*** empty log message ***

--- a/doc-src/TutorialI/CTL/CTL.thy	Sat Jan 06 10:36:19 2001 +0100
+++ b/doc-src/TutorialI/CTL/CTL.thy	Sat Jan 06 11:27:09 2001 +0100
@@ -62,7 +62,7 @@
 "mc(Neg f)   = -mc f"
 "mc(And f g) = mc f \<inter> mc g"
 "mc(AX f)    = {s. \<forall>t. (s,t) \<in> M  \<longrightarrow> t \<in> mc f}"
-"mc(EF f)    = lfp(\<lambda>T. mc f \<union> M^-1 ^^ T)"(*>*)
+"mc(EF f)    = lfp(\<lambda>T. mc f \<union> M^-1 ``` T)"(*>*)
 "mc(AF f)    = lfp(af(mc f))";
 
 text{*\noindent
@@ -75,12 +75,12 @@
 apply blast;
 done
 (*<*)
-lemma mono_ef: "mono(\<lambda>T. A \<union> M^-1 ^^ T)";
+lemma mono_ef: "mono(\<lambda>T. A \<union> M^-1 ``` T)";
 apply(rule monoI);
 by(blast);
 
 lemma EF_lemma:
-  "lfp(\<lambda>T. A \<union> M^-1 ^^ T) = {s. \<exists>t. (s,t) \<in> M^* \<and> t \<in> A}";
+  "lfp(\<lambda>T. A \<union> M^-1 ``` T) = {s. \<exists>t. (s,t) \<in> M^* \<and> t \<in> A}";
 apply(rule equalityI);
  apply(rule subsetI);
  apply(simp);
@@ -366,7 +366,7 @@
 Note that @{term EU} is not definable in terms of the other operators!
 
 Model checking @{term EU} is again a least fixed point construction:
-@{text[display]"mc(EU f g) = lfp(\<lambda>T. mc g \<union> mc f \<inter> (M^-1 ^^ T))"}
+@{text[display]"mc(EU f g) = lfp(\<lambda>T. mc g \<union> mc f \<inter> (M^-1 ``` T))"}
 
 \begin{exercise}
 Extend the datatype of formulae by the above until operator
@@ -382,7 +382,7 @@
 (*<*)
 constdefs
  eufix :: "state set \<Rightarrow> state set \<Rightarrow> state set \<Rightarrow> state set"
-"eufix A B T \<equiv> B \<union> A \<inter> (M^-1 ^^ T)"
+"eufix A B T \<equiv> B \<union> A \<inter> (M^-1 ``` T)"
 
 lemma "lfp(eufix A B) \<subseteq> eusem A B"
 apply(rule lfp_lowerbound)

--- a/doc-src/TutorialI/CTL/PDL.thy	Sat Jan 06 10:36:19 2001 +0100
+++ b/doc-src/TutorialI/CTL/PDL.thy	Sat Jan 06 11:27:09 2001 +0100
@@ -58,14 +58,14 @@
 "mc(Neg f)   = -mc f"
 "mc(And f g) = mc f \<inter> mc g"
 "mc(AX f)    = {s. \<forall>t. (s,t) \<in> M  \<longrightarrow> t \<in> mc f}"
-"mc(EF f)    = lfp(\<lambda>T. mc f \<union> M^-1 ^^ T)"
+"mc(EF f)    = lfp(\<lambda>T. mc f \<union> M^-1 ``` T)"
 
 text{*\noindent
 Only the equation for @{term EF} deserves some comments. Remember that the
-postfix @{text"^-1"} and the infix @{text"^^"} are predefined and denote the
+postfix @{text"^-1"} and the infix @{text"```"} are predefined and denote the
 converse of a relation and the application of a relation to a set. Thus
-@{term "M^-1 ^^ T"} is the set of all predecessors of @{term T} and the least
-fixed point (@{term lfp}) of @{term"\<lambda>T. mc f \<union> M^-1 ^^ T"} is the least set
+@{term "M^-1 ``` T"} is the set of all predecessors of @{term T} and the least
+fixed point (@{term lfp}) of @{term"\<lambda>T. mc f \<union> M^-1 ``` T"} is the least set
 @{term T} containing @{term"mc f"} and all predecessors of @{term T}. If you
 find it hard to see that @{term"mc(EF f)"} contains exactly those states from
 which there is a path to a state where @{term f} is true, do not worry---that
@@ -74,7 +74,7 @@
 First we prove monotonicity of the function inside @{term lfp}
 *}
 
-lemma mono_ef: "mono(\<lambda>T. A \<union> M^-1 ^^ T)"
+lemma mono_ef: "mono(\<lambda>T. A \<union> M^-1 ``` T)"
 apply(rule monoI)
 apply blast
 done
@@ -87,7 +87,7 @@
 *}
 
 lemma EF_lemma:
-  "lfp(\<lambda>T. A \<union> M^-1 ^^ T) = {s. \<exists>t. (s,t) \<in> M^* \<and> t \<in> A}"
+  "lfp(\<lambda>T. A \<union> M^-1 ``` T) = {s. \<exists>t. (s,t) \<in> M^* \<and> t \<in> A}"
 
 txt{*\noindent
 The equality is proved in the canonical fashion by proving that each set

--- a/doc-src/TutorialI/CTL/document/CTL.tex	Sat Jan 06 10:36:19 2001 +0100
+++ b/doc-src/TutorialI/CTL/document/CTL.tex	Sat Jan 06 11:27:09 2001 +0100
@@ -300,7 +300,7 @@
 
 Model checking \isa{EU} is again a least fixed point construction:
 \begin{isabelle}%
-\ \ \ \ \ mc{\isacharparenleft}EU\ f\ g{\isacharparenright}\ {\isacharequal}\ lfp{\isacharparenleft}{\isasymlambda}T{\isachardot}\ mc\ g\ {\isasymunion}\ mc\ f\ {\isasyminter}\ {\isacharparenleft}M{\isacharcircum}{\isacharminus}{\isadigit{1}}\ {\isacharcircum}{\isacharcircum}\ T{\isacharparenright}{\isacharparenright}%
+\ \ \ \ \ mc{\isacharparenleft}EU\ f\ g{\isacharparenright}\ {\isacharequal}\ lfp{\isacharparenleft}{\isasymlambda}T{\isachardot}\ mc\ g\ {\isasymunion}\ mc\ f\ {\isasyminter}\ {\isacharparenleft}M{\isacharcircum}{\isacharminus}{\isadigit{1}}\ {\isacharbackquote}{\isacharbackquote}{\isacharbackquote}\ T{\isacharparenright}{\isacharparenright}%
 \end{isabelle}
 
 \begin{exercise}

--- a/doc-src/TutorialI/CTL/document/PDL.tex	Sat Jan 06 10:36:19 2001 +0100
+++ b/doc-src/TutorialI/CTL/document/PDL.tex	Sat Jan 06 11:27:09 2001 +0100
@@ -58,14 +58,14 @@
 {\isachardoublequote}mc{\isacharparenleft}Neg\ f{\isacharparenright}\ \ \ {\isacharequal}\ {\isacharminus}mc\ f{\isachardoublequote}\isanewline
 {\isachardoublequote}mc{\isacharparenleft}And\ f\ g{\isacharparenright}\ {\isacharequal}\ mc\ f\ {\isasyminter}\ mc\ g{\isachardoublequote}\isanewline
 {\isachardoublequote}mc{\isacharparenleft}AX\ f{\isacharparenright}\ \ \ \ {\isacharequal}\ {\isacharbraceleft}s{\isachardot}\ {\isasymforall}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}t{\isacharparenright}\ {\isasymin}\ M\ \ {\isasymlongrightarrow}\ t\ {\isasymin}\ mc\ f{\isacharbraceright}{\isachardoublequote}\isanewline
-{\isachardoublequote}mc{\isacharparenleft}EF\ f{\isacharparenright}\ \ \ \ {\isacharequal}\ lfp{\isacharparenleft}{\isasymlambda}T{\isachardot}\ mc\ f\ {\isasymunion}\ M{\isacharcircum}{\isacharminus}{\isadigit{1}}\ {\isacharcircum}{\isacharcircum}\ T{\isacharparenright}{\isachardoublequote}%
+{\isachardoublequote}mc{\isacharparenleft}EF\ f{\isacharparenright}\ \ \ \ {\isacharequal}\ lfp{\isacharparenleft}{\isasymlambda}T{\isachardot}\ mc\ f\ {\isasymunion}\ M{\isacharcircum}{\isacharminus}{\isadigit{1}}\ {\isacharbackquote}{\isacharbackquote}{\isacharbackquote}\ T{\isacharparenright}{\isachardoublequote}%
 \begin{isamarkuptext}%
 \noindent
 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
+postfix \isa{{\isacharcircum}{\isacharminus}{\isadigit{1}}} and the infix \isa{{\isacharbackquote}{\isacharbackquote}{\isacharbackquote}} are predefined and denote the
 converse of a relation and the application of a relation to a set. Thus
-\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{M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}{\isacharbackquote}\ 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}\ {\isacharbackquote}{\isacharbackquote}{\isacharbackquote}\ 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
@@ -73,7 +73,7 @@
 
