author | wenzelm |
Thu, 05 May 2011 23:15:11 +0200 | |
changeset 42704 | 3f19e324ff59 |
parent 42662 | 2080fe35abea |
child 42705 | 528a2ba8fa74 |
permissions | -rw-r--r-- |
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\begin{isabellebody}% |
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\def\isabellecontext{Generic}% |
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\isadelimtheory |
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\endisadelimtheory |
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\isatagtheory |
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\isacommand{theory}\isamarkupfalse% |
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\ Generic\isanewline |
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\isakeyword{imports}\ Base\ Main\isanewline |
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\isakeyword{begin}% |
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\endisatagtheory |
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{\isafoldtheory}% |
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\isadelimtheory |
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\endisadelimtheory |
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\isamarkupchapter{Generic tools and packages \label{ch:gen-tools}% |
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} |
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\isamarkuptrue% |
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% |
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\isamarkupsection{Configuration options \label{sec:config}% |
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} |
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\isamarkuptrue% |
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% |
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\begin{isamarkuptext}% |
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Isabelle/Pure maintains a record of named configuration |
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options within the theory or proof context, with values of type |
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\verb|bool|, \verb|int|, \verb|real|, or \verb|string|. Tools may declare options in ML, and then refer to these |
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values (relative to the context). Thus global reference variables |
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are easily avoided. The user may change the value of a |
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configuration option by means of an associated attribute of the same |
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name. This form of context declaration works particularly well with |
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commands such as \hyperlink{command.declare}{\mbox{\isa{\isacommand{declare}}}} or \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}} like |
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this:% |
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\end{isamarkuptext}% |
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\isamarkuptrue% |
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\isacommand{declare}\isamarkupfalse% |
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\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5B}{\isacharbrackleft}}show{\isaliteral{5F}{\isacharunderscore}}main{\isaliteral{5F}{\isacharunderscore}}goal\ {\isaliteral{3D}{\isacharequal}}\ false{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5D}{\isacharbrackright}}\isanewline |
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\isanewline |
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\isacommand{notepad}\isamarkupfalse% |
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\isanewline |
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\isakeyword{begin}\isanewline |
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\isadelimproof |
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\ \ % |
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\endisadelimproof |
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% |
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\isatagproof |
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\isacommand{note}\isamarkupfalse% |
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\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5B}{\isacharbrackleft}}show{\isaliteral{5F}{\isacharunderscore}}main{\isaliteral{5F}{\isacharunderscore}}goal\ {\isaliteral{3D}{\isacharequal}}\ true{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5D}{\isacharbrackright}}% |
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\endisatagproof |
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{\isafoldproof}% |
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% |
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\isadelimproof |
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\isanewline |
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% |
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\endisadelimproof |
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\isacommand{end}\isamarkupfalse% |
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% |
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\begin{isamarkuptext}% |
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For historical reasons, some tools cannot take the full proof |
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context into account and merely refer to the background theory. |
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This is accommodated by configuration options being declared as |
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``global'', which may not be changed within a local context. |
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\begin{matharray}{rcll} |
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\indexdef{}{command}{print\_configs}\hypertarget{command.print-configs}{\hyperlink{command.print-configs}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}configs}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
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\end{matharray} |
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\begin{railoutput} |
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\rail@begin{6}{} |
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\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
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\rail@bar |
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\rail@term{\isa{true}}[] |
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\rail@nextbar{2} |
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\rail@term{\isa{false}}[] |
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\rail@nextbar{3} |
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\rail@nont{\hyperlink{syntax.int}{\mbox{\isa{int}}}}[] |
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\rail@nextbar{4} |
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\rail@nont{\hyperlink{syntax.float}{\mbox{\isa{float}}}}[] |
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\rail@nextbar{5} |
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\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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\rail@endbar |
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\rail@endbar |
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\rail@end |
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\end{railoutput} |
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\begin{description} |
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\item \hyperlink{command.print-configs}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}configs}}}} prints the available configuration |
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options, with names, types, and current values. |
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\item \isa{{\isaliteral{22}{\isachardoublequote}}name\ {\isaliteral{3D}{\isacharequal}}\ value{\isaliteral{22}{\isachardoublequote}}} as an attribute expression modifies the |
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named option, with the syntax of the value depending on the option's |
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type. For \verb|bool| the default value is \isa{true}. Any |
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attempt to change a global option in a local context is ignored. |
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\end{description}% |
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\end{isamarkuptext}% |
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\isamarkuptrue% |
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% |
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\isamarkupsection{Basic proof tools% |
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} |
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\isamarkuptrue% |
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% |
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\isamarkupsubsection{Miscellaneous methods and attributes \label{sec:misc-meth-att}% |
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} |
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\isamarkuptrue% |
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% |
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\begin{isamarkuptext}% |
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\begin{matharray}{rcl} |
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\indexdef{}{method}{unfold}\hypertarget{method.unfold}{\hyperlink{method.unfold}{\mbox{\isa{unfold}}}} & : & \isa{method} \\ |
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\indexdef{}{method}{fold}\hypertarget{method.fold}{\hyperlink{method.fold}{\mbox{\isa{fold}}}} & : & \isa{method} \\ |
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\indexdef{}{method}{insert}\hypertarget{method.insert}{\hyperlink{method.insert}{\mbox{\isa{insert}}}} & : & \isa{method} \\[0.5ex] |
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\indexdef{}{method}{erule}\hypertarget{method.erule}{\hyperlink{method.erule}{\mbox{\isa{erule}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
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\indexdef{}{method}{drule}\hypertarget{method.drule}{\hyperlink{method.drule}{\mbox{\isa{drule}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
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\indexdef{}{method}{frule}\hypertarget{method.frule}{\hyperlink{method.frule}{\mbox{\isa{frule}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
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\indexdef{}{method}{succeed}\hypertarget{method.succeed}{\hyperlink{method.succeed}{\mbox{\isa{succeed}}}} & : & \isa{method} \\ |
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\indexdef{}{method}{fail}\hypertarget{method.fail}{\hyperlink{method.fail}{\mbox{\isa{fail}}}} & : & \isa{method} \\ |
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\end{matharray} |
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\begin{railoutput} |
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\rail@begin{3}{} |
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\rail@bar |
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\rail@term{\hyperlink{method.fold}{\mbox{\isa{fold}}}}[] |
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\rail@nextbar{1} |
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\rail@term{\hyperlink{method.unfold}{\mbox{\isa{unfold}}}}[] |
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\rail@nextbar{2} |
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\rail@term{\hyperlink{method.insert}{\mbox{\isa{insert}}}}[] |
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\rail@endbar |
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\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
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\rail@end |
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\rail@begin{3}{} |
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\rail@bar |
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\rail@term{\hyperlink{method.erule}{\mbox{\isa{erule}}}}[] |
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\rail@nextbar{1} |
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\rail@term{\hyperlink{method.drule}{\mbox{\isa{drule}}}}[] |
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\rail@nextbar{2} |
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\rail@term{\hyperlink{method.frule}{\mbox{\isa{frule}}}}[] |
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\rail@endbar |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
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\rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[] |
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\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
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\rail@endbar |
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\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
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\rail@end |
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\end{railoutput} |
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\begin{description} |
