2748
|
1 |
(*<*)
|
|
2 |
theory Slides5
|
|
3 |
imports "~~/src/HOL/Library/LaTeXsugar" "Nominal"
|
|
4 |
begin
|
|
5 |
|
|
6 |
notation (latex output)
|
|
7 |
set ("_") and
|
|
8 |
Cons ("_::/_" [66,65] 65)
|
|
9 |
|
|
10 |
(*>*)
|
|
11 |
|
|
12 |
|
|
13 |
text_raw {*
|
2750
|
14 |
%% shallow, deep, and recursive binders
|
|
15 |
%%
|
2748
|
16 |
%%\renewcommand{\slidecaption}{Cambridge, 8.~June 2010}
|
|
17 |
%%\renewcommand{\slidecaption}{Uppsala, 3.~March 2011}
|
|
18 |
\renewcommand{\slidecaption}{Saarbrücken, 31.~March 2011}
|
|
19 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
20 |
\mode<presentation>{
|
|
21 |
\begin{frame}<1>[t]
|
|
22 |
\frametitle{%
|
|
23 |
\begin{tabular}{@ {\hspace{-3mm}}c@ {}}
|
|
24 |
\\
|
2750
|
25 |
\LARGE General Bindings and\\
|
|
26 |
\LARGE Alpha-Equivalence\\
|
|
27 |
\LARGE in Nominal Isabelle\\[3mm]
|
|
28 |
\Large Or, Nominal Isabelle 2\\[-5mm]
|
2748
|
29 |
\end{tabular}}
|
|
30 |
\begin{center}
|
|
31 |
Christian Urban
|
|
32 |
\end{center}
|
|
33 |
\begin{center}
|
|
34 |
joint work with {\bf Cezary Kaliszyk}\\[0mm]
|
|
35 |
\end{center}
|
|
36 |
\end{frame}}
|
|
37 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
38 |
|
|
39 |
*}
|
|
40 |
|
|
41 |
text_raw {*
|
|
42 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
43 |
\mode<presentation>{
|
|
44 |
\begin{frame}<1-2>
|
|
45 |
\frametitle{\begin{tabular}{c}Binding in Old Nominal\end{tabular}}
|
|
46 |
\mbox{}\\[-6mm]
|
|
47 |
|
|
48 |
\begin{itemize}
|
|
49 |
\item the old Nominal Isabelle provided a reasoning infrastructure for single binders\medskip
|
|
50 |
|
|
51 |
\begin{center}
|
|
52 |
Lam [a].(Var a)
|
|
53 |
\end{center}\bigskip
|
|
54 |
|
|
55 |
\item<2-> but representing
|
|
56 |
|
|
57 |
\begin{center}
|
|
58 |
$\forall\{a_1,\ldots,a_n\}.\; T$
|
|
59 |
\end{center}\medskip
|
|
60 |
|
|
61 |
with single binders and reasoning about it is a \alert{\bf major} pain;
|
|
62 |
take my word for it!
|
|
63 |
\end{itemize}
|
|
64 |
|
|
65 |
\only<1>{
|
|
66 |
\begin{textblock}{6}(1.5,11)
|
|
67 |
\small
|
|
68 |
for example\\
|
|
69 |
\begin{tabular}{l@ {\hspace{2mm}}l}
|
|
70 |
& a $\fresh$ Lam [a]. t\\
|
|
71 |
& Lam [a]. (Var a) \alert{$=$} Lam [b]. (Var b)\\
|
|
72 |
& Barendregt-style reasoning about bound variables\\
|
|
73 |
\end{tabular}
|
|
74 |
\end{textblock}}
|
|
75 |
|
|
76 |
\end{frame}}
|
|
77 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
78 |
*}
|
|
79 |
|
2750
|
80 |
|
|
81 |
|
|
82 |
text_raw {*
|
|
83 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
84 |
\mode<presentation>{
|
2751
|
85 |
\begin{frame}<1-6>
|
2750
|
86 |
\frametitle{New Types in HOL}
|
|
87 |
|
2751
|
88 |
\begin{center}
|
|
89 |
\begin{tikzpicture}[scale=1.5]
|
|
90 |
%%%\draw[step=2mm] (-4,-1) grid (4,1);
|
|
91 |
|
|
92 |
\onslide<2-4,6>{\draw[very thick] (0.7,0.4) circle (4.25mm);}
|
|
93 |
\onslide<1-4,6>{\draw[rounded corners=1mm, very thick] ( 0.0,-0.8) rectangle ( 1.8, 0.9);}
|
|
94 |
\onslide<3-5,6>{\draw[rounded corners=1mm, very thick] (-1.95,0.85) rectangle (-2.85,-0.05);}
|
2750
|
95 |
|
2751
|
96 |
\onslide<3-4,6>{\draw (-2.0, 0.845) -- (0.7,0.845);}
|
|
97 |
\onslide<3-4,6>{\draw (-2.0,-0.045) -- (0.7,-0.045);}
|
|
98 |
|
|
99 |
\onslide<4-4,6>{\alert{\draw ( 0.7, 0.4) node {\footnotesize\begin{tabular}{@ {}c@ {}}$\alpha$-\\[-1mm]classes\end{tabular}};}}
|
|
100 |
\onslide<4-5,6>{\alert{\draw (-2.4, 0.4) node {\footnotesize\begin{tabular}{@ {}c@ {}}$\alpha$-eq.\\[-1mm]terms\end{tabular}};}}
|
|
101 |
\onslide<1-4,6>{\draw (1.8, 0.48) node[right=-0.1mm]
|
|
102 |
{\footnotesize\begin{tabular}{@ {}l@ {}}existing\\[-1mm] type\\ \onslide<4-4,6>{\alert{(sets of raw terms)}}\end{tabular}};}
|
|
103 |
\onslide<2-4,6>{\draw (0.9, -0.35) node {\footnotesize\begin{tabular}{@ {}l@ {}}non-empty\\[-1mm]subset\end{tabular}};}
|
|
104 |
\onslide<3-5,6>{\draw (-3.25, 0.55) node {\footnotesize\begin{tabular}{@ {}l@ {}}new\\[-1mm]type\end{tabular}};}
|
|
105 |
|
|
106 |
\onslide<3-4,6>{\draw[<->, very thick] (-1.8, 0.3) -- (-0.1,0.3);}
|
|
107 |
\onslide<3-4,6>{\draw (-0.95, 0.3) node[above=0mm] {\footnotesize{}isomorphism};}
|
|
108 |
|
|
109 |
\onslide<6>{\draw[->, line width=2mm, red] (-1.0,-0.4) -- (0.35,0.16);}
|
|
110 |
\end{tikzpicture}
|
|
111 |
\end{center}
|
|
112 |
|
|
113 |
\begin{center}
|
|
114 |
\textcolor{red}{\large\bf\onslide<6>{define $\alpha$-equivalence}}
|
|
115 |
\end{center}
|
|
116 |
|
2750
|
117 |
\end{frame}}
|
|
118 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
119 |
*}
|
|
120 |
|
|
121 |
|
|
122 |
|
2748
|
123 |
text_raw {*
|
|
124 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
125 |
\mode<presentation>{
|
|
126 |
\begin{frame}<1-4>
|
|
127 |
\frametitle{\begin{tabular}{c}Binding Sets of Names\end{tabular}}
|
|
128 |
\mbox{}\\[-3mm]
|
|
129 |
|
|
130 |
\begin{itemize}
|
|
131 |
\item binding sets of names has some interesting properties:\medskip
|
|
132 |
|
|
133 |
\begin{center}
|
|
134 |
\begin{tabular}{l}
|
2751
|
135 |
\textcolor{blue}{$\forall\{x, y\}.\, x \rightarrow y \;\;\approx_\alpha\;\; \forall\{y, x\}.\, y \rightarrow x$}
|
2748
|
136 |
\bigskip\smallskip\\
|
|
137 |
|
|
138 |
\onslide<2->{%
|
2751
|
139 |
\textcolor{blue}{$\forall\{x, y\}.\, x \rightarrow y \;\;\not\approx_\alpha\;\; \forall\{z\}.\, z \rightarrow z$}
|
2748
|
140 |
}\bigskip\smallskip\\
|
|
141 |
|
|
142 |
\onslide<3->{%
|
2751
|
143 |
\textcolor{blue}{$\forall\{x\}.\, x \rightarrow y \;\;\approx_\alpha\;\; \forall\{x, \alert{z}\}.\, x \rightarrow y$}
|
2748
|
144 |
}\medskip\\
|
|
145 |
\onslide<3->{\hspace{4cm}\small provided $z$ is fresh for the type}
|
|
146 |
\end{tabular}
|
|
147 |
\end{center}
|
|
148 |
\end{itemize}
|
|
149 |
|
|
150 |
\begin{textblock}{8}(2,14.5)
|
|
151 |
\footnotesize $^*$ $x$, $y$, $z$ are assumed to be distinct
|
|
152 |
\end{textblock}
|
|
153 |
|
|
154 |
\only<4>{
|
|
155 |
\begin{textblock}{6}(2.5,4)
|
|
156 |
\begin{tikzpicture}
|
|
157 |
\draw (0,0) node[inner sep=3mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
|
|
158 |
{\normalsize\color{darkgray}
|
|
159 |
\begin{minipage}{8cm}\raggedright
|
|
160 |
For type-schemes the order of bound names does not matter, and
|
2751
|
161 |
$\alpha$-equivalence is preserved under \alert{vacuous} binders.
|
2748
|
162 |
\end{minipage}};
|
|
163 |
\end{tikzpicture}
|
|
164 |
\end{textblock}}
|
|
165 |
\end{frame}}
|
|
166 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
167 |
*}
|
|
168 |
|
|
169 |
text_raw {*
|
|
170 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
171 |
\mode<presentation>{
|
|
172 |
\begin{frame}<1-3>
|
|
173 |
\frametitle{\begin{tabular}{c}Other Binding Modes\end{tabular}}
|
|
174 |
\mbox{}\\[-3mm]
|
|
175 |
|
|
176 |
\begin{itemize}
|
|
177 |
\item alpha-equivalence being preserved under vacuous binders is \underline{not} always
|
|
178 |
wanted:\bigskip\bigskip\normalsize
|
|
179 |
|
2751
|
180 |
\textcolor{blue}{\begin{tabular}{@ {\hspace{-8mm}}l}
|
2748
|
181 |
$\text{let}\;x = 3\;\text{and}\;y = 2\;\text{in}\;x - y\;\text{end}$\medskip\\
|
|
182 |
\onslide<2->{$\;\;\;\only<2>{\approx_\alpha}\only<3>{\alert{\not\approx_\alpha}}
|
|
183 |
\text{let}\;y = 2\;\text{and}\;x = 3\only<3->{\alert{\;\text{and}
|
|
184 |
\;z = \text{loop}}}\;\text{in}\;x - y\;\text{end}$}
|
2751
|
185 |
\end{tabular}}
|
2748
|
186 |
|
|
187 |
|
|
188 |
\end{itemize}
|
|
189 |
|
|
190 |
\end{frame}}
|
|
191 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
192 |
*}
|
|
193 |
|
|
194 |
text_raw {*
|
|
195 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
196 |
\mode<presentation>{
|
|
197 |
\begin{frame}<1>
|
|
198 |
\frametitle{\begin{tabular}{c}\LARGE{}Even Another Binding Mode\end{tabular}}
|
|
199 |
\mbox{}\\[-3mm]
|
|
200 |
|
|
201 |
\begin{itemize}
|
|
202 |
\item sometimes one wants to abstract more than one name, but the order \underline{does} matter\bigskip
|
|
203 |
|
|
204 |
\begin{center}
|
2751
|
205 |
\textcolor{blue}{\begin{tabular}{@ {\hspace{-8mm}}l}
|
2748
|
206 |
$\text{let}\;(x, y) = (3, 2)\;\text{in}\;x - y\;\text{end}$\medskip\\
|
|
207 |
$\;\;\;\not\approx_\alpha
|
|
208 |
\text{let}\;(y, x) = (3, 2)\;\text{in}\;x - y\;\text{end}$
|
2751
|
209 |
\end{tabular}}
|
2748
|
210 |
\end{center}
|
|
211 |
|
|
212 |
|
|
213 |
\end{itemize}
|
|
214 |
|
|
215 |
\end{frame}}
|
|
216 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
217 |
*}
|
|
218 |
|
|
219 |
text_raw {*
|
|
220 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
221 |
\mode<presentation>{
|
|
222 |
\begin{frame}<1-2>
|
|
223 |
\frametitle{\begin{tabular}{c}\LARGE{}Three Binding Modes\end{tabular}}
|
|
224 |
\mbox{}\\[-3mm]
|
|
225 |
|
|
226 |
\begin{itemize}
|
|
227 |
\item the order does not matter and alpha-equivelence is preserved under
|
|
228 |
vacuous binders \textcolor{gray}{(restriction)}\medskip
|
|
229 |
|
|
230 |
\item the order does not matter, but the cardinality of the binders
|
|
231 |
must be the same \textcolor{gray}{(abstraction)}\medskip
|
|
232 |
|
|
233 |
\item the order does matter \textcolor{gray}{(iterated single binders)}
|
|
234 |
\end{itemize}
|
|
235 |
|
|
236 |
\onslide<2->{
|
|
237 |
\begin{center}
|
|
238 |
\isacommand{bind (set+)}\hspace{6mm}
|
|
239 |
\isacommand{bind (set)}\hspace{6mm}
|
|
240 |
\isacommand{bind}
|
|
241 |
\end{center}}
|
|
242 |
|
|
243 |
\end{frame}}
|
|
244 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
245 |
*}
|
|
246 |
|
|
247 |
text_raw {*
|
|
248 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
249 |
\mode<presentation>{
|
|
250 |
\begin{frame}<1-3>
|
|
251 |
\frametitle{\begin{tabular}{c}Specification of Binding\end{tabular}}
|
|
252 |
\mbox{}\\[-6mm]
|
|
253 |
|
|
254 |
\mbox{}\hspace{10mm}
|
|
255 |
\begin{tabular}{ll}
|
|
256 |
\multicolumn{2}{l}{\isacommand{nominal\_datatype} trm $=$}\\
|
|
257 |
\hspace{5mm}\phantom{$|$} Var name\\
|
|
258 |
\hspace{5mm}$|$ App trm trm\\
|
|
259 |
\hspace{5mm}$|$ Lam \only<2->{x::}name \only<2->{t::}trm
|
|
260 |
& \onslide<2->{\isacommand{bind} x \isacommand{in} t}\\
|
2750
|
261 |
\hspace{5mm}$|$ Let \only<2->{as::}assns \only<2->{t::}trm
|
2748
|
262 |
& \onslide<2->{\isacommand{bind} bn(as) \isacommand{in} t}\\
|
2750
|
263 |
\multicolumn{2}{l}{\isacommand{and} assns $=$}\\
|
2748
|
264 |
\multicolumn{2}{l}{\hspace{5mm}\phantom{$|$} ANil}\\
|
2750
|
265 |
\multicolumn{2}{l}{\hspace{5mm}$|$ ACons name trm assns}\\
|
2748
|
266 |
\multicolumn{2}{l}{\onslide<3->{\isacommand{binder} bn \isacommand{where}}}\\
|
|
267 |
\multicolumn{2}{l}{\onslide<3->{\hspace{5mm}\phantom{$|$} bn(ANil) $=$ []}}\\
|
|
268 |
\multicolumn{2}{l}{\onslide<3->{\hspace{5mm}$|$ bn(ACons a t as) $=$ [a] @ bn(as)}}\\
|
|
269 |
\end{tabular}
|
|
270 |
|
|
271 |
|
|
272 |
|
|
273 |
\end{frame}}
|
|
274 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
275 |
*}
|
|
276 |
|
|
277 |
|
|
278 |
text_raw {*
|
|
279 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
280 |
\mode<presentation>{
|
|
281 |
\begin{frame}<1-8>
|
|
282 |
\frametitle{\begin{tabular}{c}Alpha-Equivalence\end{tabular}}
|
|
283 |
\mbox{}\\[-3mm]
|
|
284 |
|
|
285 |
\begin{itemize}
|
|
286 |
\item lets first look at pairs\bigskip\medskip
|
|
287 |
|
2751
|
288 |
\textcolor{blue}{\begin{tabular}{@ {\hspace{1cm}}l}
|
|
289 |
$(as, x) \onslide<2->{\approx\!}\makebox[5mm][l]{\only<2-6>{${}_{\text{set}}$}%
|
2748
|
290 |
\only<7>{${}_{\text{\alert{list}}}$}%
|
|
291 |
\only<8>{${}_{\text{\alert{set+}}}$}}%
|
2751
|
292 |
\,\onslide<2->{(bs,y)}$
|
|
293 |
\end{tabular}}\bigskip
|
2748
|
294 |
\end{itemize}
|
|
295 |
|
|
296 |
\only<1>{
|
|
297 |
\begin{textblock}{8}(3,8.5)
|
|
298 |
\begin{tabular}{l@ {\hspace{2mm}}p{8cm}}
|
2751
|
299 |
& \textcolor{blue}{$as$} is a set of names\ldots the binders\\
|
|
300 |
& \textcolor{blue}{$x$} is the body (might be a tuple)\\
|
|
301 |
& \textcolor{blue}{$\approx_{\text{set}}$} is where the cardinality
|
2748
|
302 |
of the binders has to be the same\\
|
|
303 |
\end{tabular}
|
|
304 |
\end{textblock}}
|
|
305 |
|
|
306 |
\only<4->{
|
|
307 |
\begin{textblock}{12}(5,8)
|
2751
|
308 |
\textcolor{blue}{
|
2748
|
309 |
\begin{tabular}{ll@ {\hspace{1mm}}l}
|
|
310 |
$\dn$ & \onslide<5->{$\exists \pi.\,$} & $\text{fv}(x) - as = \text{fv}(y) - bs$\\[1mm]
|
|
311 |
& \onslide<5->{$\;\;\;\wedge$} & \onslide<5->{$\text{fv}(x) - as \fresh^* \pi$}\\[1mm]
|
2751
|
312 |
& \onslide<5->{$\;\;\;\wedge$} & \onslide<5->{$(\pi \act x) = y$}\\[1mm]
|
|
313 |
& \only<6-7>{$\;\;\;\wedge$}\only<8>{\textcolor{gray}{\xout{$\;\;\;\wedge$}}} &
|
|
314 |
\only<6-7>{$\pi \act as = bs$}\only<8>{\textcolor{gray}{\xout{$\pi \act as = bs$}}}\\
|
|
315 |
\end{tabular}}
|
2748
|
316 |
\end{textblock}}
|
|
317 |
|
|
318 |
\only<7>{
|
|
319 |
\begin{textblock}{7}(3,13.8)
|
|
320 |
\footnotesize $^*$ $as$ and $bs$ are \alert{lists} of names
|
|
321 |
\end{textblock}}
|
|
322 |
\end{frame}}
|
|
323 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
324 |
*}
|
|
325 |
|
|
326 |
text_raw {*
|
|
327 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
328 |
\mode<presentation>{
|
|
329 |
\begin{frame}<1-3>
|
|
330 |
\frametitle{\begin{tabular}{c}Examples\end{tabular}}
|
|
331 |
\mbox{}\\[-3mm]
|
|
332 |
|
|
333 |
\begin{itemize}
|
2751
|
334 |
\item lets look at type-schemes:\medskip\medskip
|
2748
|
335 |
|
|
336 |
\begin{center}
|
2751
|
337 |
\textcolor{blue}{$(as, x) \approx\!\makebox[5mm][l]{${}_{\text{set}}$} (bs, y)$}
|
2748
|
338 |
\end{center}\medskip
|
|
339 |
|
|
340 |
\onslide<2->{
|
|
341 |
\begin{center}
|
2751
|
342 |
\textcolor{blue}{
|
2748
|
343 |
\begin{tabular}{l}
|
|
344 |
$\text{fv}(x) = \{x\}$\\[1mm]
|
|
345 |
$\text{fv}(T_1 \rightarrow T_2) = \text{fv}(T_1) \cup \text{fv}(T_2)$\\
|
2751
|
346 |
\end{tabular}}
|
2748
|
347 |
\end{center}}
|
|
348 |
\end{itemize}
|
|
349 |
|
|
350 |
|
|
351 |
\only<3->{
|
|
352 |
\begin{textblock}{4}(0.3,12)
|
|
353 |
\begin{tikzpicture}
|
|
354 |
\draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
|
|
355 |
{\tiny\color{darkgray}
|
|
356 |
\begin{minipage}{3.4cm}\raggedright
|
|
357 |
\begin{tabular}{r@ {\hspace{1mm}}l}
|
|
358 |
\multicolumn{2}{@ {}l}{set+:}\\
|
|
359 |
$\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
|
|
360 |
$\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
|
|
361 |
$\wedge$ & $\pi \cdot x = y$\\
|
|
362 |
\\
|
|
363 |
\end{tabular}
|
|
364 |
\end{minipage}};
|
|
365 |
\end{tikzpicture}
|
|
366 |
\end{textblock}}
|
|
367 |
\only<3->{
|
|
368 |
\begin{textblock}{4}(5.2,12)
|
|
369 |
\begin{tikzpicture}
|
|
370 |
\draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
|
|
371 |
{\tiny\color{darkgray}
|
|
372 |
\begin{minipage}{3.4cm}\raggedright
|
|
373 |
\begin{tabular}{r@ {\hspace{1mm}}l}
|
|
374 |
\multicolumn{2}{@ {}l}{set:}\\
|
|
375 |
$\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
|
|
376 |
$\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
|
|
377 |
$\wedge$ & $\pi \cdot x = y$\\
|
|
378 |
$\wedge$ & $\pi \cdot as = bs$\\
|
|
379 |
\end{tabular}
|
|
380 |
\end{minipage}};
|
|
381 |
\end{tikzpicture}
|
|
382 |
\end{textblock}}
|
|
383 |
\only<3->{
|
|
384 |
\begin{textblock}{4}(10.2,12)
|
|
385 |
\begin{tikzpicture}
|
|
386 |
\draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
|
|
387 |
{\tiny\color{darkgray}
|
|
388 |
\begin{minipage}{3.4cm}\raggedright
|
|
389 |
\begin{tabular}{r@ {\hspace{1mm}}l}
|
|
390 |
\multicolumn{2}{@ {}l}{list:}\\
|
|
391 |
$\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
|
|
392 |
$\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
|
|
393 |
$\wedge$ & $\pi \cdot x = y$\\
|
|
394 |
$\wedge$ & $\pi \cdot as = bs$\\
|
|
395 |
\end{tabular}
|
|
396 |
\end{minipage}};
|
|
397 |
\end{tikzpicture}
|
|
398 |
\end{textblock}}
|
|
399 |
|
|
400 |
\end{frame}}
|
|
401 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
402 |
*}
|
|
403 |
|
|
404 |
text_raw {*
|
|
405 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
406 |
\mode<presentation>{
|
|
407 |
\begin{frame}<1-2>
|
|
408 |
\frametitle{\begin{tabular}{c}Examples\end{tabular}}
|
|
409 |
\mbox{}\\[-3mm]
|
|
410 |
|
|
411 |
\begin{center}
|
2751
|
412 |
\textcolor{blue}{
|
2748
|
413 |
\only<1>{$(\{x, y\}, x \rightarrow y) \approx_? (\{x, y\}, y \rightarrow x)$}
|
2751
|
414 |
\only<2>{$([x, y], x \rightarrow y) \approx_? ([x, y], y \rightarrow x)$}}
|
2748
|
415 |
\end{center}
|
|
416 |
|
|
417 |
\begin{itemize}
|
2751
|
418 |
\item \textcolor{blue}{$\approx_{\text{set+}}$, $\approx_{\text{set}}$%
|
|
419 |
\only<2>{, \alert{$\not\approx_{\text{list}}$}}}
|
2748
|
420 |
\end{itemize}
|
|
421 |
|
|
422 |
|
|
423 |
\only<1->{
|
|
424 |
\begin{textblock}{4}(0.3,12)
|
|
425 |
\begin{tikzpicture}
|
|
426 |
\draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
|
|
427 |
{\tiny\color{darkgray}
|
|
428 |
\begin{minipage}{3.4cm}\raggedright
|
|
429 |
\begin{tabular}{r@ {\hspace{1mm}}l}
|
|
430 |
\multicolumn{2}{@ {}l}{set+:}\\
|
|
431 |
$\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
|
|
432 |
$\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
|
|
433 |
$\wedge$ & $\pi \cdot x = y$\\
|
|
434 |
\\
|
|
435 |
\end{tabular}
|
|
436 |
\end{minipage}};
|
|
437 |
\end{tikzpicture}
|
|
438 |
\end{textblock}}
|
|
439 |
\only<1->{
|
|
440 |
\begin{textblock}{4}(5.2,12)
|
|
441 |
\begin{tikzpicture}
|
|
442 |
\draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
|
|
443 |
{\tiny\color{darkgray}
|
|
444 |
\begin{minipage}{3.4cm}\raggedright
|
|
445 |
\begin{tabular}{r@ {\hspace{1mm}}l}
|
|
446 |
\multicolumn{2}{@ {}l}{set:}\\
|
|
447 |
$\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
|
|
448 |
$\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
|
|
449 |
$\wedge$ & $\pi \cdot x = y$\\
|
|
450 |
$\wedge$ & $\pi \cdot as = bs$\\
|
|
451 |
\end{tabular}
|
|
452 |
\end{minipage}};
|
|
453 |
\end{tikzpicture}
|
|
454 |
\end{textblock}}
|
|
455 |
\only<1->{
|
|
456 |
\begin{textblock}{4}(10.2,12)
|
|
457 |
\begin{tikzpicture}
|
|
458 |
\draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
|
|
459 |
{\tiny\color{darkgray}
|
|
460 |
\begin{minipage}{3.4cm}\raggedright
|
|
461 |
\begin{tabular}{r@ {\hspace{1mm}}l}
|
|
462 |
\multicolumn{2}{@ {}l}{list:}\\
|
|
463 |
$\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
|
|
464 |
$\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
|
|
465 |
$\wedge$ & $\pi \cdot x = y$\\
|
|
466 |
$\wedge$ & $\pi \cdot as = bs$\\
|
|
467 |
\end{tabular}
|
|
468 |
\end{minipage}};
|
|
469 |
\end{tikzpicture}
|
|
470 |
\end{textblock}}
|
|
471 |
|
|
472 |
\end{frame}}
|
|
473 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
474 |
*}
|
|
475 |
|
|
476 |
text_raw {*
|
|
477 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
478 |
\mode<presentation>{
|
|
479 |
\begin{frame}<1-2>
|
|
480 |
\frametitle{\begin{tabular}{c}Examples\end{tabular}}
|
|
481 |
\mbox{}\\[-3mm]
|
|
482 |
|
|
483 |
\begin{center}
|
2751
|
484 |
\textcolor{blue}{\only<1>{$(\{x\}, x) \approx_? (\{x, y\}, x)$}}
|
2748
|
485 |
\end{center}
|
|
486 |
|
|
487 |
\begin{itemize}
|
2751
|
488 |
\item \textcolor{blue}{$\approx_{\text{set+}}$, $\not\approx_{\text{set}}$,
|
|
489 |
$\not\approx_{\text{list}}$}
|
2748
|
490 |
\end{itemize}
|
|
491 |
|
|
492 |
|
|
493 |
\only<1->{
|
|
494 |
\begin{textblock}{4}(0.3,12)
|
|
495 |
\begin{tikzpicture}
|
|
496 |
\draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
|
|
497 |
{\tiny\color{darkgray}
|
|
498 |
\begin{minipage}{3.4cm}\raggedright
|
|
499 |
\begin{tabular}{r@ {\hspace{1mm}}l}
|
|
500 |
\multicolumn{2}{@ {}l}{set+:}\\
|
|
501 |
$\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
|
|
502 |
$\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
|
|
503 |
$\wedge$ & $\pi \cdot x = y$\\
|
|
504 |
\\
|
|
505 |
