Initial commit.

Examples/DMZ/DMZ.thy

@@ -0,0 +1,75 @@
+(*****************************************************************************
+ * 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.
+ *****************************************************************************)
+
+section {* A Simple DMZ Setup *}
+theory 
+  DMZ
+imports 
+  DMZDatatype
+  DMZInteger
+begin
+
+text{* This scenario is slightly more complicated than the SimpleDMZ
+one, as we now also model specific servers within one
+network. Therefore, we cannot use anymore the modelling using
+datatype synonym, but only use the one where an address is modelled as an
+integer (with ports).
+
+The scenario is the following:
+
+\begin{labeling}{Networks:}
+\item[Networks:]
+  \begin{itemize}
+  \item Intranet (Company intern network)
+  \item DMZ (demilitarised zone, servers, etc), containing
+     at least two distinct servers ``mail'' and ``web''
+  \item Internet (``all others'') 
+  \end{itemize}
+\item[Policy:]
+  \begin{itemize}
+  \item allow http(s) from Intranet to Internet
+  \item deny all trafic from Internet to Intranet
+  \item allo imaps and smtp from intranet to mailserver
+  \item allow smtp from Internet to mailserver
+  \item allow http(s) from Internet to webserver 
+  \item deny everything else
+  \end{itemize}
+  
+\end{labeling}
+*}
+
+end

Examples/DMZ/DMZDatatype.thy

@@ -0,0 +1,120 @@
+(*****************************************************************************
+ * 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 {* DMZ Datatype *}
+theory 
+  DMZDatatype
+imports 
+    "../../UPF-Firewall"
+begin
+
+text{* This is the fourth scenario, slightly more complicated than the
+previous one, as we now also model specific servers within one
+network. Therefore, we could not use anymore the modelling using
+datatype synonym, but only use the one where an address is modelled as an
+integer (with ports). 
+
+Just for comparison, this theory is the same scenario with datatype synonym
+anyway, but with four distinct networks instead of one contained in
+another. As there is no corresponding network model included, we need
+to define a custom one.  *}
+
+
+datatype Adr = Intranet | Internet | Mail | Web | DMZ
+instance Adr::adr ..
+type_synonym port = int
+type_synonym Networks = "Adr \<times> port"
+
+
+definition
+  intranet::"Networks net" where
+ "intranet = {{(a,b). a= Intranet}}"
+definition
+  dmz :: "Networks net" where
+ "dmz = {{(a,b). a= DMZ}}"
+definition
+  mail :: "Networks net" where
+ "mail = {{(a,b). a=Mail}}" 
+definition
+  web :: "Networks net" where
+ "web = {{(a,b). a=Web}}" 
+definition
+  internet :: "Networks net" where 
+ "internet = {{(a,b). a= Internet}}"
+
+definition 
+  Intranet_mail_port :: "(Networks ,DummyContent) FWPolicy" where
+  "Intranet_mail_port = (allow_from_ports_to {21::port,14} intranet mail)" 
+
+definition
+  Intranet_Internet_port :: "(Networks,DummyContent) FWPolicy" where
+  "Intranet_Internet_port = allow_from_ports_to {80::port,90} intranet internet"
+     
+definition
+  Internet_web_port :: "(Networks,DummyContent) FWPolicy" where
+  "Internet_web_port = (allow_from_ports_to {80::port,90} internet web)"
+          
+definition
+  Internet_mail_port :: "(Networks,DummyContent) FWPolicy" where
+  "Internet_mail_port =  (allow_all_from_port_to internet (21::port) dmz)"
+
+definition 
+  policyPort :: "(Networks, DummyContent) FWPolicy" where
+ "policyPort = deny_all ++ 
+                  Intranet_Internet_port ++ 
+                  Intranet_mail_port ++  
+                  Internet_mail_port ++ 
+                  Internet_web_port"
+
+
+text {* We only want to create test cases which are sent between the
+three main networks --- e.g. not between the mailserver and the
+dmz. Therefore, the constraint looks as follows. *}
+
+definition
+ not_in_same_net :: "(Networks,DummyContent) packet \<Rightarrow> bool" where
+ "not_in_same_net x  =  ((src x \<sqsubset> internet \<longrightarrow> \<not> dest x \<sqsubset> internet) \<and> 
+                        (src x \<sqsubset> intranet \<longrightarrow> \<not> dest x \<sqsubset> intranet) \<and> 
+                        (src x \<sqsubset> dmz \<longrightarrow> \<not> dest x \<sqsubset> dmz))"
+
+lemmas PolicyLemmas =   dmz_def internet_def intranet_def mail_def web_def 
+                       Internet_web_port_def Internet_mail_port_def
+                       Intranet_Internet_port_def Intranet_mail_port_def 
+                       src_def dest_def src_port dest_port in_subnet_def
+
+
+end

Examples/DMZ/DMZInteger.thy

@@ -0,0 +1,133 @@
+(*****************************************************************************
+ * 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 {* DMZ: Integer *}
+theory 
+  DMZInteger
+imports 
+  "../../UPF-Firewall"
+begin
+
+text{* This scenario is slightly more complicated than the SimpleDMZ
+one, as we now also model specific servers within one
+network. Therefore, we cannot use anymore the modelling using
+datatype synonym, but only use the one where an address is modelled as an
+integer (with ports).
+
+The scenario is the following:
+
+\begin{labeling}{Networks:}
+\item[Networks:]
+  \begin{itemize}
+  \item Intranet (Company intern network)
+  \item DMZ (demilitarised zone, servers, etc), containing
+     at least two distinct servers ``mail'' and ``web''
+  \item Internet (``all others'') 
+  \end{itemize}
+\item[Policy:]
+  \begin{itemize}
+  \item allow http(s) from Intranet to Internet
+  \item deny all trafic from Internet to Intranet
+  \item allo imaps and smtp from intranet to mailserver
+  \item allow smtp from Internet to mailserver
+  \item allow http(s) from Internet to webserver 
+  \item deny everything else
+  \end{itemize}
+  
+\end{labeling}
+*}
+
+
+definition
+   intranet::"adr\<^sub>i\<^sub>p net" where
+   "intranet = {{(a,b) . (a > 1 \<and> a < 4) }}"
+definition
+  dmz :: "adr\<^sub>i\<^sub>p net" where
+  "dmz = {{(a,b). (a > 6) \<and> (a < 11)}}" 
+definition
+  mail :: "adr\<^sub>i\<^sub>p net" where
+  "mail = {{(a,b). a = 7}}"
+definition
+  web :: "adr\<^sub>i\<^sub>p net" where
+  "web = {{(a,b). a = 8 }}"
+definition
+  internet :: "adr\<^sub>i\<^sub>p net" where
+  "internet = {{(a,b).  \<not> ( (a > 1 \<and> a < 4) \<or> (a > 6) \<and> (a < 11))   }}"
+
+
+definition 
+  Intranet_mail_port :: "(adr\<^sub>i\<^sub>p,'b) FWPolicy" where
+  "Intranet_mail_port = (allow_from_to_ports {21::port,14} intranet mail)" 
+
+definition
+  Intranet_Internet_port :: "(adr\<^sub>i\<^sub>p,'b) FWPolicy" where
+  "Intranet_Internet_port = allow_from_to_ports {80::port,90} intranet internet"
+     
+definition
+  Internet_web_port :: "(adr\<^sub>i\<^sub>p,'b) FWPolicy" where
+  "Internet_web_port = (allow_from_to_ports {80::port,90} internet web)"
+          
+definition
+  Internet_mail_port :: "(adr\<^sub>i\<^sub>p,'b) FWPolicy" where
+  "Internet_mail_port =  (allow_all_from_port_to internet (21::port) dmz )"
+
+
+
+definition 
+  policyPort :: "(adr\<^sub>i\<^sub>p, DummyContent) FWPolicy" where
+ "policyPort = deny_all ++ 
+                  Intranet_Internet_port ++ 
+                  Intranet_mail_port ++  
+                  Internet_mail_port ++ 
+                  Internet_web_port"
+
+
+text {* We only want to create test cases which are sent between the three main networks ---
+ e.g. not between the mailserver and the dmz. Therefore, the constraint looks as follows. *}
+
+definition
+ not_in_same_net :: "(adr\<^sub>i\<^sub>p,DummyContent) packet \<Rightarrow> bool" where
+ "not_in_same_net x  =  ((src x \<sqsubset> internet \<longrightarrow> \<not> dest x \<sqsubset> internet) \<and> 
+                        (src x \<sqsubset> intranet \<longrightarrow> \<not> dest x \<sqsubset> intranet) \<and> 
+                        (src x \<sqsubset> dmz \<longrightarrow> \<not> dest x \<sqsubset> dmz))"
+
+lemmas PolicyLemmas =  policyPort_def  dmz_def internet_def intranet_def mail_def web_def 
+                       Intranet_Internet_port_def Intranet_mail_port_def Internet_web_port_def 
+                       Internet_mail_port_def src_def dest_def IntegerPort.src_port
+                       in_subnet_def IntegerPort.dest_port
+
+end

