
wenzelm@26840: %
wenzelm@26840: \begin{isabellebody}%
wenzelm@40685: \def\isabellecontext{HOL{\isaliteral{5F}{\isacharunderscore}}Specific}%
wenzelm@26840: %
wenzelm@26840: \isadelimtheory
wenzelm@26840: %
wenzelm@26840: \endisadelimtheory
wenzelm@26840: %
wenzelm@26840: \isatagtheory
wenzelm@26840: \isacommand{theory}\isamarkupfalse%
wenzelm@40685: \ HOL{\isaliteral{5F}{\isacharunderscore}}Specific\isanewline
wenzelm@26849: \isakeyword{imports}\ Main\isanewline
wenzelm@43498: \isakeyword{uses}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2F}{\isacharslash}}antiquote{\isaliteral{5F}{\isacharunderscore}}setup{\isaliteral{2E}{\isachardot}}ML{\isaliteral{22}{\isachardoublequoteclose}}\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@35757: \isamarkupsection{Typedef axiomatization \label{sec:hol-typedef}%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@26849: \begin{matharray}{rcl}
wenzelm@40685:     \indexdef{HOL}{command}{typedef}\hypertarget{command.HOL.typedef}{\hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\isa{altname}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nont{\isa{abstype}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[]
wenzelm@43467: \rail@nont{\isa{repset}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{3}{\isa{altname}}
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{\isakeyword{open}}}[]
wenzelm@43467: \rail@nextbar{2}
wenzelm@43467: \rail@term{\isa{\isakeyword{open}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{abstype}}
wenzelm@43467: \rail@nont{\hyperlink{syntax.typespecsorts}{\mbox{\isa{typespecsorts}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.mixfix}{\mbox{\isa{mixfix}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{repset}}
wenzelm@43467: \rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{\isakeyword{morphisms}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
wenzelm@26849: 
wenzelm@26849: 
wenzelm@28788:   \begin{description}
wenzelm@42994: 
wenzelm@40685:   \item \hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}\ t\ {\isaliteral{3D}{\isacharequal}}\ A{\isaliteral{22}{\isachardoublequote}}}
wenzelm@35757:   axiomatizes a Gordon/HOL-style type definition in the background
wenzelm@35757:   theory of the current context, depending on a non-emptiness result
wenzelm@35757:   of the set \isa{A} (which needs to be proven interactively).
wenzelm@35757: 
wenzelm@35757:   The raw type may not depend on parameters or assumptions of the
wenzelm@35757:   context --- this is logically impossible in Isabelle/HOL --- but the
wenzelm@35757:   non-emptiness property can be local, potentially resulting in
wenzelm@35757:   multiple interpretations in target contexts.  Thus the established
wenzelm@35757:   bijection between the representing set \isa{A} and the new type
wenzelm@35757:   \isa{t} may semantically depend on local assumptions.
wenzelm@42994: 
wenzelm@35757:   By default, \hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}} defines both a type \isa{t}
wenzelm@35757:   and a set (term constant) of the same name, unless an alternative
wenzelm@40685:   base name is given in parentheses, or the ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}open{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}''
wenzelm@35757:   declaration is used to suppress a separate constant definition
wenzelm@40685:   altogether.  The injection from type to set is called \isa{Rep{\isaliteral{5F}{\isacharunderscore}}t},
wenzelm@40685:   its inverse \isa{Abs{\isaliteral{5F}{\isacharunderscore}}t} --- this may be changed via an explicit
wenzelm@35757:   \hyperlink{keyword.HOL.morphisms}{\mbox{\isa{\isakeyword{morphisms}}}} declaration.
wenzelm@42994: 
wenzelm@40685:   Theorems \isa{Rep{\isaliteral{5F}{\isacharunderscore}}t}, \isa{Rep{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{5F}{\isacharunderscore}}inverse}, and \isa{Abs{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{5F}{\isacharunderscore}}inverse} provide the most basic characterization as a
wenzelm@26849:   corresponding injection/surjection pair (in both directions).  Rules
wenzelm@40685:   \isa{Rep{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{5F}{\isacharunderscore}}inject} and \isa{Abs{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{5F}{\isacharunderscore}}inject} provide a slightly
wenzelm@26849:   more convenient view on the injectivity part, suitable for automated
wenzelm@26902:   proof tools (e.g.\ in \hyperlink{attribute.simp}{\mbox{\isa{simp}}} or \hyperlink{attribute.iff}{\mbox{\isa{iff}}}
wenzelm@40685:   declarations).  Rules \isa{Rep{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{5F}{\isacharunderscore}}cases}/\isa{Rep{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{5F}{\isacharunderscore}}induct}, and
wenzelm@40685:   \isa{Abs{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{5F}{\isacharunderscore}}cases}/\isa{Abs{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{5F}{\isacharunderscore}}induct} provide alternative views
wenzelm@26895:   on surjectivity; these are already declared as set or type rules for
wenzelm@26902:   the generic \hyperlink{method.cases}{\mbox{\isa{cases}}} and \hyperlink{method.induct}{\mbox{\isa{induct}}} methods.
wenzelm@42994: 
wenzelm@35757:   An alternative name for the set definition (and other derived
wenzelm@35757:   entities) may be specified in parentheses; the default is to use
wenzelm@35757:   \isa{t} as indicated before.
wenzelm@26849: 
wenzelm@35757:   \end{description}%
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@43467:     \indexdef{HOL}{attribute}{split\_format}\hypertarget{attribute.HOL.split-format}{\hyperlink{attribute.HOL.split-format}{\mbox{\isa{split{\isaliteral{5F}{\isacharunderscore}}format}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{attribute} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{attribute.HOL.split-format}{\mbox{\isa{split{\isaliteral{5F}{\isacharunderscore}}format}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@term{\isa{complete}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
wenzelm@43467: 
wenzelm@26849: 
wenzelm@28788:   \begin{description}
wenzelm@42994: 
wenzelm@40685:   \item \hyperlink{attribute.HOL.split-format}{\mbox{\isa{split{\isaliteral{5F}{\isacharunderscore}}format}}}\ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}complete{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} causes
wenzelm@28788:   arguments in function applications to be represented canonically
wenzelm@28788:   according to their tuple type structure.
wenzelm@26849: 
krauss@40634:   Note that this operation tends to invent funny names for new local
krauss@40634:   parameters introduced.
wenzelm@26849: 
wenzelm@28788:   \end{description}%
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@40685:     fixed & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ B{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     schematic & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ m{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} &
wenzelm@40685:       \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ B{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ M{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@26849:   \end{tabular}
wenzelm@26849:   \end{center}
wenzelm@26849: 
wenzelm@40685:   \noindent The ASCII representation of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} is \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{7C}{\isacharbar}}\ x\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}.
wenzelm@26849: 
wenzelm@40685:   A fixed record \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} has field \isa{x} of value
wenzelm@26849:   \isa{a} and field \isa{y} of value \isa{b}.  The corresponding
wenzelm@40685:   type is \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ B{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}, assuming that \isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{22}{\isachardoublequote}}}
wenzelm@40685:   and \isa{{\isaliteral{22}{\isachardoublequote}}b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ B{\isaliteral{22}{\isachardoublequote}}}.
wenzelm@26849: 
wenzelm@40685:   A record scheme like \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ m{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} contains fields
wenzelm@26849:   \isa{x} and \isa{y} as before, but also possibly further fields
wenzelm@40685:   as indicated by the ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}'' notation (which is actually part
wenzelm@40685:   of the syntax).  The improper field ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\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@40685:   previous scheme may get instantiated to \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ z\ {\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ m{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}, where \isa{m{\isaliteral{27}{\isacharprime}}} refers to a different more part.
wenzelm@26849:   Fixed records are special instances of record schemes, where
wenzelm@40685:   ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}'' is properly terminated by the \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ unit{\isaliteral{22}{\isachardoublequote}}}
wenzelm@40685:   element.  In fact, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} is just an abbreviation
wenzelm@40685:   for \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}.
wenzelm@42994: 
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@40685:     \indexdef{HOL}{command}{record}\hypertarget{command.HOL.record}{\hyperlink{command.HOL.record}{\mbox{\isa{\isacommand{record}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.record}{\mbox{\isa{\isacommand{record}}}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.typespecsorts}{\mbox{\isa{typespecsorts}}}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.type}{\mbox{\isa{type}}}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{2B}{\isacharplus}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.constdecl}{\mbox{\isa{constdecl}}}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
wenzelm@43467: 
wenzelm@26849: 
wenzelm@28788:   \begin{description}
wenzelm@26849: 
wenzelm@40685:   \item \hyperlink{command.HOL.record}{\mbox{\isa{\isacommand{record}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}\ t\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\ {\isaliteral{2B}{\isacharplus}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} defines extensible record type \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}},
wenzelm@40685:   derived from the optional parent record \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}} by adding new
wenzelm@40685:   field components \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} etc.
wenzelm@26849: 
wenzelm@40685:   The type variables of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} need to be
wenzelm@40685:   covered by the (distinct) parameters \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}}.  Type constructor \isa{t} has to be new, while \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} needs to specify an instance of an existing record type.  At
wenzelm@40685:   least one new field \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\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@40685:   The parent record specification \isa{{\isaliteral{5C3C7461753E}{\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@40685:   For convenience, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}} is made a
wenzelm@40685:   type abbreviation for the fixed record type \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}, likewise is \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{5F}{\isacharunderscore}}scheme{\isaliteral{22}{\isachardoublequote}}} made an abbreviation for
wenzelm@40685:   \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}.
wenzelm@26849: 
wenzelm@28788:   \end{description}%
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@40685:   presentation below, we assume for now that \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}} is a root record with fields \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\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@40685:     \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{5F}{\isacharunderscore}}update{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@40685:   There is special syntax for application of updates: \isa{{\isaliteral{22}{\isachardoublequote}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} abbreviates term \isa{{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{5F}{\isacharunderscore}}update\ a\ r{\isaliteral{22}{\isachardoublequote}}}.  Further notation for
wenzelm@40685:   repeated updates is also available: \isa{{\isaliteral{22}{\isachardoublequote}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}z\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} may be written \isa{{\isaliteral{22}{\isachardoublequote}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ z\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\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@40685:   function applications, fields may be freely permuted in \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ z\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\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@40685:     \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}make{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\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@40685:   Assuming that \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}} has ancestor
wenzelm@40685:   fields \isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C72686F3E}{\isasymrho}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub k\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C72686F3E}{\isasymrho}}\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{22}{\isachardoublequote}}},
wenzelm@26849:   the above record operations will get the following types:
wenzelm@26849: 
wenzelm@26852:   \medskip
wenzelm@26852:   \begin{tabular}{lll}
wenzelm@40685:     \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{5F}{\isacharunderscore}}update{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}make{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C72686F3E}{\isasymrho}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C72686F3E}{\isasymrho}}\isaliteral{5C3C5E7375623E}{}\isactrlsub k\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@26852:   \end{tabular}
wenzelm@26852:   \medskip
wenzelm@26849: 
wenzelm@26852:   \noindent Some further operations address the extension aspect of a
wenzelm@40685:   derived record scheme specifically: \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}fields{\isaliteral{22}{\isachardoublequote}}} produces a
wenzelm@26849:   record fragment consisting of exactly the new fields introduced here
wenzelm@40685:   (the result may serve as a more part elsewhere); \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}extend{\isaliteral{22}{\isachardoublequote}}}
wenzelm@40685:   takes a fixed record and adds a given more part; \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}truncate{\isaliteral{22}{\isachardoublequote}}} restricts a record scheme to a fixed record.
wenzelm@26849: 
wenzelm@26852:   \medskip
wenzelm@26852:   \begin{tabular}{lll}
wenzelm@40685:     \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}fields{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}extend{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}truncate{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@26852:   \end{tabular}
wenzelm@26852:   \medskip
wenzelm@26849: 
wenzelm@40685:   \noindent Note that \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}make{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}fields{\isaliteral{22}{\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@42994: 
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@26902:   the \hyperlink{method.simp}{\mbox{\isa{simp}}} method without further arguments.  These rules
wenzelm@40685:   are available as \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}simps{\isaliteral{22}{\isachardoublequote}}}, too.
wenzelm@42994: 
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@40685:   \item Inject equations of a form analogous to \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ x\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ y\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequote}}} are declared to the Simplifier and Classical
wenzelm@26902:   Reasoner as \hyperlink{attribute.iff}{\mbox{\isa{iff}}} rules.  These rules are available as
wenzelm@40685:   \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}iffs{\isaliteral{22}{\isachardoublequote}}}.
wenzelm@26849: 
wenzelm@40685:   \item The introduction rule for record equality analogous to \isa{{\isaliteral{22}{\isachardoublequote}}x\ r\ {\isaliteral{3D}{\isacharequal}}\ x\ r{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ y\ r\ {\isaliteral{3D}{\isacharequal}}\ y\ r{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ r\ {\isaliteral{3D}{\isacharequal}}\ r{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequote}}} is declared to the Simplifier,
wenzelm@40685:   and as the basic rule context as ``\hyperlink{attribute.intro}{\mbox{\isa{intro}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}''.
wenzelm@40685:   The rule is called \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}equality{\isaliteral{22}{\isachardoublequote}}}.
wenzelm@26849: 
wenzelm@26849:   \item Representations of arbitrary record expressions as canonical
wenzelm@26902:   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,
wenzelm@26849:   \secref{sec:cases-induct}).  Several variations are available, for
wenzelm@26849:   fixed records, record schemes, more parts etc.
wenzelm@42994: 
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@40685:   expression: users just need to apply something like ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}cases\ r{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' to a certain proof problem.
