40 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    40 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    41 \begin{frame}[c]

    41 % \begin{frame}[c]

    42 \frametitle{Survey: Thanks!}

    42 % \frametitle{Survey: Thanks!}

    43 \small

    43 % \small

    44 

    44 

    45 \begin{itemize}

    45 % \begin{itemize}

    46 \item {\bf My Voice} ``could be a bit louder''

    46 % \item {\bf My Voice} ``could be a bit louder''

    47 \item {\bf Writing} ``sometimes a bit difficult to read''

    47 % \item {\bf Writing} ``sometimes a bit difficult to read''

    48 \item {\bf Recording} ``video caps of blackboard''

    48 % \item {\bf Recording} ``video caps of blackboard''

    49 \item ``It's all great''

    49 % \item ``It's all great''

    50 \end{itemize}

    50 % \end{itemize}

    52 \end{frame}

    52 % \end{frame}

    53 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

    53 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   206 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   206 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   207 \begin{frame}[t]

   207 % \begin{frame}[t]

   208 

   208 

   209 \begin{center}

   209 % \begin{center}

   210 \bl{$\only<1>{(b \cdot c)}%

   210 % \bl{$\only<1>{(b \cdot c)}%

   211      \only<2-3>{(\underline{b \cdot c})}%

   211 %      \only<2-3>{(\underline{b \cdot c})}%

   212      \only<1-3>{+}% 

   212 %      \only<1-3>{+}% 

   213      \only<1>{(\ZERO + \ONE)}%

   213 %      \only<1>{(\ZERO + \ONE)}%

   214      \only<2-3>{(\underline{\ZERO + \ONE})}$}%

   214 %      \only<2-3>{(\underline{\ZERO + \ONE})}$}%

   215 \only<4->{%

   215 % \only<4->{%

   216 \bl{$\underline{(b \cdot c) + (\ZERO + \ONE)}$}%

   216 % \bl{$\underline{(b \cdot c) + (\ZERO + \ONE)}$}%

   217 }

   217 % }

   218 $\mapsto$

   218 % $\mapsto$

   219 \bl{$(b \cdot c) + \ONE$}

   219 % \bl{$(b \cdot c) + \ONE$}

   220 \end{center}\bigskip

   220 % \end{center}\bigskip

   221 

   221 

   222 \onslide<3->{%

   222 % \onslide<3->{%

   223 \begin{center}

   223 % \begin{center}

   224 \begin{tabular}{lcl}

   224 % \begin{tabular}{lcl}

   225 \bl{$f_{s1}$} & \bl{$=$} & \bl{$\lambda v.v$}\\

   225 % \bl{$f_{s1}$} & \bl{$=$} & \bl{$\lambda v.v$}\\

   226 \bl{$f_{s2}$} & \bl{$=$} & \bl{$\lambda v. \textit{Right}(v)$}

   226 % \bl{$f_{s2}$} & \bl{$=$} & \bl{$\lambda v. \textit{Right}(v)$}

   227 \end{tabular}

   227 % \end{tabular}

   228 \end{center}}

   228 % \end{center}}

   229 

   229 

   230 \only<4>{%

   230 % \only<4>{%

   231 \begin{center}

   231 % \begin{center}

   232 \begin{tabular}{@{}l@{\hspace{1mm}}l@{}}

   232 % \begin{tabular}{@{}l@{\hspace{1mm}}l@{}}

   233 \bl{$f_{alt}(f_{s1}, f_{s2}) \dn$}\\

   233 % \bl{$f_{alt}(f_{s1}, f_{s2}) \dn$}\\

   234 \quad \bl{$\lambda v.\,$} 

   234 % \quad \bl{$\lambda v.\,$} 

   235         case \bl{$v = Left(v')$}: 

   235 %         case \bl{$v = Left(v')$}: 

   236       & return \bl{$Left(f_{s1}(v'))$}\\

   236 %       & return \bl{$Left(f_{s1}(v'))$}\\

   237 \quad \phantom{$\lambda v.\,$} 

   237 % \quad \phantom{$\lambda v.\,$} 

   238         case \bl{$v = Right(v')$}: 

   238 %         case \bl{$v = Right(v')$}: 

   239       & return \bl{$Right(f_{s2}(v'))$}\\ 

   239 %       & return \bl{$Right(f_{s2}(v'))$}\\ 

   240 \end{tabular}

   240 % \end{tabular}

   241 \end{center}}%

   241 % \end{center}}%

   242 \only<5->{%

   242 % \only<5->{%

   243 \begin{center}

   243 % \begin{center}

   244 \begin{tabular}{@{}l@{\hspace{1mm}}l@{}}

   244 % \begin{tabular}{@{}l@{\hspace{1mm}}l@{}}

   245 \only<5->{\phantom{\bl{$f_{alt}(f_{s1}, f_{s2}) \dn$}}}\\

   245 % \only<5->{\phantom{\bl{$f_{alt}(f_{s1}, f_{s2}) \dn$}}}\\

   246 \quad \bl{$\lambda v.\,$} 

   246 % \quad \bl{$\lambda v.\,$} 

   247         case \bl{$v = Left(v')$}: 

   247 %         case \bl{$v = Left(v')$}: 

   248       & return \bl{$Left(v')$}\\

   248 %       & return \bl{$Left(v')$}\\

   249 \quad \phantom{$\lambda v.\,$} 

   249 % \quad \phantom{$\lambda v.\,$} 

   250         case \bl{$v = Right(v')$}: 

   250 %         case \bl{$v = Right(v')$}: 

   251       & return \bl{$Right(Right(v'))$}\\ 

   251 %       & return \bl{$Right(Right(v'))$}\\ 

   252 \end{tabular}

   252 % \end{tabular}

   253 \end{center}}%

   253 % \end{center}}%

   254 

   254 

   255 \only<6->{%

   255 % \only<6->{%

   256 \begin{center}

   256 % \begin{center}

   257 \begin{tabular}{@{}l@{\hspace{4mm}}l@{}}

   257 % \begin{tabular}{@{}l@{\hspace{4mm}}l@{}}

   258 \bl{$\textit{mkeps}$} simplified case: &

   258 % \bl{$\textit{mkeps}$} simplified case: &

   259 \bl{$\textit{Right}(\textit{Empty})$}\\

   259 % \bl{$\textit{Right}(\textit{Empty})$}\\

   260 rectified case: &

   260 % rectified case: &

   261 \bl{$\textit{Right}(\textit{Right}(\textit{Empty}))$}

   261 % \bl{$\textit{Right}(\textit{Right}(\textit{Empty}))$}

   262 \end{tabular}

   262 % \end{tabular}

   263 \end{center}}%

   263 % \end{center}}%

   264 

   264 

   265 \end{frame}

   265 % \end{frame}

   266 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   266 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   374 \frametitle{Two Rules}

   374 \frametitle{Coursework: Nullable}

   375 

   375 

   376 \begin{itemize}

   376 \begin{center}

   377 \item Longest match rule (``maximal munch rule''): The 

   377 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}

   378 longest initial substring matched by any regular expression is taken

   378   \bl{$nullable([c_1 c_2 \ldots c_n])$}  & \bl{$\dn$} & $?$\\

   379 as next token.\bigskip

   379   \bl{$nullable(r^+)$}                   & \bl{$\dn$} & $?$\\

   380 

   380   \bl{$nullable(r^?)$}                   & \bl{$\dn$} & $?$\\

   381 \item Rule priority:

   381   \bl{$nullable(r^{\{n\}})$}              & \bl{$\dn$} & $?$\\

   382 For a particular longest initial substring, the first regular

   382   \bl{$nullable(r^{\{n..\}})$}            & \bl{$\dn$} & $?$\\

   383 expression that can match determines the token.

   383   \bl{$nullable(r^{\{..n\}})$}            & \bl{$\dn$} & $?$\\

   384 

   384   \bl{$nullable(r^{\{n..m\}})$}           & \bl{$\dn$} & $?$\\

   385 \end{itemize}

   385   \bl{$nullable(\sim{}r)$}               & \bl{$\dn$} & $?$\\

   386 

   386                                                         

   387 %\url{http://www.technologyreview.com/tr10/?year=2011}

   387 \end{tabular}

   388 \end{center}

   389 

   390 \end{frame}

   391 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   392 

   393 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   394 \begin{frame}[c]

