theory Flask+
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imports Main Flask_type OS_type_def File_renaming +
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begin+
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+
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(****** Policy-language-level rule match/auxiliary functions ******)+
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+
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fun patt_match :: "'a patt \<Rightarrow> 'a \<Rightarrow> bool"+
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where+
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  "patt_match (Single x) y = (x = y)"+
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| "patt_match (Set s)    x = (x \<in> s)"+
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| "patt_match (Tilde s)  x = (x \<notin> s)"+
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| "patt_match Asterisk   x = True"+
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+
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(* match a target with a patt, but including the SELF special +
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 * patt_match_self patt target source +
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 *)+
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fun patt_match_self :: "(type_t patt) target_with_self_t \<Rightarrow> type_t \<Rightarrow> type_t \<Rightarrow> bool"+
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where+
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  "patt_match_self Self                  tt st = (tt = st)"+
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| "patt_match_self (Not_self (Single p)) tt st = (tt = p)"+
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| "patt_match_self (Not_self (Set p))    tt st = (tt \<in> p)"+
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| "patt_match_self (Not_self (Tilde p))  tt st = (tt \<notin> p)"+
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| "patt_match_self (Not_self Asterisk)   tt st = True"+
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+
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(* list lookup: find the first one *)+
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fun lookup :: "'a list \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> 'a option"+
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where+
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  "lookup [] P = None"+
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| "lookup (x # xs) P = (if (P x) then Some x else lookup xs P)"+
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+
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(* list member: if exists an element satisfy predicate P *)+
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fun member :: "'a list \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> bool"+
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where+
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  "member [] P = False"+
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| "member (x # xs) P = (if (P x) then True else member xs P)"+
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+
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(******* socket related aux functions ********)+
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fun is_remote_request :: "t_event \<Rightarrow> bool"    +
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where+
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  "is_remote_request (Accept p fd addr port fd' i)  = True"+
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| "is_remote_request (Connect p fd addr)   = True"+
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| "is_remote_request (SendSock p fd) = True"+
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| "is_remote_request (RecvSock p fd) = True"+
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| "is_remote_request e         = False"+
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+
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fun ip_of_addr:: "t_sock_addr \<Rightarrow> t_inet_addr"+
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where+
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  "ip_of_addr (INET_ADDR saddr sport) = saddr"+
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+
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fun port_of_addr:: "t_sock_addr \<Rightarrow> t_socket_port"+
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where+
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  "port_of_addr (INET_ADDR saddr sport) = sport"+
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+
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fun after_bind:: "t_sock_state option \<Rightarrow> bool"+
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where+
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  "after_bind None = False"+
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| "after_bind (Some SS_create) = False"+
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| "after_bind _= True" (* after bind , it should have local addr *)+
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+
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fun after_conacc:: "t_sock_state option \<Rightarrow> bool"+
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where+
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  "after_conacc None = False"+
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| "after_conacc (Some SS_create) = False"+
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| "after_conacc (Some SS_bind) = False"+
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| "after_conacc (Some SS_listen) = False"+
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| "after_conacc _ = True"  (* after connect or accept, it should have remote addr *)+
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+
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(* inet_addr_compare addr1 addr2 \<equiv> addr1 \<le> addr2; but in \<le>'s def,there is a \<exists>, is not a function*)+
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fun subnet_addr :: "t_inet_addr \<Rightarrow> t_inet_addr \<Rightarrow> bool"+
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where+
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  "subnet_addr []     addr   = True"+
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| "subnet_addr (x#xs) []     = False"+
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| "subnet_addr (x#xs) (y#ys) = ((x = y) \<and> subnet_addr xs ys)"+
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+
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definition port_in_range :: "t_socket_port \<Rightarrow> t_socket_port \<Rightarrow> t_socket_port \<Rightarrow> bool"+
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where+
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  "port_in_range minp maxp p \<equiv> ((p < maxp \<or> p = maxp) \<and> (p > minp \<or> p = minp))"+
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+
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(* initial value of initiate state constrains aux function *)+
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definition bidirect_in_init :: "'a set \<Rightarrow> ('a \<Rightarrow> 'b option) \<Rightarrow> bool"+
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where+
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  "bidirect_in_init S f \<equiv>  (\<forall> a. a \<in> S \<longrightarrow> (\<exists> b. f a = Some b)) \<and> +
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                           (\<forall> a b. f a = Some b \<longrightarrow> a \<in> S)" +
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+
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fun is_file_itag :: "t_inode_tag \<Rightarrow> bool"+
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where+
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  "is_file_itag Tag_FILE = True"+
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| "is_file_itag tag      = False"+
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+
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fun is_dir_itag :: "t_inode_tag \<Rightarrow> bool"+
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where+
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  "is_dir_itag Tag_DIR = True"+
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| "is_dir_itag tag     = False"+
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+
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fun is_file_dir_itag :: "t_inode_tag \<Rightarrow> bool"+
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where+
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  "is_file_dir_itag Tag_FILE = True"+
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| "is_file_dir_itag Tag_DIR  = True"+
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| "is_file_dir_itag tag      = False"+
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+
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fun is_tcp_itag :: "t_inode_tag \<Rightarrow> bool"+
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where+
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  "is_tcp_itag Tag_TCP_SOCK = True"+
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| "is_tcp_itag tag      = False"+
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+
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fun is_udp_itag :: "t_inode_tag \<Rightarrow> bool"+
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where+
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  "is_udp_itag Tag_UDP_SOCK = True"+
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| "is_udp_itag tag     = False"+
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+
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fun is_sock_itag :: "t_inode_tag \<Rightarrow> bool"+
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where+
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  "is_sock_itag Tag_TCP_SOCK = True"+
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| "is_sock_itag Tag_UDP_SOCK = True"+
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| "is_sock_itag tag          = False"+
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+
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+
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locale init = +
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  fixes +
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      init_files :: "t_file set"+
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  and init_procs :: "t_process set"+
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  and init_nodes :: "t_node set"+
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  and init_sockets :: "t_socket set"+
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  and init_users :: "user_t set"+
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+
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  and init_file_of_proc_fd ::   "t_process \<Rightarrow> t_fd \<rightharpoonup> t_file"+
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  and init_fds_of_proc ::       "t_process \<Rightarrow> t_fd set"+
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  and init_oflags_of_proc_fd::  "t_process \<Rightarrow> t_fd \<rightharpoonup> t_open_flags"+
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  and init_inum_of_file ::      "t_file \<rightharpoonup> t_inode_num"+
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  and init_inum_of_socket::     "t_socket  \<rightharpoonup> t_inode_num" +
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  and init_itag_of_inum::       "t_inode_num \<rightharpoonup> t_inode_tag"+
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  and init_files_hung_by_del :: "t_file set"+
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(*+
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  and init_file_at_writing_by:: "t_file \<Rightarrow> (t_process \<times> t_fd) set"+
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*)+
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  and init_socket_state ::      "t_socket \<rightharpoonup> t_sock_state"+
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+
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  and init_msgqs :: "t_msgq set"+
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  and init_msgs_of_queue:: "t_msgq \<Rightarrow> t_msg list"+
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  and init_shms :: "t_shm set"+
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  and init_procs_of_shm :: "t_shm \<Rightarrow> (t_process \<times> t_shm_attach_flag) set" +
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  and init_flag_of_proc_shm :: "t_process \<Rightarrow> t_shm \<rightharpoonup> t_shm_attach_flag"+
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+
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  assumes+
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      parent_file_in_init: "\<And> f pf. \<lbrakk>parent f = Some pf; f \<in> init_files\<rbrakk> \<Longrightarrow> pf \<in> init_files"+
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  and root_is_dir: "\<exists> i. init_inum_of_file [] = Some i \<and> init_itag_of_inum i = Some Tag_DIR"+
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  and init_file_has_inum:  "\<And> f. f \<in> init_files \<Longrightarrow> \<exists> im. init_inum_of_file f = Some im"+
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  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)"+
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  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)"+
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  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"+
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+
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  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)"+
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  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> +
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                                         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'))"+
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+
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  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)"+
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  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)"+
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  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"+
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+
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  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"+
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  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"+
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  and init_msgs_distinct:      "\<And> q. distinct (init_msgs_of_queue q)"+
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  and init_msgs_valid:         "\<And> m q. m \<in> set (init_msgs_of_queue q) \<Longrightarrow> q \<in> init_msgqs"+
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+
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  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"+
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  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)"+
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(*+
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  and init_netobj_has_state:   "bidirect_in_init init_netobjs init_netobj_state"+
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  and init_netobj_has_socktype:"bidirect_in_init init_netobjs init_netobj_socktype"+
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  and init_netobj_has_laddr:   "\<And> s. after_bind (init_netobj_state s) \<Longrightarrow> init_netobj_localaddr s \<noteq> None"+
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  and init_netobj_has_raddr:   "\<And> s. after_conacc (init_netobj_state s) \<Longrightarrow> init_netobj_remoteaddr s \<noteq> None"+
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*)+
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+
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  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" +
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+
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begin +
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+
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definition is_init_file:: "t_file \<Rightarrow> bool"+
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where+
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  "is_init_file f \<equiv> (case (init_inum_of_file f) of+
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                       Some i \<Rightarrow> (case (init_itag_of_inum i) of+
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                                    Some Tag_FILE \<Rightarrow> True+
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                                  | _             \<Rightarrow> False)+
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                     | _      \<Rightarrow> False)"+
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+
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definition is_init_dir:: "t_file \<Rightarrow> bool"+
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where+
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  "is_init_dir f \<equiv> (case (init_inum_of_file f) of+
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                      Some i \<Rightarrow> (case (init_itag_of_inum i) of+
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                                   Some Tag_DIR \<Rightarrow> True+
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                                 | _            \<Rightarrow> False)+
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                    | _      \<Rightarrow> False)"+
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+
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definition is_init_tcp_sock:: "t_socket \<Rightarrow> bool"+
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where+
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  "is_init_tcp_sock s \<equiv> (case (init_inum_of_socket s) of+
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                           Some i \<Rightarrow> (case (init_itag_of_inum i) of+
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                                        Some Tag_TCP_SOCK \<Rightarrow> True+
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                                      | _                 \<Rightarrow> False)+
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                         | _      \<Rightarrow> False)"+
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+
