doc-src/IsarRef/Thy/document/HOL_Specific.tex
author wenzelm
Tue Aug 12 21:27:46 2008 +0200 (2008-08-12)
changeset 27834 04562d200f02
parent 27452 5c1fb7d262bf
child 28562 4e74209f113e
permissions -rw-r--r--
updated generated file;
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%
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\begin{isabellebody}%
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\def\isabellecontext{HOL{\isacharunderscore}Specific}%
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%
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\isadelimtheory
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\isanewline
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\isanewline
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%
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\endisadelimtheory
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%
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\isatagtheory
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\isacommand{theory}\isamarkupfalse%
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\ HOL{\isacharunderscore}Specific\isanewline
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\isakeyword{imports}\ Main\isanewline
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\isakeyword{begin}%
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\endisatagtheory
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{\isafoldtheory}%
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%
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\isadelimtheory
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%
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\endisadelimtheory
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%
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\isamarkupchapter{Isabelle/HOL \label{ch:hol}%
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}
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\isamarkuptrue%
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%
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\isamarkupsection{Primitive types \label{sec:hol-typedef}%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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\begin{matharray}{rcl}
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    \indexdef{HOL}{command}{typedecl}\hypertarget{command.HOL.typedecl}{\hyperlink{command.HOL.typedecl}{\mbox{\isa{\isacommand{typedecl}}}}} & : & \isartrans{theory}{theory} \\
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    \indexdef{HOL}{command}{typedef}\hypertarget{command.HOL.typedef}{\hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}}} & : & \isartrans{theory}{proof(prove)} \\
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  \end{matharray}
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  \begin{rail}
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    'typedecl' typespec infix?
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    ;
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    'typedef' altname? abstype '=' repset
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    ;
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    altname: '(' (name | 'open' | 'open' name) ')'
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    ;
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    abstype: typespec infix?
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    ;
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    repset: term ('morphisms' name name)?
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    ;
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  \end{rail}
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  \begin{descr}
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  \item [\hyperlink{command.HOL.typedecl}{\mbox{\isa{\isacommand{typedecl}}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t{\isachardoublequote}}] is similar to the original \hyperlink{command.typedecl}{\mbox{\isa{\isacommand{typedecl}}}} of
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  Isabelle/Pure (see \secref{sec:types-pure}), but also declares type
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  arity \isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}type{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ type{\isacharparenright}\ type{\isachardoublequote}}, making \isa{t} an
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  actual HOL type constructor.   %FIXME check, update
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  \item [\hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t\ {\isacharequal}\ A{\isachardoublequote}}] sets up a goal stating non-emptiness of the set \isa{A}.
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  After finishing the proof, the theory will be augmented by a
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  Gordon/HOL-style type definition, which establishes a bijection
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  between the representing set \isa{A} and the new type \isa{t}.
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  Technically, \hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}} defines both a type \isa{t} and a set (term constant) of the same name (an alternative base
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  name may be given in parentheses).  The injection from type to set
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  is called \isa{Rep{\isacharunderscore}t}, its inverse \isa{Abs{\isacharunderscore}t} (this may be
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  changed via an explicit \hyperlink{keyword.HOL.morphisms}{\mbox{\isa{\isakeyword{morphisms}}}} declaration).
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  Theorems \isa{Rep{\isacharunderscore}t}, \isa{Rep{\isacharunderscore}t{\isacharunderscore}inverse}, and \isa{Abs{\isacharunderscore}t{\isacharunderscore}inverse} provide the most basic characterization as a
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  corresponding injection/surjection pair (in both directions).  Rules
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  \isa{Rep{\isacharunderscore}t{\isacharunderscore}inject} and \isa{Abs{\isacharunderscore}t{\isacharunderscore}inject} provide a slightly
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  more convenient view on the injectivity part, suitable for automated
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  proof tools (e.g.\ in \hyperlink{attribute.simp}{\mbox{\isa{simp}}} or \hyperlink{attribute.iff}{\mbox{\isa{iff}}}
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  declarations).  Rules \isa{Rep{\isacharunderscore}t{\isacharunderscore}cases}/\isa{Rep{\isacharunderscore}t{\isacharunderscore}induct}, and
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  \isa{Abs{\isacharunderscore}t{\isacharunderscore}cases}/\isa{Abs{\isacharunderscore}t{\isacharunderscore}induct} provide alternative views
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  on surjectivity; these are already declared as set or type rules for
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  the generic \hyperlink{method.cases}{\mbox{\isa{cases}}} and \hyperlink{method.induct}{\mbox{\isa{induct}}} methods.
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  An alternative name may be specified in parentheses; the default is
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  to use \isa{t} as indicated before.  The ``\isa{{\isachardoublequote}{\isacharparenleft}open{\isacharparenright}{\isachardoublequote}}''
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  declaration suppresses a separate constant definition for the
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  representing set.
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  \end{descr}
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  Note that raw type declarations are rarely used in practice; the
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  main application is with experimental (or even axiomatic!) theory
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  fragments.  Instead of primitive HOL type definitions, user-level
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  theories usually refer to higher-level packages such as \hyperlink{command.HOL.record}{\mbox{\isa{\isacommand{record}}}} (see \secref{sec:hol-record}) or \hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}} (see \secref{sec:hol-datatype}).%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\isamarkupsection{Adhoc tuples%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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\begin{matharray}{rcl}
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    \hyperlink{attribute.HOL.split-format}{\mbox{\isa{split{\isacharunderscore}format}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isaratt \\
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  \end{matharray}
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  \begin{rail}
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    'split\_format' (((name *) + 'and') | ('(' 'complete' ')'))
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    ;
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  \end{rail}
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  \begin{descr}
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  \item [\hyperlink{attribute.HOL.split-format}{\mbox{\isa{split{\isacharunderscore}format}}}~\isa{{\isachardoublequote}p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub m\ {\isasymAND}\ {\isasymdots}\ {\isasymAND}\ q\isactrlsub {\isadigit{1}}\ {\isasymdots}\ q\isactrlsub n{\isachardoublequote}}] puts expressions of
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  low-level tuple types into canonical form as specified by the
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  arguments given; the \isa{i}-th collection of arguments refers to
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  occurrences in premise \isa{i} of the rule.  The ``\isa{{\isachardoublequote}{\isacharparenleft}complete{\isacharparenright}{\isachardoublequote}}'' option causes \emph{all} arguments in function
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  applications to be represented canonically according to their tuple
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  type structure.
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  Note that these operations tend to invent funny names for new local
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  parameters to be introduced.
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  \end{descr}%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\isamarkupsection{Records \label{sec:hol-record}%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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In principle, records merely generalize the concept of tuples, where
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  components may be addressed by labels instead of just position.  The
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  logical infrastructure of records in Isabelle/HOL is slightly more
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  advanced, though, supporting truly extensible record schemes.  This
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  admits operations that are polymorphic with respect to record
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  extension, yielding ``object-oriented'' effects like (single)
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  inheritance.  See also \cite{NaraschewskiW-TPHOLs98} for more
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  details on object-oriented verification and record subtyping in HOL.%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\isamarkupsubsection{Basic concepts%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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Isabelle/HOL supports both \emph{fixed} and \emph{schematic} records
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  at the level of terms and types.  The notation is as follows:
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  \begin{center}
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  \begin{tabular}{l|l|l}
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    & record terms & record types \\ \hline
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    fixed & \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isasymrparr}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharcolon}{\isacharcolon}\ A{\isacharcomma}\ y\ {\isacharcolon}{\isacharcolon}\ B{\isasymrparr}{\isachardoublequote}} \\
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    schematic & \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ m{\isasymrparr}{\isachardoublequote}} &
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      \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharcolon}{\isacharcolon}\ A{\isacharcomma}\ y\ {\isacharcolon}{\isacharcolon}\ B{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ M{\isasymrparr}{\isachardoublequote}} \\
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  \end{tabular}
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  \end{center}
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  \noindent The ASCII representation of \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isasymrparr}{\isachardoublequote}} is \isa{{\isachardoublequote}{\isacharparenleft}{\isacharbar}\ x\ {\isacharequal}\ a\ {\isacharbar}{\isacharparenright}{\isachardoublequote}}.
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  A fixed record \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isasymrparr}{\isachardoublequote}} has field \isa{x} of value
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  \isa{a} and field \isa{y} of value \isa{b}.  The corresponding
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  type is \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharcolon}{\isacharcolon}\ A{\isacharcomma}\ y\ {\isacharcolon}{\isacharcolon}\ B{\isasymrparr}{\isachardoublequote}}, assuming that \isa{{\isachardoublequote}a\ {\isacharcolon}{\isacharcolon}\ A{\isachardoublequote}}
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  and \isa{{\isachardoublequote}b\ {\isacharcolon}{\isacharcolon}\ B{\isachardoublequote}}.
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  A record scheme like \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ m{\isasymrparr}{\isachardoublequote}} contains fields
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  \isa{x} and \isa{y} as before, but also possibly further fields
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  as indicated by the ``\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}'' notation (which is actually part
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  of the syntax).  The improper field ``\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}'' of a record
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  scheme is called the \emph{more part}.  Logically it is just a free
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  variable, which is occasionally referred to as ``row variable'' in
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  the literature.  The more part of a record scheme may be
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  instantiated by zero or more further components.  For example, the
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  previous scheme may get instantiated to \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isacharcomma}\ z\ {\isacharequal}\ c{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ m{\isacharprime}{\isasymrparr}{\isachardoublequote}}, where \isa{m{\isacharprime}} refers to a different more part.
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  Fixed records are special instances of record schemes, where
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  ``\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}'' is properly terminated by the \isa{{\isachardoublequote}{\isacharparenleft}{\isacharparenright}\ {\isacharcolon}{\isacharcolon}\ unit{\isachardoublequote}}
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  element.  In fact, \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isasymrparr}{\isachardoublequote}} is just an abbreviation
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  for \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ {\isacharparenleft}{\isacharparenright}{\isasymrparr}{\isachardoublequote}}.
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  \medskip Two key observations make extensible records in a simply
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  typed language like HOL work out:
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  \begin{enumerate}
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  \item the more part is internalized, as a free term or type
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  variable,
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  \item field names are externalized, they cannot be accessed within
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  the logic as first-class values.
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  \end{enumerate}
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  \medskip In Isabelle/HOL record types have to be defined explicitly,
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  fixing their field names and types, and their (optional) parent
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  record.  Afterwards, records may be formed using above syntax, while
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  obeying the canonical order of fields as given by their declaration.
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  The record package provides several standard operations like
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  selectors and updates.  The common setup for various generic proof
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  tools enable succinct reasoning patterns.  See also the Isabelle/HOL
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  tutorial \cite{isabelle-hol-book} for further instructions on using
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  records in practice.%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\isamarkupsubsection{Record specifications%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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\begin{matharray}{rcl}
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    \indexdef{HOL}{command}{record}\hypertarget{command.HOL.record}{\hyperlink{command.HOL.record}{\mbox{\isa{\isacommand{record}}}}} & : & \isartrans{theory}{theory} \\
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  \end{matharray}
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  \begin{rail}
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    'record' typespec '=' (type '+')? (constdecl +)
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    ;
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  \end{rail}
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  \begin{descr}
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  \item [\hyperlink{command.HOL.record}{\mbox{\isa{\isacommand{record}}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharparenright}\ t\ {\isacharequal}\ {\isasymtau}\ {\isacharplus}\ c\isactrlsub {\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ c\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub n{\isachardoublequote}}] defines
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  extensible record type \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharparenright}\ t{\isachardoublequote}},
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  derived from the optional parent record \isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}} by adding new
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  field components \isa{{\isachardoublequote}c\isactrlsub i\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub i{\isachardoublequote}} etc.
