Theory IntegerPort_TCPUDP

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subsection ‹Integer Addresses with Ports and Protocols›
theory 
  IntegerPort_TCPUDP
  imports 
    NetworkCore
begin

text‹A theory describing addresses which are modelled as a pair of Integers - the first being 
       the host address, the second the port number.›

type_synonym 
  address = int

type_synonym 
  port = int 

type_synonym 
  adripp = "address × port × protocol" 

instance protocol :: adr ..

overloading src_port_int_TCPUDP  "src_port :: (::adr,) packet  ::port" 
begin 
definition 
  "src_port_int_TCPUDP (x::(adripp,) packet)   (fst o snd o fst  o snd) x"
end 

overloading dest_port_int_TCPUDP  "dest_port :: (::adr,) packet  ::port"
begin
definition 
  "dest_port_int_TCPUDP (x::(adripp,) packet)  (fst o snd o fst o  snd o snd) x"
end 

overloading subnet_of_int_TCPUDP  "subnet_of :: ::adr   net"
begin 
definition
  "subnet_of_int_TCPUDP (x::(adripp))  {{(a,b,c). a = fst x}}::adripp net" 
end

overloading src_protocol_int_TCPUDP  "src_protocol :: (::adr,) packet  protocol"
begin
definition 
  "src_protocol_int_TCPUDP (x::(adripp,) packet)  (snd o snd o fst o snd) x"
end

overloading dest_protocol_int_TCPUDP  "dest_protocol :: (::adr,) packet  protocol"
begin
definition 
  "dest_protocol_int_TCPUDP (x::(adripp,) packet)  (snd o snd o fst o snd o snd) x"
end

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

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

text ‹Common test constraints:›

definition port_positive :: "(adripp,'b) packet  bool" where
  "port_positive x = (dest_port x > (0::port))"

definition fix_values :: "(adripp,DummyContent) packet  bool" where
  "fix_values x =  (src_port x = (1::port)  src_protocol x = udp  content x = data  id x = 1)"


lemmas adrippLemmas = src_port dest_port src_port_int_TCPUDP_def dest_port_int_TCPUDP_def 
  src_protocol_int_TCPUDP_def dest_protocol_int_TCPUDP_def subnet_of_int_TCPUDP_def 

lemmas adrippTestConstraints = port_positive_def fix_values_def
  
end