
diff -r 6c0d02f416ba -r 2fffd5ac487f doc-src/Codegen/Thy/document/Inductive_Predicate.tex
--- a/doc-src/Codegen/Thy/document/Inductive_Predicate.tex	Mon Aug 16 10:54:08 2010 +0200
+++ b/doc-src/Codegen/Thy/document/Inductive_Predicate.tex	Mon Aug 16 11:18:28 2010 +0200
@@ -10,7 +10,8 @@
 \isacommand{theory}\isamarkupfalse%
 \ Inductive{\isacharunderscore}Predicate\isanewline
 \isakeyword{imports}\ Setup\isanewline
-\isakeyword{begin}%
+\isakeyword{begin}\isanewline
+%
 \endisatagtheory
 {\isafoldtheory}%
 %
@@ -18,16 +19,32 @@
 %
 \endisadelimtheory
 %
+\isadeliminvisible
+%
+\endisadeliminvisible
+%
+\isataginvisible
+%
+\endisataginvisible
+{\isafoldinvisible}%
+%
+\isadeliminvisible
+%
+\endisadeliminvisible
+%
 \isamarkupsection{Inductive Predicates \label{sec:inductive}%
 }
 \isamarkuptrue%
 %
 \begin{isamarkuptext}%
-To execute inductive predicates, a special preprocessor, the predicate
- compiler, generates code equations from the introduction rules of the predicates.
-The mechanisms of this compiler are described in \cite{Berghofer-Bulwahn-Haftmann:2009:TPHOL}.
-Consider the simple predicate \isa{append} given by these two
-introduction rules:%
+The \isa{predicate{\isacharunderscore}compiler} is an extension of the code generator
+  which turns inductive specifications into equational ones, from
+  which in turn executable code can be generated.  The mechanisms of
+  this compiler are described in detail in
+  \cite{Berghofer-Bulwahn-Haftmann:2009:TPHOL}.
+
+  Consider the simple predicate \isa{append} given by these two
+  introduction rules:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
@@ -38,8 +55,8 @@
 \isatagquote
 %
 \begin{isamarkuptext}%
-\isa{append\ {\isacharbrackleft}{\isacharbrackright}\ ys\ ys}\\
-\noindent\isa{append\ xs\ ys\ zs\ {\isasymLongrightarrow}\ append\ {\isacharparenleft}x\ {\isacharhash}\ xs{\isacharparenright}\ ys\ {\isacharparenleft}x\ {\isacharhash}\ zs{\isacharparenright}}%
+\isa{append\ {\isacharbrackleft}{\isacharbrackright}\ ys\ ys} \\
+  \isa{append\ xs\ ys\ zs\ {\isasymLongrightarrow}\ append\ {\isacharparenleft}x\ {\isacharhash}\ xs{\isacharparenright}\ ys\ {\isacharparenleft}x\ {\isacharhash}\ zs{\isacharparenright}}%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
@@ -71,22 +88,21 @@
 \endisadelimquote
 %
 \begin{isamarkuptext}%
-\noindent The \hyperlink{command.code-pred}{\mbox{\isa{\isacommand{code{\isacharunderscore}pred}}}} command takes the name
-of the inductive predicate and then you put a period to discharge
-a trivial correctness proof. 
-The compiler infers possible modes 
-for the predicate and produces the derived code equations.
-Modes annotate which (parts of the) arguments are to be taken as input,
-and which output. Modes are similar to types, but use the notation \isa{i}
-for input and \isa{o} for output.
+\noindent The \hyperlink{command.code-pred}{\mbox{\isa{\isacommand{code{\isacharunderscore}pred}}}} command takes the name of the
+  inductive predicate and then you put a period to discharge a trivial
+  correctness proof.  The compiler infers possible modes for the
+  predicate and produces the derived code equations.  Modes annotate
+  which (parts of the) arguments are to be taken as input, and which
+  output. Modes are similar to types, but use the notation \isa{i}
+  for input and \isa{o} for output.