 First we prove monotonicity of the function inside \isa{lfp}%
 \end{isamarkuptext}%
-\isacommand{lemma}\ mono{\isacharunderscore}ef{\isacharcolon}\ {\isachardoublequote}mono{\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isacharcircum}{\isacharminus}{\isadigit{1}}\ {\isacharcircum}{\isacharcircum}\ T{\isacharparenright}{\isachardoublequote}\isanewline
+\isacommand{lemma}\ mono{\isacharunderscore}ef{\isacharcolon}\ {\isachardoublequote}mono{\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isacharcircum}{\isacharminus}{\isadigit{1}}\ {\isacharbackquote}{\isacharbackquote}{\isacharbackquote}\ T{\isacharparenright}{\isachardoublequote}\isanewline
 \isacommand{apply}{\isacharparenleft}rule\ monoI{\isacharparenright}\isanewline
 \isacommand{apply}\ blast\isanewline
 \isacommand{done}%
@@ -85,7 +85,7 @@
 a separate lemma:%
 \end{isamarkuptext}%
 \isacommand{lemma}\ EF{\isacharunderscore}lemma{\isacharcolon}\isanewline
-\ \ {\isachardoublequote}lfp{\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isacharcircum}{\isacharminus}{\isadigit{1}}\ {\isacharcircum}{\isacharcircum}\ T{\isacharparenright}\ {\isacharequal}\ {\isacharbraceleft}s{\isachardot}\ {\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}t{\isacharparenright}\ {\isasymin}\ M{\isacharcircum}{\isacharasterisk}\ {\isasymand}\ t\ {\isasymin}\ A{\isacharbraceright}{\isachardoublequote}%
+\ \ {\isachardoublequote}lfp{\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isacharcircum}{\isacharminus}{\isadigit{1}}\ {\isacharbackquote}{\isacharbackquote}{\isacharbackquote}\ T{\isacharparenright}\ {\isacharequal}\ {\isacharbraceleft}s{\isachardot}\ {\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}t{\isacharparenright}\ {\isasymin}\ M{\isacharcircum}{\isacharasterisk}\ {\isasymand}\ t\ {\isasymin}\ A{\isacharbraceright}{\isachardoublequote}%
 \begin{isamarkuptxt}%
 \noindent
 The equality is proved in the canonical fashion by proving that each set
@@ -98,7 +98,7 @@
 \noindent
 Simplification leaves us with the following first subgoal
 \begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}s{\isachardot}\ s\ {\isasymin}\ lfp\ {\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharcircum}{\isacharcircum}\ T{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\isactrlsup {\isacharasterisk}\ {\isasymand}\ t\ {\isasymin}\ A%
+\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}s{\isachardot}\ s\ {\isasymin}\ lfp\ {\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}{\isacharbackquote}\ T{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\isactrlsup {\isacharasterisk}\ {\isasymand}\ t\ {\isasymin}\ A%
 \end{isabelle}
 which is proved by \isa{lfp}-induction:%
 \end{isamarkuptxt}%
@@ -127,7 +127,7 @@
 \noindent
 After simplification and clarification we are left with
 \begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ t{\isachardot}\ {\isasymlbrakk}{\isacharparenleft}x{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\isactrlsup {\isacharasterisk}{\isacharsemicolon}\ t\ {\isasymin}\ A{\isasymrbrakk}\ {\isasymLongrightarrow}\ x\ {\isasymin}\ lfp\ {\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharcircum}{\isacharcircum}\ T{\isacharparenright}%
+\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ t{\isachardot}\ {\isasymlbrakk}{\isacharparenleft}x{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\isactrlsup {\isacharasterisk}{\isacharsemicolon}\ t\ {\isasymin}\ A{\isasymrbrakk}\ {\isasymLongrightarrow}\ x\ {\isasymin}\ lfp\ {\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}{\isacharbackquote}\ T{\isacharparenright}%
 \end{isabelle}
 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
@@ -148,14 +148,14 @@
 \noindent
 The base case
 \begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ t{\isachardot}\ t\ {\isasymin}\ A\ {\isasymLongrightarrow}\ t\ {\isasymin}\ lfp\ {\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharcircum}{\isacharcircum}\ T{\isacharparenright}%
+\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ t{\isachardot}\ t\ {\isasymin}\ A\ {\isasymLongrightarrow}\ t\ {\isasymin}\ lfp\ {\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}{\isacharbackquote}\ T{\isacharparenright}%
 \end{isabelle}
 is solved by unrolling \isa{lfp} once%
 \end{isamarkuptxt}%
 \ \isacommand{apply}{\isacharparenleft}rule\ ssubst{\isacharbrackleft}OF\ lfp{\isacharunderscore}unfold{\isacharbrackleft}OF\ mono{\isacharunderscore}ef{\isacharbrackright}{\isacharbrackright}{\isacharparenright}%
 \begin{isamarkuptxt}%
 \begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ t{\isachardot}\ t\ {\isasymin}\ A\ {\isasymLongrightarrow}\ t\ {\isasymin}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharcircum}{\isacharcircum}\ lfp\ {\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharcircum}{\isacharcircum}\ T{\isacharparenright}%
+\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ t{\isachardot}\ t\ {\isasymin}\ A\ {\isasymLongrightarrow}\ t\ {\isasymin}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}{\isacharbackquote}\ lfp\ {\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}{\isacharbackquote}\ T{\isacharparenright}%
 \end{isabelle}
 and disposing of the resulting trivial subgoal automatically:%
 \end{isamarkuptxt}%

--- a/doc-src/TutorialI/fp.tex	Sat Jan 06 10:36:19 2001 +0100
+++ b/doc-src/TutorialI/fp.tex	Sat Jan 06 11:27:09 2001 +0100
@@ -160,8 +160,7 @@
 \isaindexbold{hd} (``head'') and \isaindexbold{tl} (``tail'') return the first
 element and the remainder of a list. (However, pattern-matching is usually
 preferable to \isa{hd} and \isa{tl}.)  
-Also available are the higher-order
-functions \isa{map}, \isa{filter}, \isa{foldl} and \isa{foldr}.
+Also available are higher-order functions like \isa{map} and \isa{filter}.
 Theory \isa{List} also contains
 more syntactic sugar: \isa{[}$x@1$\isa{,}\dots\isa{,}$x@n$\isa{]} abbreviates
 $x@1$\isa{\#}\dots\isa{\#}$x@n$\isa{\#[]}.  In the rest of the tutorial we