# HG changeset patch
# User Christian Urban <urbanc@in.tum.de>
# Date 1278757624 -3600
# Node ID 842969a598f2aaeeef74a7cba7e2fe1091f149c9
# Parent  0a5320c6a7e6076227fcf5052446fae92e834c05
added material for slides

diff -r 0a5320c6a7e6 -r 842969a598f2 IsaMakefile
--- a/IsaMakefile	Fri Jul 09 23:04:51 2010 +0100
+++ b/IsaMakefile	Sat Jul 10 11:27:04 2010 +0100
@@ -62,20 +62,38 @@
 
 ## Slides
 
-session1: Slides/ROOT.ML \
+session1: Slides/ROOT1.ML \
          Slides/document/root* \
          Slides/Slides1.thy
-	@$(USEDIR) -D generated1 -f ROOT.ML HOL-Nominal Slides
-	@perl -i -p -e "s/..isachardoublequoteopen./\\\begin{innerdouble}/g" Sl
-	@perl -i -p -e "s/..isachardoublequoteclose./\\\end{innerdouble}/g" Sli
-	@perl -i -p -e "s/..isacharbackquoteopen./\\\begin{innersingle}/g" Slid
-	@perl -i -p -e "s/..isacharbackquoteclose./\\\end{innersingle}/g" Slide
+	@$(USEDIR) -D generated1 -f ROOT1.ML HOL-Nominal Slides
 
 slides1: session1
 	rm -f Slides/generated1/*.aux # otherwise latex will fall over
 	cd Slides/generated1 ; $(ISABELLE_TOOL) latex -o pdf root.beamer.tex
 	cd Slides/generated1 ; $(ISABELLE_TOOL) latex -o pdf root.beamer.tex
-	cp Slides/generated1/root.beamer.pdf Slides/slides.pdf     
+	cp Slides/generated1/root.beamer.pdf Slides/slides1.pdf     
+
+session2: Slides/ROOT2.ML \
+         Slides/document/root* \
+         Slides/Slides2.thy
+	@$(USEDIR) -D generated2 -f ROOT2.ML HOL-Nominal Slides
+
+slides2: session2
+	rm -f Slides/generated2/*.aux # otherwise latex will fall over
+	cd Slides/generated2 ; $(ISABELLE_TOOL) latex -o pdf root.beamer.tex
+	cd Slides/generated2 ; $(ISABELLE_TOOL) latex -o pdf root.beamer.tex
+	cp Slides/generated2/root.beamer.pdf Slides/slides2.pdf 
+
+session3: Slides/ROOT3.ML \
+         Slides/document/root* \
+         Slides/Slides3.thy
+	@$(USEDIR) -D generated3 -f ROOT3.ML HOL-Nominal Slides
+
+slides3: session3
+	rm -f Slides/generated3/*.aux # otherwise latex will fall over
+	cd Slides/generated3 ; $(ISABELLE_TOOL) latex -o pdf root.beamer.tex
+	cd Slides/generated3 ; $(ISABELLE_TOOL) latex -o pdf root.beamer.tex
+	cp Slides/generated3/root.beamer.pdf Slides/slides3.pdf 
 
 slides: slides1
 
diff -r 0a5320c6a7e6 -r 842969a598f2 Slides/ROOT.ML
--- a/Slides/ROOT.ML	Fri Jul 09 23:04:51 2010 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,6 +0,0 @@
-show_question_marks := false;
-quick_and_dirty := true;
-
-no_document use_thy "LaTeXsugar";
-
-use_thy "Slides1"
\ No newline at end of file
diff -r 0a5320c6a7e6 -r 842969a598f2 Slides/ROOT1.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Slides/ROOT1.ML	Sat Jul 10 11:27:04 2010 +0100
@@ -0,0 +1,6 @@
+show_question_marks := false;
+quick_and_dirty := true;
+
+no_document use_thy "LaTeXsugar";
+
+use_thy "Slides1"
\ No newline at end of file
diff -r 0a5320c6a7e6 -r 842969a598f2 Slides/ROOT2.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Slides/ROOT2.ML	Sat Jul 10 11:27:04 2010 +0100
@@ -0,0 +1,6 @@
+show_question_marks := false;
+quick_and_dirty := true;
+
+no_document use_thy "LaTeXsugar";
+
+use_thy "Slides2"
\ No newline at end of file
diff -r 0a5320c6a7e6 -r 842969a598f2 Slides/ROOT3.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Slides/ROOT3.ML	Sat Jul 10 11:27:04 2010 +0100
@@ -0,0 +1,6 @@
+show_question_marks := false;
+quick_and_dirty := true;
+
+no_document use_thy "LaTeXsugar";
+
+use_thy "Slides3"
\ No newline at end of file
diff -r 0a5320c6a7e6 -r 842969a598f2 Slides/Slides2.thy
--- /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
diff -r 0a5320c6a7e6 -r 842969a598f2 Slides/Slides3.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Slides/Slides3.thy	Sat Jul 10 11:27:04 2010 +0100
@@ -0,0 +1,997 @@
+(*<*)
+theory Slides3
+imports "LaTeXsugar" "Nominal"
+begin
+
+notation (latex output)
+  set ("_") and
+  Cons  ("_::/_" [66,65] 65) 
+
+(*>*)
+
+
+text_raw {*
+  \renewcommand{\slidecaption}{Cambridge, 8.~June 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/HOL\\[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 old Nominal 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}<1-4>
+  \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}
+  $\forall\{x, y\}.\, x \rightarrow y \;\;\approx_\alpha\;\; \forall\{y, x\}.\, y \rightarrow x$
+  \bigskip\smallskip\\
+
+  \onslide<2->{%
+  $\forall\{x, y\}.\, x \rightarrow y \;\;\not\approx_\alpha\;\; \forall\{z\}.\, z \rightarrow z$
+  }\bigskip\smallskip\\
+
+  \onslide<3->{%
+  $\forall\{x\}.\, x \rightarrow y \;\;\approx_\alpha\;\; \forall\{x, \alert{z}\}.\, x \rightarrow y$
+  }\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
+  
+  \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}
+  \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
+  \end{itemize}
+
+  \onslide<2->{
+  \begin{center}
+  \isacommand{bind\_res}\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::}assn \only<2->{t::}trm
+  & \onslide<2->{\isacommand{bind} bn(as) \isacommand{in} t}\\
+  \multicolumn{2}{l}{\isacommand{and} assn $=$}\\
+  \multicolumn{2}{l}{\hspace{5mm}\phantom{$|$} ANil}\\
+  \multicolumn{2}{l}{\hspace{5mm}$|$ ACons name trm assn}\\
+  \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}<1-5>
+  \frametitle{\begin{tabular}{c}Inspiration from Ott\end{tabular}}
+  \mbox{}\\[-3mm]
+
+  \begin{itemize}
+  \item this way of specifying binding is inspired by 
+  Ott\onslide<2->{, \alert{\bf but} we made adjustments:}\medskip
+  
+
+  \only<2>{
+  \begin{itemize}
+  \item Ott allows specifications like\smallskip
+  \begin{center}
+  $t ::= t\;t\; |\;\lambda x.t$
+  \end{center}
+  \end{itemize}}
+
+  \only<3-4>{
+  \begin{itemize}
+  \item whether something is bound can depend in Ott on other bound things\smallskip
+  \begin{center}
+  \begin{tikzpicture}
+  \node (A) at (-0.5,1) {Foo $(\lambda y. \lambda x. t)$};
+  \node (B) at ( 1.1,1) {$s$};
+  \onslide<4>{\node (C) at (0.5,0) {$\{y, x\}$};}
+  \onslide<4>{\draw[->,red,line width=1mm] (A) -- (C);}
+  \onslide<4>{\draw[->,red,line width=1mm] (C) -- (B);}
+  \end{tikzpicture}
+  \end{center}
+  \onslide<4>{this might make sense for ``raw'' terms, but not at all 
+  for $\alpha$-equated terms}
+  \end{itemize}}
+
+  \only<5>{
+  \begin{itemize}
+  \item we allow multiple binders and bodies\smallskip
+  \begin{center}
+  \isacommand{bind} a b c \isacommand{in} x y z
+  \end{center}\bigskip\medskip
+  the reason is that in general
+  \begin{center}
+  \begin{tabular}{rcl}
+  \isacommand{bind\_res} as \isacommand{in} x y & $\not\Leftrightarrow$ &
+  \begin{tabular}{@ {}l}
+  \isacommand{bind\_res} as \isacommand{in} x,\\
+  \isacommand{bind\_res} as \isacommand{in} y
+  \end{tabular}
+  \end{tabular}
+  \end{center}\smallskip
+
+  same with \isacommand{bind\_set}
+  \end{itemize}}
+  \end{itemize}
+
+
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1>
+  \frametitle{\begin{tabular}{c}Alpha-Equivalence\end{tabular}}
+  \mbox{}\\[-3mm]
+
+  \begin{itemize}
+  \item in old Nominal, we represented single binders as partial functions:\bigskip
+  
+  \begin{center}
+  \begin{tabular}{l}
+  Lam [$a$].\,$t$ $\;{^\text{``}}\!\dn{}\!^{\text{''}}$\\[2mm]
+  \;\;\;\;$\lambda b.$\;$\text{if}\;a = b\;\text{then}\;t\;\text{else}$\\
+  \phantom{\;\;\;\;$\lambda b.$\;\;\;\;\;\;}$\text{if}\;b \fresh t\;
+  \text{then}\;(a\;b)\act t\;\text{else}\;\text{error}$ 
+  \end{tabular}
+  \end{center}
+  \end{itemize}
+
+  \begin{textblock}{10}(2,14)
+  \footnotesize $^*$ alpha-equality coincides with equality on functions
+  \end{textblock}
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1->
+  \frametitle{\begin{tabular}{c}New Design\end{tabular}}
+  \mbox{}\\[4mm]
+
+  \begin{center}
+  \begin{tikzpicture}
+  \alt<2>
+  {\draw (0,0) node[inner sep=3mm, ultra thick, draw=red, rounded corners=2mm]
+  (A) {\textcolor{red}{\begin{minipage}{1.1cm}bind.\\spec.\end{minipage}}};}
+  {\draw (0,0) node[inner sep=3mm, ultra thick, draw=white, rounded corners=2mm]
+  (A) {\begin{minipage}{1.1cm}bind.\\spec.\end{minipage}};}
+  
+  \alt<3>
+  {\draw (3,0) node[inner sep=3mm, ultra thick, draw=red, rounded corners=2mm]
+  (B) {\textcolor{red}{\begin{minipage}{1.1cm}raw\\terms\end{minipage}}};}
+  {\draw (3,0) node[inner sep=3mm, ultra thick, draw=white, rounded corners=2mm]
+  (B) {\begin{minipage}{1.1cm}raw\\terms\end{minipage}};}
+
+  \alt<4>
+  {\draw (6,0) node[inner sep=3mm, ultra thick, draw=red, rounded corners=2mm]
+  (C) {\textcolor{red}{\begin{minipage}{1.1cm}$\alpha$-\\equiv.\end{minipage}}};}
+  {\draw (6,0) node[inner sep=3mm, ultra thick, draw=white, rounded corners=2mm]
+  (C) {\begin{minipage}{1.1cm}$\alpha$-\\equiv.\end{minipage}};}
+  
+  \alt<5>
+  {\draw (0,-3) node[inner sep=3mm, ultra thick, draw=red, rounded corners=2mm]
+  (D) {\textcolor{red}{\begin{minipage}{1.1cm}quot.\\type\end{minipage}}};}
+  {\draw (0,-3) node[inner sep=3mm, ultra thick, draw=white, rounded corners=2mm]
+  (D) {\begin{minipage}{1.1cm}quot.\\type\end{minipage}};}
+
+  \alt<6>
+  {\draw (3,-3) node[inner sep=3mm, ultra thick, draw=red, rounded corners=2mm]
+  (E) {\textcolor{red}{\begin{minipage}{1.1cm}lift\\thms\end{minipage}}};}
+  {\draw (3,-3) node[inner sep=3mm, ultra thick, draw=white, rounded corners=2mm]
+  (E) {\begin{minipage}{1.1cm}lift\\thms\end{minipage}};}
+
+  \alt<7>
+  {\draw (6,-3) node[inner sep=3mm, ultra thick, draw=red, rounded corners=2mm]
+  (F) {\textcolor{red}{\begin{minipage}{1.1cm}add.\\thms\end{minipage}}};}
+  {\draw (6,-3) node[inner sep=3mm, ultra thick, draw=white, rounded corners=2mm]
+  (F) {\begin{minipage}{1.1cm}add.\\thms\end{minipage}};}
+  
+  \draw[->,white!50,line width=1mm] (A) -- (B);
+  \draw[->,white!50,line width=1mm] (B) -- (C);
+  \draw[->,white!50,line width=1mm, line join=round, rounded corners=2mm] 
+  (C) -- (8,0) -- (8,-1.5) -- (-2,-1.5) -- (-2,-3) -- (D);
+  \draw[->,white!50,line width=1mm] (D) -- (E);
+  \draw[->,white!50,line width=1mm] (E) -- (F);
+  \end{tikzpicture}
+  \end{center}
+
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1-9>
+  \frametitle{\begin{tabular}{c}Alpha-Equivalence\end{tabular}}
+  \mbox{}\\[-3mm]
+
+  \begin{itemize}
+  \item lets first look at pairs\bigskip\medskip
+
+  \begin{tabular}{@ {\hspace{1cm}}l}
+  $(as, x) \onslide<2->{\approx\!}\makebox[0mm][l]{\only<2-7>{${}_{\text{set}}$}%
+           \only<8>{${}_{\text{\alert{list}}}$}%
+           \only<9>{${}_{\text{\alert{res}}}$}}%
+           \onslide<3->{^{R,\text{fv}}}\,\onslide<2->{(bs,y)}$
+  \end{tabular}\bigskip
+  \end{itemize}
+
+  \only<1>{
+  \begin{textblock}{8}(3,8.5)
+  \begin{tabular}{l@ {\hspace{2mm}}p{8cm}}
+   & $as$ is a set of atoms\ldots the binders\\
+   & $x$ is the body\\
+   & $\approx_{\text{set}}$ is where the cardinality 
+  of the binders has to be the same\\
+  \end{tabular}
+  \end{textblock}}
+
+  \only<4->{
+  \begin{textblock}{12}(5,8)
+  \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<6->{$\;\;\;\wedge$} & \onslide<6->{$(\pi \act x)\;R\;y$}\\[1mm]
+        & \onslide<7-8>{$\;\;\;\wedge$} & \onslide<7-8>{$\pi \act as = bs$}\\
+  \end{tabular}
+  \end{textblock}}
+  
+  \only<8>{
+  \begin{textblock}{8}(3,13.8)
+  \footnotesize $^*$ $as$ and $bs$ are \alert{lists} of atoms 
+  \end{textblock}}
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1-2>
+  \frametitle{\begin{tabular}{c}Examples\end{tabular}}
+  \mbox{}\\[-3mm]
+
+  \begin{itemize}
+  \item lets look at ``type-schemes'':\medskip\medskip
+
+  \begin{center}
+  $(as, x) \approx\!\makebox[0mm][l]{${}_{\text{set}}$}\only<1>{{}^{R,\text{fv}}}\only<2->{{}^{\alert{=},\alert{\text{fv}}}} (bs, y)$
+  \end{center}\medskip
+
+  \onslide<2->{
+  \begin{center}
+  \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<2->{
+  \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}{res:}\\
+  $\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
+  $\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
+  $\wedge$ & $\pi \cdot x = y$\\
+  \\
+  \end{tabular}
+  \end{minipage}};
+  \end{tikzpicture}
+  \end{textblock}}
+  \only<2->{
+  \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<2->{
+  \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}
+  \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 $\approx_{\text{res}}$, $\approx_{\text{set}}$% 
+  \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}{res:}\\
+  $\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
+  $\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
+  $\wedge$ & $\pi \cdot x = y$\\
+  \\
+  \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>
+  \frametitle{\begin{tabular}{c}Examples\end{tabular}}
+  \mbox{}\\[-3mm]
+
+  \begin{center}
+  \only<1>{$(\{x\}, x) \approx_? (\{x, y\}, x)$}
+  \end{center}
+
+  \begin{itemize}
+  \item $\approx_{\text{res}}$, $\not\approx_{\text{set}}$,
+        $\not\approx_{\text{list}}$
+  \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}{res:}\\
+  $\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
+  $\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
+  $\wedge$ & $\pi \cdot x = y$\\
+  \\
+  \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}<1-3>
+  \frametitle{\begin{tabular}{c}General Abstractions\end{tabular}}
+  \mbox{}\\[-7mm]
+
+  \begin{itemize}
+  \item we take $(as, x) \approx\!\makebox[0mm][l]{${}_{\star}$}^{=,\text{supp}} (bs, y)$\medskip
+  \item they are equivalence relations\medskip
+  \item we can therefore use the quotient package to introduce the 
+  types $\beta\;\text{abs}_\star$\bigskip
+  \begin{center}
+  \only<1>{$[as].\,x$}
+  \only<2>{$\text{supp}([as].x) = \text{supp}(x) - as$}
+  \only<3>{%
+  \begin{tabular}{r@ {\hspace{1mm}}l}
+  \multicolumn{2}{@ {\hspace{-7mm}}l}{$[as]. x \alert{=}  [bs].y\;\;\;\text{if\!f}$}\\[2mm]
+  $\exists \pi.$ & $\text{supp}(x) - as = \text{supp}(y) - bs$\\
+  $\wedge$       & $\text{supp}(x) - as \fresh^* \pi$\\
+  $\wedge$       & $\pi \act x = y $\\
+  $(\wedge$       & $\pi \act as = bs)\;^\star$\\
+  \end{tabular}}
+  \end{center}
+  \end{itemize}
+
+  
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1>
+  \frametitle{\begin{tabular}{c}One Problem\end{tabular}}
+  \mbox{}\\[-3mm]
+
+  \begin{center}
+  $\text{let}\;x_1=t_1 \ldots x_n=t_n\;\text{in}\;s$
+  \end{center}
+
+  \begin{itemize}
+  \item we cannot represent this as\medskip
+  \begin{center}
+  $\text{let}\;[x_1,\ldots,x_n]\alert{.}s\;\;[t_1,\ldots,t_n]$
+  \end{center}\bigskip
+
+  because\medskip
+  \begin{center}
+  $\text{let}\;[x].s\;\;[t_1,t_2]$
+  \end{center}
+  \end{itemize}
+
+  
+  \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::assn t::trm
+  & \isacommand{bind} bn(as) \isacommand{in} t\\
+  \multicolumn{2}{l}{\isacommand{and} assn $=$}\\
+  \multicolumn{2}{l}{\hspace{5mm}\phantom{$|$} ANil}\\
+  \multicolumn{2}{l}{\hspace{5mm}$|$ ACons name trm assn}\\
+  \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}<1-2>
+  \frametitle{\begin{tabular}{c}``Raw'' Definitions\end{tabular}}
+  \mbox{}\\[-6mm]
+
+  \mbox{}\hspace{10mm}
+  \begin{tabular}{ll}
+  \multicolumn{2}{l}{\isacommand{datatype} trm $=$}\\
+  \hspace{5mm}\phantom{$|$} Var name\\
+  \hspace{5mm}$|$ App trm trm\\
+  \hspace{5mm}$|$ Lam name trm\\
+  \hspace{5mm}$|$ Let assn trm\\
+  \multicolumn{2}{l}{\isacommand{and} assn $=$}\\
+  \multicolumn{2}{l}{\hspace{5mm}\phantom{$|$} ANil}\\
+  \multicolumn{2}{l}{\hspace{5mm}$|$ ACons name trm assn}\\[5mm]
+  \multicolumn{2}{l}{\isacommand{function} 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}
+
+  \only<2>{
+  \begin{textblock}{5}(10,5)
+  $+$ \begin{tabular}{l}automatically\\ 
+  generate fv's\end{tabular}
+  \end{textblock}}
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1>
