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