Examples/Examples.thy

@@ -0,0 +1,50 @@
+(*****************************************************************************
+ * 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.
+ *****************************************************************************)
+
+chapter {* Examples *}
+theory  
+  Examples
+imports 
+  "DMZ/DMZ"
+  "VoIP/VoIP"
+  "Transformation/Transformation"
+  "NAT-FW/NAT-FW"
+  "PersonalFirewall/PersonalFirewall"
+begin
+
+end
+

Examples/NAT-FW/NAT-FW.thy

@@ -0,0 +1,292 @@
+(*****************************************************************************
+ * 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.
+ *****************************************************************************)
+
+section {* Example: NAT *} 
+theory 
+  "NAT-FW"
+imports
+  "../../UPF-Firewall"
+begin
+
+
+definition subnet1 :: "adr\<^sub>i\<^sub>p net" where
+ "subnet1 = {{(d,e). d > 1 \<and> d < 256}}"
+
+definition subnet2 :: "adr\<^sub>i\<^sub>p net" where
+ "subnet2 = {{(d,e). d > 500 \<and> d < 1256}}"
+
+
+definition
+  "accross_subnets x  \<equiv> 
+ ((src x \<sqsubset> subnet1 \<and> (dest x \<sqsubset> subnet2)) \<or>
+  (src x \<sqsubset> subnet2 \<and> (dest x \<sqsubset> subnet1)))"
+
+definition
+   filter :: "(adr\<^sub>i\<^sub>p, DummyContent) FWPolicy" where
+  "filter = allow_from_port_to (1::port) subnet1 subnet2 ++
+             allow_from_port_to (2::port) subnet1 subnet2 ++
+             allow_from_port_to (3::port) subnet1 subnet2 ++ deny_all"
+
+definition 
+ nat_0  where 
+ "nat_0 = (A\<^sub>f(\<lambda>x. {x}))"
+
+
+lemmas UnfoldPolicy0 =filter_def nat_0_def 
+                      NATLemmas 
+                      ProtocolPortCombinators.ProtocolCombinators 
+                      adr\<^sub>i\<^sub>pLemmas
+                      packet_defs accross_subnets_def
+                      subnet1_def subnet2_def
+
+
+lemmas subnets = subnet1_def subnet2_def 
+
+
+
+
+
+definition Adr11 :: "int set"
+where "Adr11 = {d. d > 2 \<and> d < 3}"
+
+definition Adr21 :: "int set" where
+ "Adr21 = {d. d > 502 \<and> d < 503}"
+
+
+definition nat_1 where
+ "nat_1 = nat_0 ++ (srcPat2pool_IntPort Adr11 Adr21)"
+
+
+definition policy_1 where
+ "policy_1 = ((\<lambda> (x,y). x) o_f 
+ ((nat_1 \<Otimes>\<^sub>2 filter) o (\<lambda> x. (x,x))))"
+
+
+lemmas UnfoldPolicy1 = UnfoldPolicy0 nat_1_def Adr11_def Adr21_def policy_1_def
+
+
+
+
+definition Adr12 :: "int set"
+where "Adr12 = {d. d > 4 \<and> d < 6}"
+
+definition Adr22 :: "int set" where
+ "Adr22 = {d. d > 504 \<and> d < 506}"
+
+
+definition nat_2 where
+ "nat_2 = nat_1 ++ (srcPat2pool_IntPort Adr12 Adr22)"
+
+
+definition policy_2 where
+ "policy_2 = ((\<lambda> (x,y). x) o_f 
+ ((nat_2 \<Otimes>\<^sub>2 filter) o (\<lambda> x. (x,x))))"
+
+
+lemmas UnfoldPolicy2 = UnfoldPolicy1 nat_2_def Adr12_def Adr22_def policy_2_def
+
+
+
+
+definition Adr13 :: "int set"
+where "Adr13 = {d. d > 6 \<and> d < 9}"
+
+definition Adr23 :: "int set" where
+ "Adr23 = {d. d > 506 \<and> d < 509}"
+
+
+definition nat_3 where
+ "nat_3 = nat_2 ++ (srcPat2pool_IntPort Adr13 Adr23)"
+
+
+definition policy_3 where
+ "policy_3 = ((\<lambda> (x,y). x) o_f 
+ ((nat_3 \<Otimes>\<^sub>2 filter) o (\<lambda> x. (x,x))))"
+
+
+lemmas UnfoldPolicy3 = UnfoldPolicy2 nat_3_def Adr13_def Adr23_def policy_3_def
+
+
+
+
+definition Adr14 :: "int set"
+where "Adr14 = {d. d > 8 \<and> d < 12}"
+
+definition Adr24 :: "int set" where
+ "Adr24 = {d. d > 508 \<and> d < 512}"
+
+
+definition nat_4 where
+ "nat_4 = nat_3 ++ (srcPat2pool_IntPort Adr14 Adr24)"
+
+
+definition policy_4 where
+ "policy_4 = ((\<lambda> (x,y). x) o_f 
+ ((nat_4 \<Otimes>\<^sub>2 filter) o (\<lambda> x. (x,x))))"
+
+
+lemmas UnfoldPolicy4 = UnfoldPolicy3 nat_4_def Adr14_def Adr24_def policy_4_def
+
+
+
+
+definition Adr15 :: "int set"
+where "Adr15 = {d. d > 10 \<and> d < 15}"
+
+definition Adr25 :: "int set" where
+ "Adr25 = {d. d > 510 \<and> d < 515}"
+
+
+definition nat_5 where
+ "nat_5 = nat_4 ++ (srcPat2pool_IntPort Adr15 Adr25)"
+
+
+definition policy_5 where
+ "policy_5 = ((\<lambda> (x,y). x) o_f 
+ ((nat_5 \<Otimes>\<^sub>2 filter) o (\<lambda> x. (x,x))))"
+
+
+lemmas UnfoldPolicy5 = UnfoldPolicy4 nat_5_def Adr15_def Adr25_def policy_5_def
+
+
+
+
+definition Adr16 :: "int set"
+where "Adr16 = {d. d > 12 \<and> d < 18}"
+
+definition Adr26 :: "int set" where
+ "Adr26 = {d. d > 512 \<and> d < 518}"
+
+
+definition nat_6 where
+ "nat_6 = nat_5 ++ (srcPat2pool_IntPort Adr16 Adr26)"
+
+
+definition policy_6 where
+ "policy_6 = ((\<lambda> (x,y). x) o_f 
+ ((nat_6 \<Otimes>\<^sub>2 filter) o (\<lambda> x. (x,x))))"
+
+
+lemmas UnfoldPolicy6 = UnfoldPolicy5 nat_6_def Adr16_def Adr26_def policy_6_def
+
+
+
+
+definition Adr17 :: "int set"
+where "Adr17 = {d. d > 14 \<and> d < 21}"
+
+definition Adr27 :: "int set" where
+ "Adr27 = {d. d > 514 \<and> d < 521}"
+
+
+definition nat_7 where
+ "nat_7 = nat_6 ++ (srcPat2pool_IntPort Adr17 Adr27)"
+
+
+definition policy_7 where
+ "policy_7 = ((\<lambda> (x,y). x) o_f 
+ ((nat_7 \<Otimes>\<^sub>2 filter) o (\<lambda> x. (x,x))))"
+
+
+lemmas UnfoldPolicy7 = UnfoldPolicy6 nat_7_def Adr17_def Adr27_def policy_7_def
+
+
+
+
+definition Adr18 :: "int set"
+where "Adr18 = {d. d > 16 \<and> d < 24}"
+
+definition Adr28 :: "int set" where
+ "Adr28 = {d. d > 516 \<and> d < 524}"
+
+
+definition nat_8 where
+ "nat_8 = nat_7 ++ (srcPat2pool_IntPort Adr18 Adr28)"
+
+
+definition policy_8 where
+ "policy_8 = ((\<lambda> (x,y). x) o_f 
+ ((nat_8 \<Otimes>\<^sub>2 filter) o (\<lambda> x. (x,x))))"
+
+
+lemmas UnfoldPolicy8 = UnfoldPolicy7 nat_8_def Adr18_def Adr28_def policy_8_def
+
+
+
+
+definition Adr19 :: "int set"
+where "Adr19 = {d. d > 18 \<and> d < 27}"
+
+definition Adr29 :: "int set" where
+ "Adr29 = {d. d > 518 \<and> d < 527}"
+
+
+definition nat_9 where
+ "nat_9 = nat_8 ++ (srcPat2pool_IntPort Adr19 Adr29)"
+
+
+definition policy_9 where
+ "policy_9 = ((\<lambda> (x,y). x) o_f 
+ ((nat_9 \<Otimes>\<^sub>2 filter) o (\<lambda> x. (x,x))))"
+
+
+lemmas UnfoldPolicy9 = UnfoldPolicy8 nat_9_def Adr19_def Adr29_def policy_9_def
+
+
+
+
+definition Adr110 :: "int set"
+where "Adr110 = {d. d > 20 \<and> d < 30}"
+
+definition Adr210 :: "int set" where
+ "Adr210 = {d. d > 520 \<and> d < 530}"
+
+
+definition nat_10 where
+ "nat_10 = nat_9 ++ (srcPat2pool_IntPort Adr110 Adr210)"
+
+
+definition policy_10 where
+ "policy_10 = ((\<lambda> (x,y). x) o_f 
+ ((nat_10 \<Otimes>\<^sub>2 filter) o (\<lambda> x. (x,x))))"
+
+
+lemmas UnfoldPolicy10 = UnfoldPolicy9 nat_10_def Adr110_def Adr210_def policy_10_def
+
+
+
+end

Examples/PersonalFirewall/PersonalFirewall.thy

@@ -0,0 +1,45 @@
+(*****************************************************************************
+ * 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.
+ *****************************************************************************)
+
+section {* Personal Firewall *}
+theory 
+  PersonalFirewall
+imports 
+  PersonalFirewallInt
+  PersonalFirewallIpv4
+begin 
+end

Examples/PersonalFirewall/PersonalFirewallDatatype.thy

@@ -0,0 +1,108 @@
+(*****************************************************************************
+ * 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 {* Personal Firewall: Datatype *}
+theory 
+  PersonalFirewallDatatype
+imports 
+  FWTesting
+begin
+
+text{* The most basic firewall scenario; there is a personal PC on one
+side and the Internet on the other.  There are two policies: the first
+one allows all traffic from the PC to the Internet and denies all
+coming into the PC. The second policy only allows specific ports from
+the PC. This scenario comes in three variants: the first one specifies
+the allowed protocols directly, the second together with their
+respective port numbers, the third one only with the port numbers.  *}
+
+datatype Adr = pc | internet
+
+type_synonym DatatypeTwoNets = "Adr \<times> int"
+
+instance Adr::adr ..
+
+defs (overloaded)
+ src_port_def: "src_port (x::(DatatypeTwoNets,'b) packet) \<equiv> snd (src x)"
+ dest_port_def: "dest_port (x::(DatatypeTwoNets,'b) packet) \<equiv> snd (dest x)"
+
+definition
+ PC :: "DatatypeTwoNets net" where
+"PC = {{(a,b). a = pc}}"
+
+definition
+ Internet :: "DatatypeTwoNets net" where
+"Internet = {{(a,b). a = internet}}"
+
+
+text{*
+Definition of the testing constraint
+*}
+
+definition
+ not_in_same_net :: "(DatatypeTwoNets,DummyContent) packet \<Rightarrow> bool" where
+"not_in_same_net x = ((src x \<sqsubset> PC \<longrightarrow> dest x \<sqsubset> Internet) \<and> (src x \<sqsubset> Internet \<longrightarrow> dest x \<sqsubset> PC))" 
+
+text {*
+Definitions of the policies 
+
+In fact, the short definitions wouldn't have to be written down - they
+are the automatically simplified versions of their big counterparts.
+
+*}
+
+definition
+ strictPolicy :: "(DatatypeTwoNets,DummyContent) FWPolicy" where
+"strictPolicy = deny_all ++ allow_all_from_to PC Internet"
+
+definition
+ PortPolicy :: "(DatatypeTwoNets,'b) FWPolicy" where
+"PortPolicy = deny_all ++ allow_from_ports_to {80::port,24,21} PC Internet"
+
+definition
+ PortPolicyBig :: "(DatatypeTwoNets,'b) FWPolicy" where
+"PortPolicyBig =  
+                 allow_from_port_to (80::port) PC Internet \<Oplus> 
+                 allow_from_port_to (24::port) PC Internet \<Oplus> 
+                 allow_from_port_to (21::port) PC Internet \<Oplus> 
+                 deny_all"
+
+
+lemmas policyLemmas = strictPolicy_def PortPolicy_def PC_def Internet_def PortPolicyBig_def src_def dest_def src_port_def dest_port_def  
+                      PolicyCombinators PortCombinators in_subnet_def
+
+end

Examples/PersonalFirewall/PersonalFirewallInt.thy

@@ -0,0 +1,113 @@
+(*****************************************************************************
+ * 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{* Personal Firewall: Integer *}
+theory 
+  PersonalFirewallInt
+imports 
+  "../../UPF-Firewall"
+begin
+
+text{*
+The most basic firewall scenario; there is a personal PC on one side and the Internet on the other. 
+There are two policies: the first one allows all traffic from the PC to the Internet and denies
+all coming into the PC. The second policy only allows specific ports from the PC. This scenario
+comes in three variants: the first one specifies the allowed protocols directly, the second together 
+with their respective port numbers, the third one only with the port numbers.
+*}
+
+
+
+text{*
+Definitions of the subnets 
+*}
+
+definition
+ PC :: "(adr\<^sub>i\<^sub>p net)" where
+"PC = {{(a,b). a = 3}}"
+
+definition
+ Internet :: "adr\<^sub>i\<^sub>p net" where
+"Internet = {{(a,b). \<not> (a = 3)}}"
+
+
+
+text{*
+Definition of the testing constraint
+*}
+
+
+
+definition
+ not_in_same_net :: "(adr\<^sub>i\<^sub>p,DummyContent) packet \<Rightarrow> bool" where
+"not_in_same_net x = ((src x \<sqsubset> PC \<longrightarrow> dest x \<sqsubset> Internet) \<and> (src x \<sqsubset> Internet \<longrightarrow> dest x \<sqsubset> PC))" 
+
+text {*
+Definitions of the policies 
+*}
+
+
+
+definition
+ strictPolicy :: "(adr\<^sub>i\<^sub>p,DummyContent) FWPolicy" where
+"strictPolicy = deny_all ++ allow_all_from_to PC Internet"
+
+definition 
+ PortPolicy :: "(adr\<^sub>i\<^sub>p,DummyContent) FWPolicy" where
+"PortPolicy = deny_all ++ allow_from_ports_to {http,smtp,ftp} PC Internet"
+
+definition
+ PortPolicyBig :: "(adr\<^sub>i\<^sub>p,DummyContent) FWPolicy" where
+"PortPolicyBig = deny_all ++ 
+                 allow_from_port_to http PC Internet ++ 
+                 allow_from_port_to smtp PC Internet ++ 
+                 allow_from_port_to ftp PC Internet"
+
+
+lemmas policyLemmas = strictPolicy_def PortPolicy_def PC_def
+                      Internet_def PortPolicyBig_def src_def dest_def
+                      adr\<^sub>i\<^sub>pLemmas content_def
+                      PortCombinators in_subnet_def PortPolicyBig_def id_def
+
+
+declare Ports [simp add]
+
+definition wellformed_packet::"(adr\<^sub>i\<^sub>p,DummyContent) packet \<Rightarrow> bool" where
+ "wellformed_packet p = (content p = data)"
+
+
+end

Examples/PersonalFirewall/PersonalFirewallIpv4.thy

@@ -0,0 +1,103 @@
+(*****************************************************************************
+ * 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 {* Personal Firewall IPv4 *}
+theory 
+  PersonalFirewallIpv4
+imports 
+  "../../UPF-Firewall"
+begin
+
+
+text{*
+
+The most basic firewall scenario; there is a personal PC on one side and the Internet on the other. 
+There are two policies: the first one allows all traffic from the PC to the Internet and denies
+all coming into the PC. The second policy only allows specific ports from the PC. This scenario
+comes in three variants: the first one specifies the allowed protocols directly, the second together 
+with their respective port numbers, the third one only with the port numbers.
+
+*}
+
+
+text{*
+Definitions of the subnets 
+*}
+
+definition 
+ PC :: "(ipv4 net)" where
+"PC = {{((a,b,c,d),e). a = 1 \<and> b = 3 \<and> c = 5 \<and> d = 2}}"
+
+definition
+ Internet :: "ipv4 net" where
+"Internet = {{((a,b,c,d),e). \<not> (a = 1 \<and> b = 3 \<and> c = 5 \<and> d = 2)}}"
+
+
+text{*
+Definition of the testing constraint
+*}
+
+definition
+ not_in_same_net :: "(ipv4,DummyContent) packet \<Rightarrow> bool" where
+"not_in_same_net x = ((src x \<sqsubset> PC \<longrightarrow> dest x \<sqsubset> Internet) \<and> (src x \<sqsubset> Internet \<longrightarrow> dest x \<sqsubset> PC))" 
+
+text {*
+Definitions of the policies 
+*}
+
+definition
+ strictPolicy :: "(ipv4,DummyContent) FWPolicy" where
+"strictPolicy = deny_all ++ allow_all_from_to PC Internet"
+
+definition
+ PortPolicy :: "(ipv4,DummyContent) FWPolicy" where
+"PortPolicy = deny_all ++ allow_from_ports_to {80::port,24,21} PC Internet"
+
+definition
+ PortPolicyBig :: "(ipv4,DummyContent) FWPolicy" where
+"PortPolicyBig = deny_all ++ allow_from_port_to (80::port) PC Internet++ allow_from_port_to (24::port) PC Internet++ allow_from_port_to (21::port) PC Internet"
+
+
+lemmas policyLemmas = strictPolicy_def PortPolicy_def PC_def
+                      Internet_def PortPolicyBig_def src_def dest_def
+                      IPv4.src_port
+                      IPv4.dest_port PolicyCombinators
+                      PortCombinators in_subnet_def PortPolicyBig_def
+
+
+
+end

Examples/Transformation/Transformation.thy

@@ -0,0 +1,44 @@
+(*****************************************************************************
+ * 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.
+ *****************************************************************************)
+
+section {* Demonstrating Policy Transformations *}
+theory Transformation
+imports 
+  Transformation01
+  Transformation02
+begin
+end

Examples/Transformation/Transformation01.thy

@@ -0,0 +1,268 @@
+(*****************************************************************************
+ * 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 {* Transformation Example 1 *}
+theory 
+  Transformation01
+imports 
+  "../../UPF-Firewall"
+begin
+
+definition
+ FWLink :: "adr\<^sub>i\<^sub>p net" where
+"FWLink = {{(a,b). a = 1}}"
+
+definition
+ any :: "adr\<^sub>i\<^sub>p net" where
+"any = {{(a,b). a > 5}}"
+
+definition
+ i4:: "adr\<^sub>i\<^sub>p net" where
+"i4 = {{(a,b). a = 2 }}" 
+
+definition
+ i27:: "adr\<^sub>i\<^sub>p net" where
+"i27 = {{(a,b). a = 3 }}" 
+ 
+definition
+ eth_intern:: "adr\<^sub>i\<^sub>p net" where
+"eth_intern = {{(a,b). a = 4 }}"
+ 
+definition
+ eth_private:: "adr\<^sub>i\<^sub>p net" where
+"eth_private = {{(a,b). a = 5 }}"
+
+
+definition
+(* Mandatory: Global *)
+
+ MG2 :: "(adr\<^sub>i\<^sub>p net,port) Combinators" where
+"MG2 = AllowPortFromTo i27 any 1 \<oplus> 
+       AllowPortFromTo i27 any 2 \<oplus>
+       AllowPortFromTo i27 any 3"
+
+definition
+ MG3 :: "(adr\<^sub>i\<^sub>p net,port) Combinators" where
+"MG3 = AllowPortFromTo any FWLink 1"
+
+definition
+ MG4 :: "(adr\<^sub>i\<^sub>p net,port) Combinators" where
+"MG4 = AllowPortFromTo FWLink FWLink 4"
+ 
+definition
+ MG7 :: "(adr\<^sub>i\<^sub>p net,port) Combinators" where
+"MG7 = AllowPortFromTo FWLink i4 6 \<oplus>
+       AllowPortFromTo FWLink i4 7"
+
+definition
+ MG8 :: "(adr\<^sub>i\<^sub>p net,port) Combinators" where
+"MG8 = AllowPortFromTo FWLink i4 6 \<oplus>
+       AllowPortFromTo FWLink i4 7"
+
+(* Default Global *)
+
+definition
+ DG3:: "(adr\<^sub>i\<^sub>p net,port) Combinators" where
+"DG3 = AllowPortFromTo any any 7"
+
+ 
+
+definition
+"Policy = DenyAll \<oplus> MG8 \<oplus>  MG7 \<oplus> MG4 \<oplus> MG3 \<oplus> MG2 \<oplus> DG3"   
+ 
+ 
+
+ lemmas PolicyLemmas =  Policy_def
+ FWLink_def
+ any_def
+ 
+ i27_def
+ i4_def
+ 
+ eth_intern_def
+ eth_private_def
+ 
+ MG2_def MG3_def MG4_def MG7_def MG8_def  
+ DG3_def
+ 
+
+lemmas PolicyL =  MG2_def MG3_def MG4_def MG7_def MG8_def  
+ DG3_def Policy_def
+
+definition 
+ not_in_same_net :: "(adr\<^sub>i\<^sub>p,DummyContent) packet \<Rightarrow> bool" where
+"not_in_same_net x =  (((src x \<sqsubset> i27) \<longrightarrow> ( \<not> (dest x \<sqsubset> i27))) \<and>
+                      ((src x \<sqsubset>  i4) \<longrightarrow> ( \<not> (dest x \<sqsubset> i4))) \<and>
+                      ((src x \<sqsubset>  eth_intern) \<longrightarrow> ( \<not> (dest x \<sqsubset> eth_intern))) \<and>
+                      ((src x \<sqsubset>  eth_private) \<longrightarrow> ( \<not> (dest x \<sqsubset> eth_private))))"
+                   
+consts fixID :: id
+consts fixContent :: DummyContent
+
+definition "fixElements p = (id p = fixID \<and> content p = fixContent)"
+
+lemmas fixDefs = fixElements_def NetworkCore.id_def NetworkCore.content_def
+
+
+
+lemma sets_distinct1: "(n::int) \<noteq> m \<Longrightarrow> {(a,b). a = n} \<noteq> {(a,b). a = m}"
+apply auto
+done
+
+lemma sets_distinct2: "(m::int) \<noteq> n \<Longrightarrow> {(a,b). a = n} \<noteq> {(a,b). a = m}"
+apply auto
+done
+
+
+
+lemma sets_distinct3: "{((a::int),(b::int)). a = n} \<noteq> {(a,b). a > n}"
+apply auto
+done
+
+
+lemma sets_distinct4: "{((a::int),(b::int)). a > n} \<noteq> {(a,b). a = n}"
+apply auto
+done
+
+
+lemma aux: "\<lbrakk>a \<in> c; a \<notin> d; c = d\<rbrakk> \<Longrightarrow> False"
+apply auto
+done
+
+
+lemma sets_distinct5: "(s::int) < g \<Longrightarrow> {(a::int, b::int). a = s} \<noteq> {(a::int, b::int).  g < a}"
+apply (auto simp: sets_distinct3)
+apply (subgoal_tac "(s,4) \<in> {(a::int,b::int). a = (s)}")
+apply (subgoal_tac "(s,4) \<notin> {(a::int,b::int). g < a}")
+apply (erule aux)
+apply assumption+
+apply simp
+by blast
+
+
+lemma sets_distinct6: "(s::int) < g \<Longrightarrow> {(a::int, b::int).  g < a} \<noteq> {(a::int, b::int).  a = s}"
+apply (rule not_sym)
+apply (rule sets_distinct5)
+by simp
+
+
+lemma distinctNets: "FWLink \<noteq>  any \<and> FWLink \<noteq>  i4 \<and> FWLink \<noteq>  i27 \<and> FWLink \<noteq>  eth_intern \<and> FWLink \<noteq>   eth_private \<and> 
+any \<noteq>  FWLink \<and> any \<noteq>  i4 \<and> any \<noteq>  i27 \<and> any \<noteq>  eth_intern \<and> any \<noteq>  eth_private \<and> i4 \<noteq>  FWLink \<and> 
+i4 \<noteq>  any \<and> i4 \<noteq>  i27 \<and> i4 \<noteq>  eth_intern \<and> i4 \<noteq>  eth_private \<and> i27 \<noteq>  FWLink \<and> i27 \<noteq>  any \<and> 
+i27 \<noteq>  i4 \<and> i27 \<noteq>  eth_intern \<and> i27 \<noteq>  eth_private \<and> eth_intern \<noteq>  FWLink \<and> eth_intern \<noteq>  any \<and> 
+eth_intern \<noteq>  i4 \<and> eth_intern \<noteq>  i27 \<and> eth_intern \<noteq>  eth_private \<and> eth_private \<noteq>  FWLink \<and> 
+eth_private \<noteq>  any \<and> eth_private \<noteq>  i4 \<and> eth_private \<noteq>  i27 \<and> eth_private \<noteq>  eth_intern"
+apply (simp add: PolicyLemmas sets_distinct1 sets_distinct2 sets_distinct3 sets_distinct4 sets_distinct5 sets_distinct6)
+done
+
+
+
+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}"
+  apply auto
+done
+
+
+lemma aux2: "{a,b} = {b,a}"
+  apply auto
+done
+
+(*
+lemma noMT: "\<forall> x \<in> set (policy2list Policy). dom (C x) \<noteq> {}"
+apply (simp add: PolicyLemmas)
+apply (simp add: PLemmas PolicyLemmas)
+by arith
+*)
+
+
+lemma ANDex: "allNetsDistinct (policy2list Policy)"
+apply (simp add: PolicyL allNetsDistinct_def distinctNets)
+apply (auto simp: PLemmas PolicyLemmas netsDistinct_def sets_distinct5 sets_distinct6)
+done
+
+(*
+lemma count_the_rules: "(int (length(policy2list (list2FWpolicy(normalize Policy)))) = post) \<and> 
+(int(length (policy2list Policy)) = pre) \<and>
+ (int (length((normalize Policy))) = Partitions)"
+apply (insert distinctNets noMT)
+apply (simp add: normalize_def PolicyL bothNets_def aux5 aux2 Nets_List_def, thin_tac "?X",thin_tac "?S")
+oops
+
+
+
+lemma normedPolicy: "normalize Policy = X"
+apply (insert distinctNets noMT)
+apply (simp add: normalize_def PolicyL bothNets_def aux5 aux2 Nets_List_def, thin_tac "?X",thin_tac "?S")
+oops
+*)
+
+fun (sequential) numberOfRules where 
+ "numberOfRules (a\<oplus>b) = numberOfRules a + numberOfRules b"
+ |"numberOfRules a = (1::int)" 
+
+
+
+
+fun numberOfRulesList where 
+ "numberOfRulesList  (x#xs) = ((numberOfRules x)#(numberOfRulesList xs)) "
+ |"numberOfRulesList [] = []" 
+
+(*
+lemma "numberOfRulesList (normalize Policy) = X"
+apply (insert distinctNets noMT)
+apply (simp add: normalize_def PolicyL bothNets_def aux5 aux2 Nets_List_def, thin_tac "?X",thin_tac "?S")
+oops
+*)
+
+lemma all_in_list: "all_in_list (policy2list Policy) (Nets_List Policy)"
+apply (simp add: PolicyL)
+apply (unfold Nets_List_def)
+apply (unfold bothNets_def)
+apply (insert distinctNets)
+apply simp
+done
+
+lemmas normalizeUnfold =   normalize_def Policy_def Nets_List_def bothNets_def aux aux2 bothNets_def
+
+(*
+lemma noMT2: "\<forall> x \<in> set (policy2list Policy). dom (C x) \<noteq> {}"
+apply (simp add: PLemmas  normalize_def bothNets_def
+                 PolicyLemmas aux5 aux2 Nets_List_def ) 
+by (metis zless_add1_eq)
+*)
+
+
+end

Examples/Transformation/Transformation02.thy

@@ -0,0 +1,219 @@
+(*****************************************************************************
+ * 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 {* Transforamtion Example 2 *}
+theory 
+  Transformation02
+imports 
+   "../../UPF-Firewall"
+begin
+
+definition
+ FWLink :: "adr\<^sub>i\<^sub>p net" where
+"FWLink = {{(a,b). a = 1}}"
+
+definition
+ any :: "adr\<^sub>i\<^sub>p net" where
+"any = {{(a,b). a > 5}}"
+
+definition
+ i4_32:: "adr\<^sub>i\<^sub>p net" where
+"i4_32 = {{(a,b). a = 2 }}" 
+
+definition
+ i10_32:: "adr\<^sub>i\<^sub>p net" where
+"i10_32 = {{(a,b). a = 3 }}" 
+ 
+definition
+ eth_intern:: "adr\<^sub>i\<^sub>p net" where
+"eth_intern = {{(a,b). a = 4 }}"
+ 
+definition
+ eth_private:: "adr\<^sub>i\<^sub>p net" where
+"eth_private = {{(a,b). a = 5 }}"
+
+
+
+definition
+ D1a :: "(adr\<^sub>i\<^sub>p net, port) Combinators" where
+"D1a = AllowPortFromTo eth_intern any 1 \<oplus> 
+       AllowPortFromTo eth_intern any 2"
+
+
+definition
+ D1b :: "(adr\<^sub>i\<^sub>p net, port) Combinators" where
+"D1b = AllowPortFromTo eth_private any 1 \<oplus>
+       AllowPortFromTo eth_private any 2"
+
+definition
+ D2a :: "(adr\<^sub>i\<^sub>p net, port) Combinators" where
+"D2a = AllowPortFromTo  any i4_32 21"
+
+
+definition
+ D2b :: "(adr\<^sub>i\<^sub>p net, port) Combinators" where
+"D2b = AllowPortFromTo any i10_32 21 \<oplus> 
+       AllowPortFromTo any i10_32 43"
+
+
+
+definition
+ Policy :: "(adr\<^sub>i\<^sub>p net, port) Combinators" where
+"Policy = DenyAll \<oplus> D2b \<oplus> D2a \<oplus> D1b \<oplus> D1a"
+
+lemmas PolicyLemmas = Policy_def D1a_def D1b_def D2a_def D2b_def 
+ 
+
+ lemmas PolicyL =  Policy_def
+ FWLink_def
+ any_def
+ i10_32_def
+ i4_32_def
+ eth_intern_def
+ eth_private_def
+ D1a_def D1b_def D2a_def D2b_def 
+                    
+consts fixID :: id
+consts fixContent :: DummyContent
+
+definition "fixElements p = (id p = fixID \<and> content p = fixContent)"
+
+lemmas fixDefs = fixElements_def NetworkCore.id_def NetworkCore.content_def
+
+
+
+lemma sets_distinct1: "(n::int) \<noteq> m \<Longrightarrow> {(a,b). a = n} \<noteq> {(a,b). a = m}"
+apply auto
+done
+
+lemma sets_distinct2: "(m::int) \<noteq> n \<Longrightarrow> {(a,b). a = n} \<noteq> {(a,b). a = m}"
+apply auto
+done
+
+
+
+lemma sets_distinct3: "{((a::int),(b::int)). a = n} \<noteq> {(a,b). a > n}"
+apply auto
+done
+
+
+lemma sets_distinct4: "{((a::int),(b::int)). a > n} \<noteq> {(a,b). a = n}"
+apply auto
+done
+
+
+lemma aux: "\<lbrakk>a \<in> c; a \<notin> d; c = d\<rbrakk> \<Longrightarrow> False"
+apply auto
+done
+
+
+lemma sets_distinct5: "(s::int) < g \<Longrightarrow> {(a::int, b::int). a = s} \<noteq> {(a::int, b::int).  g < a}"
+apply (auto simp: sets_distinct3)
+apply (subgoal_tac "(s,4) \<in> {(a::int,b::int). a = (s)}")
+apply (subgoal_tac "(s,4) \<notin> {(a::int,b::int). g < a}")
+apply (erule aux)
+apply assumption+
+apply simp
+by blast
+
+lemma sets_distinct6: "(s::int) < g \<Longrightarrow> {(a::int, b::int).  g < a} \<noteq> {(a::int, b::int).  a = s}"
+apply (rule not_sym)
+apply (rule sets_distinct5)
+by simp
+
+
+lemma distinctNets: "FWLink \<noteq> any \<and> FWLink \<noteq> i4_32 \<and> FWLink \<noteq> i10_32 \<and>
+FWLink \<noteq> eth_intern \<and> FWLink \<noteq> eth_private \<and> any \<noteq> FWLink \<and> any \<noteq>
+i4_32 \<and> any \<noteq> i10_32 \<and> any \<noteq> eth_intern \<and> any \<noteq> eth_private \<and> i4_32 \<noteq>
+FWLink \<and> i4_32 \<noteq> any \<and> i4_32 \<noteq> i10_32 \<and> i4_32 \<noteq> eth_intern \<and> i4_32 \<noteq>
+eth_private \<and> i10_32 \<noteq> FWLink \<and> i10_32 \<noteq> any \<and> i10_32 \<noteq> i4_32 \<and> i10_32
+\<noteq> eth_intern \<and> i10_32 \<noteq> eth_private \<and> eth_intern \<noteq> FWLink \<and> eth_intern
+\<noteq> any \<and> eth_intern \<noteq> i4_32 \<and> eth_intern \<noteq> i10_32 \<and> eth_intern \<noteq>
+eth_private \<and> eth_private \<noteq> FWLink \<and> eth_private \<noteq> any \<and> eth_private \<noteq>
+i4_32 \<and> eth_private \<noteq> i10_32 \<and> eth_private \<noteq> eth_intern " 
+apply (simp add: PolicyL sets_distinct1 sets_distinct2 sets_distinct3
+  sets_distinct4 sets_distinct5 sets_distinct6) 
+done
+
+
+
+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}"
+  apply auto
+done
+
+
+lemma aux2: "{a,b} = {b,a}"
+  apply auto
+done
+
+
+
+
+lemma ANDex: "allNetsDistinct (policy2list Policy)"
+apply (simp add: PolicyLemmas allNetsDistinct_def distinctNets)
+apply (simp add: PolicyL)
+apply (auto simp: PLemmas PolicyL netsDistinct_def sets_distinct5 sets_distinct6 sets_distinct1 sets_distinct2)
+done
+
+fun (sequential) numberOfRules where 
+ "numberOfRules (a\<oplus>b) = numberOfRules a + numberOfRules b"
+ |"numberOfRules a = (1::int)" 
+
+
+
+
+fun numberOfRulesList where 
+ "numberOfRulesList  (x#xs) = ((numberOfRules x)#(numberOfRulesList xs)) "
+ |"numberOfRulesList [] = []" 
+
+
+
+lemma all_in_list: "all_in_list (policy2list Policy) (Nets_List Policy)"
+apply (simp add: PolicyLemmas)
+apply (unfold Nets_List_def)
+apply (unfold bothNets_def)
+apply (insert distinctNets)
+apply simp
+done
+
+
+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
+
+
+end
+
+

