author | wenzelm |
Sat, 30 Oct 2010 16:33:58 +0200 | |
changeset 40291 | 012ed4426fda |
parent 40255 | 9ffbc25e1606 |
child 40406 | 313a24b66a8d |
permissions | -rw-r--r-- |
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% |
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\begin{isabellebody}% |
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\def\isabellecontext{Generic}% |
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% |
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\isadelimtheory |
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% |
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\endisadelimtheory |
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% |
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\isatagtheory |
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\isacommand{theory}\isamarkupfalse% |
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\ Generic\isanewline |
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\isakeyword{imports}\ Main\isanewline |
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\isakeyword{begin}% |
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\endisatagtheory |
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{\isafoldtheory}% |
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% |
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\isadelimtheory |
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% |
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\endisadelimtheory |
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% |
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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% |
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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}}}}. |
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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{\isacharunderscore}configs}}}}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\ |
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\end{matharray} |
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||
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\begin{rail} |
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name ('=' ('true' | 'false' | int | float | name))? |
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\end{rail} |
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||
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\begin{description} |
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|
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\item \hyperlink{command.print-configs}{\mbox{\isa{\isacommand{print{\isacharunderscore}configs}}}} prints the available configuration |
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options, with names, types, and current values. |
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\item \isa{{\isachardoublequote}name\ {\isacharequal}\ value{\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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|
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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{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\ |
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\indexdef{}{method}{drule}\hypertarget{method.drule}{\hyperlink{method.drule}{\mbox{\isa{drule}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\ |
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\indexdef{}{method}{frule}\hypertarget{method.frule}{\hyperlink{method.frule}{\mbox{\isa{frule}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\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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||
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\begin{rail} |
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('fold' | 'unfold' | 'insert') thmrefs |
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; |
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('erule' | 'drule' | 'frule') ('('nat')')? thmrefs |
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; |
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\end{rail} |
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||
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\begin{description} |
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|
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\item \hyperlink{method.unfold}{\mbox{\isa{unfold}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} and \hyperlink{method.fold}{\mbox{\isa{fold}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\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{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\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{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}, \hyperlink{method.drule}{\mbox{\isa{drule}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}, and \hyperlink{method.frule}{\mbox{\isa{frule}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\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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||
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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{{\isachardoublequote}{\isacharcomma}{\isachardoublequote}}'' method combinator (cf.\ |
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\secref{sec:proof-meth}). |
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|
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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{{\isachardoublequote}{\isacharbar}{\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{\isacharunderscore}format}}}} & : & \isa{attribute} \\ |
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\indexdef{}{attribute}{standard}\hypertarget{attribute.standard}{\hyperlink{attribute.standard}{\mbox{\isa{standard}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{attribute} \\ |
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\indexdef{}{attribute}{no\_vars}\hypertarget{attribute.no-vars}{\hyperlink{attribute.no-vars}{\mbox{\isa{no{\isacharunderscore}vars}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{attribute} \\ |
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\end{matharray} |
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||
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\begin{rail} |
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'tagged' name name |
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; |
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'untagged' name |
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; |
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('THEN' | 'COMP') ('[' nat ']')? thmref |
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; |
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('unfolded' | 'folded') thmrefs |
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; |
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'rotated' ( int )? |
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\end{rail} |
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\begin{description} |
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|
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\item \hyperlink{attribute.tagged}{\mbox{\isa{tagged}}}~\isa{{\isachardoublequote}name\ value{\isachardoublequote}} and \hyperlink{attribute.untagged}{\mbox{\isa{untagged}}}~\isa{name} add and remove \emph{tags} of some theorem. |
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Tags may be any list of string pairs that serve as formal comment. |
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The first string is considered the tag name, the second its value. |
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Note that \hyperlink{attribute.untagged}{\mbox{\isa{untagged}}} removes any tags of the same name. |
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\item \hyperlink{attribute.THEN}{\mbox{\isa{THEN}}}~\isa{a} and \hyperlink{attribute.COMP}{\mbox{\isa{COMP}}}~\isa{a} |
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compose rules by resolution. \hyperlink{attribute.THEN}{\mbox{\isa{THEN}}} resolves with the |
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first premise of \isa{a} (an alternative position may be also |
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specified); the \hyperlink{attribute.COMP}{\mbox{\isa{COMP}}} version skips the automatic |
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lifting process that is normally intended (cf.\ \verb|op RS| and |
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\verb|op COMP| in \cite{isabelle-implementation}). |
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\item \hyperlink{attribute.unfolded}{\mbox{\isa{unfolded}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} and \hyperlink{attribute.folded}{\mbox{\isa{folded}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} expand and fold back again the given |
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definitions throughout a rule. |
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\item \hyperlink{attribute.rotated}{\mbox{\isa{rotated}}}~\isa{n} rotate the premises of a |
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theorem by \isa{n} (default 1). |
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\item \hyperlink{attribute.Pure.elim-format}{\mbox{\isa{elim{\isacharunderscore}format}}} turns a destruction rule into |
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elimination rule format, by resolving with the rule \isa{{\isachardoublequote}PROP\ A\ {\isasymLongrightarrow}\ {\isacharparenleft}PROP\ A\ {\isasymLongrightarrow}\ PROP\ B{\isacharparenright}\ {\isasymLongrightarrow}\ PROP\ B{\isachardoublequote}}. |
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Note that the Classical Reasoner (\secref{sec:classical}) provides |
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its own version of this operation. |
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\item \hyperlink{attribute.standard}{\mbox{\isa{standard}}} puts a theorem into the standard form of |
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object-rules at the outermost theory level. Note that this |
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operation violates the local proof context (including active |
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locales). |
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||
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\item \hyperlink{attribute.no-vars}{\mbox{\isa{no{\isacharunderscore}vars}}} replaces schematic variables by free |
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ones; this is mainly for tuning output of pretty printed theorems. |
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||
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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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\isamarkupsubsection{Low-level equational reasoning% |
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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}{subst}\hypertarget{method.subst}{\hyperlink{method.subst}{\mbox{\isa{subst}}}} & : & \isa{method} \\ |
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\indexdef{}{method}{hypsubst}\hypertarget{method.hypsubst}{\hyperlink{method.hypsubst}{\mbox{\isa{hypsubst}}}} & : & \isa{method} \\ |
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\indexdef{}{method}{split}\hypertarget{method.split}{\hyperlink{method.split}{\mbox{\isa{split}}}} & : & \isa{method} \\ |
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\end{matharray} |
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\begin{rail} |
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'subst' ('(' 'asm' ')')? ('(' (nat+) ')')? thmref |
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; |
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'split' ('(' 'asm' ')')? thmrefs |
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; |
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\end{rail} |
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These methods provide low-level facilities for equational reasoning |
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that are intended for specialized applications only. Normally, |
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single step calculations would be performed in a structured text |
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(see also \secref{sec:calculation}), while the Simplifier methods |
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provide the canonical way for automated normalization (see |
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\secref{sec:simplifier}). |
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||
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\begin{description} |
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|
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\item \hyperlink{method.subst}{\mbox{\isa{subst}}}~\isa{eq} performs a single substitution step |
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using rule \isa{eq}, which may be either a meta or object |
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equality. |
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||
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\item \hyperlink{method.subst}{\mbox{\isa{subst}}}~\isa{{\isachardoublequote}{\isacharparenleft}asm{\isacharparenright}\ eq{\isachardoublequote}} substitutes in an |
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assumption. |
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||
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\item \hyperlink{method.subst}{\mbox{\isa{subst}}}~\isa{{\isachardoublequote}{\isacharparenleft}i\ {\isasymdots}\ j{\isacharparenright}\ eq{\isachardoublequote}} performs several |
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substitutions in the conclusion. The numbers \isa{i} to \isa{j} |
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indicate the positions to substitute at. Positions are ordered from |
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the top of the term tree moving down from left to right. For |
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example, in \isa{{\isachardoublequote}{\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ {\isacharplus}\ {\isacharparenleft}c\ {\isacharplus}\ d{\isacharparenright}{\isachardoublequote}} there are three positions |
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where commutativity of \isa{{\isachardoublequote}{\isacharplus}{\isachardoublequote}} is applicable: 1 refers to \isa{{\isachardoublequote}a\ {\isacharplus}\ b{\isachardoublequote}}, 2 to the whole term, and 3 to \isa{{\isachardoublequote}c\ {\isacharplus}\ d{\isachardoublequote}}. |
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If the positions in the list \isa{{\isachardoublequote}{\isacharparenleft}i\ {\isasymdots}\ j{\isacharparenright}{\isachardoublequote}} are non-overlapping |
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(e.g.\ \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{2}}\ {\isadigit{3}}{\isacharparenright}{\isachardoublequote}} in \isa{{\isachardoublequote}{\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ {\isacharplus}\ {\isacharparenleft}c\ {\isacharplus}\ d{\isacharparenright}{\isachardoublequote}}) you may |
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assume all substitutions are performed simultaneously. Otherwise |
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the behaviour of \isa{subst} is not specified. |
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||
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\item \hyperlink{method.subst}{\mbox{\isa{subst}}}~\isa{{\isachardoublequote}{\isacharparenleft}asm{\isacharparenright}\ {\isacharparenleft}i\ {\isasymdots}\ j{\isacharparenright}\ eq{\isachardoublequote}} performs the |
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substitutions in the assumptions. The positions refer to the |
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assumptions in order from left to right. For example, given in a |
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goal of the form \isa{{\isachardoublequote}P\ {\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}c\ {\isacharplus}\ d{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymdots}{\isachardoublequote}}, position 1 of |
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commutativity of \isa{{\isachardoublequote}{\isacharplus}{\isachardoublequote}} is the subterm \isa{{\isachardoublequote}a\ {\isacharplus}\ b{\isachardoublequote}} and |
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position 2 is the subterm \isa{{\isachardoublequote}c\ {\isacharplus}\ d{\isachardoublequote}}. |
|
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|
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\item \hyperlink{method.hypsubst}{\mbox{\isa{hypsubst}}} performs substitution using some |
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assumption; this only works for equations of the form \isa{{\isachardoublequote}x\ {\isacharequal}\ t{\isachardoublequote}} where \isa{x} is a free or bound variable. |
246 |
||
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\item \hyperlink{method.split}{\mbox{\isa{split}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} performs single-step case |
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splitting using the given rules. By default, splitting is performed |
|
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in the conclusion of a goal; the \isa{{\isachardoublequote}{\isacharparenleft}asm{\isacharparenright}{\isachardoublequote}} option indicates to |
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operate on assumptions instead. |
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|
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Note that the \hyperlink{method.simp}{\mbox{\isa{simp}}} method already involves repeated |
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application of split rules as declared in the current context. |
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||
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\end{description}% |
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\end{isamarkuptext}% |
257 |
\isamarkuptrue% |
|
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% |
|
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\isamarkupsubsection{Further tactic emulations \label{sec:tactics}% |
260 |
} |
|
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\isamarkuptrue% |
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% |
|
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\begin{isamarkuptext}% |
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The following improper proof methods emulate traditional tactics. |
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These admit direct access to the goal state, which is normally |
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considered harmful! In particular, this may involve both numbered |
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goal addressing (default 1), and dynamic instantiation within the |
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scope of some subgoal. |
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||
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\begin{warn} |
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Dynamic instantiations refer to universally quantified parameters |
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of a subgoal (the dynamic context) rather than fixed variables and |
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term abbreviations of a (static) Isar context. |
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\end{warn} |
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||
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Tactic emulation methods, unlike their ML counterparts, admit |
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simultaneous instantiation from both dynamic and static contexts. |
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If names occur in both contexts goal parameters hide locally fixed |
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variables. Likewise, schematic variables refer to term |
|
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abbreviations, if present in the static context. Otherwise the |
|
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schematic variable is interpreted as a schematic variable and left |
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to be solved by unification with certain parts of the subgoal. |
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||
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Note that the tactic emulation proof methods in Isabelle/Isar are |
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consistently named \isa{foo{\isacharunderscore}tac}. Note also that variable names |
|
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occurring on left hand sides of instantiations must be preceded by a |
|
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question mark if they coincide with a keyword or contain dots. This |
|
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is consistent with the attribute \hyperlink{attribute.where}{\mbox{\isa{where}}} (see |
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\secref{sec:pure-meth-att}). |
290 |
||
291 |
\begin{matharray}{rcl} |
|
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\indexdef{}{method}{rule\_tac}\hypertarget{method.rule-tac}{\hyperlink{method.rule-tac}{\mbox{\isa{rule{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\ |
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\indexdef{}{method}{erule\_tac}\hypertarget{method.erule-tac}{\hyperlink{method.erule-tac}{\mbox{\isa{erule{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\ |
|
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\indexdef{}{method}{drule\_tac}\hypertarget{method.drule-tac}{\hyperlink{method.drule-tac}{\mbox{\isa{drule{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\ |
|
295 |
\indexdef{}{method}{frule\_tac}\hypertarget{method.frule-tac}{\hyperlink{method.frule-tac}{\mbox{\isa{frule{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\ |
|
296 |
\indexdef{}{method}{cut\_tac}\hypertarget{method.cut-tac}{\hyperlink{method.cut-tac}{\mbox{\isa{cut{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\ |
|
297 |
\indexdef{}{method}{thin\_tac}\hypertarget{method.thin-tac}{\hyperlink{method.thin-tac}{\mbox{\isa{thin{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\ |
|
298 |
\indexdef{}{method}{subgoal\_tac}\hypertarget{method.subgoal-tac}{\hyperlink{method.subgoal-tac}{\mbox{\isa{subgoal{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\ |
|
299 |
\indexdef{}{method}{rename\_tac}\hypertarget{method.rename-tac}{\hyperlink{method.rename-tac}{\mbox{\isa{rename{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\ |
|
300 |
\indexdef{}{method}{rotate\_tac}\hypertarget{method.rotate-tac}{\hyperlink{method.rotate-tac}{\mbox{\isa{rotate{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\ |
|
301 |
\indexdef{}{method}{tactic}\hypertarget{method.tactic}{\hyperlink{method.tactic}{\mbox{\isa{tactic}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\ |
|
302 |
\indexdef{}{method}{raw\_tactic}\hypertarget{method.raw-tactic}{\hyperlink{method.raw-tactic}{\mbox{\isa{raw{\isacharunderscore}tactic}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\ |
|
26782 | 303 |
\end{matharray} |
304 |
||
305 |
\begin{rail} |
|
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|
306 |
( 'rule_tac' | 'erule_tac' | 'drule_tac' | 'frule_tac' | 'cut_tac' | 'thin_tac' ) goalspec? |
26782 | 307 |
( insts thmref | thmrefs ) |
308 |
; |
|
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|
309 |
'subgoal_tac' goalspec? (prop +) |
26782 | 310 |
; |
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311 |
'rename_tac' goalspec? (name +) |
26782 | 312 |
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|
313 |
'rotate_tac' goalspec? int? |
26782 | 314 |
; |
27224 | 315 |
('tactic' | 'raw_tactic') text |
26782 | 316 |
; |
317 |
||
318 |
insts: ((name '=' term) + 'and') 'in' |
|
319 |
; |
|
320 |
\end{rail} |
|
321 |
||
28788 | 322 |
\begin{description} |
26782 | 323 |
|
28788 | 324 |
\item \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isacharunderscore}tac}}} etc. do resolution of rules with explicit |
30397 | 325 |
instantiation. This works the same way as the ML tactics \verb|res_inst_tac| etc. (see \cite{isabelle-implementation}) |
26782 | 326 |
|
327 |
Multiple rules may be only given if there is no instantiation; then |
|
26907 | 328 |
\hyperlink{method.rule-tac}{\mbox{\isa{rule{\isacharunderscore}tac}}} is the same as \verb|resolve_tac| in ML (see |
30397 | 329 |
\cite{isabelle-implementation}). |
26782 | 330 |
|
28788 | 331 |
\item \hyperlink{method.cut-tac}{\mbox{\isa{cut{\isacharunderscore}tac}}} inserts facts into the proof state as |
27210 | 332 |
assumption of a subgoal, see also \verb|Tactic.cut_facts_tac| in |
30397 | 333 |
\cite{isabelle-implementation}. Note that the scope of schematic |
26782 | 334 |
variables is spread over the main goal statement. Instantiations |
28788 | 335 |
may be given as well, see also ML tactic \verb|cut_inst_tac| in |
30397 | 336 |
\cite{isabelle-implementation}. |
26782 | 337 |
|
28788 | 338 |
\item \hyperlink{method.thin-tac}{\mbox{\isa{thin{\isacharunderscore}tac}}}~\isa{{\isasymphi}} deletes the specified assumption |
339 |
from a subgoal; note that \isa{{\isasymphi}} may contain schematic variables. |
|
30397 | 340 |
See also \verb|thin_tac| in \cite{isabelle-implementation}. |
28788 | 341 |
|
342 |
\item \hyperlink{method.subgoal-tac}{\mbox{\isa{subgoal{\isacharunderscore}tac}}}~\isa{{\isasymphi}} adds \isa{{\isasymphi}} as an |
|
30397 | 343 |
assumption to a subgoal. See also \verb|subgoal_tac| and \verb|subgoals_tac| in \cite{isabelle-implementation}. |
26782 | 344 |
|
28788 | 345 |
\item \hyperlink{method.rename-tac}{\mbox{\isa{rename{\isacharunderscore}tac}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n{\isachardoublequote}} renames parameters of a |
346 |
goal according to the list \isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub n{\isachardoublequote}}, which refers to the |
|
347 |
\emph{suffix} of variables. |
|
26782 | 348 |
|
28788 | 349 |
\item \hyperlink{method.rotate-tac}{\mbox{\isa{rotate{\isacharunderscore}tac}}}~\isa{n} rotates the assumptions of a |
26782 | 350 |
goal by \isa{n} positions: from right to left if \isa{n} is |
351 |
positive, and from left to right if \isa{n} is negative; the |
|
352 |
default value is 1. See also \verb|rotate_tac| in |
|
30397 | 353 |
\cite{isabelle-implementation}. |
26782 | 354 |
|
28788 | 355 |
\item \hyperlink{method.tactic}{\mbox{\isa{tactic}}}~\isa{{\isachardoublequote}text{\isachardoublequote}} produces a proof method from |
26782 | 356 |
any ML text of type \verb|tactic|. Apart from the usual ML |
27224 | 357 |
environment and the current proof context, the ML code may refer to |
358 |
the locally bound values \verb|facts|, which indicates any |
|
359 |
current facts used for forward-chaining. |
|
26782 | 360 |
|
28788 | 361 |
\item \hyperlink{method.raw-tactic}{\mbox{\isa{raw{\isacharunderscore}tactic}}} is similar to \hyperlink{method.tactic}{\mbox{\isa{tactic}}}, but |
27224 | 362 |
presents the goal state in its raw internal form, where simultaneous |
363 |
subgoals appear as conjunction of the logical framework instead of |
|
364 |
the usual split into several subgoals. While feature this is useful |
|
365 |
for debugging of complex method definitions, it should not never |
|
366 |
appear in production theories. |
|
26782 | 367 |
|
28788 | 368 |
\end{description}% |
26782 | 369 |
\end{isamarkuptext}% |
370 |
\isamarkuptrue% |
|
371 |
% |
|
27042 | 372 |
\isamarkupsection{The Simplifier \label{sec:simplifier}% |
26782 | 373 |
} |
374 |
\isamarkuptrue% |
|
375 |
% |
|
27042 | 376 |
\isamarkupsubsection{Simplification methods% |
26782 | 377 |
} |
378 |
\isamarkuptrue% |
|
379 |
% |
|
380 |
\begin{isamarkuptext}% |
|
381 |
\begin{matharray}{rcl} |
|
28788 | 382 |
\indexdef{}{method}{simp}\hypertarget{method.simp}{\hyperlink{method.simp}{\mbox{\isa{simp}}}} & : & \isa{method} \\ |
383 |
\indexdef{}{method}{simp\_all}\hypertarget{method.simp-all}{\hyperlink{method.simp-all}{\mbox{\isa{simp{\isacharunderscore}all}}}} & : & \isa{method} \\ |
|
26782 | 384 |
\end{matharray} |
385 |
||
386 |
\indexouternonterm{simpmod} |
|
387 |
\begin{rail} |
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|
388 |
('simp' | 'simp_all') opt? (simpmod *) |
26782 | 389 |
; |
390 |
||
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|
391 |
opt: '(' ('no_asm' | 'no_asm_simp' | 'no_asm_use' | 'asm_lr' ) ')' |
26782 | 392 |
; |
393 |
simpmod: ('add' | 'del' | 'only' | 'cong' (() | 'add' | 'del') | |
|
394 |
'split' (() | 'add' | 'del')) ':' thmrefs |
|
395 |
; |
|
396 |
\end{rail} |
|
397 |
||
28788 | 398 |
\begin{description} |
26782 | 399 |
|
28788 | 400 |
\item \hyperlink{method.simp}{\mbox{\isa{simp}}} invokes the Simplifier, after declaring |
26782 | 401 |
additional rules according to the arguments given. Note that the |
402 |
\railtterm{only} modifier first removes all other rewrite rules, |
|
403 |
congruences, and looper tactics (including splits), and then behaves |
|
404 |
like \railtterm{add}. |
|
405 |
||
406 |
\medskip The \railtterm{cong} modifiers add or delete Simplifier |
|
407 |
congruence rules (see also \cite{isabelle-ref}), the default is to |
|
408 |
add. |
|
409 |
||
410 |
\medskip The \railtterm{split} modifiers add or delete rules for the |
|
411 |
Splitter (see also \cite{isabelle-ref}), the default is to add. |
|
412 |
This works only if the Simplifier method has been properly setup to |
|
413 |
include the Splitter (all major object logics such HOL, HOLCF, FOL, |
|
414 |
ZF do this already). |
|
415 |
||
28788 | 416 |
\item \hyperlink{method.simp-all}{\mbox{\isa{simp{\isacharunderscore}all}}} is similar to \hyperlink{method.simp}{\mbox{\isa{simp}}}, but acts on |
26782 | 417 |
all goals (backwards from the last to the first one). |
418 |
||
28788 | 419 |
\end{description} |
26782 | 420 |
|
421 |
By default the Simplifier methods take local assumptions fully into |
|
422 |
account, using equational assumptions in the subsequent |
|
423 |
normalization process, or simplifying assumptions themselves (cf.\ |
|
30397 | 424 |
\verb|asm_full_simp_tac| in \cite{isabelle-ref}). In structured |
425 |
proofs this is usually quite well behaved in practice: just the |
|
426 |
local premises of the actual goal are involved, additional facts may |
|
427 |
be inserted via explicit forward-chaining (via \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}, |
|
35613 | 428 |
\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}, \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}} etc.). |
26782 | 429 |
|
430 |
Additional Simplifier options may be specified to tune the behavior |
|
431 |
further (mostly for unstructured scripts with many accidental local |
|
26842 | 432 |
facts): ``\isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharparenright}{\isachardoublequote}}'' means assumptions are ignored |
433 |
completely (cf.\ \verb|simp_tac|), ``\isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharunderscore}simp{\isacharparenright}{\isachardoublequote}}'' means |
|
26782 | 434 |
assumptions are used in the simplification of the conclusion but are |
26842 | 435 |
not themselves simplified (cf.\ \verb|asm_simp_tac|), and ``\isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharunderscore}use{\isacharparenright}{\isachardoublequote}}'' means assumptions are simplified but are not used |
26782 | 436 |
in the simplification of each other or the conclusion (cf.\ \verb|full_simp_tac|). For compatibility reasons, there is also an option |
26842 | 437 |
``\isa{{\isachardoublequote}{\isacharparenleft}asm{\isacharunderscore}lr{\isacharparenright}{\isachardoublequote}}'', which means that an assumption is only used |
26782 | 438 |
for simplifying assumptions which are to the right of it (cf.\ \verb|asm_lr_simp_tac|). |
439 |
||
27094 | 440 |
The configuration option \isa{{\isachardoublequote}depth{\isacharunderscore}limit{\isachardoublequote}} limits the number of |
26782 | 441 |
recursive invocations of the simplifier during conditional |
442 |
rewriting. |
|
443 |
||
444 |
\medskip The Splitter package is usually configured to work as part |
|
26842 | 445 |
of the Simplifier. The effect of repeatedly applying \verb|split_tac| can be simulated by ``\isa{{\isachardoublequote}{\isacharparenleft}simp\ only{\isacharcolon}\ split{\isacharcolon}\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharparenright}{\isachardoublequote}}''. There is also a separate \isa{split} |
26782 | 446 |
method available for single-step case splitting.% |
447 |
\end{isamarkuptext}% |
|
448 |
\isamarkuptrue% |
|
449 |
% |
|
27042 | 450 |
\isamarkupsubsection{Declaring rules% |
26782 | 451 |
} |
452 |
\isamarkuptrue% |
|
453 |
% |
|
454 |
\begin{isamarkuptext}% |
|
455 |
\begin{matharray}{rcl} |
|
28788 | 456 |
\indexdef{}{command}{print\_simpset}\hypertarget{command.print-simpset}{\hyperlink{command.print-simpset}{\mbox{\isa{\isacommand{print{\isacharunderscore}simpset}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\ |
457 |
\indexdef{}{attribute}{simp}\hypertarget{attribute.simp}{\hyperlink{attribute.simp}{\mbox{\isa{simp}}}} & : & \isa{attribute} \\ |
|
458 |
\indexdef{}{attribute}{cong}\hypertarget{attribute.cong}{\hyperlink{attribute.cong}{\mbox{\isa{cong}}}} & : & \isa{attribute} \\ |
|
459 |
\indexdef{}{attribute}{split}\hypertarget{attribute.split}{\hyperlink{attribute.split}{\mbox{\isa{split}}}} & : & \isa{attribute} \\ |
|
26782 | 460 |
\end{matharray} |
461 |
||
462 |
\begin{rail} |
|
463 |
('simp' | 'cong' | 'split') (() | 'add' | 'del') |
|
464 |
; |
|
465 |
\end{rail} |
|
466 |
||
28788 | 467 |
\begin{description} |
26782 | 468 |
|
28788 | 469 |
\item \hyperlink{command.print-simpset}{\mbox{\isa{\isacommand{print{\isacharunderscore}simpset}}}} prints the collection of rules |
26782 | 470 |
declared to the Simplifier, which is also known as ``simpset'' |
471 |
internally \cite{isabelle-ref}. |
|
472 |
||
28788 | 473 |
\item \hyperlink{attribute.simp}{\mbox{\isa{simp}}} declares simplification rules. |
26782 | 474 |
|
28788 | 475 |
\item \hyperlink{attribute.cong}{\mbox{\isa{cong}}} declares congruence rules. |
26782 | 476 |
|
28788 | 477 |
\item \hyperlink{attribute.split}{\mbox{\isa{split}}} declares case split rules. |
26782 | 478 |
|
28788 | 479 |
\end{description}% |
26782 | 480 |
\end{isamarkuptext}% |
481 |
\isamarkuptrue% |
|
482 |
% |
|
27042 | 483 |
\isamarkupsubsection{Simplification procedures% |
26782 | 484 |
} |
485 |
\isamarkuptrue% |
|
486 |
% |
|
487 |
\begin{isamarkuptext}% |
|
488 |
\begin{matharray}{rcl} |
|
28788 | 489 |
\indexdef{}{command}{simproc\_setup}\hypertarget{command.simproc-setup}{\hyperlink{command.simproc-setup}{\mbox{\isa{\isacommand{simproc{\isacharunderscore}setup}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\ |
490 |
simproc & : & \isa{attribute} \\ |
|
26782 | 491 |
\end{matharray} |
492 |
||
493 |
\begin{rail} |
|
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|
494 |
'simproc_setup' name '(' (term + '|') ')' '=' text \\ ('identifier' (nameref+))? |
26782 | 495 |
; |
496 |
||
497 |
'simproc' (('add' ':')? | 'del' ':') (name+) |
|
498 |
; |
|
499 |
\end{rail} |
|
500 |
||
28788 | 501 |
\begin{description} |
26782 | 502 |
|
28788 | 503 |
\item \hyperlink{command.simproc-setup}{\mbox{\isa{\isacommand{simproc{\isacharunderscore}setup}}}} defines a named simplification |
26782 | 504 |
procedure that is invoked by the Simplifier whenever any of the |
505 |
given term patterns match the current redex. The implementation, |
|
30269
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30172
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changeset
|
506 |
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 |
26842 | 507 |
supposed to be some proven rewrite rule \isa{{\isachardoublequote}r\ {\isasymequiv}\ r{\isacharprime}{\isachardoublequote}} (or a |
26782 | 508 |
generalized version), or \verb|NONE| to indicate failure. The |
509 |
\verb|simpset| argument holds the full context of the current |
|
510 |
Simplifier invocation, including the actual Isar proof context. The |
|
511 |
\verb|morphism| informs about the difference of the original |
|
512 |
compilation context wrt.\ the one of the actual application later |
|
26902 | 513 |
on. The optional \hyperlink{keyword.identifier}{\mbox{\isa{\isakeyword{identifier}}}} specifies theorems that |
26782 | 514 |
represent the logical content of the abstract theory of this |
515 |
simproc. |
|
516 |
||
517 |
Morphisms and identifiers are only relevant for simprocs that are |
|
518 |
defined within a local target context, e.g.\ in a locale. |
|
519 |
||
28788 | 520 |
\item \isa{{\isachardoublequote}simproc\ add{\isacharcolon}\ name{\isachardoublequote}} and \isa{{\isachardoublequote}simproc\ del{\isacharcolon}\ name{\isachardoublequote}} |
26782 | 521 |
add or delete named simprocs to the current Simplifier context. The |
26907 | 522 |
default is to add a simproc. Note that \hyperlink{command.simproc-setup}{\mbox{\isa{\isacommand{simproc{\isacharunderscore}setup}}}} |
26782 | 523 |
already adds the new simproc to the subsequent context. |
524 |
||
28788 | 525 |
\end{description}% |
26782 | 526 |
\end{isamarkuptext}% |
527 |
\isamarkuptrue% |
|
528 |
% |
|
27042 | 529 |
\isamarkupsubsection{Forward simplification% |
26782 | 530 |
} |
531 |
\isamarkuptrue% |
|
532 |
% |
|
533 |
\begin{isamarkuptext}% |
|
534 |
\begin{matharray}{rcl} |
|
28788 | 535 |
\indexdef{}{attribute}{simplified}\hypertarget{attribute.simplified}{\hyperlink{attribute.simplified}{\mbox{\isa{simplified}}}} & : & \isa{attribute} \\ |
26782 | 536 |
\end{matharray} |
537 |
||
538 |
\begin{rail} |
|
539 |
'simplified' opt? thmrefs? |
|
540 |
; |
|
541 |
||
40255
9ffbc25e1606
eliminated obsolete \_ escapes in rail environments;
wenzelm
parents:
35613
diff
changeset
|
542 |
opt: '(' ('no_asm' | 'no_asm_simp' | 'no_asm_use') ')' |
26782 | 543 |
; |
544 |
\end{rail} |
|
545 |
||
28788 | 546 |
\begin{description} |
26782 | 547 |
|
28788 | 548 |
\item \hyperlink{attribute.simplified}{\mbox{\isa{simplified}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} causes a theorem to |
549 |
be simplified, either by exactly the specified rules \isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n{\isachardoublequote}}, or the implicit Simplifier context if no arguments are given. |
|
550 |
The result is fully simplified by default, including assumptions and |
|
551 |
conclusion; the options \isa{no{\isacharunderscore}asm} etc.\ tune the Simplifier in |
|
552 |
the same way as the for the \isa{simp} method. |
|
26782 | 553 |
|
554 |
Note that forward simplification restricts the simplifier to its |
|
555 |
most basic operation of term rewriting; solver and looper tactics |
|
556 |
\cite{isabelle-ref} are \emph{not} involved here. The \isa{simplified} attribute should be only rarely required under normal |
|
557 |
circumstances. |
|
558 |
||
28788 | 559 |
\end{description}% |
26782 | 560 |
\end{isamarkuptext}% |
561 |
\isamarkuptrue% |
|
562 |
% |
|
27042 | 563 |
\isamarkupsection{The Classical Reasoner \label{sec:classical}% |
26782 | 564 |
} |
565 |
\isamarkuptrue% |
|
566 |
% |
|
27042 | 567 |
\isamarkupsubsection{Basic methods% |
26782 | 568 |
} |
569 |
\isamarkuptrue% |
|
570 |
% |
|
571 |
\begin{isamarkuptext}% |
|
572 |
\begin{matharray}{rcl} |
|
28788 | 573 |
\indexdef{}{method}{rule}\hypertarget{method.rule}{\hyperlink{method.rule}{\mbox{\isa{rule}}}} & : & \isa{method} \\ |
574 |
\indexdef{}{method}{contradiction}\hypertarget{method.contradiction}{\hyperlink{method.contradiction}{\mbox{\isa{contradiction}}}} & : & \isa{method} \\ |
|
575 |
\indexdef{}{method}{intro}\hypertarget{method.intro}{\hyperlink{method.intro}{\mbox{\isa{intro}}}} & : & \isa{method} \\ |
|
576 |
\indexdef{}{method}{elim}\hypertarget{method.elim}{\hyperlink{method.elim}{\mbox{\isa{elim}}}} & : & \isa{method} \\ |
|
26782 | 577 |
\end{matharray} |
578 |
||
579 |
\begin{rail} |
|
580 |
('rule' | 'intro' | 'elim') thmrefs? |
|
581 |
; |
|
582 |
\end{rail} |
|
583 |
||
28788 | 584 |
\begin{description} |
26782 | 585 |
|
28788 | 586 |
\item \hyperlink{method.rule}{\mbox{\isa{rule}}} as offered by the Classical Reasoner is a |
26782 | 587 |
refinement over the primitive one (see \secref{sec:pure-meth-att}). |
588 |
Both versions essentially work the same, but the classical version |
|
589 |
observes the classical rule context in addition to that of |
|
590 |
Isabelle/Pure. |
|
591 |
||
592 |
Common object logics (HOL, ZF, etc.) declare a rich collection of |
|
593 |
classical rules (even if these would qualify as intuitionistic |
|
594 |
ones), but only few declarations to the rule context of |
|
595 |
Isabelle/Pure (\secref{sec:pure-meth-att}). |
|
596 |
||
28788 | 597 |
\item \hyperlink{method.contradiction}{\mbox{\isa{contradiction}}} solves some goal by contradiction, |
26842 | 598 |
deriving any result from both \isa{{\isachardoublequote}{\isasymnot}\ A{\isachardoublequote}} and \isa{A}. Chained |
26782 | 599 |
facts, which are guaranteed to participate, may appear in either |
600 |
order. |
|
601 |
||
28788 | 602 |
\item \hyperlink{method.intro}{\mbox{\isa{intro}}} and \hyperlink{method.elim}{\mbox{\isa{elim}}} repeatedly refine some goal |
603 |
by intro- or elim-resolution, after having inserted any chained |
|
26902 | 604 |
facts. Exactly the rules given as arguments are taken into account; |
605 |
this allows fine-tuned decomposition of a proof problem, in contrast |
|
606 |
to common automated tools. |
|
26782 | 607 |
|
28788 | 608 |
\end{description}% |
26782 | 609 |
\end{isamarkuptext}% |
610 |
\isamarkuptrue% |
|
611 |
% |
|
27042 | 612 |
\isamarkupsubsection{Automated methods% |
26782 | 613 |
} |
614 |
\isamarkuptrue% |
|
615 |
% |
|
616 |
\begin{isamarkuptext}% |
|
617 |
\begin{matharray}{rcl} |
|
28788 | 618 |
\indexdef{}{method}{blast}\hypertarget{method.blast}{\hyperlink{method.blast}{\mbox{\isa{blast}}}} & : & \isa{method} \\ |
619 |
\indexdef{}{method}{fast}\hypertarget{method.fast}{\hyperlink{method.fast}{\mbox{\isa{fast}}}} & : & \isa{method} \\ |
|
620 |
\indexdef{}{method}{slow}\hypertarget{method.slow}{\hyperlink{method.slow}{\mbox{\isa{slow}}}} & : & \isa{method} \\ |
|
621 |
\indexdef{}{method}{best}\hypertarget{method.best}{\hyperlink{method.best}{\mbox{\isa{best}}}} & : & \isa{method} \\ |
|
622 |
\indexdef{}{method}{safe}\hypertarget{method.safe}{\hyperlink{method.safe}{\mbox{\isa{safe}}}} & : & \isa{method} \\ |
|
623 |
\indexdef{}{method}{clarify}\hypertarget{method.clarify}{\hyperlink{method.clarify}{\mbox{\isa{clarify}}}} & : & \isa{method} \\ |
|
26782 | 624 |
\end{matharray} |
625 |
||
626 |
\indexouternonterm{clamod} |
|
627 |
\begin{rail} |
|
35613 | 628 |
'blast' nat? (clamod *) |
26782 | 629 |
; |
35613 | 630 |
('fast' | 'slow' | 'best' | 'safe' | 'clarify') (clamod *) |
26782 | 631 |
; |
632 |
||
633 |
clamod: (('intro' | 'elim' | 'dest') ('!' | () | '?') | 'del') ':' thmrefs |
|
634 |
; |
|
635 |
\end{rail} |
|
636 |
||
28788 | 637 |
\begin{description} |
26782 | 638 |
|
28788 | 639 |
\item \hyperlink{method.blast}{\mbox{\isa{blast}}} refers to the classical tableau prover (see |
30397 | 640 |
\verb|blast_tac| in \cite{isabelle-ref}). The optional argument |
641 |
specifies a user-supplied search bound (default 20). |
|
26782 | 642 |
|
28788 | 643 |
\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 | 644 |
reasoner. See \verb|fast_tac|, \verb|slow_tac|, \verb|best_tac|, \verb|safe_tac|, and \verb|clarify_tac| in \cite{isabelle-ref} for more |
645 |
information. |
|
26782 | 646 |
|
28788 | 647 |
\end{description} |
26782 | 648 |
|
649 |
Any of the above methods support additional modifiers of the context |
|
650 |
of classical rules. Their semantics is analogous to the attributes |
|
651 |
given before. Facts provided by forward chaining are inserted into |
|
35613 | 652 |
the goal before commencing proof search.% |
26782 | 653 |
\end{isamarkuptext}% |
654 |
\isamarkuptrue% |
|
655 |
% |
|
27042 | 656 |
\isamarkupsubsection{Combined automated methods \label{sec:clasimp}% |
26782 | 657 |
} |
658 |
\isamarkuptrue% |
|
659 |
% |
|
660 |
\begin{isamarkuptext}% |
|
661 |
\begin{matharray}{rcl} |
|
28788 | 662 |
\indexdef{}{method}{auto}\hypertarget{method.auto}{\hyperlink{method.auto}{\mbox{\isa{auto}}}} & : & \isa{method} \\ |
663 |
\indexdef{}{method}{force}\hypertarget{method.force}{\hyperlink{method.force}{\mbox{\isa{force}}}} & : & \isa{method} \\ |
|
664 |
\indexdef{}{method}{clarsimp}\hypertarget{method.clarsimp}{\hyperlink{method.clarsimp}{\mbox{\isa{clarsimp}}}} & : & \isa{method} \\ |
|
665 |
\indexdef{}{method}{fastsimp}\hypertarget{method.fastsimp}{\hyperlink{method.fastsimp}{\mbox{\isa{fastsimp}}}} & : & \isa{method} \\ |
|
666 |
\indexdef{}{method}{slowsimp}\hypertarget{method.slowsimp}{\hyperlink{method.slowsimp}{\mbox{\isa{slowsimp}}}} & : & \isa{method} \\ |
|
667 |
\indexdef{}{method}{bestsimp}\hypertarget{method.bestsimp}{\hyperlink{method.bestsimp}{\mbox{\isa{bestsimp}}}} & : & \isa{method} \\ |
|
26782 | 668 |
\end{matharray} |
669 |
||
670 |
\indexouternonterm{clasimpmod} |
|
671 |
\begin{rail} |
|
35613 | 672 |
'auto' (nat nat)? (clasimpmod *) |
26782 | 673 |
; |
35613 | 674 |
('force' | 'clarsimp' | 'fastsimp' | 'slowsimp' | 'bestsimp') (clasimpmod *) |
26782 | 675 |
; |
676 |
||
677 |
clasimpmod: ('simp' (() | 'add' | 'del' | 'only') | |
|
678 |
('cong' | 'split') (() | 'add' | 'del') | |
|
679 |
'iff' (((() | 'add') '?'?) | 'del') | |
|
680 |
(('intro' | 'elim' | 'dest') ('!' | () | '?') | 'del')) ':' thmrefs |
|
681 |
\end{rail} |
|
682 |
||
28788 | 683 |
\begin{description} |
26782 | 684 |
|
28788 | 685 |
\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 |
686 |
to Isabelle's combined simplification and classical reasoning |
|
26782 | 687 |
tactics. These correspond to \verb|auto_tac|, \verb|force_tac|, \verb|clarsimp_tac|, and Classical Reasoner tactics with the Simplifier |
30397 | 688 |
added as wrapper, see \cite{isabelle-ref} for more information. The |
689 |
modifier arguments correspond to those given in |
|
26782 | 690 |
\secref{sec:simplifier} and \secref{sec:classical}. Just note that |
691 |
the ones related to the Simplifier are prefixed by \railtterm{simp} |
|
692 |
here. |
|
693 |
||
694 |
Facts provided by forward chaining are inserted into the goal before |
|
35613 | 695 |
doing the search. |
26782 | 696 |
|
28788 | 697 |
\end{description}% |
26782 | 698 |
\end{isamarkuptext}% |
699 |
\isamarkuptrue% |
|
700 |
% |
|
27042 | 701 |
\isamarkupsubsection{Declaring rules% |
26782 | 702 |
} |
703 |
\isamarkuptrue% |
|
704 |
% |
|
705 |
\begin{isamarkuptext}% |
|
706 |
\begin{matharray}{rcl} |
|
28788 | 707 |
\indexdef{}{command}{print\_claset}\hypertarget{command.print-claset}{\hyperlink{command.print-claset}{\mbox{\isa{\isacommand{print{\isacharunderscore}claset}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\ |
708 |
\indexdef{}{attribute}{intro}\hypertarget{attribute.intro}{\hyperlink{attribute.intro}{\mbox{\isa{intro}}}} & : & \isa{attribute} \\ |
|
709 |
\indexdef{}{attribute}{elim}\hypertarget{attribute.elim}{\hyperlink{attribute.elim}{\mbox{\isa{elim}}}} & : & \isa{attribute} \\ |
|
710 |
\indexdef{}{attribute}{dest}\hypertarget{attribute.dest}{\hyperlink{attribute.dest}{\mbox{\isa{dest}}}} & : & \isa{attribute} \\ |
|
711 |
\indexdef{}{attribute}{rule}\hypertarget{attribute.rule}{\hyperlink{attribute.rule}{\mbox{\isa{rule}}}} & : & \isa{attribute} \\ |
|
712 |
\indexdef{}{attribute}{iff}\hypertarget{attribute.iff}{\hyperlink{attribute.iff}{\mbox{\isa{iff}}}} & : & \isa{attribute} \\ |
|
26782 | 713 |
\end{matharray} |
714 |
||
715 |
\begin{rail} |
|
716 |
('intro' | 'elim' | 'dest') ('!' | () | '?') nat? |
|
717 |
; |
|
718 |
'rule' 'del' |
|
719 |
; |
|
720 |
'iff' (((() | 'add') '?'?) | 'del') |
|
721 |
; |
|
722 |
\end{rail} |
|
723 |
||
28788 | 724 |
\begin{description} |
26782 | 725 |
|
28788 | 726 |
\item \hyperlink{command.print-claset}{\mbox{\isa{\isacommand{print{\isacharunderscore}claset}}}} prints the collection of rules |
26782 | 727 |
declared to the Classical Reasoner, which is also known as |
728 |
``claset'' internally \cite{isabelle-ref}. |
|
729 |
||
28788 | 730 |
\item \hyperlink{attribute.intro}{\mbox{\isa{intro}}}, \hyperlink{attribute.elim}{\mbox{\isa{elim}}}, and \hyperlink{attribute.dest}{\mbox{\isa{dest}}} |
26782 | 731 |
declare introduction, elimination, and destruction rules, |
732 |
respectively. By default, rules are considered as \emph{unsafe} |
|
26842 | 733 |
(i.e.\ not applied blindly without backtracking), while ``\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}'' classifies as \emph{safe}. Rule declarations marked by |
734 |
``\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}'' coincide with those of Isabelle/Pure, cf.\ |
|
26782 | 735 |
\secref{sec:pure-meth-att} (i.e.\ are only applied in single steps |
26902 | 736 |
of the \hyperlink{method.rule}{\mbox{\isa{rule}}} method). The optional natural number |
26782 | 737 |
specifies an explicit weight argument, which is ignored by automated |
738 |
tools, but determines the search order of single rule steps. |
|
739 |
||
28788 | 740 |
\item \hyperlink{attribute.rule}{\mbox{\isa{rule}}}~\isa{del} deletes introduction, |
26782 | 741 |
elimination, or destruction rules from the context. |
742 |
||
28788 | 743 |
\item \hyperlink{attribute.iff}{\mbox{\isa{iff}}} declares logical equivalences to the |
26782 | 744 |
Simplifier and the Classical reasoner at the same time. |
745 |
Non-conditional rules result in a ``safe'' introduction and |
|
746 |
elimination pair; conditional ones are considered ``unsafe''. Rules |
|
26842 | 747 |
with negative conclusion are automatically inverted (using \isa{{\isachardoublequote}{\isasymnot}{\isachardoublequote}}-elimination internally). |
26782 | 748 |
|
26902 | 749 |
The ``\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}'' version of \hyperlink{attribute.iff}{\mbox{\isa{iff}}} declares rules to |
26782 | 750 |
the Isabelle/Pure context only, and omits the Simplifier |
751 |
declaration. |
|
752 |
||
28788 | 753 |
\end{description}% |
26782 | 754 |
\end{isamarkuptext}% |
755 |
\isamarkuptrue% |
|
756 |
% |
|
27042 | 757 |
\isamarkupsubsection{Classical operations% |
26782 | 758 |
} |
759 |
\isamarkuptrue% |
|
760 |
% |
|
761 |
\begin{isamarkuptext}% |
|
762 |
\begin{matharray}{rcl} |
|
28788 | 763 |
\indexdef{}{attribute}{swapped}\hypertarget{attribute.swapped}{\hyperlink{attribute.swapped}{\mbox{\isa{swapped}}}} & : & \isa{attribute} \\ |
26782 | 764 |
\end{matharray} |
765 |
||
28788 | 766 |
\begin{description} |
26782 | 767 |
|
28788 | 768 |
\item \hyperlink{attribute.swapped}{\mbox{\isa{swapped}}} turns an introduction rule into an |
26842 | 769 |
elimination, by resolving with the classical swap principle \isa{{\isachardoublequote}{\isacharparenleft}{\isasymnot}\ B\ {\isasymLongrightarrow}\ A{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymnot}\ A\ {\isasymLongrightarrow}\ B{\isacharparenright}{\isachardoublequote}}. |
26782 | 770 |
|
28788 | 771 |
\end{description}% |
26782 | 772 |
\end{isamarkuptext}% |
773 |
\isamarkuptrue% |
|
774 |
% |
|
27047 | 775 |
\isamarkupsection{Object-logic setup \label{sec:object-logic}% |
26790 | 776 |
} |
777 |
\isamarkuptrue% |
|
778 |
% |
|
779 |
\begin{isamarkuptext}% |
|
780 |
\begin{matharray}{rcl} |
|
28788 | 781 |
\indexdef{}{command}{judgment}\hypertarget{command.judgment}{\hyperlink{command.judgment}{\mbox{\isa{\isacommand{judgment}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\ |
782 |
\indexdef{}{method}{atomize}\hypertarget{method.atomize}{\hyperlink{method.atomize}{\mbox{\isa{atomize}}}} & : & \isa{method} \\ |
|
783 |
\indexdef{}{attribute}{atomize}\hypertarget{attribute.atomize}{\hyperlink{attribute.atomize}{\mbox{\isa{atomize}}}} & : & \isa{attribute} \\ |
|
784 |
\indexdef{}{attribute}{rule\_format}\hypertarget{attribute.rule-format}{\hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isacharunderscore}format}}}} & : & \isa{attribute} \\ |
|
785 |
\indexdef{}{attribute}{rulify}\hypertarget{attribute.rulify}{\hyperlink{attribute.rulify}{\mbox{\isa{rulify}}}} & : & \isa{attribute} \\ |
|
26790 | 786 |
\end{matharray} |
787 |
||
788 |
The very starting point for any Isabelle object-logic is a ``truth |
|
789 |
judgment'' that links object-level statements to the meta-logic |
|
790 |
(with its minimal language of \isa{prop} that covers universal |
|
26842 | 791 |
quantification \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}} and implication \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}}). |
26790 | 792 |
|
793 |
Common object-logics are sufficiently expressive to internalize rule |
|
26842 | 794 |
statements over \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}} within their own |
26790 | 795 |
language. This is useful in certain situations where a rule needs |
796 |
to be viewed as an atomic statement from the meta-level perspective, |
|
26842 | 797 |
e.g.\ \isa{{\isachardoublequote}{\isasymAnd}x{\isachardot}\ x\ {\isasymin}\ A\ {\isasymLongrightarrow}\ P\ x{\isachardoublequote}} versus \isa{{\isachardoublequote}{\isasymforall}x\ {\isasymin}\ A{\isachardot}\ P\ x{\isachardoublequote}}. |
26790 | 798 |
|
26902 | 799 |
From the following language elements, only the \hyperlink{method.atomize}{\mbox{\isa{atomize}}} |
26907 | 800 |
method and \hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isacharunderscore}format}}} attribute are occasionally |
26790 | 801 |
required by end-users, the rest is for those who need to setup their |
802 |
own object-logic. In the latter case existing formulations of |
|
803 |
Isabelle/FOL or Isabelle/HOL may be taken as realistic examples. |
|
804 |
||
805 |
Generic tools may refer to the information provided by object-logic |
|
806 |
declarations internally. |
|
807 |
||
808 |
\begin{rail} |
|
809 |
'judgment' constdecl |
|
810 |
; |
|
811 |
'atomize' ('(' 'full' ')')? |
|
812 |
; |
|
40255
9ffbc25e1606
eliminated obsolete \_ escapes in rail environments;
wenzelm
parents:
35613
diff
changeset
|
813 |
'rule_format' ('(' 'noasm' ')')? |
26790 | 814 |
; |
815 |
\end{rail} |
|
816 |
||
28788 | 817 |
\begin{description} |
26790 | 818 |
|
28788 | 819 |
\item \hyperlink{command.judgment}{\mbox{\isa{\isacommand{judgment}}}}~\isa{{\isachardoublequote}c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\ {\isacharparenleft}mx{\isacharparenright}{\isachardoublequote}} declares constant |
820 |
\isa{c} as the truth judgment of the current object-logic. Its |
|
821 |
type \isa{{\isasymsigma}} should specify a coercion of the category of |
|
822 |
object-level propositions to \isa{prop} of the Pure meta-logic; |
|
823 |
the mixfix annotation \isa{{\isachardoublequote}{\isacharparenleft}mx{\isacharparenright}{\isachardoublequote}} would typically just link the |
|
824 |
object language (internally of syntactic category \isa{logic}) |
|
825 |
with that of \isa{prop}. Only one \hyperlink{command.judgment}{\mbox{\isa{\isacommand{judgment}}}} |
|
826 |
declaration may be given in any theory development. |
|
26790 | 827 |
|
28788 | 828 |
\item \hyperlink{method.atomize}{\mbox{\isa{atomize}}} (as a method) rewrites any non-atomic |
26790 | 829 |
premises of a sub-goal, using the meta-level equations declared via |
26902 | 830 |
\hyperlink{attribute.atomize}{\mbox{\isa{atomize}}} (as an attribute) beforehand. As a result, |
26790 | 831 |
heavily nested goals become amenable to fundamental operations such |
26902 | 832 |
as resolution (cf.\ the \hyperlink{method.rule}{\mbox{\isa{rule}}} method). Giving the ``\isa{{\isachardoublequote}{\isacharparenleft}full{\isacharparenright}{\isachardoublequote}}'' option here means to turn the whole subgoal into an |
26790 | 833 |
object-statement (if possible), including the outermost parameters |
834 |
and assumptions as well. |
|
835 |
||
26902 | 836 |
A typical collection of \hyperlink{attribute.atomize}{\mbox{\isa{atomize}}} rules for a particular |
26790 | 837 |
object-logic would provide an internalization for each of the |
26842 | 838 |
connectives of \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}}, \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}}, and \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}}. |
26790 | 839 |
Meta-level conjunction should be covered as well (this is |
840 |
particularly important for locales, see \secref{sec:locale}). |
|
841 |
||
28788 | 842 |
\item \hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isacharunderscore}format}}} rewrites a theorem by the equalities |
843 |
declared as \hyperlink{attribute.rulify}{\mbox{\isa{rulify}}} rules in the current object-logic. |
|
844 |
By default, the result is fully normalized, including assumptions |
|
845 |
and conclusions at any depth. The \isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharparenright}{\isachardoublequote}} option |
|
846 |
restricts the transformation to the conclusion of a rule. |
|
26790 | 847 |
|
26907 | 848 |
In common object-logics (HOL, FOL, ZF), the effect of \hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isacharunderscore}format}}} is to replace (bounded) universal quantification |
26842 | 849 |
(\isa{{\isachardoublequote}{\isasymforall}{\isachardoublequote}}) and implication (\isa{{\isachardoublequote}{\isasymlongrightarrow}{\isachardoublequote}}) by the corresponding |
850 |
rule statements over \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}}. |
|
26790 | 851 |
|
28788 | 852 |
\end{description}% |
26790 | 853 |
\end{isamarkuptext}% |
854 |
\isamarkuptrue% |
|
855 |
% |
|
26782 | 856 |
\isadelimtheory |
857 |
% |
|
858 |
\endisadelimtheory |
|
859 |
% |
|
860 |
\isatagtheory |
|
861 |
\isacommand{end}\isamarkupfalse% |
|
862 |
% |
|
863 |
\endisatagtheory |
|
864 |
{\isafoldtheory}% |
|
865 |
% |
|
866 |
\isadelimtheory |
|
867 |
% |
|
868 |
\endisadelimtheory |
|
869 |
\isanewline |
|
870 |
\end{isabellebody}% |
|
871 |
%%% Local Variables: |
|
872 |
%%% mode: latex |
|
873 |
%%% TeX-master: "root" |
|
874 |
%%% End: |