afl-material: comparison slides/slides02.tex

equal deleted inserted replaced

-:7c80b9b6f713
+:885ac2b6c27d
 & \bl{$\mid$} & \bl{$r_1 + r_2$}      & alternative / choice\\
 & \bl{$\mid$} & \bl{$r^*$}            & star (zero or more)\\
 \end{tabular}
 \end{textblock}
+\only<2->{\footnotesize
+\begin{textblock}{9}(2,0.5)
+\begin{bubble}[9.8cm]
+\lstinputlisting{../progs/app01.scala}
+\end{bubble}
+\end{textblock}}
 \end{frame}
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 \bl{$der\,c\,r$} gives the answer, Brzozowski 1964
 \end{frame}
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-\mode<presentation>{
 \begin{frame}[c]
 \frametitle{The Derivative of a Rexp}
 \begin{center}
 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}
 \bl{$\textit{ders}\, []\, r$}     & \bl{$\dn$} & \bl{$r$} & \\
 \bl{$\textit{ders}\, (c\!::\!s)\, r$} & \bl{$\dn$} & \bl{$\textit{ders}\,s\,(der\,c\,r)$} & \\
 \end{tabular}
 \end{center}
-\end{frame}}
+\end{frame}
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 \begin{frame}[c]
 \frametitle{Examples}
 \end{frame}
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-\mode<presentation>{
 \begin{frame}[t]
 \frametitle{The Algorithm}
 \begin{center}
 \begin{tabular}{@{}rll@{}}
 \bl{\textit{false}}$\\
 \end{tabular}
 \end{center}
-\end{frame}}
+\end{frame}
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 \begin{frame}[c]
 \frametitle{The Idea of the Algorithm}
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 \begin{frame}[c]
-\frametitle{\begin{tabular}{c}\bl{$(a?\{n\}) \cdot a\{n\}$}\end{tabular}}
+\frametitle{\bl{$(a?\{n\}) \cdot a\{n\}$}}
 \begin{center}
 \begin{tikzpicture}
 \begin{axis}[
 xlabel={\pcode{a}s},
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
+\begin{frame}[c]
-\begin{frame}[c]
+\frametitle{Examples}
-\frametitle{\begin{tabular}{c}Examples\end{tabular}}
 Recall the example of \bl{$r \dn ((a \cdot b) + b)^*$} with
 \begin{center}
 \begin{tabular}{l}
 \end{tabular}
 \end{center}
 What are these regular expressions equivalent to?
-\end{frame}}
+\end{frame}
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-\mode<presentation>{
+\begin{frame}[t]
-\begin{frame}[t]
+\frametitle{\bl{$(a?\{n\}) \cdot a\{n\}$}}
-\frametitle{\begin{tabular}{c}\bl{$(a?\{n\}) \cdot a\{n\}$}\end{tabular}}
 \begin{center}
 \begin{tikzpicture}
 \begin{axis}[
 xlabel={\pcode{a}s},
 \addplot[black,mark=square*,mark options={fill=white}] table {re3.data};
 \end{axis}
 \end{tikzpicture}
 \end{center}
-\end{frame}}
+\end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
+\begin{frame}[t]
-\begin{frame}[t]
+\frametitle{Proofs about Rexps}
-\frametitle{\begin{tabular}{c}Proofs about Rexps\end{tabular}}
 Remember their inductive definition:\\[5cm]
 \begin{textblock}{6}(5,5)
 \begin{tabular}{@ {}rrl}
 \bl{$r$} & \bl{$::=$}  & \bl{$\varnothing$}\\
-& \bl{$\mid$} & \bl{$\epsilon$}       \\
+& \bl{$\mid$} & \bl{$\epsilon$}     \\
-& \bl{$\mid$} & \bl{$c$}                        \\
+& \bl{$\mid$} & \bl{$c$}            \\
 & \bl{$\mid$} & \bl{$r_1 \cdot r_2$}\\
-& \bl{$\mid$} & \bl{$r_1 + r_2$}  \\
+& \bl{$\mid$} & \bl{$r_1 + r_2$}    \\
-& \bl{$\mid$} & \bl{$r^*$}                  \\
+& \bl{$\mid$} & \bl{$r^*$}          \\
 \end{tabular}
 \end{textblock}
 If we want to prove something, say a property \bl{$P(r)$}, for all regular expressions \bl{$r$} then \ldots
-\end{frame}}
+\end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
+\begin{frame}[c]
-\begin{frame}[c]
+\frametitle{Proofs about Rexp (2)}
-\frametitle{\begin{tabular}{c}Proofs about Rexp (2)\end{tabular}}
 \begin{itemize}
 \item \bl{$P$} holds for \bl{$\varnothing$}, \bl{$\epsilon$} and \bl{c}\bigskip
 \item \bl{$P$} holds for \bl{$r_1 + r_2$} under the assumption that \bl{$P$} already
 holds for \bl{$r_1$} and \bl{$r_2$}.\bigskip
 holds for \bl{$r_1$} and \bl{$r_2$}.\bigskip
 \item \bl{$P$} holds for \bl{$r^*$} under the assumption that \bl{$P$} already
 holds for \bl{$r$}.
 \end{itemize}
-\end{frame}}
+\end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
+\begin{frame}[c]
-\begin{frame}[c]
+\frametitle{Proofs about Rexp (3)}
-\frametitle{\begin{tabular}{c}Proofs about Rexp (3)\end{tabular}}
 Assume \bl{$P(r)$} is the property:
 \begin{center}
 \bl{$nullable(r)$} if and only if \bl{$[] \in L(r)$}
 \end{center}
-\end{frame}}
+\end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
+\begin{frame}[c]
-\begin{frame}[c]
+\frametitle{Proofs about Rexp (4)}
-\frametitle{\begin{tabular}{c}Proofs about Rexp (4)\end{tabular}}
 \begin{center}
 \bl{\begin{tabular}{r@{\hspace{1mm}}c@{\hspace{1mm}}l}
 $rev(\varnothing)$   & $\dn$ & $\varnothing$\\
 $rev(\epsilon)$         & $\dn$ & $\epsilon$\\
 \bl{$L(rev(r)) = \{s^{-1} \;|\; s \in L(r)\}$}
 \end{center}
 by induction on \bl{$r$}.
-\end{frame}}
+\end{frame}
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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
+\begin{frame}[c]
-\begin{frame}[c]
+\frametitle{Proofs about Rexp (5)}
-\frametitle{\begin{tabular}{c}Proofs about Rexp (5)\end{tabular}}
 Let \bl{$Der\,c\,A$} be the set defined as
 \begin{center}
 \bl{$Der\,c\,A \dn \{ s \;|\;  c\!::\!s \in A\}$ }
 \bl{$L(der\,c\,r) = Der\,c\,(L(r))$}
 \end{center}
 by induction on \bl{$r$}.
-\end{frame}}
+\end{frame}
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 \mode<presentation>{

changeset 337	885ac2b6c27d
parent 336	7c80b9b6f713
child 338	f16120cb4e19