diff -r 78d828f43cdf -r 4b4742aa43f2 Slides/Slides5.thy
--- a/Slides/Slides5.thy	Sat Dec 17 16:58:11 2011 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,784 +0,0 @@
-(*<*)
-theory Slides5
-imports "~~/src/HOL/Library/LaTeXsugar" "Nominal"
-begin
-
-notation (latex output)
-  set ("_") and
-  Cons  ("_::/_" [66,65] 65) 
-
-(*>*)
-
-
-text_raw {*
-  %% shallow, deep, and recursive binders
-  %%
-  %%\renewcommand{\slidecaption}{Cambridge, 8.~June 2010}
-  %%\renewcommand{\slidecaption}{Uppsala, 3.~March 2011}
-  \renewcommand{\slidecaption}{Saarbrücken, 31.~March 2011}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1>[t]
-  \frametitle{%
-  \begin{tabular}{@ {\hspace{-3mm}}c@ {}}
-  \\
-  \LARGE General Bindings and\\ 
-  \LARGE Alpha-Equivalence\\ 
-  \LARGE in Nominal Isabelle\\[3mm] 
-  \Large Or, Nominal Isabelle 2\\[-5mm]
-  \end{tabular}}
-  \begin{center}
-  Christian Urban
-  \end{center}
-  \begin{center}
-  joint work with {\bf Cezary Kaliszyk}\\[0mm] 
-  \end{center}
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1-2>
-  \frametitle{\begin{tabular}{c}Binding in Old Nominal\end{tabular}}
-  \mbox{}\\[-6mm]
-
-  \begin{itemize}
-  \item the old Nominal Isabelle provided a reasoning infrastructure for single binders\medskip
-  
-  \begin{center}
-  Lam [a].(Var a)
-  \end{center}\bigskip
-
-  \item<2-> but representing 
-
-  \begin{center}
-  $\forall\{a_1,\ldots,a_n\}.\; T$ 
-  \end{center}\medskip
-
-  with single binders and reasoning about it is a \alert{\bf major} pain; 
-  take my word for it!
-  \end{itemize}
-
-  \only<1>{
-  \begin{textblock}{6}(1.5,11)
-  \small
-  for example\\
-  \begin{tabular}{l@ {\hspace{2mm}}l}
-   & a $\fresh$ Lam [a]. t\\
-   & Lam [a]. (Var a) \alert{$=$} Lam [b]. (Var b)\\
-   & Barendregt-style reasoning about bound variables\\
-  \end{tabular}
-  \end{textblock}}
-  
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1-6>
-  \frametitle{New Types in HOL}
-
-   \begin{center}
-  \begin{tikzpicture}[scale=1.5]
-  %%%\draw[step=2mm] (-4,-1) grid (4,1);
-  
-  \onslide<2-4,6>{\draw[very thick] (0.7,0.4) circle (4.25mm);}
-  \onslide<1-4,6>{\draw[rounded corners=1mm, very thick] ( 0.0,-0.8) rectangle ( 1.8, 0.9);}
-  \onslide<3-5,6>{\draw[rounded corners=1mm, very thick] (-1.95,0.85) rectangle (-2.85,-0.05);}
-  
-  \onslide<3-4,6>{\draw (-2.0, 0.845) --  (0.7,0.845);}
-  \onslide<3-4,6>{\draw (-2.0,-0.045)  -- (0.7,-0.045);}
-
-  \onslide<4-4,6>{\alert{\draw ( 0.7, 0.4) node {\footnotesize\begin{tabular}{@ {}c@ {}}$\alpha$-\\[-1mm]classes\end{tabular}};}}
-  \onslide<4-5,6>{\alert{\draw (-2.4, 0.4) node {\footnotesize\begin{tabular}{@ {}c@ {}}$\alpha$-eq.\\[-1mm]terms\end{tabular}};}}
-  \onslide<1-4,6>{\draw (1.8, 0.48) node[right=-0.1mm]
-    {\footnotesize\begin{tabular}{@ {}l@ {}}existing\\[-1mm] type\\ \onslide<4-4,6>{\alert{(sets of raw terms)}}\end{tabular}};}
-  \onslide<2-4,6>{\draw (0.9, -0.35) node {\footnotesize\begin{tabular}{@ {}l@ {}}non-empty\\[-1mm]subset\end{tabular}};}
-  \onslide<3-5,6>{\draw (-3.25, 0.55) node {\footnotesize\begin{tabular}{@ {}l@ {}}new\\[-1mm]type\end{tabular}};}
-  
-  \onslide<3-4,6>{\draw[<->, very thick] (-1.8, 0.3) -- (-0.1,0.3);}
-  \onslide<3-4,6>{\draw (-0.95, 0.3) node[above=0mm] {\footnotesize{}isomorphism};}
-
-  \onslide<6>{\draw[->, line width=2mm, red] (-1.0,-0.4) -- (0.35,0.16);}
-  \end{tikzpicture}
-  \end{center}
-  
-  \begin{center}
-  \textcolor{red}{\large\bf\onslide<6>{define $\alpha$-equivalence}}
-  \end{center}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1-4>
-  \frametitle{\begin{tabular}{c}Binding Sets of Names\end{tabular}}
-  \mbox{}\\[-3mm]
-
-  \begin{itemize}
-  \item binding sets of names has some interesting properties:\medskip
-  
-  \begin{center}
-  \begin{tabular}{l}
-  \textcolor{blue}{$\forall\{x, y\}.\, x \rightarrow y \;\;\approx_\alpha\;\; \forall\{y, x\}.\, y \rightarrow x$}
-  \bigskip\smallskip\\
-
-  \onslide<2->{%
-  \textcolor{blue}{$\forall\{x, y\}.\, x \rightarrow y \;\;\not\approx_\alpha\;\; \forall\{z\}.\, z \rightarrow z$}
-  }\bigskip\smallskip\\
-
-  \onslide<3->{%
-  \textcolor{blue}{$\forall\{x\}.\, x \rightarrow y \;\;\approx_\alpha\;\; \forall\{x, \alert{z}\}.\, x \rightarrow y$}
-  }\medskip\\
-  \onslide<3->{\hspace{4cm}\small provided $z$ is fresh for the type}
-  \end{tabular}
-  \end{center}
-  \end{itemize}
-  
-  \begin{textblock}{8}(2,14.5)
-  \footnotesize $^*$ $x$, $y$, $z$ are assumed to be distinct
-  \end{textblock}
-
-  \only<4>{
-  \begin{textblock}{6}(2.5,4)
-  \begin{tikzpicture}
-  \draw (0,0) node[inner sep=3mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
-  {\normalsize\color{darkgray}
-  \begin{minipage}{8cm}\raggedright
-  For type-schemes the order of bound names does not matter, and
-  $\alpha$-equivalence is preserved under \alert{vacuous} binders.
-  \end{minipage}};
-  \end{tikzpicture}
-  \end{textblock}}
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1-3>
-  \frametitle{\begin{tabular}{c}Other Binding Modes\end{tabular}}
-  \mbox{}\\[-3mm]
-
-  \begin{itemize}
-  \item alpha-equivalence being preserved under vacuous binders is \underline{not} always
-  wanted:\bigskip\bigskip\normalsize
-  
-  \textcolor{blue}{\begin{tabular}{@ {\hspace{-8mm}}l}
-  $\text{let}\;x = 3\;\text{and}\;y = 2\;\text{in}\;x - y\;\text{end}$\medskip\\
-  \onslide<2->{$\;\;\;\only<2>{\approx_\alpha}\only<3>{\alert{\not\approx_\alpha}}
-   \text{let}\;y = 2\;\text{and}\;x = 3\only<3->{\alert{\;\text{and}
-    \;z = \text{loop}}}\;\text{in}\;x - y\;\text{end}$}
-  \end{tabular}}
-  
-
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1>
-  \frametitle{\begin{tabular}{c}\LARGE{}Even Another Binding Mode\end{tabular}}
-  \mbox{}\\[-3mm]
-
-  \begin{itemize}
-  \item sometimes one wants to abstract more than one name, but the order \underline{does} matter\bigskip
-  
-  \begin{center}
-  \textcolor{blue}{\begin{tabular}{@ {\hspace{-8mm}}l}
-  $\text{let}\;(x, y) = (3, 2)\;\text{in}\;x - y\;\text{end}$\medskip\\
-  $\;\;\;\not\approx_\alpha
-   \text{let}\;(y, x) = (3, 2)\;\text{in}\;x - y\;\text{end}$
-  \end{tabular}}
-  \end{center}
-  
-
-  \end{itemize}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1-2>
-  \frametitle{\begin{tabular}{c}\LARGE{}Three Binding Modes\end{tabular}}
-  \mbox{}\\[-3mm]
-
-  \begin{itemize}
-  \item the order does not matter and alpha-equivelence is preserved under
-  vacuous binders \textcolor{gray}{(restriction)}\medskip
-  
-  \item the order does not matter, but the cardinality of the binders 
-  must be the same \textcolor{gray}{(abstraction)}\medskip
-
-  \item the order does matter \textcolor{gray}{(iterated single binders)}
-  \end{itemize}
-
-  \onslide<2->{
-  \begin{center}
-  \isacommand{bind (set+)}\hspace{6mm}
-  \isacommand{bind (set)}\hspace{6mm}
-  \isacommand{bind}
-  \end{center}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1-3>
-  \frametitle{\begin{tabular}{c}Specification of Binding\end{tabular}}
-  \mbox{}\\[-6mm]
-
-  \mbox{}\hspace{10mm}
-  \begin{tabular}{ll}
-  \multicolumn{2}{l}{\isacommand{nominal\_datatype} trm $=$}\\
-  \hspace{5mm}\phantom{$|$} Var name\\
-  \hspace{5mm}$|$ App trm trm\\
-  \hspace{5mm}$|$ Lam \only<2->{x::}name \only<2->{t::}trm
-  & \onslide<2->{\isacommand{bind} x \isacommand{in} t}\\
-  \hspace{5mm}$|$ Let \only<2->{as::}assns \only<2->{t::}trm
-  & \onslide<2->{\isacommand{bind} bn(as) \isacommand{in} t}\\
-  \multicolumn{2}{l}{\isacommand{and} assns $=$}\\
-  \multicolumn{2}{l}{\hspace{5mm}\phantom{$|$} ANil}\\
-  \multicolumn{2}{l}{\hspace{5mm}$|$ ACons name trm assns}\\
-  \multicolumn{2}{l}{\onslide<3->{\isacommand{binder} bn \isacommand{where}}}\\
-  \multicolumn{2}{l}{\onslide<3->{\hspace{5mm}\phantom{$|$} bn(ANil) $=$ []}}\\
-  \multicolumn{2}{l}{\onslide<3->{\hspace{5mm}$|$ bn(ACons a t as) $=$ [a] @ bn(as)}}\\
-  \end{tabular}
-
-
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1-8>
-  \frametitle{\begin{tabular}{c}Alpha-Equivalence\end{tabular}}
-  \mbox{}\\[-3mm]
-
-  \begin{itemize}
-  \item lets first look at pairs\bigskip\medskip
-
-  \textcolor{blue}{\begin{tabular}{@ {\hspace{1cm}}l}
-  $(as, x) \onslide<2->{\approx\!}\makebox[5mm][l]{\only<2-6>{${}_{\text{set}}$}%
-           \only<7>{${}_{\text{\alert{list}}}$}%
-           \only<8>{${}_{\text{\alert{set+}}}$}}%
-           \,\onslide<2->{(bs,y)}$
-  \end{tabular}}\bigskip
-  \end{itemize}
-
-  \only<1>{
-  \begin{textblock}{8}(3,8.5)
-  \begin{tabular}{l@ {\hspace{2mm}}p{8cm}}
-   & \textcolor{blue}{$as$} is a set of names\ldots the binders\\
-   & \textcolor{blue}{$x$} is the body (might be a tuple)\\
-   & \textcolor{blue}{$\approx_{\text{set}}$} is where the cardinality 
-  of the binders has to be the same\\
-  \end{tabular}
-  \end{textblock}}
-
-  \only<4->{
-  \begin{textblock}{12}(5,8)
-  \textcolor{blue}{
-  \begin{tabular}{ll@ {\hspace{1mm}}l}
-  $\dn$ & \onslide<5->{$\exists \pi.\,$} & $\text{fv}(x) - as = \text{fv}(y) - bs$\\[1mm]
-        & \onslide<5->{$\;\;\;\wedge$} & \onslide<5->{$\text{fv}(x) - as \fresh^* \pi$}\\[1mm]
-        & \onslide<5->{$\;\;\;\wedge$} & \onslide<5->{$(\pi \act x) = y$}\\[1mm]
-        & \only<6-7>{$\;\;\;\wedge$}\only<8>{\textcolor{gray}{\xout{$\;\;\;\wedge$}}} & 
-          \only<6-7>{$\pi \act as = bs$}\only<8>{\textcolor{gray}{\xout{$\pi \act as = bs$}}}\\
-  \end{tabular}}
-  \end{textblock}}
-  
-  \only<7>{
-  \begin{textblock}{7}(3,13.8)
-  \footnotesize $^*$ $as$ and $bs$ are \alert{lists} of names 
-  \end{textblock}}
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1-3>
-  \frametitle{\begin{tabular}{c}Examples\end{tabular}}
-  \mbox{}\\[-3mm]
-
-  \begin{itemize}
-  \item lets look at type-schemes:\medskip\medskip
-
-  \begin{center}
-  \textcolor{blue}{$(as, x) \approx\!\makebox[5mm][l]{${}_{\text{set}}$} (bs, y)$}
-  \end{center}\medskip
-
-  \onslide<2->{
-  \begin{center}
-  \textcolor{blue}{
-  \begin{tabular}{l}
-  $\text{fv}(x) = \{x\}$\\[1mm]
-  $\text{fv}(T_1 \rightarrow T_2) = \text{fv}(T_1) \cup \text{fv}(T_2)$\\
-  \end{tabular}}
-  \end{center}}
-  \end{itemize}
-
-  
-  \only<3->{
-  \begin{textblock}{4}(0.3,12)
-  \begin{tikzpicture}
-  \draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
-  {\tiny\color{darkgray}
-  \begin{minipage}{3.4cm}\raggedright
-  \begin{tabular}{r@ {\hspace{1mm}}l}
-  \multicolumn{2}{@ {}l}{set+:}\\
-  $\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
-  $\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
-  $\wedge$ & $\pi \cdot x = y$\\
-  \\
-  \end{tabular}
-  \end{minipage}};
-  \end{tikzpicture}
-  \end{textblock}}
-  \only<3->{
-  \begin{textblock}{4}(5.2,12)
-  \begin{tikzpicture}
-  \draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
-  {\tiny\color{darkgray}
-  \begin{minipage}{3.4cm}\raggedright
-  \begin{tabular}{r@ {\hspace{1mm}}l}
-  \multicolumn{2}{@ {}l}{set:}\\
-  $\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
-  $\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
-  $\wedge$ & $\pi \cdot x = y$\\