  
-For \isa{append}, the compiler can infer the following modes:
-\begin{itemize}
-\item \isa{i\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ bool}
-\item \isa{i\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool}
-\item \isa{o\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ bool}
-\end{itemize}
-You can compute sets of predicates using \indexdef{}{command}{values}\hypertarget{command.values}{\hyperlink{command.values}{\mbox{\isa{\isacommand{values}}}}}:%
+  For \isa{append}, the compiler can infer the following modes:
+  \begin{itemize}
+    \item \isa{i\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ bool}
+    \item \isa{i\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool}
+    \item \isa{o\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ bool}
+  \end{itemize}
+  You can compute sets of predicates using \indexdef{}{command}{values}\hypertarget{command.values}{\hyperlink{command.values}{\mbox{\isa{\isacommand{values}}}}}:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
@@ -129,10 +145,10 @@
 \isamarkuptrue%
 %
 \begin{isamarkuptext}%
-\noindent If you are only interested in the first elements of the set
-comprehension (with respect to a depth-first search on the introduction rules), you can
-pass an argument to
-\hyperlink{command.values}{\mbox{\isa{\isacommand{values}}}} to specify the number of elements you want:%
+\noindent If you are only interested in the first elements of the
+  set comprehension (with respect to a depth-first search on the
+  introduction rules), you can pass an argument to \hyperlink{command.values}{\mbox{\isa{\isacommand{values}}}}
+  to specify the number of elements you want:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
@@ -142,9 +158,9 @@
 %
 \isatagquote
 \isacommand{values}\isamarkupfalse%
-\ {\isadigit{1}}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharparenleft}xs{\isacharcomma}\ ys{\isacharparenright}{\isachardot}\ append\ xs\ ys\ {\isacharbrackleft}{\isacharparenleft}{\isadigit{1}}{\isacharcolon}{\isacharcolon}nat{\isacharparenright}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbrackright}{\isacharbraceright}{\isachardoublequoteclose}\isanewline
+\ {\isadigit{1}}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharparenleft}xs{\isacharcomma}\ ys{\isacharparenright}{\isachardot}\ append\ xs\ ys\ {\isacharbrackleft}{\isacharparenleft}{\isadigit{1}}{\isacharcolon}{\isacharcolon}nat{\isacharparenright}{\isacharcomma}\ {\isadigit{2}}{\isacharcomma}\ {\isadigit{3}}{\isacharcomma}\ {\isadigit{4}}{\isacharbrackright}{\isacharbraceright}{\isachardoublequoteclose}\isanewline
 \isacommand{values}\isamarkupfalse%
-\ {\isadigit{3}}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharparenleft}xs{\isacharcomma}\ ys{\isacharparenright}{\isachardot}\ append\ xs\ ys\ {\isacharbrackleft}{\isacharparenleft}{\isadigit{1}}{\isacharcolon}{\isacharcolon}nat{\isacharparenright}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbrackright}{\isacharbraceright}{\isachardoublequoteclose}%
+\ {\isadigit{3}}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharparenleft}xs{\isacharcomma}\ ys{\isacharparenright}{\isachardot}\ append\ xs\ ys\ {\isacharbrackleft}{\isacharparenleft}{\isadigit{1}}{\isacharcolon}{\isacharcolon}nat{\isacharparenright}{\isacharcomma}\ {\isadigit{2}}{\isacharcomma}\ {\isadigit{3}}{\isacharcomma}\ {\isadigit{4}}{\isacharbrackright}{\isacharbraceright}{\isachardoublequoteclose}%
 \endisatagquote
 {\isafoldquote}%
 %
@@ -154,10 +170,10 @@
 %
 \begin{isamarkuptext}%
 \noindent The \hyperlink{command.values}{\mbox{\isa{\isacommand{values}}}} command can only compute set
- comprehensions for which a mode has been inferred.
+  comprehensions for which a mode has been inferred.
 
-The code equations for a predicate are made available as theorems with
- the suffix \isa{equation}, and can be inspected with:%
+  The code equations for a predicate are made available as theorems with
+  the suffix \isa{equation}, and can be inspected with:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
@@ -180,14 +196,13 @@
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
-\isamarkupsubsubsection{Alternative names for functions%
+\isamarkupsubsection{Alternative names for functions%
 }
 \isamarkuptrue%
 %
 \begin{isamarkuptext}%
-By default, the functions generated from a predicate are named after the predicate with the
-mode mangled into the name (e.g., \isa{append{\isacharunderscore}i{\isacharunderscore}i{\isacharunderscore}o}).
-You can specify your own names as follows:%
+By default, the functions generated from a predicate are named after
+  the predicate with the mode mangled into the name (e.g., \isa{append{\isacharunderscore}i{\isacharunderscore}i{\isacharunderscore}o}).  You can specify your own names as follows:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
@@ -208,18 +223,18 @@
 %
 \endisadelimquote
 %
-\isamarkupsubsubsection{Alternative introduction rules%
+\isamarkupsubsection{Alternative introduction rules%
 }
 \isamarkuptrue%
 %
 \begin{isamarkuptext}%
-Sometimes the introduction rules of an predicate are not executable because they contain
-non-executable constants or specific modes could not be inferred.
