1 theory Flask

     2 imports Main Flask_type OS_type_def File_renaming 

     3 begin

     4 

     5 (****** Policy-language-level rule match/auxiliary functions ******)

     6 

     7 fun patt_match :: "'a patt \<Rightarrow> 'a \<Rightarrow> bool"

     8 where

     9   "patt_match (Single x) y = (x = y)"

    10 | "patt_match (Set s)    x = (x \<in> s)"

    11 | "patt_match (Tilde s)  x = (x \<notin> s)"

    12 | "patt_match Asterisk   x = True"

    13 

    14 (* match a target with a patt, but including the SELF special 

    15  * patt_match_self patt target source 

    16  *)

    17 fun patt_match_self :: "(type_t patt) target_with_self_t \<Rightarrow> type_t \<Rightarrow> type_t \<Rightarrow> bool"

    18 where

    19   "patt_match_self Self                  tt st = (tt = st)"

    20 | "patt_match_self (Not_self (Single p)) tt st = (tt = p)"

    21 | "patt_match_self (Not_self (Set p))    tt st = (tt \<in> p)"

    22 | "patt_match_self (Not_self (Tilde p))  tt st = (tt \<notin> p)"

    23 | "patt_match_self (Not_self Asterisk)   tt st = True"

    24 

    25 (* list lookup: find the first one *)

    26 fun lookup :: "'a list \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> 'a option"

    27 where

    28   "lookup [] P = None"

    29 | "lookup (x # xs) P = (if (P x) then Some x else lookup xs P)"

    30 

    31 (* list member: if exists an element satisfy predicate P *)

    32 fun member :: "'a list \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> bool"

    33 where

    34   "member [] P = False"

    35 | "member (x # xs) P = (if (P x) then True else member xs P)"

    36 

    37 (******* socket related aux functions ********)

    38 fun is_remote_request :: "t_event \<Rightarrow> bool"    

    39 where

    40   "is_remote_request (Accept p fd addr port fd' i)  = True"

    41 | "is_remote_request (Connect p fd addr)   = True"

    42 | "is_remote_request (SendSock p fd) = True"

    43 | "is_remote_request (RecvSock p fd) = True"

    44 | "is_remote_request e         = False"

    45 

    46 fun ip_of_addr:: "t_sock_addr \<Rightarrow> t_inet_addr"

    47 where

    48   "ip_of_addr (INET_ADDR saddr sport) = saddr"

    49 

    50 fun port_of_addr:: "t_sock_addr \<Rightarrow> t_socket_port"

    51 where

    52   "port_of_addr (INET_ADDR saddr sport) = sport"

    53 

    54 fun after_bind:: "t_sock_state option \<Rightarrow> bool"

    55 where

    56   "after_bind None = False"

    57 | "after_bind (Some SS_create) = False"

    58 | "after_bind _= True" (* after bind , it should have local addr *)

    59 

    60 fun after_conacc:: "t_sock_state option \<Rightarrow> bool"

    61 where

    62   "after_conacc None = False"

    63 | "after_conacc (Some SS_create) = False"

    64 | "after_conacc (Some SS_bind) = False"

    65 | "after_conacc (Some SS_listen) = False"

    66 | "after_conacc _ = True"  (* after connect or accept, it should have remote addr *)

    67 

    68 (* inet_addr_compare addr1 addr2 \<equiv> addr1 \<le> addr2; but in \<le>'s def,there is a \<exists>, is not a function*)

    69 fun subnet_addr :: "t_inet_addr \<Rightarrow> t_inet_addr \<Rightarrow> bool"

    70 where

    71   "subnet_addr []     addr   = True"

    72 | "subnet_addr (x#xs) []     = False"

    73 | "subnet_addr (x#xs) (y#ys) = ((x = y) \<and> subnet_addr xs ys)"

    74 

    75 definition port_in_range :: "t_socket_port \<Rightarrow> t_socket_port \<Rightarrow> t_socket_port \<Rightarrow> bool"

    76 where

    77   "port_in_range minp maxp p \<equiv> ((p < maxp \<or> p = maxp) \<and> (p > minp \<or> p = minp))"

    78 

    79 (* initial value of initiate state constrains aux function *)

    80 definition bidirect_in_init :: "'a set \<Rightarrow> ('a \<Rightarrow> 'b option) \<Rightarrow> bool"

    81 where

    82   "bidirect_in_init S f \<equiv>  (\<forall> a. a \<in> S \<longrightarrow> (\<exists> b. f a = Some b)) \<and> 

    83                            (\<forall> a b. f a = Some b \<longrightarrow> a \<in> S)" 

    84 

    85 fun is_file_itag :: "t_inode_tag \<Rightarrow> bool"

    86 where

    87   "is_file_itag Tag_FILE = True"

    88 | "is_file_itag tag      = False"

    89 

    90 fun is_dir_itag :: "t_inode_tag \<Rightarrow> bool"

    91 where

    92   "is_dir_itag Tag_DIR = True"

    93 | "is_dir_itag tag     = False"

    94 

    95 fun is_file_dir_itag :: "t_inode_tag \<Rightarrow> bool"

    96 where

    97   "is_file_dir_itag Tag_FILE = True"

    98 | "is_file_dir_itag Tag_DIR  = True"

    99 | "is_file_dir_itag tag      = False"

   100 

   101 fun is_tcp_itag :: "t_inode_tag \<Rightarrow> bool"

   102 where

   103   "is_tcp_itag Tag_TCP_SOCK = True"

   104 | "is_tcp_itag tag      = False"

   105 

   106 fun is_udp_itag :: "t_inode_tag \<Rightarrow> bool"

   107 where

   108   "is_udp_itag Tag_UDP_SOCK = True"

   109 | "is_udp_itag tag     = False"

   110 

   111 fun is_sock_itag :: "t_inode_tag \<Rightarrow> bool"

   112 where

   113   "is_sock_itag Tag_TCP_SOCK = True"

   114 | "is_sock_itag Tag_UDP_SOCK = True"

   115 | "is_sock_itag tag          = False"

   116 

   117 

   118 locale init = 

   119   fixes 

   120       init_files :: "t_file set"

   121   and init_procs :: "t_process set"

   122   and init_nodes :: "t_node set"

   123   and init_sockets :: "t_socket set"

   124   and init_users :: "user_t set"

   125 

   126   and init_file_of_proc_fd ::   "t_process \<Rightarrow> t_fd \<rightharpoonup> t_file"

   127   and init_fds_of_proc ::       "t_process \<Rightarrow> t_fd set"

   128   and init_oflags_of_proc_fd::  "t_process \<Rightarrow> t_fd \<rightharpoonup> t_open_flags"

   129   and init_inum_of_file ::      "t_file \<rightharpoonup> t_inode_num"

   130   and init_inum_of_socket::     "t_socket  \<rightharpoonup> t_inode_num" 

   131   and init_itag_of_inum::       "t_inode_num \<rightharpoonup> t_inode_tag"

   132   and init_files_hung_by_del :: "t_file set"

   133 (*

   134   and init_file_at_writing_by:: "t_file \<Rightarrow> (t_process \<times> t_fd) set"

   135 *)

   136   and init_socket_state ::      "t_socket \<rightharpoonup> t_sock_state"

   137 

   138   and init_msgqs :: "t_msgq set"

   139   and init_msgs_of_queue:: "t_msgq \<Rightarrow> t_msg list"

   140   and init_shms :: "t_shm set"

   141   and init_procs_of_shm :: "t_shm \<Rightarrow> (t_process \<times> t_shm_attach_flag) set" 

   142 

   143   assumes

   144       parent_file_in_init: "\<And> f pf. \<lbrakk>parent f = Some pf; f \<in> init_files\<rbrakk> \<Longrightarrow> pf \<in> init_files"

   145   and root_is_dir: "\<exists> i. init_inum_of_file [] = Some i \<and> init_itag_of_inum i = Some Tag_DIR"

   146   and init_file_has_inum:  "\<And> f. f \<in> init_files \<Longrightarrow> \<exists> im. init_inum_of_file f = Some im"

   147   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)"

   148   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)"

   149   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"

   150 

   151   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)"

   152   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> 

   153                                          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'))"

   154 

   155   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)"

   156   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)"

   157   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"

   158 

   159   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"

   160   and init_msgs_distinct:      "\<And> q. distinct (init_msgs_of_queue q)"

   161 

   162   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"

   163   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)"

   164 (*

   165   and init_netobj_has_state:   "bidirect_in_init init_netobjs init_netobj_state"

   166   and init_netobj_has_socktype:"bidirect_in_init init_netobjs init_netobj_socktype"

   167   and init_netobj_has_laddr:   "\<And> s. after_bind (init_netobj_state s) \<Longrightarrow> init_netobj_localaddr s \<noteq> None"

   168   and init_netobj_has_raddr:   "\<And> s. after_conacc (init_netobj_state s) \<Longrightarrow> init_netobj_remoteaddr s \<noteq> None"

   169 *)

   170 

   171   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" 

   172 

   173 begin 

   174 

   175 definition is_init_file:: "t_file \<Rightarrow> bool"

   176 where

   177   "is_init_file f \<equiv> (case (init_inum_of_file f) of

   178                        Some i \<Rightarrow> (case (init_itag_of_inum i) of

   179                                     Some Tag_FILE \<Rightarrow> True

   180                                   | _             \<Rightarrow> False)

   181                      | _      \<Rightarrow> False)"

   182 

   183 definition is_init_dir:: "t_file \<Rightarrow> bool"

   184 where

   185   "is_init_dir f \<equiv> (case (init_inum_of_file f) of

   186                       Some i \<Rightarrow> (case (init_itag_of_inum i) of

   187                                    Some Tag_DIR \<Rightarrow> True

   188                                  | _            \<Rightarrow> False)

   189                     | _      \<Rightarrow> False)"

   190 

   191 definition is_init_tcp_sock:: "t_socket \<Rightarrow> bool"

   192 where

   193   "is_init_tcp_sock s \<equiv> (case (init_inum_of_socket s) of

   194                            Some i \<Rightarrow> (case (init_itag_of_inum i) of

   195                                         Some Tag_TCP_SOCK \<Rightarrow> True

   196                                       | _                 \<Rightarrow> False)

   197                          | _      \<Rightarrow> False)"

   198 

   199 definition is_init_udp_sock:: "t_socket \<Rightarrow> bool"

   200 where

   201   "is_init_udp_sock s \<equiv> (case (init_inum_of_socket s) of

   202                            Some i \<Rightarrow> (case (init_itag_of_inum i) of

   203                                         Some Tag_UDP_SOCK \<Rightarrow> True

   204                                       | _                 \<Rightarrow> False)

   205                          | _      \<Rightarrow> False)"

   206 

   207 fun init_alive :: "t_object \<Rightarrow> bool"

   208 where

   209   "init_alive (O_proc p)     = (p \<in> init_procs)"

   210 | "init_alive (O_file f)     = (is_init_file f)"

   211 | "init_alive (O_dir  f)     = (is_init_dir  f)"

   212 | "init_alive (O_fd p fd)    = (fd \<in> init_fds_of_proc p)"

   213 | "init_alive (O_node n)     = (n \<in> init_nodes)"

   214 | "init_alive (O_tcp_sock k) = (is_init_tcp_sock k)"

   215 | "init_alive (O_udp_sock k) = (is_init_udp_sock k)"

   216 | "init_alive (O_shm  h)     = (h \<in> init_shms)"

   217 | "init_alive (O_msgq q)     = (q \<in> init_msgqs)"

   218 | "init_alive (O_msg q m)    = (m \<in> set (init_msgs_of_queue q) \<and> q \<in> init_msgqs)"

   219 

   220 

   221 (************ system listeners, event-related ***********)

   222 

   223 fun file_of_proc_fd ::  "t_state \<Rightarrow> t_process \<Rightarrow> t_fd \<Rightarrow> t_file option"

   224 where

   225   "file_of_proc_fd [] p' fd' = (init_file_of_proc_fd p' fd')"

   226 | "file_of_proc_fd (Open p f flags fd iopt # \<tau>) p' fd' = 

   227      (if (p' = p \<and> fd = fd') then Some f else file_of_proc_fd \<tau> p' fd')"

   228 | "file_of_proc_fd (CloseFd p fd # \<tau>) p' fd' = 

   229      (if (p = p' \<and> fd = fd') then None else file_of_proc_fd \<tau> p' fd')"

   230 (*deleted: if (f\<^isub>3 \<preceq> f\<^isub>1) then None else *)

   231 (*

   232 | "file_of_proc_fd (Rename p f\<^isub>2 f\<^isub>3 # \<tau>) p' fd = 

   233      (case (file_of_proc_fd \<tau> p' fd) of

   234         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) 

   235                     else Some f\<^isub>1)

   236       | None    \<Rightarrow> None )"

   237 *)

   238 | "file_of_proc_fd (Execve p f fds # \<tau>) p' fd = 

   239      (if (p' = p \<and> fd \<in> fds) then file_of_proc_fd \<tau> p fd 

   240       else if (p' = p) then None

   241       else file_of_proc_fd \<tau> p' fd) "

   242 | "file_of_proc_fd (Clone p p' fds shms # \<tau>) p'' fd = 

   243      (if (p'' = p' \<and> fd \<in> fds) then file_of_proc_fd \<tau> p fd

   244       else if (p'' = p') then None

   245       else file_of_proc_fd \<tau> p'' fd)"

   246 | "file_of_proc_fd (Kill p\<^isub> p\<^isub>' # \<tau>) p'' fd = 

   247      (if (p'' = p\<^isub>') then None else file_of_proc_fd \<tau> p'' fd)"

   248 | "file_of_proc_fd (Exit p # \<tau>) p' fd = 

   249      (if (p = p') then None else file_of_proc_fd \<tau> p' fd)"

   250 | "file_of_proc_fd (_ # \<tau>) p fd = file_of_proc_fd \<tau> p fd"

   251 

   252 definition proc_fd_of_file :: "t_state \<Rightarrow> t_file \<Rightarrow> (t_process \<times> t_fd) set"

   253 where

   254   "proc_fd_of_file \<tau> f = {(p, fd) | p fd. file_of_proc_fd \<tau> p fd = Some f}"

   255 

   256 

   257 (****** files and directories ******)

   258 

   259 fun files_hung_by_del :: "t_state \<Rightarrow> t_file set"

   260 where

   261   "files_hung_by_del [] = init_files_hung_by_del"

   262 | "files_hung_by_del (UnLink p f # \<tau>) = (

   263      if (proc_fd_of_file \<tau> f = {}) then files_hung_by_del \<tau> 

   264      else insert f (files_hung_by_del \<tau>))"

   265 (* | files_hung_by_del (Rmdir p f) is not need, for open can only apply to file not dir *)

   266 | "files_hung_by_del (CloseFd p fd # \<tau>) = (

   267      case (file_of_proc_fd \<tau> p fd) of

   268        Some f \<Rightarrow> (if (proc_fd_of_file \<tau> f = {(p, fd)}) 

   269                   then files_hung_by_del \<tau> - {f}

   270                   else files_hung_by_del \<tau>)

   271      | None   \<Rightarrow> files_hung_by_del \<tau>            )"

   272 (*

   273 | "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 *)

   274 *)

   275 | "files_hung_by_del (e # \<tau>) = files_hung_by_del \<tau>"

   276 declare files_hung_by_del.simps [simp del]

   277 

   278 fun inum_of_file :: "t_state \<Rightarrow> (t_file \<rightharpoonup> t_inode_num)"

   279 where

   280   "inum_of_file [] = init_inum_of_file"

   281 | "inum_of_file (Open p f flags fd (Some inum) # \<tau>) = (inum_of_file \<tau>) (f := Some inum)" 

   282 | "inum_of_file (CloseFd p fd # \<tau>) = (

   283      case (file_of_proc_fd \<tau> p fd) of

   284        Some f \<Rightarrow> ( if ((proc_fd_of_file \<tau> f = {(p, fd)}) \<and> (f \<in> files_hung_by_del \<tau>)) 

   285                    then (inum_of_file \<tau>) (f := None)

   286                    else inum_of_file \<tau> )

   287      | _      \<Rightarrow> (inum_of_file \<tau>)    )"

   288 | "inum_of_file (UnLink p f # \<tau>) = (

   289      if (proc_fd_of_file \<tau> f = {}) 

   290      then (inum_of_file \<tau>) (f := None)

   291      else inum_of_file \<tau>            )" 

   292 | "inum_of_file (Rmdir p f # \<tau>) = (

   293      if (proc_fd_of_file \<tau> f = {}) 

   294      then (inum_of_file \<tau>) (f := None)

   295      else inum_of_file \<tau>          )" 

   296 | "inum_of_file (Mkdir p f ino # \<tau>) = (inum_of_file \<tau>) (f:=  Some ino)"

   297 | "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)"

   298 (*

   299 | "inum_of_file (Rename p f\<^isub>2 f\<^isub>3 # \<tau>) = (\<lambda> f. 

   300      if (f\<^isub>2 \<preceq> f) then None

   301      else if (f\<^isub>3 \<preceq> f) then inum_of_file \<tau> (file_before_rename f\<^isub>2 f\<^isub>3 f)

   302      else inum_of_file \<tau> f         )"

   303 *)

   304 | "inum_of_file (e # \<tau>) = inum_of_file \<tau>" 

   305 

   306 definition current_files :: "t_state \<Rightarrow> t_file set"

   307 where

   308   "current_files \<tau> = {f. \<exists> i. inum_of_file \<tau> f = Some i}" 

   309 

   310 definition has_same_inode :: "t_state \<Rightarrow> t_file \<Rightarrow> t_file \<Rightarrow> bool"

   311 where 

   312   "has_same_inode \<tau> fa fb = 

   313      (\<exists>i. inum_of_file \<tau> fa = Some i \<and> inum_of_file \<tau> fb = Some i)"

   314 

   315 fun inum_of_socket :: "t_state \<Rightarrow> (t_socket \<rightharpoonup> t_inode_num)"

   316 where

   317   "inum_of_socket [] = init_inum_of_socket"

   318 | "inum_of_socket (CloseFd p fd # \<tau>) = 

   319      (inum_of_socket \<tau>) ((p, fd):= None)"

   320 | "inum_of_socket (CreateSock p af st fd ino # \<tau>) = 

   321      (inum_of_socket \<tau>) ((p, fd) := Some ino)"

   322 | "inum_of_socket (Accept p fd addr lport' fd' ino # \<tau>) = 

   323      (inum_of_socket \<tau>) ((p, fd') := Some ino)"

   324 | "inum_of_socket (Clone p p' fds shms # \<tau>) = 

   325      (\<lambda> (p'', fd). if (p'' = p' \<and> fd \<in> fds) then inum_of_socket \<tau> (p, fd) 

   326                    else if (p'' = p') then None

   327                    else inum_of_socket \<tau> (p'',fd))" 

   328 | "inum_of_socket (Execve p f fds # \<tau>) = 

   329      (\<lambda> (p', fd). if (p' = p \<and> fd \<in> fds) then inum_of_socket \<tau> (p, fd)

   330                   else if (p' = p) then None

   331                   else inum_of_socket \<tau> (p', fd))"

   332 | "inum_of_socket (Kill p\<^isub>1 p\<^isub>2 # \<tau>) = 

   333      (\<lambda> (p, fd). if (p = p\<^isub>2) then None else inum_of_socket \<tau> (p, fd) )"

   334 | "inum_of_socket (Exit p # \<tau>) = 

   335      (\<lambda> (p', fd). if (p' = p) then None else inum_of_socket \<tau> (p', fd))"

   336 | "inum_of_socket (_ # \<tau>) = inum_of_socket \<tau>" 

   337 

   338 definition current_sockets :: "t_state \<Rightarrow> t_socket set"

   339 where

   340   "current_sockets \<tau> = {s. \<exists> i. inum_of_socket \<tau> s = Some i}"

   341 

   342 (* 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 !!! *)  

   343 (* 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>*)

   344 fun itag_of_inum :: "t_state \<Rightarrow> (t_inode_num \<rightharpoonup> t_inode_tag)"

   345 where

   346   "itag_of_inum [] = init_itag_of_inum"

   347 | "itag_of_inum (Open p f flags fd (Some ino) # \<tau>) = (itag_of_inum \<tau>) (ino := Some Tag_FILE)"

   348 | "itag_of_inum (Mkdir p f ino # \<tau>) = (itag_of_inum \<tau>) (ino := Some Tag_DIR)" 

   349 | "itag_of_inum (CreateSock p af st fd ino # \<tau>) = 

   350      (case st of 

   351         STREAM \<Rightarrow> (itag_of_inum \<tau>) (ino := Some Tag_TCP_SOCK)

   352       | DGRAM  \<Rightarrow> (itag_of_inum \<tau>) (ino := Some Tag_UDP_SOCK) )"

   353 | "itag_of_inum (Accept p fd addr lport' fd' ino # \<tau>) = 

   354      (itag_of_inum \<tau>) (ino := Some Tag_TCP_SOCK)"

   355 | "itag_of_inum (_ # \<tau>) = itag_of_inum \<tau>"  (* may be sth wrong with nettemp representing addr \<times> netdev in statical analysis ??? *)

   356 

   357 definition is_file:: "t_state \<Rightarrow> t_file \<Rightarrow> bool"

   358 where

   359   "is_file \<tau> f \<equiv> (case (inum_of_file \<tau> f) of

   360                     Some i \<Rightarrow> (case (itag_of_inum \<tau> i) of

   361                                  Some Tag_FILE \<Rightarrow> True

   362                                | _             \<Rightarrow> False)

   363                   | _      \<Rightarrow> False)"

   364 

   365 definition is_dir:: "t_state \<Rightarrow> t_file \<Rightarrow> bool"

   366 where

   367   "is_dir \<tau> f \<equiv> (case (inum_of_file \<tau> f) of

   368                     Some i \<Rightarrow> (case (itag_of_inum \<tau> i) of

   369                                  Some Tag_DIR \<Rightarrow> True

   370                                | _            \<Rightarrow> False)

   371                   | _      \<Rightarrow> False)"

   372 

   373 definition dir_is_empty :: "t_state \<Rightarrow> t_file \<Rightarrow> bool"

   374 where

   375   "dir_is_empty \<tau> f \<equiv> is_dir \<tau> f \<and> \<not> (\<exists> f'. f' \<in> current_files \<tau> \<and> f \<prec> f')"

   376 

   377 definition is_tcp_sock :: "t_state \<Rightarrow> t_socket \<Rightarrow> bool"

   378 where

   379   "is_tcp_sock \<tau> s \<equiv> (case (inum_of_socket \<tau> s) of

   380                         Some i \<Rightarrow> (case (itag_of_inum \<tau> i) of

   381                                      Some Tag_TCP_SOCK \<Rightarrow> True

   382                                    | _                 \<Rightarrow> False)

   383                       | _      \<Rightarrow> False)"

   384 

   385 definition is_udp_sock :: "t_state \<Rightarrow> t_socket \<Rightarrow> bool"

   386 where

   387   "is_udp_sock \<tau> s \<equiv> (case (inum_of_socket \<tau> s) of

   388                         Some i \<Rightarrow> (case (itag_of_inum \<tau> i) of

   389                                      Some Tag_UDP_SOCK \<Rightarrow> True

   390                                    | _                 \<Rightarrow> False)

   391                       | _      \<Rightarrow> False)"

   392 

   393 fun current_procs :: "t_state \<Rightarrow> t_process set"

   394 where

   395   "current_procs [] = init_procs"

   396 | "current_procs (Clone p p' fds shms # \<tau>) = (insert p' (current_procs \<tau>))"

   397 | "current_procs (Exit p # \<tau>) = (current_procs \<tau> - {p})"

   398 | "current_procs (Kill p p' # \<tau>) = (current_procs \<tau> - {p'})"

   399 | "current_procs (_ # \<tau>) = current_procs \<tau>" 

   400 

   401 fun current_proc_fds :: "t_state \<Rightarrow> t_process \<Rightarrow> t_fd set" 

   402 where  

   403   "current_proc_fds [] = init_fds_of_proc"

   404 | "current_proc_fds (Open p f flags fd iopt # \<tau>) = 

   405      (current_proc_fds \<tau>) (p:= insert fd (current_proc_fds \<tau> p))"

   406 | "current_proc_fds (CreateSock p sf st newfd newi # \<tau>) =

   407      (current_proc_fds \<tau>) (p:= insert newfd (current_proc_fds \<tau> p))" 

   408 | "current_proc_fds (Accept p fd raddr port fd' ino # \<tau>) = 

   409      (current_proc_fds \<tau>) (p:= insert fd' (current_proc_fds \<tau> p))"

   410 | "current_proc_fds (CloseFd p fd # \<tau>) = 

   411      (current_proc_fds \<tau>) (p:= (current_proc_fds \<tau> p) - {fd})"

   412 | "current_proc_fds (Clone p p' fds shms # \<tau>) = 

   413      (current_proc_fds \<tau>) (p':= fds)"

   414 | "current_proc_fds (Execve p f fds # \<tau>) = 

   415      (current_proc_fds \<tau>) (p:= fds)"

   416 | "current_proc_fds (Exit p # \<tau>) = (current_proc_fds \<tau>) (p := {})"

   417 | "current_proc_fds (Kill p p' # \<tau>) = (current_proc_fds \<tau>) (p' := {})"

   418 | "current_proc_fds (_ # \<tau>) = current_proc_fds \<tau>"

   419 

   420 fun current_shms :: "t_state \<Rightarrow> t_shm set"

   421 where

   422   "current_shms [] = init_shms"

   423 | "current_shms (CreateShM p newshm # \<tau>) = insert newshm (current_shms \<tau>)"

   424 | "current_shms (DeleteShM p s # \<tau>) = (current_shms \<tau>) - {s}"

   425 | "current_shms (e # \<tau>) = current_shms \<tau> "

   426 

   427 fun procs_of_shm :: "t_state \<Rightarrow> t_shm \<Rightarrow> (t_process \<times> t_shm_attach_flag) set"

   428 where

   429   "procs_of_shm [] = init_procs_of_shm"

   430 | "procs_of_shm (CreateShM p h # \<tau>) = 

   431     (procs_of_shm \<tau>) (h := {})"  (* creator may not be the sharer of the shm *)

   432 | "procs_of_shm (Attach p h flag # \<tau>) = 

   433     (procs_of_shm \<tau>) (h := insert (p, flag) (procs_of_shm \<tau> h))"

   434 | "procs_of_shm (Detach p h # \<tau>) =

   435     (procs_of_shm \<tau>) (h := (procs_of_shm \<tau> h) - {(p,flag). \<exists> flag. (p, flag) \<in> procs_of_shm \<tau> h})"

   436 | "procs_of_shm (DeleteShM p h # \<tau>) = (procs_of_shm \<tau>) (h := {})"

   437 | "procs_of_shm (Clone p p' fds shms # \<tau>) = 

   438     (\<lambda> h. if (h \<in> shms) 

   439           then (procs_of_shm \<tau> h) \<union> {(p', flag). \<exists> flag. (p, flag) \<in> procs_of_shm \<tau> h}

   440           else procs_of_shm \<tau> h)"

   441 | "procs_of_shm (Execve p f fds # \<tau>) = 

   442     (\<lambda> h. procs_of_shm \<tau> h - {(p, flag). \<exists> flag. (p, flag) \<in> procs_of_shm \<tau> h})"

   443 | "procs_of_shm (e # \<tau>)          = procs_of_shm \<tau>"

   444 

   445 definition info_flow_shm :: "t_state \<Rightarrow> t_process \<Rightarrow> t_process \<Rightarrow> bool"

   446 where

   447   "info_flow_shm \<tau> from to \<equiv> (from = to) \<or> (\<exists> h \<in> current_shms \<tau>. \<exists> toflag. 

   448     (((from, SHM_RDWR) \<in> procs_of_shm \<tau> h) \<and> ((to, toflag) \<in> procs_of_shm \<tau> h)))"

   449 

   450 fun current_msgqs :: "t_state \<Rightarrow> t_msg set"

   451 where

   452   "current_msgqs [] = init_msgqs"

   453 | "current_msgqs (CreateMsgq p q # \<tau>) = insert q (current_msgqs \<tau>)"

   454 | "current_msgqs (RemoveMsgq p q # \<tau>) = (current_msgqs \<tau>) - {q}"

   455 | "current_msgqs (_ # \<tau>) = current_msgqs \<tau>"

   456 

   457 fun msgs_of_queue :: "t_state \<Rightarrow> t_msgq \<Rightarrow> t_msg list"

   458 where

   459   "msgs_of_queue [] = init_msgs_of_queue"

   460 | "msgs_of_queue (CreateMsgq p q # \<tau>) = (msgs_of_queue \<tau>)(q := [])"

   461 | "msgs_of_queue (SendMsg p q m  # \<tau>) = (msgs_of_queue \<tau>)(q := msgs_of_queue \<tau> q @ [m])"

   462 | "msgs_of_queue (RecvMsg p q m  # \<tau>) = (msgs_of_queue \<tau>)(q := tl (msgs_of_queue \<tau> q))"

   463 | "msgs_of_queue (RemoveMsgq p q # \<tau>) = (msgs_of_queue \<tau>)(q := [])" 

   464 | "msgs_of_queue (_ # \<tau>) = msgs_of_queue \<tau>"         

   465 

   466 definition current_file_inums :: "t_state \<Rightarrow> t_inode_num set"

   467 where

   468   "current_file_inums \<tau> \<equiv> {im. \<exists> f. inum_of_file \<tau> f = Some im}"

   469 

   470 definition current_sock_inums :: "t_state \<Rightarrow> t_inode_num set"

   471 where

   472   "current_sock_inums \<tau> = {im. \<exists> s. inum_of_socket \<tau> s = Some im}"

   473 

   474 definition current_inode_nums :: "t_state \<Rightarrow> nat set"

   475 where

   476   "current_inode_nums \<tau> = current_file_inums \<tau> \<union> current_sock_inums \<tau>"

   477 

   478 fun flags_of_proc_fd :: "t_state \<Rightarrow> t_process \<Rightarrow> t_fd \<Rightarrow> t_open_flags option"

   479 where

   480   "flags_of_proc_fd [] p fd = init_oflags_of_proc_fd p fd" 

   481 | "flags_of_proc_fd (Open p f flags fd iopt # \<tau>) p' fd' = 

   482      (if (p = p' \<and> fd = fd') then Some flags else flags_of_proc_fd \<tau> p' fd')"

   483 | "flags_of_proc_fd (CloseFd p fd # \<tau>) p' fd' = 

   484      (if (p = p' \<and> fd = fd') then None else flags_of_proc_fd \<tau> p' fd')"

   485 | "flags_of_proc_fd (CreateSock p af st fd ino # \<tau>) p' fd' = 

   486      (if (p = p' \<and> fd = fd') then None else flags_of_proc_fd \<tau> p' fd')"

   487 | "flags_of_proc_fd (Accept p fd addr lport' fd' ino # \<tau>) p' fd'' = 

   488      (if (p = p' \<and> fd' = fd'') then None else flags_of_proc_fd \<tau> p' fd'')"

   489 | "flags_of_proc_fd (Clone p p' fds shms # \<tau>) p'' fd = 

   490      (if (p' = p'' \<and> fd \<in> fds) then flags_of_proc_fd \<tau> p fd else flags_of_proc_fd \<tau> p'' fd)"  

   491 | "flags_of_proc_fd (Execve p f fds # \<tau>) p' fd = 

   492      (if (p' = p \<and> fd \<in> fds) then flags_of_proc_fd \<tau> p fd else flags_of_proc_fd \<tau> p' fd)"

   493 | "flags_of_proc_fd (Kill p\<^isub>1 p\<^isub>2 # \<tau>) p fd = 

   494      (if (p = p\<^isub>2) then None else flags_of_proc_fd \<tau> p fd)"

   495 | "flags_of_proc_fd (Exit p # \<tau>) p' fd' = 

   496      (if (p = p') then None else flags_of_proc_fd \<tau> p' fd')"

   497 | "flags_of_proc_fd (e # \<tau>) p fd = flags_of_proc_fd \<tau> p fd" 

   498 

   499 (* 

   500 fun file_at_writing_by:: "t_state \<Rightarrow> t_file \<Rightarrow> (t_process \<times> t_fd) set"

   501 where

   502   "file_at_writing_by [] f = init_file_at_writing_by f"  

   503 | "file_at_writing_by (Open p f flags fd (Some inum) # \<tau>) f' = (

   504      if (f' = f) 

   505      then ( if (is_write_flag flags) 

   506             then {(p, fd)}

   507             else {} )

   508      else file_at_writing_by \<tau> f'                              )"

   509 | "file_at_writing_by (Open p f flags fd None # \<tau>) f' = (

   510      if (f' = f \<and> is_write_flag flags) 

   511      then insert (p, fd) (file_at_writing_by \<tau> f) 

   512      else file_at_writing_by \<tau> f'                       )"

   513 | "file_at_writing_by (Mkdir p f inum # \<tau>) f' = 

   514      (if (f' = f) then {} else file_at_writing_by \<tau> f')"

   515 | "file_at_writing_by (LinkHard p f f' # \<tau>) f'' = 

   516      (if (f'' = f') then file_at_writing_by \<tau> f else file_at_writing_by \<tau> f'')"

   517 | "file_at_writing_by (Rename p f\<^isub>2 f\<^isub>3 # \<tau>) f = (

   518      if (f\<^isub>3 \<preceq> f) then file_at_writing_by \<tau> (file_before_rename f\<^isub>2 f\<^isub>3 f)

   519      else file_at_writing_by \<tau> f               )"

   520 | "file_at_writing_by (CloseFd p fd # \<tau>) f = 

   521      (file_at_writing_by \<tau> f - {(p, fd)})"

   522 | "file_at_writing_by (Clone p p' fds shms # \<tau>) f = 

   523      (file_at_writing_by \<tau> f) \<union> {(p',fd)| fd. fd \<in> fds \<and> (p, fd) \<in> file_at_writing_by \<tau> f}"

   524 | "file_at_writing_by (Execve p f fds # \<tau>) f' = 

   525      (if (f' = f) then {} else file_at_writing_by \<tau> f')"

   526 | "file_at_writing_by (Exit p # \<tau>) f = 

   527      (file_at_writing_by \<tau> f - {(p, fd)| fd. (p, fd) \<in> file_at_writing_by \<tau> f})"

   528 | "file_at_writing_by (Kill p p' # \<tau>) f = 

   529      (file_at_writing_by \<tau> f - {(p', fd)| fd. (p', fd) \<in> file_at_writing_by \<tau> f})"

   530 | "file_at_writing_by (e # \<tau>) f            =  file_at_writing_by \<tau> f"

   531 *)

   532 

   533 definition current_users :: "t_state \<Rightarrow> user_t set"

   534 where

   535   "current_users \<tau> \<equiv> init_users"  

   536 

   537 fun update_with_shuthow :: "t_sock_state option \<Rightarrow> t_shutdown_how \<Rightarrow> t_sock_state option"

   538 where

   539   "update_with_shuthow (Some (SS_trans Trans_Recv)) SHUT_RD = Some (SS_trans Trans_No)"

   540 | "update_with_shuthow (Some (SS_trans Trans_RS))   SHUT_RD = Some (SS_trans Trans_Send)"

   541 | "update_with_shuthow (Some (SS_trans Trans_Send)) SHUT_RD = Some (SS_trans Trans_Send)"

   542 | "update_with_shuthow (Some (SS_trans Trans_No))   SHUT_RD = Some (SS_trans Trans_No)"

   543 | "update_with_shuthow (Some (SS_trans Trans_Recv)) SHUT_WR = Some (SS_trans Trans_Recv)"

   544 | "update_with_shuthow (Some (SS_trans Trans_RS))   SHUT_WR = Some (SS_trans Trans_Recv)"

   545 | "update_with_shuthow (Some (SS_trans Trans_Send)) SHUT_WR = Some (SS_trans Trans_No)"

   546 | "update_with_shuthow (Some (SS_trans Trans_No))   SHUT_WR = Some (SS_trans Trans_No)"

   547 | "update_with_shuthow (Some (SS_trans Trans_Recv)) SHUT_RDWR = Some (SS_trans Trans_No)"

   548 | "update_with_shuthow (Some (SS_trans Trans_RS))   SHUT_RDWR = Some (SS_trans Trans_No)"

   549 | "update_with_shuthow (Some (SS_trans Trans_Send)) SHUT_RDWR = Some (SS_trans Trans_No)"

   550 | "update_with_shuthow (Some (SS_trans Trans_No))   SHUT_RDWR = Some (SS_trans Trans_No)"

   551 | "update_with_shuthow opt1                         how       = None" 

   552 

   553 fun socket_state :: "t_state \<Rightarrow> t_socket \<Rightarrow> t_sock_state option"

   554 where

   555   "socket_state [] = init_socket_state"

   556 | "socket_state (CloseFd p fd # \<tau>) = 

   557      (socket_state \<tau>) ((p, fd):= None)"

   558 | "socket_state (CreateSock p af st fd ino # \<tau>) = 

   559      (socket_state \<tau>) ((p, fd) := Some SS_create)"

   560 | "socket_state (Bind p fd addr # \<tau>) = 

   561      (socket_state \<tau>) ((p, fd) := Some SS_bind)"

   562 | "socket_state (Connect p fd addr # \<tau>) = 

   563      (socket_state \<tau>) ((p, fd) := Some (SS_trans Trans_RS))"

   564 | "socket_state (Listen p fd # \<tau>) = 

   565      (socket_state \<tau>) ((p, fd) := Some SS_listen)"

   566 | "socket_state (Accept p fd addr lport' fd' ino # \<tau>) = 

   567      (socket_state \<tau>) ((p, fd') := Some (SS_trans Trans_RS))"

   568 | "socket_state (Shutdown p fd sh # \<tau>) = 

   569      (socket_state \<tau>) ((p, fd) := update_with_shuthow (socket_state \<tau> (p, fd)) sh)"

   570 | "socket_state (Clone p p' fds shms # \<tau>) = 

   571      (\<lambda> (p'', fd). if (p'' = p' \<and> fd \<in> fds) then socket_state \<tau> (p, fd) 

   572                    else if (p'' = p') then None

   573                    else socket_state \<tau> (p'', fd))" 

   574 | "socket_state (Execve p f fds # \<tau>) = 

   575      (\<lambda> (p', fd). if (p' = p \<and> fd \<in> fds) then socket_state \<tau> (p, fd) 

   576                   else if (p' = p) then None 

   577                   else socket_state \<tau> (p', fd))" 

   578 | "socket_state (Kill p\<^isub>1 p\<^isub>2 # \<tau>) = 

   579      (\<lambda> (p, fd). if (p = p\<^isub>2) then None else socket_state \<tau> (p, fd))"

   580 | "socket_state (Exit p # \<tau>) = 

   581      (\<lambda> (p', fd'). if (p = p') then None else socket_state \<tau> (p', fd'))"

   582 | "socket_state (e # \<tau>) = socket_state \<tau>"  

   583 

   584 definition socket_in_trans :: "t_state \<Rightarrow> t_socket \<Rightarrow> bool"

   585 where

   586   "socket_in_trans \<tau> s \<equiv> (case (socket_state \<tau> s) of

   587                             Some st \<Rightarrow> (case st of 

   588                                           SS_trans para \<Rightarrow> True

   589                                         | _             \<Rightarrow> False)

   590                           | _       \<Rightarrow> False)"

   591 

   592 definition socket_in_sending :: "t_state \<Rightarrow> t_socket \<Rightarrow> bool"

   593 where

   594   "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))"

   595 

   596 definition socket_in_recving :: "t_state \<Rightarrow> t_socket \<Rightarrow> bool"

   597 where

   598   "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))"

   599 

   600 

   601 (******* admissable check by the OS *******)

   602 fun os_grant :: "t_state \<Rightarrow> t_event \<Rightarrow> bool"

   603 where

   604   "os_grant \<tau> (Open p f flags fd inumopt) = (

   605      case inumopt of

   606        Some ino \<Rightarrow>

   607     (p \<in> current_procs \<tau> \<and> f \<notin> current_files \<tau> \<and> 

   608      (\<exists> pf. parent f = Some pf \<and> pf \<in> current_files \<tau> \<and> is_dir \<tau> pf \<and> pf \<notin> files_hung_by_del \<tau>) \<and>

   609      is_creat_flag flags \<and> fd \<notin> (current_proc_fds \<tau> p) \<and> ino \<notin> (current_inode_nums \<tau>))

   610    |   None     \<Rightarrow>

   611     (p \<in> current_procs \<tau> \<and> f \<in> current_files \<tau> \<and> \<not> is_creat_excl_flag flags \<and> is_file \<tau> f \<and>

   612      fd \<notin> (current_proc_fds \<tau> p))           )"

   613 (*(if (is_dir \<tau> f) then (is_dir_flag flags \<and> \<not> is_write_flag flags) else (\<not> is_dir_flag flags)),

   614   here open is not applied to directories, readdir is for that, but it is not security-related *)

   615 | "os_grant \<tau> (CloseFd p fd)                  = 

   616     (p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p)"

   617 | "os_grant \<tau> (UnLink p f)                    = 

   618     (p \<in> current_procs \<tau> \<and> f \<in> current_files \<tau> \<and> is_file \<tau> f \<and> f \<notin> files_hung_by_del \<tau>)"

   619 | "os_grant \<tau> (Rmdir p f)                     = 

   620     (p \<in> current_procs \<tau> \<and> f \<in> current_files \<tau> \<and> dir_is_empty \<tau> f \<and> f \<notin> files_hung_by_del \<tau> \<and> f \<noteq> [])" (* root file cannot be deleted *)

   621 | "os_grant \<tau> (Mkdir p f ino)                 = 

   622     (p \<in> current_procs \<tau> \<and> f \<notin> current_files \<tau> \<and> 

   623      (\<exists> pf. parent f = Some pf \<and> pf \<in> current_files \<tau> \<and> is_dir \<tau> pf \<and> pf \<notin> files_hung_by_del \<tau>) \<and>

   624      ino \<notin> (current_inode_nums \<tau>))"

   625 | "os_grant \<tau> (LinkHard p f\<^isub>1 f\<^isub>2)              = 

   626     (p \<in> current_procs \<tau> \<and> f\<^isub>1 \<in> current_files \<tau> \<and> f\<^isub>2 \<notin> current_files \<tau> \<and> 

   627      (\<exists> pf\<^isub>2. parent f\<^isub>2 = Some pf\<^isub>2 \<and> pf\<^isub>2 \<in> current_files \<tau> \<and> is_dir \<tau> pf\<^isub>2 \<and> 

   628              pf\<^isub>2 \<notin> files_hung_by_del \<tau>) \<and> is_file \<tau> f\<^isub>1)"

   629 | "os_grant \<tau> (Truncate p f len)              = 

   630     (p \<in> current_procs \<tau> \<and> f \<in> current_files \<tau> \<and> is_file \<tau> f)"

   631 (*

   632 | "os_grant \<tau> (FTruncate p fd len)            = 

   633     (p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> 

   634      (\<exists> f. file_of_proc_fd \<tau> p fd = Some f \<and> f \<in> current_files \<tau> \<and> is_file \<tau> f) \<and> 

   635      (\<exists> flags. flags_of_proc_fd \<tau> p fd = Some flags \<and> is_write_flag flags))"

   636 *)

   637 | "os_grant \<tau> (ReadFile p fd)                 = 

   638     (p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> 

   639      (\<exists> f. file_of_proc_fd \<tau> p fd = Some f \<and> f \<in> current_files \<tau>) \<and> 

   640      (\<exists> flags. flags_of_proc_fd \<tau> p fd = Some flags \<and> is_read_flag flags))"

   641 | "os_grant \<tau> (WriteFile p fd)                = 

   642     (p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> 

   643      (\<exists> f. file_of_proc_fd \<tau> p fd = Some f \<and> f \<in> current_files \<tau>) \<and> 

   644      (\<exists> flags. flags_of_proc_fd \<tau> p fd = Some flags \<and> is_write_flag flags))"

   645 | "os_grant \<tau> (Execve p f fds)                = 

   646     (p \<in> current_procs \<tau> \<and> f \<in> current_files \<tau> \<and> is_file \<tau> f \<and> fds \<subseteq> current_proc_fds \<tau> p)" (* file_at_writing_by \<tau> f = {} *)

   647 (*

   648 | "os_grant \<tau> (Rename p f\<^isub>2 f\<^isub>3)                = 

   649     (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>

   650      (\<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> 

   651              pf\<^isub>3 \<notin> files_hung_by_del \<tau>) )"

   652 *)

   653 | "os_grant \<tau> (CreateMsgq p q)                = 

   654     (p \<in> current_procs \<tau> \<and> q \<notin> (current_msgqs \<tau>))"

   655 | "os_grant \<tau> (SendMsg p q m)                 = 

   656     (p \<in> current_procs \<tau> \<and> q \<in> current_msgqs \<tau> \<and> m \<notin> (set (msgs_of_queue \<tau> q)))"

   657 | "os_grant \<tau> (RecvMsg p q m)                 = 

   658     (p \<in> current_procs \<tau> \<and> q \<in> current_msgqs \<tau> \<and> m = hd (msgs_of_queue \<tau> q))"

   659 | "os_grant \<tau> (RemoveMsgq p q)                = 

   660     (p \<in> current_procs \<tau> \<and> q \<in> current_msgqs \<tau>)"

   661 | "os_grant \<tau> (CreateShM p h)                 = 

   662     (p \<in> current_procs \<tau> \<and> h \<notin> (current_shms \<tau>))"

   663 | "os_grant \<tau> (Attach p h flag)               = 

   664     (p \<in> current_procs \<tau> \<and> h \<in> current_shms \<tau> \<and> \<not> (\<exists> flag. (p, flag) \<in> procs_of_shm \<tau> h))"

   665 | "os_grant \<tau> (Detach p h)                    = 

   666     (p \<in> current_procs \<tau> \<and> h \<in> current_shms \<tau> \<and> (\<exists> flag. (p, flag) \<in> procs_of_shm \<tau> h))"

   667 | "os_grant \<tau> (DeleteShM p h)                 = 

   668     (p \<in> current_procs \<tau> \<and> h \<in> current_shms \<tau>)"

   669 | "os_grant \<tau> (CreateSock p af st fd ino)     = 

   670     (p \<in> current_procs \<tau> \<and> af = AF_INET \<and> fd \<notin> (current_proc_fds \<tau> p) \<and> 

   671      ino \<notin> (current_inode_nums \<tau>))"

   672 | "os_grant \<tau> (Accept p fd addr port fd' ino) = 

   673     (p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> (p, fd) \<in> current_sockets \<tau> \<and> 

   674      fd' \<notin> (current_proc_fds \<tau> p) \<and> socket_state \<tau> (p, fd) = Some SS_listen \<and> 

   675      is_tcp_sock \<tau> (p, fd) \<and> ino \<notin> (current_inode_nums \<tau>))"

   676 | "os_grant \<tau> (Bind p fd addr)                = 

   677     (p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> (p, fd) \<in> current_sockets \<tau> \<and> 

   678      socket_state \<tau> (p, fd) = Some SS_create)" (* ?? !! (case addr of INET_ADDR ip port \<Rightarrow> ip \<in> local_ipaddrs)) *)

   679 | "os_grant \<tau> (Connect p fd addr)             = 

   680     (p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> (p, fd) \<in> current_sockets \<tau> \<and> 

   681      socket_state \<tau> (p, fd) = Some SS_bind)"

   682 | "os_grant \<tau> (Listen p fd)                   = 

   683     (p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> (p, fd) \<in> current_sockets \<tau> \<and> 

   684      socket_state \<tau> (p, fd) = Some SS_bind \<and> is_tcp_sock \<tau> (p, fd))" (* Listen and Accept should only be used for TCP sever side *)

   685 | "os_grant \<tau> (SendSock p fd)                 = 

   686     (p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> (p, fd) \<in> current_sockets \<tau> \<and> 

   687      socket_in_sending \<tau> (p, fd))"

   688 | "os_grant \<tau> (RecvSock p fd)                 = 

   689     (p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> (p, fd) \<in> current_sockets \<tau> \<and> 

   690      socket_in_recving \<tau> (p, fd))"

   691 | "os_grant \<tau> (Shutdown p fd sh)              = 

   692     (p \<in> current_procs \<tau> \<and> fd \<in> current_proc_fds \<tau> p \<and> (p, fd) \<in> current_sockets \<tau> \<and> 

   693      socket_in_trans \<tau> (p, fd))"

   694 (*

   695 | "os_grant \<tau> (ChangeOwner p u)               = (p \<in> current_procs \<tau> \<and> u \<in> current_users \<tau>)"

   696 *)

   697 | "os_grant \<tau> (Clone p p' fds shms)           = 

   698     (p \<in> current_procs \<tau> \<and> p' \<notin> (current_procs \<tau>) \<and> fds \<subseteq> current_proc_fds \<tau> p \<and>

   699      (\<forall> h \<in> shms. \<exists> flag. (p, flag) \<in> procs_of_shm \<tau> h))"

   700 | "os_grant \<tau> (Kill p\<^isub>1 p\<^isub>2)                    = 

   701     (p\<^isub>1 \<in> current_procs \<tau> \<and> p\<^isub>2 \<in> current_procs \<tau>)" (* a process can kill itself right? *)

   702 | "os_grant \<tau> (Exit p)                        = 

   703     (p \<in> current_procs \<tau>)"

   704 | "os_grant \<tau> (Ptrace p\<^isub>1 p\<^isub>2)                  = 

   705     (p\<^isub>1 \<in> current_procs \<tau> \<and> p\<^isub>2 \<in> current_procs \<tau>)" (* a process can trace itself right? *)

   706 

   707 fun alive :: "t_state \<Rightarrow> t_object \<Rightarrow> bool"

   708 where

   709   "alive s (O_proc p)     = (p \<in> current_procs s)"

   710 | "alive s (O_file f)     = (f \<in> current_files s \<and> is_file s f)"

   711 | "alive s (O_dir  f)     = (f \<in> current_files s \<and> is_dir s f)"

   712 | "alive s (O_fd p fd)    = (fd \<in> current_proc_fds s p)"

   713 | "alive s (O_node n)     = (n \<in> init_nodes)"

   714 | "alive s (O_tcp_sock k) = (k \<in> current_sockets s \<and> is_tcp_sock s k)"

   715 | "alive s (O_udp_sock k) = (k \<in> current_sockets s \<and> is_udp_sock s k)"

   716 | "alive s (O_shm  h)     = (h \<in> current_shms s)"

   717 | "alive s (O_msgq q)     = (q \<in> current_msgqs s)"

   718 | "alive s (O_msg q m)    = (m \<in> set (msgs_of_queue s q) \<and> q \<in> current_msgqs s)"

   719 

   720 (* deleted objects should be "taintable" objects, objects like fd should not be in consideration *)

   721 (* actually, deleted should be renamed as "vanished", cause "exit/closefd" *)

   722 fun deleted :: "t_object \<Rightarrow> t_event list \<Rightarrow> bool"

   723 where

   724   "deleted obj [] = False"

   725 | "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> 

   726                                   (\<exists> fd. obj = O_tcp_sock (p', fd) \<and> is_tcp_sock s (p',fd)) \<or>

   727                                   (\<exists> fd. obj = O_udp_sock (p', fd) \<and> is_udp_sock s (p',fd)) \<or>

   728                                   deleted obj s)"

   729 | "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>

   730                                      (obj = O_udp_sock (p,fd) \<and> is_udp_sock s (p, fd)) \<or> deleted obj s)"

   731 | "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> 

   732                                        (\<exists> fd. obj = O_tcp_sock (p, fd) \<and> is_tcp_sock s (p,fd) \<and> fd \<notin> fds) \<or>

   733                                        (\<exists> fd. obj = O_udp_sock (p, fd) \<and> is_udp_sock s (p,fd) \<and> fd \<notin> fds) \<or>

   734                                        deleted obj s)"

   735 | "deleted obj (UnLink p f # s) = ((obj = O_file f) \<or> deleted obj s)"

   736 | "deleted obj (Rmdir p f # s)  = ((obj = O_dir  f) \<or> deleted obj s)"

   737 | "deleted obj (Exit p # s) = ((obj = O_proc p) \<or> (\<exists> fd \<in> current_proc_fds s p. obj = O_fd p fd) \<or> 

   738                                (\<exists> fd. obj = O_tcp_sock (p, fd) \<and> is_tcp_sock s (p,fd)) \<or>

   739                                (\<exists> fd. obj = O_udp_sock (p, fd) \<and> is_udp_sock s (p,fd)) \<or> deleted obj s)"

   740 (*

   741 | "deleted obj (Rename p f f' # s)  = 

   742      (case obj of

   743         O_file f'' \<Rightarrow> f \<preceq> f'' \<or> deleted obj s

   744       | O_dir  f'' \<Rightarrow> f \<preceq> f'' \<or> deleted obj s

   745       | _ \<Rightarrow> deleted obj s)"

   746 *)

   747 | "deleted obj (RemoveMsgq p q # s) = (obj = O_msgq q \<or> (\<exists> m. obj = O_msg q m) \<or> deleted obj s)"

   748 | "deleted obj (DeleteShM p h # s) = (obj = O_shm h \<or> deleted obj s)"

   749 | "deleted obj (RecvMsg p q m # s)  = (obj = O_msg q m \<or> deleted obj s)"

   750 | "deleted obj (_ # s) = deleted obj s"

   751 

   752 

   753 end

   754 

   755 

   756 

   757 locale flask = init + 

   758  fixes

   759    (***************** Policy-specific Parameters *************)

   760       type_transition_rules :: "type_transition_rule_list_t"

   761   and allowed_rules :: "allowed_rule_list_t"

   762   and role_allowed_rules :: "role_allow_rule_list_t"

   763   and role_declaration_rules :: "role_declarations_list_t"

   764   and role_transition_rules:: "role_transition_rule_list_t"

   765   and constrains_rules :: "constrains_list_t"

   766 

   767   and init_type_of_obj :: "t_object \<rightharpoonup> type_t"

   768   and init_user_of_obj :: "t_object \<rightharpoonup> user_t"

   769   and init_role_of_proc :: "t_process \<rightharpoonup> role_t"

   770 

   771   assumes

   772    

   773       init_obj_has_type: "\<And> obj. init_alive obj \<Longrightarrow> \<exists> t. init_type_of_obj obj = Some t"

   774   and init_type_has_obj: "\<And> obj t. init_type_of_obj obj = Some t \<Longrightarrow> init_alive obj"

   775   and init_obj_has_user: "\<And> obj. init_alive obj \<Longrightarrow> \<exists> u. init_user_of_obj obj = Some u"

   776   and init_user_has_obj: "\<And> obj u. init_user_of_obj obj = Some u \<Longrightarrow> init_alive obj \<and> u \<in> init_users"

   777   and init_proc_has_role: "bidirect_in_init init_procs init_role_of_proc"

   778 

   779 begin

   780 

   781 (*********** policy-specified computations, not-event-related ************)

   782 

   783 (* security_transition_sid : type_transition_rules

   784  * It's a system-call offered by security-server? So access-control-checked too?

   785  * according to selinux, it deals only with execve and file-creation

   786  *  is_execve: if is the execve case

   787  *  is_file: if is the creation of file/dir

   788  *  change from is_execve to is_file, because the new message by default use

   789  *  the type of the sending process too. 

   790  *)

   791 

   792 definition type_transition :: "type_t \<Rightarrow> type_t \<Rightarrow> security_class_t \<Rightarrow> bool \<Rightarrow> type_t"

   793 where

   794   "type_transition st rt tc IS_file \<equiv> (

   795      case (lookup type_transition_rules 

   796              (\<lambda> (stp, rtp, tc', dt). patt_match stp st \<and> patt_match rtp rt \<and> tc = tc')) of

   797        None     \<Rightarrow> (if IS_file then rt else st)

   798      | Some (stp,rtp,tc',dt) \<Rightarrow> dt)"

   799 

   800 (* allowed_rule_list *)

   801 definition TE_allow :: "type_t \<Rightarrow> type_t \<Rightarrow> security_class_t \<Rightarrow> permission_t \<Rightarrow> bool"

   802 where

   803   "TE_allow st tt tc perm \<equiv> member allowed_rules

   804       (\<lambda> (stp, ttp, tc', pp). tc = tc' \<and> patt_match stp st \<and> patt_match_self ttp tt st \<and>

   805                               patt_match pp perm)"

   806 

   807 (* role_allow_rule_list_t *)

   808 definition role_transition :: "role_t \<Rightarrow> type_t \<Rightarrow> role_t option"

   809 where

   810   "role_transition r t \<equiv> 

   811      (case (lookup role_transition_rules (\<lambda> (pr, ft, nr). pr = r \<and> t = ft)) of

   812         None \<Rightarrow> None

   813       | Some (pr,ft,nr) \<Rightarrow> Some nr)"

   814 

   815 definition role_decl_check :: "role_t \<Rightarrow> type_t \<Rightarrow> bool"

   816 where

   817   "role_decl_check r t \<equiv> member role_declaration_rules (\<lambda> (role, types). r = role \<and> t \<in> types)"

   818 

   819 definition role_allow :: "role_t \<Rightarrow> role_t \<Rightarrow> bool"

   820 where

   821   "role_allow r nr \<equiv> member role_allowed_rules (\<lambda> (from, to). r \<in> from \<and> nr \<in> to)"

   822 

   823 (* here don't use lookup, because constrains should all be satisfied, 

   824  * while transitions always choose the "first" one 

   825  *)

   826 definition constrains_satisfied :: 

   827   "security_context_t \<Rightarrow> security_context_t \<Rightarrow> security_class_t \<Rightarrow> permission_t \<Rightarrow> bool"

   828 where

   829   "constrains_satisfied sctxt tctxt c p \<equiv> 

   830     (fold (\<lambda> (cset, pset, P) res. res \<and> (if (c \<in> cset \<and> p \<in> pset) 

   831                                             then P sctxt tctxt else True))

   832           constrains_rules True)"

   833 

   834 (* main interface for TE_allow check and constrains check *)

   835 fun permission_check:: 

   836   "security_context_t \<Rightarrow> security_context_t \<Rightarrow> security_class_t \<Rightarrow> permission_t \<Rightarrow> bool"

   837 where

   838   "permission_check (su,sr,st) (tu,tr,tt) c p =

   839     ((TE_allow st tt c p) \<and> (constrains_satisfied (su,sr,st) (tu,tr,tt) c p))"

   840 declare permission_check.simps [simp del]

   841 

   842 (* no changeowner ??? : by adding "relabel obj sectxt" event or "login" event? 

   843  * or this explanation: the running of the sever will not grant any login but running 

   844  * of the server-programs! 

   845  *)

   846 

   847 fun user_of_obj :: "t_state \<Rightarrow> t_object \<Rightarrow> user_t option"

   848 where 

   849   "user_of_obj [] = init_user_of_obj"

   850 | "user_of_obj (Clone p p' fds shms # s) = 

   851     (\<lambda> obj. case obj of 

   852               O_proc p'' \<Rightarrow> if (p'' = p') then user_of_obj s (O_proc p) else user_of_obj s obj

   853             | O_fd p'' fd  \<Rightarrow> if (p'' = p' \<and> fd \<in> fds) then user_of_obj s (O_fd p fd)

   854                               else if (p'' = p') then None

   855                                    else user_of_obj s obj

   856             | O_tcp_sock (p'',fd) \<Rightarrow> if (p'' = p' \<and> fd \<in> fds) then user_of_obj s (O_tcp_sock (p, fd))

   857                                      else if (p'' = p') then None

   858                                           else user_of_obj s obj

   859             | O_udp_sock (p'',fd) \<Rightarrow> if (p'' = p' \<and> fd \<in> fds) then user_of_obj s (O_udp_sock (p, fd))

   860                                      else if (p'' = p') then None

   861                                           else user_of_obj s obj 

   862             | _ \<Rightarrow> user_of_obj s obj)"

   863 | "user_of_obj (Open p f flags fd iopt # s) = 

   864     (case iopt of

   865        None \<Rightarrow> (user_of_obj s) ((O_fd p fd) := user_of_obj s (O_proc p))

   866      | _    \<Rightarrow> ((user_of_obj s) ((O_fd p fd) := user_of_obj s (O_proc p)))

   867                ((O_file f) := user_of_obj s (O_proc p)))"

   868 | "user_of_obj (Mkdir p f inum # s) =

   869     (user_of_obj s) ((O_dir f) := user_of_obj s (O_proc p))"

   870 | "user_of_obj (LinkHard p f f' # s) = 

   871     (user_of_obj s) ((O_file f') := user_of_obj s (O_proc p))"

   872 (*

   873 | "user_of_obj (Rename p f2 f3 # s) = 

   874     (\<lambda> obj. case obj of 

   875               O_file f \<Rightarrow> if (f3 \<preceq> f) then user_of_obj s (O_file (file_before_rename f2 f3 f))

   876                           else user_of_obj s obj

   877             | O_dir  f \<Rightarrow> if (f3 \<preceq> f) then user_of_obj s (O_dir (file_before_rename f2 f3 f))

   878                           else user_of_obj s obj

   879             | _        \<Rightarrow> user_of_obj s obj)"

   880 *)

   881 | "user_of_obj (CreateMsgq p q # s) = 

   882     (user_of_obj s) ((O_msgq q) := user_of_obj s (O_proc p))" 

   883 | "user_of_obj (SendMsg p q m # s) = 

   884     (user_of_obj s) ((O_msg q m) := user_of_obj s (O_proc p))"

   885 | "user_of_obj (CreateShM p h # s) = 

   886     (user_of_obj s) ((O_shm h) := user_of_obj s (O_proc p))"

   887 | "user_of_obj (CreateSock p af st fd inum # s) =  (\<lambda> obj. 

   888      case obj of

   889        O_fd p' fd' \<Rightarrow> if (p' = p \<and> fd' = fd) then user_of_obj s (O_proc p)

   890                       else user_of_obj s obj

   891      | O_tcp_sock (p', fd') \<Rightarrow> if (p' = p \<and> fd' = fd \<and> st = STREAM) then user_of_obj s (O_proc p)

   892                                else user_of_obj s obj

   893      | O_udp_sock (p', fd') \<Rightarrow> if (p' = p \<and> fd' = fd \<and> st = DGRAM) then user_of_obj s (O_proc p)

   894                                else user_of_obj s obj

   895      | _ \<Rightarrow> user_of_obj s obj )"

   896 | "user_of_obj (Accept p fd addr port fd' inum # s) = (\<lambda> obj. 

   897      case obj of

   898        O_fd p' fd'' \<Rightarrow> if (p' = p \<and> fd'' = fd') then user_of_obj s (O_proc p)

   899                       else user_of_obj s obj

   900      | O_tcp_sock (p', fd'') \<Rightarrow> if (p' = p \<and> fd'' = fd') then user_of_obj s (O_proc p)

   901                                else user_of_obj s obj

   902      | _ \<Rightarrow> user_of_obj s obj )"

   903 | "user_of_obj (_ # s) = user_of_obj s"

   904 

   905 fun type_of_obj :: "t_state \<Rightarrow> (t_object \<Rightarrow> type_t option)"

   906 where

   907   "type_of_obj [] = init_type_of_obj"

   908 | "type_of_obj (Clone p p' fds shms # s) = (\<lambda> obj. 

   909      case obj of 

   910        O_proc p'' \<Rightarrow> if (p'' = p') then type_of_obj s (O_proc p) else type_of_obj s obj

   911      | O_fd p'' fd \<Rightarrow> if (p'' = p' \<and> fd \<in> fds) then type_of_obj s (O_fd p fd)

   912                       else if (p'' = p') then None

   913                            else type_of_obj s obj

   914      | O_tcp_sock (p'', fd) \<Rightarrow> if (p'' = p' \<and> fd \<in> fds) then type_of_obj s (O_tcp_sock (p, fd))

   915                                else if (p'' = p') then None

   916                                     else type_of_obj s obj

   917      | O_udp_sock (p'', fd) \<Rightarrow> if (p'' = p' \<and> fd \<in> fds) then type_of_obj s (O_udp_sock (p, fd))

   918                                else if (p'' = p') then None

   919                                     else type_of_obj s obj

   920      | _ \<Rightarrow> type_of_obj s obj )"

   921 | "type_of_obj (Execve p f fds # s) = (type_of_obj s) ((O_proc p) := 

   922     (case (type_of_obj s (O_proc p), type_of_obj s (O_file f)) of 

   923        (Some tp, Some tf) \<Rightarrow> Some (type_transition tp tf C_process False)

   924      | _                  \<Rightarrow> None)                    )"

   925 | "type_of_obj (Open p f flags fd (Some inum) # s) = ((type_of_obj s) ((O_file f) := 

   926      (case (parent f) of 

   927         Some pf \<Rightarrow> (case (type_of_obj s (O_proc p), type_of_obj s (O_dir pf)) of 

   928                       (Some tp, Some tpf) \<Rightarrow> Some (type_transition tp tpf C_file True)

   929                     | _ \<Rightarrow> None)

   930       | _       \<Rightarrow> None)                              )) ((O_fd p fd) := 

   931      type_of_obj s (O_proc p))"

   932 | "type_of_obj (Open p f flags fd None # s) = (type_of_obj s) ((O_fd p fd) := 

   933      type_of_obj s (O_proc p))"

   934 | "type_of_obj (Mkdir p f inum # s) = (type_of_obj s) ((O_dir f) := 

   935      (case (parent f) of 

   936         Some pf \<Rightarrow> (case (type_of_obj s (O_proc p), type_of_obj s (O_dir pf)) of

   937                      (Some tp, Some tpf) \<Rightarrow> Some (type_transition tp tpf C_dir True)

   938                    | _ \<Rightarrow> None)

   939      | _ \<Rightarrow> None)                                 )"

   940 | "type_of_obj (LinkHard p f f' # s) = (type_of_obj s) ((O_file f') := 

   941     (case (parent f') of 

   942        Some pf \<Rightarrow> (case (type_of_obj s (O_proc p), type_of_obj s (O_dir pf)) of

   943                     (Some tp, Some tpf) \<Rightarrow> Some (type_transition tp tpf C_file True)

   944                   | _ \<Rightarrow> None)

   945      | _ \<Rightarrow> None)                                      )"

   946 (*

   947 | "type_of_obj (Rename p f f' # s) = (\<lambda> obj. 

   948       case obj of

   949         O_file f'' \<Rightarrow> (if (f' \<preceq> f'') then type_of_obj s (O_file (file_before_rename f f' f''))

   950                        else type_of_obj s (O_file f''))

   951       | O_dir f'' \<Rightarrow> (if (f' \<preceq> f'') then type_of_obj s (O_file (file_before_rename f f' f''))

   952                       else type_of_obj s (O_file f''))

   953       | _ \<Rightarrow> type_of_obj s obj   )"

   954 *)

   955 | "type_of_obj (CreateMsgq p q # s) = (type_of_obj s) ((O_msgq q) := 

   956      (case (type_of_obj s (O_proc p)) of 

   957         Some tp \<Rightarrow> Some tp

   958       | _       \<Rightarrow> None)                          )"

   959 | "type_of_obj (SendMsg p q m # s) = (type_of_obj s) ((O_msg q m) := 

   960      (case (type_of_obj s (O_proc p), type_of_obj s (O_msgq q)) of 

   961         (Some tp, Some tq) \<Rightarrow> Some (type_transition tp tq C_msg False)

   962       | _ \<Rightarrow> None)                               )"

   963 | "type_of_obj (CreateShM p h # s) = (type_of_obj s) ((O_shm h) := 

   964      (case (type_of_obj s (O_proc p)) of 

   965         Some tp \<Rightarrow> Some tp

   966       | _       \<Rightarrow> None)                          )"

   967 | "type_of_obj (CreateSock p af st fd inum # s) = (\<lambda> obj. 

   968      case obj of

   969        O_fd p' fd' \<Rightarrow> if (p' = p \<and> fd' = fd) then type_of_obj s (O_proc p)

   970                       else type_of_obj s obj

   971      | O_tcp_sock (p', fd') \<Rightarrow> if (p' = p \<and> fd' = fd \<and> st = STREAM) then type_of_obj s (O_proc p)

   972                                else type_of_obj s obj

   973      | O_udp_sock (p', fd') \<Rightarrow> if (p' = p \<and> fd' = fd \<and> st = DGRAM) then type_of_obj s (O_proc p)

   974                                else type_of_obj s obj

   975      | _ \<Rightarrow> type_of_obj s obj )"

   976 | "type_of_obj (Accept p fd addr port fd' inum # s) = (\<lambda> obj. 

