--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/doc-src/IsarRef/Quick_Reference.thy Tue Aug 28 12:45:49 2012 +0200
@@ -0,0 +1,231 @@
+theory Quick_Reference
+imports Base Main
+begin
+
+chapter {* Isabelle/Isar quick reference \label{ap:refcard} *}
+
+section {* Proof commands *}
+
+subsection {* Primitives and basic syntax *}
+
+text {*
+ \begin{tabular}{ll}
+ @{command "fix"}~@{text x} & augment context by @{text "\<And>x. \<box>"} \\
+ @{command "assume"}~@{text "a: \<phi>"} & augment context by @{text "\<phi> \<Longrightarrow> \<box>"} \\
+ @{command "then"} & indicate forward chaining of facts \\
+ @{command "have"}~@{text "a: \<phi>"} & prove local result \\
+ @{command "show"}~@{text "a: \<phi>"} & prove local result, refining some goal \\
+ @{command "using"}~@{text a} & indicate use of additional facts \\
+ @{command "unfolding"}~@{text a} & unfold definitional equations \\
+ @{command "proof"}~@{text "m\<^sub>1"}~\dots~@{command "qed"}~@{text "m\<^sub>2"} & indicate proof structure and refinements \\
+ @{command "{"}~@{text "\<dots>"}~@{command "}"} & indicate explicit blocks \\
+ @{command "next"} & switch blocks \\
+ @{command "note"}~@{text "a = b"} & reconsider facts \\
+ @{command "let"}~@{text "p = t"} & abbreviate terms by higher-order matching \\
+ @{command "write"}~@{text "c (mx)"} & declare local mixfix syntax \\
+ \end{tabular}
+
+ \medskip
+
+ \begin{tabular}{rcl}
+ @{text "proof"} & = & @{text "prfx\<^sup>*"}~@{command "proof"}~@{text "method\<^sup>? stmt\<^sup>*"}~@{command "qed"}~@{text "method\<^sup>?"} \\
+ & @{text "|"} & @{text "prfx\<^sup>*"}~@{command "done"} \\
+ @{text prfx} & = & @{command "apply"}~@{text method} \\
+ & @{text "|"} & @{command "using"}~@{text "facts"} \\
+ & @{text "|"} & @{command "unfolding"}~@{text "facts"} \\
+ @{text stmt} & = & @{command "{"}~@{text "stmt\<^sup>*"}~@{command "}"} \\
+ & @{text "|"} & @{command "next"} \\
+ & @{text "|"} & @{command "note"}~@{text "name = facts"} \\
+ & @{text "|"} & @{command "let"}~@{text "term = term"} \\
+ & @{text "|"} & @{command "write"}~@{text "name (mixfix)"} \\
+ & @{text "|"} & @{command "fix"}~@{text "var\<^sup>+"} \\
+ & @{text "|"} & @{command "assume"}~@{text "name: props"} \\
+ & @{text "|"} & @{command "then"}@{text "\<^sup>?"}~@{text goal} \\
+ @{text goal} & = & @{command "have"}~@{text "name: props proof"} \\
+ & @{text "|"} & @{command "show"}~@{text "name: props proof"} \\
+ \end{tabular}
+*}
+
+
+subsection {* Abbreviations and synonyms *}
+
+text {*
+ \begin{tabular}{rcl}
+ @{command "by"}~@{text "m\<^sub>1 m\<^sub>2"} & @{text "\<equiv>"} &
+ @{command "proof"}~@{text "m\<^sub>1"}~@{command "qed"}~@{text "m\<^sub>2"} \\
+ @{command ".."} & @{text "\<equiv>"} & @{command "by"}~@{text rule} \\
+ @{command "."} & @{text "\<equiv>"} & @{command "by"}~@{text this} \\
+ @{command "hence"} & @{text "\<equiv>"} & @{command "then"}~@{command "have"} \\
+ @{command "thus"} & @{text "\<equiv>"} & @{command "then"}~@{command "show"} \\
+ @{command "from"}~@{text a} & @{text "\<equiv>"} & @{command "note"}~@{text a}~@{command "then"} \\
+ @{command "with"}~@{text a} & @{text "\<equiv>"} & @{command "from"}~@{text "a \<AND> this"} \\
+ @{command "from"}~@{text this} & @{text "\<equiv>"} & @{command "then"} \\
+ @{command "from"}~@{text this}~@{command "have"} & @{text "\<equiv>"} & @{command "hence"} \\
+ @{command "from"}~@{text this}~@{command "show"} & @{text "\<equiv>"} & @{command "thus"} \\
+ \end{tabular}
+*}
+
+
+subsection {* Derived elements *}
+
+text {*
+ \begin{tabular}{rcl}
+ @{command "also"}@{text "\<^sub>0"} & @{text "\<approx>"} &
+ @{command "note"}~@{text "calculation = this"} \\
+ @{command "also"}@{text "\<^sub>n\<^sub>+\<^sub>1"} & @{text "\<approx>"} &
+ @{command "note"}~@{text "calculation = trans [OF calculation this]"} \\
+ @{command "finally"} & @{text "\<approx>"} &
+ @{command "also"}~@{command "from"}~@{text calculation} \\[0.5ex]
+ @{command "moreover"} & @{text "\<approx>"} &
+ @{command "note"}~@{text "calculation = calculation this"} \\
+ @{command "ultimately"} & @{text "\<approx>"} &
+ @{command "moreover"}~@{command "from"}~@{text calculation} \\[0.5ex]
+ @{command "presume"}~@{text "a: \<phi>"} & @{text "\<approx>"} &
+ @{command "assume"}~@{text "a: \<phi>"} \\
+ @{command "def"}~@{text "a: x \<equiv> t"} & @{text "\<approx>"} &
+ @{command "fix"}~@{text x}~@{command "assume"}~@{text "a: x \<equiv> t"} \\
+ @{command "obtain"}~@{text "x \<WHERE> a: \<phi>"} & @{text "\<approx>"} &
+ @{text "\<dots>"}~@{command "fix"}~@{text x}~@{command "assume"}~@{text "a: \<phi>"} \\
+ @{command "case"}~@{text c} & @{text "\<approx>"} &
+ @{command "fix"}~@{text x}~@{command "assume"}~@{text "c: \<phi>"} \\
+ @{command "sorry"} & @{text "\<approx>"} &
+ @{command "by"}~@{text cheating} \\
+ \end{tabular}
+*}
+
+
+subsection {* Diagnostic commands *}
+
+text {*
+ \begin{tabular}{ll}
+ @{command "pr"} & print current state \\
+ @{command "thm"}~@{text a} & print fact \\
+ @{command "prop"}~@{text \<phi>} & print proposition \\
+ @{command "term"}~@{text t} & print term \\
+ @{command "typ"}~@{text \<tau>} & print type \\
+ \end{tabular}
+*}
+
+
+section {* Proof methods *}
+
+text {*
+ \begin{tabular}{ll}
+ \multicolumn{2}{l}{\textbf{Single steps (forward-chaining facts)}} \\[0.5ex]
+ @{method assumption} & apply some assumption \\
+ @{method this} & apply current facts \\
+ @{method rule}~@{text a} & apply some rule \\
+ @{method rule} & apply standard rule (default for @{command "proof"}) \\
+ @{method contradiction} & apply @{text "\<not>"} elimination rule (any order) \\
+ @{method cases}~@{text t} & case analysis (provides cases) \\
+ @{method induct}~@{text x} & proof by induction (provides cases) \\[2ex]
+
+ \multicolumn{2}{l}{\textbf{Repeated steps (inserting facts)}} \\[0.5ex]
+ @{method "-"} & no rules \\
+ @{method intro}~@{text a} & introduction rules \\
+ @{method intro_classes} & class introduction rules \\
+ @{method elim}~@{text a} & elimination rules \\
+ @{method unfold}~@{text a} & definitional rewrite rules \\[2ex]
+
+ \multicolumn{2}{l}{\textbf{Automated proof tools (inserting facts)}} \\[0.5ex]
+ @{method iprover} & intuitionistic proof search \\
+ @{method blast}, @{method fast} & Classical Reasoner \\
+ @{method simp}, @{method simp_all} & Simplifier (+ Splitter) \\
+ @{method auto}, @{method force} & Simplifier + Classical Reasoner \\
+ @{method arith} & Arithmetic procedures \\
+ \end{tabular}
+*}
+
+
+section {* Attributes *}
+
+text {*
+ \begin{tabular}{ll}
+ \multicolumn{2}{l}{\textbf{Rules}} \\[0.5ex]
+ @{attribute OF}~@{text a} & rule resolved with facts (skipping ``@{text _}'') \\
+ @{attribute of}~@{text t} & rule instantiated with terms (skipping ``@{text _}'') \\
+ @{attribute "where"}~@{text "x = t"} & rule instantiated with terms, by variable name \\
+ @{attribute symmetric} & resolution with symmetry rule \\
+ @{attribute THEN}~@{text b} & resolution with another rule \\
+ @{attribute rule_format} & result put into standard rule format \\
+ @{attribute elim_format} & destruct rule turned into elimination rule format \\[1ex]
+
+ \multicolumn{2}{l}{\textbf{Declarations}} \\[0.5ex]
+ @{attribute simp} & Simplifier rule \\
+ @{attribute intro}, @{attribute elim}, @{attribute dest} & Pure or Classical Reasoner rule \\
+ @{attribute iff} & Simplifier + Classical Reasoner rule \\
+ @{attribute split} & case split rule \\
+ @{attribute trans} & transitivity rule \\
+ @{attribute sym} & symmetry rule \\
+ \end{tabular}
+*}
+
+
+section {* Rule declarations and methods *}
+
+text {*
+ \begin{tabular}{l|lllll}
+ & @{method rule} & @{method iprover} & @{method blast} & @{method simp} & @{method auto} \\
+ & & & @{method fast} & @{method simp_all} & @{method force} \\
+ \hline
+ @{attribute Pure.elim}@{text "!"} @{attribute Pure.intro}@{text "!"}
+ & @{text "\<times>"} & @{text "\<times>"} \\
+ @{attribute Pure.elim} @{attribute Pure.intro}
+ & @{text "\<times>"} & @{text "\<times>"} \\
+ @{attribute elim}@{text "!"} @{attribute intro}@{text "!"}
+ & @{text "\<times>"} & & @{text "\<times>"} & & @{text "\<times>"} \\
+ @{attribute elim} @{attribute intro}
+ & @{text "\<times>"} & & @{text "\<times>"} & & @{text "\<times>"} \\
+ @{attribute iff}
+ & @{text "\<times>"} & & @{text "\<times>"} & @{text "\<times>"} & @{text "\<times>"} \\
+ @{attribute iff}@{text "?"}
+ & @{text "\<times>"} \\
+ @{attribute elim}@{text "?"} @{attribute intro}@{text "?"}
+ & @{text "\<times>"} \\
+ @{attribute simp}
+ & & & & @{text "\<times>"} & @{text "\<times>"} \\
+ @{attribute cong}
+ & & & & @{text "\<times>"} & @{text "\<times>"} \\
+ @{attribute split}
+ & & & & @{text "\<times>"} & @{text "\<times>"} \\
+ \end{tabular}
+*}
+
+
+section {* Emulating tactic scripts *}
+
+subsection {* Commands *}
+
+text {*
+ \begin{tabular}{ll}
+ @{command "apply"}~@{text m} & apply proof method at initial position \\
+ @{command "apply_end"}~@{text m} & apply proof method near terminal position \\
+ @{command "done"} & complete proof \\
+ @{command "defer"}~@{text n} & move subgoal to end \\
+ @{command "prefer"}~@{text n} & move subgoal to beginning \\
+ @{command "back"} & backtrack last command \\
+ \end{tabular}
+*}
+
+
+subsection {* Methods *}
+
+text {*
+ \begin{tabular}{ll}
+ @{method rule_tac}~@{text insts} & resolution (with instantiation) \\
+ @{method erule_tac}~@{text insts} & elim-resolution (with instantiation) \\
+ @{method drule_tac}~@{text insts} & destruct-resolution (with instantiation) \\
+ @{method frule_tac}~@{text insts} & forward-resolution (with instantiation) \\
+ @{method cut_tac}~@{text insts} & insert facts (with instantiation) \\
+ @{method thin_tac}~@{text \<phi>} & delete assumptions \\
+ @{method subgoal_tac}~@{text \<phi>} & new claims \\
+ @{method rename_tac}~@{text x} & rename innermost goal parameters \\
+ @{method rotate_tac}~@{text n} & rotate assumptions of goal \\
+ @{method tactic}~@{text "text"} & arbitrary ML tactic \\
+ @{method case_tac}~@{text t} & exhaustion (datatypes) \\
+ @{method induct_tac}~@{text x} & induction (datatypes) \\
+ @{method ind_cases}~@{text t} & exhaustion + simplification (inductive predicates) \\
+ \end{tabular}
+*}
+
+end