
diff -r 1fead823c7c6 -r 6e15de7dd871 doc-src/TutorialI/document/Records.tex
--- a/doc-src/TutorialI/document/Records.tex	Tue Aug 28 13:15:15 2012 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,665 +0,0 @@
-%
-\begin{isabellebody}%
-\def\isabellecontext{Records}%
-%
-\isamarkupheader{Records \label{sec:records}%
-}
-\isamarkuptrue%
-%
-\isadelimtheory
-%
-\endisadelimtheory
-%
-\isatagtheory
-%
-\endisatagtheory
-{\isafoldtheory}%
-%
-\isadelimtheory
-%
-\endisadelimtheory
-%
-\begin{isamarkuptext}%
-\index{records|(}%
-  Records are familiar from programming languages.  A record of $n$
-  fields is essentially an $n$-tuple, but the record's components have
-  names, which can make expressions easier to read and reduces the
-  risk of confusing one field for another.
-
-  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
-  not in Standard ML.  If two different record types have field names
-  in common, then the ambiguity is resolved in the usual way, by
-  qualified names.
-
-  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; polymorphism
-  takes care of structural sub-typing behind the scenes.  There are
-  also explicit coercion functions between fixed record types.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Record Basics%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Record types are not primitive in Isabelle and have a delicate
-  internal representation \cite{NaraschewskiW-TPHOLs98}, 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
-  the record as a distinguished entity.  Here is a simple example:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{record}\isamarkupfalse%
-\ point\ {\isaliteral{3D}{\isacharequal}}\isanewline
-\ \ Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\isanewline
-\ \ Ycoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int%
-\begin{isamarkuptext}%
-\noindent
-  Records of type \isa{point} have two fields named \isa{Xcoord}
-  and \isa{Ycoord}, both of type~\isa{int}.  We now define a
-  constant of type \isa{point}:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{definition}\isamarkupfalse%
-\ pt{\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ point\ \isakeyword{where}\isanewline
-{\isaliteral{22}{\isachardoublequoteopen}}pt{\isadigit{1}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{7C}{\isacharbar}}\ Xcoord\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{2}}{\isadigit{3}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
-\begin{isamarkuptext}%
-\noindent
-  We see above the ASCII notation for record brackets.  You can also
-  use the symbolic brackets \isa{{\isaliteral{5C3C6C706172723E}{\isasymlparr}}} and \isa{{\isaliteral{5C3C72706172723E}{\isasymrparr}}}.  Record type
-  expressions can be also written directly with individual fields.
-  The type name above is merely an abbreviation.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{definition}\isamarkupfalse%
-\ pt{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
-{\isaliteral{22}{\isachardoublequoteopen}}pt{\isadigit{2}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{4}}{\isadigit{5}}{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{9}}{\isadigit{7}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}%
-\begin{isamarkuptext}%
-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}\isamarkupfalse%
-\ {\isaliteral{22}{\isachardoublequoteopen}}Xcoord\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ simp%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-The \emph{update}\index{update!record} operation is functional.  For
-  example, \isa{p{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}} is a record whose \isa{Xcoord}
-  value is zero and whose \isa{Ycoord} value is copied from~\isa{p}.  Updates of explicit records are also simplified automatically:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
-\ \ \ \ \ \ \ \ \ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ simp%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-\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}.