Examples/VoIP/VoIP.thy

@@ -0,0 +1,136 @@
+(*****************************************************************************
+ * 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.
+ *****************************************************************************)
+
+section {* Voice over IP *}
+theory VoIP
+imports 
+  "../../UPF-Firewall"
+begin
+
+
+text{* In this theory we generate the test data for correct runs of
+the FTP protocol. As usual, we start with definining the networks and
+the policy. We use a rather simple policy which allows only FTP
+connections starting from the Intranet and going to the Internet, and
+deny everything else. *}
+
+definition 
+  intranet :: "adr\<^sub>i\<^sub>p net" where
+  "intranet = {{(a,e) . a = 3}}"
+
+definition 
+  internet :: "adr\<^sub>i\<^sub>p net" where
+  "internet = {{(a,c). a > 4}}"
+
+definition 
+  gatekeeper :: "adr\<^sub>i\<^sub>p net" where
+  "gatekeeper = {{(a,c). a =4}}"
+
+
+definition 
+  voip_policy :: "(adr\<^sub>i\<^sub>p,address voip_msg) FWPolicy" where
+  "voip_policy = A\<^sub>U"
+
+
+text{* The next two constants check if an address is in the Intranet
+or in the Internet respectively.*}
+
+definition 
+  is_in_intranet :: "address  \<Rightarrow> bool" where
+  "is_in_intranet a = (a = 3)"
+
+definition 
+  is_gatekeeper :: "address \<Rightarrow> bool" where
+  "is_gatekeeper a =  (a = 4)"
+
+definition 
+  is_in_internet :: "address \<Rightarrow> bool" where
+  "is_in_internet a =  (a > 4)"
+
+
+text{*
+The next definition is our starting state: an empty trace and the just defined policy.*}
+
+definition 
+  "\<sigma>_0_voip" ::  "(adr\<^sub>i\<^sub>p, address voip_msg) history \<times>
+                 (adr\<^sub>i\<^sub>p, address voip_msg) FWPolicy" 
+where                                     
+  "\<sigma>_0_voip = ([],voip_policy)"
+
+text{*Next we state the conditions we have on our trace: a normal
+behaviour FTP run from the intranet to some server in the internet on
+port 21.*}
+
+definition "accept_voip" ::  "(adr\<^sub>i\<^sub>p, address voip_msg) history \<Rightarrow> bool" where
+          "accept_voip t = 
+  (\<exists> c s g i p1 p2. t \<in> NB_voip c s g i p1 p2 \<and> is_in_intranet c \<and> is_in_internet s
+                                              \<and> is_gatekeeper g)"
+
+
+
+fun packet_with_id where
+ "packet_with_id [] i = []"
+|"packet_with_id (x#xs) i = 
+  (if id x = i then (x#(packet_with_id xs i)) else (packet_with_id xs i))"
+
+
+text{*The depth of the test case generation corresponds to the maximal
+length of generated traces. 4 is the minimum to get a full FTP
+protocol run.  *}
+
+
+
+
+
+fun ids1 where
+ "ids1 i (x#xs) = (id x = i \<and> ids1 i xs)"
+|"ids1 i [] = True"
+
+lemmas ST_simps = Let_def valid_SE_def unit_SE_def bind_SE_def
+ subnet_of_int_def  p_accept_def content_def
+ is_in_intranet_def is_in_internet_def intranet_def internet_def exI
+ subnetOf_lemma subnetOf_lemma2 subnetOf_lemma3 subnetOf_lemma4 voip_policy_def
+ NetworkCore.id_def  is_arq_def is_fin_def
+ is_connect_def is_setup_def ports_open_def subnet_of_adr_def
+ VOIP.NB_voip_def \<sigma>_0_voip_def PLemmas VOIP_TRPolicy_def
+ policy2MON_def applyPolicy_def 
+
+
+
+
+
+end

FWNormalisation/ElementaryRules.thy

@@ -0,0 +1,76 @@
+(*****************************************************************************
+ * 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:firewall:2010}. They are not used elsewhere.
+*}
+
+lemma elem1:
+ "C (AllowPortFromTo x y p \<oplus> DenyAllFromTo x y) = C (DenyAllFromTo x y)"
+by (rule ext, auto simp: PLemmas)
+
+
+lemma elem2:
+ "C ((a \<oplus> b) \<oplus> c) = C (a \<oplus> (b \<oplus> c))"
+by (simp add: C.simps) 
+
+lemma elem3:
+ "C (AllowPortFromTo x y a \<oplus> AllowPortFromTo x y b) = 
+  C (AllowPortFromTo x y b \<oplus> AllowPortFromTo x y a)"
+by (rule ext, auto simp: PLemmas)
+
+lemma elem4:
+ "C (a \<oplus> DenyAll) = C DenyAll"
+by (rule ext, auto simp: PLemmas)
+
+lemma elem5:
+ "C (DenyAllFromTo x y \<oplus> DenyAllFromTo u v) = C (DenyAllFromTo u v \<oplus> DenyAllFromTo x y)"
+by (rule ext, auto simp: PLemmas)
+
+
+lemma elem6: 
+ "dom (C a) \<inter> dom (C b) = {} \<Longrightarrow> C (a \<oplus> b) = C (b \<oplus> a)"
+by (rule ext, metis C.simps(4) map_add_comm)
+
+end

FWNormalisation/FWNormalisation.thy

@@ -0,0 +1,42 @@
+(*****************************************************************************
+ * 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.
+ *****************************************************************************)
+
+chapter {* Firewall Policy Normalisation *}
+theory  FWNormalisation
+imports NormalisationIPPProofs
+begin
+
+end