   977      case obj of

   978        O_fd p' fd'' \<Rightarrow> if (p' = p \<and> fd'' = fd') then type_of_obj s (O_proc p)

   979                       else type_of_obj s obj

   980      | O_tcp_sock (p', fd'') \<Rightarrow> if (p' = p \<and> fd'' = fd') then type_of_obj s (O_proc p)

   981                                else type_of_obj s obj

   982      | _ \<Rightarrow> type_of_obj s obj )"

   983 | "type_of_obj (_ # s) = type_of_obj s"

   984 

   985 fun role_of_proc :: "t_state \<Rightarrow> (t_process \<Rightarrow> role_t option)"

   986 where

   987   "role_of_proc [] = init_role_of_proc"

   988 | "role_of_proc (Clone p p' fds shms # s) = 

   989     (role_of_proc s) (p' := role_of_proc s p)"

   990 | "role_of_proc (Execve p f fds # s) = (role_of_proc s) (p := 

   991     (case (role_of_proc s p, type_of_obj s (O_file f)) of

   992        (Some r, Some ft) \<Rightarrow> role_transition r ft

   993      | _ \<Rightarrow> None)                       )"

   994 | "role_of_proc (_ # s) = role_of_proc s"

   995 

   996 fun role_of_obj :: "t_state \<Rightarrow> t_object \<Rightarrow> role_t option"

   997 where

   998   "role_of_obj s (O_proc p) = role_of_proc s p"

   999 | "role_of_obj s _          = Some R_object"  (* object_r *)

  1000 

  1001 definition sectxt_of_obj :: "t_state \<Rightarrow> t_object \<Rightarrow> security_context_t option"

  1002 where

  1003   "sectxt_of_obj s obj = (

  1004      case (user_of_obj s obj, role_of_obj s obj, type_of_obj s obj) of

  1005        (Some u, Some r, Some t) \<Rightarrow> Some (u, r, t)

  1006      | _                        \<Rightarrow> None)"

  1007 

  1008 (******* flask granting ********

  1009  * involves three kinds of rules:

  1010  *  1. allow rule of types, allowed_rule_list_t, main

  1011  *  2. allow rule of roles, role_allow_rule_list_t, mainly for execve call

  1012  *  3. constrains, section 3.4.5, user-specifically defined.

  1013  * Passed all these 3, then grant Yes, else No 

  1014  *) 

  1015 

  1016 definition search_check_allp :: "security_context_t \<Rightarrow> security_context_t set \<Rightarrow> bool"

  1017 where

  1018   "search_check_allp pctxt sectxts = (\<forall> sec \<in> sectxts. permission_check pctxt sec C_dir P_search)"

  1019 

  1020 definition search_check_file :: "security_context_t \<Rightarrow> security_context_t \<Rightarrow> bool"

  1021 where

  1022   "search_check_file sctxt fctxt \<equiv> permission_check sctxt fctxt C_file P_search"

  1023 

  1024 definition search_check_dir :: "security_context_t \<Rightarrow> security_context_t \<Rightarrow> bool"

  1025 where

  1026   "search_check_dir sctxt fctxt \<equiv> permission_check sctxt fctxt C_dir P_search"

  1027 

  1028 fun get_parentfs_ctxts :: "t_state \<Rightarrow> t_file \<Rightarrow> (security_context_t list) option"

  1029 where

  1030   "get_parentfs_ctxts s [] = 

  1031      (case (sectxt_of_obj s (O_dir [])) of 

  1032         Some ctxt \<Rightarrow> Some [ctxt]

  1033       | _         \<Rightarrow> None)"

  1034 | "get_parentfs_ctxts s (f#pf) = 

  1035      (case (get_parentfs_ctxts s pf, sectxt_of_obj s (O_dir (f#pf))) of

  1036         (Some ctxts, Some ctxt) \<Rightarrow> Some (ctxt#ctxts)

  1037       | _ \<Rightarrow> None)"

  1038 

  1039 fun search_check :: "t_state \<Rightarrow> security_context_t \<Rightarrow> t_file \<Rightarrow> bool"

  1040 where

  1041   "search_check s pctxt [] = 

  1042      (case (sectxt_of_obj s (O_dir [])) of

  1043         Some fctxt \<Rightarrow> search_check_dir pctxt fctxt

  1044       | _          \<Rightarrow> False)"

  1045 | "search_check s pctxt (f#pf) = 

  1046      (if (is_file s (f#pf)) 

  1047       then (case (sectxt_of_obj s (O_file (f#pf)), get_parentfs_ctxts s pf) of

  1048               (Some fctxt, Some pfctxts) \<Rightarrow> (search_check_file pctxt fctxt \<and> search_check_allp pctxt (set pfctxts))

  1049             | _ \<Rightarrow> False)

  1050       else (case (sectxt_of_obj s (O_dir (f#pf)), get_parentfs_ctxts s pf) of

  1051               (Some fctxt, Some pfctxts) \<Rightarrow> (search_check_dir pctxt fctxt \<and> search_check_allp pctxt (set pfctxts))

  1052             | _ \<Rightarrow> False))"

  1053 

  1054 (* this means we should prove every current fd has a security context! *)

  1055 definition sectxts_of_fds :: "t_state \<Rightarrow> t_process \<Rightarrow> t_fd set \<Rightarrow> security_context_t set"

  1056 where

  1057   "sectxts_of_fds s p fds \<equiv> {ctxt. \<exists> fd \<in> fds. sectxt_of_obj s (O_fd p fd) = Some ctxt}"

  1058 

  1059 definition inherit_fds_check :: "t_state \<Rightarrow> security_context_t \<Rightarrow> t_process \<Rightarrow> t_fd set \<Rightarrow> bool"

  1060 where

  1061   "inherit_fds_check s npsectxt p fds \<equiv> 

  1062      (\<forall> ctxt \<in> sectxts_of_fds s p fds. permission_check npsectxt ctxt C_fd P_inherit)"

  1063 

  1064 fun npctxt_execve :: "security_context_t \<Rightarrow> security_context_t \<Rightarrow> security_context_t option"

  1065 where

  1066   "npctxt_execve (pu,pr,pt) (fu,fr,ft) = 

  1067      (case (role_transition pr ft) of

  1068         Some nr \<Rightarrow> Some (pu, nr, type_transition pt ft C_process False)

  1069       | _       \<Rightarrow>  None)"

  1070 

  1071 fun nfctxt_create :: "security_context_t \<Rightarrow> security_context_t \<Rightarrow> security_class_t \<Rightarrow> security_context_t"

  1072 where

  1073   "nfctxt_create (pu,pr,pt) (fu,fr,ft) cls = (pu, R_object, type_transition pt ft cls True)"

  1074 

  1075 fun grant_execve :: 

  1076   "security_context_t \<Rightarrow> security_context_t \<Rightarrow> security_context_t \<Rightarrow> bool"

  1077 where

  1078   "grant_execve (up,rp,tp) (uf,rf,tf) (up',nr,nt) = 

  1079          (role_decl_check nr nt \<and> role_allow rp nr \<and> 

  1080           permission_check (up,rp,tp) (uf,rf,tf) C_file P_execute \<and>

  1081           permission_check (up,nr,nt) (uf,rf,tf) C_file P_entrypoint \<and>

  1082           permission_check (up,rp,tp) (up,nr,nt) C_process P_transition \<and>

  1083           permission_check (up,nr,nt) (uf,rf,tf) C_process P_execute)"

  1084 

  1085 definition sectxts_of_shms :: "t_state \<Rightarrow> t_shm set \<Rightarrow> security_context_t set"

  1086 where

  1087   "sectxts_of_shms s shms \<equiv> {ctxt. \<exists> h \<in> shms. sectxt_of_obj s (O_shm h) = Some ctxt}"

  1088 

  1089 definition inherit_shms_check :: "t_state \<Rightarrow> security_context_t \<Rightarrow> t_shm set \<Rightarrow> bool"

  1090 where

  1091   "inherit_shms_check s npsectxt shms \<equiv> 

  1092      (\<forall> ctxt \<in> sectxts_of_shms s shms. permission_check npsectxt ctxt C_shm P_inherit)"

  1093 

  1094 fun perm_of_mflag :: "t_open_must_flag \<Rightarrow> permission_t set"

  1095 where

  1096   "perm_of_mflag OF_RDONLY = {P_read}"

  1097 | "perm_of_mflag OF_WRONLY = {P_write}"

  1098 | "perm_of_mflag OF_RDWR   = {P_read, P_write}"

  1099 

  1100 definition perm_of_oflag :: "t_open_option_flag set \<Rightarrow> permission_t set"

  1101 where

  1102   "perm_of_oflag oflags \<equiv> 

  1103     (case (OF_APPEND \<in> oflags, OF_CREAT \<in> oflags) of

  1104        (True, True) \<Rightarrow> {P_append, P_create} 

  1105      | (True, _   ) \<Rightarrow> {P_append}

  1106      | (_   , True) \<Rightarrow> {P_create}

  1107      | _            \<Rightarrow> {})"

  1108 

  1109 definition perms_of_flags :: "t_open_flags \<Rightarrow> permission_t set"

  1110 where

  1111   "perms_of_flags flags \<equiv> 

  1112     (case flags of

  1113        (mflag,oflags) \<Rightarrow> (perm_of_mflag mflag \<union> perm_of_oflag oflags))"

  1114 

  1115 (*

  1116 definition class_of_flags :: "t_open_flags \<Rightarrow> security_class_t"

  1117 where

  1118   "class_of_flags flags \<equiv> 

  1119     (case flags of

  1120       (mflag, oflags) \<Rightarrow> if (OF_DIRECTORY \<in> oflags) then C_dir else C_file)"

  1121 

  1122 definition obj_of_flags :: "t_open_flags \<Rightarrow> t_file \<Rightarrow> t_object"

  1123 where

  1124   "obj_of_flags flags f \<equiv> 

  1125     (case flags of

  1126       (mflag, oflags) \<Rightarrow> if (OF_DIRECTORY \<in> oflags) then O_dir f else O_file f)"

  1127 *)

  1128 

  1129 definition oflags_check :: "t_open_flags \<Rightarrow> security_context_t \<Rightarrow> security_context_t \<Rightarrow> bool"

  1130 where

  1131   "oflags_check flags pctxt fctxt \<equiv> 

  1132      \<forall> perm \<in> (perms_of_flags flags). permission_check pctxt fctxt C_file perm"

  1133 

  1134 fun grant :: "t_state \<Rightarrow> t_event \<Rightarrow> bool"

  1135 where