# HG changeset patch
# User wenzelm
# Date 1008964705 -3600
# Node ID e3cb192aa6ee9055896d916c44a5032f7286021e
# Parent  cf5a342ce69831f648538a1b080edac946c7186d
updated;

diff -r cf5a342ce698 -r e3cb192aa6ee doc-src/TutorialI/Types/document/Records.tex
--- a/doc-src/TutorialI/Types/document/Records.tex	Fri Dec 21 19:56:42 2001 +0100
+++ b/doc-src/TutorialI/Types/document/Records.tex	Fri Dec 21 20:58:25 2001 +0100
@@ -14,7 +14,7 @@
   names, which can make expressions easier to read and reduces the
   risk of confusing one field for another.
 
-  A basic Isabelle record covers a certain set of fields, with select
+  A record of Isabelle/HOL covers a collection of fields, with select
   and update operations.  Each field has a specified type, which may
   be polymorphic.  The field names are part of the record type, and
   the order of the fields is significant --- as it is in Pascal but
@@ -25,10 +25,9 @@
   Record types can also be defined by extending other record types.
   Extensible records make use of the reserved pseudo-field \cdx{more},
   which is present in every record type.  Generic record operations
-  work on all possible extensions of a given type scheme; naive
-  polymorphism takes care of structural sub-typing behind the scenes.
-  There are also explicit coercion functions between fixed record
-  types.%
+  work on all possible extensions of a given type scheme; polymorphism
+  takes care of structural sub-typing behind the scenes.  There are
+  also explicit coercion functions between fixed record types.%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
@@ -37,11 +36,11 @@
 \isamarkuptrue%
 %
 \begin{isamarkuptext}%
-Record types are not primitive in Isabelle and have a subtle
+Record types are not primitive in Isabelle and have a delicate
   internal representation based on nested copies of the primitive
   product type.  A \commdx{record} declaration introduces a new record
   type scheme by specifying its fields, which are packaged internally
-  to hold up the perception of records as a separate concept.%
+  to hold up the perception of the record as a distinguished entity.%
 \end{isamarkuptext}%
 \isamarkuptrue%
 \isacommand{record}\ point\ {\isacharequal}\isanewline
@@ -71,9 +70,9 @@
 \ \ {\isachardoublequote}pt{\isadigit{2}}\ {\isasymequiv}\ {\isasymlparr}Xcoord\ {\isacharequal}\ {\isacharminus}{\isadigit{4}}{\isadigit{5}}{\isacharcomma}\ Ycoord\ {\isacharequal}\ {\isadigit{9}}{\isadigit{7}}{\isasymrparr}{\isachardoublequote}\isamarkupfalse%
 %
 \begin{isamarkuptext}%
-For each field, there is a \emph{selector} function of the same
-  name.  For example, if \isa{p} has type \isa{point} then \isa{Xcoord\ p} denotes the value of the \isa{Xcoord} field of~\isa{p}.  Expressions involving field selection of explicit records are
-  simplified automatically:%
+For each field, there is a \emph{selector}\index{selector!record}
+  function of the same name.  For example, if \isa{p} has type \isa{point} then \isa{Xcoord\ p} denotes the value of the \isa{Xcoord} field of~\isa{p}.  Expressions involving field selection
+  of explicit records are simplified automatically:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 \isacommand{lemma}\ {\isachardoublequote}Xcoord\ {\isasymlparr}Xcoord\ {\isacharequal}\ a{\isacharcomma}\ Ycoord\ {\isacharequal}\ b{\isasymrparr}\ {\isacharequal}\ a{\isachardoublequote}\isanewline
@@ -81,9 +80,9 @@
 \isacommand{by}\ simp\isamarkupfalse%
 %
 \begin{isamarkuptext}%
-The \emph{update} operation is functional.  For example, \isa{p{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ {\isadigit{0}}{\isasymrparr}} is a record whose \isa{Xcoord} value is zero
-  and whose \isa{Ycoord} value is copied from~\isa{p}.  Updates
-  are also simplified automatically:%
+The \emph{update}\index{update!record} operation is functional.  For
+  example, \isa{p{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ {\isadigit{0}}{\isasymrparr}} is a record whose \isa{Xcoord}
+  value is zero and whose \isa{Ycoord} value is copied from~\isa{p}.  Updates are also simplified automatically:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 \isacommand{lemma}\ {\isachardoublequote}{\isasymlparr}Xcoord\ {\isacharequal}\ a{\isacharcomma}\ Ycoord\ {\isacharequal}\ b{\isasymrparr}{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ {\isadigit{0}}{\isasymrparr}\ {\isacharequal}\isanewline
@@ -95,8 +94,7 @@
 \begin{warn}
   Field names are declared as constants and can no longer be used as
   variables.  It would be unwise, for example, to call the fields of
-  type \isa{point} simply \isa{x} and~\isa{y}.  Each record
-  declaration introduces a constant \cdx{more}.
+  type \isa{point} simply \isa{x} and~\isa{y}.
   \end{warn}%
 \end{isamarkuptext}%
 \isamarkuptrue%
@@ -144,10 +142,11 @@
 \isacommand{by}\ simp\isamarkupfalse%
 %
 \begin{isamarkuptext}%
-This lemma applies to any record whose first two fields are \isa{Xcoord} and~\isa{Ycoord}.  Note that \isa{{\isasymlparr}Xcoord\ {\isacharequal}\ a{\isacharcomma}\ Ycoord\ {\isacharequal}\ b{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ {\isacharparenleft}{\isacharparenright}{\isasymrparr}} is actually the same as \isa{{\isasymlparr}Xcoord\ {\isacharequal}\ a{\isacharcomma}\ Ycoord\ {\isacharequal}\ b{\isasymrparr}}.
+This lemma applies to any record whose first two fields are \isa{Xcoord} and~\isa{Ycoord}.  Note that \isa{{\isasymlparr}Xcoord\ {\isacharequal}\ a{\isacharcomma}\ Ycoord\ {\isacharequal}\ b{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ {\isacharparenleft}{\isacharparenright}{\isasymrparr}} is really the same as \isa{{\isasymlparr}Xcoord\ {\isacharequal}\ a{\isacharcomma}\ Ycoord\ {\isacharequal}\ b{\isasymrparr}}.  Selectors and updates are always polymorphic wrt.\ the \isa{more} part of a record scheme, its value is just ignored (for
+  select) or copied (for update).
 
-  The pseudo-field \isa{more} can be selected in the usual way, but
-  the identifier must be qualified:%
+  The \isa{more} pseudo-field may be manipulated directly as well,
+  but the identifier needs to be qualified:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 \isacommand{lemma}\ {\isachardoublequote}point{\isachardot}more\ cpt{\isadigit{1}}\ {\isacharequal}\ {\isasymlparr}col\ {\isacharequal}\ Green{\isasymrparr}{\isachardoublequote}\isanewline
@@ -156,26 +155,27 @@
 %
 \begin{isamarkuptext}%
 We see that the colour attached to this \isa{point} is a
-  (rudimentary) record in its own right, namely \isa{{\isasymlparr}col\ {\isacharequal}\ Green{\isasymrparr}}.  In order to select or update \isa{col} in the above
-  fragment, \isa{{\isasymlparr}col\ {\isacharequal}\ Green{\isasymrparr}} needs to be put back into the
-  context of its parent type scheme, say as \isa{more} part of a
-  \isa{point}.
+  (rudimentary) record in its own right, namely \isa{{\isasymlparr}col\ {\isacharequal}\ Green{\isasymrparr}}.  In order to select or update \isa{col}, this fragment
+  needs to be put back into the context of the parent type scheme, say
+  as \isa{more} part of another \isa{point}.
 
