Theory PersonalFirewallDatatype

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subsection ‹Personal Firewall: Datatype›
theory 
  PersonalFirewallDatatype
  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.  
›

datatype Adr = pc | internet
  
type_synonym DatatypeTwoNets = "Adr × int"
  
instance Adr::adr ..
    
definition
  PC :: "DatatypeTwoNets net" where
  "PC = {{(a,b). a = pc}}"
  
definition
  Internet :: "DatatypeTwoNets net" where
  "Internet = {{(a,b). a = internet}}"
  
definition
  not_in_same_net :: "(DatatypeTwoNets,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 

  In fact, the short definitions wouldn't have to be written down - they
  are the automatically simplified versions of their big counterparts.
›

definition
  strictPolicy :: "(DatatypeTwoNets,DummyContent) FWPolicy" where
  "strictPolicy = deny_all ++ allow_all_from_to PC Internet"
  
definition
  PortPolicy :: "(DatatypeTwoNets,'b) FWPolicy" where
  "PortPolicy = deny_all ++ allow_from_ports_to {80::port,24,21} PC Internet"
  
definition
  PortPolicyBig :: "(DatatypeTwoNets,'b) FWPolicy" where
  "PortPolicyBig =  
                 allow_from_port_to (80::port) PC Internet ⨁ 
                 allow_from_port_to (24::port) PC Internet ⨁ 
                 allow_from_port_to (21::port) PC Internet ⨁ 
                 deny_all"
  
lemmas policyLemmas = strictPolicy_def PortPolicy_def PC_def Internet_def PortPolicyBig_def src_def 
                      PolicyCombinators PortCombinators in_subnet_def
  
end