Ziele Untersuchung
mit Columbo Integrität von
Datenbanken Interaktion und
Portierbarkeit Ergonomie der
Schnittstellen

Angebot Produkte Projekt Beratung

Mittel Analytik Modellierung Sprachen Algebra Logik Hardware Denken Kreativität

Zusammenhänge Gesellschaft Wirtschaft Branche Firma


products/Sources/formale Sprachen/PVS/Bernstein/ (Beweissystem der NASA Version 6.0.9^©) Datei vom 8.10.2014 mit Größe 5 kB

Quelle Outcome_adt.pvs Sprache: PVS

%%% ADT file generated from Outcome

Outcome_adt: THEORY
BEGIN

  Outcome: TYPE

  IMPORTING list[real]

  istrue?, isfalse?, unknown?: [Outcome -> boolean]

  counterexample: [(isfalse?) -> (cons?)]

  IsTrue: (istrue?)

  Counterexample: [(cons?) -> (isfalse?)]

  Unknown: (unknown?)

  Outcome_ord: [Outcome -> upto(2)]

  Outcome_ord_defaxiom: AXIOM
    Outcome_ord(IsTrue) = 0 AND
     (FORALL (counterexample: (cons?)):
        Outcome_ord(Counterexample(counterexample)) = 1)
      AND Outcome_ord(Unknown) = 2;

  ord(x: Outcome): [Outcome -> upto(2)] =
      CASES x
        OF IsTrue: 0, Counterexample(Counterexample1_var): 1, Unknown: 2
        ENDCASES

  Outcome_IsTrue_extensionality: AXIOM
    FORALL (istrue?_var: (istrue?), istrue?_var2: (istrue?)):
      istrue?_var = istrue?_var2;

  Outcome_Counterexample_extensionality: AXIOM
    FORALL (isfalse?_var: (isfalse?), isfalse?_var2: (isfalse?)):
      counterexample(isfalse?_var) = counterexample(isfalse?_var2) IMPLIES
       isfalse?_var = isfalse?_var2;

  Outcome_Counterexample_eta: AXIOM
    FORALL (isfalse?_var: (isfalse?)):
      Counterexample(counterexample(isfalse?_var)) = isfalse?_var;

  Outcome_Unknown_extensionality: AXIOM
    FORALL (unknown?_var: (unknown?), unknown?_var2: (unknown?)):
      unknown?_var = unknown?_var2;

  Outcome_counterexample_Counterexample: AXIOM
    FORALL (Counterexample1_var: (cons?)):
      counterexample(Counterexample(Counterexample1_var)) =
       Counterexample1_var;

  Outcome_inclusive: AXIOM
    FORALL (Outcome_var: Outcome):
      istrue?(Outcome_var) OR
       isfalse?(Outcome_var) OR unknown?(Outcome_var);

  Outcome_induction: AXIOM
    FORALL (p: [Outcome -> boolean]):
      p(IsTrue) AND
       (FORALL (Counterexample1_var: (cons?)):
          p(Counterexample(Counterexample1_var)))
        AND p(Unknown)
       IMPLIES (FORALL (Outcome_var: Outcome): p(Outcome_var));

  subterm(x: Outcome, y: Outcome):  boolean = x = y;

  <<:  (strict_well_founded?[Outcome]) = LAMBDA (x, y: Outcome): FALSE;

  Outcome_well_founded: AXIOM strict_well_founded?[Outcome](<<);

  reduce_nat(istrue?_fun: nat, isfalse?_fun: [(cons?) -> nat],
             unknown?_fun: nat):
        [Outcome -> nat] =
      LAMBDA (Outcome_adtvar: Outcome):
        LET red: [Outcome -> nat] =
              reduce_nat(istrue?_fun, isfalse?_fun, unknown?_fun)
          IN
          CASES Outcome_adtvar
            OF IsTrue: istrue?_fun,
               Counterexample(Counterexample1_var):
                 isfalse?_fun(Counterexample1_var),
               Unknown: unknown?_fun
            ENDCASES;

