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

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