-  \end{warn}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Extensible Records and Generic Operations%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-\index{records!extensible|(}%
-
-  Now, let us define coloured points (type \isa{cpoint}) to be
-  points extended with a field \isa{col} of type \isa{colour}:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{datatype}\isamarkupfalse%
-\ colour\ {\isaliteral{3D}{\isacharequal}}\ Red\ {\isaliteral{7C}{\isacharbar}}\ Green\ {\isaliteral{7C}{\isacharbar}}\ Blue\isanewline
-\isanewline
-\isacommand{record}\isamarkupfalse%
-\ cpoint\ {\isaliteral{3D}{\isacharequal}}\ point\ {\isaliteral{2B}{\isacharplus}}\isanewline
-\ \ col\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ colour%
-\begin{isamarkuptext}%
-\noindent
-  The fields of this new type are \isa{Xcoord}, \isa{Ycoord} and
-  \isa{col}, in that order.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{definition}\isamarkupfalse%
-\ cpt{\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ cpoint\ \isakeyword{where}\isanewline
-{\isaliteral{22}{\isachardoublequoteopen}}cpt{\isadigit{1}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{2}}{\isadigit{3}}{\isaliteral{2C}{\isacharcomma}}\ col\ {\isaliteral{3D}{\isacharequal}}\ Green{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}%
-\begin{isamarkuptext}%
-We can define generic operations that work on arbitrary
-  instances of a record scheme, e.g.\ covering \isa{point}, \isa{cpoint}, and any further extensions.  Every record structure has an
-  implicit pseudo-field, \cdx{more}, that keeps the extension as an
-  explicit value.  Its type is declared as completely
-  polymorphic:~\isa{{\isaliteral{27}{\isacharprime}}a}.  When a fixed record value is expressed
-  using just its standard fields, the value of \isa{more} is
-  implicitly set to \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}}, the empty tuple, which has type
-  \isa{unit}.  Within the record brackets, you can refer to the
-  \isa{more} field by writing ``\isa{{\isaliteral{5C3C646F74733E}{\isasymdots}}}'' (three dots):%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ {\isaliteral{22}{\isachardoublequoteopen}}Xcoord\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ p{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ simp%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-This lemma applies to any record whose first two fields are \isa{Xcoord} and~\isa{Ycoord}.  Note that \isa{{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}} is exactly the same as \isa{{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\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 \isa{more} pseudo-field may be manipulated directly as well,
-  but the identifier needs to be qualified:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ {\isaliteral{22}{\isachardoublequoteopen}}point{\isaliteral{2E}{\isachardot}}more\ cpt{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}col\ {\isaliteral{3D}{\isacharequal}}\ Green{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ cpt{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-\noindent
-  We see that the colour part attached to this \isa{point} is a
-  rudimentary record in its own right, namely \isa{{\isaliteral{5C3C6C706172723E}{\isasymlparr}}col\ {\isaliteral{3D}{\isacharequal}}\ Green{\isaliteral{5C3C72706172723E}{\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 definition of \isa{point} above has generated two
-  type abbreviations:
-
-  \medskip
-  \begin{tabular}{l}
-  \isa{point}~\isa{{\isaliteral{3D}{\isacharequal}}}~\isa{{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{5C3C72706172723E}{\isasymrparr}}} \\
-  \isa{{\isaliteral{27}{\isacharprime}}a\ point{\isaliteral{5F}{\isacharunderscore}}scheme}~\isa{{\isaliteral{3D}{\isacharequal}}}~\isa{{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C72706172723E}{\isasymrparr}}} \\
-  \end{tabular}
-  \medskip
-  
-\noindent
-  Type \isa{point} is for fixed records having exactly the two fields
-  \isa{Xcoord} and~\isa{Ycoord}, while the polymorphic type \isa{{\isaliteral{27}{\isacharprime}}a\ point{\isaliteral{5F}{\isacharunderscore}}scheme} comprises all possible extensions to those two
-  fields.  Note that \isa{unit\ point{\isaliteral{5F}{\isacharunderscore}}scheme} coincides with \isa{point}, and \isa{{\isaliteral{5C3C6C706172723E}{\isasymlparr}}col\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ colour{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ point{\isaliteral{5F}{\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{definition}\isamarkupfalse%
-\ getX\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ point{\isaliteral{5F}{\isacharunderscore}}scheme\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