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\item \hyperlink{method.unfold}{\mbox{\isa{unfold}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} and \hyperlink{method.fold}{\mbox{\isa{fold}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} expand (or fold back) the given definitions throughout |
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all goals; any chained facts provided are inserted into the goal and |
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subject to rewriting as well. |
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\item \hyperlink{method.insert}{\mbox{\isa{insert}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} inserts theorems as facts |
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into all goals of the proof state. Note that current facts |
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indicated for forward chaining are ignored. |
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\item \hyperlink{method.erule}{\mbox{\isa{erule}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}, \hyperlink{method.drule}{\mbox{\isa{drule}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}, and \hyperlink{method.frule}{\mbox{\isa{frule}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} are similar to the basic \hyperlink{method.rule}{\mbox{\isa{rule}}} |
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method (see \secref{sec:pure-meth-att}), but apply rules by |
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elim-resolution, destruct-resolution, and forward-resolution, |
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respectively \cite{isabelle-implementation}. The optional natural |
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number argument (default 0) specifies additional assumption steps to |
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be performed here. |
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Note that these methods are improper ones, mainly serving for |
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experimentation and tactic script emulation. Different modes of |
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basic rule application are usually expressed in Isar at the proof |
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language level, rather than via implicit proof state manipulations. |
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For example, a proper single-step elimination would be done using |
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the plain \hyperlink{method.rule}{\mbox{\isa{rule}}} method, with forward chaining of current |
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facts. |
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\item \hyperlink{method.succeed}{\mbox{\isa{succeed}}} yields a single (unchanged) result; it is |
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the identity of the ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}}'' method combinator (cf.\ |
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\secref{sec:proof-meth}). |
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\item \hyperlink{method.fail}{\mbox{\isa{fail}}} yields an empty result sequence; it is the |
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identity of the ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}}'' method combinator (cf.\ |
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\secref{sec:proof-meth}). |
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\end{description} |
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\begin{matharray}{rcl} |
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\indexdef{}{attribute}{tagged}\hypertarget{attribute.tagged}{\hyperlink{attribute.tagged}{\mbox{\isa{tagged}}}} & : & \isa{attribute} \\ |
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\indexdef{}{attribute}{untagged}\hypertarget{attribute.untagged}{\hyperlink{attribute.untagged}{\mbox{\isa{untagged}}}} & : & \isa{attribute} \\[0.5ex] |
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\indexdef{}{attribute}{THEN}\hypertarget{attribute.THEN}{\hyperlink{attribute.THEN}{\mbox{\isa{THEN}}}} & : & \isa{attribute} \\ |
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\indexdef{}{attribute}{COMP}\hypertarget{attribute.COMP}{\hyperlink{attribute.COMP}{\mbox{\isa{COMP}}}} & : & \isa{attribute} \\[0.5ex] |
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\indexdef{}{attribute}{unfolded}\hypertarget{attribute.unfolded}{\hyperlink{attribute.unfolded}{\mbox{\isa{unfolded}}}} & : & \isa{attribute} \\ |
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\indexdef{}{attribute}{folded}\hypertarget{attribute.folded}{\hyperlink{attribute.folded}{\mbox{\isa{folded}}}} & : & \isa{attribute} \\[0.5ex] |
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\indexdef{}{attribute}{rotated}\hypertarget{attribute.rotated}{\hyperlink{attribute.rotated}{\mbox{\isa{rotated}}}} & : & \isa{attribute} \\ |
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\indexdef{Pure}{attribute}{elim\_format}\hypertarget{attribute.Pure.elim-format}{\hyperlink{attribute.Pure.elim-format}{\mbox{\isa{elim{\isaliteral{5F}{\isacharunderscore}}format}}}} & : & \isa{attribute} \\ |
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\indexdef{}{attribute}{standard}\hypertarget{attribute.standard}{\hyperlink{attribute.standard}{\mbox{\isa{standard}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{attribute} \\ |
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\indexdef{}{attribute}{no\_vars}\hypertarget{attribute.no-vars}{\hyperlink{attribute.no-vars}{\mbox{\isa{no{\isaliteral{5F}{\isacharunderscore}}vars}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{attribute} \\ |
|
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\end{matharray} |
207 |
||
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\begin{railoutput} |
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\rail@begin{1}{} |
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\rail@term{\hyperlink{attribute.tagged}{\mbox{\isa{tagged}}}}[] |
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\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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\rail@end |
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\rail@begin{1}{} |
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\rail@term{\hyperlink{attribute.untagged}{\mbox{\isa{untagged}}}}[] |
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\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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\rail@end |
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\rail@begin{2}{} |
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\rail@bar |
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\rail@term{\hyperlink{attribute.THEN}{\mbox{\isa{THEN}}}}[] |
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\rail@nextbar{1} |
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\rail@term{\hyperlink{attribute.COMP}{\mbox{\isa{COMP}}}}[] |
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\rail@endbar |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@term{\isa{{\isaliteral{5B}{\isacharbrackleft}}}}[] |
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\rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[] |
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\rail@term{\isa{{\isaliteral{5D}{\isacharbrackright}}}}[] |
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\rail@endbar |
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\rail@nont{\hyperlink{syntax.thmref}{\mbox{\isa{thmref}}}}[] |
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\rail@end |
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\rail@begin{2}{} |
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\rail@bar |
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\rail@term{\hyperlink{attribute.unfolded}{\mbox{\isa{unfolded}}}}[] |
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\rail@nextbar{1} |
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\rail@term{\hyperlink{attribute.folded}{\mbox{\isa{folded}}}}[] |
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\rail@endbar |
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\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
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\rail@end |
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\rail@begin{2}{} |
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\rail@term{\hyperlink{attribute.rotated}{\mbox{\isa{rotated}}}}[] |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@nont{\hyperlink{syntax.int}{\mbox{\isa{int}}}}[] |
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\rail@endbar |
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\rail@end |
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\end{railoutput} |
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|
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|
28788 | 250 |
\begin{description} |
26782 | 251 |
|
40406 | 252 |
\item \hyperlink{attribute.tagged}{\mbox{\isa{tagged}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name\ value{\isaliteral{22}{\isachardoublequote}}} and \hyperlink{attribute.untagged}{\mbox{\isa{untagged}}}~\isa{name} add and remove \emph{tags} of some theorem. |
26782 | 253 |
Tags may be any list of string pairs that serve as formal comment. |
28788 | 254 |
The first string is considered the tag name, the second its value. |
255 |
Note that \hyperlink{attribute.untagged}{\mbox{\isa{untagged}}} removes any tags of the same name. |
|
26782 | 256 |
|
28788 | 257 |
\item \hyperlink{attribute.THEN}{\mbox{\isa{THEN}}}~\isa{a} and \hyperlink{attribute.COMP}{\mbox{\isa{COMP}}}~\isa{a} |
26902 | 258 |
compose rules by resolution. \hyperlink{attribute.THEN}{\mbox{\isa{THEN}}} resolves with the |
26782 | 259 |
first premise of \isa{a} (an alternative position may be also |
26902 | 260 |
specified); the \hyperlink{attribute.COMP}{\mbox{\isa{COMP}}} version skips the automatic |
30463 | 261 |
lifting process that is normally intended (cf.\ \verb|op RS| and |
262 |
\verb|op COMP| in \cite{isabelle-implementation}). |
|
26782 | 263 |
|
40406 | 264 |
\item \hyperlink{attribute.unfolded}{\mbox{\isa{unfolded}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} and \hyperlink{attribute.folded}{\mbox{\isa{folded}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} expand and fold back again the given |
28788 | 265 |
definitions throughout a rule. |
26782 | 266 |
|
28788 | 267 |
\item \hyperlink{attribute.rotated}{\mbox{\isa{rotated}}}~\isa{n} rotate the premises of a |
26782 | 268 |
theorem by \isa{n} (default 1). |
269 |
||
40406 | 270 |
\item \hyperlink{attribute.Pure.elim-format}{\mbox{\isa{elim{\isaliteral{5F}{\isacharunderscore}}format}}} turns a destruction rule into |
271 |
elimination rule format, by resolving with the rule \isa{{\isaliteral{22}{\isachardoublequote}}PROP\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}PROP\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ PROP\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ PROP\ B{\isaliteral{22}{\isachardoublequote}}}. |
|
26782 | 272 |
|
273 |
Note that the Classical Reasoner (\secref{sec:classical}) provides |
|
274 |
its own version of this operation. |
|
275 |
||
28788 | 276 |
\item \hyperlink{attribute.standard}{\mbox{\isa{standard}}} puts a theorem into the standard form of |
277 |
object-rules at the outermost theory level. Note that this |
|
26782 | 278 |
operation violates the local proof context (including active |
279 |
locales). |
|
280 |
||
40406 | 281 |
\item \hyperlink{attribute.no-vars}{\mbox{\isa{no{\isaliteral{5F}{\isacharunderscore}}vars}}} replaces schematic variables by free |
26782 | 282 |
ones; this is mainly for tuning output of pretty printed theorems. |
283 |
||
28788 | 284 |
\end{description}% |
26782 | 285 |
\end{isamarkuptext}% |
286 |
\isamarkuptrue% |
|
287 |
% |
|
27047 | 288 |
\isamarkupsubsection{Low-level equational reasoning% |
289 |
} |
|
290 |
\isamarkuptrue% |
|
291 |
% |
|
292 |
\begin{isamarkuptext}% |
|
293 |
\begin{matharray}{rcl} |
|
28788 | 294 |
\indexdef{}{method}{subst}\hypertarget{method.subst}{\hyperlink{method.subst}{\mbox{\isa{subst}}}} & : & \isa{method} \\ |
295 |
\indexdef{}{method}{hypsubst}\hypertarget{method.hypsubst}{\hyperlink{method.hypsubst}{\mbox{\isa{hypsubst}}}} & : & \isa{method} \\ |
|
296 |
\indexdef{}{method}{split}\hypertarget{method.split}{\hyperlink{method.split}{\mbox{\isa{split}}}} & : & \isa{method} \\ |
|
27047 | 297 |
\end{matharray} |
298 |
||
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\begin{railoutput} |
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\rail@begin{6}{} |
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\rail@term{\hyperlink{method.subst}{\mbox{\isa{subst}}}}[] |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
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\rail@term{\isa{asm}}[] |
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\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
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\rail@endbar |
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\rail@cr{3} |
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\rail@bar |
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\rail@nextbar{4} |
