doc-src/IsarRef/Thy/document/HOL_Specific.tex
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\begin{isabellebody}%
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\def\isabellecontext{HOL{\isacharunderscore}Specific}%
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\isadelimtheory
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\isanewline
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\isanewline
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\endisadelimtheory
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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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\isadelimtheory
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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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\isamarkupsection{Primitive types \label{sec:hol-typedef}%
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}
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\isamarkuptrue%
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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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\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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\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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  \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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  \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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  \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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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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  \begin{enumerate}
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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.
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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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  \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.
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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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  \end{enumerate}%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\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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    ;
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    'rep\_datatype' ('(' (name +) ')')? (term +)
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    ;
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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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  \end{rail}
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  \begin{descr}
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  \item [\hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}}] defines inductive datatypes in
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  HOL.
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  \item [\hyperlink{command.HOL.rep-datatype}{\mbox{\isa{\isacommand{rep{\isacharunderscore}datatype}}}}] represents existing types as
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   388
  inductive ones, generating the standard infrastructure of derived
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  concepts (primitive recursion etc.).
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   390
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  \end{descr}
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   392
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  The induction and exhaustion theorems generated provide case names
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  according to the constructors involved, while parameters are named
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  after the types (see also \secref{sec:cases-induct}).
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diff changeset
   397
  See \cite{isabelle-HOL} for more details on datatypes, but beware of
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   398
  the old-style theory syntax being used there!  Apart from proper
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   399
  proof methods for case-analysis and induction, there are also
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   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
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   401
  to refer directly to the internal structure of subgoals (including
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   402
  internally bound parameters).%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   403
\end{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   404
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   405
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   406
\isamarkupsection{Recursive functions \label{sec:recursion}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   407
}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   408
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   409
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   410
\begin{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   411
\begin{matharray}{rcl}
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   412
    \indexdef{HOL}{command}{primrec}\hypertarget{command.HOL.primrec}{\hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}}} & : & \isarkeep{local{\dsh}theory} \\
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   413
    \indexdef{HOL}{command}{fun}\hypertarget{command.HOL.fun}{\hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}}} & : & \isarkeep{local{\dsh}theory} \\
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   414
    \indexdef{HOL}{command}{function}\hypertarget{command.HOL.function}{\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}} & : & \isartrans{local{\dsh}theory}{proof(prove)} \\
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   415
    \indexdef{HOL}{command}{termination}\hypertarget{command.HOL.termination}{\hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}} & : & \isartrans{local{\dsh}theory}{proof(prove)} \\
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   416
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   417
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   418
  \begin{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   419
    'primrec' target? fixes 'where' equations
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   420
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   421
    equations: (thmdecl? prop + '|')
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   422
    ;
26987
978cefd606ad updated generated file;
wenzelm
parents: 26907
diff changeset
   423
    ('fun' | 'function') target? functionopts? fixes 'where' clauses
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   424
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   425
    clauses: (thmdecl? prop ('(' 'otherwise' ')')? + '|')
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   426
    ;
26987
978cefd606ad updated generated file;
wenzelm
parents: 26907
diff changeset
   427
    functionopts: '(' (('sequential' | 'domintros' | 'tailrec' | 'default' term) + ',') ')'
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   428
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   429
    'termination' ( term )?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   430
  \end{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   431
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   432
  \begin{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   433
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   434
  \item [\hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}}] defines primitive recursive
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   435
  functions over datatypes, see also \cite{isabelle-HOL}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   436
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   437
  \item [\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}] defines functions by general
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   438
  wellfounded recursion. A detailed description with examples can be
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   439
  found in \cite{isabelle-function}. The function is specified by a
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   440
  set of (possibly conditional) recursive equations with arbitrary
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   441
  pattern matching. The command generates proof obligations for the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   442
  completeness and the compatibility of patterns.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   443
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   444
  The defined function is considered partial, and the resulting
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   445
  simplification rules (named \isa{{\isachardoublequote}f{\isachardot}psimps{\isachardoublequote}}) and induction rule
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   446
  (named \isa{{\isachardoublequote}f{\isachardot}pinduct{\isachardoublequote}}) are guarded by a generated domain
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   447
  predicate \isa{{\isachardoublequote}f{\isacharunderscore}dom{\isachardoublequote}}. The \hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   448
  command can then be used to establish that the function is total.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   449
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   450
  \item [\hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}}] is a shorthand notation for
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   451
  ``\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}~\isa{{\isachardoublequote}{\isacharparenleft}sequential{\isacharparenright}{\isachardoublequote}}, followed by
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   452
  automated proof attempts regarding pattern matching and termination.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   453
  See \cite{isabelle-function} for further details.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   454
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   455
  \item [\hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}~\isa{f}] commences a
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   456
  termination proof for the previously defined function \isa{f}.  If
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   457
  this is omitted, the command refers to the most recent function
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   458
  definition.  After the proof is closed, the recursive equations and
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   459
  the induction principle is established.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   460
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   461
  \end{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   462
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   463
  %FIXME check
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   464
27452
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27124
diff changeset
   465
  Recursive definitions introduced by the \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27124
diff changeset
   466
  command accommodate
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   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)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   468
  refers to a specific induction rule, with parameters named according
27452
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27124
diff changeset
   469
  to the user-specified equations.
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27124
diff changeset
   470
  For the \hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}} the induction principle coincides
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27124
diff changeset
   471
  with structural recursion on the datatype the recursion is carried
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27124
diff changeset
   472
  out.
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27124
diff changeset
   473
  Case names of \hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}} are that of the datatypes involved, while those of
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   474
  \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} are numbered (starting from 1).