-  $\wedge$ & $\pi \cdot as = bs$\\
-  \end{tabular}
-  \end{minipage}};
-  \end{tikzpicture}
-  \end{textblock}}
-  \only<3->{
-  \begin{textblock}{4}(10.2,12)
-  \begin{tikzpicture}
-  \draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
-  {\tiny\color{darkgray}
-  \begin{minipage}{3.4cm}\raggedright
-  \begin{tabular}{r@ {\hspace{1mm}}l}
-  \multicolumn{2}{@ {}l}{list:}\\
-  $\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
-  $\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
-  $\wedge$ & $\pi \cdot x = y$\\
-  $\wedge$ & $\pi \cdot as = bs$\\
-  \end{tabular}
-  \end{minipage}};
-  \end{tikzpicture}
-  \end{textblock}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1-2>
-  \frametitle{\begin{tabular}{c}Examples\end{tabular}}
-  \mbox{}\\[-3mm]
-
-  \begin{center}
-  \textcolor{blue}{
-  \only<1>{$(\{x, y\}, x \rightarrow y) \approx_? (\{x, y\}, y \rightarrow x)$}
-  \only<2>{$([x, y], x \rightarrow y) \approx_? ([x, y], y \rightarrow x)$}}
-  \end{center}
-
-  \begin{itemize}
-  \item \textcolor{blue}{$\approx_{\text{set+}}$, $\approx_{\text{set}}$% 
-  \only<2>{, \alert{$\not\approx_{\text{list}}$}}}
-  \end{itemize}
-
-  
-  \only<1->{
-  \begin{textblock}{4}(0.3,12)
-  \begin{tikzpicture}
-  \draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
-  {\tiny\color{darkgray}
-  \begin{minipage}{3.4cm}\raggedright
-  \begin{tabular}{r@ {\hspace{1mm}}l}
-  \multicolumn{2}{@ {}l}{set+:}\\
-  $\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
-  $\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
-  $\wedge$ & $\pi \cdot x = y$\\
-  \\
-  \end{tabular}
-  \end{minipage}};
-  \end{tikzpicture}
-  \end{textblock}}
-  \only<1->{
-  \begin{textblock}{4}(5.2,12)
-  \begin{tikzpicture}
-  \draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
-  {\tiny\color{darkgray}
-  \begin{minipage}{3.4cm}\raggedright
-  \begin{tabular}{r@ {\hspace{1mm}}l}
-  \multicolumn{2}{@ {}l}{set:}\\
-  $\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
-  $\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
-  $\wedge$ & $\pi \cdot x = y$\\
-  $\wedge$ & $\pi \cdot as = bs$\\
-  \end{tabular}
-  \end{minipage}};
-  \end{tikzpicture}
-  \end{textblock}}
-  \only<1->{
-  \begin{textblock}{4}(10.2,12)
-  \begin{tikzpicture}
-  \draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
-  {\tiny\color{darkgray}
-  \begin{minipage}{3.4cm}\raggedright
-  \begin{tabular}{r@ {\hspace{1mm}}l}
-  \multicolumn{2}{@ {}l}{list:}\\
-  $\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
-  $\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
-  $\wedge$ & $\pi \cdot x = y$\\
-  $\wedge$ & $\pi \cdot as = bs$\\
-  \end{tabular}
-  \end{minipage}};
-  \end{tikzpicture}
-  \end{textblock}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1-2>
-  \frametitle{\begin{tabular}{c}Examples\end{tabular}}
-  \mbox{}\\[-3mm]
-
-  \begin{center}
-  \textcolor{blue}{\only<1>{$(\{x\}, x) \approx_? (\{x, y\}, x)$}}
-  \end{center}
-
-  \begin{itemize}
-  \item \textcolor{blue}{$\approx_{\text{set+}}$, $\not\approx_{\text{set}}$,
