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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 
  adr\<^sub>i\<^sub>p\<^sub>p = "address \<times> port \<times> protocol" 

instance protocol :: adr ..

overloading src_port_int_TCPUDP \<equiv> "src_port :: ('\<alpha>::adr,'\<beta>) packet \<Rightarrow> '\<gamma>::port" 
begin 
definition 
   "src_port_int_TCPUDP (x::(adr\<^sub>i\<^sub>p\<^sub>p,'\<beta>) packet)  \<equiv> (fst o snd o fst  o snd) x"
end 

overloading dest_port_int_TCPUDP \<equiv> "dest_port :: ('\<alpha>::adr,'\<beta>) packet \<Rightarrow> '\<gamma>::port"
begin
definition 
  "dest_port_int_TCPUDP (x::(adr\<^sub>i\<^sub>p\<^sub>p,'\<beta>) packet) \<equiv> (fst o snd o fst o  snd o snd) x"
end 

overloading subnet_of_int_TCPUDP \<equiv> "subnet_of :: '\<alpha>::adr \<Rightarrow> '\<alpha> net"
begin 
definition
  "subnet_of_int_TCPUDP (x::(adr\<^sub>i\<^sub>p\<^sub>p)) \<equiv> {{(a,b,c). a = fst x}}::adr\<^sub>i\<^sub>p\<^sub>p net" 
end

overloading src_protocol_int_TCPUDP \<equiv> "src_protocol :: ('\<alpha>::adr,'\<beta>) packet \<Rightarrow> protocol"
begin
definition 
  "src_protocol_int_TCPUDP (x::(adr\<^sub>i\<^sub>p\<^sub>p,'\<beta>) packet) \<equiv> (snd o snd o fst o snd) x"
end

overloading dest_protocol_int_TCPUDP \<equiv> "dest_protocol :: ('\<alpha>::adr,'\<beta>) packet \<Rightarrow> protocol"
begin
definition 
  "dest_protocol_int_TCPUDP (x::(adr\<^sub>i\<^sub>p\<^sub>p,'\<beta>) packet) \<equiv> (snd o snd o fst o snd o snd) x"
end

lemma src_port: "src_port (a,x::adr\<^sub>i\<^sub>p\<^sub>p,d,e) = fst (snd x)"
  by (simp add: src_port_int_TCPUDP_def in_subnet)

lemma dest_port: "dest_port (a,d,x::adr\<^sub>i\<^sub>p\<^sub>p,e) = fst (snd x)"
  by (simp add: dest_port_int_TCPUDP_def in_subnet)

text {* Common test constraints: *}


definition port_positive :: "(adr\<^sub>i\<^sub>p\<^sub>p,'b) packet \<Rightarrow> bool" where
 "port_positive x = (dest_port x > (0::port))"

definition fix_values :: "(adr\<^sub>i\<^sub>p\<^sub>p,DummyContent) packet \<Rightarrow> bool" where
 "fix_values x =  (src_port x = (1::port) \<and> src_protocol x = udp \<and> content x = data \<and> id x = 1)"


lemmas adr\<^sub>i\<^sub>p\<^sub>pLemmas = 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 adr\<^sub>i\<^sub>p\<^sub>pTestConstraints = port_positive_def fix_values_def

end