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   475
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   476
  The equations provided by these packages may be referred later as
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   477
  theorem list \isa{{\isachardoublequote}f{\isachardot}simps{\isachardoublequote}}, where \isa{f} is the (collective)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   478
  name of the functions defined.  Individual equations may be named
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   479
  explicitly as well.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   480
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   481
  The \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} command accepts the following
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   482
  options.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   483
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   484
  \begin{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   485
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   486
  \item [\isa{sequential}] enables a preprocessor which
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   487
  disambiguates overlapping patterns by making them mutually disjoint.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   488
  Earlier equations take precedence over later ones.  This allows to
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   489
  give the specification in a format very similar to functional
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   490
  programming.  Note that the resulting simplification and induction
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   491
  rules correspond to the transformed specification, not the one given
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   492
  originally. This usually means that each equation given by the user
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   493
  may result in several theroems.  Also note that this automatic
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   494
  transformation only works for ML-style datatype patterns.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   495
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   496
  \item [\isa{domintros}] enables the automated generation of
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   497
  introduction rules for the domain predicate. While mostly not
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   498
  needed, they can be helpful in some proofs about partial functions.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   499
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   500
  \item [\isa{tailrec}] generates the unconstrained recursive
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   501
  equations even without a termination proof, provided that the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   502
  function is tail-recursive. This currently only works
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   503
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   504
  \item [\isa{{\isachardoublequote}default\ d{\isachardoublequote}}] allows to specify a default value for a
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   505
  (partial) function, which will ensure that \isa{{\isachardoublequote}f\ x\ {\isacharequal}\ d\ x{\isachardoublequote}}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   506
  whenever \isa{{\isachardoublequote}x\ {\isasymnotin}\ f{\isacharunderscore}dom{\isachardoublequote}}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   507
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   508
  \end{descr}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   509
\end{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   510
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   511
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   512
\isamarkupsubsection{Proof methods related to recursive definitions%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   513
}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   514
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   515
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   516
\begin{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   517
\begin{matharray}{rcl}
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   518
    \indexdef{HOL}{method}{pat\_completeness}\hypertarget{method.HOL.pat-completeness}{\hyperlink{method.HOL.pat-completeness}{\mbox{\isa{pat{\isacharunderscore}completeness}}}} & : & \isarmeth \\
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   519
    \indexdef{HOL}{method}{relation}\hypertarget{method.HOL.relation}{\hyperlink{method.HOL.relation}{\mbox{\isa{relation}}}} & : & \isarmeth \\
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   520
    \indexdef{HOL}{method}{lexicographic\_order}\hypertarget{method.HOL.lexicographic-order}{\hyperlink{method.HOL.lexicographic-order}{\mbox{\isa{lexicographic{\isacharunderscore}order}}}} & : & \isarmeth \\
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   521
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   522
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   523
  \begin{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   524
    'relation' term
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   525
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   526
    'lexicographic\_order' (clasimpmod *)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   527
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   528
  \end{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   529
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   530
  \begin{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   531
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   532
  \item [\hyperlink{method.HOL.pat-completeness}{\mbox{\isa{pat{\isacharunderscore}completeness}}}] is a specialized method to
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   533
  solve goals regarding the completeness of pattern matching, as
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   534
  required by the \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} package (cf.\
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   535
  \cite{isabelle-function}).
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   536
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   537
  \item [\hyperlink{method.HOL.relation}{\mbox{\isa{relation}}}~\isa{R}] introduces a termination
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   538
  proof using the relation \isa{R}.  The resulting proof state will
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   539
  contain goals expressing that \isa{R} is wellfounded, and that the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   540
  arguments of recursive calls decrease with respect to \isa{R}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   541
  Usually, this method is used as the initial proof step of manual
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   542
  termination proofs.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   543
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   544
  \item [\hyperlink{method.HOL.lexicographic-order}{\mbox{\isa{lexicographic{\isacharunderscore}order}}}] attempts a fully
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   545
  automated termination proof by searching for a lexicographic
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   546
  combination of size measures on the arguments of the function. The
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   547
  method accepts the same arguments as the \hyperlink{method.auto}{\mbox{\isa{auto}}} method,
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   548
  which it uses internally to prove local descents.  The same context
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   549
  modifiers as for \hyperlink{method.auto}{\mbox{\isa{auto}}} are accepted, see
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   550
  \secref{sec:clasimp}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   551
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   552
  In case of failure, extensive information is printed, which can help
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   553
  to analyse the situation (cf.\ \cite{isabelle-function}).
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   554
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   555
  \end{descr}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   556
\end{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   557
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   558
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   559
\isamarkupsubsection{Old-style recursive function definitions (TFL)%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   560
}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   561
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   562
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   563
\begin{isamarkuptext}%
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   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.
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   565
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   566
  \begin{matharray}{rcl}
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   567
    \indexdef{HOL}{command}{recdef}\hypertarget{command.HOL.recdef}{\hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}}} & : & \isartrans{theory}{theory} \\
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   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)} \\
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   569
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   570
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   571
  \begin{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   572
    'recdef' ('(' 'permissive' ')')? \\ name term (prop +) hints?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   573
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   574
    recdeftc thmdecl? tc
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   575
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   576
    hints: '(' 'hints' (recdefmod *) ')'
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   577
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   578
    recdefmod: (('recdef\_simp' | 'recdef\_cong' | 'recdef\_wf') (() | 'add' | 'del') ':' thmrefs) | clasimpmod
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   579
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   580
    tc: nameref ('(' nat ')')?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   581
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   582
  \end{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   583
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   584
  \begin{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   585
  
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   586
  \item [\hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}}] defines general well-founded
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   587
  recursive functions (using the TFL package), see also
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   588
  \cite{isabelle-HOL}.  The ``\isa{{\isachardoublequote}{\isacharparenleft}permissive{\isacharparenright}{\isachardoublequote}}'' option tells
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   589
  TFL to recover from failed proof attempts, returning unfinished
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   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
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   591
  automated proof process of TFL.  Additional \hyperlink{syntax.clasimpmod}{\mbox{\isa{clasimpmod}}}
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   592
  declarations (cf.\ \secref{sec:clasimp}) may be given to tune the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   593
  context of the Simplifier (cf.\ \secref{sec:simplifier}) and
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   594
  Classical reasoner (cf.\ \secref{sec:classical}).
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   595
  
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   596
  \item [\hyperlink{command.HOL.recdef-tc}{\mbox{\isa{\isacommand{recdef{\isacharunderscore}tc}}}}~\isa{{\isachardoublequote}c\ {\isacharparenleft}i{\isacharparenright}{\isachardoublequote}}] recommences the
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   597
  proof for leftover termination condition number \isa{i} (default
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   598
  1) as generated by a \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} definition of
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   599
  constant \isa{c}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   600
  
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   601
  Note that in most cases, \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} is able to finish
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   602
  its internal proofs without manual intervention.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   603
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   604
  \end{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   605
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   606
  \medskip Hints for \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} may be also declared
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   607
  globally, using the following attributes.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   608
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   609
  \begin{matharray}{rcl}
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   610
    \indexdef{HOL}{attribute}{recdef\_simp}\hypertarget{attribute.HOL.recdef-simp}{\hyperlink{attribute.HOL.recdef-simp}{\mbox{\isa{recdef{\isacharunderscore}simp}}}} & : & \isaratt \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   611
    \indexdef{HOL}{attribute}{recdef\_cong}\hypertarget{attribute.HOL.recdef-cong}{\hyperlink{attribute.HOL.recdef-cong}{\mbox{\isa{recdef{\isacharunderscore}cong}}}} & : & \isaratt \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   612
    \indexdef{HOL}{attribute}{recdef\_wf}\hypertarget{attribute.HOL.recdef-wf}{\hyperlink{attribute.HOL.recdef-wf}{\mbox{\isa{recdef{\isacharunderscore}wf}}}} & : & \isaratt \\
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   613
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   614
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   615
  \begin{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   616
    ('recdef\_simp' | 'recdef\_cong' | 'recdef\_wf') (() | 'add' | 'del')
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   617
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   618
  \end{rail}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   619
\end{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   620
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   621
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   622
\isamarkupsection{Inductive and coinductive definitions \label{sec:hol-inductive}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   623
}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   624
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   625
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   626
\begin{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   627
An \textbf{inductive definition} specifies the least predicate (or
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   628
  set) \isa{R} closed under given rules: applying a rule to elements
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   629
  of \isa{R} yields a result within \isa{R}.  For example, a
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   630
  structural operational semantics is an inductive definition of an
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   631
  evaluation relation.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   632
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   633
  Dually, a \textbf{coinductive definition} specifies the greatest
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   634
  predicate~/ set \isa{R} that is consistent with given rules: every
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   635
  element of \isa{R} can be seen as arising by applying a rule to
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   636
  elements of \isa{R}.  An important example is using bisimulation
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   637
  relations to formalise equivalence of processes and infinite data
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   638
  structures.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   639
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   640
  \medskip The HOL package is related to the ZF one, which is
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   641
  described in a separate paper,\footnote{It appeared in CADE
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   642
  \cite{paulson-CADE}; a longer version is distributed with Isabelle.}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   643
  which you should refer to in case of difficulties.  The package is
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   644
  simpler than that of ZF thanks to implicit type-checking in HOL.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   645
  The types of the (co)inductive predicates (or sets) determine the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   646
  domain of the fixedpoint definition, and the package does not have
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   647
  to use inference rules for type-checking.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   648
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   649
  \begin{matharray}{rcl}
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   650
    \indexdef{HOL}{command}{inductive}\hypertarget{command.HOL.inductive}{\hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}}} & : & \isarkeep{local{\dsh}theory} \\
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   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} \\
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   652
    \indexdef{HOL}{command}{coinductive}\hypertarget{command.HOL.coinductive}{\hyperlink{command.HOL.coinductive}{\mbox{\isa{\isacommand{coinductive}}}}} & : & \isarkeep{local{\dsh}theory} \\
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   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} \\
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   654
    \indexdef{HOL}{attribute}{mono}\hypertarget{attribute.HOL.mono}{\hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}}} & : & \isaratt \\
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   655
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   656
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   657
  \begin{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   658
    ('inductive' | 'inductive\_set' | 'coinductive' | 'coinductive\_set') target? fixes ('for' fixes)? \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   659
    ('where' clauses)? ('monos' thmrefs)?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   660
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   661
    clauses: (thmdecl? prop + '|')
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   662
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   663
    'mono' (() | 'add' | 'del')
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   664
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   665
  \end{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   666
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   667
  \begin{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   668
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   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
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   670
  introduction rules given in the \hyperlink{keyword.where}{\mbox{\isa{\isakeyword{where}}}} part.  The
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   671
  optional \hyperlink{keyword.for}{\mbox{\isa{\isakeyword{for}}}} part contains a list of parameters of the
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   672
  (co)inductive predicates that remain fixed throughout the
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   673
  definition.  The optional \hyperlink{keyword.monos}{\mbox{\isa{\isakeyword{monos}}}} section contains
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   674
  \emph{monotonicity theorems}, which are required for each operator
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   675
  applied to a recursive set in the introduction rules.  There
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   676
  \emph{must} be a theorem of the form \isa{{\isachardoublequote}A\ {\isasymle}\ B\ {\isasymLongrightarrow}\ M\ A\ {\isasymle}\ M\ B{\isachardoublequote}},
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   677
  for each premise \isa{{\isachardoublequote}M\ R\isactrlsub i\ t{\isachardoublequote}} in an introduction rule!
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   678
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   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,
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   680
  allowing the definition of (co)inductive sets.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   681
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   682
  \item [\hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}}] declares monotonicity rules.  These
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   683
  rule are involved in the automated monotonicity proof of \hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}}.
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   684
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   685
  \end{descr}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   686
\end{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   687
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   688
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   689
\isamarkupsubsection{Derived rules%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   690
}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   691
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   692
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   693
\begin{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   694
Each (co)inductive definition \isa{R} adds definitions to the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   695
  theory and also proves some theorems:
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   696
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   697
  \begin{description}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   698
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   699
  \item [\isa{R{\isachardot}intros}] is the list of introduction rules as proven
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   700
  theorems, for the recursive predicates (or sets).  The rules are
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   701
  also available individually, using the names given them in the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   702
  theory file;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   703
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   704
  \item [\isa{R{\isachardot}cases}] is the case analysis (or elimination) rule;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   705
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   706
  \item [\isa{R{\isachardot}induct} or \isa{R{\isachardot}coinduct}] is the (co)induction
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   707
  rule.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   708
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   709
  \end{description}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   710
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   711
  When several predicates \isa{{\isachardoublequote}R\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ R\isactrlsub n{\isachardoublequote}} are
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   712
  defined simultaneously, the list of introduction rules is called
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   713
  \isa{{\isachardoublequote}R\isactrlsub {\isadigit{1}}{\isacharunderscore}{\isasymdots}{\isacharunderscore}R\isactrlsub n{\isachardot}intros{\isachardoublequote}}, the case analysis rules are
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   714
  called \isa{{\isachardoublequote}R\isactrlsub {\isadigit{1}}{\isachardot}cases{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ R\isactrlsub n{\isachardot}cases{\isachardoublequote}}, and the list
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   715
  of mutual induction rules is called \isa{{\isachardoublequote}R\isactrlsub {\isadigit{1}}{\isacharunderscore}{\isasymdots}{\isacharunderscore}R\isactrlsub n{\isachardot}inducts{\isachardoublequote}}.%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   716
\end{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   717
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   718
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   719
\isamarkupsubsection{Monotonicity theorems%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   720
}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   721
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   722
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   723
\begin{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   724
Each theory contains a default set of theorems that are used in
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   725
  monotonicity proofs.  New rules can be added to this set via the
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   726
  \hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}} attribute.  The HOL theory \isa{Inductive}
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   727
  shows how this is done.  In general, the following monotonicity
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   728
  theorems may be added:
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   729
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   730
  \begin{itemize}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   731
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   732
  \item Theorems of the form \isa{{\isachardoublequote}A\ {\isasymle}\ B\ {\isasymLongrightarrow}\ M\ A\ {\isasymle}\ M\ B{\isachardoublequote}}, for proving
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   733
  monotonicity of inductive definitions whose introduction rules have
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   734
  premises involving terms such as \isa{{\isachardoublequote}M\ R\isactrlsub i\ t{\isachardoublequote}}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   735
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   736
  \item Monotonicity theorems for logical operators, which are of the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   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
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   738
  the case of the operator \isa{{\isachardoublequote}{\isasymor}{\isachardoublequote}}, the corresponding theorem is
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   739
  \[
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   740
  \infer{\isa{{\isachardoublequote}P\isactrlsub {\isadigit{1}}\ {\isasymor}\ P\isactrlsub {\isadigit{2}}\ {\isasymlongrightarrow}\ Q\isactrlsub {\isadigit{1}}\ {\isasymor}\ Q\isactrlsub {\isadigit{2}}{\isachardoublequote}}}{\isa{{\isachardoublequote}P\isactrlsub {\isadigit{1}}\ {\isasymlongrightarrow}\ Q\isactrlsub {\isadigit{1}}{\isachardoublequote}} & \isa{{\isachardoublequote}P\isactrlsub {\isadigit{2}}\ {\isasymlongrightarrow}\ Q\isactrlsub {\isadigit{2}}{\isachardoublequote}}}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   741
  \]
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   742
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   743
  \item De Morgan style equations for reasoning about the ``polarity''
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   744
  of expressions, e.g.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   745
  \[
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   746
  \isa{{\isachardoublequote}{\isasymnot}\ {\isasymnot}\ P\ {\isasymlongleftrightarrow}\ P{\isachardoublequote}} \qquad\qquad
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   747
  \isa{{\isachardoublequote}{\isasymnot}\ {\isacharparenleft}P\ {\isasymand}\ Q{\isacharparenright}\ {\isasymlongleftrightarrow}\ {\isasymnot}\ P\ {\isasymor}\ {\isasymnot}\ Q{\isachardoublequote}}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   748
  \]
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   749
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   750
  \item Equations for reducing complex operators to more primitive
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   751
  ones whose monotonicity can easily be proved, e.g.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   752
  \[
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   753
  \isa{{\isachardoublequote}{\isacharparenleft}P\ {\isasymlongrightarrow}\ Q{\isacharparenright}\ {\isasymlongleftrightarrow}\ {\isasymnot}\ P\ {\isasymor}\ Q{\isachardoublequote}} \qquad\qquad
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   754
  \isa{{\isachardoublequote}Ball\ A\ P\ {\isasymequiv}\ {\isasymforall}x{\isachardot}\ x\ {\isasymin}\ A\ {\isasymlongrightarrow}\ P\ x{\isachardoublequote}}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   755
  \]
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   756
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   757
  \end{itemize}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   758
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   759
  %FIXME: Example of an inductive definition%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   760
\end{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   761
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   762
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   763
\isamarkupsection{Arithmetic proof support%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   764
}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   765
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   766
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   767
\begin{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   768
\begin{matharray}{rcl}
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   769
    \indexdef{HOL}{method}{arith}\hypertarget{method.HOL.arith}{\hyperlink{method.HOL.arith}{\mbox{\isa{arith}}}} & : & \isarmeth \\
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   770
    \indexdef{HOL}{attribute}{arith\_split}\hypertarget{attribute.HOL.arith-split}{\hyperlink{attribute.HOL.arith-split}{\mbox{\isa{arith{\isacharunderscore}split}}}} & : & \isaratt \\
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   771
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   772
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   773
  The \hyperlink{method.HOL.arith}{\mbox{\isa{arith}}} method decides linear arithmetic problems
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   774
  (on types \isa{nat}, \isa{int}, \isa{real}).  Any current
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   775
  facts are inserted into the goal before running the procedure.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   776
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   777
  The \hyperlink{attribute.HOL.arith-split}{\mbox{\isa{arith{\isacharunderscore}split}}} attribute declares case split
26895
d066f9db833b updated generated file;
wenzelm
parents: 26861
diff changeset
   778
  rules to be expanded before the arithmetic procedure is invoked.
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   779
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   780
  Note that a simpler (but faster) version of arithmetic reasoning is
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   781
  already performed by the Simplifier.%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   782
\end{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   783
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   784
%
28603
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   785
\isamarkupsection{Invoking automated reasoning tools -- The Sledgehammer%
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   786
}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   787
\isamarkuptrue%
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   788
%
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   789
\begin{isamarkuptext}%
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   790
Isabelle/HOL includes a generic \emph{ATP manager} that allows
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   791
  external automated reasoning tools to crunch a pending goal.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   792
  Supported provers include E\footnote{\url{http://www.eprover.org}},
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   793
  SPASS\footnote{\url{http://www.spass-prover.org/}}, and Vampire.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   794
  There is also a wrapper to invoke provers remotely via the
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   795
  SystemOnTPTP\footnote{\url{http://www.cs.miami.edu/~tptp/cgi-bin/SystemOnTPTP}}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   796
  web service.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   797
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   798
  The problem passed to external provers consists of the goal together
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   799
  with a smart selection of lemmas from the current theory context.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   800
  The result of a successful proof search is some source text that
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   801
  usually reconstructs the proof within Isabelle, without requiring
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   802
  external provers again.  The Metis
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   803
  prover\footnote{\url{http://www.gilith.com/software/metis/}} that is
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   804
  integrated into Isabelle/HOL is being used here.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   805
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   806
  In this mode of operation, heavy means of automated reasoning are
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   807
  used as a strong relevance filter, while the main proof checking
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   808
  works via explicit inferences going through the Isabelle kernel.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   809
  Moreover, rechecking Isabelle proof texts with already specified
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   810
  auxiliary facts is much faster than performing fully automated
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   811
  search over and over again.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   812
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   813
  \begin{matharray}{rcl}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   814
    \indexdef{HOL}{command}{sledgehammer}\hypertarget{command.HOL.sledgehammer}{\hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{proof} \\
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   815
    \indexdef{HOL}{command}{print\_atps}\hypertarget{command.HOL.print-atps}{\hyperlink{command.HOL.print-atps}{\mbox{\isa{\isacommand{print{\isacharunderscore}atps}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   816
    \indexdef{HOL}{command}{atp\_info}\hypertarget{command.HOL.atp-info}{\hyperlink{command.HOL.atp-info}{\mbox{\isa{\isacommand{atp{\isacharunderscore}info}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{\cdot} \\
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   817
    \indexdef{HOL}{command}{atp\_kill}\hypertarget{command.HOL.atp-kill}{\hyperlink{command.HOL.atp-kill}{\mbox{\isa{\isacommand{atp{\isacharunderscore}kill}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{\cdot} \\
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   818
    \indexdef{HOL}{method}{metis}\hypertarget{method.HOL.metis}{\hyperlink{method.HOL.metis}{\mbox{\isa{metis}}}} & : & \isarmeth \\
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   819
  \end{matharray}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   820
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   821
  \begin{rail}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   822
  'sledgehammer' (nameref *)
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   823
  ;
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   824
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   825
  'metis' thmrefs
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   826
  ;
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   827
  \end{rail}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   828
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   829
  \begin{descr}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   830
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   831
  \item [\hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}}~\isa{{\isachardoublequote}prover\isactrlsub {\isadigit{1}}\ {\isasymdots}\ prover\isactrlsub n{\isachardoublequote}}] invokes the specified automated theorem provers on
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   832
  the first subgoal.  Provers are run in parallel, the first
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   833
  successful result is displayed, and the other attempts are
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   834
  terminated.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   835
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   836
  Provers are defined in the theory context, see also \hyperlink{command.HOL.print-atps}{\mbox{\isa{\isacommand{print{\isacharunderscore}atps}}}}.  If no provers are given as arguments to \hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}}, the system refers to the default defined as
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   837
  ``ATP provers'' preference by the user interface.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   838
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   839
  There are additional preferences for timeout (default: 60 seconds),
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   840
  and the maximum number of independent prover processes (default: 5);
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   841
  excessive provers are automatically terminated.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   842
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   843
  \item [\hyperlink{command.HOL.print-atps}{\mbox{\isa{\isacommand{print{\isacharunderscore}atps}}}}] prints the list of automated
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   844
  theorem provers available to the \hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   845
  command.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   846
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   847
  \item [\hyperlink{command.HOL.atp-info}{\mbox{\isa{\isacommand{atp{\isacharunderscore}info}}}}] prints information about presently
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   848
  running provers, including elapsed runtime, and the remaining time
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   849
  until timeout.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   850
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   851
  \item [\hyperlink{command.HOL.atp-kill}{\mbox{\isa{\isacommand{atp{\isacharunderscore}kill}}}}] terminates all presently running
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   852
  provers.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   853
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   854
  \item [\hyperlink{method.HOL.metis}{\mbox{\isa{metis}}}~\isa{{\isachardoublequote}facts{\isachardoublequote}}] invokes the Metis
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   855
  prover with the given facts.  Metis is an automated proof tool of
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   856
  medium strength, but is fully integrated into Isabelle/HOL, with
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   857
  explicit inferences going through the kernel.  Thus its results are
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   858
  guaranteed to be ``correct by construction''.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   859
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   860
  Note that all facts used with Metis need to be specified as explicit
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   861
  arguments.  There are no rule declarations as for other Isabelle
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   862
  provers, like \hyperlink{method.blast}{\mbox{\isa{blast}}} or \hyperlink{method.fast}{\mbox{\isa{fast}}}.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   863
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   864
  \end{descr}%
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   865
\end{isamarkuptext}%
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   866
\isamarkuptrue%
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   867
%
27124
e02d6e655e60 updated generated file;
wenzelm
parents: 27103
diff changeset
   868
\isamarkupsection{Unstructured cases analysis and induction \label{sec:hol-induct-tac}%
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   869
}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   870
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   871
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   872
\begin{isamarkuptext}%
27124
e02d6e655e60 updated generated file;
wenzelm
parents: 27103
diff changeset
   873
The following tools of Isabelle/HOL support cases analysis and
e02d6e655e60 updated generated file;
wenzelm
parents: 27103
diff changeset
   874
  induction in unstructured tactic scripts; see also
e02d6e655e60 updated generated file;
wenzelm
parents: 27103
diff changeset
   875
  \secref{sec:cases-induct} for proper Isar versions of similar ideas.
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   876
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   877
  \begin{matharray}{rcl}
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   878
    \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 \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   879
    \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 \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   880
    \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 \\
27124
e02d6e655e60 updated generated file;
wenzelm
parents: 27103
diff changeset
   881
    \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} \\
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   882
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   883
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   884
  \begin{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   885
    'case\_tac' goalspec? term rule?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   886
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   887
    'induct\_tac' goalspec? (insts * 'and') rule?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   888
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   889
    'ind\_cases' (prop +) ('for' (name +)) ?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   890
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   891
    'inductive\_cases' (thmdecl? (prop +) + 'and')
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   892
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   893
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   894
    rule: ('rule' ':' thmref)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   895
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   896
  \end{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   897
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   898
  \begin{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   899
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   900
  \item [\hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isacharunderscore}tac}}} and \hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isacharunderscore}tac}}}]
27124
e02d6e655e60 updated generated file;
wenzelm
parents: 27103
diff changeset
   901
  admit to reason about inductive types.  Rules are selected according
e02d6e655e60 updated generated file;
wenzelm
parents: 27103
diff changeset
   902
  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.
e02d6e655e60 updated generated file;
wenzelm
parents: 27103
diff changeset
   903
e02d6e655e60 updated generated file;
wenzelm
parents: 27103
diff changeset
   904
  These unstructured tactics feature both goal addressing and dynamic
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   905
  instantiation.  Note that named rule cases are \emph{not} provided
27124
e02d6e655e60 updated generated file;
wenzelm
parents: 27103
diff changeset
   906
  as would be by the proper \hyperlink{method.cases}{\mbox{\isa{cases}}} and \hyperlink{method.induct}{\mbox{\isa{induct}}} proof
e02d6e655e60 updated generated file;
wenzelm
parents: 27103
diff changeset
   907
  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
e02d6e655e60 updated generated file;
wenzelm
parents: 27103
diff changeset
   908
  statements, only the compact object-logic conclusion of the subgoal
e02d6e655e60 updated generated file;
wenzelm
parents: 27103
diff changeset
   909
  being addressed.
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   910
  
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   911
  \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
26861
e6fe036ec21d updated generated file;
wenzelm
parents: 26854
diff changeset
   912
  forward manner.
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   913
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   914
  While \hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isacharunderscore}cases}}} is a proof method to apply the
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   915
  result immediately as elimination rules, \hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isacharunderscore}cases}}}} provides case split theorems at the theory level
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   916
  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
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   917
  be generalized before applying the resulting rule.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   918
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   919
  \end{descr}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   920
\end{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   921
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   922
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   923
\isamarkupsection{Executable code%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   924
}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   925
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   926
%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   927
\begin{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   928
Isabelle/Pure provides two generic frameworks to support code
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   929
  generation from executable specifications.  Isabelle/HOL
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   930
  instantiates these mechanisms in a way that is amenable to end-user
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   931
  applications.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   932
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   933
  One framework generates code from both functional and relational
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   934
  programs to SML.  See \cite{isabelle-HOL} for further information
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   935
  (this actually covers the new-style theory format as well).
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   936
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   937
  \begin{matharray}{rcl}
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   938
    \indexdef{HOL}{command}{value}\hypertarget{command.HOL.value}{\hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   939
    \indexdef{HOL}{command}{code\_module}\hypertarget{command.HOL.code-module}{\hyperlink{command.HOL.code-module}{\mbox{\isa{\isacommand{code{\isacharunderscore}module}}}}} & : & \isartrans{theory}{theory} \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   940
    \indexdef{HOL}{command}{code\_library}\hypertarget{command.HOL.code-library}{\hyperlink{command.HOL.code-library}{\mbox{\isa{\isacommand{code{\isacharunderscore}library}}}}} & : & \isartrans{theory}{theory} \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   941
    \indexdef{HOL}{command}{consts\_code}\hypertarget{command.HOL.consts-code}{\hyperlink{command.HOL.consts-code}{\mbox{\isa{\isacommand{consts{\isacharunderscore}code}}}}} & : & \isartrans{theory}{theory} \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
   942
    \indexdef{HOL}{command}{types\_code}\hypertarget{command.HOL.types-code}{\hyperlink{command.HOL.types-code}{\mbox{\isa{\isacommand{types{\isacharunderscore}code}}}}} & : & \isartrans{theory}{theory} \\  
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   943
    \indexdef{HOL}{attribute}{code}\hypertarget{attribute.HOL.code}{\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}} & : & \isaratt \\
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   944
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   945
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   946
  \begin{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   947
  'value' term
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   948
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   949
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   950
  ( 'code\_module' | 'code\_library' ) modespec ? name ? \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   951
    ( 'file' name ) ? ( 'imports' ( name + ) ) ? \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   952
    'contains' ( ( name '=' term ) + | term + )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   953
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   954
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   955
  modespec: '(' ( name * ) ')'
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   956
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   957
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   958
  'consts\_code' (codespec +)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   959
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   960
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   961
  codespec: const template attachment ?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   962
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   963
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   964
  'types\_code' (tycodespec +)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   965
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   966
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   967
  tycodespec: name template attachment ?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   968
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   969
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   970
  const: term
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   971
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   972
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   973
  template: '(' string ')'
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   974
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   975
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   976
  attachment: 'attach' modespec ? verblbrace text verbrbrace
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   977
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   978
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   979
  'code' (name)?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   980
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   981
  \end{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   982
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   983
  \begin{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   984
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
   985
  \item [\hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}~\isa{t}] evaluates and prints a
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   986
  term using the code generator.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   987
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   988
  \end{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   989
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   990
  \medskip The other framework generates code from functional programs
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   991
  (including overloading using type classes) to SML \cite{SML}, OCaml
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   992
  \cite{OCaml} and Haskell \cite{haskell-revised-report}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   993
  Conceptually, code generation is split up in three steps:
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   994
  \emph{selection} of code theorems, \emph{translation} into an
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   995
  abstract executable view and \emph{serialization} to a specific
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   996
  \emph{target language}.  See \cite{isabelle-codegen} for an
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   997
  introduction on how to use it.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   998
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   999
  \begin{matharray}{rcl}
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1000
    \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} \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1001
    \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} \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1002
    \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} \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1003
    \indexdef{HOL}{command}{code\_datatype}\hypertarget{command.HOL.code-datatype}{\hyperlink{command.HOL.code-datatype}{\mbox{\isa{\isacommand{code{\isacharunderscore}datatype}}}}} & : & \isartrans{theory}{theory} \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1004
    \indexdef{HOL}{command}{code\_const}\hypertarget{command.HOL.code-const}{\hyperlink{command.HOL.code-const}{\mbox{\isa{\isacommand{code{\isacharunderscore}const}}}}} & : & \isartrans{theory}{theory} \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1005
    \indexdef{HOL}{command}{code\_type}\hypertarget{command.HOL.code-type}{\hyperlink{command.HOL.code-type}{\mbox{\isa{\isacommand{code{\isacharunderscore}type}}}}} & : & \isartrans{theory}{theory} \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1006
    \indexdef{HOL}{command}{code\_class}\hypertarget{command.HOL.code-class}{\hyperlink{command.HOL.code-class}{\mbox{\isa{\isacommand{code{\isacharunderscore}class}}}}} & : & \isartrans{theory}{theory} \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1007
    \indexdef{HOL}{command}{code\_instance}\hypertarget{command.HOL.code-instance}{\hyperlink{command.HOL.code-instance}{\mbox{\isa{\isacommand{code{\isacharunderscore}instance}}}}} & : & \isartrans{theory}{theory} \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1008
    \indexdef{HOL}{command}{code\_monad}\hypertarget{command.HOL.code-monad}{\hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isacharunderscore}monad}}}}} & : & \isartrans{theory}{theory} \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1009
    \indexdef{HOL}{command}{code\_reserved}\hypertarget{command.HOL.code-reserved}{\hyperlink{command.HOL.code-reserved}{\mbox{\isa{\isacommand{code{\isacharunderscore}reserved}}}}} & : & \isartrans{theory}{theory} \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1010
    \indexdef{HOL}{command}{code\_include}\hypertarget{command.HOL.code-include}{\hyperlink{command.HOL.code-include}{\mbox{\isa{\isacommand{code{\isacharunderscore}include}}}}} & : & \isartrans{theory}{theory} \\
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1011
    \indexdef{HOL}{command}{code\_modulename}\hypertarget{command.HOL.code-modulename}{\hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isacharunderscore}modulename}}}}} & : & \isartrans{theory}{theory} \\
27103
d8549f4d900b major refactorings in code generator modules
haftmann
parents: 27047
diff changeset
  1012
    \indexdef{HOL}{command}{code\_abort}\hypertarget{command.HOL.code-abort}{\hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isacharunderscore}abort}}}}} & : & \isartrans{theory}{theory} \\
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1013
    \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} \\
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
  1014
    \indexdef{HOL}{attribute}{code}\hypertarget{attribute.HOL.code}{\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}} & : & \isaratt \\
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1015
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1016
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1017
  \begin{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1018
    'export\_code' ( constexpr + ) ? \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1019
      ( ( 'in' target ( 'module\_name' string ) ? \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1020
        ( 'file' ( string | '-' ) ) ? ( '(' args ')' ) ?) + ) ?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1021
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1022
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1023
    'code\_thms' ( constexpr + ) ?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1024
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1025
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1026
    'code\_deps' ( constexpr + ) ?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1027
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1028
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1029
    const: term
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1030
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1031
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1032
    constexpr: ( const | 'name.*' | '*' )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1033
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1034
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1035
    typeconstructor: nameref
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1036
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1037
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1038
    class: nameref
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1039
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1040
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1041
    target: 'OCaml' | 'SML' | 'Haskell'
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1042
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1043
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1044
    'code\_datatype' const +
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1045
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1046
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1047
    'code\_const' (const + 'and') \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1048
      ( ( '(' target ( syntax ? + 'and' ) ')' ) + )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1049
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1050
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1051
    'code\_type' (typeconstructor + 'and') \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1052
      ( ( '(' target ( syntax ? + 'and' ) ')' ) + )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1053
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1054
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1055
    'code\_class' (class + 'and') \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1056
      ( ( '(' target \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1057
        ( ( string ('where' \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1058
          ( const ( '==' | equiv ) string ) + ) ? ) ? + 'and' ) ')' ) + )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1059
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1060
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1061
    'code\_instance' (( typeconstructor '::' class ) + 'and') \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1062
      ( ( '(' target ( '-' ? + 'and' ) ')' ) + )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1063
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1064
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1065
    'code\_monad' const const target
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1066
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1067
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1068
    'code\_reserved' target ( string + )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1069
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1070
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1071
    'code\_include' target ( string ( string | '-') )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1072
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1073
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1074
    'code\_modulename' target ( ( string string ) + )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1075
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1076
27452
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27124
diff changeset
  1077
    'code\_abort' ( const + )
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1078
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1079
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1080
    syntax: string | ( 'infix' | 'infixl' | 'infixr' ) nat string
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1081
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1082
28562
4e74209f113e `code func` now just `code`
haftmann
parents: 27834
diff changeset
  1083
    'code' ( 'inline' ) ? ( 'del' ) ?