-{\isaliteral{22}{\isachardoublequoteopen}}getX\ r\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ Xcoord\ r{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
-\isacommand{definition}\isamarkupfalse%
-\ setX\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ point{\isaliteral{5F}{\isacharunderscore}}scheme\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ point{\isaliteral{5F}{\isacharunderscore}}scheme{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
-{\isaliteral{22}{\isachardoublequoteopen}}setX\ r\ a\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}%
-\begin{isamarkuptext}%
-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} (including \isa{cpoint} etc.):%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{definition}\isamarkupfalse%
-\ incX\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ point{\isaliteral{5F}{\isacharunderscore}}scheme\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ point{\isaliteral{5F}{\isacharunderscore}}scheme{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
-{\isaliteral{22}{\isachardoublequoteopen}}incX\ r\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\isanewline
-\ \ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ r\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord\ r{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ point{\isaliteral{2E}{\isachardot}}more\ r{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}%
-\begin{isamarkuptext}%
-Generic theorems can be proved about generic methods.  This trivial
-  lemma relates \isa{incX} to \isa{getX} and \isa{setX}:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ {\isaliteral{22}{\isachardoublequoteopen}}incX\ r\ {\isaliteral{3D}{\isacharequal}}\ setX\ r\ {\isaliteral{28}{\isacharparenleft}}getX\ r\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ getX{\isaliteral{5F}{\isacharunderscore}}def\ setX{\isaliteral{5F}{\isacharunderscore}}def\ incX{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-\begin{warn}
-  If you use the symbolic record brackets \isa{{\isaliteral{5C3C6C706172723E}{\isasymlparr}}} and \isa{{\isaliteral{5C3C72706172723E}{\isasymrparr}}},
-  then you must also use the symbolic ellipsis, ``\isa{{\isaliteral{5C3C646F74733E}{\isasymdots}}}'', rather
-  than three consecutive periods, ``\isa{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}''.  Mixing the ASCII
-  and symbolic versions causes a syntax error.  (The two versions are
-  more distinct on screen than they are on paper.)
-  \end{warn}%
-  \index{records!extensible|)}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Record Equality%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Two records are equal\index{equality!of records} if all pairs of
-  corresponding fields are equal.  Concrete record equalities are
-  simplified automatically:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
-\ \ \ \ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ b\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ simp%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-The following equality is similar, but generic, in that \isa{r}
-  can be any instance of \isa{{\isaliteral{27}{\isacharprime}}a\ point{\isaliteral{5F}{\isacharunderscore}}scheme}:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ {\isaliteral{22}{\isachardoublequoteopen}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\ r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Ycoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ simp%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-\noindent
-  We see above the syntax for iterated updates.  We could equivalently
-  have written the left-hand side as \isa{r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Ycoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}}.
-
-  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}\isamarkupfalse%
-\ {\isaliteral{22}{\isachardoublequoteopen}}r\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ r{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord\ r{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ simp%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-\noindent
-  The generic version of this equality includes the pseudo-field
-  \isa{more}:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ {\isaliteral{22}{\isachardoublequoteopen}}r\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ r{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord\ r{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ point{\isaliteral{2E}{\isachardot}}more\ r{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ simp%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-The simplifier can prove many record equalities
-  automatically, but general equality reasoning can be tricky.