   To define generic operations, we need to know a bit more about
-  records.  Our declaration of \isa{point} above generated two type
+  records.  Our definition of \isa{point} above generated two type
   abbreviations:
 
-  \smallskip
+  \medskip
   \begin{tabular}{l}
   \isa{point}~\isa{{\isacharequal}}~\isa{{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharcolon}\ int{\isacharcomma}\ Ycoord\ {\isacharcolon}{\isacharcolon}\ int{\isasymrparr}} \\
   \isa{{\isacharprime}a\ point{\isacharunderscore}scheme}~\isa{{\isacharequal}}~\isa{{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharcolon}\ int{\isacharcomma}\ Ycoord\ {\isacharcolon}{\isacharcolon}\ int{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a{\isasymrparr}} \\
   \end{tabular}
-  \smallskip
+  \medskip
 
-  Type \isa{point} is for rigid records having exactly the two fields
+  Type \isa{point} is for fixed records having exactly the two fields
   \isa{Xcoord} and~\isa{Ycoord}, while the polymorphic type \isa{{\isacharprime}a\ point{\isacharunderscore}scheme} comprises all possible extensions to those two
-  fields, recall that \isa{unit\ point{\isacharunderscore}scheme} coincides with \isa{point}.  For example, let us define two operations --- methods, if
-  we regard records as objects --- to get and set any point's \isa{Xcoord} field.%
+  fields.  Note that \isa{unit\ point{\isacharunderscore}scheme} coincides with \isa{point}, and \isa{{\isasymlparr}col\ {\isacharcolon}{\isacharcolon}\ colour{\isasymrparr}\ point{\isacharunderscore}scheme} with \isa{cpoint}.
+
+  In the following example we define two operations --- methods, if we
+  regard records as objects --- to get and set any point's \isa{Xcoord} field.%
 \end{isamarkuptext}%
 \isamarkuptrue%
 \isacommand{constdefs}\isanewline
@@ -188,7 +188,7 @@
 Here is a generic method that modifies a point, incrementing its
   \isa{Xcoord} field.  The \isa{Ycoord} and \isa{more} fields
   are copied across.  It works for any record type scheme derived from
-  \isa{point}, such as \isa{cpoint}:%
+  \isa{point} (including \isa{cpoint} etc.):%
 \end{isamarkuptext}%
 \isamarkuptrue%
 \isacommand{constdefs}\isanewline
@@ -233,7 +233,7 @@
 %
 \begin{isamarkuptext}%
 The following equality is similar, but generic, in that \isa{r}
-  can be any instance of \isa{point{\isacharunderscore}scheme}:%
+  can be any instance of \isa{{\isacharprime}a\ point{\isacharunderscore}scheme}:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 \isacommand{lemma}\ {\isachardoublequote}r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isacharcomma}\ Ycoord\ {\isacharcolon}{\isacharequal}\ b{\isasymrparr}\ {\isacharequal}\ r{\isasymlparr}Ycoord\ {\isacharcolon}{\isacharequal}\ b{\isacharcomma}\ Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}{\isachardoublequote}\isanewline
@@ -242,11 +242,11 @@
 %
 \begin{isamarkuptext}%
 We see above the syntax for iterated updates.  We could equivalently
-  have written the left-hand side as \isa{r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isacharcomma}\ Ycoord\ {\isacharcolon}{\isacharequal}\ b{\isasymrparr}}.
+  have written the left-hand side as \isa{r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}{\isasymlparr}Ycoord\ {\isacharcolon}{\isacharequal}\ b{\isasymrparr}}.
 
-  Record equality is \emph{extensional}: \index{extensionality!for
-  records} a record is determined entirely by the values of its
-  fields.%
+  \medskip Record equality is \emph{extensional}:
+  \index{extensionality!for records} a record is determined entirely
+  by the values of its fields.%
 \end{isamarkuptext}%
 \isamarkuptrue%
 \isacommand{lemma}\ {\isachardoublequote}r\ {\isacharequal}\ {\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ r{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ r{\isasymrparr}{\isachardoublequote}\isanewline
@@ -254,7 +254,8 @@
 \isacommand{by}\ simp\isamarkupfalse%
 %
 \begin{isamarkuptext}%
-The generic version of this equality includes the field \isa{more}:%
+The generic version of this equality includes the pseudo-field
+  \isa{more}:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 \isacommand{lemma}\ {\isachardoublequote}r\ {\isacharequal}\ {\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ r{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ r{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ point{\isachardot}more\ r{\isasymrparr}{\isachardoublequote}\isanewline
@@ -262,10 +263,7 @@
 \isacommand{by}\ simp\isamarkupfalse%
 %
 \begin{isamarkuptext}%
-Note that the \isa{r} is of a different (more general) type than
-  the previous one.
-
-  \medskip The simplifier can prove many record equalities
+\medskip The simplifier can prove many record equalities
   automatically, but general equality reasoning can be tricky.
   Consider proving this obvious fact:%
 \end{isamarkuptext}%
@@ -277,8 +275,8 @@
 \isacommand{oops}\isamarkupfalse%
 %
 \begin{isamarkuptext}%
-The simplifier can do nothing, since general record equality is not
-  eliminated automatically.  One way to proceed is by an explicit
+Here the simplifier can do nothing, since general record equality is
+  not eliminated automatically.  One way to proceed is by an explicit
   forward step that applies the selector \isa{Xcoord} to both sides
   of the assumed record equality:%
 \end{isamarkuptext}%
@@ -300,17 +298,17 @@
 \isacommand{done}\isamarkupfalse%
 %
 \begin{isamarkuptext}%
-The \isa{cases} method is preferable to such a forward proof.
-  State the desired lemma again:%
+The \isa{cases} method is preferable to such a forward proof.  We
+  state the desired lemma again:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 \isacommand{lemma}\ {\isachardoublequote}r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}\ {\isacharequal}\ r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isacharprime}{\isasymrparr}\ {\isasymLongrightarrow}\ a\ {\isacharequal}\ a{\isacharprime}{\isachardoublequote}\isamarkupfalse%
 %
 \begin{isamarkuptxt}%
-The \methdx{cases} method adds an equality to replace the named
-    record variable by an explicit record, listing all fields.  It
-    even includes the pseudo-field \isa{more}, since the record
-    equality stated above is generic.%
+The \methdx{cases} method adds an equality to replace the
+  named record term by an explicit record expression, listing all
+  fields.  It even includes the pseudo-field \isa{more}, since the
+  record equality stated here is generic for all extensions.%
 \end{isamarkuptxt}%
 \ \ \isamarkuptrue%
 \isacommand{apply}\ {\isacharparenleft}cases\ r{\isacharparenright}\isamarkupfalse%
@@ -321,32 +319,42 @@
 \isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymlbrakk}r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}\ {\isacharequal}\ r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isacharprime}{\isasymrparr}{\isacharsemicolon}\isanewline
 \isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ \ \ \ }r\ {\isacharequal}\ {\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ more{\isasymrparr}{\isasymrbrakk}\isanewline
 \isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymLongrightarrow}\ a\ {\isacharequal}\ a{\isacharprime}%
-\end{isabelle}
-    Again, \isa{simp} finishes the proof.  Because \isa{r} has
-    become an explicit record expression, the updates can be applied
-    and the record equality can be replaced by equality of the
-    corresponding fields (due to injectivity).%
+\end{isabelle} Again, \isa{simp} finishes the proof.  Because \isa{r} is now represented as
+  an explicit record construction, the updates can be applied and the
+  record equality can be replaced by equality of the corresponding
+  fields (due to injectivity).%
 \end{isamarkuptxt}%
 \ \ \isamarkuptrue%
 \isacommand{apply}\ simp\isanewline
 \ \ \isamarkupfalse%
 \isacommand{done}\isamarkupfalse%
 %
+\begin{isamarkuptext}%
+The generic cases method does not admit references to locally bound
+  parameters of a goal.  In longer proof scripts one might have to
+  fall back on the primitive \isa{rule{\isacharunderscore}tac} used together with the
+  internal representation rules of records.  E.g.\ the above use of
+  \isa{{\isacharparenleft}cases\ r{\isacharparenright}} would become \isa{{\isacharparenleft}rule{\isacharunderscore}tac\ r\ {\isacharequal}\ r\ in\ point{\isachardot}cases{\isacharunderscore}scheme{\isacharparenright}}.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
 \isamarkupsubsection{Extending and Truncating Records%
 }
 \isamarkuptrue%
 %
 \begin{isamarkuptext}%
-Each record declaration introduces functions to refer collectively
-  to a record's fields and to convert between related record types.
-  They can, for instance, convert between types \isa{point} and \isa{cpoint}.  We can add a colour to a point or to convert a \isa{cpoint} to a \isa{point} by forgetting its colour.
+Each record declaration introduces a number of derived operations to
+  refer collectively to a record's fields and to convert between fixed
+  record types.  They can, for instance, convert between types \isa{point} and \isa{cpoint}.  We can add a colour to a point or convert
+  a \isa{cpoint} to a \isa{point} by forgetting its colour.
 
   \begin{itemize}
 
   \item Function \cdx{make} takes as arguments all of the record's
-  fields.  It returns the corresponding record.
+  fields (including those inherited from ancestors).  It returns the
+  corresponding record.
 
