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theory Dynamic_static
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imports Main Flask Static Init_prop Valid_prop Tainted_prop Delete_prop Co2sobj_prop S2ss_prop S2ss_prop2
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Temp
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begin
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context tainting_s begin
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definition enrich:: "t_state \<Rightarrow> t_object set \<Rightarrow> t_state \<Rightarrow> bool"
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where
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"enrich s objs s' \<equiv> \<forall> obj \<in> objs. \<exists> obj'. obj' \<notin> objs \<and> alive s' obj \<and> co2sobj s' obj' = co2sobj s' obj"
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definition reserve:: "t_state \<Rightarrow> t_object set \<Rightarrow> t_state \<Rightarrow> bool"
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where
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"reserve s objs s' \<equiv> \<forall> obj. alive s obj \<longrightarrow> alive s' obj \<and> co2sobj s' obj = co2sobj s obj"
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definition enrichable :: "t_state \<Rightarrow> t_object set \<Rightarrow> bool"
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where
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"enrichable s objs \<equiv> \<exists> s'. valid s' \<and> s2ss s' = s2ss s \<and> enrich s objs s' \<and> reserve s objs s'"
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definition is_created :: "t_state \<Rightarrow> t_object \<Rightarrow> bool"
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where
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"is_created s obj \<equiv> init_alive obj \<longrightarrow> deleted obj s"
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definition is_inited :: "t_state \<Rightarrow> t_object \<Rightarrow> bool"
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where
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"is_inited s obj \<equiv> init_alive obj \<and> \<not> deleted obj s"
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lemma is_inited_eq_not_created:
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"is_inited s obj = (\<not> is_created s obj)"
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by (auto simp:is_created_def is_inited_def)
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lemma d2s_main_execve:
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"valid (Execve p f fds # s) \<Longrightarrow> s2ss (Execve p f fds # s) \<in> static"
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apply (frule vd_cons, frule vt_grant_os, clarsimp simp:s2ss_execve)
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sorry
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lemma d2s_main:
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"valid s \<Longrightarrow> s2ss s \<propto> static"
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apply (induct s, simp add:s2ss_nil_prop init_ss_in_def)
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apply (rule_tac x = "init_static_state" in bexI, simp, simp add:s_init)
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apply (frule vd_cons, frule vt_grant_os, simp)
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apply (case_tac a)
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apply (clarsimp simp add:s2ss_execve)
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apply (rule conjI, rule impI)
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sorry
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lemma many_sq_imp_sms:
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"\<lbrakk>S_msgq (Create, sec, sms) \<in> ss; ss \<in> static\<rbrakk> \<Longrightarrow> \<forall> sm \<in> (set sms). is_many_smsg sm"
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sorry
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(* recorded in our static world *)
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fun recorded :: "t_object \<Rightarrow> bool"
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where
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"recorded (O_proc p) = True"
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| "recorded (O_file f) = True"
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| "recorded (O_dir f) = True"
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| "recorded (O_node n) = False" (* cause socket is temperary not considered *)
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| "recorded (O_shm h) = True"
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| "recorded (O_msgq q) = True"
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| "recorded _ = False"
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lemma enrichability:
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"\<lbrakk>valid s; \<forall> obj \<in> objs. alive s obj \<and> is_created s obj \<and> recorded obj\<rbrakk>
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\<Longrightarrow> enrichable s objs"
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proof (induct s arbitrary:objs)
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case Nil
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hence "objs = {}"
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apply (auto simp:is_created_def)
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apply (erule_tac x = x in ballE)
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apply (auto simp:init_alive_prop)
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done
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thus ?case using Nil unfolding enrichable_def enrich_def reserve_def
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by (rule_tac x = "[]" in exI, auto)
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next
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case (Cons e s)
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hence p1: "\<And> objs. \<forall> obj \<in> objs. alive s obj \<and> is_created s obj \<and> recorded obj \<Longrightarrow> enrichable s objs"
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and p2: "valid (e # s)" and p3: "\<forall>obj\<in>objs. alive (e # s) obj \<and> is_created (e # s) obj \<and> recorded obj"
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and os: "os_grant s e" and se: "grant s e" and vd: "valid s"
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by (auto dest:vt_grant_os vd_cons vt_grant)
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show ?case sorry (*
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proof (cases e)
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case (Execve p f fds)
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hence p4: "e = Execve p f fds" by simp
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from p3 have p5: "is_inited s (O_proc p) \<Longrightarrow> (O_proc p) \<notin> objs"
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by (auto simp:is_created_def is_inited_def p4 elim!:ballE[where x = "O_proc p"])
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show "enrichable (e # s) objs"
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proof (case "is_inited s (O_proc p)")
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apply (simp add:enrichable_def p4)
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apply auto
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apply (auto simp:enrichable_def)
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apply (induct s)
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done
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*)
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qed
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lemma s2d_main:
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"ss \<in> static \<Longrightarrow> \<exists> s. valid s \<and> s2ss s = ss"
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apply (erule static.induct)
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apply (rule_tac x = "[]" in exI, simp add:s2ss_nil_prop valid.intros)
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apply (erule exE|erule conjE)+
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apply (simp add:update_ss_def)
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sorry
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end
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end |