\end{tabular}
|
|
506 |
\end{minipage}};
|
|
507 |
\end{tikzpicture}
|
|
508 |
\end{textblock}}
|
|
509 |
\only<1->{
|
|
510 |
\begin{textblock}{4}(5.2,12)
|
|
511 |
\begin{tikzpicture}
|
|
512 |
\draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
|
|
513 |
{\tiny\color{darkgray}
|
|
514 |
\begin{minipage}{3.4cm}\raggedright
|
|
515 |
\begin{tabular}{r@ {\hspace{1mm}}l}
|
|
516 |
\multicolumn{2}{@ {}l}{set:}\\
|
|
517 |
$\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
|
|
518 |
$\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
|
|
519 |
$\wedge$ & $\pi \cdot x = y$\\
|
|
520 |
$\wedge$ & $\pi \cdot as = bs$\\
|
|
521 |
\end{tabular}
|
|
522 |
\end{minipage}};
|
|
523 |
\end{tikzpicture}
|
|
524 |
\end{textblock}}
|
|
525 |
\only<1->{
|
|
526 |
\begin{textblock}{4}(10.2,12)
|
|
527 |
\begin{tikzpicture}
|
|
528 |
\draw (0,0) node[inner sep=1mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
|
|
529 |
{\tiny\color{darkgray}
|
|
530 |
\begin{minipage}{3.4cm}\raggedright
|
|
531 |
\begin{tabular}{r@ {\hspace{1mm}}l}
|
|
532 |
\multicolumn{2}{@ {}l}{list:}\\
|
|
533 |
$\exists\pi.$ & $\text{fv}(x) - as = \text{fv}(y) - bs$\\
|
|
534 |
$\wedge$ & $\text{fv}(x) - as \fresh^* \pi$\\
|
|
535 |
$\wedge$ & $\pi \cdot x = y$\\
|
|
536 |
$\wedge$ & $\pi \cdot as = bs$\\
|
|
537 |
\end{tabular}
|
|
538 |
\end{minipage}};
|
|
539 |
\end{tikzpicture}
|
|
540 |
\end{textblock}}
|
|
541 |
|
|
542 |
\only<2>{
|
|
543 |
\begin{textblock}{6}(2.5,4)
|
|
544 |
\begin{tikzpicture}
|
|
545 |
\draw (0,0) node[inner sep=5mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
|
|
546 |
{\normalsize
|
|
547 |
\begin{minipage}{8cm}\raggedright
|
|
548 |
\begin{itemize}
|
|
549 |
\item \color{darkgray}$\alpha$-equivalences coincide when a single name is
|
|
550 |
abstracted
|
|
551 |
\item \color{darkgray}in that case they are equivalent to ``old-fashioned'' definitions of $\alpha$
|
|
552 |
\end{itemize}
|
|
553 |
\end{minipage}};
|
|
554 |
\end{tikzpicture}
|
|
555 |
\end{textblock}}
|
|
556 |
|
|
557 |
\end{frame}}
|
|
558 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
559 |
*}
|
|
560 |
|
|
561 |
text_raw {*
|
|
562 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
563 |
\mode<presentation>{
|
|
564 |
\begin{frame}<1->
|
|
565 |
\frametitle{\begin{tabular}{c}Our Specifications\end{tabular}}
|
|
566 |
\mbox{}\\[-6mm]
|
|
567 |
|
|
568 |
\mbox{}\hspace{10mm}
|
|
569 |
\begin{tabular}{ll}
|
|
570 |
\multicolumn{2}{l}{\isacommand{nominal\_datatype} trm $=$}\\
|
|
571 |
\hspace{5mm}\phantom{$|$} Var name\\
|
|
572 |
\hspace{5mm}$|$ App trm trm\\
|
|
573 |
\hspace{5mm}$|$ Lam x::name t::trm
|
|
574 |
& \isacommand{bind} x \isacommand{in} t\\
|
2750
|
575 |
\hspace{5mm}$|$ Let as::assns t::trm
|
2748
|
576 |
& \isacommand{bind} bn(as) \isacommand{in} t\\
|
2750
|
577 |
\multicolumn{2}{l}{\isacommand{and} assns $=$}\\
|
2748
|
578 |
\multicolumn{2}{l}{\hspace{5mm}\phantom{$|$} ANil}\\
|
2750
|
579 |
\multicolumn{2}{l}{\hspace{5mm}$|$ ACons name trm assns}\\
|
2748
|
580 |
\multicolumn{2}{l}{\isacommand{binder} bn \isacommand{where}}\\
|
|
581 |
\multicolumn{2}{l}{\hspace{5mm}\phantom{$|$} bn(ANil) $=$ $[]$}\\
|
|
582 |
\multicolumn{2}{l}{\hspace{5mm}$|$ bn(ACons a t as) $=$ $[$a$]$ @ bn(as)}\\
|
|
583 |
\end{tabular}
|
|
584 |
|
|
585 |
\end{frame}}
|
|
586 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
587 |
*}
|
|
588 |
|
|
589 |
text_raw {*
|
|
590 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
591 |
\mode<presentation>{
|
2751
|
592 |
\begin{frame}<1>[c]
|
|
593 |
\frametitle{\begin{tabular}{c}Binding Functions\end{tabular}}
|
2748
|
594 |
|
|
595 |
\begin{center}
|
2751
|
596 |
\begin{tikzpicture}
|
|
597 |
\node (A) at (-0.5,1) {Foo $(\lambda y. \lambda x. t)$};
|
|
598 |
\node (B) at ( 1.5,1) {$s$};
|
|
599 |
\onslide<1>{\node (C) at (0.5,-0.5) {$\{y, x\}$};}
|
|
600 |
\onslide<1>{\draw[->,red,line width=1mm] (A) -- (C);}
|
|
601 |
\onslide<1>{\draw[->,red,line width=1mm] (C) -- (B);}
|
|
602 |
\end{tikzpicture}
|
2748
|
603 |
\end{center}
|
|
604 |
|
2751
|
605 |
|
2748
|
606 |
\end{frame}}
|
|
607 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
608 |
*}
|
|
609 |
|
|
610 |
text_raw {*
|
|
611 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
612 |
\mode<presentation>{
|
2751
|
613 |
\begin{frame}<1->[t]
|
|
614 |
\frametitle{\begin{tabular}{c}Binder Clauses\end{tabular}}
|
2748
|
615 |
|
2751
|
616 |
\begin{itemize}
|
|
617 |
\item We need for a bound variable to have a `clear scope', and bound
|
|
618 |
variables should not be free and bound at the same time.\bigskip
|
|
619 |
\end{itemize}
|
2748
|
620 |
|
|
621 |
\begin{center}
|
2751
|
622 |
\only<1>{
|
|
623 |
\begin{tabular}{@ {\hspace{-5mm}}l}
|
|
624 |
\alert{\bf shallow binders}\\
|
|
625 |
\hspace{4mm}Lam x::name t::trm\hspace{4mm} \isacommand{bind} x \isacommand{in} t\\
|
|
626 |
\hspace{4mm}All xs::name set T::ty\hspace{4mm} \isacommand{bind} xs \isacommand{in} T\\
|
|
627 |
\hspace{4mm}Foo x::name t$_1$::trm t$_2$::trm\hspace{4mm}
|
|
628 |
\isacommand{bind} x \isacommand{in} t$_1$, \isacommand{bind} x \isacommand{in} t$_2$\\
|
|
629 |
\hspace{4mm}Bar x::name t$_1$::trm t$_2$::trm\hspace{4mm}
|
|
630 |
\isacommand{bind} x \isacommand{in} t$_1$ t$_2$\\
|
|
631 |
\end{tabular}}
|
|
632 |
\only<2>{
|
|
633 |
\begin{tabular}{@ {\hspace{-5mm}}l}
|
|
634 |
\alert{\bf deep binders} \\
|
|
635 |
\hspace{4mm}Let as::assns t::trm\hspace{4mm} \isacommand{bind} bn(as) \isacommand{in} t\\
|
|
636 |
\hspace{4mm}Foo as::assns t$_1$::trm t$_2$::trm\\
|
|
637 |
\hspace{20mm}\isacommand{bind} bn(as) \isacommand{in} t$_1$, \isacommand{bind} bn(as) \isacommand{in} t$_2$\\[4mm]
|
|
638 |
\makebox[0mm][l]{\alert{$\times$}}\hspace{4mm}Bar as::assns t$_1$::trm t$_2$::trm\\
|
|
639 |
\hspace{20mm}\isacommand{bind} bn$_1$(as) \isacommand{in} t$_1$, \isacommand{bind} bn$_2$(as) \isacommand{in} t$_2$\\
|
|
640 |
\end{tabular}}
|
|
641 |
\only<3>{
|
|
642 |
\begin{tabular}{@ {\hspace{-5mm}}l}
|
|
643 |
{\bf deep \alert{recursive} binders} \\
|
|
644 |
\hspace{4mm}Let\_rec as::assns t::trm\hspace{4mm} \isacommand{bind} bn(as) \isacommand{in} t as\\[4mm]
|
2748
|
645 |
|
2751
|
646 |
\makebox[0mm][l]{\alert{$\times$}}\hspace{4mm}Foo\_rec as::assns t$_1$::trm t$_2$::trm\hspace{4mm}\\
|
|
647 |
\hspace{20mm}\isacommand{bind} bn(as) \isacommand{in} t$_1$ as, \isacommand{bind} bn(as) \isacommand{in} t$_2$\\
|
2748
|
648 |
|
2751
|
649 |
\end{tabular}}
|
|
650 |
\end{center}
|
|
651 |
|
2748
|
652 |
\end{frame}}
|
|
653 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
654 |
*}
|
|
655 |
|
|
656 |
text_raw {*
|
|
657 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
658 |
\mode<presentation>{
|
2751
|
659 |
\begin{frame}<2-5>
|
|
660 |
\frametitle{\begin{tabular}{c}Our Work\end{tabular}}
|
2748
|
661 |
\mbox{}\\[-6mm]
|
|
662 |
|
2751
|
663 |
\begin{center}
|
|
664 |
\begin{tikzpicture}[scale=1.5]
|
|
665 |
%%%\draw[step=2mm] (-4,-1) grid (4,1);
|
|
666 |
|
|
667 |
\onslide<1>{\draw[very thick] (0.7,0.4) circle (4.25mm);}
|
|
668 |
\onslide<1>{\draw[rounded corners=1mm, very thick] ( 0.0,-0.8) rectangle ( 1.8, 0.9);}
|
|
669 |
\onslide<1->{\draw[rounded corners=1mm, very thick] (-1.95,0.85) rectangle (-2.85,-0.05);}
|
|
670 |
|
|
671 |
\onslide<1>{\draw (-2.0, 0.845) -- (0.7,0.845);}
|
|
672 |
\onslide<1>{\draw (-2.0,-0.045) -- (0.7,-0.045);}
|
2748
|
673 |
|
2751
|
674 |
\onslide<1>{\alert{\draw ( 0.7, 0.4) node {\footnotesize\begin{tabular}{@ {}c@ {}}$\alpha$-\\[-1mm]classes\end{tabular}};}}
|
|
675 |
\onslide<1->{\alert{\draw (-2.4, 0.4) node {\footnotesize\begin{tabular}{@ {}c@ {}}$\alpha$-eq.\\[-1mm]terms\end{tabular}};}}
|
|
676 |
\onslide<1>{\draw (1.8, 0.48) node[right=-0.1mm]
|
|
677 |
{\footnotesize\begin{tabular}{@ {}l@ {}}existing\\[-1mm] type\\ \onslide<1>{\alert{(sets of raw terms)}}\end{tabular}};}
|
|
678 |
