Theory PersonalFirewallInt

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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 :: "(adrip net)" where
  "PC = {{(a,b). a = 3}}"
  
definition
  Internet :: "adrip net" where
  "Internet = {{(a,b). ¬ (a = 3)}}"

definition
  not_in_same_net :: "(adrip,DummyContent) packet ⇒ bool" where
  "not_in_same_net x = ((src x ⊏ PC ⟶ dest x ⊏ Internet) ∧ (src x ⊏ Internet ⟶ dest x ⊏ PC))" 
  
text ‹
  Definitions of the policies 
›

definition
  strictPolicy :: "(adrip,DummyContent) FWPolicy" where
  "strictPolicy = deny_all ++ allow_all_from_to PC Internet"

definition 
  PortPolicy :: "(adrip,DummyContent) FWPolicy" where
  "PortPolicy = deny_all ++ allow_from_ports_to {http,smtp,ftp} PC Internet"
  
definition
  PortPolicyBig :: "(adrip,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
  adripLemmas content_def
  PortCombinators in_subnet_def PortPolicyBig_def id_def
  
declare Ports [simp add]
  
definition wellformed_packet::"(adrip,DummyContent) packet ⇒ bool" where
  "wellformed_packet p = (content p = data)"
  
end