
diff -r 55c0f9a8df78 -r 59961d32b1ae doc-src/TutorialI/CTL/document/CTL.tex
--- a/doc-src/TutorialI/CTL/document/CTL.tex	Fri Jan 26 15:02:04 2001 +0100
+++ b/doc-src/TutorialI/CTL/document/CTL.tex	Fri Jan 26 15:50:28 2001 +0100
@@ -15,8 +15,9 @@
 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ AF\ formula%
 \begin{isamarkuptext}%
 \noindent
-which stands for "always in the future":
-on all paths, at some point the formula holds. Formalizing the notion of an infinite path is easy
+which stands for ``\emph{A}lways in the \emph{F}uture'':
+on all infinite paths, at some point the formula holds.
+Formalizing the notion of an infinite path is easy
 in HOL: it is simply a function from \isa{nat} to \isa{state}.%
 \end{isamarkuptext}%
 \isacommand{constdefs}\ Paths\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}state\ {\isasymRightarrow}\ {\isacharparenleft}nat\ {\isasymRightarrow}\ state{\isacharparenright}set{\isachardoublequote}\isanewline
@@ -45,7 +46,7 @@
 \begin{isamarkuptext}%
 \noindent
 Because \isa{af} is monotone in its second argument (and also its first, but
-that is irrelevant) \isa{af\ A} has a least fixed point:%
+that is irrelevant), \isa{af\ A} has a least fixed point:%
 \end{isamarkuptext}%
 \isacommand{lemma}\ mono{\isacharunderscore}af{\isacharcolon}\ {\isachardoublequote}mono{\isacharparenleft}af\ A{\isacharparenright}{\isachardoublequote}\isanewline
 \isacommand{apply}{\isacharparenleft}simp\ add{\isacharcolon}\ mono{\isacharunderscore}def\ af{\isacharunderscore}def{\isacharparenright}\isanewline
@@ -111,14 +112,14 @@
 infinite \isa{A}-avoiding path starting from \isa{s}. The reason is
 that by unfolding \isa{lfp} we find that if \isa{s} is not in
 \isa{lfp\ {\isacharparenleft}af\ A{\isacharparenright}}, then \isa{s} is not in \isa{A} and there is a
-direct successor of \isa{s} that is again not in \isa{lfp\ {\isacharparenleft}af\ A{\isacharparenright}}. Iterating this argument yields the promised infinite
+direct successor of \isa{s} that is again not in \mbox{\isa{lfp\ {\isacharparenleft}af\ A{\isacharparenright}}}. Iterating this argument yields the promised infinite
 \isa{A}-avoiding path. Let us formalize this sketch.
 
 The one-step argument in the sketch above
 is proved by a variant of contraposition:%
 \end{isamarkuptext}%
 \isacommand{lemma}\ not{\isacharunderscore}in{\isacharunderscore}lfp{\isacharunderscore}afD{\isacharcolon}\isanewline
-\ {\isachardoublequote}s\ {\isasymnotin}\ lfp{\isacharparenleft}af\ A{\isacharparenright}\ {\isasymLongrightarrow}\ s\ {\isasymnotin}\ A\ {\isasymand}\ {\isacharparenleft}{\isasymexists}\ t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}t{\isacharparenright}{\isasymin}M\ {\isasymand}\ t\ {\isasymnotin}\ lfp{\isacharparenleft}af\ A{\isacharparenright}{\isacharparenright}{\isachardoublequote}\isanewline
+\ {\isachardoublequote}s\ {\isasymnotin}\ lfp{\isacharparenleft}af\ A{\isacharparenright}\ {\isasymLongrightarrow}\ s\ {\isasymnotin}\ A\ {\isasymand}\ {\isacharparenleft}{\isasymexists}\ t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ t\ {\isasymnotin}\ lfp{\isacharparenleft}af\ A{\isacharparenright}{\isacharparenright}{\isachardoublequote}\isanewline
 \isacommand{apply}{\isacharparenleft}erule\ contrapos{\isacharunderscore}np{\isacharparenright}\isanewline
 \isacommand{apply}{\isacharparenleft}rule\ ssubst{\isacharbrackleft}OF\ lfp{\isacharunderscore}unfold{\isacharbrackleft}OF\ mono{\isacharunderscore}af{\isacharbrackright}{\isacharbrackright}{\isacharparenright}\isanewline
 \isacommand{apply}{\isacharparenleft}simp\ add{\isacharcolon}af{\isacharunderscore}def{\isacharparenright}\isanewline
@@ -153,8 +154,8 @@
 \ \ \ {\isasymexists}p{\isasymin}Paths\ s{\isachardot}\ {\isasymforall}i{\isachardot}\ Q{\isacharparenleft}p\ i{\isacharparenright}{\isachardoublequote}%
 \begin{isamarkuptxt}%
 \noindent
-First we rephrase the conclusion slightly because we need to prove both the path property
-and the fact that \isa{Q} holds simultaneously:%
+First we rephrase the conclusion slightly because we need to prove simultaneously
+both the path property and the fact that \isa{Q} holds:%
 \end{isamarkuptxt}%
