Quelle sum_orders.pvs Sprache: PVS

%------------------------------------------------------------------------------
% Pointwise Ordering in Disjoint Union types
%
%       Author: David Lester <dlester@cs.man.ac.uk> Manchester University
%
%       Version 1.0          03/30/06
%------------------------------------------------------------------------------

sum_orders[T1,T2:TYPE]: THEORY

BEGIN

  r1:  VAR pred[[T1,T1]]
  r2:  VAR pred[[T2,T2]]
  x,y: VAR union[T1,T2]

  ; % syntax

  +(r1,r2)(x,y):bool = (inl?(x) AND inl?(y) AND r1(left(x), left(y))) OR
                       (inr?(x) AND inr?(y) AND r2(right(x),right(y)))

  sum_preserves_reflexive: JUDGEMENT
   +(r1:(reflexive?[T1]),r2:(reflexive?[T2]))
                                           HAS_TYPE (reflexive?[union[T1,T2]])

  sum_preserves_transitive: JUDGEMENT
   +(r1:(transitive?[T1]),r2:(transitive?[T2]))
                                           HAS_TYPE (transitive?[union[T1,T2]])

  sum_preserves_antisymmetric: JUDGEMENT
   +(r1:(antisymmetric?[T1]),r2:(antisymmetric?[T2]))
                                        HAS_TYPE (antisymmetric?[union[T1,T2]])

  sum_preserves_preorder: JUDGEMENT
   +(r1:(preorder?[T1]),r2:(preorder?[T2]))
                           HAS_TYPE (preorder?[union[T1,T2]])

  sum_preserves_partial_order: JUDGEMENT
   +(r1:(partial_order?[T1]),r2:(partial_order?[T2]))
                                        HAS_TYPE (partial_order?[union[T1,T2]])

  IMPORTING directed_orders[T1], directed_orders[T2],
            directed_orders[union[T1,T2]]

  sum_preserves_directed_complete: JUDGEMENT
   +(r1:(directed_complete?[T1]),r2:(directed_complete?[T2]))
                   HAS_TYPE (directed_complete?[union[T1,T2]])

  sum_preserves_directed_complete_partial_order: JUDGEMENT
   +(r1:(directed_complete_partial_order?[T1]),
     r2:(directed_complete_partial_order?[T2]))
                   HAS_TYPE (directed_complete_partial_order?[union[T1,T2]])

END sum_orders

quality91%

¤ Dauer der Verarbeitung: 0.1 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.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.