theory Enrichimports Main Flask Static Init_prop Valid_prop Tainted_prop Delete_prop Co2sobj_prop S2ss_prop S2ss_prop2 Tempbegincontext tainting_s begin(* enrich s target_proc duplicated_pro *)fun enrich_proc :: "t_state \<Rightarrow> t_process \<Rightarrow> t_process \<Rightarrow> t_state"where "enrich_proc [] tp dp = []"| "enrich_proc (Execve p f fds # s) tp dp = ( if (tp = p) then Execve dp f (fds \<inter> proc_file_fds s p) # Execve p f fds # (enrich_proc s tp dp) else Execve p f fds # (enrich_proc s tp dp))"| "enrich_proc (Clone p p' fds # s) tp dp = ( if (tp = p') then Clone p dp (fds \<inter> proc_file_fds s p) # Clone p p' fds # s else Clone p p' fds # (enrich_proc s tp dp))"| "enrich_proc (Open p f flags fd opt # s) tp dp = ( if (tp = p) then Open dp f (remove_create_flag flags) fd opt # Open p f flags fd opt # (enrich_proc s tp dp) else Open p f flags fd opt # (enrich_proc s tp dp))"| "enrich_proc (CloseFd p fd # s) tp dp = ( if (tp = p) then CloseFd dp fd # CloseFd p fd # (enrich_proc s tp dp) else CloseFd p fd # (enrich_proc s tp dp))"(*| "enrich_proc (Attach p h flag # s) tp dp = ( if (tp = p) then Attach dp h flag # Attach p h flag # (enrich_proc s tp dp) else Attach p h flag # (enrich_proc s tp dp))"| "enrich_proc (Detach p h # s) tp dp = ( if (tp = p) then Detach dp h # Detach p h # (enrich_proc s tp dp) else Detach p h # (enrich_proc s tp dp))"*)| "enrich_proc (Kill p p' # s) tp dp = ( if (tp = p) then Kill p p' # s else Kill p p' # (enrich_proc s tp dp))"| "enrich_proc (Exit p # s) tp dp = ( if (tp = p) then Exit p # s else Exit p # (enrich_proc s tp dp))"| "enrich_proc (e # s) tp dp = e # (enrich_proc s tp dp)"definition is_created_proc:: "t_state \<Rightarrow> t_process \<Rightarrow> bool"where "is_created_proc s p \<equiv> p \<in> init_procs \<longrightarrow> died (O_proc p) s"lemma enrich_search_check: assumes grant: "search_check s (up, rp, tp) f" and cf2sf: "\<forall> f. f \<in> current_files s \<longrightarrow> cf2sfile s' f = cf2sfile s f" and vd: "valid s" and f_in: "is_file s f" and f_in': "is_file s' f" and sec: "sectxt_of_obj s' (O_file f) = sectxt_of_obj s (O_file f)" shows "search_check s' (up, rp, tp) f"proof (cases f) case Nil with f_in vd have "False" by (auto dest:root_is_dir') thus ?thesis by simpnext case (Cons n pf) from vd f_in obtain sf where sf: "cf2sfile s f = Some sf" apply (drule_tac is_file_in_current, drule_tac current_file_has_sfile, simp) apply (erule exE, simp) done then obtain psfs where psfs: "get_parentfs_ctxts s pf = Some psfs" using Cons by (auto simp:cf2sfile_def split:option.splits if_splits) from sf cf2sf f_in have sf': "cf2sfile s' f = Some sf" by (auto dest:is_file_in_current) then obtain psfs' where psfs': "get_parentfs_ctxts s' pf = Some psfs'"using Cons by (auto simp:cf2sfile_def split:option.splits if_splits) with sf sf' psfs have psfs_eq: "set psfs' = set psfs" using Cons f_in f_in' apply (simp add:cf2sfile_def split:option.splits) apply (case_tac sf, simp) done show ?thesis using grant f_in f_in' psfs psfs' psfs_eq sec apply (simp add:Cons split:option.splits) by (case_tac a, simp)qedlemma proc_filefd_has_sfd: "\<lbrakk>fd \<in> proc_file_fds s p; valid s\<rbrakk> \<Longrightarrow> \<exists> sfd. cfd2sfd s p fd = Some sfd"apply (simp add:proc_file_fds_def)apply (auto dest: current_filefd_has_sfd)donelemma enrich_inherit_fds_check: assumes grant: "inherit_fds_check s (up, nr, nt) p fds" and vd: "valid s" and cfd2sfd: "\<forall> p fd. fd \<in> proc_file_fds s p\<longrightarrow> cfd2sfd s' p fd = cfd2sfd s p fd" and fd_in: "fds \<subseteq> proc_file_fds s p" and fd_in': "fds \<subseteq> proc_file_fds s' p" shows "inherit_fds_check s' (up, nr, nt) p fds"proof- have "\<And> fd. fd \<in> fds \<Longrightarrow> sectxt_of_obj s' (O_fd p fd) = sectxt_of_obj s (O_fd p fd)" proof- fix fd assume fd_in_fds: "fd \<in> fds" hence fd_in_cfds: "fd \<in> proc_file_fds s p" and fd_in_cfds': "fd \<in> proc_file_fds s' p" using fd_in fd_in' by auto with cfd2sfd have cfd_eq: "cfd2sfd s' p fd = cfd2sfd s p fd" by auto from fd_in_cfds obtain f where ffd: "file_of_proc_fd s p fd = Some f" by (auto simp:proc_file_fds_def) moreover have "flags_of_proc_fd s p fd \<noteq> None" using ffd vd by (auto dest:current_filefd_has_flags) moreover have "sectxt_of_obj s (O_fd p fd) \<noteq> None" using fd_in_cfds vd apply (rule_tac notI) by (auto dest!:current_has_sec' file_fds_subset_pfds[where p = p] intro:vd) moreover have "cf2sfile s f \<noteq> None" apply (rule notI) apply (drule current_file_has_sfile') using ffd by (auto simp:vd is_file_in_current dest:file_of_pfd_is_file) ultimately show "sectxt_of_obj s' (O_fd p fd) = sectxt_of_obj s (O_fd p fd)" using cfd_eq by (auto simp:cfd2sfd_def split:option.splits) qed hence "sectxts_of_fds s' p fds = sectxts_of_fds s p fds" by (simp add:sectxts_of_fds_def) thus ?thesis using grant by (simp add:inherit_fds_check_def)qedlemma not_all_procs_cons: "p \<notin> all_procs (e # s) \<Longrightarrow> p \<notin> all_procs s"by (case_tac e, auto)lemma not_all_procs_prop: "\<lbrakk>p' \<notin> all_procs s; p \<in> current_procs s; valid s\<rbrakk> \<Longrightarrow> p' \<noteq> p"apply (induct s, rule notI, simp)apply (frule vt_grant_os, frule vd_cons, frule not_all_procs_cons, simp, rule notI)apply (case_tac a, auto)donefun enrich_not_alive :: "t_state \<Rightarrow> t_object \<Rightarrow> bool"where "enrich_not_alive s (O_file f) = (f \<notin> current_files s)"| "enrich_not_alive s (O_dir f) = (f \<notin> current_files s)"| "enrich_not_alive s (O_proc p) = (p \<notin> current_procs s)"| "enrich_not_alive s (O_fd p fd) = (fd \<notin> current_proc_fds s p)"| "enrich_not_alive s (O_msgq q) = (q \<notin> current_msgqs s)"| "enrich_not_alive s (O_msg q m) = (m \<notin> set (msgs_of_queue s q) \<or> q \<notin> current_msgqs s)"| "enrich_not_alive s _ = True"lemma enrich_valid_intro_cons: assumes vs': "valid s'" and os: "os_grant s e" and grant: "grant s e" and vd: "valid s" and alive: "\<forall> obj. alive s obj \<longrightarrow> alive s' obj" and alive': "\<forall> obj. enrich_not_alive s obj \<longrightarrow> enrich_not_alive s' obj" and cp2sp: "\<forall> p. p \<in> current_procs s \<longrightarrow> cp2sproc s' p = cp2sproc s p" and cf2sf: "\<forall> f. f \<in> current_files s \<longrightarrow> cf2sfile s' f = cf2sfile s f" and ffd_remain: "\<forall> p fd f. file_of_proc_fd s p fd = Some f \<longrightarrow> file_of_proc_fd s' p fd = Some f" and cfd2sfd: "\<forall> p fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd s' p fd = cfd2sfd s p fd" shows "valid (e # s')"proof (cases e) case (Execve p f fds) have p_in: "p \<in> current_procs s'" using os alive apply (erule_tac x = "O_proc p" in allE) by (auto simp:Execve) have f_in: "is_file s' f" using os alive apply (erule_tac x = "O_file f" in allE) by (auto simp:Execve) have fd_in: "fds \<subseteq> proc_file_fds s' p" using os alive ffd_remain by (auto simp:Execve proc_file_fds_def) have "os_grant s' e" using p_in f_in fd_in by (simp add:Execve) moreover have "grant s' e" proof- from grant obtain up rp tp uf rf tf where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)" and p2: "sectxt_of_obj s (O_file f) = Some (uf, rf, tf)" by (simp add:Execve split:option.splits, blast) with grant obtain pu nr nt where p3: "npctxt_execve (up, rp, tp) (uf, rf, tf) = Some (pu, nr, nt)" by (simp add:Execve split:option.splits del:npctxt_execve.simps, blast) from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)" using os cp2sp apply (erule_tac x = p in allE) by (auto simp:Execve co2sobj.simps cp2sproc_def split:option.splits) from os have f_in': "is_file s f" by (simp add:Execve) from vd os have "\<exists> sf. cf2sfile s f = Some sf" by (auto dest!:is_file_in_current current_file_has_sfile simp:Execve) hence p2': "sectxt_of_obj s' (O_file f) = Some (uf, rf, tf)" using f_in f_in' p2 cf2sf apply (erule_tac x = f in allE) apply (auto dest:is_file_in_current simp:cf2sfile_def split:option.splits) apply (case_tac f, simp) apply (drule_tac s = s in root_is_dir', simp add:vd, simp+) done have "inherit_fds_check s' (pu, nr, nt) p fds" proof- have "fds \<subseteq> proc_file_fds s' p" using os ffd_remain Execve by (auto simp:proc_file_fds_def) thus ?thesis using Execve grant vd cfd2sfd p1 p2 p3 os apply (rule_tac s = s in enrich_inherit_fds_check) by (simp_all split:option.splits) qed moreover have "search_check s' (pu, rp, tp) f" using p1 p2 p2' vd cf2sf f_in' grant Execve p3 f_in apply (rule_tac s = s in enrich_search_check) by (simp_all split:option.splits) ultimately show ?thesis using p1' p2' p3 apply (simp add:Execve split:option.splits) using grant Execve p1 p2 by (simp add:Execve grant p1 p2) qed ultimately show ?thesis using vs' by (erule_tac valid.intros(2), simp+)next case (Clone p p' fds) have p_in: "p \<in> current_procs s'" using os alive apply (erule_tac x = "O_proc p" in allE) by (auto simp:Clone) have p'_not_in: "p' \<notin> current_procs s'" using os alive' apply (erule_tac x = "O_proc p'" in allE) by (auto simp:Clone) have fd_in: "fds \<subseteq> proc_file_fds s' p" using os alive ffd_remain by (auto simp:Clone proc_file_fds_def) have "os_grant s' e" using p_in p'_not_in fd_in by (simp add:Clone) moreover have "grant s' e" proof- from grant obtain up rp tp where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)" apply (simp add:Clone split:option.splits) by (case_tac a, auto) from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)" using os cp2sp apply (erule_tac x = p in allE) by (auto simp:Clone co2sobj.simps cp2sproc_def split:option.splits) have p2: "inherit_fds_check s' (up, rp, tp) p fds" proof- have "fds \<subseteq> proc_file_fds s' p" using os ffd_remain Clone by (auto simp:proc_file_fds_def) thus ?thesis using Clone grant vd cfd2sfd p1 os apply (rule_tac s = s in enrich_inherit_fds_check) by (simp_all split:option.splits) qed show ?thesis using p1 p2 p1' grant by (simp add:Clone) qed ultimately show ?thesis using vs' by (erule_tac valid.intros(2), simp+)nextlemma enrich_proc_prop: "\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> valid (enrich_proc s p p') \<and> (p \<in> current_procs s \<longrightarrow> co2sobj (enrich_proc s p p') (O_proc p') = co2sobj (enrich_proc s p p') (O_proc p)) \<and> (\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj) \<and> (\<forall> p'. p' \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') p' = cp2sproc s p) \<and> (\<forall> f. f \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') f = cf2sfile s f) \<and> (Tainted (enrich_proc s p p') = (Tainted s \<union> (if (O_proc p \<in> Tainted s) then {O_proc p'} else {})))"proof (induct s) case Nil thus ?case by (auto simp:is_created_proc_def)next case (Cons e s) hence p1: "\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> valid (enrich_proc s p p') \<and> (p \<in> current_procs s \<longrightarrow> co2sobj (enrich_proc s p p') (O_proc p') = co2sobj (enrich_proc s p p') (O_proc p)) \<and> (alive s obj \<longrightarrow> alive (enrich_proc s p p') obj \<and> co2sobj (enrich_proc s p p') obj = co2sobj s obj)" and p2: "valid (e # s)" and p3: "is_created_proc (e # s) p" and p4: "p' \<notin> all_procs (e # s)" by auto from p2 have vd: "valid s" and os: "os_grant s e" and grant: "grant s e" by (auto dest:vd_cons vt_grant vt_grant_os) from p4 have p4': "p' \<notin> all_procs s" by (case_tac e, auto) from p1 p4' have a1: "is_created_proc s p \<Longrightarrow> valid (enrich_proc s p p')" by (auto simp:vd) have c1: "valid (enrich_proc (e # s) p p')" apply (case_tac e) using a1 os p3 apply (auto simp:is_created_proc_def) sorry moreover have c2: "p' \<in> current_procs (enrich_proc (e # s) p p')" sorry moreover have c3: "co2sobj (enrich_proc (e # s) p p') (O_proc p') = co2sobj (enrich_proc (e # s) p p') (O_proc p)" sorry moreover have c4: "alive (e # s) obj \<longrightarrow> alive (enrich_proc (e # s) p p') obj \<and> co2sobj (enrich_proc (e # s) p p') obj = co2sobj (e # s) obj" sorry ultimately show ?case by autoqed