   395 %%\frametitle{Coursework: der}

   396 

   397 \begin{center}

   398 \begin{tabular}{@ {}l@ {\hspace{1mm}}c@ {\hspace{1mm}}l@ {}}

   399   \bl{$der\, c\, ([c_1 c_2 \ldots c_n])$}  & \bl{$\dn$} & $?$\\

   400   \bl{$der\, c\, (r^+)$}                   & \bl{$\dn$} & $?$\\

   401   \bl{$der\, c\, (r^?)$}                   & \bl{$\dn$} & $?$\\

   402   \bl{$der\, c\, (r^{\{n\}})$}              & \bl{$\dn$} &

   403      \bl{$if\;n=0\;then\;\ZERO\;else\;(der\,c\,r)\cdot r^{\{n-1\}}$}\\

   404   \bl{$der\, c\, (r^{\{n..\}})$}            & \bl{$\dn$} &

   405      \bl{$if\;n=0\;then (der\,c\,r)\cdot r^*$}\\

   406   & & \bl{$\phantom{if\;n=0\;}else \;(der\,c\,r)\cdot r^{\{n-1..\}}$}\\

   407   \bl{$der\, c\, (r^{\{..n\}})$}            & \bl{$\dn$} &

   408      \bl{$if\;n=0\;then\;\ZERO\;else\;(der\,c\,r)\cdot r^{\{..n-1\}}$}\\

   389 %finite deterministic automata/ nondeterministic automaton

   410   \bl{$der\, c\, (r^{\{n..m\}})$}          & \bl{$\dn$} &

   390 

   411      \bl{$if\;n = 0 \wedge m = 0\;then\;\ZERO\; else$}\\

   391 %\item problem with infix operations, for example i-12

   412   \multicolumn{3}{l}{\bl{$if\;n = 0 \wedge m > 0\;then\;(der\,c\,r)\cdot r^{\{..m-1\}}$}}\\

   392 

   413   \multicolumn{3}{l}{\bl{$\phantom{if\;n = 0 \wedge m > 0\;}else

   393 

   414           \;(der\,c\,r)\cdot r^{\{n-1..m-1\}}$}}\\

   394 \end{frame}

   415   \bl{$der\, c\, (\sim{}r)$}              & \bl{$\dn$} & $?$\\

   395 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

   416 \end{tabular}

   396 

   417 \end{center}

   397 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   418 

   398 \begin{frame}[c]

   419 \end{frame}

   399 \frametitle{Coursework}

   420 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   421 

   422 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   423 \begin{frame}[c]

   424 \frametitle{Coursework: CFUN}

   403 \bl{$nullable([c_1 c_2 \ldots c_n])$}  & \bl{$\dn$} & $?$\\

   428   \bl{$nullable(CFUN(\_))$}  & \bl{$\dn$} & \bl{$false$}\\

   404 \bl{$nullable(r^+)$}                   & \bl{$\dn$} & $?$\\

   429   \bl{$der\,c\,(CFUN(f))$}   & \bl{$\dn$} &

   405 \bl{$nullable(r^?)$}                   & \bl{$\dn$} & $?$\\

   430      \bl{$if\;f(c)\;then\;\ONE\;else\;\ZERO$}\bigskip\\

   406 \bl{$nullable(r^{\{n,m\}})$}            & \bl{$\dn$} & $?$\\

   431   \bl{$CHAR(c)$}                   & \bl{$\dn$} & \bl{$CFUN(\lambda{}d.\;c=d)$}\\

   407 \bl{$nullable(\sim{}r)$}               & \bl{$\dn$} & $?$\medskip\\

   432   \bl{$CSET([c_1,\ldots,c_n])$} & \bl{$\dn$} & \bl{$CFUN(\lambda{}d.\;d\in [c_1,\ldots,c_n])$}\\

   408 \bl{$der\, c\, ([c_1 c_2 \ldots c_n])$}  & \bl{$\dn$} & $?$\\

   433   \bl{$ALL$}                   & \bl{$\dn$} & \bl{$CFUN(\lambda{}d.\;true)$}\\                                                      

   409 \bl{$der\, c\, (r^+)$}                   & \bl{$\dn$} & $?$\\

   410 \bl{$der\, c\, (r^?)$}                   & \bl{$\dn$} & $?$\\

   411 \bl{$der\, c\, (r^{\{n,m\}})$}            & \bl{$\dn$} & $?$\\

   412 \bl{$der\, c\, (\sim{}r)$}               & \bl{$\dn$} & $?$\\

   814 \item then apply \bl{$q$} to the unparsed parts

   873 \item then apply \bl{$q$} to the unparsed part