-  \item Function \cdx{fields} takes the record's new fields and
+  \item Function \cdx{fields} takes the record's very own fields and
   returns a record fragment consisting of just those fields.  This may
   be filled into the \isa{more} part of the parent record scheme.
 
@@ -362,34 +370,35 @@
   These functions merely provide handsome abbreviations for standard
   record expressions involving constructors and selectors.  The
   definitions, which are \emph{not} unfolded by default, are made
-  available by the collective name of \isa{defs} (e.g.\ \isa{point{\isachardot}defs} or \isa{cpoint{\isachardot}defs}).
+  available by the collective name of \isa{defs} (\isa{point{\isachardot}defs}, \isa{cpoint{\isachardot}defs}, etc.).
 
   For example, here are the versions of those functions generated for
   record \isa{point}.  We omit \isa{point{\isachardot}fields}, which happens to
   be the same as \isa{point{\isachardot}make}.
 
   \begin{isabelle}%
-point{\isachardot}make\ {\isacharquery}Xcoord\ {\isacharquery}Ycoord\ {\isasymequiv}\ {\isasymlparr}Xcoord\ {\isacharequal}\ {\isacharquery}Xcoord{\isacharcomma}\ Ycoord\ {\isacharequal}\ {\isacharquery}Ycoord{\isasymrparr}\isanewline
-point{\isachardot}extend\ {\isacharquery}r\ {\isacharquery}more\ {\isasymequiv}\isanewline
-{\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ {\isacharquery}r{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ {\isacharquery}r{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ {\isacharquery}more{\isasymrparr}\isanewline
-point{\isachardot}truncate\ {\isacharquery}r\ {\isasymequiv}\ {\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ {\isacharquery}r{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ {\isacharquery}r{\isasymrparr}%
+point{\isachardot}make\ Xcoord\ Ycoord\ {\isasymequiv}\ {\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord{\isasymrparr}\isanewline
+point{\isachardot}extend\ r\ more\ {\isasymequiv}\isanewline
+{\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ r{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ r{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ more{\isasymrparr}\isanewline
+point{\isachardot}truncate\ r\ {\isasymequiv}\ {\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ r{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ r{\isasymrparr}%
 \end{isabelle}
 
   Contrast those with the corresponding functions for record \isa{cpoint}.  Observe \isa{cpoint{\isachardot}fields} in particular.
 
   \begin{isabelle}%
-cpoint{\isachardot}make\ {\isacharquery}Xcoord\ {\isacharquery}Ycoord\ {\isacharquery}col\ {\isasymequiv}\isanewline
-{\isasymlparr}Xcoord\ {\isacharequal}\ {\isacharquery}Xcoord{\isacharcomma}\ Ycoord\ {\isacharequal}\ {\isacharquery}Ycoord{\isacharcomma}\ col\ {\isacharequal}\ {\isacharquery}col{\isasymrparr}\isanewline
-cpoint{\isachardot}extend\ {\isacharquery}r\ {\isacharquery}more\ {\isasymequiv}\isanewline
-{\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ {\isacharquery}r{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ {\isacharquery}r{\isacharcomma}\ col\ {\isacharequal}\ col\ {\isacharquery}r{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ {\isacharquery}more{\isasymrparr}\isanewline
-cpoint{\isachardot}truncate\ {\isacharquery}r\ {\isasymequiv}\isanewline
-{\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ {\isacharquery}r{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ {\isacharquery}r{\isacharcomma}\ col\ {\isacharequal}\ col\ {\isacharquery}r{\isasymrparr}%
+cpoint{\isachardot}make\ Xcoord\ Ycoord\ col\ {\isasymequiv}\isanewline
+{\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord{\isacharcomma}\ col\ {\isacharequal}\ col{\isasymrparr}\isanewline
+cpoint{\isachardot}fields\ col\ {\isasymequiv}\ {\isasymlparr}col\ {\isacharequal}\ col{\isasymrparr}\isanewline
+cpoint{\isachardot}extend\ r\ more\ {\isasymequiv}\isanewline
+{\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ r{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ r{\isacharcomma}\ col\ {\isacharequal}\ col\ r{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ more{\isasymrparr}\isanewline
+cpoint{\isachardot}truncate\ r\ {\isasymequiv}\isanewline
+{\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ r{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ r{\isacharcomma}\ col\ {\isacharequal}\ col\ r{\isasymrparr}%
 \end{isabelle}
 
   To demonstrate these functions, we declare a new coloured point by
   extending an ordinary point.  Function \isa{point{\isachardot}extend} augments
-  \isa{pt{\isadigit{1}}} with a colour, which is converted into an appropriate
-  record fragment by \isa{cpoint{\isachardot}fields}.%
+  \isa{pt{\isadigit{1}}} with a colour value, which is converted into an
+  appropriate record fragment by \isa{cpoint{\isachardot}fields}.%
 \end{isamarkuptext}%
 \isamarkuptrue%
 \isacommand{constdefs}\isanewline
@@ -419,8 +428,7 @@
 %
 \begin{isamarkuptext}%
 In the example below, a coloured point is truncated to leave a
-  point.  We must use the \isa{truncate} function of the shorter
-  record.%
+  point.  We use the \isa{truncate} function of the target record.%
 \end{isamarkuptext}%
 \isamarkuptrue%
 \isacommand{lemma}\ {\isachardoublequote}point{\isachardot}truncate\ cpt{\isadigit{2}}\ {\isacharequal}\ pt{\isadigit{1}}{\isachardoublequote}\isanewline
@@ -429,8 +437,10 @@
 %
 \begin{isamarkuptext}%
 \begin{exercise}
-  Extend record \isa{cpoint} to have a further field, \isa{intensity}, of type~\isa{nat}.  Experiment with coercions among the
-  three record types.
+  Extend record \isa{cpoint} to have a further field, \isa{intensity}, of type~\isa{nat}.  Experiment with generic operations
+  (using polymorphic selectors and updates) and explicit coercions
+  (using \isa{extend}, \isa{truncate} etc.) among the three record
+  types.
   \end{exercise}
 
   \begin{exercise}
diff -r cf5a342ce698 -r e3cb192aa6ee doc-src/TutorialI/tutorial.ind
--- a/doc-src/TutorialI/tutorial.ind	Fri Dec 21 19:56:42 2001 +0100
+++ b/doc-src/TutorialI/tutorial.ind	Fri Dec 21 20:58:25 2001 +0100
@@ -1,139 +1,139 @@
 \begin{theindex}
 
-  \item \ttall, \bold{199}
-  \item \texttt{?}, \bold{199}
-  \item \isasymuniqex, \bold{199}
-  \item \ttuniquex, \bold{199}
-  \item {\texttt {\&}}, \bold{199}
-  \item \verb$~$, \bold{199}
-  \item \verb$~=$, \bold{199}
-  \item \ttor, \bold{199}
+  \item \ttall, \bold{201}
+  \item \texttt{?}, \bold{201}
+  \item \isasymuniqex, \bold{201}
+  \item \ttuniquex, \bold{201}
+  \item {\texttt {\&}}, \bold{201}
+  \item \verb$~$, \bold{201}
+  \item \verb$~=$, \bold{201}
+  \item \ttor, \bold{201}
   \item \texttt{[]}, \bold{9}
   \item \texttt{\#}, \bold{9}
-  \item \texttt{\at}, \bold{10}, 199
-  \item \isasymnotin, \bold{199}
-  \item \verb$~:$, \bold{199}
-  \item \isasymInter, \bold{199}
-  \item \isasymUnion, \bold{199}
-  \item \isasyminverse, \bold{199}
-  \item \verb$^-1$, \bold{199}
-  \item \isactrlsup{\isacharasterisk}, \bold{199}
-  \item \verb$^$\texttt{*}, \bold{199}
-  \item \isasymAnd, \bold{12}, \bold{199}
-  \item \ttAnd, \bold{199}
-  \item \isasymrightleftharpoons, 26
-  \item \isasymrightharpoonup, 26
-  \item \isasymleftharpoondown, 26
+  \item \texttt{\at}, \bold{10}, 201
+  \item \isasymnotin, \bold{201}
+  \item \verb$~:$, \bold{201}
+  \item \isasymInter, \bold{201}
+  \item \isasymUnion, \bold{201}
+  \item \isasyminverse, \bold{201}
+  \item \verb$^-1$, \bold{201}
+  \item \isactrlsup{\isacharasterisk}, \bold{201}
+  \item \verb$^$\texttt{*}, \bold{201}
+  \item \isasymAnd, \bold{12}, \bold{201}
+  \item \ttAnd, \bold{201}
+  \item \isasymrightleftharpoons, 55
+  \item \isasymrightharpoonup, 55
+  \item \isasymleftharpoondown, 55
   \item \emph {$\Rightarrow $}, \bold{5}
-  \item \ttlbr, \bold{199}
-  \item \ttrbr, \bold{199}
-  \item \texttt {\%}, \bold{199}
+  \item \ttlbr, \bold{201}
+  \item \ttrbr, \bold{201}
+  \item \texttt {\%}, \bold{201}
   \item \texttt {;}, \bold{7}
   \item \isa {()} (constant), 24
-  \item \isa {+} (tactical), 89
+  \item \isa {+} (tactical), 91
   \item \isa {<*lex*>}, \see{lexicographic product}{1}
-  \item \isa {?} (tactical), 89
-  \item \texttt{|} (tactical), 89
+  \item \isa {?} (tactical), 91
+  \item \texttt{|} (tactical), 91
 
