theory Enrich
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
lemma get_parentfs_ctxts_prop:
"\<lbrakk>get_parentfs_ctxts s (a # f) = Some ctxts; sectxt_of_obj s (O_dir f) = Some ctxt; valid s\<rbrakk>
\<Longrightarrow> ctxt \<in> set (ctxts)"
apply (induct f)
apply (auto split:option.splits)
done
lemma search_check_allp_intro:
"\<lbrakk>search_check s sp pf; get_parentfs_ctxts s pf = Some ctxts; valid s; is_dir s pf\<rbrakk>
\<Longrightarrow> search_check_allp sp (set ctxts)"
apply (case_tac pf)
apply (simp split:option.splits if_splits add:search_check_allp_def)
apply (rule ballI)
apply (auto simp:search_check_ctxt_def search_check_dir_def split:if_splits option.splits)
apply (auto simp:search_check_allp_def search_check_file_def)
apply (frule is_dir_not_file, simp)
done
lemma search_check_leveling_f:
"\<lbrakk>search_check s sp pf; parent f = Some pf; is_file s f; valid s;
sectxt_of_obj s (O_file f) = Some fctxt; search_check_file sp fctxt\<rbrakk>
\<Longrightarrow> search_check s sp f"
apply (case_tac f, simp+)
apply (auto split:option.splits simp:search_check_ctxt_def)
apply (frule parentf_is_dir_prop2, simp)
apply (erule get_pfs_secs_prop, simp)
apply (erule_tac search_check_allp_intro, simp_all)
apply (simp add:parentf_is_dir_prop2)
done
lemma enrich_proc_prop:
"\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk>
\<Longrightarrow> valid (enrich_proc s p p') \<and>
(\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj) \<and>
(\<forall> obj. enrich_not_alive s obj \<longrightarrow> enrich_not_alive (enrich_proc s p p') obj) \<and>
(files_hung_by_del (enrich_proc s p p') = files_hung_by_del s) \<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 f. file_of_proc_fd s tp fd = Some f \<longrightarrow> file_of_proc_fd (enrich_proc s p p') tp fd = Some f) \<and>
(\<forall> tp fd flags. flags_of_proc_fd s tp fd = Some flags \<longrightarrow>
flags_of_proc_fd (enrich_proc s p p') tp fd = Some flags) \<and>
(\<forall> q. msgs_of_queue (enrich_proc s p p') q = msgs_of_queue 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"
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 Cons have pre: "is_created_proc s p \<Longrightarrow> valid (enrich_proc s p p') \<and>
(\<forall>obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj) \<and>
(\<forall>obj. enrich_not_alive s obj \<longrightarrow> enrich_not_alive (enrich_proc s p p') obj) \<and>
files_hung_by_del (enrich_proc s p p') = files_hung_by_del s \<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 f. file_of_proc_fd s tp fd = Some f \<longrightarrow> file_of_proc_fd (enrich_proc s p p') tp fd = Some f) \<and>
(\<forall>tp fd flags.
flags_of_proc_fd s tp fd = Some flags \<longrightarrow> flags_of_proc_fd (enrich_proc s p p') tp fd = Some flags) \<and>
(\<forall>q. msgs_of_queue (enrich_proc s p p') q = msgs_of_queue 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 by auto
have alive_pre: "is_created_proc s p \<Longrightarrow> (\<forall>obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj)"
using pre by simp
hence curf_pre: "is_created_proc s p \<Longrightarrow> (\<forall>f. f \<in> current_files s \<longrightarrow> f \<in> current_files (enrich_proc s p p'))"
using vd apply auto
apply (drule is_file_or_dir, simp)
apply (erule disjE)
apply (erule_tac x = "O_file f" in allE, simp add:is_file_in_current)
apply (erule_tac x = "O_dir f" in allE, simp add:is_dir_in_current)
done
have vd_enrich_cons: "valid (enrich_proc (e # s) p p')"
proof-
from pre have pre': "is_created_proc s p \<Longrightarrow> valid (enrich_proc s p p')" by simp
have "is_created_proc s p \<Longrightarrow> valid (e # enrich_proc s p p')"
apply (frule pre')
apply (erule_tac s = s in enrich_valid_intro_cons)
apply (simp_all add:os grant vd pre)
done
moreover 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 ffd_remain: "\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow>
file_of_proc_fd (enrich_proc s p p') tp fd = Some f"
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"
proof-
from pre a2
have a4: "\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj"
by (auto)
show ?thesis using a3 a4
apply (erule_tac x = "O_file f" in allE)
by (auto dest:vt_grant_os)
qed
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')
by (auto simp:a2 curf_pre)
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 ffd_remain: "\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow>
file_of_proc_fd (enrich_proc s p p') tp fd = Some f"
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
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"
proof-
from pre a2
have a4: "\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj"
by (auto)
show ?thesis using a3 a4 None
apply (erule_tac x = "O_file f" in allE)
by (auto dest:vt_grant_os)
qed
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 curf_pre a2
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)
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'
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')
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 ffd_remain: "\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow>
file_of_proc_fd (enrich_proc s p p') tp fd = Some f"
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
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 curf_pre
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)
with alive_pre a2 have isfile_s': "is_file (enrich_proc s p p') f"
apply simp
apply (erule_tac x = "O_file f" in allE, simp)
done
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 created_cons vd_cons' all_procs_cons
apply (case_tac e)
apply (auto simp:is_created_proc_simps split:if_splits)
done
qed
moreover have "\<forall>obj. alive (e # s) obj \<longrightarrow> alive (enrich_proc (e # s) p p') obj"
proof clarify
fix obj
assume a0: "alive (e # s) obj"
have a1: "is_created_proc s p \<Longrightarrow> \<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj"
using pre by auto
show "alive (enrich_proc (e # s) p p') obj" (*
proof (cases e)
case (Execve tp f fds)
with created_cons a1
have b1: "\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj"
by (auto simp:is_created_proc_simps)
show ?thesis
using created_cons all_procs_cons vd_enrich_cons Execve b1 os a0
apply (simp add:alive_execve split:if_splits)
apply (frule_tac vd_cons) defer
apply (frule_tac vd_cons)
using vd_cons' Execve vd os
apply (auto simp:is_file_simps is_dir_simps is_created_proc_simps alive.simps
split:t_object.splits if_splits
dest:set_mp file_fds_subset_pfds)
apply (erule_tac x = "O_proc nat" in allE, simp)
apply (erule_tac x = "O_file list" in allE, simp)
apply (drule set_mp, simp)
apply (drule_tac s = s and p = tp in file_fds_subset_pfds)
apply (erule_tac x = "O_fd tp nat2" in allE, simp)
apply (auto)[1]
apply (erule_tac x = "O_fd nat1 nat2" in allE, auto dest:set_mp file_fds_subset_pfds)[1]
apply (erule_tac x = "O_dir list" in allE, simp)
sorry
show ?thesis *) sorry
moreover have "\<forall>obj. enrich_not_alive (e # s) obj \<longrightarrow> enrich_not_alive (enrich_proc (e # s) p p') obj"
thm enrich_not_alive.simps
sorry
moreover have "files_hung_by_del (enrich_proc (e # s) p p') = files_hung_by_del (e # s)"
proof-
have "is_created_proc s p \<Longrightarrow> files_hung_by_del (enrich_proc s p p') = files_hung_by_del s"
and ffd_remain: "is_created_proc s p \<Longrightarrow>
\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow>
file_of_proc_fd (enrich_proc s p p') tp fd = Some f"
using pre by auto
with created_cons all_procs_cons os vd_cons' vd
show ?thesis
apply (frule_tac not_all_procs_prop3)
apply (case_tac e)
apply (auto simp:files_hung_by_del.simps is_created_proc_simps)
apply (auto simp:enrich_proc_dup_ffd_eq proc_file_fds_def procfd_of_file_eq_fpfd''
dest:procfd_of_file_imp_fpfd procfd_of_file_imp_fpfd' procfd_of_file_non_empty
)
apply (auto simp:enrich_proc_dup_ffd_eq proc_file_fds_def split:if_splits)[1]
apply (auto simp:enrich_proc_dup_ffd_eq proc_file_fds_def files_hung_by_del.simps
split:option.splits)[1]
apply (auto split:option.splits)[1]
thm is_created_proc_simps
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 "\<forall>f. f \<in> current_files (e # s) \<longrightarrow> cf2sfile (enrich_proc (e # s) p p') f = cf2sfile (e # s) f"
sorry
moreover have "\<forall>q. q \<in> current_msgqs (e # s) \<longrightarrow> cq2smsgq (enrich_proc (e # s) p p') q = cq2smsgq (e # s) q"
sorry
moreover have "\<forall>tp fd f. file_of_proc_fd (e # s) tp fd = Some f \<longrightarrow>
file_of_proc_fd (enrich_proc (e # s) p p') tp fd = Some f"
sorry
moreover have "\<forall>tp fd flags. flags_of_proc_fd (e # s) tp fd = Some flags \<longrightarrow>
flags_of_proc_fd (enrich_proc (e # s) p p') tp fd = Some flags"
sorry
moreover have "\<forall>q. msgs_of_queue (enrich_proc (e # s) p p') q = msgs_of_queue (e # s) q"
sorry
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"
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
thm not_all_procs_prop3
apply (frule_tac not_all_procs_prop2)
apply (frule not_all_procs_prop3)
apply (auto simp add:cp2sproc_execve is_created_proc_def split:option.splits dest!:current_has_sec'
dest:vt_grant_os)
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)
apply (simp_all only:b1 b2 b3 b4 b5 b6 b7)
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
by simp
qed
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