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definition is_init_udp_sock:: "t_socket \<Rightarrow> bool"+
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where+
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  "is_init_udp_sock s \<equiv> (case (init_inum_of_socket s) of+
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                           Some i \<Rightarrow> (case (init_itag_of_inum i) of+
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                                        Some Tag_UDP_SOCK \<Rightarrow> True+
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                                      | _                 \<Rightarrow> False)+
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                         | _      \<Rightarrow> False)"+
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+
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definition init_same_inode_files :: "t_file \<Rightarrow> t_file set"+
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where+
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  "init_same_inode_files f \<equiv> if is_init_file f then {f'. init_inum_of_file f = init_inum_of_file f'} else {}"+
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+
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fun init_alive :: "t_object \<Rightarrow> bool"+
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where+
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  "init_alive (O_proc p)     = (p \<in> init_procs)"+
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| "init_alive (O_file f)     = (is_init_file f)"+
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| "init_alive (O_dir  f)     = (is_init_dir  f)"+
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| "init_alive (O_fd p fd)    = (fd \<in> init_fds_of_proc p)"+
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| "init_alive (O_node n)     = (n \<in> init_nodes)"+
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| "init_alive (O_tcp_sock k) = (is_init_tcp_sock k)"+
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| "init_alive (O_udp_sock k) = (is_init_udp_sock k)"+
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| "init_alive (O_shm  h)     = (h \<in> init_shms)"+
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| "init_alive (O_msgq q)     = (q \<in> init_msgqs)"+
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| "init_alive (O_msg q m)    = (m \<in> set (init_msgs_of_queue q) \<and> q \<in> init_msgqs)"+
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+
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+
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(************ system listeners, event-related ***********)+
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+
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fun file_of_proc_fd ::  "t_state \<Rightarrow> t_process \<Rightarrow> t_fd \<Rightarrow> t_file option"+
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where+
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  "file_of_proc_fd [] p' fd' = (init_file_of_proc_fd p' fd')"+
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| "file_of_proc_fd (Open p f flags fd iopt # \<tau>) p' fd' = +
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     (if (p' = p \<and> fd = fd') then Some f else file_of_proc_fd \<tau> p' fd')"+
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| "file_of_proc_fd (CloseFd p fd # \<tau>) p' fd' = +
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     (if (p = p' \<and> fd = fd') then None else file_of_proc_fd \<tau> p' fd')"+
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(*deleted: if (f\<^isub>3 \<preceq> f\<^isub>1) then None else *)+
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(*+
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| "file_of_proc_fd (Rename p f\<^isub>2 f\<^isub>3 # \<tau>) p' fd = +
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     (case (file_of_proc_fd \<tau> p' fd) of+
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        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) +
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                    else Some f\<^isub>1)+
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      | None    \<Rightarrow> None )"+
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*)+
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| "file_of_proc_fd (Execve p f fds # \<tau>) p' fd = +
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     (if (p' = p \<and> fd \<in> fds) then file_of_proc_fd \<tau> p fd +
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      else if (p' = p) then None+
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      else file_of_proc_fd \<tau> p' fd) "+
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| "file_of_proc_fd (Clone p p' fds shms # \<tau>) p'' fd = +
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     (if (p'' = p' \<and> fd \<in> fds) then file_of_proc_fd \<tau> p fd+
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      else if (p'' = p') then None+
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      else file_of_proc_fd \<tau> p'' fd)"+
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| "file_of_proc_fd (Kill p\<^isub> p\<^isub>' # \<tau>) p'' fd = +
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     (if (p'' = p\<^isub>') then None else file_of_proc_fd \<tau> p'' fd)"+
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| "file_of_proc_fd (Exit p # \<tau>) p' fd = +
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     (if (p = p') then None else file_of_proc_fd \<tau> p' fd)"+
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| "file_of_proc_fd (_ # \<tau>) p fd = file_of_proc_fd \<tau> p fd"+
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+
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definition proc_fd_of_file :: "t_state \<Rightarrow> t_file \<Rightarrow> (t_process \<times> t_fd) set"+
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where+
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  "proc_fd_of_file \<tau> f = {(p, fd) | p fd. file_of_proc_fd \<tau> p fd = Some f}"+
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+
−
+
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(****** files and directories ******)+
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+