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  The type variables of \isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isasymsigma}\isactrlsub i{\isachardoublequote}} need to be
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  covered by the (distinct) parameters \isa{{\isachardoublequote}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isachardoublequote}}.  Type constructor \isa{t} has to be new, while \isa{{\isasymtau}} needs to specify an instance of an existing record type.  At
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  least one new field \isa{{\isachardoublequote}c\isactrlsub i{\isachardoublequote}} has to be specified.
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  Basically, field names need to belong to a unique record.  This is
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  not a real restriction in practice, since fields are qualified by
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  the record name internally.
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  The parent record specification \isa{{\isasymtau}} is optional; if omitted
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  \isa{t} becomes a root record.  The hierarchy of all records
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  declared within a theory context forms a forest structure, i.e.\ a
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  set of trees starting with a root record each.  There is no way to
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  merge multiple parent records!
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  For convenience, \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharparenright}\ t{\isachardoublequote}} is made a
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  type abbreviation for the fixed record type \isa{{\isachardoublequote}{\isasymlparr}c\isactrlsub {\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub n{\isasymrparr}{\isachardoublequote}}, likewise is \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharcomma}\ {\isasymzeta}{\isacharparenright}\ t{\isacharunderscore}scheme{\isachardoublequote}} made an abbreviation for
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  \isa{{\isachardoublequote}{\isasymlparr}c\isactrlsub {\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub n{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}{\isachardoublequote}}.
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  \end{descr}%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\isamarkupsubsection{Record operations%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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Any record definition of the form presented above produces certain
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  standard operations.  Selectors and updates are provided for any
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  field, including the improper one ``\isa{more}''.  There are also
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  cumulative record constructor functions.  To simplify the
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  presentation below, we assume for now that \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharparenright}\ t{\isachardoublequote}} is a root record with fields \isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub n{\isachardoublequote}}.
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  \medskip \textbf{Selectors} and \textbf{updates} are available for
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  any field (including ``\isa{more}''):
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  \begin{matharray}{lll}
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    \isa{{\isachardoublequote}c\isactrlsub i{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymlparr}\isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}\ {\isasymRightarrow}\ {\isasymsigma}\isactrlsub i{\isachardoublequote}} \\
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    \isa{{\isachardoublequote}c\isactrlsub i{\isacharunderscore}update{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymsigma}\isactrlsub i\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}{\isachardoublequote}} \\
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  \end{matharray}
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  There is special syntax for application of updates: \isa{{\isachardoublequote}r{\isasymlparr}x\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}{\isachardoublequote}} abbreviates term \isa{{\isachardoublequote}x{\isacharunderscore}update\ a\ r{\isachardoublequote}}.  Further notation for
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  repeated updates is also available: \isa{{\isachardoublequote}r{\isasymlparr}x\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}{\isasymlparr}y\ {\isacharcolon}{\isacharequal}\ b{\isasymrparr}{\isasymlparr}z\ {\isacharcolon}{\isacharequal}\ c{\isasymrparr}{\isachardoublequote}} may be written \isa{{\isachardoublequote}r{\isasymlparr}x\ {\isacharcolon}{\isacharequal}\ a{\isacharcomma}\ y\ {\isacharcolon}{\isacharequal}\ b{\isacharcomma}\ z\ {\isacharcolon}{\isacharequal}\ c{\isasymrparr}{\isachardoublequote}}.  Note that
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  because of postfix notation the order of fields shown here is
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  reverse than in the actual term.  Since repeated updates are just
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  function applications, fields may be freely permuted in \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharcolon}{\isacharequal}\ a{\isacharcomma}\ y\ {\isacharcolon}{\isacharequal}\ b{\isacharcomma}\ z\ {\isacharcolon}{\isacharequal}\ c{\isasymrparr}{\isachardoublequote}}, as far as logical equality is concerned.
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  Thus commutativity of independent updates can be proven within the
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  logic for any two fields, but not as a general theorem.
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  \medskip The \textbf{make} operation provides a cumulative record
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  constructor function:
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  \begin{matharray}{lll}
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    \isa{{\isachardoublequote}t{\isachardot}make{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymsigma}\isactrlsub {\isadigit{1}}\ {\isasymRightarrow}\ {\isasymdots}\ {\isasymsigma}\isactrlsub n\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isasymrparr}{\isachardoublequote}} \\
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  \end{matharray}
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  \medskip We now reconsider the case of non-root records, which are
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  derived of some parent.  In general, the latter may depend on
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  another parent as well, resulting in a list of \emph{ancestor
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  records}.  Appending the lists of fields of all ancestors results in
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  a certain field prefix.  The record package automatically takes care
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  of this by lifting operations over this context of ancestor fields.
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  Assuming that \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharparenright}\ t{\isachardoublequote}} has ancestor
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  fields \isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isasymrho}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ b\isactrlsub k\ {\isacharcolon}{\isacharcolon}\ {\isasymrho}\isactrlsub k{\isachardoublequote}},
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  the above record operations will get the following types:
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  \medskip
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  \begin{tabular}{lll}
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    \isa{{\isachardoublequote}c\isactrlsub i{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymlparr}\isactrlvec b\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymrho}{\isacharcomma}\ \isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}\ {\isasymRightarrow}\ {\isasymsigma}\isactrlsub i{\isachardoublequote}} \\
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    \isa{{\isachardoublequote}c\isactrlsub i{\isacharunderscore}update{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymsigma}\isactrlsub i\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec b\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymrho}{\isacharcomma}\ \isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec b\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymrho}{\isacharcomma}\ \isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}{\isachardoublequote}} \\
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    \isa{{\isachardoublequote}t{\isachardot}make{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymrho}\isactrlsub {\isadigit{1}}\ {\isasymRightarrow}\ {\isasymdots}\ {\isasymrho}\isactrlsub k\ {\isasymRightarrow}\ {\isasymsigma}\isactrlsub {\isadigit{1}}\ {\isasymRightarrow}\ {\isasymdots}\ {\isasymsigma}\isactrlsub n\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec b\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymrho}{\isacharcomma}\ \isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isasymrparr}{\isachardoublequote}} \\
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  \end{tabular}
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  \medskip
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   294
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  \noindent Some further operations address the extension aspect of a
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  derived record scheme specifically: \isa{{\isachardoublequote}t{\isachardot}fields{\isachardoublequote}} produces a
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  record fragment consisting of exactly the new fields introduced here
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  (the result may serve as a more part elsewhere); \isa{{\isachardoublequote}t{\isachardot}extend{\isachardoublequote}}
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  takes a fixed record and adds a given more part; \isa{{\isachardoublequote}t{\isachardot}truncate{\isachardoublequote}} restricts a record scheme to a fixed record.
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   300
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  \medskip
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  \begin{tabular}{lll}
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    \isa{{\isachardoublequote}t{\isachardot}fields{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymsigma}\isactrlsub {\isadigit{1}}\ {\isasymRightarrow}\ {\isasymdots}\ {\isasymsigma}\isactrlsub n\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isasymrparr}{\isachardoublequote}} \\
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    \isa{{\isachardoublequote}t{\isachardot}extend{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymlparr}\isactrlvec b\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymrho}{\isacharcomma}\ \isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isasymrparr}\ {\isasymRightarrow}\ {\isasymzeta}\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec b\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymrho}{\isacharcomma}\ \isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}{\isachardoublequote}} \\
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    \isa{{\isachardoublequote}t{\isachardot}truncate{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymlparr}\isactrlvec b\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymrho}{\isacharcomma}\ \isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec b\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymrho}{\isacharcomma}\ \isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isasymrparr}{\isachardoublequote}} \\
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  \end{tabular}
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  \medskip
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   308
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  \noindent Note that \isa{{\isachardoublequote}t{\isachardot}make{\isachardoublequote}} and \isa{{\isachardoublequote}t{\isachardot}fields{\isachardoublequote}} coincide
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  for root records.%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\isamarkupsubsection{Derived rules and proof tools%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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   319
The record package proves several results internally, declaring
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  these facts to appropriate proof tools.  This enables users to
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  reason about record structures quite conveniently.  Assume that
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  \isa{t} is a record type as specified above.
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   323
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  \begin{enumerate}
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   325
  
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  \item Standard conversions for selectors or updates applied to
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  record constructor terms are made part of the default Simplifier
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  context; thus proofs by reduction of basic operations merely require
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  the \hyperlink{method.simp}{\mbox{\isa{simp}}} method without further arguments.  These rules
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  are available as \isa{{\isachardoublequote}t{\isachardot}simps{\isachardoublequote}}, too.
wenzelm@26849
   331
  
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  \item Selectors applied to updated records are automatically reduced
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  by an internal simplification procedure, which is also part of the
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  standard Simplifier setup.
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  \item Inject equations of a form analogous to \isa{{\isachardoublequote}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}x{\isacharprime}{\isacharcomma}\ y{\isacharprime}{\isacharparenright}\ {\isasymequiv}\ x\ {\isacharequal}\ x{\isacharprime}\ {\isasymand}\ y\ {\isacharequal}\ y{\isacharprime}{\isachardoublequote}} are declared to the Simplifier and Classical
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  Reasoner as \hyperlink{attribute.iff}{\mbox{\isa{iff}}} rules.  These rules are available as
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  \isa{{\isachardoublequote}t{\isachardot}iffs{\isachardoublequote}}.
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  \item The introduction rule for record equality analogous to \isa{{\isachardoublequote}x\ r\ {\isacharequal}\ x\ r{\isacharprime}\ {\isasymLongrightarrow}\ y\ r\ {\isacharequal}\ y\ r{\isacharprime}\ {\isasymdots}\ {\isasymLongrightarrow}\ r\ {\isacharequal}\ r{\isacharprime}{\isachardoublequote}} is declared to the Simplifier,
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  and as the basic rule context as ``\hyperlink{attribute.intro}{\mbox{\isa{intro}}}\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}''.
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  The rule is called \isa{{\isachardoublequote}t{\isachardot}equality{\isachardoublequote}}.
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   343
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  \item Representations of arbitrary record expressions as canonical
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  constructor terms are provided both in \hyperlink{method.cases}{\mbox{\isa{cases}}} and \hyperlink{method.induct}{\mbox{\isa{induct}}} format (cf.\ the generic proof methods of the same name,
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  \secref{sec:cases-induct}).  Several variations are available, for
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  fixed records, record schemes, more parts etc.
wenzelm@26849
   348
  
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  The generic proof methods are sufficiently smart to pick the most
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  sensible rule according to the type of the indicated record
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  expression: users just need to apply something like ``\isa{{\isachardoublequote}{\isacharparenleft}cases\ r{\isacharparenright}{\isachardoublequote}}'' to a certain proof problem.
