author wenzelm
Mon, 25 Feb 2002 20:48:14 +0100
changeset 12937 0c4fd7529467
parent 12925 99131847fb93
child 13337 f75dfc606ac7
permissions -rw-r--r--
clarified syntax of ``long'' statements: fixes/assumes/shows;

(*  Title:      HOL/Bali/Trans.thy
    ID:         $Id$
    Author:     David von Oheimb

Operational transition (small-step) semantics of the 
execution of Java expressions and statements


improvements over Java Specification 1.0 (cf.
* dynamic method lookup does not need to check the return type
* throw raises a NullPointer exception if a null reference is given, and each
  throw of a system exception yield a fresh exception object (was not specified)
* if there is not enough memory even to allocate an OutOfMemory exception,
  evaluation/execution fails, i.e. simply stops (was not specified)

design issues:
* Lit expressions and Skip statements are considered completely evaluated.
* the expr entry in rules is redundant in case of exceptions, but its full
  inclusion helps to make the rule structure independent of exception occurence.
* the rule format is such that the start state may contain an exception.
  ++ faciliates exception handling (to be added later)
  +  symmetry
* the rules are defined carefully in order to be applicable even in not
  type-correct situations (yielding undefined values),
  e.g. the_Adr (Val (Bool b)) = arbitrary.
  ++ fewer rules 
  -  less readable because of auxiliary functions like the_Adr
  Alternative: "defensive" evaluation throwing some InternalError exception
               in case of (impossible, for correct programs) type mismatches

* just simple handling (i.e. propagation) of exceptions so far
* dynamic method lookup does not check return type (should not be necessary)

Trans = Eval +

  texpr_tstmt	:: "prog  (((expr  state)  (expr  state)) +
		            ((stmt  state)  (stmt  state))) set"

syntax (symbols)
  texpr :: "[prog, expr  state, expr  state]  bool "("__ 1 _"[61,82,82] 81)
  tstmt :: "[prog, stmt  state, stmt  state]  bool "("__ 1 _"[61,82,82] 81)
  Ref   :: "loc  expr"


  "Ge_s 1 ex_s'" == "Inl (e_s, ex_s')  texpr_tstmt G"
  "Gs_s 1 s'_s'" == "Inr (s_s, s'_s')  texpr_tstmt G"
  "Ref a" == "Lit (Addr a)"

  sub_expr_expr :: "(expr  expr)  prop"
  "sub_expr_expr ef  (G e s e' s'. G(   e,s) 1 (   e',s') 
				     G(ef e,s) 1 (ef e',s'))"

inductive "texpr_tstmt G" intrs 

(* evaluation of expression *)
  (* cf. 15.5 *)
  XcptE	"v. e  Lit v 
				  G(e,Some xc,s) 1 (Lit arbitrary,Some xc,s)"

 CastXX "PROP sub_expr_expr (Cast T)"

  (* cf. 15.8.1 *)
  NewC	"new_Addr (heap s) = Some (a,x);
	  s' = assign (hupd[ainit_Obj G C]s) (x,s) 
				G(NewC C,None,s) 1 (Ref a,s')"

  (* cf. 15.9.1 *)
(*NewA1	"sub_expr_expr (NewA T)"*)
  NewA1	"G(e,None,s) 1 (e',s') 
			      G(New T[e],None,s) 1 (New T[e'],s')"
  NewA	"i = the_Intg i'; new_Addr (heap s) = Some (a, x);
	  s' = assign (hupd[ainit_Arr T i]s)(raise_if (i<#0) NegArrSize x,s) 
			G(New T[Lit i'],None,s) 1 (Ref a,s')"
  (* cf. 15.15 *)
  Cast1	"G(e,None,s) 1 (e',s') 
			      G(Cast T e,None,s) 1 (Cast T e',s')"
  Cast	"x'= raise_if (\<questiondown>G,sv fits T) ClassCast None 
		        G(Cast T (Lit v),None,s) 1 (Lit v,x',s)"

  (* cf. 15.7.1 *)
(*Lit				"G(Lit v,None,s) 1 (Lit v,None,s)"*)

  (* cf. 15.13.1, 15.2 *)
  LAcc	"v = the (locals s vn) 
			       G(LAcc vn,None,s) 1 (Lit v,None,s)"

