theory Flask
imports Main Flask_type OS_type_def File_renaming
begin
(****** Policy-language-level rule match/auxiliary functions ******)
fun patt_match :: "'a patt \<Rightarrow> 'a \<Rightarrow> bool"
where
"patt_match (Single x) y = (x = y)"
| "patt_match (Set s) x = (x \<in> s)"
| "patt_match (Tilde s) x = (x \<notin> s)"
| "patt_match Asterisk x = True"
(* match a target with a patt, but including the SELF special
* patt_match_self patt target source
*)
fun patt_match_self :: "(type_t patt) target_with_self_t \<Rightarrow> type_t \<Rightarrow> type_t \<Rightarrow> bool"
where
"patt_match_self Self tt st = (tt = st)"
| "patt_match_self (Not_self (Single p)) tt st = (tt = p)"
| "patt_match_self (Not_self (Set p)) tt st = (tt \<in> p)"
| "patt_match_self (Not_self (Tilde p)) tt st = (tt \<notin> p)"
| "patt_match_self (Not_self Asterisk) tt st = True"
(* list lookup: find the first one *)
fun lookup :: "'a list \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> 'a option"
where
"lookup [] P = None"
| "lookup (x # xs) P = (if (P x) then Some x else lookup xs P)"
(* list member: if exists an element satisfy predicate P *)
fun member :: "'a list \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> bool"
where
"member [] P = False"
| "member (x # xs) P = (if (P x) then True else member xs P)"
(******* socket related aux functions ********)
fun is_remote_request :: "t_event \<Rightarrow> bool"
where
"is_remote_request (Accept p fd addr port fd' i) = True"
| "is_remote_request (Connect p fd addr) = True"
| "is_remote_request (SendSock p fd) = True"
| "is_remote_request (RecvSock p fd) = True"
| "is_remote_request e = False"
fun ip_of_addr:: "t_sock_addr \<Rightarrow> t_inet_addr"
where
"ip_of_addr (INET_ADDR saddr sport) = saddr"
fun port_of_addr:: "t_sock_addr \<Rightarrow> t_socket_port"
where
"port_of_addr (INET_ADDR saddr sport) = sport"
fun after_bind:: "t_sock_state option \<Rightarrow> bool"
where
"after_bind None = False"
| "after_bind (Some SS_create) = False"
| "after_bind _= True" (* after bind , it should have local addr *)
fun after_conacc:: "t_sock_state option \<Rightarrow> bool"
where
"after_conacc None = False"
| "after_conacc (Some SS_create) = False"
| "after_conacc (Some SS_bind) = False"
| "after_conacc (Some SS_listen) = False"
| "after_conacc _ = True" (* after connect or accept, it should have remote addr *)
(* inet_addr_compare addr1 addr2 \<equiv> addr1 \<le> addr2; but in \<le>'s def,there is a \<exists>, is not a function*)
fun subnet_addr :: "t_inet_addr \<Rightarrow> t_inet_addr \<Rightarrow> bool"
where
"subnet_addr [] addr = True"
| "subnet_addr (x#xs) [] = False"
| "subnet_addr (x#xs) (y#ys) = ((x = y) \<and> subnet_addr xs ys)"
definition port_in_range :: "t_socket_port \<Rightarrow> t_socket_port \<Rightarrow> t_socket_port \<Rightarrow> bool"
where
"port_in_range minp maxp p \<equiv> ((p < maxp \<or> p = maxp) \<and> (p > minp \<or> p = minp))"
(* initial value of initiate state constrains aux function *)
definition bidirect_in_init :: "'a set \<Rightarrow> ('a \<Rightarrow> 'b option) \<Rightarrow> bool"
where
"bidirect_in_init S f \<equiv> (\<forall> a. a \<in> S \<longrightarrow> (\<exists> b. f a = Some b)) \<and>
(\<forall> a b. f a = Some b \<longrightarrow> a \<in> S)"
fun is_file_itag :: "t_inode_tag \<Rightarrow> bool"
where
"is_file_itag Tag_FILE = True"
| "is_file_itag tag = False"
fun is_dir_itag :: "t_inode_tag \<Rightarrow> bool"
where
"is_dir_itag Tag_DIR = True"
| "is_dir_itag tag = False"
fun is_file_dir_itag :: "t_inode_tag \<Rightarrow> bool"
where
"is_file_dir_itag Tag_FILE = True"
| "is_file_dir_itag Tag_DIR = True"
| "is_file_dir_itag tag = False"
fun is_tcp_itag :: "t_inode_tag \<Rightarrow> bool"
where
"is_tcp_itag Tag_TCP_SOCK = True"
| "is_tcp_itag tag = False"
fun is_udp_itag :: "t_inode_tag \<Rightarrow> bool"
where
"is_udp_itag Tag_UDP_SOCK = True"
| "is_udp_itag tag = False"
fun is_sock_itag :: "t_inode_tag \<Rightarrow> bool"
where
"is_sock_itag Tag_TCP_SOCK = True"
| "is_sock_itag Tag_UDP_SOCK = True"
| "is_sock_itag tag = False"
locale init =
fixes
init_files :: "t_file set"
and init_procs :: "t_process set"
and init_nodes :: "t_node set"
and init_sockets :: "t_socket set"
and init_users :: "user_t set"
and init_file_of_proc_fd :: "t_process \<Rightarrow> t_fd \<rightharpoonup> t_file"
and init_fds_of_proc :: "t_process \<Rightarrow> t_fd set"
and init_oflags_of_proc_fd:: "t_process \<Rightarrow> t_fd \<rightharpoonup> t_open_flags"
and init_inum_of_file :: "t_file \<rightharpoonup> t_inode_num"
and init_inum_of_socket:: "t_socket \<rightharpoonup> t_inode_num"
and init_itag_of_inum:: "t_inode_num \<rightharpoonup> t_inode_tag"
and init_files_hung_by_del :: "t_file set"
(*
and init_file_at_writing_by:: "t_file \<Rightarrow> (t_process \<times> t_fd) set"
*)
and init_socket_state :: "t_socket \<rightharpoonup> t_sock_state"
and init_msgqs :: "t_msgq set"
and init_msgs_of_queue:: "t_msgq \<Rightarrow> t_msg list"
and init_shms :: "t_shm set"
and init_procs_of_shm :: "t_shm \<Rightarrow> (t_process \<times> t_shm_attach_flag) set"
and init_flag_of_proc_shm :: "t_process \<Rightarrow> t_shm \<rightharpoonup> t_shm_attach_flag"
assumes
parent_file_in_init: "\<And> f pf. \<lbrakk>parent f = Some pf; f \<in> init_files\<rbrakk> \<Longrightarrow> pf \<in> init_files"
and root_is_dir: "\<exists> i. init_inum_of_file [] = Some i \<and> init_itag_of_inum i = Some Tag_DIR"
and init_file_has_inum: "\<And> f. f \<in> init_files \<Longrightarrow> \<exists> im. init_inum_of_file f = Some im"
and inof_has_file_tag: "\<And> f im. init_inum_of_file f = Some im \<Longrightarrow> f \<in> init_files \<and> (\<exists> tag. init_itag_of_inum im = Some tag \<and> is_file_dir_itag tag)"
and init_file_no_son: "\<And> f im. \<lbrakk>init_inum_of_file f = Some im; init_itag_of_inum im = Some Tag_FILE\<rbrakk> \<Longrightarrow> \<not> (\<exists> f' \<in> init_files. parent f' = Some f)"
and init_parentf_is_dir: "\<And> f pf im. \<lbrakk>parent f = Some pf; f \<in> init_files; init_inum_of_file pf = Some im\<rbrakk> \<Longrightarrow> init_itag_of_inum im = Some Tag_DIR"
and init_files_hung_valid: "\<And> f. f \<in> init_files_hung_by_del \<Longrightarrow> f \<in> init_files \<and> (\<exists> p fd. init_file_of_proc_fd p fd = Some f)"
and init_files_hung_valid': "\<And> f im. \<lbrakk>f \<in> init_files_hung_by_del; init_inum_of_file f = Some im\<rbrakk> \<Longrightarrow>
init_itag_of_inum im = Some Tag_FILE \<or> (init_itag_of_inum im = Some Tag_DIR \<and> \<not> (\<exists> f'. f' \<in> init_files \<and> f \<prec> f'))"
and init_procfds_valid: "\<And> p fd. fd \<in> init_fds_of_proc p \<Longrightarrow> p \<in> init_procs \<and> ((\<exists> f \<in> init_files. init_file_of_proc_fd p fd = Some f) \<or> (p, fd) \<in> init_sockets)"
and init_filefd_valid: "\<And> p fd f. init_file_of_proc_fd p fd = Some f \<Longrightarrow> fd \<in> init_fds_of_proc p \<and> (\<exists> im. init_inum_of_file f = Some im \<and> init_itag_of_inum im = Some Tag_FILE) \<and> p \<in> init_procs \<and> (\<exists> flags. init_oflags_of_proc_fd p fd = Some flags) \<and> (p, fd) \<notin> init_sockets"
and init_fileflag_valid: "\<And> p fd flags. init_oflags_of_proc_fd p fd = Some flags \<Longrightarrow> \<exists> f. init_file_of_proc_fd p fd = Some f"
and init_procs_has_shm: "\<And> p h flag. (p,flag) \<in> init_procs_of_shm h \<Longrightarrow> p \<in> init_procs \<and> h \<in> init_shms \<and> init_flag_of_proc_shm p h = Some flag"
and init_shmflag_has_proc: "\<And> p h flag. init_flag_of_proc_shm p h = Some flag \<Longrightarrow> (p, flag) \<in> init_procs_of_shm h"
and init_msgs_distinct: "\<And> q. distinct (init_msgs_of_queue q)"
and init_msgs_valid: "\<And> m q. m \<in> set (init_msgs_of_queue q) \<Longrightarrow> q \<in> init_msgqs"
and init_socket_has_inode: "\<And> p fd. (p, fd) \<in> init_sockets \<Longrightarrow> \<exists> im. init_inum_of_socket (p, fd) = Some im \<and> p \<in> init_procs \<and> fd \<in> init_fds_of_proc p \<and> init_file_of_proc_fd p fd = None"
and inos_has_sock_tag: "\<And> s im. init_inum_of_socket s = Some im \<Longrightarrow> s \<in> init_sockets \<and> (\<exists> tag. init_itag_of_inum im = Some tag \<and> is_sock_itag tag)"
(*
and init_netobj_has_state: "bidirect_in_init init_netobjs init_netobj_state"
and init_netobj_has_socktype:"bidirect_in_init init_netobjs init_netobj_socktype"
and init_netobj_has_laddr: "\<And> s. after_bind (init_netobj_state s) \<Longrightarrow> init_netobj_localaddr s \<noteq> None"
and init_netobj_has_raddr: "\<And> s. after_conacc (init_netobj_state s) \<Longrightarrow> init_netobj_remoteaddr s \<noteq> None"
*)
and init_finite_sets: "finite init_files \<and> finite init_procs \<and> (\<forall> p. finite (init_fds_of_proc p)) \<and> finite init_shms \<and> finite init_msgqs \<and> finite init_users"
begin
definition is_init_file:: "t_file \<Rightarrow> bool"
where
"is_init_file f \<equiv> (case (init_inum_of_file f) of
Some i \<Rightarrow> (case (init_itag_of_inum i) of
Some Tag_FILE \<Rightarrow> True
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
definition is_init_dir:: "t_file \<Rightarrow> bool"
where
"is_init_dir f \<equiv> (case (init_inum_of_file f) of
Some i \<Rightarrow> (case (init_itag_of_inum i) of
Some Tag_DIR \<Rightarrow> True
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
definition is_init_tcp_sock:: "t_socket \<Rightarrow> bool"
where
"is_init_tcp_sock s \<equiv> (case (init_inum_of_socket s) of
Some i \<Rightarrow> (case (init_itag_of_inum i) of
Some Tag_TCP_SOCK \<Rightarrow> True
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
definition is_init_udp_sock:: "t_socket \<Rightarrow> bool"
where
"is_init_udp_sock s \<equiv> (case (init_inum_of_socket s) of
Some i \<Rightarrow> (case (init_itag_of_inum i) of
Some Tag_UDP_SOCK \<Rightarrow> True
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
definition init_same_inode_files :: "t_file \<Rightarrow> t_file set"
where
"init_same_inode_files f \<equiv> if is_init_file f then {f'. init_inum_of_file f = init_inum_of_file f'} else {}"
fun init_alive :: "t_object \<Rightarrow> bool"
where
"init_alive (O_proc p) = (p \<in> init_procs)"
| "init_alive (O_file f) = (is_init_file f)"
| "init_alive (O_dir f) = (is_init_dir f)"
| "init_alive (O_fd p fd) = (fd \<in> init_fds_of_proc p)"
| "init_alive (O_node n) = (n \<in> init_nodes)"
| "init_alive (O_tcp_sock k) = (is_init_tcp_sock k)"
| "init_alive (O_udp_sock k) = (is_init_udp_sock k)"
| "init_alive (O_shm h) = (h \<in> init_shms)"
| "init_alive (O_msgq q) = (q \<in> init_msgqs)"
| "init_alive (O_msg q m) = (m \<in> set (init_msgs_of_queue q) \<and> q \<in> init_msgqs)"
(************ system listeners, event-related ***********)
fun file_of_proc_fd :: "t_state \<Rightarrow> t_process \<Rightarrow> t_fd \<Rightarrow> t_file option"
where
"file_of_proc_fd [] p' fd' = (init_file_of_proc_fd p' fd')"
| "file_of_proc_fd (Open p f flags fd iopt # \<tau>) p' fd' =
(if (p' = p \<and> fd = fd') then Some f else file_of_proc_fd \<tau> p' fd')"
| "file_of_proc_fd (CloseFd p fd # \<tau>) p' fd' =
(if (p = p' \<and> fd = fd') then None else file_of_proc_fd \<tau> p' fd')"
(*deleted: if (f\<^isub>3 \<preceq> f\<^isub>1) then None else *)
(*
| "file_of_proc_fd (Rename p f\<^isub>2 f\<^isub>3 # \<tau>) p' fd =
(case (file_of_proc_fd \<tau> p' fd) of
Some f\<^isub>1 \<Rightarrow> (if (f\<^isub>2 \<preceq> f\<^isub>1) then Some (file_after_rename f\<^isub>2 f\<^isub>3 f\<^isub>1)
else Some f\<^isub>1)
| None \<Rightarrow> None )"
*)
| "file_of_proc_fd (Execve p f fds # \<tau>) p' fd =
(if (p' = p \<and> fd \<in> fds) then file_of_proc_fd \<tau> p fd
else if (p' = p) then None
else file_of_proc_fd \<tau> p' fd) "
| "file_of_proc_fd (Clone p p' fds shms # \<tau>) p'' fd =
(if (p'' = p' \<and> fd \<in> fds) then file_of_proc_fd \<tau> p fd
else if (p'' = p') then None
else file_of_proc_fd \<tau> p'' fd)"
| "file_of_proc_fd (Kill p\<^isub> p\<^isub>' # \<tau>) p'' fd =
(if (p'' = p\<^isub>') then None else file_of_proc_fd \<tau> p'' fd)"
| "file_of_proc_fd (Exit p # \<tau>) p' fd =
(if (p = p') then None else file_of_proc_fd \<tau> p' fd)"
| "file_of_proc_fd (_ # \<tau>) p fd = file_of_proc_fd \<tau> p fd"
definition proc_fd_of_file :: "t_state \<Rightarrow> t_file \<Rightarrow> (t_process \<times> t_fd) set"
where
"proc_fd_of_file \<tau> f = {(p, fd) | p fd. file_of_proc_fd \<tau> p fd = Some f}"
definition proc_file_fds :: "t_state \<Rightarrow> t_process \<Rightarrow> t_fd set"
where
"proc_file_fds s p \<equiv> {fd. \<exists> f. file_of_proc_fd s p fd = Some f}"
definition init_proc_file_fds:: "t_process \<Rightarrow> t_fd set"
where
"init_proc_file_fds p \<equiv> {fd. \<exists> f. init_file_of_proc_fd p fd = Some f}"
(****** files and directories ******)
fun files_hung_by_del :: "t_state \<Rightarrow> t_file set"
where
"files_hung_by_del [] = init_files_hung_by_del"
| "files_hung_by_del (UnLink p f # \<tau>) = (
if (proc_fd_of_file \<tau> f = {}) then files_hung_by_del \<tau>
else insert f (files_hung_by_del \<tau>))"
(* | files_hung_by_del (Rmdir p f) is not need, for open can only apply to file not dir *)
| "files_hung_by_del (CloseFd p fd # \<tau>) = (
case (file_of_proc_fd \<tau> p fd) of
Some f \<Rightarrow> (if (proc_fd_of_file \<tau> f = {(p, fd)})
then files_hung_by_del \<tau> - {f}
else files_hung_by_del \<tau>)
| None \<Rightarrow> files_hung_by_del \<tau> )"
(*
| "files_hung_by_del (Rename p f\<^isub>2 f\<^isub>3 # \<tau>) = {file_after_rename f\<^isub>2 f\<^isub>3 f\<^isub>1| f\<^isub>1. f\<^isub>1 \<in> files_hung_by_del \<tau>}" (* for rename(2) does not infect on fd of the file, see man -S 2 rename *)
*)
| "files_hung_by_del (e # \<tau>) = files_hung_by_del \<tau>"
declare files_hung_by_del.simps [simp del]
fun inum_of_file :: "t_state \<Rightarrow> (t_file \<rightharpoonup> t_inode_num)"
where
"inum_of_file [] = init_inum_of_file"
| "inum_of_file (Open p f flags fd (Some inum) # \<tau>) = (inum_of_file \<tau>) (f := Some inum)"
| "inum_of_file (CloseFd p fd # \<tau>) = (
case (file_of_proc_fd \<tau> p fd) of
Some f \<Rightarrow> ( if ((proc_fd_of_file \<tau> f = {(p, fd)}) \<and> (f \<in> files_hung_by_del \<tau>))
then (inum_of_file \<tau>) (f := None)
else inum_of_file \<tau> )
| _ \<Rightarrow> (inum_of_file \<tau>) )"
| "inum_of_file (UnLink p f # \<tau>) = (
if (proc_fd_of_file \<tau> f = {})
then (inum_of_file \<tau>) (f := None)
else inum_of_file \<tau> )"
| "inum_of_file (Rmdir p f # \<tau>) = (inum_of_file \<tau>) (f := None)"
| "inum_of_file (Mkdir p f ino # \<tau>) = (inum_of_file \<tau>) (f:= Some ino)"
| "inum_of_file (LinkHard p f\<^isub>1 f\<^isub>2 # \<tau>) = (inum_of_file \<tau>) (f\<^isub>2 := inum_of_file \<tau> f\<^isub>1)"
(*
| "inum_of_file (Rename p f\<^isub>2 f\<^isub>3 # \<tau>) = (\<lambda> f.
if (f\<^isub>2 \<preceq> f) then None
else if (f\<^isub>3 \<preceq> f) then inum_of_file \<tau> (file_before_rename f\<^isub>2 f\<^isub>3 f)
else inum_of_file \<tau> f )"
*)
| "inum_of_file (e # \<tau>) = inum_of_file \<tau>"
definition current_files :: "t_state \<Rightarrow> t_file set"
where
"current_files \<tau> = {f. \<exists> i. inum_of_file \<tau> f = Some i}"
(* experimentary: for the delete obj's (file or socket) inode num, it is unnecessary for itag_of_inum to be NONE, cause this is the situation blocked by inum_of_file / inum_of_socket !!! *)
(* delete a file, just recycle its inode num, but not destroy its inode \<dots>, so it is irrelative to these events, like closeFd, Rmdir, UnLink \<dots>*)
fun itag_of_inum :: "t_state \<Rightarrow> (t_inode_num \<rightharpoonup> t_inode_tag)"
where
"itag_of_inum [] = init_itag_of_inum"
| "itag_of_inum (Open p f flags fd (Some ino) # \<tau>) = (itag_of_inum \<tau>) (ino := Some Tag_FILE)"
| "itag_of_inum (Mkdir p f ino # \<tau>) = (itag_of_inum \<tau>) (ino := Some Tag_DIR)"
| "itag_of_inum (CreateSock p af st fd ino # \<tau>) =
(case st of
STREAM \<Rightarrow> (itag_of_inum \<tau>) (ino := Some Tag_TCP_SOCK)
| DGRAM \<Rightarrow> (itag_of_inum \<tau>) (ino := Some Tag_UDP_SOCK) )"
| "itag_of_inum (Accept p fd addr lport' fd' ino # \<tau>) =
(itag_of_inum \<tau>) (ino := Some Tag_TCP_SOCK)"
| "itag_of_inum (_ # \<tau>) = itag_of_inum \<tau>"
definition is_file:: "t_state \<Rightarrow> t_file \<Rightarrow> bool"
where
"is_file \<tau> f \<equiv> (case (inum_of_file \<tau> f) of
Some i \<Rightarrow> (case (itag_of_inum \<tau> i) of
Some Tag_FILE \<Rightarrow> True
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
definition is_dir:: "t_state \<Rightarrow> t_file \<Rightarrow> bool"
where
"is_dir \<tau> f \<equiv> (case (inum_of_file \<tau> f) of
Some i \<Rightarrow> (case (itag_of_inum \<tau> i) of
Some Tag_DIR \<Rightarrow> True
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
definition dir_is_empty :: "t_state \<Rightarrow> t_file \<Rightarrow> bool"
where
"dir_is_empty \<tau> f \<equiv> is_dir \<tau> f \<and> \<not> (\<exists> f'. f' \<in> current_files \<tau> \<and> f \<prec> f')"
definition same_inode_files :: "t_state \<Rightarrow> t_file \<Rightarrow> t_file set"
where
"same_inode_files s f \<equiv> if is_file s f then {f'. inum_of_file s f = inum_of_file s f'} else {}"
definition has_same_inode :: "t_state \<Rightarrow> t_file \<Rightarrow> t_file \<Rightarrow> bool"
where
"has_same_inode s fa fb \<equiv> fb \<in> same_inode_files s fa"
fun inum_of_socket :: "t_state \<Rightarrow> (t_socket \<rightharpoonup> t_inode_num)"
where
"inum_of_socket [] = init_inum_of_socket"
| "inum_of_socket (CloseFd p fd # \<tau>) =
(inum_of_socket \<tau>) ((p, fd):= None)"
| "inum_of_socket (CreateSock p af st fd ino # \<tau>) =
(inum_of_socket \<tau>) ((p, fd) := Some ino)"
| "inum_of_socket (Accept p fd addr lport' fd' ino # \<tau>) =
(inum_of_socket \<tau>) ((p, fd') := Some ino)"
| "inum_of_socket (Clone p p' fds shms # \<tau>) =
(\<lambda> (p'', fd). if (p'' = p' \<and> fd \<in> fds) then inum_of_socket \<tau> (p, fd)
else if (p'' = p') then None
else inum_of_socket \<tau> (p'',fd))"
| "inum_of_socket (Execve p f fds # \<tau>) =
(\<lambda> (p', fd). if (p' = p \<and> fd \<in> fds) then inum_of_socket \<tau> (p, fd)
else if (p' = p) then None
else inum_of_socket \<tau> (p', fd))"
| "inum_of_socket (Kill p\<^isub>1 p\<^isub>2 # \<tau>) =
(\<lambda> (p, fd). if (p = p\<^isub>2) then None else inum_of_socket \<tau> (p, fd) )"
| "inum_of_socket (Exit p # \<tau>) =
(\<lambda> (p', fd). if (p' = p) then None else inum_of_socket \<tau> (p', fd))"
| "inum_of_socket (_ # \<tau>) = inum_of_socket \<tau>"
definition current_sockets :: "t_state \<Rightarrow> t_socket set"
where
"current_sockets \<tau> = {s. \<exists> i. inum_of_socket \<tau> s = Some i}"
definition is_tcp_sock :: "t_state \<Rightarrow> t_socket \<Rightarrow> bool"
where
"is_tcp_sock \<tau> s \<equiv> (case (inum_of_socket \<tau> s) of
Some i \<Rightarrow> (case (itag_of_inum \<tau> i) of
Some Tag_TCP_SOCK \<Rightarrow> True
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
definition is_udp_sock :: "t_state \<Rightarrow> t_socket \<Rightarrow> bool"
where
"is_udp_sock \<tau> s \<equiv> (case (inum_of_socket \<tau> s) of
Some i \<Rightarrow> (case (itag_of_inum \<tau> i) of
Some Tag_UDP_SOCK \<Rightarrow> True
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
fun current_procs :: "t_state \<Rightarrow> t_process set"
where
"current_procs [] = init_procs"
| "current_procs (Clone p p' fds shms # \<tau>) = (insert p' (current_procs \<tau>))"
| "current_procs (Exit p # \<tau>) = (current_procs \<tau> - {p})"
| "current_procs (Kill p p' # \<tau>) = (current_procs \<tau> - {p'})"
| "current_procs (_ # \<tau>) = current_procs \<tau>"
fun current_proc_fds :: "t_state \<Rightarrow> t_process \<Rightarrow> t_fd set"
where
"current_proc_fds [] = init_fds_of_proc"
| "current_proc_fds (Open p f flags fd iopt # \<tau>) =
(current_proc_fds \<tau>) (p:= insert fd (current_proc_fds \<tau> p))"
| "current_proc_fds (CreateSock p sf st newfd newi # \<tau>) =
(current_proc_fds \<tau>) (p:= insert newfd (current_proc_fds \<tau> p))"
| "current_proc_fds (Accept p fd raddr port fd' ino # \<tau>) =
(current_proc_fds \<tau>) (p:= insert fd' (current_proc_fds \<tau> p))"
| "current_proc_fds (CloseFd p fd # \<tau>) =
(current_proc_fds \<tau>) (p:= (current_proc_fds \<tau> p) - {fd})"
| "current_proc_fds (Clone p p' fds shms # \<tau>) =
(current_proc_fds \<tau>) (p':= fds)"
| "current_proc_fds (Execve p f fds # \<tau>) =
(current_proc_fds \<tau>) (p:= fds)"
| "current_proc_fds (Exit p # \<tau>) = (current_proc_fds \<tau>) (p := {})"
| "current_proc_fds (Kill p p' # \<tau>) = (current_proc_fds \<tau>) (p' := {})"
| "current_proc_fds (_ # \<tau>) = current_proc_fds \<tau>"
fun current_shms :: "t_state \<Rightarrow> t_shm set"
where
"current_shms [] = init_shms"
| "current_shms (CreateShM p newshm # \<tau>) = insert newshm (current_shms \<tau>)"
| "current_shms (DeleteShM p s # \<tau>) = (current_shms \<tau>) - {s}"
| "current_shms (e # \<tau>) = current_shms \<tau> "
fun flag_of_proc_shm :: "t_state \<Rightarrow> t_process \<Rightarrow> t_shm \<Rightarrow> t_shm_attach_flag option"
where
"flag_of_proc_shm [] = init_flag_of_proc_shm"
| "flag_of_proc_shm (Attach p h flag # s) = (\<lambda> p' h'.
if (p' = p \<and> h' = h) then Some flag else flag_of_proc_shm s p' h')"
| "flag_of_proc_shm (Detach p h # s) = (\<lambda> p' h'.
if (p' = p \<and> h' = h) then None else flag_of_proc_shm s p' h')"
| "flag_of_proc_shm (CreateShM p h # s) = (\<lambda> p' h'.
if (h' = h) then None else flag_of_proc_shm s p' h')"
| "flag_of_proc_shm (DeleteShM p h # s) = (\<lambda> p' h'.
if (h' = h) then None else flag_of_proc_shm s p' h')"
| "flag_of_proc_shm (Clone p p' fds shms # s) = (\<lambda> p'' h.
if (p'' = p' \<and> h \<in> shms) then flag_of_proc_shm s p h
else if (p'' = p') then None
else flag_of_proc_shm s p'' h)"
| "flag_of_proc_shm (Execve p f fds # s) = (\<lambda> p' h.
if (p' = p) then None else flag_of_proc_shm s p' h)"
| "flag_of_proc_shm (Kill p p' # s) = (\<lambda> p'' h.
if (p'' = p') then None else flag_of_proc_shm s p'' h)"
| "flag_of_proc_shm (Exit p # s) = (\<lambda> p' h.
if (p' = p) then None else flag_of_proc_shm s p' h)"
| "flag_of_proc_shm (e # s) = flag_of_proc_shm s"
fun procs_of_shm :: "t_state \<Rightarrow> t_shm \<Rightarrow> (t_process \<times> t_shm_attach_flag) set"
where
"procs_of_shm [] = init_procs_of_shm"
| "procs_of_shm (CreateShM p h # \<tau>) =
(procs_of_shm \<tau>) (h := {})" (* creator may not be the sharer of the shm *)
| "procs_of_shm (Attach p h flag # \<tau>) =
(procs_of_shm \<tau>) (h := insert (p, flag) (procs_of_shm \<tau> h))"
| "procs_of_shm (Detach p h # \<tau>) =
(procs_of_shm \<tau>) (h := (procs_of_shm \<tau> h) - {(p,flag) | flag. (p, flag) \<in> procs_of_shm \<tau> h})"
| "procs_of_shm (DeleteShM p h # \<tau>) = (procs_of_shm \<tau>) (h := {})"
| "procs_of_shm (Clone p p' fds shms # \<tau>) =
(\<lambda> h. if (h \<in> shms)
then (procs_of_shm \<tau> h) \<union> {(p', flag) | flag. (p, flag) \<in> procs_of_shm \<tau> h}
else procs_of_shm \<tau> h)"
| "procs_of_shm (Execve p f fds # \<tau>) =
(\<lambda> h. procs_of_shm \<tau> h - {(p, flag) | flag. (p, flag) \<in> procs_of_shm \<tau> h})"
| "procs_of_shm (Kill p p' # s) =
(\<lambda> h. (procs_of_shm s h) - {(p', flag) | flag. (p', flag) \<in> procs_of_shm s h})"
| "procs_of_shm (Exit p # s) =
(\<lambda> h. (procs_of_shm s h) - {(p, flag) | flag. (p, flag) \<in> procs_of_shm s h})"
| "procs_of_shm (e # \<tau>) = procs_of_shm \<tau>"
(*
inductive info_flow_shm :: "t_state \<Rightarrow> t_process \<Rightarrow> t_process \<Rightarrow> bool"
where
"p \<in> current_procs s \<Longrightarrow> info_flow_shm s p p"
| "\<lbrakk>info_flow_shm s p p'; (p', SHM_RDWR) \<in> procs_of_shm s h; (p'', flag) \<in> procs_of_shm s h; p' \<noteq> p''\<rbrakk>
\<Longrightarrow> info_flow_shm s p p''"
*)
definition one_flow_shm :: "t_state \<Rightarrow> t_shm \<Rightarrow> t_process \<Rightarrow> t_process \<Rightarrow> bool"
where
"one_flow_shm s h from to \<equiv> from \<noteq> to \<and> (from, SHM_RDWR) \<in> procs_of_shm s h \<and>
(\<exists> flag. (to, flag) \<in> procs_of_shm s h)"
fun self_shm :: "t_state \<Rightarrow> t_process \<Rightarrow> t_process \<Rightarrow> bool"
where
"self_shm s p p' = (p = p' \<and> p' \<in> current_procs s)"
definition info_flow_shm :: "t_state \<Rightarrow> t_process \<Rightarrow> t_process \<Rightarrow> bool"
where
"info_flow_shm s from to \<equiv> (self_shm s from to) \<or> (\<exists> h. one_flow_shm s h from to)"
fun current_msgqs :: "t_state \<Rightarrow> t_msg set"
where
"current_msgqs [] = init_msgqs"
| "current_msgqs (CreateMsgq p q # \<tau>) = insert q (current_msgqs \<tau>)"
| "current_msgqs (RemoveMsgq p q # \<tau>) = (current_msgqs \<tau>) - {q}"
| "current_msgqs (_ # \<tau>) = current_msgqs \<tau>"
fun msgs_of_queue :: "t_state \<Rightarrow> t_msgq \<Rightarrow> t_msg list"
where
"msgs_of_queue [] = init_msgs_of_queue"
| "msgs_of_queue (CreateMsgq p q # \<tau>) = (msgs_of_queue \<tau>)(q := [])"
| "msgs_of_queue (SendMsg p q m # \<tau>) = (msgs_of_queue \<tau>)(q := msgs_of_queue \<tau> q @ [m])"
| "msgs_of_queue (RecvMsg p q m # \<tau>) = (msgs_of_queue \<tau>)(q := tl (msgs_of_queue \<tau> q))"
| "msgs_of_queue (RemoveMsgq p q # \<tau>) = (msgs_of_queue \<tau>)(q := [])"
| "msgs_of_queue (_ # \<tau>) = msgs_of_queue \<tau>"
definition current_file_inums :: "t_state \<Rightarrow> t_inode_num set"
where
"current_file_inums \<tau> \<equiv> {im. \<exists> f. inum_of_file \<tau> f = Some im}"
definition current_sock_inums :: "t_state \<Rightarrow> t_inode_num set"
where
"current_sock_inums \<tau> = {im. \<exists> s. inum_of_socket \<tau> s = Some im}"
definition current_inode_nums :: "t_state \<Rightarrow> nat set"
where
"current_inode_nums \<tau> = current_file_inums \<tau> \<union> current_sock_inums \<tau>"
fun flags_of_proc_fd :: "t_state \<Rightarrow> t_process \<Rightarrow> t_fd \<Rightarrow> t_open_flags option"
where
"flags_of_proc_fd [] p fd = init_oflags_of_proc_fd p fd"
| "flags_of_proc_fd (Open p f flags fd iopt # \<tau>) p' fd' =
(if (p = p' \<and> fd = fd') then Some flags else flags_of_proc_fd \<tau> p' fd')"
| "flags_of_proc_fd (CloseFd p fd # \<tau>) p' fd' =
(if (p = p' \<and> fd = fd') then None else flags_of_proc_fd \<tau> p' fd')"
| "flags_of_proc_fd (CreateSock p af st fd ino # \<tau>) p' fd' =
(if (p = p' \<and> fd = fd') then None else flags_of_proc_fd \<tau> p' fd')"
| "flags_of_proc_fd (Accept p fd addr lport' fd' ino # \<tau>) p' fd'' =
(if (p = p' \<and> fd' = fd'') then None else flags_of_proc_fd \<tau> p' fd'')"
| "flags_of_proc_fd (Clone p p' fds shms # \<tau>) p'' fd =
(if (p' = p'' \<and> fd \<in> fds) then flags_of_proc_fd \<tau> p fd else flags_of_proc_fd \<tau> p'' fd)"
| "flags_of_proc_fd (Execve p f fds # \<tau>) p' fd =
(if (p' = p \<and> fd \<in> fds) then flags_of_proc_fd \<tau> p fd else flags_of_proc_fd \<tau> p' fd)"
| "flags_of_proc_fd (Kill p\<^isub>1 p\<^isub>2 # \<tau>) p fd =
(if (p = p\<^isub>2) then None else flags_of_proc_fd \<tau> p fd)"
| "flags_of_proc_fd (Exit p # \<tau>) p' fd' =
(if (p = p') then None else flags_of_proc_fd \<tau> p' fd')"
| "flags_of_proc_fd (e # \<tau>) p fd = flags_of_proc_fd \<tau> p fd"
(*
fun file_at_writing_by:: "t_state \<Rightarrow> t_file \<Rightarrow> (t_process \<times> t_fd) set"
where
"file_at_writing_by [] f = init_file_at_writing_by f"
| "file_at_writing_by (Open p f flags fd (Some inum) # \<tau>) f' = (
if (f' = f)
then ( if (is_write_flag flags)
then {(p, fd)}
else {} )
else file_at_writing_by \<tau> f' )"
| "file_at_writing_by (Open p f flags fd None # \<tau>) f' = (
if (f' = f \<and> is_write_flag flags)
then insert (p, fd) (file_at_writing_by \<tau> f)
else file_at_writing_by \<tau> f' )"
| "file_at_writing_by (Mkdir p f inum # \<tau>) f' =
(if (f' = f) then {} else file_at_writing_by \<tau> f')"
| "file_at_writing_by (LinkHard p f f' # \<tau>) f'' =
(if (f'' = f') then file_at_writing_by \<tau> f else file_at_writing_by \<tau> f'')"
| "file_at_writing_by (Rename p f\<^isub>2 f\<^isub>3 # \<tau>) f = (
if (f\<^isub>3 \<preceq> f) then file_at_writing_by \<tau> (file_before_rename f\<^isub>2 f\<^isub>3 f)
else file_at_writing_by \<tau> f )"
| "file_at_writing_by (CloseFd p fd # \<tau>) f =
(file_at_writing_by \<tau> f - {(p, fd)})"
| "file_at_writing_by (Clone p p' fds shms # \<tau>) f =
(file_at_writing_by \<tau> f) \<union> {(p',fd)| fd. fd \<in> fds \<and> (p, fd) \<in> file_at_writing_by \<tau> f}"
| "file_at_writing_by (Execve p f fds # \<tau>) f' =
(if (f' = f) then {} else file_at_writing_by \<tau> f')"
| "file_at_writing_by (Exit p # \<tau>) f =
(file_at_writing_by \<tau> f - {(p, fd)| fd. (p, fd) \<in> file_at_writing_by \<tau> f})"
| "file_at_writing_by (Kill p p' # \<tau>) f =
(file_at_writing_by \<tau> f - {(p', fd)| fd. (p', fd) \<in> file_at_writing_by \<tau> f})"
| "file_at_writing_by (e # \<tau>) f = file_at_writing_by \<tau> f"
*)
definition current_users :: "t_state \<Rightarrow> user_t set"
where
"current_users \<tau> \<equiv> init_users"
fun update_with_shuthow :: "t_sock_state option \<Rightarrow> t_shutdown_how \<Rightarrow> t_sock_state option"
where
"update_with_shuthow (Some (SS_trans Trans_Recv)) SHUT_RD = Some (SS_trans Trans_No)"
| "update_with_shuthow (Some (SS_trans Trans_RS)) SHUT_RD = Some (SS_trans Trans_Send)"
| "update_with_shuthow (Some (SS_trans Trans_Send)) SHUT_RD = Some (SS_trans Trans_Send)"
| "update_with_shuthow (Some (SS_trans Trans_No)) SHUT_RD = Some (SS_trans Trans_No)"
| "update_with_shuthow (Some (SS_trans Trans_Recv)) SHUT_WR = Some (SS_trans Trans_Recv)"
| "update_with_shuthow (Some (SS_trans Trans_RS)) SHUT_WR = Some (SS_trans Trans_Recv)"
| "update_with_shuthow (Some (SS_trans Trans_Send)) SHUT_WR = Some (SS_trans Trans_No)"
| "update_with_shuthow (Some (SS_trans Trans_No)) SHUT_WR = Some (SS_trans Trans_No)"
| "update_with_shuthow (Some (SS_trans Trans_Recv)) SHUT_RDWR = Some (SS_trans Trans_No)"
| "update_with_shuthow (Some (SS_trans Trans_RS)) SHUT_RDWR = Some (SS_trans Trans_No)"
| "update_with_shuthow (Some (SS_trans Trans_Send)) SHUT_RDWR = Some (SS_trans Trans_No)"
| "update_with_shuthow (Some (SS_trans Trans_No)) SHUT_RDWR = Some (SS_trans Trans_No)"
| "update_with_shuthow opt1 how = None"
fun socket_state :: "t_state \<Rightarrow> t_socket \<Rightarrow> t_sock_state option"
where
"socket_state [] = init_socket_state"
| "socket_state (CloseFd p fd # \<tau>) =
(socket_state \<tau>) ((p, fd):= None)"
| "socket_state (CreateSock p af st fd ino # \<tau>) =
(socket_state \<tau>) ((p, fd) := Some SS_create)"
| "socket_state (Bind p fd addr # \<tau>) =
(socket_state \<tau>) ((p, fd) := Some SS_bind)"
| "socket_state (Connect p fd addr # \<tau>) =
(socket_state \<tau>) ((p, fd) := Some (SS_trans Trans_RS))"
| "socket_state (Listen p fd # \<tau>) =
(socket_state \<tau>) ((p, fd) := Some SS_listen)"
| "socket_state (Accept p fd addr lport' fd' ino # \<tau>) =
(socket_state \<tau>) ((p, fd') := Some (SS_trans Trans_RS))"
| "socket_state (Shutdown p fd sh # \<tau>) =
(socket_state \<tau>) ((p, fd) := update_with_shuthow (socket_state \<tau> (p, fd)) sh)"
| "socket_state (Clone p p' fds shms # \<tau>) =
(\<lambda> (p'', fd). if (p'' = p' \<and> fd \<in> fds) then socket_state \<tau> (p, fd)
else if (p'' = p') then None
else socket_state \<tau> (p'', fd))"
| "socket_state (Execve p f fds # \<tau>) =
(\<lambda> (p', fd). if (p' = p \<and> fd \<in> fds) then socket_state \<tau> (p, fd)
else if (p' = p) then None
else socket_state \<tau> (p', fd))"
| "socket_state (Kill p\<^isub>1 p\<^isub>2 # \<tau>) =
(\<lambda> (p, fd). if (p = p\<^isub>2) then None else socket_state \<tau> (p, fd))"
| "socket_state (Exit p # \<tau>) =
(\<lambda> (p', fd'). if (p = p') then None else socket_state \<tau> (p', fd'))"
| "socket_state (e # \<tau>) = socket_state \<tau>"
definition socket_in_trans :: "t_state \<Rightarrow> t_socket \<Rightarrow> bool"
where
"socket_in_trans \<tau> s \<equiv> (case (socket_state \<tau> s) of
Some st \<Rightarrow> (case st of
SS_trans para \<Rightarrow> True
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
definition socket_in_sending :: "t_state \<Rightarrow> t_socket \<Rightarrow> bool"
where
"socket_in_sending \<tau> s \<equiv> (socket_state \<tau> s = Some (SS_trans Trans_Send)) \<or> (socket_state \<tau> s = Some (SS_trans Trans_RS))"
definition socket_in_recving :: "t_state \<Rightarrow> t_socket \<Rightarrow> bool"
where
"socket_in_recving \<tau> s \<equiv> (socket_state \<tau> s = Some (SS_trans Trans_Recv)) \<or> (socket_state \<tau> s = Some (SS_trans Trans_RS))"
(******* admissable check by the OS *******)
fun os_grant :: "t_state \<Rightarrow> t_event \<Rightarrow> bool"
where
"os_grant \<tau> (Open p f flags fd inumopt) = (
case inumopt of
Some ino \<Rightarrow>
(p \<in> current_procs \<tau> \<and> f \<notin> current_files \<tau> \<and>
(\<exists> pf. parent f = Some pf \<and> is_dir \<tau> pf \<and> pf \<notin> files_hung_by_del \<tau>) \<and>
is_creat_flag flags \<and> fd \<notin> (current_proc_fds \<tau> p) \<and> ino \<notin> (current_inode_nums \<tau>))
| None \<Rightarrow>
(p \<in> current_procs \<tau> \<and> \<not> is_creat_excl_flag flags \<and> is_file \<tau> f \<and>
fd \<notin> (current_proc_fds \<tau> p)) )"
(*(if (is_dir \<tau> f) then (is_dir_flag flags \<and> \<not> is_write_flag flags) else (\<not> is_dir_flag flags)),
here open is not applied to directories, readdir is for that, but it is not security-related *)
| "os_grant \<tau> (CloseFd p fd) =
(p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p)"
| "os_grant \<tau> (UnLink p f) =
(p \<in> current_procs \<tau> \<and> is_file \<tau> f \<and> f \<notin> files_hung_by_del \<tau>)"
| "os_grant \<tau> (Rmdir p f) =
(p \<in> current_procs \<tau> \<and> dir_is_empty \<tau> f \<and> f \<notin> files_hung_by_del \<tau> \<and> f \<noteq> [])" (* root file cannot be deleted *)
| "os_grant \<tau> (Mkdir p f ino) =
(p \<in> current_procs \<tau> \<and> f \<notin> current_files \<tau> \<and>
(\<exists> pf. parent f = Some pf \<and> is_dir \<tau> pf \<and> pf \<notin> files_hung_by_del \<tau>) \<and>
ino \<notin> (current_inode_nums \<tau>))"
| "os_grant \<tau> (LinkHard p f\<^isub>1 f\<^isub>2) =
(p \<in> current_procs \<tau> \<and> is_file \<tau> f\<^isub>1 \<and> f\<^isub>2 \<notin> current_files \<tau> \<and>
(\<exists> pf\<^isub>2. parent f\<^isub>2 = Some pf\<^isub>2 \<and> is_dir \<tau> pf\<^isub>2 \<and> pf\<^isub>2 \<notin> files_hung_by_del \<tau>))"
| "os_grant \<tau> (Truncate p f len) =
(p \<in> current_procs \<tau> \<and> is_file \<tau> f)"
(*
| "os_grant \<tau> (FTruncate p fd len) =
(p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and>
(\<exists> f. file_of_proc_fd \<tau> p fd = Some f \<and> f \<in> current_files \<tau> \<and> is_file \<tau> f) \<and>
(\<exists> flags. flags_of_proc_fd \<tau> p fd = Some flags \<and> is_write_flag flags))"
*)
| "os_grant \<tau> (ReadFile p fd) =
(p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and>
(\<exists> f. file_of_proc_fd \<tau> p fd = Some f \<and> f \<in> current_files \<tau>) \<and>
(\<exists> flags. flags_of_proc_fd \<tau> p fd = Some flags \<and> is_read_flag flags))"
| "os_grant \<tau> (WriteFile p fd) =
(p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and>
(\<exists> f. file_of_proc_fd \<tau> p fd = Some f \<and> f \<in> current_files \<tau>) \<and>
(\<exists> flags. flags_of_proc_fd \<tau> p fd = Some flags \<and> is_write_flag flags))"
| "os_grant \<tau> (Execve p f fds) =
(p \<in> current_procs \<tau> \<and> is_file \<tau> f \<and> fds \<subseteq> proc_file_fds \<tau> p)" (* file_at_writing_by \<tau> f = {} \<and> fds \<subseteq> current_proc_fds \<tau> p *)
(*
| "os_grant \<tau> (Rename p f\<^isub>2 f\<^isub>3) =
(p \<in> current_procs \<tau> \<and> f\<^isub>2 \<in> current_files \<tau> \<and> \<not>(f\<^isub>2 \<preceq> f\<^isub>3) \<and> f\<^isub>3 \<notin> current_files \<tau> \<and>
(\<exists> pf\<^isub>3. parent f\<^isub>3 = Some pf\<^isub>3 \<and> pf\<^isub>3 \<in> current_files \<tau> \<and> is_dir \<tau> pf\<^isub>3 \<and>
pf\<^isub>3 \<notin> files_hung_by_del \<tau>) )"
*)
| "os_grant \<tau> (CreateMsgq p q) =
(p \<in> current_procs \<tau> \<and> q \<notin> (current_msgqs \<tau>))"
| "os_grant \<tau> (SendMsg p q m) =
(p \<in> current_procs \<tau> \<and> q \<in> current_msgqs \<tau> \<and> m \<notin> (set (msgs_of_queue \<tau> q)))"
| "os_grant \<tau> (RecvMsg p q m) =
(p \<in> current_procs \<tau> \<and> q \<in> current_msgqs \<tau> \<and> m = hd (msgs_of_queue \<tau> q) \<and> msgs_of_queue \<tau> q \<noteq> [])"
| "os_grant \<tau> (RemoveMsgq p q) =
(p \<in> current_procs \<tau> \<and> q \<in> current_msgqs \<tau>)"
| "os_grant \<tau> (CreateShM p h) =
(p \<in> current_procs \<tau> \<and> h \<notin> (current_shms \<tau>))"
| "os_grant \<tau> (Attach p h flag) =
(p \<in> current_procs \<tau> \<and> h \<in> current_shms \<tau> \<and> \<not> (\<exists> flag. (p, flag) \<in> procs_of_shm \<tau> h))"
| "os_grant \<tau> (Detach p h) =
(p \<in> current_procs \<tau> \<and> h \<in> current_shms \<tau> \<and> (\<exists> flag. (p, flag) \<in> procs_of_shm \<tau> h))"
| "os_grant \<tau> (DeleteShM p h) =
(p \<in> current_procs \<tau> \<and> h \<in> current_shms \<tau>)"
| "os_grant \<tau> (CreateSock p af st fd ino) =
(p \<in> current_procs \<tau> \<and> af = AF_INET \<and> fd \<notin> (current_proc_fds \<tau> p) \<and>
ino \<notin> (current_inode_nums \<tau>))"
| "os_grant \<tau> (Accept p fd addr port fd' ino) =
(p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> (p, fd) \<in> current_sockets \<tau> \<and>
fd' \<notin> (current_proc_fds \<tau> p) \<and> socket_state \<tau> (p, fd) = Some SS_listen \<and>
is_tcp_sock \<tau> (p, fd) \<and> ino \<notin> (current_inode_nums \<tau>))"
| "os_grant \<tau> (Bind p fd addr) =
(p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> (p, fd) \<in> current_sockets \<tau> \<and>
socket_state \<tau> (p, fd) = Some SS_create)" (* ?? !! (case addr of INET_ADDR ip port \<Rightarrow> ip \<in> local_ipaddrs)) *)
| "os_grant \<tau> (Connect p fd addr) =
(p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> (p, fd) \<in> current_sockets \<tau> \<and>
socket_state \<tau> (p, fd) = Some SS_bind)"
| "os_grant \<tau> (Listen p fd) =
(p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> is_tcp_sock \<tau> (p, fd) \<and>
socket_state \<tau> (p, fd) = Some SS_bind)" (* Listen and Accept should only be used for TCP sever side *)
| "os_grant \<tau> (SendSock p fd) =
(p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> (p, fd) \<in> current_sockets \<tau> \<and>
socket_in_sending \<tau> (p, fd))"
| "os_grant \<tau> (RecvSock p fd) =
(p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> (p, fd) \<in> current_sockets \<tau> \<and>
socket_in_recving \<tau> (p, fd))"
| "os_grant \<tau> (Shutdown p fd sh) =
(p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> (p, fd) \<in> current_sockets \<tau> \<and>
socket_in_trans \<tau> (p, fd))"
(*
| "os_grant \<tau> (ChangeOwner p u) = (p \<in> current_procs \<tau> \<and> u \<in> current_users \<tau>)"
*)
| "os_grant \<tau> (Clone p p' fds shms) =
(p \<in> current_procs \<tau> \<and> p' \<notin> (current_procs \<tau>) \<and> fds \<subseteq> proc_file_fds \<tau> p \<and>
(\<forall> h \<in> shms. \<exists> flag. (p, flag) \<in> procs_of_shm \<tau> h))" (* current_proc_fds \<rightarrow> proc_file_fds *)
| "os_grant \<tau> (Kill p\<^isub>1 p\<^isub>2) =
(p\<^isub>1 \<in> current_procs \<tau> \<and> p\<^isub>2 \<in> current_procs \<tau>)" (* a process can kill itself right? *)
| "os_grant \<tau> (Exit p) =
(p \<in> current_procs \<tau>)"
| "os_grant \<tau> (Ptrace p\<^isub>1 p\<^isub>2) =
(p\<^isub>1 \<in> current_procs \<tau> \<and> p\<^isub>2 \<in> current_procs \<tau>)" (* a process can trace itself right? *)
fun alive :: "t_state \<Rightarrow> t_object \<Rightarrow> bool"
where
"alive s (O_proc p) = (p \<in> current_procs s)"
| "alive s (O_file f) = (is_file s f)"
| "alive s (O_dir f) = (is_dir s f)"
| "alive s (O_fd p fd) = (fd \<in> current_proc_fds s p)"
| "alive s (O_node n) = (n \<in> init_nodes)"
| "alive s (O_tcp_sock k) = (is_tcp_sock s k)"
| "alive s (O_udp_sock k) = (is_udp_sock s k)"
| "alive s (O_shm h) = (h \<in> current_shms s)"
| "alive s (O_msgq q) = (q \<in> current_msgqs s)"
| "alive s (O_msg q m) = (m \<in> set (msgs_of_queue s q) \<and> q \<in> current_msgqs s)"
(* deleted objects should be "taintable" objects, objects like fd should not be in consideration *)
(* actually, deleted should be renamed as "vanished", cause "exit/closefd" *)
fun deleted :: "t_object \<Rightarrow> t_event list \<Rightarrow> bool"
where
"deleted obj [] = False"
| "deleted obj (Kill p p' # s) = ((obj = O_proc p') \<or> (\<exists> fd \<in> current_proc_fds s p'. obj = O_fd p' fd) \<or>
(\<exists> fd. obj = O_tcp_sock (p', fd) \<and> is_tcp_sock s (p',fd)) \<or>
(\<exists> fd. obj = O_udp_sock (p', fd) \<and> is_udp_sock s (p',fd)) \<or>
deleted obj s)"
| "deleted obj (CloseFd p fd # s) = ((obj = O_fd p fd) \<or> (obj = O_tcp_sock (p,fd) \<and> is_tcp_sock s (p,fd)) \<or>
(obj = O_udp_sock (p,fd) \<and> is_udp_sock s (p, fd)) \<or>
(\<exists> f. obj = O_file f \<and> proc_fd_of_file s f = {(p, fd)} \<and>
f \<in> files_hung_by_del s) \<or> deleted obj s)"
| "deleted obj (Execve p f fds # s) = ((\<exists> fd \<in> current_proc_fds s p. obj = O_fd p fd \<and> fd \<notin> fds) \<or>
(\<exists> fd. obj = O_tcp_sock (p, fd) \<and> is_tcp_sock s (p,fd) \<and> fd \<notin> fds) \<or>
(\<exists> fd. obj = O_udp_sock (p, fd) \<and> is_udp_sock s (p,fd) \<and> fd \<notin> fds) \<or>
deleted obj s)"
| "deleted obj (Clone p p' fds shms # s) = ((\<exists> fd \<in> current_proc_fds s p. obj = O_fd p' fd \<and> fd \<notin> fds) \<or>
deleted obj s)"
| "deleted obj (UnLink p f # s) = ((proc_fd_of_file s f = {} \<and> obj = O_file f) \<or> deleted obj s)"
| "deleted obj (Rmdir p f # s) = ((obj = O_dir f) \<or> deleted obj s)"
| "deleted obj (Exit p # s) = ((obj = O_proc p) \<or> (\<exists> fd \<in> current_proc_fds s p. obj = O_fd p fd) \<or>
(\<exists> fd. obj = O_tcp_sock (p, fd) \<and> is_tcp_sock s (p,fd)) \<or>
(\<exists> fd. obj = O_udp_sock (p, fd) \<and> is_udp_sock s (p,fd)) \<or> deleted obj s)"
(*
| "deleted obj (Rename p f f' # s) =
(case obj of
O_file f'' \<Rightarrow> f \<preceq> f'' \<or> deleted obj s
| O_dir f'' \<Rightarrow> f \<preceq> f'' \<or> deleted obj s
| _ \<Rightarrow> deleted obj s)"
*)
| "deleted obj (RemoveMsgq p q # s) = (obj = O_msgq q \<or> (\<exists> m. obj = O_msg q m) \<or> deleted obj s)"
| "deleted obj (DeleteShM p h # s) = (obj = O_shm h \<or> deleted obj s)"
| "deleted obj (RecvMsg p q m # s) = (obj = O_msg q m \<or> deleted obj s)"
| "deleted obj (_ # s) = deleted obj s"
end
locale flask = init +
fixes
(***************** Policy-specific Parameters *************)
type_transition_rules :: "type_transition_rule_list_t"
and allowed_rules :: "allowed_rule_list_t"
and role_allowed_rules :: "role_allow_rule_list_t"
and role_declaration_rules :: "role_declarations_list_t"
and role_transition_rules:: "role_transition_rule_list_t"
and constrains_rules :: "constrains_list_t"
and init_type_of_obj :: "t_object \<rightharpoonup> type_t"
and init_user_of_obj :: "t_object \<rightharpoonup> user_t"
and init_role_of_proc :: "t_process \<rightharpoonup> role_t"
assumes
init_obj_has_type: "\<And> obj. init_alive obj \<Longrightarrow> \<exists> t. init_type_of_obj obj = Some t"
and init_type_has_obj: "\<And> obj t. init_type_of_obj obj = Some t \<Longrightarrow> init_alive obj"
and init_obj_has_user: "\<And> obj. init_alive obj \<Longrightarrow> \<exists> u. init_user_of_obj obj = Some u"
and init_user_has_obj: "\<And> obj u. init_user_of_obj obj = Some u \<Longrightarrow> init_alive obj \<and> u \<in> init_users"
and init_proc_has_role: "bidirect_in_init init_procs init_role_of_proc"
begin
(*********** policy-specified computations, not-event-related ************)
(* security_transition_sid : type_transition_rules
* It's a system-call offered by security-server? So access-control-checked too?
* according to selinux, it deals only with execve and file-creation
* is_execve: if is the execve case
* is_file: if is the creation of file/dir
* change from is_execve to is_file, because the new message by default use
* the type of the sending process too.
*)
definition type_transition :: "type_t \<Rightarrow> type_t \<Rightarrow> security_class_t \<Rightarrow> bool \<Rightarrow> type_t"
where
"type_transition st rt tc IS_file \<equiv> (
case (lookup type_transition_rules
(\<lambda> (stp, rtp, tc', dt). patt_match stp st \<and> patt_match rtp rt \<and> tc = tc')) of
None \<Rightarrow> (if IS_file then rt else st)
| Some (stp,rtp,tc',dt) \<Rightarrow> dt)"
(* allowed_rule_list *)
definition TE_allow :: "type_t \<Rightarrow> type_t \<Rightarrow> security_class_t \<Rightarrow> permission_t \<Rightarrow> bool"
where
"TE_allow st tt tc perm \<equiv> member allowed_rules
(\<lambda> (stp, ttp, tc', pp). tc = tc' \<and> patt_match stp st \<and> patt_match_self ttp tt st \<and>
patt_match pp perm)"
(* role_allow_rule_list_t *)
definition role_transition :: "role_t \<Rightarrow> type_t \<Rightarrow> role_t option"
where
"role_transition r t \<equiv>
(case (lookup role_transition_rules (\<lambda> (pr, ft, nr). pr = r \<and> t = ft)) of
None \<Rightarrow> None
| Some (pr,ft,nr) \<Rightarrow> Some nr)"
definition role_decl_check :: "role_t \<Rightarrow> type_t \<Rightarrow> bool"
where
"role_decl_check r t \<equiv> member role_declaration_rules (\<lambda> (role, types). r = role \<and> t \<in> types)"
definition role_allow :: "role_t \<Rightarrow> role_t \<Rightarrow> bool"
where
"role_allow r nr \<equiv> member role_allowed_rules (\<lambda> (from, to). r \<in> from \<and> nr \<in> to)"
(* here don't use lookup, because constrains should all be satisfied,
* while transitions always choose the "first" one
*)
definition constrains_satisfied ::
"security_context_t \<Rightarrow> security_context_t \<Rightarrow> security_class_t \<Rightarrow> permission_t \<Rightarrow> bool"
where
"constrains_satisfied sctxt tctxt c p \<equiv>
(fold (\<lambda> (cset, pset, P) res. res \<and> (if (c \<in> cset \<and> p \<in> pset)
then P sctxt tctxt else True))
constrains_rules True)"
(* main interface for TE_allow check and constrains check *)
fun permission_check::
"security_context_t \<Rightarrow> security_context_t \<Rightarrow> security_class_t \<Rightarrow> permission_t \<Rightarrow> bool"
where
"permission_check (su,sr,st) (tu,tr,tt) c p =
((TE_allow st tt c p) \<and> (constrains_satisfied (su,sr,st) (tu,tr,tt) c p))"
declare permission_check.simps [simp del]
(* no changeowner ??? : by adding "relabel obj sectxt" event or "login" event?
* or this explanation: the running of the sever will not grant any login but running
* of the server-programs!
*)
fun user_of_obj :: "t_state \<Rightarrow> t_object \<Rightarrow> user_t option"
where
"user_of_obj [] = init_user_of_obj"
| "user_of_obj (Clone p p' fds shms # s) =
(\<lambda> obj. case obj of
O_proc p'' \<Rightarrow> if (p'' = p') then user_of_obj s (O_proc p) else user_of_obj s obj
| O_fd p'' fd \<Rightarrow> if (p'' = p' \<and> fd \<in> fds) then user_of_obj s (O_fd p fd)
else if (p'' = p') then None
else user_of_obj s obj
| O_tcp_sock (p'',fd) \<Rightarrow> if (p'' = p' \<and> fd \<in> fds) then user_of_obj s (O_tcp_sock (p, fd))
else if (p'' = p') then None
else user_of_obj s obj
| O_udp_sock (p'',fd) \<Rightarrow> if (p'' = p' \<and> fd \<in> fds) then user_of_obj s (O_udp_sock (p, fd))
else if (p'' = p') then None
else user_of_obj s obj
| _ \<Rightarrow> user_of_obj s obj)"
| "user_of_obj (Open p f flags fd iopt # s) =
(case iopt of
None \<Rightarrow> (user_of_obj s) ((O_fd p fd) := user_of_obj s (O_proc p))
| _ \<Rightarrow> ((user_of_obj s) ((O_fd p fd) := user_of_obj s (O_proc p)))
((O_file f) := user_of_obj s (O_proc p)))"
| "user_of_obj (Mkdir p f inum # s) =
(user_of_obj s) ((O_dir f) := user_of_obj s (O_proc p))"
| "user_of_obj (LinkHard p f f' # s) =
(user_of_obj s) ((O_file f') := user_of_obj s (O_proc p))"
(*
| "user_of_obj (Rename p f2 f3 # s) =
(\<lambda> obj. case obj of
O_file f \<Rightarrow> if (f3 \<preceq> f) then user_of_obj s (O_file (file_before_rename f2 f3 f))
else user_of_obj s obj
| O_dir f \<Rightarrow> if (f3 \<preceq> f) then user_of_obj s (O_dir (file_before_rename f2 f3 f))
else user_of_obj s obj
| _ \<Rightarrow> user_of_obj s obj)"
*)
| "user_of_obj (CreateMsgq p q # s) =
(user_of_obj s) ((O_msgq q) := user_of_obj s (O_proc p))"
| "user_of_obj (SendMsg p q m # s) =
(user_of_obj s) ((O_msg q m) := user_of_obj s (O_proc p))"
| "user_of_obj (CreateShM p h # s) =
(user_of_obj s) ((O_shm h) := user_of_obj s (O_proc p))"
| "user_of_obj (CreateSock p af st fd inum # s) = (\<lambda> obj.
case obj of
O_fd p' fd' \<Rightarrow> if (p' = p \<and> fd' = fd) then user_of_obj s (O_proc p)
else user_of_obj s obj
| O_tcp_sock (p', fd') \<Rightarrow> if (p' = p \<and> fd' = fd \<and> st = STREAM) then user_of_obj s (O_proc p)
else user_of_obj s obj
| O_udp_sock (p', fd') \<Rightarrow> if (p' = p \<and> fd' = fd \<and> st = DGRAM) then user_of_obj s (O_proc p)
else user_of_obj s obj
| _ \<Rightarrow> user_of_obj s obj )"
| "user_of_obj (Accept p fd addr port fd' inum # s) = (\<lambda> obj.
case obj of
O_fd p' fd'' \<Rightarrow> if (p' = p \<and> fd'' = fd') then user_of_obj s (O_proc p)
else user_of_obj s obj
| O_tcp_sock (p', fd'') \<Rightarrow> if (p' = p \<and> fd'' = fd') then user_of_obj s (O_proc p)
else user_of_obj s obj
| _ \<Rightarrow> user_of_obj s obj )"
| "user_of_obj (_ # s) = user_of_obj s"
fun type_of_obj :: "t_state \<Rightarrow> (t_object \<Rightarrow> type_t option)"
where
"type_of_obj [] = init_type_of_obj"
| "type_of_obj (Clone p p' fds shms # s) = (\<lambda> obj.
case obj of
O_proc p'' \<Rightarrow> if (p'' = p') then type_of_obj s (O_proc p) else type_of_obj s obj
| O_fd p'' fd \<Rightarrow> if (p'' = p' \<and> fd \<in> fds) then type_of_obj s (O_fd p fd)
else if (p'' = p') then None
else type_of_obj s obj
| O_tcp_sock (p'', fd) \<Rightarrow> if (p'' = p' \<and> fd \<in> fds) then type_of_obj s (O_tcp_sock (p, fd))
else if (p'' = p') then None
else type_of_obj s obj
| O_udp_sock (p'', fd) \<Rightarrow> if (p'' = p' \<and> fd \<in> fds) then type_of_obj s (O_udp_sock (p, fd))
else if (p'' = p') then None
else type_of_obj s obj
| _ \<Rightarrow> type_of_obj s obj )"
| "type_of_obj (Execve p f fds # s) = (type_of_obj s) ((O_proc p) :=
(case (type_of_obj s (O_proc p), type_of_obj s (O_file f)) of
(Some tp, Some tf) \<Rightarrow> Some (type_transition tp tf C_process False)
| _ \<Rightarrow> None) )"
| "type_of_obj (Open p f flags fd (Some inum) # s) = ((type_of_obj s) ((O_file f) :=
(case (parent f) of
Some pf \<Rightarrow> (case (type_of_obj s (O_proc p), type_of_obj s (O_dir pf)) of
(Some tp, Some tpf) \<Rightarrow> Some (type_transition tp tpf C_file True)
| _ \<Rightarrow> None)
| _ \<Rightarrow> None) )) ((O_fd p fd) :=
type_of_obj s (O_proc p))"
| "type_of_obj (Open p f flags fd None # s) = (type_of_obj s) ((O_fd p fd) :=
type_of_obj s (O_proc p))"
| "type_of_obj (Mkdir p f inum # s) = (type_of_obj s) ((O_dir f) :=
(case (parent f) of
Some pf \<Rightarrow> (case (type_of_obj s (O_proc p), type_of_obj s (O_dir pf)) of
(Some tp, Some tpf) \<Rightarrow> Some (type_transition tp tpf C_dir True)
| _ \<Rightarrow> None)
| _ \<Rightarrow> None) )"
| "type_of_obj (LinkHard p f f' # s) = (type_of_obj s) ((O_file f') :=
(case (parent f') of
Some pf \<Rightarrow> (case (type_of_obj s (O_proc p), type_of_obj s (O_dir pf)) of
(Some tp, Some tpf) \<Rightarrow> Some (type_transition tp tpf C_file True)
| _ \<Rightarrow> None)
| _ \<Rightarrow> None) )"
(*
| "type_of_obj (Rename p f f' # s) = (\<lambda> obj.
case obj of
O_file f'' \<Rightarrow> (if (f' \<preceq> f'') then type_of_obj s (O_file (file_before_rename f f' f''))
else type_of_obj s (O_file f''))
| O_dir f'' \<Rightarrow> (if (f' \<preceq> f'') then type_of_obj s (O_file (file_before_rename f f' f''))
else type_of_obj s (O_file f''))
| _ \<Rightarrow> type_of_obj s obj )"
*)
| "type_of_obj (CreateMsgq p q # s) = (type_of_obj s) ((O_msgq q) :=
(case (type_of_obj s (O_proc p)) of
Some tp \<Rightarrow> Some tp
| _ \<Rightarrow> None) )"
| "type_of_obj (SendMsg p q m # s) = (type_of_obj s) ((O_msg q m) :=
(case (type_of_obj s (O_proc p), type_of_obj s (O_msgq q)) of
(Some tp, Some tq) \<Rightarrow> Some (type_transition tp tq C_msg False)
| _ \<Rightarrow> None) )"
| "type_of_obj (CreateShM p h # s) = (type_of_obj s) ((O_shm h) :=
(case (type_of_obj s (O_proc p)) of
Some tp \<Rightarrow> Some tp
| _ \<Rightarrow> None) )"
| "type_of_obj (CreateSock p af st fd inum # s) = (\<lambda> obj.
case obj of
O_fd p' fd' \<Rightarrow> if (p' = p \<and> fd' = fd) then type_of_obj s (O_proc p)
else type_of_obj s obj
| O_tcp_sock (p', fd') \<Rightarrow> if (p' = p \<and> fd' = fd \<and> st = STREAM) then type_of_obj s (O_proc p)
else type_of_obj s obj
| O_udp_sock (p', fd') \<Rightarrow> if (p' = p \<and> fd' = fd \<and> st = DGRAM) then type_of_obj s (O_proc p)
else type_of_obj s obj
| _ \<Rightarrow> type_of_obj s obj )"
| "type_of_obj (Accept p fd addr port fd' inum # s) = (\<lambda> obj.
case obj of
O_fd p' fd'' \<Rightarrow> if (p' = p \<and> fd'' = fd') then type_of_obj s (O_proc p)
else type_of_obj s obj
| O_tcp_sock (p', fd'') \<Rightarrow> if (p' = p \<and> fd'' = fd') then type_of_obj s (O_proc p)
else type_of_obj s obj
| _ \<Rightarrow> type_of_obj s obj )"
| "type_of_obj (_ # s) = type_of_obj s"
fun role_of_proc :: "t_state \<Rightarrow> (t_process \<Rightarrow> role_t option)"
where
"role_of_proc [] = init_role_of_proc"
| "role_of_proc (Clone p p' fds shms # s) =
(role_of_proc s) (p' := role_of_proc s p)"
| "role_of_proc (Execve p f fds # s) = (role_of_proc s) (p :=
(case (role_of_proc s p, type_of_obj s (O_file f)) of
(Some r, Some ft) \<Rightarrow> role_transition r ft
| _ \<Rightarrow> None) )"
| "role_of_proc (_ # s) = role_of_proc s"
fun role_of_obj :: "t_state \<Rightarrow> t_object \<Rightarrow> role_t option"
where
"role_of_obj s (O_proc p) = role_of_proc s p"
| "role_of_obj s _ = Some R_object" (* object_r *)
definition sectxt_of_obj :: "t_state \<Rightarrow> t_object \<Rightarrow> security_context_t option"
where
"sectxt_of_obj s obj = (
case (user_of_obj s obj, role_of_obj s obj, type_of_obj s obj) of
(Some u, Some r, Some t) \<Rightarrow> Some (u, r, t)
| _ \<Rightarrow> None)"
fun init_role_of_obj :: "t_object \<Rightarrow> role_t option"
where
"init_role_of_obj (O_proc p) = init_role_of_proc p"
| "init_role_of_obj _ = Some R_object"
definition init_sectxt_of_obj :: "t_object \<Rightarrow> security_context_t option"
where
"init_sectxt_of_obj obj \<equiv>
(case (init_user_of_obj obj, init_role_of_obj obj, init_type_of_obj obj) of
(Some u, Some r, Some t) \<Rightarrow> Some (u,r,t)
| _ \<Rightarrow> None)"
definition sec_of_root :: "security_context_t"
where
"sec_of_root \<equiv> (case (init_user_of_obj (O_dir []), init_type_of_obj (O_dir [])) of
(Some u, Some t) \<Rightarrow> (u, R_object, t))"
(******* flask granting ********
* involves three kinds of rules:
* 1. allow rule of types, allowed_rule_list_t, main
* 2. allow rule of roles, role_allow_rule_list_t, mainly for execve call
* 3. constrains, section 3.4.5, user-specifically defined.
* Passed all these 3, then grant Yes, else No
*)
definition search_check_allp :: "security_context_t \<Rightarrow> security_context_t set \<Rightarrow> bool"
where
"search_check_allp pctxt sectxts = (\<forall> sec \<in> sectxts. permission_check pctxt sec C_dir P_search)"
definition search_check_file :: "security_context_t \<Rightarrow> security_context_t \<Rightarrow> bool"
where
"search_check_file sctxt fctxt \<equiv> permission_check sctxt fctxt C_file P_search"
definition search_check_dir :: "security_context_t \<Rightarrow> security_context_t \<Rightarrow> bool"
where
"search_check_dir sctxt fctxt \<equiv> permission_check sctxt fctxt C_dir P_search"
fun get_parentfs_ctxts :: "t_state \<Rightarrow> t_file \<Rightarrow> (security_context_t list) option"
where
"get_parentfs_ctxts s [] =
(case (sectxt_of_obj s (O_dir [])) of
Some ctxt \<Rightarrow> Some [ctxt]
| _ \<Rightarrow> None)"
| "get_parentfs_ctxts s (f#pf) =
(case (get_parentfs_ctxts s pf, sectxt_of_obj s (O_dir (f#pf))) of
(Some ctxts, Some ctxt) \<Rightarrow> Some (ctxt#ctxts)
| _ \<Rightarrow> None)"
definition search_check_ctxt::
"security_context_t \<Rightarrow> security_context_t \<Rightarrow> security_context_t set \<Rightarrow> bool \<Rightarrow> bool"
where
"search_check_ctxt pctxt fctxt asecs if_file \<equiv> (
if if_file
then search_check_file pctxt fctxt \<and> search_check_allp pctxt asecs
else search_check_dir pctxt fctxt \<and> search_check_allp pctxt asecs )"
fun search_check :: "t_state \<Rightarrow> security_context_t \<Rightarrow> t_file \<Rightarrow> bool"
where
"search_check s pctxt [] =
(case (sectxt_of_obj s (O_dir [])) of
Some fctxt \<Rightarrow> search_check_ctxt pctxt fctxt {} False
| _ \<Rightarrow> False)"
| "search_check s pctxt (f#pf) =
(if (is_file s (f#pf))
then (case (sectxt_of_obj s (O_file (f#pf)), get_parentfs_ctxts s pf) of
(Some fctxt, Some pfctxts) \<Rightarrow> search_check_ctxt pctxt fctxt (set pfctxts) True
| _ \<Rightarrow> False)
else (case (sectxt_of_obj s (O_dir (f#pf)), get_parentfs_ctxts s pf) of
(Some fctxt, Some pfctxts) \<Rightarrow> search_check_ctxt pctxt fctxt (set pfctxts) False
| _ \<Rightarrow> False))"
(* this means we should prove every current fd has a security context! *)
definition sectxts_of_fds :: "t_state \<Rightarrow> t_process \<Rightarrow> t_fd set \<Rightarrow> security_context_t set"
where
"sectxts_of_fds s p fds \<equiv> {ctxt. \<exists> fd \<in> fds. sectxt_of_obj s (O_fd p fd) = Some ctxt}"
definition inherit_fds_check_ctxt:: "security_context_t \<Rightarrow> security_context_t set \<Rightarrow> bool"
where
"inherit_fds_check_ctxt p fds \<equiv> (\<forall> ctxt \<in> fds. permission_check p ctxt C_fd P_inherit)"
definition inherit_fds_check :: "t_state \<Rightarrow> security_context_t \<Rightarrow> t_process \<Rightarrow> t_fd set \<Rightarrow> bool"
where
"inherit_fds_check s npsectxt p fds \<equiv> inherit_fds_check_ctxt npsectxt (sectxts_of_fds s p fds)"
fun npctxt_execve :: "security_context_t \<Rightarrow> security_context_t \<Rightarrow> security_context_t option"
where
"npctxt_execve (pu,pr,pt) (fu,fr,ft) =
(case (role_transition pr ft) of
Some nr \<Rightarrow> Some (pu, nr, type_transition pt ft C_process False)
| _ \<Rightarrow> None)"
fun nfctxt_create :: "security_context_t \<Rightarrow> security_context_t \<Rightarrow> security_class_t \<Rightarrow> security_context_t"
where
"nfctxt_create (pu,pr,pt) (fu,fr,ft) cls = (pu, R_object, type_transition pt ft cls True)"
fun grant_execve ::
"security_context_t \<Rightarrow> security_context_t \<Rightarrow> security_context_t \<Rightarrow> bool"
where
"grant_execve (up,rp,tp) (uf,rf,tf) (up',nr,nt) =
(role_decl_check nr nt \<and> role_allow rp nr \<and>
permission_check (up,rp,tp) (uf,rf,tf) C_file P_execute \<and>
permission_check (up,nr,nt) (uf,rf,tf) C_file P_entrypoint \<and>
permission_check (up,rp,tp) (up,nr,nt) C_process P_transition \<and>
permission_check (up,nr,nt) (uf,rf,tf) C_process P_execute)"
definition sectxts_of_shms :: "t_state \<Rightarrow> t_shm set \<Rightarrow> security_context_t set"
where
"sectxts_of_shms s shms \<equiv> {ctxt. \<exists> h \<in> shms. sectxt_of_obj s (O_shm h) = Some ctxt}"
definition inherit_shms_check_ctxt:: "security_context_t \<Rightarrow> security_context_t set \<Rightarrow> bool"
where
"inherit_shms_check_ctxt p shms \<equiv> (\<forall> ctxt \<in> shms. permission_check p ctxt C_shm P_inherit)"
definition inherit_shms_check :: "t_state \<Rightarrow> security_context_t \<Rightarrow> t_shm set \<Rightarrow> bool"
where
"inherit_shms_check s npsectxt shms \<equiv> inherit_shms_check_ctxt npsectxt (sectxts_of_shms s shms)"
fun perm_of_mflag :: "t_open_must_flag \<Rightarrow> permission_t set"
where
"perm_of_mflag OF_RDONLY = {P_read}"
| "perm_of_mflag OF_WRONLY = {P_write}"
| "perm_of_mflag OF_RDWR = {P_read, P_write}"
definition perm_of_oflag :: "t_open_option_flag set \<Rightarrow> permission_t set"
where
"perm_of_oflag oflags \<equiv>
(case (OF_APPEND \<in> oflags, OF_CREAT \<in> oflags) of
(True, True) \<Rightarrow> {P_append, P_create}
| (True, _ ) \<Rightarrow> {P_append}
| (_ , True) \<Rightarrow> {P_create}
| _ \<Rightarrow> {})"
definition perms_of_flags :: "t_open_flags \<Rightarrow> permission_t set"
where
"perms_of_flags flags \<equiv>
(case flags of
(mflag,oflags) \<Rightarrow> (perm_of_mflag mflag \<union> perm_of_oflag oflags))"
(*
definition class_of_flags :: "t_open_flags \<Rightarrow> security_class_t"
where
"class_of_flags flags \<equiv>
(case flags of
(mflag, oflags) \<Rightarrow> if (OF_DIRECTORY \<in> oflags) then C_dir else C_file)"
definition obj_of_flags :: "t_open_flags \<Rightarrow> t_file \<Rightarrow> t_object"
where
"obj_of_flags flags f \<equiv>
(case flags of
(mflag, oflags) \<Rightarrow> if (OF_DIRECTORY \<in> oflags) then O_dir f else O_file f)"
*)
definition oflags_check :: "t_open_flags \<Rightarrow> security_context_t \<Rightarrow> security_context_t \<Rightarrow> bool"
where
"oflags_check flags pctxt fctxt \<equiv>
\<forall> perm \<in> (perms_of_flags flags). permission_check pctxt fctxt C_file perm"
fun grant :: "t_state \<Rightarrow> t_event \<Rightarrow> bool"
where
"grant s (Execve p f fds) =
(case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_file f)) of
(Some (up, rp, tp), Some (uf, rf, tf)) \<Rightarrow>
(case (npctxt_execve (up,rp,tp) (uf,rf,tf)) of
Some (pu,nr,nt) \<Rightarrow> (
search_check s (up,rp,tp) f \<and>
grant_execve (up,rp,tp) (uf,rf,tf) (up,nr,nt) \<and>
inherit_fds_check s (up,nr,nt) p fds)
| _ \<Rightarrow> False)
| _ \<Rightarrow> False )"
| "grant s (Clone p p' fds shms) =
(case (sectxt_of_obj s (O_proc p)) of
Some (up, rp, tp) \<Rightarrow>
(permission_check (up,rp,tp) (up,rp,tp) C_process P_fork \<and>
inherit_fds_check s (up,rp,tp) p fds \<and>
inherit_shms_check s (up,rp,tp) shms)
| _ \<Rightarrow> False )"
| "grant s (Kill p p') =
(case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_proc p')) of
(Some (su,sr,st), Some (tu,tr,tt)) \<Rightarrow>
permission_check (su,sr,st) (tu,tr,tt) C_process P_sigkill
| _ \<Rightarrow> False)"
| "grant s (Ptrace p p') =
(case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_proc p')) of
(Some (su,sr,st), Some (tu,tr,tt)) \<Rightarrow>
permission_check (su,sr,st) (tu,tr,tt) C_process P_ptrace
| _ \<Rightarrow> False)"
| "grant s (Exit p) = True"
| "grant s (Open p f flags fd None) =
(case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_file f)) of
(Some (pu,pr,pt), Some (fu,fr,ft)) \<Rightarrow>
search_check s (pu,pr,pt) f \<and>
oflags_check flags (pu,pr,pt) (fu,fr,ft) \<and>
permission_check (pu,pr,pt) (pu,pr,pt) C_fd P_setattr
| _ \<Rightarrow>False)"
| "grant s (Open p f flags fd (Some inum)) =
(case (parent f) of
Some pf \<Rightarrow> (case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_dir pf)) of
(Some (pu,pr,pt), Some (pfu,pfr,pft)) \<Rightarrow>
(search_check s (pu,pr,pt) pf \<and>
oflags_check flags (pu,pr,pt) (nfctxt_create (pu,pr,pt) (pfu,pfr,pft) C_file) \<and>
permission_check (pu,pr,pt) (pfu,pfr,pft) C_dir P_add_name \<and>
permission_check (pu,pr,pt) (pu,pr,pt) C_fd P_setattr)
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
| "grant s (ReadFile p fd) =
(case (file_of_proc_fd s p fd) of
Some f \<Rightarrow>
(case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_fd p fd),
sectxt_of_obj s (O_file f)) of
(Some (pu,pr,pt), Some (fdu,fdr,fdt), Some (fu,fr,ft)) \<Rightarrow>
(permission_check (pu,pr,pt) (fdu,fdr,fdt) C_fd P_setattr \<and>
permission_check (pu,pr,pt) (fu,fr,ft) C_file P_read)
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
| "grant s (WriteFile p fd) =
(case (file_of_proc_fd s p fd) of
Some f \<Rightarrow>
(case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_fd p fd),
sectxt_of_obj s (O_file f)) of
(Some (pu,pr,pt), Some (fdu,fdr,fdt), Some (fu,fr,ft)) \<Rightarrow>
(permission_check (pu,pr,pt) (fdu,fdr,fdt) C_fd P_setattr \<and>
permission_check (pu,pr,pt) (fu,fr,ft) C_file P_write)
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
| "grant s (CloseFd p fd) = True"
| "grant s (UnLink p f) =
(case (parent f) of
Some pf \<Rightarrow>
(case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_dir pf),
sectxt_of_obj s (O_file f)) of
(Some (pu,pr,pt), Some (du,dr,dt), Some (fu,fr,ft)) \<Rightarrow>
(search_check s (pu,pr,pt) f \<and>
permission_check (pu,pr,pt) (fu,fr,ft) C_file P_unlink \<and>
permission_check (pu,pr,pt) (du,dr,dt) C_dir P_remove_name)
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
| "grant s (Rmdir p f) =
(case (parent f) of
Some pf \<Rightarrow>
(case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_dir pf),
sectxt_of_obj s (O_dir f)) of
(Some (pu,pr,pt), Some (du,dr,dt), Some (fu,fr,ft)) \<Rightarrow>
(search_check s (pu,pr,pt) f \<and>
permission_check (pu,pr,pt) (fu,fr,ft) C_dir P_rmdir \<and>
permission_check (pu,pr,pt) (du,dr,dt) C_dir P_remove_name)
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
| "grant s (Mkdir p f inum) =
(case (parent f) of
Some pf \<Rightarrow>
(case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_dir pf)) of
(Some (pu,pr,pt), Some (du,dr,dt)) \<Rightarrow>
(search_check s (pu,pr,pt) f \<and>
permission_check (pu,pr,pt) (nfctxt_create (pu,pr,pt) (du,dr,dt) C_dir) C_dir P_create \<and>
permission_check (pu,pr,pt) (du,dr,dt) C_dir P_add_name)
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
| "grant s (LinkHard p f f') =
(case (parent f') of
Some pf \<Rightarrow>
(case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_dir pf),
sectxt_of_obj s (O_file f)) of
(Some (pu,pr,pt), Some (du,dr,dt), Some (fu,fr,ft)) \<Rightarrow>
(search_check s (pu,pr,pt) f \<and> search_check s (pu,pr,pt) pf \<and>
permission_check (pu,pr,pt) (fu,fr,ft) C_file P_link \<and>
permission_check (pu,pr,pt) (du,dr,dt) C_dir P_add_name)
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
| "grant s (Truncate p f len) =
(case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_file f)) of
(Some (pu,pr,pt), Some (fu,fr,ft)) \<Rightarrow>
(search_check s (pu,pr,pt) f \<and>
permission_check (pu,pr,pt) (fu,fr,ft) C_file P_setattr)
| _ \<Rightarrow> False)"
(*
| "grant s (Rename p f f') =
(case (parent f, parent f') of
(Some pf, Some pf') \<Rightarrow>
(case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_dir pf),
sectxt_of_obj s (O_file f), sectxt_of_obj s (O_dir pf')) of
(Some (pu,pr,pt), Some (pfu,pfr,pft), Some (fu,fr,ft),
Some (pfu',pfr',pft')) \<Rightarrow>
(search_check s (pu,pr,pt) f \<and>
permission_check (pu,pr,pt) (pfu,pfr,pft) C_dir P_remove_name \<and>
(if (is_file s f)
then permission_check (pu,pr,pt) (fu,fr,ft) C_file P_rename
else permission_check (pu,pr,pt) (fu,fr,ft) C_dir P_reparent) \<and>
search_check s (pu,pr,pt) pf' \<and>
permission_check (pu,pr,pt) (pfu',pfr',pft') C_dir P_add_name)
| _ \<Rightarrow> False)
| _ \<Rightarrow> False)"
*)
| "grant s (CreateMsgq p q) =
(case (sectxt_of_obj s (O_proc p)) of
Some (pu,pr,pt) \<Rightarrow>
(permission_check (pu,pr,pt) (pu,pr,pt) C_msgq P_associate \<and>
permission_check (pu,pr,pt) (pu,pr,pt) C_msgq P_create)
| _ \<Rightarrow> False)"
| "grant s (SendMsg p q m) =
(case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_msgq q)) of
(Some (pu,pr,pt), Some (qu,qr,qt)) \<Rightarrow>
(permission_check (pu,pr,pt) (qu,qr,qt) C_msgq P_enqueue \<and>
permission_check (pu,pr,pt) (qu,qr,qt) C_msgq P_write \<and>
permission_check (pu,pr,pt) (pu,pr,pt) C_msg P_send)
| _ \<Rightarrow> False)"
| "grant s (RecvMsg p q m) =
(case (sectxt_of_obj s (O_proc p),sectxt_of_obj s (O_msgq q),sectxt_of_obj s (O_msg q m)) of
(Some (pu,pr,pt), Some (qu,qr,qt), Some (mu,mr,mt)) \<Rightarrow>
permission_check (pu,pr,pt) (qu,qr,qt) C_msgq P_read \<and>
permission_check (pu,pr,pt) (mu,mr,mt) C_msg P_receive
| _ \<Rightarrow> False)"
| "grant s (RemoveMsgq p q) =
(case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_msgq q)) of
(Some (pu,pr,pt), Some (qu,qr,qt)) \<Rightarrow>
permission_check (pu,pr,pt) (qu,qr,qt) C_msgq P_destroy
| _ \<Rightarrow> False)"
| "grant s (CreateShM p h) =
(case (sectxt_of_obj s (O_proc p)) of
Some (pu,pr,pt) \<Rightarrow>
(permission_check (pu,pr,pt) (pu,pr,pt) C_shm P_associate \<and>
permission_check (pu,pr,pt) (pu,pr,pt) C_shm P_create)
| _ \<Rightarrow> False)"
| "grant s (Attach p h flag) =
(case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_shm h)) of
(Some (pu,pr,pt), Some (hu,hr,ht)) \<Rightarrow>
if flag = SHM_RDONLY
then permission_check (pu,pr,pt) (hu,hr,ht) C_shm P_read
else permission_check (pu,pr,pt) (hu,hr,ht) C_shm P_read \<and>
permission_check (pu,pr,pt) (hu,hr,ht) C_shm P_write
| _ \<Rightarrow> False)"
| "grant s (Detach p h) = True" (*?*)
| "grant s (DeleteShM p h) =
(case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_shm h)) of
(Some (pu,pr,pt), Some (hu,hr,ht)) \<Rightarrow>
permission_check (pu,pr,pt) (hu,hr,ht) C_shm P_destroy
| _ \<Rightarrow> False)"
| "grant s _ = False" (* socket event is currently not in consideration *)
inductive valid :: "t_state \<Rightarrow> bool"
where
"valid []"
| "\<lbrakk>valid s; os_grant s e; grant s e\<rbrakk> \<Longrightarrow> valid (e # s)"
(* tobj: object that can be tainted *)
fun tobj_in_init :: "t_object \<Rightarrow> bool"
where
"tobj_in_init (O_proc p) = (p \<in> init_procs)"
| "tobj_in_init (O_file f) = (is_init_file f)"
(* directory is not taintable
| "tobj_in_init (O_dir f) = (f \<in> init_files)"
*)
| "tobj_in_init (O_node n) = (n \<in> init_nodes)"
| "tobj_in_init (O_msg q m) = (m \<in> set (init_msgs_of_queue q) \<and> q \<in> init_msgqs)"
| "tobj_in_init _ = False" (* other kind of obj cannot be tainted *)
(* no use
fun no_del_event:: "t_event list \<Rightarrow> bool"
where
"no_del_event [] = True"
| "no_del_event (Kill p p' # \<tau>) = False"
| "no_del_event (CloseFd p fd # \<tau>) = False"
| "no_del_event (UnLink p f # \<tau>) = False"
| "no_del_event (Rmdir p f # \<tau>) = False"
(*
| "no_del_event (Rename p f f' # \<tau>) = False"
*)
| "no_del_event (RemoveMsgq p q # \<tau>) = False"
| "no_del_event (RecvMsg p q m # \<tau>) = False"
| "no_del_event (_ # \<tau>) = no_del_event \<tau>"
*)
end
locale tainting = flask +
fixes seeds :: "t_object set"
assumes
seeds_in_init: "\<And> obj. obj \<in> seeds \<Longrightarrow> tobj_in_init obj"
and same_inode_in_seeds: "\<And> f f'. \<lbrakk>O_file f \<in> seeds; has_same_inode [] f f'\<rbrakk> \<Longrightarrow> O_file f' \<in> seeds"
and flow_shm_in_seeds: "\<And> p p'. \<lbrakk>O_proc p \<in> seeds; info_flow_shm [] p p'\<rbrakk> \<Longrightarrow> O_proc p' \<in> seeds"
begin
inductive tainted :: "t_object \<Rightarrow> t_state \<Rightarrow> bool" ("_ \<in> tainted _" [100, 100] 100)
where
t_init: "obj \<in> seeds \<Longrightarrow> obj \<in> tainted []"
| t_clone: "\<lbrakk>O_proc p \<in> tainted s; valid (Clone p p' fds shms # s)\<rbrakk>
\<Longrightarrow> O_proc p' \<in> tainted (Clone p p' fds shms # s)"
| t_execve: "\<lbrakk>O_file f \<in> tainted s; valid (Execve p f fds # s)\<rbrakk>
\<Longrightarrow> O_proc p \<in> tainted (Execve p f fds # s)"
| t_ptrace: "\<lbrakk>O_proc p \<in> tainted s; valid (Ptrace p p' # s); info_flow_shm s p' p''\<rbrakk>
\<Longrightarrow> O_proc p'' \<in> tainted (Ptrace p p' # s)"
| t_ptrace':"\<lbrakk>O_proc p' \<in> tainted s; valid (Ptrace p p' # s); info_flow_shm s p p''\<rbrakk>
\<Longrightarrow> O_proc p'' \<in> tainted (Ptrace p p' # s)"
| t_cfile: "\<lbrakk>O_proc p \<in> tainted s; valid (Open p f flags fd (Some inum) # s)\<rbrakk>
\<Longrightarrow> O_file f \<in> tainted (Open p f flags fd (Some inum) # s)"
| t_read: "\<lbrakk>O_file f \<in> tainted s; valid (ReadFile p fd # s);
file_of_proc_fd s p fd = Some f; info_flow_shm s p p'\<rbrakk>
\<Longrightarrow> O_proc p' \<in> tainted (ReadFile p fd # s)"
| t_write: "\<lbrakk>O_proc p \<in> tainted s; valid (WriteFile p fd # s);
file_of_proc_fd s p fd = Some f; has_same_inode s f f'\<rbrakk>
\<Longrightarrow> O_file f' \<in> tainted (WriteFile p fd # s)"
(* directory is not tainted
| t_mkdir: "\<lbrakk>O_proc p \<in> tainted s; valid (Mkdir p f inum # s)\<rbrakk>
\<Longrightarrow> O_dir f \<in> tainted (Mkdir p f inum # s)"
*)
| t_link: "\<lbrakk>O_file f \<in> tainted s; valid (LinkHard p f f' # s)\<rbrakk>
\<Longrightarrow> O_file f' \<in> tainted (LinkHard p f f' # s)"
| t_trunc: "\<lbrakk>O_proc p \<in> tainted s; valid (Truncate p f len # s); len > 0; has_same_inode s f f'\<rbrakk>
\<Longrightarrow> O_file f' \<in> tainted (Truncate p f len # s)"
(*
| t_rename: "\<lbrakk>O_file f'' \<in> tainted s; valid (Rename p f f' # s);f \<preceq> f''\<rbrakk>
\<Longrightarrow> O_file (file_after_rename f f' f'') \<in> tainted (Rename p f f' # s)"
| t_rename':"\<lbrakk>O_dir f'' \<in> tainted s; valid (Rename p f f' # s);f \<preceq> f''\<rbrakk>
\<Longrightarrow> O_dir (file_after_rename f f' f'') \<in> tainted (Rename p f f' # s)"
*)
| t_attach1:"\<lbrakk>O_proc p \<in> tainted s; valid (Attach p h SHM_RDWR # s); (p', flag') \<in> procs_of_shm s h; info_flow_shm s p' p''\<rbrakk>
\<Longrightarrow> O_proc p'' \<in> tainted (Attach p h SHM_RDWR # s)"
| t_attach2:"\<lbrakk>O_proc p' \<in> tainted s; valid (Attach p h flag # s); (p', SHM_RDWR) \<in> procs_of_shm s h; info_flow_shm s p p''\<rbrakk>
\<Longrightarrow> O_proc p'' \<in> tainted (Attach p h flag # s)"
| t_sendmsg:"\<lbrakk>O_proc p \<in> tainted s; valid (SendMsg p q m # s)\<rbrakk>
\<Longrightarrow> O_msg q m \<in> tainted (SendMsg p q m # s)"
| t_recvmsg:"\<lbrakk>O_msg q m \<in> tainted s; valid (RecvMsg p q m # s); info_flow_shm s p p'\<rbrakk>
\<Longrightarrow> O_proc p' \<in> tainted (RecvMsg p q m # s)"
| t_remain: "\<lbrakk>obj \<in> tainted s; valid (e # s); alive (e # s) obj\<rbrakk>
\<Longrightarrow> obj \<in> tainted (e # s)"
(* reasonable tainted object, fd and sock and msgq and msg is excluded
* this is different from tainted, which already excluded some of them,
* tainted not excluded msg, which does not have the meaning of "tainteable", but
* but acting as a media to "pass" the virus. We normally will not say that
* a message is tableable or not.
*)
fun appropriate :: "t_object \<Rightarrow> bool"
where
"appropriate (O_proc p) = (p \<in> init_procs)"
| "appropriate (O_file f) = (is_init_file f)"
| "appropriate (O_dir f) = False"
| "appropriate (O_fd p fd) = False"
| "appropriate (O_node n) = False" (* cause socket is temperary not considered *)
| "appropriate (O_tcp_sock k) = False"
| "appropriate (O_udp_sock k) = False"
| "appropriate (O_shm h) = False"
| "appropriate (O_msgq q) = False"
| "appropriate (O_msg q m) = False"
definition taintable:: "t_object \<Rightarrow> bool"
where
"taintable obj \<equiv> init_alive obj \<and> appropriate obj \<and> (\<exists> s. obj \<in> tainted s)"
definition undeletable :: "t_object \<Rightarrow> bool"
where
"undeletable obj \<equiv> init_alive obj \<and> \<not> (\<exists> s. valid s \<and> deleted obj s)"
end
end