249 

   250 

   251 

   252 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   253 \mode<presentation>{

   254 \begin{frame}[t]

   255 \frametitle{\begin{tabular}{c}\bl{$(a?\{n\})a\{n\}$}\end{tabular}}

   256 

   257 \mbox{}\\[-13mm]

   258 

   259 \begin{tikzpicture}[y=.2cm, x=.3cm]

   260  	%axis

   261 	\draw (0,0) -- coordinate (x axis mid) (30,0);

   262     	\draw (0,0) -- coordinate (y axis mid) (0,30);

   263     	%ticks

   264     	\foreach \x in {0,5,...,30}

   265      		\draw (\x,1pt) -- (\x,-3pt)

   266 			node[anchor=north] {\x};

   267     	\foreach \y in {0,5,...,30}

   268      		\draw (1pt,\y) -- (-3pt,\y) 

   269      			node[anchor=east] {\y}; 

   270 	%labels      

   271 	\node[below=0.6cm] at (x axis mid) {\bl{a}s};

   272 	\node[rotate=90, left=1.2cm] at (y axis mid) {secs};

   273 

   274 	%plots

   275 	\draw[color=blue] plot[mark=*, mark options={fill=white}] 

   276 		file {re-python.data};

   277 	\draw[color=red] plot[mark=triangle*, mark options={fill=white} ] 

   278 		file {re1.data};

   279          \draw[color=green] plot[mark=square*, mark options={fill=white} ] 

   280 		file {re2.data};

   281          \draw[color=brown] plot[mark=pentagon*, mark options={fill=white} ] 

   282 		file {re-ruby.data};

   283     

   284 	%legend

   285 	\begin{scope}[shift={(4,20)}] 

   286 	\draw[color=blue] (0,0) -- 

   287 		plot[mark=*, mark options={fill=white}] (0.25,0) -- (0.5,0) 

   288 		node[right]{\small Python};

   289 	\draw[yshift=-\baselineskip, color=brown] (0,0) -- 

   290 		plot[mark=pentagon*, mark options={fill=white}] (0.25,0) -- (0.5,0)

   291 		node[right]{\small Ruby (Daniel Baldwin)};

   292          \draw[yshift=\baselineskip, color=red] (0,0) -- 

   293 		plot[mark=triangle*, mark options={fill=white}] (0.25,0) -- (0.5,0)

   294 		node[right]{\small Scala V1};	

   295 	 \draw[yshift=2\baselineskip, color=green] (0,0) -- 

   296 		plot[mark=square*, mark options={fill=white}] (0.25,0) -- (0.5,0)

   297 		node[right]{\small Scala V2 with simplifications};

   298 	\end{scope}

   299 \end{tikzpicture}

   300 

   301 \end{frame}}

   302 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   303 

   304 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   305 \mode<presentation>{

   306 \begin{frame}[t]

   307 

   308 \begin{tikzpicture}[y=.7cm, x=.0009cm]

   309  	%axis

   310 	\draw (0,0) -- coordinate (x axis mid) (10000,0);

   311     	\draw (0,0) -- coordinate (y axis mid) (0,6);

   312     	%ticks

   313     	\foreach \x in {0,2000,...,10000}

   314      		\draw (\x,1pt) -- (\x,-3pt)

   315 			node[anchor=north] {\x};

   316     	\foreach \y in {0,1,...,6}

   317      		\draw (1pt,\y) -- (-3pt,\y) 

   318      			node[anchor=east] {\y}; 

   319 	%labels      

   320 	\node[below=0.6cm] at (x axis mid) {\bl{a}s};

   321 	\node[rotate=90, left=1.2cm] at (y axis mid) {secs};

   322 

   323 	%plots

   324 	\draw[color=blue] plot[mark=*, mark options={fill=white}] 

   325 		file {re-internal.data};

   326 	\only<1->{	 

   327          \draw[color=red] plot[mark=triangle*, mark options={fill=white} ] 

   328 		file {re3.data};}

   329     

   330 	%legend

   331 	\begin{scope}[shift={(2000,4)}] 

   332 	\draw[color=blue] (0,0) -- 

   333 		plot[mark=*, mark options={fill=white}] (0.25,0) -- (0.5,0) 

   334 		node[right]{\small Scala Internal};

   335         \only<1->{

   336 	\draw[yshift=\baselineskip, color=red] (0,0) -- 

   337 		plot[mark=triangle*, mark options={fill=white}] (0.25,0) -- (0.5,0)

   338 		node[right]{\small Scala V3 with explicit $\_\{\_\}$};}

   339 	\end{scope}

   340 \end{tikzpicture}

   341 

   342 \begin{center}

   343 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}

   344   \\[-8mm]

   345   \bl{der c (r$_1$ $\cdot$ r$_2$)} & \bl{$\dn$}  & \bl{if nullable r$_1$}\\

   346   & & \bl{then ((der c r$_1$) $\cdot$ r$_2$) + (der c r$_2$)}\\ 

   347   & & \bl{else (der c r$_1$) $\cdot$ r$_2$}\\

   348   \bl{der c (r$\{n\}$)} & \bl{$\dn$} & \bl{if $n = 0$ then $\varnothing$}\\

   349   & & \bl{else (der c r) $\cdot$ r$\{n - 1\}$}

   350   \end{tabular}

   351 \end{center}

   352 

   353 \end{frame}}

   354 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   355