-        $\not\approx_{\text{list}}$}
-  \end{itemize}
-
-  
-  \only<1->{
-  \begin{textblock}{4}(0.3,12)
-  \begin{tikzpicture}
-  \draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
-  {\tiny\color{darkgray}
-  \begin{minipage}{3.4cm}\raggedright
-  \begin{tabular}{r@ {\hspace{1mm}}l}
-  \multicolumn{2}{@ {}l}{set+:}\\
-  $\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
-  $\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
-  $\wedge$ & $\pi \cdot x = y$\\
-  \\
-  \end{tabular}
-  \end{minipage}};
-  \end{tikzpicture}
-  \end{textblock}}
-  \only<1->{
-  \begin{textblock}{4}(5.2,12)
-  \begin{tikzpicture}
-  \draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
-  {\tiny\color{darkgray}
-  \begin{minipage}{3.4cm}\raggedright
-  \begin{tabular}{r@ {\hspace{1mm}}l}
-  \multicolumn{2}{@ {}l}{set:}\\
-  $\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
-  $\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
-  $\wedge$ & $\pi \cdot x = y$\\
-  $\wedge$ & $\pi \cdot as = bs$\\
-  \end{tabular}
-  \end{minipage}};
-  \end{tikzpicture}
-  \end{textblock}}
-  \only<1->{
-  \begin{textblock}{4}(10.2,12)
-  \begin{tikzpicture}
-  \draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
-  {\tiny\color{darkgray}
-  \begin{minipage}{3.4cm}\raggedright
-  \begin{tabular}{r@ {\hspace{1mm}}l}
-  \multicolumn{2}{@ {}l}{list:}\\
-  $\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
-  $\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
-  $\wedge$ & $\pi \cdot x = y$\\
-  $\wedge$ & $\pi \cdot as = bs$\\
-  \end{tabular}
-  \end{minipage}};
-  \end{tikzpicture}
-  \end{textblock}}
-
-  \only<2>{
-  \begin{textblock}{6}(2.5,4)
-  \begin{tikzpicture}
-  \draw (0,0) node[inner sep=5mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] 
-  {\normalsize
-  \begin{minipage}{8cm}\raggedright
-  \begin{itemize}
-  \item \color{darkgray}$\alpha$-equivalences coincide when a single name is
-  abstracted
-  \item \color{darkgray}in that case they are equivalent to ``old-fashioned'' definitions of $\alpha$ 
-  \end{itemize}
-  \end{minipage}};
-  \end{tikzpicture}
-  \end{textblock}}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->
-  \frametitle{\begin{tabular}{c}Our Specifications\end{tabular}}
-  \mbox{}\\[-6mm]
-
-  \mbox{}\hspace{10mm}
-  \begin{tabular}{ll}
-  \multicolumn{2}{l}{\isacommand{nominal\_datatype} trm $=$}\\
-  \hspace{5mm}\phantom{$|$} Var name\\
-  \hspace{5mm}$|$ App trm trm\\
-  \hspace{5mm}$|$ Lam x::name t::trm
-  & \isacommand{bind} x \isacommand{in} t\\
-  \hspace{5mm}$|$ Let as::assns t::trm
-  & \isacommand{bind} bn(as) \isacommand{in} t\\
-  \multicolumn{2}{l}{\isacommand{and} assns $=$}\\
-  \multicolumn{2}{l}{\hspace{5mm}\phantom{$|$} ANil}\\
-  \multicolumn{2}{l}{\hspace{5mm}$|$ ACons name trm assns}\\
-  \multicolumn{2}{l}{\isacommand{binder} bn \isacommand{where}}\\
-  \multicolumn{2}{l}{\hspace{5mm}\phantom{$|$} bn(ANil) $=$ $[]$}\\
-  \multicolumn{2}{l}{\hspace{5mm}$|$ bn(ACons a t as) $=$ $[$a$]$ @ bn(as)}\\
-  \end{tabular}
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1>[c]