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  \item The derived record operations \isa{{\isachardoublequote}t{\isachardot}make{\isachardoublequote}}, \isa{{\isachardoublequote}t{\isachardot}fields{\isachardoublequote}}, \isa{{\isachardoublequote}t{\isachardot}extend{\isachardoublequote}}, \isa{{\isachardoublequote}t{\isachardot}truncate{\isachardoublequote}} are \emph{not}
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  treated automatically, but usually need to be expanded by hand,
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  using the collective fact \isa{{\isachardoublequote}t{\isachardot}defs{\isachardoublequote}}.
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   357
  \end{enumerate}%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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   361
\isamarkupsection{Datatypes \label{sec:hol-datatype}%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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\begin{matharray}{rcl}
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    \indexdef{HOL}{command}{datatype}\hypertarget{command.HOL.datatype}{\hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}}} & : & \isartrans{theory}{theory} \\
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  \indexdef{HOL}{command}{rep\_datatype}\hypertarget{command.HOL.rep-datatype}{\hyperlink{command.HOL.rep-datatype}{\mbox{\isa{\isacommand{rep{\isacharunderscore}datatype}}}}} & : & \isartrans{theory}{proof} \\
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  \end{matharray}
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   371
  \begin{rail}
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    'datatype' (dtspec + 'and')
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    ;
haftmann@27452
   374
    'rep\_datatype' ('(' (name +) ')')? (term +)
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    ;
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   376
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    dtspec: parname? typespec infix? '=' (cons + '|')
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    ;
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    cons: name (type *) mixfix?
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   380
  \end{rail}
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   382
  \begin{descr}
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   383
wenzelm@26902
   384
  \item [\hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}}] defines inductive datatypes in
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   385
  HOL.
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   386
wenzelm@26907
   387
  \item [\hyperlink{command.HOL.rep-datatype}{\mbox{\isa{\isacommand{rep{\isacharunderscore}datatype}}}}] represents existing types as
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  inductive ones, generating the standard infrastructure of derived
wenzelm@26849
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  concepts (primitive recursion etc.).
wenzelm@26849
   390
wenzelm@26849
   391
  \end{descr}
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   392
wenzelm@26849
   393
  The induction and exhaustion theorems generated provide case names
wenzelm@26849
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  according to the constructors involved, while parameters are named
wenzelm@26849
   395
  after the types (see also \secref{sec:cases-induct}).
wenzelm@26849
   396
wenzelm@26849
   397
  See \cite{isabelle-HOL} for more details on datatypes, but beware of
wenzelm@26849
   398
  the old-style theory syntax being used there!  Apart from proper
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   399
  proof methods for case-analysis and induction, there are also
wenzelm@26907
   400
  emulations of ML tactics \hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isacharunderscore}tac}}} and \hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isacharunderscore}tac}}} available, see \secref{sec:hol-induct-tac}; these admit
wenzelm@26849
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  to refer directly to the internal structure of subgoals (including
wenzelm@26849
   402
  internally bound parameters).%
wenzelm@26849
   403
\end{isamarkuptext}%
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   404
\isamarkuptrue%
wenzelm@26849
   405
%
wenzelm@26849
   406
\isamarkupsection{Recursive functions \label{sec:recursion}%
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   407
}
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   408
\isamarkuptrue%
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   409
%
wenzelm@26849
   410
\begin{isamarkuptext}%
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   411
\begin{matharray}{rcl}
wenzelm@26902
   412
    \indexdef{HOL}{command}{primrec}\hypertarget{command.HOL.primrec}{\hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}}} & : & \isarkeep{local{\dsh}theory} \\
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    \indexdef{HOL}{command}{fun}\hypertarget{command.HOL.fun}{\hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}}} & : & \isarkeep{local{\dsh}theory} \\
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    \indexdef{HOL}{command}{function}\hypertarget{command.HOL.function}{\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}} & : & \isartrans{local{\dsh}theory}{proof(prove)} \\
wenzelm@26902
   415
    \indexdef{HOL}{command}{termination}\hypertarget{command.HOL.termination}{\hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}} & : & \isartrans{local{\dsh}theory}{proof(prove)} \\
wenzelm@26849
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  \end{matharray}
wenzelm@26849
   417
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   418
  \begin{rail}
wenzelm@26849
   419
    'primrec' target? fixes 'where' equations
wenzelm@26849
   420
    ;
wenzelm@26849
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    equations: (thmdecl? prop + '|')
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   422
    ;
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   423
    ('fun' | 'function') target? functionopts? fixes 'where' clauses
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   424
    ;
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   425
    clauses: (thmdecl? prop ('(' 'otherwise' ')')? + '|')
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   426
    ;
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   427
    functionopts: '(' (('sequential' | 'domintros' | 'tailrec' | 'default' term) + ',') ')'
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    ;
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    'termination' ( term )?
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   430
  \end{rail}
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   431
wenzelm@26849
   432
  \begin{descr}
wenzelm@26849
   433
wenzelm@26902
   434
  \item [\hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}}] defines primitive recursive
wenzelm@26849
   435
  functions over datatypes, see also \cite{isabelle-HOL}.
wenzelm@26849
   436
wenzelm@26902
   437
  \item [\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}] defines functions by general
wenzelm@26849
   438
  wellfounded recursion. A detailed description with examples can be
wenzelm@26849
   439
  found in \cite{isabelle-function}. The function is specified by a
wenzelm@26849
   440
  set of (possibly conditional) recursive equations with arbitrary
wenzelm@26849
   441
  pattern matching. The command generates proof obligations for the
wenzelm@26849
   442
  completeness and the compatibility of patterns.
wenzelm@26849
   443
wenzelm@26849
   444
  The defined function is considered partial, and the resulting
wenzelm@26849
   445
  simplification rules (named \isa{{\isachardoublequote}f{\isachardot}psimps{\isachardoublequote}}) and induction rule
wenzelm@26849
   446
  (named \isa{{\isachardoublequote}f{\isachardot}pinduct{\isachardoublequote}}) are guarded by a generated domain
wenzelm@26902
   447
  predicate \isa{{\isachardoublequote}f{\isacharunderscore}dom{\isachardoublequote}}. The \hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}
wenzelm@26849
   448
  command can then be used to establish that the function is total.
wenzelm@26849
   449
wenzelm@26902
   450
  \item [\hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}}] is a shorthand notation for
wenzelm@26902
   451
  ``\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}~\isa{{\isachardoublequote}{\isacharparenleft}sequential{\isacharparenright}{\isachardoublequote}}, followed by
wenzelm@26849
   452
  automated proof attempts regarding pattern matching and termination.
wenzelm@26849
   453
  See \cite{isabelle-function} for further details.
wenzelm@26849
   454
wenzelm@26902
   455
  \item [\hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}~\isa{f}] commences a
wenzelm@26849
   456
  termination proof for the previously defined function \isa{f}.  If
wenzelm@26849
   457
  this is omitted, the command refers to the most recent function
wenzelm@26849
   458
  definition.  After the proof is closed, the recursive equations and
wenzelm@26849
   459
  the induction principle is established.
wenzelm@26849
   460
wenzelm@26849
   461
  \end{descr}
wenzelm@26849
   462
wenzelm@26849
   463
  %FIXME check
wenzelm@26849
   464
haftmann@27452
   465
  Recursive definitions introduced by the \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}
haftmann@27452
   466
  command accommodate
wenzelm@26849
   467
  reasoning by induction (cf.\ \secref{sec:cases-induct}): rule \isa{{\isachardoublequote}c{\isachardot}induct{\isachardoublequote}} (where \isa{c} is the name of the function definition)
wenzelm@26849
   468
  refers to a specific induction rule, with parameters named according
haftmann@27452
   469
  to the user-specified equations.
haftmann@27452
   470
  For the \hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}} the induction principle coincides
haftmann@27452
   471
  with structural recursion on the datatype the recursion is carried
haftmann@27452
   472
  out.
haftmann@27452
   473
  Case names of \hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}} are that of the datatypes involved, while those of
wenzelm@26902
   474
  \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} are numbered (starting from 1).
wenzelm@26849
   475
wenzelm@26849
   476
  The equations provided by these packages may be referred later as
wenzelm@26849
   477
  theorem list \isa{{\isachardoublequote}f{\isachardot}simps{\isachardoublequote}}, where \isa{f} is the (collective)
wenzelm@26849
   478
  name of the functions defined.  Individual equations may be named
wenzelm@26849
   479
  explicitly as well.
wenzelm@26849
   480
wenzelm@26902
   481
  The \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} command accepts the following
wenzelm@26849
   482
  options.
wenzelm@26849
   483
wenzelm@26849
   484
  \begin{descr}
wenzelm@26849
   485
wenzelm@26849
   486
  \item [\isa{sequential}] enables a preprocessor which
wenzelm@26849
   487
  disambiguates overlapping patterns by making them mutually disjoint.
wenzelm@26849
   488
  Earlier equations take precedence over later ones.  This allows to
wenzelm@26849
   489
  give the specification in a format very similar to functional
wenzelm@26849
   490
  programming.  Note that the resulting simplification and induction
wenzelm@26849
   491
  rules correspond to the transformed specification, not the one given
wenzelm@26849
   492
  originally. This usually means that each equation given by the user
wenzelm@26849
   493
  may result in several theroems.  Also note that this automatic
wenzelm@26849
   494
  transformation only works for ML-style datatype patterns.
wenzelm@26849
   495
wenzelm@26849
   496
  \item [\isa{domintros}] enables the automated generation of
wenzelm@26849
   497
  introduction rules for the domain predicate. While mostly not
wenzelm@26849
   498
  needed, they can be helpful in some proofs about partial functions.
wenzelm@26849
   499
wenzelm@26849
   500
  \item [\isa{tailrec}] generates the unconstrained recursive
wenzelm@26849
   501
  equations even without a termination proof, provided that the
wenzelm@26849
   502
  function is tail-recursive. This currently only works
wenzelm@26849
   503
wenzelm@26849
   504
  \item [\isa{{\isachardoublequote}default\ d{\isachardoublequote}}] allows to specify a default value for a
wenzelm@26849
   505
  (partial) function, which will ensure that \isa{{\isachardoublequote}f\ x\ {\isacharequal}\ d\ x{\isachardoublequote}}
wenzelm@26849
   506
  whenever \isa{{\isachardoublequote}x\ {\isasymnotin}\ f{\isacharunderscore}dom{\isachardoublequote}}.
wenzelm@26849
   507
wenzelm@26849
   508
  \end{descr}%
wenzelm@26849
   509
\end{isamarkuptext}%
wenzelm@26849
   510
\isamarkuptrue%
wenzelm@26849
   511
%
wenzelm@26849
   512
\isamarkupsubsection{Proof methods related to recursive definitions%
wenzelm@26849
   513
}
wenzelm@26849
   514
\isamarkuptrue%
wenzelm@26849
   515
%
wenzelm@26849
   516
\begin{isamarkuptext}%
wenzelm@26849
   517
\begin{matharray}{rcl}
wenzelm@26907
   518
    \indexdef{HOL}{method}{pat\_completeness}\hypertarget{method.HOL.pat-completeness}{\hyperlink{method.HOL.pat-completeness}{\mbox{\isa{pat{\isacharunderscore}completeness}}}} & : & \isarmeth \\
wenzelm@26902
   519
    \indexdef{HOL}{method}{relation}\hypertarget{method.HOL.relation}{\hyperlink{method.HOL.relation}{\mbox{\isa{relation}}}} & : & \isarmeth \\
wenzelm@26907
   520
    \indexdef{HOL}{method}{lexicographic\_order}\hypertarget{method.HOL.lexicographic-order}{\hyperlink{method.HOL.lexicographic-order}{\mbox{\isa{lexicographic{\isacharunderscore}order}}}} & : & \isarmeth \\
wenzelm@26849
   521
  \end{matharray}
wenzelm@26849
   522
wenzelm@26849
   523
  \begin{rail}
wenzelm@26849
   524
    'relation' term
wenzelm@26849
   525
    ;
wenzelm@26849
   526
    'lexicographic\_order' (clasimpmod *)
wenzelm@26849
   527
    ;
wenzelm@26849
   528
  \end{rail}
wenzelm@26849
   529
wenzelm@26849
   530
  \begin{descr}
wenzelm@26849
   531
wenzelm@26907
   532
  \item [\hyperlink{method.HOL.pat-completeness}{\mbox{\isa{pat{\isacharunderscore}completeness}}}] is a specialized method to
wenzelm@26849
   533
  solve goals regarding the completeness of pattern matching, as
wenzelm@26902
   534
  required by the \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} package (cf.\
wenzelm@26849
   535
  \cite{isabelle-function}).
wenzelm@26849
   536
wenzelm@26902
   537
  \item [\hyperlink{method.HOL.relation}{\mbox{\isa{relation}}}~\isa{R}] introduces a termination
wenzelm@26849
   538
  proof using the relation \isa{R}.  The resulting proof state will
wenzelm@26849
   539
  contain goals expressing that \isa{R} is wellfounded, and that the
wenzelm@26849
   540
  arguments of recursive calls decrease with respect to \isa{R}.
wenzelm@26849
   541
  Usually, this method is used as the initial proof step of manual
wenzelm@26849
   542
  termination proofs.
wenzelm@26849
   543
wenzelm@26907
   544
  \item [\hyperlink{method.HOL.lexicographic-order}{\mbox{\isa{lexicographic{\isacharunderscore}order}}}] attempts a fully
wenzelm@26849
   545
  automated termination proof by searching for a lexicographic
wenzelm@26849
   546
  combination of size measures on the arguments of the function. The
wenzelm@26902
   547
  method accepts the same arguments as the \hyperlink{method.auto}{\mbox{\isa{auto}}} method,
wenzelm@26849
   548
  which it uses internally to prove local descents.  The same context
wenzelm@26902
   549
  modifiers as for \hyperlink{method.auto}{\mbox{\isa{auto}}} are accepted, see
wenzelm@26849
   550
  \secref{sec:clasimp}.
wenzelm@26849
   551
wenzelm@26849
   552
  In case of failure, extensive information is printed, which can help
wenzelm@26849
   553
  to analyse the situation (cf.\ \cite{isabelle-function}).
wenzelm@26849
   554
wenzelm@26849
   555
  \end{descr}%
wenzelm@26849
   556
\end{isamarkuptext}%
wenzelm@26849
   557
\isamarkuptrue%
wenzelm@26849
   558
%
wenzelm@26849
   559
\isamarkupsubsection{Old-style recursive function definitions (TFL)%
wenzelm@26849
   560
}
wenzelm@26849
   561
\isamarkuptrue%
wenzelm@26849
   562
%
wenzelm@26849
   563
\begin{isamarkuptext}%
wenzelm@26907
   564
The old TFL commands \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} and \hyperlink{command.HOL.recdef-tc}{\mbox{\isa{\isacommand{recdef{\isacharunderscore}tc}}}} for defining recursive are mostly obsolete; \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} or \hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}} should be used instead.
wenzelm@26849
   565
wenzelm@26849
   566
  \begin{matharray}{rcl}
wenzelm@26902
   567
    \indexdef{HOL}{command}{recdef}\hypertarget{command.HOL.recdef}{\hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}}} & : & \isartrans{theory}{theory} \\
wenzelm@26907
   568
    \indexdef{HOL}{command}{recdef\_tc}\hypertarget{command.HOL.recdef-tc}{\hyperlink{command.HOL.recdef-tc}{\mbox{\isa{\isacommand{recdef{\isacharunderscore}tc}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isartrans{theory}{proof(prove)} \\
wenzelm@26849
   569
  \end{matharray}
wenzelm@26849
   570
wenzelm@26849
   571
  \begin{rail}
wenzelm@26849
   572
    'recdef' ('(' 'permissive' ')')? \\ name term (prop +) hints?
wenzelm@26849
   573
    ;
wenzelm@26849
   574
    recdeftc thmdecl? tc
wenzelm@26849
   575
    ;
wenzelm@26849
   576
    hints: '(' 'hints' (recdefmod *) ')'
wenzelm@26849
   577
    ;
wenzelm@26849
   578
    recdefmod: (('recdef\_simp' | 'recdef\_cong' | 'recdef\_wf') (() | 'add' | 'del') ':' thmrefs) | clasimpmod
wenzelm@26849
   579
    ;
wenzelm@26849
   580
    tc: nameref ('(' nat ')')?
wenzelm@26849
   581
    ;
wenzelm@26849
   582
  \end{rail}
wenzelm@26849
   583
wenzelm@26849
   584
  \begin{descr}
wenzelm@26849
   585
  
wenzelm@26902
   586
  \item [\hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}}] defines general well-founded
wenzelm@26849
   587
  recursive functions (using the TFL package), see also
wenzelm@26849
   588
  \cite{isabelle-HOL}.  The ``\isa{{\isachardoublequote}{\isacharparenleft}permissive{\isacharparenright}{\isachardoublequote}}'' option tells
wenzelm@26849
   589
  TFL to recover from failed proof attempts, returning unfinished
wenzelm@26849
   590
  results.  The \isa{recdef{\isacharunderscore}simp}, \isa{recdef{\isacharunderscore}cong}, and \isa{recdef{\isacharunderscore}wf} hints refer to auxiliary rules to be used in the internal
wenzelm@26902
   591
  automated proof process of TFL.  Additional \hyperlink{syntax.clasimpmod}{\mbox{\isa{clasimpmod}}}
wenzelm@26849
   592
  declarations (cf.\ \secref{sec:clasimp}) may be given to tune the
wenzelm@26849
   593
  context of the Simplifier (cf.\ \secref{sec:simplifier}) and
wenzelm@26849
   594
  Classical reasoner (cf.\ \secref{sec:classical}).
wenzelm@26849
   595
  
wenzelm@26907
   596
  \item [\hyperlink{command.HOL.recdef-tc}{\mbox{\isa{\isacommand{recdef{\isacharunderscore}tc}}}}~\isa{{\isachardoublequote}c\ {\isacharparenleft}i{\isacharparenright}{\isachardoublequote}}] recommences the
wenzelm@26849
   597
  proof for leftover termination condition number \isa{i} (default
wenzelm@26902
   598
  1) as generated by a \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} definition of
wenzelm@26849
   599
  constant \isa{c}.
wenzelm@26849
   600
  
wenzelm@26902
   601
  Note that in most cases, \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} is able to finish
wenzelm@26849
   602
  its internal proofs without manual intervention.
wenzelm@26849
   603
wenzelm@26849
   604
  \end{descr}
wenzelm@26849
   605
wenzelm@26902
   606
  \medskip Hints for \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} may be also declared
wenzelm@26849
   607
  globally, using the following attributes.
wenzelm@26849
   608
wenzelm@26849
   609
  \begin{matharray}{rcl}
wenzelm@26907
   610
    \indexdef{HOL}{attribute}{recdef\_simp}\hypertarget{attribute.HOL.recdef-simp}{\hyperlink{attribute.HOL.recdef-simp}{\mbox{\isa{recdef{\isacharunderscore}simp}}}} & : & \isaratt \\
wenzelm@26907
   611
    \indexdef{HOL}{attribute}{recdef\_cong}\hypertarget{attribute.HOL.recdef-cong}{\hyperlink{attribute.HOL.recdef-cong}{\mbox{\isa{recdef{\isacharunderscore}cong}}}} & : & \isaratt \\
wenzelm@26907
   612
    \indexdef{HOL}{attribute}{recdef\_wf}\hypertarget{attribute.HOL.recdef-wf}{\hyperlink{attribute.HOL.recdef-wf}{\mbox{\isa{recdef{\isacharunderscore}wf}}}} & : & \isaratt \\
wenzelm@26849
   613
  \end{matharray}
wenzelm@26849
   614
wenzelm@26849
   615
  \begin{rail}
wenzelm@26849
   616
    ('recdef\_simp' | 'recdef\_cong' | 'recdef\_wf') (() | 'add' | 'del')
wenzelm@26849
   617
    ;
wenzelm@26849
   618
  \end{rail}%
wenzelm@26849
   619
\end{isamarkuptext}%
wenzelm@26849
   620
\isamarkuptrue%
wenzelm@26849
   621
%
wenzelm@26849
   622
\isamarkupsection{Inductive and coinductive definitions \label{sec:hol-inductive}%
wenzelm@26849
   623
}
wenzelm@26849
   624
\isamarkuptrue%
wenzelm@26849
   625
%
wenzelm@26849
   626
\begin{isamarkuptext}%
wenzelm@26849
   627
An \textbf{inductive definition} specifies the least predicate (or
wenzelm@26849
   628
  set) \isa{R} closed under given rules: applying a rule to elements
wenzelm@26849
   629
  of \isa{R} yields a result within \isa{R}.  For example, a
wenzelm@26849
   630
  structural operational semantics is an inductive definition of an
wenzelm@26849
   631
  evaluation relation.
wenzelm@26849
   632
wenzelm@26849
   633
  Dually, a \textbf{coinductive definition} specifies the greatest
wenzelm@26849
   634
  predicate~/ set \isa{R} that is consistent with given rules: every
wenzelm@26849
   635
  element of \isa{R} can be seen as arising by applying a rule to
wenzelm@26849
   636
  elements of \isa{R}.  An important example is using bisimulation
wenzelm@26849
   637
  relations to formalise equivalence of processes and infinite data
wenzelm@26849
   638
  structures.
wenzelm@26849
   639
wenzelm@26849
   640
  \medskip The HOL package is related to the ZF one, which is
wenzelm@26849
   641
  described in a separate paper,\footnote{It appeared in CADE
wenzelm@26849
   642
  \cite{paulson-CADE}; a longer version is distributed with Isabelle.}
wenzelm@26849
   643
  which you should refer to in case of difficulties.  The package is
wenzelm@26849
   644
  simpler than that of ZF thanks to implicit type-checking in HOL.
