doc-src/IsarRef/refcard.tex
author wenzelm
Tue Sep 12 22:13:23 2000 +0200 (2000-09-12)
changeset 9941 fe05af7ec816
parent 9905 14a71104a498
child 10223 31346d22bb54
permissions -rw-r--r--
renamed atts: rulify to rule_format, elimify to elim_format;
     1 
     2 \chapter{Isabelle/Isar Quick Reference}\label{ap:refcard}
     3 
     4 \section{Proof commands}
     5 
     6 \subsection{Primitives and basic syntax}
     7 
     8 \begin{tabular}{ll}
     9   $\FIX{\vec x}$ & augment context by $\All {\vec x} \Box$ \\
    10   $\ASSUME{a}{\vec\phi}$ & augment context by $\vec\phi \Imp \Box$ \\
    11   $\THEN$ & indicate forward chaining \\
    12   $\HAVE{a}{\phi}$ & prove local result \\
    13   $\SHOW{a}{\phi}$ & prove local result, establishing some goal \\
    14   $\PROOF{m@1}~\dots~\QED{m@2}$ & apply proof methods \\
    15   $\BG~\dots~\EN$ & declare explicit blocks \\
    16   $\NEXT$ & switch implicit blocks \\
    17   $\NOTE{a}{\vec b}$ & reconsider facts \\
    18   $\LET{p = t}$ & \Text{abbreviate terms by higher-order matching} \\
    19 \end{tabular}
    20 
    21 \begin{matharray}{rcl}
    22   theory{\dsh}stmt & = & \THEOREM{name}{prop} ~proof \\
    23   & \Or & \LEMMA{name}{prop}~proof \\
    24   & \Or & \TYPES~\dots \Or \CONSTS~\dots \Or \DEFS~\dots \Or \dots \\[1ex]
    25   proof & = & \PROOF{method}~stmt^*~\QED{method} \\[1ex]
    26   stmt & = & \BG~stmt^*~\EN \\
    27   & \Or & \NEXT \\
    28   & \Or & \NOTE{name}{name^+} \\
    29   & \Or & \LET{term = term} \\[0.5ex]
    30   & \Or & \FIX{var^+} \\
    31   & \Or & \ASSUME{name}{prop^+}\\
    32   & \Or & \THEN~goal{\dsh}stmt \\
    33   & \Or & goal{\dsh}stmt \\
    34   goal{\dsh}stmt & = & \HAVE{name}{prop}~proof \\
    35   & \Or & \SHOW{name}{prop}~proof \\
    36 \end{matharray}
    37 
    38 
    39 \subsection{Abbreviations and synonyms}
    40 
    41 \begin{matharray}{rcl}
    42   \BYY{m@1}{m@2} & \equiv & \PROOF{m@1}~\QED{m@2} \\
    43   \DDOT & \equiv & \BY{rule} \\
    44   \DOT & \equiv & \BY{this} \\
    45   \HENCENAME & \equiv & \THEN~\HAVENAME \\
    46   \THUSNAME & \equiv & \THEN~\SHOWNAME \\
    47   \FROM{\vec a} & \equiv & \NOTE{this}{\vec a}~\THEN \\
    48   \WITH{\vec a} & \equiv & \FROM{\vec a~this} \\[1ex]
    49   \FROM{this} & \equiv & \THEN \\
    50   \FROM{this}~\HAVENAME & \equiv & \HENCENAME \\
    51   \FROM{this}~\SHOWNAME & \equiv & \THUSNAME \\
    52 \end{matharray}
    53 
    54 
    55 \subsection{Derived elements}
    56 
    57 \begin{matharray}{rcl}
    58   \ALSO@0 & \approx & \NOTE{calculation}{this} \\
    59   \ALSO@{n+1} & \approx & \NOTE{calculation}{trans~[OF~calculation~this]} \\
    60   \FINALLY & \approx & \ALSO~\FROM{calculation} \\[0.5ex]
    61   \MOREOVER & \approx & \NOTE{calculation}{calculation~this} \\
    62   \ULTIMATELY & \approx & \MOREOVER~\FROM{calculation} \\[0.5ex]
    63   \PRESUME{a}{\vec\phi} & \approx & \ASSUME{a}{\vec\phi} \\
    64 %  & & \Text{(permissive assumption)} \\
    65   \DEF{a}{x \equiv t} & \approx & \FIX{x}~\ASSUME{a}{x \equiv t} \\
    66 %  & & \Text{(definitional assumption)} \\
    67   \OBTAIN{\vec x}{a}{\vec\phi} & \approx & \dots~\FIX{\vec x}~\ASSUME{a}{\vec\phi} \\
    68 %  & & \Text{(generalized existence)} \\
    69   \CASE{c} & \approx & \FIX{\vec x}~\ASSUME{c}{\vec\phi} \\
    70 %  & & \Text{(named context)} \\[0.5ex]
    71   \SORRY & \approx & \BY{cheating} \\
    72 \end{matharray}
    73 
    74 
    75 \subsection{Diagnostic commands}
    76 
    77 \begin{matharray}{ll}
    78   \isarkeyword{pr} & \Text{print current state} \\
    79   \isarkeyword{thm}~\vec a & \Text{print theorems} \\
    80   \isarkeyword{term}~t & \Text{print term} \\
    81   \isarkeyword{prop}~\phi & \Text{print meta-level proposition} \\
    82   \isarkeyword{typ}~\tau & \Text{print meta-level type} \\
    83 \end{matharray}
    84 
    85 
    86 \section{Proof methods}
    87 
    88 \begin{tabular}{ll}
    89   \multicolumn{2}{l}{\textbf{Single steps (forward-chaining facts)}} \\[0.5ex]
    90   $assumption$ & apply some assumption \\
    91   $this$ & apply current facts \\
    92   $rule~\vec a$ & apply some rule  \\
    93   $rule$ & apply standard rule (default for $\PROOFNAME$) \\
    94   $contradiction$ & apply $\neg{}$ elimination rule (any order) \\
    95   $cases~t$ & case analysis (provides cases) \\
    96   $induct~\vec x$ & proof by induction (provides cases) \\[2ex]
    97 
    98   \multicolumn{2}{l}{\textbf{Repeated steps (inserting facts)}} \\[0.5ex]
    99   $-$ & \Text{no rules} \\
   100   $intro~\vec a$ & \Text{introduction rules} \\
   101   $intro_classes$ & \Text{class introduction rules} \\
   102   $elim~\vec a$ & \Text{elimination rules} \\
   103   $unfold~\vec a$ & \Text{definitions} \\[2ex]
   104 
   105   \multicolumn{2}{l}{\textbf{Automated proof tools (inserting facts, or even prems!)}} \\[0.5ex]
   106   $simp$, $simp_all$ & Simplifier (+ Splitter) \\
   107   $blast$, $fast$ & Classical Reasoner \\
   108   $auto$, $force$ & Simplifier + Classical Reasoner \\
   109   $arith$ & Arithmetic procedure \\
   110 \end{tabular}
   111 
   112 
   113 \section{Attributes}
   114 
   115 \begin{tabular}{ll}
   116   \multicolumn{2}{l}{\textbf{Operations}} \\[0.5ex]
   117   $OF~\vec a$ & rule applied to facts (skipping ``$_$'') \\
   118   $of~\vec t$ & rule applied to terms (skipping ``$_$'') \\
   119   $symmetric$ & resolution with symmetry of equality \\
   120   $THEN~b$ & resolution with other rule \\
   121   $rule_format$ & result put into standard rule format \\
   122   $elim_format$ & destruct rule turned into elimination rule format \\
   123   $standard$ & result put into standard form \\[1ex]
   124 
   125   \multicolumn{2}{l}{\textbf{Declarations}} \\[0.5ex]
   126   $simp$ & Simplifier rule \\
   127   $intro$, $elim$, $dest$ & Classical Reasoner rule \\
   128   $iff$ & Simplifier + Classical Reasoner rule \\
   129   $split$ & case split rule \\
   130   $trans$ & transitivity rule \\
   131 \end{tabular}
   132 
   133 
   134 \section{Emulating tactic scripts}
   135 
   136 \subsection{Commands}
   137 
   138 \begin{tabular}{ll}
   139   $\isarkeyword{apply}~(m)$ & apply proof method at initial position \\
   140   $\isarkeyword{apply_end}~(m)$ & apply proof method near terminal position \\
   141   $\isarkeyword{done}$ & complete proof \\
   142   $\isarkeyword{defer}~n$ & move subgoal to end \\
   143   $\isarkeyword{prefer}~n$ & move subgoal to beginning \\
   144   $\isarkeyword{back}$ & backtrack last command \\
   145   $\isarkeyword{declare}$ & declare rules in current theory \\
   146 \end{tabular}
   147 
   148 \subsection{Methods}
   149 
   150 \begin{tabular}{ll}
   151   $rule_tac~insts$ & resolution (with instantiation) \\
   152   $erule_tac~insts$ & elim-resolution (with instantiation) \\
   153   $drule_tac~insts$ & destruct-resolution (with instantiation) \\
   154   $frule_tac~insts$ & forward-resolution (with instantiation) \\
   155   $cut_tac~insts$ & insert facts (with instantiation) \\
   156   $thin_tac~\phi$ & delete assumptions \\
   157   $subgoal_tac~\phi$ & new claims \\
   158   $rename_tac~\vec x$ & rename suffix of goal parameters \\
   159   $rotate_tac~n$ & rotate assumptions of goal \\
   160   $tactic~text$ & arbitrary ML tactic \\
   161   $case_tac~t$ & exhaustion (datatypes) \\
   162   $induct_tac~\vec x$ & induction (datatypes) \\
   163   $ind_cases~t$ & exhaustion + simplification (inductive sets) \\
   164 \end{tabular}
   165 
   166 
   167 %%% Local Variables:
   168 %%% mode: latex
   169 %%% TeX-master: "isar-ref"
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