
wenzelm@26840: %
wenzelm@26840: \begin{isabellebody}%
wenzelm@26840: \def\isabellecontext{HOL{\isacharunderscore}Specific}%
wenzelm@26840: %
wenzelm@26840: \isadelimtheory
wenzelm@26840: \isanewline
wenzelm@26840: \isanewline
wenzelm@26840: %
wenzelm@26840: \endisadelimtheory
wenzelm@26840: %
wenzelm@26840: \isatagtheory
wenzelm@26840: \isacommand{theory}\isamarkupfalse%
wenzelm@26840: \ HOL{\isacharunderscore}Specific\isanewline
wenzelm@26849: \isakeyword{imports}\ Main\isanewline
wenzelm@26849: \isakeyword{begin}%
wenzelm@26849: \endisatagtheory
wenzelm@26849: {\isafoldtheory}%
wenzelm@26849: %
wenzelm@26849: \isadelimtheory
wenzelm@26849: %
wenzelm@26849: \endisadelimtheory
wenzelm@26849: %
wenzelm@26852: \isamarkupchapter{Isabelle/HOL \label{ch:hol}%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsection{Primitive types \label{sec:hol-typedef}%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: \begin{matharray}{rcl}
wenzelm@26849:     \indexdef{HOL}{command}{typedecl}\mbox{\isa{\isacommand{typedecl}}} & : & \isartrans{theory}{theory} \\
wenzelm@26849:     \indexdef{HOL}{command}{typedef}\mbox{\isa{\isacommand{typedef}}} & : & \isartrans{theory}{proof(prove)} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26849:   \begin{rail}
wenzelm@26849:     'typedecl' typespec infix?
wenzelm@26849:     ;
wenzelm@26849:     'typedef' altname? abstype '=' repset
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     altname: '(' (name | 'open' | 'open' name) ')'
wenzelm@26849:     ;
wenzelm@26849:     abstype: typespec infix?
wenzelm@26849:     ;
wenzelm@26849:     repset: term ('morphisms' name name)?
wenzelm@26849:     ;
wenzelm@26849:   \end{rail}
wenzelm@26849: 
wenzelm@26849:   \begin{descr}
wenzelm@26849:   
wenzelm@26849:   \item [\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 \mbox{\isa{\isacommand{typedecl}}} of
wenzelm@26849:   Isabelle/Pure (see \secref{sec:types-pure}), but also declares type
wenzelm@26849:   arity \isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}type{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ type{\isacharparenright}\ type{\isachardoublequote}}, making \isa{t} an
wenzelm@26849:   actual HOL type constructor.   %FIXME check, update
wenzelm@26849:   
wenzelm@26849:   \item [\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}.
wenzelm@26849:   After finishing the proof, the theory will be augmented by a
wenzelm@26849:   Gordon/HOL-style type definition, which establishes a bijection
wenzelm@26849:   between the representing set \isa{A} and the new type \isa{t}.
wenzelm@26849:   
wenzelm@26849:   Technically, \mbox{\isa{\isacommand{typedef}}} defines both a type \isa{t} and a set (term constant) of the same name (an alternative base
wenzelm@26849:   name may be given in parentheses).  The injection from type to set
wenzelm@26849:   is called \isa{Rep{\isacharunderscore}t}, its inverse \isa{Abs{\isacharunderscore}t} (this may be
wenzelm@26849:   changed via an explicit \mbox{\isa{\isakeyword{morphisms}}} declaration).
wenzelm@26849:   
wenzelm@26849:   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
wenzelm@26849:   corresponding injection/surjection pair (in both directions).  Rules
wenzelm@26849:   \isa{Rep{\isacharunderscore}t{\isacharunderscore}inject} and \isa{Abs{\isacharunderscore}t{\isacharunderscore}inject} provide a slightly
wenzelm@26849:   more convenient view on the injectivity part, suitable for automated
wenzelm@26849:   proof tools (e.g.\ in \mbox{\isa{simp}} or \mbox{\isa{iff}} declarations).
wenzelm@26849:   Rules \isa{Rep{\isacharunderscore}t{\isacharunderscore}cases}/\isa{Rep{\isacharunderscore}t{\isacharunderscore}induct}, and \isa{Abs{\isacharunderscore}t{\isacharunderscore}cases}/\isa{Abs{\isacharunderscore}t{\isacharunderscore}induct} provide alternative views on
wenzelm@26849:   surjectivity; these are already declared as set or type rules for
wenzelm@26849:   the generic \mbox{\isa{cases}} and \mbox{\isa{induct}} methods.
wenzelm@26849:   
wenzelm@26849:   An alternative name may be specified in parentheses; the default is
wenzelm@26849:   to use \isa{t} as indicated before.  The ``\isa{{\isachardoublequote}{\isacharparenleft}open{\isacharparenright}{\isachardoublequote}}''
wenzelm@26849:   declaration suppresses a separate constant definition for the
wenzelm@26849:   representing set.
wenzelm@26849: 
wenzelm@26849:   \end{descr}
wenzelm@26849: 
wenzelm@26849:   Note that raw type declarations are rarely used in practice; the
wenzelm@26849:   main application is with experimental (or even axiomatic!) theory
wenzelm@26849:   fragments.  Instead of primitive HOL type definitions, user-level
wenzelm@26849:   theories usually refer to higher-level packages such as \mbox{\isa{\isacommand{record}}} (see \secref{sec:hol-record}) or \mbox{\isa{\isacommand{datatype}}} (see \secref{sec:hol-datatype}).%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsection{Adhoc tuples%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: \begin{matharray}{rcl}
wenzelm@26849:     \mbox{\isa{split{\isacharunderscore}format}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isaratt \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26849:   \begin{rail}
wenzelm@26849:     'split\_format' (((name *) + 'and') | ('(' 'complete' ')'))
wenzelm@26849:     ;
wenzelm@26849:   \end{rail}
wenzelm@26849: 
wenzelm@26849:   \begin{descr}
wenzelm@26849:   
wenzelm@26849:   \item [\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
wenzelm@26849:   low-level tuple types into canonical form as specified by the
wenzelm@26849:   arguments given; the \isa{i}-th collection of arguments refers to
wenzelm@26849:   occurrences in premise \isa{i} of the rule.  The ``\isa{{\isachardoublequote}{\isacharparenleft}complete{\isacharparenright}{\isachardoublequote}}'' option causes \emph{all} arguments in function
wenzelm@26849:   applications to be represented canonically according to their tuple
wenzelm@26849:   type structure.
wenzelm@26849: 
wenzelm@26849:   Note that these operations tend to invent funny names for new local
wenzelm@26849:   parameters to be introduced.
wenzelm@26849: 
wenzelm@26849:   \end{descr}%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsection{Records \label{sec:hol-record}%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: In principle, records merely generalize the concept of tuples, where
wenzelm@26849:   components may be addressed by labels instead of just position.  The
wenzelm@26849:   logical infrastructure of records in Isabelle/HOL is slightly more
wenzelm@26849:   advanced, though, supporting truly extensible record schemes.  This
wenzelm@26849:   admits operations that are polymorphic with respect to record
wenzelm@26849:   extension, yielding ``object-oriented'' effects like (single)
wenzelm@26849:   inheritance.  See also \cite{NaraschewskiW-TPHOLs98} for more
wenzelm@26849:   details on object-oriented verification and record subtyping in HOL.%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsubsection{Basic concepts%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: Isabelle/HOL supports both \emph{fixed} and \emph{schematic} records
wenzelm@26849:   at the level of terms and types.  The notation is as follows:
wenzelm@26849: 
wenzelm@26849:   \begin{center}
wenzelm@26849:   \begin{tabular}{l|l|l}
wenzelm@26849:     & record terms & record types \\ \hline
wenzelm@26849:     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}} \\
wenzelm@26849:     schematic & \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ m{\isasymrparr}{\isachardoublequote}} &
wenzelm@26849:       \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharcolon}{\isacharcolon}\ A{\isacharcomma}\ y\ {\isacharcolon}{\isacharcolon}\ B{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ M{\isasymrparr}{\isachardoublequote}} \\
wenzelm@26849:   \end{tabular}
wenzelm@26849:   \end{center}
wenzelm@26849: 
wenzelm@26849:   \noindent The ASCII representation of \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isasymrparr}{\isachardoublequote}} is \isa{{\isachardoublequote}{\isacharparenleft}{\isacharbar}\ x\ {\isacharequal}\ a\ {\isacharbar}{\isacharparenright}{\isachardoublequote}}.
wenzelm@26849: 
wenzelm@26849:   A fixed record \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isasymrparr}{\isachardoublequote}} has field \isa{x} of value
wenzelm@26849:   \isa{a} and field \isa{y} of value \isa{b}.  The corresponding
wenzelm@26849:   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}}
wenzelm@26849:   and \isa{{\isachardoublequote}b\ {\isacharcolon}{\isacharcolon}\ B{\isachardoublequote}}.
wenzelm@26849: 
wenzelm@26849:   A record scheme like \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ m{\isasymrparr}{\isachardoublequote}} contains fields
wenzelm@26849:   \isa{x} and \isa{y} as before, but also possibly further fields
wenzelm@26849:   as indicated by the ``\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}'' notation (which is actually part
wenzelm@26849:   of the syntax).  The improper field ``\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}'' of a record
wenzelm@26849:   scheme is called the \emph{more part}.  Logically it is just a free
wenzelm@26849:   variable, which is occasionally referred to as ``row variable'' in
wenzelm@26849:   the literature.  The more part of a record scheme may be
wenzelm@26849:   instantiated by zero or more further components.  For example, the
wenzelm@26852:   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.
wenzelm@26849:   Fixed records are special instances of record schemes, where
wenzelm@26849:   ``\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}'' is properly terminated by the \isa{{\isachardoublequote}{\isacharparenleft}{\isacharparenright}\ {\isacharcolon}{\isacharcolon}\ unit{\isachardoublequote}}
wenzelm@26849:   element.  In fact, \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isasymrparr}{\isachardoublequote}} is just an abbreviation
wenzelm@26849:   for \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ {\isacharparenleft}{\isacharparenright}{\isasymrparr}{\isachardoublequote}}.
wenzelm@26849:   
wenzelm@26849:   \medskip Two key observations make extensible records in a simply
wenzelm@26849:   typed language like HOL work out:
wenzelm@26849: 
wenzelm@26849:   \begin{enumerate}
wenzelm@26849: 
wenzelm@26849:   \item the more part is internalized, as a free term or type
wenzelm@26849:   variable,
wenzelm@26849: 
wenzelm@26852:   \item field names are externalized, they cannot be accessed within
wenzelm@26852:   the logic as first-class values.
wenzelm@26849: 
wenzelm@26849:   \end{enumerate}
wenzelm@26849: 
wenzelm@26849:   \medskip In Isabelle/HOL record types have to be defined explicitly,
wenzelm@26849:   fixing their field names and types, and their (optional) parent
wenzelm@26849:   record.  Afterwards, records may be formed using above syntax, while
wenzelm@26849:   obeying the canonical order of fields as given by their declaration.
wenzelm@26849:   The record package provides several standard operations like
wenzelm@26849:   selectors and updates.  The common setup for various generic proof
wenzelm@26849:   tools enable succinct reasoning patterns.  See also the Isabelle/HOL
wenzelm@26849:   tutorial \cite{isabelle-hol-book} for further instructions on using
wenzelm@26849:   records in practice.%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsubsection{Record specifications%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: \begin{matharray}{rcl}
wenzelm@26849:     \indexdef{HOL}{command}{record}\mbox{\isa{\isacommand{record}}} & : & \isartrans{theory}{theory} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26849:   \begin{rail}
wenzelm@26849:     'record' typespec '=' (type '+')? (constdecl +)
wenzelm@26849:     ;
wenzelm@26849:   \end{rail}
wenzelm@26849: 
wenzelm@26849:   \begin{descr}
wenzelm@26849: 
wenzelm@26849:   \item [\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
wenzelm@26849:   extensible record type \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharparenright}\ t{\isachardoublequote}},
wenzelm@26849:   derived from the optional parent record \isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}} by adding new
wenzelm@26849:   field components \isa{{\isachardoublequote}c\isactrlsub i\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub i{\isachardoublequote}} etc.
wenzelm@26849: 
wenzelm@26849:   The type variables of \isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isasymsigma}\isactrlsub i{\isachardoublequote}} need to be
wenzelm@26849:   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
wenzelm@26849:   least one new field \isa{{\isachardoublequote}c\isactrlsub i{\isachardoublequote}} has to be specified.
wenzelm@26849:   Basically, field names need to belong to a unique record.  This is
wenzelm@26849:   not a real restriction in practice, since fields are qualified by
wenzelm@26849:   the record name internally.
wenzelm@26849: 
wenzelm@26849:   The parent record specification \isa{{\isasymtau}} is optional; if omitted
wenzelm@26849:   \isa{t} becomes a root record.  The hierarchy of all records
wenzelm@26849:   declared within a theory context forms a forest structure, i.e.\ a
wenzelm@26849:   set of trees starting with a root record each.  There is no way to
wenzelm@26849:   merge multiple parent records!
wenzelm@26849: 
wenzelm@26849:   For convenience, \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharparenright}\ t{\isachardoublequote}} is made a
wenzelm@26849:   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
wenzelm@26849:   \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}}.
wenzelm@26849: 
wenzelm@26849:   \end{descr}%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsubsection{Record operations%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: Any record definition of the form presented above produces certain
wenzelm@26849:   standard operations.  Selectors and updates are provided for any
wenzelm@26849:   field, including the improper one ``\isa{more}''.  There are also
wenzelm@26849:   cumulative record constructor functions.  To simplify the
wenzelm@26849:   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}}.
wenzelm@26849: 
wenzelm@26849:   \medskip \textbf{Selectors} and \textbf{updates} are available for
wenzelm@26849:   any field (including ``\isa{more}''):
wenzelm@26849: 
wenzelm@26849:   \begin{matharray}{lll}
wenzelm@26852:     \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}} \\
wenzelm@26852:     \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}} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26849:   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
wenzelm@26849:   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
wenzelm@26849:   because of postfix notation the order of fields shown here is
wenzelm@26849:   reverse than in the actual term.  Since repeated updates are just
wenzelm@26849:   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.
wenzelm@26849:   Thus commutativity of independent updates can be proven within the
wenzelm@26849:   logic for any two fields, but not as a general theorem.
wenzelm@26849: 
wenzelm@26849:   \medskip The \textbf{make} operation provides a cumulative record
wenzelm@26849:   constructor function:
wenzelm@26849: 
wenzelm@26849:   \begin{matharray}{lll}
wenzelm@26852:     \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}} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26849:   \medskip We now reconsider the case of non-root records, which are
wenzelm@26849:   derived of some parent.  In general, the latter may depend on
wenzelm@26849:   another parent as well, resulting in a list of \emph{ancestor
wenzelm@26849:   records}.  Appending the lists of fields of all ancestors results in
wenzelm@26849:   a certain field prefix.  The record package automatically takes care
wenzelm@26849:   of this by lifting operations over this context of ancestor fields.
wenzelm@26849:   Assuming that \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharparenright}\ t{\isachardoublequote}} has ancestor
wenzelm@26849:   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}},
wenzelm@26849:   the above record operations will get the following types:
wenzelm@26849: 
wenzelm@26852:   \medskip
wenzelm@26852:   \begin{tabular}{lll}
wenzelm@26852:     \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}} \\
wenzelm@26852:     \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}} \\
wenzelm@26852:     \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}} \\
wenzelm@26852:   \end{tabular}
wenzelm@26852:   \medskip
wenzelm@26849: 
wenzelm@26852:   \noindent Some further operations address the extension aspect of a
wenzelm@26849:   derived record scheme specifically: \isa{{\isachardoublequote}t{\isachardot}fields{\isachardoublequote}} produces a
wenzelm@26849:   record fragment consisting of exactly the new fields introduced here
wenzelm@26849:   (the result may serve as a more part elsewhere); \isa{{\isachardoublequote}t{\isachardot}extend{\isachardoublequote}}
wenzelm@26849:   takes a fixed record and adds a given more part; \isa{{\isachardoublequote}t{\isachardot}truncate{\isachardoublequote}} restricts a record scheme to a fixed record.
wenzelm@26849: 
wenzelm@26852:   \medskip
wenzelm@26852:   \begin{tabular}{lll}
wenzelm@26852:     \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}} \\
wenzelm@26852:     \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}} \\
wenzelm@26852:     \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}} \\
wenzelm@26852:   \end{tabular}
wenzelm@26852:   \medskip
wenzelm@26849: 
wenzelm@26849:   \noindent Note that \isa{{\isachardoublequote}t{\isachardot}make{\isachardoublequote}} and \isa{{\isachardoublequote}t{\isachardot}fields{\isachardoublequote}} coincide
wenzelm@26849:   for root records.%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsubsection{Derived rules and proof tools%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: The record package proves several results internally, declaring
wenzelm@26849:   these facts to appropriate proof tools.  This enables users to
wenzelm@26849:   reason about record structures quite conveniently.  Assume that
wenzelm@26849:   \isa{t} is a record type as specified above.
wenzelm@26849: 
wenzelm@26849:   \begin{enumerate}
wenzelm@26849:   
wenzelm@26849:   \item Standard conversions for selectors or updates applied to
wenzelm@26849:   record constructor terms are made part of the default Simplifier
wenzelm@26849:   context; thus proofs by reduction of basic operations merely require
wenzelm@26849:   the \mbox{\isa{simp}} method without further arguments.  These rules
wenzelm@26849:   are available as \isa{{\isachardoublequote}t{\isachardot}simps{\isachardoublequote}}, too.
wenzelm@26849:   
wenzelm@26849:   \item Selectors applied to updated records are automatically reduced
wenzelm@26849:   by an internal simplification procedure, which is also part of the
wenzelm@26849:   standard Simplifier setup.
wenzelm@26849: 
wenzelm@26849:   \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
wenzelm@26849:   Reasoner as \mbox{\isa{iff}} rules.  These rules are available as
wenzelm@26849:   \isa{{\isachardoublequote}t{\isachardot}iffs{\isachardoublequote}}.
wenzelm@26849: 
wenzelm@26849:   \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,
wenzelm@26849:   and as the basic rule context as ``\mbox{\isa{intro}}\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}''.
wenzelm@26849:   The rule is called \isa{{\isachardoublequote}t{\isachardot}equality{\isachardoublequote}}.
wenzelm@26849: 
wenzelm@26849:   \item Representations of arbitrary record expressions as canonical
wenzelm@26849:   constructor terms are provided both in \mbox{\isa{cases}} and \mbox{\isa{induct}} format (cf.\ the generic proof methods of the same name,
wenzelm@26849:   \secref{sec:cases-induct}).  Several variations are available, for
wenzelm@26849:   fixed records, record schemes, more parts etc.
wenzelm@26849:   
wenzelm@26849:   The generic proof methods are sufficiently smart to pick the most
wenzelm@26849:   sensible rule according to the type of the indicated record
wenzelm@26849:   expression: users just need to apply something like ``\isa{{\isachardoublequote}{\isacharparenleft}cases\ r{\isacharparenright}{\isachardoublequote}}'' to a certain proof problem.
wenzelm@26849: 
wenzelm@26849:   \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}
wenzelm@26849:   treated automatically, but usually need to be expanded by hand,
wenzelm@26849:   using the collective fact \isa{{\isachardoublequote}t{\isachardot}defs{\isachardoublequote}}.
wenzelm@26849: 
wenzelm@26849:   \end{enumerate}%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsection{Datatypes \label{sec:hol-datatype}%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: \begin{matharray}{rcl}
wenzelm@26849:     \indexdef{HOL}{command}{datatype}\mbox{\isa{\isacommand{datatype}}} & : & \isartrans{theory}{theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{rep\_datatype}\mbox{\isa{\isacommand{rep{\isacharunderscore}datatype}}} & : & \isartrans{theory}{theory} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26849:   \begin{rail}
wenzelm@26849:     'datatype' (dtspec + 'and')
wenzelm@26849:     ;
wenzelm@26849:     'rep\_datatype' (name *) dtrules
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     dtspec: parname? typespec infix? '=' (cons + '|')
wenzelm@26849:     ;
wenzelm@26849:     cons: name (type *) mixfix?
wenzelm@26849:     ;
wenzelm@26849:     dtrules: 'distinct' thmrefs 'inject' thmrefs 'induction' thmrefs
wenzelm@26849:   \end{rail}
wenzelm@26849: 
wenzelm@26849:   \begin{descr}
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{datatype}}}] defines inductive datatypes in
wenzelm@26849:   HOL.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{rep{\isacharunderscore}datatype}}}] represents existing types as
wenzelm@26849:   inductive ones, generating the standard infrastructure of derived
wenzelm@26849:   concepts (primitive recursion etc.).
wenzelm@26849: 
wenzelm@26849:   \end{descr}
wenzelm@26849: 
wenzelm@26849:   The induction and exhaustion theorems generated provide case names
wenzelm@26849:   according to the constructors involved, while parameters are named
wenzelm@26849:   after the types (see also \secref{sec:cases-induct}).
wenzelm@26849: 
wenzelm@26849:   See \cite{isabelle-HOL} for more details on datatypes, but beware of
wenzelm@26849:   the old-style theory syntax being used there!  Apart from proper
wenzelm@26849:   proof methods for case-analysis and induction, there are also
wenzelm@26849:   emulations of ML tactics \mbox{\isa{case{\isacharunderscore}tac}} and \mbox{\isa{induct{\isacharunderscore}tac}} available, see \secref{sec:hol-induct-tac}; these admit
wenzelm@26849:   to refer directly to the internal structure of subgoals (including
wenzelm@26849:   internally bound parameters).%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsection{Recursive functions \label{sec:recursion}%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: \begin{matharray}{rcl}
wenzelm@26849:     \indexdef{HOL}{command}{primrec}\mbox{\isa{\isacommand{primrec}}} & : & \isarkeep{local{\dsh}theory} \\
wenzelm@26849:     \indexdef{HOL}{command}{fun}\mbox{\isa{\isacommand{fun}}} & : & \isarkeep{local{\dsh}theory} \\
wenzelm@26849:     \indexdef{HOL}{command}{function}\mbox{\isa{\isacommand{function}}} & : & \isartrans{local{\dsh}theory}{proof(prove)} \\
wenzelm@26849:     \indexdef{HOL}{command}{termination}\mbox{\isa{\isacommand{termination}}} & : & \isartrans{local{\dsh}theory}{proof(prove)} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26849:   \railalias{funopts}{function\_opts}  %FIXME ??
wenzelm@26849: 
wenzelm@26849:   \begin{rail}
wenzelm@26849:     'primrec' target? fixes 'where' equations
wenzelm@26849:     ;
wenzelm@26849:     equations: (thmdecl? prop + '|')
wenzelm@26849:     ;
wenzelm@26849:     ('fun' | 'function') (funopts)? fixes 'where' clauses
wenzelm@26849:     ;
wenzelm@26849:     clauses: (thmdecl? prop ('(' 'otherwise' ')')? + '|')
wenzelm@26849:     ;
wenzelm@26849:     funopts: '(' (('sequential' | 'in' name | 'domintros' | 'tailrec' |
wenzelm@26849:     'default' term) + ',') ')'
wenzelm@26849:     ;
wenzelm@26849:     'termination' ( term )?
wenzelm@26849:   \end{rail}
wenzelm@26849: 
wenzelm@26849:   \begin{descr}
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{primrec}}}] defines primitive recursive
wenzelm@26849:   functions over datatypes, see also \cite{isabelle-HOL}.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{function}}}] defines functions by general
wenzelm@26849:   wellfounded recursion. A detailed description with examples can be
wenzelm@26849:   found in \cite{isabelle-function}. The function is specified by a
wenzelm@26849:   set of (possibly conditional) recursive equations with arbitrary
wenzelm@26849:   pattern matching. The command generates proof obligations for the
wenzelm@26849:   completeness and the compatibility of patterns.
wenzelm@26849: 
wenzelm@26849:   The defined function is considered partial, and the resulting
wenzelm@26849:   simplification rules (named \isa{{\isachardoublequote}f{\isachardot}psimps{\isachardoublequote}}) and induction rule
wenzelm@26849:   (named \isa{{\isachardoublequote}f{\isachardot}pinduct{\isachardoublequote}}) are guarded by a generated domain
wenzelm@26849:   predicate \isa{{\isachardoublequote}f{\isacharunderscore}dom{\isachardoublequote}}. The \mbox{\isa{\isacommand{termination}}}
wenzelm@26849:   command can then be used to establish that the function is total.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{fun}}}] is a shorthand notation for
wenzelm@26849:   ``\mbox{\isa{\isacommand{function}}}~\isa{{\isachardoublequote}{\isacharparenleft}sequential{\isacharparenright}{\isachardoublequote}}, followed by
wenzelm@26849:   automated proof attempts regarding pattern matching and termination.
wenzelm@26849:   See \cite{isabelle-function} for further details.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{termination}}}~\isa{f}] commences a
wenzelm@26849:   termination proof for the previously defined function \isa{f}.  If
wenzelm@26849:   this is omitted, the command refers to the most recent function
wenzelm@26849:   definition.  After the proof is closed, the recursive equations and
wenzelm@26849:   the induction principle is established.
wenzelm@26849: 
wenzelm@26849:   \end{descr}
wenzelm@26849: 
wenzelm@26849:   %FIXME check
wenzelm@26849: 
wenzelm@26849:   Recursive definitions introduced by both the \mbox{\isa{\isacommand{primrec}}} and the \mbox{\isa{\isacommand{function}}} command accommodate
wenzelm@26849:   reasoning by induction (cf.\ \secref{sec:cases-induct}): rule \isa{{\isachardoublequote}c{\isachardot}induct{\isachardoublequote}} (where \isa{c} is the name of the function definition)
wenzelm@26849:   refers to a specific induction rule, with parameters named according
wenzelm@26849:   to the user-specified equations.  Case names of \mbox{\isa{\isacommand{primrec}}} are that of the datatypes involved, while those of
wenzelm@26849:   \mbox{\isa{\isacommand{function}}} are numbered (starting from 1).
wenzelm@26849: 
wenzelm@26849:   The equations provided by these packages may be referred later as
wenzelm@26849:   theorem list \isa{{\isachardoublequote}f{\isachardot}simps{\isachardoublequote}}, where \isa{f} is the (collective)
wenzelm@26849:   name of the functions defined.  Individual equations may be named
wenzelm@26849:   explicitly as well.
wenzelm@26849: 
wenzelm@26849:   The \mbox{\isa{\isacommand{function}}} command accepts the following
wenzelm@26849:   options.
wenzelm@26849: 
wenzelm@26849:   \begin{descr}
wenzelm@26849: 
wenzelm@26849:   \item [\isa{sequential}] enables a preprocessor which
wenzelm@26849:   disambiguates overlapping patterns by making them mutually disjoint.
wenzelm@26849:   Earlier equations take precedence over later ones.  This allows to
wenzelm@26849:   give the specification in a format very similar to functional
wenzelm@26849:   programming.  Note that the resulting simplification and induction
wenzelm@26849:   rules correspond to the transformed specification, not the one given
wenzelm@26849:   originally. This usually means that each equation given by the user
wenzelm@26849:   may result in several theroems.  Also note that this automatic
wenzelm@26849:   transformation only works for ML-style datatype patterns.
wenzelm@26849: 
wenzelm@26849:   \item [\isa{{\isachardoublequote}{\isasymIN}\ name{\isachardoublequote}}] gives the target for the definition.
wenzelm@26849:   %FIXME ?!?
wenzelm@26849: 
wenzelm@26849:   \item [\isa{domintros}] enables the automated generation of
wenzelm@26849:   introduction rules for the domain predicate. While mostly not
wenzelm@26849:   needed, they can be helpful in some proofs about partial functions.
wenzelm@26849: 
wenzelm@26849:   \item [\isa{tailrec}] generates the unconstrained recursive
wenzelm@26849:   equations even without a termination proof, provided that the
wenzelm@26849:   function is tail-recursive. This currently only works
wenzelm@26849: 
wenzelm@26849:   \item [\isa{{\isachardoublequote}default\ d{\isachardoublequote}}] allows to specify a default value for a
wenzelm@26849:   (partial) function, which will ensure that \isa{{\isachardoublequote}f\ x\ {\isacharequal}\ d\ x{\isachardoublequote}}
wenzelm@26849:   whenever \isa{{\isachardoublequote}x\ {\isasymnotin}\ f{\isacharunderscore}dom{\isachardoublequote}}.
wenzelm@26849: 
wenzelm@26849:   \end{descr}%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsubsection{Proof methods related to recursive definitions%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: \begin{matharray}{rcl}
wenzelm@26854:     \indexdef{HOL}{method}{pat\_completeness}\mbox{\isa{pat{\isacharunderscore}completeness}} & : & \isarmeth \\
wenzelm@26849:     \indexdef{HOL}{method}{relation}\mbox{\isa{relation}} & : & \isarmeth \\
wenzelm@26854:     \indexdef{HOL}{method}{lexicographic\_order}\mbox{\isa{lexicographic{\isacharunderscore}order}} & : & \isarmeth \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26849:   \begin{rail}
wenzelm@26849:     'relation' term
wenzelm@26849:     ;
wenzelm@26849:     'lexicographic\_order' (clasimpmod *)
wenzelm@26849:     ;
wenzelm@26849:   \end{rail}
wenzelm@26849: 
wenzelm@26849:   \begin{descr}
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{pat{\isacharunderscore}completeness}}] is a specialized method to
wenzelm@26849:   solve goals regarding the completeness of pattern matching, as
wenzelm@26849:   required by the \mbox{\isa{\isacommand{function}}} package (cf.\
wenzelm@26849:   \cite{isabelle-function}).
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{relation}}~\isa{R}] introduces a termination
wenzelm@26849:   proof using the relation \isa{R}.  The resulting proof state will
wenzelm@26849:   contain goals expressing that \isa{R} is wellfounded, and that the
wenzelm@26849:   arguments of recursive calls decrease with respect to \isa{R}.
wenzelm@26849:   Usually, this method is used as the initial proof step of manual
wenzelm@26849:   termination proofs.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{lexicographic{\isacharunderscore}order}}] attempts a fully
wenzelm@26849:   automated termination proof by searching for a lexicographic
wenzelm@26849:   combination of size measures on the arguments of the function. The
wenzelm@26849:   method accepts the same arguments as the \mbox{\isa{auto}} method,
wenzelm@26849:   which it uses internally to prove local descents.  The same context
wenzelm@26849:   modifiers as for \mbox{\isa{auto}} are accepted, see
wenzelm@26849:   \secref{sec:clasimp}.
wenzelm@26849: 
wenzelm@26849:   In case of failure, extensive information is printed, which can help
wenzelm@26849:   to analyse the situation (cf.\ \cite{isabelle-function}).
wenzelm@26849: 
wenzelm@26849:   \end{descr}%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsubsection{Old-style recursive function definitions (TFL)%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: The old TFL commands \mbox{\isa{\isacommand{recdef}}} and \mbox{\isa{\isacommand{recdef{\isacharunderscore}tc}}} for defining recursive are mostly obsolete; \mbox{\isa{\isacommand{function}}} or \mbox{\isa{\isacommand{fun}}} should be used instead.
wenzelm@26849: 
wenzelm@26849:   \begin{matharray}{rcl}
wenzelm@26849:     \indexdef{HOL}{command}{recdef}\mbox{\isa{\isacommand{recdef}}} & : & \isartrans{theory}{theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{recdef\_tc}\mbox{\isa{\isacommand{recdef{\isacharunderscore}tc}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isartrans{theory}{proof(prove)} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26849:   \begin{rail}
wenzelm@26849:     'recdef' ('(' 'permissive' ')')? \\ name term (prop +) hints?
wenzelm@26849:     ;
wenzelm@26849:     recdeftc thmdecl? tc
wenzelm@26849:     ;
wenzelm@26849:     hints: '(' 'hints' (recdefmod *) ')'
wenzelm@26849:     ;
wenzelm@26849:     recdefmod: (('recdef\_simp' | 'recdef\_cong' | 'recdef\_wf') (() | 'add' | 'del') ':' thmrefs) | clasimpmod
wenzelm@26849:     ;
wenzelm@26849:     tc: nameref ('(' nat ')')?
wenzelm@26849:     ;
wenzelm@26849:   \end{rail}
wenzelm@26849: 
wenzelm@26849:   \begin{descr}
wenzelm@26849:   
wenzelm@26849:   \item [\mbox{\isa{\isacommand{recdef}}}] defines general well-founded
wenzelm@26849:   recursive functions (using the TFL package), see also
wenzelm@26849:   \cite{isabelle-HOL}.  The ``\isa{{\isachardoublequote}{\isacharparenleft}permissive{\isacharparenright}{\isachardoublequote}}'' option tells
wenzelm@26849:   TFL to recover from failed proof attempts, returning unfinished
wenzelm@26849:   results.  The \isa{recdef{\isacharunderscore}simp}, \isa{recdef{\isacharunderscore}cong}, and \isa{recdef{\isacharunderscore}wf} hints refer to auxiliary rules to be used in the internal
wenzelm@26849:   automated proof process of TFL.  Additional \mbox{\isa{clasimpmod}}
wenzelm@26849:   declarations (cf.\ \secref{sec:clasimp}) may be given to tune the
wenzelm@26849:   context of the Simplifier (cf.\ \secref{sec:simplifier}) and
wenzelm@26849:   Classical reasoner (cf.\ \secref{sec:classical}).
wenzelm@26849:   
wenzelm@26849:   \item [\mbox{\isa{\isacommand{recdef{\isacharunderscore}tc}}}~\isa{{\isachardoublequote}c\ {\isacharparenleft}i{\isacharparenright}{\isachardoublequote}}] recommences the
wenzelm@26849:   proof for leftover termination condition number \isa{i} (default
wenzelm@26849:   1) as generated by a \mbox{\isa{\isacommand{recdef}}} definition of
wenzelm@26849:   constant \isa{c}.
wenzelm@26849:   
wenzelm@26849:   Note that in most cases, \mbox{\isa{\isacommand{recdef}}} is able to finish
wenzelm@26849:   its internal proofs without manual intervention.
wenzelm@26849: 
wenzelm@26849:   \end{descr}
wenzelm@26849: 
wenzelm@26849:   \medskip Hints for \mbox{\isa{\isacommand{recdef}}} may be also declared
wenzelm@26849:   globally, using the following attributes.
wenzelm@26849: 
wenzelm@26849:   \begin{matharray}{rcl}
wenzelm@26854:     \indexdef{HOL}{attribute}{recdef\_simp}\mbox{\isa{recdef{\isacharunderscore}simp}} & : & \isaratt \\
wenzelm@26854:     \indexdef{HOL}{attribute}{recdef\_cong}\mbox{\isa{recdef{\isacharunderscore}cong}} & : & \isaratt \\
wenzelm@26854:     \indexdef{HOL}{attribute}{recdef\_wf}\mbox{\isa{recdef{\isacharunderscore}wf}} & : & \isaratt \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26849:   \begin{rail}
wenzelm@26849:     ('recdef\_simp' | 'recdef\_cong' | 'recdef\_wf') (() | 'add' | 'del')
wenzelm@26849:     ;
wenzelm@26849:   \end{rail}%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsection{Definition by specification \label{sec:hol-specification}%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: \begin{matharray}{rcl}
wenzelm@26849:     \indexdef{HOL}{command}{specification}\mbox{\isa{\isacommand{specification}}} & : & \isartrans{theory}{proof(prove)} \\
wenzelm@26854:     \indexdef{HOL}{command}{ax\_specification}\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}} & : & \isartrans{theory}{proof(prove)} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26849:   \begin{rail}
wenzelm@26849:   ('specification' | 'ax\_specification') '(' (decl +) ')' \\ (thmdecl? prop +)
wenzelm@26849:   ;
wenzelm@26849:   decl: ((name ':')? term '(' 'overloaded' ')'?)
wenzelm@26849:   \end{rail}
wenzelm@26849: 
wenzelm@26849:   \begin{descr}
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{specification}}}~\isa{{\isachardoublequote}decls\ {\isasymphi}{\isachardoublequote}}] sets up a
wenzelm@26849:   goal stating the existence of terms with the properties specified to
wenzelm@26849:   hold for the constants given in \isa{decls}.  After finishing the
wenzelm@26849:   proof, the theory will be augmented with definitions for the given
wenzelm@26849:   constants, as well as with theorems stating the properties for these
wenzelm@26849:   constants.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}~\isa{{\isachardoublequote}decls\ {\isasymphi}{\isachardoublequote}}] sets
wenzelm@26849:   up a goal stating the existence of terms with the properties
wenzelm@26849:   specified to hold for the constants given in \isa{decls}.  After
wenzelm@26849:   finishing the proof, the theory will be augmented with axioms
wenzelm@26849:   expressing the properties given in the first place.
wenzelm@26849: 
wenzelm@26849:   \item [\isa{decl}] declares a constant to be defined by the
wenzelm@26849:   specification given.  The definition for the constant \isa{c} is
wenzelm@26849:   bound to the name \isa{c{\isacharunderscore}def} unless a theorem name is given in
wenzelm@26849:   the declaration.  Overloaded constants should be declared as such.
wenzelm@26849: 
wenzelm@26849:   \end{descr}
wenzelm@26849: 
wenzelm@26849:   Whether to use \mbox{\isa{\isacommand{specification}}} or \mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}} is to some extent a matter of style.  \mbox{\isa{\isacommand{specification}}} introduces no new axioms, and so by
wenzelm@26849:   construction cannot introduce inconsistencies, whereas \mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}} does introduce axioms, but only after the
wenzelm@26849:   user has explicitly proven it to be safe.  A practical issue must be
wenzelm@26849:   considered, though: After introducing two constants with the same
wenzelm@26849:   properties using \mbox{\isa{\isacommand{specification}}}, one can prove
wenzelm@26849:   that the two constants are, in fact, equal.  If this might be a
wenzelm@26849:   problem, one should use \mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}.%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsection{Inductive and coinductive definitions \label{sec:hol-inductive}%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: An \textbf{inductive definition} specifies the least predicate (or
wenzelm@26849:   set) \isa{R} closed under given rules: applying a rule to elements
wenzelm@26849:   of \isa{R} yields a result within \isa{R}.  For example, a
wenzelm@26849:   structural operational semantics is an inductive definition of an
wenzelm@26849:   evaluation relation.
wenzelm@26849: 
wenzelm@26849:   Dually, a \textbf{coinductive definition} specifies the greatest
wenzelm@26849:   predicate~/ set \isa{R} that is consistent with given rules: every
wenzelm@26849:   element of \isa{R} can be seen as arising by applying a rule to
wenzelm@26849:   elements of \isa{R}.  An important example is using bisimulation
wenzelm@26849:   relations to formalise equivalence of processes and infinite data
wenzelm@26849:   structures.
wenzelm@26849: 
wenzelm@26849:   \medskip The HOL package is related to the ZF one, which is
wenzelm@26849:   described in a separate paper,\footnote{It appeared in CADE
wenzelm@26849:   \cite{paulson-CADE}; a longer version is distributed with Isabelle.}
wenzelm@26849:   which you should refer to in case of difficulties.  The package is
wenzelm@26849:   simpler than that of ZF thanks to implicit type-checking in HOL.
wenzelm@26849:   The types of the (co)inductive predicates (or sets) determine the
wenzelm@26849:   domain of the fixedpoint definition, and the package does not have
wenzelm@26849:   to use inference rules for type-checking.
wenzelm@26849: 
wenzelm@26849:   \begin{matharray}{rcl}
wenzelm@26849:     \indexdef{HOL}{command}{inductive}\mbox{\isa{\isacommand{inductive}}} & : & \isarkeep{local{\dsh}theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{inductive\_set}\mbox{\isa{\isacommand{inductive{\isacharunderscore}set}}} & : & \isarkeep{local{\dsh}theory} \\
wenzelm@26849:     \indexdef{HOL}{command}{coinductive}\mbox{\isa{\isacommand{coinductive}}} & : & \isarkeep{local{\dsh}theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{coinductive\_set}\mbox{\isa{\isacommand{coinductive{\isacharunderscore}set}}} & : & \isarkeep{local{\dsh}theory} \\
wenzelm@26849:     \indexdef{HOL}{attribute}{mono}\mbox{\isa{mono}} & : & \isaratt \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26849:   \begin{rail}
wenzelm@26849:     ('inductive' | 'inductive\_set' | 'coinductive' | 'coinductive\_set') target? fixes ('for' fixes)? \\
wenzelm@26849:     ('where' clauses)? ('monos' thmrefs)?
wenzelm@26849:     ;
wenzelm@26849:     clauses: (thmdecl? prop + '|')
wenzelm@26849:     ;
wenzelm@26849:     'mono' (() | 'add' | 'del')
wenzelm@26849:     ;
wenzelm@26849:   \end{rail}
wenzelm@26849: 
wenzelm@26849:   \begin{descr}
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{inductive}}} and \mbox{\isa{\isacommand{coinductive}}}] define (co)inductive predicates from the
wenzelm@26849:   introduction rules given in the \mbox{\isa{\isakeyword{where}}} part.  The
wenzelm@26849:   optional \mbox{\isa{\isakeyword{for}}} part contains a list of parameters of the
wenzelm@26849:   (co)inductive predicates that remain fixed throughout the
wenzelm@26849:   definition.  The optional \mbox{\isa{\isakeyword{monos}}} section contains
wenzelm@26849:   \emph{monotonicity theorems}, which are required for each operator
wenzelm@26849:   applied to a recursive set in the introduction rules.  There
wenzelm@26849:   \emph{must} be a theorem of the form \isa{{\isachardoublequote}A\ {\isasymle}\ B\ {\isasymLongrightarrow}\ M\ A\ {\isasymle}\ M\ B{\isachardoublequote}},
wenzelm@26849:   for each premise \isa{{\isachardoublequote}M\ R\isactrlsub i\ t{\isachardoublequote}} in an introduction rule!
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{inductive{\isacharunderscore}set}}} and \mbox{\isa{\isacommand{coinductive{\isacharunderscore}set}}}] are wrappers for to the previous commands,
wenzelm@26849:   allowing the definition of (co)inductive sets.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{mono}}] declares monotonicity rules.  These
wenzelm@26849:   rule are involved in the automated monotonicity proof of \mbox{\isa{\isacommand{inductive}}}.
wenzelm@26849: 
wenzelm@26849:   \end{descr}%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsubsection{Derived rules%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: Each (co)inductive definition \isa{R} adds definitions to the
wenzelm@26849:   theory and also proves some theorems:
wenzelm@26849: 
wenzelm@26849:   \begin{description}
wenzelm@26849: 
wenzelm@26849:   \item [\isa{R{\isachardot}intros}] is the list of introduction rules as proven
wenzelm@26849:   theorems, for the recursive predicates (or sets).  The rules are
wenzelm@26849:   also available individually, using the names given them in the
wenzelm@26849:   theory file;
wenzelm@26849: 
wenzelm@26849:   \item [\isa{R{\isachardot}cases}] is the case analysis (or elimination) rule;
wenzelm@26849: 
wenzelm@26849:   \item [\isa{R{\isachardot}induct} or \isa{R{\isachardot}coinduct}] is the (co)induction
wenzelm@26849:   rule.
wenzelm@26849: 
wenzelm@26849:   \end{description}
wenzelm@26849: 
wenzelm@26849:   When several predicates \isa{{\isachardoublequote}R\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ R\isactrlsub n{\isachardoublequote}} are
wenzelm@26849:   defined simultaneously, the list of introduction rules is called
wenzelm@26849:   \isa{{\isachardoublequote}R\isactrlsub {\isadigit{1}}{\isacharunderscore}{\isasymdots}{\isacharunderscore}R\isactrlsub n{\isachardot}intros{\isachardoublequote}}, the case analysis rules are
wenzelm@26849:   called \isa{{\isachardoublequote}R\isactrlsub {\isadigit{1}}{\isachardot}cases{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ R\isactrlsub n{\isachardot}cases{\isachardoublequote}}, and the list
wenzelm@26849:   of mutual induction rules is called \isa{{\isachardoublequote}R\isactrlsub {\isadigit{1}}{\isacharunderscore}{\isasymdots}{\isacharunderscore}R\isactrlsub n{\isachardot}inducts{\isachardoublequote}}.%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsubsection{Monotonicity theorems%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: Each theory contains a default set of theorems that are used in
wenzelm@26849:   monotonicity proofs.  New rules can be added to this set via the
wenzelm@26849:   \mbox{\isa{mono}} attribute.  The HOL theory \isa{Inductive}
wenzelm@26849:   shows how this is done.  In general, the following monotonicity
wenzelm@26849:   theorems may be added:
wenzelm@26849: 
wenzelm@26849:   \begin{itemize}
wenzelm@26849: 
wenzelm@26849:   \item Theorems of the form \isa{{\isachardoublequote}A\ {\isasymle}\ B\ {\isasymLongrightarrow}\ M\ A\ {\isasymle}\ M\ B{\isachardoublequote}}, for proving
wenzelm@26849:   monotonicity of inductive definitions whose introduction rules have
wenzelm@26849:   premises involving terms such as \isa{{\isachardoublequote}M\ R\isactrlsub i\ t{\isachardoublequote}}.
wenzelm@26849: 
wenzelm@26849:   \item Monotonicity theorems for logical operators, which are of the
wenzelm@26849:   general form \isa{{\isachardoublequote}{\isacharparenleft}{\isasymdots}\ {\isasymlongrightarrow}\ {\isasymdots}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isacharparenleft}{\isasymdots}\ {\isasymlongrightarrow}\ {\isasymdots}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymlongrightarrow}\ {\isasymdots}{\isachardoublequote}}.  For example, in
wenzelm@26849:   the case of the operator \isa{{\isachardoublequote}{\isasymor}{\isachardoublequote}}, the corresponding theorem is
wenzelm@26849:   \[
wenzelm@26849:   \infer{\isa{{\isachardoublequote}P\isactrlsub {\isadigit{1}}\ {\isasymor}\ P\isactrlsub {\isadigit{2}}\ {\isasymlongrightarrow}\ Q\isactrlsub {\isadigit{1}}\ {\isasymor}\ Q\isactrlsub {\isadigit{2}}{\isachardoublequote}}}{\isa{{\isachardoublequote}P\isactrlsub {\isadigit{1}}\ {\isasymlongrightarrow}\ Q\isactrlsub {\isadigit{1}}{\isachardoublequote}} & \isa{{\isachardoublequote}P\isactrlsub {\isadigit{2}}\ {\isasymlongrightarrow}\ Q\isactrlsub {\isadigit{2}}{\isachardoublequote}}}
wenzelm@26849:   \]
wenzelm@26849: 
wenzelm@26849:   \item De Morgan style equations for reasoning about the ``polarity''
wenzelm@26849:   of expressions, e.g.
wenzelm@26849:   \[
wenzelm@26849:   \isa{{\isachardoublequote}{\isasymnot}\ {\isasymnot}\ P\ {\isasymlongleftrightarrow}\ P{\isachardoublequote}} \qquad\qquad
wenzelm@26849:   \isa{{\isachardoublequote}{\isasymnot}\ {\isacharparenleft}P\ {\isasymand}\ Q{\isacharparenright}\ {\isasymlongleftrightarrow}\ {\isasymnot}\ P\ {\isasymor}\ {\isasymnot}\ Q{\isachardoublequote}}
wenzelm@26849:   \]
wenzelm@26849: 
wenzelm@26849:   \item Equations for reducing complex operators to more primitive
wenzelm@26849:   ones whose monotonicity can easily be proved, e.g.
wenzelm@26849:   \[
wenzelm@26849:   \isa{{\isachardoublequote}{\isacharparenleft}P\ {\isasymlongrightarrow}\ Q{\isacharparenright}\ {\isasymlongleftrightarrow}\ {\isasymnot}\ P\ {\isasymor}\ Q{\isachardoublequote}} \qquad\qquad
wenzelm@26849:   \isa{{\isachardoublequote}Ball\ A\ P\ {\isasymequiv}\ {\isasymforall}x{\isachardot}\ x\ {\isasymin}\ A\ {\isasymlongrightarrow}\ P\ x{\isachardoublequote}}
wenzelm@26849:   \]
wenzelm@26849: 
wenzelm@26849:   \end{itemize}
wenzelm@26849: 
wenzelm@26849:   %FIXME: Example of an inductive definition%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsection{Arithmetic proof support%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: \begin{matharray}{rcl}
wenzelm@26849:     \indexdef{HOL}{method}{arith}\mbox{\isa{arith}} & : & \isarmeth \\
wenzelm@26854:     \indexdef{HOL}{method}{arith\_split}\mbox{\isa{arith{\isacharunderscore}split}} & : & \isaratt \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26849:   The \mbox{\isa{arith}} method decides linear arithmetic problems
wenzelm@26849:   (on types \isa{nat}, \isa{int}, \isa{real}).  Any current
wenzelm@26849:   facts are inserted into the goal before running the procedure.
wenzelm@26849: 
wenzelm@26849:   The \mbox{\isa{arith{\isacharunderscore}split}} attribute declares case split rules
wenzelm@26849:   to be expanded before the arithmetic procedure is invoked.
wenzelm@26849: 
wenzelm@26849:   Note that a simpler (but faster) version of arithmetic reasoning is
wenzelm@26849:   already performed by the Simplifier.%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsection{Cases and induction: emulating tactic scripts \label{sec:hol-induct-tac}%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: The following important tactical tools of Isabelle/HOL have been
wenzelm@26849:   ported to Isar.  These should be never used in proper proof texts!
wenzelm@26849: 
wenzelm@26849:   \begin{matharray}{rcl}
wenzelm@26854:     \indexdef{HOL}{method}{case\_tac}\mbox{\isa{case{\isacharunderscore}tac}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\
wenzelm@26854:     \indexdef{HOL}{method}{induct\_tac}\mbox{\isa{induct{\isacharunderscore}tac}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\
wenzelm@26854:     \indexdef{HOL}{method}{ind\_cases}\mbox{\isa{ind{\isacharunderscore}cases}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\
wenzelm@26854:     \indexdef{HOL}{command}{inductive\_cases}\mbox{\isa{\isacommand{inductive{\isacharunderscore}cases}}} & : & \isartrans{theory}{theory} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26849:   \begin{rail}
wenzelm@26849:     'case\_tac' goalspec? term rule?
wenzelm@26849:     ;
wenzelm@26849:     'induct\_tac' goalspec? (insts * 'and') rule?
wenzelm@26849:     ;
wenzelm@26849:     'ind\_cases' (prop +) ('for' (name +)) ?
wenzelm@26849:     ;
wenzelm@26849:     'inductive\_cases' (thmdecl? (prop +) + 'and')
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     rule: ('rule' ':' thmref)
wenzelm@26849:     ;
wenzelm@26849:   \end{rail}
wenzelm@26849: 
wenzelm@26849:   \begin{descr}
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{case{\isacharunderscore}tac}} and \mbox{\isa{induct{\isacharunderscore}tac}}]
wenzelm@26849:   admit to reason about inductive datatypes only (unless an
wenzelm@26849:   alternative rule is given explicitly).  Furthermore, \mbox{\isa{case{\isacharunderscore}tac}} does a classical case split on booleans; \mbox{\isa{induct{\isacharunderscore}tac}} allows only variables to be given as instantiation.
wenzelm@26849:   These tactic emulations feature both goal addressing and dynamic
wenzelm@26849:   instantiation.  Note that named rule cases are \emph{not} provided
wenzelm@26849:   as would be by the proper \mbox{\isa{induct}} and \mbox{\isa{cases}} proof
wenzelm@26849:   methods (see \secref{sec:cases-induct}).
wenzelm@26849:   
wenzelm@26861:   \item [\mbox{\isa{ind{\isacharunderscore}cases}} and \mbox{\isa{\isacommand{inductive{\isacharunderscore}cases}}}] provide an interface to the internal \verb|mk_cases| operation.  Rules are simplified in an unrestricted
wenzelm@26861:   forward manner.
wenzelm@26849: 
wenzelm@26849:   While \mbox{\isa{ind{\isacharunderscore}cases}} is a proof method to apply the
wenzelm@26849:   result immediately as elimination rules, \mbox{\isa{\isacommand{inductive{\isacharunderscore}cases}}} provides case split theorems at the theory level
wenzelm@26849:   for later use.  The \mbox{\isa{\isakeyword{for}}} argument of the \mbox{\isa{ind{\isacharunderscore}cases}} method allows to specify a list of variables that should
wenzelm@26849:   be generalized before applying the resulting rule.
wenzelm@26849: 
wenzelm@26849:   \end{descr}%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isamarkupsection{Executable code%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: Isabelle/Pure provides two generic frameworks to support code
wenzelm@26849:   generation from executable specifications.  Isabelle/HOL
wenzelm@26849:   instantiates these mechanisms in a way that is amenable to end-user
wenzelm@26849:   applications.
wenzelm@26849: 
wenzelm@26849:   One framework generates code from both functional and relational
wenzelm@26849:   programs to SML.  See \cite{isabelle-HOL} for further information
wenzelm@26849:   (this actually covers the new-style theory format as well).
wenzelm@26849: 
wenzelm@26849:   \begin{matharray}{rcl}
wenzelm@26849:     \indexdef{HOL}{command}{value}\mbox{\isa{\isacommand{value}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
wenzelm@26854:     \indexdef{HOL}{command}{code\_module}\mbox{\isa{\isacommand{code{\isacharunderscore}module}}} & : & \isartrans{theory}{theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{code\_library}\mbox{\isa{\isacommand{code{\isacharunderscore}library}}} & : & \isartrans{theory}{theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{consts\_code}\mbox{\isa{\isacommand{consts{\isacharunderscore}code}}} & : & \isartrans{theory}{theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{types\_code}\mbox{\isa{\isacommand{types{\isacharunderscore}code}}} & : & \isartrans{theory}{theory} \\  
wenzelm@26849:     \indexdef{HOL}{attribute}{code}\mbox{\isa{code}} & : & \isaratt \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26849:   \begin{rail}
wenzelm@26849:   'value' term
wenzelm@26849:   ;
wenzelm@26849: 
wenzelm@26849:   ( 'code\_module' | 'code\_library' ) modespec ? name ? \\
wenzelm@26849:     ( 'file' name ) ? ( 'imports' ( name + ) ) ? \\
wenzelm@26849:     'contains' ( ( name '=' term ) + | term + )
wenzelm@26849:   ;
wenzelm@26849: 
wenzelm@26849:   modespec: '(' ( name * ) ')'
wenzelm@26849:   ;
wenzelm@26849: 
wenzelm@26849:   'consts\_code' (codespec +)
wenzelm@26849:   ;
wenzelm@26849: 
wenzelm@26849:   codespec: const template attachment ?
wenzelm@26849:   ;
wenzelm@26849: 
wenzelm@26849:   'types\_code' (tycodespec +)
wenzelm@26849:   ;
wenzelm@26849: 
wenzelm@26849:   tycodespec: name template attachment ?
wenzelm@26849:   ;
wenzelm@26849: 
wenzelm@26849:   const: term
wenzelm@26849:   ;
wenzelm@26849: 
wenzelm@26849:   template: '(' string ')'
wenzelm@26849:   ;
wenzelm@26849: 
wenzelm@26849:   attachment: 'attach' modespec ? verblbrace text verbrbrace
wenzelm@26849:   ;
wenzelm@26849: 
wenzelm@26849:   'code' (name)?
wenzelm@26849:   ;
wenzelm@26849:   \end{rail}
wenzelm@26849: 
wenzelm@26849:   \begin{descr}
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{value}}}~\isa{t}] evaluates and prints a
wenzelm@26849:   term using the code generator.
wenzelm@26849: 
wenzelm@26849:   \end{descr}
wenzelm@26849: 
wenzelm@26849:   \medskip The other framework generates code from functional programs
wenzelm@26849:   (including overloading using type classes) to SML \cite{SML}, OCaml
wenzelm@26849:   \cite{OCaml} and Haskell \cite{haskell-revised-report}.
wenzelm@26849:   Conceptually, code generation is split up in three steps:
wenzelm@26849:   \emph{selection} of code theorems, \emph{translation} into an
wenzelm@26849:   abstract executable view and \emph{serialization} to a specific
wenzelm@26849:   \emph{target language}.  See \cite{isabelle-codegen} for an
wenzelm@26849:   introduction on how to use it.
wenzelm@26849: 
wenzelm@26849:   \begin{matharray}{rcl}
wenzelm@26854:     \indexdef{HOL}{command}{export\_code}\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
wenzelm@26854:     \indexdef{HOL}{command}{code\_thms}\mbox{\isa{\isacommand{code{\isacharunderscore}thms}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
wenzelm@26854:     \indexdef{HOL}{command}{code\_deps}\mbox{\isa{\isacommand{code{\isacharunderscore}deps}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
wenzelm@26854:     \indexdef{HOL}{command}{code\_datatype}\mbox{\isa{\isacommand{code{\isacharunderscore}datatype}}} & : & \isartrans{theory}{theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{code\_const}\mbox{\isa{\isacommand{code{\isacharunderscore}const}}} & : & \isartrans{theory}{theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{code\_type}\mbox{\isa{\isacommand{code{\isacharunderscore}type}}} & : & \isartrans{theory}{theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{code\_class}\mbox{\isa{\isacommand{code{\isacharunderscore}class}}} & : & \isartrans{theory}{theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{code\_instance}\mbox{\isa{\isacommand{code{\isacharunderscore}instance}}} & : & \isartrans{theory}{theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{code\_monad}\mbox{\isa{\isacommand{code{\isacharunderscore}monad}}} & : & \isartrans{theory}{theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{code\_reserved}\mbox{\isa{\isacommand{code{\isacharunderscore}reserved}}} & : & \isartrans{theory}{theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{code\_include}\mbox{\isa{\isacommand{code{\isacharunderscore}include}}} & : & \isartrans{theory}{theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{code\_modulename}\mbox{\isa{\isacommand{code{\isacharunderscore}modulename}}} & : & \isartrans{theory}{theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{code\_exception}\mbox{\isa{\isacommand{code{\isacharunderscore}exception}}} & : & \isartrans{theory}{theory} \\
wenzelm@26854:     \indexdef{HOL}{command}{print\_codesetup}\mbox{\isa{\isacommand{print{\isacharunderscore}codesetup}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
wenzelm@26849:     \indexdef{HOL}{attribute}{code}\mbox{\isa{code}} & : & \isaratt \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26849:   \begin{rail}
wenzelm@26849:     'export\_code' ( constexpr + ) ? \\
wenzelm@26849:       ( ( 'in' target ( 'module\_name' string ) ? \\
wenzelm@26849:         ( 'file' ( string | '-' ) ) ? ( '(' args ')' ) ?) + ) ?
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     'code\_thms' ( constexpr + ) ?
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     'code\_deps' ( constexpr + ) ?
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     const: term
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     constexpr: ( const | 'name.*' | '*' )
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     typeconstructor: nameref
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     class: nameref
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     target: 'OCaml' | 'SML' | 'Haskell'
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     'code\_datatype' const +
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     'code\_const' (const + 'and') \\
wenzelm@26849:       ( ( '(' target ( syntax ? + 'and' ) ')' ) + )
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     'code\_type' (typeconstructor + 'and') \\
wenzelm@26849:       ( ( '(' target ( syntax ? + 'and' ) ')' ) + )
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     'code\_class' (class + 'and') \\
wenzelm@26849:       ( ( '(' target \\
wenzelm@26849:         ( ( string ('where' \\
wenzelm@26849:           ( const ( '==' | equiv ) string ) + ) ? ) ? + 'and' ) ')' ) + )
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     'code\_instance' (( typeconstructor '::' class ) + 'and') \\
wenzelm@26849:       ( ( '(' target ( '-' ? + 'and' ) ')' ) + )
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     'code\_monad' const const target
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     'code\_reserved' target ( string + )
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     'code\_include' target ( string ( string | '-') )
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     'code\_modulename' target ( ( string string ) + )
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     'code\_exception' ( const + )
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     syntax: string | ( 'infix' | 'infixl' | 'infixr' ) nat string
wenzelm@26849:     ;
wenzelm@26849: 
wenzelm@26849:     'code' ('func' | 'inline') ( 'del' )?
wenzelm@26849:     ;
wenzelm@26849:   \end{rail}
wenzelm@26849: 
wenzelm@26849:   \begin{descr}
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}] is the canonical interface
wenzelm@26849:   for generating and serializing code: for a given list of constants,
wenzelm@26849:   code is generated for the specified target languages.  Abstract code
wenzelm@26849:   is cached incrementally.  If no constant is given, the currently
wenzelm@26849:   cached code is serialized.  If no serialization instruction is
wenzelm@26849:   given, only abstract code is cached.
wenzelm@26849: 
wenzelm@26849:   Constants may be specified by giving them literally, referring to
wenzelm@26849:   all executable contants within a certain theory by giving \isa{{\isachardoublequote}name{\isachardot}{\isacharasterisk}{\isachardoublequote}}, or referring to \emph{all} executable constants currently
wenzelm@26849:   available by giving \isa{{\isachardoublequote}{\isacharasterisk}{\isachardoublequote}}.
wenzelm@26849: 
wenzelm@26849:   By default, for each involved theory one corresponding name space
wenzelm@26849:   module is generated.  Alternativly, a module name may be specified
wenzelm@26849:   after the \mbox{\isa{\isakeyword{module{\isacharunderscore}name}}} keyword; then \emph{all} code is
wenzelm@26849:   placed in this module.
wenzelm@26849: 
wenzelm@26849:   For \emph{SML} and \emph{OCaml}, the file specification refers to a
wenzelm@26849:   single file; for \emph{Haskell}, it refers to a whole directory,
wenzelm@26849:   where code is generated in multiple files reflecting the module
wenzelm@26849:   hierarchy.  The file specification ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' denotes standard
wenzelm@26849:   output.  For \emph{SML}, omitting the file specification compiles
wenzelm@26849:   code internally in the context of the current ML session.
wenzelm@26849: 
wenzelm@26849:   Serializers take an optional list of arguments in parentheses.  For
wenzelm@26849:   \emph{Haskell} a module name prefix may be given using the ``\isa{{\isachardoublequote}root{\isacharcolon}{\isachardoublequote}}'' argument; ``\isa{string{\isacharunderscore}classes}'' adds a ``\verb|deriving (Read, Show)|'' clause to each appropriate datatype
wenzelm@26849:   declaration.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}thms}}}] prints a list of theorems
wenzelm@26849:   representing the corresponding program containing all given
wenzelm@26849:   constants; if no constants are given, the currently cached code
wenzelm@26849:   theorems are printed.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}deps}}}] visualizes dependencies of
wenzelm@26849:   theorems representing the corresponding program containing all given
wenzelm@26849:   constants; if no constants are given, the currently cached code
wenzelm@26849:   theorems are visualized.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}datatype}}}] specifies a constructor set
wenzelm@26849:   for a logical type.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}const}}}] associates a list of constants
wenzelm@26849:   with target-specific serializations; omitting a serialization
wenzelm@26849:   deletes an existing serialization.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}type}}}] associates a list of type
wenzelm@26849:   constructors with target-specific serializations; omitting a
wenzelm@26849:   serialization deletes an existing serialization.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}class}}}] associates a list of classes
wenzelm@26849:   with target-specific class names; in addition, constants associated
wenzelm@26849:   with this class may be given target-specific names used for instance
wenzelm@26849:   declarations; omitting a serialization deletes an existing
wenzelm@26849:   serialization.  This applies only to \emph{Haskell}.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}instance}}}] declares a list of type
wenzelm@26849:   constructor / class instance relations as ``already present'' for a
wenzelm@26849:   given target.  Omitting a ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' deletes an existing
wenzelm@26849:   ``already present'' declaration.  This applies only to
wenzelm@26849:   \emph{Haskell}.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}monad}}}] provides an auxiliary
wenzelm@26849:   mechanism to generate monadic code.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}reserved}}}] declares a list of names as
wenzelm@26849:   reserved for a given target, preventing it to be shadowed by any
wenzelm@26849:   generated code.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}include}}}] adds arbitrary named content
wenzelm@26849:   (``include'') to generated code.  A as last argument ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}''
wenzelm@26849:   will remove an already added ``include''.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}modulename}}}] declares aliasings from
wenzelm@26849:   one module name onto another.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}exception}}}] declares constants which
wenzelm@26849:   are not required to have a definition by a defining equations; these
wenzelm@26849:   are mapped on exceptions instead.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{code}}~\isa{func}] explicitly selects (or
wenzelm@26849:   with option ``\isa{{\isachardoublequote}del{\isacharcolon}{\isachardoublequote}}'' deselects) a defining equation for
wenzelm@26849:   code generation.  Usually packages introducing defining equations
wenzelm@26849:   provide a resonable default setup for selection.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{code}}\isa{inline}] declares (or with
wenzelm@26849:   option ``\isa{{\isachardoublequote}del{\isacharcolon}{\isachardoublequote}}'' removes) inlining theorems which are
wenzelm@26849:   applied as rewrite rules to any defining equation during
wenzelm@26849:   preprocessing.
wenzelm@26849: 
wenzelm@26849:   \item [\mbox{\isa{\isacommand{print{\isacharunderscore}codesetup}}}] gives an overview on
wenzelm@26849:   selected defining equations, code generator datatypes and
wenzelm@26849:   preprocessor setup.
wenzelm@26849: 
wenzelm@26849:   \end{descr}%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \isadelimtheory
wenzelm@26849: %
wenzelm@26849: \endisadelimtheory
wenzelm@26849: %
wenzelm@26849: \isatagtheory
wenzelm@26840: \isacommand{end}\isamarkupfalse%
wenzelm@26840: %
wenzelm@26840: \endisatagtheory
wenzelm@26840: {\isafoldtheory}%
wenzelm@26840: %
wenzelm@26840: \isadelimtheory
wenzelm@26840: %
wenzelm@26840: \endisadelimtheory
wenzelm@26849: \isanewline
wenzelm@26849: \isanewline
wenzelm@26840: \end{isabellebody}%
wenzelm@26840: %%% Local Variables:
wenzelm@26840: %%% mode: latex
wenzelm@26840: %%% TeX-master: "root"
wenzelm@26840: %%% End:




