selinux: comparison simple_selinux/Static.thy

equal deleted inserted replaced

-:924ab7a4e7fa
+:271e9818b6f6
+theory Static
+imports Static_type OS_type_def Flask_type Flask
+begin
+locale tainting_s = tainting
+begin
+(*
+definition init_sectxt_of_file:: "t_file \<Rightarrow> security_context_t option"
+where
+"init_sectxt_of_file f \<equiv>
+if (is_init_file f) then init_sectxt_of_obj (O_file f)
+else if (is_init_dir f) then init_sectxt_of_obj (O_dir f)
+else None"
+*)
+definition sroot :: "t_sfile"
+where
+"sroot \<equiv> (Init [], sec_of_root, None, {})"
+definition init_cf2sfile :: "t_file \<Rightarrow> t_sfile option"
+where
+"init_cf2sfile f \<equiv>
+case (parent f) of
+None \<Rightarrow> Some sroot
+| Some pf \<Rightarrow> if (is_init_file f) then
+(case (init_sectxt_of_obj (O_file f), init_sectxt_of_obj (O_dir pf), get_parentfs_ctxts [] pf) of
+(Some sec, Some psec, Some aseclist) \<Rightarrow> Some (Init f, sec, Some psec, set aseclist)
+| _ \<Rightarrow> None)    else
+(case (init_sectxt_of_obj (O_dir f), init_sectxt_of_obj (O_dir pf), get_parentfs_ctxts [] pf) of
+(Some sec, Some psec, Some aseclist) \<Rightarrow> Some (Init f, sec, Some psec, set aseclist)
+| _ \<Rightarrow> None)"
+definition init_cf2sfiles :: "t_file \<Rightarrow> t_sfile set"
+where
+"init_cf2sfiles f \<equiv> {sf. \<exists>f' \<in> init_same_inode_files f. init_cf2sfile f' = Some sf}"
+definition init_cfd2sfd :: "t_process \<Rightarrow> t_fd \<Rightarrow> (security_context_t \<times> t_open_flags \<times> t_sfile) option"
+where
+"init_cfd2sfd p fd =
+(case (init_file_of_proc_fd p fd, init_oflags_of_proc_fd p fd, init_sectxt_of_obj (O_fd p fd)) of
+(Some f, Some flags, Some sec) \<Rightarrow> (case (init_cf2sfile f) of
+Some sf \<Rightarrow> Some (sec, flags, sf)
+| _ \<Rightarrow> None)
+| _ \<Rightarrow> None)"
+definition init_cfds2sfds :: "t_process \<Rightarrow> (security_context_t \<times> t_open_flags \<times> t_sfile) set"
+where
+"init_cfds2sfds p \<equiv> { sfd. \<exists> fd \<in> init_proc_file_fds p. init_cfd2sfd p fd = Some sfd}"
+(*
+definition init_ch2sshm :: "t_shm \<Rightarrow> t_sshm option"
+where
+"init_ch2sshm h \<equiv> (case (init_sectxt_of_obj (O_shm h)) of
+Some sec \<Rightarrow> Some (Init h, sec)
+| _        \<Rightarrow> None)"
+definition init_cph2spshs
+:: "t_process \<Rightarrow> (t_sshm \<times> t_shm_attach_flag) set"
+where
+"init_cph2spshs p \<equiv> {(sh, flag)| sh flag h. (p, flag) \<in> init_procs_of_shm h \<and>
+init_ch2sshm h = Some sh}"
+*)
+definition init_cp2sproc :: "t_process \<Rightarrow> t_sproc option"
+where
+"init_cp2sproc p \<equiv> (case (init_sectxt_of_obj (O_proc p)) of
+Some sec \<Rightarrow> Some (Init p, sec, (init_cfds2sfds p))
+| None     \<Rightarrow> None)"
+(* acient files of init-file
+definition init_o2s_afs :: "t_file \<Rightarrow> security_context_t set"
+where
+"init_o2s_afs f \<equiv> {sec. \<exists> f'. f' \<preceq> f \<and> init_sectxt_of_obj (O_dir f') = Some sec}" *)
+definition init_cm2smsg :: "t_msgq \<Rightarrow> t_msg \<Rightarrow> t_smsg option"
+where
+"init_cm2smsg q m \<equiv> (case (init_sectxt_of_obj (O_msg q m)) of
+Some sec \<Rightarrow> Some (Init m, sec, (O_msg q m) \<in> seeds)
+| _ \<Rightarrow> None)"
+fun init_cqm2sms :: "t_msgq \<Rightarrow> t_msg list \<Rightarrow> (t_smsg list) option"
+where
+"init_cqm2sms q []     = Some []"
+| "init_cqm2sms q (m#ms) =
+(case (init_cqm2sms q ms, init_cm2smsg q m) of
+(Some sms, Some sm) \<Rightarrow> Some (sm # sms)
+| _        \<Rightarrow> None)"
+definition init_cq2smsgq :: "t_msgq \<Rightarrow> t_smsgq option"
+where
+"init_cq2smsgq q \<equiv> (case (init_sectxt_of_obj (O_msgq q), init_cqm2sms q (init_msgs_of_queue q)) of
+(Some sec, Some sms) \<Rightarrow> Some (Init q, sec, sms)
+| _ \<Rightarrow> None)"
+fun init_obj2sobj :: "t_object \<Rightarrow> t_sobject option"
+where
+"init_obj2sobj (O_proc p) =
+(case (init_cp2sproc p) of
+Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> seeds))
+| _ \<Rightarrow> None)"
+| "init_obj2sobj (O_file f) =
+(case (init_cf2sfile f) of
+Some sf \<Rightarrow> Some (S_file sf (O_file f \<in> seeds))
+| _       \<Rightarrow> None)"
+| "init_obj2sobj (O_dir f) =
+(case (init_cf2sfile f) of
+Some sf \<Rightarrow> Some (S_dir sf)
+| _ \<Rightarrow> None)"
+| "init_obj2sobj (O_msgq q) =
+(case (init_cq2smsgq q) of
+Some sq \<Rightarrow> Some (S_msgq sq)
+| _ \<Rightarrow> None)"
+(*
+| "init_obj2sobj (O_shm h) =
+(case (init_ch2sshm h) of
+Some sh \<Rightarrow> Some (S_shm sh)
+| _       \<Rightarrow> None)"
+| "init_obj2sobj (O_msg q m) =
+(case (init_cq2smsgq q, init_cm2smsg q m) of
+(Some sq, Some sm) \<Rightarrow> Some (S_msg sq sm)
+| _                  \<Rightarrow> None)" *)
+| "init_obj2sobj _ = None"
+definition
+"init_static_state \<equiv> {sobj. \<exists> obj. init_alive obj \<and> init_obj2sobj obj = Some sobj}"
+(**************** translation from dynamic to static *******************)
+definition cf2sfile :: "t_state \<Rightarrow> t_file \<Rightarrow> t_sfile option"
+where
+"cf2sfile s f \<equiv>
+case (parent f) of
+None \<Rightarrow> Some sroot
+| Some pf \<Rightarrow> if (is_file s f)
+then (case (sectxt_of_obj s (O_file f), sectxt_of_obj s (O_dir pf), get_parentfs_ctxts s pf) of
+(Some sec, Some psec, Some asecs) \<Rightarrow>
+Some (if (\<not> deleted (O_file f) s \<and> is_init_file f) then Init f else Created, sec, Some psec, set asecs)
+| _ \<Rightarrow> None)
+else (case (sectxt_of_obj s (O_dir f), sectxt_of_obj s (O_dir pf), get_parentfs_ctxts s pf) of
+(Some sec, Some psec, Some asecs) \<Rightarrow>
+Some (if (\<not> deleted (O_dir f) s \<and> is_init_dir f) then Init f else Created, sec, Some psec, set asecs)
+| _ \<Rightarrow> None)"
+(*
+definition cf2sfiles :: "t_state \<Rightarrow> t_file \<Rightarrow> t_sfile set"
+where
+"cf2sfiles s f \<equiv> {sf. \<exists> f' \<in> (same_inode_files s f). cf2sfile s f' = Some sf}"
+*)
+(* here cf2sfile is passed with True, because, process' fds are only for files not dirs *)
+definition cfd2sfd :: "t_state \<Rightarrow> t_process \<Rightarrow> t_fd \<Rightarrow> t_sfd option"
+where
+"cfd2sfd s p fd \<equiv>
+(case (file_of_proc_fd s p fd, flags_of_proc_fd s p fd, sectxt_of_obj s (O_fd p fd)) of
+(Some f, Some flags, Some sec) \<Rightarrow> (case (cf2sfile s f) of
+Some sf \<Rightarrow> Some (sec, flags, sf)
+| _       \<Rightarrow> None)
+| _ \<Rightarrow> None)"
+definition cpfd2sfds :: "t_state \<Rightarrow> t_process \<Rightarrow> t_sfd set"
+where
+"cpfd2sfds s p \<equiv> {sfd. \<exists> fd \<in> proc_file_fds s p. cfd2sfd s p fd = Some sfd}"
+(*
+definition ch2sshm :: "t_state \<Rightarrow> t_shm \<Rightarrow> t_sshm option"
+where
+"ch2sshm s h \<equiv> (case (sectxt_of_obj s (O_shm h)) of
+Some sec \<Rightarrow>
+Some (if (\<not> deleted (O_shm h) s \<and> h \<in> init_shms) then Init h else Created, sec)
+| _ \<Rightarrow> None)"
+definition cph2spshs :: "t_state \<Rightarrow> t_process \<Rightarrow> t_sproc_sshm set"
+where
+"cph2spshs s p \<equiv> {(sh, flag)| sh flag h. (p, flag) \<in> procs_of_shm s h \<and> ch2sshm s h = Some sh}"
+*)
+definition cp2sproc :: "t_state \<Rightarrow> t_process \<Rightarrow> t_sproc option"
+where
+"cp2sproc s p \<equiv> (case (sectxt_of_obj s (O_proc p)) of
+Some sec \<Rightarrow>
+Some (if (\<not> deleted (O_proc p) s \<and> p \<in> init_procs) then Init p else Created, sec,
+cpfd2sfds s p)
+| _ \<Rightarrow> None)"
+definition cm2smsg :: "t_state \<Rightarrow> t_msgq \<Rightarrow> t_msg \<Rightarrow> t_smsg option"
+where
+"cm2smsg s q m \<equiv> (case (sectxt_of_obj s (O_msg q m)) of
+Some sec \<Rightarrow>
+Some (if (\<not> deleted (O_msg q m) s \<and> m \<in> set (init_msgs_of_queue q)) then Init m else Created,
+sec, O_msg q m \<in> tainted s)
+| _ \<Rightarrow> None)"
+fun cqm2sms:: "t_state \<Rightarrow> t_msgq \<Rightarrow> t_msg list \<Rightarrow> (t_smsg list) option"
+where
+"cqm2sms s q [] = Some []"
+| "cqm2sms s q (m#ms) =
+(case (cqm2sms s q ms, cm2smsg s q m) of
+(Some sms, Some sm) \<Rightarrow> Some (sm#sms)
+| _ \<Rightarrow> None)"
+definition cq2smsgq :: "t_state \<Rightarrow> t_msgq \<Rightarrow> t_smsgq option"
+where
+"cq2smsgq s q \<equiv> (case (sectxt_of_obj s (O_msgq q), cqm2sms s q (msgs_of_queue s q)) of
+(Some sec, Some sms) \<Rightarrow>
+Some (if (\<not> deleted (O_msgq q) s \<and> q \<in> init_msgqs) then Init q else Created,
+sec, sms)
+| _ \<Rightarrow> None)"
+fun co2sobj :: "t_state \<Rightarrow> t_object \<Rightarrow> t_sobject option"
+where
+"co2sobj s (O_proc p) =
+(case (cp2sproc s p) of
+Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> tainted s))
+| _       \<Rightarrow> None)"
+| "co2sobj s (O_file f) =
+(case (cf2sfile s f) of
+Some sf \<Rightarrow> Some (S_file sf (O_file f \<in> tainted s))
+| _       \<Rightarrow> None)"
+| "co2sobj s (O_dir f) =
+(case (cf2sfile s f) of
+Some sf  \<Rightarrow> Some (S_dir sf)
+| _ \<Rightarrow> None)"
+| "co2sobj s (O_msgq q) =
+(case (cq2smsgq s q) of
+Some sq \<Rightarrow> Some (S_msgq sq)
+| _ \<Rightarrow> None)"
+(*
+| "co2sobj s (O_shm h) =
+(case (ch2sshm s h) of
+Some sh \<Rightarrow> Some (S_shm sh)
+| _ \<Rightarrow> None)"
+| "co2sobj s (O_msg q m) =
+(case (cq2smsgq s q, cm2smsg s q m) of
+(Some sq, Some sm) \<Rightarrow> Some (S_msg sq sm)
+| _ \<Rightarrow> None)"
+*)
+| "co2sobj s _ = None"
+definition s2ss :: "t_state \<Rightarrow> t_static_state"
+where
+"s2ss s \<equiv> {sobj. \<exists> obj. alive s obj \<and> co2sobj s obj = Some sobj}"
+(* ******************************************************** *)
+fun is_init_sfile :: "t_sfile \<Rightarrow> bool"
+where
+"is_init_sfile (Init _, sec, psec,asec) = True"
+| "is_init_sfile _ = False"
+fun is_many_sfile :: "t_sfile \<Rightarrow> bool"
+where
+"is_many_sfile (Created, sec, psec, asec) = True"
+| "is_many_sfile _ = False"
+fun is_init_sproc :: "t_sproc \<Rightarrow> bool"
+where
+"is_init_sproc (Init p, sec, fds) = True"
+| "is_init_sproc _                  = False"
+fun is_many_sproc :: "t_sproc \<Rightarrow> bool"
+where
+"is_many_sproc (Created, sec,fds) = True"
+| "is_many_sproc _                  = False"
+fun is_many_smsg :: "t_smsg \<Rightarrow> bool"
+where
+"is_many_smsg (Created,sec,tag) = True"
+| "is_many_smsg _                 = False"
+(* wrong def
+fun is_many_smsgq :: "t_smsgq \<Rightarrow> bool"
+where
+"is_many_smsgq (Created,sec,sms) = (True \<and> (\<forall> sm \<in> (set sms). is_many_smsg sm))"
+| "is_many_smsgq _                 = False"
+*)
+fun is_many_smsgq :: "t_smsgq \<Rightarrow> bool"
+where
+"is_many_smsgq (Created,sec,sms) = True"
+| "is_many_smsgq _                 = False"
+fun is_many :: "t_sobject \<Rightarrow> bool"
+where
+"is_many (S_proc sp   tag) = is_many_sproc sp"
+| "is_many (S_file sf   tag) = is_many_sfile sf"
+| "is_many (S_dir  sf      ) = is_many_sfile sf"
+| "is_many (S_msgq sq      ) = is_many_smsgq sq"
+fun is_init_smsgq :: "t_smsgq \<Rightarrow> bool"
+where
+"is_init_smsgq (Init q,sec,sms) = True"
+| "is_init_smsgq _                = False"
+fun is_init_sobj :: "t_sobject \<Rightarrow> bool"
+where
+"is_init_sobj (S_proc sp tag ) = is_init_sproc sp"
+| "is_init_sobj (S_file sf tag ) = is_init_sfile sf"
+| "is_init_sobj (S_dir  sf     ) = is_init_sfile sf"
+| "is_init_sobj (S_msgq sq     ) = is_init_smsgq sq"
+(*
+fun update_ss_sp:: "t_static_state \<Rightarrow> t_sobject \<Rightarrow> t_sobject \<Rightarrow> t_static_state"
+where
+"update_ss_sp ss (S_proc sp tag) (S_proc sp' tag') =
+(if (is_many_sproc sp) then ss \<union> {S_proc sp' tag'}
+else (ss - {S_proc sp tag}) \<union> {S_proc sp' tag'})"
+fun update_ss_sd:: "t_static_state \<Rightarrow> t_sobject \<Rightarrow> t_sobject \<Rightarrow> t_static_state"
+where
+"update_ss_sd ss (S_dir sf tag) (S_dir sf' tag') =
+(if (is_many_sfile sf) then ss \<union> {S_dir sf' tag'}
+else (ss - {S_dir sf tag}) \<union> {S_dir sf' tag'})"
+*)
+(*
+fun sparent :: "t_sfile \<Rightarrow> t_sfile option"
+where
+"sparent (Sroot si sec) = None"
+| "sparent (Sfile si sec spf) = Some spf"
+inductive is_ancesf :: "t_sfile \<Rightarrow> t_sfile \<Rightarrow> bool"
+where
+"is_ancesf sf sf"
+| "sparent sf = Some spf \<Longrightarrow> is_ancesf spf sf"
+| "\<lbrakk>sparent sf = Some spf; is_ancesf saf spf\<rbrakk> \<Longrightarrow> is_ancesf saf sf"
+definition sfile_reparent :: "t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfile"
+where
+"sfile_reparent (Sroot)"
+*)
+(*
+(* sfds rename aux definitions *)
+definition sfds_rename_notrelated
+:: "t_sfd set \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfd set \<Rightarrow> bool"
+where
+"sfds_rename_notrelated sfds from to sfds' \<equiv>
+(\<forall> sec flag sf. (sec,flag,sf) \<in> sfds \<and> (\<not> from \<preceq> sf) \<longrightarrow> (sec,flag,sf) \<in> sfds')"
+definition sfds_rename_renamed
+:: "t_sfd set \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfd set \<Rightarrow> bool"
+where
+"sfds_rename_renamed sfds sf from to sfds' \<equiv>
+(\<forall> sec flag sf'. (sec,flag,sf) \<in> sfds \<and> (sf \<preceq> sf') \<longrightarrow>
+(sec, flag, file_after_rename sf' from to) \<in> sfds' \<and> (sec,flag,sf) \<notin> sfds')"
+definition sfds_rename_remain
+:: "t_sfd set \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfd set \<Rightarrow> bool"
+where
+"sfds_rename_remain sfds sf from to sfds' \<equiv>
+(\<forall> sec flag sf'. (sec,flag,sf') \<in> sfds \<and> (sf \<preceq> sf') \<longrightarrow>
+(sec, flag, sf') \<in> sfds' \<and> (sec,flag, file_after_rename sf' from to) \<notin> sfds')"
+(* for not many, choose on renamed or not *)
+definition sfds_rename_choices
+:: "t_sfd set \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfd set \<Rightarrow> bool"
+where
+"sfds_rename_choices sfds sf from to sfds' \<equiv>
+sfds_rename_remain sfds sf from to sfds' \<or> sfds_rename_renamed sfds sf from to sfds'"
+(* for many, merge renamed with not renamed *)
+definition sfds_rename_both
+:: "t_sfd set \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfd set \<Rightarrow> bool"
+where
+"sfds_rename_both sfds sf from to sfds' \<equiv>
+(\<forall> sec flag sf'. (sec,flag,sf') \<in> sfds \<and> (sf \<preceq> sf') \<longrightarrow>
+(sec, flag, sf') \<in> sfds' \<or> (sec,flag, file_after_rename sf' from to) \<in> sfds')"
+(* added to the new sfds, are those only under the new sfile *)
+definition sfds_rename_added
+:: "t_sfd set \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfd set \<Rightarrow> bool"
+where
+"sfds_rename_added sfds from to sfds' \<equiv>
+(\<forall> sec' flag' sf' sec flag. (sec',flag',sf') \<in> sfds' \<and> (sec,flag,sf') \<notin> sfds \<longrightarrow>
+(\<exists> sf. (sec,flag,sf) \<in> sfds \<and> sf' = file_after_rename from to sf))"
+definition sproc_sfds_renamed
+:: "t_static_state \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_static_state \<Rightarrow> bool"
+where
+"sproc_sfds_renamed ss sf from to ss' \<equiv>
+(\<forall> pi sec sfds sshms tagp. S_proc (pi,sec,sfds,sshms) tagp \<in> ss \<longrightarrow>
+(\<exists> sfds'. S_proc (pi,sec,sfds',sshms) tagp \<in> ss \<and> sfds_rename_renamed sfds sf from to sfds'))"
+definition sproc_sfds_remain
+:: "t_static_state \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_static_state \<Rightarrow> bool"
+where
+"sproc_sfds_remain ss sf from to ss' \<equiv>
+(\<forall> pi sec sfds sshms tagp. S_proc (pi,sec,sfds,sshms) tagp \<in> ss \<longrightarrow>
+(\<exists> sfds'. S_proc (pi,sec,sfds',sshms) tagp \<in> ss \<and> sfds_rename_remain sfds sf from to sfds'))"
+(* for not many, choose on renamed or not *)
+definition sproc_sfds_choices
+:: "t_static_state \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_static_state \<Rightarrow> bool"
+where
+"sproc_sfds_choices ss sf from to ss' \<equiv>
+(\<forall> pi sec sfds sshms tagp. S_proc (pi,sec,sfds,sshms) tagp \<in> ss \<longrightarrow>
+(\<exists> sfds'. S_proc (pi,sec,sfds',sshms) tagp \<in> ss \<and> sfds_rename_choices sfds sf from to sfds'))"
+(* for many, merge renamed with not renamed *)
+definition sproc_sfds_both
+:: "t_static_state \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_static_state \<Rightarrow> bool"
+where
+"sproc_sfds_both ss sf from to ss' \<equiv>
+(\<forall> pi sec sfds sshms tagp. S_proc (pi,sec,sfds,sshms) tagp \<in> ss \<longrightarrow>
+(\<exists> sfds'. S_proc (pi,sec,sfds',sshms) tagp \<in> ss \<and> sfds_rename_both sfds sf from to sfds'))"
+(* remove (\<forall> sp tag. S_proc sp tag \<in> ss \<longrightarrow> S_proc sp tag \<in> ss'),
+* cause sfds contains sfs informations *)
+definition ss_rename_notrelated
+:: "t_static_state \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_static_state \<Rightarrow> bool"
+where
+"ss_rename_notrelated ss sf sf' ss' \<equiv>
+(\<forall> sq. S_msgq sq \<in> ss \<longrightarrow> S_msgq sq \<in> ss') \<and>
+(\<forall> pi sec sfds sshms tagp. S_proc (pi,sec,sfds,sshms) tagp \<in> ss \<longrightarrow> (\<exists> sfds'.
+S_proc (pi,sec,sfds',sshms) tagp \<in> ss'\<and> sfds_rename_notrelated sfds sf sf' sfds'))  \<and>
+(\<forall> sfs sf'' tag. S_file sfs tag \<in> ss \<and> sf'' \<in> sfs \<and> (\<not> sf \<preceq> sf'') \<longrightarrow> (\<exists> sfs'.
+S_file sfs tag \<in> ss' \<and> sf'' \<in> sfs')) \<and>
+(\<forall> sf'' tag. S_dir sf'' tag \<in> ss \<and> (\<not> sf \<preceq> sf'') \<longrightarrow> S_dir sf'' tag \<in> ss')"
+(* rename from to, from should definited renamed if not many *)
+definition all_descendant_sf_renamed
+:: "t_static_state \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_static_state \<Rightarrow> bool"
+where
+"all_descendant_sf_renamed ss sf from to ss' \<equiv>
+(\<forall> sfs sf' tagf. sf \<preceq> sf' \<and> S_file sfs tagf \<in> ss \<and> sf' \<in> sfs \<longrightarrow> (\<exists> sfs'.
+S_file sfs' tagf \<in> ss' \<and> file_after_rename from to sf' \<in> sfs' \<and> sf' \<notin> sfs')) \<and>
+(\<forall> sf' tagf. sf \<preceq> sf' \<and> S_dir sf' tagf \<in> ss \<longrightarrow> S_dir (file_after_rename from to sf') tagf \<in> ss' \<and> S_dir sf' tagf \<notin> ss') \<and>
+sproc_sfds_renamed ss sf from to ss'"
+(* not renamed *)
+definition all_descendant_sf_remain
+:: "t_static_state \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_static_state \<Rightarrow> bool"
+where
+"all_descendant_sf_remain ss sf from to ss' \<equiv>
+(\<forall> sfs sf' tag'. sf \<preceq> sf' \<and> S_file sfs tag' \<in> ss \<and> sf' \<in> sfs \<longrightarrow> (\<exists> sfs'.
+S_file sfs' tag' \<in> ss \<and> file_after_rename from to sf' \<notin> sfs' \<and> sf' \<in> sfs')) \<and>
+(\<forall> sf' tag'. sf \<preceq> sf' \<and> S_dir sf' tag' \<in> ss \<longrightarrow> S_dir (file_after_rename from to sf') tag' \<notin> ss' \<and> S_dir sf' tag' \<in> ss') \<and>
+sproc_sfds_remain ss sf from to ss'"
+definition all_descendant_sf_choices
+:: "t_static_state \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_static_state \<Rightarrow> bool"
+where
+"all_descendant_sf_choices ss sf from to ss' \<equiv>
+all_descendant_sf_renamed ss sf from to ss' \<or> all_descendant_sf_remain ss sf from to ss'"
+definition all_descendant_sf_both
+:: "t_static_state \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_static_state \<Rightarrow> bool"
+where
+"all_descendant_sf_both ss sf from to ss' \<equiv>
+(\<forall> sfs sf' tag'. sf \<preceq> sf' \<and> S_file sfs tag' \<in> ss \<and> sf' \<in> sfs \<longrightarrow> (\<exists> sfs'.
+S_file sfs' tag' \<in> ss \<and> file_after_rename from to sf' \<in> sfs' \<or> sf' \<in> sfs')) \<and>
+(\<forall> sf' tag'. sf \<preceq> sf' \<and> S_dir sf' tag' \<in> ss \<longrightarrow>
+S_dir (file_after_rename from to sf') tag' \<in> ss' \<or> S_dir sf' tag' \<in> ss') \<and>
+sproc_sfds_both ss sf from to ss'"
+definition ss_renamed_file
+:: "t_static_state \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_static_state \<Rightarrow> bool"
+where
+"ss_renamed_file ss sf sf' ss' \<equiv>
+(if (is_many_sfile sf)
+then all_descendant_sf_choices ss sf sf sf' ss'
+else all_descendant_sf_renamed ss sf sf sf' ss')"
+(* added to the new sfs, are those only under the new sfile *)
+definition sfs_rename_added
+:: "t_sfile set \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_sfile set \<Rightarrow> bool"
+where
+"sfs_rename_added sfs from to sfs' \<equiv>
+(\<forall> sf'. sf' \<in> sfs' \<and> sf' \<notin> sfs \<longrightarrow> (\<exists> sf. sf \<in> sfs \<and> sf' = file_after_rename from to sf))"
+(* added to the new sfile, are those only under the new sfile *)
+definition ss_rename_added
+:: "t_static_state \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_static_state \<Rightarrow> bool"
+where
+"ss_rename_added ss from to ss' \<equiv>
+(\<forall> pi sec fds fds' shms tagp. S_proc (pi, sec, fds,shms) tagp \<in> ss \<and>
+S_proc (pi,sec,fds',shms) tagp \<in> ss' \<longrightarrow> sfds_rename_added fds from to fds') \<and>
+(\<forall> sq. S_msgq sq \<in> ss' \<longrightarrow> S_msgq sq \<in> ss) \<and>
+(\<forall> sfs sfs' tagf. S_file sfs' tagf \<in> ss' \<and> S_file sfs tagf \<in> ss \<longrightarrow>
+sfs_rename_added sfs from to sfs') \<and>
+(\<forall> sf' tagf. S_dir sf' tagf \<in> ss' \<and> S_dir sf' tagf \<notin> ss \<longrightarrow>
+(\<exists> sf. S_dir sf tagf \<in> ss \<and> sf' = file_after_rename from to sf))"
+definition sfile_alive :: "t_static_state \<Rightarrow> t_sfile \<Rightarrow> bool"
+where
+"sfile_alive ss sf \<equiv> (\<exists> sfs tagf. sf \<in> sfs \<and> S_file sfs tagf \<in> ss)"
+definition sf_alive :: "t_static_state \<Rightarrow> t_sfile \<Rightarrow> bool"
+where
+"sf_alive ss sf \<equiv> (\<exists> tagd. S_dir sf tagd \<in> ss) \<or> sfile_alive ss sf"
+(* constrains that the new static state should satisfy *)
+definition ss_rename:: "t_static_state \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_static_state \<Rightarrow> bool"
+where
+"ss_rename ss sf sf' ss' \<equiv>
+ss_rename_notrelated ss sf sf' ss' \<and>
+ss_renamed_file ss sf sf' ss' \<and> ss_rename_added ss sf sf' ss' \<and>
+(\<forall> sf''. sf_alive ss sf'' \<and> sf \<prec> sf'' \<longrightarrow>
+(if (is_many_sfile sf'')
+then all_descendant_sf_choices ss sf'' sf sf' ss'
+else all_descendant_sf_both ss sf'' sf sf' ss'))"
+(* two sfile, the last fname should not be equal *)
+fun sfile_same_fname:: "t_sfile \<Rightarrow> t_sfile \<Rightarrow> bool"
+where
+"sfile_same_fname ((Init n, sec)#spf) ((Init n', sec')#spf') = (n = n')"
+| "sfile_same_fname _                   _                      = False"
+(* no same init sfile/only sfile in the target-to spf, should be in static_state addmissble check *)
+definition ss_rename_no_same_fname:: "t_static_state \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> bool"
+where
+"ss_rename_no_same_fname ss from spf \<equiv>
+\<not> (\<exists> to. sfile_same_fname from to \<and> parent to = Some spf \<and> sf_alive ss to)"
+(* is not a function, is a relation (one 2 many)
+definition update_ss_rename :: "t_static_state \<Rightarrow> t_sfile \<Rightarrow> t_sfile \<Rightarrow> t_static_state"
+where
+"update_ss_rename ss sf sf' \<equiv> if (is_many_sfile sf)
+then (ss \<union> {S_file (file_after_rename sf sf' sf'') tag | sf'' tag. sf \<preceq> sf'' \<and> S_file sf'' tag \<in> ss}
+\<union> {S_dir  (file_after_rename sf sf' sf'') tag | sf'' tag. sf \<preceq> sf'' \<and> S_dir sf'' tag \<in> ss})
+else (ss - {S_file sf'' tag | sf'' tag. sf \<preceq> sf'' \<and> S_file sf'' tag \<in> ss}
+- {S_dir  sf'' tag | sf'' tag. sf \<preceq> sf'' \<and> S_dir sf'' tag \<in> ss})
+\<union> {S_file (file_after_rename sf sf' sf'') tag | sf'' tag. sf \<preceq> sf'' \<and> S_file sf'' tag \<in> ss}
+\<union> {S_dir  (file_after_rename sf sf' sf'') tag | sf'' tag. sf \<preceq> sf'' \<and> S_dir sf'' tag \<in> ss}"
+*)
+*)
+fun sectxt_of_sproc :: "t_sproc \<Rightarrow> security_context_t"
+where
+"sectxt_of_sproc (pi,sec,fds) = sec"
+fun sectxt_of_sfile :: "t_sfile \<Rightarrow> security_context_t"
+where
+"sectxt_of_sfile (fi,sec,psec,asecs) = sec"
+fun asecs_of_sfile :: "t_sfile \<Rightarrow> security_context_t set"
+where
+"asecs_of_sfile (fi,sec,psec,asecs) = asecs"
+definition search_check_s :: "security_context_t \<Rightarrow> t_sfile \<Rightarrow> bool \<Rightarrow> bool"
+where
+"search_check_s pctxt sf if_file =
+(if if_file
+then search_check_ctxt pctxt (sectxt_of_sfile sf) (asecs_of_sfile sf) True
+else search_check_ctxt pctxt (sectxt_of_sfile sf) (asecs_of_sfile sf) False)"
+definition sectxts_of_sfds :: "t_sfd set \<Rightarrow> security_context_t set"
+where
+"sectxts_of_sfds sfds \<equiv> {ctxt. \<exists> flag sf. (ctxt, flag, sf) \<in> sfds}"
+definition inherit_fds_check_s :: "security_context_t \<Rightarrow> t_sfd set \<Rightarrow> bool"
+where
+"inherit_fds_check_s pctxt sfds \<equiv> inherit_fds_check_ctxt pctxt (sectxts_of_sfds sfds)"
+(*
+fun smsg_related :: "t_msg \<Rightarrow> t_smsg list \<Rightarrow> bool"
+where
+"smsg_related m []                   = False"
+| "smsg_related m ((mi, sec, tag)#sms) =
+(if (mi = Init m) then True else smsg_related m sms)"
+fun smsgq_smsg_related :: "t_msgq \<Rightarrow> t_msg \<Rightarrow> t_smsgq \<Rightarrow> bool"
+where
+"smsgq_smsg_related q m (qi, sec, smsgslist) = ((qi = Init q) \<and> (smsg_related m smsgslist))"
+fun smsg_relatainted :: "t_msg \<Rightarrow> t_smsg list \<Rightarrow> bool"
+where
+"smsg_relatainted m []                     = False"
+| "smsg_relatainted m ((mi, sec, tag)#sms) =
+(if (mi = Init m \<and> tag = True) then True else smsg_relatainted m sms)"
+fun smsgq_smsg_relatainted :: "t_msgq \<Rightarrow> t_msg \<Rightarrow> t_smsgq \<Rightarrow> bool"
+where
+"smsgq_smsg_relatainted q m (qi, sec, smsgslist) =
+((qi = Init q) \<and> (smsg_relatainted m smsgslist))"
+*)
+fun sfile_related :: "t_sfile \<Rightarrow> t_file \<Rightarrow> bool"
+where
+"sfile_related (fi,sec,psec,asecs) f = (fi = Init f)"
+(*
+fun sproc_related :: "t_process \<Rightarrow> t_sproc \<Rightarrow> bool"
+where
+"sproc_related p (pi, sec, fds, shms) = (pi = Init p)"
+*)
+fun init_obj_related :: "t_sobject \<Rightarrow> t_object \<Rightarrow> bool"
+where
+"init_obj_related (S_proc (pi, sec, fds) tag) (O_proc p') = (pi = Init p')"
+| "init_obj_related (S_file sf tag) (O_file f) = (sfile_related sf f)"
+| "init_obj_related (S_dir sf) (O_dir f) = (sfile_related sf f)"
+| "init_obj_related (S_msgq (qi, sec, sms)) (O_msgq q') = (qi = Init q')"
+(*
+| "init_obj_related (S_msg (qi, sec, sms) (mi, secm, tagm)) (O_msg q' m') = (qi = Init q' \<and> mi = Init m')"
+*)
+| "init_obj_related _ _ = False"
+(***************** for backward proof when Instancing static objects ******************)
+definition next_nat :: "nat set \<Rightarrow> nat"
+where
+"next_nat nset = (Max nset) + 1"
+definition new_proc :: "t_state \<Rightarrow> t_process"
+where
+"new_proc \<tau> = next_nat (current_procs \<tau>)"
+definition new_inode_num :: "t_state \<Rightarrow> nat"
+where
+"new_inode_num \<tau> = next_nat (current_inode_nums \<tau>)"
+definition new_msgq :: "t_state \<Rightarrow> t_msgq"
+where
+"new_msgq s = next_nat (current_msgqs s)"
+definition new_msg :: "t_state \<Rightarrow> t_msgq \<Rightarrow> nat"
+where
+"new_msg s q = next_nat (set (msgs_of_queue s q))"
+definition new_proc_fd :: "t_state \<Rightarrow> t_process \<Rightarrow> t_fd"
+where
+"new_proc_fd \<tau> p = next_nat (current_proc_fds \<tau> p)"
+definition all_fname_under_dir:: "t_file \<Rightarrow> t_state \<Rightarrow> t_fname set"
+where
+"all_fname_under_dir d \<tau> = {fn. \<exists> f. fn # d = f \<and> f \<in> current_files \<tau>}"
+fun fname_all_a:: "nat \<Rightarrow> t_fname"
+where
+"fname_all_a 0 = []" |
+"fname_all_a (Suc n) = ''a''@(fname_all_a n)"
+definition fname_length_set :: "t_fname set \<Rightarrow> nat set"
+where
+"fname_length_set fns = length`fns"
+definition next_fname:: "t_file \<Rightarrow> t_state \<Rightarrow> t_fname"
+where
+"next_fname pf \<tau> = fname_all_a ((Max (fname_length_set (all_fname_under_dir pf \<tau>))) + 1)"
+definition new_childf:: "t_file \<Rightarrow> t_state \<Rightarrow> t_file"
+where
+"new_childf pf \<tau> = next_fname pf \<tau> # pf"
+end
+end