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fun files_hung_by_del :: "t_state \<Rightarrow> t_file set"+
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where+
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  "files_hung_by_del [] = init_files_hung_by_del"+
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| "files_hung_by_del (UnLink p f # \<tau>) = (+
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     if (proc_fd_of_file \<tau> f = {}) then files_hung_by_del \<tau> +
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     else insert f (files_hung_by_del \<tau>))"+
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(* | files_hung_by_del (Rmdir p f) is not need, for open can only apply to file not dir *)+
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| "files_hung_by_del (CloseFd p fd # \<tau>) = (+
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     case (file_of_proc_fd \<tau> p fd) of+
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       Some f \<Rightarrow> (if (proc_fd_of_file \<tau> f = {(p, fd)}) +
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                  then files_hung_by_del \<tau> - {f}+
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                  else files_hung_by_del \<tau>)+
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     | None   \<Rightarrow> files_hung_by_del \<tau>            )"+
−
(*+
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| "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 *)+
−
*)+
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| "files_hung_by_del (e # \<tau>) = files_hung_by_del \<tau>"+
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declare files_hung_by_del.simps [simp del]+
−
+
−
fun inum_of_file :: "t_state \<Rightarrow> (t_file \<rightharpoonup> t_inode_num)"+
−
where+
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  "inum_of_file [] = init_inum_of_file"+
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| "inum_of_file (Open p f flags fd (Some inum) # \<tau>) = (inum_of_file \<tau>) (f := Some inum)" +
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| "inum_of_file (CloseFd p fd # \<tau>) = (+
−
     case (file_of_proc_fd \<tau> p fd) of+
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       Some f \<Rightarrow> ( if ((proc_fd_of_file \<tau> f = {(p, fd)}) \<and> (f \<in> files_hung_by_del \<tau>)) +
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                   then (inum_of_file \<tau>) (f := None)+
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                   else inum_of_file \<tau> )+
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     | _      \<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>            )" +
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| "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)+
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     else inum_of_file \<tau> f         )"+
−
*)+
−
| "inum_of_file (e # \<tau>) = inum_of_file \<tau>" +
−
+
−
definition current_files :: "t_state \<Rightarrow> t_file set"+
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where+
−
  "current_files \<tau> = {f. \<exists> i. inum_of_file \<tau> f = Some i}" +
−
+
−
definition has_same_inode :: "t_state \<Rightarrow> t_file \<Rightarrow> t_file \<Rightarrow> bool"+
−
where +
−
  "has_same_inode \<tau> fa fb = +
−
     (\<exists>i. inum_of_file \<tau> fa = Some i \<and> inum_of_file \<tau> fb = Some i)"+
−
+
−
fun inum_of_socket :: "t_state \<Rightarrow> (t_socket \<rightharpoonup> t_inode_num)"+
−
where+
−
  "inum_of_socket [] = init_inum_of_socket"+
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| "inum_of_socket (CloseFd p fd # \<tau>) = +
−
     (inum_of_socket \<tau>) ((p, fd):= None)"+
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| "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) +
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                   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}"+
−
+
−
(* 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 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 info_flow_shm :: "t_state \<Rightarrow> t_process \<Rightarrow> t_process \<Rightarrow> bool"+
−
where+
−
  "info_flow_shm \<tau> from to \<equiv> (from = to \<and> from \<in> current_procs \<tau>) \<or> (\<exists> h toflag. +
−
    (((from, SHM_RDWR) \<in> procs_of_shm \<tau> h) \<and> ((to, toflag) \<in> procs_of_shm \<tau> h)))" +
−
*)+
−
+
−
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>"+
−
+
−
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 {}"+
−
+
−
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> current_proc_fds \<tau> p)" (* file_at_writing_by \<tau> f = {} *)+
−
(*+
−
| "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))"+
−
| "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> current_proc_fds \<tau> p \<and>+
−
     (\<forall> h \<in> shms. \<exists> flag. (p, flag) \<in> procs_of_shm \<tau> h))"+
−
| "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"+
−
+
−
+
−
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}"+
−
+
−
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)"+
−
+
−
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_dir pctxt fctxt+
−
      | _          \<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_file pctxt fctxt \<and> search_check_allp pctxt (set pfctxts))+
−
            | _ \<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_dir pctxt fctxt \<and> search_check_allp pctxt (set pfctxts))+
−
            | _ \<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 :: "t_state \<Rightarrow> security_context_t \<Rightarrow> t_process \<Rightarrow> t_fd set \<Rightarrow> bool"+
−
where+
−
  "inherit_fds_check s npsectxt p fds \<equiv> +
−
     (\<forall> ctxt \<in> sectxts_of_fds s p fds. permission_check npsectxt ctxt C_fd P_inherit)"+
−
+
−
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 :: "t_state \<Rightarrow> security_context_t \<Rightarrow> t_shm set \<Rightarrow> bool"+
−
where+
−
  "inherit_shms_check s npsectxt shms \<equiv> +
−
     (\<forall> ctxt \<in> sectxts_of_shms s shms. permission_check npsectxt ctxt C_shm P_inherit)"+
−
+
−
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_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)"+
−
+
−
definition taintable:: "t_object \<Rightarrow> bool"+
−
where+
−
  "taintable obj \<equiv> init_alive 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+
−