  (* cf. 15.25.1 *)
  LAss1	"G(e,None,s) 1 (e',s') 
				 G(f vn:=e,None,s) 1 (vn:=e',s')"
  LAss			    "G(f vn:=Lit v,None,s) 1 (Lit v,None,lupd[vnv]s)"

  (* cf. 15.10.1, 15.2 *)
  FAcc1	"G(e,None,s) 1 (e',s') 
			       G({T}e..fn,None,s) 1 ({T}e'..fn,s')"
  FAcc	"v = the (snd (the_Obj (heap s (the_Addr a'))) (fn,T)) 
			  G({T}Lit a'..fn,None,s) 1 (Lit v,np a' None,s)"

  (* cf. 15.25.1 *)
  FAss1	"G(e1,None,s) 1 (e1',s') 
			  G(f ({T}e1..fn):=e2,None,s) 1 (f({T}e1'..fn):=e2,s')"
  FAss2	"G(e2,np a' None,s) 1 (e2',s') 
		      G(f({T}Lit a'..fn):=e2,None,s) 1 (f({T}Lit a'..fn):=e2',s')"
  FAss	"a = the_Addr a'; (c,fs) = the_Obj (heap s a);
	  s'= assign (hupd[aObj c (fs[(fn,T)v])]s) (None,s) 
		   G(f({T}Lit a'..fn):=Lit v,None,s) 1 (Lit v,s')"

  (* cf. 15.12.1 *)
  AAcc1	"G(e1,None,s) 1 (e1',s') 
				G(e1[e2],None,s) 1 (e1'[e2],s')"
  AAcc2	"G(e2,None,s) 1 (e2',s') 
			    G(Lit a'[e2],None,s) 1 (Lit a'[e2'],s')"
  AAcc	"vo = snd (the_Arr (heap s (the_Addr a'))) (the_Intg i');
	  x' = raise_if (vo = None) IndOutBound (np a' None) 
			G(Lit a'[Lit i'],None,s) 1 (Lit (the vo),x',s)"

  (* cf.,,,, 14.15 *)
  Call1	"G(e,None,s) 1 (e',s') 
			  G({pT}p),None,s) 1 (e'{pT}p),s')"
  Call2	"G(p,None,s) 1 (p',s') 
		     G(Lit a'{pT}p),None,s) 1 (Lit a'{pT}p'),s')"
  Call	"a = the_Addr a'; (md,(pn,rT),lvars,blk,res) = 
 			   the (cmethd G (fst (the_Obj (h a))) (mn,pT)) 
	    G(Lit a'{pT}Lit pv),None,(h,l)) 1 
      (Body blk res l,np a' x,(h,init_vals lvars[Thisa'][Supera'][pnpv]))"
  Body1	"G(s0,None,s) 1 (s0',s') 
		   G(Body s0    e      l,None,s) 1 (Body s0'  e  l,s')"
  Body2	"G(e ,None,s) 1 (e',s') 
		   G(Body Skip  e      l,None,s) 1 (Body Skip e' l,s')"
  Body		  "G(Body Skip (Lit v) l,None,s) 1 (Lit v,None,(heap s,l))"

(* execution of statements *)

  (* cf. 14.1 *)
  XcptS	"s0  Skip 
				 G(s0,Some xc,s) 1 (Skip,Some xc,s)"

  (* cf. 14.5 *)
(*Skip	 			 "G(Skip,None,s) 1 (Skip,None,s)"*)

  (* cf. 14.2 *)
  Comp1	"G(s1,None,s) 1 (s1',s') 
			       G(s1;; s2,None,s) 1 (s1';; s2,s')"
  Comp			    "G(Skip;; s2,None,s) 1 (s2,None,s)"

  (* cf. 14.7 *)
  Expr1	"G(e ,None,s) 1 (e',s') 
				G(Expr e,None,s) 1 (Expr e',s')"
  Expr			 "G(Expr (Lit v),None,s) 1 (Skip,None,s)"

  (* cf. 14.8.2 *)
  If1	"G(e ,None,s) 1 (e',s') 
		      G(If(e) s1 Else s2,None,s) 1 (If(e') s1 Else s2,s')"
  If		 "G(If(Lit v) s1 Else s2,None,s) 1 
		    (if the_Bool v then s1 else s2,None,s)"

  (* cf. 14.10, 14.10.1 *)
  Loop			  "G(While(e) s0,None,s) 1 
			     (If(e) (s0;; While(e) s0) Else Skip,None,s)"
  con_defs "[sub_expr_expr_def]"