doc-src/IsarRef/Thy/document/ML_Tactic.tex
changeset 40406 313a24b66a8d
parent 30172 afdf7808cfd0
child 42626 6ac8c55c657e
equal deleted inserted replaced
40405:42671298f037 40406:313a24b66a8d
     1 %
     1 %
     2 \begin{isabellebody}%
     2 \begin{isabellebody}%
     3 \def\isabellecontext{ML{\isacharunderscore}Tactic}%
     3 \def\isabellecontext{ML{\isaliteral{5F}{\isacharunderscore}}Tactic}%
     4 %
     4 %
     5 \isadelimtheory
     5 \isadelimtheory
     6 %
     6 %
     7 \endisadelimtheory
     7 \endisadelimtheory
     8 %
     8 %
     9 \isatagtheory
     9 \isatagtheory
    10 \isacommand{theory}\isamarkupfalse%
    10 \isacommand{theory}\isamarkupfalse%
    11 \ ML{\isacharunderscore}Tactic\isanewline
    11 \ ML{\isaliteral{5F}{\isacharunderscore}}Tactic\isanewline
    12 \isakeyword{imports}\ Main\isanewline
    12 \isakeyword{imports}\ Main\isanewline
    13 \isakeyword{begin}%
    13 \isakeyword{begin}%
    14 \endisatagtheory
    14 \endisatagtheory
    15 {\isafoldtheory}%
    15 {\isafoldtheory}%
    16 %
    16 %
    63   \item Abbreviations for singleton arguments (e.g.\ \verb|resolve_tac|
    63   \item Abbreviations for singleton arguments (e.g.\ \verb|resolve_tac|
    64   vs.\ \verb|rtac|).
    64   vs.\ \verb|rtac|).
    65 
    65 
    66   \end{enumerate}
    66   \end{enumerate}
    67 
    67 
    68   Basically, the set of Isar tactic emulations \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isacharunderscore}tac}}},
    68   Basically, the set of Isar tactic emulations \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}tac}}},
    69   \hyperlink{method.erule-tac}{\mbox{\isa{erule{\isacharunderscore}tac}}}, \hyperlink{method.drule-tac}{\mbox{\isa{drule{\isacharunderscore}tac}}}, \hyperlink{method.frule-tac}{\mbox{\isa{frule{\isacharunderscore}tac}}} (see
    69   \hyperlink{method.erule-tac}{\mbox{\isa{erule{\isaliteral{5F}{\isacharunderscore}}tac}}}, \hyperlink{method.drule-tac}{\mbox{\isa{drule{\isaliteral{5F}{\isacharunderscore}}tac}}}, \hyperlink{method.frule-tac}{\mbox{\isa{frule{\isaliteral{5F}{\isacharunderscore}}tac}}} (see
    70   \secref{sec:tactics}) would be sufficient to cover the four modes,
    70   \secref{sec:tactics}) would be sufficient to cover the four modes,
    71   either with or without instantiation, and either with single or
    71   either with or without instantiation, and either with single or
    72   multiple arguments.  Although it is more convenient in most cases to
    72   multiple arguments.  Although it is more convenient in most cases to
    73   use the plain \hyperlink{method.rule}{\mbox{\isa{rule}}} method (see
    73   use the plain \hyperlink{method.rule}{\mbox{\isa{rule}}} method (see
    74   \secref{sec:pure-meth-att}), or any of its ``improper'' variants
    74   \secref{sec:pure-meth-att}), or any of its ``improper'' variants
    75   \hyperlink{method.erule}{\mbox{\isa{erule}}}, \hyperlink{method.drule}{\mbox{\isa{drule}}}, \hyperlink{method.frule}{\mbox{\isa{frule}}} (see
    75   \hyperlink{method.erule}{\mbox{\isa{erule}}}, \hyperlink{method.drule}{\mbox{\isa{drule}}}, \hyperlink{method.frule}{\mbox{\isa{frule}}} (see
    76   \secref{sec:misc-meth-att}).  Note that explicit goal addressing is
    76   \secref{sec:misc-meth-att}).  Note that explicit goal addressing is
    77   only supported by the actual \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isacharunderscore}tac}}} version.
    77   only supported by the actual \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}tac}}} version.
    78 
    78 
    79   With this in mind, plain resolution tactics correspond to Isar
    79   With this in mind, plain resolution tactics correspond to Isar
    80   methods as follows.
    80   methods as follows.
    81 
    81 
    82   \medskip
    82   \medskip
    83   \begin{tabular}{lll}
    83   \begin{tabular}{lll}
    84     \verb|rtac|~\isa{{\isachardoublequote}a\ {\isadigit{1}}{\isachardoublequote}} & & \isa{{\isachardoublequote}rule\ a{\isachardoublequote}} \\
    84     \verb|rtac|~\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}rule\ a{\isaliteral{22}{\isachardoublequote}}} \\
    85     \verb|resolve_tac|~\isa{{\isachardoublequote}{\isacharbrackleft}a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}\ {\isadigit{1}}{\isachardoublequote}} & & \isa{{\isachardoublequote}rule\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}{\isachardoublequote}} \\
    85     \verb|resolve_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5D}{\isacharbrackright}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}rule\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\
    86     \verb|res_inst_tac|~\isa{{\isachardoublequote}ctxt\ {\isacharbrackleft}{\isacharparenleft}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ t\isactrlsub {\isadigit{1}}{\isacharparenright}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}\ a\ {\isadigit{1}}{\isachardoublequote}} & &
    86     \verb|res_inst_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}ctxt\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5D}{\isacharbrackright}}\ a\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & &
    87     \isa{{\isachardoublequote}rule{\isacharunderscore}tac\ x\isactrlsub {\isadigit{1}}\ {\isacharequal}\ t\isactrlsub {\isadigit{1}}\ {\isasymAND}\ {\isasymdots}\ {\isasymIN}\ a{\isachardoublequote}} \\[0.5ex]
    87     \isa{{\isaliteral{22}{\isachardoublequote}}rule{\isaliteral{5F}{\isacharunderscore}}tac\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C494E3E}{\isasymIN}}\ a{\isaliteral{22}{\isachardoublequote}}} \\[0.5ex]
    88     \verb|rtac|~\isa{{\isachardoublequote}a\ i{\isachardoublequote}} & & \isa{{\isachardoublequote}rule{\isacharunderscore}tac\ {\isacharbrackleft}i{\isacharbrackright}\ a{\isachardoublequote}} \\
    88     \verb|rtac|~\isa{{\isaliteral{22}{\isachardoublequote}}a\ i{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}rule{\isaliteral{5F}{\isacharunderscore}}tac\ {\isaliteral{5B}{\isacharbrackleft}}i{\isaliteral{5D}{\isacharbrackright}}\ a{\isaliteral{22}{\isachardoublequote}}} \\
    89     \verb|resolve_tac|~\isa{{\isachardoublequote}{\isacharbrackleft}a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}\ i{\isachardoublequote}} & & \isa{{\isachardoublequote}rule{\isacharunderscore}tac\ {\isacharbrackleft}i{\isacharbrackright}\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}{\isachardoublequote}} \\
    89     \verb|resolve_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5D}{\isacharbrackright}}\ i{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}rule{\isaliteral{5F}{\isacharunderscore}}tac\ {\isaliteral{5B}{\isacharbrackleft}}i{\isaliteral{5D}{\isacharbrackright}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\
    90     \verb|res_inst_tac|~\isa{{\isachardoublequote}ctxt\ {\isacharbrackleft}{\isacharparenleft}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ t\isactrlsub {\isadigit{1}}{\isacharparenright}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}\ a\ i{\isachardoublequote}} & &
    90     \verb|res_inst_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}ctxt\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5D}{\isacharbrackright}}\ a\ i{\isaliteral{22}{\isachardoublequote}}} & &
    91     \isa{{\isachardoublequote}rule{\isacharunderscore}tac\ {\isacharbrackleft}i{\isacharbrackright}\ x\isactrlsub {\isadigit{1}}\ {\isacharequal}\ t\isactrlsub {\isadigit{1}}\ {\isasymAND}\ {\isasymdots}\ {\isasymIN}\ a{\isachardoublequote}} \\
    91     \isa{{\isaliteral{22}{\isachardoublequote}}rule{\isaliteral{5F}{\isacharunderscore}}tac\ {\isaliteral{5B}{\isacharbrackleft}}i{\isaliteral{5D}{\isacharbrackright}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C494E3E}{\isasymIN}}\ a{\isaliteral{22}{\isachardoublequote}}} \\
    92   \end{tabular}
    92   \end{tabular}
    93   \medskip
    93   \medskip
    94 
    94 
    95   Note that explicit goal addressing may be usually avoided by
    95   Note that explicit goal addressing may be usually avoided by
    96   changing the order of subgoals with \hyperlink{command.defer}{\mbox{\isa{\isacommand{defer}}}} or \hyperlink{command.prefer}{\mbox{\isa{\isacommand{prefer}}}} (see \secref{sec:tactic-commands}).%
    96   changing the order of subgoals with \hyperlink{command.defer}{\mbox{\isa{\isacommand{defer}}}} or \hyperlink{command.prefer}{\mbox{\isa{\isacommand{prefer}}}} (see \secref{sec:tactic-commands}).%
   102 \isamarkuptrue%
   102 \isamarkuptrue%
   103 %
   103 %
   104 \begin{isamarkuptext}%
   104 \begin{isamarkuptext}%
   105 The main Simplifier tactics \verb|simp_tac| and variants (cf.\
   105 The main Simplifier tactics \verb|simp_tac| and variants (cf.\
   106   \cite{isabelle-ref}) are all covered by the \hyperlink{method.simp}{\mbox{\isa{simp}}} and
   106   \cite{isabelle-ref}) are all covered by the \hyperlink{method.simp}{\mbox{\isa{simp}}} and
   107   \hyperlink{method.simp-all}{\mbox{\isa{simp{\isacharunderscore}all}}} methods (see \secref{sec:simplifier}).  Note that
   107   \hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}} methods (see \secref{sec:simplifier}).  Note that
   108   there is no individual goal addressing available, simplification
   108   there is no individual goal addressing available, simplification
   109   acts either on the first goal (\hyperlink{method.simp}{\mbox{\isa{simp}}}) or all goals
   109   acts either on the first goal (\hyperlink{method.simp}{\mbox{\isa{simp}}}) or all goals
   110   (\hyperlink{method.simp-all}{\mbox{\isa{simp{\isacharunderscore}all}}}).
   110   (\hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}}).
   111 
   111 
   112   \medskip
   112   \medskip
   113   \begin{tabular}{lll}
   113   \begin{tabular}{lll}
   114     \verb|asm_full_simp_tac|~\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}simpset{\isacharbraceright}\ {\isadigit{1}}{\isachardoublequote}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}} \\
   114     \verb|asm_full_simp_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}simpset{\isaliteral{7D}{\isacharbraceright}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}} \\
   115     \verb|ALLGOALS|~(\verb|asm_full_simp_tac|~\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}simpset{\isacharbraceright}{\isachardoublequote}}) & & \hyperlink{method.simp-all}{\mbox{\isa{simp{\isacharunderscore}all}}} \\[0.5ex]
   115     \verb|ALLGOALS|~(\verb|asm_full_simp_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}simpset{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}}) & & \hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}} \\[0.5ex]
   116     \verb|simp_tac|~\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}simpset{\isacharbraceright}\ {\isadigit{1}}{\isachardoublequote}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}}~\isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharparenright}{\isachardoublequote}} \\
   116     \verb|simp_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}simpset{\isaliteral{7D}{\isacharbraceright}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
   117     \verb|asm_simp_tac|~\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}simpset{\isacharbraceright}\ {\isadigit{1}}{\isachardoublequote}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}}~\isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharunderscore}simp{\isacharparenright}{\isachardoublequote}} \\
   117     \verb|asm_simp_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}simpset{\isaliteral{7D}{\isacharbraceright}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
   118     \verb|full_simp_tac|~\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}simpset{\isacharbraceright}\ {\isadigit{1}}{\isachardoublequote}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}}~\isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharunderscore}use{\isacharparenright}{\isachardoublequote}} \\
   118     \verb|full_simp_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}simpset{\isaliteral{7D}{\isacharbraceright}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{5F}{\isacharunderscore}}use{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
   119     \verb|asm_lr_simp_tac|~\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}simpset{\isacharbraceright}\ {\isadigit{1}}{\isachardoublequote}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}}~\isa{{\isachardoublequote}{\isacharparenleft}asm{\isacharunderscore}lr{\isacharparenright}{\isachardoublequote}} \\
   119     \verb|asm_lr_simp_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}simpset{\isaliteral{7D}{\isacharbraceright}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}asm{\isaliteral{5F}{\isacharunderscore}}lr{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
   120   \end{tabular}
   120   \end{tabular}
   121   \medskip%
   121   \medskip%
   122 \end{isamarkuptext}%
   122 \end{isamarkuptext}%
   123 \isamarkuptrue%
   123 \isamarkuptrue%
   124 %
   124 %
   143   Isabelle/HOL, some of these also in Isabelle/FOL or Isabelle/ZF.
   143   Isabelle/HOL, some of these also in Isabelle/FOL or Isabelle/ZF.
   144   The most common ones of these may be ported to Isar as follows.
   144   The most common ones of these may be ported to Isar as follows.
   145 
   145 
   146   \medskip
   146   \medskip
   147   \begin{tabular}{lll}
   147   \begin{tabular}{lll}
   148     \verb|stac|~\isa{{\isachardoublequote}a\ {\isadigit{1}}{\isachardoublequote}} & & \isa{{\isachardoublequote}subst\ a{\isachardoublequote}} \\
   148     \verb|stac|~\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}subst\ a{\isaliteral{22}{\isachardoublequote}}} \\
   149     \verb|hyp_subst_tac|~\isa{{\isadigit{1}}} & & \isa{hypsubst} \\
   149     \verb|hyp_subst_tac|~\isa{{\isadigit{1}}} & & \isa{hypsubst} \\
   150     \verb|strip_tac|~\isa{{\isadigit{1}}} & \isa{{\isachardoublequote}{\isasymapprox}{\isachardoublequote}} & \isa{{\isachardoublequote}intro\ strip{\isachardoublequote}} \\
   150     \verb|strip_tac|~\isa{{\isadigit{1}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}intro\ strip{\isaliteral{22}{\isachardoublequote}}} \\
   151     \verb|split_all_tac|~\isa{{\isadigit{1}}} & & \isa{{\isachardoublequote}simp\ {\isacharparenleft}no{\isacharunderscore}asm{\isacharunderscore}simp{\isacharparenright}\ only{\isacharcolon}\ split{\isacharunderscore}tupled{\isacharunderscore}all{\isachardoublequote}} \\
   151     \verb|split_all_tac|~\isa{{\isadigit{1}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}simp\ {\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{29}{\isacharparenright}}\ only{\isaliteral{3A}{\isacharcolon}}\ split{\isaliteral{5F}{\isacharunderscore}}tupled{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{22}{\isachardoublequote}}} \\
   152       & \isa{{\isachardoublequote}{\isasymapprox}{\isachardoublequote}} & \isa{{\isachardoublequote}simp\ only{\isacharcolon}\ split{\isacharunderscore}tupled{\isacharunderscore}all{\isachardoublequote}} \\
   152       & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}simp\ only{\isaliteral{3A}{\isacharcolon}}\ split{\isaliteral{5F}{\isacharunderscore}}tupled{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{22}{\isachardoublequote}}} \\
   153       & \isa{{\isachardoublequote}{\isasymlless}{\isachardoublequote}} & \isa{{\isachardoublequote}clarify{\isachardoublequote}} \\
   153       & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C6C6573733E}{\isasymlless}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}clarify{\isaliteral{22}{\isachardoublequote}}} \\
   154   \end{tabular}%
   154   \end{tabular}%
   155 \end{isamarkuptext}%
   155 \end{isamarkuptext}%
   156 \isamarkuptrue%
   156 \isamarkuptrue%
   157 %
   157 %
   158 \isamarkupsection{Tacticals%
   158 \isamarkupsection{Tacticals%
   160 \isamarkuptrue%
   160 \isamarkuptrue%
   161 %
   161 %
   162 \begin{isamarkuptext}%
   162 \begin{isamarkuptext}%
   163 Classic Isabelle provides a huge amount of tacticals for combination
   163 Classic Isabelle provides a huge amount of tacticals for combination
   164   and modification of existing tactics.  This has been greatly reduced
   164   and modification of existing tactics.  This has been greatly reduced
   165   in Isar, providing the bare minimum of combinators only: ``\isa{{\isachardoublequote}{\isacharcomma}{\isachardoublequote}}'' (sequential composition), ``\isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}}'' (alternative
   165   in Isar, providing the bare minimum of combinators only: ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}}'' (sequential composition), ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}}'' (alternative
   166   choices), ``\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}'' (try), ``\isa{{\isachardoublequote}{\isacharplus}{\isachardoublequote}}'' (repeat at least
   166   choices), ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}'' (try), ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequote}}}'' (repeat at least
   167   once).  These are usually sufficient in practice; if all fails,
   167   once).  These are usually sufficient in practice; if all fails,
   168   arbitrary ML tactic code may be invoked via the \hyperlink{method.tactic}{\mbox{\isa{tactic}}}
   168   arbitrary ML tactic code may be invoked via the \hyperlink{method.tactic}{\mbox{\isa{tactic}}}
   169   method (see \secref{sec:tactics}).
   169   method (see \secref{sec:tactics}).
   170 
   170 
   171   \medskip Common ML tacticals may be expressed directly in Isar as
   171   \medskip Common ML tacticals may be expressed directly in Isar as
   172   follows:
   172   follows:
   173 
   173 
   174   \medskip
   174   \medskip
   175   \begin{tabular}{lll}
   175   \begin{tabular}{lll}
   176     \isa{{\isachardoublequote}tac\isactrlsub {\isadigit{1}}{\isachardoublequote}}~\verb|THEN|~\isa{{\isachardoublequote}tac\isactrlsub {\isadigit{2}}{\isachardoublequote}} & & \isa{{\isachardoublequote}meth\isactrlsub {\isadigit{1}}{\isacharcomma}\ meth\isactrlsub {\isadigit{2}}{\isachardoublequote}} \\
   176     \isa{{\isaliteral{22}{\isachardoublequote}}tac\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}~\verb|THEN|~\isa{{\isaliteral{22}{\isachardoublequote}}tac\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}meth\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ meth\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} \\
   177     \isa{{\isachardoublequote}tac\isactrlsub {\isadigit{1}}{\isachardoublequote}}~\verb|ORELSE|~\isa{{\isachardoublequote}tac\isactrlsub {\isadigit{2}}{\isachardoublequote}} & & \isa{{\isachardoublequote}meth\isactrlsub {\isadigit{1}}\ {\isacharbar}\ meth\isactrlsub {\isadigit{2}}{\isachardoublequote}} \\
   177     \isa{{\isaliteral{22}{\isachardoublequote}}tac\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}~\verb|ORELSE|~\isa{{\isaliteral{22}{\isachardoublequote}}tac\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}meth\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{7C}{\isacharbar}}\ meth\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} \\
   178     \verb|TRY|~\isa{tac} & & \isa{{\isachardoublequote}meth{\isacharquery}{\isachardoublequote}} \\
   178     \verb|TRY|~\isa{tac} & & \isa{{\isaliteral{22}{\isachardoublequote}}meth{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}} \\
   179     \verb|REPEAT1|~\isa{tac} & & \isa{{\isachardoublequote}meth{\isacharplus}{\isachardoublequote}} \\
   179     \verb|REPEAT1|~\isa{tac} & & \isa{{\isaliteral{22}{\isachardoublequote}}meth{\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequote}}} \\
   180     \verb|REPEAT|~\isa{tac} & & \isa{{\isachardoublequote}{\isacharparenleft}meth{\isacharplus}{\isacharparenright}{\isacharquery}{\isachardoublequote}} \\
   180     \verb|REPEAT|~\isa{tac} & & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}meth{\isaliteral{2B}{\isacharplus}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}} \\
   181     \verb|EVERY|~\isa{{\isachardoublequote}{\isacharbrackleft}tac\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}{\isachardoublequote}} & & \isa{{\isachardoublequote}meth\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isachardoublequote}} \\
   181     \verb|EVERY|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}tac\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}meth\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\
   182     \verb|FIRST|~\isa{{\isachardoublequote}{\isacharbrackleft}tac\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}{\isachardoublequote}} & & \isa{{\isachardoublequote}meth\isactrlsub {\isadigit{1}}\ {\isacharbar}\ {\isasymdots}{\isachardoublequote}} \\
   182     \verb|FIRST|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}tac\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}meth\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\
   183   \end{tabular}
   183   \end{tabular}
   184   \medskip
   184   \medskip
   185 
   185 
   186   \medskip \verb|CHANGED| (see \cite{isabelle-ref}) is usually not
   186   \medskip \verb|CHANGED| (see \cite{isabelle-ref}) is usually not
   187   required in Isar, since most basic proof methods already fail unless
   187   required in Isar, since most basic proof methods already fail unless
   188   there is an actual change in the goal state.  Nevertheless, ``\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}''  (try) may be used to accept \emph{unchanged} results as
   188   there is an actual change in the goal state.  Nevertheless, ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}''  (try) may be used to accept \emph{unchanged} results as
   189   well.
   189   well.
   190 
   190 
   191   \medskip \verb|ALLGOALS|, \verb|SOMEGOAL| etc.\ (see
   191   \medskip \verb|ALLGOALS|, \verb|SOMEGOAL| etc.\ (see
   192   \cite{isabelle-ref}) are not available in Isar, since there is no
   192   \cite{isabelle-ref}) are not available in Isar, since there is no
   193   direct goal addressing.  Nevertheless, some basic methods address
   193   direct goal addressing.  Nevertheless, some basic methods address
   194   all goals internally, notably \hyperlink{method.simp-all}{\mbox{\isa{simp{\isacharunderscore}all}}} (see
   194   all goals internally, notably \hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}} (see
   195   \secref{sec:simplifier}).  Also note that \verb|ALLGOALS| can be
   195   \secref{sec:simplifier}).  Also note that \verb|ALLGOALS| can be
   196   often replaced by ``\isa{{\isachardoublequote}{\isacharplus}{\isachardoublequote}}'' (repeat at least once), although
   196   often replaced by ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequote}}}'' (repeat at least once), although
   197   this usually has a different operational behavior, such as solving
   197   this usually has a different operational behavior, such as solving
   198   goals in a different order.
   198   goals in a different order.
   199 
   199 
   200   \medskip Iterated resolution, such as \verb|REPEAT (FIRSTGOAL|\isasep\isanewline%
   200   \medskip Iterated resolution, such as \verb|REPEAT (FIRSTGOAL|\isasep\isanewline%
   201 \verb|  (resolve_tac \<dots>))|, is usually better expressed using the \hyperlink{method.intro}{\mbox{\isa{intro}}} and \hyperlink{method.elim}{\mbox{\isa{elim}}} methods of Isar (see
   201 \verb|  (resolve_tac \<dots>))|, is usually better expressed using the \hyperlink{method.intro}{\mbox{\isa{intro}}} and \hyperlink{method.elim}{\mbox{\isa{elim}}} methods of Isar (see