diff -r a70b796d9af8 -r a50365d21144 src/HOL/MicroJava/J/State.thy
--- a/src/HOL/MicroJava/J/State.thy	Thu Feb 01 20:51:48 2001 +0100
+++ b/src/HOL/MicroJava/J/State.thy	Thu Feb 01 20:53:13 2001 +0100
@@ -6,34 +6,34 @@
 State for evaluation of Java expressions and statements
 *)
 
-State = TypeRel + Value +
+theory State = TypeRel + Value:
 
 types	fields_
-	= "(vname \\<times> cname \\<leadsto> val)" (* field name, defining class, value *)
+	= "(vname \<times> cname \<leadsto> val)" (* field name, defining class, value *)
 
-        obj = "cname \\<times> fields_"	(* class instance with class name and fields *)
+        obj = "cname \<times> fields_"	(* class instance with class name and fields *)
 
 constdefs
   obj_ty	:: "obj => ty"
  "obj_ty obj  == Class (fst obj)"
 
-  init_vars	:: "('a \\<times> ty) list => ('a \\<leadsto> val)"
- "init_vars	== map_of o map (\\<lambda>(n,T). (n,default_val T))"
+  init_vars	:: "('a \<times> ty) list => ('a \<leadsto> val)"
+ "init_vars	== map_of o map (\<lambda>(n,T). (n,default_val T))"
   
 datatype xcpt		(* exceptions *)
 	= NullPointer
 	| ClassCast
 	| OutOfMemory
 
-types	aheap  = "loc \\<leadsto> obj" (* "heap" used in a translation below *)
-        locals = "vname \\<leadsto> val"	
+types	aheap  = "loc \<leadsto> obj" (* "heap" used in a translation below *)
+        locals = "vname \<leadsto> val"	
 
         state		(* simple state, i.e. variable contents *)
-	= "aheap \\<times> locals"
+	= "aheap \<times> locals"
 	(* heap, local parameter including This *)
 
 	xstate		(* state including exception information *)
-	 = "xcpt option \\<times> state"
+	 = "xcpt option \<times> state"
 
 syntax
   heap		:: "state => aheap"
@@ -47,19 +47,98 @@
 
 constdefs
 
-  new_Addr	:: "aheap => loc \\<times> xcpt option"
- "new_Addr h == SOME (a,x). (h a = None \\<and>  x = None) |  x = Some OutOfMemory"
+  new_Addr	:: "aheap => loc \<times> xcpt option"
+ "new_Addr h == SOME (a,x). (h a = None \<and>  x = None) |  x = Some OutOfMemory"
 
   raise_if	:: "bool => xcpt => xcpt option => xcpt option"
- "raise_if c x xo == if c \\<and>  (xo = None) then Some x else xo"
+ "raise_if c x xo == if c \<and>  (xo = None) then Some x else xo"
 
   np		:: "val => xcpt option => xcpt option"
  "np v == raise_if (v = Null) NullPointer"
 
   c_hupd	:: "aheap => xstate => xstate"
- "c_hupd h'== \\<lambda>(xo,(h,l)). if xo = None then (None,(h',l)) else (xo,(h,l))"
+ "c_hupd h'== \<lambda>(xo,(h,l)). if xo = None then (None,(h',l)) else (xo,(h,l))"
 
   cast_ok	:: "'c prog => cname => aheap => val => bool"
- "cast_ok G C h v == v = Null \\<or> G\\<turnstile>obj_ty (the (h (the_Addr v)))\\<preceq> Class C"
+ "cast_ok G C h v == v = Null \<or> G\<turnstile>obj_ty (the (h (the_Addr v)))\<preceq> Class C"
+
+lemma obj_ty_def2 [simp]: "obj_ty (C,fs) = Class C"
+apply (unfold obj_ty_def)
+apply (simp (no_asm))
+done
+
+lemma new_AddrD: 
+"(a,x) = new_Addr h ==> h a = None \<and> x = None | x = Some OutOfMemory"
+apply (unfold new_Addr_def)
+apply(simp add: Pair_fst_snd_eq Eps_split)
+apply(rule someI)
+apply(rule disjI2)
+apply(rule_tac "r" = "snd (?a,Some OutOfMemory)" in trans)
+apply auto
+done
+
+
+lemma raise_if_True [simp]: "raise_if True x y \<noteq> None"
+apply (unfold raise_if_def)
+apply auto
+done
+
+lemma raise_if_False [simp]: "raise_if False x y = y"
+apply (unfold raise_if_def)
+apply auto
+done
+
+lemma raise_if_Some [simp]: "raise_if c x (Some y) \<noteq> None"
+apply (unfold raise_if_def)
+apply auto
+done
+
+lemma raise_if_Some2 [simp]: "raise_if c z (if x = None then Some y else x) \<noteq> None"
+apply (unfold raise_if_def)
+apply(induct_tac "x")
+apply auto
+done
+
+lemma raise_if_SomeD [rule_format (no_asm)]: 
+  "raise_if c x y = Some z \<longrightarrow> c \<and>  Some z = Some x |  y = Some z"
+apply (unfold raise_if_def)
+apply auto
+done
+
+lemma raise_if_NoneD [rule_format (no_asm)]: "raise_if c x y = None --> \<not> c \<and>  y = None"
+apply (unfold raise_if_def)
+apply auto
+done
+
+lemma np_NoneD [rule_format (no_asm)]: "np a' x' = None --> x' = None \<and>  a' \<noteq> Null"
+apply (unfold np_def raise_if_def)
+apply auto
+done
+
+lemma np_None [rule_format (no_asm), simp]: "a' \<noteq> Null --> np a' x' = x'"
+apply (unfold np_def raise_if_def)
+apply auto
+done
+
+lemma np_Some [simp]: "np a' (Some xc) = Some xc"
+apply (unfold np_def raise_if_def)
+apply auto
+done
+
+lemma np_Null [simp]: "np Null None = Some NullPointer"
+apply (unfold np_def raise_if_def)
+apply auto
+done
+
+lemma np_Addr [simp]: "np (Addr a) None = None"
+apply (unfold np_def raise_if_def)
+apply auto
+done
+
+lemma np_raise_if [simp]: "(np Null (raise_if c xc None)) =  
+  Some (if c then xc else NullPointer)"
+apply (unfold raise_if_def)
+apply (simp (no_asm))
+done
 
 end