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› &
    & ‹|› & 🪙‹theorem name: props if name: props for vars "proof"› java.lang.NullPointerException
    & ‹|› & 🪙‹theorem name:› java.lang.NullPointerException
    & & \quad🪙‹fixes vars› java.lang.NullPointerException
    & & \quad🪙‹assumes name: props› java.lang.NullPointerException
    & & \quad🪙‹shows name: props "proof"› java.lang.NullPointerException
    & ‹|› & 🪙‹theorem name:› java.lang.NullPointerException
    & & \quad🪙‹fixes vars› java.lang.NullPointerException
    & & \quad🪙‹assumes name: props› java.lang.NullPointerException
    & & \quad🪙‹obtains (name) vars where props | … "proof"› java.lang.NullPointerException
    ‹proof› & = & 🪙‹"refinement🪙*" proper_proof› java.lang.NullPointerException
    ‹refinement› & = &  🪙‹apply method› java.lang.NullPointerException
    & ‹|› & 🪙‹supply name = thms› java.lang.NullPointerException
    & ‹|› & 🪙‹subgoal premises name for vars "proof"› java.lang.NullPointerException
    & ‹|› & 🪙‹using thms› java.lang.NullPointerException
    & ‹|› & 🪙‹unfolding thms› java.lang.NullPointerException
    ‹proper_proof› & = & 🪙‹proof "method🪙?" "statement🪙*" qed "method🪙?"› java.lang.NullPointerException
    & ‹|› & 🪙‹done› java.lang.NullPointerException
    ‹statement› & = & 🪙‹{ "statement🪙*" }› java.lang.NullPointerException
    & ‹|› & 🪙‹next› java.lang.NullPointerException
    & ‹|› & 🪙‹note name = thms› java.lang.NullPointerException
    & ‹|› & 🪙‹let "term" = "term"› java.lang.NullPointerException
    & ‹|› & 🪙‹write name (mixfix)› java.lang.NullPointerException
    & ‹|› & 🪙‹fix vars› java.lang.NullPointerException
    & ‹|› & 🪙‹assume name: props if props for vars› java.lang.NullPointerException
    & ‹|› & 🪙‹then"🪙?" goal› java.lang.NullPointerException
    ‹goal› & = & 🪙‹have name: props if name: props for vars "proof"› java.lang.NullPointerException
    & ‹|› & 🪙‹show name: props if name: props for vars "proof"› java.lang.NullPointerException
  \end{tabular}
›

subsection ‹Primitives›

text ‹
\begin{tabular}{ll}
🪙‹fix x› &
    🪙‹assume a: A› & augment context by ‹A ==> ◻› java.lang.NullPointerException
    🪙‹then› & indicate forward chaining of facts java.lang.NullPointerException
    🪙‹have a: A› & prove local result java.lang.NullPointerException
    🪙‹show a: A› & prove local result, refining some goal java.lang.NullPointerException
    🪙‹using a› & indicate use of additional facts java.lang.NullPointerException
    🪙‹unfolding a› & unfold definitional equations java.lang.NullPointerException
    🪙‹proof m🪙1 … qed m🪙2› & indicate proof structure and refinements java.lang.NullPointerException
    🪙‹{ … }› & indicate explicit blocks java.lang.NullPointerException
    🪙‹next› & switch proof blocks java.lang.NullPointerException
    🪙‹note a = b› & reconsider and declare facts java.lang.NullPointerException
    🪙‹let p = t› & abbreviate terms by higher-order matching java.lang.NullPointerException
    🪙‹write c (mx)› & declare local mixfix syntax java.lang.NullPointerException
  \end{tabular}
›

subsection ‹Abbreviations and synonyms›

text ‹
\begin{tabular}{rcl}
🪙‹by m🪙1 m🪙2› &
    🪙‹..› & ‹≡› & 🪙‹by standard› java.lang.NullPointerException
    🪙‹.› & ‹≡› & 🪙‹by this› java.lang.NullPointerException
    🪙‹from a› & ‹≡› & 🪙‹note a then› java.lang.NullPointerException
    🪙‹with a› & ‹≡› & 🪙‹from a and this› java.lang.NullPointerException
    🪙‹from this› & ‹≡› & 🪙‹then› java.lang.NullPointerException
  \end{tabular}
›

subsection ‹Derived elements›

text ‹
\begin{tabular}{rcl}
🪙‹also"🪙0"› &
    🪙‹also"🪙n🪙+🪙1"› & ‹≈› & 🪙‹note calculation = trans [OF calculation this]› java.lang.NullPointerException
    🪙‹finally› & ‹≈› & 🪙‹also from calculation› \[0.5ex]
    🪙‹moreover› & ‹≈› & 🪙‹note calculation = calculation this› java.lang.NullPointerException
    🪙‹ultimately› & ‹≈› & 🪙‹moreover from calculation› \[0.5ex]
    🪙‹presume a: A› & ‹≈› & 🪙‹assume a: A› java.lang.NullPointerException
    🪙‹define x where "x = t"› & ‹≈› & 🪙‹fix x assume x_def: "x = t"› java.lang.NullPointerException
    🪙‹consider x where A | …› & ‹≈› & 🪙‹have thesis› java.lang.NullPointerException
    & & \quad 🪙‹if "∧x. A ==> thesis" and … for thesis› java.lang.NullPointerException
    🪙‹obtain x where a: A 🍋› & ‹≈› & 🪙‹consider x where A 🍋› java.lang.NullPointerException
    & & 🪙‹fix x assume a: A› java.lang.NullPointerException
    🪙‹case c› & ‹≈› & 🪙‹fix x assume c: A› java.lang.NullPointerException
    🪙‹sorry› & ‹≈› & 🪙‹by cheating› java.lang.NullPointerException
  \end{tabular}
›

subsection ‹Diagnostic commands›

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

section ‹Proof methods›

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

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

    \multicolumn{2}{l}{🪙‹Automated proof tools (inserting facts)›} \[0.5ex]
    @{method iprover} & intuitionistic proof search java.lang.NullPointerException
    @{method blast}, @{method fast} & Classical Reasoner java.lang.NullPointerException
    @{method simp}, @{method simp_all} & Simplifier (+ Splitter) java.lang.NullPointerException
    @{method auto}, @{method force} & Simplifier + Classical Reasoner java.lang.NullPointerException
    @{method arith} & Arithmetic procedures java.lang.NullPointerException
  \end{tabular}
›

section ‹Attributes›

text ‹
\begin{tabular}{ll}
\multicolumn{2}{l}{🪙‹Rules›}
    @{attribute OF}~‹a› & rule resolved with facts (skipping ``‹_›'') java.lang.NullPointerException
    @{attribute of}~‹t› & rule instantiated with terms (skipping ``‹_›'') java.lang.NullPointerException
    @{attribute "where"}~‹x = t› & rule instantiated with terms, by variable name java.lang.NullPointerException
    @{attribute symmetric} & resolution with symmetry rule java.lang.NullPointerException
    @{attribute THEN}~‹b› & resolution with another rule java.lang.NullPointerException
    @{attribute rule_format} & result put into standard rule format java.lang.NullPointerException
    @{attribute elim_format} & destruct rule turned into elimination rule format \[1ex]

    \multicolumn{2}{l}{🪙‹Declarations›} \[0.5ex]
    @{attribute simp} & Simplifier rule java.lang.NullPointerException
    @{attribute intro}, @{attribute elim}, @{attribute dest} & Pure or Classical Reasoner rule java.lang.NullPointerException
    @{attribute iff} & Simplifier + Classical Reasoner rule java.lang.NullPointerException
    @{attribute split} & case split rule java.lang.NullPointerException
    @{attribute trans} & transitivity rule java.lang.NullPointerException
    @{attribute sym} & symmetry rule java.lang.NullPointerException
  \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}‹!› @
      & ‹×›    & ‹×› java.lang.NullPointerException
    @{attribute Pure.elim} @{attribute Pure.intro}
      & ‹×›    & ‹×› java.lang.NullPointerException
    @{attribute elim}‹!› @{attribute intro}‹!›
      & ‹×›    &                    & ‹×›          &                     & ‹×› java.lang.NullPointerException
    @{attribute elim} @{attribute intro}
      & ‹×›    &                    & ‹×›          &                     & ‹×› java.lang.NullPointerException
    @{attribute iff}
      & ‹×›    &                    & ‹×›          & ‹×›         & ‹×› java.lang.NullPointerException
    @{attribute iff}‹?›
      & ‹×› java.lang.NullPointerException
    @{attribute elim}‹?› @{attribute intro}‹?›
      & ‹×› java.lang.NullPointerException
    @{attribute simp}
      &                &                    &                      & ‹×›         & ‹×› java.lang.NullPointerException
    @{attribute cong}
      &                &                    &                      & ‹×›         & ‹×› java.lang.NullPointerException
    @{attribute split}
      &                &                    &                      & ‹×›         & ‹×› java.lang.NullPointerException
  \end{tabular}
›

section ‹Proof scripts›

subsection ‹Commands›

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

subsection ‹Methods›

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

end

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Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

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