--- a/src/HOL/MicroJava/BV/Effect.thy Mon Mar 01 18:49:55 2010 +0100
+++ b/src/HOL/MicroJava/BV/Effect.thy Tue Mar 02 12:26:50 2010 +0100
@@ -34,33 +34,34 @@
| "succs Throw pc = [pc]"
text "Effect of instruction on the state type:"
-consts
-eff' :: "instr \<times> jvm_prog \<times> state_type \<Rightarrow> state_type"
-recdef eff' "{}"
-"eff' (Load idx, G, (ST, LT)) = (ok_val (LT ! idx) # ST, LT)"
-"eff' (Store idx, G, (ts#ST, LT)) = (ST, LT[idx:= OK ts])"
-"eff' (LitPush v, G, (ST, LT)) = (the (typeof (\<lambda>v. None) v) # ST, LT)"
-"eff' (Getfield F C, G, (oT#ST, LT)) = (snd (the (field (G,C) F)) # ST, LT)"
-"eff' (Putfield F C, G, (vT#oT#ST, LT)) = (ST,LT)"
-"eff' (New C, G, (ST,LT)) = (Class C # ST, LT)"
-"eff' (Checkcast C, G, (RefT rt#ST,LT)) = (Class C # ST,LT)"
-"eff' (Pop, G, (ts#ST,LT)) = (ST,LT)"
-"eff' (Dup, G, (ts#ST,LT)) = (ts#ts#ST,LT)"
-"eff' (Dup_x1, G, (ts1#ts2#ST,LT)) = (ts1#ts2#ts1#ST,LT)"
-"eff' (Dup_x2, G, (ts1#ts2#ts3#ST,LT)) = (ts1#ts2#ts3#ts1#ST,LT)"
-"eff' (Swap, G, (ts1#ts2#ST,LT)) = (ts2#ts1#ST,LT)"
+fun eff' :: "instr \<times> jvm_prog \<times> state_type \<Rightarrow> state_type"
+where
+"eff' (Load idx, G, (ST, LT)) = (ok_val (LT ! idx) # ST, LT)" |
+"eff' (Store idx, G, (ts#ST, LT)) = (ST, LT[idx:= OK ts])" |
+"eff' (LitPush v, G, (ST, LT)) = (the (typeof (\<lambda>v. None) v) # ST, LT)" |
+"eff' (Getfield F C, G, (oT#ST, LT)) = (snd (the (field (G,C) F)) # ST, LT)" |
+"eff' (Putfield F C, G, (vT#oT#ST, LT)) = (ST,LT)" |
+"eff' (New C, G, (ST,LT)) = (Class C # ST, LT)" |
+"eff' (Checkcast C, G, (RefT rt#ST,LT)) = (Class C # ST,LT)" |
+"eff' (Pop, G, (ts#ST,LT)) = (ST,LT)" |
+"eff' (Dup, G, (ts#ST,LT)) = (ts#ts#ST,LT)" |
+"eff' (Dup_x1, G, (ts1#ts2#ST,LT)) = (ts1#ts2#ts1#ST,LT)" |
+"eff' (Dup_x2, G, (ts1#ts2#ts3#ST,LT)) = (ts1#ts2#ts3#ts1#ST,LT)" |
+"eff' (Swap, G, (ts1#ts2#ST,LT)) = (ts2#ts1#ST,LT)" |
"eff' (IAdd, G, (PrimT Integer#PrimT Integer#ST,LT))
- = (PrimT Integer#ST,LT)"
-"eff' (Ifcmpeq b, G, (ts1#ts2#ST,LT)) = (ST,LT)"
-"eff' (Goto b, G, s) = s"
+ = (PrimT Integer#ST,LT)" |
+"eff' (Ifcmpeq b, G, (ts1#ts2#ST,LT)) = (ST,LT)" |
+"eff' (Goto b, G, s) = s" |
-- "Return has no successor instruction in the same method"
-"eff' (Return, G, s) = s"
+"eff' (Return, G, s) = s" |
-- "Throw always terminates abruptly"
-"eff' (Throw, G, s) = s"
+"eff' (Throw, G, s) = s" |
"eff' (Invoke C mn fpTs, G, (ST,LT)) = (let ST' = drop (length fpTs) ST
in (fst (snd (the (method (G,C) (mn,fpTs))))#(tl ST'),LT))"
+
+
primrec match_any :: "jvm_prog \<Rightarrow> p_count \<Rightarrow> exception_table \<Rightarrow> cname list" where
"match_any G pc [] = []"
| "match_any G pc (e#es) = (let (start_pc, end_pc, handler_pc, catch_type) = e;
@@ -77,16 +78,16 @@
"match G X pc et = (if \<exists>e \<in> set et. match_exception_entry G (Xcpt X) pc e then [Xcpt X] else [])"
by (induct et) auto
-consts
+fun
xcpt_names :: "instr \<times> jvm_prog \<times> p_count \<times> exception_table \<Rightarrow> cname list"
-recdef xcpt_names "{}"
+where
"xcpt_names (Getfield F C, G, pc, et) = match G NullPointer pc et"
- "xcpt_names (Putfield F C, G, pc, et) = match G NullPointer pc et"
- "xcpt_names (New C, G, pc, et) = match G OutOfMemory pc et"
- "xcpt_names (Checkcast C, G, pc, et) = match G ClassCast pc et"
- "xcpt_names (Throw, G, pc, et) = match_any G pc et"
- "xcpt_names (Invoke C m p, G, pc, et) = match_any G pc et"
- "xcpt_names (i, G, pc, et) = []"
+| "xcpt_names (Putfield F C, G, pc, et) = match G NullPointer pc et"
+| "xcpt_names (New C, G, pc, et) = match G OutOfMemory pc et"
+| "xcpt_names (Checkcast C, G, pc, et) = match G ClassCast pc et"
+| "xcpt_names (Throw, G, pc, et) = match_any G pc et"
+| "xcpt_names (Invoke C m p, G, pc, et) = match_any G pc et"
+| "xcpt_names (i, G, pc, et) = []"
definition xcpt_eff :: "instr \<Rightarrow> jvm_prog \<Rightarrow> p_count \<Rightarrow> state_type option \<Rightarrow> exception_table \<Rightarrow> succ_type" where
@@ -118,53 +119,53 @@
text "Conditions under which eff is applicable:"
-consts
+
+fun
app' :: "instr \<times> jvm_prog \<times> p_count \<times> nat \<times> ty \<times> state_type \<Rightarrow> bool"
-
-recdef app' "{}"
+where
"app' (Load idx, G, pc, maxs, rT, s) =
- (idx < length (snd s) \<and> (snd s) ! idx \<noteq> Err \<and> length (fst s) < maxs)"
+ (idx < length (snd s) \<and> (snd s) ! idx \<noteq> Err \<and> length (fst s) < maxs)" |
"app' (Store idx, G, pc, maxs, rT, (ts#ST, LT)) =
- (idx < length LT)"
+ (idx < length LT)" |
"app' (LitPush v, G, pc, maxs, rT, s) =
- (length (fst s) < maxs \<and> typeof (\<lambda>t. None) v \<noteq> None)"
+ (length (fst s) < maxs \<and> typeof (\<lambda>t. None) v \<noteq> None)" |
"app' (Getfield F C, G, pc, maxs, rT, (oT#ST, LT)) =
(is_class G C \<and> field (G,C) F \<noteq> None \<and> fst (the (field (G,C) F)) = C \<and>
- G \<turnstile> oT \<preceq> (Class C))"
+ G \<turnstile> oT \<preceq> (Class C))" |
"app' (Putfield F C, G, pc, maxs, rT, (vT#oT#ST, LT)) =
(is_class G C \<and> field (G,C) F \<noteq> None \<and> fst (the (field (G,C) F)) = C \<and>
- G \<turnstile> oT \<preceq> (Class C) \<and> G \<turnstile> vT \<preceq> (snd (the (field (G,C) F))))"
+ G \<turnstile> oT \<preceq> (Class C) \<and> G \<turnstile> vT \<preceq> (snd (the (field (G,C) F))))" |
"app' (New C, G, pc, maxs, rT, s) =
- (is_class G C \<and> length (fst s) < maxs)"
+ (is_class G C \<and> length (fst s) < maxs)" |
"app' (Checkcast C, G, pc, maxs, rT, (RefT rt#ST,LT)) =
- (is_class G C)"
+ (is_class G C)" |
"app' (Pop, G, pc, maxs, rT, (ts#ST,LT)) =
- True"
+ True" |
"app' (Dup, G, pc, maxs, rT, (ts#ST,LT)) =
- (1+length ST < maxs)"
+ (1+length ST < maxs)" |
"app' (Dup_x1, G, pc, maxs, rT, (ts1#ts2#ST,LT)) =
- (2+length ST < maxs)"
+ (2+length ST < maxs)" |
"app' (Dup_x2, G, pc, maxs, rT, (ts1#ts2#ts3#ST,LT)) =
- (3+length ST < maxs)"
+ (3+length ST < maxs)" |
"app' (Swap, G, pc, maxs, rT, (ts1#ts2#ST,LT)) =
- True"
+ True" |
"app' (IAdd, G, pc, maxs, rT, (PrimT Integer#PrimT Integer#ST,LT)) =
- True"
+ True" |
"app' (Ifcmpeq b, G, pc, maxs, rT, (ts#ts'#ST,LT)) =
- (0 \<le> int pc + b \<and> (isPrimT ts \<and> ts' = ts \<or> isRefT ts \<and> isRefT ts'))"
+ (0 \<le> int pc + b \<and> (isPrimT ts \<and> ts' = ts \<or> isRefT ts \<and> isRefT ts'))" |
"app' (Goto b, G, pc, maxs, rT, s) =
- (0 \<le> int pc + b)"
+ (0 \<le> int pc + b)" |
"app' (Return, G, pc, maxs, rT, (T#ST,LT)) =
- (G \<turnstile> T \<preceq> rT)"
+ (G \<turnstile> T \<preceq> rT)" |
"app' (Throw, G, pc, maxs, rT, (T#ST,LT)) =
- isRefT T"
+ isRefT T" |
"app' (Invoke C mn fpTs, G, pc, maxs, rT, s) =
(length fpTs < length (fst s) \<and>
(let apTs = rev (take (length fpTs) (fst s));
X = hd (drop (length fpTs) (fst s))
in
G \<turnstile> X \<preceq> Class C \<and> is_class G C \<and> method (G,C) (mn,fpTs) \<noteq> None \<and>
- list_all2 (\<lambda>x y. G \<turnstile> x \<preceq> y) apTs fpTs))"
+ list_all2 (\<lambda>x y. G \<turnstile> x \<preceq> y) apTs fpTs))" |
"app' (i,G, pc,maxs,rT,s) = False"
@@ -208,7 +209,7 @@
qed auto
lemma 2: "\<not>(2 < length a) \<Longrightarrow> a = [] \<or> (\<exists> l. a = [l]) \<or> (\<exists> l l'. a = [l,l'])"
-proof -;
+proof -
assume "\<not>(2 < length a)"
hence "length a < (Suc (Suc (Suc 0)))" by simp
hence * : "length a = 0 \<or> length a = Suc 0 \<or> length a = Suc (Suc 0)"
@@ -268,7 +269,7 @@
"(app (Checkcast C) G maxs rT pc et (Some s)) =
(\<exists>rT ST LT. s = (RefT rT#ST,LT) \<and> is_class G C \<and>
(\<forall>x \<in> set (match G ClassCast pc et). is_class G x))"
- by (cases s, cases "fst s", simp add: app_def) (cases "hd (fst s)", auto)
+ by (cases s, cases "fst s", simp) (cases "hd (fst s)", auto)
lemma appPop[simp]:
"(app Pop G maxs rT pc et (Some s)) = (\<exists>ts ST LT. s = (ts#ST,LT))"
@@ -359,7 +360,7 @@
assume app: "?app (a,b)"
hence "a = (rev (rev (take (length fpTs) a))) @ (drop (length fpTs) a) \<and>
length fpTs < length a" (is "?a \<and> ?l")
- by (auto simp add: app_def)
+ by auto
hence "?a \<and> 0 < length (drop (length fpTs) a)" (is "?a \<and> ?l")
by auto
hence "?a \<and> ?l \<and> length (rev (take (length fpTs) a)) = length fpTs"
@@ -374,7 +375,7 @@
hence "\<exists>apTs X ST. a = rev apTs @ X # ST \<and> length apTs = length fpTs"
by blast
with app
- show ?thesis by (unfold app_def, clarsimp) blast
+ show ?thesis by clarsimp blast
qed
with Pair
have "?app s \<Longrightarrow> ?P s" by (simp only:)