theory Tainted_prop 

imports Main Flask Flask_type Init_prop Current_files_prop Current_sockets_prop Delete_prop Proc_fd_of_file_prop Current_prop Alive_prop

begin

ML {*quick_and_dirty := true*}

context tainting begin

lemma valid_tainted_obj:

  "\<lbrakk>obj \<in> tainted s; valid s\<rbrakk> \<Longrightarrow> (\<forall> f. obj \<noteq> O_dir f) \<and> (\<forall> q. obj \<noteq> O_msgq q) \<and> (\<forall> p fd. obj \<noteq> O_fd p fd) \<and> (\<forall> s. obj \<noteq> O_tcp_sock s) \<and> (\<forall> s. obj \<noteq> O_udp_sock s)" (*(\<forall> h. obj \<noteq> O_shm h) \<and>*)

apply (induct s, simp)

apply (drule seeds_appropriate, case_tac obj, simp+)

apply (frule vd_cons, frule vt_grant_os, case_tac a)

apply (auto split:if_splits option.splits)

done

lemma dir_not_tainted: "\<lbrakk>O_dir f \<in> tainted s; valid s\<rbrakk> \<Longrightarrow> False"

by (auto dest!:valid_tainted_obj)

lemma msgq_not_tainted: "\<lbrakk>O_msgq q \<in> tainted s; valid s\<rbrakk> \<Longrightarrow> False"

by (auto dest:valid_tainted_obj)

lemma tainted_in_current:

  "\<lbrakk>obj \<in> tainted s; valid s\<rbrakk> \<Longrightarrow> alive s obj"

apply (induct s, simp)

apply (drule seeds_appropriate, case_tac obj, simp_all add:is_file_nil)

apply (frule vd_cons, frule valid_tainted_obj, simp, frule vt_grant_os, case_tac a)

apply (auto simp:alive_simps split:if_splits option.splits t_object.splits

           intro:same_inode_files_prop1 (*procs_of_shm_prop2 

            dest:info_shm_flow_in_procs *))

apply (auto simp:same_inode_files_def is_file_def split:if_splits)

done 

lemma tainted_proc_in_current:

  "\<lbrakk>O_proc p \<in> tainted s; valid s\<rbrakk> \<Longrightarrow> p \<in> current_procs s"

by (drule tainted_in_current, simp+)

(*

lemma info_flow_shm_tainted:

  "\<lbrakk>O_proc p \<in> tainted s; info_flow_shm s p p'; valid s\<rbrakk> \<Longrightarrow> O_proc p' \<in> tainted s"

proof (induct s arbitrary:p p')

  case Nil

  thus ?case by (simp add:flow_shm_in_seeds)

next

  case (Cons e s)

  hence p1: "O_proc p \<in> tainted (e # s)" and p2: "info_flow_shm (e # s) p p'" and p3: "valid (e # s)"  

    and p4: "\<And> p p'. \<lbrakk>O_proc p \<in> tainted s; info_flow_shm s p p'\<rbrakk> \<Longrightarrow> O_proc p' \<in> tainted s" 

    and p5: "valid s" and p6: "os_grant s e"

    by (auto dest:vd_cons intro:vd_cons vt_grant_os)

  have p4': 

    "\<And> p p' h flag. \<lbrakk>O_proc p \<in> tainted s; (p, SHM_RDWR) \<in> procs_of_shm s h; (p', flag) \<in> procs_of_shm s h\<rbrakk> 

                \<Longrightarrow> O_proc p' \<in> tainted s"

    by (rule p4, auto simp:info_flow_shm_def one_flow_shm_def procs_of_shm_prop2 p5)    

  from p2 p3 have p7: "p \<in> current_procs (e # s)" and p8: "p' \<in> current_procs (e # s)" 

    by (auto dest:info_shm_flow_in_procs) 

  show ?case

  proof (cases "self_shm s p p'")

    case True with p1 show ?thesis by simp

  next

    case False

    with p1 p2 p5 p6 p7 p8 p3 show ?thesis

    apply (case_tac e)(*

    prefer 7

    apply (simp add:info_flow_shm_simps split:if_splits option.splits)

    apply (rule allI|rule impI|rule conjI)+

    apply simp

    apply (case_tac "O_proc p \<in> tainted s", drule_tac p'=p' in p4, simp+)

    apply simp

    apply (auto simp:info_flow_shm_simps one_flow_shm_def dest:tainted_in_current 

  intro:p4 p4' split:if_splits option.splits)

    apply (auto simp:info_flow_shm_def one_flow_shm_def)

    apply (auto simp:one_flow_shm_def intro:p4 p4' split:if_splits option.splits)

    prefer 7

    apply (simp split:if_splits option.splits)

    apply (rule allI|rule impI|rule conjI)+

    apply (auto dest:p4'   procs_of_shm_prop2 tainted_in_current split:if_splits option.splits)[1]

    apply (erule disjE, drule_tac p = p and p' = p' in p4', simp+)