   \indexspace
 
-  \item \isa {0} (constant), 22, 23, 140
-  \item \isa {1} (constant), 23, 140, 141
+  \item \isa {0} (constant), 22, 23, 142
+  \item \isa {1} (constant), 23, 142, 143
 
   \indexspace
 
   \item abandoning a proof, \bold{13}
   \item abandoning a theory, \bold{16}
-  \item \isa {abs} (constant), 143
-  \item \texttt {abs}, \bold{199}
-  \item absolute value, 143
+  \item \isa {abs} (constant), 145
+  \item \texttt {abs}, \bold{201}
+  \item absolute value, 145
   \item \isa {add} (modifier), 29
-  \item \isa {add_ac} (theorems), 142
-  \item \isa {add_assoc} (theorem), \bold{142}
-  \item \isa {add_commute} (theorem), \bold{142}
-  \item \isa {add_mult_distrib} (theorem), \bold{141}
-  \item \texttt {ALL}, \bold{199}
-  \item \isa {All} (constant), 99
-  \item \isa {allE} (theorem), \bold{71}
-  \item \isa {allI} (theorem), \bold{70}
+  \item \isa {add_ac} (theorems), 144
+  \item \isa {add_assoc} (theorem), \bold{144}
+  \item \isa {add_commute} (theorem), \bold{144}
+  \item \isa {add_mult_distrib} (theorem), \bold{143}
+  \item \texttt {ALL}, \bold{201}
+  \item \isa {All} (constant), 101
+  \item \isa {allE} (theorem), \bold{73}
+  \item \isa {allI} (theorem), \bold{72}
   \item append function, 10--14
   \item \isacommand {apply} (command), 15
-  \item \isa {arg_cong} (theorem), \bold{86}
-  \item \isa {arith} (method), 23, 139
+  \item \isa {arg_cong} (theorem), \bold{88}
+  \item \isa {arith} (method), 23, 141
   \item arithmetic operations
     \subitem for \protect\isa{nat}, 23
-  \item \textsc {ascii} symbols, \bold{199}
-  \item associative-commutative function, 166
-  \item \isa {assumption} (method), 59
+  \item \textsc {ascii} symbols, \bold{201}
+  \item associative-commutative function, 168
+  \item \isa {assumption} (method), 61
   \item assumptions
     \subitem of subgoal, 12
-    \subitem renaming, 72--73
-    \subitem reusing, 73
-  \item \isa {auto} (method), 38, 82
-  \item \isa {axclass}, 154--160
-  \item axiom of choice, 76
-  \item axiomatic type classes, 154--160
+    \subitem renaming, 74--75
+    \subitem reusing, 75
+  \item \isa {auto} (method), 38, 84
+  \item \isa {axclass}, 156--162
+  \item axiom of choice, 78
+  \item axiomatic type classes, 156--162
 
   \indexspace
 
-  \item \isacommand {back} (command), 68
-  \item \isa {Ball} (constant), 99
-  \item \isa {ballI} (theorem), \bold{98}
-  \item \isa {best} (method), 82
-  \item \isa {Bex} (constant), 99
-  \item \isa {bexE} (theorem), \bold{98}
-  \item \isa {bexI} (theorem), \bold{98}
-  \item \isa {bij_def} (theorem), \bold{100}
-  \item bijections, 100
+  \item \isacommand {back} (command), 70
+  \item \isa {Ball} (constant), 101
+  \item \isa {ballI} (theorem), \bold{100}
+  \item \isa {best} (method), 84
+  \item \isa {Bex} (constant), 101
+  \item \isa {bexE} (theorem), \bold{100}
+  \item \isa {bexI} (theorem), \bold{100}
+  \item \isa {bij_def} (theorem), \bold{102}
+  \item bijections, 102
   \item binary trees, 18
-  \item binomial coefficients, 99
-  \item bisimulations, 106
-  \item \isa {blast} (method), 79--80, 82
+  \item binomial coefficients, 101
+  \item bisimulations, 108
+  \item \isa {blast} (method), 81--82, 84
   \item \isa {bool} (type), 4, 5
   \item boolean expressions example, 20--22
-  \item \isa {bspec} (theorem), \bold{98}
-  \item \isacommand{by} (command), 63
+  \item \isa {bspec} (theorem), \bold{100}
+  \item \isacommand{by} (command), 65
 
   \indexspace
 
-  \item \isa {card} (constant), 99
-  \item \isa {card_Pow} (theorem), \bold{99}
-  \item \isa {card_Un_Int} (theorem), \bold{99}
-  \item cardinality, 99
+  \item \isa {card} (constant), 101
+  \item \isa {card_Pow} (theorem), \bold{101}
+  \item \isa {card_Un_Int} (theorem), \bold{101}
+  \item cardinality, 101
   \item \isa {case} (symbol), 32, 33
   \item \isa {case} expressions, 5, 6, 18
   \item case distinctions, 19
   \item case splits, \bold{31}
-  \item \isa {case_tac} (method), 19, 91, 147
-  \item \isa {cases} (method), 152
-  \item \isa {clarify} (method), 81, 82
-  \item \isa {clarsimp} (method), 81, 82
-  \item \isa {classical} (theorem), \bold{63}
-  \item coinduction, \bold{106}
-  \item \isa {Collect} (constant), 99
+  \item \isa {case_tac} (method), 19, 93, 149
+  \item \isa {cases} (method), 154
+  \item \isa {clarify} (method), 83, 84
+  \item \isa {clarsimp} (method), 83, 84
+  \item \isa {classical} (theorem), \bold{65}
+  \item coinduction, \bold{108}
+  \item \isa {Collect} (constant), 101
   \item compiling expressions example, 36--38
-  \item \isa {Compl_iff} (theorem), \bold{96}
+  \item \isa {Compl_iff} (theorem), \bold{98}
   \item complement
-    \subitem of a set, 95
+    \subitem of a set, 97
   \item composition
-    \subitem of functions, \bold{100}
-    \subitem of relations, \bold{102}
+    \subitem of functions, \bold{102}
+    \subitem of relations, \bold{104}
   \item conclusion
     \subitem of subgoal, 12
   \item conditional expressions, \see{\isa{if} expressions}{1}
   \item conditional simplification rules, 31
-  \item \isa {cong} (attribute), 166
-  \item congruence rules, \bold{165}
-  \item \isa {conjE} (theorem), \bold{61}
-  \item \isa {conjI} (theorem), \bold{58}
+  \item \isa {cong} (attribute), 168
+  \item congruence rules, \bold{167}
+  \item \isa {conjE} (theorem), \bold{63}
+  \item \isa {conjI} (theorem), \bold{60}
   \item \isa {Cons} (constant), 9
   \item \isacommand {constdefs} (command), 25
   \item \isacommand {consts} (command), 10
-  \item contrapositives, 63
+  \item contrapositives, 65
   \item converse
-    \subitem of a relation, \bold{102}
-  \item \isa {converse_iff} (theorem), \bold{102}
-  \item CTL, 111--116, 181--183
+    \subitem of a relation, \bold{104}
+  \item \isa {converse_iff} (theorem), \bold{104}
+  \item CTL, 113--118, 183--185
 