 \isacommand{apply}{\isacharparenleft}subgoal{\isacharunderscore}tac\ {\isachardoublequote}{\isasymexists}p{\isachardot}\ s\ {\isacharequal}\ p\ {\isadigit{0}}\ {\isasymand}\ {\isacharparenleft}{\isasymforall}i{\isachardot}\ {\isacharparenleft}p\ i{\isacharcomma}p{\isacharparenleft}i{\isacharplus}{\isadigit{1}}{\isacharparenright}{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ Q{\isacharparenleft}p\ i{\isacharparenright}{\isacharparenright}{\isachardoublequote}{\isacharparenright}%
 \begin{isamarkuptxt}%
@@ -170,7 +171,7 @@
 \isacommand{apply}{\isacharparenleft}clarsimp{\isacharparenright}%
 \begin{isamarkuptxt}%
 \noindent
-After simplification and clarification the subgoal has the following compact form
+After simplification and clarification, the subgoal has the following form
 \begin{isabelle}%
 \ {\isadigit{1}}{\isachardot}\ {\isasymAnd}i{\isachardot}\ {\isasymlbrakk}Q\ s{\isacharsemicolon}\ {\isasymforall}s{\isachardot}\ Q\ s\ {\isasymlongrightarrow}\ {\isacharparenleft}{\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ Q\ t{\isacharparenright}{\isasymrbrakk}\isanewline
 \isaindent{\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}i{\isachardot}\ }{\isasymLongrightarrow}\ {\isacharparenleft}path\ s\ Q\ i{\isacharcomma}\ SOME\ t{\isachardot}\ {\isacharparenleft}path\ s\ Q\ i{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ Q\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\isanewline
@@ -182,7 +183,7 @@
 \ \isacommand{apply}{\isacharparenleft}simp{\isacharparenright}%
 \begin{isamarkuptxt}%
 \noindent
-After simplification the base case boils down to
+After simplification, the base case boils down to
 \begin{isabelle}%
 \ {\isadigit{1}}{\isachardot}\ {\isasymlbrakk}Q\ s{\isacharsemicolon}\ {\isasymforall}s{\isachardot}\ Q\ s\ {\isasymlongrightarrow}\ {\isacharparenleft}{\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ Q\ t{\isacharparenright}{\isasymrbrakk}\isanewline
 \isaindent{\ {\isadigit{1}}{\isachardot}\ }{\isasymLongrightarrow}\ {\isacharparenleft}s{\isacharcomma}\ SOME\ t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ Q\ t{\isacharparenright}\ {\isasymin}\ M%
@@ -281,8 +282,8 @@
 \isacommand{done}%
 \begin{isamarkuptext}%
 The language defined above is not quite CTL\@. The latter also includes an
-until-operator \isa{EU\ f\ g} with semantics ``there exists a path
-where \isa{f} is true until \isa{g} becomes true''. With the help
+until-operator \isa{EU\ f\ g} with semantics ``there \emph{E}xists a path
+where \isa{f} is true \emph{U}ntil \isa{g} becomes true''. With the help
 of an auxiliary function%
 \end{isamarkuptext}%
 \isacommand{consts}\ until{\isacharcolon}{\isacharcolon}\ {\isachardoublequote}state\ set\ {\isasymRightarrow}\ state\ set\ {\isasymRightarrow}\ state\ {\isasymRightarrow}\ state\ list\ {\isasymRightarrow}\ bool{\isachardoublequote}\isanewline
@@ -293,7 +294,7 @@
 \noindent
 the semantics of \isa{EU} is straightforward:
 \begin{isabelle}%
-\ \ \ \ \ s\ {\isasymTurnstile}\ EU\ f\ g\ {\isacharequal}\ {\isacharparenleft}{\isasymexists}p{\isachardot}\ until\ A\ B\ s\ p{\isacharparenright}%
+\ \ \ \ \ s\ {\isasymTurnstile}\ EU\ f\ g\ {\isacharequal}\ {\isacharparenleft}{\isasymexists}p{\isachardot}\ until\ {\isacharbraceleft}t{\isachardot}\ t\ {\isasymTurnstile}\ f{\isacharbraceright}\ {\isacharbraceleft}t{\isachardot}\ t\ {\isasymTurnstile}\ g{\isacharbraceright}\ s\ p{\isacharparenright}%
 \end{isabelle}
 Note that \isa{EU} is not definable in terms of the other operators!
 
@@ -320,10 +321,10 @@
 It is clear that if all sets are finite, they can be represented as lists and the usual
 set operations are easily implemented. Only \isa{lfp} requires a little thought.
 Fortunately, the HOL Library%
-\footnote{See theory \isa{While_Combinator_Example}.}
+\footnote{See theory \isa{While_Combinator}.}
 provides a theorem stating that 
 in the case of finite sets and a monotone function~\isa{F},
-the value of \isa{lfp\ F} can be computed by iterated application of \isa{F} to~\isa{{\isacharbraceleft}{\isacharbraceright}} until
+the value of \mbox{\isa{lfp\ F}} can be computed by iterated application of \isa{F} to~\isa{{\isacharbraceleft}{\isacharbraceright}} until
 a fixed point is reached. It is actually possible to generate executable functional programs
 from HOL definitions, but that is beyond the scope of the tutorial.%
 \end{isamarkuptext}%




