--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Dynamic_static.thy	Thu Oct 24 09:41:33 2013 +0800
@@ -0,0 +1,153 @@
+theory Dynamic_static
+imports Main Flask Static Init_prop Valid_prop Tainted_prop Delete_prop Co2sobj_prop S2ss_prop S2ss_prop2
+begin
+
+context tainting_s begin
+
+definition init_ss_eq:: "t_static_state \<Rightarrow> t_static_state \<Rightarrow> bool" (infix "\<doteq>" 100)
+where
+  "ss \<doteq> ss' \<equiv> ss \<subseteq> ss' \<and> {sobj. is_init_sobj sobj \<and> sobj \<in> ss'} \<subseteq> ss"
+
+lemma [simp]: "ss \<doteq> ss"
+by (auto simp:init_ss_eq_def)
+
+definition init_ss_in:: "t_static_state \<Rightarrow> t_static_state set \<Rightarrow> bool" (infix "\<propto>" 101)
+where
+  "ss \<propto> sss \<equiv> \<exists> ss' \<in> sss. ss \<doteq> ss'"
+
+lemma s2ss_included_sobj:
+  "\<lbrakk>alive s obj; co2sobj s obj= Some sobj\<rbrakk> \<Longrightarrow> sobj \<in> (s2ss s)"
+by (simp add:s2ss_def, rule_tac x = obj in exI, simp)
+
+lemma init_ss_in_prop:
+  "\<lbrakk>s2ss s \<propto> static; co2sobj s obj = Some sobj; alive s obj; init_obj_related sobj obj\<rbrakk>
+   \<Longrightarrow> \<exists> ss \<in> static. sobj \<in> ss"
+apply (simp add:init_ss_in_def init_ss_eq_def)
+apply (erule bexE, erule conjE)
+apply (rule_tac x = ss' in bexI, auto dest!:s2ss_included_sobj)
+done
+
+
+
+
+
+definition enrich:: "t_state \<Rightarrow> t_object set \<Rightarrow> t_state \<Rightarrow> bool"
+where
+  "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"
+
+definition reserve:: "t_state \<Rightarrow> t_object set \<Rightarrow> t_state \<Rightarrow> bool"
+where
+  "reserve s objs s' \<equiv> \<forall> obj. alive s obj \<longrightarrow> alive s' obj \<and> co2sobj s' obj = co2sobj s obj"
+
+definition enrichable :: "t_state \<Rightarrow> t_object set \<Rightarrow> bool"
+where
+  "enrichable s objs \<equiv> \<exists> s'. valid s' \<and> s2ss s' = s2ss s \<and> enrich s objs s' \<and> reserve s objs s'"
+
+definition is_created :: "t_state \<Rightarrow> t_object \<Rightarrow> bool"
+where
+  "is_created s obj \<equiv> init_alive obj \<longrightarrow> deleted obj s"
+
+definition is_inited :: "t_state \<Rightarrow> t_object \<Rightarrow> bool"
+where
+  "is_inited s obj \<equiv> init_alive obj \<and> \<not> deleted obj s"
+
+lemma is_inited_eq_not_created:
+  "is_inited s obj = (\<not> is_created s obj)"
+by (auto simp:is_created_def is_inited_def)
+
+(* recorded in our static world *)
+fun recorded :: "t_object \<Rightarrow> bool"
+where
+  "recorded (O_proc p)     = True"
+| "recorded (O_file f)     = True"
+| "recorded (O_dir  f)     = True"
+| "recorded (O_node n)     = False" (* cause socket is temperary not considered *)
+| "recorded (O_shm  h)     = True"
+| "recorded (O_msgq q)     = True"
+| "recorded _              = False"
+
+
+
+
+
+
+lemma d2s_main_execve:
+  "valid (Execve p f fds # s) \<Longrightarrow> s2ss (Execve p f fds # s) \<in> static"
+apply (frule vd_cons, frule vt_grant_os, clarsimp simp:s2ss_execve)
+sorry
+
+lemma d2s_main:
+  "valid s \<Longrightarrow> s2ss s \<propto> static"
+apply (induct s, simp add:s2ss_nil_prop init_ss_in_def)
+apply (rule_tac x = "init_static_state" in bexI, simp, simp add:s_init)
+apply (frule vd_cons, frule vt_grant_os, simp)
+apply (case_tac a) 
+apply (clarsimp simp add:s2ss_execve)
+apply (rule conjI, rule impI)
+
+
+
+sorry
+
+
+lemma many_sq_imp_sms:
+  "\<lbrakk>S_msgq (Create, sec, sms) \<in> ss; ss \<in> static\<rbrakk> \<Longrightarrow> \<forall> sm \<in> (set sms). is_many_smsg sm"
+sorry
+
+
+
+lemma enrichability: 
+  "\<lbrakk>valid s; \<forall> obj \<in> objs. alive s obj \<and> is_created s obj \<and> recorded obj\<rbrakk>
+   \<Longrightarrow> enrichable s objs"
+proof (induct s arbitrary:objs)
+  case Nil
+  hence "objs = {}" 
+    apply (auto simp:is_created_def)
+    apply (erule_tac x = x in ballE)
+    apply (auto simp:init_alive_prop)
+    done
+  thus ?case using Nil unfolding enrichable_def enrich_def reserve_def
+    by (rule_tac x = "[]" in exI, auto)
+next
+  case (Cons e s)
+  hence p1: "\<And> objs. \<forall> obj \<in> objs. alive s obj \<and> is_created s obj \<and> recorded obj \<Longrightarrow> enrichable s objs"
+    and p2: "valid (e # s)" and p3: "\<forall>obj\<in>objs. alive (e # s) obj \<and> is_created (e # s) obj \<and> recorded obj"
+    and os: "os_grant s e" and se: "grant s e" and vd: "valid s"
+    by (auto dest:vt_grant_os vd_cons vt_grant)
+  show ?case sorry (*
+  proof (cases e)
+    case (Execve p f fds)
+    hence p4: "e = Execve p f fds" by simp
+    from p3 have p5: "is_inited s (O_proc p) \<Longrightarrow> (O_proc p) \<notin> objs"
+      by (auto simp:is_created_def is_inited_def p4 elim!:ballE[where x = "O_proc p"])
+    show "enrichable (e # s) objs"
+    proof (case "is_inited s (O_proc p)")
+      apply (simp add:enrichable_def p4)
+
+      
+  
+    apply auto
+    apply (auto simp:enrichable_def)
+apply (induct s)
+
+
+
+done
+*)
+qed
+
+lemma s2d_main:
+  "ss \<in> static \<Longrightarrow> \<exists> s. valid s \<and> s2ss s = ss"
+apply (erule static.induct)
+apply (rule_tac x = "[]" in exI, simp add:s2ss_nil_prop valid.intros)
+
+apply (erule exE|erule conjE)+
+
+apply (simp add:update_ss_def)
+
+sorry
+
+
+end
+
+end
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