Theory JVMDefensive

theory JVMDefensive
imports JVMExec
(*  Title:      HOL/MicroJava/JVM/JVMDefensive.thy
Author: Gerwin Klein
*)


header {* \isaheader{A Defensive JVM} *}

theory JVMDefensive
imports JVMExec
begin

text {*
Extend the state space by one element indicating a type error (or
other abnormal termination) *}

datatype 'a type_error = TypeError | Normal 'a


abbreviation
fifth :: "'a × 'b × 'c × 'd × 'e × 'f => 'e"
where "fifth x == fst(snd(snd(snd(snd x))))"

fun isAddr :: "val => bool" where
"isAddr (Addr loc) = True"
| "isAddr v = False"

fun isIntg :: "val => bool" where
"isIntg (Intg i) = True"
| "isIntg v = False"

definition isRef :: "val => bool" where
"isRef v ≡ v = Null ∨ isAddr v"

primrec check_instr :: "[instr, jvm_prog, aheap, opstack, locvars,
cname, sig, p_count, nat, frame list] => bool"
where
"check_instr (Load idx) G hp stk vars C sig pc mxs frs =
(idx < length vars ∧ size stk < mxs)"


| "check_instr (Store idx) G hp stk vars Cl sig pc mxs frs =
(0 < length stk ∧ idx < length vars)"


| "check_instr (LitPush v) G hp stk vars Cl sig pc mxs frs =
(¬isAddr v ∧ size stk < mxs)"


| "check_instr (New C) G hp stk vars Cl sig pc mxs frs =
(is_class G C ∧ size stk < mxs)"


| "check_instr (Getfield F C) G hp stk vars Cl sig pc mxs frs =
(0 < length stk ∧ is_class G C ∧ field (G,C) F ≠ None ∧
(let (C', T) = the (field (G,C) F); ref = hd stk in
C' = C ∧ isRef ref ∧ (ref ≠ Null -->
hp (the_Addr ref) ≠ None ∧
(let (D,vs) = the (hp (the_Addr ref)) in
G \<turnstile> D \<preceq>C C ∧ vs (F,C) ≠ None ∧ G,hp \<turnstile> the (vs (F,C)) ::\<preceq> T))))"


| "check_instr (Putfield F C) G hp stk vars Cl sig pc mxs frs =
(1 < length stk ∧ is_class G C ∧ field (G,C) F ≠ None ∧
(let (C', T) = the (field (G,C) F); v = hd stk; ref = hd (tl stk) in
C' = C ∧ isRef ref ∧ (ref ≠ Null -->
hp (the_Addr ref) ≠ None ∧
(let (D,vs) = the (hp (the_Addr ref)) in
G \<turnstile> D \<preceq>C C ∧ G,hp \<turnstile> v ::\<preceq> T))))"


| "check_instr (Checkcast C) G hp stk vars Cl sig pc mxs frs =
(0 < length stk ∧ is_class G C ∧ isRef (hd stk))"


| "check_instr (Invoke C mn ps) G hp stk vars Cl sig pc mxs frs =
(length ps < length stk ∧
(let n = length ps; v = stk!n in
isRef v ∧ (v ≠ Null -->
hp (the_Addr v) ≠ None ∧
method (G,cname_of hp v) (mn,ps) ≠ None ∧
list_all2 (λv T. G,hp \<turnstile> v ::\<preceq> T) (rev (take n stk)) ps)))"


| "check_instr Return G hp stk0 vars Cl sig0 pc mxs frs =
(0 < length stk0 ∧ (0 < length frs -->
method (G,Cl) sig0 ≠ None ∧
(let v = hd stk0; (C, rT, body) = the (method (G,Cl) sig0) in
Cl = C ∧ G,hp \<turnstile> v ::\<preceq> rT)))"


| "check_instr Pop G hp stk vars Cl sig pc mxs frs =
(0 < length stk)"


| "check_instr Dup G hp stk vars Cl sig pc mxs frs =
(0 < length stk ∧ size stk < mxs)"


| "check_instr Dup_x1 G hp stk vars Cl sig pc mxs frs =
(1 < length stk ∧ size stk < mxs)"


| "check_instr Dup_x2 G hp stk vars Cl sig pc mxs frs =
(2 < length stk ∧ size stk < mxs)"


| "check_instr Swap G hp stk vars Cl sig pc mxs frs =
(1 < length stk)"


| "check_instr IAdd G hp stk vars Cl sig pc mxs frs =
(1 < length stk ∧ isIntg (hd stk) ∧ isIntg (hd (tl stk)))"


| "check_instr (Ifcmpeq b) G hp stk vars Cl sig pc mxs frs =
(1 < length stk ∧ 0 ≤ int pc+b)"


| "check_instr (Goto b) G hp stk vars Cl sig pc mxs frs =
(0 ≤ int pc+b)"


| "check_instr Throw G hp stk vars Cl sig pc mxs frs =
(0 < length stk ∧ isRef (hd stk))"


definition check :: "jvm_prog => jvm_state => bool" where
"check G s ≡ let (xcpt, hp, frs) = s in
(case frs of [] => True | (stk,loc,C,sig,pc)#frs' =>
(let (C',rt,mxs,mxl,ins,et) = the (method (G,C) sig); i = ins!pc in
pc < size ins ∧
check_instr i G hp stk loc C sig pc mxs frs'))"



definition exec_d :: "jvm_prog => jvm_state type_error => jvm_state option type_error" where
"exec_d G s ≡ case s of
TypeError => TypeError
| Normal s' => if check G s' then Normal (exec (G, s')) else TypeError"



definition
exec_all_d :: "jvm_prog => jvm_state type_error => jvm_state type_error => bool"
("_ \<turnstile> _ \<midarrow>jvmd-> _" [61,61,61]60) where
"G \<turnstile> s \<midarrow>jvmd-> t <->
(s,t) ∈ ({(s,t). exec_d G s = TypeError ∧ t = TypeError} ∪
{(s,t). ∃t'. exec_d G s = Normal (Some t') ∧ t = Normal t'})*"



declare split_paired_All [simp del]
declare split_paired_Ex [simp del]

lemma [dest!]:
"(if P then A else B) ≠ B ==> P"
by (cases P, auto)

lemma exec_d_no_errorI [intro]:
"check G s ==> exec_d G (Normal s) ≠ TypeError"
by (unfold exec_d_def) simp

theorem no_type_error_commutes:
"exec_d G (Normal s) ≠ TypeError ==>
exec_d G (Normal s) = Normal (exec (G, s))"

by (unfold exec_d_def, auto)


lemma defensive_imp_aggressive:
"G \<turnstile> (Normal s) \<midarrow>jvmd-> (Normal t) ==> G \<turnstile> s \<midarrow>jvm-> t"
proof -
have "!!x y. G \<turnstile> x \<midarrow>jvmd-> y ==> ∀s t. x = Normal s --> y = Normal t --> G \<turnstile> s \<midarrow>jvm-> 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) \<midarrow>jvmd-> (Normal t)"
ultimately
show "G \<turnstile> s \<midarrow>jvm-> t" by blast
qed

end