theory Enrich2
imports Main Flask Static Init_prop Valid_prop Tainted_prop Delete_prop Co2sobj_prop S2ss_prop S2ss_prop2
Temp Enrich Proc_fd_of_file_prop
begin
context tainting_s begin
fun enrich_msgq :: "t_state \<Rightarrow> t_msgq \<Rightarrow> t_msgq \<Rightarrow> t_state"
where
"enrich_msgq [] tq dq = []"
| "enrich_msgq (CreateMsgq p q # s) tq dq =
(if (tq = q)
then (CreateMsgq p dq # CreateMsgq p q # s)
else CreateMsgq p q # (enrich_msgq s tq dq))"
| "enrich_msgq (SendMsg p q m # s) tq dq =
(if (tq = q)
then (SendMsg p dq m # SendMsg p q m # (enrich_msgq s tq dq))
else SendMsg p q m # (enrich_msgq s tq dq))"
| "enrich_msgq (RecvMsg p q m # s) tq dq =
(if (tq = q)
then (RecvMsg p dq m # RecvMsg p q m # (enrich_msgq s tq dq))
else RecvMsg p q m # (enrich_msgq s tq dq))"
| "enrich_msgq (e # s) tq dq = e # (enrich_msgq s tq dq)"
lemma enrich_msgq_duq_in:
"\<lbrakk>q' \<notin> current_msgqs s; q \<in> current_msgqs s; no_del_event s; valid s\<rbrakk>
\<Longrightarrow> q' \<in> current_msgqs (enrich_msgq s q q')"
apply (induct s, simp)
apply (frule vt_grant_os, frule vd_cons, case_tac a)
apply auto
done
lemma enrich_msgq_duq_sms:
"\<lbrakk>q' \<notin> current_msgqs s; q \<in> current_msgqs s; no_del_event s; valid s\<rbrakk>
\<Longrightarrow> msgs_of_queue (enrich_msgq s q q') q' = msgs_of_queue s q"
apply (induct s, simp)
apply (frule vt_grant_os, frule vd_cons, case_tac a)
apply auto
done
lemma enrich_msgq_cur_inof:
"\<lbrakk>no_del_event s; valid s\<rbrakk>
\<Longrightarrow> inum_of_file (enrich_msgq s q q') f = inum_of_file s f"
apply (induct s arbitrary:f, simp)
apply (frule vt_grant_os, frule vd_cons, case_tac a)
apply (auto split:option.splits)
done
lemma enrich_msgq_cur_inos:
"\<lbrakk>no_del_event s; valid s\<rbrakk>
\<Longrightarrow> inum_of_socket (enrich_msgq s q q') = inum_of_socket s"
apply (rule ext)
apply (induct s, simp)
apply (frule vt_grant_os, frule vd_cons, case_tac a)
apply (auto split:option.splits)
done
lemma enrich_msgq_cur_inos':
"\<lbrakk>no_del_event s; valid s\<rbrakk>
\<Longrightarrow> inum_of_socket (enrich_msgq s q q') sock = inum_of_socket s sock"
apply (simp add:enrich_msgq_cur_inos)
done
lemma enrich_msgq_cur_inums:
"\<lbrakk>no_del_event s; valid s\<rbrakk>
\<Longrightarrow> current_inode_nums (enrich_msgq s q q') = current_inode_nums s"
apply (auto simp:current_inode_nums_def current_file_inums_def
current_sock_inums_def enrich_msgq_cur_inof enrich_msgq_cur_inos)
done
lemma enrich_msgq_cur_itag:
"\<lbrakk>no_del_event s; valid s\<rbrakk>
\<Longrightarrow> itag_of_inum (enrich_msgq s q q') = itag_of_inum s"
apply (rule ext)
apply (induct s, simp)
apply (frule vt_grant_os, frule vd_cons, case_tac a)
apply (auto split:option.splits t_socket_type.splits)
done
lemma enrich_msgq_cur_tcps:
"\<lbrakk>no_del_event s; valid s\<rbrakk>
\<Longrightarrow> is_tcp_sock (enrich_msgq s q q') = is_tcp_sock s"
apply (rule ext)
apply (auto simp:is_tcp_sock_def enrich_msgq_cur_itag enrich_msgq_cur_inos
split:option.splits t_inode_tag.splits)
done
lemma enrich_msgq_cur_udps:
"\<lbrakk>no_del_event s; valid s\<rbrakk>
\<Longrightarrow> is_udp_sock (enrich_msgq s q q') = is_udp_sock s"
apply (rule ext)
apply (auto simp:is_udp_sock_def enrich_msgq_cur_itag enrich_msgq_cur_inos
split:option.splits t_inode_tag.splits)
done
lemma enrich_msgq_cur_msgqs:
"\<lbrakk>q \<in> current_msgqs s; no_del_event s; valid s\<rbrakk>
\<Longrightarrow> current_msgqs (enrich_msgq s q q') = current_msgqs s \<union> {q'}"
apply (induct s, simp)
apply (frule vt_grant_os, frule vd_cons)
apply (case_tac a, auto)
done
lemma enrich_msgq_cur_msgs:
"\<lbrakk>q' \<notin> current_msgqs s; q \<in> current_msgqs s; no_del_event s; valid s\<rbrakk>
\<Longrightarrow> msgs_of_queue (enrich_msgq s q q') = (msgs_of_queue s) (q' := msgs_of_queue s q)"
apply (rule ext, simp, rule conjI, rule impI)
apply (simp add:enrich_msgq_duq_sms)
apply (rule impI)
apply (induct s, simp)
apply (frule vt_grant_os, frule vd_cons)
apply (case_tac a, auto)
done
lemma enrich_msgq_cur_procs:
"\<lbrakk>no_del_event s; valid s\<rbrakk>
\<Longrightarrow> current_procs (enrich_msgq s q q') = current_procs s"
apply (induct s, simp)
apply (frule vt_grant_os, frule vd_cons)
apply (case_tac a, auto)
done
lemma enrich_msgq_cur_files:
"\<lbrakk>no_del_event s; valid s\<rbrakk>
\<Longrightarrow> current_files (enrich_msgq s q q') = current_files s"
apply (auto simp:current_files_def)
apply (simp add:enrich_msgq_cur_inof)+
done
lemma enrich_msgq_cur_fds:
"\<lbrakk>no_del_event s; valid s\<rbrakk>
\<Longrightarrow> current_proc_fds (enrich_msgq s q q') = current_proc_fds s"
apply (induct s, simp)
apply (frule vt_grant_os, frule vd_cons, case_tac a)
apply auto
done
lemma enrich_msgq_filefd:
"\<lbrakk>no_del_event s; valid s\<rbrakk>
\<Longrightarrow> file_of_proc_fd (enrich_msgq s q q') = file_of_proc_fd s"
apply (rule ext, rule ext)
apply (induct s, simp)
apply (frule vt_grant_os, frule vd_cons, case_tac a)
apply auto
done
lemma enrich_msgq_flagfd:
"\<lbrakk>no_del_event s; valid s\<rbrakk>
\<Longrightarrow> flags_of_proc_fd (enrich_msgq s q q') = flags_of_proc_fd s"
apply (rule ext, rule ext)
apply (induct s, simp)
apply (frule vt_grant_os, frule vd_cons, case_tac a)
apply auto
done
lemma enrich_msgq_proc_fds:
"\<lbrakk>no_del_event s; valid s\<rbrakk>
\<Longrightarrow> proc_file_fds (enrich_msgq s q q') = proc_file_fds s"
apply (auto simp:proc_file_fds_def enrich_msgq_filefd)
done
lemma enrich_msgq_hungs:
"\<lbrakk>no_del_event s; valid s\<rbrakk>
\<Longrightarrow> files_hung_by_del (enrich_msgq s q q') = files_hung_by_del s"
apply (induct s, simp)
apply (frule vt_grant_os, frule vd_cons, case_tac a)
apply (auto simp:files_hung_by_del.simps)
done
lemma enrich_msgq_is_file:
"\<lbrakk>no_del_event s; valid s\<rbrakk>
\<Longrightarrow> is_file (enrich_msgq s q q') = is_file s"
apply (rule ext)
apply (auto simp add:is_file_def enrich_msgq_cur_itag enrich_msgq_cur_inof
split:option.splits t_inode_tag.splits)
done
lemma enrich_msgq_is_dir:
"\<lbrakk>no_del_event s; valid s\<rbrakk>
\<Longrightarrow> is_dir (enrich_msgq s q q') = is_dir s"
apply (rule ext)
apply (auto simp add:is_dir_def enrich_msgq_cur_itag enrich_msgq_cur_inof
split:option.splits t_inode_tag.splits)
done
lemma enrich_msgq_alive:
"\<lbrakk>alive s obj; valid s; q \<in> current_msgqs s; q' \<notin> current_msgqs s; no_del_event s\<rbrakk>
\<Longrightarrow> alive (enrich_msgq s q q') obj"
apply (case_tac obj)
apply (simp_all add:enrich_msgq_is_file enrich_msgq_is_dir enrich_msgq_cur_msgqs
enrich_msgq_cur_msgs enrich_msgq_cur_procs enrich_msgq_cur_fds
enrich_msgq_cur_tcps enrich_msgq_cur_udps)
apply (rule impI, simp)
done
lemma enrich_msgq_alive':
"\<lbrakk>alive (enrich_msgq s q q') obj; valid s; q \<in> current_msgqs s; q' \<notin> current_msgqs s; no_del_event s\<rbrakk>
\<Longrightarrow> alive s obj \<or> obj = O_msgq q' \<or> (\<exists> m. obj = O_msg q' m \<and> alive s (O_msg q m))"
apply (case_tac obj)
apply (simp_all add:enrich_msgq_is_file enrich_msgq_is_dir enrich_msgq_cur_msgqs
enrich_msgq_cur_msgs enrich_msgq_cur_procs enrich_msgq_cur_fds
enrich_msgq_cur_tcps enrich_msgq_cur_udps)
apply (auto split:if_splits)
done
(* enrich s target_proc duplicated_pro *)
fun enrich_proc :: "t_state \<Rightarrow> t_process \<Rightarrow> t_process \<Rightarrow> nat \<Rightarrow> t_state"
where
"enrich_proc [] tp dp n = []"
| "enrich_proc (Execve p f fds # s) tp dp n = (
if (tp = p)
then Execve dp f (fds \<inter> proc_file_fds s p) # Execve p f fds # (enrich_proc s tp dp n)
else Execve p f fds # (enrich_proc s tp dp n))"
| "enrich_proc (Clone p p' fds # s) tp dp n = (
if (tp = p')
then Clone p dp (fds \<inter> proc_file_fds s p) # Clone p p' fds # s
else Clone p p' fds # (enrich_proc s tp dp n))"
| "enrich_proc (Open p f flags fd opt # s) tp dp n= (
if (tp = p)
then Open dp f (remove_create_flag flags) fd None # Open p f flags fd opt # (enrich_proc s tp dp n)
else Open p f flags fd opt # (enrich_proc s tp dp n))"
| "enrich_proc (ReadFile p fd # s) tp dp n = (
