theory Enrich

imports Main Flask Static Init_prop Valid_prop Tainted_prop Delete_prop Co2sobj_prop S2ss_prop S2ss_prop2

 Temp

begin

datatype t_enrich_obj = 

  E_proc "t_process"

| E_file "t_file"

| E_fd   "t_process" "t_fd"

| E_inum "nat"

| E_msgq "t_msgq"

| E_msg  "t_msgq"    "t_msg"

context tainting_s begin

(* enrich s target_proc duplicated_pro *)

fun enrich_proc :: "t_state \<Rightarrow> t_process \<Rightarrow> t_process \<Rightarrow> t_state"

where 

  "enrich_proc [] tp dp = []"

| "enrich_proc (Execve p f fds # s) tp dp = (

     if (tp = p) 

     then Execve dp f (fds \<inter> proc_file_fds s p) # Execve p f fds # (enrich_proc s tp dp)

     else Execve p f fds # (enrich_proc s tp dp))"

| "enrich_proc (Clone p p' fds # s) tp dp = (

     if (tp = p') 

     then Clone p dp (fds \<inter> proc_file_fds s p) # Clone p p' fds # s

     else Clone p p' fds # (enrich_proc s tp dp))"

| "enrich_proc (Open p f flags fd opt # s) tp dp = (

     if (tp = p)

     then Open dp f (remove_create_flag flags) fd None # Open p f flags fd opt # (enrich_proc s tp dp)

     else Open p f flags fd opt # (enrich_proc s tp dp))"

| "enrich_proc (ReadFile p fd # s) tp dp = (

     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)

     then Attach dp h flag # Attach p h flag # (enrich_proc s tp dp)

     else Attach p h flag # (enrich_proc s tp dp))"

| "enrich_proc (Detach p h # s) tp dp = (

     if (tp = p) 

     then Detach dp h # Detach p h # (enrich_proc s tp dp)

     else Detach p h # (enrich_proc s tp dp))"

*)

| "enrich_proc (Kill p p' # s) tp dp = (

     if (tp = p') then Kill p p' # s

     else Kill p p' # (enrich_proc s tp dp))"

| "enrich_proc (Exit p # s) tp dp = (

     if (tp = p) then Exit p # s

     else Exit p # (enrich_proc s tp dp))"

| "enrich_proc (e # s) tp dp = e # (enrich_proc s tp dp)"

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"

  and vd: "valid s" and f_in: "is_file s f"  and f_in': "is_file s' f"

  and sec: "sectxt_of_obj s' (O_file f) = sectxt_of_obj s (O_file f)"

  shows "search_check s' (up, rp, tp) f"

proof (cases f)

  case Nil

  with f_in vd have "False" 

    by (auto dest:root_is_dir') 

  thus ?thesis by simp

next

  case (Cons n pf)

  from vd f_in obtain sf where sf: "cf2sfile s f = Some sf"

    apply (drule_tac is_file_in_current, drule_tac current_file_has_sfile, simp)

    apply (erule exE, simp)

    done

  then obtain psfs where psfs: "get_parentfs_ctxts s pf = Some psfs" using Cons

    by (auto simp:cf2sfile_def split:option.splits if_splits)

  from sf cf2sf f_in have sf': "cf2sfile s' f = Some sf" by (auto dest:is_file_in_current)

  then obtain psfs' where psfs': "get_parentfs_ctxts s' pf = Some psfs'"using Cons

    by (auto simp:cf2sfile_def split:option.splits if_splits)

  with sf sf' psfs have psfs_eq: "set psfs' = set psfs" using Cons f_in f_in'

    apply (simp add:cf2sfile_def split:option.splits)

    apply (case_tac sf, simp)

    done

  show ?thesis using grant f_in f_in' psfs psfs' psfs_eq sec

    apply (simp add:Cons split:option.splits)

    by (case_tac a, simp)

qed

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"

  and vd: "valid s" and vd': "valid s'" and f_in: "is_dir s f"  and f_in': "is_dir s' f"

  and sec: "sectxt_of_obj s' (O_dir f) = sectxt_of_obj s (O_dir f)"

  shows "search_check s' (up, rp, tp) f"

proof (cases f)

  case Nil

  have "sectxt_of_obj s' (O_dir []) = sectxt_of_obj s (O_dir [])"

    using cf2sf 

    apply (erule_tac x = "[]" in allE)

    by (auto simp:cf2sfile_def root_sec_remains vd vd')

  thus ?thesis using grant Nil 

    by auto

next

  case (Cons n pf)

  from vd f_in obtain sf where sf: "cf2sfile s f = Some sf"

    apply (drule_tac is_dir_in_current, drule_tac current_file_has_sfile, simp)

    apply (erule exE, simp)

    done

  then obtain psfs where psfs: "get_parentfs_ctxts s pf = Some psfs" using Cons

    by (auto simp:cf2sfile_def split:option.splits if_splits)

  from sf cf2sf f_in have sf': "cf2sfile s' f = Some sf" by (auto dest:is_dir_in_current)

  then obtain psfs' where psfs': "get_parentfs_ctxts s' pf = Some psfs'"using Cons

    by (auto simp:cf2sfile_def split:option.splits if_splits)

  with sf sf' psfs have psfs_eq: "set psfs' = set psfs" using Cons f_in f_in'

    apply (drule_tac is_dir_not_file)

    apply (drule is_dir_not_file)    

    apply (simp add:cf2sfile_def split:option.splits)

    apply (case_tac sf, simp)

    done

  show ?thesis using grant f_in f_in' psfs psfs' psfs_eq sec

    apply (drule_tac is_dir_not_file)

    apply (drule_tac is_dir_not_file)

    apply (simp add:Cons split:option.splits)

    by (case_tac a, simp)

qed

lemma proc_filefd_has_sfd: "\<lbrakk>fd \<in> proc_file_fds s p; valid s\<rbrakk> \<Longrightarrow> \<exists> sfd. cfd2sfd s p fd = Some sfd"

apply (simp add:proc_file_fds_def)

apply (auto dest: current_filefd_has_sfd)

done

lemma enrich_inherit_fds_check:

  assumes grant: "inherit_fds_check s (up, nr, nt) p fds"  and vd: "valid s"

  and cfd2sfd: "\<forall> p fd. fd \<in> proc_file_fds s p\<longrightarrow> cfd2sfd s' p fd = cfd2sfd s p fd"

  and fd_in: "fds \<subseteq> proc_file_fds s p" and fd_in': "fds \<subseteq> proc_file_fds s' p"

  shows "inherit_fds_check s' (up, nr, nt) p fds"

proof-

  have "\<And> fd. fd \<in> fds \<Longrightarrow> sectxt_of_obj s' (O_fd p fd) = sectxt_of_obj s (O_fd p fd)"

  proof-

    fix fd

    assume fd_in_fds: "fd \<in> fds"

    hence fd_in_cfds: "fd \<in> proc_file_fds s p" 

      and fd_in_cfds': "fd \<in> proc_file_fds s' p" 

      using fd_in fd_in' by auto

    with cfd2sfd

    have cfd_eq: "cfd2sfd s' p fd = cfd2sfd s p fd" by auto

    from fd_in_cfds obtain f where ffd: "file_of_proc_fd s p fd = Some f"

      by (auto simp:proc_file_fds_def)

    moreover have "flags_of_proc_fd s p fd \<noteq> None"

      using ffd vd by (auto dest:current_filefd_has_flags)

    moreover have "sectxt_of_obj s (O_fd p fd) \<noteq> None"

      using fd_in_cfds vd

      apply (rule_tac notI)

      by (auto dest!:current_has_sec' file_fds_subset_pfds[where p = p] intro:vd)

    moreover have "cf2sfile s f \<noteq> None"

      apply (rule notI)

      apply (drule current_file_has_sfile')

      using ffd

      by (auto simp:vd is_file_in_current dest:file_of_pfd_is_file)

    ultimately show "sectxt_of_obj s' (O_fd p fd) = sectxt_of_obj s (O_fd p fd)"

      using cfd_eq

      by (auto simp:cfd2sfd_def split:option.splits)

  qed

  hence "sectxts_of_fds s' p fds = sectxts_of_fds s p fds"

    by (simp add:sectxts_of_fds_def)

  thus ?thesis using grant

    by (simp add:inherit_fds_check_def)

qed

lemma enrich_inherit_fds_check_dup:

  assumes grant: "inherit_fds_check s (up, nr, nt) p fds"  and vd: "valid s"

  and cfd2sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd s' p' fd = cfd2sfd s p fd"

  and fd_in: "fds' \<subseteq> fds \<inter> proc_file_fds s p" 

  shows "inherit_fds_check s' (up, nr, nt) p' fds'"

proof- 

  have "sectxts_of_fds s' p' fds' \<subseteq> sectxts_of_fds s p fds"

  proof-

    have "\<And> fd sfd. \<lbrakk>fd \<in> fds'; sectxt_of_obj s' (O_fd p' fd) = Some sfd\<rbrakk> 

                     \<Longrightarrow> \<exists> fd \<in> fds. sectxt_of_obj s (O_fd p fd) = Some sfd"

    proof-

      fix fd sfd

      assume fd_in_fds': "fd \<in> fds'"

        and sec: "sectxt_of_obj s' (O_fd p' fd) = Some sfd"

      from fd_in_fds' fd_in

      have fd_in_fds: "fd \<in> fds" and fd_in_cfds: "fd \<in> proc_file_fds s p" 

        by auto

      from fd_in_cfds obtain f where ffd: "file_of_proc_fd s p fd = Some f"

        by (auto simp:proc_file_fds_def)

      moreover have "flags_of_proc_fd s p fd \<noteq> None"

        using ffd vd by (auto dest:current_filefd_has_flags)

      moreover have "cf2sfile s f \<noteq> None"

        apply (rule notI)

        apply (drule current_file_has_sfile')

        using ffd

        by (auto simp:vd is_file_in_current dest:file_of_pfd_is_file)

      moreover have "sectxt_of_obj s (O_fd p fd) \<noteq> None"

        using fd_in_cfds vd

        apply (rule_tac notI)

        by (auto dest!:current_has_sec' file_fds_subset_pfds[where p = p] intro:vd)

      ultimately 

      have "sectxt_of_obj s (O_fd p fd) = Some sfd"

        using fd_in_cfds cfd2sfd sec

        apply (erule_tac x = fd in allE)

        apply (auto simp:cfd2sfd_def split:option.splits)

        done

      thus "\<exists> fd \<in> fds. sectxt_of_obj s (O_fd p fd) = Some sfd"

        using fd_in_fds

        by (rule_tac x = fd in bexI, auto)

    qed

    thus ?thesis by (auto simp:sectxts_of_fds_def)

  qed

  thus ?thesis using grant

    by (auto simp:inherit_fds_check_def inherit_fds_check_ctxt_def)

qed

lemma enrich_valid_intro_cons:

    and alive: "\<forall> obj. alive s obj \<longrightarrow> alive s' 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"

    and cq2sq: "\<forall> q. q \<in> current_msgqs s \<longrightarrow> cq2smsgq s' q = cq2smsgq s q"

    and ffd_remain: "\<forall> p fd f. file_of_proc_fd s p fd = Some f \<longrightarrow> file_of_proc_fd s' p fd = Some f"

    and fflags_remain: "\<forall> p fd flags. flags_of_proc_fd s p fd = Some flags \<longrightarrow> flags_of_proc_fd s' p fd = Some flags"

    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"

  shows "valid (e # s')"

  show ?thesis

    have p_in: "p \<in> current_procs s'" using os alive

      apply (erule_tac x = "O_proc p" in allE)

    have f_in: "is_file s' f" using os alive

      apply (erule_tac x = "O_file f" in allE)

    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)" 

      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)

      from vd os have "\<exists> sf. cf2sfile s f = Some sf"

      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

        apply (rule_tac s = s in enrich_search_check)

        by (simp_all split:option.splits)