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507 |
507 |
508 $\bl{A}$ is the set of definitely defined variables: |
508 $\bl{A}$ is the set of definitely defined variables: |
509 |
509 |
510 \begin{center} |
510 \begin{center} |
511 \begin{tabular}{c} |
511 \begin{tabular}{c} |
512 \bl{\infer{\mbox{}}{A\;\texttt{skip}\;A}}\qquad |
512 \bl{\infer{\mbox{}}{A\triangleright\texttt{skip}\triangleright{}A}}\qquad |
513 \bl{\infer{vars(a) \subseteq A}{A\;\;(\texttt{x\,:=\,a})\;\;\{x\}\cup A}} |
513 \bl{\infer{vars(a) \subseteq A}{A\triangleright |
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514 (\texttt{x\,:=\,a})\triangleright\{x\}\cup A}} |
514 \medskip\\\pause |
515 \medskip\\\pause |
515 |
516 |
516 \bl{\infer{A_1\;s_1\;A_2\quad A_2\;s_2\;A_3}{A_1\;(s_1 ; s_2)\;A_3}} |
517 \bl{\infer{A_1\triangleright{}s_1\triangleright{}A_2 |
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518 \quad A_2\triangleright{}s_2\triangleright{}A_3} |
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519 {A_1\triangleright{}(s_1 ; s_2)\triangleright{}A_3}} |
517 \medskip\\\pause |
520 \medskip\\\pause |
518 |
521 |
519 \bl{\infer{vars(b)\subseteq A\quad A\;s_1\;A_1\quad A\;s_2\;A_2} |
522 \bl{\infer{vars(b)\subseteq A\quad A\triangleright{}s_1\triangleright{}A_1 |
520 {A\;(\texttt{if}\;b\;\texttt{then}\;s_1\;\texttt{else}\;s_2)\;A_1\cap A_2}} |
523 \quad A\triangleright{}s_2\triangleright{}A_2} |
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524 {A\triangleright(\texttt{if}\;b\;\texttt{then}\;s_1\;\texttt{else}\;s_2)\triangleright{}A_1\cap A_2}} |
521 \medskip\\\pause |
525 \medskip\\\pause |
522 |
526 |
523 \bl{\infer{vars(b)\subseteq A\quad A\;s\;A'} |
527 \bl{\infer{vars(b)\subseteq A\quad A\triangleright{}s\triangleright{}A'} |
524 {A\;(\texttt{while}\;b\;\texttt{do}\;s)\;A}}\pause |
528 {A\triangleright(\texttt{while}\;b\;\texttt{do}\;s)\triangleright{}A}}\pause |
525 \end{tabular} |
529 \end{tabular} |
526 \end{center} |
530 \end{center} |
527 |
531 |
528 \hfill we start with $\bl{A = \{\}}$ |
532 \hfill we start with $\bl{A = \{\}}$ |
529 \end{frame} |
533 \end{frame} |
620 \end{itemize} |
624 \end{itemize} |
621 |
625 |
622 \end{frame} |
626 \end{frame} |
623 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
627 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
624 |
628 |
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629 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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630 |
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631 \begin{frame}[c] |
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632 \frametitle{Next Week} |
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633 |
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634 \begin{itemize} |
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635 \item Revision Lecture\medskip |
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636 \item How many strings are in $\bl{L(a^*)}$?\pause\medskip |
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637 \item How many strings are in $\bl{L((a + b)^*)}$?\\ Are there more than |
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638 in $\bl{L(a^*)}$? |
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639 \end{itemize} |
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640 |
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641 |
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642 |
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643 \end{frame} |
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644 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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645 |
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646 |
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647 |
625 \end{document} |
648 \end{document} |
626 |
649 |
627 %%% Local Variables: |
650 %%% Local Variables: |
628 %%% mode: latex |
651 %%% mode: latex |
629 %%% TeX-master: t |
652 %%% TeX-master: t |