(*  Title:      HOL/MicroJava/J/Eval.thy

     ID:         $Id$

     Author:     David von Oheimb

     Copyright   1999 Technische Universitaet Muenchen

 Operational evaluation (big-step) semantics of the 

 execution of Java expressions and statements

 *)

 Eval = State + 

 consts

   eval  :: "javam prog \\<Rightarrow> (xstate \\<times> expr      \\<times> val      \\<times> xstate) set"

   evals :: "javam prog \\<Rightarrow> (xstate \\<times> expr list \\<times> val list \\<times> xstate) set"

   exec  :: "javam prog \\<Rightarrow> (xstate \\<times> stmt                 \\<times> xstate) set"

 syntax

   eval :: "[javam prog,xstate,expr,val,xstate] \\<Rightarrow> bool "("_\\<turnstile>_ -_\\<succ>_\\<rightarrow> _"[51,82,82,82,82]81)

   evals:: "[javam prog,xstate,expr list,

 	                      val list,xstate] \\<Rightarrow> bool "("_\\<turnstile>_ -_[\\<succ>]_\\<rightarrow> _"[51,82,51,51,82]81)

   exec :: "[javam prog,xstate,stmt,    xstate] \\<Rightarrow> bool "("_\\<turnstile>_ -_\\<rightarrow> _"  [51,82,82,   82]81)

 translations

   "G\\<turnstile>s -e \\<succ> v\\<rightarrow> (x,s')" == "(s, e, v, _args x s') \\<in> eval  G"

   "G\\<turnstile>s -e \\<succ> v\\<rightarrow>    s' " == "(s, e, v,         s') \\<in> eval  G"

   "G\\<turnstile>s -e[\\<succ>]v\\<rightarrow> (x,s')" == "(s, e, v, _args x s') \\<in> evals G"

   "G\\<turnstile>s -e[\\<succ>]v\\<rightarrow>    s' " == "(s, e, v,         s') \\<in> evals G"

   "G\\<turnstile>s -c     \\<rightarrow> (x,s')" == "(s, c,    _args x s') \\<in> exec  G"

   "G\\<turnstile>s -c     \\<rightarrow>    s' " == "(s, c,            s') \\<in> exec  G"

 inductive "eval G" "evals G" "exec G" intrs

 (* evaluation of expressions *)

   (* cf. 15.5 *)

   XcptE				  "G\\<turnstile>(Some xc,s) -e\\<succ>arbitrary\\<rightarrow> (Some xc,s)"

   (* cf. 15.8.1 *)

   NewC	"\\<lbrakk>h = heap s; (a,x) = new_Addr h;

 	  h'= h(a\\<mapsto>(C,init_vars (fields (G,C))))\\<rbrakk> \\<Longrightarrow>

 				   G\\<turnstile>Norm s -NewC C\\<succ>Addr a\\<rightarrow> c_hupd h' (x,s)"

   (* cf. 15.15 *)

   Cast	"\\<lbrakk>G\\<turnstile>Norm s0 -e\\<succ>v\\<rightarrow> (x1,s1);

 	  x2=raise_if (\\<not> cast_ok G T (heap s1) v) ClassCast x1\\<rbrakk> \\<Longrightarrow>

 			        G\\<turnstile>Norm s0 -Cast T e\\<succ>v\\<rightarrow> (x2,s1)"

   (* cf. 15.7.1 *)

   Lit				   "G\\<turnstile>Norm s -Lit v\\<succ>v\\<rightarrow> Norm s"

   (* cf. 15.13.1, 15.2 *)

   LAcc				  "G\\<turnstile>Norm s -LAcc v\\<succ>the (locals s v)\\<rightarrow> Norm s"

   (* cf. 15.25.1 *)

   LAss  "\\<lbrakk>G\\<turnstile>Norm s -e\\<succ>v\\<rightarrow>  (x,(h,l));

 	  l' = (if x = None then l(va\\<mapsto>v) else l)\\<rbrakk> \\<Longrightarrow>

 				   G\\<turnstile>Norm s -va\\<Colon>=e\\<succ>v\\<rightarrow> (x,(h,l'))"

   (* cf. 15.10.1, 15.2 *)

   FAcc	"\\<lbrakk>G\\<turnstile>Norm s0 -e\\<succ>a'\\<rightarrow> (x1,s1); 

 	  v = the (snd (the (heap s1 (the_Addr a'))) (fn,T))\\<rbrakk> \\<Longrightarrow>

 				 G\\<turnstile>Norm s0 -{T}e..fn\\<succ>v\\<rightarrow> (np a' x1,s1)"

   (* cf. 15.25.1 *)

   FAss  "\\<lbrakk>G\\<turnstile>     Norm s0  -e1\\<succ>a'\\<rightarrow> (x1,s1); a = the_Addr a';

 	  G\\<turnstile>(np a' x1,s1) -e2\\<succ>v \\<rightarrow> (x2,s2);

 	  h = heap s2; (c,fs) = the (h a);

 	  h' = h(a\\<mapsto>(c,(fs((fn,T)\\<mapsto>v))))\\<rbrakk> \\<Longrightarrow>

 			  G\\<turnstile>Norm s0 -{T}e1..fn\\<in>=e2\\<succ>v\\<rightarrow> c_hupd h' (x2,s2)"

   (* cf. 15.11.4.1, 15.11.4.2, 15.11.4.4, 15.11.4.5, 14.15 *)

   Call	"\\<lbrakk>G\\<turnstile>Norm s0 -e\\<succ>a'\\<rightarrow> s1; a = the_Addr a';

 	   G\\<turnstile>s1 -ps[\\<succ>]pvs\\<rightarrow> (x,(h,l)); dynT = fst (the (h a));

 	   (md,rT,pns,lvars,blk,res) = the (cmethd (G,dynT) (mn,pTs));

 	   G\\<turnstile>(np a' x,(h,(init_vars lvars)(pns[\\<mapsto>]pvs)(This\\<mapsto>a'))) -blk\\<rightarrow> s3;

 	   G\\<turnstile>     s3 -res\\<succ>v \\<rightarrow> (x4,s4)\\<rbrakk> \\<Longrightarrow>

 			    G\\<turnstile>Norm s0 -e..mn({pTs}ps)\\<succ>v\\<rightarrow> (x4,(heap s4,l))"

 (* evaluation of expression lists *)

   (* cf. 15.5 *)

   XcptEs			  "G\\<turnstile>(Some xc,s) -e[\\<succ>]arbitrary\\<rightarrow> (Some xc,s)"

   (* cf. 15.11.??? *)

   Nil

 				    "G\\<turnstile>Norm s0 -[][\\<succ>][]\\<rightarrow> Norm s0"

   (* cf. 15.6.4 *)

   Cons	"\\<lbrakk>G\\<turnstile>Norm s0 -e  \\<succ> v \\<rightarrow> s1;

            G\\<turnstile>     s1 -es[\\<succ>]vs\\<rightarrow> s2\\<rbrakk> \\<Longrightarrow>

 				   G\\<turnstile>Norm s0 -e#es[\\<succ>]v#vs\\<rightarrow> s2"

 (* execution of statements *)

   (* cf. 14.1 *)

   XcptS				 "G\\<turnstile>(Some xc,s) -s0\\<rightarrow> (Some xc,s)"

   (* cf. 14.5 *)

   Skip	 			    "G\\<turnstile>Norm s -Skip\\<rightarrow> Norm s"

   (* cf. 14.7 *)

   Expr	"\\<lbrakk>G\\<turnstile>Norm s0 -e\\<succ>v\\<rightarrow> s1\\<rbrakk> \\<Longrightarrow>

 				  G\\<turnstile>Norm s0 -Expr e\\<rightarrow> s1"

   (* cf. 14.2 *)

   Comp	"\\<lbrakk>G\\<turnstile>Norm s0 -s \\<rightarrow> s1;

 	  G\\<turnstile>     s1 -t \\<rightarrow> s2\\<rbrakk> \\<Longrightarrow>

 				 G\\<turnstile>Norm s0 -(s;; t)\\<rightarrow> s2"

   (* cf. 14.8.2 *)

   Cond	"\\<lbrakk>G\\<turnstile>Norm s0  -e \\<succ>v\\<rightarrow> s1;

 	  G\\<turnstile>     s1 -(if  the_Bool v then s else t)\\<rightarrow> s2\\<rbrakk> \\<Longrightarrow>

 		        G\\<turnstile>Norm s0 -(If(e) s Else t)\\<rightarrow> s2"

   (* cf. 14.10, 14.10.1 *)

   Loop	"\\<lbrakk>G\\<turnstile>Norm s0 -(If(e) (s;; While(e) s) Else Skip)\\<rightarrow> s1\\<rbrakk> \\<Longrightarrow>

 			    G\\<turnstile>Norm s0 -(While(e) s)\\<rightarrow> s1"

 end