\onslide<1>{\draw (0.9, -0.35) node {\footnotesize\begin{tabular}{@ {}l@ {}}non-empty\\[-1mm]subset\end{tabular}};}
|
|
679 |
\onslide<1->{\draw (-3.25, 0.55) node {\footnotesize\begin{tabular}{@ {}l@ {}}new\\[-1mm]type\end{tabular}};}
|
|
680 |
|
|
681 |
\onslide<1>{\draw[<->, very thick] (-1.8, 0.3) -- (-0.1,0.3);}
|
|
682 |
\onslide<1>{\draw (-0.95, 0.3) node[above=0mm] {\footnotesize{}isomorphism};}
|
2748
|
683 |
|
2751
|
684 |
\onslide<1>{\draw[->, line width=2mm, red] (-1.0,-0.4) -- (0.35,0.16);}
|
|
685 |
\end{tikzpicture}
|
|
686 |
\end{center}
|
|
687 |
|
|
688 |
\begin{textblock}{9.5}(6,3.5)
|
|
689 |
\begin{itemize}
|
|
690 |
\item<1-> defined fv and $\alpha$
|
|
691 |
\item<3-> derived a reasoning infrastructure ($\fresh$, distinctness, injectivity, cases,\ldots)
|
|
692 |
\item<4-> a (weak) induction principle
|
|
693 |
\item<5-> derive a {\bf stronger} induction principle (Barendregt variable convention built in)\\
|
|
694 |
\begin{center}
|
|
695 |
\textcolor{blue}{Foo ($\lambda x. \lambda y. t$) ($\lambda u. \lambda v. s$)}
|
|
696 |
\end{center}
|
2748
|
697 |
\end{itemize}
|
2751
|
698 |
\end{textblock}
|
2748
|
699 |
|
|
700 |
|
|
701 |
\end{frame}}
|
|
702 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
703 |
*}
|
|
704 |
|
|
705 |
|
|
706 |
text_raw {*
|
|
707 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
708 |
\mode<presentation>{
|
|
709 |
\begin{frame}<1->
|
|
710 |
\frametitle{\begin{tabular}{c}Conclusion\end{tabular}}
|
|
711 |
\mbox{}\\[-6mm]
|
|
712 |
|
|
713 |
\begin{itemize}
|
|
714 |
\item the user does not see anything of the raw level\medskip
|
|
715 |
\only<1>{\begin{center}
|
|
716 |
Lam a (Var a) \alert{$=$} Lam b (Var b)
|
|
717 |
\end{center}\bigskip}
|
|
718 |
|
2751
|
719 |
\item<2-> it took quite some time to get here, but it seems worthwhile
|
2748
|
720 |
(Barendregt's variable convention is unsound in general,
|
2751
|
721 |
found bugs in two paper proofs)\bigskip\medskip
|
|
722 |
|
|
723 |
\item<3-> \textcolor{blue}{http://isabelle.in.tum.de/nominal/}
|
2748
|
724 |
\end{itemize}
|
|
725 |
|
2751
|
726 |
|
2748
|
727 |
\end{frame}}
|
|
728 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
729 |
*}
|
|
730 |
|
|
731 |
|
|
732 |
|
|
733 |
text_raw {*
|
|
734 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
735 |
\mode<presentation>{
|
|
736 |
\begin{frame}<1->[c]
|
|
737 |
\frametitle{\begin{tabular}{c}Questions?\end{tabular}}
|
|
738 |
\mbox{}\\[-6mm]
|
|
739 |
|
|
740 |
\begin{center}
|
|
741 |
\alert{\huge{Thanks!}}
|
|
742 |
\end{center}
|
|
743 |
|
|
744 |
\end{frame}}
|
|
745 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
746 |
*}
|
|
747 |
|
|
748 |
|
|
749 |
|
|
750 |
text_raw {*
|
|
751 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
752 |
\mode<presentation>{
|
|
753 |
\begin{frame}<1-2>[c]
|
|
754 |
\frametitle{\begin{tabular}{c}Examples\end{tabular}}
|
|
755 |
\mbox{}\\[-6mm]
|
|
756 |
|
2751
|
757 |
\textcolor{blue}{
|
2748
|
758 |
\begin{center}
|
|
759 |
$(\{a,b\}, a \rightarrow b) \approx_\alpha (\{a, b\}, a \rightarrow b)$
|
|
760 |
$(\{a,b\}, a \rightarrow b) \approx_\alpha (\{a, b\}, b \rightarrow a)$
|
2751
|
761 |
\end{center}}
|
2748
|
762 |
|
2751
|
763 |
\textcolor{blue}{
|
2748
|
764 |
\begin{center}
|
|
765 |
$(\{a,b\}, (a \rightarrow b, a \rightarrow b))$\\
|
|
766 |
\hspace{17mm}$\not\approx_\alpha (\{a, b\}, (a \rightarrow b, b \rightarrow a))$
|
2751
|
767 |
\end{center}}
|
2748
|
768 |
|
|
769 |
\onslide<2->
|
|
770 |
{1.) \hspace{3mm}\isacommand{bind (set)} as \isacommand{in} $\tau_1$,
|
|
771 |
\isacommand{bind (set)} as \isacommand{in} $\tau_2$\medskip
|
|
772 |
|
|
773 |
2.) \hspace{3mm}\isacommand{bind (set)} as \isacommand{in} $\tau_1$ $\tau_2$
|
|
774 |
}
|
|
775 |
|
|
776 |
\end{frame}}
|
|
777 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
778 |
*}
|
|
779 |
|
2751
|
780 |
|
|
781 |
|
2748
|
782 |
(*<*)
|
|
783 |
end
|
|
784 |
(*>*) |