    apply (erule disjE, rule disjI2, rule disjI2, rule_tac x = h in exI, simp, rule_tac x= toflag in exI, simp)

    apply ((erule exE|erule conjE)+)

    apply (auto simp:info_flow_shm_def dest:p4'

           procs_of_shm_prop2 tainted_in_current split:if_splits option.splits)[1]

    apply (drule_tac p = p and p' = p' in p4')

    apply (erule_tac x = ha in allE, simp)

    apply (drule_tac p = "nat1" and p' = p' in p4')

    apply (auto dest:p4'[where p = nat1 and p' = p'])

apply (induct s) 

apply simp defer

apply (frule vd_cons, frule vt_grant_os, case_tac a)

apply (auto simp:info_flow_shm_def elim!:disjE)

sorry *)

  sorry

qed

qed

*)

lemma has_same_inode_comm:

  "has_same_inode s f f' = has_same_inode s f' f"

by (auto simp add:has_same_inode_def same_inode_files_def is_file_def)

(*

lemma info_flow_shm_tainted:

  "\<lbrakk>O_proc p \<in> tainted s; info_flow_shm s p p'; valid s\<rbrakk> \<Longrightarrow> O_proc p' \<in> tainted s"

by (simp only:tainted_eq_tainted info_flow_shm_tainted)

*)

lemma same_inode_files_tainted:

  "\<lbrakk>O_file f \<in> tainted s; f' \<in> same_inode_files s f; valid s\<rbrakk> \<Longrightarrow> O_file f' \<in> tainted s"

apply (induct s arbitrary:f f', simp add:same_inode_in_seeds has_same_inode_def)

apply (frule vt_grant_os, frule vd_cons, case_tac a)

prefer 6

apply (simp split:if_splits option.splits add:same_inode_files_open current_files_simps)

prefer 8

apply (frule tainted_in_current, simp, simp add:alive.simps, drule is_file_in_current)

apply (auto simp add:same_inode_files_closefd split:option.splits if_splits)[1]

prefer 8

apply (frule tainted_in_current, simp, simp add:alive.simps, drule is_file_in_current)

apply (auto simp add:same_inode_files_unlink split:option.splits if_splits)[1]

prefer 10

apply (auto split:if_splits option.splits simp:same_inode_files_linkhard current_files_simps)[1]

apply (drule tainted_in_current, simp, simp add:alive.simps is_file_in_current)

apply (drule same_inode_files_prop5, simp)

apply (drule same_inode_files_prop5, drule_tac f' = list1 and f'' = f' in same_inode_files_prop4, simp, simp)

apply (auto simp:same_inode_files_other split:if_splits)

apply (drule_tac f'' = f' and f' = f and f = fa in same_inode_files_prop4, simp+)

apply (drule_tac f'' = f' and f' = f and f = list in same_inode_files_prop4, simp+)

done

lemma has_same_inode_tainted:

  "\<lbrakk>O_file f \<in> tainted s; has_same_inode s f f'; valid s\<rbrakk> \<Longrightarrow> O_file f' \<in> tainted s"

by (simp add:has_same_inode_def same_inode_files_tainted)

lemma same_inodes_tainted:

  "\<lbrakk>f \<in> same_inode_files s f'; valid s\<rbrakk> \<Longrightarrow> (O_file f \<in> tainted s) = (O_file f' \<in> tainted s)"

apply (frule same_inode_files_prop8, frule same_inode_files_prop7)

apply (auto intro:has_same_inode_tainted)

done

lemma t_remain: "\<lbrakk>obj \<in> tainted s; valid (e # s); alive (e # s) obj\<rbrakk> 

             \<Longrightarrow> obj \<in> tainted (e # s)"

apply (frule vd_cons, frule vt_grant_os, case_tac e)

apply (auto simp:alive_simps split:option.splits if_splits)

done

lemma not_exited_cons:

  "\<not> exited obj (e # s) \<Longrightarrow> \<not> exited obj s"

apply (case_tac e, case_tac [!] obj)

by (auto)

lemma t_remain_app:

  "\<lbrakk>obj \<in> tainted s; \<not> died obj (s' @ s); valid (s' @ s)\<rbrakk> 

  \<Longrightarrow> obj \<in> tainted (s' @ s)"

apply (induct s', simp)

apply (simp (no_asm) only:cons_app_simp_aux, rule t_remain)

apply (simp_all add:not_died_cons_D vd_cons) 

apply (frule tainted_in_current)

apply (simp add:vd_cons)

apply (drule valid_tainted_obj, simp add:vd_cons) 

apply (case_tac a, auto simp:alive_simps split:t_object.splits option.splits)

done

lemma t_remain_app_deleted:

  "\<lbrakk>obj \<in> tainted s; \<not> deleted obj (s' @ s); appropriate obj; \<not> exited obj (s' @ s); valid (s' @ s)\<rbrakk>

   \<Longrightarrow> obj \<in> tainted (s' @ s)"

apply (rule t_remain_app, simp_all add:deleted_died)

done

end

end