wenzelm@26849
   645
  The types of the (co)inductive predicates (or sets) determine the
wenzelm@26849
   646
  domain of the fixedpoint definition, and the package does not have
wenzelm@26849
   647
  to use inference rules for type-checking.
wenzelm@26849
   648
wenzelm@26849
   649
  \begin{matharray}{rcl}
wenzelm@26902
   650
    \indexdef{HOL}{command}{inductive}\hypertarget{command.HOL.inductive}{\hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}}} & : & \isarkeep{local{\dsh}theory} \\
wenzelm@26907
   651
    \indexdef{HOL}{command}{inductive\_set}\hypertarget{command.HOL.inductive-set}{\hyperlink{command.HOL.inductive-set}{\mbox{\isa{\isacommand{inductive{\isacharunderscore}set}}}}} & : & \isarkeep{local{\dsh}theory} \\
wenzelm@26902
   652
    \indexdef{HOL}{command}{coinductive}\hypertarget{command.HOL.coinductive}{\hyperlink{command.HOL.coinductive}{\mbox{\isa{\isacommand{coinductive}}}}} & : & \isarkeep{local{\dsh}theory} \\
wenzelm@26907
   653
    \indexdef{HOL}{command}{coinductive\_set}\hypertarget{command.HOL.coinductive-set}{\hyperlink{command.HOL.coinductive-set}{\mbox{\isa{\isacommand{coinductive{\isacharunderscore}set}}}}} & : & \isarkeep{local{\dsh}theory} \\
wenzelm@26902
   654
    \indexdef{HOL}{attribute}{mono}\hypertarget{attribute.HOL.mono}{\hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}}} & : & \isaratt \\
wenzelm@26849
   655
  \end{matharray}
wenzelm@26849
   656
wenzelm@26849
   657
  \begin{rail}
wenzelm@26849
   658
    ('inductive' | 'inductive\_set' | 'coinductive' | 'coinductive\_set') target? fixes ('for' fixes)? \\
wenzelm@26849
   659
    ('where' clauses)? ('monos' thmrefs)?
wenzelm@26849
   660
    ;
wenzelm@26849
   661
    clauses: (thmdecl? prop + '|')
wenzelm@26849
   662
    ;
wenzelm@26849
   663
    'mono' (() | 'add' | 'del')
wenzelm@26849
   664
    ;
wenzelm@26849
   665
  \end{rail}
wenzelm@26849
   666
wenzelm@26849
   667
  \begin{descr}
wenzelm@26849
   668
wenzelm@26902
   669
  \item [\hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}} and \hyperlink{command.HOL.coinductive}{\mbox{\isa{\isacommand{coinductive}}}}] define (co)inductive predicates from the
wenzelm@26902
   670
  introduction rules given in the \hyperlink{keyword.where}{\mbox{\isa{\isakeyword{where}}}} part.  The
wenzelm@26902
   671
  optional \hyperlink{keyword.for}{\mbox{\isa{\isakeyword{for}}}} part contains a list of parameters of the
wenzelm@26849
   672
  (co)inductive predicates that remain fixed throughout the
wenzelm@26902
   673
  definition.  The optional \hyperlink{keyword.monos}{\mbox{\isa{\isakeyword{monos}}}} section contains
wenzelm@26849
   674
  \emph{monotonicity theorems}, which are required for each operator
wenzelm@26849
   675
  applied to a recursive set in the introduction rules.  There
wenzelm@26849
   676
  \emph{must} be a theorem of the form \isa{{\isachardoublequote}A\ {\isasymle}\ B\ {\isasymLongrightarrow}\ M\ A\ {\isasymle}\ M\ B{\isachardoublequote}},
wenzelm@26849
   677
  for each premise \isa{{\isachardoublequote}M\ R\isactrlsub i\ t{\isachardoublequote}} in an introduction rule!
wenzelm@26849
   678
wenzelm@26907
   679
  \item [\hyperlink{command.HOL.inductive-set}{\mbox{\isa{\isacommand{inductive{\isacharunderscore}set}}}} and \hyperlink{command.HOL.coinductive-set}{\mbox{\isa{\isacommand{coinductive{\isacharunderscore}set}}}}] are wrappers for to the previous commands,
wenzelm@26849
   680
  allowing the definition of (co)inductive sets.
wenzelm@26849
   681
wenzelm@26902
   682
  \item [\hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}}] declares monotonicity rules.  These
wenzelm@26902
   683
  rule are involved in the automated monotonicity proof of \hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}}.
wenzelm@26849
   684
wenzelm@26849
   685
  \end{descr}%
wenzelm@26849
   686
\end{isamarkuptext}%
wenzelm@26849
   687
\isamarkuptrue%
wenzelm@26849
   688
%
wenzelm@26849
   689
\isamarkupsubsection{Derived rules%
wenzelm@26849
   690
}
wenzelm@26849
   691
\isamarkuptrue%
wenzelm@26849
   692
%
wenzelm@26849
   693
\begin{isamarkuptext}%
wenzelm@26849
   694
Each (co)inductive definition \isa{R} adds definitions to the
wenzelm@26849
   695
  theory and also proves some theorems:
wenzelm@26849
   696
wenzelm@26849
   697
  \begin{description}
wenzelm@26849
   698
wenzelm@26849
   699
  \item [\isa{R{\isachardot}intros}] is the list of introduction rules as proven
wenzelm@26849
   700
  theorems, for the recursive predicates (or sets).  The rules are
wenzelm@26849
   701
  also available individually, using the names given them in the
wenzelm@26849
   702
  theory file;
wenzelm@26849
   703
wenzelm@26849
   704
  \item [\isa{R{\isachardot}cases}] is the case analysis (or elimination) rule;
wenzelm@26849
   705
wenzelm@26849
   706
  \item [\isa{R{\isachardot}induct} or \isa{R{\isachardot}coinduct}] is the (co)induction
wenzelm@26849
   707
  rule.
wenzelm@26849
   708
wenzelm@26849
   709
  \end{description}
wenzelm@26849
   710
wenzelm@26849
   711
  When several predicates \isa{{\isachardoublequote}R\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ R\isactrlsub n{\isachardoublequote}} are
wenzelm@26849
   712
  defined simultaneously, the list of introduction rules is called
wenzelm@26849
   713
  \isa{{\isachardoublequote}R\isactrlsub {\isadigit{1}}{\isacharunderscore}{\isasymdots}{\isacharunderscore}R\isactrlsub n{\isachardot}intros{\isachardoublequote}}, the case analysis rules are
wenzelm@26849
   714
  called \isa{{\isachardoublequote}R\isactrlsub {\isadigit{1}}{\isachardot}cases{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ R\isactrlsub n{\isachardot}cases{\isachardoublequote}}, and the list
wenzelm@26849
   715
  of mutual induction rules is called \isa{{\isachardoublequote}R\isactrlsub {\isadigit{1}}{\isacharunderscore}{\isasymdots}{\isacharunderscore}R\isactrlsub n{\isachardot}inducts{\isachardoublequote}}.%
wenzelm@26849
   716
\end{isamarkuptext}%
wenzelm@26849
   717
\isamarkuptrue%
wenzelm@26849
   718
%
wenzelm@26849
   719
\isamarkupsubsection{Monotonicity theorems%
wenzelm@26849
   720
}
wenzelm@26849
   721
\isamarkuptrue%
wenzelm@26849
   722
%
wenzelm@26849
   723
\begin{isamarkuptext}%
wenzelm@26849
   724
Each theory contains a default set of theorems that are used in
wenzelm@26849
   725
  monotonicity proofs.  New rules can be added to this set via the
wenzelm@26902
   726
  \hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}} attribute.  The HOL theory \isa{Inductive}
wenzelm@26849
   727
  shows how this is done.  In general, the following monotonicity
wenzelm@26849
   728
  theorems may be added:
wenzelm@26849
   729
wenzelm@26849
   730
  \begin{itemize}
wenzelm@26849
   731
wenzelm@26849
   732
  \item Theorems of the form \isa{{\isachardoublequote}A\ {\isasymle}\ B\ {\isasymLongrightarrow}\ M\ A\ {\isasymle}\ M\ B{\isachardoublequote}}, for proving
wenzelm@26849
   733
  monotonicity of inductive definitions whose introduction rules have
wenzelm@26849
   734
  premises involving terms such as \isa{{\isachardoublequote}M\ R\isactrlsub i\ t{\isachardoublequote}}.
wenzelm@26849
   735
wenzelm@26849
   736
  \item Monotonicity theorems for logical operators, which are of the
wenzelm@26849
   737
  general form \isa{{\isachardoublequote}{\isacharparenleft}{\isasymdots}\ {\isasymlongrightarrow}\ {\isasymdots}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isacharparenleft}{\isasymdots}\ {\isasymlongrightarrow}\ {\isasymdots}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymlongrightarrow}\ {\isasymdots}{\isachardoublequote}}.  For example, in
wenzelm@26849
   738
  the case of the operator \isa{{\isachardoublequote}{\isasymor}{\isachardoublequote}}, the corresponding theorem is
wenzelm@26849
   739
  \[
wenzelm@26849
   740
  \infer{\isa{{\isachardoublequote}P\isactrlsub {\isadigit{1}}\ {\isasymor}\ P\isactrlsub {\isadigit{2}}\ {\isasymlongrightarrow}\ Q\isactrlsub {\isadigit{1}}\ {\isasymor}\ Q\isactrlsub {\isadigit{2}}{\isachardoublequote}}}{\isa{{\isachardoublequote}P\isactrlsub {\isadigit{1}}\ {\isasymlongrightarrow}\ Q\isactrlsub {\isadigit{1}}{\isachardoublequote}} & \isa{{\isachardoublequote}P\isactrlsub {\isadigit{2}}\ {\isasymlongrightarrow}\ Q\isactrlsub {\isadigit{2}}{\isachardoublequote}}}
wenzelm@26849
   741
  \]
wenzelm@26849
   742
wenzelm@26849
   743
  \item De Morgan style equations for reasoning about the ``polarity''
wenzelm@26849
   744
  of expressions, e.g.
wenzelm@26849
   745
  \[
wenzelm@26849
   746
  \isa{{\isachardoublequote}{\isasymnot}\ {\isasymnot}\ P\ {\isasymlongleftrightarrow}\ P{\isachardoublequote}} \qquad\qquad
wenzelm@26849
   747
  \isa{{\isachardoublequote}{\isasymnot}\ {\isacharparenleft}P\ {\isasymand}\ Q{\isacharparenright}\ {\isasymlongleftrightarrow}\ {\isasymnot}\ P\ {\isasymor}\ {\isasymnot}\ Q{\isachardoublequote}}
wenzelm@26849
   748
  \]
wenzelm@26849
   749
wenzelm@26849
   750
  \item Equations for reducing complex operators to more primitive
wenzelm@26849
   751
  ones whose monotonicity can easily be proved, e.g.
wenzelm@26849
   752
  \[
wenzelm@26849
   753
  \isa{{\isachardoublequote}{\isacharparenleft}P\ {\isasymlongrightarrow}\ Q{\isacharparenright}\ {\isasymlongleftrightarrow}\ {\isasymnot}\ P\ {\isasymor}\ Q{\isachardoublequote}} \qquad\qquad
wenzelm@26849
   754
  \isa{{\isachardoublequote}Ball\ A\ P\ {\isasymequiv}\ {\isasymforall}x{\isachardot}\ x\ {\isasymin}\ A\ {\isasymlongrightarrow}\ P\ x{\isachardoublequote}}
wenzelm@26849
   755
  \]
wenzelm@26849
   756
wenzelm@26849
   757
  \end{itemize}
wenzelm@26849
   758
wenzelm@26849
   759
  %FIXME: Example of an inductive definition%
wenzelm@26849
   760
\end{isamarkuptext}%
wenzelm@26849
   761
\isamarkuptrue%
wenzelm@26849
   762
%
wenzelm@26849
   763
\isamarkupsection{Arithmetic proof support%
wenzelm@26849
   764
}
wenzelm@26849
   765
\isamarkuptrue%
wenzelm@26849
   766
%
wenzelm@26849
   767
\begin{isamarkuptext}%
wenzelm@26849
   768
\begin{matharray}{rcl}
wenzelm@26902
   769
    \indexdef{HOL}{method}{arith}\hypertarget{method.HOL.arith}{\hyperlink{method.HOL.arith}{\mbox{\isa{arith}}}} & : & \isarmeth \\
wenzelm@26907
   770
    \indexdef{HOL}{attribute}{arith\_split}\hypertarget{attribute.HOL.arith-split}{\hyperlink{attribute.HOL.arith-split}{\mbox{\isa{arith{\isacharunderscore}split}}}} & : & \isaratt \\
wenzelm@26849
   771
  \end{matharray}
wenzelm@26849
   772
wenzelm@26902
   773
  The \hyperlink{method.HOL.arith}{\mbox{\isa{arith}}} method decides linear arithmetic problems
wenzelm@26849
   774
  (on types \isa{nat}, \isa{int}, \isa{real}).  Any current
wenzelm@26849
   775
  facts are inserted into the goal before running the procedure.
wenzelm@26849
   776
wenzelm@26907
   777
  The \hyperlink{attribute.HOL.arith-split}{\mbox{\isa{arith{\isacharunderscore}split}}} attribute declares case split
wenzelm@26895
   778
  rules to be expanded before the arithmetic procedure is invoked.
wenzelm@26849
   779
wenzelm@26849
   780
  Note that a simpler (but faster) version of arithmetic reasoning is
wenzelm@26849
   781
  already performed by the Simplifier.%
wenzelm@26849
   782
\end{isamarkuptext}%
wenzelm@26849
   783
\isamarkuptrue%
wenzelm@26849
   784
%
wenzelm@27124
   785
\isamarkupsection{Unstructured cases analysis and induction \label{sec:hol-induct-tac}%
wenzelm@26849
   786
}
wenzelm@26849
   787
\isamarkuptrue%
wenzelm@26849
   788
%
wenzelm@26849
   789
\begin{isamarkuptext}%
wenzelm@27124
   790
The following tools of Isabelle/HOL support cases analysis and
wenzelm@27124
   791
  induction in unstructured tactic scripts; see also
wenzelm@27124
   792
  \secref{sec:cases-induct} for proper Isar versions of similar ideas.
wenzelm@26849
   793
wenzelm@26849
   794
  \begin{matharray}{rcl}
wenzelm@26907
   795
    \indexdef{HOL}{method}{case\_tac}\hypertarget{method.HOL.case-tac}{\hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\
wenzelm@26907
   796
    \indexdef{HOL}{method}{induct\_tac}\hypertarget{method.HOL.induct-tac}{\hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\
wenzelm@26907
   797
    \indexdef{HOL}{method}{ind\_cases}\hypertarget{method.HOL.ind-cases}{\hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isacharunderscore}cases}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\
wenzelm@27124
   798
    \indexdef{HOL}{command}{inductive\_cases}\hypertarget{command.HOL.inductive-cases}{\hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isacharunderscore}cases}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isartrans{theory}{theory} \\
wenzelm@26849
   799
  \end{matharray}
wenzelm@26849
   800
wenzelm@26849
   801
  \begin{rail}
wenzelm@26849
   802
    'case\_tac' goalspec? term rule?
wenzelm@26849
   803
    ;
wenzelm@26849
   804
    'induct\_tac' goalspec? (insts * 'and') rule?
wenzelm@26849
   805
    ;
wenzelm@26849
   806
    'ind\_cases' (prop +) ('for' (name +)) ?
wenzelm@26849
   807
    ;
wenzelm@26849
   808
    'inductive\_cases' (thmdecl? (prop +) + 'and')
wenzelm@26849
   809
    ;
wenzelm@26849
   810
wenzelm@26849
   811
    rule: ('rule' ':' thmref)
wenzelm@26849
   812
    ;
wenzelm@26849
   813
  \end{rail}
wenzelm@26849
   814
wenzelm@26849
   815
  \begin{descr}
wenzelm@26849
   816
wenzelm@26907
   817
  \item [\hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isacharunderscore}tac}}} and \hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isacharunderscore}tac}}}]
wenzelm@27124
   818
  admit to reason about inductive types.  Rules are selected according
wenzelm@27124
   819
  to the declarations by the \hyperlink{attribute.cases}{\mbox{\isa{cases}}} and \hyperlink{attribute.induct}{\mbox{\isa{induct}}} attributes, cf.\ \secref{sec:cases-induct}.  The \hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}} package already takes care of this.
wenzelm@27124
   820
wenzelm@27124
   821
  These unstructured tactics feature both goal addressing and dynamic
wenzelm@26849
   822
  instantiation.  Note that named rule cases are \emph{not} provided
wenzelm@27124
   823
  as would be by the proper \hyperlink{method.cases}{\mbox{\isa{cases}}} and \hyperlink{method.induct}{\mbox{\isa{induct}}} proof
wenzelm@27124
   824
  methods (see \secref{sec:cases-induct}).  Unlike the \hyperlink{method.induct}{\mbox{\isa{induct}}} method, \hyperlink{method.induct-tac}{\mbox{\isa{induct{\isacharunderscore}tac}}} does not handle structured rule
wenzelm@27124
   825
  statements, only the compact object-logic conclusion of the subgoal
wenzelm@27124
   826
  being addressed.
wenzelm@26849
   827
  
wenzelm@26907
   828
  \item [\hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isacharunderscore}cases}}} and \hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isacharunderscore}cases}}}}] provide an interface to the internal \verb|mk_cases| operation.  Rules are simplified in an unrestricted
wenzelm@26861
   829
  forward manner.
wenzelm@26849
   830
wenzelm@26907
   831
  While \hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isacharunderscore}cases}}} is a proof method to apply the
wenzelm@26907
   832
  result immediately as elimination rules, \hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isacharunderscore}cases}}}} provides case split theorems at the theory level
wenzelm@26907
   833
  for later use.  The \hyperlink{keyword.for}{\mbox{\isa{\isakeyword{for}}}} argument of the \hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isacharunderscore}cases}}} method allows to specify a list of variables that should
wenzelm@26849
   834
  be generalized before applying the resulting rule.
wenzelm@26849
   835
wenzelm@26849
   836
  \end{descr}%
wenzelm@26849
   837
\end{isamarkuptext}%
wenzelm@26849
   838
\isamarkuptrue%
wenzelm@26849
   839
%
wenzelm@26849
   840
\isamarkupsection{Executable code%
wenzelm@26849
   841
}
wenzelm@26849
   842
\isamarkuptrue%
wenzelm@26849
   843
%
wenzelm@26849
   844
\begin{isamarkuptext}%
wenzelm@26849
   845
Isabelle/Pure provides two generic frameworks to support code
wenzelm@26849
   846
  generation from executable specifications.  Isabelle/HOL
wenzelm@26849
   847
  instantiates these mechanisms in a way that is amenable to end-user
wenzelm@26849
   848
  applications.
wenzelm@26849
   849
wenzelm@26849
   850
  One framework generates code from both functional and relational
wenzelm@26849
   851
  programs to SML.  See \cite{isabelle-HOL} for further information
wenzelm@26849
   852
  (this actually covers the new-style theory format as well).
wenzelm@26849
   853
wenzelm@26849
   854
  \begin{matharray}{rcl}
wenzelm@26902
   855
    \indexdef{HOL}{command}{value}\hypertarget{command.HOL.value}{\hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
wenzelm@26907
   856
    \indexdef{HOL}{command}{code\_module}\hypertarget{command.HOL.code-module}{\hyperlink{command.HOL.code-module}{\mbox{\isa{\isacommand{code{\isacharunderscore}module}}}}} & : & \isartrans{theory}{theory} \\
wenzelm@26907
   857
    \indexdef{HOL}{command}{code\_library}\hypertarget{command.HOL.code-library}{\hyperlink{command.HOL.code-library}{\mbox{\isa{\isacommand{code{\isacharunderscore}library}}}}} & : & \isartrans{theory}{theory} \\
wenzelm@26907
   858
    \indexdef{HOL}{command}{consts\_code}\hypertarget{command.HOL.consts-code}{\hyperlink{command.HOL.consts-code}{\mbox{\isa{\isacommand{consts{\isacharunderscore}code}}}}} & : & \isartrans{theory}{theory} \\
wenzelm@26907
   859
    \indexdef{HOL}{command}{types\_code}\hypertarget{command.HOL.types-code}{\hyperlink{command.HOL.types-code}{\mbox{\isa{\isacommand{types{\isacharunderscore}code}}}}} & : & \isartrans{theory}{theory} \\  
wenzelm@26902
   860
    \indexdef{HOL}{attribute}{code}\hypertarget{attribute.HOL.code}{\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}} & : & \isaratt \\
wenzelm@26849
   861
  \end{matharray}
wenzelm@26849
   862
wenzelm@26849
   863
  \begin{rail}
wenzelm@26849
   864
  'value' term
wenzelm@26849
   865
  ;
wenzelm@26849
   866
wenzelm@26849
   867
  ( 'code\_module' | 'code\_library' ) modespec ? name ? \\
wenzelm@26849
   868
    ( 'file' name ) ? ( 'imports' ( name + ) ) ? \\
wenzelm@26849
   869
    'contains' ( ( name '=' term ) + | term + )
wenzelm@26849
   870
  ;
wenzelm@26849
   871
wenzelm@26849
   872
  modespec: '(' ( name * ) ')'
wenzelm@26849
   873
  ;
wenzelm@26849
   874
wenzelm@26849
   875
  'consts\_code' (codespec +)
wenzelm@26849
   876
  ;
wenzelm@26849
   877
wenzelm@26849
   878
  codespec: const template attachment ?
wenzelm@26849
   879
  ;
wenzelm@26849
   880
wenzelm@26849
   881
  'types\_code' (tycodespec +)
wenzelm@26849
   882
  ;
wenzelm@26849
   883
wenzelm@26849
   884
  tycodespec: name template attachment ?
wenzelm@26849
   885
  ;
wenzelm@26849
   886
wenzelm@26849
   887
  const: term
wenzelm@26849
   888
  ;
wenzelm@26849
   889
wenzelm@26849
   890
  template: '(' string ')'
wenzelm@26849
   891
  ;
wenzelm@26849
   892
wenzelm@26849
   893
  attachment: 'attach' modespec ? verblbrace text verbrbrace
wenzelm@26849
   894
  ;
wenzelm@26849
   895
wenzelm@26849
   896
  'code' (name)?
wenzelm@26849
   897
  ;
wenzelm@26849
   898
  \end{rail}
wenzelm@26849
   899
wenzelm@26849
   900
  \begin{descr}
wenzelm@26849
   901
wenzelm@26902
   902
  \item [\hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}~\isa{t}] evaluates and prints a
wenzelm@26849
   903
  term using the code generator.
wenzelm@26849
   904
wenzelm@26849
   905
  \end{descr}
wenzelm@26849
   906
wenzelm@26849
   907
  \medskip The other framework generates code from functional programs
wenzelm@26849
   908
  (including overloading using type classes) to SML \cite{SML}, OCaml
wenzelm@26849
   909
  \cite{OCaml} and Haskell \cite{haskell-revised-report}.
wenzelm@26849
   910
  Conceptually, code generation is split up in three steps:
wenzelm@26849
   911
  \emph{selection} of code theorems, \emph{translation} into an
wenzelm@26849
   912
  abstract executable view and \emph{serialization} to a specific
wenzelm@26849
   913
  \emph{target language}.  See \cite{isabelle-codegen} for an
wenzelm@26849
   914
  introduction on how to use it.
wenzelm@26849
   915
wenzelm@26849
   916
  \begin{matharray}{rcl}
wenzelm@26907
   917
    \indexdef{HOL}{command}{export\_code}\hypertarget{command.HOL.export-code}{\hyperlink{command.HOL.export-code}{\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
wenzelm@26907
   918
    \indexdef{HOL}{command}{code\_thms}\hypertarget{command.HOL.code-thms}{\hyperlink{command.HOL.code-thms}{\mbox{\isa{\isacommand{code{\isacharunderscore}thms}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
wenzelm@26907
   919
    \indexdef{HOL}{command}{code\_deps}\hypertarget{command.HOL.code-deps}{\hyperlink{command.HOL.code-deps}{\mbox{\isa{\isacommand{code{\isacharunderscore}deps}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
wenzelm@26907
   920
    \indexdef{HOL}{command}{code\_datatype}\hypertarget{command.HOL.code-datatype}{\hyperlink{command.HOL.code-datatype}{\mbox{\isa{\isacommand{code{\isacharunderscore}datatype}}}}} & : & \isartrans{theory}{theory} \\
wenzelm@26907
   921
    \indexdef{HOL}{command}{code\_const}\hypertarget{command.HOL.code-const}{\hyperlink{command.HOL.code-const}{\mbox{\isa{\isacommand{code{\isacharunderscore}const}}}}} & : & \isartrans{theory}{theory} \\
wenzelm@26907
   922
    \indexdef{HOL}{command}{code\_type}\hypertarget{command.HOL.code-type}{\hyperlink{command.HOL.code-type}{\mbox{\isa{\isacommand{code{\isacharunderscore}type}}}}} & : & \isartrans{theory}{theory} \\
wenzelm@26907
   923
    \indexdef{HOL}{command}{code\_class}\hypertarget{command.HOL.code-class}{\hyperlink{command.HOL.code-class}{\mbox{\isa{\isacommand{code{\isacharunderscore}class}}}}} & : & \isartrans{theory}{theory} \\
wenzelm@26907
   924
    \indexdef{HOL}{command}{code\_instance}\hypertarget{command.HOL.code-instance}{\hyperlink{command.HOL.code-instance}{\mbox{\isa{\isacommand{code{\isacharunderscore}instance}}}}} & : & \isartrans{theory}{theory} \\
wenzelm@26907
   925
    \indexdef{HOL}{command}{code\_monad}\hypertarget{command.HOL.code-monad}{\hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isacharunderscore}monad}}}}} & : & \isartrans{theory}{theory} \\
wenzelm@26907
   926
    \indexdef{HOL}{command}{code\_reserved}\hypertarget{command.HOL.code-reserved}{\hyperlink{command.HOL.code-reserved}{\mbox{\isa{\isacommand{code{\isacharunderscore}reserved}}}}} & : & \isartrans{theory}{theory} \\
wenzelm@26907
   927
    \indexdef{HOL}{command}{code\_include}\hypertarget{command.HOL.code-include}{\hyperlink{command.HOL.code-include}{\mbox{\isa{\isacommand{code{\isacharunderscore}include}}}}} & : & \isartrans{theory}{theory} \\
wenzelm@26907
   928
    \indexdef{HOL}{command}{code\_modulename}\hypertarget{command.HOL.code-modulename}{\hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isacharunderscore}modulename}}}}} & : & \isartrans{theory}{theory} \\
haftmann@27103
   929
    \indexdef{HOL}{command}{code\_abort}\hypertarget{command.HOL.code-abort}{\hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isacharunderscore}abort}}}}} & : & \isartrans{theory}{theory} \\
wenzelm@26907
   930
    \indexdef{HOL}{command}{print\_codesetup}\hypertarget{command.HOL.print-codesetup}{\hyperlink{command.HOL.print-codesetup}{\mbox{\isa{\isacommand{print{\isacharunderscore}codesetup}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
wenzelm@26902
   931
    \indexdef{HOL}{attribute}{code}\hypertarget{attribute.HOL.code}{\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}} & : & \isaratt \\
wenzelm@26849
   932
  \end{matharray}
wenzelm@26849
   933
wenzelm@26849
   934
  \begin{rail}
wenzelm@26849
   935
    'export\_code' ( constexpr + ) ? \\
wenzelm@26849
   936
      ( ( 'in' target ( 'module\_name' string ) ? \\
wenzelm@26849
   937
        ( 'file' ( string | '-' ) ) ? ( '(' args ')' ) ?) + ) ?
wenzelm@26849
   938
    ;
wenzelm@26849
   939
wenzelm@26849
   940
    'code\_thms' ( constexpr + ) ?
wenzelm@26849
   941
    ;
wenzelm@26849
   942
wenzelm@26849
   943
    'code\_deps' ( constexpr + ) ?
wenzelm@26849
   944
    ;
wenzelm@26849
   945
wenzelm@26849
   946
    const: term
wenzelm@26849
   947
    ;
wenzelm@26849
   948
wenzelm@26849
   949
    constexpr: ( const | 'name.*' | '*' )
wenzelm@26849
   950
    ;
wenzelm@26849
   951
wenzelm@26849
   952
    typeconstructor: nameref
wenzelm@26849
   953
    ;
wenzelm@26849
   954
wenzelm@26849
   955
    class: nameref
wenzelm@26849
   956
    ;
wenzelm@26849
   957
wenzelm@26849
   958
    target: 'OCaml' | 'SML' | 'Haskell'
wenzelm@26849
   959
    ;
wenzelm@26849
   960
wenzelm@26849
   961
    'code\_datatype' const +
wenzelm@26849
   962
    ;
wenzelm@26849
   963
wenzelm@26849
   964
    'code\_const' (const + 'and') \\
wenzelm@26849
   965
      ( ( '(' target ( syntax ? + 'and' ) ')' ) + )
wenzelm@26849
   966
    ;
wenzelm@26849
   967
wenzelm@26849
   968
    'code\_type' (typeconstructor + 'and') \\
wenzelm@26849
   969
      ( ( '(' target ( syntax ? + 'and' ) ')' ) + )
wenzelm@26849
   970
    ;
wenzelm@26849
   971
wenzelm@26849
   972
    'code\_class' (class + 'and') \\
wenzelm@26849
   973
      ( ( '(' target \\
wenzelm@26849
   974
        ( ( string ('where' \\
wenzelm@26849
   975
          ( const ( '==' | equiv ) string ) + ) ? ) ? + 'and' ) ')' ) + )
wenzelm@26849
   976
    ;
wenzelm@26849
   977
wenzelm@26849
   978
    'code\_instance' (( typeconstructor '::' class ) + 'and') \\
wenzelm@26849
   979
      ( ( '(' target ( '-' ? + 'and' ) ')' ) + )
wenzelm@26849
   980
    ;
wenzelm@26849
   981
wenzelm@26849
   982
    'code\_monad' const const target
wenzelm@26849
   983
    ;
wenzelm@26849
   984
wenzelm@26849
   985
    'code\_reserved' target ( string + )
wenzelm@26849
   986
    ;
wenzelm@26849
   987
wenzelm@26849
   988
    'code\_include' target ( string ( string | '-') )
wenzelm@26849
   989
    ;
wenzelm@26849
   990
wenzelm@26849
   991
    'code\_modulename' target ( ( string string ) + )
wenzelm@26849
   992
    ;
wenzelm@26849
   993
haftmann@27452
   994
    'code\_abort' ( const + )
wenzelm@26849
   995
    ;
wenzelm@26849
   996
wenzelm@26849
   997
    syntax: string | ( 'infix' | 'infixl' | 'infixr' ) nat string
wenzelm@26849
   998
    ;
wenzelm@26849
   999
wenzelm@26849
  1000
    'code' ('func' | 'inline') ( 'del' )?
wenzelm@26849
  1001
    ;
wenzelm@26849
  1002
  \end{rail}
wenzelm@26849
  1003
wenzelm@26849
  1004
  \begin{descr}
wenzelm@26849
  1005
wenzelm@26907
  1006
  \item [\hyperlink{command.HOL.export-code}{\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}}] is the canonical interface
wenzelm@26849
  1007
  for generating and serializing code: for a given list of constants,
wenzelm@26849
  1008
  code is generated for the specified target languages.  Abstract code
wenzelm@26849
  1009
  is cached incrementally.  If no constant is given, the currently
wenzelm@26849
  1010
  cached code is serialized.  If no serialization instruction is
wenzelm@26849
  1011
  given, only abstract code is cached.
wenzelm@26849
  1012
wenzelm@26849
  1013
  Constants may be specified by giving them literally, referring to
wenzelm@26849
  1014
  all executable contants within a certain theory by giving \isa{{\isachardoublequote}name{\isachardot}{\isacharasterisk}{\isachardoublequote}}, or referring to \emph{all} executable constants currently
wenzelm@26849
  1015
  available by giving \isa{{\isachardoublequote}{\isacharasterisk}{\isachardoublequote}}.
wenzelm@26849
  1016
wenzelm@26849
  1017
  By default, for each involved theory one corresponding name space
wenzelm@26849
  1018
  module is generated.  Alternativly, a module name may be specified
wenzelm@26907
  1019
  after the \hyperlink{keyword.module-name}{\mbox{\isa{\isakeyword{module{\isacharunderscore}name}}}} keyword; then \emph{all} code is
wenzelm@26849
  1020
  placed in this module.
wenzelm@26849
  1021
wenzelm@26849
  1022
  For \emph{SML} and \emph{OCaml}, the file specification refers to a
wenzelm@26849
  1023
  single file; for \emph{Haskell}, it refers to a whole directory,
wenzelm@26849
  1024
  where code is generated in multiple files reflecting the module
wenzelm@26849
  1025
  hierarchy.  The file specification ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' denotes standard
wenzelm@26849
  1026
  output.  For \emph{SML}, omitting the file specification compiles
wenzelm@26849
  1027
  code internally in the context of the current ML session.
wenzelm@26849
  1028
wenzelm@26849
  1029
  Serializers take an optional list of arguments in parentheses.  For
wenzelm@26849
  1030
  \emph{Haskell} a module name prefix may be given using the ``\isa{{\isachardoublequote}root{\isacharcolon}{\isachardoublequote}}'' argument; ``\isa{string{\isacharunderscore}classes}'' adds a ``\verb|deriving (Read, Show)|'' clause to each appropriate datatype
wenzelm@26849
  1031
  declaration.
wenzelm@26849
  1032
wenzelm@26907
  1033
  \item [\hyperlink{command.HOL.code-thms}{\mbox{\isa{\isacommand{code{\isacharunderscore}thms}}}}] prints a list of theorems
wenzelm@26849
  1034
  representing the corresponding program containing all given
wenzelm@26849
  1035
  constants; if no constants are given, the currently cached code
wenzelm@26849
  1036
  theorems are printed.
wenzelm@26849
  1037
wenzelm@26907
  1038
  \item [\hyperlink{command.HOL.code-deps}{\mbox{\isa{\isacommand{code{\isacharunderscore}deps}}}}] visualizes dependencies of
wenzelm@26849
  1039
  theorems representing the corresponding program containing all given
wenzelm@26849
  1040
  constants; if no constants are given, the currently cached code
wenzelm@26849
  1041
  theorems are visualized.
wenzelm@26849
  1042
wenzelm@26907
  1043
  \item [\hyperlink{command.HOL.code-datatype}{\mbox{\isa{\isacommand{code{\isacharunderscore}datatype}}}}] specifies a constructor set
wenzelm@26849
  1044
  for a logical type.
wenzelm@26849
  1045
wenzelm@26907
  1046
  \item [\hyperlink{command.HOL.code-const}{\mbox{\isa{\isacommand{code{\isacharunderscore}const}}}}] associates a list of constants
wenzelm@26849
  1047
  with target-specific serializations; omitting a serialization
wenzelm@26849
  1048
  deletes an existing serialization.
wenzelm@26849
  1049
wenzelm@26907
  1050
  \item [\hyperlink{command.HOL.code-type}{\mbox{\isa{\isacommand{code{\isacharunderscore}type}}}}] associates a list of type
wenzelm@26849
  1051
  constructors with target-specific serializations; omitting a
wenzelm@26849
  1052
  serialization deletes an existing serialization.
wenzelm@26849
  1053
wenzelm@26907
  1054
  \item [\hyperlink{command.HOL.code-class}{\mbox{\isa{\isacommand{code{\isacharunderscore}class}}}}] associates a list of classes
wenzelm@26849
  1055
  with target-specific class names; in addition, constants associated
wenzelm@26849
  1056
  with this class may be given target-specific names used for instance
wenzelm@26849
  1057
  declarations; omitting a serialization deletes an existing
wenzelm@26849
  1058
  serialization.  This applies only to \emph{Haskell}.
wenzelm@26849
  1059
wenzelm@26907
  1060
  \item [\hyperlink{command.HOL.code-instance}{\mbox{\isa{\isacommand{code{\isacharunderscore}instance}}}}] declares a list of type
wenzelm@26849
  1061
  constructor / class instance relations as ``already present'' for a
wenzelm@26849
  1062
  given target.  Omitting a ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' deletes an existing
wenzelm@26849
  1063
  ``already present'' declaration.  This applies only to
wenzelm@26849
  1064
  \emph{Haskell}.
wenzelm@26849
  1065
wenzelm@26907
  1066
  \item [\hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isacharunderscore}monad}}}}] provides an auxiliary
wenzelm@27834
  1067
  mechanism to generate monadic code for Haskell.
wenzelm@26849
  1068
wenzelm@26907
  1069
  \item [\hyperlink{command.HOL.code-reserved}{\mbox{\isa{\isacommand{code{\isacharunderscore}reserved}}}}] declares a list of names as
wenzelm@26849
  1070
  reserved for a given target, preventing it to be shadowed by any
wenzelm@26849
  1071
  generated code.
wenzelm@26849
  1072
wenzelm@26907
  1073
  \item [\hyperlink{command.HOL.code-include}{\mbox{\isa{\isacommand{code{\isacharunderscore}include}}}}] adds arbitrary named content
wenzelm@27834
  1074
  (``include'') to generated code.  A ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' as last argument
wenzelm@26849
  1075
  will remove an already added ``include''.
wenzelm@26849
  1076
wenzelm@26907
  1077
  \item [\hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isacharunderscore}modulename}}}}] declares aliasings from
wenzelm@26849
  1078
  one module name onto another.
wenzelm@26849
  1079
haftmann@27103
  1080
  \item [\hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isacharunderscore}abort}}}}] declares constants which
haftmann@27452
  1081
  are not required to have a definition by means of defining equations;
haftmann@27103
  1082
  if needed these are implemented by program abort instead.
wenzelm@26849
  1083
wenzelm@26902
  1084
  \item [\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}~\isa{func}] explicitly selects (or
wenzelm@26849
  1085
  with option ``\isa{{\isachardoublequote}del{\isacharcolon}{\isachardoublequote}}'' deselects) a defining equation for
wenzelm@26849
  1086
  code generation.  Usually packages introducing defining equations
haftmann@27452
  1087
  provide a reasonable default setup for selection.
wenzelm@26849
  1088
wenzelm@26902
  1089
  \item [\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}\isa{inline}] declares (or with
wenzelm@26849
  1090
  option ``\isa{{\isachardoublequote}del{\isacharcolon}{\isachardoublequote}}'' removes) inlining theorems which are
wenzelm@26849
  1091
  applied as rewrite rules to any defining equation during
wenzelm@26849
  1092
  preprocessing.
wenzelm@26849
  1093
wenzelm@26907
  1094
  \item [\hyperlink{command.HOL.print-codesetup}{\mbox{\isa{\isacommand{print{\isacharunderscore}codesetup}}}}] gives an overview on
wenzelm@26849
  1095
  selected defining equations, code generator datatypes and
wenzelm@26849
  1096
  preprocessor setup.
wenzelm@26849
  1097
wenzelm@26849
  1098
  \end{descr}%
wenzelm@26849
  1099
\end{isamarkuptext}%
wenzelm@26849
  1100
\isamarkuptrue%
wenzelm@26849
  1101
%
wenzelm@27047
  1102
\isamarkupsection{Definition by specification \label{sec:hol-specification}%
wenzelm@27047
  1103
}
wenzelm@27047
  1104
\isamarkuptrue%
wenzelm@27047
  1105
%
wenzelm@27047
  1106
\begin{isamarkuptext}%
wenzelm@27047
  1107
\begin{matharray}{rcl}
wenzelm@27047
  1108
    \indexdef{HOL}{command}{specification}\hypertarget{command.HOL.specification}{\hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}} & : & \isartrans{theory}{proof(prove)} \\
wenzelm@27047
  1109
    \indexdef{HOL}{command}{ax\_specification}\hypertarget{command.HOL.ax-specification}{\hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}}} & : & \isartrans{theory}{proof(prove)} \\
wenzelm@27047
  1110
  \end{matharray}
wenzelm@27047
  1111
wenzelm@27047
  1112
  \begin{rail}
wenzelm@27047
  1113
  ('specification' | 'ax\_specification') '(' (decl +) ')' \\ (thmdecl? prop +)
wenzelm@27047
  1114
  ;
wenzelm@27047
  1115
  decl: ((name ':')? term '(' 'overloaded' ')'?)
wenzelm@27047
  1116
  \end{rail}
wenzelm@27047
  1117
wenzelm@27047
  1118
  \begin{descr}
wenzelm@27047
  1119
wenzelm@27047
  1120
  \item [\hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}~\isa{{\isachardoublequote}decls\ {\isasymphi}{\isachardoublequote}}] sets up a
wenzelm@27047
  1121
  goal stating the existence of terms with the properties specified to
wenzelm@27047
  1122
  hold for the constants given in \isa{decls}.  After finishing the
wenzelm@27047
  1123
  proof, the theory will be augmented with definitions for the given
wenzelm@27047
  1124
  constants, as well as with theorems stating the properties for these
wenzelm@27047
  1125
  constants.
wenzelm@27047
  1126
wenzelm@27047
  1127
  \item [\hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}}~\isa{{\isachardoublequote}decls\ {\isasymphi}{\isachardoublequote}}] sets
wenzelm@27047
  1128
  up a goal stating the existence of terms with the properties
wenzelm@27047
  1129
  specified to hold for the constants given in \isa{decls}.  After
wenzelm@27047
  1130
  finishing the proof, the theory will be augmented with axioms
wenzelm@27047
  1131
  expressing the properties given in the first place.
wenzelm@27047
  1132
wenzelm@27047
  1133
  \item [\isa{decl}] declares a constant to be defined by the
wenzelm@27047
  1134
  specification given.  The definition for the constant \isa{c} is
wenzelm@27047
  1135
  bound to the name \isa{c{\isacharunderscore}def} unless a theorem name is given in
wenzelm@27047
  1136
  the declaration.  Overloaded constants should be declared as such.
wenzelm@27047
  1137
wenzelm@27047
  1138
  \end{descr}
wenzelm@27047
  1139
wenzelm@27047
  1140
  Whether to use \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}} or \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}} is to some extent a matter of style.  \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}} introduces no new axioms, and so by
wenzelm@27047
  1141
  construction cannot introduce inconsistencies, whereas \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}} does introduce axioms, but only after the
wenzelm@27047
  1142
  user has explicitly proven it to be safe.  A practical issue must be
wenzelm@27047
  1143
  considered, though: After introducing two constants with the same
wenzelm@27047
  1144
  properties using \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}, one can prove
wenzelm@27047
  1145
  that the two constants are, in fact, equal.  If this might be a
wenzelm@27047
  1146
  problem, one should use \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}}.%
wenzelm@27047
  1147
\end{isamarkuptext}%
wenzelm@27047
  1148
\isamarkuptrue%
wenzelm@27047
  1149
%
wenzelm@26849
  1150
\isadelimtheory
wenzelm@26849
  1151
%
wenzelm@26849
  1152
\endisadelimtheory
wenzelm@26849
  1153
%
wenzelm@26849
  1154
\isatagtheory
wenzelm@26840
  1155
\isacommand{end}\isamarkupfalse%
wenzelm@26840
  1156
%
wenzelm@26840
  1157
\endisatagtheory
wenzelm@26840
  1158
{\isafoldtheory}%
wenzelm@26840
  1159
%
wenzelm@26840
  1160
\isadelimtheory
wenzelm@26840
  1161
%
wenzelm@26840
  1162
\endisadelimtheory
wenzelm@26849
  1163
\isanewline
wenzelm@26840
  1164
\end{isabellebody}%
wenzelm@26840
  1165
%%% Local Variables:
wenzelm@26840
  1166
%%% mode: latex
wenzelm@26840
  1167
%%% TeX-master: "root"
wenzelm@26840
  1168
%%% End: