doc-src/IsarRef/Thy/document/HOL_Specific.tex
changeset 26902 8db1e960d636
parent 26895 d066f9db833b
child 26907 75466ad27dd7
equal deleted inserted replaced
26901:d1694ef6e7a7 26902:8db1e960d636
    28 }
    28 }
    29 \isamarkuptrue%
    29 \isamarkuptrue%
    30 %
    30 %
    31 \begin{isamarkuptext}%
    31 \begin{isamarkuptext}%
    32 \begin{matharray}{rcl}
    32 \begin{matharray}{rcl}
    33     \indexdef{HOL}{command}{typedecl}\mbox{\isa{\isacommand{typedecl}}} & : & \isartrans{theory}{theory} \\
    33     \indexdef{HOL}{command}{typedecl}\hypertarget{command.HOL.typedecl}{\hyperlink{command.HOL.typedecl}{\mbox{\isa{\isacommand{typedecl}}}}} & : & \isartrans{theory}{theory} \\
    34     \indexdef{HOL}{command}{typedef}\mbox{\isa{\isacommand{typedef}}} & : & \isartrans{theory}{proof(prove)} \\
    34     \indexdef{HOL}{command}{typedef}\hypertarget{command.HOL.typedef}{\hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}}} & : & \isartrans{theory}{proof(prove)} \\
    35   \end{matharray}
    35   \end{matharray}
    36 
    36 
    37   \begin{rail}
    37   \begin{rail}
    38     'typedecl' typespec infix?
    38     'typedecl' typespec infix?
    39     ;
    39     ;
    48     ;
    48     ;
    49   \end{rail}
    49   \end{rail}
    50 
    50 
    51   \begin{descr}
    51   \begin{descr}
    52   
    52   
    53   \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
    53   \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
    54   Isabelle/Pure (see \secref{sec:types-pure}), but also declares type
    54   Isabelle/Pure (see \secref{sec:types-pure}), but also declares type
    55   arity \isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}type{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ type{\isacharparenright}\ type{\isachardoublequote}}, making \isa{t} an
    55   arity \isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}type{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ type{\isacharparenright}\ type{\isachardoublequote}}, making \isa{t} an
    56   actual HOL type constructor.   %FIXME check, update
    56   actual HOL type constructor.   %FIXME check, update
    57   
    57   
    58   \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}.
    58   \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}.
    59   After finishing the proof, the theory will be augmented by a
    59   After finishing the proof, the theory will be augmented by a
    60   Gordon/HOL-style type definition, which establishes a bijection
    60   Gordon/HOL-style type definition, which establishes a bijection
    61   between the representing set \isa{A} and the new type \isa{t}.
    61   between the representing set \isa{A} and the new type \isa{t}.
    62   
    62   
    63   Technically, \mbox{\isa{\isacommand{typedef}}} defines both a type \isa{t} and a set (term constant) of the same name (an alternative base
    63   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
    64   name may be given in parentheses).  The injection from type to set
    64   name may be given in parentheses).  The injection from type to set
    65   is called \isa{Rep{\isacharunderscore}t}, its inverse \isa{Abs{\isacharunderscore}t} (this may be
    65   is called \isa{Rep{\isacharunderscore}t}, its inverse \isa{Abs{\isacharunderscore}t} (this may be
    66   changed via an explicit \mbox{\isa{\isakeyword{morphisms}}} declaration).
    66   changed via an explicit \hyperlink{keyword.HOL.morphisms}{\mbox{\isa{\isakeyword{morphisms}}}} declaration).
    67   
    67   
    68   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
    68   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
    69   corresponding injection/surjection pair (in both directions).  Rules
    69   corresponding injection/surjection pair (in both directions).  Rules
    70   \isa{Rep{\isacharunderscore}t{\isacharunderscore}inject} and \isa{Abs{\isacharunderscore}t{\isacharunderscore}inject} provide a slightly
    70   \isa{Rep{\isacharunderscore}t{\isacharunderscore}inject} and \isa{Abs{\isacharunderscore}t{\isacharunderscore}inject} provide a slightly
    71   more convenient view on the injectivity part, suitable for automated
    71   more convenient view on the injectivity part, suitable for automated
    72   proof tools (e.g.\ in \mbox{\isa{simp}} or \mbox{\isa{iff}}
    72   proof tools (e.g.\ in \hyperlink{attribute.simp}{\mbox{\isa{simp}}} or \hyperlink{attribute.iff}{\mbox{\isa{iff}}}
    73   declarations).  Rules \isa{Rep{\isacharunderscore}t{\isacharunderscore}cases}/\isa{Rep{\isacharunderscore}t{\isacharunderscore}induct}, and
    73   declarations).  Rules \isa{Rep{\isacharunderscore}t{\isacharunderscore}cases}/\isa{Rep{\isacharunderscore}t{\isacharunderscore}induct}, and
    74   \isa{Abs{\isacharunderscore}t{\isacharunderscore}cases}/\isa{Abs{\isacharunderscore}t{\isacharunderscore}induct} provide alternative views
    74   \isa{Abs{\isacharunderscore}t{\isacharunderscore}cases}/\isa{Abs{\isacharunderscore}t{\isacharunderscore}induct} provide alternative views
    75   on surjectivity; these are already declared as set or type rules for
    75   on surjectivity; these are already declared as set or type rules for
    76   the generic \mbox{\isa{cases}} and \mbox{\isa{induct}} methods.
    76   the generic \hyperlink{method.cases}{\mbox{\isa{cases}}} and \hyperlink{method.induct}{\mbox{\isa{induct}}} methods.
    77   
    77   
    78   An alternative name may be specified in parentheses; the default is
    78   An alternative name may be specified in parentheses; the default is
    79   to use \isa{t} as indicated before.  The ``\isa{{\isachardoublequote}{\isacharparenleft}open{\isacharparenright}{\isachardoublequote}}''
    79   to use \isa{t} as indicated before.  The ``\isa{{\isachardoublequote}{\isacharparenleft}open{\isacharparenright}{\isachardoublequote}}''
    80   declaration suppresses a separate constant definition for the
    80   declaration suppresses a separate constant definition for the
    81   representing set.
    81   representing set.
    83   \end{descr}
    83   \end{descr}
    84 
    84 
    85   Note that raw type declarations are rarely used in practice; the
    85   Note that raw type declarations are rarely used in practice; the
    86   main application is with experimental (or even axiomatic!) theory
    86   main application is with experimental (or even axiomatic!) theory
    87   fragments.  Instead of primitive HOL type definitions, user-level
    87   fragments.  Instead of primitive HOL type definitions, user-level
    88   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}).%
    88   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}).%
    89 \end{isamarkuptext}%
    89 \end{isamarkuptext}%
    90 \isamarkuptrue%
    90 \isamarkuptrue%
    91 %
    91 %
    92 \isamarkupsection{Adhoc tuples%
    92 \isamarkupsection{Adhoc tuples%
    93 }
    93 }
    94 \isamarkuptrue%
    94 \isamarkuptrue%
    95 %
    95 %
    96 \begin{isamarkuptext}%
    96 \begin{isamarkuptext}%
    97 \begin{matharray}{rcl}
    97 \begin{matharray}{rcl}
    98     \mbox{\isa{split{\isacharunderscore}format}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isaratt \\
    98     \hyperlink{attribute.HOL.split_format}{\mbox{\isa{split{\isacharunderscore}format}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isaratt \\
    99   \end{matharray}
    99   \end{matharray}
   100 
   100 
   101   \begin{rail}
   101   \begin{rail}
   102     'split\_format' (((name *) + 'and') | ('(' 'complete' ')'))
   102     'split\_format' (((name *) + 'and') | ('(' 'complete' ')'))
   103     ;
   103     ;
   104   \end{rail}
   104   \end{rail}
   105 
   105 
   106   \begin{descr}
   106   \begin{descr}
   107   
   107   
   108   \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
   108   \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
   109   low-level tuple types into canonical form as specified by the
   109   low-level tuple types into canonical form as specified by the
   110   arguments given; the \isa{i}-th collection of arguments refers to
   110   arguments given; the \isa{i}-th collection of arguments refers to
   111   occurrences in premise \isa{i} of the rule.  The ``\isa{{\isachardoublequote}{\isacharparenleft}complete{\isacharparenright}{\isachardoublequote}}'' option causes \emph{all} arguments in function
   111   occurrences in premise \isa{i} of the rule.  The ``\isa{{\isachardoublequote}{\isacharparenleft}complete{\isacharparenright}{\isachardoublequote}}'' option causes \emph{all} arguments in function
   112   applications to be represented canonically according to their tuple
   112   applications to be represented canonically according to their tuple
   113   type structure.
   113   type structure.
   202 }
   202 }
   203 \isamarkuptrue%
   203 \isamarkuptrue%
   204 %
   204 %
   205 \begin{isamarkuptext}%
   205 \begin{isamarkuptext}%
   206 \begin{matharray}{rcl}
   206 \begin{matharray}{rcl}
   207     \indexdef{HOL}{command}{record}\mbox{\isa{\isacommand{record}}} & : & \isartrans{theory}{theory} \\
   207     \indexdef{HOL}{command}{record}\hypertarget{command.HOL.record}{\hyperlink{command.HOL.record}{\mbox{\isa{\isacommand{record}}}}} & : & \isartrans{theory}{theory} \\
   208   \end{matharray}
   208   \end{matharray}
   209 
   209 
   210   \begin{rail}
   210   \begin{rail}
   211     'record' typespec '=' (type '+')? (constdecl +)
   211     'record' typespec '=' (type '+')? (constdecl +)
   212     ;
   212     ;
   213   \end{rail}
   213   \end{rail}
   214 
   214 
   215   \begin{descr}
   215   \begin{descr}
   216 
   216 
   217   \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
   217   \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
   218   extensible record type \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharparenright}\ t{\isachardoublequote}},
   218   extensible record type \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharparenright}\ t{\isachardoublequote}},
   219   derived from the optional parent record \isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}} by adding new
   219   derived from the optional parent record \isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}} by adding new
   220   field components \isa{{\isachardoublequote}c\isactrlsub i\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub i{\isachardoublequote}} etc.
   220   field components \isa{{\isachardoublequote}c\isactrlsub i\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub i{\isachardoublequote}} etc.
   221 
   221 
   222   The type variables of \isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isasymsigma}\isactrlsub i{\isachardoublequote}} need to be
   222   The type variables of \isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isasymsigma}\isactrlsub i{\isachardoublequote}} need to be
   324   \begin{enumerate}
   324   \begin{enumerate}
   325   
   325   
   326   \item Standard conversions for selectors or updates applied to
   326   \item Standard conversions for selectors or updates applied to
   327   record constructor terms are made part of the default Simplifier
   327   record constructor terms are made part of the default Simplifier
   328   context; thus proofs by reduction of basic operations merely require
   328   context; thus proofs by reduction of basic operations merely require
   329   the \mbox{\isa{simp}} method without further arguments.  These rules
   329   the \hyperlink{method.simp}{\mbox{\isa{simp}}} method without further arguments.  These rules
   330   are available as \isa{{\isachardoublequote}t{\isachardot}simps{\isachardoublequote}}, too.
   330   are available as \isa{{\isachardoublequote}t{\isachardot}simps{\isachardoublequote}}, too.
   331   
   331   
   332   \item Selectors applied to updated records are automatically reduced
   332   \item Selectors applied to updated records are automatically reduced
   333   by an internal simplification procedure, which is also part of the
   333   by an internal simplification procedure, which is also part of the
   334   standard Simplifier setup.
   334   standard Simplifier setup.
   335 
   335 
   336   \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
   336   \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
   337   Reasoner as \mbox{\isa{iff}} rules.  These rules are available as
   337   Reasoner as \hyperlink{attribute.iff}{\mbox{\isa{iff}}} rules.  These rules are available as
   338   \isa{{\isachardoublequote}t{\isachardot}iffs{\isachardoublequote}}.
   338   \isa{{\isachardoublequote}t{\isachardot}iffs{\isachardoublequote}}.
   339 
   339 
   340   \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,
   340   \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,
   341   and as the basic rule context as ``\mbox{\isa{intro}}\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}''.
   341   and as the basic rule context as ``\hyperlink{attribute.intro}{\mbox{\isa{intro}}}\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}''.
   342   The rule is called \isa{{\isachardoublequote}t{\isachardot}equality{\isachardoublequote}}.
   342   The rule is called \isa{{\isachardoublequote}t{\isachardot}equality{\isachardoublequote}}.
   343 
   343 
   344   \item Representations of arbitrary record expressions as canonical
   344   \item Representations of arbitrary record expressions as canonical
   345   constructor terms are provided both in \mbox{\isa{cases}} and \mbox{\isa{induct}} format (cf.\ the generic proof methods of the same name,
   345   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,
   346   \secref{sec:cases-induct}).  Several variations are available, for
   346   \secref{sec:cases-induct}).  Several variations are available, for
   347   fixed records, record schemes, more parts etc.
   347   fixed records, record schemes, more parts etc.
   348   
   348   
   349   The generic proof methods are sufficiently smart to pick the most
   349   The generic proof methods are sufficiently smart to pick the most
   350   sensible rule according to the type of the indicated record
   350   sensible rule according to the type of the indicated record
   362 }
   362 }
   363 \isamarkuptrue%
   363 \isamarkuptrue%
   364 %
   364 %
   365 \begin{isamarkuptext}%
   365 \begin{isamarkuptext}%
   366 \begin{matharray}{rcl}
   366 \begin{matharray}{rcl}
   367     \indexdef{HOL}{command}{datatype}\mbox{\isa{\isacommand{datatype}}} & : & \isartrans{theory}{theory} \\
   367     \indexdef{HOL}{command}{datatype}\hypertarget{command.HOL.datatype}{\hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}}} & : & \isartrans{theory}{theory} \\
   368     \indexdef{HOL}{command}{rep\_datatype}\mbox{\isa{\isacommand{rep{\isacharunderscore}datatype}}} & : & \isartrans{theory}{theory} \\
   368     \indexdef{HOL}{command}{rep\_datatype}\hypertarget{command.HOL.rep_datatype}{\hyperlink{command.HOL.rep_datatype}{\mbox{\isa{\isacommand{rep{\isacharunderscore}datatype}}}}} & : & \isartrans{theory}{theory} \\
   369   \end{matharray}
   369   \end{matharray}
   370 
   370 
   371   \begin{rail}
   371   \begin{rail}
   372     'datatype' (dtspec + 'and')
   372     'datatype' (dtspec + 'and')
   373     ;
   373     ;
   381     dtrules: 'distinct' thmrefs 'inject' thmrefs 'induction' thmrefs
   381     dtrules: 'distinct' thmrefs 'inject' thmrefs 'induction' thmrefs
   382   \end{rail}
   382   \end{rail}
   383 
   383 
   384   \begin{descr}
   384   \begin{descr}
   385 
   385 
   386   \item [\mbox{\isa{\isacommand{datatype}}}] defines inductive datatypes in
   386   \item [\hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}}] defines inductive datatypes in
   387   HOL.
   387   HOL.
   388 
   388 
   389   \item [\mbox{\isa{\isacommand{rep{\isacharunderscore}datatype}}}] represents existing types as
   389   \item [\hyperlink{command.HOL.rep_datatype}{\mbox{\isa{\isacommand{rep{\isacharunderscore}datatype}}}}] represents existing types as
   390   inductive ones, generating the standard infrastructure of derived
   390   inductive ones, generating the standard infrastructure of derived
   391   concepts (primitive recursion etc.).
   391   concepts (primitive recursion etc.).
   392 
   392 
   393   \end{descr}
   393   \end{descr}
   394 
   394 
   397   after the types (see also \secref{sec:cases-induct}).
   397   after the types (see also \secref{sec:cases-induct}).
   398 
   398 
   399   See \cite{isabelle-HOL} for more details on datatypes, but beware of
   399   See \cite{isabelle-HOL} for more details on datatypes, but beware of
   400   the old-style theory syntax being used there!  Apart from proper
   400   the old-style theory syntax being used there!  Apart from proper
   401   proof methods for case-analysis and induction, there are also
   401   proof methods for case-analysis and induction, there are also
   402   emulations of ML tactics \mbox{\isa{case{\isacharunderscore}tac}} and \mbox{\isa{induct{\isacharunderscore}tac}} available, see \secref{sec:hol-induct-tac}; these admit
   402   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
   403   to refer directly to the internal structure of subgoals (including
   403   to refer directly to the internal structure of subgoals (including
   404   internally bound parameters).%
   404   internally bound parameters).%
   405 \end{isamarkuptext}%
   405 \end{isamarkuptext}%
   406 \isamarkuptrue%
   406 \isamarkuptrue%
   407 %
   407 %
   409 }
   409 }
   410 \isamarkuptrue%
   410 \isamarkuptrue%
   411 %
   411 %
   412 \begin{isamarkuptext}%
   412 \begin{isamarkuptext}%
   413 \begin{matharray}{rcl}
   413 \begin{matharray}{rcl}
   414     \indexdef{HOL}{command}{primrec}\mbox{\isa{\isacommand{primrec}}} & : & \isarkeep{local{\dsh}theory} \\
   414     \indexdef{HOL}{command}{primrec}\hypertarget{command.HOL.primrec}{\hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}}} & : & \isarkeep{local{\dsh}theory} \\
   415     \indexdef{HOL}{command}{fun}\mbox{\isa{\isacommand{fun}}} & : & \isarkeep{local{\dsh}theory} \\
   415     \indexdef{HOL}{command}{fun}\hypertarget{command.HOL.fun}{\hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}}} & : & \isarkeep{local{\dsh}theory} \\
   416     \indexdef{HOL}{command}{function}\mbox{\isa{\isacommand{function}}} & : & \isartrans{local{\dsh}theory}{proof(prove)} \\
   416     \indexdef{HOL}{command}{function}\hypertarget{command.HOL.function}{\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}} & : & \isartrans{local{\dsh}theory}{proof(prove)} \\
   417     \indexdef{HOL}{command}{termination}\mbox{\isa{\isacommand{termination}}} & : & \isartrans{local{\dsh}theory}{proof(prove)} \\
   417     \indexdef{HOL}{command}{termination}\hypertarget{command.HOL.termination}{\hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}} & : & \isartrans{local{\dsh}theory}{proof(prove)} \\
   418   \end{matharray}
   418   \end{matharray}
   419 
   419 
   420   \railalias{funopts}{function\_opts}  %FIXME ??
   420   \railalias{funopts}{function\_opts}  %FIXME ??
   421 
   421 
   422   \begin{rail}
   422   \begin{rail}
   434     'termination' ( term )?
   434     'termination' ( term )?
   435   \end{rail}
   435   \end{rail}
   436 
   436 
   437   \begin{descr}
   437   \begin{descr}
   438 
   438 
   439   \item [\mbox{\isa{\isacommand{primrec}}}] defines primitive recursive
   439   \item [\hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}}] defines primitive recursive
   440   functions over datatypes, see also \cite{isabelle-HOL}.
   440   functions over datatypes, see also \cite{isabelle-HOL}.
   441 
   441 
   442   \item [\mbox{\isa{\isacommand{function}}}] defines functions by general
   442   \item [\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}] defines functions by general
   443   wellfounded recursion. A detailed description with examples can be
   443   wellfounded recursion. A detailed description with examples can be
   444   found in \cite{isabelle-function}. The function is specified by a
   444   found in \cite{isabelle-function}. The function is specified by a
   445   set of (possibly conditional) recursive equations with arbitrary
   445   set of (possibly conditional) recursive equations with arbitrary
   446   pattern matching. The command generates proof obligations for the
   446   pattern matching. The command generates proof obligations for the
   447   completeness and the compatibility of patterns.
   447   completeness and the compatibility of patterns.
   448 
   448 
   449   The defined function is considered partial, and the resulting
   449   The defined function is considered partial, and the resulting
   450   simplification rules (named \isa{{\isachardoublequote}f{\isachardot}psimps{\isachardoublequote}}) and induction rule
   450   simplification rules (named \isa{{\isachardoublequote}f{\isachardot}psimps{\isachardoublequote}}) and induction rule
   451   (named \isa{{\isachardoublequote}f{\isachardot}pinduct{\isachardoublequote}}) are guarded by a generated domain
   451   (named \isa{{\isachardoublequote}f{\isachardot}pinduct{\isachardoublequote}}) are guarded by a generated domain
   452   predicate \isa{{\isachardoublequote}f{\isacharunderscore}dom{\isachardoublequote}}. The \mbox{\isa{\isacommand{termination}}}
   452   predicate \isa{{\isachardoublequote}f{\isacharunderscore}dom{\isachardoublequote}}. The \hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}
   453   command can then be used to establish that the function is total.
   453   command can then be used to establish that the function is total.
   454 
   454 
   455   \item [\mbox{\isa{\isacommand{fun}}}] is a shorthand notation for
   455   \item [\hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}}] is a shorthand notation for
   456   ``\mbox{\isa{\isacommand{function}}}~\isa{{\isachardoublequote}{\isacharparenleft}sequential{\isacharparenright}{\isachardoublequote}}, followed by
   456   ``\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}~\isa{{\isachardoublequote}{\isacharparenleft}sequential{\isacharparenright}{\isachardoublequote}}, followed by
   457   automated proof attempts regarding pattern matching and termination.
   457   automated proof attempts regarding pattern matching and termination.
   458   See \cite{isabelle-function} for further details.
   458   See \cite{isabelle-function} for further details.
   459 
   459 
   460   \item [\mbox{\isa{\isacommand{termination}}}~\isa{f}] commences a
   460   \item [\hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}~\isa{f}] commences a
   461   termination proof for the previously defined function \isa{f}.  If
   461   termination proof for the previously defined function \isa{f}.  If
   462   this is omitted, the command refers to the most recent function
   462   this is omitted, the command refers to the most recent function
   463   definition.  After the proof is closed, the recursive equations and
   463   definition.  After the proof is closed, the recursive equations and
   464   the induction principle is established.
   464   the induction principle is established.
   465 
   465 
   466   \end{descr}
   466   \end{descr}
   467 
   467 
   468   %FIXME check
   468   %FIXME check
   469 
   469 
   470   Recursive definitions introduced by both the \mbox{\isa{\isacommand{primrec}}} and the \mbox{\isa{\isacommand{function}}} command accommodate
   470   Recursive definitions introduced by both the \hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}} and the \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} command accommodate
   471   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)
   471   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)
   472   refers to a specific induction rule, with parameters named according
   472   refers to a specific induction rule, with parameters named according
   473   to the user-specified equations.  Case names of \mbox{\isa{\isacommand{primrec}}} are that of the datatypes involved, while those of
   473   to the user-specified equations.  Case names of \hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}} are that of the datatypes involved, while those of
   474   \mbox{\isa{\isacommand{function}}} are numbered (starting from 1).
   474   \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} are numbered (starting from 1).
   475 
   475 
   476   The equations provided by these packages may be referred later as
   476   The equations provided by these packages may be referred later as
   477   theorem list \isa{{\isachardoublequote}f{\isachardot}simps{\isachardoublequote}}, where \isa{f} is the (collective)
   477   theorem list \isa{{\isachardoublequote}f{\isachardot}simps{\isachardoublequote}}, where \isa{f} is the (collective)
   478   name of the functions defined.  Individual equations may be named
   478   name of the functions defined.  Individual equations may be named
   479   explicitly as well.
   479   explicitly as well.
   480 
   480 
   481   The \mbox{\isa{\isacommand{function}}} command accepts the following
   481   The \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} command accepts the following
   482   options.
   482   options.
   483 
   483 
   484   \begin{descr}
   484   \begin{descr}
   485 
   485 
   486   \item [\isa{sequential}] enables a preprocessor which
   486   \item [\isa{sequential}] enables a preprocessor which
   516 }
   516 }
   517 \isamarkuptrue%
   517 \isamarkuptrue%
   518 %
   518 %
   519 \begin{isamarkuptext}%
   519 \begin{isamarkuptext}%
   520 \begin{matharray}{rcl}
   520 \begin{matharray}{rcl}
   521     \indexdef{HOL}{method}{pat\_completeness}\mbox{\isa{pat{\isacharunderscore}completeness}} & : & \isarmeth \\
   521     \indexdef{HOL}{method}{pat\_completeness}\hypertarget{method.HOL.pat_completeness}{\hyperlink{method.HOL.pat_completeness}{\mbox{\isa{pat{\isacharunderscore}completeness}}}} & : & \isarmeth \\
   522     \indexdef{HOL}{method}{relation}\mbox{\isa{relation}} & : & \isarmeth \\
   522     \indexdef{HOL}{method}{relation}\hypertarget{method.HOL.relation}{\hyperlink{method.HOL.relation}{\mbox{\isa{relation}}}} & : & \isarmeth \\
   523     \indexdef{HOL}{method}{lexicographic\_order}\mbox{\isa{lexicographic{\isacharunderscore}order}} & : & \isarmeth \\
   523     \indexdef{HOL}{method}{lexicographic\_order}\hypertarget{method.HOL.lexicographic_order}{\hyperlink{method.HOL.lexicographic_order}{\mbox{\isa{lexicographic{\isacharunderscore}order}}}} & : & \isarmeth \\
   524   \end{matharray}
   524   \end{matharray}
   525 
   525 
   526   \begin{rail}
   526   \begin{rail}
   527     'relation' term
   527     'relation' term
   528     ;
   528     ;
   530     ;
   530     ;
   531   \end{rail}
   531   \end{rail}
   532 
   532 
   533   \begin{descr}
   533   \begin{descr}
   534 
   534 
   535   \item [\mbox{\isa{pat{\isacharunderscore}completeness}}] is a specialized method to
   535   \item [\hyperlink{method.HOL.pat_completeness}{\mbox{\isa{pat{\isacharunderscore}completeness}}}] is a specialized method to
   536   solve goals regarding the completeness of pattern matching, as
   536   solve goals regarding the completeness of pattern matching, as
   537   required by the \mbox{\isa{\isacommand{function}}} package (cf.\
   537   required by the \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} package (cf.\
   538   \cite{isabelle-function}).
   538   \cite{isabelle-function}).
   539 
   539 
   540   \item [\mbox{\isa{relation}}~\isa{R}] introduces a termination
   540   \item [\hyperlink{method.HOL.relation}{\mbox{\isa{relation}}}~\isa{R}] introduces a termination
   541   proof using the relation \isa{R}.  The resulting proof state will
   541   proof using the relation \isa{R}.  The resulting proof state will
   542   contain goals expressing that \isa{R} is wellfounded, and that the
   542   contain goals expressing that \isa{R} is wellfounded, and that the
   543   arguments of recursive calls decrease with respect to \isa{R}.
   543   arguments of recursive calls decrease with respect to \isa{R}.
   544   Usually, this method is used as the initial proof step of manual
   544   Usually, this method is used as the initial proof step of manual
   545   termination proofs.
   545   termination proofs.
   546 
   546 
   547   \item [\mbox{\isa{lexicographic{\isacharunderscore}order}}] attempts a fully
   547   \item [\hyperlink{method.HOL.lexicographic_order}{\mbox{\isa{lexicographic{\isacharunderscore}order}}}] attempts a fully
   548   automated termination proof by searching for a lexicographic
   548   automated termination proof by searching for a lexicographic
   549   combination of size measures on the arguments of the function. The
   549   combination of size measures on the arguments of the function. The
   550   method accepts the same arguments as the \mbox{\isa{auto}} method,
   550   method accepts the same arguments as the \hyperlink{method.auto}{\mbox{\isa{auto}}} method,
   551   which it uses internally to prove local descents.  The same context
   551   which it uses internally to prove local descents.  The same context
   552   modifiers as for \mbox{\isa{auto}} are accepted, see
   552   modifiers as for \hyperlink{method.auto}{\mbox{\isa{auto}}} are accepted, see
   553   \secref{sec:clasimp}.
   553   \secref{sec:clasimp}.
   554 
   554 
   555   In case of failure, extensive information is printed, which can help
   555   In case of failure, extensive information is printed, which can help
   556   to analyse the situation (cf.\ \cite{isabelle-function}).
   556   to analyse the situation (cf.\ \cite{isabelle-function}).
   557 
   557 
   562 \isamarkupsubsection{Old-style recursive function definitions (TFL)%
   562 \isamarkupsubsection{Old-style recursive function definitions (TFL)%
   563 }
   563 }
   564 \isamarkuptrue%
   564 \isamarkuptrue%
   565 %
   565 %
   566 \begin{isamarkuptext}%
   566 \begin{isamarkuptext}%
   567 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.
   567 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.
   568 
   568 
   569   \begin{matharray}{rcl}
   569   \begin{matharray}{rcl}
   570     \indexdef{HOL}{command}{recdef}\mbox{\isa{\isacommand{recdef}}} & : & \isartrans{theory}{theory} \\
   570     \indexdef{HOL}{command}{recdef}\hypertarget{command.HOL.recdef}{\hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}}} & : & \isartrans{theory}{theory} \\
   571     \indexdef{HOL}{command}{recdef\_tc}\mbox{\isa{\isacommand{recdef{\isacharunderscore}tc}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isartrans{theory}{proof(prove)} \\
   571     \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)} \\
   572   \end{matharray}
   572   \end{matharray}
   573 
   573 
   574   \begin{rail}
   574   \begin{rail}
   575     'recdef' ('(' 'permissive' ')')? \\ name term (prop +) hints?
   575     'recdef' ('(' 'permissive' ')')? \\ name term (prop +) hints?
   576     ;
   576     ;
   584     ;
   584     ;
   585   \end{rail}
   585   \end{rail}
   586 
   586 
   587   \begin{descr}
   587   \begin{descr}
   588   
   588   
   589   \item [\mbox{\isa{\isacommand{recdef}}}] defines general well-founded
   589   \item [\hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}}] defines general well-founded
   590   recursive functions (using the TFL package), see also
   590   recursive functions (using the TFL package), see also
   591   \cite{isabelle-HOL}.  The ``\isa{{\isachardoublequote}{\isacharparenleft}permissive{\isacharparenright}{\isachardoublequote}}'' option tells
   591   \cite{isabelle-HOL}.  The ``\isa{{\isachardoublequote}{\isacharparenleft}permissive{\isacharparenright}{\isachardoublequote}}'' option tells
   592   TFL to recover from failed proof attempts, returning unfinished
   592   TFL to recover from failed proof attempts, returning unfinished
   593   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
   593   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
   594   automated proof process of TFL.  Additional \mbox{\isa{clasimpmod}}
   594   automated proof process of TFL.  Additional \hyperlink{syntax.clasimpmod}{\mbox{\isa{clasimpmod}}}
   595   declarations (cf.\ \secref{sec:clasimp}) may be given to tune the
   595   declarations (cf.\ \secref{sec:clasimp}) may be given to tune the
   596   context of the Simplifier (cf.\ \secref{sec:simplifier}) and
   596   context of the Simplifier (cf.\ \secref{sec:simplifier}) and
   597   Classical reasoner (cf.\ \secref{sec:classical}).
   597   Classical reasoner (cf.\ \secref{sec:classical}).
   598   
   598   
   599   \item [\mbox{\isa{\isacommand{recdef{\isacharunderscore}tc}}}~\isa{{\isachardoublequote}c\ {\isacharparenleft}i{\isacharparenright}{\isachardoublequote}}] recommences the
   599   \item [\hyperlink{command.HOL.recdef_tc}{\mbox{\isa{\isacommand{recdef{\isacharunderscore}tc}}}}~\isa{{\isachardoublequote}c\ {\isacharparenleft}i{\isacharparenright}{\isachardoublequote}}] recommences the
   600   proof for leftover termination condition number \isa{i} (default
   600   proof for leftover termination condition number \isa{i} (default
   601   1) as generated by a \mbox{\isa{\isacommand{recdef}}} definition of
   601   1) as generated by a \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} definition of
   602   constant \isa{c}.
   602   constant \isa{c}.
   603   
   603   
   604   Note that in most cases, \mbox{\isa{\isacommand{recdef}}} is able to finish
   604   Note that in most cases, \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} is able to finish
   605   its internal proofs without manual intervention.
   605   its internal proofs without manual intervention.
   606 
   606 
   607   \end{descr}
   607   \end{descr}
   608 
   608 
   609   \medskip Hints for \mbox{\isa{\isacommand{recdef}}} may be also declared
   609   \medskip Hints for \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} may be also declared
   610   globally, using the following attributes.
   610   globally, using the following attributes.
   611 
   611 
   612   \begin{matharray}{rcl}
   612   \begin{matharray}{rcl}
   613     \indexdef{HOL}{attribute}{recdef\_simp}\mbox{\isa{recdef{\isacharunderscore}simp}} & : & \isaratt \\
   613     \indexdef{HOL}{attribute}{recdef\_simp}\hypertarget{attribute.HOL.recdef_simp}{\hyperlink{attribute.HOL.recdef_simp}{\mbox{\isa{recdef{\isacharunderscore}simp}}}} & : & \isaratt \\
   614     \indexdef{HOL}{attribute}{recdef\_cong}\mbox{\isa{recdef{\isacharunderscore}cong}} & : & \isaratt \\
   614     \indexdef{HOL}{attribute}{recdef\_cong}\hypertarget{attribute.HOL.recdef_cong}{\hyperlink{attribute.HOL.recdef_cong}{\mbox{\isa{recdef{\isacharunderscore}cong}}}} & : & \isaratt \\
   615     \indexdef{HOL}{attribute}{recdef\_wf}\mbox{\isa{recdef{\isacharunderscore}wf}} & : & \isaratt \\
   615     \indexdef{HOL}{attribute}{recdef\_wf}\hypertarget{attribute.HOL.recdef_wf}{\hyperlink{attribute.HOL.recdef_wf}{\mbox{\isa{recdef{\isacharunderscore}wf}}}} & : & \isaratt \\
   616   \end{matharray}
   616   \end{matharray}
   617 
   617 
   618   \begin{rail}
   618   \begin{rail}
   619     ('recdef\_simp' | 'recdef\_cong' | 'recdef\_wf') (() | 'add' | 'del')
   619     ('recdef\_simp' | 'recdef\_cong' | 'recdef\_wf') (() | 'add' | 'del')
   620     ;
   620     ;
   626 }
   626 }
   627 \isamarkuptrue%
   627 \isamarkuptrue%
   628 %
   628 %
   629 \begin{isamarkuptext}%
   629 \begin{isamarkuptext}%
   630 \begin{matharray}{rcl}
   630 \begin{matharray}{rcl}
   631     \indexdef{HOL}{command}{specification}\mbox{\isa{\isacommand{specification}}} & : & \isartrans{theory}{proof(prove)} \\
   631     \indexdef{HOL}{command}{specification}\hypertarget{command.HOL.specification}{\hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}} & : & \isartrans{theory}{proof(prove)} \\
   632     \indexdef{HOL}{command}{ax\_specification}\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}} & : & \isartrans{theory}{proof(prove)} \\
   632     \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)} \\
   633   \end{matharray}
   633   \end{matharray}
   634 
   634 
   635   \begin{rail}
   635   \begin{rail}
   636   ('specification' | 'ax\_specification') '(' (decl +) ')' \\ (thmdecl? prop +)
   636   ('specification' | 'ax\_specification') '(' (decl +) ')' \\ (thmdecl? prop +)
   637   ;
   637   ;
   638   decl: ((name ':')? term '(' 'overloaded' ')'?)
   638   decl: ((name ':')? term '(' 'overloaded' ')'?)
   639   \end{rail}
   639   \end{rail}
   640 
   640 
   641   \begin{descr}
   641   \begin{descr}
   642 
   642 
   643   \item [\mbox{\isa{\isacommand{specification}}}~\isa{{\isachardoublequote}decls\ {\isasymphi}{\isachardoublequote}}] sets up a
   643   \item [\hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}~\isa{{\isachardoublequote}decls\ {\isasymphi}{\isachardoublequote}}] sets up a
   644   goal stating the existence of terms with the properties specified to
   644   goal stating the existence of terms with the properties specified to
   645   hold for the constants given in \isa{decls}.  After finishing the
   645   hold for the constants given in \isa{decls}.  After finishing the
   646   proof, the theory will be augmented with definitions for the given
   646   proof, the theory will be augmented with definitions for the given
   647   constants, as well as with theorems stating the properties for these
   647   constants, as well as with theorems stating the properties for these
   648   constants.
   648   constants.
   649 
   649 
   650   \item [\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}~\isa{{\isachardoublequote}decls\ {\isasymphi}{\isachardoublequote}}] sets
   650   \item [\hyperlink{command.HOL.ax_specification}{\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}}~\isa{{\isachardoublequote}decls\ {\isasymphi}{\isachardoublequote}}] sets
   651   up a goal stating the existence of terms with the properties
   651   up a goal stating the existence of terms with the properties
   652   specified to hold for the constants given in \isa{decls}.  After
   652   specified to hold for the constants given in \isa{decls}.  After
   653   finishing the proof, the theory will be augmented with axioms
   653   finishing the proof, the theory will be augmented with axioms
   654   expressing the properties given in the first place.
   654   expressing the properties given in the first place.
   655 
   655 
   658   bound to the name \isa{c{\isacharunderscore}def} unless a theorem name is given in
   658   bound to the name \isa{c{\isacharunderscore}def} unless a theorem name is given in
   659   the declaration.  Overloaded constants should be declared as such.
   659   the declaration.  Overloaded constants should be declared as such.
   660 
   660 
   661   \end{descr}
   661   \end{descr}
   662 
   662 
   663   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
   663   Whether to use \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}} or \hyperlink{command.HOL.ax_specification}{\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}} is to some extent a matter of style.  \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}} introduces no new axioms, and so by
   664   construction cannot introduce inconsistencies, whereas \mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}} does introduce axioms, but only after the
   664   construction cannot introduce inconsistencies, whereas \hyperlink{command.HOL.ax_specification}{\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}} does introduce axioms, but only after the
   665   user has explicitly proven it to be safe.  A practical issue must be
   665   user has explicitly proven it to be safe.  A practical issue must be
   666   considered, though: After introducing two constants with the same
   666   considered, though: After introducing two constants with the same
   667   properties using \mbox{\isa{\isacommand{specification}}}, one can prove
   667   properties using \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}, one can prove
   668   that the two constants are, in fact, equal.  If this might be a
   668   that the two constants are, in fact, equal.  If this might be a
   669   problem, one should use \mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}.%
   669   problem, one should use \hyperlink{command.HOL.ax_specification}{\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}}.%
   670 \end{isamarkuptext}%
   670 \end{isamarkuptext}%
   671 \isamarkuptrue%
   671 \isamarkuptrue%
   672 %
   672 %
   673 \isamarkupsection{Inductive and coinductive definitions \label{sec:hol-inductive}%
   673 \isamarkupsection{Inductive and coinductive definitions \label{sec:hol-inductive}%
   674 }
   674 }
   696   The types of the (co)inductive predicates (or sets) determine the
   696   The types of the (co)inductive predicates (or sets) determine the
   697   domain of the fixedpoint definition, and the package does not have
   697   domain of the fixedpoint definition, and the package does not have
   698   to use inference rules for type-checking.
   698   to use inference rules for type-checking.
   699 
   699 
   700   \begin{matharray}{rcl}
   700   \begin{matharray}{rcl}
   701     \indexdef{HOL}{command}{inductive}\mbox{\isa{\isacommand{inductive}}} & : & \isarkeep{local{\dsh}theory} \\
   701     \indexdef{HOL}{command}{inductive}\hypertarget{command.HOL.inductive}{\hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}}} & : & \isarkeep{local{\dsh}theory} \\
   702     \indexdef{HOL}{command}{inductive\_set}\mbox{\isa{\isacommand{inductive{\isacharunderscore}set}}} & : & \isarkeep{local{\dsh}theory} \\
   702     \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} \\
   703     \indexdef{HOL}{command}{coinductive}\mbox{\isa{\isacommand{coinductive}}} & : & \isarkeep{local{\dsh}theory} \\
   703     \indexdef{HOL}{command}{coinductive}\hypertarget{command.HOL.coinductive}{\hyperlink{command.HOL.coinductive}{\mbox{\isa{\isacommand{coinductive}}}}} & : & \isarkeep{local{\dsh}theory} \\
   704     \indexdef{HOL}{command}{coinductive\_set}\mbox{\isa{\isacommand{coinductive{\isacharunderscore}set}}} & : & \isarkeep{local{\dsh}theory} \\
   704     \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} \\
   705     \indexdef{HOL}{attribute}{mono}\mbox{\isa{mono}} & : & \isaratt \\
   705     \indexdef{HOL}{attribute}{mono}\hypertarget{attribute.HOL.mono}{\hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}}} & : & \isaratt \\
   706   \end{matharray}
   706   \end{matharray}
   707 
   707 
   708   \begin{rail}
   708   \begin{rail}
   709     ('inductive' | 'inductive\_set' | 'coinductive' | 'coinductive\_set') target? fixes ('for' fixes)? \\
   709     ('inductive' | 'inductive\_set' | 'coinductive' | 'coinductive\_set') target? fixes ('for' fixes)? \\
   710     ('where' clauses)? ('monos' thmrefs)?
   710     ('where' clauses)? ('monos' thmrefs)?
   715     ;
   715     ;
   716   \end{rail}
   716   \end{rail}
   717 
   717 
   718   \begin{descr}
   718   \begin{descr}
   719 
   719 
   720   \item [\mbox{\isa{\isacommand{inductive}}} and \mbox{\isa{\isacommand{coinductive}}}] define (co)inductive predicates from the
   720   \item [\hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}} and \hyperlink{command.HOL.coinductive}{\mbox{\isa{\isacommand{coinductive}}}}] define (co)inductive predicates from the
   721   introduction rules given in the \mbox{\isa{\isakeyword{where}}} part.  The
   721   introduction rules given in the \hyperlink{keyword.where}{\mbox{\isa{\isakeyword{where}}}} part.  The
   722   optional \mbox{\isa{\isakeyword{for}}} part contains a list of parameters of the
   722   optional \hyperlink{keyword.for}{\mbox{\isa{\isakeyword{for}}}} part contains a list of parameters of the
   723   (co)inductive predicates that remain fixed throughout the
   723   (co)inductive predicates that remain fixed throughout the
   724   definition.  The optional \mbox{\isa{\isakeyword{monos}}} section contains
   724   definition.  The optional \hyperlink{keyword.monos}{\mbox{\isa{\isakeyword{monos}}}} section contains
   725   \emph{monotonicity theorems}, which are required for each operator
   725   \emph{monotonicity theorems}, which are required for each operator
   726   applied to a recursive set in the introduction rules.  There
   726   applied to a recursive set in the introduction rules.  There
   727   \emph{must} be a theorem of the form \isa{{\isachardoublequote}A\ {\isasymle}\ B\ {\isasymLongrightarrow}\ M\ A\ {\isasymle}\ M\ B{\isachardoublequote}},
   727   \emph{must} be a theorem of the form \isa{{\isachardoublequote}A\ {\isasymle}\ B\ {\isasymLongrightarrow}\ M\ A\ {\isasymle}\ M\ B{\isachardoublequote}},
   728   for each premise \isa{{\isachardoublequote}M\ R\isactrlsub i\ t{\isachardoublequote}} in an introduction rule!
   728   for each premise \isa{{\isachardoublequote}M\ R\isactrlsub i\ t{\isachardoublequote}} in an introduction rule!
   729 
   729 
   730   \item [\mbox{\isa{\isacommand{inductive{\isacharunderscore}set}}} and \mbox{\isa{\isacommand{coinductive{\isacharunderscore}set}}}] are wrappers for to the previous commands,
   730   \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,
   731   allowing the definition of (co)inductive sets.
   731   allowing the definition of (co)inductive sets.
   732 
   732 
   733   \item [\mbox{\isa{mono}}] declares monotonicity rules.  These
   733   \item [\hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}}] declares monotonicity rules.  These
   734   rule are involved in the automated monotonicity proof of \mbox{\isa{\isacommand{inductive}}}.
   734   rule are involved in the automated monotonicity proof of \hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}}.
   735 
   735 
   736   \end{descr}%
   736   \end{descr}%
   737 \end{isamarkuptext}%
   737 \end{isamarkuptext}%
   738 \isamarkuptrue%
   738 \isamarkuptrue%
   739 %
   739 %
   772 \isamarkuptrue%
   772 \isamarkuptrue%
   773 %
   773 %
   774 \begin{isamarkuptext}%
   774 \begin{isamarkuptext}%
   775 Each theory contains a default set of theorems that are used in
   775 Each theory contains a default set of theorems that are used in
   776   monotonicity proofs.  New rules can be added to this set via the
   776   monotonicity proofs.  New rules can be added to this set via the
   777   \mbox{\isa{mono}} attribute.  The HOL theory \isa{Inductive}
   777   \hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}} attribute.  The HOL theory \isa{Inductive}
   778   shows how this is done.  In general, the following monotonicity
   778   shows how this is done.  In general, the following monotonicity
   779   theorems may be added:
   779   theorems may be added:
   780 
   780 
   781   \begin{itemize}
   781   \begin{itemize}
   782 
   782 
   815 }
   815 }
   816 \isamarkuptrue%
   816 \isamarkuptrue%
   817 %
   817 %
   818 \begin{isamarkuptext}%
   818 \begin{isamarkuptext}%
   819 \begin{matharray}{rcl}
   819 \begin{matharray}{rcl}
   820     \indexdef{HOL}{method}{arith}\mbox{\isa{arith}} & : & \isarmeth \\
   820     \indexdef{HOL}{method}{arith}\hypertarget{method.HOL.arith}{\hyperlink{method.HOL.arith}{\mbox{\isa{arith}}}} & : & \isarmeth \\
   821     \indexdef{HOL}{attribute}{arith\_split}\mbox{\isa{arith{\isacharunderscore}split}} & : & \isaratt \\
   821     \indexdef{HOL}{attribute}{arith\_split}\hypertarget{attribute.HOL.arith_split}{\hyperlink{attribute.HOL.arith_split}{\mbox{\isa{arith{\isacharunderscore}split}}}} & : & \isaratt \\
   822   \end{matharray}
   822   \end{matharray}
   823 
   823 
   824   The \mbox{\isa{arith}} method decides linear arithmetic problems
   824   The \hyperlink{method.HOL.arith}{\mbox{\isa{arith}}} method decides linear arithmetic problems
   825   (on types \isa{nat}, \isa{int}, \isa{real}).  Any current
   825   (on types \isa{nat}, \isa{int}, \isa{real}).  Any current
   826   facts are inserted into the goal before running the procedure.
   826   facts are inserted into the goal before running the procedure.
   827 
   827 
   828   The \mbox{\isa{arith{\isacharunderscore}split}} attribute declares case split
   828   The \hyperlink{attribute.HOL.arith_split}{\mbox{\isa{arith{\isacharunderscore}split}}} attribute declares case split
   829   rules to be expanded before the arithmetic procedure is invoked.
   829   rules to be expanded before the arithmetic procedure is invoked.
   830 
   830 
   831   Note that a simpler (but faster) version of arithmetic reasoning is
   831   Note that a simpler (but faster) version of arithmetic reasoning is
   832   already performed by the Simplifier.%
   832   already performed by the Simplifier.%
   833 \end{isamarkuptext}%
   833 \end{isamarkuptext}%
   840 \begin{isamarkuptext}%
   840 \begin{isamarkuptext}%
   841 The following important tactical tools of Isabelle/HOL have been
   841 The following important tactical tools of Isabelle/HOL have been
   842   ported to Isar.  These should be never used in proper proof texts!
   842   ported to Isar.  These should be never used in proper proof texts!
   843 
   843 
   844   \begin{matharray}{rcl}
   844   \begin{matharray}{rcl}
   845     \indexdef{HOL}{method}{case\_tac}\mbox{\isa{case{\isacharunderscore}tac}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\
   845     \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 \\
   846     \indexdef{HOL}{method}{induct\_tac}\mbox{\isa{induct{\isacharunderscore}tac}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\
   846     \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 \\
   847     \indexdef{HOL}{method}{ind\_cases}\mbox{\isa{ind{\isacharunderscore}cases}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarmeth \\
   847     \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 \\
   848     \indexdef{HOL}{command}{inductive\_cases}\mbox{\isa{\isacommand{inductive{\isacharunderscore}cases}}} & : & \isartrans{theory}{theory} \\
   848     \indexdef{HOL}{command}{inductive\_cases}\hypertarget{command.HOL.inductive_cases}{\hyperlink{command.HOL.inductive_cases}{\mbox{\isa{\isacommand{inductive{\isacharunderscore}cases}}}}} & : & \isartrans{theory}{theory} \\
   849   \end{matharray}
   849   \end{matharray}
   850 
   850 
   851   \begin{rail}
   851   \begin{rail}
   852     'case\_tac' goalspec? term rule?
   852     'case\_tac' goalspec? term rule?
   853     ;
   853     ;
   862     ;
   862     ;
   863   \end{rail}
   863   \end{rail}
   864 
   864 
   865   \begin{descr}
   865   \begin{descr}
   866 
   866 
   867   \item [\mbox{\isa{case{\isacharunderscore}tac}} and \mbox{\isa{induct{\isacharunderscore}tac}}]
   867   \item [\hyperlink{method.HOL.case_tac}{\mbox{\isa{case{\isacharunderscore}tac}}} and \hyperlink{method.HOL.induct_tac}{\mbox{\isa{induct{\isacharunderscore}tac}}}]
   868   admit to reason about inductive datatypes only (unless an
   868   admit to reason about inductive datatypes only (unless an
   869   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.
   869   alternative rule is given explicitly).  Furthermore, \hyperlink{method.HOL.case_tac}{\mbox{\isa{case{\isacharunderscore}tac}}} does a classical case split on booleans; \hyperlink{method.HOL.induct_tac}{\mbox{\isa{induct{\isacharunderscore}tac}}} allows only variables to be given as instantiation.
   870   These tactic emulations feature both goal addressing and dynamic
   870   These tactic emulations feature both goal addressing and dynamic
   871   instantiation.  Note that named rule cases are \emph{not} provided
   871   instantiation.  Note that named rule cases are \emph{not} provided
   872   as would be by the proper \mbox{\isa{induct}} and \mbox{\isa{cases}} proof
   872   as would be by the proper \hyperlink{method.induct}{\mbox{\isa{induct}}} and \hyperlink{method.cases}{\mbox{\isa{cases}}} proof
   873   methods (see \secref{sec:cases-induct}).
   873   methods (see \secref{sec:cases-induct}).
   874   
   874   
   875   \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
   875   \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
   876   forward manner.
   876   forward manner.
   877 
   877 
   878   While \mbox{\isa{ind{\isacharunderscore}cases}} is a proof method to apply the
   878   While \hyperlink{method.HOL.ind_cases}{\mbox{\isa{ind{\isacharunderscore}cases}}} is a proof method to apply the
   879   result immediately as elimination rules, \mbox{\isa{\isacommand{inductive{\isacharunderscore}cases}}} provides case split theorems at the theory level
   879   result immediately as elimination rules, \hyperlink{command.HOL.inductive_cases}{\mbox{\isa{\isacommand{inductive{\isacharunderscore}cases}}}} provides case split theorems at the theory level
   880   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
   880   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
   881   be generalized before applying the resulting rule.
   881   be generalized before applying the resulting rule.
   882 
   882 
   883   \end{descr}%
   883   \end{descr}%
   884 \end{isamarkuptext}%
   884 \end{isamarkuptext}%
   885 \isamarkuptrue%
   885 \isamarkuptrue%
   897   One framework generates code from both functional and relational
   897   One framework generates code from both functional and relational
   898   programs to SML.  See \cite{isabelle-HOL} for further information
   898   programs to SML.  See \cite{isabelle-HOL} for further information
   899   (this actually covers the new-style theory format as well).
   899   (this actually covers the new-style theory format as well).
   900 
   900 
   901   \begin{matharray}{rcl}
   901   \begin{matharray}{rcl}
   902     \indexdef{HOL}{command}{value}\mbox{\isa{\isacommand{value}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
   902     \indexdef{HOL}{command}{value}\hypertarget{command.HOL.value}{\hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
   903     \indexdef{HOL}{command}{code\_module}\mbox{\isa{\isacommand{code{\isacharunderscore}module}}} & : & \isartrans{theory}{theory} \\
   903     \indexdef{HOL}{command}{code\_module}\hypertarget{command.HOL.code_module}{\hyperlink{command.HOL.code_module}{\mbox{\isa{\isacommand{code{\isacharunderscore}module}}}}} & : & \isartrans{theory}{theory} \\
   904     \indexdef{HOL}{command}{code\_library}\mbox{\isa{\isacommand{code{\isacharunderscore}library}}} & : & \isartrans{theory}{theory} \\
   904     \indexdef{HOL}{command}{code\_library}\hypertarget{command.HOL.code_library}{\hyperlink{command.HOL.code_library}{\mbox{\isa{\isacommand{code{\isacharunderscore}library}}}}} & : & \isartrans{theory}{theory} \\
   905     \indexdef{HOL}{command}{consts\_code}\mbox{\isa{\isacommand{consts{\isacharunderscore}code}}} & : & \isartrans{theory}{theory} \\
   905     \indexdef{HOL}{command}{consts\_code}\hypertarget{command.HOL.consts_code}{\hyperlink{command.HOL.consts_code}{\mbox{\isa{\isacommand{consts{\isacharunderscore}code}}}}} & : & \isartrans{theory}{theory} \\
   906     \indexdef{HOL}{command}{types\_code}\mbox{\isa{\isacommand{types{\isacharunderscore}code}}} & : & \isartrans{theory}{theory} \\  
   906     \indexdef{HOL}{command}{types\_code}\hypertarget{command.HOL.types_code}{\hyperlink{command.HOL.types_code}{\mbox{\isa{\isacommand{types{\isacharunderscore}code}}}}} & : & \isartrans{theory}{theory} \\  
   907     \indexdef{HOL}{attribute}{code}\mbox{\isa{code}} & : & \isaratt \\
   907     \indexdef{HOL}{attribute}{code}\hypertarget{attribute.HOL.code}{\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}} & : & \isaratt \\
   908   \end{matharray}
   908   \end{matharray}
   909 
   909 
   910   \begin{rail}
   910   \begin{rail}
   911   'value' term
   911   'value' term
   912   ;
   912   ;
   944   ;
   944   ;
   945   \end{rail}
   945   \end{rail}
   946 
   946 
   947   \begin{descr}
   947   \begin{descr}
   948 
   948 
   949   \item [\mbox{\isa{\isacommand{value}}}~\isa{t}] evaluates and prints a
   949   \item [\hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}~\isa{t}] evaluates and prints a
   950   term using the code generator.
   950   term using the code generator.
   951 
   951 
   952   \end{descr}
   952   \end{descr}
   953 
   953 
   954   \medskip The other framework generates code from functional programs
   954   \medskip The other framework generates code from functional programs
   959   abstract executable view and \emph{serialization} to a specific
   959   abstract executable view and \emph{serialization} to a specific
   960   \emph{target language}.  See \cite{isabelle-codegen} for an
   960   \emph{target language}.  See \cite{isabelle-codegen} for an
   961   introduction on how to use it.
   961   introduction on how to use it.
   962 
   962 
   963   \begin{matharray}{rcl}
   963   \begin{matharray}{rcl}
   964     \indexdef{HOL}{command}{export\_code}\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
   964     \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} \\
   965     \indexdef{HOL}{command}{code\_thms}\mbox{\isa{\isacommand{code{\isacharunderscore}thms}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
   965     \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} \\
   966     \indexdef{HOL}{command}{code\_deps}\mbox{\isa{\isacommand{code{\isacharunderscore}deps}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
   966     \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} \\
   967     \indexdef{HOL}{command}{code\_datatype}\mbox{\isa{\isacommand{code{\isacharunderscore}datatype}}} & : & \isartrans{theory}{theory} \\
   967     \indexdef{HOL}{command}{code\_datatype}\hypertarget{command.HOL.code_datatype}{\hyperlink{command.HOL.code_datatype}{\mbox{\isa{\isacommand{code{\isacharunderscore}datatype}}}}} & : & \isartrans{theory}{theory} \\
   968     \indexdef{HOL}{command}{code\_const}\mbox{\isa{\isacommand{code{\isacharunderscore}const}}} & : & \isartrans{theory}{theory} \\
   968     \indexdef{HOL}{command}{code\_const}\hypertarget{command.HOL.code_const}{\hyperlink{command.HOL.code_const}{\mbox{\isa{\isacommand{code{\isacharunderscore}const}}}}} & : & \isartrans{theory}{theory} \\
   969     \indexdef{HOL}{command}{code\_type}\mbox{\isa{\isacommand{code{\isacharunderscore}type}}} & : & \isartrans{theory}{theory} \\
   969     \indexdef{HOL}{command}{code\_type}\hypertarget{command.HOL.code_type}{\hyperlink{command.HOL.code_type}{\mbox{\isa{\isacommand{code{\isacharunderscore}type}}}}} & : & \isartrans{theory}{theory} \\
   970     \indexdef{HOL}{command}{code\_class}\mbox{\isa{\isacommand{code{\isacharunderscore}class}}} & : & \isartrans{theory}{theory} \\
   970     \indexdef{HOL}{command}{code\_class}\hypertarget{command.HOL.code_class}{\hyperlink{command.HOL.code_class}{\mbox{\isa{\isacommand{code{\isacharunderscore}class}}}}} & : & \isartrans{theory}{theory} \\
   971     \indexdef{HOL}{command}{code\_instance}\mbox{\isa{\isacommand{code{\isacharunderscore}instance}}} & : & \isartrans{theory}{theory} \\
   971     \indexdef{HOL}{command}{code\_instance}\hypertarget{command.HOL.code_instance}{\hyperlink{command.HOL.code_instance}{\mbox{\isa{\isacommand{code{\isacharunderscore}instance}}}}} & : & \isartrans{theory}{theory} \\
   972     \indexdef{HOL}{command}{code\_monad}\mbox{\isa{\isacommand{code{\isacharunderscore}monad}}} & : & \isartrans{theory}{theory} \\
   972     \indexdef{HOL}{command}{code\_monad}\hypertarget{command.HOL.code_monad}{\hyperlink{command.HOL.code_monad}{\mbox{\isa{\isacommand{code{\isacharunderscore}monad}}}}} & : & \isartrans{theory}{theory} \\
   973     \indexdef{HOL}{command}{code\_reserved}\mbox{\isa{\isacommand{code{\isacharunderscore}reserved}}} & : & \isartrans{theory}{theory} \\
   973     \indexdef{HOL}{command}{code\_reserved}\hypertarget{command.HOL.code_reserved}{\hyperlink{command.HOL.code_reserved}{\mbox{\isa{\isacommand{code{\isacharunderscore}reserved}}}}} & : & \isartrans{theory}{theory} \\
   974     \indexdef{HOL}{command}{code\_include}\mbox{\isa{\isacommand{code{\isacharunderscore}include}}} & : & \isartrans{theory}{theory} \\
   974     \indexdef{HOL}{command}{code\_include}\hypertarget{command.HOL.code_include}{\hyperlink{command.HOL.code_include}{\mbox{\isa{\isacommand{code{\isacharunderscore}include}}}}} & : & \isartrans{theory}{theory} \\
   975     \indexdef{HOL}{command}{code\_modulename}\mbox{\isa{\isacommand{code{\isacharunderscore}modulename}}} & : & \isartrans{theory}{theory} \\
   975     \indexdef{HOL}{command}{code\_modulename}\hypertarget{command.HOL.code_modulename}{\hyperlink{command.HOL.code_modulename}{\mbox{\isa{\isacommand{code{\isacharunderscore}modulename}}}}} & : & \isartrans{theory}{theory} \\
   976     \indexdef{HOL}{command}{code\_exception}\mbox{\isa{\isacommand{code{\isacharunderscore}exception}}} & : & \isartrans{theory}{theory} \\
   976     \indexdef{HOL}{command}{code\_exception}\hypertarget{command.HOL.code_exception}{\hyperlink{command.HOL.code_exception}{\mbox{\isa{\isacommand{code{\isacharunderscore}exception}}}}} & : & \isartrans{theory}{theory} \\
   977     \indexdef{HOL}{command}{print\_codesetup}\mbox{\isa{\isacommand{print{\isacharunderscore}codesetup}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
   977     \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} \\
   978     \indexdef{HOL}{attribute}{code}\mbox{\isa{code}} & : & \isaratt \\
   978     \indexdef{HOL}{attribute}{code}\hypertarget{attribute.HOL.code}{\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}} & : & \isaratt \\
   979   \end{matharray}
   979   \end{matharray}
   980 
   980 
   981   \begin{rail}
   981   \begin{rail}
   982     'export\_code' ( constexpr + ) ? \\
   982     'export\_code' ( constexpr + ) ? \\
   983       ( ( 'in' target ( 'module\_name' string ) ? \\
   983       ( ( 'in' target ( 'module\_name' string ) ? \\
  1048     ;
  1048     ;
  1049   \end{rail}
  1049   \end{rail}
  1050 
  1050 
  1051   \begin{descr}
  1051   \begin{descr}
  1052 
  1052 
  1053   \item [\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}] is the canonical interface
  1053   \item [\hyperlink{command.HOL.export_code}{\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}}] is the canonical interface
  1054   for generating and serializing code: for a given list of constants,
  1054   for generating and serializing code: for a given list of constants,
  1055   code is generated for the specified target languages.  Abstract code
  1055   code is generated for the specified target languages.  Abstract code
  1056   is cached incrementally.  If no constant is given, the currently
  1056   is cached incrementally.  If no constant is given, the currently
  1057   cached code is serialized.  If no serialization instruction is
  1057   cached code is serialized.  If no serialization instruction is
  1058   given, only abstract code is cached.
  1058   given, only abstract code is cached.
