181 lines
7.0 KiB
Plaintext
181 lines
7.0 KiB
Plaintext
(*****************************************************************************
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* Copyright (c) 2005-2010 ETH Zurich, Switzerland
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* 2008-2015 Achim D. Brucker, Germany
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* 2009-2016 Université Paris-Sud, France
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* 2015-2016 The University of Sheffield, UK
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*
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are
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* met:
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*
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* * Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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*
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* * Redistributions in binary form must reproduce the above
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* copyright notice, this list of conditions and the following
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* disclaimer in the documentation and/or other materials provided
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* with the distribution.
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*
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* * Neither the name of the copyright holders nor the names of its
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* contributors may be used to endorse or promote products derived
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* from this software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*****************************************************************************)
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subsection \<open>Transforamtion Example 2\<close>
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theory
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Transformation02
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imports
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"../../UPF-Firewall"
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begin
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definition
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FWLink :: "adr\<^sub>i\<^sub>p net" where
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"FWLink = {{(a,b). a = 1}}"
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definition
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any :: "adr\<^sub>i\<^sub>p net" where
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"any = {{(a,b). a > 5}}"
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definition
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i4_32:: "adr\<^sub>i\<^sub>p net" where
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"i4_32 = {{(a,b). a = 2 }}"
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definition
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i10_32:: "adr\<^sub>i\<^sub>p net" where
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"i10_32 = {{(a,b). a = 3 }}"
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definition
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eth_intern:: "adr\<^sub>i\<^sub>p net" where
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"eth_intern = {{(a,b). a = 4 }}"
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definition
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eth_private:: "adr\<^sub>i\<^sub>p net" where
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"eth_private = {{(a,b). a = 5 }}"
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definition
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D1a :: "(adr\<^sub>i\<^sub>p net, port) Combinators" where
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"D1a = AllowPortFromTo eth_intern any 1 \<oplus>
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AllowPortFromTo eth_intern any 2"
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definition
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D1b :: "(adr\<^sub>i\<^sub>p net, port) Combinators" where
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"D1b = AllowPortFromTo eth_private any 1 \<oplus>
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AllowPortFromTo eth_private any 2"
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definition
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D2a :: "(adr\<^sub>i\<^sub>p net, port) Combinators" where
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"D2a = AllowPortFromTo any i4_32 21"
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definition
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D2b :: "(adr\<^sub>i\<^sub>p net, port) Combinators" where
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"D2b = AllowPortFromTo any i10_32 21 \<oplus>
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AllowPortFromTo any i10_32 43"
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definition
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Policy :: "(adr\<^sub>i\<^sub>p net, port) Combinators" where
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"Policy = DenyAll \<oplus> D2b \<oplus> D2a \<oplus> D1b \<oplus> D1a"
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lemmas PolicyLemmas = Policy_def D1a_def D1b_def D2a_def D2b_def
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lemmas PolicyL = Policy_def
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FWLink_def
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any_def
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i10_32_def
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i4_32_def
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eth_intern_def
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eth_private_def
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D1a_def D1b_def D2a_def D2b_def
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consts fixID :: id
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consts fixContent :: DummyContent
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definition "fixElements p = (id p = fixID \<and> content p = fixContent)"