-It is also possible that the introduction rules yield a function that loops forever
-due to the execution in a depth-first search manner.
-Therefore, you can declare alternative introduction rules for predicates with the attribute
-\hyperlink{attribute.code-pred-intro}{\mbox{\isa{code{\isacharunderscore}pred{\isacharunderscore}intro}}}.
-For example, the transitive closure is defined by:%
+Sometimes the introduction rules of an predicate are not executable
+  because they contain non-executable constants or specific modes
+  could not be inferred.  It is also possible that the introduction
+  rules yield a function that loops forever due to the execution in a
+  depth-first search manner.  Therefore, you can declare alternative
+  introduction rules for predicates with the attribute \hyperlink{attribute.code-pred-intro}{\mbox{\isa{code{\isacharunderscore}pred{\isacharunderscore}intro}}}.  For example, the transitive closure is defined
+  by:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
@@ -230,8 +245,8 @@
 \isatagquote
 %
 \begin{isamarkuptext}%
-\isa{r\ a\ b\ {\isasymLongrightarrow}\ r\isactrlsup {\isacharplus}\isactrlsup {\isacharplus}\ a\ b}\\
-\noindent \isa{{\isasymlbrakk}r\isactrlsup {\isacharplus}\isactrlsup {\isacharplus}\ a\ b{\isacharsemicolon}\ r\ b\ c{\isasymrbrakk}\ {\isasymLongrightarrow}\ r\isactrlsup {\isacharplus}\isactrlsup {\isacharplus}\ a\ c}%
+\isa{r\ a\ b\ {\isasymLongrightarrow}\ r\isactrlsup {\isacharplus}\isactrlsup {\isacharplus}\ a\ b} \\
+  \isa{r\isactrlsup {\isacharplus}\isactrlsup {\isacharplus}\ a\ b\ {\isasymLongrightarrow}\ r\ b\ c\ {\isasymLongrightarrow}\ r\isactrlsup {\isacharplus}\isactrlsup {\isacharplus}\ a\ c}%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
@@ -243,11 +258,11 @@
 \endisadelimquote
 %
 \begin{isamarkuptext}%
-\noindent These rules do not suit well for executing the transitive closure 
-with the mode \isa{{\isacharparenleft}i\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool{\isacharparenright}\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool}, as the second rule will
-cause an infinite loop in the recursive call.
-This can be avoided using the following alternative rules which are
-declared to the predicate compiler by the attribute \hyperlink{attribute.code-pred-intro}{\mbox{\isa{code{\isacharunderscore}pred{\isacharunderscore}intro}}}:%
+\noindent These rules do not suit well for executing the transitive
+  closure with the mode \isa{{\isacharparenleft}i\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool{\isacharparenright}\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool}, as
+  the second rule will cause an infinite loop in the recursive call.
+  This can be avoided using the following alternative rules which are
+  declared to the predicate compiler by the attribute \hyperlink{attribute.code-pred-intro}{\mbox{\isa{code{\isacharunderscore}pred{\isacharunderscore}intro}}}:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
@@ -270,11 +285,11 @@
 \endisadelimquote
 %
 \begin{isamarkuptext}%
-\noindent After declaring all alternative rules for the transitive closure,
-you invoke \hyperlink{command.code-pred}{\mbox{\isa{\isacommand{code{\isacharunderscore}pred}}}} as usual.
-As you have declared alternative rules for the predicate, you are urged to prove that these
-introduction rules are complete, i.e., that you can derive an elimination rule for the
-alternative rules:%
+\noindent After declaring all alternative rules for the transitive
+  closure, you invoke \hyperlink{command.code-pred}{\mbox{\isa{\isacommand{code{\isacharunderscore}pred}}}} as usual.  As you have
+  declared alternative rules for the predicate, you are urged to prove
+  that these introduction rules are complete, i.e., that you can
+  derive an elimination rule for the alternative rules:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
@@ -290,7 +305,7 @@
 \ \ \isacommand{case}\isamarkupfalse%
 \ tranclp\isanewline
 \ \ \isacommand{from}\isamarkupfalse%
-\ this\ converse{\isacharunderscore}tranclpE{\isacharbrackleft}OF\ this{\isacharparenleft}{\isadigit{1}}{\isacharparenright}{\isacharbrackright}\ \isacommand{show}\isamarkupfalse%
+\ this\ converse{\isacharunderscore}tranclpE\ {\isacharbrackleft}OF\ this{\isacharparenleft}{\isadigit{1}}{\isacharparenright}{\isacharbrackright}\ \isacommand{show}\isamarkupfalse%
 \ thesis\ \isacommand{by}\isamarkupfalse%
 \ metis\isanewline
 \isacommand{qed}\isamarkupfalse%
@@ -303,9 +318,9 @@
 \endisadelimquote
 %
 \begin{isamarkuptext}%
-\noindent Alternative rules can also be used for constants that have not
-been defined inductively. For example, the lexicographic order which
-is defined as:%
+\noindent Alternative rules can also be used for constants that have
+  not been defined inductively. For example, the lexicographic order
+  which is defined as:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
@@ -333,24 +348,11 @@
 \endisadelimquote
 %
 \begin{isamarkuptext}%
-\noindent To make it executable, you can derive the following two rules and prove the
-elimination rule:%
+\noindent To make it executable, you can derive the following two
+  rules and prove the elimination rule:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
-\isadelimproof
-%
-\endisadelimproof
-%
-\isatagproof
-%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
 \isadelimquote
 %
 \endisadelimquote
@@ -372,47 +374,45 @@
 %
 \endisadelimquote
 %
-\isamarkupsubsubsection{Options for values%
+\isamarkupsubsection{Options for values%
 }
 \isamarkuptrue%
 %
 \begin{isamarkuptext}%
-In the presence of higher-order predicates, multiple modes for some predicate could be inferred
-that are not disambiguated by the pattern of the set comprehension.
-To disambiguate the modes for the arguments of a predicate, you can state
-the modes explicitly in the \hyperlink{command.values}{\mbox{\isa{\isacommand{values}}}} command. 
-Consider the simple predicate \isa{succ}:%
+In the presence of higher-order predicates, multiple modes for some
+  predicate could be inferred that are not disambiguated by the
+  pattern of the set comprehension.  To disambiguate the modes for the
+  arguments of a predicate, you can state the modes explicitly in the
+  \hyperlink{command.values}{\mbox{\isa{\isacommand{values}}}} command.  Consider the simple predicate \isa{succ}:%
 \end{isamarkuptext}%
 \isamarkuptrue%
+%
+\isadelimquote
+%
+\endisadelimquote
+%
+\isatagquote
 \isacommand{inductive}\isamarkupfalse%
-\ succ\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
-\isakeyword{where}\isanewline
+\ succ\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
 \ \ {\isachardoublequoteopen}succ\ {\isadigit{0}}\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
 {\isacharbar}\ {\isachardoublequoteopen}succ\ x\ y\ {\isasymLongrightarrow}\ succ\ {\isacharparenleft}Suc\ x{\isacharparenright}\ {\isacharparenleft}Suc\ y{\isacharparenright}{\isachardoublequoteclose}\isanewline
 \isanewline
 \isacommand{code{\isacharunderscore}pred}\isamarkupfalse%
-\ succ%
-\isadelimproof
-\ %
-\endisadelimproof
+\ succ\ \isacommand{{\isachardot}}\isamarkupfalse%
 %
-\isatagproof
-\isacommand{{\isachardot}}\isamarkupfalse%
+\endisatagquote
+{\isafoldquote}%
 %
-\endisatagproof
-{\isafoldproof}%
+\isadelimquote
 %
-\isadelimproof
-%
-\endisadelimproof
+\endisadelimquote
 %
 \begin{isamarkuptext}%
-\noindent For this, the predicate compiler can infer modes \isa{o\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool}, \isa{i\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool},
-  \isa{o\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ bool} and \isa{i\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ bool}.
-The invocation of \hyperlink{command.values}{\mbox{\isa{\isacommand{values}}}} \isa{{\isacharbraceleft}n{\isachardot}\ tranclp\ succ\ {\isadigit{1}}{\isadigit{0}}\ n{\isacharbraceright}} loops, as multiple
-modes for the predicate \isa{succ} are possible and here the first mode \isa{o\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool}
-is chosen. To choose another mode for the argument, you can declare the mode for the argument between
-the \hyperlink{command.values}{\mbox{\isa{\isacommand{values}}}} and the number of elements.%
+\noindent For this, the predicate compiler can infer modes \isa{o\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool}, \isa{i\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool}, \isa{o\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ bool} and
+  \isa{i\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ bool}.  The invocation of \hyperlink{command.values}{\mbox{\isa{\isacommand{values}}}}
+  \isa{{\isacharbraceleft}n{\isachardot}\ tranclp\ succ\ {\isadigit{1}}{\isadigit{0}}\ n{\isacharbraceright}} loops, as multiple modes for the
+  predicate \isa{succ} are possible and here the first mode \isa{o\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool} is chosen. To choose another mode for the argument,
+  you can declare the mode for the argument between the \hyperlink{command.values}{\mbox{\isa{\isacommand{values}}}} and the number of elements.%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
@@ -432,41 +432,49 @@
 %
 \endisadelimquote
 %
-\isamarkupsubsubsection{Embedding into functional code within Isabelle/HOL%
+\isamarkupsubsection{Embedding into functional code within Isabelle/HOL%
 }
 \isamarkuptrue%
 %
 \begin{isamarkuptext}%
-To embed the computation of an inductive predicate into functions that are defined in Isabelle/HOL,
-you have a number of options:
-\begin{itemize}
-\item You want to use the first-order predicate with the mode
-  where all arguments are input. Then you can use the predicate directly, e.g.
-\begin{quote}
-  \isa{valid{\isacharunderscore}suffix\ ys\ zs\ {\isacharequal}}\\
-  \isa{{\isacharparenleft}if\ append\ {\isacharbrackleft}Suc\ {\isadigit{0}}{\isacharcomma}\ {\isadigit{2}}{\isacharbrackright}\ ys\ zs\ then\ Some\ ys\ else\ None{\isacharparenright}}
-\end{quote}
-\item If you know that the execution returns only one value (it is deterministic), then you can
-  use the combinator \isa{Predicate{\isachardot}the}, e.g., a functional concatenation of lists
-  is defined with
-\begin{quote}
-  \isa{functional{\isacharunderscore}concat\ xs\ ys\ {\isacharequal}\ Predicate{\isachardot}the\ {\isacharparenleft}append{\isacharunderscore}i{\isacharunderscore}i{\isacharunderscore}o\ xs\ ys{\isacharparenright}}
-\end{quote}
-  Note that if the evaluation does not return a unique value, it raises a run-time error
-  \isa{not{\isacharunderscore}unique}.
-\end{itemize}%
+To embed the computation of an inductive predicate into functions
+  that are defined in Isabelle/HOL, you have a number of options:
+
+  \begin{itemize}
+
+    \item You want to use the first-order predicate with the mode
+      where all arguments are input. Then you can use the predicate directly, e.g.
+
+      \begin{quote}
+        \isa{valid{\isacharunderscore}suffix\ ys\ zs\ {\isacharequal}} \\
+        \isa{{\isacharparenleft}if\ append\ {\isacharbrackleft}Suc\ {\isadigit{0}}{\isacharcomma}\ {\isadigit{2}}{\isacharbrackright}\ ys\ zs\ then\ Some\ ys\ else\ None{\isacharparenright}}
+      \end{quote}
+
+    \item If you know that the execution returns only one value (it is
+      deterministic), then you can use the combinator \isa{Predicate{\isachardot}the}, e.g., a functional concatenation of lists is
+      defined with
+
+      \begin{quote}
+        \isa{functional{\isacharunderscore}concat\ xs\ ys\ {\isacharequal}\ Predicate{\isachardot}the\ {\isacharparenleft}append{\isacharunderscore}i{\isacharunderscore}i{\isacharunderscore}o\ xs\ ys{\isacharparenright}}
+      \end{quote}
+
+      Note that if the evaluation does not return a unique value, it
+      raises a run-time error \isa{not{\isacharunderscore}unique}.
+
+  \end{itemize}%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
-\isamarkupsubsubsection{Further Examples%
+\isamarkupsubsection{Further Examples%
 }
 \isamarkuptrue%
 %
 \begin{isamarkuptext}%
 Further examples for compiling inductive predicates can be found in
-the \isa{HOL{\isacharslash}ex{\isacharslash}Predicate{\isacharunderscore}Compile{\isacharunderscore}ex} theory file.
-There are also some examples in the Archive of Formal Proofs, notably
-in the \isa{POPLmark{\isacharminus}deBruijn} and the \isa{FeatherweightJava} sessions.%
+  the \isa{HOL{\isacharslash}ex{\isacharslash}Predicate{\isacharunderscore}Compile{\isacharunderscore}ex{\isacharcomma}thy} theory file.  There are
+  also some examples in the Archive of Formal Proofs, notably in the
+  \isa{POPLmark{\isacharminus}deBruijn} and the \isa{FeatherweightJava}
+  sessions.%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %




