theory Enrichimports Main Flask Static Init_prop Valid_prop Tainted_prop Delete_prop Co2sobj_prop S2ss_prop S2ss_prop2 Temp Enrich Proc_fd_of_file_propbegincontext tainting_s beginlemma get_parentfs_ctxts_prop: "\<lbrakk>get_parentfs_ctxts s (a # f) = Some ctxts; sectxt_of_obj s (O_dir f) = Some ctxt; valid s\<rbrakk> \<Longrightarrow> ctxt \<in> set (ctxts)"apply (induct f)apply (auto split:option.splits)donelemma search_check_allp_intro: "\<lbrakk>search_check s sp pf; get_parentfs_ctxts s pf = Some ctxts; valid s; is_dir s pf\<rbrakk> \<Longrightarrow> search_check_allp sp (set ctxts)"apply (case_tac pf)apply (simp split:option.splits if_splits add:search_check_allp_def)apply (rule ballI)apply (auto simp:search_check_ctxt_def search_check_dir_def split:if_splits option.splits)apply (auto simp:search_check_allp_def search_check_file_def)apply (frule is_dir_not_file, simp)donelemma search_check_leveling_f: "\<lbrakk>search_check s sp pf; parent f = Some pf; is_file s f; valid s; sectxt_of_obj s (O_file f) = Some fctxt; search_check_file sp fctxt\<rbrakk> \<Longrightarrow> search_check s sp f"apply (case_tac f, simp+)apply (auto split:option.splits simp:search_check_ctxt_def)apply (frule parentf_is_dir_prop2, simp)apply (erule get_pfs_secs_prop, simp)apply (erule_tac search_check_allp_intro, simp_all)apply (simp add:parentf_is_dir_prop2)donelemma 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> (\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj) \<and> (\<forall> obj. enrich_not_alive s obj \<longrightarrow> enrich_not_alive (enrich_proc s p p') obj) \<and> (files_hung_by_del (enrich_proc s p p') = files_hung_by_del s) \<and> (\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp) \<and> (\<forall> f. f \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') f = cf2sfile s f) \<and> (\<forall> q. q \<in> current_msgqs s \<longrightarrow> cq2smsgq (enrich_proc s p p') q = cq2smsgq s q) \<and> (\<forall> tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> file_of_proc_fd (enrich_proc s p p') tp fd = Some f) \<and> (\<forall> tp fd flags. flags_of_proc_fd s tp fd = Some flags \<longrightarrow> flags_of_proc_fd (enrich_proc s p p') tp fd = Some flags) \<and> (\<forall> q. msgs_of_queue (enrich_proc s p p') q = msgs_of_queue s q) \<and> (\<forall> tp fd. fd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp fd = cfd2sfd s tp fd) \<and> (cp2sproc (enrich_proc s p p') p' = cp2sproc s p) \<and> (\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd)"proof (induct s) case Nil thus ?case by (auto simp:is_created_proc_def)next case (Cons e s) hence vd_cons': "valid (e # s)" and created_cons: "is_created_proc (e # s) p" and all_procs_cons: "p' \<notin> all_procs (e # s)" and vd: "valid s" and os: "os_grant s e" and grant: "grant s e" by (auto dest:vd_cons' vt_grant_os vt_grant) from all_procs_cons have all_procs: "p' \<notin> all_procs s" by (case_tac e, auto) from Cons have pre: "is_created_proc s p \<Longrightarrow> valid (enrich_proc s p p') \<and> (\<forall>obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj) \<and> (\<forall>obj. enrich_not_alive s obj \<longrightarrow> enrich_not_alive (enrich_proc s p p') obj) \<and> files_hung_by_del (enrich_proc s p p') = files_hung_by_del s \<and> (\<forall>tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp) \<and> (\<forall>f. f \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') f = cf2sfile s f) \<and> (\<forall>q. q \<in> current_msgqs s \<longrightarrow> cq2smsgq (enrich_proc s p p') q = cq2smsgq s q) \<and> (\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> file_of_proc_fd (enrich_proc s p p') tp fd = Some f) \<and> (\<forall>tp fd flags. flags_of_proc_fd s tp fd = Some flags \<longrightarrow> flags_of_proc_fd (enrich_proc s p p') tp fd = Some flags) \<and> (\<forall>q. msgs_of_queue (enrich_proc s p p') q = msgs_of_queue s q) \<and> (\<forall>tp fd. fd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp fd = cfd2sfd s tp fd) \<and> (cp2sproc (enrich_proc s p p') p' = cp2sproc s p) \<and> (\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd)" using vd all_procs by auto have alive_pre: "is_created_proc s p \<Longrightarrow> (\<forall>obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj)" using pre by simp hence curf_pre: "is_created_proc s p \<Longrightarrow> (\<forall>f. f \<in> current_files s \<longrightarrow> f \<in> current_files (enrich_proc s p p'))" using vd apply auto apply (drule is_file_or_dir, simp) apply (erule disjE) apply (erule_tac x = "O_file f" in allE, simp add:is_file_in_current) apply (erule_tac x = "O_dir f" in allE, simp add:is_dir_in_current) done have vd_enrich_cons: "valid (enrich_proc (e # s) p p')" proof- from pre have pre': "is_created_proc s p \<Longrightarrow> valid (enrich_proc s p p')" by simp have "is_created_proc s p \<Longrightarrow> valid (e # enrich_proc s p p')" apply (frule pre') apply (erule_tac s = s in enrich_valid_intro_cons) apply (simp_all add:os grant vd pre) done moreover have "\<And>f fds. \<lbrakk>valid (Execve p f fds # enrich_proc s p p'); is_created_proc s p; valid (Execve p f fds # s); p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> valid (Execve p' f (fds \<inter> proc_file_fds s p) # Execve p f fds # enrich_proc s p p')" proof- fix f fds assume a1: "valid (Execve p f fds # enrich_proc s p p')" and a2: "is_created_proc s p" and a3: "valid (Execve p f fds # s)" and a0: "p' \<notin> all_procs s" have cp2sp: "\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp" and cf2sf: "\<forall> tf. tf \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') tf = cf2sfile s tf" and cfd2sfd: "\<forall> tp tfd. tfd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp tfd = cfd2sfd s tp tfd" and ffd_remain: "\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> file_of_proc_fd (enrich_proc s p p') tp fd = Some f" and dup_sp: "cp2sproc (enrich_proc s p p') p' = cp2sproc s p" and dup_sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd" using pre a2 by auto show "valid (Execve p' f (fds \<inter> proc_file_fds s p) # Execve p f fds # enrich_proc s p p')" proof- from a0 a3 have a0': "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3) from a3 have grant: "grant s (Execve p f fds)" and os: "os_grant s (Execve p f fds)" by (auto dest:vt_grant_os vt_grant simp del:os_grant.simps) have f_in: "is_file (enrich_proc s p p') f" proof- from pre a2 have a4: "\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj" by (auto) show ?thesis using a3 a4 apply (erule_tac x = "O_file f" in allE) by (auto dest:vt_grant_os) qed moreover have a5: "proc_file_fds s p \<subseteq> proc_file_fds (Execve p f fds # enrich_proc s p p') p'" using a3 a0' apply (frule_tac vt_grant_os) apply (auto simp:proc_file_fds_def) apply (rule_tac x = fa in exI) apply (erule enrich_proc_dup_ffd) apply (simp_all add:vd all_procs a2) done ultimately have "os_grant (Execve p f fds # enrich_proc s p p') (Execve p' f (fds \<inter> proc_file_fds s p))" apply (auto simp:is_file_simps enrich_proc_dup_in a2 vd all_procs a1 enrich_proc_dup_ffds) done moreover have "grant (Execve p f fds # enrich_proc s p p') (Execve p' f (fds \<inter> proc_file_fds s p))" 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 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 split:option.splits del:npctxt_execve.simps, blast) have p1': "sectxt_of_obj (Execve p f fds # enrich_proc s p p') (O_proc p') = Some (up, rp, tp)" using p1 dup_sp a1 a0' apply (simp add:sectxt_of_obj_simps) by (simp add:cp2sproc_def split:option.splits) from os have f_in': "is_file s f" by simp from vd os have "\<exists> sf. cf2sfile s f = Some sf" by (auto dest!:is_file_in_current current_file_has_sfile) hence p2': "sectxt_of_obj (Execve p f fds # enrich_proc s p p') (O_file f) = Some (uf, rf, tf)" using f_in p2 cf2sf os a1 apply (erule_tac x = f in allE) apply (auto dest:is_file_in_current simp:cf2sfile_def sectxt_of_obj_simps split:option.splits) apply (case_tac f, simp) apply (drule_tac s = s in root_is_dir', simp add:vd, simp+) done from dup_sfd a5 have "\<forall>fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (Execve p f fds # enrich_proc s p p') p' fd = cfd2sfd s p fd" apply (rule_tac allI) apply (erule_tac x = fd in allE, clarsimp) apply (drule set_mp, simp) apply (auto simp:cfd2sfd_execve proc_file_fds_def a1) done hence "inherit_fds_check (Execve p f fds # enrich_proc s p p') (up, nr, nt) p' (fds \<inter> proc_file_fds s p)" using grant os p1 p2 p3 vd apply (clarsimp) apply (rule_tac s = s and p = p and fds = fds in enrich_inherit_fds_check_dup) apply simp_all done moreover have "search_check (Execve p f fds # enrich_proc s p p') (up, rp, tp) f" using p1 p2 p2' vd cf2sf f_in f_in' grant p3 f_in a1 apply (rule_tac s = s in enrich_search_check) apply (simp_all add:is_file_simps) apply (rule allI, rule impI, erule_tac x = fa in allE, simp) apply (drule_tac ff = fa in cf2sfile_other') by (auto simp:a2 curf_pre) ultimately show ?thesis using p1' p2' p3 apply (simp split:option.splits) using grant p1 p2 apply simp done qed ultimately show ?thesis using a1 by (erule_tac valid.intros(2), auto) qed qed moreover have "\<And>tp fds. \<lbrakk>valid (Clone tp p fds # s); p' \<noteq> p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> valid (Clone tp p' (fds \<inter> proc_file_fds s tp) # Clone tp p fds # s)" apply (frule vt_grant_os, frule vt_grant, drule not_all_procs_prop3) apply (rule valid.intros(2)) apply (simp_all split:option.splits add:sectxt_of_obj_simps) apply (auto simp add:proc_file_fds_def)[1] apply (auto simp:inherit_fds_check_def sectxt_of_obj_simps sectxts_of_fds_def inherit_fds_check_ctxt_def) done moreover have "\<And>f flags fd opt. \<lbrakk>valid (Open p f flags fd opt # enrich_proc s p p'); is_created_proc s p; valid (Open p f flags fd opt # s); p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> valid (Open p' f (remove_create_flag flags) fd None # Open p f flags fd opt # enrich_proc s p p')" proof- fix f flags fd opt assume a1: "valid (Open p f flags fd opt # enrich_proc s p p')" and a2: "is_created_proc s p" and a3: "valid (Open p f flags fd opt # s)" and a4: "p' \<notin> all_procs s" have cp2sp: "\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp" and cf2sf: "\<forall> tf. tf \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') tf = cf2sfile s tf" and cfd2sfd: "\<forall> tp tfd. tfd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp tfd = cfd2sfd s tp tfd" and ffd_remain: "\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> file_of_proc_fd (enrich_proc s p p') tp fd = Some f" and dup_sp: "cp2sproc (enrich_proc s p p') p' = cp2sproc s p" and dup_sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd" using pre a2 by auto from a4 a3 have a0: "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3 split:option.splits) have a5: "p' \<in> current_procs (enrich_proc s p p')" using a2 a3 vd apply (erule_tac enrich_proc_dup_in) by (simp_all add:vd a4) have a6: "is_file (Open p f flags fd opt # enrich_proc s p p') f" using a1 a3 by (auto simp:is_file_open dest:vt_grant_os) have a7: "fd \<notin> current_proc_fds (enrich_proc s p p') p'" using a2 a4 vd apply (simp add:enrich_proc_dup_ffds_eq_fds) apply (rule notI) apply (drule_tac p = p in file_fds_subset_pfds) apply (drule set_mp, simp) using a3 apply (drule_tac vt_grant_os) apply (auto split:option.splits) done from a1 have a8: "valid (enrich_proc s p p')" by (erule_tac valid.cases, auto) from a3 have grant: "grant s (Open p f flags fd opt)" and os: "os_grant s (Open p f flags fd opt)" by (auto dest:vt_grant_os vt_grant) show "valid (Open p' f (remove_create_flag flags) fd None # Open p f flags fd opt # enrich_proc s p p')" proof (cases opt) case None have f_in: "is_file (enrich_proc s p p') f" proof- from pre a2 have a4: "\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj" by (auto) show ?thesis using a3 a4 None apply (erule_tac x = "O_file f" in allE) by (auto dest:vt_grant_os) qed from grant None 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)" apply (simp split:option.splits) by (case_tac a, case_tac aa, blast) have p1': "sectxt_of_obj (Open p f flags fd opt # enrich_proc s p p') (O_proc p') = Some (up, rp, tp)" using p1 dup_sp a1 apply (simp add:sectxt_of_obj_simps) by (simp add:cp2sproc_def split:option.splits) from os None have f_in': "is_file s f" by simp from vd os None have "\<exists> sf. cf2sfile s f = Some sf" by (auto dest!:is_file_in_current current_file_has_sfile) hence p2': "sectxt_of_obj (Open p f flags fd opt # enrich_proc s p p') (O_file f) = Some (uf, rf, tf)" using p2 cf2sf os a1 None f_in' vd f_in apply (erule_tac x = f in allE) apply (auto dest:is_file_in_current simp:cf2sfile_def sectxt_of_obj_simps split:option.splits) apply (case_tac f, simp) apply (drule_tac s = s in root_is_dir', simp add:vd, simp+) done have "search_check (Open p f flags fd opt # enrich_proc s p p') (up, rp, tp) f" using p1 p2 p2' vd cf2sf f_in f_in' grant f_in a1 None apply (rule_tac s = s in enrich_search_check) apply (simp_all add:is_file_simps) apply (rule allI, rule impI, erule_tac x = fa in allE, simp) apply (simp add:cf2sfile_open_none) done thus ?thesis using a0 a5 a6 a7 None a1 apply (rule_tac valid.intros(2)) apply (simp_all add:a1) apply (case_tac flags, simp add:is_creat_excl_flag_def) using p1' p2' apply simp using grant p1 p2 apply (simp add:oflags_check_remove_create) done next case (Some inum) with os obtain pf where parent: "parent f = Some pf" by auto with grant Some obtain pu rp pt pfu pfr pft where p1: "sectxt_of_obj s (O_proc p) = Some (pu, rp, pt)" and p2: "sectxt_of_obj s (O_dir pf) = Some (pfu, pfr, pft)" apply (simp split:option.splits) apply (case_tac a, case_tac aa, blast) done from p1 have p1': "sectxt_of_obj (enrich_proc s p p') (O_proc p) = Some (pu, rp, pt)" using cp2sp os apply (erule_tac x = p in allE) apply (auto split:option.splits simp:cp2sproc_def) done from os parent Some have pf_in: "is_dir s pf" by auto hence "\<exists> sf. cf2sfile s pf = Some sf" using vd by (auto dest!:is_dir_in_current current_file_has_sfile) from a1 parent Some have pf_in': "is_dir (enrich_proc s p p') pf" apply (frule_tac vt_grant_os) by (clarsimp) have p2': "sectxt_of_obj (enrich_proc s p p') (O_dir pf) = Some (pfu, pfr, pft)" proof- have "cf2sfile (enrich_proc s p p') pf = cf2sfile s pf" using cf2sf pf_in apply (drule_tac is_dir_in_current) apply (erule_tac x = pf in allE) by simp with pf_in pf_in' p2 vd Some a8 show ?thesis apply (frule_tac is_dir_not_file) apply (frule_tac s = "enrich_proc s p p'" in is_dir_not_file) apply (simp add:cf2sfile_def) apply (case_tac pf, simp) apply (simp add:sroot_def root_sec_remains) by (auto split:option.splits dest!:current_has_sec' get_pfs_secs_prop' dest:parentf_is_dir_prop1) qed from p1 have dup: "sectxt_of_obj (Open p f flags fd (Some inum) # enrich_proc s p p') (O_proc p') = Some (pu, rp, pt)" using a1 Some apply (simp add:sec_open) using dup_sp apply (auto split:option.splits if_splits simp:cp2sproc_def) done have nsf: "sectxt_of_obj (Open p f flags fd (Some inum) # enrich_proc s p p') (O_file f) = Some (pu, R_object, type_transition pt pft C_file True)" using a1 Some p1 p2 parent p2' p1' by (simp add:sec_open) have "search_check (Open p f flags fd (Some inum) # enrich_proc s p p') (pu, rp, pt) f" proof- have "search_check (Open p f flags fd (Some inum) # enrich_proc s p p') (pu, rp, pt) pf" using grant Some parent p1 p2 vd a1 pf_in pf_in' p2' apply simp apply (rule_tac s = s in enrich_search_check') apply (simp_all add:is_dir_simps sectxt_of_obj_simps) apply (rule allI, rule impI) apply (case_tac "fa = f") using os Some apply simp apply (drule_tac f' = fa in cf2sfile_open) apply (simp add:current_files_simps) using curf_pre a2 apply simp apply simp using cf2sf apply simp done moreover have "is_file (Open p f flags fd (Some inum) # enrich_proc s p p') f" using a1 Some by (simp add:is_file_open) ultimately show ?thesis using parent a1 Some nsf apply (erule_tac search_check_leveling_f) apply (simp_all) apply (simp add:search_check_file_def) apply (simp add:permission_check.simps) sorry qed thus ?thesis using a0 a5 a6 a7 a1 Some apply (rule_tac valid.intros(2)) apply (simp add:a1) apply simp apply (case_tac flags, simp add:is_creat_excl_flag_def) using grant p1 p2 parent dup nsf apply (simp add:oflags_check_remove_create) done qed qed moreover have "\<And>fd. \<lbrakk>valid (CloseFd p fd # enrich_proc s p p'); is_created_proc s p; valid (CloseFd p fd # s); p' \<notin> all_procs s; fd \<in> proc_file_fds s p\<rbrakk> \<Longrightarrow> valid (CloseFd p' fd # CloseFd p fd # enrich_proc s p p')" proof- fix fd assume a1: "valid (CloseFd p fd # enrich_proc s p p')" and a2: "is_created_proc s p" and a3: "p' \<notin> all_procs s" and a4: "valid (CloseFd p fd # s)" and a5: "fd \<in> proc_file_fds s p" from a4 a3 have a0: "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3) have "p' \<in> current_procs (enrich_proc s p p')" using a2 a3 vd by (auto intro:enrich_proc_dup_in) moreover have "fd \<in> current_proc_fds (enrich_proc s p p') p'" using a5 a2 a3 vd pre' apply (simp) apply (drule_tac s = "enrich_proc s p p'" and p = p' in file_fds_subset_pfds) apply (erule set_mp) apply (simp add:enrich_proc_dup_ffds) done ultimately show "valid (CloseFd p' fd # CloseFd p fd # enrich_proc s p p')" apply (rule_tac valid.intros(2)) apply (simp_all add:a1 a0 a2 pre') done qed moreover have "\<And> fd. \<lbrakk>valid (ReadFile p fd # enrich_proc s p p'); is_created_proc s p; valid (ReadFile p fd # s); p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> valid (ReadFile p' fd # ReadFile p fd # enrich_proc s p p')" proof- fix fd assume a1: "valid (ReadFile p fd # enrich_proc s p p')" and a2: "is_created_proc s p" and a3: "valid (ReadFile p fd # s)" and a4: "p' \<notin> all_procs s" from a3 have os: "os_grant s (ReadFile p fd)" and grant: "grant s (ReadFile p fd)" by (auto dest:vt_grant_os vt_grant) have cp2sp: "\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp" and cf2sf: "\<forall> tf. tf \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') tf = cf2sfile s tf" and cfd2sfd: "\<forall> tp tfd. tfd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp tfd = cfd2sfd s tp tfd" and ffd_remain: "\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> file_of_proc_fd (enrich_proc s p p') tp fd = Some f" and dup_sp: "cp2sproc (enrich_proc s p p') p' = cp2sproc s p" and dup_sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd" using pre a2 by auto have vd_enrich: "valid (enrich_proc s p p')" using a1 by (auto dest:valid.cases) show "valid (ReadFile p' fd # ReadFile p fd # enrich_proc s p p')" proof- have "os_grant (ReadFile p fd # enrich_proc s p p') (ReadFile p' fd)" using a1 a2 a4 vd os apply (clarsimp simp:current_files_simps enrich_proc_dup_in enrich_proc_dup_ffds_eq_fds) apply (simp add:proc_file_fds_def) apply (rule conjI) apply (rule_tac x = f in exI, simp add:enrich_proc_dup_ffd) using curf_pre apply (simp) apply (drule enrich_proc_dup_fflags) apply simp_all apply (erule disjE) apply auto apply (simp add:is_read_flag_def) done moreover have "grant (ReadFile p fd # enrich_proc s p p') (ReadFile p' fd)" proof- from grant obtain f sp sfd sf where p1: "file_of_proc_fd s p fd = Some f" and p2: "sectxt_of_obj s (O_proc p) = Some sp" and p3: "sectxt_of_obj s (O_fd p fd) = Some sfd" and p4: "sectxt_of_obj s (O_file f) = Some sf" by (auto split:option.splits) from os obtain flag where p0: "flags_of_proc_fd s p fd = Some flag" by auto from os have f_in_s: "f \<in> current_files s" using p1 by simp from p1 vd have isfile_s: "is_file s f" by (erule_tac file_of_pfd_is_file, simp) with alive_pre a2 have isfile_s': "is_file (enrich_proc s p p') f" apply simp apply (erule_tac x = "O_file f" in allE, simp) done from p0 obtain flag' where p0': "flags_of_proc_fd (enrich_proc s p p') p' fd = Some flag'" and p0'': "(flag' = flag) \<or> (flag' = remove_create_flag flag)" using a2 a4 vd apply (drule_tac enrich_proc_dup_fflags) apply auto apply (case_tac flag, auto) apply (case_tac flag, auto) done from p1 have p1': "file_of_proc_fd (enrich_proc s p p') p' fd = Some f" using a2 a4 vd by (simp add:enrich_proc_dup_ffd) from p2 have p2': "sectxt_of_obj (enrich_proc s p p') (O_proc p') = Some sp" using dup_sp by (auto simp:cp2sproc_def split:option.splits) from p3 p1 p1' p0 p0' os have p3': "sectxt_of_obj (enrich_proc s p p') (O_fd p' fd) = Some sfd" using dup_sfd apply (erule_tac x = fd in allE) apply (auto simp:proc_file_fds_def cfd2sfd_def split:option.splits) apply (drule current_file_has_sfile') apply (simp add:vd, simp) apply (drule current_file_has_sfile') apply (simp add:vd, simp) done from p4 have p4': "sectxt_of_obj (enrich_proc s p p') (O_file f) = Some sf" using f_in_s cf2sf isfile_s isfile_s' a1 vd_enrich vd apply (erule_tac x = f in allE) apply (simp) apply (auto simp:cf2sfile_def split:option.splits dest!:current_has_sec' get_pfs_secs_prop' dest:parentf_is_dir is_file_in_current) apply (case_tac f, simp, drule root_is_dir', simp, simp, simp) done show ?thesis using p1' p2' p3' p4' a1 apply (simp add:sectxt_of_obj_simps) using grant p1 p2 p3 p4 apply simp done qed ultimately show ?thesis using a1 by (erule_tac valid.intros(2), simp+) qed qed ultimately show ?thesis using created_cons vd_cons' all_procs_cons apply (case_tac e) apply (auto simp:is_created_proc_simps split:if_splits) done qed moreover have "\<forall>obj. alive (e # s) obj \<longrightarrow> alive (enrich_proc (e # s) p p') obj" proof clarify fix obj assume a0: "alive (e # s) obj" have a1: "is_created_proc s p \<Longrightarrow> \<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj" using pre by auto show "alive (enrich_proc (e # s) p p') obj" (* proof (cases e) case (Execve tp f fds) with created_cons a1 have b1: "\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj" by (auto simp:is_created_proc_simps) show ?thesis using created_cons all_procs_cons vd_enrich_cons Execve b1 os a0 apply (simp add:alive_execve split:if_splits) apply (frule_tac vd_cons) defer apply (frule_tac vd_cons) using vd_cons' Execve vd os apply (auto simp:is_file_simps is_dir_simps is_created_proc_simps alive.simps split:t_object.splits if_splits dest:set_mp file_fds_subset_pfds) apply (erule_tac x = "O_proc nat" in allE, simp) apply (erule_tac x = "O_file list" in allE, simp) apply (drule set_mp, simp) apply (drule_tac s = s and p = tp in file_fds_subset_pfds) apply (erule_tac x = "O_fd tp nat2" in allE, simp) apply (auto)[1] apply (erule_tac x = "O_fd nat1 nat2" in allE, auto dest:set_mp file_fds_subset_pfds)[1] apply (erule_tac x = "O_dir list" in allE, simp) sorry show ?thesis *) sorry moreover have "\<forall>obj. enrich_not_alive (e # s) obj \<longrightarrow> enrich_not_alive (enrich_proc (e # s) p p') obj" thm enrich_not_alive.simps sorry moreover have "files_hung_by_del (enrich_proc (e # s) p p') = files_hung_by_del (e # s)" proof- have "is_created_proc s p \<Longrightarrow> files_hung_by_del (enrich_proc s p p') = files_hung_by_del s" and ffd_remain: "is_created_proc s p \<Longrightarrow> \<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> file_of_proc_fd (enrich_proc s p p') tp fd = Some f" using pre by auto with created_cons all_procs_cons os vd_cons' vd show ?thesis apply (frule_tac not_all_procs_prop3) apply (case_tac e) apply (auto simp:files_hung_by_del.simps is_created_proc_simps) apply (auto simp:enrich_proc_dup_ffd_eq proc_file_fds_def procfd_of_file_eq_fpfd'' dest:procfd_of_file_imp_fpfd procfd_of_file_imp_fpfd' procfd_of_file_non_empty ) apply (auto simp:enrich_proc_dup_ffd_eq proc_file_fds_def split:if_splits)[1] apply (auto simp:enrich_proc_dup_ffd_eq proc_file_fds_def files_hung_by_del.simps split:option.splits)[1] apply (auto split:option.splits)[1] thm is_created_proc_simps sorry moreover have "\<forall>tp. tp \<in> current_procs (e # s) \<longrightarrow> cp2sproc (enrich_proc (e # s) p p') tp = cp2sproc (e # s) tp" sorry moreover have "\<forall>f. f \<in> current_files (e # s) \<longrightarrow> cf2sfile (enrich_proc (e # s) p p') f = cf2sfile (e # s) f" sorry moreover have "\<forall>q. q \<in> current_msgqs (e # s) \<longrightarrow> cq2smsgq (enrich_proc (e # s) p p') q = cq2smsgq (e # s) q" sorry moreover have "\<forall>tp fd f. file_of_proc_fd (e # s) tp fd = Some f \<longrightarrow> file_of_proc_fd (enrich_proc (e # s) p p') tp fd = Some f" sorry moreover have "\<forall>tp fd flags. flags_of_proc_fd (e # s) tp fd = Some flags \<longrightarrow> flags_of_proc_fd (enrich_proc (e # s) p p') tp fd = Some flags" sorry moreover have "\<forall>q. msgs_of_queue (enrich_proc (e # s) p p') q = msgs_of_queue (e # s) q" sorry moreover have "\<forall>tp fd. fd \<in> proc_file_fds (e # s) tp \<longrightarrow> cfd2sfd (enrich_proc (e # s) p p') tp fd = cfd2sfd (e # s) tp fd" sorry moreover have "cp2sproc (enrich_proc (e # s) p p') p' = cp2sproc (e # s) p" proof- from pre have b0: "is_created_proc s p \<Longrightarrow> cp2sproc (enrich_proc s p p') p' = cp2sproc s p" by simp have b1: "\<And> tp f fds. \<lbrakk>valid (enrich_proc (Execve tp f fds # s) p p'); valid (Execve tp f fds # s); is_created_proc (Execve tp f fds # s) p; p' \<notin> all_procs (Execve tp f fds # s)\<rbrakk> \<Longrightarrow> cp2sproc (enrich_proc (Execve tp f fds # s) p p') p' = cp2sproc (Execve tp f fds # s) p" proof- fix tp f fds assume a1: "valid (enrich_proc (Execve tp f fds # s) p p')" and a2: "valid (Execve tp f fds # s)" and a3: "is_created_proc (Execve tp f fds # s) p" and a4: "p' \<notin> all_procs (Execve tp f fds # s)" show "cp2sproc (enrich_proc (Execve tp f fds # s) p p') p' = cp2sproc (Execve tp f fds # s) p" proof (cases "tp = p") case True show ?thesis using True a1 a2 a3 a4 b0 thm not_all_procs_prop3 apply (frule_tac not_all_procs_prop2) apply (frule not_all_procs_prop3) apply (auto simp add:cp2sproc_execve is_created_proc_def split:option.splits dest!:current_has_sec' dest:vt_grant_os) apply (auto simp:sectxt_of_obj_simps split:option.splits dest:valid.cases) sorry next case False show ?thesis sorry qed qed have b2: "\<And> tp fd. cp2sproc (enrich_proc (ReadFile tp fd # s) p p') p' = cp2sproc (ReadFile tp fd # s) p" sorry have b3: "\<And> tp. cp2sproc (enrich_proc (Exit tp # s) p p') p' = cp2sproc (Exit tp # s) p" sorry have b4: "\<And> tp tp'. cp2sproc (enrich_proc (Kill tp tp' # s) p p') p' = cp2sproc (Kill tp tp' # s) p" sorry have b5: "\<And> tp tp' fds. cp2sproc (enrich_proc (Clone tp tp' fds # s) p p') p' = cp2sproc (Clone tp tp' fds # s) p" sorry have b6: "\<And> tp f flags fd opt. cp2sproc (enrich_proc (Open tp f flags fd opt # s) p p') p' = cp2sproc (Open tp f flags fd opt # s) p" sorry have b7: "\<And> tp fd. cp2sproc (enrich_proc (CloseFd tp fd # s) p p') p' = cp2sproc (CloseFd tp fd # s) p" sorry show ?thesis using vd_enrich_cons apply (case_tac e) apply (simp_all only:b1 b2 b3 b4 b5 b6 b7) using created_cons vd_enrich_cons vd_cons' b0 apply (auto simp:cp2sproc_other is_created_proc_def) done qed moreover have "\<forall> fd. fd \<in> proc_file_fds (e # s) p \<longrightarrow> cfd2sfd (enrich_proc (e # s) p p') p' fd = cfd2sfd (e # s) p fd" sorry ultimately show ?case by simpqedlemma enrich_proc_valid: "\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> valid (enrich_proc s p p')"by (auto dest:enrich_proc_prop)lemma enrich_proc_valid: "\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> " lemma enrich_proc_tainted: "\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk> \<Longrightarrow> tainted (enrich_proc s p p') = (if (O_proc p \<in> tainted s) then tainted s \<union> {O_proc p'} else tainted s)"apply (induct s)apply (simp add:is_created_proc_def)apply (frule vt_grant_os, frule vd_cons, simp)apply (frule enrich_proc_dup_in, simp+)apply (frule not_all_procs_prop3)apply (case_tac a)prefer 3apply (simp split:if_splits)apply (rule impI|rule conjI)+apply (simp add:is_created_proc_def)apply (auto simp:is_created_proc_def split:if_splits dest:tainted_in_current)[1]apply (simp add:is_created_proc_def)prefer 4apply (simp split:if_splits)apply (rule impI|rule conjI)+apply (simp add:is_created_proc_def)apply (auto simp:is_created_proc_def split:if_splits dest:tainted_in_current)[1]apply (simp add:is_created_proc_def)prefer 4apply (auto simp:is_created_proc_def split:if_splits option.splits dest:tainted_in_current)[1]prefer 4apply (auto simp:is_created_proc_def split:if_splits option.splits dest:tainted_in_current enrich_proc_dup_ffd enrich_proc_dup_ffd')[1]lemma enrich_proc_dup_tainted: "\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk> \<Longrightarrow> (O_proc p' \<in> tainted (enrich_proc s p p')) = (O_proc p \<in> tainted s)"apply (induct s)apply (simp add:is_created_proc_def)apply (frule vt_grant_os, frule vd_cons)apply (case_tac a)apply (auto simp:is_created_proc_def)[1]lemma enrich_proc_tainted: ""endend