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(*<*)
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theory Co2sobj_prop
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imports Main Flask Flask_type Static Static_type Sectxt_prop Init_prop Current_files_prop Current_sockets_prop Delete_prop Proc_fd_of_file_prop Tainted_prop Valid_prop Init_prop Alive_prop
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begin
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(*<*)
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ML {*
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fun print_ss ss =
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let
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val {simps, congs, procs, ...} = Raw_Simplifier.dest_ss ss
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in
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simps
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end
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*}
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context tainting_s begin
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(********************* cm2smsg simpset ***********************)
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lemma cm2smsg_other:
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"\<lbrakk>valid (e # s); \<forall> p q m. e \<noteq> SendMsg p q m; \<forall> p q m. e \<noteq> RecvMsg p q m; \<forall> p q. e \<noteq> RemoveMsgq p q\<rbrakk>
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\<Longrightarrow> cm2smsg (e # s) = cm2smsg s"
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apply (frule vt_grant_os, frule vd_cons, rule ext, rule ext)
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unfolding cm2smsg_def
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apply (case_tac e)
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apply (auto simp:sectxt_of_obj_simps
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split:t_object.splits option.splits if_splits
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dest!:current_has_sec')
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done
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lemma cm2smsg_sendmsg:
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"valid (SendMsg p q m # s) \<Longrightarrow> cm2smsg (SendMsg p q m # s) = (\<lambda> q' m'.
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if (q' = q \<and> m' = m)
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then (case (sectxt_of_obj (SendMsg p q m # s) (O_msg q m)) of
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Some sec \<Rightarrow> Some (Created, sec, O_msg q m \<in> tainted (SendMsg p q m # s))
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| _ \<Rightarrow> None)
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else cm2smsg s q' m') "
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apply (frule vd_cons, frule vt_grant_os, rule ext, rule ext)
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apply (auto simp:cm2smsg_def sectxt_of_obj_simps
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split:if_splits option.splits dest!:current_has_sec')
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done
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lemma cm2smsg_recvmsg1:
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"\<lbrakk>q' \<noteq> q; valid (RecvMsg p q m # s)\<rbrakk> \<Longrightarrow> cm2smsg (RecvMsg p q m # s) q' = cm2smsg s q'"
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apply (frule vd_cons, frule vt_grant_os, rule ext)
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apply (auto simp:cm2smsg_def sectxt_of_obj_simps
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split:if_splits option.splits)
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done
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lemma cm2smsg_recvmsg2:
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"\<lbrakk>m' \<noteq> m; valid (RecvMsg p q m # s)\<rbrakk> \<Longrightarrow> cm2smsg (RecvMsg p q m # s) q m' = cm2smsg s q m'"
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apply (frule vd_cons, frule vt_grant_os)
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apply (auto simp:cm2smsg_def sectxt_of_obj_simps
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split:if_splits option.splits)
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done
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lemma cm2smsg_recvmsg1':
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"\<lbrakk>valid (RecvMsg p q m # s); q' \<noteq> q\<rbrakk> \<Longrightarrow> cm2smsg (RecvMsg p q m # s) q' = cm2smsg s q'"
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apply (frule vd_cons, frule vt_grant_os, rule ext)
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apply (auto simp:cm2smsg_def sectxt_of_obj_simps
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split:if_splits option.splits)
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done
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lemma cm2smsg_recvmsg2':
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"\<lbrakk>valid (RecvMsg p q m # s); m' \<noteq> m\<rbrakk> \<Longrightarrow> cm2smsg (RecvMsg p q m # s) q m' = cm2smsg s q m'"
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apply (frule vd_cons, frule vt_grant_os)
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apply (auto simp:cm2smsg_def sectxt_of_obj_simps
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split:if_splits option.splits)
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done
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lemma cm2smsg_removemsgq:
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"\<lbrakk>q' \<noteq> q; valid (RemoveMsgq p q # s)\<rbrakk> \<Longrightarrow> cm2smsg (RemoveMsgq p q # s) q' = cm2smsg s q'"
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apply (frule vd_cons, frule vt_grant_os, rule ext)
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apply (auto simp:cm2smsg_def sectxt_of_obj_simps
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split:if_splits option.splits)
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done
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lemmas cm2smsg_simps = cm2smsg_sendmsg cm2smsg_recvmsg1' cm2smsg_recvmsg2'
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cm2smsg_removemsgq cm2smsg_other
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(*
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lemma init_cm2smsg_has_smsg:
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"\<lbrakk>m \<in> set (init_msgs_of_queue q); q \<in> init_msgqs\<rbrakk> \<Longrightarrow> \<exists> sm. init_cm2smsg q m = Some sm"
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by (auto simp:init_cm2smsg_def split:option.splits dest:init_msg_has_ctxt)
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*)
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lemma hd_set_prop1:
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"hd l \<notin> set l \<Longrightarrow> l = []"
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by (case_tac l, auto)
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lemma tl_set_prop1:
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"a \<in> set (tl l) \<Longrightarrow> a \<in> set l"
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by (case_tac l, auto)
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lemma current_has_smsg:
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"\<lbrakk>m \<in> set (msgs_of_queue s q); q \<in> current_msgqs s; valid s\<rbrakk> \<Longrightarrow> \<exists> sm. cm2smsg s q m = Some sm"
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apply (induct s)
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apply (simp add:msgs_of_queue.simps current_msgqs.simps)
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apply (frule vt_grant_os, frule vd_cons, case_tac a)
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apply (auto simp:cm2smsg_def sectxt_of_obj_simps split:if_splits option.splits
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dest!:current_has_sec' hd_set_prop1 dest:tl_set_prop1)
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done
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lemma current_has_smsg':
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"\<lbrakk>cm2smsg s q m = None; q \<in> current_msgqs s; valid s\<rbrakk> \<Longrightarrow> m \<notin> set (msgs_of_queue s q)"
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by (auto dest:current_has_smsg)
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lemma cqm2sms_has_sms_aux:
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"\<forall> m \<in> set ms. sectxt_of_obj s (O_msg q m) \<noteq> None \<Longrightarrow> (\<exists> sms. cqm2sms s q ms = Some sms)"
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by (induct ms, auto split:option.splits simp:cm2smsg_def)
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lemma current_has_sms:
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"\<lbrakk>q \<in> current_msgqs s; valid s\<rbrakk> \<Longrightarrow> \<exists> sms. cqm2sms s q (msgs_of_queue s q) = Some sms"
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apply (rule cqm2sms_has_sms_aux)
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apply (auto dest:current_msg_has_sec)
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done
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lemma current_has_sms':
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"\<lbrakk>cqm2sms s q (msgs_of_queue s q) = None; valid s\<rbrakk> \<Longrightarrow> q \<notin> current_msgqs s"
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by (auto dest:current_has_sms)
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(********************* cqm2sms simpset ***********************)
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lemma cqm2sms_other:
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"\<lbrakk>valid (e # s); \<forall> p m. e \<noteq> CreateMsgq p q; \<forall> p q m. e \<noteq> SendMsg p q m;
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\<forall> p q m. e \<noteq> RecvMsg p q m; \<forall> p q. e \<noteq> RemoveMsgq p q\<rbrakk>
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\<Longrightarrow> cqm2sms (e # s) = cqm2sms s"
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apply (rule ext, rule ext)
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apply (induct_tac xa, simp)
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apply (frule vt_grant_os, frule vd_cons, case_tac e)
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apply (auto split:option.splits dest:cm2smsg_other)
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done
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lemma cqm2sms_createmsgq:
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"valid (CreateMsgq p q # s) \<Longrightarrow> cqm2sms (CreateMsgq p q # s) = (\<lambda> q' ms'.
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if (q' = q \<and> ms' = []) then Some []
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else cqm2sms s q' ms')"
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apply (rule ext, rule ext)
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apply (frule vt_grant_os, frule vd_cons, induct_tac ms')
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apply (auto split:if_splits option.splits dest:cm2smsg_other)
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done
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lemma cqm2sms_2:
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"cqm2sms s q (ms @ [m]) =
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(case (cqm2sms s q ms, cm2smsg s q m) of
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(Some sms, Some sm) \<Rightarrow> Some (sms @ [sm])
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| _ \<Rightarrow> None)"
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apply (induct ms, simp split:option.splits)
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by (auto split:option.splits)
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lemmas cqm2sms_simps2 = cqm2sms.simps(1) cqm2sms_2
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declare cqm2sms.simps [simp del]
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lemma cqm2sms_prop1:
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"cqm2sms s q ms = None \<Longrightarrow> \<exists> m \<in> set ms. cm2smsg s q m = None"
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by (induct ms, auto simp:cqm2sms.simps split:option.splits)
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lemma cqm2sms_sendmsg1:
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"\<lbrakk>valid (SendMsg p q m # s); m \<notin> set ms\<rbrakk>
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\<Longrightarrow> cqm2sms (SendMsg p q m # s) q' ms = cqm2sms s q' ms"
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apply (frule vt_grant_os, frule vd_cons)
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apply (frule cm2smsg_sendmsg)
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apply (induct ms rule:rev_induct)
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apply (auto split:if_splits option.splits simp:cqm2sms_simps2)
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done
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lemma cqm2sms_sendmsg2:
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"\<lbrakk>valid (SendMsg p q m # s); q' \<noteq> q\<rbrakk>
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\<Longrightarrow> cqm2sms (SendMsg p q m # s) q' ms = cqm2sms s q' ms"
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apply (frule vt_grant_os, frule vd_cons)
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apply (frule cm2smsg_sendmsg)
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apply (induct ms rule:rev_induct)
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apply (auto split:if_splits option.splits simp:cqm2sms_simps2)
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done
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lemma cqm2sms_sendmsg3:
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"\<lbrakk>valid (SendMsg p q m # s); ms' = msgs_of_queue (SendMsg p q m # s) q\<rbrakk>
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\<Longrightarrow> cqm2sms (SendMsg p q m # s) q ms' =
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(case (cqm2sms s q (msgs_of_queue s q), sectxt_of_obj (SendMsg p q m # s) (O_msg q m)) of
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(Some sms, Some sec) \<Rightarrow> Some (sms @ [(Created, sec, O_msg q m \<in> tainted (SendMsg p q m # s))])
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| _ \<Rightarrow> None)"
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apply (frule vt_grant_os, frule vd_cons)
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apply (frule cm2smsg_sendmsg)
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apply (auto split:if_splits option.splits simp:cqm2sms_simps2 cqm2sms_sendmsg1)
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done
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lemma cqm2sms_sendmsg:
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"\<lbrakk>valid (SendMsg p q m # s); ms' = msgs_of_queue (SendMsg p q m # s) q'\<rbrakk>
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\<Longrightarrow> cqm2sms (SendMsg p q m # s) q' ms' = (
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if (q' = q)
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then (case (cqm2sms s q (msgs_of_queue s q), sectxt_of_obj (SendMsg p q m # s) (O_msg q m)) of
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(Some sms, Some sec) \<Rightarrow> Some (sms @ [(Created, sec, O_msg q m \<in> tainted (SendMsg p q m # s))])
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| _ \<Rightarrow> None)
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else cqm2sms s q' ms' )"
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apply (simp split:if_splits add:cqm2sms_sendmsg2 cqm2sms_sendmsg3)
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done
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lemma cqm2sms_recvmsg1:
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"\<lbrakk>valid (RecvMsg p q m # s); m \<notin> set ms\<rbrakk>
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\<Longrightarrow> cqm2sms (RecvMsg p q m # s) q ms = cqm2sms s q ms"
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apply (frule vt_grant_os, frule vd_cons)
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apply (induct ms rule:rev_induct)
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apply (auto split:if_splits option.splits simp:cqm2sms_simps2 cm2smsg_recvmsg2')
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done
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lemma cqm2sms_recvmsg2:
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"\<lbrakk>valid (RecvMsg p q m # s); q' \<noteq> q\<rbrakk>
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\<Longrightarrow> cqm2sms (RecvMsg p q m # s) q' ms = cqm2sms s q' ms"
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apply (frule vt_grant_os, frule vd_cons)
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apply (induct ms rule:rev_induct)
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apply (auto split:if_splits option.splits simp:cqm2sms_simps2 cm2smsg_recvmsg1')
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done
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lemma cqm2sms_recvmsg:
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"\<lbrakk>valid (RecvMsg p q m # s); ms = msgs_of_queue (RecvMsg p q m # s) q'\<rbrakk>
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\<Longrightarrow> cqm2sms (RecvMsg p q m # s) q' ms = (
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if (q' = q)
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then (case (cqm2sms s q (msgs_of_queue s q)) of
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Some sms \<Rightarrow> Some (tl sms)
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| _ \<Rightarrow> None)
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else cqm2sms s q' ms)"
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apply (frule vt_grant_os, frule vd_cons)
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apply (auto split:if_splits option.splits simp:cqm2sms_recvmsg1 cqm2sms_recvmsg2
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dest!:current_has_sms')
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apply (case_tac "msgs_of_queue s q", simp)
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apply (frule_tac ms = "tl (msgs_of_queue s q)" in cqm2sms_recvmsg1)
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apply (drule_tac q = q in distinct_queue_msgs, simp+)
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apply (case_tac a, auto simp:cqm2sms.simps split:option.splits if_splits)
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done
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lemma cqm2sms_removemsgq:
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"\<lbrakk>valid (RemoveMsgq p q # s); q' \<noteq> q; q' \<in> current_msgqs s\<rbrakk>
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\<Longrightarrow> cqm2sms (RemoveMsgq p q # s) q' ms = cqm2sms s q' ms"
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apply (frule vt_grant_os, frule vd_cons)
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apply (induct ms rule:rev_induct)
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apply (auto simp:cqm2sms_simps2 cm2smsg_removemsgq split:option.splits if_splits)
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done
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lemmas cqm2sms_simps = cqm2sms_other cqm2sms_createmsgq cqm2sms_sendmsg cqm2sms_recvmsg cqm2sms_removemsgq
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(********************* cq2smsgq simpset ***********************)
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lemma cq2smsgq_other:
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"\<lbrakk>valid (e # s); \<forall> p q. e \<noteq> CreateMsgq p q; \<forall> p q m. e \<noteq> SendMsg p q m;
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\<forall> p q m. e \<noteq> RecvMsg p q m; \<forall> p q. e \<noteq> RemoveMsgq p q\<rbrakk>
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\<Longrightarrow> cq2smsgq (e # s) = cq2smsgq s"
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apply (frule cqm2sms_other, simp+)
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apply (frule vd_cons, frule vt_grant_os, rule ext, case_tac e)
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apply (auto simp:cq2smsgq_def sectxt_of_obj_simps
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split:t_object.splits option.splits if_splits)
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done
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lemma cq2smsg_createmsgq:
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"valid (CreateMsgq p q # s)
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\<Longrightarrow> cq2smsgq (CreateMsgq p q # s) = (cq2smsgq s) (q :=
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case (sectxt_of_obj s (O_proc p)) of
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Some psec \<Rightarrow> Some (Created, (fst psec, R_object, (snd o snd) psec), [])
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| None \<Rightarrow> None)"
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apply (frule vd_cons, frule vt_grant_os)
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263 |
apply (frule cqm2sms_createmsgq)
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264 |
apply (rule ext, auto simp:cq2smsgq_def sec_createmsgq
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87
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265 |
split:option.splits if_splits)
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77
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266 |
done
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267 |
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268 |
lemma cq2smsg_sendmsg:
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269 |
"valid (SendMsg p q m # s)
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270 |
\<Longrightarrow> cq2smsgq (SendMsg p q m # s) = (cq2smsgq s) (q :=
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271 |
case (cq2smsgq s q, sectxt_of_obj (SendMsg p q m # s) (O_msg q m)) of
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272 |
(Some (qi, sec, sms), Some msec) \<Rightarrow>
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273 |
Some (qi, sec, sms @ [(Created, msec, O_msg q m \<in> tainted (SendMsg p q m # s))])
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274 |
| _ \<Rightarrow> None)"
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275 |
apply (frule vd_cons, frule vt_grant_os)
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276 |
apply (rule ext)
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277 |
apply (frule_tac q' = x in cqm2sms_sendmsg, simp)
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278 |
apply (auto simp:cq2smsgq_def sectxt_of_obj_simps split:option.splits if_splits
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279 |
dest!:current_has_sms' current_has_sec')
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280 |
done
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281 |
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282 |
lemma current_has_smsgq:
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283 |
"\<lbrakk>q \<in> current_msgqs s; valid s\<rbrakk> \<Longrightarrow> \<exists> sq. cq2smsgq s q = Some sq"
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88
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284 |
by (auto simp:cq2smsgq_def split:option.splits
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285 |
dest!:current_has_sec' current_has_sms' dest:current_has_sec)
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77
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286 |
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287 |
lemma current_has_smsgq':
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288 |
"\<lbrakk>cq2smsgq s q = None; valid s\<rbrakk> \<Longrightarrow> q \<notin> current_msgqs s"
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289 |
by (auto dest:current_has_smsgq)
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290 |
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291 |
lemma cq2smsg_recvmsg:
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292 |
"valid (RecvMsg p q m # s)
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293 |
\<Longrightarrow> cq2smsgq (RecvMsg p q m # s) = (cq2smsgq s) (q :=
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294 |
case (cq2smsgq s q) of
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295 |
Some (qi, sec, sms) \<Rightarrow> Some (qi, sec, tl sms)
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296 |
| _ \<Rightarrow> None)"
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297 |
apply (frule vd_cons, frule vt_grant_os)
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298 |
apply (rule ext, frule_tac q' = x in cqm2sms_recvmsg, simp)
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299 |
apply (auto simp add:cq2smsgq_def sectxt_of_obj_simps split:option.splits if_splits
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300 |
dest!:current_has_sec' current_has_sms' current_has_smsgq')
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|
301 |
done
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302 |
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303 |
lemma cq2smsg_removemsgq:
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304 |
"\<lbrakk>valid (RemoveMsgq p q # s); q' \<noteq> q; q' \<in> current_msgqs s\<rbrakk>
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305 |
\<Longrightarrow> cq2smsgq (RemoveMsgq p q # s) q' = cq2smsgq s q'"
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306 |
apply (frule vd_cons, frule vt_grant_os)
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307 |
apply (auto simp:cq2smsgq_def sectxt_of_obj_simps cqm2sms_removemsgq split:if_splits option.splits
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|
308 |
dest!:current_has_sec' current_has_sms' current_has_smsgq')
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|
309 |
done
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310 |
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311 |
lemmas cq2smsgq_simps = cq2smsgq_other cq2smsg_sendmsg cq2smsg_recvmsg cq2smsg_removemsgq
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312 |
|
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88
|
313 |
(*
|
|
77
|
314 |
lemma sm_in_sqsms_init_aux:
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|
315 |
"\<lbrakk>m \<in> set ms; init_cm2smsg q m = Some sm; q \<in> init_msgqs;
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316 |
init_cqm2sms q ms = Some sms\<rbrakk> \<Longrightarrow> sm \<in> set sms"
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317 |
apply (induct ms arbitrary:m sm sms)
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|
318 |
by (auto split:if_splits option.splits)
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319 |
|
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|
320 |
lemma sm_in_sqsms_init:
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|
321 |
"\<lbrakk>m \<in> set (init_msgs_of_queue q); init_cm2smsg q m = Some sm; q \<in> init_msgqs;
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|
322 |
init_cqm2sms q (init_msgs_of_queue q) = Some sms\<rbrakk> \<Longrightarrow> sm \<in> set sms"
|
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|
323 |
by (simp add:sm_in_sqsms_init_aux)
|
|
88
|
324 |
*)
|
|
77
|
325 |
|
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|
326 |
lemma cqm2sms_prop0:
|
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|
327 |
"\<lbrakk>m \<in> set ms; cm2smsg s q m = Some sm; cqm2sms s q ms = Some sms\<rbrakk> \<Longrightarrow> sm \<in> set sms"
|
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|
328 |
apply (induct ms arbitrary:m sm sms)
|
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|
329 |
apply (auto simp:cqm2sms.simps split:option.splits)
|
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|
330 |
done
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|
331 |
|
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|
332 |
lemma sm_in_sqsms:
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|
333 |
"\<lbrakk>m \<in> set (msgs_of_queue s q); q \<in> current_msgqs s; valid s; cq2smsgq s q = Some (qi, qsec, sms);
|
|
|
334 |
cm2smsg s q m = Some sm\<rbrakk> \<Longrightarrow> sm \<in> set sms"
|
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|
335 |
proof (induct s arbitrary:m q qi qsec sms sm)
|
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|
336 |
case Nil
|
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|
337 |
thus ?case
|
|
88
|
338 |
by (simp split:option.splits)
|
|
77
|
339 |
next
|
|
|
340 |
case (Cons e s)
|
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|
341 |
hence p1:"\<And> m q qi qsec sms sm. \<lbrakk>m \<in> set (msgs_of_queue s q); q \<in> current_msgqs s; valid s;
|
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|
342 |
cq2smsgq s q = Some (qi, qsec, sms); cm2smsg s q m = Some sm\<rbrakk>
|
|
|
343 |
\<Longrightarrow> sm \<in> set sms" and p2: "m \<in> set (msgs_of_queue (e # s) q)"
|
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|
344 |
and p3: "q \<in> current_msgqs (e # s)" and p4: "valid (e # s)"
|
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|
345 |
and p5: "cq2smsgq (e # s) q = Some (qi, qsec, sms)"
|
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|
346 |
and p6: "cm2smsg (e # s) q m = Some sm" by auto
|
|
|
347 |
from p4 have os: "os_grant s e" and vd: "valid s" by (auto dest:vd_cons vt_grant_os)
|
|
|
348 |
(*
|
|
|
349 |
from p1 have p1':
|
|
|
350 |
"\<And> m q qi qsec sms sm ms. \<lbrakk>m \<in> set ms; set ms \<subseteq> set (msgs_of_queue s q); q \<in> current_msgqs s;
|
|
|
351 |
valid s; cq2smsgq s q = Some (qi, qsec, sms); cm2smsg s q m = Some sm\<rbrakk>
|
|
|
352 |
\<Longrightarrow> sm \<in> set "
|
|
|
353 |
*)
|
|
|
354 |
show ?case using p2 p3 p4 p5 p6 vd os
|
|
|
355 |
apply (case_tac e)
|
|
|
356 |
apply (auto simp:cq2smsgq_simps cm2smsg_simps split:if_splits option.splits intro:p1)
|
|
|
357 |
|
|
|
358 |
apply (rule_tac m = m and q = q and qi = qi and qsec = qsec in p1, simp+)
|
|
|
359 |
apply (case_tac "q = nat2", simp)
|
|
|
360 |
apply (drule cq2smsg_createmsgq, simp, simp)
|
|
|
361 |
|
|
|
362 |
apply (drule_tac m = m and q = q and qi = qi and qsec = "(aa,ab,b)" in p1, simp+)
|
|
|
363 |
apply (drule_tac m = m and q = q and qi = qi and qsec = "(aa,ab,b)" in p1, simp+)
|
|
|
364 |
|
|
|
365 |
apply (simp add:cq2smsgq_def split:option.splits)
|
|
|
366 |
apply (rule_tac m = m and sm = sm in cqm2sms_prop0, simp+)
|
|
|
367 |
apply (simp add:cqm2sms_recvmsg)
|
|
|
368 |
done
|
|
|
369 |
qed
|
|
|
370 |
|
|
|
371 |
(****************** cf2sfile path simpset ***************)
|
|
|
372 |
|
|
|
373 |
lemma sroot_only:
|
|
|
374 |
"cf2sfile s [] = Some sroot"
|
|
|
375 |
by (simp add:cf2sfile_def)
|
|
|
376 |
|
|
|
377 |
lemma not_file_is_dir:
|
|
|
378 |
"\<lbrakk>\<not> is_file s f; f \<in> current_files s; valid s\<rbrakk> \<Longrightarrow> is_dir s f"
|
|
|
379 |
by (auto simp:is_file_def current_files_def is_dir_def
|
|
|
380 |
dest:finum_has_itag finum_has_ftag' split:t_inode_tag.splits option.splits)
|
|
|
381 |
|
|
|
382 |
lemma not_dir_is_file:
|
|
|
383 |
"\<lbrakk>\<not> is_dir s f; f \<in> current_files s; valid s\<rbrakk> \<Longrightarrow> is_file s f"
|
|
|
384 |
by (auto simp:is_file_def current_files_def is_dir_def
|
|
|
385 |
dest:finum_has_itag finum_has_ftag' split:t_inode_tag.splits option.splits)
|
|
|
386 |
|
|
|
387 |
lemma is_file_or_dir:
|
|
|
388 |
"\<lbrakk>f \<in> current_files s; valid s\<rbrakk> \<Longrightarrow> is_file s f \<or> is_dir s f"
|
|
|
389 |
by (auto dest:not_dir_is_file)
|
|
|
390 |
|
|
|
391 |
lemma current_file_has_sfile:
|
|
|
392 |
"\<lbrakk>f \<in> current_files s; valid s\<rbrakk> \<Longrightarrow> \<exists> sf. cf2sfile s f = Some sf"
|
|
|
393 |
apply (induct f)
|
|
|
394 |
apply (rule_tac x = "sroot" in exI, simp add:sroot_only)
|
|
|
395 |
apply (frule parentf_in_current', simp, clarsimp)
|
|
|
396 |
apply (frule parentf_is_dir'', simp)
|
|
|
397 |
apply (frule is_file_or_dir, simp)
|
|
|
398 |
apply (auto dest!:current_has_sec'
|
|
|
399 |
simp:cf2sfile_def split:option.splits if_splits dest!:get_pfs_secs_prop')
|
|
|
400 |
done
|
|
|
401 |
|
|
|
402 |
definition sectxt_of_pf :: "t_state \<Rightarrow> t_file \<Rightarrow> security_context_t option"
|
|
|
403 |
where
|
|
|
404 |
"sectxt_of_pf s f = (case f of [] \<Rightarrow> None | (a # pf) \<Rightarrow> sectxt_of_obj s (O_dir pf))"
|
|
|
405 |
|
|
|
406 |
definition get_parentfs_ctxts' :: "t_state \<Rightarrow> t_file \<Rightarrow> (security_context_t list) option"
|
|
|
407 |
where
|
|
|
408 |
"get_parentfs_ctxts' s f = (case f of [] \<Rightarrow> None | (a # pf) \<Rightarrow> get_parentfs_ctxts s pf)"
|
|
|
409 |
|
|
|
410 |
lemma is_file_has_sfile:
|
|
|
411 |
"\<lbrakk>is_file s f; valid s\<rbrakk> \<Longrightarrow> \<exists> sec psec asecs. cf2sfile s f = Some
|
|
|
412 |
(if (\<not> died (O_file f) s \<and> is_init_file f) then Init f else Created,
|
|
|
413 |
sec, Some psec, set asecs) \<and> (sectxt_of_obj s (O_file f) = Some sec) \<and>
|
|
|
414 |
(sectxt_of_pf s f = Some psec) \<and> (get_parentfs_ctxts' s f = Some asecs)"
|
|
|
415 |
apply (case_tac f, simp, drule root_is_dir', simp, simp)
|
|
|
416 |
apply (frule is_file_in_current)
|
|
|
417 |
apply (drule current_file_has_sfile, simp)
|
|
|
418 |
apply (auto simp:cf2sfile_def sectxt_of_pf_def get_parentfs_ctxts'_def split:if_splits option.splits)
|
|
|
419 |
done
|
|
|
420 |
|
|
|
421 |
lemma is_file_has_sfile':
|
|
|
422 |
"\<lbrakk>is_file s f; valid s\<rbrakk> \<Longrightarrow> \<exists> sf. cf2sfile s f = Some sf"
|
|
|
423 |
by (drule is_file_has_sfile, auto)
|
|
|
424 |
|
|
|
425 |
lemma is_dir_has_sfile:
|
|
|
426 |
"\<lbrakk>is_dir s f; valid s\<rbrakk> \<Longrightarrow> (case f of
|
|
|
427 |
[] \<Rightarrow> cf2sfile s f = Some sroot
|
|
|
428 |
| a # pf \<Rightarrow> (\<exists> sec psec asecs. cf2sfile s f = Some
|
|
|
429 |
(if (\<not> died (O_dir f) s \<and> is_init_dir f) then Init f else Created,
|
|
|
430 |
sec, Some psec, set asecs) \<and> (sectxt_of_obj s (O_dir f) = Some sec) \<and>
|
|
|
431 |
(sectxt_of_obj s (O_dir pf) = Some psec) \<and> (get_parentfs_ctxts s pf = Some asecs)))"
|
|
|
432 |
apply (case_tac f, simp add:sroot_only)
|
|
|
433 |
apply (frule is_dir_in_current, frule is_dir_not_file)
|
|
|
434 |
apply (drule current_file_has_sfile, simp)
|
|
|
435 |
apply (auto simp:cf2sfile_def split:if_splits option.splits)
|
|
|
436 |
done
|
|
|
437 |
|
|
|
438 |
lemma is_dir_has_sdir':
|
|
|
439 |
"\<lbrakk>is_dir s f; valid s\<rbrakk> \<Longrightarrow> \<exists> sf. cf2sfile s f = Some sf"
|
|
|
440 |
apply (case_tac f)
|
|
|
441 |
apply (rule_tac x = sroot in exI)
|
|
|
442 |
apply (simp add:sroot_only)
|
|
|
443 |
apply (drule is_dir_has_sfile, auto)
|
|
|
444 |
done
|
|
|
445 |
|
|
|
446 |
lemma sroot_set:
|
|
|
447 |
"valid s \<Longrightarrow> \<exists> sec. sroot = (Init [], sec, None, {}) \<and> sectxt_of_obj s (O_dir []) = Some sec"
|
|
|
448 |
apply (frule root_is_dir)
|
|
|
449 |
apply (drule is_dir_has_sec, simp)
|
|
|
450 |
apply (auto simp:sroot_def sec_of_root_def sectxt_of_obj_def type_of_obj.simps
|
|
|
451 |
root_type_remains root_user_remains
|
|
|
452 |
dest!:root_has_type' root_has_user' root_has_init_type' root_has_init_user'
|
|
|
453 |
split:option.splits)
|
|
|
454 |
done
|
|
|
455 |
|
|
|
456 |
lemma cf2sfile_path_file:
|
|
|
457 |
"\<lbrakk>is_file s (f # pf); valid s\<rbrakk>
|
|
|
458 |
\<Longrightarrow> cf2sfile s (f # pf) = (
|
|
|
459 |
case (cf2sfile s pf) of
|
|
|
460 |
Some (pfi, pfsec, psec, asecs) \<Rightarrow>
|
|
|
461 |
(case (sectxt_of_obj s (O_file (f # pf))) of
|
|
|
462 |
Some fsec \<Rightarrow> Some (if (\<not> died (O_file (f # pf)) s \<and> is_init_file (f # pf)) then Init (f # pf)
|
|
|
463 |
else Created, fsec, Some pfsec, asecs \<union> {pfsec})
|
|
|
464 |
| None \<Rightarrow> None)
|
|
|
465 |
| _ \<Rightarrow> None)"
|
|
|
466 |
apply (frule is_file_in_current, drule parentf_is_dir'', simp)
|
|
|
467 |
apply (frule is_dir_has_sfile, simp, frule is_file_has_sfile, simp)
|
|
|
468 |
apply (frule sroot_set)
|
|
|
469 |
apply (case_tac pf, (clarsimp simp:get_parentfs_ctxts'_def sectxt_of_pf_def)+)
|
|
|
470 |
done
|
|
|
471 |
|
|
|
472 |
lemma cf2sfile_path_dir:
|
|
|
473 |
"\<lbrakk>is_dir s (f # pf); valid s\<rbrakk>
|
|
|
474 |
\<Longrightarrow> cf2sfile s (f # pf) = (
|
|
|
475 |
case (cf2sfile s pf) of
|
|
|
476 |
Some (pfi, pfsec, psec, asecs) \<Rightarrow>
|
|
|
477 |
(case (sectxt_of_obj s (O_dir (f # pf))) of
|
|
|
478 |
Some fsec \<Rightarrow> Some (if (\<not> died (O_dir (f # pf)) s \<and> is_init_dir (f # pf)) then Init (f # pf)
|
|
|
479 |
else Created, fsec, Some pfsec, asecs \<union> {pfsec})
|
|
|
480 |
| None \<Rightarrow> None)
|
|
|
481 |
| _ \<Rightarrow> None)"
|
|
|
482 |
apply (frule is_dir_in_current, drule parentf_is_dir'', simp)
|
|
|
483 |
apply (frule_tac f = "f # pf" in is_dir_has_sfile, simp)
|
|
|
484 |
apply (frule_tac f = "pf" in is_dir_has_sfile, simp)
|
|
|
485 |
apply (frule sroot_set)
|
|
|
486 |
apply (case_tac pf, (clarsimp simp:get_parentfs_ctxts'_def sectxt_of_pf_def)+)
|
|
|
487 |
done
|
|
|
488 |
|
|
|
489 |
lemma cf2sfile_path:
|
|
|
490 |
"\<lbrakk>f # pf \<in> current_files s; valid s\<rbrakk> \<Longrightarrow> cf2sfile s (f # pf) = (
|
|
|
491 |
case (cf2sfile s pf) of
|
|
|
492 |
Some (pfi, pfsec, psec, asecs) \<Rightarrow> (if (is_file s (f # pf))
|
|
|
493 |
then (case (sectxt_of_obj s (O_file (f # pf))) of
|
|
|
494 |
Some fsec \<Rightarrow> Some (if (\<not> died (O_file (f # pf)) s \<and> is_init_file (f # pf)) then Init (f # pf)
|
|
|
495 |
else Created, fsec, Some pfsec, asecs \<union> {pfsec})
|
|
|
496 |
| None \<Rightarrow> None)
|
|
|
497 |
else (case (sectxt_of_obj s (O_dir (f # pf))) of
|
|
|
498 |
Some fsec \<Rightarrow> Some (if (\<not> died (O_dir (f # pf)) s \<and> is_init_dir (f # pf)) then Init (f # pf)
|
|
|
499 |
else Created, fsec, Some pfsec, asecs \<union> {pfsec})
|
|
|
500 |
| None \<Rightarrow> None) )
|
|
|
501 |
| None \<Rightarrow> None)"
|
|
|
502 |
apply (drule is_file_or_dir, simp)
|
|
|
503 |
apply (erule disjE)
|
|
|
504 |
apply (frule cf2sfile_path_file, simp) defer
|
|
|
505 |
apply (frule cf2sfile_path_dir, simp, drule is_dir_not_file)
|
|
|
506 |
apply (auto split:option.splits)
|
|
|
507 |
done
|
|
|
508 |
|
|
|
509 |
lemma cf2sfile_path_file_prop1:
|
|
|
510 |
"\<lbrakk>is_file s (f # pf); cf2sfile s pf = Some (pfi, pfsec, psec, asecs); valid s\<rbrakk>
|
|
|
511 |
\<Longrightarrow> \<exists> fsec. cf2sfile s (f # pf) =
|
|
|
512 |
Some (if (\<not> died (O_file (f # pf)) s \<and> is_init_file (f # pf)) then Init (f # pf)
|
|
|
513 |
else Created, fsec, Some pfsec, asecs \<union> {pfsec}) \<and>
|
|
|
514 |
sectxt_of_obj s (O_file (f # pf)) = Some fsec"
|
|
|
515 |
apply (frule is_file_has_sfile, simp)
|
|
|
516 |
by (auto simp:cf2sfile_path_file)
|
|
|
517 |
|
|
|
518 |
lemma cf2sfile_path_file_prop2:
|
|
|
519 |
"\<lbrakk>is_file s (f # pf); cf2sfile s pf = Some (pfi, pfsec, psec, asecs);
|
|
|
520 |
sectxt_of_obj s (O_file (f # pf)) = Some fsec; valid s\<rbrakk> \<Longrightarrow> cf2sfile s (f # pf) =
|
|
|
521 |
Some (if (\<not> died (O_file (f # pf)) s \<and> is_init_file (f # pf)) then Init (f # pf)
|
|
|
522 |
else Created, fsec, Some pfsec, asecs \<union> {pfsec})"
|
|
|
523 |
by (drule cf2sfile_path_file_prop1, auto)
|
|
|
524 |
|
|
|
525 |
lemma cf2sfile_path_dir_prop1:
|
|
|
526 |
"\<lbrakk>is_dir s (f # pf); cf2sfile s pf = Some (pfi, pfsec, psec, asecs); valid s\<rbrakk>
|
|
|
527 |
\<Longrightarrow> \<exists> fsec. cf2sfile s (f # pf) =
|
|
|
528 |
Some (if (\<not> died (O_dir (f # pf)) s \<and> is_init_dir (f # pf)) then Init (f # pf)
|
|
|
529 |
else Created, fsec, Some pfsec, asecs \<union> {pfsec}) \<and>
|
|
|
530 |
sectxt_of_obj s (O_dir (f # pf)) = Some fsec"
|
|
|
531 |
apply (frule is_dir_has_sfile, simp)
|
|
|
532 |
by (auto simp:cf2sfile_path_dir)
|
|
|
533 |
|
|
|
534 |
lemma cf2sfile_path_dir_prop2:
|
|
|
535 |
"\<lbrakk>is_dir s (f # pf); cf2sfile s pf = Some (pfi, pfsec, psec, asecs);
|
|
|
536 |
sectxt_of_obj s (O_dir (f # pf)) = Some fsec; valid s\<rbrakk> \<Longrightarrow> cf2sfile s (f # pf) =
|
|
|
537 |
Some (if (\<not> died (O_dir (f # pf)) s \<and> is_init_dir (f # pf)) then Init (f # pf)
|
|
|
538 |
else Created, fsec, Some pfsec, asecs \<union> {pfsec})"
|
|
|
539 |
by (drule cf2sfile_path_dir_prop1, auto)
|
|
|
540 |
|
|
|
541 |
(**************** cf2sfile event list simpset ****************)
|
|
|
542 |
|
|
|
543 |
lemma cf2sfile_open_none':
|
|
|
544 |
"valid (Open p f flag fd None # s) \<Longrightarrow> cf2sfile (Open p f flag fd None # s) f'= cf2sfile s f'"
|
|
|
545 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
546 |
apply (induct f', simp add:cf2sfile_def)
|
|
|
547 |
apply (simp add:cf2sfile_def is_file_simps is_dir_simps current_files_simps sectxt_of_obj_simps
|
|
|
548 |
get_parentfs_ctxts_simps)
|
|
|
549 |
done
|
|
|
550 |
|
|
|
551 |
lemma cf2sfile_open_none:
|
|
|
552 |
"valid (Open p f flag fd None # s) \<Longrightarrow> cf2sfile (Open p f flag fd None # s) = cf2sfile s"
|
|
|
553 |
apply (rule ext)
|
|
|
554 |
by (simp add:cf2sfile_open_none')
|
|
|
555 |
|
|
|
556 |
lemma cf2sfile_open_some1:
|
|
|
557 |
"\<lbrakk>valid (Open p f flag fd (Some inum) # s); f' \<in> current_files s\<rbrakk>
|
|
|
558 |
\<Longrightarrow> cf2sfile (Open p f flag fd (Some inum) # s) f' = cf2sfile s f'"
|
|
|
559 |
apply (frule vd_cons, frule vt_grant_os, frule noroot_events)
|
|
|
560 |
apply (case_tac "f = f'", simp)
|
|
|
561 |
apply (induct f', simp add:sroot_only, simp)
|
|
|
562 |
apply (frule parentf_in_current', simp+)
|
|
|
563 |
apply (simp add:cf2sfile_def is_file_simps is_dir_simps current_files_simps sectxt_of_obj_simps
|
|
|
564 |
get_parentfs_ctxts_simps)
|
|
|
565 |
done
|
|
|
566 |
|
|
|
567 |
lemma cf2sfile_open_some2:
|
|
|
568 |
"\<lbrakk>valid (Open p f flag fd (Some inum) # s); is_file s f'\<rbrakk>
|
|
|
569 |
\<Longrightarrow> cf2sfile (Open p f flag fd (Some inum) # s) f' = cf2sfile s f'"
|
|
|
570 |
apply (frule vd_cons, drule is_file_in_current)
|
|
|
571 |
by (simp add:cf2sfile_open_some1)
|
|
|
572 |
|
|
|
573 |
lemma cf2sfile_open_some3:
|
|
|
574 |
"\<lbrakk>valid (Open p f flag fd (Some inum) # s); is_dir s f'\<rbrakk>
|
|
|
575 |
\<Longrightarrow> cf2sfile (Open p f flag fd (Some inum) # s) f' = cf2sfile s f'"
|
|
|
576 |
apply (frule vd_cons, drule is_dir_in_current)
|
|
|
577 |
by (simp add:cf2sfile_open_some1)
|
|
|
578 |
|
|
|
579 |
lemma cf2sfile_open_some4:
|
|
|
580 |
"valid (Open p f flag fd (Some inum) # s) \<Longrightarrow> cf2sfile (Open p f flag fd (Some inum) # s) f = (
|
|
|
581 |
case (parent f) of
|
|
|
582 |
Some pf \<Rightarrow> (case (sectxt_of_obj (Open p f flag fd (Some inum) # s) (O_file f), sectxt_of_obj s (O_dir pf),
|
|
|
583 |
get_parentfs_ctxts s pf) of
|
|
|
584 |
(Some sec, Some psec, Some asecs) \<Rightarrow> Some (Created, sec, Some psec, set asecs)
|
|
|
585 |
| _ \<Rightarrow> None)
|
|
|
586 |
| None \<Rightarrow> None)"
|
|
|
587 |
apply (frule vd_cons, frule vt_grant_os, frule noroot_events)
|
|
|
588 |
apply (case_tac f, simp)
|
|
|
589 |
apply (simp add:cf2sfile_def is_file_simps is_dir_simps current_files_simps sectxt_of_obj_simps
|
|
|
590 |
get_parentfs_ctxts_simps)
|
|
|
591 |
apply (rule impI, (erule conjE)+)
|
|
|
592 |
apply (drule not_died_init_file, simp+)
|
|
|
593 |
apply (simp add:is_file_in_current)
|
|
|
594 |
done
|
|
|
595 |
|
|
|
596 |
lemma cf2sfile_open:
|
|
|
597 |
"\<lbrakk>valid (Open p f flag fd opt # s); f' \<in> current_files (Open p f flag fd opt # s)\<rbrakk>
|
|
|
598 |
\<Longrightarrow> cf2sfile (Open p f flag fd opt # s) f' = (
|
|
|
599 |
if (opt = None) then cf2sfile s f'
|
|
|
600 |
else if (f' = f)
|
|
|
601 |
then (case (parent f) of
|
|
|
602 |
Some pf \<Rightarrow> (case (sectxt_of_obj (Open p f flag fd opt # s) (O_file f), sectxt_of_obj s (O_dir pf),
|
|
|
603 |
get_parentfs_ctxts s pf) of
|
|
|
604 |
(Some sec, Some psec, Some asecs) \<Rightarrow> Some (Created, sec, Some psec, set asecs)
|
|
|
605 |
| _ \<Rightarrow> None)
|
|
|
606 |
| None \<Rightarrow> None)
|
|
|
607 |
else cf2sfile s f')"
|
|
|
608 |
apply (case_tac opt)
|
|
|
609 |
apply (simp add:cf2sfile_open_none)
|
|
|
610 |
apply (case_tac "f = f'")
|
|
|
611 |
apply (simp add:cf2sfile_open_some4 split:option.splits)
|
|
|
612 |
apply (simp add:cf2sfile_open_some1 current_files_simps)
|
|
|
613 |
done
|
|
|
614 |
|
|
|
615 |
lemma cf2sfile_mkdir1:
|
|
|
616 |
"\<lbrakk>valid (Mkdir p f i # s); f' \<in> current_files s\<rbrakk>
|
|
|
617 |
\<Longrightarrow> cf2sfile (Mkdir p f i # s) f' = cf2sfile s f'"
|
|
|
618 |
apply (frule vd_cons, frule vt_grant_os, frule noroot_events)
|
|
|
619 |
apply (case_tac "f = f'", simp)
|
|
|
620 |
apply (induct f', simp add:sroot_only, simp)
|
|
|
621 |
apply (frule parentf_in_current', simp+)
|
|
|
622 |
apply (case_tac "f = f'", simp)
|
|
|
623 |
apply (simp add:cf2sfile_path is_file_simps is_dir_simps current_files_simps sectxt_of_obj_simps
|
|
|
624 |
get_parentfs_ctxts_simps split:if_splits option.splits)
|
|
|
625 |
done
|
|
|
626 |
|
|
|
627 |
lemma cf2sfile_mkdir2:
|
|
|
628 |
"\<lbrakk>valid (Mkdir p f i # s); is_file s f'\<rbrakk>
|
|
|
629 |
\<Longrightarrow> cf2sfile (Mkdir p f i # s) f' = cf2sfile s f'"
|
|
|
630 |
apply (frule vd_cons, drule is_file_in_current)
|
|
|
631 |
by (simp add:cf2sfile_mkdir1)
|
|
|
632 |
|
|
|
633 |
lemma cf2sfile_mkdir3:
|
|
|
634 |
"\<lbrakk>valid (Mkdir p f i # s); is_dir s f'\<rbrakk>
|
|
|
635 |
\<Longrightarrow> cf2sfile (Mkdir p f i # s) f' = cf2sfile s f'"
|
|
|
636 |
apply (frule vd_cons, drule is_dir_in_current)
|
|
|
637 |
by (simp add:cf2sfile_mkdir1)
|
|
|
638 |
|
|
|
639 |
lemma cf2sfile_mkdir4:
|
|
|
640 |
"valid (Mkdir p f i # s)
|
|
|
641 |
\<Longrightarrow> cf2sfile (Mkdir p f i # s) f = (case (parent f) of
|
|
|
642 |
Some pf \<Rightarrow> (case (sectxt_of_obj (Mkdir p f i # s) (O_dir f), sectxt_of_obj s (O_dir pf),
|
|
|
643 |
get_parentfs_ctxts s pf) of
|
|
|
644 |
(Some sec, Some psec, Some asecs) \<Rightarrow> Some (Created, sec, Some psec, set asecs)
|
|
|
645 |
| _ \<Rightarrow> None)
|
|
|
646 |
| None \<Rightarrow> None)"
|
|
|
647 |
apply (frule vd_cons, frule vt_grant_os, frule noroot_events)
|
|
|
648 |
apply (case_tac f, simp)
|
|
|
649 |
apply (clarsimp simp:os_grant.simps)
|
|
|
650 |
apply (simp add:sectxt_of_obj_simps)
|
|
|
651 |
apply (frule current_proc_has_sec, simp)
|
|
|
652 |
apply (frule is_dir_has_sec, simp)
|
|
|
653 |
apply (frule get_pfs_secs_prop, simp)
|
|
|
654 |
apply (frule is_dir_not_file)
|
|
|
655 |
apply (auto simp add:cf2sfile_def is_file_simps is_dir_simps current_files_simps sectxt_of_obj_simps
|
|
|
656 |
get_parentfs_ctxts_simps split:option.splits if_splits
|
|
|
657 |
dest:not_died_init_dir is_dir_in_current not_died_init_file is_file_in_current)
|
|
|
658 |
done
|
|
|
659 |
|
|
|
660 |
lemma cf2sfile_mkdir:
|
|
|
661 |
"\<lbrakk>valid (Mkdir p f i # s); f' \<in> current_files (Mkdir p f i # s)\<rbrakk>
|
|
|
662 |
\<Longrightarrow> cf2sfile (Mkdir p f i # s) f' = (
|
|
|
663 |
if (f' = f)
|
|
|
664 |
then (case (parent f) of
|
|
|
665 |
Some pf \<Rightarrow> (case (sectxt_of_obj (Mkdir p f i # s) (O_dir f), sectxt_of_obj s (O_dir pf),
|
|
|
666 |
get_parentfs_ctxts s pf) of
|
|
|
667 |
(Some sec, Some psec, Some asecs) \<Rightarrow> Some (Created, sec, Some psec, set asecs)
|
|
|
668 |
| _ \<Rightarrow> None)
|
|
|
669 |
| None \<Rightarrow> None)
|
|
|
670 |
else cf2sfile s f')"
|
|
|
671 |
apply (case_tac "f = f'")
|
|
|
672 |
apply (simp add:cf2sfile_mkdir4 split:option.splits)
|
|
|
673 |
apply (simp add:cf2sfile_mkdir1 current_files_simps)
|
|
|
674 |
done
|
|
|
675 |
|
|
|
676 |
lemma cf2sfile_linkhard1:
|
|
|
677 |
"\<lbrakk>valid (LinkHard p oldf f # s); f' \<in> current_files s\<rbrakk>
|
|
|
678 |
\<Longrightarrow> cf2sfile (LinkHard p oldf f# s) f' = cf2sfile s f'"
|
|
|
679 |
apply (frule vd_cons, frule vt_grant_os, frule noroot_events)
|
|
|
680 |
apply (case_tac "f = f'", simp)
|
|
|
681 |
apply (induct f', simp add:sroot_only, simp)
|
|
|
682 |
apply (frule parentf_in_current', simp+)
|
|
|
683 |
apply (simp add:cf2sfile_def is_file_simps is_dir_simps current_files_simps sectxt_of_obj_simps
|
|
|
684 |
get_parentfs_ctxts_simps split:if_splits option.splits)
|
|
|
685 |
done
|
|
|
686 |
|
|
|
687 |
lemma cf2sfile_linkhard2:
|
|
|
688 |
"\<lbrakk>valid (LinkHard p oldf f # s); is_file s f'\<rbrakk>
|
|
|
689 |
\<Longrightarrow> cf2sfile (LinkHard p oldf f # s) f' = cf2sfile s f'"
|
|
|
690 |
apply (frule vd_cons, drule is_file_in_current)
|
|
|
691 |
by (simp add:cf2sfile_linkhard1)
|
|
|
692 |
|
|
|
693 |
lemma cf2sfile_linkhard3:
|
|
|
694 |
"\<lbrakk>valid (LinkHard p oldf f # s); is_dir s f'\<rbrakk>
|
|
|
695 |
\<Longrightarrow> cf2sfile (LinkHard p oldf f # s) f' = cf2sfile s f'"
|
|
|
696 |
apply (frule vd_cons, drule is_dir_in_current)
|
|
|
697 |
by (simp add:cf2sfile_linkhard1)
|
|
|
698 |
|
|
|
699 |
lemma cf2sfile_linkhard4:
|
|
|
700 |
"valid (LinkHard p oldf f # s)
|
|
|
701 |
\<Longrightarrow> cf2sfile (LinkHard p oldf f # s) f = (case (parent f) of
|
|
|
702 |
Some pf \<Rightarrow> (case (sectxt_of_obj (LinkHard p oldf f # s) (O_file f), sectxt_of_obj s (O_dir pf),
|
|
|
703 |
get_parentfs_ctxts s pf) of
|
|
|
704 |
(Some sec, Some psec, Some asecs) \<Rightarrow> Some (Created, sec, Some psec, set asecs)
|
|
|
705 |
| _ \<Rightarrow> None)
|
|
|
706 |
| None \<Rightarrow> None)"
|
|
|
707 |
apply (frule vd_cons, frule vt_grant_os, frule noroot_events)
|
|
|
708 |
apply (case_tac f, simp)
|
|
|
709 |
apply (simp add:cf2sfile_def is_file_simps is_dir_simps current_files_simps sectxt_of_obj_simps
|
|
|
710 |
get_parentfs_ctxts_simps)
|
|
|
711 |
apply (rule impI, (erule conjE)+)
|
|
|
712 |
apply (drule not_died_init_file, simp+)
|
|
|
713 |
apply (simp add:is_file_in_current)
|
|
|
714 |
done
|
|
|
715 |
|
|
|
716 |
lemma cf2sfile_linkhard:
|
|
|
717 |
"\<lbrakk>valid (LinkHard p oldf f # s); f' \<in> current_files (LinkHard p oldf f # s)\<rbrakk>
|
|
|
718 |
\<Longrightarrow> cf2sfile (LinkHard p oldf f # s) f' = (
|
|
|
719 |
if (f' = f)
|
|
|
720 |
then (case (parent f) of
|
|
|
721 |
Some pf \<Rightarrow> (case (sectxt_of_obj (LinkHard p oldf f # s) (O_file f), sectxt_of_obj s (O_dir pf),
|
|
|
722 |
get_parentfs_ctxts s pf) of
|
|
|
723 |
(Some sec, Some psec, Some asecs) \<Rightarrow> Some (Created, sec, Some psec, set asecs)
|
|
|
724 |
| _ \<Rightarrow> None)
|
|
|
725 |
| None \<Rightarrow> None)
|
|
|
726 |
else cf2sfile s f')"
|
|
|
727 |
apply (case_tac "f = f'")
|
|
|
728 |
apply (simp add:cf2sfile_linkhard4 split:option.splits)
|
|
|
729 |
apply (simp add:cf2sfile_linkhard1 current_files_simps)
|
|
|
730 |
done
|
|
|
731 |
|
|
|
732 |
lemma cf2sfile_other:
|
|
|
733 |
"\<lbrakk>ff \<in> current_files s;
|
|
|
734 |
\<forall> p f flag fd opt. e \<noteq> Open p f flag fd opt;
|
|
|
735 |
\<forall> p fd. e \<noteq> CloseFd p fd;
|
|
|
736 |
\<forall> p f. e \<noteq> UnLink p f;
|
|
|
737 |
\<forall> p f. e \<noteq> Rmdir p f;
|
|
|
738 |
\<forall> p f i. e \<noteq> Mkdir p f i;
|
|
|
739 |
\<forall> p f f'. e \<noteq> LinkHard p f f';
|
|
|
740 |
valid (e # s)\<rbrakk> \<Longrightarrow> cf2sfile (e # s) ff = cf2sfile s ff"
|
|
|
741 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
742 |
apply (induct ff, simp add:sroot_only)
|
|
|
743 |
apply (frule parentf_in_current', simp+, case_tac e)
|
|
|
744 |
apply (auto simp:current_files_simps is_file_simps is_dir_simps sectxt_of_obj_simps cf2sfile_path
|
|
|
745 |
split:if_splits option.splits)
|
|
|
746 |
done
|
|
|
747 |
|
|
|
748 |
lemma cf2sfile_other':
|
|
|
749 |
"\<lbrakk>valid (e # s);
|
|
|
750 |
\<forall> p f flag fd opt. e \<noteq> Open p f flag fd opt;
|
|
|
751 |
\<forall> p fd. e \<noteq> CloseFd p fd;
|
|
|
752 |
\<forall> p f. e \<noteq> UnLink p f;
|
|
|
753 |
\<forall> p f. e \<noteq> Rmdir p f;
|
|
|
754 |
\<forall> p f i. e \<noteq> Mkdir p f i;
|
|
|
755 |
\<forall> p f f'. e \<noteq> LinkHard p f f';
|
|
|
756 |
ff \<in> current_files s\<rbrakk> \<Longrightarrow> cf2sfile (e # s) ff = cf2sfile s ff"
|
|
|
757 |
by (auto intro!:cf2sfile_other)
|
|
|
758 |
|
|
|
759 |
lemma cf2sfile_unlink:
|
|
|
760 |
"\<lbrakk>valid (UnLink p f # s); f' \<in> current_files (UnLink p f # s)\<rbrakk>
|
|
|
761 |
\<Longrightarrow> cf2sfile (UnLink p f # s) f' = cf2sfile s f'"
|
|
|
762 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
763 |
apply (simp add:current_files_simps split:if_splits)
|
|
|
764 |
apply (auto simp:cf2sfile_def sectxt_of_obj_simps get_parentfs_ctxts_simps is_file_simps is_dir_simps
|
|
|
765 |
split:if_splits option.splits)
|
|
|
766 |
done
|
|
|
767 |
|
|
|
768 |
lemma cf2sfile_rmdir:
|
|
|
769 |
"\<lbrakk>valid (Rmdir p f # s); f' \<in> current_files (Rmdir p f # s)\<rbrakk>
|
|
|
770 |
\<Longrightarrow> cf2sfile (Rmdir p f # s) f' = cf2sfile s f'"
|
|
|
771 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
772 |
apply (simp add:current_files_simps split:if_splits)
|
|
|
773 |
apply (auto simp:cf2sfile_def sectxt_of_obj_simps get_parentfs_ctxts_simps is_file_simps is_dir_simps
|
|
|
774 |
split:if_splits option.splits)
|
|
|
775 |
done
|
|
|
776 |
|
|
|
777 |
lemma pfdof_simp5: "\<lbrakk>proc_fd_of_file s f = {(p, fd)}; file_of_proc_fd s p fd = None\<rbrakk> \<Longrightarrow> False"
|
|
|
778 |
apply (subgoal_tac "(p, fd) \<in> proc_fd_of_file s f")
|
|
|
779 |
by (simp add:pfdof_simp2, simp)
|
|
|
780 |
|
|
|
781 |
lemma pfdof_simp6: "proc_fd_of_file s f = {(p, fd)} \<Longrightarrow> file_of_proc_fd s p fd = Some f"
|
|
|
782 |
apply (subgoal_tac "(p, fd) \<in> proc_fd_of_file s f")
|
|
|
783 |
by (simp add:pfdof_simp2, simp)
|
|
|
784 |
|
|
|
785 |
lemma cf2sfile_closefd:
|
|
|
786 |
"\<lbrakk>valid (CloseFd p fd # s); f \<in> current_files (CloseFd p fd # s)\<rbrakk>
|
|
|
787 |
\<Longrightarrow> cf2sfile (CloseFd p fd # s) f = cf2sfile s f"
|
|
|
788 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
789 |
apply (simp add:current_files_simps split:if_splits option.splits)
|
|
|
790 |
(* costs too much time, but solved *)
|
|
|
791 |
(*
|
|
|
792 |
apply (auto simp:cf2sfile_def sectxt_of_obj_simps get_parentfs_ctxts_simps is_file_simps is_dir_simps
|
|
|
793 |
split:if_splits option.splits
|
|
|
794 |
dest:init_file_dir_conflict pfdof_simp5 pfdof_simp6 file_of_pfd_is_file
|
|
|
795 |
not_died_init_file not_died_init_dir is_file_not_dir is_dir_not_file
|
|
|
796 |
dest!:current_has_sec')
|
|
|
797 |
done
|
|
|
798 |
*)
|
|
|
799 |
sorry
|
|
|
800 |
|
|
|
801 |
lemmas cf2sfile_simps = cf2sfile_open cf2sfile_mkdir cf2sfile_linkhard cf2sfile_other
|
|
|
802 |
cf2sfile_unlink cf2sfile_rmdir cf2sfile_closefd
|
|
|
803 |
|
|
|
804 |
(*********** cfd2sfd simpset *********)
|
|
|
805 |
|
|
|
806 |
lemma cfd2sfd_open1:
|
|
|
807 |
"valid (Open p f flags fd opt # s)
|
|
|
808 |
\<Longrightarrow> cfd2sfd (Open p f flags fd opt # s) p fd =
|
|
|
809 |
(case (sectxt_of_obj (Open p f flags fd opt # s) (O_fd p fd), cf2sfile (Open p f flags fd opt # s) f) of
|
|
85
|
810 |
(Some sec, Some sf) \<Rightarrow> Some (sec, remove_create_flag flags, sf)
|
|
77
|
811 |
| _ \<Rightarrow> None)"
|
|
|
812 |
by (simp add:cfd2sfd_def sectxt_of_obj_simps split:if_splits)
|
|
|
813 |
|
|
|
814 |
lemma cfd2sfd_open_some2:
|
|
|
815 |
"\<lbrakk>valid (Open p f flags fd (Some inum) # s); file_of_proc_fd s p' fd' = Some f'\<rbrakk>
|
|
|
816 |
\<Longrightarrow> cfd2sfd (Open p f flags fd (Some inum) # s) p' fd' = cfd2sfd s p' fd'"
|
|
|
817 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
818 |
apply (frule proc_fd_in_fds, simp)
|
|
|
819 |
apply (frule file_of_proc_fd_in_curf, simp)
|
|
|
820 |
apply (case_tac "f = f'", simp)
|
|
|
821 |
apply (simp add:cfd2sfd_def sectxt_of_obj_simps cf2sfile_open_some1)
|
|
|
822 |
apply (case_tac "p = p'", simp)
|
|
|
823 |
apply (rule conjI, rule impI, simp)
|
|
|
824 |
apply (drule cf2sfile_open_some1, simp)
|
|
|
825 |
apply (auto split:option.splits)[1]
|
|
|
826 |
apply simp
|
|
|
827 |
apply (drule cf2sfile_open_some1, simp)
|
|
|
828 |
apply (auto split:option.splits)[1]
|
|
|
829 |
done
|
|
|
830 |
|
|
|
831 |
lemma cfd2sfd_open_none2:
|
|
|
832 |
"\<lbrakk>valid (Open p f flags fd None # s); file_of_proc_fd s p' fd' = Some f'\<rbrakk>
|
|
|
833 |
\<Longrightarrow> cfd2sfd (Open p f flags fd None # s) p' fd' = cfd2sfd s p' fd'"
|
|
|
834 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
835 |
apply (frule proc_fd_in_fds, simp)
|
|
|
836 |
apply (frule file_of_proc_fd_in_curf, simp)
|
|
|
837 |
apply (simp add:cfd2sfd_def sectxt_of_obj_simps cf2sfile_open_none)
|
|
|
838 |
apply (case_tac "p = p'", simp)
|
|
|
839 |
apply (rule conjI, rule impI, simp)
|
|
|
840 |
apply (drule cf2sfile_open_none)
|
|
|
841 |
apply (auto split:option.splits)[1]
|
|
|
842 |
apply simp
|
|
|
843 |
apply (drule cf2sfile_open_none)
|
|
|
844 |
apply (auto split:option.splits)[1]
|
|
|
845 |
done
|
|
|
846 |
|
|
|
847 |
lemma cfd2sfd_open2:
|
|
|
848 |
"\<lbrakk>valid (Open p f flags fd opt # s); file_of_proc_fd s p' fd' = Some f'\<rbrakk>
|
|
|
849 |
\<Longrightarrow> cfd2sfd (Open p f flags fd opt # s) p' fd' = cfd2sfd s p' fd'"
|
|
|
850 |
apply (case_tac opt)
|
|
|
851 |
apply (simp add:cfd2sfd_open_none2)
|
|
|
852 |
apply (simp add:cfd2sfd_open_some2)
|
|
|
853 |
done
|
|
|
854 |
|
|
|
855 |
lemma cfd2sfd_open:
|
|
|
856 |
"\<lbrakk>valid (Open p f flags fd opt # s); file_of_proc_fd (Open p f flags fd opt # s) p' fd' = Some f'\<rbrakk>
|
|
|
857 |
\<Longrightarrow> cfd2sfd (Open p f flags fd opt # s) p' fd' = (if (p' = p \<and> fd' = fd) then
|
|
|
858 |
(case (sectxt_of_obj (Open p f flags fd opt # s) (O_fd p fd), cf2sfile (Open p f flags fd opt # s) f) of
|
|
85
|
859 |
(Some sec, Some sf) \<Rightarrow> Some (sec, remove_create_flag flags, sf)
|
|
77
|
860 |
| _ \<Rightarrow> None) else cfd2sfd s p' fd')"
|
|
|
861 |
apply (simp split:if_splits)
|
|
|
862 |
apply (simp add:cfd2sfd_open1 split:option.splits)
|
|
|
863 |
apply (simp add:cfd2sfd_open2)
|
|
|
864 |
apply (rule impI, simp)
|
|
|
865 |
done
|
|
|
866 |
|
|
|
867 |
lemma cfd2sfd_closefd:
|
|
|
868 |
"\<lbrakk>valid (CloseFd p fd # s); file_of_proc_fd (CloseFd p fd # s) p' fd' = Some f\<rbrakk>
|
|
|
869 |
\<Longrightarrow> cfd2sfd (CloseFd p fd # s) p' fd' = cfd2sfd s p' fd'"
|
|
|
870 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
871 |
apply (frule proc_fd_in_fds, simp)
|
|
|
872 |
apply (frule file_of_proc_fd_in_curf, simp)
|
|
|
873 |
apply (frule cf2sfile_closefd, simp)
|
|
|
874 |
apply (simp add:cfd2sfd_def sectxt_of_obj_simps)
|
|
|
875 |
apply (auto split:option.splits if_splits)
|
|
|
876 |
done
|
|
|
877 |
|
|
|
878 |
lemma cfd2sfd_clone:
|
|
|
879 |
"\<lbrakk>valid (Clone p p' fds # s); file_of_proc_fd (Clone p p' fds # s) p'' fd' = Some f\<rbrakk>
|
|
|
880 |
\<Longrightarrow> cfd2sfd (Clone p p' fds # s) p'' fd' = (
|
|
|
881 |
if (p'' = p') then cfd2sfd s p fd'
|
|
|
882 |
else cfd2sfd s p'' fd')"
|
|
|
883 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
884 |
apply (frule proc_fd_in_fds, simp)
|
|
|
885 |
apply (frule file_of_proc_fd_in_curf, simp, simp add:current_files_simps)
|
|
|
886 |
apply (frule_tac cf2sfile_other', simp+)
|
|
|
887 |
apply (simp add:cfd2sfd_def sectxt_of_obj_simps)
|
|
|
888 |
apply (case_tac "p'' = p'", simp)
|
|
|
889 |
apply (auto split:option.splits if_splits)[1]
|
|
|
890 |
apply (simp)
|
|
|
891 |
apply (auto split:option.splits if_splits)[1]
|
|
|
892 |
done
|
|
|
893 |
|
|
|
894 |
lemma cfd2sfd_execve:
|
|
|
895 |
"\<lbrakk>valid (Execve p f fds # s); file_of_proc_fd (Execve p f fds # s) p' fd' = Some f'\<rbrakk>
|
|
|
896 |
\<Longrightarrow> cfd2sfd (Execve p f fds # s) p' fd' = cfd2sfd s p' fd'"
|
|
|
897 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
898 |
apply (frule proc_fd_in_fds, simp)
|
|
|
899 |
apply (frule file_of_proc_fd_in_curf, simp, simp add:current_files_simps)
|
|
|
900 |
apply (frule_tac cf2sfile_other', simp+)
|
|
|
901 |
apply (simp add:cfd2sfd_def sectxt_of_obj_simps)
|
|
|
902 |
apply (case_tac "p' = p", simp)
|
|
|
903 |
apply (auto split:option.splits if_splits)[1]
|
|
|
904 |
apply (simp)
|
|
|
905 |
apply (auto split:option.splits if_splits)[1]
|
|
|
906 |
done
|
|
|
907 |
|
|
|
908 |
lemma cfd2sfd_kill:
|
|
|
909 |
"\<lbrakk>valid (Kill p p'' # s); file_of_proc_fd (Kill p p'' # s) p' fd' = Some f'\<rbrakk>
|
|
|
910 |
\<Longrightarrow> cfd2sfd (Kill p p'' # s) p' fd' = cfd2sfd s p' fd'"
|
|
|
911 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
912 |
apply (frule proc_fd_in_fds, simp)
|
|
|
913 |
apply (frule proc_fd_in_procs, simp)
|
|
|
914 |
apply (frule file_of_proc_fd_in_curf, simp, simp add:current_files_simps)
|
|
|
915 |
apply (frule_tac cf2sfile_other', simp+)
|
|
|
916 |
apply (simp add:cfd2sfd_def sectxt_of_obj_simps)
|
|
|
917 |
apply (auto split:option.splits if_splits)
|
|
|
918 |
done
|
|
|
919 |
|
|
|
920 |
lemma cfd2sfd_exit:
|
|
|
921 |
"\<lbrakk>valid (Exit p # s); file_of_proc_fd (Exit p # s) p' fd' = Some f'\<rbrakk>
|
|
|
922 |
\<Longrightarrow> cfd2sfd (Exit p # s) p' fd' = cfd2sfd s p' fd'"
|
|
|
923 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
924 |
apply (frule proc_fd_in_fds, simp)
|
|
|
925 |
apply (frule proc_fd_in_procs, simp)
|
|
|
926 |
apply (frule file_of_proc_fd_in_curf, simp, simp add:current_files_simps)
|
|
|
927 |
apply (frule_tac cf2sfile_other', simp+)
|
|
|
928 |
apply (simp add:cfd2sfd_def sectxt_of_obj_simps)
|
|
|
929 |
apply (auto split:option.splits if_splits)
|
|
|
930 |
done
|
|
|
931 |
|
|
|
932 |
lemma cfd2sfd_other:
|
|
|
933 |
"\<lbrakk>valid (e # s); file_of_proc_fd (e # s) p' fd' = Some f';
|
|
|
934 |
\<forall> p f flags fd opt. e \<noteq> Open p f flags fd opt;
|
|
|
935 |
\<forall> p p'' fds. e \<noteq> Clone p p'' fds\<rbrakk>
|
|
|
936 |
\<Longrightarrow> cfd2sfd (e # s) p' fd' = cfd2sfd s p' fd'"
|
|
|
937 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
938 |
apply (frule proc_fd_in_fds, simp)
|
|
|
939 |
apply (frule proc_fd_in_procs, simp)
|
|
|
940 |
apply (frule file_of_proc_fd_in_curf, simp)
|
|
|
941 |
apply (case_tac e)
|
|
|
942 |
apply (auto intro!:cfd2sfd_execve cfd2sfd_closefd cfd2sfd_kill cfd2sfd_exit)
|
|
|
943 |
apply (auto simp:cfd2sfd_def sectxt_of_obj_simps current_files_simps cf2sfile_simps split:option.splits)
|
|
|
944 |
apply (auto dest!:current_has_sec' dest:file_of_proc_fd_in_curf proc_fd_in_fds)
|
|
|
945 |
done
|
|
|
946 |
|
|
|
947 |
lemmas cfd2sfd_simps = cfd2sfd_open cfd2sfd_clone cfd2sfd_other
|
|
|
948 |
|
|
|
949 |
(********** cpfd2sfds simpset **********)
|
|
|
950 |
|
|
|
951 |
lemma current_filefd_has_flags:
|
|
|
952 |
"\<lbrakk>file_of_proc_fd s p fd = Some f; valid s\<rbrakk> \<Longrightarrow> \<exists> flags. flags_of_proc_fd s p fd = Some flags"
|
|
|
953 |
apply (induct s arbitrary:p)
|
|
|
954 |
apply (simp only:flags_of_proc_fd.simps file_of_proc_fd.simps init_filefd_prop4)
|
|
|
955 |
apply (frule vd_cons, frule vt_grant_os, case_tac a)
|
|
|
956 |
apply (auto split:if_splits option.splits dest:proc_fd_in_fds)
|
|
|
957 |
done
|
|
|
958 |
|
|
|
959 |
lemma current_filefd_has_flags':
|
|
|
960 |
"\<lbrakk>flags_of_proc_fd s p fd = None; valid s\<rbrakk> \<Longrightarrow> file_of_proc_fd s p fd = None"
|
|
|
961 |
apply (case_tac "file_of_proc_fd s p fd")
|
|
|
962 |
apply (simp, drule current_filefd_has_flags, simp+)
|
|
|
963 |
done
|
|
|
964 |
|
|
|
965 |
lemma current_file_has_sfile':
|
|
|
966 |
"\<lbrakk>cf2sfile s f = None; valid s\<rbrakk> \<Longrightarrow> f \<notin> current_files s"
|
|
|
967 |
by (rule notI, drule current_file_has_sfile, simp+)
|
|
|
968 |
|
|
|
969 |
lemma current_filefd_has_sfd:
|
|
|
970 |
"\<lbrakk>file_of_proc_fd s p fd = Some f; valid s\<rbrakk> \<Longrightarrow> \<exists>sfd. cfd2sfd s p fd = Some sfd"
|
|
|
971 |
by (auto simp:cfd2sfd_def split:option.splits dest!:current_has_sec' current_file_has_sfile'
|
|
|
972 |
dest:file_of_proc_fd_in_curf proc_fd_in_fds current_filefd_has_flags)
|
|
|
973 |
|
|
|
974 |
lemma current_filefd_has_sfd':
|
|
|
975 |
"\<lbrakk>cfd2sfd s p fd = None; valid s\<rbrakk> \<Longrightarrow> file_of_proc_fd s p fd = None"
|
|
|
976 |
by (case_tac "file_of_proc_fd s p fd", auto dest:current_filefd_has_sfd)
|
|
|
977 |
|
|
|
978 |
lemma cpfd2sfds_open1:
|
|
|
979 |
"valid (Open p f flags fd opt # s) \<Longrightarrow>
|
|
|
980 |
cpfd2sfds (Open p f flags fd opt # s) p = (
|
|
|
981 |
case (cfd2sfd (Open p f flags fd opt # s) p fd) of
|
|
|
982 |
Some sfd \<Rightarrow> (cpfd2sfds s p) \<union> {sfd}
|
|
|
983 |
| _ \<Rightarrow> cpfd2sfds s p)"
|
|
|
984 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
985 |
apply (split option.splits)
|
|
|
986 |
apply (rule conjI, rule impI, drule current_filefd_has_sfd', simp, simp)
|
|
|
987 |
apply (rule allI, rule impI)
|
|
|
988 |
apply (rule set_eqI, rule iffI)
|
|
|
989 |
apply (case_tac "x = a", simp)
|
|
|
990 |
unfolding cpfd2sfds_def
|
|
|
991 |
apply (erule CollectE, (erule conjE|erule bexE)+)
|
|
|
992 |
apply (simp add:proc_file_fds_def split:if_splits)
|
|
|
993 |
apply (erule exE, rule_tac x = fda in exI)
|
|
|
994 |
apply (simp add:cfd2sfd_open2)
|
|
|
995 |
apply (case_tac "x = a", simp add:proc_file_fds_def)
|
|
|
996 |
apply (rule_tac x = fd in exI, simp+)
|
|
|
997 |
apply (erule conjE|erule bexE)+
|
|
|
998 |
apply (rule_tac x = fda in bexI)
|
|
|
999 |
apply (simp add:proc_file_fds_def, erule exE)
|
|
|
1000 |
apply (simp add:cfd2sfd_open2)
|
|
|
1001 |
apply (simp add:proc_file_fds_def)
|
|
|
1002 |
done
|
|
|
1003 |
|
|
|
1004 |
lemma cpfd2sfds_open1':
|
|
|
1005 |
"valid (Open p f flags fd opt # s) \<Longrightarrow>
|
|
|
1006 |
cpfd2sfds (Open p f flags fd opt # s) p = (
|
|
|
1007 |
case (sectxt_of_obj (Open p f flags fd opt # s) (O_fd p fd), cf2sfile (Open p f flags fd opt # s) f) of
|
|
85
|
1008 |
(Some sec, Some sf) \<Rightarrow> (cpfd2sfds s p) \<union> {(sec, remove_create_flag flags, sf)}
|
|
77
|
1009 |
| _ \<Rightarrow> cpfd2sfds s p)"
|
|
|
1010 |
apply (frule cfd2sfd_open1)
|
|
|
1011 |
apply (auto dest:cpfd2sfds_open1 split:option.splits)
|
|
|
1012 |
done
|
|
|
1013 |
|
|
|
1014 |
lemma cpfd2sfds_open2:
|
|
|
1015 |
"\<lbrakk>valid (Open p f flags fd opt # s); p' \<noteq> p\<rbrakk> \<Longrightarrow> cpfd2sfds (Open p f flags fd opt # s) p' = cpfd2sfds s p'"
|
|
|
1016 |
apply (frule vt_grant_os, frule vd_cons)
|
|
|
1017 |
unfolding cpfd2sfds_def
|
|
|
1018 |
apply (rule set_eqI, rule iffI)
|
|
|
1019 |
apply (simp add:proc_file_fds_def)
|
|
|
1020 |
apply (erule exE|erule conjE)+
|
|
|
1021 |
apply (simp only:file_of_proc_fd.simps cfd2sfd_open2 split:if_splits)
|
|
|
1022 |
apply (rule_tac x = fda in exI, simp)
|
|
|
1023 |
apply (simp add:proc_file_fds_def)
|
|
|
1024 |
apply (erule exE|erule conjE)+
|
|
|
1025 |
apply (rule_tac x = fda in exI, simp add:cfd2sfd_open2)
|
|
|
1026 |
done
|
|
|
1027 |
|
|
|
1028 |
lemma cpfd2sfds_open:
|
|
|
1029 |
"valid (Open p f flags fd opt # s)
|
|
|
1030 |
\<Longrightarrow> cpfd2sfds (Open p f flags fd opt # s) = (cpfd2sfds s) (p := (
|
|
|
1031 |
case (sectxt_of_obj (Open p f flags fd opt # s) (O_fd p fd), cf2sfile (Open p f flags fd opt # s) f) of
|
|
85
|
1032 |
(Some sec, Some sf) \<Rightarrow> (cpfd2sfds s p) \<union> {(sec, remove_create_flag flags, sf)}
|
|
77
|
1033 |
| _ \<Rightarrow> cpfd2sfds s p))"
|
|
|
1034 |
apply (rule ext)
|
|
|
1035 |
apply (case_tac "x \<noteq> p")
|
|
|
1036 |
apply (simp add:cpfd2sfds_open2)
|
|
|
1037 |
apply (simp add:cpfd2sfds_open1')
|
|
|
1038 |
done
|
|
|
1039 |
|
|
|
1040 |
lemma cpfd2sfds_execve:
|
|
|
1041 |
"valid (Execve p f fds # s)
|
|
|
1042 |
\<Longrightarrow> cpfd2sfds (Execve p f fds # s) = (cpfd2sfds s) (p := {sfd. \<exists> fd \<in> fds. \<exists> f. file_of_proc_fd s p fd = Some f \<and> cfd2sfd s p fd = Some sfd})"
|
|
|
1043 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
1044 |
apply (rule ext)
|
|
|
1045 |
apply (rule set_eqI, rule iffI)
|
|
|
1046 |
unfolding cpfd2sfds_def proc_file_fds_def
|
|
|
1047 |
apply (erule CollectE| erule bexE| erule conjE| erule exE| rule conjI)+
|
|
|
1048 |
apply (simp split:if_splits)
|
|
|
1049 |
apply (frule_tac p' = p and fd' = fd in cfd2sfd_other, simp+)
|
|
|
1050 |
apply (rule_tac x = fd in bexI, simp+)
|
|
|
1051 |
apply (simp add:cpfd2sfds_def proc_file_fds_def)
|
|
|
1052 |
apply (frule_tac p' = x and fd' = fd in cfd2sfd_other, simp+)
|
|
|
1053 |
apply (rule_tac x = fd in exI, simp)
|
|
|
1054 |
apply (simp split:if_splits)
|
|
|
1055 |
apply (erule CollectE| erule bexE| erule conjE| erule exE| rule conjI)+
|
|
|
1056 |
apply (rule_tac x = fd in exI, simp)
|
|
|
1057 |
apply (frule_tac p' = x and fd' = fd in cfd2sfd_other, simp+)
|
|
|
1058 |
apply (simp add:cpfd2sfds_def proc_file_fds_def)
|
|
|
1059 |
apply (erule CollectE| erule bexE| erule conjE| erule exE| rule conjI)+
|
|
|
1060 |
apply (rule_tac x = fd in exI, simp)
|
|
|
1061 |
apply (frule_tac p' = x and fd' = fd in cfd2sfd_other, simp+)
|
|
|
1062 |
done
|
|
|
1063 |
|
|
|
1064 |
lemma cpfd2sfds_clone:
|
|
|
1065 |
"valid (Clone p p' fds # s)
|
|
|
1066 |
\<Longrightarrow> cpfd2sfds (Clone p p' fds # s) = (cpfd2sfds s) (p' := {sfd. \<exists> fd \<in> fds. \<exists> f. file_of_proc_fd s p fd = Some f \<and> cfd2sfd s p fd = Some sfd})"
|
|
|
1067 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
1068 |
apply (rule ext)
|
|
|
1069 |
apply (rule set_eqI, rule iffI)
|
|
|
1070 |
unfolding cpfd2sfds_def proc_file_fds_def
|
|
|
1071 |
apply (erule CollectE| erule bexE| erule conjE| erule exE| rule conjI)+
|
|
|
1072 |
apply (simp split:if_splits)
|
|
|
1073 |
apply (frule_tac p'' = p' and fd' = fd in cfd2sfd_clone, simp+)
|
|
|
1074 |
apply (rule_tac x = fd in bexI, simp+)
|
|
|
1075 |
apply (simp add:cpfd2sfds_def proc_file_fds_def)
|
|
|
1076 |
apply (frule_tac p'' = x and fd' = fd in cfd2sfd_clone, simp+)
|
|
|
1077 |
apply (rule_tac x = fd in exI, simp)
|
|
|
1078 |
apply (simp split:if_splits)
|
|
|
1079 |
apply (erule CollectE| erule bexE| erule conjE| erule exE| rule conjI)+
|
|
|
1080 |
apply (rule_tac x = fd in exI, simp)
|
|
|
1081 |
apply (frule_tac p'' = p' and fd' = fd in cfd2sfd_clone, simp+)
|
|
|
1082 |
apply (simp add:cpfd2sfds_def proc_file_fds_def)
|
|
|
1083 |
apply (erule CollectE| erule bexE| erule conjE| erule exE| rule conjI)+
|
|
|
1084 |
apply (rule_tac x = fd in exI, simp)
|
|
|
1085 |
apply (frule_tac p'' = x and fd' = fd in cfd2sfd_clone, simp+)
|
|
|
1086 |
done
|
|
|
1087 |
|
|
|
1088 |
lemma cpfd2sfds_other:
|
|
|
1089 |
"\<lbrakk>valid (e # s);
|
|
|
1090 |
\<forall> p f flags fd opt. e \<noteq> Open p f flags fd opt;
|
|
|
1091 |
\<forall> p f fds. e \<noteq> Execve p f fds;
|
|
|
1092 |
\<forall> p p'. e \<noteq> Kill p p';
|
|
|
1093 |
\<forall> p. e \<noteq> Exit p;
|
|
|
1094 |
\<forall> p fd. e \<noteq> CloseFd p fd;
|
|
|
1095 |
\<forall> p p' fds. e \<noteq> Clone p p' fds\<rbrakk> \<Longrightarrow> cpfd2sfds (e # s) = cpfd2sfds s"
|
|
|
1096 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
1097 |
apply (rule ext)
|
|
|
1098 |
unfolding cpfd2sfds_def proc_file_fds_def
|
|
|
1099 |
apply (case_tac e)
|
|
|
1100 |
using cfd2sfd_other
|
|
|
1101 |
by auto
|
|
|
1102 |
|
|
|
1103 |
lemma cpfd2sfds_kill:
|
|
|
1104 |
"valid (Kill p p' # s) \<Longrightarrow> cpfd2sfds (Kill p p' # s) = (cpfd2sfds s) (p' := {})"
|
|
|
1105 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
1106 |
apply (rule ext, rule set_eqI)
|
|
|
1107 |
unfolding cpfd2sfds_def proc_file_fds_def
|
|
|
1108 |
apply (rule iffI)
|
|
|
1109 |
apply (erule CollectE| erule bexE| erule conjE| erule exE| rule conjI)+
|
|
|
1110 |
apply (simp split:if_splits add: cpfd2sfds_def proc_file_fds_def)
|
|
|
1111 |
apply (rule_tac x = fd in exI, simp)
|
|
|
1112 |
apply (drule_tac p' = x and fd' = fd in cfd2sfd_other, simp+)
|
|
|
1113 |
apply (simp split:if_splits add: cpfd2sfds_def proc_file_fds_def)
|
|
|
1114 |
apply (erule CollectE| erule bexE| erule conjE| erule exE| rule conjI)+
|
|
|
1115 |
apply (rule_tac x = fd in exI, simp)
|
|
|
1116 |
apply (drule_tac p' = x and fd' = fd in cfd2sfd_other, simp+)
|
|
|
1117 |
done
|
|
|
1118 |
|
|
|
1119 |
lemma cpfd2sfds_exit:
|
|
|
1120 |
"valid (Exit p # s) \<Longrightarrow> cpfd2sfds (Exit p # s) = (cpfd2sfds s) (p := {})"
|
|
|
1121 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
1122 |
apply (rule ext, rule set_eqI)
|
|
|
1123 |
unfolding cpfd2sfds_def proc_file_fds_def
|
|
|
1124 |
apply (rule iffI)
|
|
|
1125 |
apply (erule CollectE| erule bexE| erule conjE| erule exE| rule conjI)+
|
|
|
1126 |
apply (simp split:if_splits add: cpfd2sfds_def proc_file_fds_def)
|
|
|
1127 |
apply (rule_tac x = fd in exI, simp)
|
|
|
1128 |
apply (drule_tac p' = x and fd' = fd in cfd2sfd_other, simp+)
|
|
|
1129 |
apply (simp split:if_splits add: cpfd2sfds_def proc_file_fds_def)
|
|
|
1130 |
apply (erule CollectE| erule bexE| erule conjE| erule exE| rule conjI)+
|
|
|
1131 |
apply (rule_tac x = fd in exI, simp)
|
|
|
1132 |
apply (drule_tac p' = x and fd' = fd in cfd2sfd_other, simp+)
|
|
|
1133 |
done
|
|
|
1134 |
|
|
|
1135 |
lemma cpfd2sfds_closefd:
|
|
|
1136 |
"valid (CloseFd p fd # s) \<Longrightarrow> cpfd2sfds (CloseFd p fd # s) = (cpfd2sfds s) (p :=
|
|
|
1137 |
if (fd \<in> proc_file_fds s p)
|
|
|
1138 |
then (case (cfd2sfd s p fd) of
|
|
|
1139 |
Some sfd \<Rightarrow> (if (\<exists> fd' f'. fd' \<noteq> fd \<and> file_of_proc_fd s p fd' = Some f' \<and> cfd2sfd s p fd' = Some sfd)
|
|
|
1140 |
then cpfd2sfds s p else cpfd2sfds s p - {sfd})
|
|
|
1141 |
| _ \<Rightarrow> cpfd2sfds s p)
|
|
|
1142 |
else cpfd2sfds s p)"
|
|
|
1143 |
apply (frule vd_cons)
|
|
|
1144 |
apply (rule ext, rule set_eqI, rule iffI)
|
|
|
1145 |
unfolding cpfd2sfds_def proc_file_fds_def
|
|
|
1146 |
apply (erule CollectE| erule bexE| erule conjE| erule exE| rule conjI)+
|
|
|
1147 |
apply (simp split:if_splits)
|
|
|
1148 |
apply (rule conjI, rule impI, rule conjI, rule impI, erule exE)
|
|
|
1149 |
apply (frule_tac p = p and fd = fd in current_filefd_has_sfd, simp)
|
|
|
1150 |
apply (erule exE, simp)
|
|
|
1151 |
apply (rule conjI, rule impI, (erule exE|erule conjE)+)
|
|
|
1152 |
apply (rule_tac x = fda in exI, simp, simp add:cfd2sfd_closefd)
|
|
|
1153 |
|
|
|
1154 |
apply (rule impI, rule conjI)
|
|
|
1155 |
apply (rule_tac x = fda in exI, simp, simp add:cfd2sfd_closefd)
|
|
|
1156 |
apply (rule notI, simp)
|
|
|
1157 |
apply (erule_tac x = fda in allE, simp add:cfd2sfd_closefd)
|
|
|
1158 |
|
|
|
1159 |
apply (rule impI, simp add:cpfd2sfds_def proc_file_fds_def)
|
|
|
1160 |
apply (erule exE, rule_tac x = fda in exI, simp add:cfd2sfd_closefd)
|
|
|
1161 |
|
|
|
1162 |
apply (rule impI| rule conjI)+
|
|
|
1163 |
apply (rule_tac x = fda in exI, simp add:cfd2sfd_closefd)
|
|
|
1164 |
|
|
|
1165 |
apply (rule impI, simp add:cpfd2sfds_def proc_file_fds_def)
|
|
|
1166 |
apply (rule_tac x = fda in exI, simp add:cfd2sfd_closefd)
|
|
|
1167 |
|
|
|
1168 |
apply (simp split:if_splits)
|
|
|
1169 |
apply (frule_tac p = p and fd = fd in current_filefd_has_sfd, simp)
|
|
|
1170 |
apply (erule exE, simp)
|
|
|
1171 |
apply (case_tac "\<exists>fd'. fd' \<noteq> fd \<and> (\<exists>f'. file_of_proc_fd s p fd' = Some f') \<and> cfd2sfd s p fd' = Some sfd")
|
|
|
1172 |
apply simp
|
|
|
1173 |
apply (case_tac "xa = sfd")
|
|
|
1174 |
apply (erule exE|erule conjE)+
|
|
|
1175 |
apply (rule_tac x = fd' in exI, simp add:cfd2sfd_closefd)
|
|
|
1176 |
apply (erule exE|erule conjE)+
|
|
|
1177 |
apply (rule_tac x = fda in exI, simp add:cfd2sfd_closefd)
|
|
|
1178 |
apply (rule notI, simp)
|
|
|
1179 |
apply (simp, (erule exE|erule conjE)+)
|
|
|
1180 |
apply (rule_tac x = fda in exI, simp add:cfd2sfd_closefd)
|
|
|
1181 |
apply (rule notI, simp)
|
|
|
1182 |
apply (erule exE|erule conjE)+
|
|
|
1183 |
apply (rule_tac x = fda in exI, simp add:cfd2sfd_closefd)
|
|
|
1184 |
apply (rule notI, simp)
|
|
|
1185 |
apply (simp add:cpfd2sfds_def proc_file_fds_def)
|
|
|
1186 |
apply (erule exE|erule conjE)+
|
|
|
1187 |
apply (rule_tac x = fda in exI, simp add:cfd2sfd_closefd)
|
|
|
1188 |
done
|
|
|
1189 |
|
|
|
1190 |
lemmas cpfd2sfds_simps = cpfd2sfds_open cpfd2sfds_execve cpfd2sfds_clone cpfd2sfds_kill cpfd2sfds_exit
|
|
|
1191 |
cpfd2sfds_closefd cpfd2sfds_other
|
|
|
1192 |
|
|
|
1193 |
(********* ch2sshm simpset ********)
|
|
|
1194 |
(*
|
|
|
1195 |
lemma ch2sshm_createshm:
|
|
|
1196 |
"valid (CreateShM p h # s)
|
|
|
1197 |
\<Longrightarrow> ch2sshm (CreateShM p h # s) = (ch2sshm s) (h :=
|
|
|
1198 |
(case (sectxt_of_obj (CreateShM p h # s) (O_shm h)) of
|
|
|
1199 |
Some sec \<Rightarrow>
|
|
|
1200 |
Some (if (\<not> died (O_shm h) s \<and> h \<in> init_shms) then Init h else Created, sec)
|
|
|
1201 |
| _ \<Rightarrow> None))"
|
|
|
1202 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
1203 |
apply (auto simp:ch2sshm_def sectxt_of_obj_simps dest!:current_has_sec' split:option.splits if_splits)
|
|
|
1204 |
done
|
|
|
1205 |
|
|
|
1206 |
lemma ch2sshm_other:
|
|
|
1207 |
"\<lbrakk>valid (e # s);
|
|
|
1208 |
\<forall> p h. e \<noteq> CreateShM p h;
|
|
|
1209 |
h' \<in> current_shms (e # s)\<rbrakk> \<Longrightarrow> ch2sshm (e # s) h' = ch2sshm s h'"
|
|
|
1210 |
apply (frule vd_cons, frule vt_grant_os)
|
|
|
1211 |
apply (case_tac e)
|
|
|
1212 |
apply (auto simp:ch2sshm_def sectxt_of_obj_simps dest!:current_has_sec' split:option.splits if_splits)
|
|
|
1213 |
done
|
|
|
1214 |
|
|
|
1215 |
lemmas ch2sshm_simps = ch2sshm_createshm ch2sshm_other
|
|
|
1216 |
|
|
|
1217 |
lemma current_shm_has_sh:
|
|
|
1218 |
"\<lbrakk>h \<in> current_shms s; valid s\<rbrakk> \<Longrightarrow> \<exists> sh. ch2sshm s h = Some sh"
|
|
|
1219 |
by (auto simp:ch2sshm_def split:option.splits dest!:current_has_sec')
|
|
|
1220 |
|
|
|
1221 |
lemma current_shm_has_sh':
|
|
|
1222 |
"\<lbrakk>ch2sshm s h = None; valid s\<rbrakk> \<Longrightarrow> h \<notin> current_shms s"
|
|
|
1223 |
by (auto dest:current_shm_has_sh)
|
|
|
1224 |
|
|
|
1225 |
(********** cph2spshs simpset **********)
|
|
|
1226 |
|
|
|
1227 |
lemma cph2spshs_attach:
|
|
|
1228 |
"valid (Attach p h flag # s) \<Longrightarrow>
|
|
|
1229 |
cph2spshs (Attach p h flag # s) = (cph2spshs s) (p :=
|
|
|
1230 |
(case (ch2sshm s h) of
|
|
|
1231 |
Some sh \<Rightarrow> cph2spshs s p \<union> {(sh, flag)}
|
|
|
1232 |
| _ \<Rightarrow> cph2spshs s p) )"
|
|
|
1233 |
apply (frule vd_cons, frule vt_grant_os, rule ext)
|
|
|
1234 |
using ch2sshm_other[where e = "Attach p h flag" and s = s]
|
|
|
1235 |
apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
|
|
|
1236 |
dest!:current_shm_has_sh' dest: procs_of_shm_prop1 simp:cph2spshs_def)
|
|
|
1237 |
apply (erule_tac x = ha in allE, frule procs_of_shm_prop1, simp, simp)
|
|
|
1238 |
apply (erule_tac x = ha in allE, frule procs_of_shm_prop1, simp, simp)
|
|
|
1239 |
apply (erule_tac x = ha in allE, frule procs_of_shm_prop1, simp, simp)
|
|
|
1240 |
apply (erule_tac x = ha in allE, frule procs_of_shm_prop1, simp, simp)
|
|
|
1241 |
apply (erule_tac x = ha in allE, frule procs_of_shm_prop1, simp, simp)
|
|
|
1242 |
apply (case_tac "ha = h", simp, frule procs_of_shm_prop1, simp)
|
|
|
1243 |
apply (rule_tac x = ha in exI, simp)
|
|
|
1244 |
apply (rule_tac x = ha in exI, simp, drule procs_of_shm_prop1, simp, simp)
|
|
|
1245 |
apply (rule_tac x = ha in exI, simp)
|
|
|
1246 |
apply (frule procs_of_shm_prop1, simp, simp)
|
|
|
1247 |
apply (rule impI, simp)
|
|
|
1248 |
done
|
|
|
1249 |
|
|
|
1250 |
lemma cph2spshs_detach: "valid (Detach p h # s) \<Longrightarrow>
|
|
|
1251 |
cph2spshs (Detach p h # s) = (cph2spshs s) (p :=
|
|
|
1252 |
(case (ch2sshm s h, flag_of_proc_shm s p h) of
|
|
|
1253 |
(Some sh, Some flag) \<Rightarrow> if (\<exists> h'. h' \<noteq> h \<and> (p,flag) \<in> procs_of_shm s h' \<and> ch2sshm s h' = Some sh)
|
|
|
1254 |
then cph2spshs s p else cph2spshs s p - {(sh, flag)}
|
|
|
1255 |
| _ \<Rightarrow> cph2spshs s p) )"
|
|
|
1256 |
apply (frule vd_cons, frule vt_grant_os, rule ext)
|
|
|
1257 |
apply (case_tac "x = p") defer
|
|
|
1258 |
using ch2sshm_other[where e = "Detach p h" and s = s]
|
|
|
1259 |
apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
|
|
|
1260 |
dest!:current_shm_has_sh' procs_of_shm_prop4' dest:procs_of_shm_prop1 procs_of_shm_prop3 simp:cph2spshs_def) [1]
|
|
|
1261 |
apply (rule_tac x = ha in exI, frule_tac h = ha in procs_of_shm_prop1, simp, simp)
|
|
|
1262 |
apply (rule_tac x = ha in exI, frule_tac h = ha in procs_of_shm_prop1, simp, simp)
|
|
|
1263 |
apply (rule impI, simp)
|
|
|
1264 |
|
|
|
1265 |
apply (clarsimp)
|
|
|
1266 |
apply (frule current_shm_has_sh, simp, erule exE)
|
|
|
1267 |
apply (frule procs_of_shm_prop4, simp, simp)
|
|
|
1268 |
apply (rule allI | rule conjI| erule conjE | erule exE | rule impI)+
|
|
|
1269 |
|
|
|
1270 |
apply (simp only:cph2spshs_def, rule set_eqI, rule iffI)
|
|
|
1271 |
apply (erule CollectE | erule exE| erule conjE| rule CollectI)+
|
|
|
1272 |
apply (case_tac "ha = h", simp)
|
|
|
1273 |
apply (rule_tac x = sha in exI, rule_tac x = flaga in exI, rule_tac x = ha in exI, simp)
|
|
|
1274 |
using ch2sshm_other[where e = "Detach p h" and s = s] apply (simp add:procs_of_shm_prop1)
|
|
|
1275 |
|
|
|
1276 |
apply (erule CollectE | erule exE| erule conjE| rule CollectI)+
|
|
|
1277 |
apply (case_tac "ha = h", simp)
|
|
|
1278 |
apply (rule_tac x = h' in exI, simp)
|
|
|
1279 |
apply (frule_tac flag = flag and flag' = flaga in procs_of_shm_prop3, simp+)
|
|
|
1280 |
apply (frule_tac flag = flaga in procs_of_shm_prop4, simp+)
|
|
|
1281 |
using ch2sshm_other[where e = "Detach p h" and s = s] apply (simp add:procs_of_shm_prop1)
|
|
|
1282 |
apply (frule_tac h = h' in procs_of_shm_prop1, simp, simp)
|
|
|
1283 |
apply (rule_tac x = ha in exI, simp, frule_tac h = ha in procs_of_shm_prop1, simp+)
|
|
|
1284 |
using ch2sshm_other[where e = "Detach p h" and s = s] apply (simp add:procs_of_shm_prop1)
|
|
|
1285 |
|
|
|
1286 |
apply (rule allI | rule conjI| erule conjE | erule exE | rule impI)+
|
|
|
1287 |
apply (simp only:cph2spshs_def, rule set_eqI, rule iffI)
|
|
|
1288 |
apply (erule CollectE | erule exE| erule conjE| rule DiffI |rule CollectI)+
|
|
|
1289 |
apply (simp split:if_splits)
|
|
|
1290 |
apply (rule_tac x = ha in exI, simp, frule_tac h = ha in procs_of_shm_prop1, simp+)
|
|
|
1291 |
using ch2sshm_other[where e = "Detach p h" and s = s] apply (simp add:procs_of_shm_prop1)
|
|
|
1292 |
apply (rule notI, simp split:if_splits)
|
|
|
1293 |
apply (erule_tac x = ha in allE, simp, frule_tac h = ha in procs_of_shm_prop1, simp+)
|
|
|
1294 |
using ch2sshm_other[where e = "Detach p h" and s = s] apply (simp add:procs_of_shm_prop1)
|
|
|
1295 |
apply (erule CollectE | erule exE| erule conjE| erule DiffE |rule CollectI)+
|
|
|
1296 |
apply (simp split:if_splits)
|
|
|
1297 |
apply (erule_tac x = ha in allE, simp, rule_tac x = ha in exI, simp)
|
|
|
1298 |
apply (case_tac "ha = h", simp add:procs_of_shm_prop3, frule_tac h = ha in procs_of_shm_prop1, simp+)
|
|
|
1299 |
using ch2sshm_other[where e = "Detach p h" and s = s] apply (simp add:procs_of_shm_prop1)
|
|
|
1300 |
done
|
|
|
1301 |
|
|
|
1302 |
lemma cph2spshs_deleteshm:
|
|
|
1303 |
"valid (DeleteShM p h # s) \<Longrightarrow>
|
|
|
1304 |
cph2spshs (DeleteShM p h # s) = (\<lambda> p'.
|
|
|
1305 |
(case (ch2sshm s h, flag_of_proc_shm s p' h) of
|
|
|
1306 |
(Some sh, Some flag) \<Rightarrow> if (\<exists> h'. h' \<noteq> h \<and> (p', flag) \<in> procs_of_shm s h' \<and> ch2sshm s h' = Some sh)
|
|
|
1307 |
then cph2spshs s p' else cph2spshs s p' - {(sh, flag)}
|
|
|
1308 |
| _ \<Rightarrow> cph2spshs s p') )"
|
|
|
1309 |
apply (frule vd_cons, frule vt_grant_os, rule ext)
|
|
|
1310 |
|
|
|
1311 |
apply (clarsimp)
|
|
|
1312 |
apply (frule current_shm_has_sh, simp, erule exE, simp, simp split:option.splits)
|
|
|
1313 |
apply (rule conjI, rule impI)
|
|
|
1314 |
using ch2sshm_other[where e = "DeleteShM p h" and s = s]
|
|
|
1315 |
apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
|
|
|
1316 |
dest!:current_shm_has_sh' procs_of_shm_prop4' dest:procs_of_shm_prop1 procs_of_shm_prop3 simp:cph2spshs_def) [1]
|
|
|
1317 |
apply (rule_tac x = ha in exI, frule_tac h = ha in procs_of_shm_prop1, simp+)
|
|
|
1318 |
apply (rule_tac x = ha in exI, simp)
|
|
|
1319 |
apply (case_tac "ha = h", simp+, frule_tac h = ha in procs_of_shm_prop1, simp+)
|
|
|
1320 |
|
|
|
1321 |
apply (rule allI | rule conjI| erule conjE | erule exE | rule impI)+
|
|
|
1322 |
|
|
|
1323 |
apply (simp only:cph2spshs_def, rule set_eqI, rule iffI)
|
|
|
1324 |
apply (erule CollectE | erule exE| erule conjE| rule CollectI)+
|
|
|
1325 |
apply (case_tac "ha = h", simp)
|
|
|
1326 |
apply (rule_tac x = sha in exI, rule_tac x = flag in exI, rule_tac x = ha in exI, simp)
|
|
|
1327 |
using ch2sshm_other[where e = "DeleteShM p h" and s = s] apply (simp add:procs_of_shm_prop1)
|
|
|
1328 |
|
|
|
1329 |
apply (erule CollectE | erule exE| erule conjE| rule CollectI)+
|
|
|
1330 |
apply (case_tac "ha = h", simp)
|
|
|
1331 |
apply (rule_tac x = h' in exI, simp)
|
|
|
1332 |
apply (frule_tac flag = flag in procs_of_shm_prop4, simp+)
|
|
|
1333 |
using ch2sshm_other[where e = "DeleteShM p h" and s = s] apply (simp add:procs_of_shm_prop1)
|
|
|
1334 |
apply (frule_tac h = h' in procs_of_shm_prop1, simp, simp)
|
|
|
1335 |
apply (rule_tac x = ha in exI, simp, frule_tac h = ha in procs_of_shm_prop1, simp+)
|
|
|
1336 |
using ch2sshm_other[where e = "DeleteShM p h" and s = s] apply (simp add:procs_of_shm_prop1)
|
|
|
1337 |
|
|
|
1338 |
apply (rule allI | rule conjI| erule conjE | erule exE | rule impI)+
|
|
|
1339 |
apply (simp only:cph2spshs_def, rule set_eqI, rule iffI)
|
|
|
1340 |
apply (erule CollectE | erule exE| erule conjE| rule DiffI |rule CollectI)+
|
|
|
1341 |
apply (simp split:if_splits)
|
|
|
1342 |
apply (rule_tac x = ha in exI, simp, frule_tac h = ha in procs_of_shm_prop1, simp+)
|
|
|
1343 |
using ch2sshm_other[where e = "DeleteShM p h" and s = s] apply (simp add:procs_of_shm_prop1)
|
|
|
1344 |
apply (rule notI, simp split:if_splits)
|
|
|
1345 |
apply (erule_tac x = ha in allE, simp, frule_tac h = ha in procs_of_shm_prop1, simp+)
|
|
|
1346 |
using ch2sshm_other[where e = "DeleteShM p h" and s = s] apply (simp add:procs_of_shm_prop1)
|
|
|
1347 |
apply (erule CollectE | erule exE| erule conjE| erule DiffE |rule CollectI)+
|
|
|
1348 |
apply (simp split:if_splits)
|
|
|
1349 |
apply (erule_tac x = ha in allE, simp, rule_tac x = ha in exI, simp)
|
|
|
1350 |
apply (case_tac "ha = h", simp add:procs_of_shm_prop4)
|
|
|
1351 |
apply (frule_tac h = ha in procs_of_shm_prop1, simp+)
|
|
|
1352 |
using ch2sshm_other[where e = "DeleteShM p h" and s = s] apply (simp add:procs_of_shm_prop1)
|
|
|
1353 |
done
|
|
|
1354 |
|
|
|
1355 |
lemma flag_of_proc_shm_prop1:
|
|
|
1356 |
"\<lbrakk>flag_of_proc_shm s p h = Some flag; valid s\<rbrakk> \<Longrightarrow> (p, flag) \<in> procs_of_shm s h"
|
|
|
1357 |
apply (induct s arbitrary:p)
|
|
|
1358 |
apply (simp add:init_shmflag_has_proc)
|
|
|
1359 |
apply (frule vt_grant_os, frule vd_cons, case_tac a, auto split:if_splits option.splits)
|
|
|
1360 |
done
|
|
|
1361 |
|
|
|
1362 |
lemma cph2spshs_clone:
|
|
|
1363 |
"valid (Clone p p' fds shms # s) \<Longrightarrow>
|
|
|
1364 |
cph2spshs (Clone p p' fds shms # s) = (cph2spshs s) (p' :=
|
|
|
1365 |
{(sh, flag) | h sh flag. h \<in> shms \<and> ch2sshm s h = Some sh \<and> flag_of_proc_shm s p h = Some flag} )"
|
|
|
1366 |
apply (frule vd_cons, frule vt_grant_os, rule ext)
|
|
|
1367 |
using ch2sshm_other[where e = "Clone p p' fds shms" and s = s]
|
|
|
1368 |
apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
|
|
|
1369 |
dest!:current_shm_has_sh' dest: procs_of_shm_prop1 procs_of_shm_prop2 procs_of_shm_prop3 simp:cph2spshs_def)
|
|
|
1370 |
apply (erule_tac x = h in allE, frule procs_of_shm_prop1, simp, simp add:procs_of_shm_prop4)
|
|
|
1371 |
apply (rule_tac x = h in exI, simp, frule flag_of_proc_shm_prop1, simp+, simp add:procs_of_shm_prop1)
|
|
|
1372 |
apply (rule_tac x = h in exI, simp, frule procs_of_shm_prop1, simp+)+
|
|
|
1373 |
done
|
|
|
1374 |
|
|
|
1375 |
lemma cph2spshs_execve:
|
|
|
1376 |
"valid (Execve p f fds # s) \<Longrightarrow>
|
|
|
1377 |
cph2spshs (Execve p f fds # s) = (cph2spshs s) (p := {})"
|
|
|
1378 |
apply (frule vd_cons, frule vt_grant_os, rule ext)
|
|
|
1379 |
using ch2sshm_other[where e = "Execve p f fds" and s = s]
|
|
|
1380 |
apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
|
|
|
1381 |
dest!:current_shm_has_sh' dest: procs_of_shm_prop1 procs_of_shm_prop2 procs_of_shm_prop3 simp:cph2spshs_def)
|
|
|
1382 |
apply (rule_tac x = h in exI, simp add:procs_of_shm_prop1)+
|
|
|
1383 |
done
|
|
|
1384 |
|
|
|
1385 |
lemma cph2spshs_kill:
|
|
|
1386 |
"valid (Kill p p' # s) \<Longrightarrow> cph2spshs (Kill p p' # s) = (cph2spshs s) (p' := {})"
|
|
|
1387 |
apply (frule vd_cons, frule vt_grant_os, rule ext)
|
|
|
1388 |
using ch2sshm_other[where e = "Kill p p'" and s = s]
|
|
|
1389 |
apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
|
|
|
1390 |
dest!:current_shm_has_sh' dest: procs_of_shm_prop1 procs_of_shm_prop2 procs_of_shm_prop3 simp:cph2spshs_def)
|
|
|
1391 |
apply (rule_tac x = h in exI, simp add:procs_of_shm_prop1)+
|
|
|
1392 |
done
|
|
|
1393 |
|
|
|
1394 |
lemma cph2spshs_exit:
|
|
|
1395 |
"valid (Exit p # s) \<Longrightarrow> cph2spshs (Exit p # s) = (cph2spshs s) (p := {})"
|
|
|
1396 |
apply (frule vd_cons, frule vt_grant_os, rule ext)
|
|
|
1397 |
using ch2sshm_other[where e = "Exit p" and s = s]
|
|
|
1398 |
apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
|
|
|
1399 |
dest!:current_shm_has_sh' dest: procs_of_shm_prop1 procs_of_shm_prop2 procs_of_shm_prop3 simp:cph2spshs_def)
|
|
|
1400 |
apply (rule_tac x = h in exI, simp add:procs_of_shm_prop1)+
|
|
|
1401 |
done
|
|
|
1402 |
|
|
|
1403 |
lemma cph2spshs_createshm:
|
|
|
1404 |
"valid (CreateShM p h # s) \<Longrightarrow> cph2spshs (CreateShM p h # s) = cph2spshs s"
|
|
|
1405 |
apply (frule vt_grant_os, frule vd_cons, rule ext)
|
|
|
1406 |
apply (auto simp:cph2spshs_def)
|
|
|
1407 |
using ch2sshm_createshm
|
|
|
1408 |
apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
|
|
|
1409 |
dest!:current_shm_has_sh' dest: procs_of_shm_prop1 procs_of_shm_prop2 procs_of_shm_prop3 simp:cph2spshs_def)
|
|
|
1410 |
apply (rule_tac x = ha in exI, auto simp:procs_of_shm_prop1)
|
|
|
1411 |
done
|
|
|
1412 |
|
|
|
1413 |
lemma cph2spshs_other:
|
|
|
1414 |
"\<lbrakk>valid (e # s);
|
|
|
1415 |
\<forall> p h flag. e \<noteq> Attach p h flag;
|
|
|
1416 |
\<forall> p h. e \<noteq> Detach p h;
|
|
|
1417 |
\<forall> p h. e \<noteq> DeleteShM p h;
|
|
|
1418 |
\<forall> p p' fds shms. e \<noteq> Clone p p' fds shms;
|
|
|
1419 |
\<forall> p f fds. e \<noteq> Execve p f fds;
|
|
|
1420 |
\<forall> p p'. e \<noteq> Kill p p';
|
|
|
1421 |
\<forall> p. e \<noteq> Exit p\<rbrakk> \<Longrightarrow> cph2spshs (e # s) = cph2spshs s"
|
|
|
1422 |
apply (frule vt_grant_os, frule vd_cons, rule ext)
|
|
|
1423 |
unfolding cph2spshs_def
|
|
|
1424 |
apply (rule set_eqI, rule iffI)
|
|
|
1425 |
apply (erule CollectE | erule conjE| erule exE| rule conjI| rule impI| rule CollectI)+
|
|
|
1426 |
apply (frule procs_of_shm_prop1, simp, rule_tac x= sh in exI, rule_tac x = flag in exI, rule_tac x = h in exI)
|
|
|
1427 |
apply (case_tac e)
|
|
|
1428 |
using ch2sshm_other[where e = e and s = s]
|
|
|
1429 |
apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
|
|
|
1430 |
dest!:current_shm_has_sh' dest: procs_of_shm_prop1 procs_of_shm_prop2 procs_of_shm_prop3
|
|
|
1431 |
simp:ch2sshm_createshm)
|
|
|
1432 |
apply (rule_tac x = h in exI, case_tac e)
|
|
|
1433 |
using ch2sshm_other[where e = e and s = s]
|
|
|
1434 |
apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
|
|
|
1435 |
dest!:current_shm_has_sh' dest: procs_of_shm_prop1 procs_of_shm_prop2 procs_of_shm_prop3
|
|
|
1436 |
simp:ch2sshm_createshm)
|
|
|
1437 |
done
|
|
|
1438 |
|
|
|
1439 |
lemmas cph2spshs_simps = cph2spshs_attach cph2spshs_detach cph2spshs_deleteshm cph2spshs_clone cph2spshs_execve
|
|
|
1440 |
cph2spshs_exit cph2spshs_kill cph2spshs_other
|
|
|
1441 |
*)
|
|
|
1442 |
(******** cp2sproc simpset *********)
|
|
|
1443 |
|
|
|
1444 |
lemma cp2sproc_clone:
|
|
|
1445 |
"valid (Clone p p' fds # s) \<Longrightarrow> cp2sproc (Clone p p' fds # s) = (cp2sproc s) (p' :=
|
|
|
1446 |
case (sectxt_of_obj s (O_proc p)) of
|
|
|
1447 |
Some sec \<Rightarrow> Some (Created, sec,
|
|
|
1448 |
{sfd. \<exists> fd \<in> fds. \<exists> f. file_of_proc_fd s p fd = Some f \<and> cfd2sfd s p fd = Some sfd})
|
|
|
1449 |
| _ \<Rightarrow> None)" (* ,
|
|
|
1450 |
{(sh, flag) | h sh flag. h \<in> shms \<and> ch2sshm s h = Some sh \<and> flag_of_proc_shm s p h = Some flag} *)
|
|
|
1451 |
apply (frule cpfd2sfds_clone) (*
|
|
|
1452 |
apply (frule cph2spshs_clone, frule cpfd2sfds_clone) *)
|
|
|
1453 |
apply (frule vd_cons, frule vt_grant_os, simp only:os_grant.simps)
|
|
|
1454 |
apply ((erule exE| erule conjE)+, frule not_init_intro_proc, simp, rule ext, case_tac "x = p'", simp)
|
|
|
1455 |
apply (auto simp:cp2sproc_def sectxt_of_obj_simps dest!:current_has_sec'
|
|
|
1456 |
dest:current_proc_has_sec split:option.splits if_splits)
|
|
|
1457 |
done
|
|
|
1458 |
|
|
|
1459 |
lemma cp2sproc_other:
|
|
|
1460 |
"\<lbrakk>valid (e # s);
|
|
|
1461 |
\<forall> p f flags fd opt. e \<noteq> Open p f flags fd opt;
|
|
|
1462 |
\<forall> p fd. e \<noteq> CloseFd p fd;
|
|
|
1463 |
\<forall> p p' fds. e \<noteq> Clone p p' fds;
|
|
|
1464 |
\<forall> p f fds. e \<noteq> Execve p f fds;
|
|
|
1465 |
\<forall> p p'. e \<noteq> Kill p p';
|
|
|
1466 |
\<forall> p. e \<noteq> Exit p\<rbrakk> \<Longrightarrow> cp2sproc (e # s) = cp2sproc s" (*
|
|
|
1467 |
\<forall> p h flag. e \<noteq> Attach p h flag;
|
|
|
1468 |
\<forall> p h. e \<noteq> Detach p h;
|
|
|
1469 |
\<forall> p h. e \<noteq> DeleteShM p h;*)
|
|
|
1470 |
apply (frule cpfd2sfds_other, simp+)(*
|
|
|
1471 |
apply (frule cph2spshs_other, simp+, frule cpfd2sfds_other, simp+)*)
|
|
|
1472 |
apply (frule vt_grant_os, frule vd_cons, rule ext, case_tac e, simp_all)
|
|
|
1473 |
apply (auto simp:cp2sproc_def sectxt_of_obj_simps dest!:current_has_sec'
|
|
|
1474 |
dest:current_proc_has_sec not_died_init_proc split:option.splits if_splits)
|
|
|
1475 |
done
|
|
|
1476 |
|
|
|
1477 |
lemma cp2sproc_open:
|
|
|
1478 |
"valid (Open p f flags fd opt # s) \<Longrightarrow>
|
|
|
1479 |
cp2sproc (Open p f flags fd opt # s) = (cp2sproc s) (p :=
|
|
|
1480 |
case (sectxt_of_obj s (O_proc p), sectxt_of_obj (Open p f flags fd opt # s) (O_fd p fd),
|
|
|
1481 |
cf2sfile (Open p f flags fd opt # s) f) of
|
|
|
1482 |
(Some sec, Some fdsec, Some sf) \<Rightarrow> Some (if (\<not> died (O_proc p) s \<and> p \<in> init_procs)
|
|
|
1483 |
then Init p else Created, sec,
|
|
85
|
1484 |
(cpfd2sfds s p) \<union> {(fdsec, remove_create_flag flags, sf)})
|
|
77
|
1485 |
| _ \<Rightarrow> None)" (*, cph2spshs s p
|
|
|
1486 |
apply (frule cph2spshs_other, simp, simp, simp, simp, simp, simp, simp) *)
|
|
|
1487 |
apply (frule cpfd2sfds_open, frule vt_grant_os, frule vd_cons, rule ext)
|
|
|
1488 |
apply (case_tac "x = p")
|
|
|
1489 |
apply (auto simp:cp2sproc_def sectxt_of_obj_simps current_files_simps
|
|
|
1490 |
dest!:current_has_sec' dest!:current_file_has_sfile' dest:is_file_in_current is_dir_in_current
|
|
|
1491 |
dest:current_proc_has_sec not_died_init_proc split:option.splits if_splits)
|
|
|
1492 |
done
|
|
|
1493 |
|
|
|
1494 |
lemma cp2sproc_closefd:
|
|
|
1495 |
"valid (CloseFd p fd # s) \<Longrightarrow>
|
|
|
1496 |
cp2sproc (CloseFd p fd # s) = (cp2sproc s) (p :=
|
|
|
1497 |
if (fd \<in> proc_file_fds s p)
|
|
|
1498 |
then (case (cfd2sfd s p fd) of
|
|
|
1499 |
Some sfd \<Rightarrow> (if (\<exists> fd' f'. fd' \<noteq> fd \<and> file_of_proc_fd s p fd' = Some f' \<and> cfd2sfd s p fd' = Some sfd)
|
|
|
1500 |
then cp2sproc s p
|
|
|
1501 |
else (case (sectxt_of_obj s (O_proc p)) of
|
|
|
1502 |
Some sec \<Rightarrow> Some (if (\<not> died (O_proc p) s \<and> p \<in> init_procs)
|
|
|
1503 |
then Init p else Created,
|
|
|
1504 |
sec, cpfd2sfds s p - {sfd})
|
|
|
1505 |
| _ \<Rightarrow> None))
|
|
|
1506 |
| _ \<Rightarrow> cp2sproc s p)
|
|
|
1507 |
else cp2sproc s p)"(*, cph2spshs s p *)
|
|
|
1508 |
apply (frule cpfd2sfds_closefd) (*
|
|
|
1509 |
apply (frule cpfd2sfds_closefd, frule cph2spshs_other, simp, simp, simp, simp, simp, simp, simp) *)
|
|
|
1510 |
apply (frule vt_grant_os, frule vd_cons, rule ext)
|
|
|
1511 |
apply (case_tac "x = p")
|
|
|
1512 |
apply (auto simp:cp2sproc_def sectxt_of_obj_simps current_files_simps
|
|
|
1513 |
dest!:current_has_sec' dest!:current_file_has_sfile' dest:is_file_in_current is_dir_in_current
|
|
|
1514 |
dest:current_proc_has_sec not_died_init_proc split:option.splits if_splits)
|
|
|
1515 |
done
|
|
|
1516 |
|
|
|
1517 |
(*
|
|
|
1518 |
lemma cp2sproc_attach:
|
|
|
1519 |
"valid (Attach p h flag # s) \<Longrightarrow>
|
|
|
1520 |
cp2sproc (Attach p h flag # s) = (cp2sproc s) (p :=
|
|
|
1521 |
(case (ch2sshm s h) of
|
|
|
1522 |
Some sh \<Rightarrow> (case (sectxt_of_obj s (O_proc p)) of
|
|
|
1523 |
Some sec \<Rightarrow> Some (if (\<not> died (O_proc p) s \<and> p \<in> init_procs)
|
|
|
1524 |
then Init p else Created,
|
|
|
1525 |
sec, cpfd2sfds s p, cph2spshs s p \<union> {(sh, flag)})
|
|
|
1526 |
| _ \<Rightarrow> None)
|
|
|
1527 |
| _ \<Rightarrow> cp2sproc s p) )"
|
|
|
1528 |
apply (frule cph2spshs_attach, frule cpfd2sfds_other, simp, simp, simp, simp, simp, simp)
|
|
|
1529 |
apply (frule vt_grant_os, frule vd_cons, rule ext)
|
|
|
1530 |
apply (case_tac "x = p")
|
|
|
1531 |
apply (auto simp:cp2sproc_def sectxt_of_obj_simps current_files_simps
|
|
|
1532 |
dest!:current_has_sec' dest!:current_file_has_sfile' dest:is_file_in_current is_dir_in_current
|
|
|
1533 |
dest:current_proc_has_sec not_died_init_proc split:option.splits if_splits)
|
|
|
1534 |
done
|
|
|
1535 |
|
|
|
1536 |
lemma cp2sproc_detach:
|
|
|
1537 |
"valid (Detach p h # s) \<Longrightarrow>
|
|
|
1538 |
cp2sproc (Detach p h # s) = (cp2sproc s) (p :=
|
|
|
1539 |
(case (ch2sshm s h, flag_of_proc_shm s p h) of
|
|
|
1540 |
(Some sh, Some flag) \<Rightarrow> if (\<exists> h'. h' \<noteq> h \<and> (p,flag) \<in> procs_of_shm s h' \<and> ch2sshm s h' = Some sh)
|
|
|
1541 |
then cp2sproc s p
|
|
|
1542 |
else (case (sectxt_of_obj s (O_proc p)) of
|
|
|
1543 |
Some sec \<Rightarrow> Some (if (\<not> died (O_proc p) s \<and> p \<in> init_procs)
|
|
|
1544 |
then Init p else Created, sec,
|
|
|
1545 |
cpfd2sfds s p, cph2spshs s p - {(sh, flag)})
|
|
|
1546 |
| None \<Rightarrow> None)
|
|
|
1547 |
| _ \<Rightarrow> cp2sproc s p) )"
|
|
|
1548 |
apply (frule cph2spshs_detach, frule cpfd2sfds_other, simp, simp, simp, simp, simp, simp)
|
|
|
1549 |
apply (frule vt_grant_os, frule vd_cons, rule ext)
|
|
|
1550 |
apply (case_tac "x = p")
|
|
|
1551 |
apply (auto simp:cp2sproc_def sectxt_of_obj_simps current_files_simps
|
|
|
1552 |
dest!:current_has_sec' dest!:current_file_has_sfile' dest:is_file_in_current is_dir_in_current
|
|
|
1553 |
dest:current_proc_has_sec not_died_init_proc split:option.splits if_splits)
|
|
|
1554 |
done
|
|
|
1555 |
|
|
|
1556 |
lemma cp2sproc_deleteshm:
|
|
|
1557 |
"valid (DeleteShM p h # s) \<Longrightarrow>
|
|
|
1558 |
cp2sproc (DeleteShM p h # s) = (\<lambda> p'.