-  Consider proving this obvious fact:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ {\isaliteral{22}{\isachardoublequoteopen}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\ r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{apply}\isamarkupfalse%
-\ simp{\isaliteral{3F}{\isacharquery}}\isanewline
-\ \ \isacommand{oops}\isamarkupfalse%
-%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-\noindent
-  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}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ {\isaliteral{22}{\isachardoublequoteopen}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\ r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{apply}\isamarkupfalse%
-\ {\isaliteral{28}{\isacharparenleft}}drule{\isaliteral{5F}{\isacharunderscore}}tac\ f\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ \isakeyword{in}\ arg{\isaliteral{5F}{\isacharunderscore}}cong{\isaliteral{29}{\isacharparenright}}%
-\begin{isamarkuptxt}%
-\begin{isabelle}%
-\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ Xcoord\ {\isaliteral{28}{\isacharparenleft}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ {\isaliteral{28}{\isacharparenleft}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}%
-\end{isabelle}
-    Now, \isa{simp} will reduce the assumption to the desired
-    conclusion.%
-\end{isamarkuptxt}%
-\isamarkuptrue%
-\ \ \isacommand{apply}\isamarkupfalse%
-\ simp\isanewline
-\ \ \isacommand{done}\isamarkupfalse%
-%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-The \isa{cases} method is preferable to such a forward proof.  We
-  state the desired lemma again:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ {\isaliteral{22}{\isachardoublequoteopen}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\ r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}%
-\isadelimproof
-%
-\endisadelimproof
-%
-\isatagproof
-%
-\begin{isamarkuptxt}%
-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}\isamarkupfalse%
-\ {\isaliteral{28}{\isacharparenleft}}cases\ r{\isaliteral{29}{\isacharparenright}}%
-\begin{isamarkuptxt}%
-\begin{isabelle}%
-\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}Xcoord\ Ycoord\ more{\isaliteral{2E}{\isachardot}}\isanewline
-\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\ r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
-\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ \ }r\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ more{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
-\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}%
-\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}\isamarkupfalse%
-\ simp\isanewline
-\ \ \isacommand{done}\isamarkupfalse%
-%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\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{\isaliteral{5F}{\isacharunderscore}}tac} used together with the
-  internal field representation rules of records.  The above use of
-  \isa{{\isaliteral{28}{\isacharparenleft}}cases\ r{\isaliteral{29}{\isacharparenright}}} would become \isa{{\isaliteral{28}{\isacharparenleft}}rule{\isaliteral{5F}{\isacharunderscore}}tac\ r\ {\isaliteral{3D}{\isacharequal}}\ r\ in\ point{\isaliteral{2E}{\isachardot}}cases{\isaliteral{5F}{\isacharunderscore}}scheme{\isaliteral{29}{\isacharparenright}}}.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Extending and Truncating Records%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-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 (including those inherited from ancestors).  It returns the
-  corresponding record.
-
-  \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.
-
-  \item Function \cdx{extend} takes two arguments: a record to be
-  extended and a record containing the new fields.
-
-  \item Function \cdx{truncate} takes a record (possibly an extension
-  of the original record type) and returns a fixed record, removing
-  any additional fields.
-
-  \end{itemize}
-  These functions provide useful 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} (\isa{point{\isaliteral{2E}{\isachardot}}defs}, \isa{cpoint{\isaliteral{2E}{\isachardot}}defs}, etc.).
-  For example, here are the versions of those functions generated for
-  record \isa{point}.  We omit \isa{point{\isaliteral{2E}{\isachardot}}fields}, which happens to
-  be the same as \isa{point{\isaliteral{2E}{\isachardot}}make}.
-
-  \begin{isabelle}%
-point{\isaliteral{2E}{\isachardot}}make\ Xcoord\ Ycoord\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord{\isaliteral{5C3C72706172723E}{\isasymrparr}}\isasep\isanewline%
-point{\isaliteral{2E}{\isachardot}}extend\ r\ more\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\isanewline
-{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ r{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord\ r{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ more{\isaliteral{5C3C72706172723E}{\isasymrparr}}\isasep\isanewline%
-point{\isaliteral{2E}{\isachardot}}truncate\ r\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ r{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord\ r{\isaliteral{5C3C72706172723E}{\isasymrparr}}%
-\end{isabelle}
-  Contrast those with the corresponding functions for record \isa{cpoint}.  Observe \isa{cpoint{\isaliteral{2E}{\isachardot}}fields} in particular.
-  \begin{isabelle}%
-cpoint{\isaliteral{2E}{\isachardot}}make\ Xcoord\ Ycoord\ col\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\isanewline
-{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord{\isaliteral{2C}{\isacharcomma}}\ col\ {\isaliteral{3D}{\isacharequal}}\ col{\isaliteral{5C3C72706172723E}{\isasymrparr}}\isasep\isanewline%
-cpoint{\isaliteral{2E}{\isachardot}}fields\ col\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}col\ {\isaliteral{3D}{\isacharequal}}\ col{\isaliteral{5C3C72706172723E}{\isasymrparr}}\isasep\isanewline%
-cpoint{\isaliteral{2E}{\isachardot}}extend\ r\ more\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\isanewline
-{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ r{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord\ r{\isaliteral{2C}{\isacharcomma}}\ col\ {\isaliteral{3D}{\isacharequal}}\ col\ r{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ more{\isaliteral{5C3C72706172723E}{\isasymrparr}}\isasep\isanewline%
-cpoint{\isaliteral{2E}{\isachardot}}truncate\ r\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\isanewline
-{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ r{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord\ r{\isaliteral{2C}{\isacharcomma}}\ col\ {\isaliteral{3D}{\isacharequal}}\ col\ r{\isaliteral{5C3C72706172723E}{\isasymrparr}}%
-\end{isabelle}
-
-  To demonstrate these functions, we declare a new coloured point by
-  extending an ordinary point.  Function \isa{point{\isaliteral{2E}{\isachardot}}extend} augments
-  \isa{pt{\isadigit{1}}} with a colour value, which is converted into an
-  appropriate record fragment by \isa{cpoint{\isaliteral{2E}{\isachardot}}fields}.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{definition}\isamarkupfalse%
-\ cpt{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ cpoint\ \isakeyword{where}\isanewline
-{\isaliteral{22}{\isachardoublequoteopen}}cpt{\isadigit{2}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ point{\isaliteral{2E}{\isachardot}}extend\ pt{\isadigit{1}}\ {\isaliteral{28}{\isacharparenleft}}cpoint{\isaliteral{2E}{\isachardot}}fields\ Green{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
-\begin{isamarkuptext}%
-The coloured points \isa{cpt{\isadigit{1}}} and \isa{cpt{\isadigit{2}}} are equal.  The
-  proof is trivial, by unfolding all the definitions.  We deliberately
-  omit the definition of~\isa{pt{\isadigit{1}}} in order to reveal the underlying
-  comparison on type \isa{point}.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ {\isaliteral{22}{\isachardoublequoteopen}}cpt{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ cpt{\isadigit{2}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{apply}\isamarkupfalse%
-\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ cpt{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}def\ cpt{\isadigit{2}}{\isaliteral{5F}{\isacharunderscore}}def\ point{\isaliteral{2E}{\isachardot}}defs\ cpoint{\isaliteral{2E}{\isachardot}}defs{\isaliteral{29}{\isacharparenright}}%
-\begin{isamarkuptxt}%
-\begin{isabelle}%
-\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ Xcoord\ pt{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Ycoord\ pt{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{2}}{\isadigit{3}}%
-\end{isabelle}%
-\end{isamarkuptxt}%
-\isamarkuptrue%
-\ \ \isacommand{apply}\isamarkupfalse%
-\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ pt{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
-\ \ \isacommand{done}\isamarkupfalse%
-%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-In the example below, a coloured point is truncated to leave a
-  point.  We use the \isa{truncate} function of the target record.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ {\isaliteral{22}{\isachardoublequoteopen}}point{\isaliteral{2E}{\isachardot}}truncate\ cpt{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ pt{\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ pt{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}def\ cpt{\isadigit{2}}{\isaliteral{5F}{\isacharunderscore}}def\ point{\isaliteral{2E}{\isachardot}}defs{\isaliteral{29}{\isacharparenright}}%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-\begin{exercise}
-  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}
-  (For Java programmers.)
-  Model a small class hierarchy using records.
-  \end{exercise}
-  \index{records|)}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimtheory
-%
-\endisadelimtheory
-%
-\isatagtheory
-%
-\endisatagtheory
-{\isafoldtheory}%
-%
-\isadelimtheory
-%
-\endisadelimtheory
-\end{isabellebody}%
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "root"
-%%% End:




