Quelle coalition_fun.pvs Sprache: PVS

%---------------------------------------------------------------------
% A formal theory of cooperative TU-games in PVS 4.2
%
% Author: Erik Martin-Dorel,
% University Montpellier 2 & University of Perpignan
%
%   THEORIES players_set[U] and
%            coalition_fun[U,N]
%
%   Version 1.0    2009/05/01    Initial version
%   Version 1.1    2009/05/10    Identifiers renamed
%   Version 1.2    2009/05/14    Lemmas added
%   Version 1.3    2009/10/03    Conversion avoided in Judgement proof
%
% This work has been done at the University of Perpignan
% within the Master's Thesis, under the supervision of
% Marc Daumas and Annick Truffert, with the help of Michel Ventou
%
% This library is available under GNU Lesser General Public License,
% either version 3 of the Licence, or any later version
%---------------------------------------------------------------------

%players_set[U: TYPE+]: THEORY
% BEGIN
%  elt: U
%  players_set: TYPE+ = non_empty_finite_set[U] CONTAINING singleton(elt)
% END players_set

coalition_fun[U: TYPE+,       (IMPORTING players_set[U])
              N: players_set]: THEORY
BEGIN

  IMPORTING players_set[U]

  powset: TYPE = setof[(N)] % rather than (powerset[U](N))

  fullN: powset = fullset[(N)]

  v: VAR [powset -> real]
  S: VAR powset
  x, y: VAR [(N) -> real]
  i: VAR (N)
  c: VAR real
  a: VAR nzreal

  zero_fun(S): real = 0
  coalition_fun?(v): bool = v(emptyset) = 0
  coalition_fun: TYPE+ = (coalition_fun?) CONTAINING zero_fun

  subsets_are_finite: JUDGEMENT setof[(N)] SUBTYPE_OF finite_set[(N)]

  IMPORTING %finite_sets@finite_sets_sum[(N),real,0,+],
            finite_sets@finite_sets_sum_real[(N)]

  tot(S, x): real = sum(S, x)

  tot_S_0: LEMMA tot(S, LAMBDA i: 0) = 0
  tot_distrib: LEMMA tot(S, LAMBDA i: x(i) + y(i)) = tot(S, x) + tot(S, y)
  tot_mult_const:  LEMMA tot(S, LAMBDA i: c * x(i)) = c * tot(S,x)
  tot_distrib_sub: LEMMA tot(S, LAMBDA i: x(i) - y(i)) = tot(S, x) - tot(S, y)
  tot_div_const:   LEMMA tot(S, LAMBDA i: x(i) / a) = tot(S,x) / a

  set_vect: TYPE = setof[[(N) -> real]]

END coalition_fun

%---------------------------------------------------------------------
% License for use and distribution
%
% Copyright (C) 2009 Erik Martin-Dorel.
%
% GNU LGPL information:
% ---------------------
%
% This library is free software: you can redistribute it and/or
% modify it under the terms of the GNU Lesser General Public License
% as published by the Free Software Foundation, either version 3 of
% the License, or (at your option) any later version.
%
% This library is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU Lesser General Public
% License along with this library.
% If not, see <http://www.gnu.org/licenses/>.
%---------------------------------------------------------------------

quality65%

¤ Dauer der Verarbeitung: 0.14 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.