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\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
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\rail@plus |
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\rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[] |
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\rail@nextplus{5} |
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\rail@endplus |
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\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
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\rail@endbar |
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\rail@nont{\hyperlink{syntax.thmref}{\mbox{\isa{thmref}}}}[] |
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\rail@end |
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\rail@begin{2}{} |
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\rail@term{\hyperlink{method.split}{\mbox{\isa{split}}}}[] |
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\rail@bar |
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\rail@nextbar{1} |
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\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
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\rail@term{\isa{asm}}[] |
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\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
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\rail@endbar |
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\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
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\rail@end |
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\end{railoutput} |
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|
27047 | 332 |
|
333 |
These methods provide low-level facilities for equational reasoning |
|
334 |
that are intended for specialized applications only. Normally, |
|
335 |
single step calculations would be performed in a structured text |
|
336 |
(see also \secref{sec:calculation}), while the Simplifier methods |
|
337 |
provide the canonical way for automated normalization (see |
|
338 |
\secref{sec:simplifier}). |
|
339 |
||
28788 | 340 |
\begin{description} |
27047 | 341 |
|
28788 | 342 |
\item \hyperlink{method.subst}{\mbox{\isa{subst}}}~\isa{eq} performs a single substitution step |
343 |
using rule \isa{eq}, which may be either a meta or object |
|
27047 | 344 |
equality. |
345 |
||
40406 | 346 |
\item \hyperlink{method.subst}{\mbox{\isa{subst}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}asm{\isaliteral{29}{\isacharparenright}}\ eq{\isaliteral{22}{\isachardoublequote}}} substitutes in an |
27047 | 347 |
assumption. |
348 |
||
40406 | 349 |
\item \hyperlink{method.subst}{\mbox{\isa{subst}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ j{\isaliteral{29}{\isacharparenright}}\ eq{\isaliteral{22}{\isachardoublequote}}} performs several |
27047 | 350 |
substitutions in the conclusion. The numbers \isa{i} to \isa{j} |
351 |
indicate the positions to substitute at. Positions are ordered from |
|
352 |
the top of the term tree moving down from left to right. For |
|
40406 | 353 |
example, in \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2B}{\isacharplus}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}c\ {\isaliteral{2B}{\isacharplus}}\ d{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} there are three positions |
354 |
where commutativity of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequote}}} is applicable: 1 refers to \isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{2B}{\isacharplus}}\ b{\isaliteral{22}{\isachardoublequote}}}, 2 to the whole term, and 3 to \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{2B}{\isacharplus}}\ d{\isaliteral{22}{\isachardoublequote}}}. |
|
27047 | 355 |
|
40406 | 356 |
If the positions in the list \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ j{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} are non-overlapping |
357 |
(e.g.\ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}\ {\isadigit{3}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} in \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2B}{\isacharplus}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}c\ {\isaliteral{2B}{\isacharplus}}\ d{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}) you may |
|
27047 | 358 |
assume all substitutions are performed simultaneously. Otherwise |
359 |
the behaviour of \isa{subst} is not specified. |
|
360 |
||
40406 | 361 |
\item \hyperlink{method.subst}{\mbox{\isa{subst}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}asm{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ j{\isaliteral{29}{\isacharparenright}}\ eq{\isaliteral{22}{\isachardoublequote}}} performs the |
27072 | 362 |
substitutions in the assumptions. The positions refer to the |
363 |
assumptions in order from left to right. For example, given in a |
|
40406 | 364 |
goal of the form \isa{{\isaliteral{22}{\isachardoublequote}}P\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2B}{\isacharplus}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ {\isaliteral{28}{\isacharparenleft}}c\ {\isaliteral{2B}{\isacharplus}}\ d{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}, position 1 of |
365 |
commutativity of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequote}}} is the subterm \isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{2B}{\isacharplus}}\ b{\isaliteral{22}{\isachardoublequote}}} and |
|
366 |
position 2 is the subterm \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{2B}{\isacharplus}}\ d{\isaliteral{22}{\isachardoublequote}}}. |
|
27047 | 367 |
|
28788 | 368 |
\item \hyperlink{method.hypsubst}{\mbox{\isa{hypsubst}}} performs substitution using some |
40406 | 369 |
assumption; this only works for equations of the form \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{22}{\isachardoublequote}}} where \isa{x} is a free or bound variable. |
27047 | 370 |
|
40406 | 371 |
\item \hyperlink{method.split}{\mbox{\isa{split}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} performs single-step case |
28788 | 372 |
splitting using the given rules. By default, splitting is performed |
40406 | 373 |
in the conclusion of a goal; the \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}asm{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option indicates to |
28788 | 374 |
operate on assumptions instead. |
27047 | 375 |
|
376 |
Note that the \hyperlink{method.simp}{\mbox{\isa{simp}}} method already involves repeated |
|
377 |
application of split rules as declared in the current context. |
|
378 |
||
28788 | 379 |
\end{description}% |
27047 | 380 |
\end{isamarkuptext}% |
381 |
\isamarkuptrue% |
|
382 |
% |
|
26782 | 383 |
\isamarkupsubsection{Further tactic emulations \label{sec:tactics}% |
384 |
} |
|
385 |
\isamarkuptrue% |
|
386 |
% |
|
387 |
\begin{isamarkuptext}% |
|
388 |
The following improper proof methods emulate traditional tactics. |
|
389 |
These admit direct access to the goal state, which is normally |
|
390 |
considered harmful! In particular, this may involve both numbered |
|
391 |
goal addressing (default 1), and dynamic instantiation within the |
|
392 |
scope of some subgoal. |
|
393 |
||
394 |
\begin{warn} |
|
395 |
Dynamic instantiations refer to universally quantified parameters |
|
396 |
of a subgoal (the dynamic context) rather than fixed variables and |
|
397 |
term abbreviations of a (static) Isar context. |
|
398 |
\end{warn} |
|
399 |
||
400 |
Tactic emulation methods, unlike their ML counterparts, admit |
|
401 |
simultaneous instantiation from both dynamic and static contexts. |
|
402 |
If names occur in both contexts goal parameters hide locally fixed |
|
403 |
variables. Likewise, schematic variables refer to term |
|
404 |
abbreviations, if present in the static context. Otherwise the |
|
405 |
schematic variable is interpreted as a schematic variable and left |
|
406 |
to be solved by unification with certain parts of the subgoal. |
|
407 |
||
408 |
Note that the tactic emulation proof methods in Isabelle/Isar are |
|
40406 | 409 |
consistently named \isa{foo{\isaliteral{5F}{\isacharunderscore}}tac}. Note also that variable names |
26782 | 410 |
occurring on left hand sides of instantiations must be preceded by a |
411 |
question mark if they coincide with a keyword or contain dots. This |
|
26902 | 412 |
is consistent with the attribute \hyperlink{attribute.where}{\mbox{\isa{where}}} (see |
26782 | 413 |
\secref{sec:pure-meth-att}). |
414 |
||
415 |
\begin{matharray}{rcl} |
|
40406 | 416 |
\indexdef{}{method}{rule\_tac}\hypertarget{method.rule-tac}{\hyperlink{method.rule-tac}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
417 |
\indexdef{}{method}{erule\_tac}\hypertarget{method.erule-tac}{\hyperlink{method.erule-tac}{\mbox{\isa{erule{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
|
418 |
\indexdef{}{method}{drule\_tac}\hypertarget{method.drule-tac}{\hyperlink{method.drule-tac}{\mbox{\isa{drule{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
|
419 |
\indexdef{}{method}{frule\_tac}\hypertarget{method.frule-tac}{\hyperlink{method.frule-tac}{\mbox{\isa{frule{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
|
420 |
\indexdef{}{method}{cut\_tac}\hypertarget{method.cut-tac}{\hyperlink{method.cut-tac}{\mbox{\isa{cut{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
|
421 |
\indexdef{}{method}{thin\_tac}\hypertarget{method.thin-tac}{\hyperlink{method.thin-tac}{\mbox{\isa{thin{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
|
422 |
\indexdef{}{method}{subgoal\_tac}\hypertarget{method.subgoal-tac}{\hyperlink{method.subgoal-tac}{\mbox{\isa{subgoal{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
|
423 |
\indexdef{}{method}{rename\_tac}\hypertarget{method.rename-tac}{\hyperlink{method.rename-tac}{\mbox{\isa{rename{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
|
424 |
\indexdef{}{method}{rotate\_tac}\hypertarget{method.rotate-tac}{\hyperlink{method.rotate-tac}{\mbox{\isa{rotate{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
|
425 |
\indexdef{}{method}{tactic}\hypertarget{method.tactic}{\hyperlink{method.tactic}{\mbox{\isa{tactic}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
|
426 |
\indexdef{}{method}{raw\_tactic}\hypertarget{method.raw-tactic}{\hyperlink{method.raw-tactic}{\mbox{\isa{raw{\isaliteral{5F}{\isacharunderscore}}tactic}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\ |
|
26782 | 427 |
\end{matharray} |
428 |
||
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\begin{railoutput} |
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\rail@begin{9}{} |
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431 |
\rail@bar |
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\rail@term{\hyperlink{method.rule-tac}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}tac}}}}[] |
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\rail@nextbar{1} |
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\rail@term{\hyperlink{method.erule-tac}{\mbox{\isa{erule{\isaliteral{5F}{\isacharunderscore}}tac}}}}[] |
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435 |
\rail@nextbar{2} |
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436 |
\rail@term{\hyperlink{method.drule-tac}{\mbox{\isa{drule{\isaliteral{5F}{\isacharunderscore}}tac}}}}[] |
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\rail@nextbar{3} |
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438 |
\rail@term{\hyperlink{method.frule-tac}{\mbox{\isa{frule{\isaliteral{5F}{\isacharunderscore}}tac}}}}[] |
6c621a9d612a
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439 |
\rail@nextbar{4} |
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440 |
\rail@term{\hyperlink{method.cut-tac}{\mbox{\isa{cut{\isaliteral{5F}{\isacharunderscore}}tac}}}}[] |
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441 |
\rail@nextbar{5} |
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442 |
\rail@term{\hyperlink{method.thin-tac}{\mbox{\isa{thin{\isaliteral{5F}{\isacharunderscore}}tac}}}}[] |
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443 |
\rail@endbar |
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modernized rail diagrams using @{rail} antiquotation;
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444 |
\rail@bar |
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modernized rail diagrams using @{rail} antiquotation;
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445 |
\rail@nextbar{1} |
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|
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\rail@nont{\hyperlink{syntax.goalspec}{\mbox{\isa{goalspec}}}}[] |
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\rail@endbar |
42704 | 448 |
\rail@cr{7} |
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\rail@bar |
42617 | 450 |
\rail@nont{\isa{dynamic{\isaliteral{5F}{\isacharunderscore}}insts}}[] |
451 |
\rail@term{\isa{\isakeyword{in}}}[] |
|
42596
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|
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\rail@nont{\hyperlink{syntax.thmref}{\mbox{\isa{thmref}}}}[] |
42704 | 453 |
\rail@nextbar{8} |
42596
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|
454 |
\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
6c621a9d612a
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|
455 |
\rail@endbar |
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modernized rail diagrams using @{rail} antiquotation;
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|
456 |
\rail@end |
42662 | 457 |
\rail@begin{2}{} |
42596
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modernized rail diagrams using @{rail} antiquotation;
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|
458 |
\rail@term{\hyperlink{method.subgoal-tac}{\mbox{\isa{subgoal{\isaliteral{5F}{\isacharunderscore}}tac}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
459 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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diff
changeset
|
460 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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diff
changeset
|
461 |
\rail@nont{\hyperlink{syntax.goalspec}{\mbox{\isa{goalspec}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
462 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
463 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
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diff
changeset
|
464 |
\rail@nont{\hyperlink{syntax.prop}{\mbox{\isa{prop}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
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diff
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|
465 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
466 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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diff
changeset
|
467 |
\rail@end |
42662 | 468 |
\rail@begin{2}{} |
42596
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modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
469 |
\rail@term{\hyperlink{method.rename-tac}{\mbox{\isa{rename{\isaliteral{5F}{\isacharunderscore}}tac}}}}[] |
6c621a9d612a
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parents:
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diff
changeset
|
470 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
471 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
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diff
changeset
|
472 |
\rail@nont{\hyperlink{syntax.goalspec}{\mbox{\isa{goalspec}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
473 |
\rail@endbar |
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modernized rail diagrams using @{rail} antiquotation;
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diff
changeset
|
474 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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changeset
|
475 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
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|
476 |
\rail@nextplus{1} |
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diff
changeset
|
477 |
\rail@endplus |
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changeset
|
478 |
\rail@end |
42662 | 479 |
\rail@begin{2}{} |
42596
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parents:
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diff
changeset
|
480 |
\rail@term{\hyperlink{method.rotate-tac}{\mbox{\isa{rotate{\isaliteral{5F}{\isacharunderscore}}tac}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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diff
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|
481 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
482 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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diff
changeset
|
483 |
\rail@nont{\hyperlink{syntax.goalspec}{\mbox{\isa{goalspec}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
484 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
485 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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parents:
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diff
changeset
|
486 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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diff
changeset
|
487 |
\rail@nont{\hyperlink{syntax.int}{\mbox{\isa{int}}}}[] |
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|
488 |
\rail@endbar |
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modernized rail diagrams using @{rail} antiquotation;
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changeset
|
489 |
\rail@end |
42662 | 490 |
\rail@begin{2}{} |
42596
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modernized rail diagrams using @{rail} antiquotation;
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changeset
|
491 |
\rail@bar |
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modernized rail diagrams using @{rail} antiquotation;
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|
492 |
\rail@term{\hyperlink{method.tactic}{\mbox{\isa{tactic}}}}[] |
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\rail@nextbar{1} |
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|
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\rail@term{\hyperlink{method.raw-tactic}{\mbox{\isa{raw{\isaliteral{5F}{\isacharunderscore}}tactic}}}}[] |
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|
495 |
\rail@endbar |
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\rail@nont{\hyperlink{syntax.text}{\mbox{\isa{text}}}}[] |
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\rail@end |
42617 | 498 |
\rail@begin{2}{\isa{dynamic{\isaliteral{5F}{\isacharunderscore}}insts}} |
42596
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|
499 |
\rail@plus |
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\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
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\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
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\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
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\rail@nextplus{1} |
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\rail@cterm{\isa{\isakeyword{and}}}[] |
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\rail@endplus |
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|
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\rail@end |
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507 |
\end{railoutput} |
42617 | 508 |
|
26782 | 509 |
|
28788 | 510 |
\begin{description} |
26782 | 511 |
|
40406 | 512 |
\item \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}tac}}} etc. do resolution of rules with explicit |
30397 | 513 |
instantiation. This works the same way as the ML tactics \verb|res_inst_tac| etc. (see \cite{isabelle-implementation}) |
26782 | 514 |
|
515 |
Multiple rules may be only given if there is no instantiation; then |
|
40406 | 516 |
\hyperlink{method.rule-tac}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}tac}}} is the same as \verb|resolve_tac| in ML (see |
30397 | 517 |
\cite{isabelle-implementation}). |
26782 | 518 |
|
40406 | 519 |
\item \hyperlink{method.cut-tac}{\mbox{\isa{cut{\isaliteral{5F}{\isacharunderscore}}tac}}} inserts facts into the proof state as |
27210 | 520 |
assumption of a subgoal, see also \verb|Tactic.cut_facts_tac| in |
30397 | 521 |
\cite{isabelle-implementation}. Note that the scope of schematic |
26782 | 522 |
variables is spread over the main goal statement. Instantiations |
28788 | 523 |
may be given as well, see also ML tactic \verb|cut_inst_tac| in |
30397 | 524 |
\cite{isabelle-implementation}. |
26782 | 525 |
|
40406 | 526 |
\item \hyperlink{method.thin-tac}{\mbox{\isa{thin{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} deletes the specified assumption |
527 |
from a subgoal; note that \isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} may contain schematic variables. |
|
30397 | 528 |
See also \verb|thin_tac| in \cite{isabelle-implementation}. |
28788 | 529 |
|
40406 | 530 |
\item \hyperlink{method.subgoal-tac}{\mbox{\isa{subgoal{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} adds \isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} as an |
30397 | 531 |
assumption to a subgoal. See also \verb|subgoal_tac| and \verb|subgoals_tac| in \cite{isabelle-implementation}. |
26782 | 532 |
|
40406 | 533 |
\item \hyperlink{method.rename-tac}{\mbox{\isa{rename{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} renames parameters of a |
534 |
goal according to the list \isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}, which refers to the |
|
28788 | 535 |
\emph{suffix} of variables. |
26782 | 536 |
|
40406 | 537 |
\item \hyperlink{method.rotate-tac}{\mbox{\isa{rotate{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{n} rotates the assumptions of a |
26782 | 538 |
goal by \isa{n} positions: from right to left if \isa{n} is |
539 |
positive, and from left to right if \isa{n} is negative; the |
|
540 |
default value is 1. See also \verb|rotate_tac| in |
|
30397 | 541 |
\cite{isabelle-implementation}. |
26782 | 542 |
|
40406 | 543 |
\item \hyperlink{method.tactic}{\mbox{\isa{tactic}}}~\isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}} produces a proof method from |
26782 | 544 |
any ML text of type \verb|tactic|. Apart from the usual ML |
27224 | 545 |
environment and the current proof context, the ML code may refer to |
546 |
the locally bound values \verb|facts|, which indicates any |
|
547 |
current facts used for forward-chaining. |
|
26782 | 548 |
|
40406 | 549 |
\item \hyperlink{method.raw-tactic}{\mbox{\isa{raw{\isaliteral{5F}{\isacharunderscore}}tactic}}} is similar to \hyperlink{method.tactic}{\mbox{\isa{tactic}}}, but |
27224 | 550 |
presents the goal state in its raw internal form, where simultaneous |
551 |
subgoals appear as conjunction of the logical framework instead of |
|
552 |
the usual split into several subgoals. While feature this is useful |
|
553 |
for debugging of complex method definitions, it should not never |
|
554 |
appear in production theories. |
|
26782 | 555 |
|
28788 | 556 |
\end{description}% |
26782 | 557 |
\end{isamarkuptext}% |
558 |
\isamarkuptrue% |
|
559 |
% |
|
27042 | 560 |
\isamarkupsection{The Simplifier \label{sec:simplifier}% |
26782 | 561 |
} |
562 |
\isamarkuptrue% |
|
563 |
% |
|
27042 | 564 |
\isamarkupsubsection{Simplification methods% |
26782 | 565 |
} |
566 |
\isamarkuptrue% |
|
567 |
% |
|
568 |
\begin{isamarkuptext}% |
|
569 |
\begin{matharray}{rcl} |
|
28788 | 570 |
\indexdef{}{method}{simp}\hypertarget{method.simp}{\hyperlink{method.simp}{\mbox{\isa{simp}}}} & : & \isa{method} \\ |
40406 | 571 |
\indexdef{}{method}{simp\_all}\hypertarget{method.simp-all}{\hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}}} & : & \isa{method} \\ |
26782 | 572 |
\end{matharray} |
573 |
||
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574 |
\begin{railoutput} |
42662 | 575 |
\rail@begin{2}{} |
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\rail@bar |
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\rail@term{\hyperlink{method.simp}{\mbox{\isa{simp}}}}[] |
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\rail@nextbar{1} |
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\rail@term{\hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}}}[] |
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\rail@endbar |
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581 |
\rail@bar |
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582 |
\rail@nextbar{1} |
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\rail@nont{\isa{opt}}[] |
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\rail@endbar |
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\rail@plus |
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\rail@nextplus{1} |
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\rail@cnont{\hyperlink{syntax.simpmod}{\mbox{\isa{simpmod}}}}[] |
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\rail@endplus |
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589 |
\rail@end |
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\rail@begin{4}{\isa{opt}} |
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\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
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\rail@bar |
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\rail@term{\isa{no{\isaliteral{5F}{\isacharunderscore}}asm}}[] |
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\rail@nextbar{1} |
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\rail@term{\isa{no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{5F}{\isacharunderscore}}simp}}[] |
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\rail@nextbar{2} |
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\rail@term{\isa{no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{5F}{\isacharunderscore}}use}}[] |
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\rail@nextbar{3} |
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\rail@term{\isa{asm{\isaliteral{5F}{\isacharunderscore}}lr}}[] |
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\rail@endbar |
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\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
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\rail@end |
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\rail@begin{9}{\indexdef{}{syntax}{simpmod}\hypertarget{syntax.simpmod}{\hyperlink{syntax.simpmod}{\mbox{\isa{simpmod}}}}} |
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\rail@bar |
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\rail@term{\isa{add}}[] |
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\rail@nextbar{1} |
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\rail@term{\isa{del}}[] |
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\rail@nextbar{2} |
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\rail@term{\isa{only}}[] |
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\rail@nextbar{3} |
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\rail@term{\isa{cong}}[] |
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\rail@bar |
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\rail@nextbar{4} |
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\rail@term{\isa{add}}[] |
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\rail@nextbar{5} |
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\rail@term{\isa{del}}[] |
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\rail@endbar |
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\rail@nextbar{6} |
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\rail@term{\isa{split}}[] |
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\rail@bar |
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\rail@nextbar{7} |
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\rail@term{\isa{add}}[] |
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\rail@nextbar{8} |
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\rail@term{\isa{del}}[] |
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\rail@endbar |
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\rail@endbar |
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\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[] |
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\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
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\rail@end |
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\end{railoutput} |
26782 | 631 |
|
632 |
||
28788 | 633 |
\begin{description} |
26782 | 634 |
|
28788 | 635 |
\item \hyperlink{method.simp}{\mbox{\isa{simp}}} invokes the Simplifier, after declaring |
26782 | 636 |
additional rules according to the arguments given. Note that the |
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\isa{only} modifier first removes all other rewrite rules, |
26782 | 638 |
congruences, and looper tactics (including splits), and then behaves |
42596
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like \isa{add}. |
26782 | 640 |
|
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641 |
\medskip The \isa{cong} modifiers add or delete Simplifier |
26782 | 642 |
congruence rules (see also \cite{isabelle-ref}), the default is to |
643 |
add. |
|
644 |
||
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\medskip The \isa{split} modifiers add or delete rules for the |
26782 | 646 |
Splitter (see also \cite{isabelle-ref}), the default is to add. |
647 |
This works only if the Simplifier method has been properly setup to |
|
648 |
include the Splitter (all major object logics such HOL, HOLCF, FOL, |
|
649 |
ZF do this already). |
|
650 |
||
40406 | 651 |
\item \hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}} is similar to \hyperlink{method.simp}{\mbox{\isa{simp}}}, but acts on |
26782 | 652 |
all goals (backwards from the last to the first one). |
653 |
||
28788 | 654 |
\end{description} |
26782 | 655 |
|
656 |
By default the Simplifier methods take local assumptions fully into |
|
657 |
account, using equational assumptions in the subsequent |
|
658 |
normalization process, or simplifying assumptions themselves (cf.\ |
|
30397 | 659 |
\verb|asm_full_simp_tac| in \cite{isabelle-ref}). In structured |
660 |
proofs this is usually quite well behaved in practice: just the |
|
661 |
local premises of the actual goal are involved, additional facts may |
|
662 |
be inserted via explicit forward-chaining (via \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}, |
|
35613 | 663 |
\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}, \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}} etc.). |
26782 | 664 |
|
665 |
Additional Simplifier options may be specified to tune the behavior |
|
666 |
further (mostly for unstructured scripts with many accidental local |
|
40406 | 667 |
facts): ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' means assumptions are ignored |
668 |
completely (cf.\ \verb|simp_tac|), ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' means |
|
26782 | 669 |
assumptions are used in the simplification of the conclusion but are |
40406 | 670 |
not themselves simplified (cf.\ \verb|asm_simp_tac|), and ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{5F}{\isacharunderscore}}use{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' means assumptions are simplified but are not used |
26782 | 671 |
in the simplification of each other or the conclusion (cf.\ \verb|full_simp_tac|). For compatibility reasons, there is also an option |
40406 | 672 |
``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}asm{\isaliteral{5F}{\isacharunderscore}}lr{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'', which means that an assumption is only used |
26782 | 673 |
for simplifying assumptions which are to the right of it (cf.\ \verb|asm_lr_simp_tac|). |
674 |
||
40406 | 675 |
The configuration option \isa{{\isaliteral{22}{\isachardoublequote}}depth{\isaliteral{5F}{\isacharunderscore}}limit{\isaliteral{22}{\isachardoublequote}}} limits the number of |
26782 | 676 |
recursive invocations of the simplifier during conditional |
677 |
rewriting. |
|
678 |
||
679 |
\medskip The Splitter package is usually configured to work as part |
|
40406 | 680 |
of the Simplifier. The effect of repeatedly applying \verb|split_tac| can be simulated by ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}simp\ only{\isaliteral{3A}{\isacharcolon}}\ split{\isaliteral{3A}{\isacharcolon}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}''. There is also a separate \isa{split} |
26782 | 681 |
method available for single-step case splitting.% |
682 |
\end{isamarkuptext}% |
|
683 |
\isamarkuptrue% |
|
684 |
% |
|
27042 | 685 |
\isamarkupsubsection{Declaring rules% |
26782 | 686 |
} |
687 |
\isamarkuptrue% |
|
688 |
% |
|
689 |
\begin{isamarkuptext}% |
|
690 |
\begin{matharray}{rcl} |
|
40406 | 691 |
\indexdef{}{command}{print\_simpset}\hypertarget{command.print-simpset}{\hyperlink{command.print-simpset}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}simpset}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
28788 | 692 |
\indexdef{}{attribute}{simp}\hypertarget{attribute.simp}{\hyperlink{attribute.simp}{\mbox{\isa{simp}}}} & : & \isa{attribute} \\ |
693 |
\indexdef{}{attribute}{cong}\hypertarget{attribute.cong}{\hyperlink{attribute.cong}{\mbox{\isa{cong}}}} & : & \isa{attribute} \\ |
|
694 |
\indexdef{}{attribute}{split}\hypertarget{attribute.split}{\hyperlink{attribute.split}{\mbox{\isa{split}}}} & : & \isa{attribute} \\ |
|
26782 | 695 |
\end{matharray} |
696 |
||
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697 |
\begin{railoutput} |
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\rail@begin{3}{} |
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699 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
700 |
\rail@term{\hyperlink{attribute.simp}{\mbox{\isa{simp}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
701 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
702 |
\rail@term{\hyperlink{attribute.cong}{\mbox{\isa{cong}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
703 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
704 |
\rail@term{\hyperlink{attribute.split}{\mbox{\isa{split}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
705 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
706 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
707 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
708 |
\rail@term{\isa{add}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
709 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
710 |
\rail@term{\isa{del}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
711 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
712 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
713 |
\end{railoutput} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
714 |
|
26782 | 715 |
|
28788 | 716 |
\begin{description} |
26782 | 717 |
|
40406 | 718 |
\item \hyperlink{command.print-simpset}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}simpset}}}} prints the collection of rules |
26782 | 719 |
declared to the Simplifier, which is also known as ``simpset'' |
720 |
internally \cite{isabelle-ref}. |
|
721 |
||
28788 | 722 |
\item \hyperlink{attribute.simp}{\mbox{\isa{simp}}} declares simplification rules. |
26782 | 723 |
|
28788 | 724 |
\item \hyperlink{attribute.cong}{\mbox{\isa{cong}}} declares congruence rules. |
26782 | 725 |
|
28788 | 726 |
\item \hyperlink{attribute.split}{\mbox{\isa{split}}} declares case split rules. |
26782 | 727 |
|
28788 | 728 |
\end{description}% |
26782 | 729 |
\end{isamarkuptext}% |
730 |
\isamarkuptrue% |
|
731 |
% |
|
27042 | 732 |
\isamarkupsubsection{Simplification procedures% |
26782 | 733 |
} |
734 |
\isamarkuptrue% |
|
735 |
% |
|
736 |
\begin{isamarkuptext}% |
|
737 |
\begin{matharray}{rcl} |
|
40406 | 738 |
\indexdef{}{command}{simproc\_setup}\hypertarget{command.simproc-setup}{\hyperlink{command.simproc-setup}{\mbox{\isa{\isacommand{simproc{\isaliteral{5F}{\isacharunderscore}}setup}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\ |
28788 | 739 |
simproc & : & \isa{attribute} \\ |
26782 | 740 |
\end{matharray} |
741 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
742 |
\begin{railoutput} |
42662 | 743 |
\rail@begin{6}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
744 |
\rail@term{\hyperlink{command.simproc-setup}{\mbox{\isa{\isacommand{simproc{\isaliteral{5F}{\isacharunderscore}}setup}}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
745 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
746 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
747 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
748 |
\rail@nont{\hyperlink{syntax.term}{\mbox{\isa{term}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
749 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
750 |
\rail@cterm{\isa{{\isaliteral{7C}{\isacharbar}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
751 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
752 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
753 |
\rail@term{\isa{{\isaliteral{3D}{\isacharequal}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
754 |
\rail@nont{\hyperlink{syntax.text}{\mbox{\isa{text}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
755 |
\rail@cr{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
756 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
757 |
\rail@nextbar{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
758 |
\rail@term{\isa{\isakeyword{identifier}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
759 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
760 |
\rail@nont{\hyperlink{syntax.nameref}{\mbox{\isa{nameref}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
761 |
\rail@nextplus{5} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
762 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
763 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
764 |
\rail@end |
42662 | 765 |
\rail@begin{3}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
766 |
\rail@term{\hyperlink{attribute.simproc}{\mbox{\isa{simproc}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
767 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
768 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
769 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
770 |
\rail@term{\isa{add}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
771 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
772 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
773 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
774 |
\rail@term{\isa{del}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
775 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
776 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
777 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
778 |
\rail@nont{\hyperlink{syntax.name}{\mbox{\isa{name}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
779 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
780 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
781 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
782 |
\end{railoutput} |
26782 | 783 |
|
784 |
||
28788 | 785 |
\begin{description} |
26782 | 786 |
|
40406 | 787 |
\item \hyperlink{command.simproc-setup}{\mbox{\isa{\isacommand{simproc{\isaliteral{5F}{\isacharunderscore}}setup}}}} defines a named simplification |
26782 | 788 |
procedure that is invoked by the Simplifier whenever any of the |
789 |
given term patterns match the current redex. The implementation, |
|
30269
2fab27ea2a1f
updated generated file -- changed since @{ML} now ignores source flag;
wenzelm
parents:
30172
diff
changeset
|
790 |
which is provided as ML source text, needs to be of type \verb|morphism -> simpset -> cterm -> thm option|, where the \verb|cterm| represents the current redex \isa{r} and the result is |
40406 | 791 |
supposed to be some proven rewrite rule \isa{{\isaliteral{22}{\isachardoublequote}}r\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ r{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequote}}} (or a |
26782 | 792 |
generalized version), or \verb|NONE| to indicate failure. The |
793 |
\verb|simpset| argument holds the full context of the current |
|
794 |
Simplifier invocation, including the actual Isar proof context. The |
|
795 |
\verb|morphism| informs about the difference of the original |
|
796 |
compilation context wrt.\ the one of the actual application later |
|
26902 | 797 |
on. The optional \hyperlink{keyword.identifier}{\mbox{\isa{\isakeyword{identifier}}}} specifies theorems that |
26782 | 798 |
represent the logical content of the abstract theory of this |
799 |
simproc. |
|
800 |
||
801 |
Morphisms and identifiers are only relevant for simprocs that are |
|
802 |
defined within a local target context, e.g.\ in a locale. |
|
803 |
||
40406 | 804 |
\item \isa{{\isaliteral{22}{\isachardoublequote}}simproc\ add{\isaliteral{3A}{\isacharcolon}}\ name{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}simproc\ del{\isaliteral{3A}{\isacharcolon}}\ name{\isaliteral{22}{\isachardoublequote}}} |
26782 | 805 |
add or delete named simprocs to the current Simplifier context. The |
40406 | 806 |
default is to add a simproc. Note that \hyperlink{command.simproc-setup}{\mbox{\isa{\isacommand{simproc{\isaliteral{5F}{\isacharunderscore}}setup}}}} |
26782 | 807 |
already adds the new simproc to the subsequent context. |
808 |
||
28788 | 809 |
\end{description}% |
26782 | 810 |
\end{isamarkuptext}% |
811 |
\isamarkuptrue% |
|
812 |
% |
|
27042 | 813 |
\isamarkupsubsection{Forward simplification% |
26782 | 814 |
} |
815 |
\isamarkuptrue% |
|
816 |
% |
|
817 |
\begin{isamarkuptext}% |
|
818 |
\begin{matharray}{rcl} |
|
28788 | 819 |
\indexdef{}{attribute}{simplified}\hypertarget{attribute.simplified}{\hyperlink{attribute.simplified}{\mbox{\isa{simplified}}}} & : & \isa{attribute} \\ |
26782 | 820 |
\end{matharray} |
821 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
822 |
\begin{railoutput} |
42662 | 823 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
824 |
\rail@term{\hyperlink{attribute.simplified}{\mbox{\isa{simplified}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
825 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
826 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
827 |
\rail@nont{\isa{opt}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
828 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
829 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
830 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
831 |
\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
832 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
833 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
834 |
\rail@begin{3}{\isa{opt}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
835 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
836 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
837 |
\rail@term{\isa{no{\isaliteral{5F}{\isacharunderscore}}asm}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
838 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
839 |
\rail@term{\isa{no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{5F}{\isacharunderscore}}simp}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
840 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
841 |
\rail@term{\isa{no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{5F}{\isacharunderscore}}use}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
842 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
843 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
844 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
845 |
\end{railoutput} |
26782 | 846 |
|
847 |
||
28788 | 848 |
\begin{description} |
26782 | 849 |
|
40406 | 850 |
\item \hyperlink{attribute.simplified}{\mbox{\isa{simplified}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} causes a theorem to |
851 |
be simplified, either by exactly the specified rules \isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}, or the implicit Simplifier context if no arguments are given. |
|
28788 | 852 |
The result is fully simplified by default, including assumptions and |
40406 | 853 |
conclusion; the options \isa{no{\isaliteral{5F}{\isacharunderscore}}asm} etc.\ tune the Simplifier in |
28788 | 854 |
the same way as the for the \isa{simp} method. |
26782 | 855 |
|
856 |
Note that forward simplification restricts the simplifier to its |
|
857 |
most basic operation of term rewriting; solver and looper tactics |
|
858 |
\cite{isabelle-ref} are \emph{not} involved here. The \isa{simplified} attribute should be only rarely required under normal |
|
859 |
circumstances. |
|
860 |
||
28788 | 861 |
\end{description}% |
26782 | 862 |
\end{isamarkuptext}% |
863 |
\isamarkuptrue% |
|
864 |
% |
|
27042 | 865 |
\isamarkupsection{The Classical Reasoner \label{sec:classical}% |
26782 | 866 |
} |
867 |
\isamarkuptrue% |
|
868 |
% |
|
27042 | 869 |
\isamarkupsubsection{Basic methods% |
26782 | 870 |
} |
871 |
\isamarkuptrue% |
|
872 |
% |
|
873 |
\begin{isamarkuptext}% |
|
874 |
\begin{matharray}{rcl} |
|
28788 | 875 |
\indexdef{}{method}{rule}\hypertarget{method.rule}{\hyperlink{method.rule}{\mbox{\isa{rule}}}} & : & \isa{method} \\ |
876 |
\indexdef{}{method}{contradiction}\hypertarget{method.contradiction}{\hyperlink{method.contradiction}{\mbox{\isa{contradiction}}}} & : & \isa{method} \\ |
|
877 |
\indexdef{}{method}{intro}\hypertarget{method.intro}{\hyperlink{method.intro}{\mbox{\isa{intro}}}} & : & \isa{method} \\ |
|
878 |
\indexdef{}{method}{elim}\hypertarget{method.elim}{\hyperlink{method.elim}{\mbox{\isa{elim}}}} & : & \isa{method} \\ |
|
26782 | 879 |
\end{matharray} |
880 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
881 |
\begin{railoutput} |
42662 | 882 |
\rail@begin{3}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
883 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
884 |
\rail@term{\hyperlink{method.rule}{\mbox{\isa{rule}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
885 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
886 |
\rail@term{\hyperlink{method.intro}{\mbox{\isa{intro}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
887 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
888 |
\rail@term{\hyperlink{method.elim}{\mbox{\isa{elim}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
889 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
890 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
891 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
892 |
\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
893 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
894 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
895 |
\end{railoutput} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
896 |
|
26782 | 897 |
|
28788 | 898 |
\begin{description} |
26782 | 899 |
|
28788 | 900 |
\item \hyperlink{method.rule}{\mbox{\isa{rule}}} as offered by the Classical Reasoner is a |
26782 | 901 |
refinement over the primitive one (see \secref{sec:pure-meth-att}). |
902 |
Both versions essentially work the same, but the classical version |
|
903 |
observes the classical rule context in addition to that of |
|
904 |
Isabelle/Pure. |
|
905 |
||
906 |
Common object logics (HOL, ZF, etc.) declare a rich collection of |
|
907 |
classical rules (even if these would qualify as intuitionistic |
|
908 |
ones), but only few declarations to the rule context of |
|
909 |
Isabelle/Pure (\secref{sec:pure-meth-att}). |
|
910 |
||
28788 | 911 |
\item \hyperlink{method.contradiction}{\mbox{\isa{contradiction}}} solves some goal by contradiction, |
40406 | 912 |
deriving any result from both \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A{\isaliteral{22}{\isachardoublequote}}} and \isa{A}. Chained |
26782 | 913 |
facts, which are guaranteed to participate, may appear in either |
914 |
order. |
|
915 |
||
28788 | 916 |
\item \hyperlink{method.intro}{\mbox{\isa{intro}}} and \hyperlink{method.elim}{\mbox{\isa{elim}}} repeatedly refine some goal |
917 |
by intro- or elim-resolution, after having inserted any chained |
|
26902 | 918 |
facts. Exactly the rules given as arguments are taken into account; |
919 |
this allows fine-tuned decomposition of a proof problem, in contrast |
|
920 |
to common automated tools. |
|
26782 | 921 |
|
28788 | 922 |
\end{description}% |
26782 | 923 |
\end{isamarkuptext}% |
924 |
\isamarkuptrue% |
|
925 |
% |
|
27042 | 926 |
\isamarkupsubsection{Automated methods% |
26782 | 927 |
} |
928 |
\isamarkuptrue% |
|
929 |
% |
|
930 |
\begin{isamarkuptext}% |
|
931 |
\begin{matharray}{rcl} |
|
28788 | 932 |
\indexdef{}{method}{blast}\hypertarget{method.blast}{\hyperlink{method.blast}{\mbox{\isa{blast}}}} & : & \isa{method} \\ |
933 |
\indexdef{}{method}{fast}\hypertarget{method.fast}{\hyperlink{method.fast}{\mbox{\isa{fast}}}} & : & \isa{method} \\ |
|
934 |
\indexdef{}{method}{slow}\hypertarget{method.slow}{\hyperlink{method.slow}{\mbox{\isa{slow}}}} & : & \isa{method} \\ |
|
935 |
\indexdef{}{method}{best}\hypertarget{method.best}{\hyperlink{method.best}{\mbox{\isa{best}}}} & : & \isa{method} \\ |
|
936 |
\indexdef{}{method}{safe}\hypertarget{method.safe}{\hyperlink{method.safe}{\mbox{\isa{safe}}}} & : & \isa{method} \\ |
|
937 |
\indexdef{}{method}{clarify}\hypertarget{method.clarify}{\hyperlink{method.clarify}{\mbox{\isa{clarify}}}} & : & \isa{method} \\ |
|
26782 | 938 |
\end{matharray} |
939 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
940 |
\begin{railoutput} |
42662 | 941 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
942 |
\rail@term{\hyperlink{method.blast}{\mbox{\isa{blast}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
943 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
944 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
945 |
\rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
946 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
947 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
948 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
949 |
\rail@cnont{\hyperlink{syntax.clamod}{\mbox{\isa{clamod}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
950 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
951 |
\rail@end |
42662 | 952 |
\rail@begin{5}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
953 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
954 |
\rail@term{\hyperlink{method.fast}{\mbox{\isa{fast}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
955 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
956 |
\rail@term{\hyperlink{method.slow}{\mbox{\isa{slow}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
957 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
958 |
\rail@term{\hyperlink{method.best}{\mbox{\isa{best}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
959 |
\rail@nextbar{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
960 |
\rail@term{\hyperlink{method.safe}{\mbox{\isa{safe}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
961 |
\rail@nextbar{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
962 |
\rail@term{\hyperlink{method.clarify}{\mbox{\isa{clarify}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
963 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
964 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
965 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
966 |
\rail@cnont{\hyperlink{syntax.clamod}{\mbox{\isa{clamod}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
967 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
968 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
969 |
\rail@begin{4}{\indexdef{}{syntax}{clamod}\hypertarget{syntax.clamod}{\hyperlink{syntax.clamod}{\mbox{\isa{clamod}}}}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
970 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
971 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
972 |
\rail@term{\isa{intro}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
973 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
974 |
\rail@term{\isa{elim}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
975 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
976 |
\rail@term{\isa{dest}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
977 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
978 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
979 |
\rail@term{\isa{{\isaliteral{21}{\isacharbang}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
980 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
981 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
982 |
\rail@term{\isa{{\isaliteral{3F}{\isacharquery}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
983 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
984 |
\rail@nextbar{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
985 |
\rail@term{\isa{del}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
986 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
987 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
988 |
\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
989 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
990 |
\end{railoutput} |
26782 | 991 |
|
992 |
||
28788 | 993 |
\begin{description} |
26782 | 994 |
|
28788 | 995 |
\item \hyperlink{method.blast}{\mbox{\isa{blast}}} refers to the classical tableau prover (see |
30397 | 996 |
\verb|blast_tac| in \cite{isabelle-ref}). The optional argument |
997 |
specifies a user-supplied search bound (default 20). |
|
26782 | 998 |
|
28788 | 999 |
\item \hyperlink{method.fast}{\mbox{\isa{fast}}}, \hyperlink{method.slow}{\mbox{\isa{slow}}}, \hyperlink{method.best}{\mbox{\isa{best}}}, \hyperlink{method.safe}{\mbox{\isa{safe}}}, and \hyperlink{method.clarify}{\mbox{\isa{clarify}}} refer to the generic classical |
30397 | 1000 |
reasoner. See \verb|fast_tac|, \verb|slow_tac|, \verb|best_tac|, \verb|safe_tac|, and \verb|clarify_tac| in \cite{isabelle-ref} for more |
1001 |
information. |
|
26782 | 1002 |
|
28788 | 1003 |
\end{description} |
26782 | 1004 |
|
1005 |
Any of the above methods support additional modifiers of the context |
|
1006 |
of classical rules. Their semantics is analogous to the attributes |
|
1007 |
given before. Facts provided by forward chaining are inserted into |
|
35613 | 1008 |
the goal before commencing proof search.% |
26782 | 1009 |
\end{isamarkuptext}% |
1010 |
\isamarkuptrue% |
|
1011 |
% |
|
27042 | 1012 |
\isamarkupsubsection{Combined automated methods \label{sec:clasimp}% |
26782 | 1013 |
} |
1014 |
\isamarkuptrue% |
|
1015 |
% |
|
1016 |
\begin{isamarkuptext}% |
|
1017 |
\begin{matharray}{rcl} |
|
28788 | 1018 |
\indexdef{}{method}{auto}\hypertarget{method.auto}{\hyperlink{method.auto}{\mbox{\isa{auto}}}} & : & \isa{method} \\ |
1019 |
\indexdef{}{method}{force}\hypertarget{method.force}{\hyperlink{method.force}{\mbox{\isa{force}}}} & : & \isa{method} \\ |
|
1020 |
\indexdef{}{method}{clarsimp}\hypertarget{method.clarsimp}{\hyperlink{method.clarsimp}{\mbox{\isa{clarsimp}}}} & : & \isa{method} \\ |
|
1021 |
\indexdef{}{method}{fastsimp}\hypertarget{method.fastsimp}{\hyperlink{method.fastsimp}{\mbox{\isa{fastsimp}}}} & : & \isa{method} \\ |
|
1022 |
\indexdef{}{method}{slowsimp}\hypertarget{method.slowsimp}{\hyperlink{method.slowsimp}{\mbox{\isa{slowsimp}}}} & : & \isa{method} \\ |
|
1023 |
\indexdef{}{method}{bestsimp}\hypertarget{method.bestsimp}{\hyperlink{method.bestsimp}{\mbox{\isa{bestsimp}}}} & : & \isa{method} \\ |
|
26782 | 1024 |
\end{matharray} |
1025 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1026 |
\begin{railoutput} |
42662 | 1027 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1028 |
\rail@term{\hyperlink{method.auto}{\mbox{\isa{auto}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1029 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1030 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1031 |
\rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1032 |
\rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1033 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1034 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1035 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1036 |
\rail@cnont{\hyperlink{syntax.clasimpmod}{\mbox{\isa{clasimpmod}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1037 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1038 |
\rail@end |
42662 | 1039 |
\rail@begin{5}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1040 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1041 |
\rail@term{\hyperlink{method.force}{\mbox{\isa{force}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1042 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1043 |
\rail@term{\hyperlink{method.clarsimp}{\mbox{\isa{clarsimp}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1044 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1045 |
\rail@term{\hyperlink{method.fastsimp}{\mbox{\isa{fastsimp}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1046 |
\rail@nextbar{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1047 |
\rail@term{\hyperlink{method.slowsimp}{\mbox{\isa{slowsimp}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1048 |
\rail@nextbar{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1049 |
\rail@term{\hyperlink{method.bestsimp}{\mbox{\isa{bestsimp}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1050 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1051 |
\rail@plus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1052 |
\rail@nextplus{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1053 |
\rail@cnont{\hyperlink{syntax.clasimpmod}{\mbox{\isa{clasimpmod}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1054 |
\rail@endplus |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1055 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1056 |
\rail@begin{14}{\indexdef{}{syntax}{clasimpmod}\hypertarget{syntax.clasimpmod}{\hyperlink{syntax.clasimpmod}{\mbox{\isa{clasimpmod}}}}} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1057 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1058 |
\rail@term{\isa{simp}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1059 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1060 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1061 |
\rail@term{\isa{add}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1062 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1063 |
\rail@term{\isa{del}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1064 |
\rail@nextbar{3} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1065 |
\rail@term{\isa{only}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1066 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1067 |
\rail@nextbar{4} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1068 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1069 |
\rail@term{\isa{cong}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1070 |
\rail@nextbar{5} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1071 |
\rail@term{\isa{split}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1072 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1073 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1074 |
\rail@nextbar{5} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1075 |
\rail@term{\isa{add}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1076 |
\rail@nextbar{6} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1077 |
\rail@term{\isa{del}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1078 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1079 |
\rail@nextbar{7} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1080 |
\rail@term{\isa{iff}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1081 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1082 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1083 |
\rail@nextbar{8} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1084 |
\rail@term{\isa{add}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1085 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1086 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1087 |
\rail@nextbar{8} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1088 |
\rail@term{\isa{{\isaliteral{3F}{\isacharquery}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1089 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1090 |
\rail@nextbar{9} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1091 |
\rail@term{\isa{del}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1092 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1093 |
\rail@nextbar{10} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1094 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1095 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1096 |
\rail@term{\isa{intro}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1097 |
\rail@nextbar{11} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1098 |
\rail@term{\isa{elim}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1099 |
\rail@nextbar{12} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1100 |
\rail@term{\isa{dest}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1101 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1102 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1103 |
\rail@term{\isa{{\isaliteral{21}{\isacharbang}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1104 |
\rail@nextbar{11} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1105 |
\rail@nextbar{12} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1106 |
\rail@term{\isa{{\isaliteral{3F}{\isacharquery}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1107 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1108 |
\rail@nextbar{13} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1109 |
\rail@term{\isa{del}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1110 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1111 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1112 |
\rail@term{\isa{{\isaliteral{3A}{\isacharcolon}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1113 |
\rail@nont{\hyperlink{syntax.thmrefs}{\mbox{\isa{thmrefs}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1114 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1115 |
\end{railoutput} |
26782 | 1116 |
|
1117 |
||
28788 | 1118 |
\begin{description} |
26782 | 1119 |
|
28788 | 1120 |
\item \hyperlink{method.auto}{\mbox{\isa{auto}}}, \hyperlink{method.force}{\mbox{\isa{force}}}, \hyperlink{method.clarsimp}{\mbox{\isa{clarsimp}}}, \hyperlink{method.fastsimp}{\mbox{\isa{fastsimp}}}, \hyperlink{method.slowsimp}{\mbox{\isa{slowsimp}}}, and \hyperlink{method.bestsimp}{\mbox{\isa{bestsimp}}} provide access |
1121 |
to Isabelle's combined simplification and classical reasoning |
|
26782 | 1122 |
tactics. These correspond to \verb|auto_tac|, \verb|force_tac|, \verb|clarsimp_tac|, and Classical Reasoner tactics with the Simplifier |
30397 | 1123 |
added as wrapper, see \cite{isabelle-ref} for more information. The |
1124 |
modifier arguments correspond to those given in |
|
26782 | 1125 |
\secref{sec:simplifier} and \secref{sec:classical}. Just note that |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1126 |
the ones related to the Simplifier are prefixed by \isa{simp} |
26782 | 1127 |
here. |
1128 |
||
1129 |
Facts provided by forward chaining are inserted into the goal before |
|
35613 | 1130 |
doing the search. |
26782 | 1131 |
|
28788 | 1132 |
\end{description}% |
26782 | 1133 |
\end{isamarkuptext}% |
1134 |
\isamarkuptrue% |
|
1135 |
% |
|
27042 | 1136 |
\isamarkupsubsection{Declaring rules% |
26782 | 1137 |
} |
1138 |
\isamarkuptrue% |
|
1139 |
% |
|
1140 |
\begin{isamarkuptext}% |
|
1141 |
\begin{matharray}{rcl} |
|
40406 | 1142 |
\indexdef{}{command}{print\_claset}\hypertarget{command.print-claset}{\hyperlink{command.print-claset}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}claset}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\ |
28788 | 1143 |
\indexdef{}{attribute}{intro}\hypertarget{attribute.intro}{\hyperlink{attribute.intro}{\mbox{\isa{intro}}}} & : & \isa{attribute} \\ |
1144 |
\indexdef{}{attribute}{elim}\hypertarget{attribute.elim}{\hyperlink{attribute.elim}{\mbox{\isa{elim}}}} & : & \isa{attribute} \\ |
|
1145 |
\indexdef{}{attribute}{dest}\hypertarget{attribute.dest}{\hyperlink{attribute.dest}{\mbox{\isa{dest}}}} & : & \isa{attribute} \\ |
|
1146 |
\indexdef{}{attribute}{rule}\hypertarget{attribute.rule}{\hyperlink{attribute.rule}{\mbox{\isa{rule}}}} & : & \isa{attribute} \\ |
|
1147 |
\indexdef{}{attribute}{iff}\hypertarget{attribute.iff}{\hyperlink{attribute.iff}{\mbox{\isa{iff}}}} & : & \isa{attribute} \\ |
|
26782 | 1148 |
\end{matharray} |
1149 |
||
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1150 |
\begin{railoutput} |
42662 | 1151 |
\rail@begin{3}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1152 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1153 |
\rail@term{\hyperlink{attribute.intro}{\mbox{\isa{intro}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1154 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1155 |
\rail@term{\hyperlink{attribute.elim}{\mbox{\isa{elim}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1156 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1157 |
\rail@term{\hyperlink{attribute.dest}{\mbox{\isa{dest}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1158 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1159 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1160 |
\rail@term{\isa{{\isaliteral{21}{\isacharbang}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1161 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1162 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1163 |
\rail@term{\isa{{\isaliteral{3F}{\isacharquery}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1164 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1165 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1166 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1167 |
\rail@nont{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1168 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1169 |
\rail@end |
42662 | 1170 |
\rail@begin{1}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1171 |
\rail@term{\hyperlink{attribute.rule}{\mbox{\isa{rule}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1172 |
\rail@term{\isa{del}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1173 |
\rail@end |
42662 | 1174 |
\rail@begin{3}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1175 |
\rail@term{\hyperlink{attribute.iff}{\mbox{\isa{iff}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1176 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1177 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1178 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1179 |
\rail@term{\isa{add}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1180 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1181 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1182 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1183 |
\rail@term{\isa{{\isaliteral{3F}{\isacharquery}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1184 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1185 |
\rail@nextbar{2} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1186 |
\rail@term{\isa{del}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1187 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1188 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1189 |
\end{railoutput} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1190 |
|
26782 | 1191 |
|
28788 | 1192 |
\begin{description} |
26782 | 1193 |
|
40406 | 1194 |
\item \hyperlink{command.print-claset}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}claset}}}} prints the collection of rules |
26782 | 1195 |
declared to the Classical Reasoner, which is also known as |
1196 |
``claset'' internally \cite{isabelle-ref}. |
|
1197 |
||
28788 | 1198 |
\item \hyperlink{attribute.intro}{\mbox{\isa{intro}}}, \hyperlink{attribute.elim}{\mbox{\isa{elim}}}, and \hyperlink{attribute.dest}{\mbox{\isa{dest}}} |
26782 | 1199 |
declare introduction, elimination, and destruction rules, |
1200 |
respectively. By default, rules are considered as \emph{unsafe} |
|
40406 | 1201 |
(i.e.\ not applied blindly without backtracking), while ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}}'' classifies as \emph{safe}. Rule declarations marked by |
1202 |
``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}'' coincide with those of Isabelle/Pure, cf.\ |
|
26782 | 1203 |
\secref{sec:pure-meth-att} (i.e.\ are only applied in single steps |
26902 | 1204 |
of the \hyperlink{method.rule}{\mbox{\isa{rule}}} method). The optional natural number |
26782 | 1205 |
specifies an explicit weight argument, which is ignored by automated |
1206 |
tools, but determines the search order of single rule steps. |
|
1207 |
||
28788 | 1208 |
\item \hyperlink{attribute.rule}{\mbox{\isa{rule}}}~\isa{del} deletes introduction, |
26782 | 1209 |
elimination, or destruction rules from the context. |
1210 |
||
28788 | 1211 |
\item \hyperlink{attribute.iff}{\mbox{\isa{iff}}} declares logical equivalences to the |
26782 | 1212 |
Simplifier and the Classical reasoner at the same time. |
1213 |
Non-conditional rules result in a ``safe'' introduction and |
|
1214 |
elimination pair; conditional ones are considered ``unsafe''. Rules |
|
40406 | 1215 |
with negative conclusion are automatically inverted (using \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}{\isaliteral{22}{\isachardoublequote}}}-elimination internally). |
26782 | 1216 |
|
40406 | 1217 |
The ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}'' version of \hyperlink{attribute.iff}{\mbox{\isa{iff}}} declares rules to |
26782 | 1218 |
the Isabelle/Pure context only, and omits the Simplifier |
1219 |
declaration. |
|
1220 |
||
28788 | 1221 |
\end{description}% |
26782 | 1222 |
\end{isamarkuptext}% |
1223 |
\isamarkuptrue% |
|
1224 |
% |
|
27042 | 1225 |
\isamarkupsubsection{Classical operations% |
26782 | 1226 |
} |
1227 |
\isamarkuptrue% |
|
1228 |
% |
|
1229 |
\begin{isamarkuptext}% |
|
1230 |
\begin{matharray}{rcl} |
|
28788 | 1231 |
\indexdef{}{attribute}{swapped}\hypertarget{attribute.swapped}{\hyperlink{attribute.swapped}{\mbox{\isa{swapped}}}} & : & \isa{attribute} \\ |
26782 | 1232 |
\end{matharray} |
1233 |
||
28788 | 1234 |
\begin{description} |
26782 | 1235 |
|
28788 | 1236 |
\item \hyperlink{attribute.swapped}{\mbox{\isa{swapped}}} turns an introduction rule into an |
40406 | 1237 |
elimination, by resolving with the classical swap principle \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}. |
26782 | 1238 |
|
28788 | 1239 |
\end{description}% |
26782 | 1240 |
\end{isamarkuptext}% |
1241 |
\isamarkuptrue% |
|
1242 |
% |
|
27047 | 1243 |
\isamarkupsection{Object-logic setup \label{sec:object-logic}% |
26790 | 1244 |
} |
1245 |
\isamarkuptrue% |
|
1246 |
% |
|
1247 |
\begin{isamarkuptext}% |
|
1248 |
\begin{matharray}{rcl} |
|
40406 | 1249 |
\indexdef{}{command}{judgment}\hypertarget{command.judgment}{\hyperlink{command.judgment}{\mbox{\isa{\isacommand{judgment}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\ |
28788 | 1250 |
\indexdef{}{method}{atomize}\hypertarget{method.atomize}{\hyperlink{method.atomize}{\mbox{\isa{atomize}}}} & : & \isa{method} \\ |
1251 |
\indexdef{}{attribute}{atomize}\hypertarget{attribute.atomize}{\hyperlink{attribute.atomize}{\mbox{\isa{atomize}}}} & : & \isa{attribute} \\ |
|
40406 | 1252 |
\indexdef{}{attribute}{rule\_format}\hypertarget{attribute.rule-format}{\hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}format}}}} & : & \isa{attribute} \\ |
28788 | 1253 |
\indexdef{}{attribute}{rulify}\hypertarget{attribute.rulify}{\hyperlink{attribute.rulify}{\mbox{\isa{rulify}}}} & : & \isa{attribute} \\ |
26790 | 1254 |
\end{matharray} |
1255 |
||
1256 |
The very starting point for any Isabelle object-logic is a ``truth |
|
1257 |
judgment'' that links object-level statements to the meta-logic |
|
1258 |
(with its minimal language of \isa{prop} that covers universal |
|
40406 | 1259 |
quantification \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{22}{\isachardoublequote}}} and implication \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}}). |
26790 | 1260 |
|
1261 |
Common object-logics are sufficiently expressive to internalize rule |
|
40406 | 1262 |
statements over \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}} within their own |
26790 | 1263 |
language. This is useful in certain situations where a rule needs |
1264 |
to be viewed as an atomic statement from the meta-level perspective, |
|
40406 | 1265 |
e.g.\ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ x{\isaliteral{22}{\isachardoublequote}}} versus \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{22}{\isachardoublequote}}}. |
26790 | 1266 |
|
26902 | 1267 |
From the following language elements, only the \hyperlink{method.atomize}{\mbox{\isa{atomize}}} |
40406 | 1268 |
method and \hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}format}}} attribute are occasionally |
26790 | 1269 |
required by end-users, the rest is for those who need to setup their |
1270 |
own object-logic. In the latter case existing formulations of |
|
1271 |
Isabelle/FOL or Isabelle/HOL may be taken as realistic examples. |
|
1272 |
||
1273 |
Generic tools may refer to the information provided by object-logic |
|
1274 |
declarations internally. |
|
1275 |
||
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6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
1276 |
\begin{railoutput} |
42662 | 1277 |
\rail@begin{1}{} |
42596
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modernized rail diagrams using @{rail} antiquotation;
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|
1278 |
\rail@term{\hyperlink{command.judgment}{\mbox{\isa{\isacommand{judgment}}}}}[] |
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|
1279 |
\rail@nont{\hyperlink{syntax.constdecl}{\mbox{\isa{constdecl}}}}[] |
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modernized rail diagrams using @{rail} antiquotation;
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changeset
|
1280 |
\rail@end |
42662 | 1281 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1282 |
\rail@term{\hyperlink{attribute.atomize}{\mbox{\isa{atomize}}}}[] |
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modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1283 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1284 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1285 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
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changeset
|
1286 |
\rail@term{\isa{full}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
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changeset
|
1287 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
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changeset
|
1288 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
1289 |
\rail@end |
42662 | 1290 |
\rail@begin{2}{} |
42596
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1291 |
\rail@term{\hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}format}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
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changeset
|
1292 |
\rail@bar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
1293 |
\rail@nextbar{1} |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1294 |
\rail@term{\isa{{\isaliteral{28}{\isacharparenleft}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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changeset
|
1295 |
\rail@term{\isa{noasm}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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diff
changeset
|
1296 |
\rail@term{\isa{{\isaliteral{29}{\isacharparenright}}}}[] |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1297 |
\rail@endbar |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
40406
diff
changeset
|
1298 |
\rail@end |
6c621a9d612a
modernized rail diagrams using @{rail} antiquotation;
wenzelm
parents:
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changeset
|
1299 |
\end{railoutput} |
6c621a9d612a
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|
1300 |
|
26790 | 1301 |
|
28788 | 1302 |
\begin{description} |
26790 | 1303 |
|
40406 | 1304 |
\item \hyperlink{command.judgment}{\mbox{\isa{\isacommand{judgment}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\ {\isaliteral{28}{\isacharparenleft}}mx{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} declares constant |
28788 | 1305 |
\isa{c} as the truth judgment of the current object-logic. Its |
40406 | 1306 |
type \isa{{\isaliteral{5C3C7369676D613E}{\isasymsigma}}} should specify a coercion of the category of |
28788 | 1307 |
object-level propositions to \isa{prop} of the Pure meta-logic; |
40406 | 1308 |
the mixfix annotation \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}mx{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} would typically just link the |
28788 | 1309 |
object language (internally of syntactic category \isa{logic}) |
1310 |
with that of \isa{prop}. Only one \hyperlink{command.judgment}{\mbox{\isa{\isacommand{judgment}}}} |
|
1311 |
declaration may be given in any theory development. |
|
26790 | 1312 |
|
28788 | 1313 |
\item \hyperlink{method.atomize}{\mbox{\isa{atomize}}} (as a method) rewrites any non-atomic |
26790 | 1314 |
premises of a sub-goal, using the meta-level equations declared via |
26902 | 1315 |
\hyperlink{attribute.atomize}{\mbox{\isa{atomize}}} (as an attribute) beforehand. As a result, |
26790 | 1316 |
heavily nested goals become amenable to fundamental operations such |
42626 | 1317 |
as resolution (cf.\ the \hyperlink{method.Pure.rule}{\mbox{\isa{rule}}} method). Giving the ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}full{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' option here means to turn the whole subgoal into an |
26790 | 1318 |
object-statement (if possible), including the outermost parameters |
1319 |
and assumptions as well. |
|
1320 |
||
26902 | 1321 |
A typical collection of \hyperlink{attribute.atomize}{\mbox{\isa{atomize}}} rules for a particular |
26790 | 1322 |
object-logic would provide an internalization for each of the |
40406 | 1323 |
connectives of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}}, and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}}. |
26790 | 1324 |
Meta-level conjunction should be covered as well (this is |
1325 |
particularly important for locales, see \secref{sec:locale}). |
|
1326 |
||
40406 | 1327 |
\item \hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}format}}} rewrites a theorem by the equalities |
28788 | 1328 |
declared as \hyperlink{attribute.rulify}{\mbox{\isa{rulify}}} rules in the current object-logic. |
1329 |
By default, the result is fully normalized, including assumptions |
|
40406 | 1330 |
and conclusions at any depth. The \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option |
28788 | 1331 |
restricts the transformation to the conclusion of a rule. |
26790 | 1332 |
|
40406 | 1333 |
In common object-logics (HOL, FOL, ZF), the effect of \hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}format}}} is to replace (bounded) universal quantification |
1334 |
(\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}{\isaliteral{22}{\isachardoublequote}}}) and implication (\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}{\isaliteral{22}{\isachardoublequote}}}) by the corresponding |
|
1335 |
rule statements over \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}}. |
|
26790 | 1336 |
|
28788 | 1337 |
\end{description}% |
26790 | 1338 |
\end{isamarkuptext}% |
1339 |
\isamarkuptrue% |
|
1340 |
% |
|
26782 | 1341 |
\isadelimtheory |
1342 |
% |
|
1343 |
\endisadelimtheory |
|
1344 |
% |
|
1345 |
\isatagtheory |
|
1346 |
\isacommand{end}\isamarkupfalse% |
|
1347 |
% |
|
1348 |
\endisatagtheory |
|
1349 |
{\isafoldtheory}% |
|
1350 |
% |
|
1351 |
\isadelimtheory |
|
1352 |
% |
|
1353 |
\endisadelimtheory |
|
1354 |
\isanewline |
|
1355 |
\end{isabellebody}% |
|
1356 |
%%% Local Variables: |
|
1357 |
%%% mode: latex |
|
1358 |
%%% TeX-master: "root" |
|
1359 |
%%% End: |