  REDUCE_nat(istrue?_fun: [Outcome -> nat],
             isfalse?_fun: [[(cons?), Outcome] -> nat],
             unknown?_fun: [Outcome -> nat]):
        [Outcome -> nat] =
      LAMBDA (Outcome_adtvar: Outcome):
        LET red: [Outcome -> nat] =
              REDUCE_nat(istrue?_fun, isfalse?_fun, unknown?_fun)
          IN
          CASES Outcome_adtvar
            OF IsTrue: istrue?_fun(Outcome_adtvar),
               Counterexample(Counterexample1_var):
                 isfalse?_fun(Counterexample1_var, Outcome_adtvar),
               Unknown: unknown?_fun(Outcome_adtvar)
            ENDCASES;

  reduce_ordinal(istrue?_fun: ordinal, isfalse?_fun: [(cons?) -> ordinal],
                 unknown?_fun: ordinal):
        [Outcome -> ordinal] =
      LAMBDA (Outcome_adtvar: Outcome):
        LET red: [Outcome -> ordinal] =
              reduce_ordinal(istrue?_fun, isfalse?_fun, unknown?_fun)
          IN
          CASES Outcome_adtvar
            OF IsTrue: istrue?_fun,
               Counterexample(Counterexample1_var):
                 isfalse?_fun(Counterexample1_var),
               Unknown: unknown?_fun
            ENDCASES;

  REDUCE_ordinal(istrue?_fun: [Outcome -> ordinal],
                 isfalse?_fun: [[(cons?), Outcome] -> ordinal],
                 unknown?_fun: [Outcome -> ordinal]):
        [Outcome -> ordinal] =
      LAMBDA (Outcome_adtvar: Outcome):
        LET red: [Outcome -> ordinal] =
              REDUCE_ordinal(istrue?_fun, isfalse?_fun, unknown?_fun)
          IN
          CASES Outcome_adtvar
            OF IsTrue: istrue?_fun(Outcome_adtvar),
               Counterexample(Counterexample1_var):
                 isfalse?_fun(Counterexample1_var, Outcome_adtvar),
               Unknown: unknown?_fun(Outcome_adtvar)
            ENDCASES;
END Outcome_adt

Outcome_adt_reduce[range: TYPE]: THEORY
BEGIN

  IMPORTING Outcome_adt

  IMPORTING list[real]

  reduce(istrue?_fun: range, isfalse?_fun: [(cons?) -> range],
         unknown?_fun: range):
        [Outcome -> range] =
      LAMBDA (Outcome_adtvar: Outcome):
        LET red: [Outcome -> range] =
              reduce(istrue?_fun, isfalse?_fun, unknown?_fun)
          IN
          CASES Outcome_adtvar
            OF IsTrue: istrue?_fun,
               Counterexample(Counterexample1_var):
                 isfalse?_fun(Counterexample1_var),
               Unknown: unknown?_fun
            ENDCASES;

  REDUCE(istrue?_fun: [Outcome -> range],
         isfalse?_fun: [[(cons?), Outcome] -> range],
         unknown?_fun: [Outcome -> range]):
        [Outcome -> range] =
      LAMBDA (Outcome_adtvar: Outcome):
        LET red: [Outcome -> range] =
              REDUCE(istrue?_fun, isfalse?_fun, unknown?_fun)
          IN
          CASES Outcome_adtvar
            OF IsTrue: istrue?_fun(Outcome_adtvar),
               Counterexample(Counterexample1_var):
                 isfalse?_fun(Counterexample1_var, Outcome_adtvar),
               Unknown: unknown?_fun(Outcome_adtvar)
            ENDCASES;
END Outcome_adt_reduce

quality92%

¤ Dauer der Verarbeitung: 0.10 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.