-  \frametitle{\begin{tabular}{c}Binding Functions\end{tabular}}
-
-  \begin{center}
-  \begin{tikzpicture}
-  \node (A) at (-0.5,1) {Foo $(\lambda y. \lambda x. t)$};
-  \node (B) at ( 1.5,1) {$s$};
-  \onslide<1>{\node (C) at (0.5,-0.5) {$\{y, x\}$};}
-  \onslide<1>{\draw[->,red,line width=1mm] (A) -- (C);}
-  \onslide<1>{\draw[->,red,line width=1mm] (C) -- (B);}
-  \end{tikzpicture}
-  \end{center}
-
-  
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[t]
-  \frametitle{\begin{tabular}{c}Binder Clauses\end{tabular}}
-
-  \begin{itemize}
-  \item We need for a bound variable to have a `clear scope', and bound
-  variables should not be free and bound at the same time.\bigskip
-  \end{itemize}
-
-  \begin{center}
-  \only<1>{
-  \begin{tabular}{@ {\hspace{-5mm}}l}
-  \alert{\bf shallow binders}\\ 
-  \hspace{4mm}Lam x::name t::trm\hspace{4mm} \isacommand{bind} x \isacommand{in} t\\
-  \hspace{4mm}All xs::name set T::ty\hspace{4mm} \isacommand{bind} xs \isacommand{in} T\\
-  \hspace{4mm}Foo x::name t$_1$::trm t$_2$::trm\hspace{4mm} 
-     \isacommand{bind} x \isacommand{in} t$_1$, \isacommand{bind} x \isacommand{in} t$_2$\\
-  \hspace{4mm}Bar x::name t$_1$::trm t$_2$::trm\hspace{4mm} 
-     \isacommand{bind} x \isacommand{in} t$_1$ t$_2$\\
-  \end{tabular}}
-  \only<2>{
-  \begin{tabular}{@ {\hspace{-5mm}}l}
-  \alert{\bf deep binders} \\
-  \hspace{4mm}Let as::assns t::trm\hspace{4mm} \isacommand{bind} bn(as) \isacommand{in} t\\
-  \hspace{4mm}Foo as::assns t$_1$::trm t$_2$::trm\\
-  \hspace{20mm}\isacommand{bind} bn(as) \isacommand{in} t$_1$, \isacommand{bind} bn(as) \isacommand{in} t$_2$\\[4mm]
-  \makebox[0mm][l]{\alert{$\times$}}\hspace{4mm}Bar as::assns t$_1$::trm t$_2$::trm\\
-  \hspace{20mm}\isacommand{bind} bn$_1$(as) \isacommand{in} t$_1$, \isacommand{bind} bn$_2$(as) \isacommand{in} t$_2$\\
-  \end{tabular}}
-  \only<3>{
-  \begin{tabular}{@ {\hspace{-5mm}}l}
-  {\bf deep \alert{recursive} binders} \\
-  \hspace{4mm}Let\_rec as::assns t::trm\hspace{4mm} \isacommand{bind} bn(as) \isacommand{in} t as\\[4mm]
-
-  \makebox[0mm][l]{\alert{$\times$}}\hspace{4mm}Foo\_rec as::assns t$_1$::trm t$_2$::trm\hspace{4mm}\\ 
-  \hspace{20mm}\isacommand{bind} bn(as) \isacommand{in} t$_1$ as, \isacommand{bind} bn(as) \isacommand{in} t$_2$\\
-
-  \end{tabular}}
-  \end{center}
-  
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<2-5>
-  \frametitle{\begin{tabular}{c}Our Work\end{tabular}}
-  \mbox{}\\[-6mm]
-
-    \begin{center}
-  \begin{tikzpicture}[scale=1.5]
-  %%%\draw[step=2mm] (-4,-1) grid (4,1);
-  
-  \onslide<1>{\draw[very thick] (0.7,0.4) circle (4.25mm);}
-  \onslide<1>{\draw[rounded corners=1mm, very thick] ( 0.0,-0.8) rectangle ( 1.8, 0.9);}
-  \onslide<1->{\draw[rounded corners=1mm, very thick] (-1.95,0.85) rectangle (-2.85,-0.05);}
-  
-  \onslide<1>{\draw (-2.0, 0.845) --  (0.7,0.845);}
-  \onslide<1>{\draw (-2.0,-0.045)  -- (0.7,-0.045);}
-
-  \onslide<1>{\alert{\draw ( 0.7, 0.4) node {\footnotesize\begin{tabular}{@ {}c@ {}}$\alpha$-\\[-1mm]classes\end{tabular}};}}