+  \frametitle{\begin{tabular}{c}\LARGE``Raw'' Alpha-Equivalence\end{tabular}}
+  \mbox{}\\[6mm]
+
+  \begin{center}
+  Lam x::name t::trm \hspace{10mm}\isacommand{bind} x \isacommand{in} t\\
+  \end{center}
+
+
+  \[
+  \infer[\text{Lam-}\!\approx_\alpha]
+  {\text{Lam}\;x\;t \approx_\alpha \text{Lam}\;x'\;t'}
+  {([x], t) \approx\!\makebox[0mm][l]{${}_{\text{list}}$}
+    ^{\approx_\alpha,\text{fv}} ([x'], t')}
+  \]
+
+
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1>
+  \frametitle{\begin{tabular}{c}\LARGE``Raw'' Alpha-Equivalence\end{tabular}}
+  \mbox{}\\[6mm]
+
+  \begin{center}
+  Lam x::name y::name t::trm s::trm \hspace{5mm}\isacommand{bind} x y \isacommand{in} t s\\
+  \end{center}
+
+
+  \[
+  \infer[\text{Lam-}\!\approx_\alpha]
+  {\text{Lam}\;x\;y\;t\;s \approx_\alpha \text{Lam}\;x'\;y'\;t'\;s'}
+  {([x, y], (t, s)) \approx\!\makebox[0mm][l]{${}_{\text{list}}$}
+    ^{R, fv} ([x', y'], (t', s'))}
+  \]
+
+  \footnotesize
+  where $R =\;\approx_\alpha\times\approx_\alpha$ and $fv = \text{fv}\cup\text{fv}$
+
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1-2>
+  \frametitle{\begin{tabular}{c}\LARGE``Raw'' Alpha-Equivalence\end{tabular}}
+  \mbox{}\\[6mm]
+
+  \begin{center}
+  Let as::assn t::trm \hspace{10mm}\isacommand{bind} bn(as) \isacommand{in} t\\
+  \end{center}
+
+
+  \[
+  \infer[\text{Let-}\!\approx_\alpha]
+  {\text{Let}\;as\;t \approx_\alpha \text{Let}\;as'\;t'}
+  {(\text{bn}(as), t) \approx\!\makebox[0mm][l]{${}_{\text{list}}$}
+    ^{\approx_\alpha,\text{fv}} (\text{bn}(as'), t') &
+   \onslide<2>{as \approx_\alpha^{\text{bn}} as'}}
+  \]
+
+
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1->
+  \frametitle{\begin{tabular}{c}\LARGE{}$\alpha$ for Binding Functions\end{tabular}}
+  \mbox{}\\[-6mm]
+
+  \mbox{}\hspace{10mm}
+  \begin{tabular}{l}
+  \ldots\\
+  \isacommand{binder} bn \isacommand{where}\\
+  \phantom{$|$} bn(ANil) $=$ $[]$\\
+  $|$ bn(ACons a t as) $=$ $[$a$]$ @ bn(as)\\
+  \end{tabular}\bigskip
+
+  \begin{center}
+  \mbox{\infer{\text{ANil} \approx_\alpha^{\text{bn}} \text{ANil}}{}}\bigskip
+
+  \mbox{\infer{\text{ACons}\;a\;t\;as \approx_\alpha^{\text{bn}} \text{ACons}\;a'\;t'\;as'}
+  {t \approx_\alpha t' & as \approx_\alpha^{bn} as'}}
+  \end{center}
+
+
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1->
+  \frametitle{\begin{tabular}{c}Automatic Proofs\end{tabular}}
+  \mbox{}\\[-6mm]
+
+  \begin{itemize}
+  \item we can show that $\alpha$'s are equivalence relations\medskip
+  \item as a result we can use the quotient package to introduce the type(s)
+  of $\alpha$-equated terms
+
+  \[
+  \infer
+  {\text{Lam}\;x\;t \alert{=} \text{Lam}\;x'\;t'}
+  {\only<1>{([x], t) \approx\!\makebox[0mm][l]{${}_{\text{list}}$}
+    ^{=,\text{supp}} ([x'], t')}%
+   \only<2>{[x].t = [x'].t'}}
+  \]
+
+
+  \item the properties for support are implied by the properties of $[\_].\_$
+  \item we can derive strong induction principles (almost automatic---just a matter of
+  another week or two)
+  \end{itemize}
+
+
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1>[t]
+  \frametitle{\begin{tabular}{c}Runtime is Acceptable\end{tabular}}
+  \mbox{}\\[-7mm]\mbox{}
+
+  \footnotesize
+  \begin{center}
+  \begin{tikzpicture}
+  \draw (0,0) node[inner sep=2mm, ultra thick, draw=white, rounded corners=2mm]
+  (A) {\begin{minipage}{0.8cm}bind.\\spec.\end{minipage}};
+  
+  \draw (2,0) node[inner sep=2mm, ultra thick, draw=white, rounded corners=2mm]
+  (B) {\begin{minipage}{0.8cm}raw\\terms\end{minipage}};
+
+  \draw (4,0) node[inner sep=2mm, ultra thick, draw=white, rounded corners=2mm]
+  (C) {\begin{minipage}{0.8cm}$\alpha$-\\equiv.\end{minipage}};
+  
+  \draw (0,-2) node[inner sep=2mm, ultra thick, draw=white, rounded corners=2mm]
+  (D) {\begin{minipage}{0.8cm}quot.\\type\end{minipage}};
+
+  \draw (2,-2) node[inner sep=2mm, ultra thick, draw=white, rounded corners=2mm]
+  (E) {\begin{minipage}{0.8cm}lift\\thms\end{minipage}};
