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