src/Doc/Isar_Ref/Quick_Reference.thy
 author wenzelm Wed Mar 25 11:39:52 2015 +0100 (2015-03-25) changeset 59809 87641097d0f3 parent 58618 782f0b662cae child 60618 4c79543cc376 permissions -rw-r--r--
tuned signature;
 wenzelm@26779  1 theory Quick_Reference  wenzelm@42651  2 imports Base Main  wenzelm@26779  3 begin  wenzelm@26779  4 wenzelm@58618  5 chapter \Isabelle/Isar quick reference \label{ap:refcard}\  wenzelm@26779  6 wenzelm@58618  7 section \Proof commands\  wenzelm@26779  8 wenzelm@58618  9 subsection \Primitives and basic syntax\  wenzelm@26779  10 wenzelm@58618  11 text \  wenzelm@26779  12  \begin{tabular}{ll}  wenzelm@26779  13  @{command "fix"}~@{text x} & augment context by @{text "\x. \"} \\  wenzelm@26779  14  @{command "assume"}~@{text "a: \"} & augment context by @{text "\ \ \"} \\  wenzelm@26779  15  @{command "then"} & indicate forward chaining of facts \\  wenzelm@26779  16  @{command "have"}~@{text "a: \"} & prove local result \\  wenzelm@26779  17  @{command "show"}~@{text "a: \"} & prove local result, refining some goal \\  wenzelm@26779  18  @{command "using"}~@{text a} & indicate use of additional facts \\  wenzelm@26779  19  @{command "unfolding"}~@{text a} & unfold definitional equations \\  wenzelm@26779  20  @{command "proof"}~@{text "m\<^sub>1"}~\dots~@{command "qed"}~@{text "m\<^sub>2"} & indicate proof structure and refinements \\  wenzelm@26852  21  @{command "{"}~@{text "\"}~@{command "}"} & indicate explicit blocks \\  wenzelm@26779  22  @{command "next"} & switch blocks \\  wenzelm@26779  23  @{command "note"}~@{text "a = b"} & reconsider facts \\  wenzelm@26779  24  @{command "let"}~@{text "p = t"} & abbreviate terms by higher-order matching \\  wenzelm@40535  25  @{command "write"}~@{text "c (mx)"} & declare local mixfix syntax \\  wenzelm@26779  26  \end{tabular}  wenzelm@26779  27 wenzelm@26852  28  \medskip  wenzelm@26852  29 wenzelm@26852  30  \begin{tabular}{rcl}  wenzelm@29724  31  @{text "proof"} & = & @{text "prfx\<^sup>*"}~@{command "proof"}~@{text "method\<^sup>? stmt\<^sup>*"}~@{command "qed"}~@{text "method\<^sup>?"} \\  wenzelm@42667  32  & @{text "|"} & @{text "prfx\<^sup>*"}~@{command "done"} \\  wenzelm@26779  33  @{text prfx} & = & @{command "apply"}~@{text method} \\  wenzelm@26852  34  & @{text "|"} & @{command "using"}~@{text "facts"} \\  wenzelm@26852  35  & @{text "|"} & @{command "unfolding"}~@{text "facts"} \\  wenzelm@26779  36  @{text stmt} & = & @{command "{"}~@{text "stmt\<^sup>*"}~@{command "}"} \\  wenzelm@26852  37  & @{text "|"} & @{command "next"} \\  wenzelm@26852  38  & @{text "|"} & @{command "note"}~@{text "name = facts"} \\  wenzelm@26852  39  & @{text "|"} & @{command "let"}~@{text "term = term"} \\  wenzelm@40535  40  & @{text "|"} & @{command "write"}~@{text "name (mixfix)"} \\  wenzelm@26852  41  & @{text "|"} & @{command "fix"}~@{text "var\<^sup>+"} \\  wenzelm@26852  42  & @{text "|"} & @{command "assume"}~@{text "name: props"} \\  wenzelm@26852  43  & @{text "|"} & @{command "then"}@{text "\<^sup>?"}~@{text goal} \\  wenzelm@26780  44  @{text goal} & = & @{command "have"}~@{text "name: props proof"} \\  wenzelm@26852  45  & @{text "|"} & @{command "show"}~@{text "name: props proof"} \\  wenzelm@26852  46  \end{tabular}  wenzelm@58618  47 \  wenzelm@26779  48 wenzelm@26779  49 wenzelm@58618  50 subsection \Abbreviations and synonyms\  wenzelm@26779  51 wenzelm@58618  52 text \  wenzelm@26852  53  \begin{tabular}{rcl}  wenzelm@26852  54  @{command "by"}~@{text "m\<^sub>1 m\<^sub>2"} & @{text "\"} &  wenzelm@26852  55  @{command "proof"}~@{text "m\<^sub>1"}~@{command "qed"}~@{text "m\<^sub>2"} \\  wenzelm@26852  56  @{command ".."} & @{text "\"} & @{command "by"}~@{text rule} \\  wenzelm@26852  57  @{command "."} & @{text "\"} & @{command "by"}~@{text this} \\  wenzelm@26852  58  @{command "hence"} & @{text "\"} & @{command "then"}~@{command "have"} \\  wenzelm@26852  59  @{command "thus"} & @{text "\"} & @{command "then"}~@{command "show"} \\  wenzelm@26852  60  @{command "from"}~@{text a} & @{text "\"} & @{command "note"}~@{text a}~@{command "then"} \\  wenzelm@42667  61  @{command "with"}~@{text a} & @{text "\"} & @{command "from"}~@{text "a \ this"} \\  wenzelm@26852  62  @{command "from"}~@{text this} & @{text "\"} & @{command "then"} \\  wenzelm@26852  63  @{command "from"}~@{text this}~@{command "have"} & @{text "\"} & @{command "hence"} \\  wenzelm@26852  64  @{command "from"}~@{text this}~@{command "show"} & @{text "\"} & @{command "thus"} \\  wenzelm@26852  65  \end{tabular}  wenzelm@58618  66 \  wenzelm@26779  67 wenzelm@26779  68 wenzelm@58618  69 subsection \Derived elements\  wenzelm@26779  70 wenzelm@58618  71 text \  wenzelm@26852  72  \begin{tabular}{rcl}  wenzelm@26852  73  @{command "also"}@{text "\<^sub>0"} & @{text "\"} &  wenzelm@26852  74  @{command "note"}~@{text "calculation = this"} \\  wenzelm@26852  75  @{command "also"}@{text "\<^sub>n\<^sub>+\<^sub>1"} & @{text "\"} &  wenzelm@26852  76  @{command "note"}~@{text "calculation = trans [OF calculation this]"} \\  wenzelm@26852  77  @{command "finally"} & @{text "\"} &  wenzelm@26852  78  @{command "also"}~@{command "from"}~@{text calculation} \\[0.5ex]  wenzelm@26852  79  @{command "moreover"} & @{text "\"} &  wenzelm@26852  80  @{command "note"}~@{text "calculation = calculation this"} \\  wenzelm@26852  81  @{command "ultimately"} & @{text "\"} &  wenzelm@26852  82  @{command "moreover"}~@{command "from"}~@{text calculation} \\[0.5ex]  wenzelm@26852  83  @{command "presume"}~@{text "a: \"} & @{text "\"} &  wenzelm@26852  84  @{command "assume"}~@{text "a: \"} \\  wenzelm@26852  85  @{command "def"}~@{text "a: x \ t"} & @{text "\"} &  wenzelm@26852  86  @{command "fix"}~@{text x}~@{command "assume"}~@{text "a: x \ t"} \\  wenzelm@26852  87  @{command "obtain"}~@{text "x \ a: \"} & @{text "\"} &  wenzelm@26852  88  @{text "\"}~@{command "fix"}~@{text x}~@{command "assume"}~@{text "a: \"} \\  wenzelm@26852  89  @{command "case"}~@{text c} & @{text "\"} &  wenzelm@26852  90  @{command "fix"}~@{text x}~@{command "assume"}~@{text "c: \"} \\  wenzelm@26852  91  @{command "sorry"} & @{text "\"} &  wenzelm@26852  92  @{command "by"}~@{text cheating} \\  wenzelm@26852  93  \end{tabular}  wenzelm@58618  94 \  wenzelm@26779  95 wenzelm@26779  96 wenzelm@58618  97 subsection \Diagnostic commands\  wenzelm@26779  98 wenzelm@58618  99 text \  wenzelm@26779  100  \begin{tabular}{ll}  wenzelm@57479  101  @{command "print_state"} & print proof state \\  wenzelm@57479  102  @{command "print_statement"} & print fact in long statement form \\  wenzelm@26779  103  @{command "thm"}~@{text a} & print fact \\  wenzelm@40536  104  @{command "prop"}~@{text \} & print proposition \\  wenzelm@26779  105  @{command "term"}~@{text t} & print term \\  wenzelm@40536  106  @{command "typ"}~@{text \} & print type \\  wenzelm@26779  107  \end{tabular}  wenzelm@58618  108 \  wenzelm@26779  109 wenzelm@26779  110 wenzelm@58618  111 section \Proof methods\  wenzelm@26779  112 wenzelm@58618  113 text \  wenzelm@26779  114  \begin{tabular}{ll}  wenzelm@26779  115  \multicolumn{2}{l}{\textbf{Single steps (forward-chaining facts)}} \\[0.5ex]  wenzelm@26779  116  @{method assumption} & apply some assumption \\  wenzelm@26779  117  @{method this} & apply current facts \\  wenzelm@26779  118  @{method rule}~@{text a} & apply some rule \\  wenzelm@26779  119  @{method rule} & apply standard rule (default for @{command "proof"}) \\  wenzelm@26779  120  @{method contradiction} & apply @{text "\"} elimination rule (any order) \\  wenzelm@26779  121  @{method cases}~@{text t} & case analysis (provides cases) \\  wenzelm@26779  122  @{method induct}~@{text x} & proof by induction (provides cases) \\[2ex]  wenzelm@26779  123 wenzelm@26779  124  \multicolumn{2}{l}{\textbf{Repeated steps (inserting facts)}} \\[0.5ex]  wenzelm@26779  125  @{method "-"} & no rules \\  wenzelm@26779  126  @{method intro}~@{text a} & introduction rules \\  wenzelm@26779  127  @{method intro_classes} & class introduction rules \\  wenzelm@26779  128  @{method elim}~@{text a} & elimination rules \\  wenzelm@26779  129  @{method unfold}~@{text a} & definitional rewrite rules \\[2ex]  wenzelm@26779  130 wenzelm@26779  131  \multicolumn{2}{l}{\textbf{Automated proof tools (inserting facts)}} \\[0.5ex]  wenzelm@26779  132  @{method iprover} & intuitionistic proof search \\  wenzelm@26779  133  @{method blast}, @{method fast} & Classical Reasoner \\  wenzelm@26779  134  @{method simp}, @{method simp_all} & Simplifier (+ Splitter) \\  wenzelm@26779  135  @{method auto}, @{method force} & Simplifier + Classical Reasoner \\  wenzelm@26779  136  @{method arith} & Arithmetic procedures \\  wenzelm@26779  137  \end{tabular}  wenzelm@58618  138 \  wenzelm@26779  139 wenzelm@26779  140 wenzelm@58618  141 section \Attributes\  wenzelm@26779  142 wenzelm@58618  143 text \  wenzelm@26779  144  \begin{tabular}{ll}  wenzelm@42667  145  \multicolumn{2}{l}{\textbf{Rules}} \\[0.5ex]  wenzelm@26779  146  @{attribute OF}~@{text a} & rule resolved with facts (skipping @{text _}'') \\  wenzelm@26779  147  @{attribute of}~@{text t} & rule instantiated with terms (skipping @{text _}'') \\  wenzelm@26779  148  @{attribute "where"}~@{text "x = t"} & rule instantiated with terms, by variable name \\  wenzelm@26779  149  @{attribute symmetric} & resolution with symmetry rule \\  wenzelm@26779  150  @{attribute THEN}~@{text b} & resolution with another rule \\  wenzelm@26779  151  @{attribute rule_format} & result put into standard rule format \\  wenzelm@26779  152  @{attribute elim_format} & destruct rule turned into elimination rule format \\[1ex]  wenzelm@26779  153 wenzelm@26779  154  \multicolumn{2}{l}{\textbf{Declarations}} \\[0.5ex]  wenzelm@26779  155  @{attribute simp} & Simplifier rule \\  wenzelm@26779  156  @{attribute intro}, @{attribute elim}, @{attribute dest} & Pure or Classical Reasoner rule \\  wenzelm@26779  157  @{attribute iff} & Simplifier + Classical Reasoner rule \\  wenzelm@26779  158  @{attribute split} & case split rule \\  wenzelm@26779  159  @{attribute trans} & transitivity rule \\  wenzelm@26779  160  @{attribute sym} & symmetry rule \\  wenzelm@26779  161  \end{tabular}  wenzelm@58618  162 \  wenzelm@26779  163 wenzelm@26779  164 wenzelm@58618  165 section \Rule declarations and methods\  wenzelm@26779  166 wenzelm@58618  167 text \  wenzelm@26779  168  \begin{tabular}{l|lllll}  wenzelm@26779  169  & @{method rule} & @{method iprover} & @{method blast} & @{method simp} & @{method auto} \\  wenzelm@26779  170  & & & @{method fast} & @{method simp_all} & @{method force} \\  wenzelm@26779  171  \hline  wenzelm@26779  172  @{attribute Pure.elim}@{text "!"} @{attribute Pure.intro}@{text "!"}  wenzelm@26779  173  & @{text "\"} & @{text "\"} \\  wenzelm@26779  174  @{attribute Pure.elim} @{attribute Pure.intro}  wenzelm@26779  175  & @{text "\"} & @{text "\"} \\  wenzelm@26779  176  @{attribute elim}@{text "!"} @{attribute intro}@{text "!"}  wenzelm@26779  177  & @{text "\"} & & @{text "\"} & & @{text "\"} \\  wenzelm@26779  178  @{attribute elim} @{attribute intro}  wenzelm@26779  179  & @{text "\"} & & @{text "\"} & & @{text "\"} \\  wenzelm@26779  180  @{attribute iff}  wenzelm@26779  181  & @{text "\"} & & @{text "\"} & @{text "\"} & @{text "\"} \\  wenzelm@26779  182  @{attribute iff}@{text "?"}  wenzelm@26779  183  & @{text "\"} \\  wenzelm@26779  184  @{attribute elim}@{text "?"} @{attribute intro}@{text "?"}  wenzelm@26779  185  & @{text "\"} \\  wenzelm@26779  186  @{attribute simp}  wenzelm@26779  187  & & & & @{text "\"} & @{text "\"} \\  wenzelm@26779  188  @{attribute cong}  wenzelm@26779  189  & & & & @{text "\"} & @{text "\"} \\  wenzelm@26779  190  @{attribute split}  wenzelm@26779  191  & & & & @{text "\"} & @{text "\"} \\  wenzelm@26779  192  \end{tabular}  wenzelm@58618  193 \  wenzelm@26779  194 wenzelm@26779  195 wenzelm@58618  196 section \Emulating tactic scripts\  wenzelm@26779  197 wenzelm@58618  198 subsection \Commands\  wenzelm@26779  199 wenzelm@58618  200 text \  wenzelm@26779  201  \begin{tabular}{ll}  wenzelm@26779  202  @{command "apply"}~@{text m} & apply proof method at initial position \\  wenzelm@26779  203  @{command "apply_end"}~@{text m} & apply proof method near terminal position \\  wenzelm@26779  204  @{command "done"} & complete proof \\  wenzelm@26779  205  @{command "defer"}~@{text n} & move subgoal to end \\  wenzelm@26779  206  @{command "prefer"}~@{text n} & move subgoal to beginning \\  wenzelm@26779  207  @{command "back"} & backtrack last command \\  wenzelm@26779  208  \end{tabular}  wenzelm@58618  209 \  wenzelm@26779  210 wenzelm@26779  211 wenzelm@58618  212 subsection \Methods\  wenzelm@26779  213 wenzelm@58618  214 text \  wenzelm@26779  215  \begin{tabular}{ll}  wenzelm@26779  216  @{method rule_tac}~@{text insts} & resolution (with instantiation) \\  wenzelm@26779  217  @{method erule_tac}~@{text insts} & elim-resolution (with instantiation) \\  wenzelm@26779  218  @{method drule_tac}~@{text insts} & destruct-resolution (with instantiation) \\  wenzelm@26779  219  @{method frule_tac}~@{text insts} & forward-resolution (with instantiation) \\  wenzelm@26779  220  @{method cut_tac}~@{text insts} & insert facts (with instantiation) \\  wenzelm@26779  221  @{method thin_tac}~@{text \} & delete assumptions \\  wenzelm@26779  222  @{method subgoal_tac}~@{text \} & new claims \\  wenzelm@26779  223  @{method rename_tac}~@{text x} & rename innermost goal parameters \\  wenzelm@26779  224  @{method rotate_tac}~@{text n} & rotate assumptions of goal \\  wenzelm@26779  225  @{method tactic}~@{text "text"} & arbitrary ML tactic \\  wenzelm@26779  226  @{method case_tac}~@{text t} & exhaustion (datatypes) \\  wenzelm@26779  227  @{method induct_tac}~@{text x} & induction (datatypes) \\  wenzelm@26779  228  @{method ind_cases}~@{text t} & exhaustion + simplification (inductive predicates) \\  wenzelm@26779  229  \end{tabular}  wenzelm@58618  230 \  wenzelm@26779  231 wenzelm@26779  232 end