  1061   all executable contants within a certain theory by giving \isa{{\isachardoublequote}name{\isachardot}{\isacharasterisk}{\isachardoublequote}}, or referring to \emph{all} executable constants currently
  1061   all executable contants within a certain theory by giving \isa{{\isachardoublequote}name{\isachardot}{\isacharasterisk}{\isachardoublequote}}, or referring to \emph{all} executable constants currently
  1062   available by giving \isa{{\isachardoublequote}{\isacharasterisk}{\isachardoublequote}}.
  1062   available by giving \isa{{\isachardoublequote}{\isacharasterisk}{\isachardoublequote}}.
  1063 
  1063 
  1064   By default, for each involved theory one corresponding name space
  1064   By default, for each involved theory one corresponding name space
  1065   module is generated.  Alternativly, a module name may be specified
  1065   module is generated.  Alternativly, a module name may be specified
  1066   after the \mbox{\isa{\isakeyword{module{\isacharunderscore}name}}} keyword; then \emph{all} code is
  1066   after the \hyperlink{keyword.module_name}{\mbox{\isa{\isakeyword{module{\isacharunderscore}name}}}} keyword; then \emph{all} code is
  1067   placed in this module.
  1067   placed in this module.
  1068 
  1068 
  1069   For \emph{SML} and \emph{OCaml}, the file specification refers to a
  1069   For \emph{SML} and \emph{OCaml}, the file specification refers to a
  1070   single file; for \emph{Haskell}, it refers to a whole directory,
  1070   single file; for \emph{Haskell}, it refers to a whole directory,
  1071   where code is generated in multiple files reflecting the module
  1071   where code is generated in multiple files reflecting the module
  1075 
  1075 
  1076   Serializers take an optional list of arguments in parentheses.  For
  1076   Serializers take an optional list of arguments in parentheses.  For
  1077   \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
  1077   \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
  1078   declaration.
  1078   declaration.
  1079 
  1079 
  1080   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}thms}}}] prints a list of theorems
  1080   \item [\hyperlink{command.HOL.code_thms}{\mbox{\isa{\isacommand{code{\isacharunderscore}thms}}}}] prints a list of theorems
  1081   representing the corresponding program containing all given
  1081   representing the corresponding program containing all given
  1082   constants; if no constants are given, the currently cached code
  1082   constants; if no constants are given, the currently cached code
  1083   theorems are printed.
  1083   theorems are printed.
  1084 
  1084 
  1085   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}deps}}}] visualizes dependencies of
  1085   \item [\hyperlink{command.HOL.code_deps}{\mbox{\isa{\isacommand{code{\isacharunderscore}deps}}}}] visualizes dependencies of
  1086   theorems representing the corresponding program containing all given
  1086   theorems representing the corresponding program containing all given
  1087   constants; if no constants are given, the currently cached code
  1087   constants; if no constants are given, the currently cached code
  1088   theorems are visualized.
  1088   theorems are visualized.
  1089 
  1089 
  1090   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}datatype}}}] specifies a constructor set
  1090   \item [\hyperlink{command.HOL.code_datatype}{\mbox{\isa{\isacommand{code{\isacharunderscore}datatype}}}}] specifies a constructor set
  1091   for a logical type.
  1091   for a logical type.
  1092 
  1092 
  1093   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}const}}}] associates a list of constants
  1093   \item [\hyperlink{command.HOL.code_const}{\mbox{\isa{\isacommand{code{\isacharunderscore}const}}}}] associates a list of constants
  1094   with target-specific serializations; omitting a serialization
  1094   with target-specific serializations; omitting a serialization
  1095   deletes an existing serialization.
  1095   deletes an existing serialization.
  1096 
  1096 
  1097   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}type}}}] associates a list of type
  1097   \item [\hyperlink{command.HOL.code_type}{\mbox{\isa{\isacommand{code{\isacharunderscore}type}}}}] associates a list of type
  1098   constructors with target-specific serializations; omitting a
  1098   constructors with target-specific serializations; omitting a
  1099   serialization deletes an existing serialization.
  1099   serialization deletes an existing serialization.
  1100 
  1100 
  1101   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}class}}}] associates a list of classes
  1101   \item [\hyperlink{command.HOL.code_class}{\mbox{\isa{\isacommand{code{\isacharunderscore}class}}}}] associates a list of classes
  1102   with target-specific class names; in addition, constants associated
  1102   with target-specific class names; in addition, constants associated
  1103   with this class may be given target-specific names used for instance
  1103   with this class may be given target-specific names used for instance
  1104   declarations; omitting a serialization deletes an existing
  1104   declarations; omitting a serialization deletes an existing
  1105   serialization.  This applies only to \emph{Haskell}.
  1105   serialization.  This applies only to \emph{Haskell}.
  1106 
  1106 
  1107   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}instance}}}] declares a list of type
  1107   \item [\hyperlink{command.HOL.code_instance}{\mbox{\isa{\isacommand{code{\isacharunderscore}instance}}}}] declares a list of type
  1108   constructor / class instance relations as ``already present'' for a
  1108   constructor / class instance relations as ``already present'' for a
  1109   given target.  Omitting a ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' deletes an existing
  1109   given target.  Omitting a ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' deletes an existing
  1110   ``already present'' declaration.  This applies only to
  1110   ``already present'' declaration.  This applies only to
  1111   \emph{Haskell}.
  1111   \emph{Haskell}.
  1112 
  1112 
  1113   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}monad}}}] provides an auxiliary
  1113   \item [\hyperlink{command.HOL.code_monad}{\mbox{\isa{\isacommand{code{\isacharunderscore}monad}}}}] provides an auxiliary
  1114   mechanism to generate monadic code.
  1114   mechanism to generate monadic code.
  1115 
  1115 
  1116   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}reserved}}}] declares a list of names as
  1116   \item [\hyperlink{command.HOL.code_reserved}{\mbox{\isa{\isacommand{code{\isacharunderscore}reserved}}}}] declares a list of names as
  1117   reserved for a given target, preventing it to be shadowed by any
  1117   reserved for a given target, preventing it to be shadowed by any
  1118   generated code.
  1118   generated code.
  1119 
  1119 
  1120   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}include}}}] adds arbitrary named content
  1120   \item [\hyperlink{command.HOL.code_include}{\mbox{\isa{\isacommand{code{\isacharunderscore}include}}}}] adds arbitrary named content
  1121   (``include'') to generated code.  A as last argument ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}''
  1121   (``include'') to generated code.  A as last argument ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}''
  1122   will remove an already added ``include''.
  1122   will remove an already added ``include''.
  1123 
  1123 
  1124   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}modulename}}}] declares aliasings from
  1124   \item [\hyperlink{command.HOL.code_modulename}{\mbox{\isa{\isacommand{code{\isacharunderscore}modulename}}}}] declares aliasings from
  1125   one module name onto another.
  1125   one module name onto another.
  1126 
  1126 
  1127   \item [\mbox{\isa{\isacommand{code{\isacharunderscore}exception}}}] declares constants which
  1127   \item [\hyperlink{command.HOL.code_exception}{\mbox{\isa{\isacommand{code{\isacharunderscore}exception}}}}] declares constants which
  1128   are not required to have a definition by a defining equations; these
  1128   are not required to have a definition by a defining equations; these
  1129   are mapped on exceptions instead.
  1129   are mapped on exceptions instead.
  1130 
  1130 
  1131   \item [\mbox{\isa{code}}~\isa{func}] explicitly selects (or
  1131   \item [\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}~\isa{func}] explicitly selects (or
  1132   with option ``\isa{{\isachardoublequote}del{\isacharcolon}{\isachardoublequote}}'' deselects) a defining equation for
  1132   with option ``\isa{{\isachardoublequote}del{\isacharcolon}{\isachardoublequote}}'' deselects) a defining equation for
  1133   code generation.  Usually packages introducing defining equations
  1133   code generation.  Usually packages introducing defining equations
  1134   provide a resonable default setup for selection.
  1134   provide a resonable default setup for selection.
  1135 
  1135 
  1136   \item [\mbox{\isa{code}}\isa{inline}] declares (or with
  1136   \item [\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}\isa{inline}] declares (or with
  1137   option ``\isa{{\isachardoublequote}del{\isacharcolon}{\isachardoublequote}}'' removes) inlining theorems which are
  1137   option ``\isa{{\isachardoublequote}del{\isacharcolon}{\isachardoublequote}}'' removes) inlining theorems which are
  1138   applied as rewrite rules to any defining equation during
  1138   applied as rewrite rules to any defining equation during
  1139   preprocessing.
  1139   preprocessing.
  1140 
  1140 
  1141   \item [\mbox{\isa{\isacommand{print{\isacharunderscore}codesetup}}}] gives an overview on
  1141   \item [\hyperlink{command.HOL.print_codesetup}{\mbox{\isa{\isacommand{print{\isacharunderscore}codesetup}}}}] gives an overview on
  1142   selected defining equations, code generator datatypes and
  1142   selected defining equations, code generator datatypes and
  1143   preprocessor setup.
  1143   preprocessor setup.
  1144 
  1144 
  1145   \end{descr}%
  1145   \end{descr}%
  1146 \end{isamarkuptext}%
  1146 \end{isamarkuptext}%