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1084
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1085
  \end{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1086
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1087
  \begin{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1088
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1089
  \item [\hyperlink{command.HOL.export-code}{\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}}] is the canonical interface
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1090
  for generating and serializing code: for a given list of constants,
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1091
  code is generated for the specified target languages.  Abstract code
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1092
  is cached incrementally.  If no constant is given, the currently
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1093
  cached code is serialized.  If no serialization instruction is
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1094
  given, only abstract code is cached.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1095
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1096
  Constants may be specified by giving them literally, referring to
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1097
  all executable contants within a certain theory by giving \isa{{\isachardoublequote}name{\isachardot}{\isacharasterisk}{\isachardoublequote}}, or referring to \emph{all} executable constants currently
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1098
  available by giving \isa{{\isachardoublequote}{\isacharasterisk}{\isachardoublequote}}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1099
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1100
  By default, for each involved theory one corresponding name space
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1101
  module is generated.  Alternativly, a module name may be specified
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1102
  after the \hyperlink{keyword.module-name}{\mbox{\isa{\isakeyword{module{\isacharunderscore}name}}}} keyword; then \emph{all} code is
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1103
  placed in this module.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1104
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1105
  For \emph{SML} and \emph{OCaml}, the file specification refers to a
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1106
  single file; for \emph{Haskell}, it refers to a whole directory,
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1107
  where code is generated in multiple files reflecting the module
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1108
  hierarchy.  The file specification ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' denotes standard
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1109
  output.  For \emph{SML}, omitting the file specification compiles
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1110
  code internally in the context of the current ML session.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1111
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1112
  Serializers take an optional list of arguments in parentheses.  For
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1113
  \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
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1114
  declaration.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1115
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1116
  \item [\hyperlink{command.HOL.code-thms}{\mbox{\isa{\isacommand{code{\isacharunderscore}thms}}}}] prints a list of theorems
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1117
  representing the corresponding program containing all given
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1118
  constants; if no constants are given, the currently cached code
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1119
  theorems are printed.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1120
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1121
  \item [\hyperlink{command.HOL.code-deps}{\mbox{\isa{\isacommand{code{\isacharunderscore}deps}}}}] visualizes dependencies of
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1122
  theorems representing the corresponding program containing all given
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1123
  constants; if no constants are given, the currently cached code
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1124
  theorems are visualized.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1125
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1126
  \item [\hyperlink{command.HOL.code-datatype}{\mbox{\isa{\isacommand{code{\isacharunderscore}datatype}}}}] specifies a constructor set
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1127
  for a logical type.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1128
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1129
  \item [\hyperlink{command.HOL.code-const}{\mbox{\isa{\isacommand{code{\isacharunderscore}const}}}}] associates a list of constants
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1130
  with target-specific serializations; omitting a serialization
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1131
  deletes an existing serialization.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1132
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1133
  \item [\hyperlink{command.HOL.code-type}{\mbox{\isa{\isacommand{code{\isacharunderscore}type}}}}] associates a list of type
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1134
  constructors with target-specific serializations; omitting a
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1135
  serialization deletes an existing serialization.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1136
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1137
  \item [\hyperlink{command.HOL.code-class}{\mbox{\isa{\isacommand{code{\isacharunderscore}class}}}}] associates a list of classes
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1138
  with target-specific class names; in addition, constants associated
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1139
  with this class may be given target-specific names used for instance
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1140
  declarations; omitting a serialization deletes an existing
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1141
  serialization.  This applies only to \emph{Haskell}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1142
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1143
  \item [\hyperlink{command.HOL.code-instance}{\mbox{\isa{\isacommand{code{\isacharunderscore}instance}}}}] declares a list of type
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1144
  constructor / class instance relations as ``already present'' for a
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1145
  given target.  Omitting a ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' deletes an existing
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1146
  ``already present'' declaration.  This applies only to
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1147
  \emph{Haskell}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1148
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1149
  \item [\hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isacharunderscore}monad}}}}] provides an auxiliary
27834
04562d200f02 updated generated file;
wenzelm
parents: 27452
diff changeset
  1150
  mechanism to generate monadic code for Haskell.
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1151
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1152
  \item [\hyperlink{command.HOL.code-reserved}{\mbox{\isa{\isacommand{code{\isacharunderscore}reserved}}}}] declares a list of names as
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1153
  reserved for a given target, preventing it to be shadowed by any
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1154
  generated code.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1155
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1156
  \item [\hyperlink{command.HOL.code-include}{\mbox{\isa{\isacommand{code{\isacharunderscore}include}}}}] adds arbitrary named content
27834
04562d200f02 updated generated file;
wenzelm
parents: 27452
diff changeset
  1157
  (``include'') to generated code.  A ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' as last argument
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1158
  will remove an already added ``include''.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1159
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1160
  \item [\hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isacharunderscore}modulename}}}}] declares aliasings from
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1161
  one module name onto another.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1162
27103
d8549f4d900b major refactorings in code generator modules
haftmann
parents: 27047
diff changeset
  1163
  \item [\hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isacharunderscore}abort}}}}] declares constants which
27452
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27124
diff changeset
  1164
  are not required to have a definition by means of defining equations;
27103
d8549f4d900b major refactorings in code generator modules
haftmann
parents: 27047
diff changeset
  1165
  if needed these are implemented by program abort instead.
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1166
28562
4e74209f113e `code func` now just `code`
haftmann
parents: 27834
diff changeset
  1167
  \item [\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}] explicitly selects (or
4e74209f113e `code func` now just `code`
haftmann
parents: 27834
diff changeset
  1168
  with option ``\isa{{\isachardoublequote}del{\isachardoublequote}}'' deselects) a defining equation for
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1169
  code generation.  Usually packages introducing defining equations
27452
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27124
diff changeset
  1170
  provide a reasonable default setup for selection.
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1171
26902
8db1e960d636 updated generated file;
wenzelm
parents: 26895
diff changeset
  1172
  \item [\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}\isa{inline}] declares (or with
28562
4e74209f113e `code func` now just `code`
haftmann
parents: 27834
diff changeset
  1173
  option ``\isa{{\isachardoublequote}del{\isachardoublequote}}'' removes) inlining theorems which are
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1174
  applied as rewrite rules to any defining equation during
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1175
  preprocessing.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1176
26907
75466ad27dd7 updated generated file;
wenzelm
parents: 26902
diff changeset
  1177
  \item [\hyperlink{command.HOL.print-codesetup}{\mbox{\isa{\isacommand{print{\isacharunderscore}codesetup}}}}] gives an overview on
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1178
  selected defining equations, code generator datatypes and
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1179
  preprocessor setup.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1180
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1181
  \end{descr}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1182
\end{isamarkuptext}%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1183
\isamarkuptrue%
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1184
%
27047
2dcdea037385 updated generated file;
wenzelm
parents: 27042
diff changeset
  1185
\isamarkupsection{Definition by specification \label{sec:hol-specification}%
2dcdea037385 updated generated file;
wenzelm
parents: 27042
diff changeset
  1186
}
2dcdea037385 updated generated file;
wenzelm
parents: 27042
diff changeset
  1187
\isamarkuptrue%
2dcdea037385 updated generated file;
wenzelm
parents: 27042
diff changeset
  1188
%
2dcdea037385 updated generated file;
wenzelm
parents: 27042
diff changeset
  1189
\begin{isamarkuptext}%
2dcdea037385 updated generated file;
wenzelm
parents: 27042
diff changeset
  1190
\begin{matharray}{rcl}
2dcdea037385 updated generated file;
wenzelm
parents: 27042
diff changeset
  1191
    \indexdef{HOL}{command}{specification}\hypertarget{command.HOL.specification}{\hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}} & : & \isartrans{theory}{proof(prove)} \\
2dcdea037385 updated generated file;
wenzelm
parents: 27042
diff changeset
  1192
    \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)} \\
2dcdea037385 updated generated file;
wenzelm
parents: 27042
diff changeset
  1193
  \end{matharray}
2dcdea037385 updated generated file;
wenzelm
parents: 27042
diff changeset