+
+  \draw (4,-2) node[inner sep=2mm, ultra thick, draw=white, rounded corners=2mm]
+  (F) {\begin{minipage}{0.8cm}add.\\thms\end{minipage}};
+  
+  \draw[->,white!50,line width=1mm] (A) -- (B);
+  \draw[->,white!50,line width=1mm] (B) -- (C);
+  \draw[->,white!50,line width=1mm, line join=round, rounded corners=2mm] 
+  (C) -- (5,0) -- (5,-1) -- (-1,-1) -- (-1,-2) -- (D);
+  \draw[->,white!50,line width=1mm] (D) -- (E);
+  \draw[->,white!50,line width=1mm] (E) -- (F);
+  \end{tikzpicture}
+  \end{center}
+
+  \begin{itemize}
+  \item Core Haskell: 11 types, 49 term-constructors, 
+  \end{itemize}
+
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+
+text_raw {*
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+  \mode<presentation>{
+  \begin{frame}<1->
+  \frametitle{\begin{tabular}{c}Interesting Phenomenon\end{tabular}}
+  \mbox{}\\[-6mm]
+
+  \small
+  \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::assn t::trm
+  & \isacommand{bind} bn(as) \isacommand{in} t\\
+  \multicolumn{2}{l}{\isacommand{and} assn $=$}\\
+  \multicolumn{2}{l}{\hspace{5mm}\phantom{$|$} ANil}\\
+  \multicolumn{2}{l}{\hspace{5mm}$|$ ACons name trm assn}\\
+  \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}\bigskip\medskip
+
+  we cannot quotient assn: ACons a \ldots $\not\approx_\alpha$ ACons b \ldots
+
+  \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-> we have not yet done function definitions (will come soon and
+  we hope to make improvements over the old way there too)\medskip
+  \item<3-> 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, quotient package, POPL 2011 tutorial)\medskip
+  \end{itemize}
+
+
+  \end{frame}}
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
+*}
+
+(*<*)
+end
+(*>*)
\ No newline at end of file
diff -r 0a5320c6a7e6 -r 842969a598f2 Slides/document/beamerthemeplaincudark.sty
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Slides/document/beamerthemeplaincudark.sty	Sat Jul 10 11:27:04 2010 +0100
@@ -0,0 +1,171 @@
+\ProvidesPackage{beamerthemeplaincu}[2003/11/07 ver 0.93]
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]
+
+% Copyright 2003 by Till Tantau <tantau@cs.tu-berlin.de>.
+%
+% This program can be redistributed and/or modified under the terms
+% of the LaTeX Project Public License Distributed from CTAN
+% archives in directory macros/latex/base/lppl.txt.
+
+\newcommand{\slidecaption}{}
+
+\mode<presentation>
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% comic fonts fonts
+\DeclareFontFamily{T1}{comic}{}%
+\DeclareFontShape{T1}{comic}{m}{n}{<->s*[.9]comic8t}{}%
+\DeclareFontShape{T1}{comic}{m}{it}{<->s*[.9]comic8t}{}%
+\DeclareFontShape{T1}{comic}{m}{sc}{<->s*[.9]comic8t}{}%
+\DeclareFontShape{T1}{comic}{b}{n}{<->s*[.9]comicbd8t}{}%
+\DeclareFontShape{T1}{comic}{b}{it}{<->s*[.9]comicbd8t}{}%
+\DeclareFontShape{T1}{comic}{m}{sl}{<->ssub * comic/m/it}{}%
+\DeclareFontShape{T1}{comic}{b}{sc}{<->sub * comic/m/sc}{}%
+\DeclareFontShape{T1}{comic}{b}{sl}{<->ssub * comic/b/it}{}%
+\DeclareFontShape{T1}{comic}{bx}{n}{<->ssub * comic/b/n}{}%
+\DeclareFontShape{T1}{comic}{bx}{it}{<->ssub * comic/b/it}{}%
+\DeclareFontShape{T1}{comic}{bx}{sc}{<->sub * comic/m/sc}{}%
+\DeclareFontShape{T1}{comic}{bx}{sl}{<->ssub * comic/b/it}{}%
+%
+\renewcommand{\rmdefault}{comic}%
+\renewcommand{\sfdefault}{comic}%
+\renewcommand{\mathfamilydefault}{cmr}% mathfont should be still the old one
+%
+\DeclareMathVersion{bold}% mathfont needs to be bold
+\DeclareSymbolFont{operators}{OT1}{cmr}{b}{n}%
+\SetSymbolFont{operators}{bold}{OT1}{cmr}{b}{n}%
+\DeclareSymbolFont{letters}{OML}{cmm}{b}{it}%
+\SetSymbolFont{letters}{bold}{OML}{cmm}{b}{it}%
+\DeclareSymbolFont{symbols}{OMS}{cmsy}{b}{n}%
+\SetSymbolFont{symbols}{bold}{OMS}{cmsy}{b}{n}%
+\DeclareSymbolFont{largesymbols}{OMX}{cmex}{b}{n}%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% colours
+\setbeamercolor{normal text}{fg=white}
+%%%\setbeamercolor{background canvas}{bg=black} 
+\setbeamertemplate{background canvas}[vertical shading]
+  [bottom=white!5!black,top=white!5!black,middle=white!25!black]
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Frametitles
+\setbeamerfont{frametitle}{size={\huge}}
+\setbeamerfont{frametitle}{family={\usefont{T1}{ptm}{b}{n}}}
+\setbeamercolor{frametitle}{fg=white!80!black}
+
+\setbeamertemplate{frametitle}{%
+\vskip 2mm  % distance from the top margin
+\hskip -3mm % distance from left margin
+\vbox{%
+\begin{minipage}{1.05\textwidth}%
+\centering%
+\insertframetitle%
+\end{minipage}}%
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Foot
+%
+\setbeamertemplate{navigation symbols}{} 
+\usefoottemplate{%
+\vbox{%
+  \tinyline{%
+    \tiny\hfill\textcolor{gray!50}{\slidecaption{} --
+      p.~\insertframenumber/\inserttotalframenumber}}}%
+}
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%\beamertemplateballitem
+\setbeamertemplate{itemize items}[ball]
+\setbeamercolor{item}{fg=red}
+
+\pgfdeclareradialshading[bg,parent.bg]{bigsphere}{\pgfpoint{-0.1849315ex}{.2260273ex}}%
+{%
+  color(0cm)=(bg!15);
+  color(0.1643835ex)=(bg!75);
+  color(0.3287671ex)=(bg!70!black);
+  color(0.4520547ex)=(bg!50!black)}
+
+\pgfdeclareradialshading{bigspherered}{\pgfpoint{-0.1849315ex}{.2260273ex}}%
+{%
+  color(0cm)=(red!15);
+  color(0.1643835ex)=(red!75);
+  color(0.3287671ex)=(red!70!black);
+  color(0.4520547ex)=(red!50!black)}
+
+\pgfdeclareradialshading[bg,parent.bg]{smallsphere}{\pgfpoint{-0.1479452ex}{0.18287671ex}}%
+{%
+  color(0cm)=(bg!15); 
+  color(0.1315068ex)=(bg!75);
+  color(0.2630136ex)=(bg!70!black);
+  color(0.36164383ex)=(bg!50!black)}
+
+\setlength\leftmargini{2mm}
+\setlength\leftmarginii{0.6cm}
+\setlength\leftmarginiii{1.5cm}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% blocks
+%\definecolor{cream}{rgb}{1,1,.65}
+\definecolor{cream}{rgb}{1,1,.8}
+
+\setbeamerfont{block title}{size=\normalsize}
+\setbeamercolor{block title}{fg=black,bg=cream}
+\setbeamercolor{block body}{fg=black,bg=cream}
+\setbeamertemplate{blocks}[rounded][shadow=true]
+\setbeamercolor{boxcolor}{fg=red,bg=cream}
+
+
+% 
+% Boxed environment with semi-transparent shadow. 
+% 
+\newlength{\boxw} 
+\newlength{\boxh} 
+\newlength{\shadowsize} 
+\newlength{\boxroundness} 
+\newlength{\tmpa} 
+\newsavebox{\shadowblockbox} 
+
+\setlength{\shadowsize}{6pt} 
+\setlength{\boxroundness}{3pt} 
+
+\newenvironment{shadowblock}[1]% 
+{\begin{lrbox}{\shadowblockbox}\begin{minipage}{#1}}% 
+{\end{minipage}\end{lrbox}% 
+\settowidth{\boxw}{\usebox{\shadowblockbox}}% 
+\settodepth{\tmpa}{\usebox{\shadowblockbox}}% 
+\settoheight{\boxh}{\usebox{\shadowblockbox}}% 
+\addtolength{\boxh}{\tmpa}% 
+\begin{tikzpicture} 
+    \addtolength{\boxw}{\boxroundness * 2} 
+    \addtolength{\boxh}{\boxroundness * 2} 
+
+    \foreach \x in {0,.05,...,1} 
+    { 
+        \setlength{\tmpa}{\shadowsize * \real{\x}} 
+        \fill[xshift=\shadowsize - 1pt,yshift=-\shadowsize + 1pt,
+              black,opacity=.04,rounded corners=\boxroundness] 
+            (\tmpa, \tmpa) rectangle +(\boxw - \tmpa - \tmpa, \boxh - \tmpa - \tmpa); 
+    } 
+
+    \filldraw[fill=cream, draw=black, rounded corners=\boxroundness] 
+             (0, 0) rectangle (\boxw, \boxh); 
+    \draw node[xshift=\boxroundness,yshift=\boxroundness,inner sep=0pt,
+               outer sep=0pt,anchor=south west] (0,0) {\usebox{\shadowblockbox}}; 
+\end{tikzpicture}} 
+
+
+\mode
+<all>
+
+
+
+
+
+
diff -r 0a5320c6a7e6 -r 842969a598f2 Slides/document/beamerthemeplainculight.sty
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Slides/document/beamerthemeplainculight.sty	Sat Jul 10 11:27:04 2010 +0100
@@ -0,0 +1,101 @@
+\ProvidesPackage{beamerthemeplaincu}[2003/11/07 ver 0.93]
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]
+
+% Copyright 2003 by Till Tantau <tantau@cs.tu-berlin.de>.
