|
7
|
1 |
\documentclass[dvipsnames,14pt,t]{beamer}
|
|
|
2 |
\usepackage{beamerthemeplainculight}
|
|
|
3 |
\usepackage[T1]{fontenc}
|
|
|
4 |
\usepackage[latin1]{inputenc}
|
|
|
5 |
\usepackage{mathpartir}
|
|
|
6 |
\usepackage[absolute,overlay]{textpos}
|
|
|
7 |
\usepackage{ifthen}
|
|
|
8 |
\usepackage{tikz}
|
|
|
9 |
\usepackage{pgf}
|
|
|
10 |
\usepackage{calc}
|
|
|
11 |
\usepackage{ulem}
|
|
|
12 |
\usepackage{courier}
|
|
|
13 |
\usepackage{listings}
|
|
|
14 |
\renewcommand{\uline}[1]{#1}
|
|
|
15 |
\usetikzlibrary{arrows}
|
|
|
16 |
\usetikzlibrary{automata}
|
|
|
17 |
\usetikzlibrary{shapes}
|
|
|
18 |
\usetikzlibrary{shadows}
|
|
|
19 |
\usetikzlibrary{positioning}
|
|
|
20 |
\usetikzlibrary{calc}
|
|
|
21 |
\usepackage{graphicx}
|
|
|
22 |
|
|
|
23 |
\definecolor{javared}{rgb}{0.6,0,0} % for strings
|
|
|
24 |
\definecolor{javagreen}{rgb}{0.25,0.5,0.35} % comments
|
|
|
25 |
\definecolor{javapurple}{rgb}{0.5,0,0.35} % keywords
|
|
|
26 |
\definecolor{javadocblue}{rgb}{0.25,0.35,0.75} % javadoc
|
|
|
27 |
|
|
|
28 |
\lstset{language=Java,
|
|
|
29 |
basicstyle=\ttfamily,
|
|
|
30 |
keywordstyle=\color{javapurple}\bfseries,
|
|
|
31 |
stringstyle=\color{javagreen},
|
|
|
32 |
commentstyle=\color{javagreen},
|
|
|
33 |
morecomment=[s][\color{javadocblue}]{/**}{*/},
|
|
|
34 |
numbers=left,
|
|
|
35 |
numberstyle=\tiny\color{black},
|
|
|
36 |
stepnumber=1,
|
|
|
37 |
numbersep=10pt,
|
|
|
38 |
tabsize=2,
|
|
|
39 |
showspaces=false,
|
|
|
40 |
showstringspaces=false}
|
|
|
41 |
|
|
|
42 |
\lstdefinelanguage{scala}{
|
|
|
43 |
morekeywords={abstract,case,catch,class,def,%
|
|
|
44 |
do,else,extends,false,final,finally,%
|
|
|
45 |
for,if,implicit,import,match,mixin,%
|
|
|
46 |
new,null,object,override,package,%
|
|
|
47 |
private,protected,requires,return,sealed,%
|
|
|
48 |
super,this,throw,trait,true,try,%
|
|
|
49 |
type,val,var,while,with,yield},
|
|
|
50 |
otherkeywords={=>,<-,<\%,<:,>:,\#,@},
|
|
|
51 |
sensitive=true,
|
|
|
52 |
morecomment=[l]{//},
|
|
|
53 |
morecomment=[n]{/*}{*/},
|
|
|
54 |
morestring=[b]",
|
|
|
55 |
morestring=[b]',
|
|
|
56 |
morestring=[b]"""
|
|
|
57 |
}
|
|
|
58 |
|
|
|
59 |
\lstset{language=Scala,
|
|
|
60 |
basicstyle=\ttfamily,
|
|
|
61 |
keywordstyle=\color{javapurple}\bfseries,
|
|
|
62 |
stringstyle=\color{javagreen},
|
|
|
63 |
commentstyle=\color{javagreen},
|
|
|
64 |
morecomment=[s][\color{javadocblue}]{/**}{*/},
|
|
|
65 |
numbers=left,
|
|
|
66 |
numberstyle=\tiny\color{black},
|
|
|
67 |
stepnumber=1,
|
|
|
68 |
numbersep=10pt,
|
|
|
69 |
tabsize=2,
|
|
|
70 |
showspaces=false,
|
|
|
71 |
showstringspaces=false}
|
|
|
72 |
|
|
|
73 |
% beamer stuff
|
|
11
|
74 |
\renewcommand{\slidecaption}{AFL 02, King's College London, 3.~October 2012}
|
|
|
75 |
\newcommand{\bl}[1]{\textcolor{blue}{#1}}
|
|
|
76 |
\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
|
|
7
|
77 |
|
|
|
78 |
\begin{document}
|
|
|
79 |
|
|
|
80 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
81 |
\mode<presentation>{
|
|
|
82 |
\begin{frame}<1>[t]
|
|
|
83 |
\frametitle{%
|
|
|
84 |
\begin{tabular}{@ {}c@ {}}
|
|
|
85 |
\\[-3mm]
|
|
|
86 |
\LARGE Automata and \\[-2mm]
|
|
11
|
87 |
\LARGE Formal Languages (2)\\[-3mm]
|
|
7
|
88 |
\end{tabular}}
|
|
|
89 |
|
|
|
90 |
\begin{center}
|
|
|
91 |
\includegraphics[scale=0.3]{pics/ante1.jpg}\hspace{5mm}
|
|
|
92 |
\includegraphics[scale=0.31]{pics/ante2.jpg}\\
|
|
|
93 |
\footnotesize\textcolor{gray}{Antikythera automaton, 100 BC (Archimedes?)}
|
|
|
94 |
\end{center}
|
|
|
95 |
|
|
|
96 |
\normalsize
|
|
|
97 |
\begin{center}
|
|
|
98 |
\begin{tabular}{ll}
|
|
|
99 |
Email: & christian.urban at kcl.ac.uk\\
|
|
|
100 |
Of$\!$fice: & S1.27 (1st floor Strand Building)\\
|
|
|
101 |
Slides: & KEATS
|
|
|
102 |
\end{tabular}
|
|
|
103 |
\end{center}
|
|
|
104 |
|
|
|
105 |
|
|
|
106 |
\end{frame}}
|
|
|
107 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
108 |
|
|
|
109 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
110 |
\mode<presentation>{
|
|
15
|
111 |
\begin{frame}[t]
|
|
7
|
112 |
\frametitle{\begin{tabular}{c}Regular Expressions\end{tabular}}
|
|
|
113 |
|
|
15
|
114 |
Their inductive definition:
|
|
|
115 |
|
|
|
116 |
|
|
|
117 |
\begin{textblock}{6}(2,5)
|
|
7
|
118 |
\begin{tabular}{@ {}rrl@ {\hspace{13mm}}l}
|
|
|
119 |
\bl{r} & \bl{$::=$} & \bl{$\varnothing$} & null\\
|
|
|
120 |
& \bl{$\mid$} & \bl{$\epsilon$} & empty string / "" / []\\
|
|
|
121 |
& \bl{$\mid$} & \bl{c} & character\\
|
|
|
122 |
& \bl{$\mid$} & \bl{r$_1$ $\cdot$ r$_2$} & sequence\\
|
|
|
123 |
& \bl{$\mid$} & \bl{r$_1$ + r$_2$} & alternative / choice\\
|
|
|
124 |
& \bl{$\mid$} & \bl{r$^*$} & star (zero or more)\\
|
|
|
125 |
\end{tabular}
|
|
|
126 |
\end{textblock}
|
|
|
127 |
|
|
|
128 |
\end{frame}}
|
|
|
129 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
130 |
|
|
|
131 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
132 |
\mode<presentation>{
|
|
|
133 |
\begin{frame}[c]
|
|
|
134 |
\frametitle{\begin{tabular}{c}The Meaning of a\\[-2mm] Regular Expression\end{tabular}}
|
|
|
135 |
|
|
|
136 |
\begin{textblock}{15}(1,4)
|
|
|
137 |
\begin{tabular}{@ {}rcl}
|
|
|
138 |
\bl{$L$($\varnothing$)} & \bl{$\dn$} & \bl{$\varnothing$}\\
|
|
|
139 |
\bl{$L$($\epsilon$)} & \bl{$\dn$} & \bl{$\{$""$\}$}\\
|
|
|
140 |
\bl{$L$(c)} & \bl{$\dn$} & \bl{$\{$"c"$\}$}\\
|
|
|
141 |
\bl{$L$(r$_1$ + r$_2$)} & \bl{$\dn$} & \bl{$L$(r$_1$) $\cup$ $L$(r$_2$)}\\
|
|
11
|
142 |
\bl{$L$(r$_1$ $\cdot$ r$_2$)} & \bl{$\dn$} & \bl{$L$(r$_1$) @ $L$(r$_2$)}\\
|
|
|
143 |
\bl{$L$(r$^*$)} & \bl{$\dn$} & \bl{$\bigcup_{n \ge 0}$ $L$(r)$^n$}\\
|
|
7
|
144 |
\end{tabular}\bigskip
|
|
|
145 |
|
|
11
|
146 |
\hspace{5mm}\textcolor{gray}{$L$(r)$^0$ $\;\dn\;$ $\{$""$\}$}\\
|
|
|
147 |
\textcolor{gray}{$L$(r)$^{n+1}$ $\;\dn\;$ $L$(r) @ $L$(r)$^n$}
|
|
|
148 |
\end{textblock}
|
|
7
|
149 |
|
|
|
150 |
\end{frame}}
|
|
|
151 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
152 |
|
|
11
|
153 |
\newcommand{\YES}{\textcolor{gray}{yes}}
|
|
|
154 |
\newcommand{\NO}{\textcolor{gray}{no}}
|
|
|
155 |
\newcommand{\FORALLR}{\textcolor{gray}{$\forall$ r.}}
|
|
7
|
156 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
157 |
\mode<presentation>{
|
|
|
158 |
\begin{frame}[c]
|
|
11
|
159 |
\frametitle{\begin{tabular}{c}Reg Exp Equivalences\end{tabular}}
|
|
7
|
160 |
|
|
|
161 |
\begin{center}
|
|
11
|
162 |
\begin{tabular}{lrcl@ {\hspace{7mm}}l}
|
|
|
163 |
&\bl{(a + b) + c} & \bl{$\equiv^?$} & \bl{a + (b + c)} & \onslide<2->{\YES}\\
|
|
|
164 |
&\bl{a + a} & \bl{$\equiv^?$} & \bl{a} & \onslide<3->{\YES}\\
|
|
|
165 |
&\bl{(a $\cdot$ b) $\cdot$ c} & \bl{$\equiv^?$} & \bl{a $\cdot$ (b $\cdot$ c)} & \onslide<4->{\YES}\\
|
|
|
166 |
&\bl{a $\cdot$ a} & \bl{$\equiv^?$} & \bl{a} & \onslide<5->{\NO}\\
|
|
|
167 |
&\bl{$\epsilon^*$} & \bl{$\equiv^?$} & \bl{$\epsilon$} & \onslide<6->{\YES}\\
|
|
|
168 |
&\bl{$\varnothing^*$} & \bl{$\equiv^?$} & \bl{$\varnothing$} & \onslide<7->{\NO}\\
|
|
|
169 |
\FORALLR &\bl{r $\cdot$ $\epsilon$} & \bl{$\equiv^?$} & \bl{r} & \onslide<8->{\YES}\\
|
|
|
170 |
\FORALLR &\bl{r + $\epsilon$} & \bl{$\equiv^?$} & \bl{r} & \onslide<9->{\NO}\\
|
|
|
171 |
\FORALLR &\bl{r + $\varnothing$} & \bl{$\equiv^?$} & \bl{r} & \onslide<10->{\YES}\\
|
|
|
172 |
\FORALLR &\bl{r $\cdot$ $\varnothing$} & \bl{$\equiv^?$} & \bl{r} & \onslide<11->{\NO}\\
|
|
|
173 |
&\bl{c $\cdot$ (a + b)} & \bl{$\equiv^?$} & \bl{(c $\cdot$ a) + (c $\cdot$ b)} & \onslide<12->{\YES}\\
|
|
|
174 |
&\bl{a$^*$} & \bl{$\equiv^?$} & \bl{$\epsilon$ + (a $\cdot$ a$^*$)} & \onslide<13->{\YES}
|
|
|
175 |
\end{tabular}
|
|
7
|
176 |
\end{center}
|
|
|
177 |
|
|
|
178 |
\end{frame}}
|
|
|
179 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
180 |
|
|
|
181 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
182 |
\mode<presentation>{
|
|
|
183 |
\begin{frame}[c]
|
|
11
|
184 |
\frametitle{\begin{tabular}{c}The Meaning of Matching\end{tabular}}
|
|
|
185 |
|
|
|
186 |
\large
|
|
|
187 |
a regular expression \bl{r} matches a string \bl{s} is defined as
|
|
|
188 |
|
|
|
189 |
\begin{center}
|
|
|
190 |
\bl{s $\in$ $L$(r)}\\
|
|
|
191 |
\end{center}\bigskip\bigskip\pause
|
|
|
192 |
|
|
|
193 |
\small
|
|
|
194 |
if \bl{r$_1$ $\equiv$ r$_2$}, then \bl{$s$ $\in$ $L$(r$_1$)} iff \bl{$s$ $\in$ $L$(r$_2$)}
|
|
|
195 |
|
|
|
196 |
\end{frame}}
|
|
|
197 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
198 |
|
|
|
199 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
200 |
\mode<presentation>{
|
|
|
201 |
\begin{frame}[t]
|
|
|
202 |
\frametitle{\begin{tabular}{c}A Matching Algorithm\end{tabular}}
|
|
|
203 |
|
|
|
204 |
\begin{itemize}
|
|
|
205 |
\item given a regular expression \bl{r} and a string \bl{s}, say yes or no for whether
|
|
|
206 |
\begin{center}
|
|
|
207 |
\bl{s $\in$ $L$(r)}
|
|
