Theory IPv4_TCPUDP

(*****************************************************************************
 * 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 ‹IPv4 with Ports and Protocols›
theory 
  IPv4_TCPUDP
  imports IPv4
begin

type_synonym 
  ipv4_TCPUDP    =  "(ipv4_ip × port × protocol)"
 
instance protocol :: adr ..

overloading src_port_ipv4_TCPUDP ≡ "src_port :: ('α::adr,'β) packet ⇒ 'γ::port" 
begin 
definition 
  "src_port_ipv4_TCPUDP (x::(ipv4_TCPUDP,'β) packet) ≡ (fst o snd o fst o snd) x"
end 

overloading dest_port_ipv4_TCPUDP ≡ "dest_port :: ('α::adr,'β) packet ⇒ 'γ::port"
begin
definition 
  "dest_port_ipv4_TCPUDP  (x::(ipv4_TCPUDP,'β) packet) ≡ (fst o snd o fst o snd o snd) x"
end 

overloading subnet_of_ipv4_TCPUDP ≡ "subnet_of :: 'α::adr ⇒ 'α net"
begin 
definition
  "subnet_of_ipv4_TCPUDP (x::ipv4_TCPUDP) ≡ {{(a,b). a = fst x}}::(ipv4_TCPUDP net)" 
end

overloading dest_protocol_ipv4_TCPUDP ≡ "dest_protocol :: ('α::adr,'β) packet ⇒ protocol"
begin
definition 
  "dest_protocol_ipv4_TCPUDP (x::(ipv4_TCPUDP,'β) packet) ≡ (snd o snd o fst o snd o snd) x"
end

definition subnet_of_ip :: "ipv4_ip ⇒ ipv4_TCPUDP net"
  where "subnet_of_ip ip = {{(a,b). (a = ip)}}"

lemma src_port: "src_port (a,(x::ipv4_TCPUDP),d,e) = fst (snd x)"
  by (simp add: src_port_ipv4_TCPUDP_def in_subnet)

lemma dest_port: "dest_port (a,d,(x::ipv4_TCPUDP),e) = fst (snd x)"
  by (simp add: dest_port_ipv4_TCPUDP_def in_subnet)

lemmas Ipv4_TCPUDPLemmas = src_port dest_port src_port_ipv4_TCPUDP_def dest_port_ipv4_TCPUDP_def 
  dest_protocol_ipv4_TCPUDP_def subnet_of_ipv4_TCPUDP_def
end