if (tp = p)
then ReadFile dp fd # ReadFile p fd # (enrich_proc s tp dp n)
else ReadFile p fd # (enrich_proc s tp dp n))"
| "enrich_proc (RecvMsg p q m # s) tp dp n = (
if (tp = p)
then RecvMsg dp n m # RecvMsg p q m # (enrich_msgq (enrich_proc s tp dp (n+1)) q n)
else RecvMsg p q m # (enrich_proc s tp dp n))"
(*
| "enrich_proc (CloseFd p fd # s) tp dp = (
if (tp = p \<and> fd \<in> proc_file_fds s p)
then CloseFd dp fd # CloseFd p fd # (enrich_proc s tp dp)
else CloseFd p fd # (enrich_proc s tp dp))"
*)
(*
| "enrich_proc (Attach p h flag # s) tp dp = (
if (tp = p)
then Attach dp h flag # Attach p h flag # (enrich_proc s tp dp)
else Attach p h flag # (enrich_proc s tp dp))"
| "enrich_proc (Detach p h # s) tp dp = (
if (tp = p)
then Detach dp h # Detach p h # (enrich_proc s tp dp)
else Detach p h # (enrich_proc s tp dp))"
*)
(*
| "enrich_proc (Kill p p' # s) tp dp = (
if (tp = p') then Kill p p' # s
else Kill p p' # (enrich_proc s tp dp))"
| "enrich_proc (Exit p # s) tp dp = (
if (tp = p) then Exit p # s
else Exit p # (enrich_proc s tp dp))"
*)
| "enrich_proc (e # s) tp dp n = e # (enrich_proc s tp dp n)"
definition is_created_proc:: "t_state \<Rightarrow> t_process \<Rightarrow> bool"
where
"is_created_proc s p \<equiv> p \<in> current_procs s \<and> (p \<in> init_procs \<longrightarrow> died (O_proc p) s)"
definition is_created_proc':: "t_state \<Rightarrow> t_process \<Rightarrow> bool"
where
"is_created_proc' s p \<equiv> p \<in> current_procs s \<and> p \<notin> init_procs"
lemma created_proc_clone:
"valid (Clone p p' fds # s) \<Longrightarrow>
is_created_proc (Clone p p' fds # s) tp = (if (tp = p') then True else is_created_proc s tp)"
apply (drule vt_grant_os)
apply (auto simp:is_created_proc_def dest:not_all_procs_prop2)
using not_died_init_proc
by auto
lemma created_proc_exit:
"is_created_proc (Exit p # s) tp = (if (tp = p) then False else is_created_proc s tp)"
by (simp add:is_created_proc_def)
lemma created_proc_kill:
"is_created_proc (Kill p p' # s) tp = (if (tp = p') then False else is_created_proc s tp)"
by (simp add:is_created_proc_def)
lemma created_proc_other:
"\<lbrakk>\<And> p p' fds. e \<noteq> Clone p p' fds;
\<And> p. e \<noteq> Exit p;
\<And> p p'. e \<noteq> Kill p p'\<rbrakk> \<Longrightarrow> is_created_proc (e # s) tp = is_created_proc s tp"
by (case_tac e, auto simp:is_created_proc_def)
lemmas is_created_proc_simps = created_proc_clone created_proc_exit created_proc_kill created_proc_other
lemma no_del_died:
"\<lbrakk>no_del_event s; died obj s\<rbrakk> \<Longrightarrow> (\<exists> p fd. obj = O_fd p fd \<or> obj = O_tcp_sock (p, fd) \<or> obj = O_udp_sock (p, fd))
\<or> (\<exists> q m. obj = O_msg q m) "
apply (induct s)
apply simp
apply (case_tac a)
apply (auto split:option.splits)
done
lemma no_del_created_eq:
"no_del_event s \<Longrightarrow> is_created_proc s p = is_created_proc' s p"
apply (induct s)
apply (simp add:is_created_proc_def is_created_proc'_def)
apply (case_tac a)
apply (auto simp add:is_created_proc_def is_created_proc'_def dest:no_del_died)
done
lemma enrich_proc_dup_in:
"\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; no_del_event s; valid s\<rbrakk>
\<Longrightarrow> p' \<in> current_procs (enrich_proc s p p' i)"
apply (induct s, simp add:is_created_proc_def)
apply (frule vt_grant_os, frule vd_cons)
apply (case_tac a)
apply ( auto simp:is_created_proc_def Let_def enrich_msgq_cur_procs
dest:not_all_procs_prop3)
sorry
lemma enrich_proc_dup_ffd:
"\<lbrakk>file_of_proc_fd s p fd = Some f; is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk>
\<Longrightarrow> file_of_proc_fd (enrich_proc s p p' i) p' fd = Some f"
apply (induct s, simp add:is_created_proc_def)
apply (frule vt_grant_os, frule vd_cons)
apply (case_tac a, auto simp:is_created_proc_def proc_file_fds_def Let_def
dest:not_all_procs_prop3 split:if_splits option.splits)
sorry
lemma enrich_proc_dup_ffd':
"\<lbrakk>file_of_proc_fd (enrich_proc s p p' i) p' fd = Some f; is_created_proc s p; p' \<notin> all_procs s;
no_del_event s; valid s\<rbrakk>
\<Longrightarrow> file_of_proc_fd s p fd = Some f"
apply (induct s, simp add:is_created_proc_def)
apply (frule vt_grant_os, frule vd_cons)
apply (case_tac a, auto simp:is_created_proc_def proc_file_fds_def Let_def
dest:not_all_procs_prop3 split:if_splits option.splits)
sorry
lemma enrich_proc_dup_ffd_eq:
"\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; no_del_event s; valid s\<rbrakk>
\<Longrightarrow> file_of_proc_fd (enrich_proc s p p' i) p' fd = file_of_proc_fd s p fd"
apply (case_tac "file_of_proc_fd s p fd")
apply (case_tac[!] "file_of_proc_fd (enrich_proc s p p' i) p' fd")
apply (auto dest:enrich_proc_dup_ffd enrich_proc_dup_ffd')
apply (drule_tac i = i in enrich_proc_dup_ffd, simp+)
done
lemma enrich_proc_cur_msgqs:
"\<lbrakk>valid s\<rbrakk> \<Longrightarrow> current_msgqs (enrich_proc s p p' i) = current_msgqs s \<union> {q'. q' \<ge> new_msgq s \<and> q' \<le> new_msgq s + (nums_of_recvmsg s p) - 1}"
apply (induct s, simp)
apply (auto)[1]
apply (drule new_msgq_1, simp, simp)
apply (frule vt_grant_os, frule vd_cons)
sorry
lemma enrich_proc_not_alive:
"\<lbrakk>enrich_not_alive s (E_proc p' (new_msgq s) (new_msgq s + (nums_of_recvmsg s p) - 1)) obj;
is_created_proc s p; p' \<notin> all_procs s; no_del_event s; valid s\<rbrakk>
\<Longrightarrow> enrich_not_alive (enrich_proc s p p' (new_msgq s)) (E_proc p' (new_msgq s) (new_msgq s + (nums_of_recvmsg s p) - 1)) obj"
apply (case_tac obj, simp_all)
prefer 5
apply (simp add:enrich_proc_cur_msgqs)
apply (rule impI, rule notI)
apply simp
apply (auto)[1]
defer
apply simp
apply (rule impI, rule notI)
defer
apply (subgoal_tac "new_msgq s \<noteq> 0")
apply simp
apply arith
apply (simp_all add:enrich_proc_cur_procs enrich_proc_cur_files enrich_proc_cur_inums
enrich_proc_cur_msgqs enrich_proc_cur_msgs enrich_proc_cur_fds)
defer
apply (rule impI, rule notI)
sorry
lemma enrich_proc_dup_fflags:
"\<lbrakk>flags_of_proc_fd s p fd = Some flag; is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk>
\<Longrightarrow> flags_of_proc_fd (enrich_proc s p p') p' fd = Some (remove_create_flag flag) \<or>
flags_of_proc_fd (enrich_proc s p p') p' fd = Some flag"
apply (induct s arbitrary:p, simp add:is_created_proc_def)
apply (frule vt_grant_os, frule vd_cons)
apply (case_tac a, auto simp:is_created_proc_def proc_file_fds_def is_creat_flag_def Let_def
dest:not_all_procs_prop3 split:if_splits option.splits)
sorry
lemma enrich_proc_dup_ffds:
"\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; no_del_event s; valid s\<rbrakk>
\<Longrightarrow> proc_file_fds (enrich_proc s p p') p' = proc_file_fds s p"
apply (auto simp:proc_file_fds_def)
apply (rule_tac x = f in exI)
apply (erule enrich_proc_dup_ffd', simp+)
apply (rule_tac x = f in exI)
apply (erule enrich_proc_dup_ffd, simp+)
done
lemma enrich_proc_dup_ffds_eq_fds:
"\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; no_del_event s; valid s\<rbrakk>
\<Longrightarrow> current_proc_fds (enrich_proc s p p') p' = proc_file_fds s p"
apply (induct s arbitrary:p)
apply (simp add: is_created_proc_def)
apply (frule not_all_procs_prop3)
apply (frule vd_cons, frule vt_grant_os, case_tac a)
apply (auto split:if_splits option.splits dest:proc_fd_in_fds set_mp not_all_procs_prop3
simp:proc_file_fds_def is_created_proc_def Let_def)
sorry
lemma enrich_proc_dup_ffds':
"\<lbrakk>fd \<notin> current_proc_fds (enrich_proc s p p') p'; is_created_proc s p; p' \<notin> all_procs s; no_del_event s; valid s\<rbrakk>
\<Longrightarrow> fd \<notin> proc_file_fds s p \<and> file_of_proc_fd s p fd = None"
apply (auto simp:enrich_proc_dup_ffds_eq_fds)
apply (simp add:proc_file_fds_def)
done
lemma enrich_proc_cur_inof:
"\<lbrakk>valid s; no_del_event s\<rbrakk> \<Longrightarrow> inum_of_file (enrich_proc s p p') f = inum_of_file s f"
apply (induct s arbitrary:f)
apply simp
apply (frule vd_cons, frule vt_grant_os, frule vt_grant)
apply (case_tac a, auto)
apply (auto split:option.splits simp del:grant.simps simp add:Let_def)
