src/Doc/Isar_Ref/Quick_Reference.thy
author wenzelm
Mon Oct 09 21:12:22 2017 +0200 (23 months ago)
changeset 66822 4642cf4a7ebb
parent 63531 847eefdca90d
permissions -rw-r--r--
tuned signature;
wenzelm@61656
     1
(*:maxLineLen=78:*)
wenzelm@61656
     2
wenzelm@26779
     3
theory Quick_Reference
wenzelm@63531
     4
  imports Main Base
wenzelm@26779
     5
begin
wenzelm@26779
     6
wenzelm@58618
     7
chapter \<open>Isabelle/Isar quick reference \label{ap:refcard}\<close>
wenzelm@26779
     8
wenzelm@58618
     9
section \<open>Proof commands\<close>
wenzelm@26779
    10
wenzelm@62278
    11
subsection \<open>Main grammar \label{ap:main-grammar}\<close>
wenzelm@62270
    12
wenzelm@62270
    13
text \<open>
wenzelm@62270
    14
  \begin{tabular}{rcl}
wenzelm@62270
    15
    \<open>main\<close> & = & \<^theory_text>\<open>notepad begin "statement\<^sup>*" end\<close> \\
wenzelm@63292
    16
    & \<open>|\<close> & \<^theory_text>\<open>theorem name: props if name: props for vars "proof"\<close> \\
wenzelm@62270
    17
    & \<open>|\<close> & \<^theory_text>\<open>theorem name:\<close> \\
wenzelm@63285
    18
    & & \quad\<^theory_text>\<open>fixes vars\<close> \\
wenzelm@62270
    19
    & & \quad\<^theory_text>\<open>assumes name: props\<close> \\
wenzelm@62270
    20
    & & \quad\<^theory_text>\<open>shows name: props "proof"\<close> \\
wenzelm@63286
    21
    & \<open>|\<close> & \<^theory_text>\<open>theorem name:\<close> \\
wenzelm@63286
    22
    & & \quad\<^theory_text>\<open>fixes vars\<close> \\
wenzelm@63286
    23
    & & \quad\<^theory_text>\<open>assumes name: props\<close> \\
wenzelm@63286
    24
    & & \quad\<^theory_text>\<open>obtains (name) vars where props | \<dots> "proof"\<close> \\
wenzelm@63298
    25
    \<open>proof\<close> & = & \<^theory_text>\<open>"refinement\<^sup>*" proper_proof\<close> \\
wenzelm@62270
    26
    \<open>refinement\<close> & = &  \<^theory_text>\<open>apply method\<close> \\
wenzelm@63292
    27
    & \<open>|\<close> & \<^theory_text>\<open>supply name = thms\<close> \\
wenzelm@63286
    28
    & \<open>|\<close> & \<^theory_text>\<open>subgoal premises name for vars "proof"\<close> \\
wenzelm@63292
    29
    & \<open>|\<close> & \<^theory_text>\<open>using thms\<close> \\
wenzelm@63292
    30
    & \<open>|\<close> & \<^theory_text>\<open>unfolding thms\<close> \\
wenzelm@63298
    31
    \<open>proper_proof\<close> & = & \<^theory_text>\<open>proof "method\<^sup>?" "statement\<^sup>*" qed "method\<^sup>?"\<close> \\
wenzelm@63293
    32
    & \<open>|\<close> & \<^theory_text>\<open>done\<close> \\
wenzelm@62270
    33
    \<open>statement\<close> & = & \<^theory_text>\<open>{ "statement\<^sup>*" }\<close> \\
wenzelm@62270
    34
    & \<open>|\<close> & \<^theory_text>\<open>next\<close> \\
wenzelm@63292
    35
    & \<open>|\<close> & \<^theory_text>\<open>note name = thms\<close> \\
wenzelm@62270
    36
    & \<open>|\<close> & \<^theory_text>\<open>let "term" = "term"\<close> \\
wenzelm@62270
    37
    & \<open>|\<close> & \<^theory_text>\<open>write name  (mixfix)\<close> \\
wenzelm@63285
    38
    & \<open>|\<close> & \<^theory_text>\<open>fix vars\<close> \\
wenzelm@63285
    39
    & \<open>|\<close> & \<^theory_text>\<open>assume name: props if props for vars\<close> \\
wenzelm@62270
    40
    & \<open>|\<close> & \<^theory_text>\<open>then"\<^sup>?" goal\<close> \\
wenzelm@63286
    41
    \<open>goal\<close> & = & \<^theory_text>\<open>have name: props if name: props for vars "proof"\<close> \\
wenzelm@63285
    42
    & \<open>|\<close> & \<^theory_text>\<open>show name: props if name: props for vars "proof"\<close> \\
wenzelm@62270
    43
  \end{tabular}
wenzelm@62270
