(***************************************************************************** * Copyright (c) 2005-2010 ETH Zurich, Switzerland * 2008-2015 Achim D. Brucker, Germany * 2009-2016 Université Paris-Sud, France * 2015-2016 The University of Sheffield, UK * * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions are * met: * * * Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * * Redistributions in binary form must reproduce the above * copyright notice, this list of conditions and the following * disclaimer in the documentation and/or other materials provided * with the distribution. * * * Neither the name of the copyright holders nor the names of its * contributors may be used to endorse or promote products derived * from this software without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. *****************************************************************************) subsection ‹Elementary Firewall Policy Transformation Rules› theory ElementaryRules imports FWNormalisationCore begin text‹ This theory contains those elementary transformation rules which are presented in the ICST 2010 paper~\<^cite>‹"brucker.ea:icst:2010"›. They are not used elsewhere. › lemma elem1: "C (AllowPortFromTo x y p ⊕ DenyAllFromTo x y) = C (DenyAllFromTo x y)" by (rule ext, auto simp: PLemmas) lemma elem2: "C ((a ⊕ b) ⊕ c) = C (a ⊕ (b ⊕ c))" by (simp add: C.simps) lemma elem3: "C (AllowPortFromTo x y a ⊕ AllowPortFromTo x y b) = C (AllowPortFromTo x y b ⊕ AllowPortFromTo x y a)" by (rule ext, auto simp: PLemmas) lemma elem4: "C (a ⊕ DenyAll) = C DenyAll" by (rule ext, auto simp: PLemmas) lemma elem5: "C (DenyAllFromTo x y ⊕ DenyAllFromTo u v) = C (DenyAllFromTo u v ⊕ DenyAllFromTo x y)" by (rule ext, auto simp: PLemmas) lemma elem6: "dom (C a) ∩ dom (C b) = {} ⟹ C (a ⊕ b) = C (b ⊕ a)" by (rule ext, metis C.simps(4) map_add_comm) end