|
208 |
\end{center}\bigskip\bigskip\pause
|
|
|
209 |
\only<2>{\item foo}%
|
|
|
210 |
\only<3>{\item bar}
|
|
|
211 |
\end{itemize}
|
|
|
212 |
|
|
|
213 |
|
|
|
214 |
\end{frame}}
|
|
|
215 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
216 |
|
|
|
217 |
|
|
|
218 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
219 |
\mode<presentation>{
|
|
|
220 |
\begin{frame}[c]
|
|
15
|
221 |
\frametitle{\begin{tabular}{c}A Matching Algorithm\end{tabular}}
|
|
7
|
222 |
|
|
|
223 |
\small
|
|
|
224 |
whether a regular expression matches the empty string:\medskip
|
|
|
225 |
|
|
|
226 |
|
|
|
227 |
{\lstset{language=Scala}\fontsize{8}{10}\selectfont
|
|
|
228 |
\texttt{\lstinputlisting{app5.scala}}}
|
|
|
229 |
|
|
|
230 |
|
|
|
231 |
|
|
|
232 |
\end{frame}}
|
|
|
233 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
234 |
|
|
|
235 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
236 |
\mode<presentation>{
|
|
|
237 |
\begin{frame}[c]
|
|
15
|
238 |
\frametitle{\begin{tabular}{c}The Derivative of a Rexp\end{tabular}}
|
|
7
|
239 |
|
|
|
240 |
\large
|
|
|
241 |
If \bl{r} matches the string \bl{c::s}, what is a regular expression that matches \bl{s}?\bigskip\bigskip\bigskip\bigskip
|
|
|
242 |
|
|
|
243 |
\small
|
|
|
244 |
\bl{der c r} gives the answer
|
|
|
245 |
\end{frame}}
|
|
|
246 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
247 |
|
|
|
248 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
249 |
\mode<presentation>{
|
|
|
250 |
\begin{frame}[c]
|
|
|
251 |
\frametitle{\begin{tabular}{c}The Derivative\end{tabular}}
|
|
|
252 |
|
|
|
253 |
\begin{center}
|
|
|
254 |
\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}
|
|
|
255 |
\bl{der c ($\varnothing$)} & \bl{$\dn$} & \bl{$\varnothing$} & \\
|
|
|
256 |
\bl{der c ($\epsilon$)} & \bl{$\dn$} & \bl{$\varnothing$} & \\
|
|
|
257 |
\bl{der c (d)} & \bl{$\dn$} & \bl{if c $=$ d then [] else $\varnothing$} & \\
|
|
|
258 |
\bl{der c (r$_1$ + r$_2$)} & \bl{$\dn$} & \bl{(der c r$_1$) + (der c r$_2$)} & \\
|
|
|
259 |
\bl{der c (r$_1$ $\cdot$ r$_2$)} & \bl{$\dn$} & \bl{((der c r$_1$) $\cdot$ r$_2$) + } & \\
|
|
|
260 |
& & \bl{\hspace{3mm}(if nullable r$_1$ then der c r$_2$ else $\varnothing$)}\\
|
|
|
261 |
\bl{der c (r$^*$)} & \bl{$\dn$} & \bl{(der c r) $\cdot$ (r$^*$)} &\smallskip\\\pause
|
|
|
262 |
|
|
|
263 |
\bl{ders [] r} & \bl{$\dn$} & \bl{r} & \\
|
|
|
264 |
\bl{ders (c::s) r} & \bl{$\dn$} & \bl{ders s (der c r)} & \\
|
|
|
265 |
\end{tabular}
|
|
|
266 |
\end{center}
|
|
|
267 |
|
|
|
268 |
\end{frame}}
|
|
|
269 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
270 |
|
|
|
271 |
|
|
|
272 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
273 |
\mode<presentation>{
|
|
|
274 |
\begin{frame}[c]
|
|
|
275 |
\frametitle{\begin{tabular}{c}The Derivative\end{tabular}}
|
|
|
276 |
|
|
|
277 |
|
|
|
278 |
{\lstset{language=Scala}\fontsize{8}{10}\selectfont
|
|
|
279 |
\texttt{\lstinputlisting{app6.scala}}}
|
|
|
280 |
|
|
|
281 |
|
|
|
282 |
|
|
|
283 |
\end{frame}}
|
|
|
284 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
285 |
|
|
|
286 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
287 |
\mode<presentation>{
|
|
|
288 |
\begin{frame}[c]
|
|
|
289 |
\frametitle{\begin{tabular}{c}The Rexp Matcher\end{tabular}}
|
|
|
290 |
|
|
|
291 |
|
|
|
292 |
{\lstset{language=Scala}\fontsize{8}{10}\selectfont
|
|
|
293 |
\texttt{\lstinputlisting{app7.scala}}}
|
|
|
294 |
|
|
|
295 |
|
|
|
296 |
|
|
|
297 |
\end{frame}}
|
|
|
298 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
299 |
|
|
|
300 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
301 |
\mode<presentation>{
|
|
|
302 |
\begin{frame}[c]
|
|
|
303 |
\frametitle{\begin{tabular}{c}This Course\end{tabular}}
|
|
|
304 |
|
|
|
305 |
We will have a look at:
|
|
|
306 |
|
|
|
307 |
\begin{itemize}
|
|
|
308 |
\item regular expressions / regular expression matching
|
|
|
309 |
\item automata
|
|
|
310 |
\item the Myhill-Nerode theorem
|
|
|
311 |
\item parsing
|
|
|
312 |
\item grammars
|
|
|
313 |
\item a small interpreter / web browser
|
|
|
314 |
\end{itemize}
|
|
|
315 |
|
|
|
316 |
\end{frame}}
|
|
|
317 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
318 |
|
|
|
319 |
|
|
|
320 |
|
|
|
321 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
322 |
\mode<presentation>{
|
|
|
323 |
\begin{frame}[c]
|
|
|
324 |
\frametitle{\begin{tabular}{c}Exam\end{tabular}}
|
|
|
325 |
|
|
|
326 |
\begin{itemize}
|
|
|
327 |
\item The question ``Is this relevant for the exam?'' is not appreciated!\bigskip\\
|
|
|
328 |
|
|
|
329 |
Whatever is in the homework sheets (and is not marked optional) is relevant for the
|
|
|
330 |
exam.\\ No code needs to be written.
|
|
|
331 |
\end{itemize}
|
|
|
332 |
|
|
|
333 |
\end{frame}}
|
|
|
334 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
335 |
|
|
|
336 |
|
|
|
337 |
|
|
|
338 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
339 |
\mode<presentation>{
|
|
|
340 |
\begin{frame}[t]
|
|
|
341 |
\frametitle{\begin{tabular}{c}Maps in Scala\end{tabular}}
|
|
|
342 |
|
|
|
343 |
\begin{itemize}
|
|
|
344 |
\item {\bf\texttt{map}} takes a function, say f, and applies it to every element of the list:
|
|
|
345 |
\end{itemize}
|
|
|
346 |
|
|
|
347 |
\begin{textblock}{15}(2,7)
|
|
|
348 |
\fontsize{13}{14}\selectfont
|
|
|
349 |
\bf\texttt{List(1, 2, 3, 4, 5, 6, 7, 8, 9)}
|
|
|
350 |
\end{textblock}
|
|
|
351 |
|
|
|
352 |
\begin{textblock}{15}(2,10)
|
|
|
353 |
\fontsize{13}{14}\selectfont
|
|
|
354 |
\bf\texttt{List(1, 4, 9, 16, 25, 36, 49, 64, 81)}
|
|
|
355 |
\end{textblock}
|
|
|
356 |
|
|
|
357 |
\end{frame}}
|
|
|
358 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
359 |
|
|
|
360 |
|
|
|
361 |
\end{document}
|
|
|
362 |
|
|
|
363 |
%%% Local Variables:
|
|
|
364 |
%%% mode: latex
|
|
|
365 |
%%% TeX-master: t
|
|
|
366 |
%%% End:
|
|
|
367 |
|