+%
+% This program can be redistributed and/or modified under the terms
+% of the LaTeX Project Public License Distributed from CTAN
+% archives in directory macros/latex/base/lppl.txt.
+
+\newcommand{\slidecaption}{}
+
+\mode<presentation>
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% comic fonts fonts
+\DeclareFontFamily{T1}{comic}{}%
+\DeclareFontShape{T1}{comic}{m}{n}{<->s*[.9]comic8t}{}%
+\DeclareFontShape{T1}{comic}{m}{it}{<->s*[.9]comic8t}{}%
+\DeclareFontShape{T1}{comic}{m}{sc}{<->s*[.9]comic8t}{}%
+\DeclareFontShape{T1}{comic}{b}{n}{<->s*[.9]comicbd8t}{}%
+\DeclareFontShape{T1}{comic}{b}{it}{<->s*[.9]comicbd8t}{}%
+\DeclareFontShape{T1}{comic}{m}{sl}{<->ssub * comic/m/it}{}%
+\DeclareFontShape{T1}{comic}{b}{sc}{<->sub * comic/m/sc}{}%
+\DeclareFontShape{T1}{comic}{b}{sl}{<->ssub * comic/b/it}{}%
+\DeclareFontShape{T1}{comic}{bx}{n}{<->ssub * comic/b/n}{}%
+\DeclareFontShape{T1}{comic}{bx}{it}{<->ssub * comic/b/it}{}%
+\DeclareFontShape{T1}{comic}{bx}{sc}{<->sub * comic/m/sc}{}%
+\DeclareFontShape{T1}{comic}{bx}{sl}{<->ssub * comic/b/it}{}%
+%
+\renewcommand{\rmdefault}{comic}%
+\renewcommand{\sfdefault}{comic}%
+\renewcommand{\mathfamilydefault}{cmr}% mathfont should be still the old one
+%
+\DeclareMathVersion{bold}% mathfont needs to be bold
+\DeclareSymbolFont{operators}{OT1}{cmr}{b}{n}%
+\SetSymbolFont{operators}{bold}{OT1}{cmr}{b}{n}%
+\DeclareSymbolFont{letters}{OML}{cmm}{b}{it}%
+\SetSymbolFont{letters}{bold}{OML}{cmm}{b}{it}%
+\DeclareSymbolFont{symbols}{OMS}{cmsy}{b}{n}%
+\SetSymbolFont{symbols}{bold}{OMS}{cmsy}{b}{n}%
+\DeclareSymbolFont{largesymbols}{OMX}{cmex}{b}{n}%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Frametitles
+\setbeamerfont{frametitle}{size={\huge}}
+\setbeamerfont{frametitle}{family={\usefont{T1}{ptm}{b}{n}}}
+\setbeamercolor{frametitle}{fg=gray,bg=white}
+
+\setbeamertemplate{frametitle}{%
+\vskip 2mm  % distance from the top margin
+\hskip -3mm % distance from left margin
+\vbox{%
+\begin{minipage}{1.05\textwidth}%
+\centering%
+\insertframetitle%
+\end{minipage}}%
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Foot
+%
+\setbeamertemplate{navigation symbols}{} 
+\usefoottemplate{%
+\vbox{%
+  \tinyline{%
+    \tiny\hfill\textcolor{gray!50}{\slidecaption{} --
+      p.~\insertframenumber/\inserttotalframenumber}}}%
+}
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\beamertemplateballitem
+\setlength\leftmargini{2mm}
+\setlength\leftmarginii{0.6cm}
+\setlength\leftmarginiii{1.5cm}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% blocks
+%\definecolor{cream}{rgb}{1,1,.65}
+\definecolor{cream}{rgb}{1,1,.8}
+\setbeamerfont{block title}{size=\normalsize}
+\setbeamercolor{block title}{fg=black,bg=cream}
+\setbeamercolor{block body}{fg=black,bg=cream}
+
+\setbeamertemplate{blocks}[rounded][shadow=true]
+
+\setbeamercolor{boxcolor}{fg=black,bg=cream}
+
+\mode
+<all>
+
+
+
+
+
+
diff -r 0a5320c6a7e6 -r 842969a598f2 Slides/document/root.tex
--- a/Slides/document/root.tex	Fri Jul 09 23:04:51 2010 +0100
+++ b/Slides/document/root.tex	Sat Jul 10 11:27:04 2010 +0100
@@ -1,4 +1,4 @@
-\usepackage{beamerthemeplaincu}
+\usepackage{beamerthemeplainculight}
 \usepackage[T1]{fontenc}
 \usepackage{proof}
 \usepackage{german}