   \indexspace
 
@@ -141,179 +141,179 @@
   \item datatypes, 17--22
     \subitem and nested recursion, 40, 44
     \subitem mutually recursive, 38
-    \subitem nested, 170
-  \item \isacommand {defer} (command), 16, 90
+    \subitem nested, 172
+  \item \isacommand {defer} (command), 16, 92
   \item Definitional Approach, 26
   \item definitions, \bold{25}
     \subitem unfolding, \bold{30}
   \item \isacommand {defs} (command), 25
   \item \isa {del} (modifier), 29
-  \item description operators, 75--77
+  \item description operators, 77--79
   \item descriptions
-    \subitem definite, 75
-    \subitem indefinite, 76
-  \item \isa {dest} (attribute), 92
-  \item destruction rules, 61
-  \item \isa {diff_mult_distrib} (theorem), \bold{141}
+    \subitem definite, 77
+    \subitem indefinite, 78
+  \item \isa {dest} (attribute), 94
+  \item destruction rules, 63
+  \item \isa {diff_mult_distrib} (theorem), \bold{143}
   \item difference
-    \subitem of sets, \bold{96}
-  \item \isa {disjCI} (theorem), \bold{64}
-  \item \isa {disjE} (theorem), \bold{60}
+    \subitem of sets, \bold{98}
+  \item \isa {disjCI} (theorem), \bold{66}
+  \item \isa {disjE} (theorem), \bold{62}
   \item \isa {div} (symbol), 23
-  \item divides relation, 74, 85, 91--94, 142
+  \item divides relation, 76, 87, 93--96, 144
   \item division
-    \subitem by negative numbers, 143
-    \subitem by zero, 142
-    \subitem for type \protect\isa{nat}, 141
+    \subitem by negative numbers, 145
+    \subitem by zero, 144
+    \subitem for type \protect\isa{nat}, 143
   \item domain
-    \subitem of a relation, 102
-  \item \isa {Domain_iff} (theorem), \bold{102}
+    \subitem of a relation, 104
+  \item \isa {Domain_iff} (theorem), \bold{104}
   \item \isacommand {done} (command), 13
-  \item \isa {drule_tac} (method), 66, 86
-  \item \isa {dvd_add} (theorem), \bold{142}
-  \item \isa {dvd_anti_sym} (theorem), \bold{142}
-  \item \isa {dvd_def} (theorem), \bold{142}
+  \item \isa {drule_tac} (method), 68, 88
+  \item \isa {dvd_add} (theorem), \bold{144}
+  \item \isa {dvd_anti_sym} (theorem), \bold{144}
+  \item \isa {dvd_def} (theorem), \bold{144}
 
   \indexspace
 
-  \item \isa {elim!} (attribute), 121
-  \item elimination rules, 59--60
+  \item \isa {elim!} (attribute), 123
+  \item elimination rules, 61--62
   \item \isacommand {end} (command), 14
-  \item \isa {Eps} (constant), 99
+  \item \isa {Eps} (constant), 101
   \item equality, 5
-    \subitem of functions, \bold{99}
-    \subitem of records, 151
-    \subitem of sets, \bold{96}
-  \item \isa {equalityE} (theorem), \bold{96}
-  \item \isa {equalityI} (theorem), \bold{96}
-  \item \isa {erule} (method), 60
-  \item \isa {erule_tac} (method), 66
-  \item Euclid's algorithm, 91--94
+    \subitem of functions, \bold{101}
+    \subitem of records, 153
+    \subitem of sets, \bold{98}
+  \item \isa {equalityE} (theorem), \bold{98}
+  \item \isa {equalityI} (theorem), \bold{98}
+  \item \isa {erule} (method), 62
+  \item \isa {erule_tac} (method), 68
+  \item Euclid's algorithm, 93--96
   \item even numbers
-    \subitem defining inductively, 117--121
-  \item \texttt {EX}, \bold{199}
-  \item \isa {Ex} (constant), 99
-  \item \isa {exE} (theorem), \bold{72}
-  \item \isa {exI} (theorem), \bold{72}
-  \item \isa {ext} (theorem), \bold{99}
-  \item \isa {extend} (constant), 153
+    \subitem defining inductively, 119--123
+  \item \texttt {EX}, \bold{201}
+  \item \isa {Ex} (constant), 101
+  \item \isa {exE} (theorem), \bold{74}
+  \item \isa {exI} (theorem), \bold{74}
+  \item \isa {ext} (theorem), \bold{101}
+  \item \isa {extend} (constant), 155
   \item extensionality
-    \subitem for functions, \bold{99, 100}
-    \subitem for records, 151
-    \subitem for sets, \bold{96}
-  \item \ttEXU, \bold{199}
+    \subitem for functions, \bold{101, 102}
+    \subitem for records, 153
+    \subitem for sets, \bold{98}
+  \item \ttEXU, \bold{201}
 
   \indexspace
 
   \item \isa {False} (constant), 5
-  \item \isa {fast} (method), 82, 114
+  \item \isa {fast} (method), 84, 116
   \item Fibonacci function, 47
-  \item \isa {fields} (constant), 153
-  \item \isa {finite} (symbol), 99
-  \item \isa {Finites} (constant), 99
-  \item fixed points, 106
+  \item \isa {fields} (constant), 155
+  \item \isa {finite} (symbol), 101
+  \item \isa {Finites} (constant), 101
+  \item fixed points, 108
   \item flags, 5, 6, 33
     \subitem setting and resetting, 5
-  \item \isa {force} (method), 81, 82
+  \item \isa {force} (method), 83, 84
   \item formulae, 5--6
-  \item forward proof, 82--88
-  \item \isa {frule} (method), 73
-  \item \isa {frule_tac} (method), 66
+  \item forward proof, 84--90
+  \item \isa {frule} (method), 75
+  \item \isa {frule_tac} (method), 68
   \item \isa {fst} (constant), 24
   \item function types, 5
-  \item functions, 99--101
-    \subitem partial, 172
+  \item functions, 101--103
+    \subitem partial, 174
     \subitem total, 11, 46--52
-    \subitem underdefined, 173
+    \subitem underdefined, 175
 
   \indexspace
 
-  \item \isa {gcd} (constant), 83--84, 91--94
-  \item generalizing for induction, 119
+  \item \isa {gcd} (constant), 85--86, 93--96
+  \item generalizing for induction, 121
   \item generalizing induction formulae, 35
-  \item Girard, Jean-Yves, \fnote{61}
+  \item Girard, Jean-Yves, \fnote{63}
   \item Gordon, Mike, 3
   \item grammars
-    \subitem defining inductively, 130--135
-  \item ground terms example, 125--130
+    \subitem defining inductively, 132--137
+  \item ground terms example, 127--132
 
   \indexspace
 
   \item \isa {hd} (constant), 17, 37
-  \item Hilbert's $\varepsilon$-operator, 76
+  \item Hilbert's $\varepsilon$-operator, 78
   \item HOLCF, 43
-  \item Hopcroft, J. E., 135
-  \item \isa {hypreal} (type), 145
+  \item Hopcroft, J. E., 137
+  \item \isa {hypreal} (type), 147
 
