--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/MicroJava/JVM/JVMDefensive.thy Tue Oct 08 10:49:19 2002 +0200
@@ -0,0 +1,183 @@
+(* Title: HOL/MicroJava/JVM/JVMDefensive.thy
+ ID: $Id$
+ Author: Gerwin Klein
+ Copyright GPL
+*)
+
+header {* \isaheader{A Defensive JVM} *}
+
+theory JVMDefensive = JVMExec:
+
+text {*
+ Extend the state space by one element indicating a type error (or
+ other abnormal termination) *}
+datatype 'a type_error = TypeError | Normal 'a
+
+
+syntax "fifth" :: "'a \<times> 'b \<times> 'c \<times> 'd \<times> 'e \<times> 'f \<Rightarrow> 'e"
+translations
+ "fifth x" == "fst(snd(snd(snd(snd x))))"
+
+
+consts isAddr :: "val \<Rightarrow> bool"
+recdef isAddr "{}"
+ "isAddr (Addr loc) = True"
+ "isAddr v = False"
+
+consts isIntg :: "val \<Rightarrow> bool"
+recdef isIntg "{}"
+ "isIntg (Intg i) = True"
+ "isIntg v = False"
+
+constdefs
+ isRef :: "val \<Rightarrow> bool"
+ "isRef v \<equiv> v = Null \<or> isAddr v"
+
+
+consts
+ check_instr :: "[instr, jvm_prog, aheap, opstack, locvars,
+ cname, sig, p_count, p_count, frame list] \<Rightarrow> bool"
+primrec
+ "check_instr (Load idx) G hp stk vars C sig pc maxpc frs =
+ (idx < length vars)"
+
+ "check_instr (Store idx) G hp stk vars Cl sig pc maxpc frs =
+ (0 < length stk \<and> idx < length vars)"
+
+ "check_instr (LitPush v) G hp stk vars Cl sig pc maxpc frs =
+ (\<not>isAddr v)"
+
+ "check_instr (New C) G hp stk vars Cl sig pc maxpc frs =
+ is_class G C"
+
+ "check_instr (Getfield F C) G hp stk vars Cl sig pc maxpc frs =
+ (0 < length stk \<and> is_class G C \<and> field (G,C) F \<noteq> None \<and>
+ (let (C', T) = the (field (G,C) F); ref = hd stk in
+ C' = C \<and> isRef ref \<and> (ref \<noteq> Null \<longrightarrow>
+ hp (the_Addr ref) \<noteq> None \<and>
+ (let (D,vs) = the (hp (the_Addr ref)) in
+ G \<turnstile> D \<preceq>C C \<and> vs (F,C) \<noteq> None \<and> G,hp \<turnstile> the (vs (F,C)) ::\<preceq> T))))"
+
+ "check_instr (Putfield F C) G hp stk vars Cl sig pc maxpc frs =
+ (1 < length stk \<and> is_class G C \<and> field (G,C) F \<noteq> None \<and>
+ (let (C', T) = the (field (G,C) F); v = hd stk; ref = hd (tl stk) in
+ C' = C \<and> isRef ref \<and> (ref \<noteq> Null \<longrightarrow>
+ hp (the_Addr ref) \<noteq> None \<and>
+ (let (D,vs) = the (hp (the_Addr ref)) in
+ G \<turnstile> D \<preceq>C C \<and> G,hp \<turnstile> v ::\<preceq> T))))"
+
+ "check_instr (Checkcast C) G hp stk vars Cl sig pc maxpc frs =
+ (0 < length stk \<and> is_class G C \<and> isRef (hd stk))"
+
+
+ "check_instr (Invoke C mn ps) G hp stk vars Cl sig pc maxpc frs =
+ (length ps < length stk \<and>
+ (let n = length ps; v = stk!n in
+ isRef v \<and> (v \<noteq> Null \<longrightarrow>
+ hp (the_Addr v) \<noteq> None \<and>
+ method (G,cname_of hp v) (mn,ps) \<noteq> None \<and>
+ list_all2 (\<lambda>v T. G,hp \<turnstile> v ::\<preceq> T) (rev (take n stk)) ps)))"
+
+ "check_instr Return G hp stk0 vars Cl sig0 pc maxpc frs =
+ (0 < length stk0 \<and> (0 < length frs \<longrightarrow>
+ method (G,Cl) sig0 \<noteq> None \<and>
+ (let v = hd stk0; (C, rT, body) = the (method (G,Cl) sig0) in
+ Cl = C \<and> G,hp \<turnstile> v ::\<preceq> rT)))"
+
+ "check_instr Pop G hp stk vars Cl sig pc maxpc frs =
+ (0 < length stk)"
+
+ "check_instr Dup G hp stk vars Cl sig pc maxpc frs =
+ (0 < length stk)"
