Quelle csequence_list.pvs Sprache: PVS

%-----------------------------------------------------------------------------
% Conversions between sequences of countable length and the prelude list type.
%
% Author: Jerry James <loganjerry@gmail.com>
%
% This file and its accompanying proof file are distributed under the CC0 1.0
% Universal license: http://creativecommons.org/publicdomain/zero/1.0/.
%
% Version history:
%   2007 Feb 14: PVS 4.0 version
%   2011 May  6: PVS 5.0 version
%   2013 Jan 14: PVS 6.0 version
%-----------------------------------------------------------------------------
csequence_list[T: TYPE]: THEORY
BEGIN

  IMPORTING list[T], list_props[T], csequence_nth[T]

  n: VAR nat
  l: VAR list
  fseq: VAR finite_csequence

  % Convert a list to a finite_csequence
  from_list(l): RECURSIVE finite_csequence =
    IF null?(l) THEN empty_cseq ELSE add(car(l), from_list(cdr(l))) ENDIF
     MEASURE l BY <<

  from_list_length: THEOREM FORALL l: length(from_list(l)) = length(l)

  from_list_index: THEOREM
    FORALL l, n: index?(from_list(l))(n) IFF n < length(l)

  from_list_nth: THEOREM
    FORALL l, (n: below[length(l)]): nth(from_list(l), n) = nth(l, n)

  % Convert a finite_csequence to a list
  to_list(fseq): RECURSIVE list =
    IF empty?(fseq) THEN null
    ELSE cons(first(fseq), to_list(rest(fseq)))
    ENDIF
     MEASURE length(fseq)

  to_list_length: THEOREM FORALL fseq: length(to_list(fseq)) = length(fseq)

  to_list_index: THEOREM
    FORALL fseq, n: n < length(to_list(fseq)) IFF index?(fseq)(n)

  to_list_nth: THEOREM
    FORALL fseq, (n: indexes(fseq)): nth(to_list(fseq), n) = nth(fseq, n)

  % Applying both conversions gives you back what you started with

  to_from_list: THEOREM FORALL l: to_list(from_list(l)) = l

  from_to_list: THEOREM FORALL fseq: from_list(to_list(fseq)) = fseq

END csequence_list

quality91%

¤ Dauer der Verarbeitung: 0.15 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.