# HG changeset patch # User wenzelm # Date 972926880 -3600 # Node ID c20f78a9606f5d569f1ceeda9d1c504eae55bdcc # Parent 807992b67eddeb80c858a416c42b29b70445563f updated; diff -r 807992b67edd -r c20f78a9606f doc-src/AxClass/generated/isabellesym.sty --- a/doc-src/AxClass/generated/isabellesym.sty Mon Oct 30 18:26:14 2000 +0100 +++ b/doc-src/AxClass/generated/isabellesym.sty Mon Oct 30 18:28:00 2000 +0100 @@ -127,7 +127,7 @@ \newcommand{\isasymLongleftrightarrow}{\isamath{\Longleftrightarrow}} \newcommand{\isasymbar}{\isamath{\mid}} \newcommand{\isasymhyphen}{\isatext{\rm-}} -\newcommand{\isasymmacron}{\isatext{\rm\=\relax}} +\newcommand{\isasyminverse}{\isamath{{}^{-1}}} \newcommand{\isasymexclamdown}{\isatext{\rm\textexclamdown}} \newcommand{\isasymquestiondown}{\isatext{\rm\textquestiondown}} \newcommand{\isasymguillemotleft}{\isatext{\flqq}} %requires babel diff -r 807992b67edd -r c20f78a9606f doc-src/TutorialI/CTL/document/PDL.tex --- a/doc-src/TutorialI/CTL/document/PDL.tex Mon Oct 30 18:26:14 2000 +0100 +++ b/doc-src/TutorialI/CTL/document/PDL.tex Mon Oct 30 18:28:00 2000 +0100 @@ -63,8 +63,8 @@ Only the equation for \isa{EF} deserves some comments. Remember that the postfix \isa{{\isacharcircum}{\isacharminus}{\isadigit{1}}} and the infix \isa{{\isacharcircum}{\isacharcircum}} are predefined and denote the converse of a relation and the application of a relation to a set. Thus -\isa{M{\isacharcircum}{\isacharminus}{\isadigit{1}}\ {\isacharcircum}{\isacharcircum}\ T} is the set of all predecessors of \isa{T} and the least -fixed point (\isa{lfp}) of \isa{{\isasymlambda}T{\isachardot}\ mc\ f\ {\isasymunion}\ M{\isacharcircum}{\isacharminus}{\isadigit{1}}\ {\isacharcircum}{\isacharcircum}\ T} is the least set +\isa{M{\isasyminverse}\ {\isacharcircum}{\isacharcircum}\ T} is the set of all predecessors of \isa{T} and the least +fixed point (\isa{lfp}) of \isa{{\isasymlambda}T{\isachardot}\ mc\ f\ {\isasymunion}\ M{\isasyminverse}\ {\isacharcircum}{\isacharcircum}\ T} is the least set \isa{T} containing \isa{mc\ f} and all predecessors of \isa{T}. If you find it hard to see that \isa{mc\ {\isacharparenleft}EF\ f{\isacharparenright}} contains exactly those states from which there is a path to a state where \isa{f} is true, do not worry---that @@ -128,17 +128,17 @@ \begin{isabelle} \ \isadigit{1}{\isachardot}\ {\isasymAnd}s\ t{\isachardot}\ {\isasymlbrakk}{\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M{\isacharcircum}{\isacharasterisk}{\isacharsemicolon}\ t\ {\isasymin}\ A{\isasymrbrakk}\ {\isasymLongrightarrow}\ s\ {\isasymin}\ lfp\ {\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isacharcircum}{\isacharminus}\isadigit{1}\ {\isacharcircum}{\isacharcircum}\ T{\isacharparenright} \end{isabelle} -This goal is proved by induction on \isa{{\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M{\isacharcircum}{\isacharasterisk}}. But since the model +This goal is proved by induction on \isa{{\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\isactrlsup {\isacharasterisk}}. But since the model checker works backwards (from \isa{t} to \isa{s}), we cannot use the induction theorem \isa{rtrancl{\isacharunderscore}induct} because it works in the forward direction. Fortunately the converse induction theorem \isa{converse{\isacharunderscore}rtrancl{\isacharunderscore}induct} already exists: \begin{isabelle}% -\ \ \ \ \ {\isasymlbrakk}{\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\ {\isasymin}\ r{\isacharcircum}{\isacharasterisk}{\isacharsemicolon}\ P\ b{\isacharsemicolon}\isanewline -\ \ \ \ \ \ \ \ {\isasymAnd}y\ z{\isachardot}\ {\isasymlbrakk}{\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharsemicolon}\ {\isacharparenleft}z{\isacharcomma}\ b{\isacharparenright}\ {\isasymin}\ r{\isacharcircum}{\isacharasterisk}{\isacharsemicolon}\ P\ z{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ y{\isasymrbrakk}\isanewline +\ \ \ \ \ {\isasymlbrakk}{\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\ {\isasymin}\ r\isactrlsup {\isacharasterisk}{\isacharsemicolon}\ P\ b{\isacharsemicolon}\isanewline +\ \ \ \ \ \ \ \ {\isasymAnd}y\ z{\isachardot}\ {\isasymlbrakk}{\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharsemicolon}\ {\isacharparenleft}z{\isacharcomma}\ b{\isacharparenright}\ {\isasymin}\ r\isactrlsup {\isacharasterisk}{\isacharsemicolon}\ P\ z{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ y{\isasymrbrakk}\isanewline \ \ \ \ \ {\isasymLongrightarrow}\ P\ a% \end{isabelle} -It says that if \isa{{\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\ {\isasymin}\ r{\isacharcircum}{\isacharasterisk}} and we know \isa{P\ b} then we can infer +It says that if \isa{{\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\ {\isasymin}\ r\isactrlsup {\isacharasterisk}} and we know \isa{P\ b} then we can infer \isa{P\ a} provided each step backwards from a predecessor \isa{z} of \isa{b} preserves \isa{P}.% \end{isamarkuptxt}% diff -r 807992b67edd -r c20f78a9606f doc-src/TutorialI/isabellesym.sty --- a/doc-src/TutorialI/isabellesym.sty Mon Oct 30 18:26:14 2000 +0100 +++ b/doc-src/TutorialI/isabellesym.sty Mon Oct 30 18:28:00 2000 +0100 @@ -127,7 +127,7 @@ \newcommand{\isasymLongleftrightarrow}{\isamath{\Longleftrightarrow}} \newcommand{\isasymbar}{\isamath{\mid}} \newcommand{\isasymhyphen}{\isatext{\rm-}} -\newcommand{\isasymmacron}{\isatext{\rm\=\relax}} +\newcommand{\isasyminverse}{\isamath{{}^{-1}}} \newcommand{\isasymexclamdown}{\isatext{\rm\textexclamdown}} \newcommand{\isasymquestiondown}{\isatext{\rm\textquestiondown}} \newcommand{\isasymguillemotleft}{\isatext{\flqq}} %requires babel