   \indexspace
 
-  \item \isa {Id_def} (theorem), \bold{102}
-  \item \isa {id_def} (theorem), \bold{100}
+  \item \isa {Id_def} (theorem), \bold{104}
+  \item \isa {id_def} (theorem), \bold{102}
   \item identifiers, \bold{6}
     \subitem qualified, \bold{4}
-  \item identity function, \bold{100}
-  \item identity relation, \bold{102}
+  \item identity function, \bold{102}
+  \item identity relation, \bold{104}
   \item \isa {if} expressions, 5, 6
     \subitem simplification of, 33
     \subitem splitting of, 31, 49
   \item if-and-only-if, 6
-  \item \isa {iff} (attribute), 80, 92, 120
-  \item \isa {iffD1} (theorem), \bold{84}
-  \item \isa {iffD2} (theorem), \bold{84}
+  \item \isa {iff} (attribute), 82, 94, 122
+  \item \isa {iffD1} (theorem), \bold{86}
+  \item \isa {iffD2} (theorem), \bold{86}
   \item image
-    \subitem under a function, \bold{101}
-    \subitem under a relation, \bold{102}
-  \item \isa {image_def} (theorem), \bold{101}
-  \item \isa {Image_iff} (theorem), \bold{102}
-  \item \isa {impI} (theorem), \bold{62}
-  \item implication, 62--63
-  \item \isa {ind_cases} (method), 121
-  \item \isa {induct_tac} (method), 12, 19, 52, 180
-  \item induction, 176--183
-    \subitem complete, 178
-    \subitem deriving new schemas, 180
-    \subitem on a term, 177
+    \subitem under a function, \bold{103}
+    \subitem under a relation, \bold{104}
+  \item \isa {image_def} (theorem), \bold{103}
+  \item \isa {Image_iff} (theorem), \bold{104}
+  \item \isa {impI} (theorem), \bold{64}
+  \item implication, 64--65
+  \item \isa {ind_cases} (method), 123
+  \item \isa {induct_tac} (method), 12, 19, 52, 182
+  \item induction, 178--185
+    \subitem complete, 180
+    \subitem deriving new schemas, 182
+    \subitem on a term, 179
     \subitem recursion, 51--52
     \subitem structural, 19
-    \subitem well-founded, 105
+    \subitem well-founded, 107
   \item induction heuristics, 34--36
-  \item \isacommand {inductive} (command), 117
+  \item \isacommand {inductive} (command), 119
   \item inductive definition
-    \subitem simultaneous, 131
-  \item inductive definitions, 117--135
-  \item \isacommand {inductive\_cases} (command), 121, 129
+    \subitem simultaneous, 133
+  \item inductive definitions, 119--137
+  \item \isacommand {inductive\_cases} (command), 123, 131
   \item infinitely branching trees, 43
   \item \isacommand{infixr} (annotation), 10
-  \item \isa {inj_on_def} (theorem), \bold{100}
-  \item injections, 100
-  \item \isa {insert} (constant), 97
-  \item \isa {insert} (method), 87--88
-  \item instance, \bold{155}
-  \item \texttt {INT}, \bold{199}
-  \item \texttt {Int}, \bold{199}
-  \item \isa {int} (type), 143--144
-  \item \isa {INT_iff} (theorem), \bold{98}
-  \item \isa {IntD1} (theorem), \bold{95}
-  \item \isa {IntD2} (theorem), \bold{95}
-  \item integers, 143--144
-  \item \isa {INTER} (constant), 99
-  \item \texttt {Inter}, \bold{199}
-  \item \isa {Inter_iff} (theorem), \bold{98}
-  \item intersection, 95
-    \subitem indexed, 98
-  \item \isa {IntI} (theorem), \bold{95}
-  \item \isa {intro} (method), 64
-  \item \isa {intro!} (attribute), 118
-  \item \isa {intro_classes} (method), 155
-  \item introduction rules, 58--59
-  \item \isa {inv} (constant), 76
-  \item \isa {inv_image_def} (theorem), \bold{105}
+  \item \isa {inj_on_def} (theorem), \bold{102}
+  \item injections, 102
+  \item \isa {insert} (constant), 99
+  \item \isa {insert} (method), 89--90
+  \item instance, \bold{158}
+  \item \texttt {INT}, \bold{201}
+  \item \texttt {Int}, \bold{201}
+  \item \isa {int} (type), 145--146
+  \item \isa {INT_iff} (theorem), \bold{100}
+  \item \isa {IntD1} (theorem), \bold{97}
+  \item \isa {IntD2} (theorem), \bold{97}
+  \item integers, 145--146
+  \item \isa {INTER} (constant), 101
+  \item \texttt {Inter}, \bold{201}
+  \item \isa {Inter_iff} (theorem), \bold{100}
+  \item intersection, 97
+    \subitem indexed, 100
+  \item \isa {IntI} (theorem), \bold{97}
+  \item \isa {intro} (method), 66
+  \item \isa {intro!} (attribute), 120
+  \item \isa {intro_classes} (method), 158
+  \item introduction rules, 60--61
+  \item \isa {inv} (constant), 78
+  \item \isa {inv_image_def} (theorem), \bold{107}
   \item inverse
-    \subitem of a function, \bold{100}
-    \subitem of a relation, \bold{102}
+    \subitem of a function, \bold{102}
+    \subitem of a relation, \bold{104}
   \item inverse image
-    \subitem of a function, 101
-    \subitem of a relation, 104
+    \subitem of a function, 103
+    \subitem of a relation, 106
   \item \isa {itrev} (constant), 34
 
   \indexspace
@@ -324,99 +324,99 @@
 
   \item $\lambda$ expressions, 5
   \item LCF, 43
-  \item \isa {LEAST} (symbol), 23, 75
-  \item least number operator, \see{\protect\isa{LEAST}}{75}
+  \item \isa {LEAST} (symbol), 23, 77
+  \item least number operator, \see{\protect\isa{LEAST}}{77}
   \item \isacommand {lemma} (command), 13
-  \item \isacommand {lemmas} (command), 83, 92
+  \item \isacommand {lemmas} (command), 85, 94
   \item \isa {length} (symbol), 18
-  \item \isa {length_induct}, \bold{180}
-  \item \isa {less_than} (constant), 104
-  \item \isa {less_than_iff} (theorem), \bold{104}
+  \item \isa {length_induct}, \bold{182}
+  \item \isa {less_than} (constant), 106
+  \item \isa {less_than_iff} (theorem), \bold{106}
   \item \isa {let} expressions, 5, 6, 31
   \item \isa {Let_def} (theorem), 31
-  \item \isa {lex_prod_def} (theorem), \bold{105}
-  \item lexicographic product, \bold{105}, 168
+  \item \isa {lex_prod_def} (theorem), \bold{107}
+  \item lexicographic product, \bold{107}, 170
   \item {\texttt{lfp}}
-    \subitem applications of, \see{CTL}{106}
+    \subitem applications of, \see{CTL}{108}
   \item Library, 4
-  \item linear arithmetic, 22--24, 139
+  \item linear arithmetic, 22--24, 141
   \item \isa {List} (theory), 17
   \item \isa {list} (type), 5, 9, 17
   \item \isa {list.split} (theorem), 32
-  \item \isa {lists_mono} (theorem), \bold{127}
-  \item Lowe, Gavin, 186--187
+  \item \isa {lists_mono} (theorem), \bold{129}
+  \item Lowe, Gavin, 188--189
 
   \indexspace
 
   \item \isa {Main} (theory), 4
-  \item major premise, \bold{65}
-  \item \isa {make} (constant), 153
+  \item major premise, \bold{67}
+  \item \isa {make} (constant), 155
   \item \isa {max} (constant), 23, 24
-  \item measure functions, 47, 104
-  \item \isa {measure_def} (theorem), \bold{105}
-  \item meta-logic, \bold{70}
+  \item measure functions, 47, 106
+  \item \isa {measure_def} (theorem), \bold{107}
+  \item meta-logic, \bold{72}
   \item methods, \bold{16}
   \item \isa {min} (constant), 23, 24
   \item \isa {mod} (symbol), 23
-  \item \isa {mod_div_equality} (theorem), \bold{141}
-  \item \isa {mod_mult_distrib} (theorem), \bold{141}
-  \item model checking example, 106--116
-  \item \emph{modus ponens}, 57, 62
-  \item \isa {mono_def} (theorem), \bold{106}
-  \item monotone functions, \bold{106}, 129
-    \subitem and inductive definitions, 127--128
-  \item \isa {more} (constant), 148--150
-  \item \isa {mp} (theorem), \bold{62}
-  \item \isa {mult_ac} (theorems), 142
-  \item multiple inheritance, \bold{159}
-  \item multiset ordering, \bold{105}
+  \item \isa {mod_div_equality} (theorem), \bold{143}
+  \item \isa {mod_mult_distrib} (theorem), \bold{143}
+  \item model checking example, 108--118
+  \item \emph{modus ponens}, 59, 64
+  \item \isa {mono_def} (theorem), \bold{108}
+  \item monotone functions, \bold{108}, 131
+    \subitem and inductive definitions, 129--130
+  \item \isa {more} (constant), 150, 152
+  \item \isa {mp} (theorem), \bold{64}
+  \item \isa {mult_ac} (theorems), 144
+  \item multiple inheritance, \bold{161}
+  \item multiset ordering, \bold{107}
 