FWNormalisation/FWNormalisationCore.thy

@@ -0,0 +1,654 @@
+(*****************************************************************************
+ * 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 {* Policy Normalisation: Core Definitions *}
+theory
+  FWNormalisationCore
+imports
+  "../PacketFilter/PacketFilter"
+begin
+
+text{* 
+  This theory contains all the definitions used for policy normalisation as described 
+  in~\cite{brucker.ea:icst:2010,brucker.ea:formal-fw-testing:2014}.
+
+  The normalisation procedure transforms policies into semantically equivalent  ones which are 
+  ``easier'' to test. It is organized into nine phases. We impose the following two restrictions 
+  on the input policies: 
+  \begin{itemize}
+  \item Each policy must contain a $\mathtt{DenyAll}$ rule. If this restriction were to be lifted, 
+        the $\mathtt{insertDenies}$ phase would have to be adjusted accordingly.
+  \item For each pair of networks $n_1$ and $n_2$, the networks are either disjoint or equal. If 
+        this restriction were to be lifted, we would need some additional phases before the start 
+        of the normalisation procedure presented below. This rule would split single rules into 
+        several by splitting up the networks such that they are all pairwise disjoint or equal. 
+        Such a transformation is clearly semantics-preserving and the condition would hold after
+        these phases.
+  \end{itemize}
+  As a result, the procedure generates a list of policies, in which:
+  \begin{itemize}
+  \item each element of the list contains a policy which completely specifies the blocking behavior 
+        between two networks, and
+  \item there are no shadowed rules.
+  \end{itemize}
+  This result is desirable since the test case generation for rules between networks $A$ and $B$ 
+  is independent of the rules that specify the behavior for traffic flowing between networks $C$ 
+  and $D$. Thus, the different segments of the policy can be processed individually. The 
+  normalization procedure does not aim to minimize the number of rules. While it does remove 
+  unnecessary ones, it also adds new ones, enabling a policy to be split into several independent
+  parts.
+*}
+
+text{* 
+  Policy transformations are functions that map policies to policies.  We decided to represent
+  policy transformations as \emph{syntactic rules}; this choice paves the way for expressing the 
+  entire normalisation process inside HOL by functions manipulating abstract policy syntax. 
+*}
+
+
+subsubsection{* Basics *}
+text{* We define a very simple policy language: *}
+
+datatype ('\<alpha>,'\<beta>) Combinators = 
+  DenyAll
+| DenyAllFromTo '\<alpha> '\<alpha> 
+| AllowPortFromTo '\<alpha> '\<alpha> '\<beta> 
+| Conc "(('\<alpha>,'\<beta>) Combinators)" "(('\<alpha>,'\<beta>) Combinators)" (infixr "\<oplus>" 80)
+
+text{* 
+  And define the semantic interpretation of it. For technical reasons, we fix here the type to 
+  policies over IntegerPort addresses. However, we could easily provide definitions for other
+  address types as well, using a generic consts for the type definition and a primitive recursive 
+  definition for each desired address model.  *}
+
+subsubsection{* Auxiliary definitions and functions. *}
+text{*
+  This subsubsection defines several functions which are useful later for the combinators, invariants, 
+  and proofs. 
+*}
+fun srcNet where 
+ "srcNet (DenyAllFromTo x y) = x"
+|"srcNet (AllowPortFromTo x y p) = x"
+|"srcNet DenyAll = undefined"
+|"srcNet (v \<oplus> va) = undefined" 
+
+fun destNet where 
+ "destNet (DenyAllFromTo x y) = y"
+|"destNet (AllowPortFromTo x y p) = y"
+|"destNet DenyAll = undefined"
+|"destNet (v \<oplus> va) = undefined" 
+
+fun srcnets where
+ "srcnets DenyAll = [] " 
+|"srcnets (DenyAllFromTo x y) = [x] " 
+|"srcnets (AllowPortFromTo x y p) = [x] " 
+|"(srcnets (x \<oplus> y)) = (srcnets x)@(srcnets y)"
+
+fun destnets where
+ "destnets DenyAll = [] " 
+|"destnets (DenyAllFromTo x y) = [y] " 
+|"destnets (AllowPortFromTo x y p) = [y] "
+|"(destnets (x \<oplus> y)) = (destnets x)@(destnets y)"
+
+fun (sequential) net_list_aux where
+ "net_list_aux [] = []"
+|"net_list_aux (DenyAll#xs) = net_list_aux xs"
+|"net_list_aux ((DenyAllFromTo x y)#xs) = x#y#(net_list_aux xs)"
+|"net_list_aux ((AllowPortFromTo x y p)#xs) = x#y#(net_list_aux xs)"
+|"net_list_aux ((x\<oplus>y)#xs) = (net_list_aux [x])@(net_list_aux [y])@(net_list_aux xs)"
+
+fun net_list where "net_list p = remdups (net_list_aux p)"
+
+definition bothNets where "bothNets x = (zip (srcnets x) (destnets x))"
+
+fun (sequential) normBothNets where 
+ "normBothNets ((a,b)#xs) = (if ((b,a) \<in> set xs) \<or> (a,b) \<in> set (xs) 
+                            then (normBothNets xs)
+                            else (a,b)#(normBothNets xs))"
+|"normBothNets x = x" 
+
+fun makeSets where 
+ "makeSets ((a,b)#xs) = ({a,b}#(makeSets xs))"
+|"makeSets [] = []"
+
+fun bothNet where
+ "bothNet DenyAll = {}"
+|"bothNet (DenyAllFromTo a b) = {a,b}"
+|"bothNet (AllowPortFromTo a b p) = {a,b}"
+|"bothNet (v \<oplus> va) = undefined "
+
+text{* 
+  $Nets\_List$ provides from a list of rules a list where the entries are the appearing sets of 
+  source and destination network of each rule. 
+*}
+
+definition Nets_List 
+  where 
+  "Nets_List x = makeSets (normBothNets (bothNets x))"
+
+fun (sequential) first_srcNet where 
+  "first_srcNet (x\<oplus>y) = first_srcNet x"
+| "first_srcNet x = srcNet x"
+
+fun (sequential) first_destNet where 
+  "first_destNet (x\<oplus>y) = first_destNet x"
+| "first_destNet x = destNet x"
+
+fun (sequential) first_bothNet where
+ "first_bothNet (x\<oplus>y) = first_bothNet x"
+|"first_bothNet x = bothNet x"
+
+fun (sequential) in_list where 
+ "in_list DenyAll l = True"
+|"in_list x l = (bothNet x \<in> set l)"
+
+fun all_in_list where 
+ "all_in_list [] l = True"
+|"all_in_list (x#xs) l = (in_list x l \<and> all_in_list xs l)" 
+
+fun (sequential) member where
+ "member a (x\<oplus>xs) = ((member a x) \<or> (member a xs))"
+|"member a x = (a = x)"
+
+fun sdnets where
+  "sdnets DenyAll = {}"
+| "sdnets (DenyAllFromTo a b) = {(a,b)}"
+| "sdnets (AllowPortFromTo a b c) = {(a,b)}"
+| "sdnets (a \<oplus> b) = sdnets a \<union> sdnets b"
+
+definition packet_Nets  where "packet_Nets x a b = ((src x \<sqsubset> a \<and> dest x \<sqsubset> b) \<or>
+                                                    (src x \<sqsubset> b \<and> dest x \<sqsubset> a))"
+
+definition subnetsOfAdr where "subnetsOfAdr a = {x. a \<sqsubset> x}"
+
+definition fst_set where "fst_set s = {a. \<exists> b. (a,b) \<in> s}"
+
+definition snd_set where "snd_set s = {a. \<exists> b. (b,a) \<in> s}"
+
+fun memberP where
+ "memberP r (x#xs) = (member r x \<or> memberP r xs)"
+|"memberP r [] = False"
+
+fun firstList where 
+ "firstList (x#xs) = (first_bothNet x)"
+|"firstList [] = {}"
+
+subsubsection{* Invariants *}
+
+text{* If there is a DenyAll, it is at the first position *}
+fun wellformed_policy1:: "(('\<alpha>, '\<beta>) Combinators) list \<Rightarrow> bool" where 
+  "wellformed_policy1 [] = True"
+| "wellformed_policy1 (x#xs) = (DenyAll \<notin> (set xs))" 
+
+text{* There is a DenyAll at the first position *}
+fun wellformed_policy1_strong:: "(('\<alpha>, '\<beta>) Combinators) list \<Rightarrow> bool"
+where 
+  "wellformed_policy1_strong [] = False"
+| "wellformed_policy1_strong (x#xs) = (x=DenyAll \<and> (DenyAll \<notin> (set xs)))" 
+
+
+text{* All two networks are either disjoint or equal. *}
+definition netsDistinct where "netsDistinct a b = (\<not> (\<exists> x. x \<sqsubset> a \<and> x \<sqsubset> b))"
+
+definition twoNetsDistinct where
+  "twoNetsDistinct a b c d = (netsDistinct a c \<or> netsDistinct b d)"
+
+definition allNetsDistinct where 
+  "allNetsDistinct p = (\<forall> a b. (a \<noteq> b \<and> a \<in> set (net_list p) \<and>
+                        b \<in> set (net_list p)) \<longrightarrow> netsDistinct a b)"
+
+definition disjSD_2 where 
+ "disjSD_2 x y = (\<forall> a b c d. ((a,b)\<in>sdnets x \<and>  (c,d) \<in>sdnets y \<longrightarrow>
+      (twoNetsDistinct a b c d \<and> twoNetsDistinct a b d c)))"
+
+text{* The policy is given as a list of single rules. *}
+fun singleCombinators where 
+"singleCombinators [] = True"
+|"singleCombinators ((x\<oplus>y)#xs) = False"
+|"singleCombinators (x#xs) = singleCombinators xs"
+
+definition onlyTwoNets where
+ "onlyTwoNets x = ((\<exists> a b. (sdnets x = {(a,b)})) \<or> (\<exists> a b. sdnet