaign)
|
|
700 |
\item suite of compiler tools
|
|
701 |
\item SSA-based intermediate language
|
|
702 |
\item no need to allocate registers
|
686
|
703 |
\item source languages: C, C++, Rust, Go, Swift
|
|
704 |
\item target CPUs: x86, ARM, PowerPC, \ldots
|
685
|
705 |
\end{itemize}
|
|
706 |
\end{frame}
|
|
707 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
702
|
708 |
|
598
|
709 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
666
|
710 |
%\begin{frame}[c]
|
|
711 |
% \frametitle{Coursework: MkEps}
|
|
712 |
%
|
|
713 |
%\begin{center}
|
|
714 |
%\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
|
|
715 |
% \bl{$mkeps([c_1 c_2 \ldots c_n])$} & \bl{$\dn$} & $\bl{undefined}$\\
|
|
716 |
% \bl{$mkeps(r^*)$} & \bl{$\dn$} & $\bl{Stars\,[]}$\\
|
|
717 |
% \bl{$mkeps(r^{\{n\}})$} & \bl{$\dn$} & $\bl{Stars\,(mkeps(r))^n}$\\
|
|
718 |
% \bl{$mkeps(r^{\{n..\}})$} & \bl{$\dn$} & $\bl{Stars\,(mkeps(r))^n}$\\
|
|
719 |
% \bl{$mkeps(r^{\{..n\}})$} & \bl{$\dn$} & $\bl{Stars\,[]}$\\
|
|
720 |
% \bl{$mkeps(r^{\{n..m\}})$} & \bl{$\dn$} & $\bl{Stars\,(mkeps(r))^n}$\medskip\\
|
|
721 |
%
|
|
722 |
% \bl{$mkeps(r^+)$} & \bl{$\dn$} & \bl{$mkeps(r^{\{1..\}})$}\\
|
|
723 |
% \bl{$mkeps(r^?)$} & \bl{$\dn$} & \bl{$mkeps(r^{\{..1\}})$}\\
|
|
724 |
%\end{tabular}
|
|
725 |
%\end{center}
|
|
726 |
%
|
|
727 |
%\end{frame}
|
|
728 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
729 |
%
|
|
730 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
731 |
%\begin{frame}[c]
|
|
732 |
% \frametitle{Coursework: Inj}
|
|
733 |
%
|
|
734 |
%\begin{center}
|
|
735 |
%\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
|
|
736 |
% \bl{$inj([c_1 c_2 \ldots c_n])\,c\,Empty$} & \bl{$\dn$} & $\bl{Chr\,c}$\\
|
|
737 |
% \bl{$inj(r^*)\,c\;(Seq\,v\,(Stars\,vs))$} & \bl{$\dn$} & $\bl{Stars\,(inj\,r\,c\,v::vs)}$\\
|
|
738 |
% \bl{$inj(r^{\{n\}})\,c\;(Seq\,v\,(Stars\,vs))$} & \bl{$\dn$} & $\bl{Stars\,(inj\,r\,c\,v::vs)}$\\
|
|
739 |
% \bl{$inj(r^{\{n..\}})\,c\;(Seq\,v\,(Stars\,vs))$} & \bl{$\dn$} & $\bl{Stars\,(inj\,r\,c\,v::vs)}$\\
|
|
740 |
% \bl{$inj(r^{\{..n\}})\,c\;(Seq\,v\,(Stars\,vs))$} & \bl{$\dn$} & $\bl{Stars\,(inj\,r\,c\,v::vs)}$\\
|
|
741 |
% \bl{$inj(r^{\{n..m\}})\,c\;(Seq\,v\,(Stars\,vs))$} & \bl{$\dn$} & $\bl{Stars\,(inj\,r\,c\,v::vs)}$\medskip\\
|
|
742 |
%
|
|
743 |
% \bl{$inj(r^+)\,c\,v$} & \bl{$\dn$} & \bl{$inj(r^{\{1..\}})\,c\,v$}\\
|
|
744 |
% \bl{$inj(r^?)\,c\,v$} & \bl{$\dn$} & \bl{$inj(r^{\{..1\}})\,c\,v$}\\
|
|
745 |
%\end{tabular}
|
|
746 |
%\end{center}
|
|
747 |
%
|
|
748 |
%\end{frame}
|
|
749 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
702
|
750 |
%
|
598
|
751 |
|
49
|
752 |
\end{document}
|
|
753 |
|
|
754 |
%%% Local Variables:
|
|
755 |
%%% mode: latex
|
|
756 |
%%% TeX-master: t
|
|
757 |
%%% End:
|
|
758 |
|