sorry
lemma not_all_procs_sock:
"\<lbrakk>p' \<notin> all_procs s; valid s\<rbrakk> \<Longrightarrow> inum_of_socket s (p', fd) = None"
apply (frule not_all_procs_prop3)
apply (case_tac "inum_of_socket s (p', fd)", simp_all)
apply (drule cn_in_curp', simp+)
done
lemma enrich_proc_cur_inos:
"\<lbrakk>valid s; no_del_event s; p' \<notin> all_procs s\<rbrakk>
\<Longrightarrow> inum_of_socket (enrich_proc s p p') (tp, fd) = inum_of_socket s (tp, fd)"
apply (induct s arbitrary:tp)
apply simp
apply (frule vd_cons, frule vt_grant_os)
apply (case_tac a, auto split:option.splits simp:not_all_procs_sock Let_def)
apply (simp add:proc_file_fds_def, erule exE)
apply (case_tac "inum_of_socket s (nat1, fd)", simp_all)
apply (drule filefd_socket_conflict, simp_all add:current_sockets_def)
sorry
lemma enrich_proc_cur_inums:
"\<lbrakk>p' \<notin> all_procs s; no_del_event s; valid s\<rbrakk>
\<Longrightarrow> current_inode_nums (enrich_proc s p p') = current_inode_nums s"
apply (auto simp:current_inode_nums_def current_file_inums_def
current_sock_inums_def enrich_proc_cur_inof enrich_proc_cur_inos)
done
lemma enrich_proc_cur_itag:
"\<lbrakk>valid s; no_del_event s; p' \<notin> all_procs s\<rbrakk>
\<Longrightarrow> itag_of_inum (enrich_proc s p p') i = itag_of_inum s i"
apply (induct s)
apply simp
apply (frule vd_cons, frule vt_grant_os)
apply (case_tac a, auto split:option.splits t_socket_type.splits simp:Let_def)
sorry
lemma enrich_proc_cur_tcps:
"\<lbrakk>valid s; no_del_event s; p' \<notin> all_procs s\<rbrakk>
\<Longrightarrow> is_tcp_sock (enrich_proc s p p') = is_tcp_sock s"
apply (rule ext, case_tac x)
apply (auto simp add:is_tcp_sock_def enrich_proc_cur_itag enrich_proc_cur_inos
split:option.splits t_inode_tag.splits)
done
lemma enrich_proc_cur_udps:
"\<lbrakk>valid s; no_del_event s; p' \<notin> all_procs s\<rbrakk>
\<Longrightarrow> is_udp_sock (enrich_proc s p p') = is_udp_sock s"
apply (rule ext, case_tac x)
apply (auto simp add:is_udp_sock_def enrich_proc_cur_itag enrich_proc_cur_inos
split:option.splits t_inode_tag.splits)
done
lemma enrich_proc_cur_msgqs:
"\<lbrakk>q \<in> current_msgqs s; valid s\<rbrakk> \<Longrightarrow> q \<in> current_msgqs (enrich_proc s p p')"
apply (induct s, simp)
apply (frule vt_grant_os, frule vd_cons)
apply (case_tac a, auto simp:Let_def)
sorry
lemma enrich_proc_cur_msgs:
"\<lbrakk>q \<in> current_msgqs s; valid s\<rbrakk> \<Longrightarrow> msgs_of_queue (enrich_proc s p p') q = msgs_of_queue s q"
apply (induct s, simp)
apply (frule_tac p = p and p' = p' in enrich_proc_cur_msgqs, simp)
apply (frule vt_grant_os, frule vd_cons)
apply (case_tac a, auto simp:Let_def)
sorry
lemma enrich_proc_cur_procs:
"\<lbrakk>p' \<notin> all_procs s; no_del_event s; is_created_proc s p; valid s\<rbrakk>
\<Longrightarrow> current_procs (enrich_proc s p p') = current_procs s \<union> {p'}"
apply (induct s, simp add:is_created_proc_def)
apply (frule vt_grant_os, frule vd_cons)
apply (case_tac a, auto simp:is_created_proc_simps Let_def)
sorry
lemma enrich_proc_cur_files:
"\<lbrakk>valid s; no_del_event s\<rbrakk> \<Longrightarrow> current_files (enrich_proc s p p') = current_files s"
apply (auto simp:current_files_def)
apply (simp add: enrich_proc_cur_inof)+
done
lemma enrich_proc_cur_fds1:
"\<lbrakk>p' \<notin> all_procs s; no_del_event s; is_created_proc s p; valid s; tp \<in> current_procs s\<rbrakk>
\<Longrightarrow> current_proc_fds (enrich_proc s p p') tp = current_proc_fds s tp"
apply (induct s, simp add:is_created_proc_def)
apply (frule vt_grant_os, frule vd_cons)
apply (frule not_all_procs_prop3)
apply (case_tac a)
sorry
(*
apply (auto simp:is_created_proc_simps)
done
*)
lemma enrich_proc_cur_fds1':
"\<lbrakk>p' \<notin> all_procs s; no_del_event s; is_created_proc s p; valid s; tp \<noteq> p'\<rbrakk>
\<Longrightarrow> current_proc_fds (enrich_proc s p p') tp = current_proc_fds s tp"
apply (induct s, simp add:is_created_proc_def)
apply (frule vt_grant_os, frule vd_cons)
apply (frule not_all_procs_prop3) sorry (*
apply (case_tac a)
apply (auto simp:is_created_proc_simps)
done
*)
lemma enrich_proc_cur_fds:
"\<lbrakk>p' \<notin> all_procs s; no_del_event s; is_created_proc s p; valid s\<rbrakk>
\<Longrightarrow> current_proc_fds (enrich_proc s p p') tp = (if (tp = p') then proc_file_fds s p else current_proc_fds s tp)"
apply (simp add:enrich_proc_cur_fds1' enrich_proc_dup_ffds_eq_fds split:if_splits)
done
lemma enrich_proc_not_alive:
"\<lbrakk>enrich_not_alive s (E_proc p') obj; is_created_proc s p; p' \<notin> all_procs s; no_del_event s; valid s\<rbrakk>
\<Longrightarrow> enrich_not_alive (enrich_proc s p p') (E_proc p') obj"
apply (case_tac obj)
apply (simp_all add:enrich_proc_cur_procs enrich_proc_cur_files enrich_proc_cur_inums
enrich_proc_cur_msgqs enrich_proc_cur_msgs enrich_proc_cur_fds)
defer
apply (rule impI, rule notI)
sorry
lemma enrich_proc_filefd:
"\<lbrakk>file_of_proc_fd s tp fd = Some f; is_created_proc s p; p' \<notin> all_procs s; no_del_event s; valid s\<rbrakk>
\<Longrightarrow> file_of_proc_fd (enrich_proc s p p') tp fd = Some f"
apply (induct s arbitrary:tp, simp add:is_created_proc_def)
apply (frule vt_grant_os, frule vd_cons)
apply (frule not_all_procs_prop3)
apply (case_tac a)
apply (auto simp:is_created_proc_simps dest:proc_fd_in_procs split:if_splits)
sorry
lemma enrich_proc_flagfd:
"\<lbrakk>flags_of_proc_fd s tp fd = Some f; is_created_proc s p; p' \<notin> all_procs s; no_del_event s; valid s\<rbrakk>
\<Longrightarrow> flags_of_proc_fd (enrich_proc s p p') tp fd = Some f"
apply (induct s arbitrary:tp, simp add:is_created_proc_def)
apply (frule vt_grant_os, frule vd_cons)
apply (frule not_all_procs_prop3)
apply (case_tac a)
apply (auto simp:is_created_proc_simps dest:proc_fd_in_procs current_fflag_has_ffd split:if_splits option.splits)
sorry
lemma enrich_proc_hungs:
"\<lbrakk>valid s; no_del_event s\<rbrakk> \<Longrightarrow> files_hung_by_del (enrich_proc s p p') = files_hung_by_del s"
apply (induct s, simp)
apply (frule vt_grant_os, frule vd_cons)
apply (case_tac a, auto simp:files_hung_by_del.simps)
sorry
lemma enrich_proc_is_file:
"\<lbrakk>valid s; no_del_event s; p' \<notin> all_procs s\<rbrakk>
\<Longrightarrow> is_file (enrich_proc s p p') = is_file s"
apply (rule ext, case_tac x)
apply (auto simp add:is_file_def enrich_proc_cur_itag enrich_proc_cur_inof
split:option.splits t_inode_tag.splits)
done
lemma enrich_proc_is_dir:
"\<lbrakk>valid s; no_del_event s; p' \<notin> all_procs s\<rbrakk>
\<Longrightarrow> is_dir (enrich_proc s p p') = is_dir s"
apply (rule ext, case_tac x)
apply (auto simp add:is_dir_def enrich_proc_cur_itag enrich_proc_cur_inof
split:option.splits t_inode_tag.splits)
done
lemma enrich_proc_alive:
"\<lbrakk>alive s obj; valid s; is_created_proc s p; p' \<notin> all_procs s; no_del_event s\<rbrakk>
\<Longrightarrow> alive (enrich_proc s p p') obj"
apply (case_tac obj)
apply (simp_all add:enrich_proc_is_file enrich_proc_is_dir enrich_proc_cur_msgqs
enrich_proc_cur_msgs enrich_proc_cur_procs enrich_proc_cur_fds
enrich_proc_cur_tcps enrich_proc_cur_udps)
apply (rule impI, simp)
apply (drule current_proc_fds_in_curp, simp, simp add:not_all_procs_prop3)
done
lemma enrich_proc_prop:
"\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s; no_del_event s\<rbrakk>
\<Longrightarrow> valid (enrich_proc s p p') \<and>
(\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp) \<and>
(\<forall> f. f \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') f = cf2sfile s f) \<and>
(\<forall> q. q \<in> current_msgqs s \<longrightarrow> cq2smsgq (enrich_proc s p p') q = cq2smsgq s q) \<and>
(\<forall> tp fd. fd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp fd = cfd2sfd s tp fd) \<and>
(cp2sproc (enrich_proc s p p') p' = cp2sproc s p) \<and>
(\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd)"
proof (induct s)
case Nil
thus ?case by (auto simp:is_created_proc_def)
next
case (Cons e s)
hence vd_cons': "valid (e # s)" and created_cons: "is_created_proc (e # s) p"
and all_procs_cons: "p' \<notin> all_procs (e # s)" and vd: "valid s"
and os: "os_grant s e" and grant: "grant s e"
and nodel_cons: "no_del_event (e # s)"
by (auto dest:vd_cons' vt_grant_os vt_grant)
from all_procs_cons have all_procs: "p' \<notin> all_procs s" by (case_tac e, auto)
from nodel_cons have nodel: "no_del_event s" by (case_tac e, auto)
from Cons have pre: "is_created_proc s p \<Longrightarrow> valid (enrich_proc s p p') \<and>
(\<forall>tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp) \<and>
(\<forall>f. f \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') f = cf2sfile s f) \<and>
(\<forall>q. q \<in> current_msgqs s \<longrightarrow> cq2smsgq (enrich_proc s p p') q = cq2smsgq s q) \<and>
(\<forall>tp fd. fd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp fd = cfd2sfd s tp fd) \<and>
(cp2sproc (enrich_proc s p p') p' = cp2sproc s p) \<and>
(\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd)"
using vd all_procs nodel by auto
from pre have pre_vd: "is_created_proc s p \<Longrightarrow> valid (enrich_proc s p p')" by simp
have vd_enrich:"is_created_proc s p \<Longrightarrow> valid (e # enrich_proc s p p')"
apply (frule pre_vd)
apply (erule_tac s = s and obj' = "E_proc p'" in enrich_valid_intro_cons)
apply (simp_all add: pre nodel_cons all_procs_cons vd_cons')
apply (clarsimp simp:enrich_proc_alive nodel all_procs vd)
apply (rule allI, rule impI, erule enrich_proc_not_alive)
apply (simp_all add:nodel all_procs vd enrich_proc_hungs enrich_proc_cur_msgs)
apply ((rule allI| rule impI)+, erule enrich_proc_filefd)
apply (simp_all add:nodel all_procs vd)
apply ((rule allI| rule impI)+, erule enrich_proc_flagfd)
apply (simp_all add:nodel all_procs vd)
done
have vd_enrich_cons: "valid (enrich_proc (e # s) p p')"
proof-
have "\<And>f fds. \<lbrakk>valid (Execve p f fds # enrich_proc s p p'); is_created_proc s p;
valid (Execve p f fds # s); p' \<notin> all_procs s\<rbrakk>
\<Longrightarrow> valid (Execve p' f (fds \<inter> proc_file_fds s p) # Execve p f fds # enrich_proc s p p')"
proof-
fix f fds
assume a1: "valid (Execve p f fds # enrich_proc s p p')" and a2: "is_created_proc s p"
and a3: "valid (Execve p f fds # s)" and a0: "p' \<notin> all_procs s"
have cp2sp: "\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp"
and cf2sf: "\<forall> tf. tf \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') tf = cf2sfile s tf"
and cfd2sfd: "\<forall> tp tfd. tfd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp tfd = cfd2sfd s tp tfd"
and dup_sp: "cp2sproc (enrich_proc s p p') p' = cp2sproc s p"
and dup_sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd"
using pre a2
by auto
show "valid (Execve p' f (fds \<inter> proc_file_fds s p) # Execve p f fds # enrich_proc s p p')"
proof-
from a0 a3 have a0': "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3)
from a3 have grant: "grant s (Execve p f fds)" and os: "os_grant s (Execve p f fds)"
by (auto dest:vt_grant_os vt_grant simp del:os_grant.simps)
have f_in: "is_file (enrich_proc s p p') f"
using vd nodel os all_procs
by (auto dest:vt_grant_os simp:enrich_proc_is_file)
moreover have a5: "proc_file_fds s p \<subseteq> proc_file_fds (Execve p f fds # enrich_proc s p p') p'"
using a3 a0'
apply (frule_tac vt_grant_os)
apply (auto simp:proc_file_fds_def)
apply (rule_tac x = fa in exI)
apply (erule enrich_proc_dup_ffd)
apply (simp_all add:vd all_procs a2)
done
ultimately have "os_grant (Execve p f fds # enrich_proc s p p') (Execve p' f (fds \<inter> proc_file_fds s p))"
apply (auto simp:is_file_simps enrich_proc_dup_in a2 vd all_procs a1 enrich_proc_dup_ffds)
done
moreover have "grant (Execve p f fds # enrich_proc s p p') (Execve p' f (fds \<inter> proc_file_fds s p))"
proof-
from grant obtain up rp tp uf rf tf
where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
and p2: "sectxt_of_obj s (O_file f) = Some (uf, rf, tf)"
by (simp split:option.splits, blast)
with grant obtain pu nr nt where p3: "npctxt_execve (up, rp, tp) (uf, rf, tf) = Some (pu, nr, nt)"
by (simp split:option.splits del:npctxt_execve.simps, blast)
have p1': "sectxt_of_obj (Execve p f fds # enrich_proc s p p') (O_proc p') = Some (up, rp, tp)"
using p1 dup_sp a1 a0'
apply (simp add:sectxt_of_obj_simps)
by (simp add:cp2sproc_def split:option.splits)
from os have f_in': "is_file s f" by simp
from vd os have "\<exists> sf. cf2sfile s f = Some sf"
by (auto dest!:is_file_in_current current_file_has_sfile)
hence p2': "sectxt_of_obj (Execve p f fds # enrich_proc s p p') (O_file f) = Some (uf, rf, tf)"
using f_in p2 cf2sf os a1
apply (erule_tac x = f in allE)
apply (auto dest:is_file_in_current simp:cf2sfile_def sectxt_of_obj_simps split:option.splits)
apply (case_tac f, simp)
apply (drule_tac s = s in root_is_dir', simp add:vd, simp+)
done
from dup_sfd a5 have "\<forall>fd. fd \<in> proc_file_fds s p \<longrightarrow>
cfd2sfd (Execve p f fds # enrich_proc s p p') p' fd = cfd2sfd s p fd"
apply (rule_tac allI)
apply (erule_tac x = fd in allE, clarsimp)
apply (drule set_mp, simp)
apply (auto simp:cfd2sfd_execve proc_file_fds_def a1)
done
hence "inherit_fds_check (Execve p f fds # enrich_proc s p p') (up, nr, nt) p' (fds \<inter> proc_file_fds s p)"
using grant os p1 p2 p3 vd
apply (clarsimp)
apply (rule_tac s = s and p = p and fds = fds in enrich_inherit_fds_check_dup)
apply simp_all
done
moreover have "search_check (Execve p f fds # enrich_proc s p p') (up, rp, tp) f"
using p1 p2 p2' vd cf2sf f_in f_in' grant p3 f_in a1
apply (rule_tac s = s in enrich_search_check)
apply (simp_all add:is_file_simps)
apply (rule allI, rule impI, erule_tac x = fa in allE, simp)
apply (drule_tac ff = fa in cf2sfile_other')
apply (auto simp:a2 enrich_proc_cur_files nodel)
done
ultimately show ?thesis
using p1' p2' p3
apply (simp split:option.splits)
using grant p1 p2
apply simp
done
qed
ultimately show ?thesis using a1
by (erule_tac valid.intros(2), auto)
qed
qed
moreover have "\<And>tp fds. \<lbrakk>valid (Clone tp p fds # s); p' \<noteq> p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow>
valid (Clone tp p' (fds \<inter> proc_file_fds s tp) # Clone tp p fds # s)"
apply (frule vt_grant_os, frule vt_grant, drule not_all_procs_prop3)
apply (rule valid.intros(2))
apply (simp_all split:option.splits add:sectxt_of_obj_simps)
apply (auto simp add:proc_file_fds_def)[1]
apply (auto simp:inherit_fds_check_def sectxt_of_obj_simps sectxts_of_fds_def inherit_fds_check_ctxt_def)
done
moreover have "\<And>f flags fd opt. \<lbrakk>valid (Open p f flags fd opt # enrich_proc s p p');
is_created_proc s p; valid (Open p f flags fd opt # s); p' \<notin> all_procs s\<rbrakk>
\<Longrightarrow> valid (Open p' f (remove_create_flag flags) fd None # Open p f flags fd opt # enrich_proc s p p')"
proof-
fix f flags fd opt
assume a1: "valid (Open p f flags fd opt # enrich_proc s p p')" and a2: "is_created_proc s p"
and a3: "valid (Open p f flags fd opt # s)" and a4: "p' \<notin> all_procs s"
have cp2sp: "\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp"
and cf2sf: "\<forall> tf. tf \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') tf = cf2sfile s tf"
and cfd2sfd: "\<forall> tp tfd. tfd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp tfd = cfd2sfd s tp tfd"
and dup_sp: "cp2sproc (enrich_proc s p p') p' = cp2sproc s p"
and dup_sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd"
using pre a2 by auto
from a4 a3 have a0: "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3 split:option.splits)
have a5: "p' \<in> current_procs (enrich_proc s p p')"
using a2 a3 vd
apply (erule_tac enrich_proc_dup_in)
by (simp_all add:vd a4)
have a6: "is_file (Open p f flags fd opt # enrich_proc s p p') f"
using a1 a3
by (auto simp:is_file_open dest:vt_grant_os)
have a7: "fd \<notin> current_proc_fds (enrich_proc s p p') p'"
using a2 a4 vd nodel
apply (simp add:enrich_proc_dup_ffds_eq_fds)
apply (rule notI)
apply (drule_tac p = p in file_fds_subset_pfds)
apply (drule set_mp, simp)
using a3
apply (drule_tac vt_grant_os)