   \indexspace
 
-  \item \isa {nat} (type), 4, 22, 141--143
-  \item \isa {nat_less_induct} (theorem), 178
-  \item natural deduction, 57--58
-  \item natural numbers, 22, 141--143
-  \item Needham-Schroeder protocol, 185--187
-  \item negation, 63--65
+  \item \isa {nat} (type), 4, 22, 143--145
+  \item \isa {nat_less_induct} (theorem), 180
+  \item natural deduction, 59--60
+  \item natural numbers, 22, 143--145
+  \item Needham-Schroeder protocol, 187--189
+  \item negation, 65--67
   \item \isa {Nil} (constant), 9
   \item \isa {no_asm} (modifier), 29
   \item \isa {no_asm_simp} (modifier), 30
   \item \isa {no_asm_use} (modifier), 30
-  \item non-standard reals, 145
+  \item non-standard reals, 147
   \item \isa {None} (constant), \bold{24}
-  \item \isa {notE} (theorem), \bold{63}
-  \item \isa {notI} (theorem), \bold{63}
-  \item numbers, 139--145
-  \item numeric literals, 140
-    \subitem for type \protect\isa{nat}, 141
-    \subitem for type \protect\isa{real}, 145
+  \item \isa {notE} (theorem), \bold{65}
+  \item \isa {notI} (theorem), \bold{65}
+  \item numbers, 141--147
+  \item numeric literals, 142
+    \subitem for type \protect\isa{nat}, 143
+    \subitem for type \protect\isa{real}, 147
 
   \indexspace
 
-  \item \isa {O} (symbol), 102
-  \item \texttt {o}, \bold{199}
-  \item \isa {o_def} (theorem), \bold{100}
-  \item \isa {OF} (attribute), 85--86
-  \item \isa {of} (attribute), 83, 86
+  \item \isa {O} (symbol), 104
+  \item \texttt {o}, \bold{201}
+  \item \isa {o_def} (theorem), \bold{102}
+  \item \isa {OF} (attribute), 87--88
+  \item \isa {of} (attribute), 85, 88
   \item \isa {only} (modifier), 29
   \item \isacommand {oops} (command), 13
   \item \isa {option} (type), \bold{24}
-  \item ordered rewriting, \bold{166}
-  \item overloading, 23, 154--157
-    \subitem and arithmetic, 140
+  \item ordered rewriting, \bold{168}
+  \item overloading, 23, 157--159
+    \subitem and arithmetic, 142
 
   \indexspace
 
-  \item pairs and tuples, 24, 145--148
+  \item pairs and tuples, 24, 147--150
   \item parent theories, \bold{4}
   \item pattern matching
     \subitem and \isacommand{recdef}, 47
   \item patterns
-    \subitem higher-order, \bold{167}
-  \item PDL, 108--110
-  \item \isacommand {pr} (command), 16, 90
-  \item \isacommand {prefer} (command), 16, 90
+    \subitem higher-order, \bold{169}
+  \item PDL, 110--112
+  \item \isacommand {pr} (command), 16, 92
+  \item \isacommand {prefer} (command), 16, 92
   \item primitive recursion, \see{recursion, primitive}{1}
   \item \isacommand {primrec} (command), 10, 18, 38--43
   \item product type, \see{pairs and tuples}{1}
@@ -424,75 +424,77 @@
   \item proof state, 12
   \item proofs
     \subitem abandoning, \bold{13}
-    \subitem examples of failing, 77--79
+    \subitem examples of failing, 79--81
   \item protocols
-    \subitem security, 185--195
+    \subitem security, 187--197
 
   \indexspace
 
   \item quantifiers, 6
-    \subitem and inductive definitions, 125--127
-    \subitem existential, 72
-    \subitem for sets, 98
-    \subitem instantiating, 74
-    \subitem universal, 69--72
+    \subitem and inductive definitions, 127--129
+    \subitem existential, 74
+    \subitem for sets, 100
+    \subitem instantiating, 76
+    \subitem universal, 71--74
 
   \indexspace
 
-  \item \isa {r_into_rtrancl} (theorem), \bold{102}
-  \item \isa {r_into_trancl} (theorem), \bold{103}
+  \item \isa {r_into_rtrancl} (theorem), \bold{104}
+  \item \isa {r_into_trancl} (theorem), \bold{105}
   \item range
-    \subitem of a function, 101
-    \subitem of a relation, 102
-  \item \isa {range} (symbol), 101
-  \item \isa {Range_iff} (theorem), \bold{102}
-  \item \isa {Real} (theory), 145
-  \item \isa {real} (type), 144--145
-  \item real numbers, 144--145
-  \item \isacommand {recdef} (command), 46--52, 104, 168--176
-    \subitem and numeric literals, 140
-  \item \isa {recdef_cong} (attribute), 172
+    \subitem of a function, 103
+    \subitem of a relation, 104
+  \item \isa {range} (symbol), 103
+  \item \isa {Range_iff} (theorem), \bold{104}
+  \item \isa {Real} (theory), 147
+  \item \isa {real} (type), 146--147
+  \item real numbers, 146--147
+  \item \isacommand {recdef} (command), 46--52, 106, 170--178
+    \subitem and numeric literals, 142
+  \item \isa {recdef_cong} (attribute), 174
   \item \isa {recdef_simp} (attribute), 49
-  \item \isa {recdef_wf} (attribute), 170
-  \item \isacommand {record} (command), 149
-  \item records, 148--154
-    \subitem extensible, 150
+  \item \isa {recdef_wf} (attribute), 172
+  \item \isacommand {record} (command), 151
+  \item records, 150--156
+    \subitem extensible, 152
   \item recursion
-    \subitem guarded, 173
+    \subitem guarded, 175
     \subitem primitive, 18
-    \subitem well-founded, \bold{169}
+    \subitem well-founded, \bold{171}
   \item recursion induction, 51--52
   \item \isacommand {redo} (command), 16
-  \item reflexive and transitive closure, 102--104
+  \item reflexive and transitive closure, 104--106
   \item reflexive transitive closure
-    \subitem defining inductively, 122--125
-  \item \isa {rel_comp_def} (theorem), \bold{102}
-  \item relations, 101--104
-    \subitem well-founded, 104--105
-  \item \isa {rename_tac} (method), 72--73
+    \subitem defining inductively, 124--127
+  \item \isa {rel_comp_def} (theorem), \bold{104}
+  \item relations, 103--106
+    \subitem well-founded, 106--107
+  \item \isa {rename_tac} (method), 74--75
   \item \isa {rev} (constant), 10--14, 34
   \item rewrite rules, \bold{27}
-    \subitem permutative, \bold{166}
+    \subitem permutative, \bold{168}
   \item rewriting, \bold{27}
   \item \isa {rotate_tac} (method), 30
-  \item \isa {rtrancl_refl} (theorem), \bold{102}
-  \item \isa {rtrancl_trans} (theorem), \bold{102}
-  \item rule induction, 118--120
-  \item rule inversion, 120--121, 129--130
-  \item \isa {rule_format} (attribute), 177
-  \item \isa {rule_tac} (method), 66
-    \subitem and renaming, 73
+  \item \isa {rtrancl_refl} (theorem), \bold{104}
+  \item \isa {rtrancl_trans} (theorem), \bold{104}
+  \item rule induction, 120--122
+  \item rule inversion, 122--123, 131--132
+  \item \isa {rule_format} (attribute), 179
+  \item \isa {rule_tac} (method), 68
+    \subitem and renaming, 75
 