+
+ "check_instr Dup_x1 G hp stk vars Cl sig pc maxpc frs =
+ (1 < length stk)"
+
+ "check_instr Dup_x2 G hp stk vars Cl sig pc maxpc frs =
+ (2 < length stk)"
+
+ "check_instr Swap G hp stk vars Cl sig pc maxpc frs =
+ (1 < length stk)"
+
+ "check_instr IAdd G hp stk vars Cl sig pc maxpc frs =
+ (1 < length stk \<and> isIntg (hd stk) \<and> isIntg (hd (tl stk)))"
+
+ "check_instr (Ifcmpeq b) G hp stk vars Cl sig pc maxpc frs =
+ (1 < length stk \<and> 0 \<le> int pc+b \<and> nat(int pc+b) < maxpc)"
+
+ "check_instr (Goto b) G hp stk vars Cl sig pc maxpc frs =
+ (0 \<le> int pc+b \<and> nat(int pc+b) < maxpc)"
+
+ "check_instr Throw G hp stk vars Cl sig pc maxpc frs =
+ (0 < length stk \<and> isRef (hd stk))"
+
+constdefs
+ check :: "jvm_prog \<Rightarrow> jvm_state \<Rightarrow> bool"
+ "check G s \<equiv> let (xcpt, hp, frs) = s in
+ (case frs of [] \<Rightarrow> True | (stk,loc,C,sig,pc)#frs' \<Rightarrow>
+ (let ins = fifth (the (method (G,C) sig)); i = ins!pc in
+ check_instr i G hp stk loc C sig pc (length ins) frs'))"
+
+
+ exec_d :: "jvm_prog \<Rightarrow> jvm_state type_error \<Rightarrow> jvm_state option type_error"
+ "exec_d G s \<equiv> case s of
+ TypeError \<Rightarrow> TypeError
+ | Normal s' \<Rightarrow> if check G s' then Normal (exec (G, s')) else TypeError"
+
+
+consts
+ "exec_all_d" :: "jvm_prog \<Rightarrow> jvm_state type_error \<Rightarrow> jvm_state type_error \<Rightarrow> bool"
+ ("_ |- _ -jvmd-> _" [61,61,61]60)
+
+syntax (xsymbols)
+ "exec_all_d" :: "jvm_prog \<Rightarrow> jvm_state type_error \<Rightarrow> jvm_state type_error \<Rightarrow> bool"
+ ("_ \<turnstile> _ -jvmd\<rightarrow> _" [61,61,61]60)
+
+defs
+ exec_all_d_def:
+ "G \<turnstile> s -jvmd\<rightarrow> t \<equiv>
+ (s,t) \<in> ({(s,t). exec_d G s = TypeError \<and> t = TypeError} \<union>
+ {(s,t). \<exists>t'. exec_d G s = Normal (Some t') \<and> t = Normal t'})\<^sup>*"
+
+
+declare split_paired_All [simp del]
+declare split_paired_Ex [simp del]
+
+lemma [dest!]:
+ "(if P then A else B) \<noteq> B \<Longrightarrow> P"
+ by (cases P, auto)
+
+lemma exec_d_no_errorI [intro]:
+ "check G s \<Longrightarrow> exec_d G (Normal s) \<noteq> TypeError"
+ by (unfold exec_d_def) simp
+
+theorem no_type_error_commutes:
+ "exec_d G (Normal s) \<noteq> TypeError \<Longrightarrow>
+ exec_d G (Normal s) = Normal (exec (G, s))"
+ by (unfold exec_d_def, auto)
+
+
+lemma defensive_imp_aggressive:
+ "G \<turnstile> (Normal s) -jvmd\<rightarrow> (Normal t) \<Longrightarrow> G \<turnstile> s -jvm\<rightarrow> t"
+proof -
+ have "\<And>x y. G \<turnstile> x -jvmd\<rightarrow> y \<Longrightarrow> \<forall>s t. x = Normal s \<longrightarrow> y = Normal t \<longrightarrow> G \<turnstile> s -jvm\<rightarrow> t"
+ apply (unfold exec_all_d_def)
+ apply (erule rtrancl_induct)
+ apply (simp add: exec_all_def)
+ apply (fold exec_all_d_def)
+ apply simp
+ apply (intro allI impI)
+ apply (erule disjE, simp)
+ apply (elim exE conjE)
+ apply (erule allE, erule impE, assumption)
+ apply (simp add: exec_all_def exec_d_def split: type_error.splits split_if_asm)
+ apply (rule rtrancl_trans, assumption)
+ apply blast
+ done
+ moreover
+ assume "G \<turnstile> (Normal s) -jvmd\<rightarrow> (Normal t)"
+ ultimately
+ show "G \<turnstile> s -jvm\<rightarrow> t" by blast
+qed
+
+end
\ No newline at end of file