--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Slides/Slides2.thy	Sat Jul 10 11:27:04 2010 +0100
@@ -0,0 +1,225 @@
+(*<*)
+theory Slides2
+imports "LaTeXsugar" "Nominal"
+begin
+
+notation (latex output)
+  set ("_") and
+  Cons  ("_::/_" [66,65] 65) 
+
+(*>*)
+
+
+text_raw {*
+  \renewcommand{\slidecaption}{TU Munich, 28.~May 2010}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1>[t]
+  \frametitle{%
+  \begin{tabular}{@ {\hspace{-3mm}}c@ {}}
+  \\
+  \huge Nominal 2\\[-2mm] 
+  \large Or, How to Reason Conveniently with\\[-5mm]
+  \large General Bindings in Isabelle\\[15mm]
+  \end{tabular}}
+  \begin{center}
+  joint work with {\bf Cezary} and Brian Huf\!fman\\[0mm] 
+  \end{center}
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+
+*}
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1-2>
+  \frametitle{\begin{tabular}{c}Part I: Nominal Theory\end{tabular}}
+  \mbox{}\\[-3mm]
+
+  \begin{itemize}
+  \item sorted atoms and sort-respecting permutations\medskip
+
+  \onslide<2->{
+  \item[] in old Nominal: atoms have \underline{dif\!ferent} type\medskip
+
+  \begin{center}
+  \begin{tabular}{c@ {\hspace{7mm}}c}
+  $[]\;\act\;c \dn c$ &
+  $(a\;b)\!::\!\pi\;\act\;c \dn$ 
+  $\begin{cases}
+  b & \text{if}\; \pi \act c = a\\
+  a & \text{if}\; \pi \act c = b\\
+  \pi \act c & \text{otherwise}
+  \end{cases}$
+  \end{tabular}
+  \end{center}}
+  \end{itemize}
+
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1>
+  \frametitle{\begin{tabular}{c}Problems\end{tabular}}
+  \mbox{}\\[-3mm]
+
+  \begin{itemize}
+  \item @{text "_ \<bullet> _ :: \<alpha> perm \<Rightarrow> \<beta> \<Rightarrow> \<beta>"}\bigskip
+
+  \item @{text "supp _ :: \<beta> \<Rightarrow> \<alpha> set"}
+
+  \begin{center}
+  $\text{finite} (\text{supp}\;x)_{\,\alpha_1\,\text{set}}$ \ldots 
+  $\text{finite} (\text{supp}\;x)_{\,\alpha_n\,\text{set}}$
+  \end{center}\bigskip
+  
+  \item $\forall \pi_{\alpha_1} \ldots \pi_{\alpha_n}\;.\; P$\bigskip
+
+  \item type-classes
+  \end{itemize}
+
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1-4>
+  \frametitle{\begin{tabular}{c}Our New Solution\end{tabular}}
+  \mbox{}\\[-3mm]
+*}
+datatype atom = Atom string nat
+
+text_raw {*
+  \mbox{}\bigskip
+  \begin{itemize}
+  \item<2-> permutations are (restricted) bijective functions from @{text "atom \<Rightarrow> atom"}
+
+     \begin{itemize}
+     \item sort-respecting \hspace{5mm}($\forall a.\;\text{sort}(f a) = \text{sort}(a)$)
+     \item finite domain \hspace{5mm}($\text{finite} \{a.\;f a \not= a\}$)
+     \end{itemize}\medskip
+
+  \item<3-> swappings:
+     \small
+     \[
+     \begin{array}{l@ {\hspace{1mm}}l}
+     (a\;b) \dn & \text{if}\;\text{sort}(a) = \text{sort}(b)\\
+        & \text{then}\;\lambda  c. \text{if}\;a = c\;\text{then}\;b\;\text{else}\;
+          \text{if}\;b = c\;\text{then}\;a\;\text{else}\;c\\
+        & \text{else}\;\only<3>{\mbox{\textcolor{red}{\bf ?}}}\only<4->{\text{id}}
+     \end{array}
+     \]
+  \end{itemize}
+
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1-6>
+  \frametitle{\begin{tabular}{c}\LARGE{}A Smoother Nominal Theory\end{tabular}}
+  \mbox{}\\[-3mm]
+
+  \begin{itemize}
+  \item<1-> $(a\;b) = (b\;a) \onslide<3->{= (a\;c) + (b\;c) + (a\;c)}$\bigskip  
+
+  \item<2-> permutations are an instance of group\_add\\ $0$, $\pi_1 + \pi_2$, $- \pi$\bigskip
+
+  \item<5-> $\_\;\act\;\_ :: \text{perm} \Rightarrow \alpha \Rightarrow \alpha$\medskip
+  
+   \begin{itemize}
+   \item $0\;\act\;x = x$\\
+   \item $(\pi_1 + \pi_2)\;\act\;x = \pi_1\;\act\;(\pi_2\;\act\;x)$
+   \end{itemize}
+
+   \small
+   \onslide<6->{$\text{finite}(\text{supp}\;x)$, $\forall \pi. P$}
+  \end{itemize}
+
+  \only<4>{
+  \begin{textblock}{6}(2.5,11)
+  \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
+  This is slightly odd, since in general: 
+  \begin{center}$\pi_1 + \pi_2 \alert{\not=} \pi_2 + \pi_1$\end{center}
+  \end{minipage}};
+  \end{tikzpicture}
+  \end{textblock}}
+
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1-3>
+  \frametitle{\begin{tabular}{c}Very Few Snatches\end{tabular}}
+  \mbox{}\\[-3mm]
+
+  \begin{itemize}
+  \item \underline{concrete} atoms:
+  \end{itemize}
+*}
+(*<*)
+consts sort :: "atom \<Rightarrow> string"
+(*>*)
+
+typedef name = "{a :: atom. sort a = ''name''}" (*<*)sorry(*>*)
+typedef ident = "{a :: atom. sort a = ''ident''}" (*<*)sorry(*>*)
+
+text_raw {*
+  \mbox{}\bigskip\bigskip
+  \begin{itemize}
+  \item<2-> there is an overloaded  function \underline{atom}, which injects concrete 
+  atoms into generic ones\medskip 
+  \begin{center}
+  \begin{tabular}{l}
+  $\text{atom}(a) \fresh x$\\
+  $(a \leftrightarrow b) \dn (\text{atom}(a)\;\;\text{atom}(b))$
+  \end{tabular}
+  \end{center}\bigskip\medskip
+
+  \onslide<3->
+  {I would like to have $a \fresh x$, $(a\; b)$, \ldots}
+
+  \end{itemize}
+
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1-2>[c]
+  \frametitle{\begin{tabular}{c}\LARGE{}End of Part I\end{tabular}}
+  \mbox{}\\[-3mm]
+
+  \begin{itemize}
+  \item the formalised version of the nominal theory is now much nicer to 
+  work with (sorts are occasionally explicit)\bigskip
+
+  \item permutations: ``be as abstract as you can'' (group\_add is a slight oddity)\bigskip
+
+  \item allow sort-disrespecting swappings\onslide<2->{: just define them as the identity}
+  \end{itemize}
+
+  
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+(*<*)
+end
+(*>*)
\ No newline at end of file