--- a/no_shm_selinux/Enrich.thy Mon Dec 23 19:47:17 2013 +0800
+++ b/no_shm_selinux/Enrich.thy Thu Dec 26 10:56:50 2013 +0800
@@ -3,6 +3,7 @@
Temp
begin
+(* objects that need dynamic indexing, all nature-numbers *)
datatype t_enrich_obj =
E_proc "t_process"
| E_file "t_file"
@@ -13,6 +14,110 @@
context tainting_s begin
+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 (Exit p # s) = 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>"
+
+fun all_inums :: "t_state \<Rightarrow> t_inode_num set"
+where
+ "all_inums [] = current_inode_nums []"
+| "all_inums (Open p f flags fd opt # s) = (
+ case opt of
+ None \<Rightarrow> all_inums s
+ | Some i \<Rightarrow> all_inums s \<union> {i} )"
+| "all_inums (Mkdir p f i # s) = (all_inums s \<union> {i})"
+| "all_inums (CreateSock p af st fd i # s) = (all_inums s \<union> {i})"
+| "all_inums (Accept p fd addr lport fd' i # s) = (all_inums s \<union> {i})"
+| "all_inums (_ # s) = all_inums s"
+
+fun all_fds :: "t_state \<Rightarrow> t_process \<Rightarrow> t_fd set"
+where
+ "all_fds [] = init_fds_of_proc"
+| "all_fds (Open p f flags fd ipt # s) = (all_fds s) (p := all_fds s p \<union> {fd})"
+| "all_fds (CreateSock p sf st fd i # s) = (all_fds s) (p := all_fds s p \<union> {fd})"
+| "all_fds (Accept p fd' raddr port fd i # s) = (all_fds s) (p := all_fds s p \<union> {fd})"
+| "all_fds (Clone p p' fds # s) = (all_fds s) (p' := fds)"
+| "all_fds (_ # s) = all_fds s"
+
+fun all_msgqs:: "t_state \<Rightarrow> t_msgq set"
+where
+ "all_msgqs [] = init_msgqs"
+| "all_msgqs (CreateMsgq p q # s) = all_msgqs s \<union> {q}"
+| "all_msgqs (e # s) = all_msgqs s"
+
+fun all_msgs:: "t_state \<Rightarrow> t_msgq \<Rightarrow> t_msg set"
+where
+ "all_msgs [] q = set (init_msgs_of_queue q)"
+| "all_msgs (CreateMsgq p q # s) q' = (if q' = q then {} else all_msgs s q')"
+| "all_msgs (SendMsg p q m # s) q' = (if q' = q then all_msgs s q \<union> {m} else all_msgs s q')"
+| "all_msgs (_ # s) q' = all_msgs s q'"
+
+fun all_files:: "t_state \<Rightarrow> t_file set"
+where
+ "all_files [] = init_files "
+| "all_files (Open p f flags fd opt # s) = (if opt = None then all_files s else (all_files s \<union> {f}))"
+| "all_files (Mkdir p f inum # s) = all_files s \<union> {f}"
+| "all_files (LinkHard p f f' # s) = all_files s \<union> {f'}"
+| "all_files (e # s) = all_files s"
+
+fun notin_all:: "t_state \<Rightarrow> t_enrich_obj \<Rightarrow> bool"
+where
+ "notin_all s (E_proc p) = (p \<notin> all_procs s)"
+| "notin_all s (E_file f) = (f \<notin> all_files s \<and> (\<exists> pf. parent f = Some pf \<and> is_dir s pf))"
+| "notin_all s (E_fd p fd) = (fd \<notin> all_fds s p)"
+| "notin_all s (E_inum i) = (i \<notin> all_inums s)"
+| "notin_all s (E_msgq q) = (q \<notin> all_msgqs s)"
+| "notin_all s (E_msg q m) = (m \<notin> all_msgs s q)"
+
+lemma not_all_procs_cons:
+ "p \<notin> all_procs (e # s) \<Longrightarrow> p \<notin> all_procs s"
+by (case_tac e, auto)
+
+lemma not_all_procs_prop:
+ "\<lbrakk>p' \<notin> all_procs s; p \<in> current_procs s; valid s\<rbrakk> \<Longrightarrow> p' \<noteq> p"
+apply (induct s, rule notI, simp)
+apply (frule vt_grant_os, frule vd_cons, frule not_all_procs_cons, simp, rule notI)
+apply (case_tac a, auto)
+done
+
+lemma not_all_procs_prop2:
+ "p' \<notin> all_procs s \<Longrightarrow> p' \<notin> init_procs"
+apply (induct s, simp)
+by (case_tac a, auto)
+
+lemma not_all_procs_prop3:
+ "p' \<notin> all_procs s \<Longrightarrow> p' \<notin> current_procs s"
+apply (induct s, simp)
+by (case_tac a, auto)
+
+fun enrich_not_alive :: "t_state \<Rightarrow> t_enrich_obj \<Rightarrow> t_enrich_obj \<Rightarrow> bool"
+where
+ "enrich_not_alive s obj (E_file f) = (f \<notin> current_files s \<and> E_file f \<noteq> obj)"
+| "enrich_not_alive s obj (E_proc p) = (p \<notin> current_procs s \<and> E_proc p \<noteq> obj)"
+| "enrich_not_alive s obj (E_fd p fd) = ((p \<in> current_procs s \<longrightarrow> fd \<notin> current_proc_fds s p) \<and> E_fd p fd \<noteq> obj)"
+| "enrich_not_alive s obj (E_msgq q) = (q \<notin> current_msgqs s \<and> E_msgq q \<noteq> obj)"
+| "enrich_not_alive s obj (E_inum i) = (i \<notin> current_inode_nums s \<and> E_inum i \<noteq> obj)"
+| "enrich_not_alive s obj (E_msg q m) = ((q \<in> current_msgqs s \<longrightarrow> m \<notin> set (msgs_of_queue s q)) \<and> E_msg q m \<noteq> obj)"
+
+lemma file_has_parent: "\<lbrakk>is_file s f; valid s\<rbrakk> \<Longrightarrow> \<exists> pf. is_dir s pf \<and> parent f = Some pf"
+apply (case_tac f)
+apply (simp, drule root_is_dir', simp+)
+apply (simp add:parentf_is_dir_prop2)
+done
+
(* enrich s target_proc duplicated_pro *)
fun enrich_proc :: "t_state \<Rightarrow> t_process \<Rightarrow> t_process \<Rightarrow> t_state"
where
@@ -33,10 +138,12 @@
if (tp = p)
then ReadFile dp fd # ReadFile p fd # (enrich_proc s tp dp)
else ReadFile p fd # (enrich_proc s tp dp))"
+(*
| "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)
@@ -47,14 +154,41 @@
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 = e # (enrich_proc s tp dp)"
+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 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_search_check:
assumes grant: "search_check s (up, rp, tp) f"
and cf2sf: "\<forall> f. f \<in> current_files s \<longrightarrow> cf2sfile s' f = cf2sfile s f"
@@ -214,37 +348,11 @@
by (auto simp:inherit_fds_check_def inherit_fds_check_ctxt_def)
qed
-lemma not_all_procs_cons:
- "p \<notin> all_procs (e # s) \<Longrightarrow> p \<notin> all_procs s"
-by (case_tac e, auto)
-
-lemma not_all_procs_prop:
- "\<lbrakk>p' \<notin> all_procs s; p \<in> current_procs s; valid s\<rbrakk> \<Longrightarrow> p' \<noteq> p"
-apply (induct s, rule notI, simp)
-apply (frule vt_grant_os, frule vd_cons, frule not_all_procs_cons, simp, rule notI)
-apply (case_tac a, auto)
-done
-
-fun enrich_not_alive :: "t_state \<Rightarrow> t_enrich_obj \<Rightarrow> bool"
-where
- "enrich_not_alive s (E_file f) = (f \<notin> current_files s)"
-| "enrich_not_alive s (E_proc p) = (p \<notin> current_procs s)"
-| "enrich_not_alive s (E_fd p fd) = (p \<in> current_procs s \<longrightarrow> fd \<notin> current_proc_fds s p)"
-| "enrich_not_alive s (E_msgq q) = (q \<notin> current_msgqs s)"
-| "enrich_not_alive s (E_inum i) = (i \<notin> current_inode_nums s)"
-| "enrich_not_alive s (E_msg q m) = (q \<in> current_msgqs s \<longrightarrow> m \<notin> set (msgs_of_queue s q))"
-
-lemma file_has_parent: "\<lbrakk>is_file s f; valid s\<rbrakk> \<Longrightarrow> \<exists> pf. is_dir s pf \<and> parent f = Some pf"
-apply (case_tac f)
-apply (simp, drule root_is_dir', simp+)
-apply (simp add:parentf_is_dir_prop2)
-done
lemma enrich_valid_intro_cons:
- assumes vs': "valid s'"
- and os: "os_grant s e" and grant: "grant s e" and vd: "valid s"
+ assumes vs': "valid s'" and vd': "valid (e # s)"
and alive: "\<forall> obj. alive s obj \<longrightarrow> alive s' obj"
- and alive': "\<forall> obj. enrich_not_alive s obj \<longrightarrow> enrich_not_alive s' obj"
+ and alive': "\<forall> obj. enrich_not_alive s obj' obj \<longrightarrow> enrich_not_alive s' obj' obj"
and hungs: "files_hung_by_del s' = files_hung_by_del s"
and cp2sp: "\<forall> p. p \<in> current_procs s \<longrightarrow> cp2sproc s' p = cp2sproc s p"
and cf2sf: "\<forall> f. f \<in> current_files s \<longrightarrow> cf2sfile s' f = cf2sfile s f"
@@ -254,244 +362,569 @@
and sms_remain: "\<forall> q. msgs_of_queue s' q = msgs_of_queue s q"
(* and empty_remain: "\<forall> f. dir_is_empty s f \<longrightarrow> dir_is_empty s' f" *)
and cfd2sfd: "\<forall> p fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd s' p fd = cfd2sfd s p fd"
+ and nodel: "no_del_event (e # s)"
+ and notin_all: "notin_all (e # s) obj'"
shows "valid (e # s')"
-proof (cases e)
- case (Execve p f fds)
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:Execve)
- have f_in: "is_file s' f" using os alive
- apply (erule_tac x = "O_file f" in allE)
- by (auto simp:Execve)
- have fd_in: "fds \<subseteq> proc_file_fds s' p" using os alive ffd_remain
- by (auto simp:Execve proc_file_fds_def)
- have "os_grant s' e" using p_in f_in fd_in by (simp add:Execve)
- moreover have "grant s' e"
- 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 add:Execve 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 add:Execve split:option.splits del:npctxt_execve.simps, blast)
- from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
- using os cp2sp
- apply (erule_tac x = p in allE)
- by (auto simp:Execve co2sobj.simps cp2sproc_def split:option.splits)
- from os have f_in': "is_file s f" by (simp add:Execve)
- from vd os have "\<exists> sf. cf2sfile s f = Some sf"
- by (auto dest!:is_file_in_current current_file_has_sfile simp:Execve)
- hence p2': "sectxt_of_obj s' (O_file f) = Some (uf, rf, tf)" using f_in f_in' p2 cf2sf
- apply (erule_tac x = f in allE)
- apply (auto dest:is_file_in_current simp:cf2sfile_def split:option.splits)
- apply (case_tac f, simp)
- apply (drule_tac s = s in root_is_dir', simp add:vd, simp+)
- done
- have "inherit_fds_check s' (pu, nr, nt) p fds"
- proof-
- have "fds \<subseteq> proc_file_fds s' p" using os ffd_remain Execve
- by (auto simp:proc_file_fds_def)
- thus ?thesis using Execve grant vd cfd2sfd p1 p2 p3 os
- apply (rule_tac s = s in enrich_inherit_fds_check)
- by (simp_all split:option.splits)
- qed
- moreover have "search_check s' (pu, rp, tp) f"
- using p1 p2 p2' vd cf2sf f_in' grant Execve p3 f_in
- apply (rule_tac s = s in enrich_search_check)
- by (simp_all split:option.splits)
- ultimately show ?thesis using p1' p2' p3
- apply (simp add:Execve split:option.splits)
- using grant Execve p1 p2
- by (simp add:Execve grant p1 p2)
- qed
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (Clone p p' fds)
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:Clone)
- have p'_not_in: "p' \<notin> current_procs s'" using os alive'
- apply (erule_tac x = "E_proc p'" in allE)
- by (auto simp:Clone)
- have fd_in: "fds \<subseteq> proc_file_fds s' p" using os alive ffd_remain
- by (auto simp:Clone proc_file_fds_def)
- have "os_grant s' e" using p_in p'_not_in fd_in by (simp add:Clone)
- moreover have "grant s' e"
- proof-
- from grant obtain up rp tp
- where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
- apply (simp add:Clone split:option.splits)
- by (case_tac a, auto)
- from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
- using os cp2sp
- apply (erule_tac x = p in allE)
- by (auto simp:Clone co2sobj.simps cp2sproc_def split:option.splits)
- have p2: "inherit_fds_check s' (up, rp, tp) p fds"
- proof-
- have "fds \<subseteq> proc_file_fds s' p" using os ffd_remain Clone
- by (auto simp:proc_file_fds_def)
- thus ?thesis using Clone grant vd cfd2sfd p1 os
- apply (rule_tac s = s in enrich_inherit_fds_check)
- by (simp_all split:option.splits)
- qed
- show ?thesis using p1 p2 p1' grant
- by (simp add:Clone)
- qed
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (Kill p p')
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:Kill)
- have p'_in: "p' \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p'" in allE)
- by (auto simp:Kill)
- have "os_grant s' e" using p_in p'_in by (simp add:Kill)
- moreover have "grant s' e"
- proof-
- from grant obtain up rp tp up' rp' tp'
- where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
- and p'1: "sectxt_of_obj s (O_proc p') = Some (up', rp', tp')"
- apply (simp add:Kill split:option.splits)
- by (case_tac a, case_tac aa, blast)
- from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
- using os cp2sp
- apply (erule_tac x = p in allE)
- by (auto simp:Kill co2sobj.simps cp2sproc_def split:option.splits)
- from p'1 have p'1': "sectxt_of_obj s' (O_proc p') = Some (up', rp', tp')"
- using os cp2sp
- apply (erule_tac x = p' in allE)
- by (auto simp:Kill co2sobj.simps cp2sproc_def split:option.splits)
- show ?thesis using p1 p'1 p1' p'1' grant
- by (simp add:Kill)
- qed
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (Ptrace p p')
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:Ptrace)
- have p'_in: "p' \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p'" in allE)
- by (auto simp:Ptrace)
- have "os_grant s' e" using p_in p'_in by (simp add:Ptrace)
- moreover have "grant s' e"
- proof-
- from grant obtain up rp tp up' rp' tp'
- where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
- and p'1: "sectxt_of_obj s (O_proc p') = Some (up', rp', tp')"
- apply (simp add:Ptrace split:option.splits)
- by (case_tac a, case_tac aa, blast)
- from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
- using os cp2sp
- apply (erule_tac x = p in allE)
- by (auto simp:Ptrace co2sobj.simps cp2sproc_def split:option.splits)
- from p'1 have p'1': "sectxt_of_obj s' (O_proc p') = Some (up', rp', tp')"
- using os cp2sp
- apply (erule_tac x = p' in allE)
- by (auto simp:Ptrace co2sobj.simps cp2sproc_def split:option.splits)
- show ?thesis using p1 p'1 p1' p'1' grant
- by (simp add:Ptrace)
- qed
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (Exit p)
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:Exit)
- have "os_grant s' e" using p_in by (simp add:Exit)
- moreover have "grant s' e"
- by (simp add:Exit)
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (Open p f flags fd opt)
+proof-
+ from vd' have os: "os_grant s e" and grant: "grant s e" and vd: "valid s"
+ by (auto dest:vt_grant_os vt_grant vd_cons)
show ?thesis
- proof (cases opt)
- case None
+ proof (cases e)
+ case (Execve p f fds)
have p_in: "p \<in> current_procs s'" using os alive
apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:Open None)
+ by (auto simp:Execve)
have f_in: "is_file s' f" using os alive
apply (erule_tac x = "O_file f" in allE)
- by (auto simp:Open None)
- have fd_not_in: "fd \<notin> current_proc_fds s' p"
- using os alive' p_in
- apply (erule_tac x = "E_fd p fd" in allE)
- by (simp add:Open None)
- have "os_grant s' e" using p_in f_in fd_not_in os
- by (simp add:Open None)
- moreover have "grant s' e"
+ by (auto simp:Execve)
+ have fd_in: "fds \<subseteq> proc_file_fds s' p" using os alive ffd_remain
+ by (auto simp:Execve proc_file_fds_def)
+ have "os_grant s' e" using p_in f_in fd_in by (simp add:Execve)
+ moreover have "grant s' e"
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)"
- apply (simp add:Open None split:option.splits)
- by (case_tac a, case_tac aa, blast)
+ by (simp add:Execve 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 add:Execve split:option.splits del:npctxt_execve.simps, blast)
from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
using os cp2sp
apply (erule_tac x = p in allE)
- by (auto simp:Open None co2sobj.simps cp2sproc_def split:option.splits)
- from os have f_in': "is_file s f" by (simp add:Open None)
+ by (auto simp:Execve co2sobj.simps cp2sproc_def split:option.splits)
+ from os have f_in': "is_file s f" by (simp add:Execve)
from vd os have "\<exists> sf. cf2sfile s f = Some sf"
- by (auto dest!:is_file_in_current current_file_has_sfile simp:Open None)
+ by (auto dest!:is_file_in_current current_file_has_sfile simp:Execve)
hence p2': "sectxt_of_obj s' (O_file f) = Some (uf, rf, tf)" using f_in f_in' p2 cf2sf
apply (erule_tac x = f in allE)
apply (auto dest:is_file_in_current simp:cf2sfile_def 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 s' (up, rp, tp) f"
- using p1 p2 p2' vd cf2sf f_in' grant Open None f_in
+ have "inherit_fds_check s' (pu, nr, nt) p fds"
+ proof-
+ have "fds \<subseteq> proc_file_fds s' p" using os ffd_remain Execve
+ by (auto simp:proc_file_fds_def)
+ thus ?thesis using Execve grant vd cfd2sfd p1 p2 p3 os
+ apply (rule_tac s = s in enrich_inherit_fds_check)
+ by (simp_all split:option.splits)
+ qed
+ moreover have "search_check s' (pu, rp, tp) f"
+ using p1 p2 p2' vd cf2sf f_in' grant Execve p3 f_in
apply (rule_tac s = s in enrich_search_check)
by (simp_all split:option.splits)
- thus ?thesis using p1' p2'
- apply (simp add:Open None split:option.splits)
- using grant Open None p1 p2
+ ultimately show ?thesis using p1' p2' p3
+ apply (simp add:Execve split:option.splits)
+ using grant Execve p1 p2
+ by (simp add:Execve grant p1 p2)
+ qed
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ next
+ case (Clone p p' fds)
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:Clone)
+ have p'_not_in: "p' \<notin> current_procs s'" using alive' notin_all os Clone
+ apply (erule_tac x = "E_proc p'" in allE)
+ apply (auto dest:not_all_procs_prop3)
+ done
+ have fd_in: "fds \<subseteq> proc_file_fds s' p" using os alive ffd_remain
+ by (auto simp:Clone proc_file_fds_def)
+ have "os_grant s' e" using p_in p'_not_in fd_in by (simp add:Clone)
+ moreover have "grant s' e"
+ proof-
+ from grant obtain up rp tp
+ where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
+ apply (simp add:Clone split:option.splits)
+ by (case_tac a, auto)
+ from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
+ using os cp2sp
+ apply (erule_tac x = p in allE)
+ by (auto simp:Clone co2sobj.simps cp2sproc_def split:option.splits)
+ have p2: "inherit_fds_check s' (up, rp, tp) p fds"
+ proof-
+ have "fds \<subseteq> proc_file_fds s' p" using os ffd_remain Clone
+ by (auto simp:proc_file_fds_def)
+ thus ?thesis using Clone grant vd cfd2sfd p1 os
+ apply (rule_tac s = s in enrich_inherit_fds_check)
+ by (simp_all split:option.splits)
+ qed
+ show ?thesis using p1 p2 p1' grant
+ by (simp add:Clone)
+ qed
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ next
+ case (Kill p p')
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:Kill)
+ have p'_in: "p' \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p'" in allE)
+ by (auto simp:Kill)
+ have "os_grant s' e" using p_in p'_in by (simp add:Kill)
+ moreover have "grant s' e"
+ proof-
+ from grant obtain up rp tp up' rp' tp'
+ where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
+ and p'1: "sectxt_of_obj s (O_proc p') = Some (up', rp', tp')"
+ apply (simp add:Kill split:option.splits)
+ by (case_tac a, case_tac aa, blast)
+ from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
+ using os cp2sp
+ apply (erule_tac x = p in allE)
+ by (auto simp:Kill co2sobj.simps cp2sproc_def split:option.splits)
+ from p'1 have p'1': "sectxt_of_obj s' (O_proc p') = Some (up', rp', tp')"
+ using os cp2sp
+ apply (erule_tac x = p' in allE)
+ by (auto simp:Kill co2sobj.simps cp2sproc_def split:option.splits)
+ show ?thesis using p1 p'1 p1' p'1' grant
+ by (simp add:Kill)
+ qed
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ next
+ case (Ptrace p p')
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:Ptrace)
+ have p'_in: "p' \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p'" in allE)
+ by (auto simp:Ptrace)
+ have "os_grant s' e" using p_in p'_in by (simp add:Ptrace)
+ moreover have "grant s' e"
+ proof-
+ from grant obtain up rp tp up' rp' tp'
+ where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
+ and p'1: "sectxt_of_obj s (O_proc p') = Some (up', rp', tp')"
+ apply (simp add:Ptrace split:option.splits)
+ by (case_tac a, case_tac aa, blast)
+ from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
+ using os cp2sp
+ apply (erule_tac x = p in allE)
+ by (auto simp:Ptrace co2sobj.simps cp2sproc_def split:option.splits)
+ from p'1 have p'1': "sectxt_of_obj s' (O_proc p') = Some (up', rp', tp')"
+ using os cp2sp
+ apply (erule_tac x = p' in allE)
+ by (auto simp:Ptrace co2sobj.simps cp2sproc_def split:option.splits)
+ show ?thesis using p1 p'1 p1' p'1' grant
+ by (simp add:Ptrace)
+ qed
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ next
+ case (Exit p)
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:Exit)
+ have "os_grant s' e" using p_in by (simp add:Exit)
+ moreover have "grant s' e"
+ by (simp add:Exit)
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ next
+ case (Open p f flags fd opt)
+ show ?thesis
+ proof (cases opt)
+ case None
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:Open None)
+ have f_in: "is_file s' f" using os alive
+ apply (erule_tac x = "O_file f" in allE)
+ by (auto simp:Open None)
+ have fd_not_in: "fd \<notin> current_proc_fds s' p"
+ using os alive' p_in notin_all Open None
+ apply (erule_tac x = "E_fd p fd" in allE)
+ apply (case_tac obj')
+ by auto
+ have "os_grant s' e" using p_in f_in fd_not_in os
+ by (simp add:Open None)
+ moreover have "grant s' e"
+ 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)"
+ apply (simp add:Open None split:option.splits)
+ by (case_tac a, case_tac aa, blast)
+ from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
+ using os cp2sp
+ apply (erule_tac x = p in allE)
+ by (auto simp:Open None co2sobj.simps cp2sproc_def split:option.splits)
+ from os have f_in': "is_file s f" by (simp add:Open None)
+ from vd os have "\<exists> sf. cf2sfile s f = Some sf"
+ by (auto dest!:is_file_in_current current_file_has_sfile simp:Open None)
+ hence p2': "sectxt_of_obj s' (O_file f) = Some (uf, rf, tf)" using f_in f_in' p2 cf2sf
+ apply (erule_tac x = f in allE)
+ apply (auto dest:is_file_in_current simp:cf2sfile_def 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 s' (up, rp, tp) f"
+ using p1 p2 p2' vd cf2sf f_in' grant Open None f_in
+ apply (rule_tac s = s in enrich_search_check)
+ by (simp_all split:option.splits)
+ thus ?thesis using p1' p2'
+ apply (simp add:Open None split:option.splits)
+ using grant Open None p1 p2
+ by simp
+ qed
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ next
+ case (Some inum)
+ from os obtain pf where pf_in_s: "is_dir s pf" and parent: "parent f = Some pf"
+ by (auto simp:Open Some)
+ have pf_in: "is_dir s' pf" using pf_in_s alive
+ apply (erule_tac x = "O_dir pf" in allE)
+ by simp
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:Open Some)
+ have f_not_in: "f \<notin> current_files s'" using os alive' Open Some notin_all
+ apply (erule_tac x = "E_file f" in allE)
+ apply (case_tac obj')
+ by auto
+ have fd_not_in: "fd \<notin> current_proc_fds s' p"
+ using os alive' p_in Open Some notin_all
+ apply (erule_tac x = "E_fd p fd" in allE)
+ apply (case_tac obj', auto)
+ done
+ have inum_not_in: "inum \<notin> current_inode_nums s'"
+ using os alive' Open Some notin_all
+ apply (erule_tac x = "E_inum inum" in allE)
+ by (case_tac obj', auto)
+ have "os_grant s' e" using p_in pf_in parent f_not_in fd_not_in inum_not_in os
+ by (simp add:Open Some hungs)
+ moreover have "grant s' e"
+ proof-
+ from grant parent 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_dir pf) = Some (uf, rf, tf)"
+ apply (simp add:Open Some split:option.splits)
+ by (case_tac a, case_tac aa, blast)
+ from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
+ using os cp2sp
+ apply (erule_tac x = p in allE)
+ by (auto simp:Open Some co2sobj.simps cp2sproc_def split:option.splits)
+ from vd os pf_in_s have "\<exists> sf. cf2sfile s pf = Some sf"
+ by (auto dest!:is_dir_in_current current_file_has_sfile simp:Open Some)
+ hence p2': "sectxt_of_obj s' (O_dir pf) = Some (uf, rf, tf)" using p2 cf2sf pf_in pf_in_s
+ apply (erule_tac x = pf in allE)
+ apply (erule exE, frule_tac s = s in is_dir_in_current, simp)
+ apply (drule is_dir_not_file, drule is_dir_not_file)
+ apply (auto simp:cf2sfile_def split:option.splits)
+ apply (case_tac pf, simp_all)
+ by (simp add:sroot_def root_sec_remains vd vs')
+ have "search_check s' (up, rp, tp) pf"
+ using p1 p2 p2' vd cf2sf pf_in grant Open Some pf_in_s parent vs'
+ apply (rule_tac s = s in enrich_search_check')
+ by (simp_all split:option.splits)
+ thus ?thesis using p1' p2' parent
+ apply (simp add:Open Some split:option.splits)
+ using grant Open Some p1 p2
+ by simp
+ qed
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ qed
+ next
+ case (ReadFile p fd)
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:ReadFile)
+ have fd_in: "fd \<in> current_proc_fds s' p" using os alive
+ apply (erule_tac x = "O_fd p fd" in allE)
+ by (auto simp:ReadFile)
+ obtain f where ffd: "file_of_proc_fd s p fd = Some f"
+ using os ReadFile by auto
+ hence f_in_s: "is_file s f" using vd
+ by (auto intro:file_of_pfd_is_file)
+ obtain flags where fflag: "flags_of_proc_fd s p fd = Some flags"
+ using os ReadFile by auto
+ have ffd_in: "file_of_proc_fd s' p fd = Some f"
+ using ffd_remain ffd by auto
+ hence f_in: "is_file s' f" using vs'
+ by (auto intro:file_of_pfd_is_file)
+ have flags_in: "flags_of_proc_fd s' p fd = Some flags"
+ using fflags_remain fflag by auto
+ have "os_grant s' e" using p_in fd_in ffd_in flags_in fflag os f_in
+ by (auto simp add:ReadFile is_file_in_current)
+ moreover have "grant s' e"
+ proof-
+ from grant ffd obtain up rp tp uf rf tf ufd rfd tfd
+ 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)"
+ and p3: "sectxt_of_obj s (O_fd p fd) = Some (ufd, rfd, tfd)"
+ apply (simp add:ReadFile split:option.splits)
+ by (case_tac a, case_tac aa, case_tac ab, blast)
+ from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
+ using os cp2sp
+ apply (erule_tac x = p in allE)
+ by (auto simp:ReadFile co2sobj.simps cp2sproc_def split:option.splits)
+ from vd f_in_s have "\<exists> sf. cf2sfile s f = Some sf"
+ by (auto dest!:is_file_in_current current_file_has_sfile)
+ hence p2': "sectxt_of_obj s' (O_file f) = Some (uf, rf, tf)" using f_in f_in_s p2 cf2sf
+ apply (erule_tac x = f in allE)
+ apply (auto dest:is_file_in_current simp:cf2sfile_def split:option.splits)
+ apply (case_tac f, simp)
+ apply (drule_tac s = s in root_is_dir', simp add:vd, simp+)
+ done
+ have p3': "sectxt_of_obj s' (O_fd p fd) = Some (ufd, rfd, tfd)"
+ using cfd2sfd ffd_in ffd p3 f_in f_in_s vd
+ apply (erule_tac x = p in allE)
+ apply (erule_tac x = fd in allE)
+ apply (simp add:proc_file_fds_def)
+ apply (auto simp:cfd2sfd_def fflag flags_in p3 split:option.splits
+ dest!:current_file_has_sfile' simp:is_file_in_current)
+ done
+ show ?thesis using p1' p2' p3' ffd_in ffd
+ apply (simp add:ReadFile split:option.splits)
+ using grant p1 p2 p3 ReadFile
by simp
qed
ultimately show ?thesis using vs'
by (erule_tac valid.intros(2), simp+)
next
- case (Some inum)
+ case (WriteFile p fd)
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:WriteFile)
+ have fd_in: "fd \<in> current_proc_fds s' p" using os alive
+ apply (erule_tac x = "O_fd p fd" in allE)
+ by (auto simp:WriteFile)
+ obtain f where ffd: "file_of_proc_fd s p fd = Some f"
+ using os WriteFile by auto
+ hence f_in_s: "is_file s f" using vd
+ by (auto intro:file_of_pfd_is_file)
+ obtain flags where fflag: "flags_of_proc_fd s p fd = Some flags"
+ using os WriteFile by auto
+ have ffd_in: "file_of_proc_fd s' p fd = Some f"
+ using ffd_remain ffd by auto
+ hence f_in: "is_file s' f" using vs'
+ by (auto intro:file_of_pfd_is_file)
+ have flags_in: "flags_of_proc_fd s' p fd = Some flags"
+ using fflags_remain fflag by auto
+ have "os_grant s' e" using p_in fd_in ffd_in flags_in fflag os f_in
+ by (auto simp add:WriteFile is_file_in_current)
+ moreover have "grant s' e"
+ proof-
+ from grant ffd obtain up rp tp uf rf tf ufd rfd tfd
+ 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)"
+ and p3: "sectxt_of_obj s (O_fd p fd) = Some (ufd, rfd, tfd)"
+ apply (simp add:WriteFile split:option.splits)
+ by (case_tac a, case_tac aa, case_tac ab, blast)
+ from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
+ using os cp2sp
+ apply (erule_tac x = p in allE)
+ by (auto simp:WriteFile co2sobj.simps cp2sproc_def split:option.splits)
+ from vd f_in_s have "\<exists> sf. cf2sfile s f = Some sf"
+ by (auto dest!:is_file_in_current current_file_has_sfile)
+ hence p2': "sectxt_of_obj s' (O_file f) = Some (uf, rf, tf)" using f_in f_in_s p2 cf2sf
+ apply (erule_tac x = f in allE)
+ apply (auto dest:is_file_in_current simp:cf2sfile_def split:option.splits)
+ apply (case_tac f, simp)
+ apply (drule_tac s = s in root_is_dir', simp add:vd, simp+)
+ done
+ have p3': "sectxt_of_obj s' (O_fd p fd) = Some (ufd, rfd, tfd)"
+ using cfd2sfd ffd_in ffd p3 f_in f_in_s vd
+ apply (erule_tac x = p in allE)
+ apply (erule_tac x = fd in allE)
+ apply (simp add:proc_file_fds_def)
+ apply (auto simp:cfd2sfd_def fflag flags_in p3 split:option.splits
+ dest!:current_file_has_sfile' simp:is_file_in_current)
+ done
+ show ?thesis using p1' p2' p3' ffd_in ffd
+ apply (simp add:WriteFile split:option.splits)
+ using grant p1 p2 p3 WriteFile
+ by simp
+ qed
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ next
+ case (CloseFd p fd)
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:CloseFd)
+ have fd_in: "fd \<in> current_proc_fds s' p" using os alive
+ apply (erule_tac x = "O_fd p fd" in allE)
+ by (auto simp:CloseFd)
+ have "os_grant s' e" using p_in fd_in
+ by (auto simp add:CloseFd)
+ moreover have "grant s' e"
+ by(simp add:CloseFd)
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ next
+ case (UnLink p f)
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:UnLink)
+ have f_in: "is_file s' f" using os alive
+ apply (erule_tac x = "O_file f" in allE)
+ by (auto simp:UnLink)
+ from os vd obtain pf where pf_in_s: "is_dir s pf"
+ and parent: "parent f = Some pf"
+ by (auto simp:UnLink dest!:file_has_parent)
+ from pf_in_s alive have pf_in: "is_dir s' pf"
+ apply (erule_tac x = "O_dir pf" in allE)
+ by (auto simp:UnLink)
+ have "os_grant s' e" using p_in f_in os
+ by (simp add:UnLink hungs)
+ moreover have "grant s' e"
+ proof-
+ from grant parent obtain up rp tp uf rf tf upf rpf tpf
+ 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)"
+ and p3: "sectxt_of_obj s (O_dir pf) = Some (upf, rpf, tpf)"
+ apply (simp add:UnLink split:option.splits)
+ by (case_tac a, case_tac aa, case_tac ab, blast)
+ from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
+ using os cp2sp
+ apply (erule_tac x = p in allE)
+ by (auto simp:UnLink co2sobj.simps cp2sproc_def split:option.splits)
+ from vd os pf_in_s have "\<exists> sf. cf2sfile s f = Some sf"
+ by (auto dest!:is_file_in_current current_file_has_sfile simp:UnLink)
+ hence p2': "sectxt_of_obj s' (O_file f) = Some (uf, rf, tf)"
+ using p2 cf2sf f_in os parent
+ apply (erule_tac x = f in allE)
+ apply (erule exE, clarsimp simp:UnLink)
+ apply (frule_tac s = s in is_file_in_current, simp)
+ by (auto simp:cf2sfile_def split:option.splits)
+ from vd os pf_in_s have "\<exists> sf. cf2sfile s pf = Some sf"
+ by (auto dest!:is_dir_in_current current_file_has_sfile simp:UnLink)
+ hence p3': "sectxt_of_obj s' (O_dir pf) = Some (upf, rpf, tpf)" using p3 cf2sf pf_in pf_in_s
+ apply (erule_tac x = pf in allE)
+ apply (erule exE, frule_tac s = s in is_dir_in_current, simp)
+ apply (drule is_dir_not_file, drule is_dir_not_file)
+ apply (auto simp:cf2sfile_def split:option.splits)
+ apply (case_tac pf, simp_all)
+ by (simp add:sroot_def root_sec_remains vd vs')
+ have "search_check s' (up, rp, tp) f"
+ using p1 p2 p2' vd cf2sf f_in grant UnLink os parent vs'
+ apply (rule_tac s = s in enrich_search_check)
+ by (simp_all split:option.splits)
+ thus ?thesis using p1' p2' p3' parent
+ apply (simp add:UnLink split:option.splits)
+ using grant UnLink p1 p2 p3
+ by simp
+ qed
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ next
+ case (Rmdir p f)
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:Rmdir)
+ have f_in: "is_dir s' f" using os alive
+ apply (erule_tac x = "O_dir f" in allE)
+ by (auto simp:Rmdir dir_is_empty_def)
+ have not_root: "f \<noteq> []" using os
+ by (auto simp:Rmdir)
+ from os vd obtain pf where pf_in_s: "is_dir s pf"
+ and parent: "parent f = Some pf"
+ apply (auto simp:Rmdir dir_is_empty_def)
+ apply (case_tac f, simp+)
+ apply (drule parentf_is_dir_prop1, auto)
+ done
+ from pf_in_s alive have pf_in: "is_dir s' pf"
+ apply (erule_tac x = "O_dir pf" in allE)
+ by (auto simp:Rmdir)
+ have empty_in: "dir_is_empty s' f" using os Rmdir notin_all
+ apply (clarsimp simp add:dir_is_empty_def f_in)
+ using alive'
+ apply (erule_tac x = "E_file f'" in allE)
+ apply simp
+ apply (erule disjE)
+ apply (erule_tac x = f' in allE, simp)
+ apply (case_tac obj', simp_all)
+ apply (clarsimp)
+ apply (drule_tac f' = f in parent_ancen)
+ apply (simp, rule notI, simp add:noJ_Anc)
+ apply (case_tac "f = pf")
+ using vd' Rmdir
+ apply (simp_all add:is_dir_rmdir)
+ apply (erule_tac x = pf in allE)
+ apply (drule_tac f = pf in is_dir_in_current)
+ apply (simp add:noJ_Anc)
+ done
+ have "os_grant s' e" using p_in f_in os empty_in
+ by (simp add:Rmdir hungs)
+ moreover have "grant s' e"
+ proof-
+ from grant parent obtain up rp tp uf rf tf upf rpf tpf
+ where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
+ and p2: "sectxt_of_obj s (O_dir f) = Some (uf, rf, tf)"
+ and p3: "sectxt_of_obj s (O_dir pf) = Some (upf, rpf, tpf)"
+ apply (simp add:Rmdir split:option.splits)
+ by (case_tac a, case_tac aa, case_tac ab, blast)
+ from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
+ using os cp2sp
+ apply (erule_tac x = p in allE)
+ by (auto simp:Rmdir co2sobj.simps cp2sproc_def split:option.splits)
+ from vd os pf_in_s have "\<exists> sf. cf2sfile s f = Some sf"
+ by (auto dest!:is_dir_in_current current_file_has_sfile simp:dir_is_empty_def Rmdir)
+ hence p2': "sectxt_of_obj s' (O_dir f) = Some (uf, rf, tf)"
+ using p2 cf2sf f_in os parent
+ apply (erule_tac x = f in allE)
+ apply (erule exE, clarsimp simp:Rmdir dir_is_empty_def)
+ apply (frule_tac s = s in is_dir_in_current, simp)
+ apply (drule is_dir_not_file, drule is_dir_not_file)
+ by (auto simp:cf2sfile_def split:option.splits)
+ from vd os pf_in_s have "\<exists> sf. cf2sfile s pf = Some sf"
+ by (auto dest!:is_dir_in_current current_file_has_sfile simp:Rmdir)
+ hence p3': "sectxt_of_obj s' (O_dir pf) = Some (upf, rpf, tpf)" using p3 cf2sf pf_in pf_in_s
+ apply (erule_tac x = pf in allE)
+ apply (erule exE, frule_tac s = s in is_dir_in_current, simp)
+ apply (drule is_dir_not_file, drule is_dir_not_file)
+ apply (auto simp:cf2sfile_def split:option.splits)
+ apply (case_tac pf, simp_all)
+ by (simp add:sroot_def root_sec_remains vd vs')
+ have "search_check s' (up, rp, tp) f"
+ using p1 p2 p2' vd cf2sf f_in grant Rmdir os parent vs'
+ apply (rule_tac s = s in enrich_search_check')
+ by (simp_all add:dir_is_empty_def split:option.splits)
+ thus ?thesis using p1' p2' p3' parent
+ apply (simp add:Rmdir split:option.splits)
+ using grant Rmdir p1 p2 p3
+ by simp
+ qed
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ next
+ case (Mkdir p f inum)
from os obtain pf where pf_in_s: "is_dir s pf" and parent: "parent f = Some pf"
- by (auto simp:Open Some)
+ by (auto simp:Mkdir)
have pf_in: "is_dir s' pf" using pf_in_s alive
apply (erule_tac x = "O_dir pf" in allE)
by simp
have p_in: "p \<in> current_procs s'" using os alive
apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:Open Some)
- have f_not_in: "f \<notin> current_files s'" using os alive'
+ by (auto simp:Mkdir)
+ have f_not_in: "f \<notin> current_files s'" using os alive' Mkdir notin_all
apply (erule_tac x = "E_file f" in allE)
- by (auto simp:Open Some)
- have fd_not_in: "fd \<notin> current_proc_fds s' p"
- using os alive' p_in
- apply (erule_tac x = "E_fd p fd" in allE)
- by (simp add:Open Some)
+ by (auto)
have inum_not_in: "inum \<notin> current_inode_nums s'"
- using os alive'
+ using os alive' Mkdir notin_all
apply (erule_tac x = "E_inum inum" in allE)
- by (simp add:Open Some)
- have "os_grant s' e" using p_in pf_in parent f_not_in fd_not_in inum_not_in os
- by (simp add:Open Some hungs)
+ by (auto)
+ have "os_grant s' e" using p_in pf_in parent f_not_in os inum_not_in
+ by (simp add:Mkdir hungs)
moreover have "grant s' e"
proof-
from grant parent 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_dir pf) = Some (uf, rf, tf)"
- apply (simp add:Open Some split:option.splits)
+ apply (simp add:Mkdir split:option.splits)
by (case_tac a, case_tac aa, blast)
from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
using os cp2sp
apply (erule_tac x = p in allE)
- by (auto simp:Open Some co2sobj.simps cp2sproc_def split:option.splits)
+ by (auto simp:Mkdir co2sobj.simps cp2sproc_def split:option.splits)
from vd os pf_in_s have "\<exists> sf. cf2sfile s pf = Some sf"
- by (auto dest!:is_dir_in_current current_file_has_sfile simp:Open Some)
+ by (auto dest!:is_dir_in_current current_file_has_sfile simp:Mkdir)
hence p2': "sectxt_of_obj s' (O_dir pf) = Some (uf, rf, tf)" using p2 cf2sf pf_in pf_in_s
apply (erule_tac x = pf in allE)
apply (erule exE, frule_tac s = s in is_dir_in_current, simp)
@@ -500,610 +933,296 @@
apply (case_tac pf, simp_all)
by (simp add:sroot_def root_sec_remains vd vs')
have "search_check s' (up, rp, tp) pf"
- using p1 p2 p2' vd cf2sf pf_in grant Open Some pf_in_s parent vs'
+ using p1 p2 p2' vd cf2sf pf_in grant Mkdir pf_in_s parent vs'
apply (rule_tac s = s in enrich_search_check')
+ apply (simp_all split:option.splits)
+ done
+ thus ?thesis using p1' p2' parent
+ apply (simp add:Mkdir split:option.splits)
+ using grant Mkdir p1 p2
+ apply simp
+ done
+ qed
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ next
+ case (LinkHard p f f')
+ from os obtain pf where pf_in_s: "is_dir s pf" and parent: "parent f' = Some pf"
+ by (auto simp:LinkHard)
+ have pf_in: "is_dir s' pf" using pf_in_s alive
+ apply (erule_tac x = "O_dir pf" in allE)
+ by simp
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:LinkHard)
+ have f'_not_in: "f' \<notin> current_files s'" using os alive' LinkHard notin_all
+ apply (erule_tac x = "E_file f'" in allE)
+ by (auto simp:LinkHard)
+ have f_in: "is_file s' f" using os alive
+ apply (erule_tac x = "O_file f" in allE)
+ by (auto simp:LinkHard)
+ have "os_grant s' e" using p_in pf_in parent os f_in f'_not_in
+ by (simp add:LinkHard hungs)
+ moreover have "grant s' e"
+ proof-
+ from grant parent obtain up rp tp uf rf tf upf rpf tpf
+ 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)"
+ and p3: "sectxt_of_obj s (O_dir pf) = Some (upf, rpf, tpf)"
+ apply (simp add:LinkHard split:option.splits)
+ by (case_tac a, case_tac aa, case_tac ab, blast)
+ from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
+ using os cp2sp
+ apply (erule_tac x = p in allE)
+ by (auto simp:LinkHard co2sobj.simps cp2sproc_def split:option.splits)
+ from vd os pf_in_s have "\<exists> sf. cf2sfile s f = Some sf"
+ by (auto dest!:is_file_in_current current_file_has_sfile simp:LinkHard)
+ hence p2': "sectxt_of_obj s' (O_file f) = Some (uf, rf, tf)"
+ using p2 cf2sf f_in os parent
+ apply (erule_tac x = f in allE)
+ apply (erule exE, clarsimp simp:LinkHard)
+ apply (frule_tac s = s in is_file_in_current, simp)
+ apply (auto simp:cf2sfile_def split:option.splits)
+ apply (case_tac f, simp)
+ by (drule_tac s = s in root_is_dir', simp add:vd, simp+)
+ from vd os pf_in_s have "\<exists> sf. cf2sfile s pf = Some sf"
+ by (auto dest!:is_dir_in_current current_file_has_sfile simp:LinkHard)
+ hence p3': "sectxt_of_obj s' (O_dir pf) = Some (upf, rpf, tpf)" using p3 cf2sf pf_in pf_in_s
+ apply (erule_tac x = pf in allE)
+ apply (erule exE, frule_tac s = s in is_dir_in_current, simp)
+ apply (drule is_dir_not_file, drule is_dir_not_file)
+ apply (auto simp:cf2sfile_def split:option.splits)
+ apply (case_tac pf, simp_all)
+ by (simp add:sroot_def root_sec_remains vd vs')
+ have "search_check s' (up, rp, tp) f"
+ using p1 p2 p2' vd cf2sf f_in grant LinkHard os parent vs'
+ apply (rule_tac s = s in enrich_search_check)
by (simp_all split:option.splits)
- thus ?thesis using p1' p2' parent
- apply (simp add:Open Some split:option.splits)
- using grant Open Some p1 p2
+ moreover have "search_check s' (up, rp, tp) pf"
+ using p1 p3 p3' vd cf2sf pf_in grant LinkHard os parent vs'
+ apply (rule_tac s = s in enrich_search_check')
+ apply (simp_all split:option.splits)
+ done
+ ultimately show ?thesis using p1' p2' p3' parent
+ apply (simp add:LinkHard split:option.splits)
+ using grant LinkHard p1 p2 p3
+ apply simp
+ done
+ qed
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ next
+ case (Truncate p f len)
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:Truncate)
+ have f_in: "is_file s' f" using os alive
+ apply (erule_tac x = "O_file f" in allE)
+ by (auto simp:Truncate)
+ have "os_grant s' e" using p_in f_in by (simp add:Truncate)
+ moreover have "grant s' e"
+ 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)"
+ apply (simp add:Truncate split:option.splits)
+ by (case_tac a, case_tac aa, blast)
+ from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
+ using os cp2sp
+ apply (erule_tac x = p in allE)
+ by (auto simp:Truncate co2sobj.simps cp2sproc_def split:option.splits)
+ from os have f_in': "is_file s f" by (simp add:Truncate)
+ from vd os have "\<exists> sf. cf2sfile s f = Some sf"
+ by (auto dest!:is_file_in_current current_file_has_sfile simp:Truncate)
+ hence p2': "sectxt_of_obj s' (O_file f) = Some (uf, rf, tf)" using f_in f_in' p2 cf2sf
+ apply (erule_tac x = f in allE)
+ apply (auto dest:is_file_in_current simp:cf2sfile_def 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 s' (up, rp, tp) f"
+ using p1 p2 p2' vd cf2sf f_in' grant Truncate f_in
+ apply (rule_tac s = s in enrich_search_check)
+ by (simp_all split:option.splits)
+ thus ?thesis using p1' p2'
+ apply (simp add:Truncate split:option.splits)
+ using grant Truncate p1 p2
+ by (simp add:Truncate grant p1 p2)
+ qed
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ next
+ case (CreateMsgq p q)
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:CreateMsgq)
+ have q_not_in: "q \<notin> current_msgqs s'" using os alive' CreateMsgq notin_all
+ apply (erule_tac x = "E_msgq q" in allE)
+ by auto
+ have "os_grant s' e" using p_in q_not_in by (simp add:CreateMsgq)
+ moreover have "grant s' e"
+ proof-
+ from grant obtain up rp tp
+ where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
+ apply (simp add:CreateMsgq split:option.splits)
+ by (case_tac a, blast)
+ from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
+ using os cp2sp
+ apply (erule_tac x = p in allE)
+ by (auto simp:CreateMsgq co2sobj.simps cp2sproc_def split:option.splits)
+ show ?thesis using p1'
+ apply (simp add:CreateMsgq split:option.splits)
+ using grant CreateMsgq p1
by simp
qed
ultimately show ?thesis using vs'
by (erule_tac valid.intros(2), simp+)
- qed
-next
- case (ReadFile p fd)
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:ReadFile)
- have fd_in: "fd \<in> current_proc_fds s' p" using os alive
- apply (erule_tac x = "O_fd p fd" in allE)
- by (auto simp:ReadFile)
- obtain f where ffd: "file_of_proc_fd s p fd = Some f"
- using os ReadFile by auto
- hence f_in_s: "is_file s f" using vd
- by (auto intro:file_of_pfd_is_file)
- obtain flags where fflag: "flags_of_proc_fd s p fd = Some flags"
- using os ReadFile by auto
- have ffd_in: "file_of_proc_fd s' p fd = Some f"
- using ffd_remain ffd by auto
- hence f_in: "is_file s' f" using vs'
- by (auto intro:file_of_pfd_is_file)
- have flags_in: "flags_of_proc_fd s' p fd = Some flags"
- using fflags_remain fflag by auto
- have "os_grant s' e" using p_in fd_in ffd_in flags_in fflag os f_in
- by (auto simp add:ReadFile is_file_in_current)
- moreover have "grant s' e"
- proof-
- from grant ffd obtain up rp tp uf rf tf ufd rfd tfd
- 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)"
- and p3: "sectxt_of_obj s (O_fd p fd) = Some (ufd, rfd, tfd)"
- apply (simp add:ReadFile split:option.splits)
- by (case_tac a, case_tac aa, case_tac ab, blast)
- from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
- using os cp2sp
- apply (erule_tac x = p in allE)
- by (auto simp:ReadFile co2sobj.simps cp2sproc_def split:option.splits)
- from vd f_in_s have "\<exists> sf. cf2sfile s f = Some sf"
- by (auto dest!:is_file_in_current current_file_has_sfile)
- hence p2': "sectxt_of_obj s' (O_file f) = Some (uf, rf, tf)" using f_in f_in_s p2 cf2sf
- apply (erule_tac x = f in allE)
- apply (auto dest:is_file_in_current simp:cf2sfile_def split:option.splits)
- apply (case_tac f, simp)
- apply (drule_tac s = s in root_is_dir', simp add:vd, simp+)
- done
- have p3': "sectxt_of_obj s' (O_fd p fd) = Some (ufd, rfd, tfd)"
- using cfd2sfd ffd_in ffd p3 f_in f_in_s vd
- apply (erule_tac x = p in allE)
- apply (erule_tac x = fd in allE)
- apply (simp add:proc_file_fds_def)
- apply (auto simp:cfd2sfd_def fflag flags_in p3 split:option.splits
- dest!:current_file_has_sfile' simp:is_file_in_current)
- done
- show ?thesis using p1' p2' p3' ffd_in ffd
- apply (simp add:ReadFile split:option.splits)
- using grant p1 p2 p3 ReadFile
- by simp
- qed
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (WriteFile p fd)
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:WriteFile)
- have fd_in: "fd \<in> current_proc_fds s' p" using os alive
- apply (erule_tac x = "O_fd p fd" in allE)
- by (auto simp:WriteFile)
- obtain f where ffd: "file_of_proc_fd s p fd = Some f"
- using os WriteFile by auto
- hence f_in_s: "is_file s f" using vd
- by (auto intro:file_of_pfd_is_file)
- obtain flags where fflag: "flags_of_proc_fd s p fd = Some flags"
- using os WriteFile by auto
- have ffd_in: "file_of_proc_fd s' p fd = Some f"
- using ffd_remain ffd by auto
- hence f_in: "is_file s' f" using vs'
- by (auto intro:file_of_pfd_is_file)
- have flags_in: "flags_of_proc_fd s' p fd = Some flags"
- using fflags_remain fflag by auto
- have "os_grant s' e" using p_in fd_in ffd_in flags_in fflag os f_in
- by (auto simp add:WriteFile is_file_in_current)
- moreover have "grant s' e"
- proof-
- from grant ffd obtain up rp tp uf rf tf ufd rfd tfd
- 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)"
- and p3: "sectxt_of_obj s (O_fd p fd) = Some (ufd, rfd, tfd)"
- apply (simp add:WriteFile split:option.splits)
- by (case_tac a, case_tac aa, case_tac ab, blast)
- from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
- using os cp2sp
- apply (erule_tac x = p in allE)
- by (auto simp:WriteFile co2sobj.simps cp2sproc_def split:option.splits)
- from vd f_in_s have "\<exists> sf. cf2sfile s f = Some sf"
- by (auto dest!:is_file_in_current current_file_has_sfile)
- hence p2': "sectxt_of_obj s' (O_file f) = Some (uf, rf, tf)" using f_in f_in_s p2 cf2sf
- apply (erule_tac x = f in allE)
- apply (auto dest:is_file_in_current simp:cf2sfile_def split:option.splits)
- apply (case_tac f, simp)
- apply (drule_tac s = s in root_is_dir', simp add:vd, simp+)
- done
- have p3': "sectxt_of_obj s' (O_fd p fd) = Some (ufd, rfd, tfd)"
- using cfd2sfd ffd_in ffd p3 f_in f_in_s vd
- apply (erule_tac x = p in allE)
- apply (erule_tac x = fd in allE)
- apply (simp add:proc_file_fds_def)
- apply (auto simp:cfd2sfd_def fflag flags_in p3 split:option.splits
- dest!:current_file_has_sfile' simp:is_file_in_current)
- done
- show ?thesis using p1' p2' p3' ffd_in ffd
- apply (simp add:WriteFile split:option.splits)
- using grant p1 p2 p3 WriteFile
- by simp
- qed
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (CloseFd p fd)
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:CloseFd)
- have fd_in: "fd \<in> current_proc_fds s' p" using os alive
- apply (erule_tac x = "O_fd p fd" in allE)
- by (auto simp:CloseFd)
- have "os_grant s' e" using p_in fd_in
- by (auto simp add:CloseFd)
- moreover have "grant s' e"
- by(simp add:CloseFd)
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (UnLink p f)
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:UnLink)
- have f_in: "is_file s' f" using os alive
- apply (erule_tac x = "O_file f" in allE)
- by (auto simp:UnLink)
- from os vd obtain pf where pf_in_s: "is_dir s pf"
- and parent: "parent f = Some pf"
- by (auto simp:UnLink dest!:file_has_parent)
- from pf_in_s alive have pf_in: "is_dir s' pf"
- apply (erule_tac x = "O_dir pf" in allE)
- by (auto simp:UnLink)
- have "os_grant s' e" using p_in f_in os
- by (simp add:UnLink hungs)
- moreover have "grant s' e"
- proof-
- from grant parent obtain up rp tp uf rf tf upf rpf tpf
- 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)"
- and p3: "sectxt_of_obj s (O_dir pf) = Some (upf, rpf, tpf)"
- apply (simp add:UnLink split:option.splits)
- by (case_tac a, case_tac aa, case_tac ab, blast)
- from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
- using os cp2sp
- apply (erule_tac x = p in allE)
- by (auto simp:UnLink co2sobj.simps cp2sproc_def split:option.splits)
- from vd os pf_in_s have "\<exists> sf. cf2sfile s f = Some sf"
- by (auto dest!:is_file_in_current current_file_has_sfile simp:UnLink)
- hence p2': "sectxt_of_obj s' (O_file f) = Some (uf, rf, tf)"
- using p2 cf2sf f_in os parent
- apply (erule_tac x = f in allE)
- apply (erule exE, clarsimp simp:UnLink)
- apply (frule_tac s = s in is_file_in_current, simp)
- by (auto simp:cf2sfile_def split:option.splits)
- from vd os pf_in_s have "\<exists> sf. cf2sfile s pf = Some sf"
- by (auto dest!:is_dir_in_current current_file_has_sfile simp:UnLink)
- hence p3': "sectxt_of_obj s' (O_dir pf) = Some (upf, rpf, tpf)" using p3 cf2sf pf_in pf_in_s
- apply (erule_tac x = pf in allE)
- apply (erule exE, frule_tac s = s in is_dir_in_current, simp)
- apply (drule is_dir_not_file, drule is_dir_not_file)
- apply (auto simp:cf2sfile_def split:option.splits)
- apply (case_tac pf, simp_all)
- by (simp add:sroot_def root_sec_remains vd vs')
- have "search_check s' (up, rp, tp) f"
- using p1 p2 p2' vd cf2sf f_in grant UnLink os parent vs'
- apply (rule_tac s = s in enrich_search_check)
- by (simp_all split:option.splits)
- thus ?thesis using p1' p2' p3' parent
- apply (simp add:UnLink split:option.splits)
- using grant UnLink p1 p2 p3
- by simp
- qed
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (Rmdir p f)
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:Rmdir)
- have f_in: "is_dir s' f" using os alive
- apply (erule_tac x = "O_dir f" in allE)
- by (auto simp:Rmdir dir_is_empty_def)
- have not_root: "f \<noteq> []" using os
- by (auto simp:Rmdir)
- from os vd obtain pf where pf_in_s: "is_dir s pf"
- and parent: "parent f = Some pf"
- apply (auto simp:Rmdir dir_is_empty_def)
- apply (case_tac f, simp+)
- apply (drule parentf_is_dir_prop1, auto)
- done
- from pf_in_s alive have pf_in: "is_dir s' pf"
- apply (erule_tac x = "O_dir pf" in allE)
- by (auto simp:Rmdir)
- have empty_in: "dir_is_empty s' f" using os
- apply (simp add:dir_is_empty_def f_in)
- apply auto using alive'
- apply (erule_tac x = "E_file f'" in allE)
- by (simp add:Rmdir dir_is_empty_def)
- have "os_grant s' e" using p_in f_in os empty_in
- by (simp add:Rmdir hungs)
- moreover have "grant s' e"
- proof-
- from grant parent obtain up rp tp uf rf tf upf rpf tpf
- where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
- and p2: "sectxt_of_obj s (O_dir f) = Some (uf, rf, tf)"
- and p3: "sectxt_of_obj s (O_dir pf) = Some (upf, rpf, tpf)"
- apply (simp add:Rmdir split:option.splits)
- by (case_tac a, case_tac aa, case_tac ab, blast)
- from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
- using os cp2sp
- apply (erule_tac x = p in allE)
- by (auto simp:Rmdir co2sobj.simps cp2sproc_def split:option.splits)
- from vd os pf_in_s have "\<exists> sf. cf2sfile s f = Some sf"
- by (auto dest!:is_dir_in_current current_file_has_sfile simp:dir_is_empty_def Rmdir)
- hence p2': "sectxt_of_obj s' (O_dir f) = Some (uf, rf, tf)"
- using p2 cf2sf f_in os parent
- apply (erule_tac x = f in allE)
- apply (erule exE, clarsimp simp:Rmdir dir_is_empty_def)
- apply (frule_tac s = s in is_dir_in_current, simp)
- apply (drule is_dir_not_file, drule is_dir_not_file)
- by (auto simp:cf2sfile_def split:option.splits)
- from vd os pf_in_s have "\<exists> sf. cf2sfile s pf = Some sf"
- by (auto dest!:is_dir_in_current current_file_has_sfile simp:Rmdir)
- hence p3': "sectxt_of_obj s' (O_dir pf) = Some (upf, rpf, tpf)" using p3 cf2sf pf_in pf_in_s
- apply (erule_tac x = pf in allE)
- apply (erule exE, frule_tac s = s in is_dir_in_current, simp)
- apply (drule is_dir_not_file, drule is_dir_not_file)
- apply (auto simp:cf2sfile_def split:option.splits)
- apply (case_tac pf, simp_all)
- by (simp add:sroot_def root_sec_remains vd vs')
- have "search_check s' (up, rp, tp) f"
- using p1 p2 p2' vd cf2sf f_in grant Rmdir os parent vs'
- apply (rule_tac s = s in enrich_search_check')
- by (simp_all add:dir_is_empty_def split:option.splits)
- thus ?thesis using p1' p2' p3' parent
- apply (simp add:Rmdir split:option.splits)
- using grant Rmdir p1 p2 p3
- by simp
- qed
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (Mkdir p f inum)
- from os obtain pf where pf_in_s: "is_dir s pf" and parent: "parent f = Some pf"
- by (auto simp:Mkdir)
- have pf_in: "is_dir s' pf" using pf_in_s alive
- apply (erule_tac x = "O_dir pf" in allE)
- by simp
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:Mkdir)
- have f_not_in: "f \<notin> current_files s'" using os alive'
- apply (erule_tac x = "E_file f" in allE)
- by (auto simp:Mkdir)
- have inum_not_in: "inum \<notin> current_inode_nums s'"
- using os alive'
- apply (erule_tac x = "E_inum inum" in allE)
- by (simp add:Mkdir)
- have "os_grant s' e" using p_in pf_in parent f_not_in os inum_not_in
- by (simp add:Mkdir hungs)
- moreover have "grant s' e"
- proof-
- from grant parent 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_dir pf) = Some (uf, rf, tf)"
- apply (simp add:Mkdir split:option.splits)
- by (case_tac a, case_tac aa, blast)
- from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
- using os cp2sp
- apply (erule_tac x = p in allE)
- by (auto simp:Mkdir co2sobj.simps cp2sproc_def split:option.splits)
- from vd os pf_in_s have "\<exists> sf. cf2sfile s pf = Some sf"
- by (auto dest!:is_dir_in_current current_file_has_sfile simp:Mkdir)
- hence p2': "sectxt_of_obj s' (O_dir pf) = Some (uf, rf, tf)" using p2 cf2sf pf_in pf_in_s
- apply (erule_tac x = pf in allE)
- apply (erule exE, frule_tac s = s in is_dir_in_current, simp)
- apply (drule is_dir_not_file, drule is_dir_not_file)
- apply (auto simp:cf2sfile_def split:option.splits)
- apply (case_tac pf, simp_all)
- by (simp add:sroot_def root_sec_remains vd vs')
- have "search_check s' (up, rp, tp) pf"
- using p1 p2 p2' vd cf2sf pf_in grant Mkdir pf_in_s parent vs'
- apply (rule_tac s = s in enrich_search_check')
- apply (simp_all split:option.splits)
- done
- thus ?thesis using p1' p2' parent
- apply (simp add:Mkdir split:option.splits)
- using grant Mkdir p1 p2
- apply simp
- done
- qed
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (LinkHard p f f')
- from os obtain pf where pf_in_s: "is_dir s pf" and parent: "parent f' = Some pf"
- by (auto simp:LinkHard)
- have pf_in: "is_dir s' pf" using pf_in_s alive
- apply (erule_tac x = "O_dir pf" in allE)
- by simp
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:LinkHard)
- have f'_not_in: "f' \<notin> current_files s'" using os alive'
- apply (erule_tac x = "E_file f'" in allE)
- by (auto simp:LinkHard)
- have f_in: "is_file s' f" using os alive
- apply (erule_tac x = "O_file f" in allE)
- by (auto simp:LinkHard)
- have "os_grant s' e" using p_in pf_in parent os f_in f'_not_in
- by (simp add:LinkHard hungs)
- moreover have "grant s' e"
- proof-
- from grant parent obtain up rp tp uf rf tf upf rpf tpf
- 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)"
- and p3: "sectxt_of_obj s (O_dir pf) = Some (upf, rpf, tpf)"
- apply (simp add:LinkHard split:option.splits)
- by (case_tac a, case_tac aa, case_tac ab, blast)
- from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
- using os cp2sp
- apply (erule_tac x = p in allE)
- by (auto simp:LinkHard co2sobj.simps cp2sproc_def split:option.splits)
- from vd os pf_in_s have "\<exists> sf. cf2sfile s f = Some sf"
- by (auto dest!:is_file_in_current current_file_has_sfile simp:LinkHard)
- hence p2': "sectxt_of_obj s' (O_file f) = Some (uf, rf, tf)"
- using p2 cf2sf f_in os parent
- apply (erule_tac x = f in allE)
- apply (erule exE, clarsimp simp:LinkHard)
- apply (frule_tac s = s in is_file_in_current, simp)
- apply (auto simp:cf2sfile_def split:option.splits)
- apply (case_tac f, simp)
- by (drule_tac s = s in root_is_dir', simp add:vd, simp+)
- from vd os pf_in_s have "\<exists> sf. cf2sfile s pf = Some sf"
- by (auto dest!:is_dir_in_current current_file_has_sfile simp:LinkHard)
- hence p3': "sectxt_of_obj s' (O_dir pf) = Some (upf, rpf, tpf)" using p3 cf2sf pf_in pf_in_s
- apply (erule_tac x = pf in allE)
- apply (erule exE, frule_tac s = s in is_dir_in_current, simp)
- apply (drule is_dir_not_file, drule is_dir_not_file)
- apply (auto simp:cf2sfile_def split:option.splits)
- apply (case_tac pf, simp_all)
- by (simp add:sroot_def root_sec_remains vd vs')
- have "search_check s' (up, rp, tp) f"
- using p1 p2 p2' vd cf2sf f_in grant LinkHard os parent vs'
- apply (rule_tac s = s in enrich_search_check)
- by (simp_all split:option.splits)
- moreover have "search_check s' (up, rp, tp) pf"
- using p1 p3 p3' vd cf2sf pf_in grant LinkHard os parent vs'
- apply (rule_tac s = s in enrich_search_check')
- apply (simp_all split:option.splits)
- done
- ultimately show ?thesis using p1' p2' p3' parent
- apply (simp add:LinkHard split:option.splits)
- using grant LinkHard p1 p2 p3
- apply simp
- done
- qed
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (Truncate p f len)
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:Truncate)
- have f_in: "is_file s' f" using os alive
- apply (erule_tac x = "O_file f" in allE)
- by (auto simp:Truncate)
- have "os_grant s' e" using p_in f_in by (simp add:Truncate)
- moreover have "grant s' e"
- 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)"
- apply (simp add:Truncate split:option.splits)
- by (case_tac a, case_tac aa, blast)
- from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
- using os cp2sp
- apply (erule_tac x = p in allE)
- by (auto simp:Truncate co2sobj.simps cp2sproc_def split:option.splits)
- from os have f_in': "is_file s f" by (simp add:Truncate)
- from vd os have "\<exists> sf. cf2sfile s f = Some sf"
- by (auto dest!:is_file_in_current current_file_has_sfile simp:Truncate)
- hence p2': "sectxt_of_obj s' (O_file f) = Some (uf, rf, tf)" using f_in f_in' p2 cf2sf
- apply (erule_tac x = f in allE)
- apply (auto dest:is_file_in_current simp:cf2sfile_def 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 s' (up, rp, tp) f"
- using p1 p2 p2' vd cf2sf f_in' grant Truncate f_in
- apply (rule_tac s = s in enrich_search_check)
- by (simp_all split:option.splits)
- thus ?thesis using p1' p2'
- apply (simp add:Truncate split:option.splits)
- using grant Truncate p1 p2
- by (simp add:Truncate grant p1 p2)
- qed
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (CreateMsgq p q)
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:CreateMsgq)
- have q_not_in: "q \<notin> current_msgqs s'" using os alive'
- apply (erule_tac x = "E_msgq q" in allE)
- by (simp add:CreateMsgq)
- have "os_grant s' e" using p_in q_not_in by (simp add:CreateMsgq)
- moreover have "grant s' e"
- proof-
- from grant obtain up rp tp
- where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
- apply (simp add:CreateMsgq split:option.splits)
- by (case_tac a, blast)
- from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
- using os cp2sp
- apply (erule_tac x = p in allE)
- by (auto simp:CreateMsgq co2sobj.simps cp2sproc_def split:option.splits)
- show ?thesis using p1'
- apply (simp add:CreateMsgq split:option.splits)
- using grant CreateMsgq p1
- by simp
- qed
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (RemoveMsgq p q)
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:RemoveMsgq)
- have q_in: "q \<in> current_msgqs s'" using os alive
- apply (erule_tac x = "O_msgq q" in allE)
- by (simp add:RemoveMsgq)
- have "os_grant s' e" using p_in q_in by (simp add:RemoveMsgq)
- moreover have "grant s' e"
- proof-
- from grant obtain up rp tp uq rq tq
- where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
- and p2: "sectxt_of_obj s (O_msgq q) = Some (uq, rq, tq)"
- apply (simp add:RemoveMsgq split:option.splits)
- by (case_tac a, case_tac aa, blast)
- from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
- using os cp2sp
- apply (erule_tac x = p in allE)
- by (auto simp:RemoveMsgq co2sobj.simps cp2sproc_def split:option.splits)
- from p2 have p2': "sectxt_of_obj s' (O_msgq q) = Some (uq, rq, tq)"
- using os cq2sq vd
- apply (erule_tac x = q in allE)
- by (auto simp:RemoveMsgq co2sobj.simps cq2smsgq_def dest!:current_has_sms' split:option.splits)
- show ?thesis using p1' p2' grant p1 p2
+ next
+ case (RemoveMsgq p q)
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:RemoveMsgq)
+ have q_in: "q \<in> current_msgqs s'" using os alive
+ apply (erule_tac x = "O_msgq q" in allE)
by (simp add:RemoveMsgq)
- qed
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (SendMsg p q m)
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:SendMsg)
- have q_in: "q \<in> current_msgqs s'" using os alive
- apply (erule_tac x = "O_msgq q" in allE)
- by (simp add:SendMsg)
- have m_not_in: "m \<notin> set (msgs_of_queue s' q)" using os alive'
- apply (erule_tac x = "E_msg q m" in allE)
- by (simp add:SendMsg q_in)
- have "os_grant s' e" using p_in q_in m_not_in
- by (simp add:SendMsg)
- moreover have "grant s' e"
- proof-
- from grant obtain up rp tp uq rq tq
- where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
- and p2: "sectxt_of_obj s (O_msgq q) = Some (uq, rq, tq)"
- apply (simp add:SendMsg split:option.splits)
- by (case_tac a, case_tac aa, blast)
- from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
- using os cp2sp
- apply (erule_tac x = p in allE)
- by (auto simp:SendMsg co2sobj.simps cp2sproc_def split:option.splits)
- from p2 have p2': "sectxt_of_obj s' (O_msgq q) = Some (uq, rq, tq)"
- using os cq2sq vd
- apply (erule_tac x = q in allE)
- by (auto simp:SendMsg co2sobj.simps cq2smsgq_def dest!:current_has_sms' split:option.splits)
- show ?thesis using p1' p2' grant p1 p2
+ have "os_grant s' e" using p_in q_in by (simp add:RemoveMsgq)
+ moreover have "grant s' e"
+ proof-
+ from grant obtain up rp tp uq rq tq
+ where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
+ and p2: "sectxt_of_obj s (O_msgq q) = Some (uq, rq, tq)"
+ apply (simp add:RemoveMsgq split:option.splits)
+ by (case_tac a, case_tac aa, blast)
+ from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