apply (auto split:option.splits)
done
from a1 have a8: "valid (enrich_proc s p p')" by (erule_tac valid.cases, auto)
from a3 have grant: "grant s (Open p f flags fd opt)" and os: "os_grant s (Open p f flags fd opt)"
by (auto dest:vt_grant_os vt_grant)
show "valid (Open p' f (remove_create_flag flags) fd None # Open p f flags fd opt # enrich_proc s p p')"
proof (cases opt)
case None
have f_in: "is_file (enrich_proc s p p') f"
using vd nodel os all_procs None
by (auto dest:vt_grant_os simp:enrich_proc_is_file)
from grant None obtain up rp tp uf rf tf
where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
and p2: "sectxt_of_obj s (O_file f) = Some (uf, rf, tf)"
apply (simp split:option.splits)
by (case_tac a, case_tac aa, blast)
have p1': "sectxt_of_obj (Open p f flags fd opt # enrich_proc s p p') (O_proc p') = Some (up, rp, tp)"
using p1 dup_sp a1
apply (simp add:sectxt_of_obj_simps)
by (simp add:cp2sproc_def split:option.splits)
from os None have f_in': "is_file s f" by simp
from vd os None have "\<exists> sf. cf2sfile s f = Some sf"
by (auto dest!:is_file_in_current current_file_has_sfile)
hence p2': "sectxt_of_obj (Open p f flags fd opt # enrich_proc s p p') (O_file f) = Some (uf, rf, tf)"
using p2 cf2sf os a1 None f_in' vd f_in
apply (erule_tac x = f in allE)
apply (auto dest:is_file_in_current simp:cf2sfile_def sectxt_of_obj_simps split:option.splits)
apply (case_tac f, simp)
apply (drule_tac s = s in root_is_dir', simp add:vd, simp+)
done
have "search_check (Open p f flags fd opt # enrich_proc s p p') (up, rp, tp) f"
using p1 p2 p2' vd cf2sf f_in f_in' grant f_in a1 None
apply (rule_tac s = s in enrich_search_check)
apply (simp_all add:is_file_simps)
apply (rule allI, rule impI, erule_tac x = fa in allE, simp)
apply (simp add:cf2sfile_open_none)
done
thus ?thesis using a0 a5 a6 a7 None a1
apply (rule_tac valid.intros(2))
apply (simp_all add:a1)
apply (case_tac flags, simp add:is_creat_excl_flag_def)
using p1' p2'
apply simp
using grant p1 p2
apply (simp add:oflags_check_remove_create)
done
next
case (Some inum)
with os obtain pf where parent: "parent f = Some pf" by auto
with grant Some obtain pu rp pt pfu pfr pft where
p1: "sectxt_of_obj s (O_proc p) = Some (pu, rp, pt)"
and p2: "sectxt_of_obj s (O_dir pf) = Some (pfu, pfr, pft)"
apply (simp split:option.splits)
apply (case_tac a, case_tac aa, blast)
done
from p1 have p1': "sectxt_of_obj (enrich_proc s p p') (O_proc p) = Some (pu, rp, pt)"
using cp2sp os
apply (erule_tac x = p in allE)
apply (auto split:option.splits simp:cp2sproc_def)
done
from os parent Some
have pf_in: "is_dir s pf" by auto
hence "\<exists> sf. cf2sfile s pf = Some sf" using vd
by (auto dest!:is_dir_in_current current_file_has_sfile)
from a1 parent Some have pf_in': "is_dir (enrich_proc s p p') pf"
apply (frule_tac vt_grant_os)
by (clarsimp)
have p2': "sectxt_of_obj (enrich_proc s p p') (O_dir pf) = Some (pfu, pfr, pft)"
proof-
have "cf2sfile (enrich_proc s p p') pf = cf2sfile s pf"
using cf2sf pf_in
apply (drule_tac is_dir_in_current)
apply (erule_tac x = pf in allE)
by simp
with pf_in pf_in' p2 vd Some a8
show ?thesis
apply (frule_tac is_dir_not_file)
apply (frule_tac s = "enrich_proc s p p'" in is_dir_not_file)
apply (simp add:cf2sfile_def)
apply (case_tac pf, simp)
apply (simp add:sroot_def root_sec_remains)
by (auto split:option.splits dest!:current_has_sec' get_pfs_secs_prop' dest:parentf_is_dir_prop1)
qed
from p1 have dup: "sectxt_of_obj (Open p f flags fd (Some inum) # enrich_proc s p p') (O_proc p')
= Some (pu, rp, pt)"
using a1 Some
apply (simp add:sec_open)
using dup_sp
apply (auto split:option.splits if_splits simp:cp2sproc_def)
done
have nsf: "sectxt_of_obj (Open p f flags fd (Some inum) # enrich_proc s p p') (O_file f)
= Some (pu, R_object, type_transition pt pft C_file True)"
using a1 Some p1 p2 parent p2' p1'
by (simp add:sec_open)
have "search_check (Open p f flags fd (Some inum) # enrich_proc s p p') (pu, rp, pt) f"
proof-
have "search_check (Open p f flags fd (Some inum) # enrich_proc s p p') (pu, rp, pt) pf"
using grant Some parent p1 p2 vd a1 pf_in pf_in' p2'
apply simp
apply (rule_tac s = s in enrich_search_check')
apply (simp_all add:is_dir_simps sectxt_of_obj_simps)
apply (rule allI, rule impI)
apply (case_tac "fa = f")
using os Some
apply simp
apply (drule_tac f' = fa in cf2sfile_open)
apply (simp add:current_files_simps)
using enrich_proc_cur_files a2 nodel
apply simp
apply simp
using cf2sf
apply simp
done
moreover have "is_file (Open p f flags fd (Some inum) # enrich_proc s p p') f"
using a1 Some
by (simp add:is_file_open)
ultimately
show ?thesis
using parent a1 Some nsf
apply (erule_tac search_check_leveling_f)
apply (simp_all)
apply (simp add:search_check_file_def)
(* create new file, grant only check pf's SEARCH permission, not newfile itself, so we make assumptions of this case in the locale *)
apply (simp add:permission_check.simps)
sorry
qed
thus ?thesis using a0 a5 a6 a7 a1 Some
apply (rule_tac valid.intros(2))
apply (simp add:a1)
apply simp
apply (case_tac flags, simp add:is_creat_excl_flag_def)
using grant p1 p2 parent dup nsf
apply (simp add:oflags_check_remove_create)
done
qed
qed
moreover have "\<And>fd. \<lbrakk>valid (CloseFd p fd # enrich_proc s p p'); is_created_proc s p;
valid (CloseFd p fd # s); p' \<notin> all_procs s; fd \<in> proc_file_fds s p\<rbrakk>
\<Longrightarrow> valid (CloseFd p' fd # CloseFd p fd # enrich_proc s p p')"
proof-
fix fd
assume a1: "valid (CloseFd p fd # enrich_proc s p p')" and a2: "is_created_proc s p"
and a3: "p' \<notin> all_procs s" and a4: "valid (CloseFd p fd # s)"
and a5: "fd \<in> proc_file_fds s p"
from a4 a3 have a0: "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3)
have "p' \<in> current_procs (enrich_proc s p p')"
using a2 a3 vd
by (auto intro:enrich_proc_dup_in)
moreover have "fd \<in> current_proc_fds (enrich_proc s p p') p'"
using a5 a2 a3 vd pre_vd nodel
apply (simp)
apply (drule_tac s = "enrich_proc s p p'" and p = p' in file_fds_subset_pfds)
apply (erule set_mp)
apply (simp add:enrich_proc_dup_ffds)
done
ultimately show "valid (CloseFd p' fd # CloseFd p fd # enrich_proc s p p')"
apply (rule_tac valid.intros(2))
apply (simp_all add:a1 a0 a2 pre_vd)
done
qed
moreover have "\<And> fd. \<lbrakk>valid (ReadFile p fd # enrich_proc s p p');
is_created_proc s p; valid (ReadFile p fd # s); p' \<notin> all_procs s\<rbrakk>
\<Longrightarrow> valid (ReadFile p' fd # ReadFile p fd # enrich_proc s p p')"
proof-
fix fd
assume a1: "valid (ReadFile p fd # enrich_proc s p p')" and a2: "is_created_proc s p"
and a3: "valid (ReadFile p fd # s)" and a4: "p' \<notin> all_procs s"
from a3 have os: "os_grant s (ReadFile p fd)" and grant: "grant s (ReadFile p fd)"
by (auto dest:vt_grant_os vt_grant)
have cp2sp: "\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp"
and cf2sf: "\<forall> tf. tf \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') tf = cf2sfile s tf"
and cfd2sfd: "\<forall> tp tfd. tfd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp tfd = cfd2sfd s tp tfd"
and dup_sp: "cp2sproc (enrich_proc s p p') p' = cp2sproc s p"
and dup_sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd"
using pre a2 by auto
have vd_enrich: "valid (enrich_proc s p p')" using a1 by (auto dest:valid.cases)
show "valid (ReadFile p' fd # ReadFile p fd # enrich_proc s p p')"
proof-
have "os_grant (ReadFile p fd # enrich_proc s p p') (ReadFile p' fd)"
using a1 a2 a4 vd os nodel
apply (clarsimp simp:current_files_simps enrich_proc_dup_in enrich_proc_dup_ffds_eq_fds)
apply (simp add:proc_file_fds_def)
apply (rule conjI)
apply (rule_tac x = f in exI, simp add:enrich_proc_dup_ffd)
using enrich_proc_cur_files
apply (simp)
apply (drule enrich_proc_dup_fflags)
apply simp_all
apply (erule disjE)
apply auto
apply (simp add:is_read_flag_def)
done
moreover have "grant (ReadFile p fd # enrich_proc s p p') (ReadFile p' fd)"
proof-
from grant obtain f sp sfd sf where p1: "file_of_proc_fd s p fd = Some f"
and p2: "sectxt_of_obj s (O_proc p) = Some sp"
and p3: "sectxt_of_obj s (O_fd p fd) = Some sfd"
and p4: "sectxt_of_obj s (O_file f) = Some sf"
by (auto split:option.splits)
from os obtain flag where p0: "flags_of_proc_fd s p fd = Some flag"
by auto
from os have f_in_s: "f \<in> current_files s" using p1 by simp
from p1 vd have isfile_s: "is_file s f" by (erule_tac file_of_pfd_is_file, simp)
hence isfile_s': "is_file (enrich_proc s p p') f"
using vd nodel all_procs a2
by (auto simp:enrich_proc_is_file)
from p0 obtain flag' where p0': "flags_of_proc_fd (enrich_proc s p p') p' fd = Some flag'"
and p0'': "(flag' = flag) \<or> (flag' = remove_create_flag flag)"
using a2 a4 vd
apply (drule_tac enrich_proc_dup_fflags)
apply auto
apply (case_tac flag, auto)
apply (case_tac flag, auto)
done
from p1 have p1': "file_of_proc_fd (enrich_proc s p p') p' fd = Some f"
using a2 a4 vd
by (simp add:enrich_proc_dup_ffd)
from p2 have p2': "sectxt_of_obj (enrich_proc s p p') (O_proc p') = Some sp"
using dup_sp
by (auto simp:cp2sproc_def split:option.splits)
from p3 p1 p1' p0 p0' os have p3': "sectxt_of_obj (enrich_proc s p p') (O_fd p' fd) = Some sfd"
using dup_sfd
apply (erule_tac x = fd in allE)
apply (auto simp:proc_file_fds_def cfd2sfd_def split:option.splits)
apply (drule current_file_has_sfile')
apply (simp add:vd, simp)
apply (drule current_file_has_sfile')
apply (simp add:vd, simp)
done
from p4 have p4': "sectxt_of_obj (enrich_proc s p p') (O_file f) = Some sf"
using f_in_s cf2sf isfile_s isfile_s' a1 vd_enrich vd
apply (erule_tac x = f in allE)
apply (simp)
apply (auto simp:cf2sfile_def split:option.splits
dest!:current_has_sec' get_pfs_secs_prop' dest:parentf_is_dir is_file_in_current)
apply (case_tac f, simp, drule root_is_dir', simp, simp, simp)
done
show ?thesis using p1' p2' p3' p4' a1
apply (simp add:sectxt_of_obj_simps)
using grant p1 p2 p3 p4
apply simp
done
qed
ultimately show ?thesis
using a1
by (erule_tac valid.intros(2), simp+)
qed
qed
ultimately show ?thesis
using vd_enrich created_cons vd_cons' all_procs_cons
apply (case_tac e)
apply (auto simp:is_created_proc_simps split:if_splits)
done
qed
have sec_proc:
"\<And> tp. \<lbrakk>tp \<in> current_procs s; is_created_proc s p\<rbrakk>
\<Longrightarrow> sectxt_of_obj (enrich_proc s p p') (O_proc tp) = sectxt_of_obj s (O_proc tp)"
using pre
apply (clarsimp)
apply (erule_tac x = tp in allE, auto simp:cp2sproc_def split:option.splits)
done
have sf_cons:
"\<forall>f. f \<in> current_files (e # s) \<longrightarrow> cf2sfile (enrich_proc (e # s) p p') f = cf2sfile (e # s) f"
proof clarify
fix f
assume a1: "f \<in> current_files (e # s)"
from pre have pre_sf: "\<And> f. \<lbrakk>f \<in> current_files s; is_created_proc s p\<rbrakk>
\<Longrightarrow> cf2sfile (enrich_proc s p p') f = cf2sfile s f"
by auto
from a1 have a1': "f \<in> current_files (enrich_proc (e # s) p p')"
using vd_cons' nodel_cons
by (simp add:enrich_proc_cur_files)
from a1 have a1'': "f \<in> current_files (e # enrich_proc s p p')"
using vd_cons' nodel_cons os vd vd_enrich created_cons
apply (case_tac e)
apply (auto simp:enrich_proc_cur_files current_files_simps is_created_proc_simps
dest:is_file_in_current is_dir_in_current split:option.splits)
done
have sec_dir:
"\<And> tf. \<lbrakk>is_dir s tf; is_created_proc s p\<rbrakk>
\<Longrightarrow> sectxt_of_obj (enrich_proc s p p') (O_dir tf) = sectxt_of_obj s (O_dir tf)"
proof-
fix tf
assume a1: "is_dir s tf" and a2: "is_created_proc s p"
from a2 pre
have pre': "\<And>f. f \<in> current_files s \<Longrightarrow> cf2sfile (enrich_proc s p p') f = cf2sfile s f"
and vd_enrich: "valid (enrich_proc s p p')"
by auto
hence csf: "cf2sfile (enrich_proc s p p') tf = cf2sfile s tf"
using a1 by (auto simp:is_dir_in_current)
from a1 obtain sf where csf_some: "cf2sfile s tf = Some sf"
apply (case_tac "cf2sfile s tf")
apply (drule current_file_has_sfile')
apply (simp add:vd, simp add:is_dir_in_current, simp)
done
from a1 have a1': "is_dir (enrich_proc s p p') tf"
using enrich_proc_is_dir vd nodel all_procs by simp
from a1 have a3: "\<not> is_file s tf" using vd by (simp add:is_dir_not_file)
from a1' vd have a3': "\<not> is_file (enrich_proc s p p') tf" by (simp add:is_dir_not_file)
show "sectxt_of_obj (enrich_proc s p p') (O_dir tf) = sectxt_of_obj s (O_dir tf)"
using csf csf_some a3 a3' vd_enrich vd
apply (auto simp:cf2sfile_def split:option.splits)
apply (case_tac tf)
apply (simp add:root_sec_remains, simp)
done
qed
have sec_file:
"\<And> tf. \<lbrakk>is_file s tf; is_created_proc s p\<rbrakk>
\<Longrightarrow> sectxt_of_obj (enrich_proc s p p') (O_file tf) = sectxt_of_obj s (O_file tf)"
proof-
fix tf
assume a1: "is_file s tf" and a2: "is_created_proc s p"
from a2 pre
have pre': "\<And>f. f \<in> current_files s \<Longrightarrow> cf2sfile (enrich_proc s p p') f = cf2sfile s f"
and vd_enrich: "valid (enrich_proc s p p')"
by auto
hence csf: "cf2sfile (enrich_proc s p p') tf = cf2sfile s tf"
using a1 by (auto simp:is_file_in_current)
from a1 obtain sf where csf_some: "cf2sfile s tf = Some sf"
apply (case_tac "cf2sfile s tf")
apply (drule current_file_has_sfile')
apply (simp add:vd, simp add:is_file_in_current, simp)
done
from a1 have a1': "is_file (enrich_proc s p p') tf"
using vd nodel all_procs by (simp add:enrich_proc_is_file)
show "sectxt_of_obj (enrich_proc s p p') (O_file tf) = sectxt_of_obj s (O_file tf)"
using csf csf_some vd_enrich vd a1 a1'
apply (auto simp:cf2sfile_def split:option.splits if_splits)
apply (case_tac tf, simp_all)
apply (drule root_is_dir', simp+)
done
qed
have secs_dir:
"\<And> tf ctxts'. \<lbrakk>is_dir s tf; is_created_proc s p; get_parentfs_ctxts s tf = Some ctxts'\<rbrakk>
\<Longrightarrow> \<exists> ctxts. get_parentfs_ctxts (enrich_proc s p p') tf = Some ctxts \<and> set ctxts = set ctxts'"
proof-
fix tf ctxts'
assume a1: "is_dir s tf" and a2: "is_created_proc s p"
and a4: "get_parentfs_ctxts s tf = Some ctxts'"
from a2 pre
have pre': "\<And>f. f \<in> current_files s \<Longrightarrow> cf2sfile (enrich_proc s p p') f = cf2sfile s f"
and vd_enrich': "valid (enrich_proc s p p')"
by auto
hence csf: "cf2sfile (enrich_proc s p p') tf = cf2sfile s tf"
using a1 by (auto simp:is_dir_in_current)
from a1 obtain sf where csf_some: "cf2sfile s tf = Some sf"
apply (case_tac "cf2sfile s tf")
apply (drule current_file_has_sfile')
apply (simp add:vd, simp add:is_dir_in_current, simp)
done
from a1 have a1': "is_dir (enrich_proc s p p') tf"
using enrich_proc_is_dir vd nodel all_procs by simp
from a1 have a5: "\<not> is_file s tf" using vd by (simp add:is_dir_not_file)
from a1' vd have a5': "\<not> is_file (enrich_proc s p p') tf" by (simp add:is_dir_not_file)
from a1' pre_vd a2 obtain ctxts
where a3: "get_parentfs_ctxts (enrich_proc s p p') tf = Some ctxts"
apply (case_tac "get_parentfs_ctxts (enrich_proc s p p') tf")
apply (drule get_pfs_secs_prop', simp+)
done
moreover have "set ctxts = set ctxts'"
proof (cases tf)
case Nil
with a3 a4 vd vd_enrich'
show ?thesis
by (simp add:get_parentfs_ctxts.simps root_sec_remains split:option.splits)
next
case (Cons a ff)
with csf csf_some a5 a5' vd_enrich' vd a3 a4
show ?thesis
apply (auto simp:cf2sfile_def split:option.splits if_splits)
done
qed
ultimately
show "\<exists> ctxts. get_parentfs_ctxts (enrich_proc s p p') tf = Some ctxts \<and> set ctxts = set ctxts'"
by auto
qed
have b1: "\<And> proc f' flags fd' opt. e = Open proc f' flags fd' opt
\<Longrightarrow> cf2sfile (enrich_proc (e # s) p p') f = cf2sfile (e # s) f"
proof-
fix proc f' flags fd' opt
assume ev: "e = Open proc f' flags fd' opt"
have b1': "cf2sfile (e # enrich_proc s p p') f = cf2sfile (e # s) f"
proof (cases opt)
case None
thus ?thesis
using vd_cons' vd_enrich a1 created_cons
by (simp add:cf2sfile_open_none ev pre_sf
is_created_proc_simps current_files_simps)
next
case (Some inum)
show ?thesis
proof (cases "f' = f")
case True
from a1 obtain sf where csf: "cf2sfile (e # s) f = Some sf"
apply (case_tac "cf2sfile (e # s) f")
apply (drule current_file_has_sfile')
apply (simp add:vd_cons', simp, simp)
done
from a1 ev os Some True obtain pf where parent: "parent f = Some pf"