    44
\<close>
wenzelm@62270
    45
wenzelm@62270
    46
wenzelm@62270
    47
subsection \<open>Primitives\<close>
wenzelm@26779
    48
wenzelm@58618
    49
text \<open>
wenzelm@26779
    50
  \begin{tabular}{ll}
wenzelm@62270
    51
    \<^theory_text>\<open>fix x\<close> & augment context by \<open>\<And>x. \<box>\<close> \\
wenzelm@62270
    52
    \<^theory_text>\<open>assume a: A\<close> & augment context by \<open>A \<Longrightarrow> \<box>\<close> \\
wenzelm@62270
    53
    \<^theory_text>\<open>then\<close> & indicate forward chaining of facts \\
wenzelm@62270
    54
    \<^theory_text>\<open>have a: A\<close> & prove local result \\
wenzelm@62270
    55
    \<^theory_text>\<open>show a: A\<close> & prove local result, refining some goal \\
wenzelm@62270
    56
    \<^theory_text>\<open>using a\<close> & indicate use of additional facts \\
wenzelm@62270
    57
    \<^theory_text>\<open>unfolding a\<close> & unfold definitional equations \\
wenzelm@62270
    58
    \<^theory_text>\<open>proof m\<^sub>1 \<dots> qed m\<^sub>2\<close> & indicate proof structure and refinements \\
wenzelm@62270
    59
    \<^theory_text>\<open>{ \<dots> }\<close> & indicate explicit blocks \\
wenzelm@62270
    60
    \<^theory_text>\<open>next\<close> & switch proof blocks \\
wenzelm@62270
    61
    \<^theory_text>\<open>note a = b\<close> & reconsider and declare facts \\
wenzelm@62270
    62
    \<^theory_text>\<open>let p = t\<close> & abbreviate terms by higher-order matching \\
wenzelm@62270
    63
    \<^theory_text>\<open>write c  (mx)\<close> & declare local mixfix syntax \\
wenzelm@26852
    64
  \end{tabular}
wenzelm@58618
    65
\<close>
wenzelm@26779
    66
wenzelm@26779
    67
wenzelm@58618
    68
subsection \<open>Abbreviations and synonyms\<close>
wenzelm@26779
    69
wenzelm@58618
    70
text \<open>
wenzelm@26852
    71
  \begin{tabular}{rcl}
wenzelm@62270
    72
    \<^theory_text>\<open>by m\<^sub>1 m\<^sub>2\<close> & \<open>\<equiv>\<close> & \<^theory_text>\<open>proof m\<^sub>1 qed m\<^sub>2\<close> \\
wenzelm@62270
    73
    \<^theory_text>\<open>..\<close> & \<open>\<equiv>\<close> & \<^theory_text>\<open>by standard\<close> \\
wenzelm@62270
    74
    \<^theory_text>\<open>.\<close> & \<open>\<equiv>\<close> & \<^theory_text>\<open>by this\<close> \\
wenzelm@62270
    75
    \<^theory_text>\<open>from a\<close> & \<open>\<equiv>\<close> & \<^theory_text>\<open>note a then\<close> \\
wenzelm@62270
    76
    \<^theory_text>\<open>with a\<close> & \<open>\<equiv>\<close> & \<^theory_text>\<open>from a and this\<close> \\
wenzelm@62270
    77
    \<^theory_text>\<open>from this\<close> & \<open>\<equiv>\<close> & \<^theory_text>\<open>then\<close> \\
wenzelm@26852
    78
  \end{tabular}
wenzelm@58618
    79
\<close>
wenzelm@26779
    80
wenzelm@26779
    81
wenzelm@58618
    82
subsection \<open>Derived elements\<close>
wenzelm@26779
    83
wenzelm@58618
    84
text \<open>
wenzelm@26852
    85
  \begin{tabular}{rcl}
wenzelm@62270
    86
    \<^theory_text>\<open>also"\<^sub>0"\<close> & \<open>\<approx>\<close> & \<^theory_text>\<open>note calculation = this\<close> \\
wenzelm@62270
    87
    \<^theory_text>\<open>also"\<^sub>n\<^sub>+\<^sub>1"\<close> & \<open>\<approx>\<close> & \<^theory_text>\<open>note calculation = trans [OF calculation this]\<close> \\
wenzelm@62270
    88
    \<^theory_text>\<open>finally\<close> & \<open>\<approx>\<close> & \<^theory_text>\<open>also from calculation\<close> \\[0.5ex]
wenzelm@62270
    89
    \<^theory_text>\<open>moreover\<close> & \<open>\<approx>\<close> & \<^theory_text>\<open>note calculation = calculation this\<close> \\
wenzelm@62270
    90
    \<^theory_text>\<open>ultimately\<close> & \<open>\<approx>\<close> & \<^theory_text>\<open>moreover from calculation\<close> \\[0.5ex]
wenzelm@62270
    91
    \<^theory_text>\<open>presume a: A\<close> & \<open>\<approx>\<close> & \<^theory_text>\<open>assume a: A\<close> \\
wenzelm@63039
    92
    \<^theory_text>\<open>define x where "x = t"\<close> & \<open>\<approx>\<close> & \<^theory_text>\<open>fix x assume x_def: "x = t"\<close> \\
wenzelm@62270
    93
    \<^theory_text>\<open>consider x where A | \<dots>\<close> & \<open>\<approx>\<close> & \<^theory_text>\<open>have thesis\<close> \\
wenzelm@62270
    94
    & & \quad \<^theory_text>\<open>if "\<And>x. A \<Longrightarrow> thesis" and \<dots> for thesis\<close> \\
wenzelm@62270
    95
    \<^theory_text>\<open>obtain x where a: A \<proof>\<close> & \<open>\<approx>\<close> & \<^theory_text>\<open>consider x where A \<proof>\<close> \\
wenzelm@62270
    96
    & & \<^theory_text>\<open>fix x assume a: A\<close> \\
wenzelm@62270
    97
    \<^theory_text>\<open>case c\<close> & \<open>\<approx>\<close> & \<^theory_text>\<open>fix x assume c: A\<close> \\
wenzelm@62270
    98
    \<^theory_text>\<open>sorry\<close> & \<open>\<approx>\<close> & \<^theory_text>\<open>by cheating\<close> \\
wenzelm@26852
    99
  \end{tabular}
wenzelm@58618
   100
\<close>
wenzelm@26779
   101
wenzelm@26779
   102
wenzelm@58618
   103
subsection \<open>Diagnostic commands\<close>
wenzelm@26779
   104
wenzelm@58618
   105
text \<open>
wenzelm@26779
   106
  \begin{tabular}{ll}
wenzelm@62270
   107
    \<^theory_text>\<open>typ \<tau>\<close> & print type \\
wenzelm@62270
   108
    \<^theory_text>\<open>term t\<close> & print term \\
wenzelm@62270
   109
    \<^theory_text>\<open>prop \<phi>\<close> & print proposition \\
wenzelm@62270
   110
    \<^theory_text>\<open>thm a\<close> & print fact \\
wenzelm@62270
   111
    \<^theory_text>\<open>print_statement a\<close> & print fact in long statement form \\
wenzelm@26779
   112
  \end{tabular}
wenzelm@58618
   113
\<close>
wenzelm@26779
   114
wenzelm@26779
   115
wenzelm@58618
   116
section \<open>Proof methods\<close>
wenzelm@26779
   117
wenzelm@58618
   118
text \<open>
wenzelm@26779
   119
  \begin{tabular}{ll}
wenzelm@61477
   120
    \multicolumn{2}{l}{\<^bold>\<open>Single steps (forward-chaining facts)\<close>} \\[0.5ex]
wenzelm@62270
   121
    @{method assumption} & apply some goal assumption \\
wenzelm@26779
   122
    @{method this} & apply current facts \\
wenzelm@61493
   123
    @{method rule}~\<open>a\<close> & apply some rule  \\
wenzelm@60618
   124
    @{method standard} & apply standard rule (default for @{command "proof"}) \\
wenzelm@61493
   125
    @{method contradiction} & apply \<open>\<not>\<close> elimination rule (any order) \\
wenzelm@61493
   126
    @{method cases}~\<open>t\<close> & case analysis (provides cases) \\
wenzelm@61493
   127
    @{method induct}~\<open>x\<close> & proof by induction (provides cases) \\[2ex]
wenzelm@26779
   128
wenzelm@61477
   129
    \multicolumn{2}{l}{\<^bold>\<open>Repeated steps (inserting facts)\<close>} \\[0.5ex]
wenzelm@26779
   130
    @{method "-"} & no rules \\
wenzelm@61493
   131
    @{method intro}~\<open>a\<close> & introduction rules \\
wenzelm@26779
   132
    @{method intro_classes} & class introduction rules \\
wenzelm@62270
   133
    @{method intro_locales} & locale introduction rules (without body) \\
wenzelm@62270
   134
    @{method unfold_locales} & locale introduction rules (with body) \\
wenzelm@61493
   135
    @{method elim}~\<open>a\<close> & elimination rules \\
wenzelm@61493
   136
    @{method unfold}~\<open>a\<close> & definitional rewrite rules \\[2ex]
wenzelm@26779
   137
wenzelm@61477
   138
    \multicolumn{2}{l}{\<^bold>\<open>Automated proof tools (inserting facts)\<close>} \\[0.5ex]
wenzelm@26779
   139
    @{method iprover} & intuitionistic proof search \\
wenzelm@26779
   140
    @{method blast}, @{method fast} & Classical Reasoner \\
wenzelm@26779
   141
    @{method simp}, @{method simp_all} & Simplifier (+ Splitter) \\
wenzelm@26779
   142
    @{method auto}, @{method force} & Simplifier + Classical Reasoner \\
wenzelm@26779
   143
    @{method arith} & Arithmetic procedures \\
wenzelm@26779
   144
  \end{tabular}
wenzelm@58618
   145
\<close>
wenzelm@26779
   146
wenzelm@26779
   147
wenzelm@58618
   148
section \<open>Attributes\<close>
wenzelm@26779
   149
wenzelm@58618
   150
text \<open>
wenzelm@26779
   151
  \begin{tabular}{ll}
wenzelm@61477
   152
    \multicolumn{2}{l}{\<^bold>\<open>Rules\<close>} \\[0.5ex]
wenzelm@61493
   153
    @{attribute OF}~\<open>a\<close> & rule resolved with facts (skipping ``\<open>_\<close>'') \\
wenzelm@61493
   154
    @{attribute of}~\<open>t\<close> & rule instantiated with terms (skipping ``\<open>_\<close>'') \\
wenzelm@61493
   155
    @{attribute "where"}~\<open>x = t\<close> & rule instantiated with terms, by variable name \\
wenzelm@26779
   156
    @{attribute symmetric} & resolution with symmetry rule \\
wenzelm@61493
   157
    @{attribute THEN}~\<open>b\<close> & resolution with another rule \\
wenzelm@26779
   158
    @{attribute rule_format} & result put into standard rule format \\
wenzelm@26779
   159
    @{attribute elim_format} & destruct rule turned into elimination rule format \\[1ex]
wenzelm@26779
   160
wenzelm@61477
   161
    \multicolumn{2}{l}{\<^bold>\<open>Declarations\<close>} \\[0.5ex]
wenzelm@26779
   162
    @{attribute simp} & Simplifier rule \\
wenzelm@26779
   163
    @{attribute intro}, @{attribute elim}, @{attribute dest} & Pure or Classical Reasoner rule \\
wenzelm@26779
   164
    @{attribute iff} & Simplifier + Classical Reasoner rule \\
wenzelm@26779
   165
    @{attribute split} & case split rule \\
wenzelm@26779
   166
    @{attribute trans} & transitivity rule \\
wenzelm@26779
   167
    @{attribute sym} & symmetry rule \\
wenzelm@26779
   168
  \end{tabular}
wenzelm@58618
   169
\<close>
wenzelm@26779
   170
wenzelm@26779
   171
wenzelm@58618
   172
section \<open>Rule declarations and methods\<close>
wenzelm@26779
   173
wenzelm@58618
   174
text \<open>
wenzelm@26779
   175
  \begin{tabular}{l|lllll}
wenzelm@26779
   176
      & @{method rule} & @{method iprover} & @{method blast} & @{method simp} & @{method auto} \\
wenzelm@26779
   177
      &                &                   & @{method fast} & @{method simp_all} & @{method force} \\
wenzelm@26779
   178
    \hline
wenzelm@61493
   179
    @{attribute Pure.elim}\<open>!\<close> @{attribute Pure.intro}\<open>!\<close>
wenzelm@61493
   180
      & \<open>\<times>\<close>    & \<open>\<times>\<close> \\
wenzelm@26779
   181
    @{attribute Pure.elim} @{attribute Pure.intro}
wenzelm@61493
   182
      & \<open>\<times>\<close>    & \<open>\<times>\<close> \\
wenzelm@61493
   183
    @{attribute elim}\<open>!\<close> @{attribute intro}\<open>!\<close>
wenzelm@61493
   184
      & \<open>\<times>\<close>    &                    & \<open>\<times>\<close>          &                     & \<open>\<times>\<close> \\
wenzelm@26779
   185
    @{attribute elim} @{attribute intro}
wenzelm@61493
   186
      & \<open>\<times>\<close>    &                    & \<open>\<times>\<close>          &                     & \<open>\<times>\<close> \\
wenzelm@26779
   187
    @{attribute iff}
wenzelm@61493
   188
      & \<open>\<times>\<close>    &                    & \<open>\<times>\<close>          & \<open>\<times>\<close>         & \<open>\<times>\<close> \\
wenzelm@61493
   189
    @{attribute iff}\<open>?\<close>
wenzelm@61493
   190
      & \<open>\<times>\<close> \\
wenzelm@61493
   191
    @{attribute elim}\<open>?\<close> @{attribute intro}\<open>?\<close>
wenzelm@61493
   192
      & \<open>\<times>\<close> \\
wenzelm@26779
   193
    @{attribute simp}
wenzelm@61493
   194
      &                &                    &                      & \<open>\<times>\<close>         & \<open>\<times>\<close> \\
wenzelm@26779
   195
    @{attribute cong}
wenzelm@61493
   196
      &                &                    &                      & \<open>\<times>\<close>         & \<open>\<times>\<close> \\
wenzelm@26779
   197
    @{attribute split}
wenzelm@61493
   198
      &                &                    &                      & \<open>\<times>\<close>         & \<open>\<times>\<close> \\
wenzelm@26779
   199
  \end{tabular}
wenzelm@58618
   200
\<close>
wenzelm@26779
   201
wenzelm@26779
   202
wenzelm@62270
   203
section \<open>Proof scripts\<close>
wenzelm@26779
   204
wenzelm@58618
   205
subsection \<open>Commands\<close>
wenzelm@26779
   206
wenzelm@58618
   207
text \<open>
wenzelm@26779
   208
  \begin{tabular}{ll}
wenzelm@62270
   209
    \<^theory_text>\<open>apply m\<close> & apply proof method during backwards refinement \\
wenzelm@62270
   210
    \<^theory_text>\<open>apply_end m\<close> & apply proof method (as if in terminal position) \\
wenzelm@62270
   211
    \<^theory_text>\<open>supply a\<close> & supply facts during backwards refinement \\
wenzelm@62270
   212
    \<^theory_text>\<open>subgoal\<close> & nested proof during backwards refinement \\
wenzelm@62270
   213
    \<^theory_text>\<open>defer n\<close> & move subgoal to end \\
wenzelm@62270
   214
    \<^theory_text>\<open>prefer n\<close> & move subgoal to start \\
wenzelm@62270
   215
    \<^theory_text>\<open>back\<close> & backtrack last command \\
wenzelm@62270
   216
    \<^theory_text>\<open>done\<close> & complete proof \\
wenzelm@26779
   217
  \end{tabular}
wenzelm@58618
   218
\<close>
wenzelm@26779
   219
wenzelm@26779
   220
wenzelm@58618
   221
subsection \<open>Methods\<close>
wenzelm@26779
   222
wenzelm@58618
   223
text \<open>
wenzelm@26779
   224
  \begin{tabular}{ll}
wenzelm@61493
   225
    @{method rule_tac}~\<open>insts\<close> & resolution (with instantiation) \\
wenzelm@61493
   226
    @{method erule_tac}~\<open>insts\<close> & elim-resolution (with instantiation) \\
wenzelm@61493
   227
    @{method drule_tac}~\<open>insts\<close> & destruct-resolution (with instantiation) \\
wenzelm@61493
   228
    @{method frule_tac}~\<open>insts\<close> & forward-resolution (with instantiation) \\
wenzelm@61493
   229
    @{method cut_tac}~\<open>insts\<close> & insert facts (with instantiation) \\
wenzelm@61493
   230
    @{method thin_tac}~\<open>\<phi>\<close> & delete assumptions \\
wenzelm@61493
   231
    @{method subgoal_tac}~\<open>\<phi>\<close> & new claims \\
wenzelm@61493
   232
    @{method rename_tac}~\<open>x\<close> & rename innermost goal parameters \\
wenzelm@61493
   233
    @{method rotate_tac}~\<open>n\<close> & rotate assumptions of goal \\
wenzelm@61493
   234
    @{method tactic}~\<open>text\<close> & arbitrary ML tactic \\
wenzelm@61493
   235
    @{method case_tac}~\<open>t\<close> & exhaustion (datatypes) \\
wenzelm@61493
   236
    @{method induct_tac}~\<open>x\<close> & induction (datatypes) \\
wenzelm@61493
   237
    @{method ind_cases}~\<open>t\<close> & exhaustion + simplification (inductive predicates) \\
wenzelm@26779
   238
  \end{tabular}
wenzelm@58618
   239
\<close>
wenzelm@26779
   240
wenzelm@26779
   241
end