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lemmas fixDefs = fixElements_def NetworkCore.id_def NetworkCore.content_def
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lemma sets_distinct1: "(n::int) \<noteq> m \<Longrightarrow> {(a,b). a = n} \<noteq> {(a,b). a = m}"
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by auto
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lemma sets_distinct2: "(m::int) \<noteq> n \<Longrightarrow> {(a,b). a = n} \<noteq> {(a,b). a = m}"
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by auto
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lemma sets_distinct3: "{((a::int),(b::int)). a = n} \<noteq> {(a,b). a > n}"
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by auto
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lemma sets_distinct4: "{((a::int),(b::int)). a > n} \<noteq> {(a,b). a = n}"
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by auto
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lemma aux: "\<lbrakk>a \<in> c; a \<notin> d; c = d\<rbrakk> \<Longrightarrow> False"
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by auto
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lemma sets_distinct5: "(s::int) < g \<Longrightarrow> {(a::int, b::int). a = s} \<noteq> {(a::int, b::int). g < a}"
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apply (auto simp: sets_distinct3)
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apply (subgoal_tac "(s,4) \<in> {(a::int,b::int). a = (s)}")
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apply (subgoal_tac "(s,4) \<notin> {(a::int,b::int). g < a}")
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apply (erule aux)
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apply assumption+
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apply simp
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by blast
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lemma sets_distinct6: "(s::int) < g \<Longrightarrow> {(a::int, b::int). g < a} \<noteq> {(a::int, b::int). a = s}"
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apply (rule not_sym)
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apply (rule sets_distinct5)
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by simp
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lemma distinctNets: "FWLink \<noteq> any \<and> FWLink \<noteq> i4_32 \<and> FWLink \<noteq> i10_32 \<and>
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FWLink \<noteq> eth_intern \<and> FWLink \<noteq> eth_private \<and> any \<noteq> FWLink \<and> any \<noteq>
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i4_32 \<and> any \<noteq> i10_32 \<and> any \<noteq> eth_intern \<and> any \<noteq> eth_private \<and> i4_32 \<noteq>
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FWLink \<and> i4_32 \<noteq> any \<and> i4_32 \<noteq> i10_32 \<and> i4_32 \<noteq> eth_intern \<and> i4_32 \<noteq>
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eth_private \<and> i10_32 \<noteq> FWLink \<and> i10_32 \<noteq> any \<and> i10_32 \<noteq> i4_32 \<and> i10_32
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\<noteq> eth_intern \<and> i10_32 \<noteq> eth_private \<and> eth_intern \<noteq> FWLink \<and> eth_intern
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\<noteq> any \<and> eth_intern \<noteq> i4_32 \<and> eth_intern \<noteq> i10_32 \<and> eth_intern \<noteq>
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eth_private \<and> eth_private \<noteq> FWLink \<and> eth_private \<noteq> any \<and> eth_private \<noteq>
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i4_32 \<and> eth_private \<noteq> i10_32 \<and> eth_private \<noteq> eth_intern "
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by (simp add: PolicyL sets_distinct1 sets_distinct2 sets_distinct3
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sets_distinct4 sets_distinct5 sets_distinct6)
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lemma aux5: "\<lbrakk>x \<noteq> a; y\<noteq>b; (x \<noteq> y \<and> x \<noteq> b) \<or> (a \<noteq> b \<and> a \<noteq> y)\<rbrakk> \<Longrightarrow> {x,a} \<noteq> {y,b}"
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by auto
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lemma aux2: "{a,b} = {b,a}"
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by auto
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lemma ANDex: "allNetsDistinct (policy2list Policy)"
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apply (simp add: PolicyLemmas allNetsDistinct_def distinctNets)
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apply (simp add: PolicyL)
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by (auto simp: PLemmas PolicyL netsDistinct_def sets_distinct5 sets_distinct6 sets_distinct1
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sets_distinct2)
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fun (sequential) numberOfRules where
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"numberOfRules (a\<oplus>b) = numberOfRules a + numberOfRules b"
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|"numberOfRules a = (1::int)"
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fun numberOfRulesList where
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"numberOfRulesList (x#xs) = ((numberOfRules x)#(numberOfRulesList xs)) "
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|"numberOfRulesList [] = []"
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lemma all_in_list: "all_in_list (policy2list Policy) (Nets_List Policy)"
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apply (simp add: PolicyLemmas)
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apply (unfold Nets_List_def)
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apply (unfold bothNets_def)
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apply (insert distinctNets)
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by simp
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lemmas normalizeUnfold = normalize_def PolicyL Nets_List_def bothNets_def aux aux2 bothNets_def sets_distinct1 sets_distinct2 sets_distinct3 sets_distinct4 sets_distinct5 sets_distinct6 aux5 aux2
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end
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