   \indexspace
 
-  \item \isa {safe} (method), 81, 82
-  \item safe rules, \bold{80}
-  \item \isa {set} (type), 5, 95
-  \item set comprehensions, 97--98
-  \item \isa {set_ext} (theorem), \bold{96}
-  \item sets, 95--99
-    \subitem finite, 99
-    \subitem notation for finite, \bold{97}
+  \item \isa {safe} (method), 83, 84
+  \item safe rules, \bold{82}
+  \item selector
+    \subitem record, 151
+  \item \isa {set} (type), 5, 97
+  \item set comprehensions, 99--100
+  \item \isa {set_ext} (theorem), \bold{98}
+  \item sets, 97--101
+    \subitem finite, 101
+    \subitem notation for finite, \bold{99}
   \item settings, \see{flags}{1}
   \item \isa {show_brackets} (flag), 6
   \item \isa {show_types} (flag), 5, 16
@@ -500,61 +502,61 @@
   \item \isa {simp} (method), \bold{28}
   \item \isa {simp} del (attribute), 28
   \item \isa {simp_all} (method), 29, 38
-  \item simplification, 27--33, 165--168
+  \item simplification, 27--33, 167--170
     \subitem of \isa{let}-expressions, 31
     \subitem with definitions, 30
     \subitem with/of assumptions, 29
-  \item simplification rule, 167--168
+  \item simplification rule, 169--170
   \item simplification rules, 28
     \subitem adding and deleting, 29
-  \item \isa {simplified} (attribute), 83, 86
+  \item \isa {simplified} (attribute), 85, 88
   \item \isa {size} (constant), 17
   \item \isa {snd} (constant), 24
-  \item \isa {SOME} (symbol), 76
-  \item \texttt {SOME}, \bold{199}
+  \item \isa {SOME} (symbol), 78
+  \item \texttt {SOME}, \bold{201}
   \item \isa {Some} (constant), \bold{24}
-  \item \isa {some_equality} (theorem), \bold{76}
-  \item \isa {someI} (theorem), \bold{76}
-  \item \isa {someI2} (theorem), \bold{76}
-  \item \isa {someI_ex} (theorem), \bold{77}
-  \item sorts, 159
-  \item \isa {spec} (theorem), \bold{70}
+  \item \isa {some_equality} (theorem), \bold{78}
+  \item \isa {someI} (theorem), \bold{78}
+  \item \isa {someI2} (theorem), \bold{78}
+  \item \isa {someI_ex} (theorem), \bold{79}
+  \item sorts, 162
+  \item \isa {spec} (theorem), \bold{72}
   \item \isa {split} (attribute), 32
-  \item \isa {split} (constant), 146
-  \item \isa {split} (method), 31, 146
+  \item \isa {split} (constant), 148
+  \item \isa {split} (method), 31, 148
   \item \isa {split} (modifier), 32
   \item split rule, \bold{32}
   \item \isa {split_if} (theorem), 32
   \item \isa {split_if_asm} (theorem), 32
-  \item \isa {ssubst} (theorem), \bold{67}
+  \item \isa {ssubst} (theorem), \bold{69}
   \item structural induction, \see{induction, structural}{1}
-  \item subclasses, 154, 158
+  \item subclasses, 156, 161
   \item subgoal numbering, 46
-  \item \isa {subgoal_tac} (method), 88
+  \item \isa {subgoal_tac} (method), 90
   \item subgoals, 12
-  \item subset relation, \bold{96}
-  \item \isa {subsetD} (theorem), \bold{96}
-  \item \isa {subsetI} (theorem), \bold{96}
-  \item \isa {subst} (method), 67
-  \item substitution, 67--69
+  \item subset relation, \bold{98}
+  \item \isa {subsetD} (theorem), \bold{98}
+  \item \isa {subsetI} (theorem), \bold{98}
+  \item \isa {subst} (method), 69
+  \item substitution, 69--71
   \item \isa {Suc} (constant), 22
-  \item \isa {surj_def} (theorem), \bold{100}
-  \item surjections, 100
-  \item \isa {sym} (theorem), \bold{84}
+  \item \isa {surj_def} (theorem), \bold{102}
+  \item surjections, 102
+  \item \isa {sym} (theorem), \bold{86}
   \item syntax, 6, 11
-  \item syntax translations, 26
+  \item syntax translations, 55--56
 
   \indexspace
 
-  \item tacticals, 89
+  \item tacticals, 91
   \item tactics, 12
   \item \isacommand {term} (command), 16
   \item term rewriting, \bold{27}
   \item termination, \see{functions, total}{1}
   \item terms, 5
-  \item \isa {THE} (symbol), 75
-  \item \isa {the_equality} (theorem), \bold{75}
-  \item \isa {THEN} (attribute), \bold{84}, 86, 92
+  \item \isa {THE} (symbol), 77
+  \item \isa {the_equality} (theorem), \bold{77}
+  \item \isa {THEN} (attribute), \bold{86}, 88, 94
   \item \isacommand {theorem} (command), \bold{11}, 13
   \item theories, 4
     \subitem abandoning, \bold{16}
@@ -565,12 +567,12 @@
   \item \isa {ToyList} example, 9--14
   \item \isa {trace_simp} (flag), 33
   \item tracing the simplifier, \bold{33}
-  \item \isa {trancl_trans} (theorem), \bold{103}
-  \item transition systems, 107
-  \item \isacommand {translations} (command), 26
+  \item \isa {trancl_trans} (theorem), \bold{105}
+  \item transition systems, 109
+  \item \isacommand {translations} (command), 55--56
   \item tries, 44--46
   \item \isa {True} (constant), 5
-  \item \isa {truncate} (constant), 153
+  \item \isa {truncate} (constant), 155
   \item tuples, \see{pairs and tuples}{1}
   \item \isacommand {typ} (command), 16
   \item type constraints, \bold{6}
@@ -578,58 +580,60 @@
   \item type inference, \bold{5}
   \item type synonyms, 25
   \item type variables, 5
-  \item \isacommand {typedecl} (command), 107, 161
-  \item \isacommand {typedef} (command), 161--164
+  \item \isacommand {typedecl} (command), 109, 163
+  \item \isacommand {typedef} (command), 163--166
   \item types, 4--5
-    \subitem declaring, 161
-    \subitem defining, 161--164
+    \subitem declaring, 163
+    \subitem defining, 163--166
   \item \isacommand {types} (command), 25
 
   \indexspace
 
-  \item Ullman, J. D., 135
-  \item \texttt {UN}, \bold{199}
-  \item \texttt {Un}, \bold{199}
-  \item \isa {UN_E} (theorem), \bold{98}
-  \item \isa {UN_I} (theorem), \bold{98}
-  \item \isa {UN_iff} (theorem), \bold{98}
-  \item \isa {Un_subset_iff} (theorem), \bold{96}
+  \item Ullman, J. D., 137
+  \item \texttt {UN}, \bold{201}
+  \item \texttt {Un}, \bold{201}
+  \item \isa {UN_E} (theorem), \bold{100}
+  \item \isa {UN_I} (theorem), \bold{100}
+  \item \isa {UN_iff} (theorem), \bold{100}
+  \item \isa {Un_subset_iff} (theorem), \bold{98}
   \item \isacommand {undo} (command), 16
   \item \isa {unfold} (method), \bold{31}
-  \item unification, 66--69
-  \item \isa {UNION} (constant), 99
-  \item \texttt {Union}, \bold{199}
+  \item unification, 68--71
+  \item \isa {UNION} (constant), 101
+  \item \texttt {Union}, \bold{201}
   \item union
-    \subitem indexed, 98
-  \item \isa {Union_iff} (theorem), \bold{98}
+    \subitem indexed, 100
+  \item \isa {Union_iff} (theorem), \bold{100}
   \item \isa {unit} (type), 24
-  \item unknowns, 7, \bold{58}
-  \item unsafe rules, \bold{80}
-  \item updating a function, \bold{99}
+  \item unknowns, 7, \bold{60}
+  \item unsafe rules, \bold{82}
+  \item update
+    \subitem record, 151
+  \item updating a function, \bold{101}
 
   \indexspace
 
   \item variables, 7
     \subitem schematic, 7
     \subitem type, 5
-  \item \isa {vimage_def} (theorem), \bold{101}
+  \item \isa {vimage_def} (theorem), \bold{103}
 
   \indexspace
 
   \item Wenzel, Markus, vii
-  \item \isa {wf_induct} (theorem), \bold{105}
-  \item \isa {wf_inv_image} (theorem), \bold{105}
-  \item \isa {wf_less_than} (theorem), \bold{104}
-  \item \isa {wf_lex_prod} (theorem), \bold{105}
-  \item \isa {wf_measure} (theorem), \bold{105}
-  \item \isa {wf_subset} (theorem), 170
-  \item \isa {while} (constant), 175
-  \item \isa {While_Combinator} (theory), 175
-  \item \isa {while_rule} (theorem), 175
+  \item \isa {wf_induct} (theorem), \bold{107}
+  \item \isa {wf_inv_image} (theorem), \bold{107}
+  \item \isa {wf_less_than} (theorem), \bold{106}
+  \item \isa {wf_lex_prod} (theorem), \bold{107}
+  \item \isa {wf_measure} (theorem), \bold{107}
+  \item \isa {wf_subset} (theorem), 172
+  \item \isa {while} (constant), 177
+  \item \isa {While_Combinator} (theory), 177
+  \item \isa {while_rule} (theorem), 177
 
   \indexspace
 
-  \item \isa {zadd_ac} (theorems), 143
-  \item \isa {zmult_ac} (theorems), 143
+  \item \isa {zadd_ac} (theorems), 145
+  \item \isa {zmult_ac} (theorems), 145
 
 \end{theindex}