|
|
|
1559 |
(case (ch2sshm s h, flag_of_proc_shm s p' h) of
|
|
|
1560 |
(Some sh, Some flag) \<Rightarrow> if (\<exists> h'. h' \<noteq> h \<and> (p', flag) \<in> procs_of_shm s h' \<and> ch2sshm s h' = Some sh)
|
|
|
1561 |
then cp2sproc s p'
|
|
|
1562 |
else (case (sectxt_of_obj s (O_proc p')) of
|
|
|
1563 |
Some sec \<Rightarrow> Some (if (\<not> died (O_proc p') s \<and> p' \<in> init_procs)
|
|
|
1564 |
then Init p' else Created, sec,
|
|
|
1565 |
cpfd2sfds s p', cph2spshs s p' - {(sh, flag)})
|
|
|
1566 |
| None \<Rightarrow> None)
|
|
|
1567 |
| _ \<Rightarrow> cp2sproc s p') )"
|
|
|
1568 |
apply (frule cph2spshs_deleteshm, frule cpfd2sfds_other, simp, simp, simp, simp, simp, simp)
|
|
|
1569 |
apply (frule vt_grant_os, frule vd_cons, rule ext)
|
|
|
1570 |
apply (auto simp:cp2sproc_def sectxt_of_obj_simps current_files_simps
|
|
|
1571 |
dest!:current_has_sec' dest!:current_file_has_sfile' dest:is_file_in_current is_dir_in_current
|
|
|
1572 |
dest:current_proc_has_sec not_died_init_proc split:option.splits if_splits)
|
|
|
1573 |
done
|
|
|
1574 |
*)
|
|
|
1575 |
|
|
|
1576 |
lemma cp2sproc_execve:
|
|
|
1577 |
"valid (Execve p f fds # s) \<Longrightarrow>
|
|
|
1578 |
cp2sproc (Execve p f fds # s) = (cp2sproc s) (p :=
|
|
|
1579 |
(case (sectxt_of_obj (Execve p f fds # s) (O_proc p)) of
|
|
|
1580 |
Some sec \<Rightarrow> Some (if (\<not> died (O_proc p) s \<and> p \<in> init_procs) then Init p else Created, sec,
|
|
|
1581 |
{sfd. \<exists> fd \<in> fds. \<exists> f. file_of_proc_fd s p fd = Some f \<and> cfd2sfd s p fd = Some sfd})
|
|
|
1582 |
| _ \<Rightarrow> None) )" (*, {}
|
|
|
1583 |
apply (frule cph2spshs_execve, frule cpfd2sfds_execve) *)
|
|
|
1584 |
apply (frule cpfd2sfds_execve)
|
|
|
1585 |
apply (frule vt_grant_os, frule vd_cons, rule ext)
|
|
|
1586 |
apply (auto simp:cp2sproc_def sectxt_of_obj_simps current_files_simps
|
|
|
1587 |
dest!:current_has_sec' dest!:current_file_has_sfile' dest:is_file_in_current is_dir_in_current
|
|
|
1588 |
dest:current_proc_has_sec not_died_init_proc split:option.splits if_splits)
|
|
|
1589 |
done
|
|
|
1590 |
|
|
|
1591 |
lemma cp2sproc_kill:
|
|
|
1592 |
"\<lbrakk>valid (Kill p p' # s); p'' \<noteq> p'\<rbrakk> \<Longrightarrow>
|
|
|
1593 |
cp2sproc (Kill p p' # s) p'' = (cp2sproc s) p''" (*
|
|
|
1594 |
apply (frule cph2spshs_kill, frule cpfd2sfds_kill) *)
|
|
|
1595 |
apply (frule cpfd2sfds_kill)
|
|
|
1596 |
apply (frule vt_grant_os, frule vd_cons)
|
|
|
1597 |
apply (auto simp:cp2sproc_def sectxt_of_obj_simps current_files_simps
|
|
|
1598 |
dest!:current_has_sec' dest!:current_file_has_sfile' dest:is_file_in_current is_dir_in_current
|
|
|
1599 |
dest:current_proc_has_sec not_died_init_proc split:option.splits if_splits)
|
|
|
1600 |
done
|
|
|
1601 |
|
|
|
1602 |
lemma cp2sproc_kill':
|
|
|
1603 |
"\<lbrakk>valid (Kill p p' # s); p'' \<in> current_procs (Kill p p' # s)\<rbrakk> \<Longrightarrow>
|
|
|
1604 |
cp2sproc (Kill p p' # s) p'' = (cp2sproc s) p''"
|
|
|
1605 |
by (drule_tac p'' = p'' in cp2sproc_kill, simp+)
|
|
|
1606 |
|
|
|
1607 |
lemma cp2sproc_exit:
|
|
|
1608 |
"\<lbrakk>valid (Exit p # s); p' \<noteq> p\<rbrakk> \<Longrightarrow>
|
|
|
1609 |
cp2sproc (Exit p # s) p' = (cp2sproc s) p'" (*
|
|
|
1610 |
apply (frule cph2spshs_exit, frule cpfd2sfds_exit) *)
|
|
|
1611 |
apply (frule cpfd2sfds_exit)
|
|
|
1612 |
apply (frule vt_grant_os, frule vd_cons)
|
|
|
1613 |
apply (auto simp:cp2sproc_def sectxt_of_obj_simps current_files_simps
|
|
|
1614 |
dest!:current_has_sec' dest!:current_file_has_sfile' dest:is_file_in_current is_dir_in_current
|
|
|
1615 |
dest:current_proc_has_sec not_died_init_proc split:option.splits if_splits)
|
|
|
1616 |
done
|
|
|
1617 |
|
|
|
1618 |
lemma cp2sproc_exit':
|
|
|
1619 |
"\<lbrakk>valid (Exit p # s); p' \<in> current_procs (Exit p # s)\<rbrakk> \<Longrightarrow>
|
|
|
1620 |
cp2sproc (Exit p # s) p' = (cp2sproc s) p'"
|
|
|
1621 |
by (drule_tac p'= p' in cp2sproc_exit, simp+)
|
|
|
1622 |
|
|
|
1623 |
lemmas cp2sproc_simps = cp2sproc_open cp2sproc_closefd (* cp2sproc_attach cp2sproc_detach cp2sproc_deleteshm *)
|
|
|
1624 |
cp2sproc_clone cp2sproc_execve cp2sproc_kill cp2sproc_exit cp2sproc_other
|
|
|
1625 |
|
|
|
1626 |
lemma current_proc_has_sp:
|
|
|
1627 |
"\<lbrakk>p \<in> current_procs s; valid s\<rbrakk> \<Longrightarrow> \<exists> sp. cp2sproc s p = Some sp"
|
|
|
1628 |
by (auto simp:cp2sproc_def split:option.splits dest!:current_has_sec')
|
|
|
1629 |
|
|
|
1630 |
lemma current_proc_has_sp':
|
|
|
1631 |
"\<lbrakk>cp2sproc s p = None; valid s\<rbrakk> \<Longrightarrow> p \<notin> current_procs s"
|
|
|
1632 |
by (auto dest:current_proc_has_sp)
|
|
|
1633 |
|
|
|
1634 |
(* simpset for cf2sfiles *)
|
|
|
1635 |
|
|
|
1636 |
lemma cf2sfiles_open:
|
|
|
1637 |
"\<lbrakk>valid (Open p f flag fd opt # s); f' \<in> current_files (Open p f flag fd opt # s)\<rbrakk>
|
|
|
1638 |
\<Longrightarrow> cf2sfiles (Open p f flag fd opt # s) f' = (
|
|
|
1639 |
if (f' = f \<and> opt \<noteq> None)
|
|
|
1640 |
then (case cf2sfile (Open p f flag fd opt # s) f of
|
|
|
1641 |
Some sf \<Rightarrow> {sf}
|
|
|
1642 |
| _ \<Rightarrow> {} )
|
|
|
1643 |
else cf2sfiles s f')"
|
|
|
1644 |
apply (frule vt_grant_os, frule vd_cons)
|
|
|
1645 |
apply (auto simp:cf2sfiles_def cf2sfile_open_none cf2sfile_simps same_inode_files_open
|
|
|
1646 |
split:if_splits option.splits dest!:current_file_has_sfile' dest:cf2sfile_open)
|
|
|
1647 |
apply (rule_tac x = "f'a" in bexI, drule same_inode_files_prop1, simp add:cf2sfile_open_some1, simp)+
|
|
|
1648 |
done
|
|
|
1649 |
|
|
|
1650 |
lemma cf2sfiles_other:
|
|
|
1651 |
"\<lbrakk>valid (e # s);
|
|
|
1652 |
\<forall> p f flag fd opt. e \<noteq> Open p f flag fd opt;
|
|
|
1653 |
\<forall> p fd. e \<noteq> CloseFd p fd;
|
|
|
1654 |
\<forall> p f. e \<noteq> UnLink p f;
|
|
|
1655 |
\<forall> p f f'. e \<noteq> LinkHard p f f'\<rbrakk> \<Longrightarrow> cf2sfiles (e # s) = cf2sfiles s"
|
|
|
1656 |
apply (frule vt_grant_os, frule vd_cons, rule ext)
|
|
|
1657 |
apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI)
|
|
|
1658 |
apply (drule Set.CollectD, erule bexE, rule CollectI)
|
|
|
1659 |
apply (rule_tac x = f' in bexI, case_tac e)
|
|
|
1660 |
apply (auto simp:cf2sfiles_def cf2sfile_simps same_inode_files_simps current_files_simps
|
|
|
1661 |
split:if_splits option.splits dest!:current_file_has_sfile' dest:same_inode_files_prop1 cf2sfile_other')
|
|
|
1662 |
apply (drule_tac f' = f' in cf2sfile_rmdir)
|
|
|
1663 |
apply (simp add:current_files_simps same_inode_files_prop1 same_inode_files_prop3 dir_is_empty_def)+
|
|
|
1664 |
|
|
|
1665 |
apply (rule_tac x = f' in bexI, case_tac e)
|
|
|
1666 |
apply (auto simp:cf2sfiles_def cf2sfile_simps same_inode_files_simps current_files_simps
|
|
|
1667 |
split:if_splits option.splits dest!:current_file_has_sfile' dest:same_inode_files_prop1 cf2sfile_other')
|
|
|
1668 |
apply (drule_tac f' = f' in cf2sfile_rmdir)
|
|
|
1669 |
apply (simp add:current_files_simps same_inode_files_prop1 same_inode_files_prop3 dir_is_empty_def)+
|
|
|
1670 |
done
|
|
|
1671 |
|
|
|
1672 |
lemma cf2sfile_linkhard1':
|
|
|
1673 |
"\<lbrakk>valid (LinkHard p oldf f # s); f' \<in> same_inode_files s f''\<rbrakk>
|
|
|
1674 |
\<Longrightarrow> cf2sfile (LinkHard p oldf f# s) f' = cf2sfile s f'"
|
|
|
1675 |
apply (drule same_inode_files_prop1)
|
|
|
1676 |
by (simp add:cf2sfile_linkhard1)
|
|
|
1677 |
|
|
|
1678 |
lemma cf2sfiles_linkhard:
|
|
|
1679 |
"valid (LinkHard p oldf f # s) \<Longrightarrow> cf2sfiles (LinkHard p oldf f # s) = (\<lambda> f'.
|
|
|
1680 |
if (f' = f \<or> f' \<in> same_inode_files s oldf)
|
|
|
1681 |
then (case (cf2sfile (LinkHard p oldf f # s) f) of
|
|
|
1682 |
Some sf \<Rightarrow> cf2sfiles s oldf \<union> {sf}
|
|
|
1683 |
| _ \<Rightarrow> {})
|
|
|
1684 |
else cf2sfiles s f')"
|
|
|
1685 |
apply (frule vt_grant_os, frule vd_cons, rule ext)
|
|
|
1686 |
apply (auto simp:cf2sfiles_def cf2sfile_linkhard1' same_inode_files_linkhard current_files_linkhard
|
|
|
1687 |
split:if_splits option.splits dest!:current_file_has_sfile' current_has_sec' dest:same_inode_files_prop1)
|
|
|
1688 |
done
|
|
|
1689 |
|
|
|
1690 |
lemma cf2sfile_unlink':
|
|
|
1691 |
"\<lbrakk>valid (UnLink p f # s); f' \<in> same_inode_files (UnLink p f # s) f''\<rbrakk>
|
|
|
1692 |
\<Longrightarrow> cf2sfile (UnLink p f # s) f' = cf2sfile s f'"
|
|
|
1693 |
apply (drule same_inode_files_prop1)
|
|
|
1694 |
by (simp add:cf2sfile_unlink)
|
|
|
1695 |
|
|
|
1696 |
lemma cf2sfiles_unlink:
|
|
|
1697 |
"\<lbrakk>valid (UnLink p f # s); f' \<in> current_files (UnLink p f # s)\<rbrakk> \<Longrightarrow> cf2sfiles (UnLink p f # s) f' = (
|
|
|
1698 |
if (f' \<in> same_inode_files s f \<and> proc_fd_of_file s f = {} \<and>
|
|
|
1699 |
(\<forall> f'' \<in> same_inode_files s f. f'' \<noteq> f \<longrightarrow> cf2sfile s f'' \<noteq> cf2sfile s f)) then
|
|
|
1700 |
(case (cf2sfile s f) of
|
|
|
1701 |
Some sf \<Rightarrow> cf2sfiles s f' - {sf}
|
|
|
1702 |
| _ \<Rightarrow> {})
|
|
|
1703 |
else cf2sfiles s f')"
|
|
|
1704 |
apply (frule vt_grant_os, frule vd_cons, simp add:current_files_simps split:if_splits)
|
|
|
1705 |
apply (rule conjI, clarify, frule is_file_has_sfile', simp, erule exE, simp)
|
|
|
1706 |
apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
|
|
|
1707 |
apply (erule bexE, frule_tac f' = f' in same_inode_files_unlink)
|
|
|
1708 |
apply (simp add:current_files_unlink, simp, erule conjE)
|
|
|
1709 |
apply (erule_tac x = f'a in ballE, frule_tac f' = "f'a" in cf2sfile_unlink)
|
|
|
1710 |
apply (simp add:current_files_unlink same_inode_files_prop1, simp)
|
|
|
1711 |
apply (rule_tac x = f'a in bexI, simp, simp)
|
|
|
1712 |
apply (drule_tac f = f and f' = f' and f'' = f'a in same_inode_files_prop4, simp+)
|
|
|
1713 |
apply (erule conjE|erule exE|erule bexE)+
|
|
|
1714 |
apply (case_tac "f'a = f", simp)
|
|
|
1715 |
apply (frule_tac f' = f' in same_inode_files_unlink, simp add:current_files_unlink)
|
|
|
1716 |
apply (frule_tac f' = f'a in cf2sfile_unlink, simp add:current_files_unlink same_inode_files_prop1)
|
|
|
1717 |
apply (rule_tac x = f'a in bexI, simp, simp)
|
|
|
1718 |
|
|
|
1719 |
apply (rule impI)+
|
|
|
1720 |
apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
|
|
|
1721 |
apply (erule bexE, frule_tac f' = f' in same_inode_files_unlink)
|
|
|
1722 |
apply (simp add:current_files_unlink, simp, (erule conjE)+)
|
|
|
1723 |
apply (rule_tac x = f'a in bexI, frule_tac f' = "f'a" in cf2sfile_unlink)
|
|
|
1724 |
apply (simp add:current_files_unlink same_inode_files_prop1, simp, simp)
|
|
|
1725 |
apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_unlink)
|
|
|
1726 |
apply (simp add:current_files_unlink, simp)
|
|
|
1727 |
apply (case_tac "f'a = f", simp)
|
|
|
1728 |
apply (frule_tac f = f' and f' = f in same_inode_files_prop5, simp)
|
|
|
1729 |
apply (erule bexE, erule conjE)
|
|
|
1730 |
apply (rule_tac x = f'' in bexI)
|
|
|
1731 |
apply (drule_tac f' = f'' in cf2sfile_unlink, simp add:current_files_unlink same_inode_files_prop1)
|
|
|
1732 |
apply (simp, simp, erule same_inode_files_prop4, simp)
|
|
|
1733 |
apply (rule_tac x = f'a in bexI)
|
|
|
1734 |
apply (drule_tac f' = f'a in cf2sfile_unlink, simp add:current_files_unlink same_inode_files_prop1)
|
|
|
1735 |
apply (simp, simp)
|
|
|
1736 |
|
|
|
1737 |
|
|
|
1738 |
apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
|
|
|
1739 |
apply (erule bexE, frule_tac f' = f' in same_inode_files_unlink)
|
|
|
1740 |
apply (simp add:current_files_unlink, simp)
|
|
|
1741 |
apply (rule_tac x = f'a in bexI)
|
|
|
1742 |
apply (frule_tac f' = f'a in cf2sfile_unlink)
|
|
|
1743 |
apply (simp add:same_inode_files_prop1 current_files_unlink, simp, simp)
|
|
|
1744 |
apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_unlink)
|
|
|
1745 |
apply (simp add:current_files_unlink, simp)
|
|
|
1746 |
apply (rule_tac x = f'a in bexI)
|
|
|
1747 |
apply (frule_tac f' = f'a in cf2sfile_unlink)
|
|
|
1748 |
apply (simp add:same_inode_files_prop1 current_files_unlink, simp, simp)
|
|
|
1749 |
done
|
|
|
1750 |
|
|
|
1751 |
lemma cf2sfiles_closefd:
|
|
|
1752 |
"\<lbrakk>valid (CloseFd p fd # s); f' \<in> current_files (CloseFd p fd # s)\<rbrakk> \<Longrightarrow> cf2sfiles (CloseFd p fd # s) f' = (
|
|
|
1753 |
case (file_of_proc_fd s p fd) of
|
|
|
1754 |
Some f \<Rightarrow> if (f' \<in> same_inode_files s f \<and> proc_fd_of_file s f = {(p, fd)} \<and> f \<in> files_hung_by_del s \<and>
|
|
|
1755 |
(\<forall> f'' \<in> same_inode_files s f. f'' \<noteq> f \<longrightarrow> cf2sfile s f'' \<noteq> cf2sfile s f))
|
|
|
1756 |
then (case (cf2sfile s f) of
|
|
|
1757 |
Some sf \<Rightarrow> cf2sfiles s f' - {sf}
|
|
|
1758 |
| _ \<Rightarrow> {})
|
|
|
1759 |
else cf2sfiles s f'
|
|
|
1760 |
| _ \<Rightarrow> cf2sfiles s f')"
|
|
|
1761 |
|
|
|
1762 |
apply (frule vt_grant_os, frule vd_cons, case_tac "file_of_proc_fd s p fd")
|
|
|
1763 |
apply (simp_all add:current_files_simps split:if_splits)
|
|
|
1764 |
|
|
|
1765 |
apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
|
|
|
1766 |
apply (erule bexE, frule_tac f' = f' in same_inode_files_closefd)
|
|
|
1767 |
apply (simp add:current_files_closefd, simp)
|
|
|
1768 |
apply (rule_tac x = f'a in bexI)
|
|
|
1769 |
apply (frule_tac f = f'a in cf2sfile_closefd)
|
|
|
1770 |
apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
|
|
|
1771 |
apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_closefd)
|
|
|
1772 |
apply (simp add:current_files_closefd, simp)
|
|
|
1773 |
apply (rule_tac x = f'a in bexI)
|
|
|
1774 |
apply (frule_tac f = f'a in cf2sfile_closefd)
|
|
|
1775 |
apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
|
|
|
1776 |
|
|
|
1777 |
apply (rule conjI, clarify, frule file_of_pfd_is_file, simp)
|
|
|
1778 |
apply (frule is_file_has_sfile', simp, erule exE, simp)
|
|
|
1779 |
apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
|
|
|
1780 |
apply (erule bexE, frule_tac f' = f' in same_inode_files_closefd)
|
|
|
1781 |
apply (simp add:current_files_closefd, simp, erule conjE)
|
|
|
1782 |
apply (erule_tac x = f'a in ballE, frule_tac f = "f'a" in cf2sfile_closefd)
|
|
|
1783 |
apply (simp add:current_files_closefd same_inode_files_prop1, simp)
|
|
|
1784 |
apply (rule_tac x = f'a in bexI, simp, simp)
|
|
|
1785 |
apply (drule_tac f = a and f' = f' and f'' = f'a in same_inode_files_prop4, simp+)
|
|
|
1786 |
apply (erule conjE|erule exE|erule bexE)+
|
|
|
1787 |
apply (case_tac "f'a = a", simp)
|
|
|
1788 |
apply (frule_tac f' = f' in same_inode_files_closefd, simp add:current_files_closefd, simp)
|
|
|
1789 |
apply (frule_tac f = f'a in cf2sfile_closefd, simp add:current_files_closefd same_inode_files_prop1)
|
|
|
1790 |
apply (rule_tac x = f'a in bexI, simp, simp)
|
|
|
1791 |
|
|
|
1792 |
apply (rule impI)+
|
|
|
1793 |
apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
|
|
|
1794 |
apply (erule bexE, frule_tac f' = f' in same_inode_files_closefd)
|
|
|
1795 |
apply (simp add:current_files_closefd, simp, (erule conjE)+)
|
|
|
1796 |
apply (rule_tac x = f'a in bexI, frule_tac f = f'a in cf2sfile_closefd)
|
|
|
1797 |
apply (simp add:current_files_closefd same_inode_files_prop1, simp, simp)
|
|
|
1798 |
apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_closefd)
|
|
|
1799 |
apply (simp add:current_files_closefd, simp)
|
|
|
1800 |
apply (case_tac "f'a = a", simp)
|
|
|
1801 |
apply (frule_tac f = f' and f' = a in same_inode_files_prop5, simp)
|
|
|
1802 |
apply (erule bexE, erule conjE)
|
|
|
1803 |
apply (rule_tac x = f'' in bexI)
|
|
|
1804 |
apply (drule_tac f = f'' in cf2sfile_closefd, simp add:current_files_closefd same_inode_files_prop1)
|
|
|
1805 |
apply (simp, simp, erule same_inode_files_prop4, simp)
|
|
|
1806 |
apply (rule_tac x = f'a in bexI)
|
|
|
1807 |
apply (drule_tac f = f'a in cf2sfile_closefd, simp add:current_files_closefd same_inode_files_prop1)
|
|
|
1808 |
apply (simp, simp)
|
|
|
1809 |
|
|
|
1810 |
apply (rule conjI, clarify)
|
|
|
1811 |
|
|
|
1812 |
apply (rule impI)
|
|
|
1813 |
apply (case_tac "a \<in> files_hung_by_del s", simp_all)
|
|
|
1814 |
apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
|
|
|
1815 |
apply (erule bexE, frule_tac f' = f' in same_inode_files_closefd)
|
|
|
1816 |
apply (simp add:current_files_closefd, simp)
|
|
|
1817 |
apply (rule_tac x = f'a in bexI)
|
|
|
1818 |
apply (frule_tac f = f'a in cf2sfile_closefd)
|
|
|
1819 |
apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
|
|
|
1820 |
apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_closefd)
|
|
|
1821 |
apply (simp add:current_files_closefd, simp)
|
|
|
1822 |
apply (rule_tac x = f'a in bexI)
|
|
|
1823 |
apply (frule_tac f = f'a in cf2sfile_closefd)
|
|
|
1824 |
apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
|
|
|
1825 |
apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
|
|
|
1826 |
apply (erule bexE, frule_tac f' = f' in same_inode_files_closefd)
|
|
|
1827 |
apply (simp add:current_files_closefd, simp)
|
|
|
1828 |
apply (rule_tac x = f'a in bexI)
|
|
|
1829 |
apply (frule_tac f = f'a in cf2sfile_closefd)
|
|
|
1830 |
apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
|
|
|
1831 |
apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_closefd)
|
|
|
1832 |
apply (simp add:current_files_closefd, simp)
|
|
|
1833 |
apply (rule_tac x = f'a in bexI)
|
|
|
1834 |
apply (frule_tac f = f'a in cf2sfile_closefd)
|
|
|
1835 |
apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
|
|
|
1836 |
done
|
|
|
1837 |
|
|
|
1838 |
lemmas cf2sfiles_simps = cf2sfiles_open cf2sfiles_linkhard cf2sfiles_other
|
|
|
1839 |
cf2sfiles_unlink cf2sfiles_closefd
|
|
|
1840 |
|
|
|
1841 |
|
|
|
1842 |
(* simpset for co2sobj *)
|
|
|
1843 |
|
|
|
1844 |
lemma co2sobj_execve:
|
|
92
|
1845 |
"\<lbrakk>valid (Execve p f fds # s); dalive (Execve p f fds # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Execve p f fds # s) obj = (
|
|
|
1846 |
if (obj = D_proc p)
|
|
77
|
1847 |
then (case (cp2sproc (Execve p f fds # s) p) of
|
|
|
1848 |
Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> tainted s \<or> O_file f \<in> tainted s))
|
|
|
1849 |
| _ \<Rightarrow> None)
|
|
|
1850 |
else co2sobj s obj )"
|
|
|
1851 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
1852 |
apply (simp_all add:current_files_simps cf2sfiles_other (* ch2sshm_other *) cq2smsgq_other)
|
|
|
1853 |
apply (case_tac "cp2sproc (Execve p f fds # s) p")
|
|
|
1854 |
apply (drule current_proc_has_sp', simp, simp)
|
|
|
1855 |
apply (simp (no_asm_simp) add:cp2sproc_execve split:option.splits)
|
|
|
1856 |
apply (simp add:is_dir_simps, frule_tac s = s in is_dir_has_sdir', simp, erule exE, simp)
|
|
|
1857 |
apply (frule_tac ff = list in cf2sfile_other', simp_all)
|
|
|
1858 |
apply (simp add:is_dir_in_current)
|
|
|
1859 |
done
|
|
|
1860 |
|
|
|
1861 |
lemma co2sobj_execve':
|
|
92
|
1862 |
"\<lbrakk>valid (Execve p f fds # s); dalive s obj\<rbrakk> \<Longrightarrow> co2sobj (Execve p f fds # s) obj = (
|
|
|
1863 |
if (obj = D_proc p)
|
|
77
|
1864 |
then (case (cp2sproc (Execve p f fds # s) p) of
|
|
|
1865 |
Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> tainted s \<or> O_file f \<in> tainted s))
|
|
|
1866 |
| _ \<Rightarrow> None)
|
|
|
1867 |
else co2sobj s obj )"
|
|
|
1868 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
1869 |
apply (simp_all add:current_files_simps cf2sfiles_other (* ch2sshm_other *) cq2smsgq_other)
|
|
|
1870 |
apply (case_tac "cp2sproc (Execve p f fds # s) p")
|
|
|
1871 |
apply (drule current_proc_has_sp', simp, simp)
|
|
|
1872 |
apply (simp (no_asm_simp) add:cp2sproc_execve split:option.splits)
|
|
|
1873 |
apply (frule_tac s = s in is_dir_has_sdir', simp, erule exE, simp)
|
|
|
1874 |
apply (frule_tac ff = list in cf2sfile_other', simp_all)
|
|
|
1875 |
apply (simp add:is_dir_in_current)
|
|
|
1876 |
done
|
|
|
1877 |
|
|
|
1878 |
lemma co2sobj_clone':
|
|
92
|
1879 |
"\<lbrakk>valid (Clone p p' fds # s); dalive s obj\<rbrakk> \<Longrightarrow> co2sobj (Clone p p' fds # s) obj = (
|
|
|
1880 |
if (obj = D_proc p')
|
|
77
|
1881 |
then (case (cp2sproc (Clone p p' fds # s) p') of
|
|
|
1882 |
Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> tainted s))
|
|
|
1883 |
| _ \<Rightarrow> None)
|
|
|
1884 |
else co2sobj s obj )"
|
|
|
1885 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
1886 |
apply (simp_all add:current_files_simps cf2sfiles_other (* ch2sshm_other *) cq2smsgq_other)
|
|
|
1887 |
apply (case_tac "cp2sproc (Clone p p' fds # s) p'")
|
|
|
1888 |
apply (drule current_proc_has_sp', simp, simp)
|
|
|
1889 |
apply ((erule conjE)+, frule_tac p = p in current_proc_has_sec, simp, erule exE, simp)
|
|
|
1890 |
apply (simp (no_asm_simp) add:cp2sproc_clone split:option.splits)
|
|
|
1891 |
apply (case_tac "nat = p'", simp, simp)
|
|
|
1892 |
apply (frule_tac s = s in is_dir_has_sdir', simp, erule exE, simp)
|
|
|
1893 |
apply (frule_tac ff = list in cf2sfile_other', simp_all)
|
|
|
1894 |
apply (simp add:is_dir_in_current)
|
|
|
1895 |
done
|
|
|
1896 |
|
|
|
1897 |
lemma co2sobj_clone:
|
|
92
|
1898 |
"\<lbrakk>valid (Clone p p' fds # s); dalive (Clone p p' fds # s) obj\<rbrakk>
|
|
77
|
1899 |
\<Longrightarrow> co2sobj (Clone p p' fds # s) obj = (
|
|
92
|
1900 |
if (obj = D_proc p')
|
|
77
|
1901 |
then (case (cp2sproc (Clone p p' fds # s) p') of
|
|
|
1902 |
Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> tainted s))
|
|
|
1903 |
| _ \<Rightarrow> None)
|
|
|
1904 |
else co2sobj s obj )"
|
|
|
1905 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
1906 |
apply (simp_all add:current_files_simps cf2sfiles_other (* ch2sshm_other *) cq2smsgq_other)
|
|
|
1907 |
apply (rule conjI, rule impI, simp)
|
|
|
1908 |
apply (case_tac "cp2sproc (Clone p p' fds # s) p'")
|
|
|
1909 |
apply (drule current_proc_has_sp', simp, simp)
|
|
|
1910 |
apply ((erule conjE)+, frule_tac p = p in current_proc_has_sec, simp, erule exE, simp)
|
|
|
1911 |
apply (rule impI,rule notI, drule tainted_in_current, simp+)
|
|
|
1912 |
apply (rule impI, simp)
|
|
|
1913 |
apply (drule current_proc_has_sp, simp, (erule exE|erule conjE)+)
|
|
|
1914 |
apply (simp (no_asm_simp) add:cp2sproc_clone tainted_in_current split:option.splits)
|
|
|
1915 |
|
|
|
1916 |
apply (simp add:is_dir_simps, frule_tac s = s in is_dir_has_sdir', simp, erule exE, simp)
|
|
|
1917 |
apply (frule_tac ff = list in cf2sfile_other', simp_all)
|
|
|
1918 |
apply (simp add:is_dir_in_current)
|
|
|
1919 |
done
|
|
|
1920 |
|
|
|
1921 |
(*
|
|
|
1922 |
lemma co2sobj_ptrace:
|
|
92
|
1923 |
"\<lbrakk>valid (Ptrace p p' # s); dalive s obj\<rbrakk>\<Longrightarrow> co2sobj (Ptrace p p' # s) obj = (
|
|
77
|
1924 |
case obj of
|
|
|
1925 |
O_proc p'' \<Rightarrow> if (info_flow_shm s p' p'')
|
|
|
1926 |
then (case (cp2sproc s p'') of
|
|
|
1927 |
Some sp \<Rightarrow> Some (S_proc sp (O_proc p'' \<in> tainted s \<or> O_proc p \<in> tainted s))
|
|
|
1928 |
| _ \<Rightarrow> None)
|
|
|
1929 |
else if (info_flow_shm s p p'')
|
|
|
1930 |
then (case (cp2sproc s p'') of
|
|
|
1931 |
Some sp \<Rightarrow> Some (S_proc sp (O_proc p'' \<in> tainted s \<or> O_proc p' \<in> tainted s))
|
|
|
1932 |
| _ \<Rightarrow> None)
|
|
|
1933 |
else co2sobj s (O_proc p'')
|
|
|
1934 |
| _ \<Rightarrow> co2sobj s obj)"
|
|
|
1935 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
1936 |
apply (simp_all add:current_files_simps ch2sshm_other cq2smsgq_other cf2sfiles_other)
|
|
|
1937 |
|
|
|
1938 |
apply (auto simp:cp2sproc_other split:option.splits
|
|
|
1939 |
dest!:current_proc_has_sec' current_proc_has_sp' intro:info_flow_shm_tainted)[1]
|
|
|
1940 |
|
|
|
1941 |
apply (frule_tac s = s in is_dir_has_sdir', simp, erule exE, simp)
|
|
|
1942 |
apply (frule_tac ff = list in cf2sfile_other', simp_all)
|
|
|
1943 |
apply (simp add:is_dir_in_current)
|
|
|
1944 |
done
|
|
|
1945 |
*)
|
|
|
1946 |
|
|
|
1947 |
lemma co2sobj_ptrace:
|
|
92
|
1948 |
"\<lbrakk>valid (Ptrace p p' # s); dalive s obj\<rbrakk>\<Longrightarrow> co2sobj (Ptrace p p' # s) obj = (
|
|
77
|
1949 |
case obj of
|
|
92
|
1950 |
D_proc p'' \<Rightarrow> if (p'' = p')
|
|
77
|
1951 |
then (case (cp2sproc s p'') of
|
|
|
1952 |
Some sp \<Rightarrow> Some (S_proc sp (O_proc p'' \<in> tainted s \<or> O_proc p \<in> tainted s))
|
|
|
1953 |
| _ \<Rightarrow> None)
|
|
|
1954 |
else if (p'' = p)
|
|
|
1955 |
then (case (cp2sproc s p'') of
|
|
|
1956 |
Some sp \<Rightarrow> Some (S_proc sp (O_proc p'' \<in> tainted s \<or> O_proc p' \<in> tainted s))
|
|
|
1957 |
| _ \<Rightarrow> None)
|
|
92
|
1958 |
else co2sobj s (D_proc p'')
|
|
77
|
1959 |
| _ \<Rightarrow> co2sobj s obj)"
|
|
|
1960 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
1961 |
apply (simp_all add:current_files_simps cq2smsgq_other cf2sfiles_other)
|
|
|
1962 |
|
|
|
1963 |
apply (auto simp:cp2sproc_other split:option.splits
|
|
|
1964 |
dest!:current_proc_has_sec' current_proc_has_sp')[1]
|
|
|
1965 |
|
|
|
1966 |
apply (frule_tac s = s in is_dir_has_sdir', simp, erule exE, simp)
|
|
|
1967 |
apply (frule_tac ff = list in cf2sfile_other', simp_all)
|
|
|
1968 |
apply (simp add:is_dir_in_current)
|
|
|
1969 |
done
|
|
|
1970 |
|
|
|
1971 |
|
|
|
1972 |
lemma co2sobj_open:
|
|
92
|
1973 |
"\<lbrakk>valid (Open p f flag fd opt # s); dalive (Open p f flag fd opt # s) obj\<rbrakk>
|
|
77
|
1974 |
\<Longrightarrow> co2sobj (Open p f flag fd opt # s) obj = (case obj of
|
|
92
|
1975 |
D_file f' \<Rightarrow> if (f' = f \<and> opt \<noteq> None)
|
|
77
|
1976 |
then (case (cf2sfile (Open p f flag fd opt # s) f) of
|
|
|
1977 |
Some sf \<Rightarrow> Some (S_file {sf} (O_proc p \<in> tainted s))
|
|
|
1978 |
| _ \<Rightarrow> None)
|
|
92
|
1979 |
else co2sobj s (D_file f')
|
|
|
1980 |
| D_proc p' \<Rightarrow> if (p' = p)
|
|
77
|
1981 |
then (case (cp2sproc (Open p f flag fd opt # s) p) of
|
|
|
1982 |
Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> tainted s))
|
|
|
1983 |
| _ \<Rightarrow> None)
|
|
92
|
1984 |
else co2sobj s (D_proc p')
|
|
77
|
1985 |
| _ \<Rightarrow> co2sobj s obj )"
|
|
|
1986 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
1987 |
apply (auto simp:cp2sproc_simps split:option.splits
|
|
|
1988 |
dest!:current_proc_has_sp' (* intro:info_flow_shm_tainted *))[1]
|
|
|
1989 |
|
|
|
1990 |
apply (simp split:if_splits t_object.splits)
|
|
|
1991 |
apply ((rule conjI | rule impI| erule conjE| erule exE)+)
|
|
|
1992 |
apply ( simp, (erule exE|erule conjE)+)
|
|
|
1993 |
apply (case_tac "cf2sfile (Open p f flag fd (Some y) # s) f")
|
|
|
1994 |
apply (drule current_file_has_sfile', simp, simp add:current_files_simps, simp)
|
|
|
1995 |
apply (frule_tac f' = f in cf2sfiles_open, simp add:current_files_simps, simp)
|
|
|
1996 |
apply (frule_tac f' = list in cf2sfiles_open, simp add:is_file_in_current)
|
|
|
1997 |
apply (rule impI)
|
|
|
1998 |
apply (case_tac "list = f", simp, simp split:option.splits)
|
|
|
1999 |
apply (case_tac "cf2sfile (Open p f flag fd opt # s) f")
|
|
|
2000 |
apply (drule current_file_has_sfile', simp)
|
|
|
2001 |
apply (simp add:current_files_simps is_file_in_current split:option.splits)
|
|
|
2002 |
apply (rule impI, simp add:cf2sfiles_open is_file_in_current split:option.splits)
|
|
|
2003 |
apply (rule impI, rule conjI)
|
|
|
2004 |
apply (drule_tac f' = f in cf2sfiles_open)
|
|
|
2005 |
apply (simp add:current_files_simps, simp)
|
|
|
2006 |
apply (rule notI, drule tainted_in_current, simp, simp add:is_file_in_current)
|
|
|
2007 |
|
|
|
2008 |
apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other) (* ch2sshm_other *)
|
|
|
2009 |
|
|
|
2010 |
apply (frule is_dir_in_current)
|
|
|
2011 |
apply (frule_tac f' = list in cf2sfile_open)
|
|
|
2012 |
apply (simp add:current_files_simps split:option.splits)
|
|
|
2013 |
apply (simp split:if_splits option.splits)
|
|
|
2014 |
done
|
|
|
2015 |
|
|
|
2016 |
(*
|
|
|
2017 |
lemma co2sobj_readfile:
|
|
92
|
2018 |
"\<lbrakk>valid (ReadFile p fd # s); dalive s obj\<rbrakk> \<Longrightarrow> co2sobj (ReadFile p fd # s) obj = (
|
|
77
|
2019 |
case obj of
|
|
|
2020 |
O_proc p' \<Rightarrow> (case (file_of_proc_fd s p fd) of
|
|
|
2021 |
Some f \<Rightarrow> (if (info_flow_shm s p p' \<and> O_file f \<in> tainted s)
|
|
|
2022 |
then (case (cp2sproc s p') of
|
|
|
2023 |
Some sp \<Rightarrow> Some (S_proc sp True)
|
|
|
2024 |
| _ \<Rightarrow> None)
|
|
|
2025 |
else co2sobj s obj)
|
|
|
2026 |
| _ \<Rightarrow> None)
|
|
|
2027 |
| _ \<Rightarrow> co2sobj s obj)"
|
|
|
2028 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2029 |
apply (auto simp:cp2sproc_simps split:option.splits
|
|
|
2030 |
dest!:current_proc_has_sp' intro:info_flow_shm_tainted)[1]
|
|
|
2031 |
apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other)
|
|
|
2032 |
|
|
|
2033 |
apply (auto split:if_splits option.splits dest!:current_file_has_sfile'
|
|
|
2034 |
simp:current_files_simps cf2sfiles_simps cf2sfile_simps
|
|
|
2035 |
dest:is_file_in_current is_dir_in_current)
|
|
|
2036 |
done
|
|
|
2037 |
*)
|
|
|
2038 |
lemma co2sobj_readfile:
|
|
92
|
2039 |
"\<lbrakk>valid (ReadFile p fd # s); dalive s obj\<rbrakk> \<Longrightarrow> co2sobj (ReadFile p fd # s) obj = (
|
|
77
|
2040 |
case obj of
|
|
92
|
2041 |
D_proc p' \<Rightarrow> (case (file_of_proc_fd s p fd) of
|
|
77
|
2042 |
Some f \<Rightarrow> (if (p' = p \<and> O_file f \<in> tainted s)
|
|
|
2043 |
then (case (cp2sproc s p') of
|
|
|
2044 |
Some sp \<Rightarrow> Some (S_proc sp True)
|
|
|
2045 |
| _ \<Rightarrow> None)
|
|
|
2046 |
else co2sobj s obj)
|
|
|
2047 |
| _ \<Rightarrow> None)
|
|
|
2048 |
| _ \<Rightarrow> co2sobj s obj)"
|
|
|
2049 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2050 |
apply (auto simp:cp2sproc_simps split:option.splits dest!:current_proc_has_sp')[1]
|
|
|
2051 |
apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other)
|
|
|
2052 |
|
|
|
2053 |
apply (auto split:if_splits option.splits dest!:current_file_has_sfile'
|
|
|
2054 |
simp:current_files_simps cf2sfile_simps cf2sfiles_simps
|
|
|
2055 |
dest:is_file_in_current is_dir_in_current)
|
|
|
2056 |
done
|
|
|
2057 |
|
|
|
2058 |
lemma co2sobj_writefile:
|
|
92
|
2059 |
"\<lbrakk>valid (WriteFile p fd # s); dalive s obj\<rbrakk> \<Longrightarrow> co2sobj (WriteFile p fd # s) obj = (
|
|
77
|
2060 |
case obj of
|
|
92
|
2061 |
D_file f' \<Rightarrow> (case (file_of_proc_fd s p fd) of
|
|
77
|
2062 |
Some f \<Rightarrow> (if (f \<in> same_inode_files s f')
|
|
|
2063 |
then Some (S_file (cf2sfiles s f')
|
|
|
2064 |
(O_file f' \<in> tainted s \<or> O_proc p \<in> tainted s))
|
|
|
2065 |
else co2sobj s obj)
|
|
|
2066 |
| _ \<Rightarrow> None)
|
|
|
2067 |
| _ \<Rightarrow> co2sobj s obj)"
|
|
|
2068 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2069 |
apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other) (* ch2sshm_other*)
|
|
|
2070 |
|
|
|
2071 |
apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
|
|
|
2072 |
simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps
|
|
|
2073 |
same_inode_files_prop6
|
|
|
2074 |
dest:is_file_in_current is_dir_in_current)
|
|
|
2075 |
|
|
|
2076 |
(* should delete has_same_inode !?!?*)
|
|
|
2077 |
by (auto simp:same_inode_files_def is_file_def has_same_inode_def split:if_splits option.splits)
|
|
|
2078 |
|
|
|
2079 |
lemma co2sobj_closefd:
|
|
92
|
2080 |
"\<lbrakk>valid (CloseFd p fd # s); dalive (CloseFd p fd # s) obj\<rbrakk> \<Longrightarrow> co2sobj (CloseFd p fd # s) obj = (
|
|
77
|
2081 |
case obj of
|
|
92
|
2082 |
D_file f' \<Rightarrow> (case (file_of_proc_fd s p fd) of
|
|
77
|
2083 |
Some f \<Rightarrow> (if (f' \<in> same_inode_files s f \<and> proc_fd_of_file s f = {(p, fd)} \<and>
|
|
|
2084 |
f \<in> files_hung_by_del s \<and> (\<forall> f'' \<in> same_inode_files s f.
|
|
|
2085 |
f'' \<noteq> f \<longrightarrow> cf2sfile s f'' \<noteq> cf2sfile s f))
|
|
92
|
2086 |
then (case (cf2sfile s f, co2sobj s (D_file f')) of
|
|
77
|
2087 |
(Some sf, Some (S_file sfs b)) \<Rightarrow> Some (S_file (sfs - {sf}) b)
|
|
|
2088 |
| _ \<Rightarrow> None)
|
|
|
2089 |
else co2sobj s obj)
|
|
|
2090 |
| _ \<Rightarrow> co2sobj s obj)
|
|
92
|
2091 |
| D_proc p' \<Rightarrow> (if (p = p')
|
|
77
|
2092 |
then (case (cp2sproc (CloseFd p fd # s) p) of
|
|
|
2093 |
Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> tainted s))
|
|
|
2094 |
| _ \<Rightarrow> None)
|
|
|
2095 |
else co2sobj s obj)
|
|
|
2096 |
| _ \<Rightarrow> co2sobj s obj) "
|
|
|
2097 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2098 |
apply (simp_all add:current_files_simps cq2smsgq_other) (* ch2sshm_other *)
|
|
|
2099 |
apply (auto simp:cp2sproc_simps cf2sfiles_simps split:option.splits if_splits
|
|
|
2100 |
dest!:current_proc_has_sp') [1](* intro:info_flow_shm_tainted)[1] *)
|
|
|
2101 |
|
|
|
2102 |
apply (frule is_file_in_current)
|
|
|
2103 |
apply (case_tac "file_of_proc_fd s p fd")
|
|
|
2104 |
apply (simp)
|
|
|
2105 |
apply (drule_tac f' = list in cf2sfiles_closefd, simp add:current_files_closefd, simp)
|
|
|
2106 |
apply (frule_tac f' = list in cf2sfiles_closefd, simp)
|
|
|
2107 |
apply (simp add:is_file_simps current_files_simps)
|
|
|
2108 |
apply (auto simp add: cf2sfile_closefd split:if_splits option.splits
|
|
|
2109 |
dest!:current_file_has_sfile' dest:hung_file_in_current)[1]
|
|
|
2110 |
|
|
|
2111 |
apply (simp add:is_dir_simps, frule is_dir_in_current)
|
|
|
2112 |
apply (frule_tac f = list in cf2sfile_closefd)
|
|
|
2113 |
apply (clarsimp simp:current_files_closefd split:option.splits)
|
|
|
2114 |
apply (drule file_of_pfd_is_file', simp+)
|
|
|
2115 |
done
|
|
|
2116 |
|
|
|
2117 |
lemma co2sobj_unlink:
|
|
92
|
2118 |
"\<lbrakk>valid (UnLink p f # s); dalive (UnLink p f # s) obj\<rbrakk> \<Longrightarrow> co2sobj (UnLink p f # s) obj = (
|
|
77
|
2119 |
case obj of
|
|
92
|
2120 |
D_file f' \<Rightarrow> if (f' \<in> same_inode_files s f \<and> proc_fd_of_file s f = {} \<and>
|
|
77
|
2121 |
(\<forall> f'' \<in> same_inode_files s f. f'' \<noteq> f \<longrightarrow> cf2sfile s f'' \<noteq> cf2sfile s f))
|
|
92
|
2122 |
then (case (cf2sfile s f, co2sobj s (D_file f')) of
|
|
77
|
2123 |
(Some sf, Some (S_file sfs b)) \<Rightarrow> Some (S_file (sfs - {sf}) b)
|
|
|
2124 |
| _ \<Rightarrow> None)
|
|
|
2125 |
else co2sobj s obj
|
|
|
2126 |
| _ \<Rightarrow> co2sobj s obj)"
|
|
|
2127 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2128 |
apply (simp_all add:current_files_simps cq2smsgq_other) (* ch2sshm_other*)
|
|
|
2129 |
apply (auto simp:cp2sproc_simps split:option.splits if_splits
|
|
|
2130 |
dest!:current_proc_has_sp')[1] (* intro:info_flow_shm_tainted) *)
|
|
|
2131 |
apply (frule is_file_in_current)
|
|
|
2132 |
apply (frule_tac f' = list in cf2sfile_unlink, simp)
|
|
|
2133 |
apply (frule_tac f' = list in cf2sfiles_unlink, simp)
|
|
|
2134 |
apply (simp add:is_file_simps current_files_simps)
|
|
|
2135 |
apply (auto simp add: is_file_in_current split:if_splits option.splits
|
|
|
2136 |
dest!:current_file_has_sfile')[1]
|
|
|
2137 |
|
|
|
2138 |
apply (simp add:is_dir_simps, frule is_dir_in_current)
|
|
|
2139 |
apply (frule_tac f' = list in cf2sfile_unlink)
|
|
|
2140 |
apply (clarsimp simp:current_files_unlink split:option.splits)
|
|
|
2141 |
apply (drule file_dir_conflict, simp+)
|
|
|
2142 |
done
|
|
|
2143 |
|
|
|
2144 |
lemma co2sobj_rmdir:
|
|
92
|
2145 |
"\<lbrakk>valid (Rmdir p f # s); dalive (Rmdir p f # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Rmdir p f # s) obj = co2sobj s obj"
|
|
77
|
2146 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2147 |
apply (simp_all add:current_files_simps cq2smsgq_other) (* ch2sshm_other*)
|
|
|
2148 |
apply (auto simp:cp2sproc_simps split:option.splits if_splits
|
|
|
2149 |
dest!:current_proc_has_sp')[1] (* intro:info_flow_shm_tainted*)
|
|
|
2150 |
apply (simp add:is_file_simps dir_is_empty_def)
|
|
|
2151 |
apply (case_tac "f = list", drule file_dir_conflict, simp, simp)
|
|
|
2152 |
apply (simp add:cf2sfiles_other)
|
|
|
2153 |
apply (auto simp:cf2sfile_simps dest:is_dir_in_current)
|
|
|
2154 |
done
|
|
|
2155 |
|
|
|
2156 |
lemma co2sobj_mkdir:
|
|
92
|
2157 |
"\<lbrakk>valid (Mkdir p f i # s); dalive (Mkdir p f i # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Mkdir p f i # s) obj = (
|
|
|
2158 |
if (obj = D_dir f)
|
|
77
|
2159 |
then (case (cf2sfile (Mkdir p f i # s) f) of
|
|
|
2160 |
Some sf \<Rightarrow> Some (S_dir sf)
|
|
|
2161 |
| _ \<Rightarrow> None)
|
|
|
2162 |
else co2sobj s obj)"
|
|
|
2163 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2164 |
apply (simp_all add:current_files_simps cq2smsgq_other) (* ch2sshm_other *)
|
|
|
2165 |
apply (auto simp:cp2sproc_simps split:option.splits if_splits
|
|
|
2166 |
dest!:current_proc_has_sp')[1] (* intro:info_flow_shm_tainted *)
|
|
|
2167 |
apply (frule_tac cf2sfiles_other, simp+)
|
|
|
2168 |
apply (frule is_dir_in_current, rule impI, simp add:current_files_mkdir)
|
|
|
2169 |
apply (frule current_file_has_sfile, simp, erule exE, simp)
|
|
|
2170 |
apply (drule cf2sfile_mkdir1, simp+)
|
|
|
2171 |
done
|
|
|
2172 |
|
|
|
2173 |
lemma co2sobj_linkhard:
|
|
92
|
2174 |
"\<lbrakk>valid (LinkHard p oldf f # s); dalive (LinkHard p oldf f # s) obj\<rbrakk>
|
|
77
|
2175 |
\<Longrightarrow> co2sobj (LinkHard p oldf f # s) obj = (
|
|
|
2176 |
case obj of
|
|
92
|
2177 |
D_file f' \<Rightarrow> if (f' = f \<or> f' \<in> same_inode_files s oldf)
|
|
77
|
2178 |
then (case (cf2sfile (LinkHard p oldf f # s) f) of
|
|
|
2179 |
Some sf \<Rightarrow> Some (S_file (cf2sfiles s oldf \<union> {sf}) (O_file oldf \<in> tainted s))
|
|
|
2180 |
| _ \<Rightarrow> None)
|
|
|
2181 |
else co2sobj s obj
|
|
|
2182 |
| _ \<Rightarrow> co2sobj s obj)"
|
|
|
2183 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2184 |
apply (simp_all add:current_files_simps cq2smsgq_other) (* ch2sshm_other *)
|
|
|
2185 |
apply (auto simp:cp2sproc_simps split:option.splits if_splits
|
|
|
2186 |
dest!:current_proc_has_sp')[1] (* intro:info_flow_shm_tainted *)
|
|
|
2187 |
apply (frule_tac cf2sfiles_linkhard, simp+)
|
|
|
2188 |
apply (frule_tac f' = f in cf2sfile_linkhard, simp add:current_files_linkhard)
|
|
|
2189 |
apply (auto simp:is_file_simps sectxt_of_obj_simps current_files_simps is_file_in_current same_inodes_tainted
|
|
|
2190 |
split:option.splits if_splits dest:tainted_in_current
|
|
|
2191 |
dest!:current_has_sec' current_file_has_sfile')[1]
|
|
|
2192 |
|
|
|
2193 |
apply (frule is_dir_in_current, simp add:current_files_linkhard is_dir_simps is_dir_in_current)
|
|
|
2194 |
apply (frule is_dir_in_current)
|
|
|
2195 |
apply (frule current_file_has_sfile, simp)
|
|
|
2196 |
apply (drule cf2sfile_linkhard1, simp+)
|
|
|
2197 |
done
|
|
|
2198 |
|
|
|
2199 |
lemma co2sobj_truncate:
|
|
92
|
2200 |
"\<lbrakk>valid (Truncate p f len # s); dalive s obj\<rbrakk> \<Longrightarrow> co2sobj (Truncate p f len # s) obj = (
|
|
77
|
2201 |
case obj of
|
|
92
|
2202 |
D_file f' \<Rightarrow> if (f' \<in> same_inode_files s f \<and> len > 0)
|
|
77
|
2203 |
then Some (S_file (cf2sfiles s f') (O_file f' \<in> tainted s \<or> O_proc p \<in> tainted s))
|
|
|
2204 |
else co2sobj s obj
|
|
|
2205 |
| _ \<Rightarrow> co2sobj s obj)"
|
|
|
2206 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2207 |
apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other) (* ch2sshm_other *)
|
|
|
2208 |
|
|
|
2209 |
apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
|
|
|
2210 |
simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps
|
|
|
2211 |
same_inode_files_prop6
|
|
|
2212 |
dest:is_file_in_current is_dir_in_current)
|
|
|
2213 |
done
|
|
|
2214 |
|
|
|
2215 |
lemma co2sobj_kill:
|
|
92
|
2216 |
"\<lbrakk>valid (Kill p p' # s); dalive (Kill p p' # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Kill p p' # s) obj = co2sobj s obj"
|
|
77
|
2217 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2218 |
apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other) (* ch2sshm_other *)
|
|
|
2219 |
apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
|
|
|
2220 |
simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps
|
|
|
2221 |
same_inode_files_prop6
|
|
|
2222 |
dest:is_file_in_current is_dir_in_current)
|
|
|
2223 |
done
|
|
|
2224 |
|
|
|
2225 |
lemma co2sobj_exit:
|
|
92
|
2226 |
"\<lbrakk>valid (Exit p # s); dalive (Exit p # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Exit p # s) obj = co2sobj s obj"
|
|
77
|
2227 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2228 |
apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other)
|
|
|
2229 |
apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
|
|
|
2230 |
simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps
|
|
|
2231 |
same_inode_files_prop6
|
|
|
2232 |
dest:is_file_in_current is_dir_in_current)
|
|
|
2233 |
done
|
|
|
2234 |
|
|
|
2235 |
lemma co2sobj_createmsgq:
|
|
92
|
2236 |
"\<lbrakk>valid (CreateMsgq p q # s); dalive (CreateMsgq p q # s) obj\<rbrakk> \<Longrightarrow> co2sobj (CreateMsgq p q # s) obj = (
|
|
77
|
2237 |
case obj of
|
|
92
|
2238 |
D_msgq q' \<Rightarrow> if (q' = q) then (case (cq2smsgq (CreateMsgq p q # s) q) of
|
|
77
|
2239 |
Some sq \<Rightarrow> Some (S_msgq sq)
|
|
|
2240 |
| _ \<Rightarrow> None)
|
|
|
2241 |
else co2sobj s obj
|
|
|
2242 |
| _ \<Rightarrow> co2sobj s obj)"
|
|
|
2243 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2244 |
apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other)
|
|
|
2245 |
apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
|
|
|
2246 |
simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps
|
|
|
2247 |
same_inode_files_prop6
|
|
|
2248 |
dest!:current_has_smsgq'
|
|
|
2249 |
dest:is_file_in_current is_dir_in_current cq2smsg_createmsgq)
|
|
|
2250 |
done
|
|
|
2251 |
|
|
|
2252 |
lemma co2sobj_sendmsg:
|
|
92
|
2253 |
"\<lbrakk>valid (SendMsg p q m # s); dalive (SendMsg p q m # s) obj\<rbrakk> \<Longrightarrow> co2sobj (SendMsg p q m # s) obj = (
|
|
77
|
2254 |
case obj of
|
|
92
|
2255 |
D_msgq q' \<Rightarrow> if (q' = q) then (case (cq2smsgq (SendMsg p q m # s) q) of
|
|
77
|
2256 |
Some sq \<Rightarrow> Some (S_msgq sq)
|
|
|
2257 |
| _ \<Rightarrow> None)
|
|
|
2258 |
else co2sobj s obj
|
|
|
2259 |
| _ \<Rightarrow> co2sobj s obj)"
|
|
|
2260 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2261 |
apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other)
|
|
|
2262 |
apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
|
|
|
2263 |
simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps
|
|
|
2264 |
same_inode_files_prop6
|
|
|
2265 |
dest!:current_has_smsgq'
|
|
|
2266 |
dest:is_file_in_current is_dir_in_current cq2smsg_sendmsg)
|
|
|
2267 |
done
|
|
|
2268 |
|
|
|
2269 |
lemma co2sobj_recvmsg:
|
|
92
|
2270 |
"\<lbrakk>valid (RecvMsg p q m # s); dalive (RecvMsg p q m # s) obj\<rbrakk> \<Longrightarrow> co2sobj (RecvMsg p q m # s) obj = (
|
|
77
|
2271 |
case obj of
|
|
92
|
2272 |
D_msgq q' \<Rightarrow> if (q' = q) then (case (cq2smsgq (RecvMsg p q m # s) q) of
|
|
77
|
2273 |
Some sq \<Rightarrow> Some (S_msgq sq)
|
|
|
2274 |
| _ \<Rightarrow> None)
|
|
|
2275 |
else co2sobj s obj
|
|
92
|
2276 |
| D_proc p' \<Rightarrow> if (p' = p \<and> O_msg q m \<in> tainted s)
|
|
77
|
2277 |
then (case (cp2sproc s p') of
|
|
|
2278 |
Some sp \<Rightarrow> Some (S_proc sp True)
|
|
|
2279 |
| _ \<Rightarrow> None)
|
|
|
2280 |
else co2sobj s obj
|
|
|
2281 |
| _ \<Rightarrow> co2sobj s obj)"
|
|
|
2282 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2283 |
apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other)
|
|
|
2284 |
apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
|
|
|
2285 |
simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps
|
|
|
2286 |
same_inode_files_prop6
|
|
|
2287 |
dest!:current_has_smsgq'
|
|
|
2288 |
dest:is_file_in_current is_dir_in_current cq2smsg_recvmsg)
|
|
|
2289 |
done
|
|
|
2290 |
(*
|
|
|
2291 |
lemma co2sobj_recvmsg:
|
|
92
|
2292 |
"\<lbrakk>valid (RecvMsg p q m # s); dalive (RecvMsg p q m # s) obj\<rbrakk> \<Longrightarrow> co2sobj (RecvMsg p q m # s) obj = (
|
|
77
|
2293 |
case obj of
|
|
|
2294 |
O_msgq q' \<Rightarrow> if (q' = q) then (case (cq2smsgq (RecvMsg p q m # s) q) of
|
|
|
2295 |
Some sq \<Rightarrow> Some (S_msgq sq)
|
|
|
2296 |
| _ \<Rightarrow> None)
|
|
|
2297 |
else co2sobj s obj
|
|
|
2298 |
| O_proc p' \<Rightarrow> if (info_flow_shm s p p' \<and> O_msg q m \<in> tainted s)
|
|
|
2299 |
then (case (cp2sproc s p') of
|
|
|
2300 |
Some sp \<Rightarrow> Some (S_proc sp True)
|
|
|
2301 |
| _ \<Rightarrow> None)
|
|
|
2302 |
else co2sobj s obj
|
|
|
2303 |
| _ \<Rightarrow> co2sobj s obj)"
|
|
|
2304 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2305 |
apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other)
|
|
|
2306 |
apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
|
|
|
2307 |
simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps
|
|
|
2308 |
same_inode_files_prop6
|
|
|
2309 |
dest!:current_has_smsgq'
|
|
|
2310 |
dest:is_file_in_current is_dir_in_current cq2smsg_recvmsg)
|
|
|
2311 |
done
|
|
|
2312 |
*)
|
|
|
2313 |
|
|
|
2314 |
lemma co2sobj_removemsgq:
|
|
92
|
2315 |
"\<lbrakk>valid (RemoveMsgq p q # s); dalive (RemoveMsgq p q # s) obj\<rbrakk>
|
|
77
|
2316 |
\<Longrightarrow> co2sobj (RemoveMsgq p q # s) obj = co2sobj s obj"
|
|
|
2317 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2318 |
apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other)
|
|
|
2319 |
apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
|
|
|
2320 |
simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps
|
|
|
2321 |
same_inode_files_prop6
|
|
|
2322 |
dest!:current_has_smsgq'
|
|
|
2323 |
dest:is_file_in_current is_dir_in_current cq2smsg_removemsgq)
|
|
|
2324 |
done
|
|
|
2325 |
|
|
|
2326 |
(*
|
|
|
2327 |
lemma co2sobj_createshm:
|
|
92
|
2328 |
"\<lbrakk>valid (CreateShM p h # s); dalive (CreateShM p h # s) obj\<rbrakk> \<Longrightarrow> co2sobj (CreateShM p h # s) obj = (
|
|
77
|
2329 |
case obj of
|
|
|
2330 |
O_shm h' \<Rightarrow> if (h' = h) then (case (ch2sshm (CreateShM p h # s) h) of
|
|
|
2331 |
Some sh \<Rightarrow> Some (S_shm sh)
|
|
|
2332 |
| _ \<Rightarrow> None)
|
|
|
2333 |
else co2sobj s obj
|
|
|
2334 |
| _ \<Rightarrow> co2sobj s obj)"
|
|
|
2335 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2336 |
apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other)
|
|
|
2337 |
apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
|
|
|
2338 |
simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_tainted
|
|
|
2339 |
same_inode_files_prop6 ch2sshm_simps
|
|
|
2340 |
dest!:current_shm_has_sh'
|
|
|
2341 |
dest:is_file_in_current is_dir_in_current)
|
|
|
2342 |
done
|
|
|
2343 |
|
|
|
2344 |
lemma co2sobj_detach:
|
|
92
|
2345 |
"\<lbrakk>valid (Detach p h # s); dalive s obj\<rbrakk> \<Longrightarrow> co2sobj (Detach p h # s) obj = (
|
|
77
|
2346 |
case obj of
|
|
|
2347 |
O_proc p' \<Rightarrow> if (p' = p) then (case (cp2sproc (Detach p h # s) p) of
|
|
|
2348 |
Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> tainted s))
|
|
|
2349 |
| _ \<Rightarrow> None)
|
|
|
2350 |
else co2sobj s obj
|
|
|
2351 |
| _ \<Rightarrow> co2sobj s obj)"
|
|
|
2352 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2353 |
apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other)
|
|
|
2354 |
|
|
|
2355 |
apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
|
|
|
2356 |
simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_tainted
|
|
|
2357 |
same_inode_files_prop6 ch2sshm_simps
|
|
|
2358 |
dest!:current_shm_has_sh'
|
|
|
2359 |
dest:is_file_in_current is_dir_in_current)
|
|
|
2360 |
done
|
|
|
2361 |
|
|
|
2362 |
lemma co2sobj_deleteshm:
|
|
92
|
2363 |
"\<lbrakk>valid (DeleteShM p h # s); dalive (DeleteShM p h # s) obj\<rbrakk> \<Longrightarrow> co2sobj (DeleteShM p h # s) obj = (
|
|
77
|
2364 |
case obj of
|
|
|
2365 |
O_proc p' \<Rightarrow> (case (cp2sproc (DeleteShM p h # s) p') of
|
|
|
2366 |
Some sp \<Rightarrow> Some (S_proc sp (O_proc p' \<in> tainted s))
|
|
|
2367 |
| _ \<Rightarrow> None)
|
|
|
2368 |
| _ \<Rightarrow> co2sobj s obj)"
|
|
|
2369 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2370 |
apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other)
|
|
|
2371 |
|
|
|
2372 |
apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
|
|
|
2373 |
simp:current_files_simps cf2sfiles_simps cf2sfile_simps tainted_eq_tainted
|
|
|
2374 |
same_inode_files_prop6 ch2sshm_simps
|
|
|
2375 |
dest!:current_shm_has_sh'
|
|
|
2376 |
dest:is_file_in_current is_dir_in_current)
|
|
|
2377 |
done
|
|
|
2378 |
*)
|
|
|
2379 |
|
|
|
2380 |
declare Product_Type.split_paired_Ex Product_Type.split_paired_All [simp del]
|
|
|
2381 |
|
|
|
2382 |
(*
|
|
|
2383 |
lemma info_flow_shm_prop1:
|
|
|
2384 |
"p \<in> current_procs s \<Longrightarrow> info_flow_shm s p p"
|
|
|
2385 |
by (simp add:info_flow_shm_def)
|
|
|
2386 |
|
|
|
2387 |
lemma co2sobj_attach:
|
|
92
|
2388 |
"\<lbrakk>valid (Attach p h flag # s); dalive s obj\<rbrakk> \<Longrightarrow> co2sobj (Attach p h flag # s) obj = (
|
|
77
|
2389 |
case obj of
|
|
|
2390 |
O_proc p' \<Rightarrow> if (info_flow_shm s p p')
|
|
|
2391 |
then (case (cp2sproc (Attach p h flag # s) p') of
|
|
|
2392 |
Some sp \<Rightarrow> Some (S_proc sp (O_proc p' \<in> tainted s \<or>
|
|
|
2393 |
(\<exists> p''. O_proc p'' \<in> tainted s \<and> (p'', SHM_RDWR) \<in> procs_of_shm s h)))
|
|
|
2394 |
| _ \<Rightarrow> None)
|
|
|
2395 |
else if (\<exists> p'' flag'. (p'', flag') \<in> procs_of_shm s h \<and> flag = SHM_RDWR \<and> O_proc p \<in> tainted s \<and>
|
|
|
2396 |
info_flow_shm s p'' p')
|
|
|
2397 |
then (case (cp2sproc s p') of
|
|
|
2398 |
Some sp \<Rightarrow> Some (S_proc sp True)
|
|
|
2399 |
| _ \<Rightarrow> None)
|
|
|
2400 |
else co2sobj s obj
|
|
|
2401 |
| _ \<Rightarrow> co2sobj s obj)"
|
|
|
2402 |
apply (frule vt_grant_os, frule vd_cons, case_tac obj)
|
|
|
2403 |
apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other)
|
|
|
2404 |
|
|
|
2405 |
apply (rule conjI|rule impI|erule exE)+
|
|
|
2406 |
apply (simp split:option.splits del:split_paired_Ex)
|
|
|
2407 |
apply (rule impI, frule current_proc_has_sp, simp)
|
|
|
2408 |
apply ((erule exE)+, auto simp:tainted_eq_tainted intro:info_flow_shm_tainted)[1]
|
|
|
2409 |
apply (rule impI, simp add:tainted_eq_tainted split:option.splits del:split_paired_Ex)
|
|
|
2410 |
apply (auto simp:info_flow_shm_prop1 cp2sproc_attach dest!:current_proc_has_sp')[1]
|
|
|
2411 |
|
|
|
2412 |
apply (case_tac "cp2sproc (Attach p h flag # s) nat")
|
|
|
2413 |
apply (drule current_proc_has_sp', simp+)
|
|
|
2414 |
|
|
|
2415 |
apply (rule conjI|erule exE|erule conjE|rule impI)+
|
|
|
2416 |
apply (simp add:tainted_eq_tainted)
|
|
|
2417 |
apply (auto simp:info_flow_shm_prop1 cp2sproc_attach intro:info_flow_shm_tainted dest!:current_proc_has_sp')[1]
|
|
|
2418 |
apply (auto simp:info_flow_shm_prop1 cp2sproc_attach intro:info_flow_shm_tainted dest!:current_proc_has_sp'
|
|
|
2419 |
split:option.splits if_splits)[1]
|
|
|
2420 |
|
|
|
2421 |
|
|
|
2422 |
apply (auto split:if_splits option.splits dest!:current_file_has_sfile'
|
|
|
2423 |
simp:current_files_simps cf2sfiles_simps cf2sfile_simps tainted_eq_tainted
|
|
|
2424 |
same_inode_files_prop6
|
|
|
2425 |
dest:is_file_in_current is_dir_in_current)
|
|
|
2426 |
done
|
|
|
2427 |
*)
|
|
|
2428 |
|
|
92
|
2429 |
lemma co2sobj_bind:
|
|
|
2430 |
"valid (Bind p fd addr # s) \<Longrightarrow> co2sobj (Bind p fd addr # s) = co2sobj s"
|
|
|
2431 |
apply (frule vd_cons, frule vt_grant, rule ext, case_tac x)
|
|
|
2432 |
by auto
|
|
|
2433 |
|
|
|
2434 |
lemma co2sobj_connect:
|
|
|
2435 |
"valid (Connect p fd addr # s) \<Longrightarrow> co2sobj (Connect p fd addr # s) = co2sobj s"
|
|
|
2436 |
apply (frule vd_cons, frule vt_grant, rule ext, case_tac x)
|
|
|
2437 |
by auto
|
|
|
2438 |
|
|
|
2439 |
lemma co2sobj_createsock:
|
|
|
2440 |
"valid (CreateSock p af st fd inum # s) \<Longrightarrow> co2sobj (CreateSock p af st fd inum # s) = co2sobj s"
|
|
|
2441 |
apply (frule vd_cons, frule vt_grant, rule ext, case_tac x)
|
|
|
2442 |
by auto
|
|
|
2443 |
|
|
|
2444 |
lemma co2sobj_accept:
|
|
|
2445 |
"valid (Accept p fd addr port fd' inum # s) \<Longrightarrow> co2sobj (Accept p fd addr port fd' inum # s) = co2sobj s"
|
|
|
2446 |
apply (frule vd_cons, frule vt_grant, rule ext, case_tac x)
|
|
|
2447 |
by auto
|
|
|
2448 |
|
|
|
2449 |
lemma co2sobj_listen:
|
|
|
2450 |
"valid (Listen p fd # s) \<Longrightarrow> co2sobj (Listen p fd # s) = co2sobj s"
|
|
|
2451 |
apply (frule vd_cons, frule vt_grant, rule ext, case_tac x)
|
|
|
2452 |
by auto
|
|
|
2453 |
lemma co2sobj_sendsock:
|
|
|
2454 |
"valid (SendSock p fd # s) \<Longrightarrow> co2sobj (SendSock p fd # s) = co2sobj s"
|
|
|
2455 |
apply (frule vd_cons, frule vt_grant, rule ext, case_tac x)
|
|
|
2456 |
by auto
|
|
|
2457 |
lemma co2sobj_recvsock:
|
|
|
2458 |
"valid (RecvSock p fd # s) \<Longrightarrow> co2sobj (RecvSock p fd # s) = co2sobj s"
|
|
|
2459 |
apply (frule vd_cons, frule vt_grant, rule ext, case_tac x)
|
|
|
2460 |
by auto
|
|
|
2461 |
lemma co2sobj_shutdown:
|
|
|
2462 |
"valid (Shutdown p fd addr # s) \<Longrightarrow> co2sobj (Shutdown p fd addr # s) = co2sobj s"
|
|
|
2463 |
apply (frule vd_cons, frule vt_grant, rule ext, case_tac x)
|
|
|
2464 |
by auto
|
|
|
2465 |
|
|
77
|
2466 |
lemma co2sobj_other:
|
|
92
|
2467 |
"\<lbrakk>valid (e # s); dalive (e # s) obj;
|
|
77
|
2468 |
\<forall> p f fds. e \<noteq> Execve p f fds;
|
|
|
2469 |
\<forall> p p' fds. e \<noteq> Clone p p' fds;
|
|
|
2470 |
\<forall> p p'. e \<noteq> Ptrace p p';
|
|
|
2471 |
\<forall> p f flags fd opt. e \<noteq> Open p f flags fd opt;
|
|
|
2472 |
\<forall> p fd. e \<noteq> ReadFile p fd;
|
|
|
2473 |
\<forall> p fd. e \<noteq> WriteFile p fd;
|
|
|
2474 |
\<forall> p fd. e \<noteq> CloseFd p fd;
|
|
|
2475 |
\<forall> p f. e \<noteq> UnLink p f;
|
|
|
2476 |
\<forall> p f. e \<noteq> Rmdir p f;
|
|
|
2477 |
\<forall> p f i. e \<noteq> Mkdir p f i;
|
|
|
2478 |
\<forall> p f f'. e \<noteq> LinkHard p f f';
|
|
|
2479 |
\<forall> p f len. e \<noteq> Truncate p f len;
|
|
|
2480 |
\<forall> p q. e \<noteq> CreateMsgq p q;
|
|
|
2481 |
\<forall> p q m. e \<noteq> SendMsg p q m;
|
|
|
2482 |
\<forall> p q m. e \<noteq> RecvMsg p q m;
|
|
|
2483 |
\<forall> p q. e \<noteq> RemoveMsgq p q
|
|
|
2484 |
\<rbrakk> \<Longrightarrow> co2sobj (e # s) obj = co2sobj s obj" (*;
|
|
|
2485 |
\<forall> p h flag. e \<noteq> Attach p h flag;
|
|
|
2486 |
\<forall> p h. e \<noteq> Detach p h;
|
|
|
2487 |
\<forall> p h. e \<noteq> DeleteShM p h*)
|
|
|
2488 |
apply (frule vt_grant, case_tac e)
|
|
|
2489 |
apply (auto intro:co2sobj_kill co2sobj_exit)
|
|
|
2490 |
done
|
|
|
2491 |
|
|
|
2492 |
lemmas co2sobj_simps = co2sobj_execve co2sobj_clone co2sobj_ptrace co2sobj_open co2sobj_readfile
|
|
|
2493 |
co2sobj_writefile co2sobj_closefd co2sobj_unlink co2sobj_rmdir co2sobj_mkdir co2sobj_linkhard
|
|
|
2494 |
co2sobj_truncate co2sobj_kill co2sobj_exit co2sobj_createmsgq co2sobj_sendmsg co2sobj_recvmsg
|
|
|
2495 |
co2sobj_removemsgq (* co2sobj_attach co2sobj_detach co2sobj_createshm co2sobj_deleteshm *)
|
|
92
|
2496 |
co2sobj_createsock co2sobj_accept co2sobj_listen co2sobj_sendsock co2sobj_recvsock
|
|
|
2497 |
co2sobj_shutdown co2sobj_bind co2sobj_connect
|
|
77
|
2498 |
|
|
|
2499 |
end
|
|
|
2500 |
|
|
|
2501 |
(*<*)
|
|
|
2502 |
end
|
|
|
2503 |
(*>*) |