+ using os cp2sp
+ apply (erule_tac x = p in allE)
+ by (auto simp:RemoveMsgq co2sobj.simps cp2sproc_def split:option.splits)
+ from p2 have p2': "sectxt_of_obj s' (O_msgq q) = Some (uq, rq, tq)"
+ using os cq2sq vd
+ apply (erule_tac x = q in allE)
+ by (auto simp:RemoveMsgq co2sobj.simps cq2smsgq_def dest!:current_has_sms' split:option.splits)
+ show ?thesis using p1' p2' grant p1 p2
+ by (simp add:RemoveMsgq)
+ qed
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ next
+ case (SendMsg p q m)
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:SendMsg)
+ have q_in: "q \<in> current_msgqs s'" using os alive
+ apply (erule_tac x = "O_msgq q" in allE)
+ by (simp add:SendMsg)
+ have m_not_in: "m \<notin> set (msgs_of_queue s' q)" using os alive' notin_all SendMsg q_in
+ apply (erule_tac x = "E_msg q m" in allE)
+ apply (case_tac obj')
+ by auto
+ have "os_grant s' e" using p_in q_in m_not_in
by (simp add:SendMsg)
- qed
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (RecvMsg p q m)
- have p_in: "p \<in> current_procs s'" using os alive
- apply (erule_tac x = "O_proc p" in allE)
- by (auto simp:RecvMsg)
- have q_in: "q \<in> current_msgqs s'" using os alive
- apply (erule_tac x = "O_msgq q" in allE)
- by (simp add:RecvMsg)
- have m_in: "m = hd (msgs_of_queue s' q)"
- and sms_not_empty: "msgs_of_queue s' q \<noteq> []"
- using os sms_remain
- by (auto simp:RecvMsg)
- have "os_grant s' e" using p_in q_in m_in sms_not_empty os
- by (simp add:RecvMsg)
- moreover have "grant s' e"
- proof-
- from grant obtain up rp tp uq rq tq um rm tm
- where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
- and p2: "sectxt_of_obj s (O_msgq q) = Some (uq, rq, tq)"
- and p3: "sectxt_of_obj s (O_msg q m) = Some (um, rm, tm)"
- apply (simp add:RecvMsg split:option.splits)
- by (case_tac a, case_tac aa, case_tac ab, blast)
- from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
- using os cp2sp
- apply (erule_tac x = p in allE)
- by (auto simp:RecvMsg co2sobj.simps cp2sproc_def split:option.splits)
- from p2 have p2': "sectxt_of_obj s' (O_msgq q) = Some (uq, rq, tq)"
- using os cq2sq vd
- apply (erule_tac x = q in allE)
- by (auto simp:RecvMsg co2sobj.simps cq2smsgq_def dest!:current_has_sms' split:option.splits)
- from p3 have p3': "sectxt_of_obj s' (O_msg q m) = Some (um, rm, tm)"
- using sms_remain cq2sq vd os p2 p2' p3
- apply (erule_tac x = q in allE)
- apply (erule_tac x = q in allE)
- apply (clarsimp simp:RecvMsg)
- apply (simp add:cq2smsgq_def split:option.splits if_splits)
- apply (drule current_has_sms', simp, simp)
- apply (case_tac "msgs_of_queue s q", simp)
- apply (simp add:cqm2sms.simps split:option.splits)
- apply (auto simp add:cm2smsg_def split:option.splits if_splits)[1]
- apply (case_tac "msgs_of_queue s q", simp)
- apply (simp add:cqm2sms.simps split:option.splits)
- apply (auto simp add:cm2smsg_def split:option.splits if_splits)[1]
- done
- show ?thesis using p1' p2' p3' grant p1 p2 p3
+ moreover have "grant s' e"
+ proof-
+ from grant obtain up rp tp uq rq tq
+ where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
+ and p2: "sectxt_of_obj s (O_msgq q) = Some (uq, rq, tq)"
+ apply (simp add:SendMsg split:option.splits)
+ by (case_tac a, case_tac aa, blast)
+ from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
+ using os cp2sp
+ apply (erule_tac x = p in allE)
+ by (auto simp:SendMsg co2sobj.simps cp2sproc_def split:option.splits)
+ from p2 have p2': "sectxt_of_obj s' (O_msgq q) = Some (uq, rq, tq)"
+ using os cq2sq vd
+ apply (erule_tac x = q in allE)
+ by (auto simp:SendMsg co2sobj.simps cq2smsgq_def dest!:current_has_sms' split:option.splits)
+ show ?thesis using p1' p2' grant p1 p2
+ by (simp add:SendMsg)
+ qed
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ next
+ case (RecvMsg p q m)
+ have p_in: "p \<in> current_procs s'" using os alive
+ apply (erule_tac x = "O_proc p" in allE)
+ by (auto simp:RecvMsg)
+ have q_in: "q \<in> current_msgqs s'" using os alive
+ apply (erule_tac x = "O_msgq q" in allE)
+ by (simp add:RecvMsg)
+ have m_in: "m = hd (msgs_of_queue s' q)"
+ and sms_not_empty: "msgs_of_queue s' q \<noteq> []"
+ using os sms_remain
+ by (auto simp:RecvMsg)
+ have "os_grant s' e" using p_in q_in m_in sms_not_empty os
by (simp add:RecvMsg)
- qed
- ultimately show ?thesis using vs'
- by (erule_tac valid.intros(2), simp+)
-next
- case (CreateSock p af st fd inum)
- show ?thesis using grant
- by (simp add:CreateSock)
-next
- case (Bind p fd addr)
- show ?thesis using grant
- by (simp add:Bind)
-next
- case (Connect p fd addr)
- show ?thesis using grant
- by (simp add:Connect)
-next
- case (Listen p fd)
- show ?thesis using grant
- by (simp add:Listen)
-next
- case (Accept p fd addr port fd' inum)
- show ?thesis using grant
- by (simp add:Accept)
-next
- case (SendSock p fd)
- show ?thesis using grant
- by (simp add:SendSock)
-next
- case (RecvSock p fd)
- show ?thesis using grant
- by (simp add:RecvSock)
-next
- case (Shutdown p fd how)
- show ?thesis using grant
- by (simp add:Shutdown)
-qed
-
-lemma not_all_procs_prop2:
- "p' \<notin> all_procs s \<Longrightarrow> p' \<notin> init_procs"
-apply (induct s, simp)
-by (case_tac a, auto)
-
-lemma not_all_procs_prop3:
- "p' \<notin> all_procs s \<Longrightarrow> p' \<notin> current_procs s"
-apply (induct s, simp)
-by (case_tac a, auto)
-
-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)"
+ moreover have "grant s' e"
+ proof-
+ from grant obtain up rp tp uq rq tq um rm tm
+ where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
+ and p2: "sectxt_of_obj s (O_msgq q) = Some (uq, rq, tq)"
+ and p3: "sectxt_of_obj s (O_msg q m) = Some (um, rm, tm)"
+ apply (simp add:RecvMsg split:option.splits)
+ by (case_tac a, case_tac aa, case_tac ab, blast)
+ from p1 have p1': "sectxt_of_obj s' (O_proc p) = Some (up, rp, tp)"
+ using os cp2sp
+ apply (erule_tac x = p in allE)
+ by (auto simp:RecvMsg co2sobj.simps cp2sproc_def split:option.splits)
+ from p2 have p2': "sectxt_of_obj s' (O_msgq q) = Some (uq, rq, tq)"
+ using os cq2sq vd
+ apply (erule_tac x = q in allE)
+ by (auto simp:RecvMsg co2sobj.simps cq2smsgq_def dest!:current_has_sms' split:option.splits)
+ from p3 have p3': "sectxt_of_obj s' (O_msg q m) = Some (um, rm, tm)"
+ using sms_remain cq2sq vd os p2 p2' p3
+ apply (erule_tac x = q in allE)
+ apply (erule_tac x = q in allE)
+ apply (clarsimp simp:RecvMsg)
+ apply (simp add:cq2smsgq_def split:option.splits if_splits)
+ apply (drule current_has_sms', simp, simp)
+ apply (case_tac "msgs_of_queue s q", simp)
+ apply (simp add:cqm2sms.simps split:option.splits)
+ apply (auto simp add:cm2smsg_def split:option.splits if_splits)[1]
+ apply (case_tac "msgs_of_queue s q", simp)
+ apply (simp add:cqm2sms.simps split:option.splits)
+ apply (auto simp add:cm2smsg_def split:option.splits if_splits)[1]
+ done
+ show ?thesis using p1' p2' p3' grant p1 p2 p3
+ by (simp add:RecvMsg)
+ qed
+ ultimately show ?thesis using vs'
+ by (erule_tac valid.intros(2), simp+)
+ next
+ case (CreateSock p af st fd inum)
+ show ?thesis using grant
+ by (simp add:CreateSock)
+ next
+ case (Bind p fd addr)
+ show ?thesis using grant
+ by (simp add:Bind)
+ next
+ case (Connect p fd addr)
+ show ?thesis using grant
+ by (simp add:Connect)
+ next
+ case (Listen p fd)
+ show ?thesis using grant
+ by (simp add:Listen)
+ next
+ case (Accept p fd addr port fd' inum)
+ show ?thesis using grant
+ by (simp add:Accept)
+ next
+ case (SendSock p fd)
+ show ?thesis using grant
+ by (simp add:SendSock)
+ next
+ case (RecvSock p fd)
+ show ?thesis using grant
+ by (simp add:RecvSock)
+ next
+ case (Shutdown p fd how)
+ show ?thesis using grant
+ by (simp add:Shutdown)
+ qed
+qed
lemma created_proc_clone:
"valid (Clone p p' fds # s) \<Longrightarrow>
@@ -1157,7 +1276,8 @@
done
lemma enrich_proc_dup_ffd':
- "\<lbrakk>file_of_proc_fd (enrich_proc s p p') p' fd = Some f; is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk>
+ "\<lbrakk>file_of_proc_fd (enrich_proc s p p') 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)
@@ -1165,6 +1285,14 @@
dest:not_all_procs_prop3 split:if_splits option.splits)
done
+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') 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') p' fd")
+apply (auto dest:enrich_proc_dup_ffd enrich_proc_dup_ffd')
+done
+
lemma current_fflag_in_fds:
"\<lbrakk>flags_of_proc_fd s p fd = Some flag; valid s\<rbrakk> \<Longrightarrow> fd \<in> current_proc_fds s p"
apply (induct s arbitrary:p)
@@ -1192,7 +1320,7 @@
done
lemma enrich_proc_dup_ffds:
- "\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk>
+ "\<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)
@@ -1202,7 +1330,7 @@
done
lemma enrich_proc_dup_ffds_eq_fds:
- "\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk>
+ "\<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)