7 set ("_") and |
7 set ("_") and |
8 Cons ("_::/_" [66,65] 65) |
8 Cons ("_::/_" [66,65] 65) |
9 |
9 |
10 (*>*) |
10 (*>*) |
11 |
11 |
12 |
12 text_raw {* |
13 text_raw {* |
13 \renewcommand{\slidecaption}{UNIF, Edinburgh, 14.~July 2010} |
14 \renewcommand{\slidecaption}{Cambridge, 8.~June 2010} |
14 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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15 \mode<presentation>{ |
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16 \begin{frame}<1>[c] |
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17 \frametitle{Quiz} |
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18 |
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19 Assuming that \smath{a} and \smath{b} are distinct variables,\\ |
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20 is it possible to find $\lambda$-terms \smath{M_1} to \smath{M_7} |
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21 that make the following pairs \alert{$\alpha$-equivalent}? |
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22 |
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23 \begin{tabular}{@ {\hspace{14mm}}p{12cm}} |
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24 \begin{itemize} |
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25 \item \smath{\lambda a.\lambda b. (M_1\,b)\;} and |
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26 \smath{\lambda b.\lambda a. (a\,M_1)\;} |
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27 |
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28 \item \smath{\lambda a.\lambda b. (M_2\,b)\;} and |
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29 \smath{\lambda b.\lambda a. (a\,M_3)\;} |
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30 |
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31 \item \smath{\lambda a.\lambda b. (b\,M_4)\;} and |
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32 \smath{\lambda b.\lambda a. (a\,M_5)\;} |
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33 |
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34 \item \smath{\lambda a.\lambda b. (b\,M_6)\;} and |
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35 \smath{\lambda a.\lambda a. (a\,M_7)\;} |
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36 \end{itemize} |
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37 \end{tabular} |
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38 |
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39 If there is one solution for a pair, can you describe all its solutions? |
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40 |
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41 \end{frame}} |
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42 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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43 *} |
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44 |
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45 text_raw {* |
15 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
46 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
16 \mode<presentation>{ |
47 \mode<presentation>{ |
17 \begin{frame}<1>[t] |
48 \begin{frame}<1>[t] |
18 \frametitle{% |
49 \frametitle{% |
19 \begin{tabular}{@ {\hspace{-3mm}}c@ {}} |
50 \begin{tabular}{@ {\hspace{-3mm}}c@ {}} |
20 \\ |
51 \\ |
21 \huge Nominal 2\\[-2mm] |
52 \huge Nominal Unification\\[-2mm] |
22 \large Or, How to Reason Conveniently with\\[-5mm] |
53 \Large Hitting a Sweet Spot\\[5mm] |
23 \large General Bindings in Isabelle/HOL\\[5mm] |
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24 \end{tabular}} |
54 \end{tabular}} |
25 \begin{center} |
55 \begin{center} |
26 Christian Urban |
56 Christian Urban |
27 \end{center} |
57 \end{center} |
28 \begin{center} |
58 \begin{center} |
29 joint work with {\bf Cezary Kaliszyk}\\[0mm] |
59 \small initial work with Andy Pitts and Jamie Gabbay\\[0mm] |
30 \end{center} |
60 \end{center} |
31 \end{frame}} |
61 \end{frame}} |
32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
62 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
33 |
63 |
34 *} |
64 *} |