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: