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 "print_state"} & 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