Quelle Quick_Reference.thy

Sprache: Isabelle

(*:maxLineLen=78:*)

theory Quick_Reference
imports Main Base
begin

chapter ‹Isabelle/Isar quick reference \label{ap:refcard}›

section ‹Proof commands›

subsection ‹Main grammar \label{ap:main-grammar}›

text ‹
\begin{tabular}{rcl}
‹main› & = & 🪙‹notepad begin "statement^*" end› \\
& ‹|› & nd='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹theorem name: props if name: props for vars "proof"› \\
& ‹|› & nd='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹theorem name:› \\
& & \quad🪙‹fixes vars› \\
& & \quad🪙‹assumes name: props› \\
& & \quad🪙‹shows name: props "proof"› \\
& ‹|› & nd='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹theorem name:› \\
& & \quad🪙‹fixes vars› \\
& & \quad🪙‹assumes name: props› \\
& & \quad🪙‹obtains (name) vars where props | … "proof"› \\
‹proof› & = & 🪙‹"refinement^*" proper_proof› \\
‹refinement› & = & 🪙‹apply method› \\
& ‹|› & nd='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹supply name = thms› \\
& ‹|› & nd='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹subgoal premises name for vars "proof"› \\
& ‹|› & nd='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹using thms› \\
& ‹|› & nd='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹unfolding thms› \\
‹proper_proof› & = & 🪙‹proof "method^?" "statement^*" qed "method^?"› \\
& ‹|› & nd='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹done› \\
‹statement› & = & 🪙‹{ "statement^*" }› \\
& ‹|› & nd='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹next› \\
& ‹|› & nd='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹note name = thms› \\
& ‹|› & nd='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹let "term" = "term"› \\
& ‹|› & nd='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹write name (mixfix)› \\
& ‹|› & nd='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹fix vars› \\
& ‹|› & nd='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹assume name: props if props for vars› \\
& ‹|› & nd='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹then"^?" goal› \\
‹goal› & = & 🪙‹have name: props if name: props for vars "proof"› \\
& ‹|› & nd='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹show name: props if name: props for vars "proof"› \\
\end{tabular}
›

subsection ‹Primitives›

text ‹
\begin{tabular}{ll}
🪙‹fix x› & augment context by ‹∧x. ◻› \\
🪙‹assume a: A› & augment context by ‹A ==> ◻› \\
🪙‹then› & indicate forward chaining of facts \\
🪙‹have a: A› & prove local result \\
🪙‹show a: A› & prove local result, refining some goal \\
🪙‹using a› & indicate use of additional facts \\
🪙‹unfolding a› & unfold definitional equations \\
🪙‹proof m₁ … qed m₂› & indicate proof structure and refinements \\
🪙‹{ … }› & indicate explicit blocks \\
🪙‹next› & switch proof blocks \\
🪙‹note a = b› & reconsider and declare facts \\
🪙‹let p = t› & abbreviate terms by higher-order matching \\
🪙‹write c (mx)› & declare local mixfix syntax \\
\end{tabular}
›

subsection ‹Abbreviations and synonyms›

text ‹
\begin{tabular}{rcl}
🪙‹by m₁ m₂› & ‹≡› & 🪙‹proof m₁ qed m₂› \\
🪙‹..› & ‹≡› & ntouchend='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹by standard› \\
🪙‹.› & ‹≡› & touchend='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹by this› \\
🪙‹from a› & ‹≡› & 🪙‹note a then› \\
🪙‹with a› & ‹≡› & 🪙‹from a and this› \\
🪙‹from this› & ‹≡› & 🪙‹then› \\
\end{tabular}
›

subsection ‹Derived elements›

text ‹
\begin{tabular}{rcl}
🪙‹also"₀"› & ‹≈› & 🪙‹note calculation = this› \\
🪙‹also"_n₊₁"› & ‹≈› & 🪙‹note calculation = trans [OF calculation this]› \\
🪙‹finally› & ‹≈› & 🪙‹also from calculation› \\[0.5ex]
🪙‹moreover› & ‹≈› & 🪙‹note calculation = calculation this› \\
🪙‹ultimately› & ‹≈› & 🪙‹moreover from calculation› \\[0.5ex]
🪙‹presume a: A› & ‹≈› & 🪙‹assume a: A› \\
🪙‹define x where "x = t"› & ‹≈› & 🪙‹fix x assume x_def: "x = t"› \\
🪙‹consider x where A | …› & ‹≈› & 🪙‹have thesis› \\
& & \quad 🪙‹if "∧x. A ==> thesis" and … for thesis› \\
🪙‹obtain x where a: A 🍋› & ‹≈› & 🪙‹consider x where A 🍋› \\
& & 🪙‹fix x assume a: A› \\
🪙‹case c› & ‹≈› & 🪙‹fix x assume c: A› \\
🪙‹sorry› & ‹≈› & ontouchend='alert("unbekannte/s Formatierung/Symbol theory_text");' >🪙‹by cheating› \\
\end{tabular}
›

subsection ‹Diagnostic commands›

text ‹
\begin{tabular}{ll}
🪙‹typ τ› & print type \\
🪙‹term t› & print term \\
🪙‹prop φ› & print proposition \\
🪙‹thm a› & print fact \\
🪙‹print_statement a› & print fact in long statement form \\
\end{tabular}
›

section ‹Proof methods›

text ‹
\begin{tabular}{ll}
\multicolumn{2}{l}{\‹Single steps (forward-chaining facts)›} \\[0.5ex]
@{method assumption} & apply some goal assumption \\
@{method this} & apply current facts \\
@{method rule}~‹a› & apply some rule \\
@{method standard} & apply standard rule (default for @{command "proof"}) \\
@{method contradiction} & apply ‹¬› elimination rule (any order) \\
@{method cases}~‹t› & case analysis (provides cases) \\
@{method induct}~‹x› & proof by induction (provides cases) \\[2ex]

\multicolumn{2}{l}{\‹Repeated steps (inserting facts)›} \\[0.5ex]
@{method "-"} & no rules \\
@{method intro}~‹a› & introduction rules \\
@{method intro_classes} & class introduction rules \\
@{method intro_locales} & locale introduction rules (without body) \\
@{method unfold_locales} & locale introduction rules (with body) \\
@{method elim}~‹a› & elimination rules \\
@{method unfold}~‹a› & definitional rewrite rules \\[2ex]

\multicolumn{2}{l}{\‹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}{\‹Rules›} \\[0.5ex]
@{attribute OF}~‹a› & rule resolved with facts (skipping ``‹_›'') \\
@{attribute of}~‹t› & rule instantiated with terms (skipping ``‹_›'') \\
@{attribute "where"}~‹x = t› & rule instantiated with terms, by variable name \\
@{attribute symmetric} & resolution with symmetry rule \\
@{attribute THEN}~‹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}{\‹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}‹!› @{attribute Pure.intro}‹!›
& ‹×› & ‹×› \\
@{attribute Pure.elim} @{attribute Pure.intro}
& ‹×› & ‹×› \\
@{attribute elim}‹!› @{attribute intro}‹!›
& ‹×› & & ‹×› & & ‹×› \\
@{attribute elim} @{attribute intro}
& ‹×› & & ‹×› & & ‹×› \\
@{attribute iff}
& ‹×› & & ‹×› & ‹×› & ‹×› \\
@{attribute iff}‹?›
& ‹×› \\
@{attribute elim}‹?› @{attribute intro}‹?›
& ‹×› \\
@{attribute simp}
& & & & ‹×› & ‹×› \\
@{attribute cong}
& & & & ‹×› & ‹×› \\
@{attribute split}
& & & & ‹×› & ‹×› \\
\end{tabular}
›

section ‹Proof scripts›

subsection ‹Commands›

text ‹
\begin{tabular}{ll}
🪙‹apply m› & apply proof method during backwards refinement \\
🪙‹apply_end m› & apply proof method (as if in terminal position) \\
🪙‹supply a› & supply facts during backwards refinement \\
🪙‹subgoal› & nested proof during backwards refinement \\
🪙‹defer n› & move subgoal to end \\
🪙‹prefer n› & move subgoal to start \\
🪙‹back› & backtrack last command \\
🪙‹done› & complete proof \\
\end{tabular}
›

subsection ‹Methods›

text ‹
\begin{tabular}{ll}
@{method rule_tac}~‹insts› & resolution (with instantiation) \\
@{method erule_tac}~‹insts› & elim-resolution (with instantiation) \\
@{method drule_tac}~‹insts› & destruct-resolution (with instantiation) \\
@{method frule_tac}~‹insts› & forward-resolution (with instantiation) \\
@{method cut_tac}~‹insts› & insert facts (with instantiation) \\
@{method thin_tac}~‹φ› & delete assumptions \\
@{method subgoal_tac}~‹φ› & new claims \\
@{method rename_tac}~‹x› & rename innermost goal parameters \\
@{method rotate_tac}~‹n› & rotate assumptions of goal \\
@{method tactic}~‹text› & arbitrary ML tactic \\
@{method case_tac}~‹t› & exhaustion (datatypes) \\
@{method induct_tac}~‹x› & induction (datatypes) \\
@{method ind_cases}~‹t› & exhaustion + simplification (inductive predicates) \\
\end{tabular}
›

end

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