and pdir: "is_dir s pf" and proc_in: "proc \<in> current_procs s" by auto
have f_in: "f \<in> current_files (e # enrich_proc s p p')"
using ev True Some
by (simp add:current_files_open)
thus ?thesis using ev Some csf vd_enrich True created_cons vd_cons' a1 parent pdir proc_in
apply (simp add:is_created_proc_simps cf2sfile_open)
apply (simp add:sectxt_of_obj_simps sec_dir sec_proc split:option.splits)
apply (drule_tac tf = pf in secs_dir, simp+)
apply (erule exE, erule conjE, simp)
apply (case_tac aa, simp)
done
next
case False
have f_in: "f \<in> current_files (e # enrich_proc s p p')"
using ev False Some vd_enrich a1 created_cons nodel vd
by (simp add:current_files_open is_created_proc_simps enrich_proc_cur_files)
with ev Some a1 vd_enrich vd_cons' created_cons False
show ?thesis
apply (simp add:is_created_proc_simps cf2sfile_open)
apply (simp add:current_files_simps pre_sf)
done
qed
qed
show "cf2sfile (enrich_proc (e # s) p p') f = cf2sfile (e # s) f"
using ev vd_enrich_cons
apply simp
apply (rule conjI, rule impI)
apply (simp add:cf2sfile_open_none)
using b1' apply (auto dest:vd_cons)
done
qed
have b2: "\<And> proc f' inum. e = Mkdir proc f' inum
\<Longrightarrow> cf2sfile (enrich_proc (e # s) p p') f = cf2sfile (e # s) f"
proof-
fix proc f' inum
assume ev: "e = Mkdir proc f' inum"
show "cf2sfile (enrich_proc (e # s) p p') f = cf2sfile (e # s) f"
proof (cases "f' = f")
case True
from a1 obtain sf where csf: "cf2sfile (e # s) f = Some sf"
apply (case_tac "cf2sfile (e # s) f")
apply (drule current_file_has_sfile')
apply (simp add:vd_cons', simp, simp)
done
from a1 ev os True obtain pf where parent: "parent f = Some pf"
and pdir: "is_dir s pf" and proc_in: "proc \<in> current_procs s" by auto
have f_in: "f \<in> current_files (e # enrich_proc s p p')"
using ev True
by (simp add:current_files_mkdir)
thus ?thesis using ev csf vd_enrich True created_cons vd_cons' a1 parent pdir proc_in
apply (simp add:is_created_proc_simps cf2sfile_mkdir)
apply (simp add:sectxt_of_obj_simps sec_dir sec_proc split:option.splits)
apply (drule_tac tf = pf in secs_dir, simp+)
apply (erule exE, erule conjE, simp)
apply (case_tac aa, simp)
done
next
case False
have f_in: "f \<in> current_files (e # enrich_proc s p p')"
using ev False vd_enrich a1 created_cons nodel vd
by (simp add:current_files_mkdir is_created_proc_simps enrich_proc_cur_files)
with ev a1 vd_enrich vd_cons' created_cons False
show ?thesis
apply (simp add:is_created_proc_simps cf2sfile_mkdir)
apply (simp add:current_files_simps pre_sf)
done
qed
qed
have b3: "\<And> proc f' f''. e = LinkHard proc f' f''
\<Longrightarrow> cf2sfile (enrich_proc (e # s) p p') f = cf2sfile (e # s) f"
proof-
fix proc f' f''
assume ev: "e = LinkHard proc f' f''"
show "cf2sfile (enrich_proc (e # s) p p') f = cf2sfile (e # s) f"
proof (cases "f'' = f")
case True
from a1 obtain sf where csf: "cf2sfile (e # s) f = Some sf"
apply (case_tac "cf2sfile (e # s) f")
apply (drule current_file_has_sfile')
apply (simp add:vd_cons', simp, simp)
done
from a1 ev os True obtain pf where parent: "parent f'' = Some pf"
and pdir: "is_dir s pf" and proc_in: "proc \<in> current_procs s" by auto
have f_in: "f \<in> current_files (e # enrich_proc s p p')"
using ev True vd_enrich created_cons
by (simp add:current_files_simps is_created_proc_simps)
thus ?thesis using ev csf vd_enrich True created_cons vd_cons' a1 parent pdir proc_in
apply (simp add:is_created_proc_simps cf2sfile_linkhard)
apply (simp add:sectxt_of_obj_simps sec_dir sec_proc split:option.splits)
apply (drule_tac tf = pf in secs_dir, simp+)
apply (erule exE, erule conjE, simp)
apply (case_tac aa, simp)
done
next
case False
have f_in: "f \<in> current_files (e # enrich_proc s p p')"
using ev False vd_enrich a1 created_cons nodel vd vd_cons'
by (simp add:current_files_linkhard is_created_proc_simps enrich_proc_cur_files)
with ev a1 vd_enrich vd_cons' created_cons False
show ?thesis
apply (simp add:is_created_proc_simps cf2sfile_linkhard)
apply (simp add:current_files_simps pre_sf)
done
qed
qed
show "cf2sfile (enrich_proc (e # s) p p') f = cf2sfile (e # s) f"
apply (case_tac e)
prefer 6 apply (erule b1)
prefer 11 apply (erule b2)
prefer 11 apply (erule b3)
using vd created_cons nodel_cons vd_enrich_cons vd_cons' a1 a1'
apply (auto intro!:pre_sf simp:cf2sfile_simps is_created_proc_simps current_files_simps
split:if_splits dest:vd_cons cf2sfile_other')
done
qed
moreover have "\<forall>tp fd. fd \<in> proc_file_fds (e # s) tp \<longrightarrow>
cfd2sfd (enrich_proc (e # s) p p') tp fd = cfd2sfd (e # s) tp fd"
proof clarify
fix tp fd
assume a1: "fd \<in> proc_file_fds (e # s) tp"
from a1 obtain f where a1': "file_of_proc_fd (e # s) tp fd = Some f"
by (auto simp:proc_file_fds_def)
from pre have pre_sfd: "\<And> tp fd. \<lbrakk>fd \<in> proc_file_fds s tp; is_created_proc s p\<rbrakk> \<Longrightarrow>
cfd2sfd (enrich_proc s p p') tp fd = cfd2sfd s tp fd" by auto
hence pre_sfd': "\<And> tp fd f. \<lbrakk>file_of_proc_fd s tp fd = Some f; is_created_proc s p\<rbrakk> \<Longrightarrow>
cfd2sfd (enrich_proc s p p') tp fd = cfd2sfd s tp fd" by (auto simp:proc_file_fds_def)
hence pre_sfd'': "\<And> tp fd f proc. \<lbrakk>file_of_proc_fd s tp fd = Some f; is_created_proc s p; p = proc\<rbrakk> \<Longrightarrow>
cfd2sfd (enrich_proc s proc p') tp fd = cfd2sfd s tp fd" by (auto simp:proc_file_fds_def)
from a1' all_procs_cons vd_cons' have a2: "tp \<noteq> p'"
apply (drule_tac not_all_procs_prop3)
apply (drule proc_fd_in_procs, simp)
by (rule notI, simp)
have a3: "p' \<noteq> p" using all_procs_cons created_cons
apply (drule_tac not_all_procs_prop3)
apply (rule notI, simp add:is_created_proc_def)
done
have a4: "file_of_proc_fd (enrich_proc (e # s) p p') tp fd = Some f"
using a1' nodel_cons all_procs_cons a1' created_cons vd_cons'
apply (frule_tac enrich_proc_filefd, simp_all)
done
have sec_proc:
"\<And> tp. \<lbrakk>tp \<in> current_procs s; is_created_proc s p\<rbrakk>
\<Longrightarrow> sectxt_of_obj (enrich_proc s p p') (O_proc tp) = sectxt_of_obj s (O_proc tp)"
using pre
apply (clarsimp)
apply (erule_tac x = tp in allE, auto simp:cp2sproc_def split:option.splits)
done
have sec_proc':
"\<And> tp. \<lbrakk>tp \<in> current_procs s; is_created_proc s p; p = tp\<rbrakk>
\<Longrightarrow> sectxt_of_obj (enrich_proc s tp p') (O_proc tp) = sectxt_of_obj s (O_proc tp)"
apply (drule_tac sec_proc, simp+)
done
show "cfd2sfd (enrich_proc (e # s) p p') tp fd = cfd2sfd (e # s) tp fd"
proof-
have b1: "\<And> proc f' fds. e = Execve proc f' fds
\<Longrightarrow> cfd2sfd (enrich_proc (e # s) p p') tp fd = cfd2sfd (e # s) tp fd"
using a4 vd_enrich_cons a1' vd_cons' created_cons
apply (simp split:if_splits del:file_of_proc_fd.simps add:a2)
apply (simp only:cfd2sfd_execve)
apply (drule_tac s = "Execve proc f' fds # enrich_proc s proc p'" in vd_cons)
apply (simp split:if_splits add:a2)
apply (drule_tac p' = proc and fd' = fd and s = "enrich_proc s proc p'" in cfd2sfd_execve, simp+)
apply (erule_tac pre_sfd'', simp add:is_created_proc_simps, simp)
apply (drule_tac p' = tp and fd' = fd in cfd2sfd_execve, simp+)
apply (erule_tac pre_sfd'', simp add:is_created_proc_simps, simp)
apply (simp only:cfd2sfd_execve)
apply (rule_tac pre_sfd')
apply (auto split:if_splits simp:is_created_proc_simps)
done
have b2: "\<And> proc proc' fds. e = Clone proc proc' fds
\<Longrightarrow> cfd2sfd (enrich_proc (e # s) p p') tp fd = cfd2sfd (e # s) tp fd"
using a4 vd_enrich_cons a1' vd_cons' created_cons
apply (simp split:if_splits del:file_of_proc_fd.simps)
apply (simp add:cfd2sfd_clone add:a2)
apply (simp add:cfd2sfd_clone split:if_splits)
apply (erule pre_sfd'', simp add:is_created_proc_simps, simp)
apply (erule pre_sfd', simp add:is_created_proc_simps)
done
have b3: "\<And> proc f' flags fd' opt. e = Open proc f' flags fd' opt
\<Longrightarrow> cfd2sfd (enrich_proc (e # s) p p') tp fd = cfd2sfd (e # s) tp fd"
using a4 a1' vd_enrich_cons vd_cons' created_cons
apply (simp split:if_splits del:file_of_proc_fd.simps)
apply (simp add:cfd2sfd_open sec_open is_created_proc_simps a2 del:file_of_proc_fd.simps)
apply (tactic {*my_clarify_tac 1*})
apply (drule vd_cons)
apply (simp add:cfd2sfd_open sec_open a3 a2 split:if_splits)
apply (case_tac "proc \<in> current_procs s")
apply (simp add:sec_proc')
apply (case_tac "sectxt_of_obj s (O_proc proc)", simp+)
apply (case_tac "f \<in> current_files (e # s)")
apply (drule sf_cons[rule_format], simp)
using vd_enrich_cons
apply (simp add:cf2sfile_open_none)
using os
apply (simp add:current_files_simps is_file_in_current split:option.splits)
using os
apply (simp split:option.splits)
apply (rule impI)
apply (simp add:cfd2sfd_open sec_open a3 a2 split:if_splits)
apply (drule vd_cons)
apply (drule_tac p' = tp and fd' = fd and f' = f and s = "enrich_proc s proc p'" in cfd2sfd_open)
apply (simp, rule impI, simp)
apply (simp split:if_splits, rule conjI, rule impI, simp)
apply (drule pre_sfd', simp, simp)
apply (simp add:cfd2sfd_open sec_open is_created_proc_simps a2 del:file_of_proc_fd.simps)
apply (case_tac "proc \<in> current_procs s")
apply (simp add:sec_proc)
apply (case_tac "f' \<in> current_files (e # s)")
apply (drule sf_cons[rule_format], simp)
apply (simp split:option.splits)
apply (rule impI|rule conjI)+
apply (drule current_has_sec', simp add:vd, simp add:os)
apply (rule impI, rule impI)
apply (simp split:if_splits)
apply (simp add:pre_sfd')
using os
apply (simp add:current_files_simps is_file_in_current split:option.splits)
using os
apply (simp split:option.splits)
done
have b4: "\<And> proc fd'. e = ReadFile proc fd'
\<Longrightarrow> cfd2sfd (enrich_proc (e # s) p p') tp fd = cfd2sfd (e # s) tp fd"
using a4 vd_enrich_cons a1' vd_cons' created_cons
apply (simp split:if_splits del:file_of_proc_fd.simps)
apply (frule_tac s = "ReadFile proc fd' # enrich_proc s proc p'" in vd_cons)
apply (simp add:cfd2sfd_other)
apply (erule pre_sfd'', simp add:is_created_proc_simps, simp)
apply (simp add:cfd2sfd_other)
apply (erule pre_sfd', simp add:is_created_proc_simps)
done
show ?thesis
apply (case_tac e)
apply (erule b1, erule b2)
prefer 4 apply (erule b3) prefer 4 apply (erule b4)
using vd created_cons nodel_cons a1' a4 vd_enrich_cons vd_cons'
apply (auto intro!:pre_sfd' simp:cfd2sfd_simps is_created_proc_simps
simp del:file_of_proc_fd.simps split:if_splits dest:vd_cons enrich_proc_filefd)
apply (simp_all)
done
qed
qed
moreover have "\<forall>q. q \<in> current_msgqs (e # s) \<longrightarrow> cq2smsgq (enrich_proc (e # s) p p') q = cq2smsgq (e # s) q"
proof clarify
fix q
assume a1: "q \<in> current_msgqs (e # s)"
from pre have pre_smsgq: "\<And> q. \<lbrakk>q \<in> current_msgqs s; is_created_proc s p\<rbrakk>
\<Longrightarrow> cq2smsgq (enrich_proc s p p') q = cq2smsgq s q"
by auto
show "cq2smsgq (enrich_proc (e # s) p p') q = cq2smsgq (e # s) q"
using vd_enrich_cons a1 created_cons nodel_cons vd_cons' os
apply (case_tac e)
apply (auto simp:cq2smsgq_simps cq2smsg_createmsgq is_created_proc_simps sec_proc
dest:cq2smsgq_other intro!:pre_smsgq split:if_splits dest:vd_cons)
apply (simp add:sectxt_of_obj_simps split:option.splits)
thm sec_proc
thm cq2smsgq_simps
thm cq2smsg_createmsgq
sorry
moreover have "\<forall>tp. tp \<in> current_procs (e # s) \<longrightarrow> cp2sproc (enrich_proc (e # s) p p') tp = cp2sproc (e # s) tp"
sorry
moreover have "cp2sproc (enrich_proc (e # s) p p') p' = cp2sproc (e # s) p"
proof-
from pre have b0: "is_created_proc s p \<Longrightarrow> cp2sproc (enrich_proc s p p') p' = cp2sproc s p" by simp
have b1: "\<And> tp f fds. \<lbrakk>valid (enrich_proc (Execve tp f fds # s) p p'); valid (Execve tp f fds # s);
is_created_proc (Execve tp f fds # s) p; p' \<notin> all_procs (Execve tp f fds # s)\<rbrakk>
\<Longrightarrow> cp2sproc (enrich_proc (Execve tp f fds # s) p p') p' = cp2sproc (Execve tp f fds # s) p"
proof-
fix tp f fds
assume a1: "valid (enrich_proc (Execve tp f fds # s) p p')"
and a2: "valid (Execve tp f fds # s)" and a3: "is_created_proc (Execve tp f fds # s) p"
and a4: "p' \<notin> all_procs (Execve tp f fds # s)"
show "cp2sproc (enrich_proc (Execve tp f fds # s) p p') p' = cp2sproc (Execve tp f fds # s) p"
proof (cases "tp = p")
case True
show ?thesis using True a1 a2 a3 a4 b0 vd
thm not_all_procs_prop3
apply (frule_tac not_all_procs_prop2)
apply (frule not_all_procs_prop3)
apply (simp add:is_created_proc_simps)
apply (frule vd_cons) (*
apply (frule_tac vt_grant_os)
apply (frule_tac \<tau> = "enrich_proc s p p'" in vt_grant_os) *)
apply (frule_tac s = "enrich_proc s p p'" in vd_cons)
apply (frule_tac \<tau> = s in vt_grant_os)
apply (case_tac "p' = p", simp) (*
apply (auto simp add:cp2sproc_execve sectxt_of_obj_simps enrich_proc_dup_in
split:option.splits dest!:current_has_sec' dest:vt_grant is_file)
apply (simp_all add:is_created_proc_def)
apply (auto simp:cp2sproc_def)
apply (simp_all add:enrich_proc_dup_in)
apply (auto simp:sectxt_of_obj_simps split:option.splits dest:valid.cases)
*)
sorry
next
case False
show ?thesis sorry
qed
qed
have b2: "\<And> tp fd. cp2sproc (enrich_proc (ReadFile tp fd # s) p p') p' = cp2sproc (ReadFile tp fd # s) p"
sorry
have b3: "\<And> tp. cp2sproc (enrich_proc (Exit tp # s) p p') p' = cp2sproc (Exit tp # s) p"
sorry
have b4: "\<And> tp tp'. cp2sproc (enrich_proc (Kill tp tp' # s) p p') p' = cp2sproc (Kill tp tp' # s) p"
sorry
have b5: "\<And> tp tp' fds. cp2sproc (enrich_proc (Clone tp tp' fds # s) p p') p' =
cp2sproc (Clone tp tp' fds # s) p"
sorry
have b6: "\<And> tp f flags fd opt. cp2sproc (enrich_proc (Open tp f flags fd opt # s) p p') p' =
cp2sproc (Open tp f flags fd opt # s) p"
sorry
have b7: "\<And> tp fd. cp2sproc (enrich_proc (CloseFd tp fd # s) p p') p' = cp2sproc (CloseFd tp fd # s) p"
sorry
show ?thesis using vd_enrich_cons
apply (case_tac e)
using vd_cons' created_cons all_procs_cons
apply (auto intro!:b1 b2 b3 b4 b5 b6 b7 simp del:enrich_proc.simps)
using created_cons vd_enrich_cons vd_cons' b0
apply (auto simp:cp2sproc_other is_created_proc_def)
done
qed
moreover have "\<forall> fd. fd \<in> proc_file_fds (e # s) p \<longrightarrow>
cfd2sfd (enrich_proc (e # s) p p') p' fd = cfd2sfd (e # s) p fd"
sorry
ultimately show ?case using vd_enrich_cons
by simp
qed
lemma enrich_proc_s2ss:
"\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> s2ss (enrich_proc s p p') = s2ss s"
lemma enrich_proc_valid:
"\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> valid (enrich_proc s p p')"
by (auto dest:enrich_proc_prop)
lemma enrich_proc_valid:
"\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> "
lemma enrich_proc_tainted:
"\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk>
\<Longrightarrow> tainted (enrich_proc s p p') = (if (O_proc p \<in> tainted s)
then tainted s \<union> {O_proc p'} else tainted s)"
apply (induct s)
apply (simp add:is_created_proc_def)
apply (frule vt_grant_os, frule vd_cons, simp)
apply (frule enrich_proc_dup_in, simp+)
apply (frule not_all_procs_prop3)
apply (case_tac a)
prefer 3
apply (simp split:if_splits)
apply (rule impI|rule conjI)+
apply (simp add:is_created_proc_def)
apply (auto simp:is_created_proc_def split:if_splits dest:tainted_in_current)[1]
apply (simp add:is_created_proc_def)
prefer 4
apply (simp split:if_splits)
apply (rule impI|rule conjI)+
apply (simp add:is_created_proc_def)
apply (auto simp:is_created_proc_def split:if_splits dest:tainted_in_current)[1]
apply (simp add:is_created_proc_def)
prefer 4
apply (auto simp:is_created_proc_def split:if_splits option.splits dest:tainted_in_current)[1]
prefer 4
apply (auto simp:is_created_proc_def split:if_splits option.splits dest:tainted_in_current enrich_proc_dup_ffd enrich_proc_dup_ffd')[1]
lemma enrich_proc_dup_tainted:
"\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk>
\<Longrightarrow> (O_proc p' \<in> tainted (enrich_proc s p p')) = (O_proc p \<in> tainted s)"
apply (induct s)
apply (simp add:is_created_proc_def)
apply (frule vt_grant_os, frule vd_cons)
apply (case_tac a)
apply (auto simp:is_created_proc_def)[1]
lemma enrich_proc_tainted:
end
end