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 
  adr⇩i⇩p⇩p = "address × port × protocol" 

instance protocol :: adr ..

overloading src_port_int_TCPUDP ≡ "src_port :: ('α::adr,'β) packet ⇒ 'γ::port" 
begin 
definition 
  "src_port_int_TCPUDP (x::(adr⇩i⇩p⇩p,'β) packet)  ≡ (fst o snd o fst  o snd) x"
end 

overloading dest_port_int_TCPUDP ≡ "dest_port :: ('α::adr,'β) packet ⇒ 'γ::port"
begin
definition 
  "dest_port_int_TCPUDP (x::(adr⇩i⇩p⇩p,'β) packet) ≡ (fst o snd o fst o  snd o snd) x"
end 

overloading subnet_of_int_TCPUDP ≡ "subnet_of :: 'α::adr ⇒ 'α net"
begin 
definition
  "subnet_of_int_TCPUDP (x::(adr⇩i⇩p⇩p)) ≡ {{(a,b,c). a = fst x}}::adr⇩i⇩p⇩p net" 
end

overloading src_protocol_int_TCPUDP ≡ "src_protocol :: ('α::adr,'β) packet ⇒ protocol"
begin
definition 
  "src_protocol_int_TCPUDP (x::(adr⇩i⇩p⇩p,'β) packet) ≡ (snd o snd o fst o snd) x"
end

overloading dest_protocol_int_TCPUDP ≡ "dest_protocol :: ('α::adr,'β) packet ⇒ protocol"
begin
definition 
  "dest_protocol_int_TCPUDP (x::(adr⇩i⇩p⇩p,'β) packet) ≡ (snd o snd o fst o snd o snd) x"
end

lemma src_port: "src_port (a,x::adr⇩i⇩p⇩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⇩i⇩p⇩p,e) = fst (snd x)"
  by (simp add: dest_port_int_TCPUDP_def in_subnet)

text ‹Common test constraints:›

definition port_positive :: "(adr⇩i⇩p⇩p,'b) packet ⇒ bool" where
  "port_positive x = (dest_port x > (0::port))"

definition fix_values :: "(adr⇩i⇩p⇩p,DummyContent) packet ⇒ bool" where
  "fix_values x =  (src_port x = (1::port) ∧ src_protocol x = udp ∧ content x = data ∧ id x = 1)"


lemmas adr⇩i⇩p⇩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⇩i⇩p⇩pTestConstraints = port_positive_def fix_values_def
  
end