-  \onslide<1->{\alert{\draw (-2.4, 0.4) node {\footnotesize\begin{tabular}{@ {}c@ {}}$\alpha$-eq.\\[-1mm]terms\end{tabular}};}}
-  \onslide<1>{\draw (1.8, 0.48) node[right=-0.1mm]
-    {\footnotesize\begin{tabular}{@ {}l@ {}}existing\\[-1mm] type\\ \onslide<1>{\alert{(sets of raw terms)}}\end{tabular}};}
-  \onslide<1>{\draw (0.9, -0.35) node {\footnotesize\begin{tabular}{@ {}l@ {}}non-empty\\[-1mm]subset\end{tabular}};}
-  \onslide<1->{\draw (-3.25, 0.55) node {\footnotesize\begin{tabular}{@ {}l@ {}}new\\[-1mm]type\end{tabular}};}
-  
-  \onslide<1>{\draw[<->, very thick] (-1.8, 0.3) -- (-0.1,0.3);}
-  \onslide<1>{\draw (-0.95, 0.3) node[above=0mm] {\footnotesize{}isomorphism};}
-
-  \onslide<1>{\draw[->, line width=2mm, red] (-1.0,-0.4) -- (0.35,0.16);}
-  \end{tikzpicture}
-  \end{center}
-  
-  \begin{textblock}{9.5}(6,3.5)
-  \begin{itemize}
-  \item<1-> defined fv and $\alpha$
-  \item<3-> derived a reasoning infrastructure ($\fresh$, distinctness, injectivity, cases,\ldots) 
-  \item<4-> a (weak) induction principle
-  \item<5-> derive a {\bf stronger} induction principle (Barendregt variable convention built in)\\
-  \begin{center}
-  \textcolor{blue}{Foo ($\lambda x. \lambda y. t$) ($\lambda u. \lambda v. s$)} 
-  \end{center}
-  \end{itemize}
-  \end{textblock}
-
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->
-  \frametitle{\begin{tabular}{c}Conclusion\end{tabular}}
-  \mbox{}\\[-6mm]
-
-  \begin{itemize}
-  \item the user does not see anything of the raw level\medskip
-  \only<1>{\begin{center}
-  Lam a (Var a) \alert{$=$} Lam b (Var b)
-  \end{center}\bigskip}
-
-  \item<2-> it took quite some time to get here, but it seems worthwhile 
-  (Barendregt's variable convention is unsound in general, 
-  found bugs in two paper proofs)\bigskip\medskip
-  
-  \item<3-> \textcolor{blue}{http://isabelle.in.tum.de/nominal/}
-  \end{itemize}
-
-  
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1->[c]
-  \frametitle{\begin{tabular}{c}Questions?\end{tabular}}
-  \mbox{}\\[-6mm]
-
-  \begin{center}
-  \alert{\huge{Thanks!}}
-  \end{center}
-  
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-
-
-text_raw {*
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \mode<presentation>{
-  \begin{frame}<1-2>[c]
-  \frametitle{\begin{tabular}{c}Examples\end{tabular}}
-  \mbox{}\\[-6mm]
-
-  \textcolor{blue}{
-  \begin{center}
-  $(\{a,b\}, a \rightarrow b) \approx_\alpha (\{a, b\}, a \rightarrow b)$
-  $(\{a,b\}, a \rightarrow b) \approx_\alpha (\{a, b\}, b \rightarrow a)$
-  \end{center}}
-
-  \textcolor{blue}{
-  \begin{center}
-  $(\{a,b\}, (a \rightarrow b, a \rightarrow b))$\\ 
-  \hspace{17mm}$\not\approx_\alpha (\{a, b\}, (a \rightarrow b, b \rightarrow a))$
-  \end{center}}
-  
-  \onslide<2->
-  {1.) \hspace{3mm}\isacommand{bind (set)} as \isacommand{in} $\tau_1$, 
-   \isacommand{bind (set)} as \isacommand{in} $\tau_2$\medskip
-
-   2.) \hspace{3mm}\isacommand{bind (set)} as \isacommand{in} $\tau_1$ $\tau_2$ 
-  }
-
-  \end{frame}}
-  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-*}
-
-
-
-(*<*)
-end
-(*>*)
\ No newline at end of file