wenzelm@26849: 
wenzelm@40685:   \item The derived record operations \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}make{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}fields{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}extend{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}truncate{\isaliteral{22}{\isachardoublequote}}} are \emph{not}
wenzelm@26849:   treated automatically, but usually need to be expanded by hand,
wenzelm@40685:   using the collective fact \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}defs{\isaliteral{22}{\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@40685:     \indexdef{HOL}{command}{datatype}\hypertarget{command.HOL.datatype}{\hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
haftmann@41644:     \indexdef{HOL}{command}{rep\_datatype}\hypertarget{command.HOL.rep-datatype}{\hyperlink{command.HOL.rep-datatype}{\mbox{\isa{\isacommand{rep{\isaliteral{5F}{\isacharunderscore}}datatype}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\isa{dtspec}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@cterm{\isa{\isakeyword{and}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{3}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.rep-datatype}{\mbox{\isa{\isacommand{rep{\isaliteral{5F}{\isacharunderscore}}datatype}}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@nextplus{2}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{dtspec}}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.parname}{\mbox{\isa{parname}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nont{\hyperlink{syntax.typespec}{\mbox{\isa{typespec}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.mixfix}{\mbox{\isa{mixfix}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\isa{cons}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@cterm{\isa{{\isaliteral{7C}{\isacharbar}}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{cons}}
wenzelm@43467: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@cnont{\hyperlink{syntax.type}{\mbox{\isa{type}}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.mixfix}{\mbox{\isa{mixfix}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
wenzelm@26849: 
wenzelm@26849: 
wenzelm@28788:   \begin{description}
wenzelm@26849: 
wenzelm@28788:   \item \hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}} defines inductive datatypes in
wenzelm@26849:   HOL.
wenzelm@26849: 
wenzelm@40685:   \item \hyperlink{command.HOL.rep-datatype}{\mbox{\isa{\isacommand{rep{\isaliteral{5F}{\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@28788:   \end{description}
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@40685:   emulations of ML tactics \hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}tac}}} and \hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\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: %
haftmann@41644: \isamarkupsection{Functorial structure of types%
haftmann@41644: }
haftmann@41644: \isamarkuptrue%
haftmann@41644: %
haftmann@41644: \begin{isamarkuptext}%
haftmann@41644: \begin{matharray}{rcl}
haftmann@41753:     \indexdef{HOL}{command}{enriched\_type}\hypertarget{command.HOL.enriched-type}{\hyperlink{command.HOL.enriched-type}{\mbox{\isa{\isacommand{enriched{\isaliteral{5F}{\isacharunderscore}}type}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}
haftmann@41644:   \end{matharray}
haftmann@41644: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.enriched-type}{\mbox{\isa{\isacommand{enriched{\isaliteral{5F}{\isacharunderscore}}type}}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43488: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
wenzelm@43488: 
haftmann@41644: 
haftmann@41644:   \begin{description}
haftmann@41644: 
wenzelm@43488:   \item \hyperlink{command.HOL.enriched-type}{\mbox{\isa{\isacommand{enriched{\isaliteral{5F}{\isacharunderscore}}type}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}prefix{\isaliteral{3A}{\isacharcolon}}\ m{\isaliteral{22}{\isachardoublequote}}} allows to
wenzelm@43488:   prove and register properties about the functorial structure of type
wenzelm@43488:   constructors.  These properties then can be used by other packages
wenzelm@43488:   to deal with those type constructors in certain type constructions.
wenzelm@43488:   Characteristic theorems are noted in the current local theory.  By
wenzelm@43488:   default, they are prefixed with the base name of the type
wenzelm@43488:   constructor, an explicit prefix can be given alternatively.
haftmann@41644: 
haftmann@41644:   The given term \isa{{\isaliteral{22}{\isachardoublequote}}m{\isaliteral{22}{\isachardoublequote}}} is considered as \emph{mapper} for the
haftmann@41644:   corresponding type constructor and must conform to the following
haftmann@41644:   type pattern:
haftmann@41644: 
haftmann@41644:   \begin{matharray}{lll}
haftmann@41644:     \isa{{\isaliteral{22}{\isachardoublequote}}m{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} &
haftmann@41644:       \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E697375623E}{}\isactrlisub k\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}\ t\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}} \\
haftmann@41644:   \end{matharray}
haftmann@41644: 
haftmann@41644:   \noindent where \isa{t} is the type constructor, \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{22}{\isachardoublequote}}} are distinct
haftmann@41644:   type variables free in the local theory and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}},
haftmann@41644:   \ldots, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E697375623E}{}\isactrlisub k{\isaliteral{22}{\isachardoublequote}}} is a subsequence of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}, \ldots,
haftmann@41644:   \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{22}{\isachardoublequote}}}.
haftmann@41644: 
haftmann@41644:   \end{description}%
haftmann@41644: \end{isamarkuptext}%
haftmann@41644: \isamarkuptrue%
haftmann@41644: %
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@40685:     \indexdef{HOL}{command}{primrec}\hypertarget{command.HOL.primrec}{\hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{fun}\hypertarget{command.HOL.fun}{\hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{function}\hypertarget{command.HOL.function}{\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{termination}\hypertarget{command.HOL.termination}{\hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.target}{\mbox{\isa{target}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nont{\hyperlink{syntax.fixes}{\mbox{\isa{fixes}}}}[]
wenzelm@43467: \rail@term{\isa{\isakeyword{where}}}[]
wenzelm@43467: \rail@nont{\isa{equations}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{4}{\isa{}}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@term{\hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}}}[]
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.target}{\mbox{\isa{target}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\isa{functionopts}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nont{\hyperlink{syntax.fixes}{\mbox{\isa{fixes}}}}[]
wenzelm@43467: \rail@cr{3}
wenzelm@43467: \rail@term{\isa{\isakeyword{where}}}[]
wenzelm@43467: \rail@nont{\isa{equations}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{3}{\isa{equations}}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.thmdecl}{\mbox{\isa{thmdecl}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[]
wenzelm@43467: \rail@nextplus{2}
wenzelm@43467: \rail@cterm{\isa{{\isaliteral{7C}{\isacharbar}}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{3}{\isa{functionopts}}
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@term{\isa{sequential}}[]
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{domintros}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nextplus{2}
wenzelm@43467: \rail@cterm{\isa{{\isaliteral{2C}{\isacharcomma}}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
wenzelm@43467: 
wenzelm@26849: 
wenzelm@28788:   \begin{description}
wenzelm@26849: 
wenzelm@28788:   \item \hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}} defines primitive recursive
wenzelm@26849:   functions over datatypes, see also \cite{isabelle-HOL}.
wenzelm@26849: 
wenzelm@28788:   \item \hyperlink{command.HOL.function}{\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@40685:   simplification rules (named \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{2E}{\isachardot}}psimps{\isaliteral{22}{\isachardoublequote}}}) and induction rule
wenzelm@40685:   (named \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{2E}{\isachardot}}pinduct{\isaliteral{22}{\isachardoublequote}}}) are guarded by a generated domain
wenzelm@40685:   predicate \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{5F}{\isacharunderscore}}dom{\isaliteral{22}{\isachardoublequote}}}. The \hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}
wenzelm@26849:   command can then be used to establish that the function is total.
wenzelm@26849: 
wenzelm@40685:   \item \hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}} is a shorthand notation for ``\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}sequential{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}, followed by automated
wenzelm@28788:   proof attempts regarding pattern matching and termination.  See
wenzelm@28788:   \cite{isabelle-function} for further details.
wenzelm@26849: 
wenzelm@28788:   \item \hyperlink{command.HOL.termination}{\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@28788:   \end{description}
wenzelm@26849: 
haftmann@27452:   Recursive definitions introduced by the \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}
haftmann@27452:   command accommodate
wenzelm@40685:   reasoning by induction (cf.\ \secref{sec:cases-induct}): rule \isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{2E}{\isachardot}}induct{\isaliteral{22}{\isachardoublequote}}} (where \isa{c} is the name of the function definition)
wenzelm@26849:   refers to a specific induction rule, with parameters named according
krauss@33857:   to the user-specified equations. Cases are numbered (starting from 1).
krauss@33857: 
krauss@33857:   For \hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}}, the induction principle coincides
haftmann@27452:   with structural recursion on the datatype the recursion is carried
haftmann@27452:   out.
wenzelm@26849: 
wenzelm@26849:   The equations provided by these packages may be referred later as
wenzelm@40685:   theorem list \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{2E}{\isachardot}}simps{\isaliteral{22}{\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@26902:   The \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} command accepts the following
wenzelm@26849:   options.
wenzelm@26849: 
wenzelm@28788:   \begin{description}
wenzelm@26849: 
wenzelm@28788:   \item \isa{sequential} enables a preprocessor which disambiguates
wenzelm@28788:   overlapping patterns by making them mutually disjoint.  Earlier
wenzelm@28788:   equations take precedence over later ones.  This allows to give the
wenzelm@28788:   specification in a format very similar to functional programming.
wenzelm@28788:   Note that the resulting simplification and induction rules
wenzelm@28788:   correspond to the transformed specification, not the one given
wenzelm@26849:   originally. This usually means that each equation given by the user
hoelzl@36137:   may result in several theorems.  Also note that this automatic
wenzelm@26849:   transformation only works for ML-style datatype patterns.
wenzelm@26849: 
wenzelm@28788:   \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@28788:   \end{description}%
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@40685:     \indexdef{HOL}{method}{pat\_completeness}\hypertarget{method.HOL.pat-completeness}{\hyperlink{method.HOL.pat-completeness}{\mbox{\isa{pat{\isaliteral{5F}{\isacharunderscore}}completeness}}}} & : & \isa{method} \\
wenzelm@28788:     \indexdef{HOL}{method}{relation}\hypertarget{method.HOL.relation}{\hyperlink{method.HOL.relation}{\mbox{\isa{relation}}}} & : & \isa{method} \\
wenzelm@40685:     \indexdef{HOL}{method}{lexicographic\_order}\hypertarget{method.HOL.lexicographic-order}{\hyperlink{method.HOL.lexicographic-order}{\mbox{\isa{lexicographic{\isaliteral{5F}{\isacharunderscore}}order}}}} & : & \isa{method} \\
wenzelm@40685:     \indexdef{HOL}{method}{size\_change}\hypertarget{method.HOL.size-change}{\hyperlink{method.HOL.size-change}{\mbox{\isa{size{\isaliteral{5F}{\isacharunderscore}}change}}}} & : & \isa{method} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{1}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{method.HOL.relation}{\mbox{\isa{relation}}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{method.HOL.lexicographic-order}{\mbox{\isa{lexicographic{\isaliteral{5F}{\isacharunderscore}}order}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@cnont{\hyperlink{syntax.clasimpmod}{\mbox{\isa{clasimpmod}}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{method.HOL.size-change}{\mbox{\isa{size{\isaliteral{5F}{\isacharunderscore}}change}}}}[]
wenzelm@43467: \rail@nont{\isa{orders}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@cnont{\hyperlink{syntax.clasimpmod}{\mbox{\isa{clasimpmod}}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{4}{\isa{orders}}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@term{\isa{max}}[]
wenzelm@43467: \rail@nextbar{2}
wenzelm@43467: \rail@term{\isa{min}}[]
wenzelm@43467: \rail@nextbar{3}
wenzelm@43467: \rail@term{\isa{ms}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
wenzelm@43467: 
wenzelm@26849: 
wenzelm@28788:   \begin{description}
wenzelm@26849: 
wenzelm@40685:   \item \hyperlink{method.HOL.pat-completeness}{\mbox{\isa{pat{\isaliteral{5F}{\isacharunderscore}}completeness}}} is a specialized method to
wenzelm@26849:   solve goals regarding the completeness of pattern matching, as
wenzelm@26902:   required by the \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} package (cf.\
wenzelm@26849:   \cite{isabelle-function}).
wenzelm@26849: 
wenzelm@28788:   \item \hyperlink{method.HOL.relation}{\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@40685:   \item \hyperlink{method.HOL.lexicographic-order}{\mbox{\isa{lexicographic{\isaliteral{5F}{\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@26902:   method accepts the same arguments as the \hyperlink{method.auto}{\mbox{\isa{auto}}} method,
wenzelm@26849:   which it uses internally to prove local descents.  The same context
wenzelm@26902:   modifiers as for \hyperlink{method.auto}{\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@40685:   \item \hyperlink{method.HOL.size-change}{\mbox{\isa{size{\isaliteral{5F}{\isacharunderscore}}change}}} also works on termination goals,
krauss@33858:   using a variation of the size-change principle, together with a
krauss@33858:   graph decomposition technique (see \cite{krauss_phd} for details).
krauss@33858:   Three kinds of orders are used internally: \isa{max}, \isa{min},
krauss@33858:   and \isa{ms} (multiset), which is only available when the theory
krauss@33858:   \isa{Multiset} is loaded. When no order kinds are given, they are
krauss@33858:   tried in order. The search for a termination proof uses SAT solving
krauss@33858:   internally.
krauss@33858: 
krauss@33858:  For local descent proofs, the same context modifiers as for \hyperlink{method.auto}{\mbox{\isa{auto}}} are accepted, see \secref{sec:clasimp}.
krauss@33858: 
wenzelm@28788:   \end{description}%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
krauss@40412: \isamarkupsubsection{Functions with explicit partiality%
krauss@40412: }
krauss@40412: \isamarkuptrue%
krauss@40412: %
krauss@40412: \begin{isamarkuptext}%
krauss@40412: \begin{matharray}{rcl}
wenzelm@40685:     \indexdef{HOL}{command}{partial\_function}\hypertarget{command.HOL.partial-function}{\hyperlink{command.HOL.partial-function}{\mbox{\isa{\isacommand{partial{\isaliteral{5F}{\isacharunderscore}}function}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{attribute}{partial\_function\_mono}\hypertarget{attribute.HOL.partial-function-mono}{\hyperlink{attribute.HOL.partial-function-mono}{\mbox{\isa{partial{\isaliteral{5F}{\isacharunderscore}}function{\isaliteral{5F}{\isacharunderscore}}mono}}}} & : & \isa{attribute} \\
krauss@40412:   \end{matharray}
krauss@40412: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{5}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.partial-function}{\mbox{\isa{\isacommand{partial{\isaliteral{5F}{\isacharunderscore}}function}}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.target}{\mbox{\isa{target}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43488: \rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.fixes}{\mbox{\isa{fixes}}}}[]
wenzelm@43467: \rail@cr{3}
wenzelm@43467: \rail@term{\isa{\isakeyword{where}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{4}
wenzelm@43467: \rail@nont{\hyperlink{syntax.thmdecl}{\mbox{\isa{thmdecl}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
wenzelm@43488: 
krauss@40412: 
krauss@40412:   \begin{description}
krauss@40412: 
wenzelm@43488:   \item \hyperlink{command.HOL.partial-function}{\mbox{\isa{\isacommand{partial{\isaliteral{5F}{\isacharunderscore}}function}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}mode{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} defines
wenzelm@43488:   recursive functions based on fixpoints in complete partial
wenzelm@43488:   orders. No termination proof is required from the user or
wenzelm@43488:   constructed internally. Instead, the possibility of non-termination
wenzelm@43488:   is modelled explicitly in the result type, which contains an
wenzelm@43488:   explicit bottom element.
krauss@40412: 
krauss@40412:   Pattern matching and mutual recursion are currently not supported.
krauss@40412:   Thus, the specification consists of a single function described by a
krauss@40412:   single recursive equation.
krauss@40412: 
krauss@40412:   There are no fixed syntactic restrictions on the body of the
krauss@40412:   function, but the induced functional must be provably monotonic
krauss@40412:   wrt.\ the underlying order.  The monotonicitity proof is performed
krauss@40412:   internally, and the definition is rejected when it fails. The proof
krauss@40412:   can be influenced by declaring hints using the
wenzelm@40685:   \hyperlink{attribute.HOL.partial-function-mono}{\mbox{\isa{partial{\isaliteral{5F}{\isacharunderscore}}function{\isaliteral{5F}{\isacharunderscore}}mono}}} attribute.
krauss@40412: 
krauss@40412:   The mandatory \isa{mode} argument specifies the mode of operation
krauss@40412:   of the command, which directly corresponds to a complete partial
krauss@40412:   order on the result type. By default, the following modes are
wenzelm@42994:   defined:
krauss@40412: 
krauss@40412:   \begin{description}
krauss@40412:   \item \isa{option} defines functions that map into the \isa{option} type. Here, the value \isa{None} is used to model a
krauss@40412:   non-terminating computation. Monotonicity requires that if \isa{None} is returned by a recursive call, then the overall result
krauss@40412:   must also be \isa{None}. This is best achieved through the use of
wenzelm@40685:   the monadic operator \isa{{\isaliteral{22}{\isachardoublequote}}Option{\isaliteral{2E}{\isachardot}}bind{\isaliteral{22}{\isachardoublequote}}}.
wenzelm@42994: 
krauss@40412:   \item \isa{tailrec} defines functions with an arbitrary result
wenzelm@40685:   type and uses the slightly degenerated partial order where \isa{{\isaliteral{22}{\isachardoublequote}}undefined{\isaliteral{22}{\isachardoublequote}}} is the bottom element.  Now, monotonicity requires that
krauss@40412:   if \isa{undefined} is returned by a recursive call, then the
krauss@40412:   overall result must also be \isa{undefined}. In practice, this is
krauss@40412:   only satisfied when each recursive call is a tail call, whose result
krauss@40412:   is directly returned. Thus, this mode of operation allows the
krauss@40412:   definition of arbitrary tail-recursive functions.
krauss@40412:   \end{description}
krauss@40412: 
krauss@40412:   Experienced users may define new modes by instantiating the locale
wenzelm@40685:   \isa{{\isaliteral{22}{\isachardoublequote}}partial{\isaliteral{5F}{\isacharunderscore}}function{\isaliteral{5F}{\isacharunderscore}}definitions{\isaliteral{22}{\isachardoublequote}}} appropriately.
krauss@40412: 
wenzelm@40685:   \item \hyperlink{attribute.HOL.partial-function-mono}{\mbox{\isa{partial{\isaliteral{5F}{\isacharunderscore}}function{\isaliteral{5F}{\isacharunderscore}}mono}}} declares rules for
krauss@40412:   use in the internal monononicity proofs of partial function
krauss@40412:   definitions.
krauss@40412: 
krauss@40412:   \end{description}%
krauss@40412: \end{isamarkuptext}%
krauss@40412: \isamarkuptrue%
krauss@40412: %
wenzelm@26849: \isamarkupsubsection{Old-style recursive function definitions (TFL)%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@40685: The old TFL commands \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} and \hyperlink{command.HOL.recdef-tc}{\mbox{\isa{\isacommand{recdef{\isaliteral{5F}{\isacharunderscore}}tc}}}} for defining recursive are mostly obsolete; \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} or \hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}} should be used instead.
wenzelm@26849: 
wenzelm@26849:   \begin{matharray}{rcl}
wenzelm@40685:     \indexdef{HOL}{command}{recdef}\hypertarget{command.HOL.recdef}{\hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{recdef\_tc}\hypertarget{command.HOL.recdef-tc}{\hyperlink{command.HOL.recdef-tc}{\mbox{\isa{\isacommand{recdef{\isaliteral{5F}{\isacharunderscore}}tc}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{5}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@term{\isa{\isakeyword{permissive}}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@cr{3}
wenzelm@43467: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[]
wenzelm@43467: \rail@nextplus{4}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{4}
wenzelm@43467: \rail@nont{\isa{hints}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@nont{\isa{recdeftc}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.thmdecl}{\mbox{\isa{thmdecl}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nont{\isa{tc}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{hints}}
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@term{\isa{\isakeyword{hints}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@cnont{\isa{recdefmod}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{4}{\isa{recdefmod}}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@term{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}simp}}[]
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}cong}}[]
wenzelm@43467: \rail@nextbar{2}
wenzelm@43467: \rail@term{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}wf}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{add}}[]
wenzelm@43467: \rail@nextbar{2}
wenzelm@43467: \rail@term{\isa{del}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[]
wenzelm@43467: \rail@nextbar{3}
wenzelm@43467: \rail@nont{\hyperlink{syntax.clasimpmod}{\mbox{\isa{clasimpmod}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{tc}}
wenzelm@43467: \rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
wenzelm@43467: 
wenzelm@26849: 
wenzelm@28788:   \begin{description}
wenzelm@42994: 
wenzelm@28788:   \item \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} defines general well-founded
wenzelm@26849:   recursive functions (using the TFL package), see also
wenzelm@40685:   \cite{isabelle-HOL}.  The ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}permissive{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' option tells
wenzelm@26849:   TFL to recover from failed proof attempts, returning unfinished
wenzelm@40685:   results.  The \isa{recdef{\isaliteral{5F}{\isacharunderscore}}simp}, \isa{recdef{\isaliteral{5F}{\isacharunderscore}}cong}, and \isa{recdef{\isaliteral{5F}{\isacharunderscore}}wf} hints refer to auxiliary rules to be used in the internal
wenzelm@26902:   automated proof process of TFL.  Additional \hyperlink{syntax.clasimpmod}{\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@42994: 
wenzelm@40685:   \item \hyperlink{command.HOL.recdef-tc}{\mbox{\isa{\isacommand{recdef{\isaliteral{5F}{\isacharunderscore}}tc}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{28}{\isacharparenleft}}i{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} recommences the
wenzelm@26849:   proof for leftover termination condition number \isa{i} (default
wenzelm@26902:   1) as generated by a \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} definition of
wenzelm@26849:   constant \isa{c}.
wenzelm@42994: 
wenzelm@26902:   Note that in most cases, \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} is able to finish
wenzelm@26849:   its internal proofs without manual intervention.
wenzelm@26849: 
wenzelm@28788:   \end{description}
wenzelm@26849: 
wenzelm@26902:   \medskip Hints for \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} may be also declared
wenzelm@26849:   globally, using the following attributes.
wenzelm@26849: 
wenzelm@26849:   \begin{matharray}{rcl}
wenzelm@40685:     \indexdef{HOL}{attribute}{recdef\_simp}\hypertarget{attribute.HOL.recdef-simp}{\hyperlink{attribute.HOL.recdef-simp}{\mbox{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}simp}}}} & : & \isa{attribute} \\
wenzelm@40685:     \indexdef{HOL}{attribute}{recdef\_cong}\hypertarget{attribute.HOL.recdef-cong}{\hyperlink{attribute.HOL.recdef-cong}{\mbox{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}cong}}}} & : & \isa{attribute} \\
wenzelm@40685:     \indexdef{HOL}{attribute}{recdef\_wf}\hypertarget{attribute.HOL.recdef-wf}{\hyperlink{attribute.HOL.recdef-wf}{\mbox{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}wf}}}} & : & \isa{attribute} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{3}{\isa{}}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@term{\hyperlink{attribute.HOL.recdef-simp}{\mbox{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}simp}}}}[]
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\hyperlink{attribute.HOL.recdef-cong}{\mbox{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}cong}}}}[]
wenzelm@43467: \rail@nextbar{2}
wenzelm@43467: \rail@term{\hyperlink{attribute.HOL.recdef-wf}{\mbox{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}wf}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{add}}[]
wenzelm@43467: \rail@nextbar{2}
wenzelm@43467: \rail@term{\isa{del}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}%
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@40685:     \indexdef{HOL}{command}{inductive}\hypertarget{command.HOL.inductive}{\hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{inductive\_set}\hypertarget{command.HOL.inductive-set}{\hyperlink{command.HOL.inductive-set}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{coinductive}\hypertarget{command.HOL.coinductive}{\hyperlink{command.HOL.coinductive}{\mbox{\isa{\isacommand{coinductive}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{coinductive\_set}\hypertarget{command.HOL.coinductive-set}{\hyperlink{command.HOL.coinductive-set}{\mbox{\isa{\isacommand{coinductive{\isaliteral{5F}{\isacharunderscore}}set}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@28788:     \indexdef{HOL}{attribute}{mono}\hypertarget{attribute.HOL.mono}{\hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}}} & : & \isa{attribute} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{7}{\isa{}}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@term{\hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}}}[]
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.inductive-set}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}}}}}[]
wenzelm@43467: \rail@nextbar{2}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.coinductive}{\mbox{\isa{\isacommand{coinductive}}}}}[]
wenzelm@43467: \rail@nextbar{3}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.coinductive-set}{\mbox{\isa{\isacommand{coinductive{\isaliteral{5F}{\isacharunderscore}}set}}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.target}{\mbox{\isa{target}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nont{\hyperlink{syntax.fixes}{\mbox{\isa{fixes}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{\isakeyword{for}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.fixes}{\mbox{\isa{fixes}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@cr{5}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{6}
wenzelm@43467: \rail@term{\isa{\isakeyword{where}}}[]
wenzelm@43467: \rail@nont{\isa{clauses}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{6}
wenzelm@43467: \rail@term{\isa{\isakeyword{monos}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{3}{\isa{clauses}}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.thmdecl}{\mbox{\isa{thmdecl}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[]
wenzelm@43467: \rail@nextplus{2}
wenzelm@43467: \rail@cterm{\isa{{\isaliteral{7C}{\isacharbar}}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{3}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{add}}[]
wenzelm@43467: \rail@nextbar{2}
wenzelm@43467: \rail@term{\isa{del}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
wenzelm@43467: 
wenzelm@26849: 
wenzelm@28788:   \begin{description}
wenzelm@26849: 
wenzelm@28788:   \item \hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}} and \hyperlink{command.HOL.coinductive}{\mbox{\isa{\isacommand{coinductive}}}} define (co)inductive predicates from the
wenzelm@26902:   introduction rules given in the \hyperlink{keyword.where}{\mbox{\isa{\isakeyword{where}}}} part.  The
wenzelm@26902:   optional \hyperlink{keyword.for}{\mbox{\isa{\isakeyword{for}}}} part contains a list of parameters of the
wenzelm@26849:   (co)inductive predicates that remain fixed throughout the
wenzelm@26902:   definition.  The optional \hyperlink{keyword.monos}{\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@40685:   \emph{must} be a theorem of the form \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C6C653E}{\isasymle}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ M\ A\ {\isaliteral{5C3C6C653E}{\isasymle}}\ M\ B{\isaliteral{22}{\isachardoublequote}}},
wenzelm@40685:   for each premise \isa{{\isaliteral{22}{\isachardoublequote}}M\ R\isaliteral{5C3C5E7375623E}{}\isactrlsub i\ t{\isaliteral{22}{\isachardoublequote}}} in an introduction rule!
wenzelm@26849: 
wenzelm@40685:   \item \hyperlink{command.HOL.inductive-set}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}}}} and \hyperlink{command.HOL.coinductive-set}{\mbox{\isa{\isacommand{coinductive{\isaliteral{5F}{\isacharunderscore}}set}}}} are wrappers for to the previous commands,
wenzelm@26849:   allowing the definition of (co)inductive sets.
wenzelm@26849: 
wenzelm@28788:   \item \hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}} declares monotonicity rules.  These
wenzelm@26902:   rule are involved in the automated monotonicity proof of \hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}}.
wenzelm@26849: 
wenzelm@28788:   \end{description}%
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@40685:   \item \isa{R{\isaliteral{2E}{\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@40685:   \item \isa{R{\isaliteral{2E}{\isachardot}}cases} is the case analysis (or elimination) rule;
wenzelm@26849: 
wenzelm@40685:   \item \isa{R{\isaliteral{2E}{\isachardot}}induct} or \isa{R{\isaliteral{2E}{\isachardot}}coinduct} is the (co)induction
wenzelm@26849:   rule.
wenzelm@26849: 
wenzelm@26849:   \end{description}
wenzelm@26849: 
wenzelm@40685:   When several predicates \isa{{\isaliteral{22}{\isachardoublequote}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ R\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} are
wenzelm@26849:   defined simultaneously, the list of introduction rules is called
wenzelm@40685:   \isa{{\isaliteral{22}{\isachardoublequote}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5F}{\isacharunderscore}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{2E}{\isachardot}}intros{\isaliteral{22}{\isachardoublequote}}}, the case analysis rules are
wenzelm@40685:   called \isa{{\isaliteral{22}{\isachardoublequote}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2E}{\isachardot}}cases{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ R\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{2E}{\isachardot}}cases{\isaliteral{22}{\isachardoublequote}}}, and the list
wenzelm@40685:   of mutual induction rules is called \isa{{\isaliteral{22}{\isachardoublequote}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5F}{\isacharunderscore}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{2E}{\isachardot}}inducts{\isaliteral{22}{\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@26902:   \hyperlink{attribute.HOL.mono}{\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@40685:   \item Theorems of the form \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C6C653E}{\isasymle}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ M\ A\ {\isaliteral{5C3C6C653E}{\isasymle}}\ M\ B{\isaliteral{22}{\isachardoublequote}}}, for proving
wenzelm@26849:   monotonicity of inductive definitions whose introduction rules have
wenzelm@40685:   premises involving terms such as \isa{{\isaliteral{22}{\isachardoublequote}}M\ R\isaliteral{5C3C5E7375623E}{}\isactrlsub i\ t{\isaliteral{22}{\isachardoublequote}}}.
wenzelm@26849: 
wenzelm@26849:   \item Monotonicity theorems for logical operators, which are of the
wenzelm@40685:   general form \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}.  For example, in
wenzelm@40685:   the case of the operator \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6F723E}{\isasymor}}{\isaliteral{22}{\isachardoublequote}}}, the corresponding theorem is
wenzelm@26849:   \[
wenzelm@40685:   \infer{\isa{{\isaliteral{22}{\isachardoublequote}}P\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ P\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ Q\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}}}{\isa{{\isaliteral{22}{\isachardoublequote}}P\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}P\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}}}
wenzelm@26849:   \]
wenzelm@26849: 
wenzelm@26849:   \item De Morgan style equations for reasoning about the ``polarity''
wenzelm@26849:   of expressions, e.g.
wenzelm@26849:   \[
wenzelm@40685:   \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ P\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ P{\isaliteral{22}{\isachardoublequote}}} \qquad\qquad
wenzelm@40685:   \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{28}{\isacharparenleft}}P\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ P\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ Q{\isaliteral{22}{\isachardoublequote}}}
wenzelm@26849:   \]
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:   \[
wenzelm@40685:   \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}P\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ P\ {\isaliteral{5C3C6F723E}{\isasymor}}\ Q{\isaliteral{22}{\isachardoublequote}}} \qquad\qquad
wenzelm@40685:   \isa{{\isaliteral{22}{\isachardoublequote}}Ball\ A\ P\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ P\ x{\isaliteral{22}{\isachardoublequote}}}
wenzelm@26849:   \]
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@28788:     \indexdef{HOL}{method}{arith}\hypertarget{method.HOL.arith}{\hyperlink{method.HOL.arith}{\mbox{\isa{arith}}}} & : & \isa{method} \\
nipkow@30863:     \indexdef{HOL}{attribute}{arith}\hypertarget{attribute.HOL.arith}{\hyperlink{attribute.HOL.arith}{\mbox{\isa{arith}}}} & : & \isa{attribute} \\
wenzelm@40685:     \indexdef{HOL}{attribute}{arith\_split}\hypertarget{attribute.HOL.arith-split}{\hyperlink{attribute.HOL.arith-split}{\mbox{\isa{arith{\isaliteral{5F}{\isacharunderscore}}split}}}} & : & \isa{attribute} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@26902:   The \hyperlink{method.HOL.arith}{\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: 
nipkow@30863:   The \hyperlink{attribute.HOL.arith}{\mbox{\isa{arith}}} attribute declares facts that are
nipkow@30863:   always supplied to the arithmetic provers implicitly.
nipkow@30863: 
wenzelm@40685:   The \hyperlink{attribute.HOL.arith-split}{\mbox{\isa{arith{\isaliteral{5F}{\isacharunderscore}}split}}} attribute declares case split
wenzelm@30865:   rules to be expanded before \hyperlink{method.HOL.arith}{\mbox{\isa{arith}}} is invoked.
wenzelm@26849: 
nipkow@30863:   Note that a simpler (but faster) arithmetic prover is
nipkow@30863:   already invoked by the Simplifier.%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@30172: \isamarkupsection{Intuitionistic proof search%
wenzelm@30172: }
wenzelm@30172: \isamarkuptrue%
wenzelm@30172: %
wenzelm@30172: \begin{isamarkuptext}%
wenzelm@30172: \begin{matharray}{rcl}
wenzelm@30172:     \indexdef{HOL}{method}{iprover}\hypertarget{method.HOL.iprover}{\hyperlink{method.HOL.iprover}{\mbox{\isa{iprover}}}} & : & \isa{method} \\
wenzelm@30172:   \end{matharray}
wenzelm@30172: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{method.HOL.iprover}{\mbox{\isa{iprover}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@cnont{\hyperlink{syntax.rulemod}{\mbox{\isa{rulemod}}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
wenzelm@43467: 
wenzelm@30172: 
wenzelm@30172:   The \hyperlink{method.HOL.iprover}{\mbox{\isa{iprover}}} method performs intuitionistic proof
wenzelm@30172:   search, depending on specifically declared rules from the context,
wenzelm@30172:   or given as explicit arguments.  Chained facts are inserted into the
wenzelm@35613:   goal before commencing proof search.
wenzelm@35613: 
wenzelm@30172:   Rules need to be classified as \hyperlink{attribute.Pure.intro}{\mbox{\isa{intro}}},
wenzelm@30172:   \hyperlink{attribute.Pure.elim}{\mbox{\isa{elim}}}, or \hyperlink{attribute.Pure.dest}{\mbox{\isa{dest}}}; here the
wenzelm@40685:   ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}}'' indicator refers to ``safe'' rules, which may be
wenzelm@30172:   applied aggressively (without considering back-tracking later).
wenzelm@40685:   Rules declared with ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}'' are ignored in proof search (the
wenzelm@43497:   single-step \hyperlink{method.Pure.rule}{\mbox{\isa{rule}}} method still observes these).  An
wenzelm@30172:   explicit weight annotation may be given as well; otherwise the
wenzelm@30172:   number of rule premises will be taken into account here.%
wenzelm@30172: \end{isamarkuptext}%
wenzelm@30172: \isamarkuptrue%
wenzelm@30172: %
wenzelm@30172: \isamarkupsection{Coherent Logic%
wenzelm@30172: }
wenzelm@30172: \isamarkuptrue%
wenzelm@30172: %
wenzelm@30172: \begin{isamarkuptext}%
wenzelm@30172: \begin{matharray}{rcl}
wenzelm@30172:     \indexdef{HOL}{method}{coherent}\hypertarget{method.HOL.coherent}{\hyperlink{method.HOL.coherent}{\mbox{\isa{coherent}}}} & : & \isa{method} \\
wenzelm@30172:   \end{matharray}
wenzelm@30172: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{method.HOL.coherent}{\mbox{\isa{coherent}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
wenzelm@43467: 
wenzelm@30172: 
wenzelm@30172:   The \hyperlink{method.HOL.coherent}{\mbox{\isa{coherent}}} method solves problems of
wenzelm@30172:   \emph{Coherent Logic} \cite{Bezem-Coquand:2005}, which covers
wenzelm@30172:   applications in confluence theory, lattice theory and projective
wenzelm@41052:   geometry.  See \verb|~~/src/HOL/ex/Coherent.thy| for some
wenzelm@30172:   examples.%
wenzelm@30172: \end{isamarkuptext}%
wenzelm@30172: \isamarkuptrue%
wenzelm@30172: %
blanchet@43082: \isamarkupsection{Proving propositions%
blanchet@43082: }
blanchet@43082: \isamarkuptrue%
blanchet@43082: %
blanchet@43082: \begin{isamarkuptext}%
blanchet@43082: In addition to the standard proof methods, a number of diagnosis
blanchet@43082:   tools search for proofs and provide an Isar proof snippet on success.
blanchet@43082:   These tools are available via the following commands.
blanchet@43082: 
blanchet@43082:   \begin{matharray}{rcl}
blanchet@43082:     \indexdef{HOL}{command}{solve\_direct}\hypertarget{command.HOL.solve-direct}{\hyperlink{command.HOL.solve-direct}{\mbox{\isa{\isacommand{solve{\isaliteral{5F}{\isacharunderscore}}direct}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
blanchet@43082:     \indexdef{HOL}{command}{try}\hypertarget{command.HOL.try}{\hyperlink{command.HOL.try}{\mbox{\isa{\isacommand{try}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
blanchet@43082:     \indexdef{HOL}{command}{sledgehammer}\hypertarget{command.HOL.sledgehammer}{\hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
blanchet@43082:     \indexdef{HOL}{command}{sledgehammer\_params}\hypertarget{command.HOL.sledgehammer-params}{\hyperlink{command.HOL.sledgehammer-params}{\mbox{\isa{\isacommand{sledgehammer{\isaliteral{5F}{\isacharunderscore}}params}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}}
blanchet@43082:   \end{matharray}
blanchet@43082: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{6}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.try}{\mbox{\isa{\isacommand{try}}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@term{\isa{simp}}[]
wenzelm@43467: \rail@nextbar{2}
wenzelm@43467: \rail@term{\isa{intro}}[]
wenzelm@43467: \rail@nextbar{3}
wenzelm@43467: \rail@term{\isa{elim}}[]
wenzelm@43467: \rail@nextbar{4}
wenzelm@43467: \rail@term{\isa{dest}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[]
wenzelm@43467: \rail@nextplus{5}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{{\isaliteral{5B}{\isacharbrackleft}}}}[]
wenzelm@43467: \rail@nont{\isa{args}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{5D}{\isacharbrackright}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\isa{facts}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.sledgehammer-params}{\mbox{\isa{\isacommand{sledgehammer{\isaliteral{5F}{\isacharunderscore}}params}}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{{\isaliteral{5B}{\isacharbrackleft}}}}[]
wenzelm@43467: \rail@nont{\isa{args}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{5D}{\isacharbrackright}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{args}}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[]
wenzelm@43467: \rail@nont{\isa{value}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@cterm{\isa{{\isaliteral{2C}{\isacharcomma}}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{5}{\isa{facts}}
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{2}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@term{\isa{add}}[]
wenzelm@43467: \rail@nextbar{3}
wenzelm@43467: \rail@term{\isa{del}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[]
wenzelm@43467: \rail@nextplus{4}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
wenzelm@43467:  % FIXME try: proper clasimpmod!?
wenzelm@43467:   % FIXME check args "value"
blanchet@43082: 
blanchet@43082:   \begin{description}
blanchet@43082: 
blanchet@43082:   \item \hyperlink{command.HOL.solve-direct}{\mbox{\isa{\isacommand{solve{\isaliteral{5F}{\isacharunderscore}}direct}}}} checks whether the current subgoals can
blanchet@43082:     be solved directly by an existing theorem. Duplicate lemmas can be detected
blanchet@43082:     in this way.
blanchet@43082: 
blanchet@43082:   \item \hyperlink{command.HOL.try}{\mbox{\isa{\isacommand{try}}}} attempts to prove a subgoal using a combination
blanchet@43082:     of standard proof methods (\isa{auto}, \isa{simp}, \isa{blast}, etc.).
blanchet@43082:     Additional facts supplied via \isa{{\isaliteral{22}{\isachardoublequote}}simp{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}intro{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}},
blanchet@43082:     \isa{{\isaliteral{22}{\isachardoublequote}}elim{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}}, and \isa{{\isaliteral{22}{\isachardoublequote}}dest{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} are passed to the appropriate proof
blanchet@43082:     methods.
blanchet@43082: 
blanchet@43082:   \item \hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}} attempts to prove a subgoal using external
blanchet@43082:     automatic provers (resolution provers and SMT solvers). See the Sledgehammer
blanchet@43082:     manual \cite{isabelle-sledgehammer} for details.
blanchet@43082: 
blanchet@43082:   \item \hyperlink{command.HOL.sledgehammer-params}{\mbox{\isa{\isacommand{sledgehammer{\isaliteral{5F}{\isacharunderscore}}params}}}} changes
blanchet@43082:     \hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}} configuration options persistently.
blanchet@43082: 
blanchet@43082:   \end{description}%
blanchet@43082: \end{isamarkuptext}%
blanchet@43082: \isamarkuptrue%
blanchet@43082: %
haftmann@31907: \isamarkupsection{Checking and refuting propositions%
haftmann@31907: }
haftmann@31907: \isamarkuptrue%
haftmann@31907: %
haftmann@31907: \begin{isamarkuptext}%
haftmann@31907: Identifying incorrect propositions usually involves evaluation of
blanchet@43082:   particular assignments and systematic counterexample search.  This
haftmann@31907:   is supported by the following commands.
haftmann@31907: 
haftmann@31907:   \begin{matharray}{rcl}
wenzelm@40685:     \indexdef{HOL}{command}{value}\hypertarget{command.HOL.value}{\hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{quickcheck}\hypertarget{command.HOL.quickcheck}{\hyperlink{command.HOL.quickcheck}{\mbox{\isa{\isacommand{quickcheck}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
blanchet@43082:     \indexdef{HOL}{command}{refute}\hypertarget{command.HOL.refute}{\hyperlink{command.HOL.refute}{\mbox{\isa{\isacommand{refute}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
blanchet@43082:     \indexdef{HOL}{command}{nitpick}\hypertarget{command.HOL.nitpick}{\hyperlink{command.HOL.nitpick}{\mbox{\isa{\isacommand{nitpick}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
blanchet@43082:     \indexdef{HOL}{command}{quickcheck\_params}\hypertarget{command.HOL.quickcheck-params}{\hyperlink{command.HOL.quickcheck-params}{\mbox{\isa{\isacommand{quickcheck{\isaliteral{5F}{\isacharunderscore}}params}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
blanchet@43082:     \indexdef{HOL}{command}{refute\_params}\hypertarget{command.HOL.refute-params}{\hyperlink{command.HOL.refute-params}{\mbox{\isa{\isacommand{refute{\isaliteral{5F}{\isacharunderscore}}params}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
blanchet@43082:     \indexdef{HOL}{command}{nitpick\_params}\hypertarget{command.HOL.nitpick-params}{\hyperlink{command.HOL.nitpick-params}{\mbox{\isa{\isacommand{nitpick{\isaliteral{5F}{\isacharunderscore}}params}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}}
haftmann@31907:   \end{matharray}
haftmann@31907: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{{\isaliteral{5B}{\isacharbrackleft}}}}[]
wenzelm@43467: \rail@nont{\isa{name}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{5D}{\isacharbrackright}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\isa{modes}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{3}{\isa{}}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@term{\hyperlink{command.HOL.quickcheck}{\mbox{\isa{\isacommand{quickcheck}}}}}[]
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.refute}{\mbox{\isa{\isacommand{refute}}}}}[]
wenzelm@43467: \rail@nextbar{2}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.nitpick}{\mbox{\isa{\isacommand{nitpick}}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{{\isaliteral{5B}{\isacharbrackleft}}}}[]
wenzelm@43467: \rail@nont{\isa{args}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{5D}{\isacharbrackright}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{3}{\isa{}}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@term{\hyperlink{command.HOL.quickcheck-params}{\mbox{\isa{\isacommand{quickcheck{\isaliteral{5F}{\isacharunderscore}}params}}}}}[]
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.refute-params}{\mbox{\isa{\isacommand{refute{\isaliteral{5F}{\isacharunderscore}}params}}}}}[]
wenzelm@43467: \rail@nextbar{2}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.nitpick-params}{\mbox{\isa{\isacommand{nitpick{\isaliteral{5F}{\isacharunderscore}}params}}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{{\isaliteral{5B}{\isacharbrackleft}}}}[]
wenzelm@43467: \rail@nont{\isa{args}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{5D}{\isacharbrackright}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{modes}}
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{args}}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[]
wenzelm@43467: \rail@nont{\isa{value}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@cterm{\isa{{\isaliteral{2C}{\isacharcomma}}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
wenzelm@43467:  % FIXME check "value"
haftmann@31907: 
haftmann@31907:   \begin{description}
haftmann@31907: 
haftmann@31907:   \item \hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}~\isa{t} evaluates and prints a
haftmann@31907:     term; optionally \isa{modes} can be specified, which are
haftmann@31907:     appended to the current print mode (see also \cite{isabelle-ref}).
haftmann@31907:     Internally, the evaluation is performed by registered evaluators,
haftmann@31907:     which are invoked sequentially until a result is returned.
haftmann@31907:     Alternatively a specific evaluator can be selected using square
haftmann@37419:     brackets; typical evaluators use the current set of code equations
haftmann@37419:     to normalize and include \isa{simp} for fully symbolic evaluation
haftmann@37419:     using the simplifier, \isa{nbe} for \emph{normalization by evaluation}
haftmann@37419:     and \emph{code} for code generation in SML.
haftmann@31907: 
haftmann@31907:   \item \hyperlink{command.HOL.quickcheck}{\mbox{\isa{\isacommand{quickcheck}}}} tests the current goal for
blanchet@43082:     counterexamples using a series of assignments for its
haftmann@31907:     free variables; by default the first subgoal is tested, an other
haftmann@31907:     can be selected explicitly using an optional goal index.
wenzelm@41185:     Assignments can be chosen exhausting the search space upto a given
wenzelm@41185:     size or using a fixed number of random assignments in the search space.
wenzelm@41185:     By default, quickcheck uses exhaustive testing.
haftmann@31907:     A number of configuration options are supported for
haftmann@31907:     \hyperlink{command.HOL.quickcheck}{\mbox{\isa{\isacommand{quickcheck}}}}, notably:
haftmann@31907: 
haftmann@31907:     \begin{description}
haftmann@31907: 
wenzelm@41185:     \item[\isa{tester}] specifies how to explore the search space
wenzelm@41185:       (e.g. exhaustive or random).
wenzelm@41185:       An unknown configuration option is treated as an argument to tester,
wenzelm@41185:       making \isa{{\isaliteral{22}{\isachardoublequote}}tester\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}} optional.
wenzelm@40515:     \item[\isa{size}] specifies the maximum size of the search space
wenzelm@40515:     for assignment values.
haftmann@31907: 
wenzelm@42994:     \item[\isa{eval}] takes a term or a list of terms and evaluates
wenzelm@42994:       these terms under the variable assignment found by quickcheck.
wenzelm@42994: 
wenzelm@40515:     \item[\isa{iterations}] sets how many sets of assignments are
wenzelm@40515:     generated for each particular size.
haftmann@31907: 
wenzelm@40685:     \item[\isa{no{\isaliteral{5F}{\isacharunderscore}}assms}] specifies whether assumptions in
wenzelm@40515:     structured proofs should be ignored.
wenzelm@40515: 
wenzelm@40515:     \item[\isa{timeout}] sets the time limit in seconds.
wenzelm@40515: 
wenzelm@40685:     \item[\isa{default{\isaliteral{5F}{\isacharunderscore}}type}] sets the type(s) generally used to
wenzelm@40515:     instantiate type variables.
wenzelm@40515: 
wenzelm@40515:     \item[\isa{report}] if set quickcheck reports how many tests
wenzelm@40515:     fulfilled the preconditions.
wenzelm@40515: 
wenzelm@40515:     \item[\isa{quiet}] if not set quickcheck informs about the
wenzelm@40515:     current size for assignment values.
wenzelm@40515: 
wenzelm@40515:     \item[\isa{expect}] can be used to check if the user's
wenzelm@40685:     expectation was met (\isa{no{\isaliteral{5F}{\isacharunderscore}}expectation}, \isa{no{\isaliteral{5F}{\isacharunderscore}}counterexample}, or \isa{counterexample}).
wenzelm@35352: 
haftmann@31907:     \end{description}
haftmann@31907: 
haftmann@31907:     These option can be given within square brackets.
haftmann@31907: 
blanchet@43082:   \item \hyperlink{command.HOL.quickcheck-params}{\mbox{\isa{\isacommand{quickcheck{\isaliteral{5F}{\isacharunderscore}}params}}}} changes
blanchet@43082:     \hyperlink{command.HOL.quickcheck}{\mbox{\isa{\isacommand{quickcheck}}}} configuration options persistently.
blanchet@43082: 
blanchet@43082:   \item \hyperlink{command.HOL.refute}{\mbox{\isa{\isacommand{refute}}}} tests the current goal for
blanchet@43082:     counterexamples using a reduction to SAT. The following configuration
blanchet@43082:     options are supported:
blanchet@43082: 
blanchet@43082:     \begin{description}
blanchet@43082: 
blanchet@43082:     \item[\isa{minsize}] specifies the minimum size (cardinality) of the
blanchet@43082:       models to search for.
blanchet@43082: 
blanchet@43082:     \item[\isa{maxsize}] specifies the maximum size (cardinality) of the
blanchet@43082:       models to search for. Nonpositive values mean $\infty$.
blanchet@43082: 
blanchet@43082:     \item[\isa{maxvars}] specifies the maximum number of Boolean variables
blanchet@43082:     to use when transforming the term into a propositional formula.
blanchet@43082:     Nonpositive values mean $\infty$.
blanchet@43082: 
blanchet@43082:     \item[\isa{satsolver}] specifies the SAT solver to use.
blanchet@43082: 
blanchet@43082:     \item[\isa{no{\isaliteral{5F}{\isacharunderscore}}assms}] specifies whether assumptions in
blanchet@43082:     structured proofs should be ignored.
blanchet@43082: 
blanchet@43082:     \item[\isa{maxtime}] sets the time limit in seconds.
blanchet@43082: 
blanchet@43082:     \item[\isa{expect}] can be used to check if the user's
blanchet@43082:     expectation was met (\isa{genuine}, \isa{potential},
blanchet@43082:     \isa{none}, or \isa{unknown}).
blanchet@43082: 
blanchet@43082:     \end{description}
blanchet@43082: 
blanchet@43082:     These option can be given within square brackets.
blanchet@43082: 
blanchet@43082:   \item \hyperlink{command.HOL.refute-params}{\mbox{\isa{\isacommand{refute{\isaliteral{5F}{\isacharunderscore}}params}}}} changes
blanchet@43082:     \hyperlink{command.HOL.refute}{\mbox{\isa{\isacommand{refute}}}} configuration options persistently.
blanchet@43082: 
blanchet@43082:   \item \hyperlink{command.HOL.nitpick}{\mbox{\isa{\isacommand{nitpick}}}} tests the current goal for counterexamples
blanchet@43082:     using a reduction to first-order relational logic. See the Nitpick manual
blanchet@43082:     \cite{isabelle-nitpick} for details.
blanchet@43082: 
blanchet@43082:   \item \hyperlink{command.HOL.nitpick-params}{\mbox{\isa{\isacommand{nitpick{\isaliteral{5F}{\isacharunderscore}}params}}}} changes
blanchet@43082:     \hyperlink{command.HOL.nitpick}{\mbox{\isa{\isacommand{nitpick}}}} configuration options persistently.
haftmann@31907: 
haftmann@31907:   \end{description}%
haftmann@31907: \end{isamarkuptext}%
haftmann@31907: \isamarkuptrue%
haftmann@31907: %
wenzelm@28788: \isamarkupsection{Unstructured case analysis and induction \label{sec:hol-induct-tac}%
wenzelm@26849: }
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@26849: \begin{isamarkuptext}%
wenzelm@27124: The following tools of Isabelle/HOL support cases analysis and
wenzelm@27124:   induction in unstructured tactic scripts; see also
wenzelm@27124:   \secref{sec:cases-induct} for proper Isar versions of similar ideas.
wenzelm@26849: 
wenzelm@26849:   \begin{matharray}{rcl}
wenzelm@40685:     \indexdef{HOL}{method}{case\_tac}\hypertarget{method.HOL.case-tac}{\hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
wenzelm@40685:     \indexdef{HOL}{method}{induct\_tac}\hypertarget{method.HOL.induct-tac}{\hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
wenzelm@40685:     \indexdef{HOL}{method}{ind\_cases}\hypertarget{method.HOL.ind-cases}{\hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
wenzelm@40685:     \indexdef{HOL}{command}{inductive\_cases}\hypertarget{command.HOL.inductive-cases}{\hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}cases}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}tac}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.goalspec}{\mbox{\isa{goalspec}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\isa{rule}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{3}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}tac}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.goalspec}{\mbox{\isa{goalspec}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.insts}{\mbox{\isa{insts}}}}[]
wenzelm@43467: \rail@nextplus{2}
wenzelm@43467: \rail@cterm{\isa{\isakeyword{and}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\isa{rule}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{3}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{\isakeyword{for}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@nextplus{2}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{3}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}cases}}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.thmdecl}{\mbox{\isa{thmdecl}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@nextplus{2}
wenzelm@43467: \rail@cterm{\isa{\isakeyword{and}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{1}{\isa{rule}}
wenzelm@43467: \rail@term{\isa{rule}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.thmref}{\mbox{\isa{thmref}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
wenzelm@26849: 
wenzelm@26849: 
wenzelm@28788:   \begin{description}
wenzelm@26849: 
wenzelm@40685:   \item \hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}tac}}} and \hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}tac}}} admit
wenzelm@28788:   to reason about inductive types.  Rules are selected according to
wenzelm@28788:   the declarations by the \hyperlink{attribute.cases}{\mbox{\isa{cases}}} and \hyperlink{attribute.induct}{\mbox{\isa{induct}}}
wenzelm@28788:   attributes, cf.\ \secref{sec:cases-induct}.  The \hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}} package already takes care of this.
wenzelm@27124: 
wenzelm@27124:   These unstructured tactics feature both goal addressing and dynamic
wenzelm@26849:   instantiation.  Note that named rule cases are \emph{not} provided
wenzelm@27124:   as would be by the proper \hyperlink{method.cases}{\mbox{\isa{cases}}} and \hyperlink{method.induct}{\mbox{\isa{induct}}} proof
wenzelm@40685:   methods (see \secref{sec:cases-induct}).  Unlike the \hyperlink{method.induct}{\mbox{\isa{induct}}} method, \hyperlink{method.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}tac}}} does not handle structured rule
wenzelm@27124:   statements, only the compact object-logic conclusion of the subgoal
wenzelm@27124:   being addressed.
wenzelm@42994: 
wenzelm@40685:   \item \hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}} and \hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\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@40685:   While \hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}} is a proof method to apply the
wenzelm@40685:   result immediately as elimination rules, \hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}cases}}}} provides case split theorems at the theory level
wenzelm@40685:   for later use.  The \hyperlink{keyword.for}{\mbox{\isa{\isakeyword{for}}}} argument of the \hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}} method allows to specify a list of variables that should
wenzelm@26849:   be generalized before applying the resulting rule.
wenzelm@26849: 
wenzelm@28788:   \end{description}%
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@43498: For validation purposes, it is often useful to \emph{execute}
wenzelm@43498:   specifications.  In principle, execution could be simulated by
wenzelm@43498:   Isabelle's inference kernel, i.e. by a combination of resolution and
wenzelm@43498:   simplification.  Unfortunately, this approach is rather inefficient.
wenzelm@43498:   A more efficient way of executing specifications is to translate
wenzelm@43498:   them into a functional programming language such as ML.
wenzelm@26849: 
wenzelm@43498:   Isabelle provides two generic frameworks to support code generation
wenzelm@43498:   from executable specifications.  Isabelle/HOL instantiates these
wenzelm@43498:   mechanisms in a way that is amenable to end-user applications.%
wenzelm@43498: \end{isamarkuptext}%
wenzelm@43498: \isamarkuptrue%
wenzelm@43498: %
wenzelm@43498: \isamarkupsubsection{The new code generator (F. Haftmann)%
wenzelm@43498: }
wenzelm@43498: \isamarkuptrue%
wenzelm@43498: %
wenzelm@43498: \begin{isamarkuptext}%
wenzelm@43498: This framework generates code from functional programs
haftmann@37397:   (including overloading using type classes) to SML \cite{SML}, OCaml
haftmann@39048:   \cite{OCaml}, Haskell \cite{haskell-revised-report} and Scala
wenzelm@43498:   \cite{scala-overview-tech-report}.  Conceptually, code generation is
wenzelm@43498:   split up in three steps: \emph{selection} of code theorems,
wenzelm@43498:   \emph{translation} into an abstract executable view and
wenzelm@43498:   \emph{serialization} to a specific \emph{target language}.
wenzelm@43498:   Inductive specifications can be executed using the predicate
wenzelm@43498:   compiler which operates within HOL.  See \cite{isabelle-codegen} for
wenzelm@43498:   an introduction.
haftmann@37397: 
haftmann@37397:   \begin{matharray}{rcl}
wenzelm@40685:     \indexdef{HOL}{command}{export\_code}\hypertarget{command.HOL.export-code}{\hyperlink{command.HOL.export-code}{\mbox{\isa{\isacommand{export{\isaliteral{5F}{\isacharunderscore}}code}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
haftmann@37397:     \indexdef{HOL}{attribute}{code}\hypertarget{attribute.HOL.code}{\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}} & : & \isa{attribute} \\
wenzelm@40685:     \indexdef{HOL}{command}{code\_abort}\hypertarget{command.HOL.code-abort}{\hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}abort}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{code\_datatype}\hypertarget{command.HOL.code-datatype}{\hyperlink{command.HOL.code-datatype}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}datatype}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{print\_codesetup}\hypertarget{command.HOL.print-codesetup}{\hyperlink{command.HOL.print-codesetup}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}codesetup}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{attribute}{code\_inline}\hypertarget{attribute.HOL.code-inline}{\hyperlink{attribute.HOL.code-inline}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}inline}}}} & : & \isa{attribute} \\
wenzelm@40685:     \indexdef{HOL}{attribute}{code\_post}\hypertarget{attribute.HOL.code-post}{\hyperlink{attribute.HOL.code-post}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}post}}}} & : & \isa{attribute} \\
wenzelm@40685:     \indexdef{HOL}{command}{print\_codeproc}\hypertarget{command.HOL.print-codeproc}{\hyperlink{command.HOL.print-codeproc}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}codeproc}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{code\_thms}\hypertarget{command.HOL.code-thms}{\hyperlink{command.HOL.code-thms}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}thms}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{code\_deps}\hypertarget{command.HOL.code-deps}{\hyperlink{command.HOL.code-deps}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}deps}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{code\_const}\hypertarget{command.HOL.code-const}{\hyperlink{command.HOL.code-const}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}const}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{code\_type}\hypertarget{command.HOL.code-type}{\hyperlink{command.HOL.code-type}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}type}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{code\_class}\hypertarget{command.HOL.code-class}{\hyperlink{command.HOL.code-class}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}class}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{code\_instance}\hypertarget{command.HOL.code-instance}{\hyperlink{command.HOL.code-instance}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}instance}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{code\_reserved}\hypertarget{command.HOL.code-reserved}{\hyperlink{command.HOL.code-reserved}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reserved}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{code\_monad}\hypertarget{command.HOL.code-monad}{\hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}monad}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{code\_include}\hypertarget{command.HOL.code-include}{\hyperlink{command.HOL.code-include}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}include}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{code\_modulename}\hypertarget{command.HOL.code-modulename}{\hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}modulename}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{code\_reflect}\hypertarget{command.HOL.code-reflect}{\hyperlink{command.HOL.code-reflect}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reflect}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}}
haftmann@37397:   \end{matharray}
haftmann@37397: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{11}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.export-code}{\mbox{\isa{\isacommand{export{\isaliteral{5F}{\isacharunderscore}}code}}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\isa{constexpr}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@cr{3}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{4}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@term{\isa{\isakeyword{in}}}[]
wenzelm@43467: \rail@nont{\isa{target}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{5}
wenzelm@43467: \rail@term{\isa{\isakeyword{module{\isaliteral{5F}{\isacharunderscore}}name}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@cr{7}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{8}
wenzelm@43467: \rail@term{\isa{\isakeyword{file}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[]
wenzelm@43467: \rail@nextbar{9}
wenzelm@43467: \rail@term{\isa{{\isaliteral{2D}{\isacharminus}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{8}
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@nont{\isa{args}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nextplus{10}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{1}{\isa{const}}
wenzelm@43467: \rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{3}{\isa{constexpr}}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nont{\isa{const}}[]
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{name{\isaliteral{2E}{\isachardot}}{\isaliteral{5F}{\isacharunderscore}}}}[]
wenzelm@43467: \rail@nextbar{2}
wenzelm@43467: \rail@term{\isa{{\isaliteral{5F}{\isacharunderscore}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{1}{\isa{typeconstructor}}
wenzelm@43467: \rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{1}{\isa{class}}
wenzelm@43467: \rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{4}{\isa{target}}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@term{\isa{SML}}[]
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{OCaml}}[]
wenzelm@43467: \rail@nextbar{2}
wenzelm@43467: \rail@term{\isa{Haskell}}[]
wenzelm@43467: \rail@nextbar{3}
wenzelm@43467: \rail@term{\isa{Scala}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{4}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@term{\isa{del}}[]
wenzelm@43467: \rail@nextbar{2}
wenzelm@43467: \rail@term{\isa{abstype}}[]
wenzelm@43467: \rail@nextbar{3}
wenzelm@43467: \rail@term{\isa{abstract}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}abort}}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\isa{const}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.code-datatype}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}datatype}}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\isa{const}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{attribute.HOL.code-inline}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}inline}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{del}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{attribute.HOL.code-post}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}post}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{del}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{3}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.code-thms}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}thms}}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\isa{constexpr}}[]
wenzelm@43467: \rail@nextplus{2}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{3}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.code-deps}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}deps}}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\isa{constexpr}}[]
wenzelm@43467: \rail@nextplus{2}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{7}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.code-const}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}const}}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\isa{const}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@cterm{\isa{\isakeyword{and}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@cr{3}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@nont{\isa{target}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{4}
wenzelm@43467: \rail@nont{\isa{syntax}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nextplus{5}
wenzelm@43467: \rail@cterm{\isa{\isakeyword{and}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@nextplus{6}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{7}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.code-type}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}type}}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\isa{typeconstructor}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@cterm{\isa{\isakeyword{and}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@cr{3}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@nont{\isa{target}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{4}
wenzelm@43467: \rail@nont{\isa{syntax}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nextplus{5}
wenzelm@43467: \rail@cterm{\isa{\isakeyword{and}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@nextplus{6}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{9}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.code-class}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}class}}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\isa{class}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@cterm{\isa{\isakeyword{and}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@cr{3}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@nont{\isa{target}}[]
wenzelm@43467: \rail@cr{5}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{6}
wenzelm@43467: \rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nextplus{7}
wenzelm@43467: \rail@cterm{\isa{\isakeyword{and}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@nextplus{8}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{7}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.code-instance}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}instance}}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\isa{typeconstructor}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}}}[]
wenzelm@43467: \rail@nont{\isa{class}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@cterm{\isa{\isakeyword{and}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@cr{3}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@nont{\isa{target}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{4}
wenzelm@43467: \rail@term{\isa{{\isaliteral{2D}{\isacharminus}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nextplus{5}
wenzelm@43467: \rail@cterm{\isa{\isakeyword{and}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@nextplus{6}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.code-reserved}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reserved}}}}}[]
wenzelm@43467: \rail@nont{\isa{target}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{1}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}monad}}}}}[]
wenzelm@43467: \rail@nont{\isa{const}}[]
wenzelm@43467: \rail@nont{\isa{const}}[]
wenzelm@43467: \rail@nont{\isa{target}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.code-include}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}include}}}}}[]
wenzelm@43467: \rail@nont{\isa{target}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[]
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{{\isaliteral{2D}{\isacharminus}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}modulename}}}}}[]
wenzelm@43467: \rail@nont{\isa{target}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{11}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.code-reflect}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reflect}}}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[]
wenzelm@43467: \rail@cr{2}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{3}
wenzelm@43467: \rail@term{\isa{\isakeyword{datatypes}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@term{\isa{{\isaliteral{5F}{\isacharunderscore}}}}[]
wenzelm@43467: \rail@nextbar{4}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[]
wenzelm@43467: \rail@nextplus{5}
wenzelm@43467: \rail@cterm{\isa{{\isaliteral{7C}{\isacharbar}}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@nextplus{6}
wenzelm@43467: \rail@cterm{\isa{\isakeyword{and}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@cr{8}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{9}
wenzelm@43467: \rail@term{\isa{\isakeyword{functions}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[]
wenzelm@43467: \rail@nextplus{10}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{9}
wenzelm@43467: \rail@term{\isa{\isakeyword{file}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{4}{\isa{syntax}}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[]
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@term{\isa{\isakeyword{infix}}}[]
wenzelm@43467: \rail@nextbar{2}
wenzelm@43467: \rail@term{\isa{\isakeyword{infixl}}}[]
wenzelm@43467: \rail@nextbar{3}
wenzelm@43467: \rail@term{\isa{\isakeyword{infixr}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
haftmann@37397: 
haftmann@37397: 
haftmann@37397:   \begin{description}
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{command.HOL.export-code}{\mbox{\isa{\isacommand{export{\isaliteral{5F}{\isacharunderscore}}code}}}} generates code for a given list
haftmann@39832:   of constants in the specified target language(s).  If no
haftmann@39832:   serialization instruction is given, only abstract code is generated
haftmann@39832:   internally.
haftmann@37397: 
haftmann@37397:   Constants may be specified by giving them literally, referring to
wenzelm@40685:   all executable contants within a certain theory by giving \isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{2E}{\isachardot}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}, or referring to \emph{all} executable constants currently
wenzelm@40685:   available by giving \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}.
haftmann@37397: 
haftmann@37397:   By default, for each involved theory one corresponding name space
haftmann@37397:   module is generated.  Alternativly, a module name may be specified
wenzelm@40685:   after the \hyperlink{keyword.module-name}{\mbox{\isa{\isakeyword{module{\isaliteral{5F}{\isacharunderscore}}name}}}} keyword; then \emph{all} code is
haftmann@37397:   placed in this module.
haftmann@37397: 
haftmann@39832:   For \emph{SML}, \emph{OCaml} and \emph{Scala} the file specification
haftmann@39832:   refers to a single file; for \emph{Haskell}, it refers to a whole
haftmann@39832:   directory, where code is generated in multiple files reflecting the
haftmann@39832:   module hierarchy.  Omitting the file specification denotes standard
haftmann@37748:   output.
haftmann@37397: 
haftmann@37397:   Serializers take an optional list of arguments in parentheses.  For
wenzelm@40685:   \emph{SML} and \emph{OCaml}, ``\isa{no{\isaliteral{5F}{\isacharunderscore}}signatures}`` omits
haftmann@37397:   explicit module signatures.
wenzelm@42994: 
haftmann@39832:   For \emph{Haskell} a module name prefix may be given using the
wenzelm@40685:   ``\isa{{\isaliteral{22}{\isachardoublequote}}root{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}}'' argument; ``\isa{string{\isaliteral{5F}{\isacharunderscore}}classes}'' adds a
haftmann@39832:   ``\verb|deriving (Read, Show)|'' clause to each appropriate
haftmann@39832:   datatype declaration.
haftmann@37397: 
haftmann@37397:   \item \hyperlink{attribute.HOL.code}{\mbox{\isa{code}}} explicitly selects (or with option
wenzelm@40685:   ``\isa{{\isaliteral{22}{\isachardoublequote}}del{\isaliteral{22}{\isachardoublequote}}}'' deselects) a code equation for code generation.
haftmann@38706:   Usually packages introducing code equations provide a reasonable
wenzelm@40685:   default setup for selection.  Variants \isa{{\isaliteral{22}{\isachardoublequote}}code\ abstype{\isaliteral{22}{\isachardoublequote}}} and
wenzelm@40685:   \isa{{\isaliteral{22}{\isachardoublequote}}code\ abstract{\isaliteral{22}{\isachardoublequote}}} declare abstract datatype certificates or
haftmann@38706:   code equations on abstract datatype representations respectively.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}abort}}}} declares constants which are not
haftmann@39832:   required to have a definition by means of code equations; if needed
haftmann@39832:   these are implemented by program abort instead.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{command.HOL.code-datatype}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}datatype}}}} specifies a constructor set
haftmann@37397:   for a logical type.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{command.HOL.print-codesetup}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}codesetup}}}} gives an overview on
haftmann@37397:   selected code equations and code generator datatypes.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{attribute.HOL.code-inline}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}inline}}} declares (or with option
wenzelm@40685:   ``\isa{{\isaliteral{22}{\isachardoublequote}}del{\isaliteral{22}{\isachardoublequote}}}'' removes) inlining theorems which are applied as
haftmann@39832:   rewrite rules to any code equation during preprocessing.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{attribute.HOL.code-post}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}post}}} declares (or with option ``\isa{{\isaliteral{22}{\isachardoublequote}}del{\isaliteral{22}{\isachardoublequote}}}'' removes) theorems which are applied as rewrite rules to any
haftmann@39832:   result of an evaluation.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{command.HOL.print-codeproc}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}codeproc}}}} prints the setup of the code
haftmann@39832:   generator preprocessor.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{command.HOL.code-thms}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}thms}}}} prints a list of theorems
haftmann@37397:   representing the corresponding program containing all given
haftmann@37397:   constants after preprocessing.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{command.HOL.code-deps}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}deps}}}} visualizes dependencies of
haftmann@37397:   theorems representing the corresponding program containing all given
haftmann@37397:   constants after preprocessing.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{command.HOL.code-const}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}const}}}} associates a list of constants
haftmann@37397:   with target-specific serializations; omitting a serialization
haftmann@37397:   deletes an existing serialization.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{command.HOL.code-type}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}type}}}} associates a list of type
haftmann@37397:   constructors with target-specific serializations; omitting a
haftmann@37397:   serialization deletes an existing serialization.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{command.HOL.code-class}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}class}}}} associates a list of classes
haftmann@37397:   with target-specific class names; omitting a serialization deletes
haftmann@37397:   an existing serialization.  This applies only to \emph{Haskell}.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{command.HOL.code-instance}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}instance}}}} declares a list of type
haftmann@37397:   constructor / class instance relations as ``already present'' for a
wenzelm@40685:   given target.  Omitting a ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{22}{\isachardoublequote}}}'' deletes an existing
haftmann@37397:   ``already present'' declaration.  This applies only to
haftmann@37397:   \emph{Haskell}.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{command.HOL.code-reserved}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reserved}}}} declares a list of names as
haftmann@37397:   reserved for a given target, preventing it to be shadowed by any
haftmann@37397:   generated code.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}monad}}}} provides an auxiliary mechanism
haftmann@37397:   to generate monadic code for Haskell.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{command.HOL.code-include}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}include}}}} adds arbitrary named content
wenzelm@40685:   (``include'') to generated code.  A ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{22}{\isachardoublequote}}}'' as last argument
haftmann@37397:   will remove an already added ``include''.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}modulename}}}} declares aliasings from one
haftmann@37397:   module name onto another.
haftmann@37397: 
wenzelm@40685:   \item \hyperlink{command.HOL.code-reflect}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reflect}}}} without a ``\isa{{\isaliteral{22}{\isachardoublequote}}file{\isaliteral{22}{\isachardoublequote}}}''
haftmann@39832:   argument compiles code into the system runtime environment and
haftmann@39832:   modifies the code generator setup that future invocations of system
wenzelm@40685:   runtime code generation referring to one of the ``\isa{{\isaliteral{22}{\isachardoublequote}}datatypes{\isaliteral{22}{\isachardoublequote}}}'' or ``\isa{{\isaliteral{22}{\isachardoublequote}}functions{\isaliteral{22}{\isachardoublequote}}}'' entities use these precompiled
wenzelm@40685:   entities.  With a ``\isa{{\isaliteral{22}{\isachardoublequote}}file{\isaliteral{22}{\isachardoublequote}}}'' argument, the corresponding code
haftmann@39832:   is generated into that specified file without modifying the code
haftmann@39832:   generator setup.
haftmann@39832: 
wenzelm@43498:   \end{description}%
wenzelm@43498: \end{isamarkuptext}%
wenzelm@43498: \isamarkuptrue%
wenzelm@43498: %
wenzelm@43498: \isamarkupsubsection{The old code generator (S. Berghofer)%
wenzelm@43498: }
wenzelm@43498: \isamarkuptrue%
wenzelm@43498: %
wenzelm@43498: \begin{isamarkuptext}%
wenzelm@43498: This framework generates code from both functional and
wenzelm@43498:   relational programs to SML, as explained below.
wenzelm@26849: 
wenzelm@26849:   \begin{matharray}{rcl}
wenzelm@43498:     \indexdef{}{command}{code\_module}\hypertarget{command.code-module}{\hyperlink{command.code-module}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}module}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@43498:     \indexdef{}{command}{code\_library}\hypertarget{command.code-library}{\hyperlink{command.code-library}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}library}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@43498:     \indexdef{}{command}{consts\_code}\hypertarget{command.consts-code}{\hyperlink{command.consts-code}{\mbox{\isa{\isacommand{consts{\isaliteral{5F}{\isacharunderscore}}code}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@43498:     \indexdef{}{command}{types\_code}\hypertarget{command.types-code}{\hyperlink{command.types-code}{\mbox{\isa{\isacommand{types{\isaliteral{5F}{\isacharunderscore}}code}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@43497:     \indexdef{}{attribute}{code}\hypertarget{attribute.code}{\hyperlink{attribute.code}{\mbox{\isa{code}}}} & : & \isa{attribute} \\
wenzelm@26849:   \end{matharray}
wenzelm@26849: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{11}{\isa{}}
wenzelm@43467: \rail@bar
wenzelm@43498: \rail@term{\hyperlink{command.code-module}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}module}}}}}[]
wenzelm@43467: \rail@nextbar{1}
wenzelm@43498: \rail@term{\hyperlink{command.code-library}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}library}}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\isa{modespec}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@cr{3}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{4}
wenzelm@43467: \rail@term{\isa{\isakeyword{file}}}[]
wenzelm@43467: \rail@nont{\isa{name}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{4}
wenzelm@43467: \rail@term{\isa{\isakeyword{imports}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@nextplus{5}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@cr{7}
wenzelm@43467: \rail@term{\isa{\isakeyword{contains}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[]
wenzelm@43467: \rail@nextplus{8}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@nextbar{9}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[]
wenzelm@43467: \rail@nextplus{10}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{modespec}}
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@cnont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.consts-code}{\mbox{\isa{\isacommand{consts{\isaliteral{5F}{\isacharunderscore}}code}}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\isa{codespec}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{codespec}}
wenzelm@43467: \rail@nont{\isa{const}}[]
wenzelm@43467: \rail@nont{\isa{template}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\isa{attachment}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.types-code}{\mbox{\isa{\isacommand{types{\isaliteral{5F}{\isacharunderscore}}code}}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\isa{tycodespec}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{tycodespec}}
wenzelm@43467: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@nont{\isa{template}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\isa{attachment}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{1}{\isa{const}}
wenzelm@43467: \rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{1}{\isa{template}}
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.string}{\mbox{\isa{string}}}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{attachment}}
wenzelm@43467: \rail@term{\isa{attach}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\isa{modespec}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@term{\isa{{\isaliteral{7B}{\isacharbraceleft}}}}[]
wenzelm@43467: \rail@nont{\hyperlink{syntax.text}{\mbox{\isa{text}}}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{7D}{\isacharbraceright}}}}[]
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{}}
wenzelm@43497: \rail@term{\hyperlink{attribute.code}{\mbox{\isa{code}}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\isa{name}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}%
wenzelm@26849: \end{isamarkuptext}%
wenzelm@26849: \isamarkuptrue%
wenzelm@26849: %
wenzelm@43498: \isamarkupsubsubsection{Invoking the code generator%
wenzelm@43498: }
wenzelm@43498: \isamarkuptrue%
wenzelm@43498: %
wenzelm@43498: \begin{isamarkuptext}%
wenzelm@43498: The code generator is invoked via the \hyperlink{command.code-module}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}module}}}}
wenzelm@43498:   and \hyperlink{command.code-library}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}library}}}} commands, which correspond to
wenzelm@43498:   \emph{incremental} and \emph{modular} code generation, respectively.
wenzelm@43498: 
wenzelm@43498:   \begin{description}
wenzelm@43498: 
wenzelm@43498:   \item [Modular] For each theory, an ML structure is generated,
wenzelm@43498:   containing the code generated from the constants defined in this
wenzelm@43498:   theory.
wenzelm@43498: 
wenzelm@43498:   \item [Incremental] All the generated code is emitted into the same
wenzelm@43498:   structure.  This structure may import code from previously generated
wenzelm@43498:   structures, which can be specified via \hyperlink{keyword.imports}{\mbox{\isa{\isakeyword{imports}}}}.
wenzelm@43498:   Moreover, the generated structure may also be referred to in later
wenzelm@43498:   invocations of the code generator.
wenzelm@43498: 
wenzelm@43498:   \end{description}
wenzelm@43498: 
wenzelm@43498:   After the \hyperlink{command.code-module}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}module}}}} and \hyperlink{command.code-library}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}library}}}}
wenzelm@43498:   keywords, the user may specify an optional list of ``modes'' in
wenzelm@43498:   parentheses. These can be used to instruct the code generator to
wenzelm@43498:   emit additional code for special purposes, e.g.\ functions for
wenzelm@43498:   converting elements of generated datatypes to Isabelle terms, or
wenzelm@43498:   test data generators. The list of modes is followed by a module
wenzelm@43498:   name.  The module name is optional for modular code generation, but
wenzelm@43498:   must be specified for incremental code generation.
wenzelm@43498: 
wenzelm@43498:   The code can either be written to a file, in which case a file name
wenzelm@43498:   has to be specified after the \hyperlink{keyword.file}{\mbox{\isa{\isakeyword{file}}}} keyword, or be loaded
wenzelm@43498:   directly into Isabelle's ML environment. In the latter case, the
wenzelm@43498:   \hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}} theory command can be used to inspect the results
wenzelm@43498:   interactively, for example.
wenzelm@43498: 
wenzelm@43498:   The terms from which to generate code can be specified after the
wenzelm@43498:   \hyperlink{keyword.contains}{\mbox{\isa{\isakeyword{contains}}}} keyword, either as a list of bindings, or just
wenzelm@43498:   as a list of terms. In the latter case, the code generator just
wenzelm@43498:   produces code for all constants and types occuring in the term, but
wenzelm@43498:   does not bind the compiled terms to ML identifiers.
wenzelm@43498: 
wenzelm@43498:   Here is an example:%
wenzelm@43498: \end{isamarkuptext}%
wenzelm@43498: \isamarkuptrue%
wenzelm@43498: \isacommand{code{\isaliteral{5F}{\isacharunderscore}}module}\isamarkupfalse%
wenzelm@43498: \ Test\isanewline
wenzelm@43498: \ \ \isakeyword{contains}\ test\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequoteopen}}foldl\ op\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{3}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{4}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{5}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}%
wenzelm@43498: \begin{isamarkuptext}%
wenzelm@43498: \noindent This binds the result of compiling the given term to
wenzelm@43498:   the ML identifier \verb|Test.test|.%
wenzelm@43498: \end{isamarkuptext}%
wenzelm@43498: \isamarkuptrue%
wenzelm@43498: %
wenzelm@43498: \isadelimML
wenzelm@43498: %
wenzelm@43498: \endisadelimML
wenzelm@43498: %
wenzelm@43498: \isatagML
wenzelm@43498: \isacommand{ML}\isamarkupfalse%
wenzelm@43498: \ {\isaliteral{7B2A}{\isacharverbatimopen}}\ %
wenzelm@43498: \isaantiq
wenzelm@43498: assert{}%
wenzelm@43498: \endisaantiq
wenzelm@43498: \ {\isaliteral{28}{\isacharparenleft}}Test{\isaliteral{2E}{\isachardot}}test\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isadigit{5}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}%
wenzelm@43498: \endisatagML
wenzelm@43498: {\isafoldML}%
wenzelm@43498: %
wenzelm@43498: \isadelimML
wenzelm@43498: %
wenzelm@43498: \endisadelimML
wenzelm@43498: %
wenzelm@43498: \isamarkupsubsubsection{Configuring the code generator%
wenzelm@43498: }
wenzelm@43498: \isamarkuptrue%
wenzelm@43498: %
wenzelm@43498: \begin{isamarkuptext}%
wenzelm@43498: When generating code for a complex term, the code generator
wenzelm@43498:   recursively calls itself for all subterms.  When it arrives at a
wenzelm@43498:   constant, the default strategy of the code generator is to look up
wenzelm@43498:   its definition and try to generate code for it.  Constants which
wenzelm@43498:   have no definitions that are immediately executable, may be
wenzelm@43498:   associated with a piece of ML code manually using the \indexref{}{command}{consts\_code}\hyperlink{command.consts-code}{\mbox{\isa{\isacommand{consts{\isaliteral{5F}{\isacharunderscore}}code}}}} command.  It takes a list whose elements consist of a
wenzelm@43498:   constant (given in usual term syntax -- an explicit type constraint
wenzelm@43498:   accounts for overloading), and a mixfix template describing the ML
wenzelm@43498:   code. The latter is very much the same as the mixfix templates used
wenzelm@43498:   when declaring new constants.  The most notable difference is that
wenzelm@43498:   terms may be included in the ML template using antiquotation
wenzelm@43498:   brackets \verb|{|\verb|*|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{22}{\isachardoublequote}}}~\verb|*|\verb|}|.
wenzelm@43498: 
wenzelm@43498:   A similar mechanism is available for types: \indexref{}{command}{types\_code}\hyperlink{command.types-code}{\mbox{\isa{\isacommand{types{\isaliteral{5F}{\isacharunderscore}}code}}}} associates type constructors with specific ML code.
wenzelm@43498: 
wenzelm@43498:   For example, the following declarations copied from \verb|~~/src/HOL/Product_Type.thy| describe how the product type of
wenzelm@43498:   Isabelle/HOL should be compiled to ML.%
wenzelm@43498: \end{isamarkuptext}%
wenzelm@43498: \isamarkuptrue%
wenzelm@43498: \isacommand{typedecl}\isamarkupfalse%
wenzelm@43498: \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ prod\isanewline
wenzelm@43498: \isacommand{consts}\isamarkupfalse%
wenzelm@43498: \ Pair\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ prod{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
wenzelm@43498: \isanewline
wenzelm@43498: \isacommand{types{\isaliteral{5F}{\isacharunderscore}}code}\isamarkupfalse%
wenzelm@43498: \ prod\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2F}{\isacharslash}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
wenzelm@43498: \isacommand{consts{\isaliteral{5F}{\isacharunderscore}}code}\isamarkupfalse%
wenzelm@43498: \ Pair\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{2F}{\isacharslash}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}%
wenzelm@43498: \begin{isamarkuptext}%
wenzelm@43498: Sometimes, the code associated with a constant or type may
wenzelm@43498:   need to refer to auxiliary functions, which have to be emitted when
wenzelm@43498:   the constant is used. Code for such auxiliary functions can be
wenzelm@43498:   declared using \hyperlink{keyword.attach}{\mbox{\isa{\isakeyword{attach}}}}. For example, the \isa{wfrec}
wenzelm@43498:   function can be implemented as follows:%
wenzelm@43498: \end{isamarkuptext}%
wenzelm@43498: \isamarkuptrue%
wenzelm@43498: \isacommand{consts{\isaliteral{5F}{\isacharunderscore}}code}\isamarkupfalse%
wenzelm@43498: \ wfrec\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6D6F64756C653E}{\isasymmodule}}wfrec{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\ \ \isanewline
wenzelm@43498: \ \ \isakeyword{attach}\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ fun\ wfrec\ f\ x\ {\isaliteral{3D}{\isacharequal}}\ f\ {\isaliteral{28}{\isacharparenleft}}wfrec\ f{\isaliteral{29}{\isacharparenright}}\ x\ {\isaliteral{2A7D}{\isacharverbatimclose}}%
wenzelm@43498: \begin{isamarkuptext}%
wenzelm@43498: If the code containing a call to \isa{wfrec} resides in an
wenzelm@43498:   ML structure different from the one containing the function
wenzelm@43498:   definition attached to \isa{wfrec}, the name of the ML structure
wenzelm@43498:   (followed by a ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2E}{\isachardot}}{\isaliteral{22}{\isachardoublequote}}}'')  is inserted in place of ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6D6F64756C653E}{\isasymmodule}}{\isaliteral{22}{\isachardoublequote}}}'' in the above template.  The ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}''  means that
wenzelm@43498:   the code generator should ignore the first argument of \isa{wfrec}, i.e.\ the termination relation, which is usually not
wenzelm@43498:   executable.
wenzelm@43498: 
wenzelm@43498:   \medskip Another possibility of configuring the code generator is to
wenzelm@43498:   register theorems to be used for code generation. Theorems can be
wenzelm@43498:   registered via the \hyperlink{attribute.code}{\mbox{\isa{code}}} attribute. It takes an optional
wenzelm@43498:   name as an argument, which indicates the format of the
wenzelm@43498:   theorem. Currently supported formats are equations (this is the
wenzelm@43498:   default when no name is specified) and horn clauses (this is
wenzelm@43498:   indicated by the name \texttt{ind}). The left-hand sides of
wenzelm@43498:   equations may only contain constructors and distinct variables,
wenzelm@43498:   whereas horn clauses must have the same format as introduction rules
wenzelm@43498:   of inductive definitions.
wenzelm@43498: 
wenzelm@43498:   The following example specifies three equations from which to
wenzelm@43498:   generate code for \isa{{\isaliteral{22}{\isachardoublequote}}op\ {\isaliteral{3C}{\isacharless}}{\isaliteral{22}{\isachardoublequote}}} on natural numbers (see also
wenzelm@43498:   \verb|~~/src/HOL/Nat.thy|).%
wenzelm@43498: \end{isamarkuptext}%
wenzelm@43498: \isamarkuptrue%
wenzelm@43498: \isacommand{lemma}\isamarkupfalse%
wenzelm@43498: \ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}Suc\ m\ {\isaliteral{3C}{\isacharless}}\ Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}m\ {\isaliteral{3C}{\isacharless}}\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
wenzelm@43498: \ \ \isakeyword{and}\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}n{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3C}{\isacharless}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ False{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
wenzelm@43498: \ \ \isakeyword{and}\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}\ {\isaliteral{3C}{\isacharless}}\ Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ True{\isaliteral{22}{\isachardoublequoteclose}}%
wenzelm@43498: \isadelimproof
wenzelm@43498: \ %
wenzelm@43498: \endisadelimproof
wenzelm@43498: %
wenzelm@43498: \isatagproof
wenzelm@43498: \isacommand{by}\isamarkupfalse%
wenzelm@43498: \ simp{\isaliteral{5F}{\isacharunderscore}}all%
wenzelm@43498: \endisatagproof
wenzelm@43498: {\isafoldproof}%
wenzelm@43498: %
wenzelm@43498: \isadelimproof
wenzelm@43498: %
wenzelm@43498: \endisadelimproof
wenzelm@43498: %
wenzelm@43498: \isamarkupsubsubsection{Specific HOL code generators%
wenzelm@43498: }
wenzelm@43498: \isamarkuptrue%
wenzelm@43498: %
wenzelm@43498: \begin{isamarkuptext}%
wenzelm@43498: The basic code generator framework offered by Isabelle/Pure
wenzelm@43498:   has already been extended with additional code generators for
wenzelm@43498:   specific HOL constructs. These include datatypes, recursive
wenzelm@43498:   functions and inductive relations. The code generator for inductive
wenzelm@43498:   relations can handle expressions of the form \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{22}{\isachardoublequote}}}, where \isa{{\isaliteral{22}{\isachardoublequote}}r{\isaliteral{22}{\isachardoublequote}}} is an inductively defined relation. If at
wenzelm@43498:   least one of the \isa{{\isaliteral{22}{\isachardoublequote}}t\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} is a dummy pattern ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequote}}}'',
wenzelm@43498:   the above expression evaluates to a sequence of possible answers. If
wenzelm@43498:   all of the \isa{{\isaliteral{22}{\isachardoublequote}}t\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} are proper terms, the expression evaluates
wenzelm@43498:   to a boolean value.
wenzelm@43498: 
wenzelm@43498:   %FIXME
wenzelm@43498:   %\begin{ttbox}
wenzelm@43498:   %  theory Test = Lambda:
wenzelm@43498:   %
wenzelm@43498:   %  code_module Test
wenzelm@43498:   %  contains
wenzelm@43498:   %    test1 = "Abs (Var 0) \(\circ\) Var 0 -> Var 0"
wenzelm@43498:   %    test2 = "Abs (Abs (Var 0 \(\circ\) Var 0) \(\circ\) (Abs (Var 0) \(\circ\) Var 0)) -> _"
wenzelm@43498:   %\end{ttbox}
wenzelm@43498:   %In the above example, \texttt{Test.test1} evaluates to the boolean
wenzelm@43498:   %value \texttt{true}, whereas \texttt{Test.test2} is a sequence whose
wenzelm@43498:   %elements can be inspected using \texttt{Seq.pull} or similar functions.
wenzelm@43498:   %\begin{ttbox}
wenzelm@43498:   %ML \{* Seq.pull Test.test2 *\}  -- \{* This is the first answer *\}
wenzelm@43498:   %ML \{* Seq.pull (snd (the it)) *\}  -- \{* This is the second answer *\}
wenzelm@43498:   %\end{ttbox}
wenzelm@43498: 
wenzelm@43498:   \medskip The theory underlying the HOL code generator is described
wenzelm@43498:   more detailed in \cite{Berghofer-Nipkow:2002}. More examples that
wenzelm@43498:   illustrate the usage of the code generator can be found e.g.\ in
wenzelm@43498:   \verb|~~/src/HOL/MicroJava/J/JListExample.thy| and \verb|~~/src/HOL/MicroJava/JVM/JVMListExample.thy|.%
wenzelm@43498: \end{isamarkuptext}%
wenzelm@43498: \isamarkuptrue%
wenzelm@43498: %
wenzelm@27047: \isamarkupsection{Definition by specification \label{sec:hol-specification}%
wenzelm@27047: }
wenzelm@27047: \isamarkuptrue%
wenzelm@27047: %
wenzelm@27047: \begin{isamarkuptext}%
wenzelm@27047: \begin{matharray}{rcl}
wenzelm@40685:     \indexdef{HOL}{command}{specification}\hypertarget{command.HOL.specification}{\hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@40685:     \indexdef{HOL}{command}{ax\_specification}\hypertarget{command.HOL.ax-specification}{\hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
wenzelm@27047:   \end{matharray}
wenzelm@27047: 
wenzelm@43467:   \begin{railoutput}
wenzelm@43467: \rail@begin{6}{\isa{}}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@term{\hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}}[]
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@nont{\isa{decl}}[]
wenzelm@43467: \rail@nextplus{1}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@cr{3}
wenzelm@43467: \rail@plus
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{4}
wenzelm@43467: \rail@nont{\hyperlink{syntax.thmdecl}{\mbox{\isa{thmdecl}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[]
wenzelm@43467: \rail@nextplus{5}
wenzelm@43467: \rail@endplus
wenzelm@43467: \rail@end
wenzelm@43467: \rail@begin{2}{\isa{decl}}
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[]
wenzelm@43467: \rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[]
wenzelm@43467: \rail@term{\isa{\isakeyword{overloaded}}}[]
wenzelm@43467: \rail@bar
wenzelm@43467: \rail@nextbar{1}
wenzelm@43467: \rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[]
wenzelm@43467: \rail@endbar
wenzelm@43467: \rail@end
wenzelm@43467: \end{railoutput}
wenzelm@43467: 
wenzelm@27047: 
wenzelm@28788:   \begin{description}
wenzelm@27047: 
wenzelm@40685:   \item \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}decls\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} sets up a
wenzelm@27047:   goal stating the existence of terms with the properties specified to
wenzelm@27047:   hold for the constants given in \isa{decls}.  After finishing the
wenzelm@27047:   proof, the theory will be augmented with definitions for the given
wenzelm@27047:   constants, as well as with theorems stating the properties for these
wenzelm@27047:   constants.
wenzelm@27047: 
wenzelm@40685:   \item \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}decls\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} sets up
wenzelm@28788:   a goal stating the existence of terms with the properties specified
wenzelm@28788:   to hold for the constants given in \isa{decls}.  After finishing
wenzelm@28788:   the proof, the theory will be augmented with axioms expressing the
wenzelm@28788:   properties given in the first place.
wenzelm@27047: 
wenzelm@28788:   \item \isa{decl} declares a constant to be defined by the
wenzelm@27047:   specification given.  The definition for the constant \isa{c} is
wenzelm@40685:   bound to the name \isa{c{\isaliteral{5F}{\isacharunderscore}}def} unless a theorem name is given in
wenzelm@27047:   the declaration.  Overloaded constants should be declared as such.
wenzelm@27047: 
wenzelm@28788:   \end{description}
wenzelm@27047: 
wenzelm@40685:   Whether to use \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}} or \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}} is to some extent a matter of style.  \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}} introduces no new axioms, and so by
wenzelm@40685:   construction cannot introduce inconsistencies, whereas \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}} does introduce axioms, but only after the
wenzelm@27047:   user has explicitly proven it to be safe.  A practical issue must be
wenzelm@27047:   considered, though: After introducing two constants with the same
wenzelm@27047:   properties using \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}, one can prove
wenzelm@27047:   that the two constants are, in fact, equal.  If this might be a
wenzelm@40685:   problem, one should use \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}}.%
wenzelm@27047: \end{isamarkuptext}%
wenzelm@27047: \isamarkuptrue%
wenzelm@27047: %
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@26840: \end{isabellebody}%
wenzelm@26840: %%% Local Variables:
wenzelm@26840: %%% mode: latex
wenzelm@26840: %%% TeX-master: "root"
wenzelm@26840: %%% End:




