diff -r 8d5221bf765b -r 1f99296758c2 src/HOL/MicroJava/BV/Step.thy
--- a/src/HOL/MicroJava/BV/Step.thy	Tue Aug 08 16:57:44 2000 +0200
+++ b/src/HOL/MicroJava/BV/Step.thy	Wed Aug 09 11:53:00 2000 +0200
@@ -10,7 +10,7 @@
 theory Step = Convert :
 
 
-(* effect of instruction on the state type *)
+text "Effect of instruction on the state type"
 consts 
 step :: "instr \\<times> jvm_prog \\<times> state_type \\<Rightarrow> state_type option"
 
@@ -39,7 +39,7 @@
 "step (i,G,s)                           = None"
 
 
-(* conditions under which step is applicable *)
+text "Conditions under which step is applicable"
 consts
 app :: "instr \\<times> jvm_prog \\<times> ty \\<times> state_type \\<Rightarrow> bool"
 
@@ -84,7 +84,8 @@
 "app (i,G,rT,s)                            = False"
 
 
-(* p_count of successor instructions *)
+text {* \isa{p_count} of successor instructions *}
+
 consts
 succs :: "instr \\<Rightarrow> p_count \\<Rightarrow> p_count set"
 
@@ -131,15 +132,21 @@
   with * show ?thesis by (auto dest: 0)
 qed
 
+text {* 
+\mdeskip
+simp rules for \isa{app} without patterns, better suited for proofs
+\medskip
+*}
+
 lemma appStore[simp]:
-"app (Store idx, G, rT, s) = (\\<exists> ts ST LT. s = (ts#ST,LT) \\<and> idx < length LT)" (is "?app s = ?P s")
+"app (Store idx, G, rT, s) = (\\<exists> ts ST LT. s = (ts#ST,LT) \\<and> idx < length LT)"
 by (cases s, cases "2 < length (fst s)", auto dest: 1 2)
 
 
 lemma appGetField[simp]:
 "app (Getfield F C, G, rT, s) = (\\<exists> oT ST LT. s = (oT#ST, LT) \\<and> is_class G C \\<and> 
                                  fst (the (field (G,C) F)) = C \\<and>
-                                 field (G,C) F \\<noteq> None \\<and> G \\<turnstile> oT \\<preceq> (Class C))" (is "?app s = ?P s")
+                                 field (G,C) F \\<noteq> None \\<and> G \\<turnstile> oT \\<preceq> (Class C))"
 by (cases s, cases "2 < length (fst s)", auto dest: 1 2)
 
 
@@ -147,36 +154,36 @@
 "app (Putfield F C, G, rT, s) = (\\<exists> vT oT ST LT. s = (vT#oT#ST, LT) \\<and> 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))))" (is "?app s = ?P s")
+                                 G \\<turnstile> vT \\<preceq> (snd (the (field (G,C) F))))" 
 by (cases s, cases "2 < length (fst s)", auto dest: 1 2)
 
 
 lemma appCheckcast[simp]:
-"app (Checkcast C, G, rT, s) = (\\<exists>rT ST LT. s = (RefT rT#ST,LT) \\<and> is_class G C)" (is "?app s = ?P s")
+"app (Checkcast C, G, rT, s) = (\\<exists>rT ST LT. s = (RefT rT#ST,LT) \\<and> is_class G C)"
 by (cases s, cases "fst s", simp, cases "hd (fst s)", auto)
 
 lemma appPop[simp]:
-"app (Pop, G, rT, s) = (\\<exists>ts ST LT. s = (ts#ST,LT))" (is "?app s = ?P s")
+"app (Pop, G, rT, s) = (\\<exists>ts ST LT. s = (ts#ST,LT))" 
 by (cases s, cases "2 < length (fst s)", auto dest: 1 2)
 
 
 lemma appDup[simp]:
-"app (Dup, G, rT, s) = (\\<exists>ts ST LT. s = (ts#ST,LT))" (is "?app s = ?P s")
+"app (Dup, G, rT, s) = (\\<exists>ts ST LT. s = (ts#ST,LT))" 
 by (cases s, cases "2 < length (fst s)", auto dest: 1 2)
 
 
 lemma appDup_x1[simp]:
-"app (Dup_x1, G, rT, s) = (\\<exists>ts1 ts2 ST LT. s = (ts1#ts2#ST,LT))" (is "?app s = ?P s")
+"app (Dup_x1, G, rT, s) = (\\<exists>ts1 ts2 ST LT. s = (ts1#ts2#ST,LT))" 
 by (cases s, cases "2 < length (fst s)", auto dest: 1 2)
 
 
 lemma appDup_x2[simp]:
-"app (Dup_x2, G, rT, s) = (\\<exists>ts1 ts2 ts3 ST LT. s = (ts1#ts2#ts3#ST,LT))"(is "?app s = ?P s")
+"app (Dup_x2, G, rT, s) = (\\<exists>ts1 ts2 ts3 ST LT. s = (ts1#ts2#ts3#ST,LT))"
 by (cases s, cases "2 < length (fst s)", auto dest: 1 2)
 
 
 lemma appSwap[simp]:
-"app (Swap, G, rT, s) = (\\<exists>ts1 ts2 ST LT. s = (ts1#ts2#ST,LT))" (is "?app s = ?P s")
+"app (Swap, G, rT, s) = (\\<exists>ts1 ts2 ST LT. s = (ts1#ts2#ST,LT))" 
 by (cases s, cases "2 < length (fst s)", auto dest: 1 2)
 
 
@@ -250,469 +257,5 @@
 qed 
 
 lemmas [simp del] = app_invoke
-lemmas [trans] = sup_loc_trans
-
-ML_setup {* bind_thm ("widen_RefT", widen_RefT) *}
-ML_setup {* bind_thm ("widen_RefT2", widen_RefT2) *}
-
-
-
-lemma app_step_some:
-"\\<lbrakk>app (i,G,rT,s); succs i pc \\<noteq> {} \\<rbrakk> \\<Longrightarrow> step (i,G,s) \\<noteq> None";
-by (cases s, cases i, auto)
-
-lemma sup_state_length:
-"G \\<turnstile> s2 <=s s1 \\<Longrightarrow> length (fst s2) = length (fst s1) \\<and> length (snd s2) = length (snd s1)"
-  by (cases s1, cases s2, simp add: sup_state_length_fst sup_state_length_snd)
-  
-lemma PrimT_PrimT: "(G \\<turnstile> xb \\<preceq> PrimT p) = (xb = PrimT p)"
-proof
-  show "xb = PrimT p \\<Longrightarrow> G \\<turnstile> xb \\<preceq> PrimT p" by blast
-
-  show "G\\<turnstile> xb \\<preceq> PrimT p \\<Longrightarrow> xb = PrimT p"
-  proof (cases xb)
-    fix prim
-    assume "xb = PrimT prim" "G\\<turnstile>xb\\<preceq>PrimT p"
-    thus ?thesis by simp
-  next
-    fix ref
-    assume "G\\<turnstile>xb\\<preceq>PrimT p" "xb = RefT ref"
-    thus ?thesis by simp (rule widen_RefT [elimify], auto)
-  qed
-qed
-
-lemma sup_loc_some [rulify]:
-"\\<forall> y n. (G \\<turnstile> b <=l y) \\<longrightarrow> n < length y \\<longrightarrow> y!n = Some t \\<longrightarrow> (\\<exists>t. b!n = Some t \\<and> (G \\<turnstile> (b!n) <=o (y!n)))" (is "?P b")
-proof (induct "?P" b)
-  show "?P []" by simp
-
-  case Cons
-  show "?P (a#list)"
-  proof (clarsimp simp add: list_all2_Cons1 sup_loc_def)
-    fix z zs n
-    assume * : 
-      "G \\<turnstile> a <=o z" "list_all2 (sup_ty_opt G) list zs" 
-      "n < Suc (length zs)" "(z # zs) ! n = Some t"
-
-    show "(\\<exists>t. (a # list) ! n = Some t) \\<and> G \\<turnstile>(a # list) ! n <=o Some t" 
-    proof (cases n) 
-      case 0
-      with * show ?thesis by (simp add: sup_ty_opt_some)
-    next
-      case Suc
-      with Cons *
-      show ?thesis by (simp add: sup_loc_def)
-    qed
-  qed
-qed
-   
-
-lemma all_widen_is_sup_loc:
-"\\<forall>b. length a = length b \\<longrightarrow> (\\<forall>x\\<in>set (zip a b). x \\<in> widen G) = (G \\<turnstile> (map Some a) <=l (map Some b))" 
- (is "\\<forall>b. length a = length b \\<longrightarrow> ?Q a b" is "?P a")
-proof (induct "a")
-  show "?P []" by simp
-
-  fix l ls assume Cons: "?P ls"
-
-  show "?P (l#ls)" 
-  proof (intro allI impI)
-    fix b 
-    assume "length (l # ls) = length (b::ty list)" 
-    with Cons
-    show "?Q (l # ls) b" by - (cases b, auto)
-  qed
-qed
- 
-
-lemma append_length_n: "\\<forall>n. n \\<le> length x \\<longrightarrow> (\\<exists>a b. x = a@b \\<and> length a = n)" (is "?P x")
-proof (induct "?P" "x")
-  show "?P []" by simp
-
-  fix l ls assume Cons: "?P ls"
-
-  show "?P (l#ls)"
-  proof (intro allI impI)
-    fix n
-    assume l: "n \\<le> length (l # ls)"
-
-    show "\\<exists>a b. l # ls = a @ b \\<and> length a = n" 
-    proof (cases n)
-      assume "n=0" thus ?thesis by simp
-    next
-      fix "n'" assume s: "n = Suc n'"
-      with l 
-      have  "n' \\<le> length ls" by simp 
-      hence "\\<exists>a b. ls = a @ b \\<and> length a = n'" by (rule Cons [rulify])
-      thus ?thesis
-      proof elim
-        fix a b 
-        assume "ls = a @ b" "length a = n'"
-        with s
-        have "l # ls = (l#a) @ b \\<and> length (l#a) = n" by simp
-        thus ?thesis by blast
-      qed
-    qed
-  qed
-qed
-
-
-
-lemma rev_append_cons:
-"\\<lbrakk>n < length x\\<rbrakk> \\<Longrightarrow> \\<exists>a b c. x = (rev a) @ b # c \\<and> length a = n"
-proof -
-  assume n: "n < length x"
-  hence "n \\<le> length x" by simp
-  hence "\\<exists>a b. x = a @ b \\<and> length a = n" by (rule append_length_n [rulify])
-  thus ?thesis
-  proof elim
-    fix r d assume x: "x = r@d" "length r = n"
-    with n
-    have "\\<exists>b c. d = b#c" by (simp add: neq_Nil_conv)
-    
-    thus ?thesis 
-    proof elim
-      fix b c 
-      assume "d = b#c"
-      with x
-      have "x = (rev (rev r)) @ b # c \\<and> length (rev r) = n" by simp
-      thus ?thesis by blast
-    qed
-  qed
-qed
-
-
-lemma app_mono: 
-"\\<lbrakk>G \\<turnstile> s2 <=s s1; app (i, G, rT, s1)\\<rbrakk> \\<Longrightarrow> app (i, G, rT, s2)";
-proof -
-  assume G:   "G \\<turnstile> s2 <=s s1"
-  assume app: "app (i, G, rT, s1)"
-  
-  show ?thesis
-  proof (cases i)
-    case Load
-    
-    from G
-    have l: "length (snd s1) = length (snd s2)" by (simp add: sup_state_length)
-
-    from G Load app
-    have "G \\<turnstile> snd s2 <=l snd s1" by (auto simp add: sup_state_def)
-    
-    with G Load app l
-    show ?thesis by clarsimp (drule sup_loc_some, simp+)
-  next
-    case Store
-    with G app
-    show ?thesis
-      by - (cases s2,
-            auto dest: map_hd_tl simp add: sup_loc_Cons2 sup_loc_length sup_state_def)
-  next
-    case Bipush
-    thus ?thesis by simp 
-  next
-    case Aconst_null
-    thus ?thesis by simp
-  next
-    case New
-    with app
-    show ?thesis by simp
-  next
-    case Getfield
-    with app G
-    show ?thesis
-      by - (cases s2, clarsimp simp add: sup_state_Cons2, rule widen_trans)
-  next
-    case Putfield
-
-    with app 
-    obtain vT oT ST LT b
-      where s1: "s1 = (vT # oT # ST, LT)" and
-                "field (G, cname) vname = Some (cname, b)" 
-                "is_class G cname" and
-            oT: "G\\<turnstile> oT\\<preceq> (Class cname)" and
-            vT: "G\\<turnstile> vT\\<preceq> b"
-      by simp (elim exE conjE, simp, rule that)
-    moreover
-    from s1 G
-    obtain vT' oT' ST' LT'
-      where s2:  "s2 = (vT' # oT' # ST', LT')" and
-            oT': "G\\<turnstile> oT' \\<preceq> oT" and
-            vT': "G\\<turnstile> vT' \\<preceq> vT"
-      by - (cases s2, simp add: sup_state_Cons2, elim exE conjE, simp, rule that)
-    moreover
-    from vT' vT
-    have "G \\<turnstile> vT' \\<preceq> b" by (rule widen_trans)
-    moreover
-    from oT' oT
-    have "G\\<turnstile> oT' \\<preceq> (Class cname)" by (rule widen_trans)
-    ultimately
-    show ?thesis
-      by (auto simp add: Putfield)
-  next
-    case Checkcast
-    with app G
-    show ?thesis 
-      by - (cases s2, auto intro: widen_RefT2 simp add: sup_state_Cons2)
-  next
-    case Return
-    with app G
-    show ?thesis
-      by - (cases s2, clarsimp simp add: sup_state_Cons2, rule widen_trans)
-  next
-    case Pop
-    with app G
-    show ?thesis
-      by - (cases s2, clarsimp simp add: sup_state_Cons2)
-  next
-    case Dup
-    with app G
-    show ?thesis
-      by - (cases s2, clarsimp simp add: sup_state_Cons2)
-  next
-    case Dup_x1
-    with app G
-    show ?thesis
-      by - (cases s2, clarsimp simp add: sup_state_Cons2)
-  next
-    case Dup_x2
-    with app G
-    show ?thesis
-      by - (cases s2, clarsimp simp add: sup_state_Cons2)
-  next
-    case Swap
-    with app G
-    show ?thesis
-      by - (cases s2, clarsimp simp add: sup_state_Cons2)
-  next
-    case IAdd
-    with app G
-    show ?thesis
-      by - (cases s2, auto simp add: sup_state_Cons2 PrimT_PrimT)
-  next
-    case Goto 
-    with app
-    show ?thesis by simp
-  next
-    case Ifcmpeq
-    with app G
-    show ?thesis
-      by - (cases s2, auto simp add: sup_state_Cons2 PrimT_PrimT widen_RefT2)
-  next
-    case Invoke
-
-    with app
-    obtain apTs X ST LT where
-      s1: "s1 = (rev apTs @ X # ST, LT)" and
-      l:  "length apTs = length list" and
-      C:  "G \\<turnstile> X \\<preceq> Class cname" and
-      w:  "\\<forall>x \\<in> set (zip apTs list). x \\<in> widen G" and
-      m:  "method (G, cname) (mname, list) \\<noteq> None"
-      by (simp del: not_None_eq, elim exE conjE) (rule that)
-
-    obtain apTs' X' ST' LT' where
-      s2: "s2 = (rev apTs' @ X' # ST', LT')" and
-      l': "length apTs' = length list"
-    proof -
-      from l s1 G 
-      have "length list < length (fst s2)" 
-        by (simp add: sup_state_length)
-      hence "\\<exists>a b c. (fst s2) = rev a @ b # c \\<and> length a = length list"
-        by (rule rev_append_cons [rulify])
-      thus ?thesis
-        by -  (cases s2, elim exE conjE, simp, rule that) 
-    qed
-
-    from l l'
-    have "length (rev apTs') = length (rev apTs)" by simp
-    
-    from this s1 s2 G 
-    obtain
-      G': "G \\<turnstile> (apTs',LT') <=s (apTs,LT)" 
-          "G \\<turnstile>  X' \\<preceq> X" "G \\<turnstile> (ST',LT') <=s (ST,LT)"
-      by (simp add: sup_state_rev_fst sup_state_append_fst sup_state_Cons1);
-        
-    with C
-    have C': "G \\<turnstile> X' \\<preceq> Class cname"
-      by - (rule widen_trans, auto)
-    
-    from G'
-    have "G \\<turnstile> map Some apTs' <=l map Some apTs"
-      by (simp add: sup_state_def)
-    also
-    from l w
-    have "G \\<turnstile> map Some apTs <=l map Some list" 
-      by (simp add: all_widen_is_sup_loc)
-    finally
-    have "G \\<turnstile> map Some apTs' <=l map Some list" .
-
-    with l'
-    have w': "\\<forall>x \\<in> set (zip apTs' list). x \\<in> widen G"
-      by (simp add: all_widen_is_sup_loc)
-
-    from Invoke s2 l' w' C' m
-    show ?thesis 
-      by simp blast
-  qed
-qed
-    
-
-lemma step_mono:
-"\\<lbrakk>succs i pc \\<noteq> {}; app (i,G,rT,s2); G \\<turnstile> s1 <=s s2\\<rbrakk> \\<Longrightarrow> 
-  G \\<turnstile> the (step (i,G,s1)) <=s the (step (i,G,s2))"
-proof (cases s1, cases s2) 
-  fix a1 b1 a2 b2
-  assume s: "s1 = (a1,b1)" "s2 = (a2,b2)"
-  assume succs: "succs i pc \\<noteq> {}"
-  assume app2: "app (i,G,rT,s2)"
-  assume G: "G \\<turnstile> s1 <=s s2"
-
-  from G app2
-  have app1: "app (i,G,rT,s1)" by (rule app_mono)
-
-  from app1 app2 succs
-  obtain a1' b1' a2' b2'
-    where step: "step (i,G,s1) = Some (a1',b1')" "step (i,G,s2) = Some (a2',b2')";
-    by (auto dest: app_step_some);
-
-  have "G \\<turnstile> (a1',b1') <=s (a2',b2')"
-  proof (cases i)
-    case Load
-
-    with s app1
-    obtain y where
-       y:  "nat < length b1" "b1 ! nat = Some y" by clarsimp
-
-    from Load s app2
-    obtain y' where
-       y': "nat < length b2" "b2 ! nat = Some y'" by clarsimp
-
-    from G s 
-    have "G \\<turnstile> b1 <=l b2" by (simp add: sup_state_def)
-
-    with y y'
-    have "G \\<turnstile> y \\<preceq> y'" 
-      by - (drule sup_loc_some, simp+)
-    
-    with Load G y y' s step app1 app2 
-    show ?thesis by (clarsimp simp add: sup_state_def)
-  next
-    case Store
-    with G s step app1 app2
-    show ?thesis
-      by (clarsimp simp add: sup_state_def sup_loc_update)
-  next
-    case Bipush
-    with G s step app1 app2
-    show ?thesis
-      by (clarsimp simp add: sup_state_Cons1)
-  next
-    case New
-    with G s step app1 app2
-    show ?thesis
-      by (clarsimp simp add: sup_state_Cons1)
-  next
-    case Aconst_null
-    with G s step app1 app2
-    show ?thesis
-      by (clarsimp simp add: sup_state_Cons1)
-  next
-    case Getfield
-    with G s step app1 app2
-    show ?thesis
-      by (clarsimp simp add: sup_state_Cons1)
-  next
-    case Putfield
-    with G s step app1 app2
-    show ?thesis
-      by (clarsimp simp add: sup_state_Cons1)
-  next
-    case Checkcast
-    with G s step app1 app2
-    show ?thesis
-      by (clarsimp simp add: sup_state_Cons1)
-  next
-    case Invoke
-
-    with s app1
-    obtain a X ST where
-      s1: "s1 = (a @ X # ST, b1)" and
-      l:  "length a = length list"
-      by (simp, elim exE conjE, simp)
-
-    from Invoke s app2
-    obtain a' X' ST' where
-      s2: "s2 = (a' @ X' # ST', b2)" and
-      l': "length a' = length list"
-      by (simp, elim exE conjE, simp)
-
-    from l l'
-    have lr: "length a = length a'" by simp
-      
-    from lr G s s1 s2 
-    have "G \\<turnstile> (ST, b1) <=s (ST', b2)"
-      by (simp add: sup_state_append_fst sup_state_Cons1)
-    
-    moreover
-    
-    from Invoke G s step app1 app2
-    have "b1 = b1' \\<and> b2 = b2'" by simp
-
-    ultimately 
-
-    have "G \\<turnstile> (ST, b1') <=s (ST', b2')" by simp
-
-    with Invoke G s step app1 app2 s1 s2 l l'
-    show ?thesis 
-      by (clarsimp simp add: sup_state_def)
-  next
-    case Return
-    with succs have "False" by simp
-    thus ?thesis by blast
-  next
-    case Pop
-    with G s step app1 app2
-    show ?thesis
-      by (clarsimp simp add: sup_state_Cons1)
-  next
-    case Dup
-    with G s step app1 app2
-    show ?thesis
-      by (clarsimp simp add: sup_state_Cons1)
-  next
-    case Dup_x1
-    with G s step app1 app2
-    show ?thesis
-      by (clarsimp simp add: sup_state_Cons1)
-  next 
-    case Dup_x2
-    with G s step app1 app2
-    show ?thesis
-      by (clarsimp simp add: sup_state_Cons1)
-  next
-    case Swap
-    with G s step app1 app2
-    show ?thesis
-      by (clarsimp simp add: sup_state_Cons1)
-  next
-    case IAdd
-    with G s step app1 app2
-    show ?thesis
-      by (clarsimp simp add: sup_state_Cons1)
-  next
-    case Goto
-    with G s step app1 app2
-    show ?thesis by simp
-  next
-    case Ifcmpeq
-    with G s step app1 app2
-    show ?thesis
-      by (clarsimp simp add: sup_state_Cons1)   
-  qed
-
-  with step
-  show ?thesis by auto  
-qed
-
-
 
 end