(* Title: HOL/Bali/Trans.thy
ID: $Id$
Author: David von Oheimb
License: GPL (GNU GENERAL PUBLIC LICENSE)
Operational transition (small-step) semantics of the
execution of Java expressions and statements
PRELIMINARY!!!!!!!!
improvements over Java Specification 1.0 (cf. 15.11.4.4):
* 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
simplifications:
* just simple handling (i.e. propagation) of exceptions so far
* dynamic method lookup does not check return type (should not be necessary)
*)
Trans = Eval +
consts
texpr_tstmt :: "prog ë (((expr ò state) ò (expr ò state)) +
((stmt ò state) ò (stmt ò state))) set"
syntax (symbols)
texpr :: "[prog, expr ò state, expr ò state] ë bool "("_É_ è1 _"[61,82,82] 81)
tstmt :: "[prog, stmt ò state, stmt ò state] ë bool "("_É_ í1 _"[61,82,82] 81)
Ref :: "loc ë expr"
translations
"GÉe_s è1 ex_s'" == "Inl (e_s, ex_s') Î texpr_tstmt G"
"GÉs_s í1 s'_s'" == "Inr (s_s, s'_s') Î texpr_tstmt G"
"Ref a" == "Lit (Addr a)"
constdefs
sub_expr_expr :: "(expr ë expr) ë prop"
"sub_expr_expr ef Ú (ÄG e s e' s'. GÉ( e,s) è1 ( e',s') êë
GÉ(ef e,s) è1 (ef e',s'))"
inductive "texpr_tstmt G" intrs
(* evaluation of expression *)
(* cf. 15.5 *)
XcptE "ËÂv. e Û Lit vÌ êë
GÉ(e,Some xc,s) è1 (Lit arbitrary,Some xc,s)"
CastXX "PROP sub_expr_expr (Cast T)"
(*
(* cf. 15.8.1 *)
NewC "Ënew_Addr (heap s) = Some (a,x);
s' = assign (hupd[aíinit_Obj G C]s) (x,s)Ì êë
GÉ(NewC C,None,s) è1 (Ref a,s')"
(* cf. 15.9.1 *)
(*NewA1 "sub_expr_expr (NewA T)"*)
NewA1 "ËGÉ(e,None,s) è1 (e',s')Ì êë
GÉ(New T[e],None,s) è1 (New T[e'],s')"
NewA "Ëi = the_Intg i'; new_Addr (heap s) = Some (a, x);
s' = assign (hupd[aíinit_Arr T i]s)(raise_if (i<#0) NegArrSize x,s)Ì êë
GÉ(New T[Lit i'],None,s) è1 (Ref a,s')"
(* cf. 15.15 *)
Cast1 "ËGÉ(e,None,s) è1 (e',s')Ì êë
GÉ(Cast T e,None,s) è1 (Cast T e',s')"
Cast "Ëx'= raise_if (\<questiondown>G,sÉv fits T) ClassCast NoneÌ êë
GÉ(Cast T (Lit v),None,s) è1 (Lit v,x',s)"
(* cf. 15.7.1 *)
(*Lit "GÉ(Lit v,None,s) è1 (Lit v,None,s)"*)
(* cf. 15.13.1, 15.2 *)
LAcc "Ëv = the (locals s vn)Ì êë
GÉ(LAcc vn,None,s) è1 (Lit v,None,s)"
(* cf. 15.25.1 *)
LAss1 "ËGÉ(e,None,s) è1 (e',s')Ì êë
GÉ(f vn:=e,None,s) è1 (vn:=e',s')"
LAss "GÉ(f vn:=Lit v,None,s) è1 (Lit v,None,lupd[vnív]s)"
(* cf. 15.10.1, 15.2 *)
FAcc1 "ËGÉ(e,None,s) è1 (e',s')Ì êë
GÉ({T}e..fn,None,s) è1 ({T}e'..fn,s')"
FAcc "Ëv = the (snd (the_Obj (heap s (the_Addr a'))) (fn,T))Ì êë
GÉ({T}Lit a'..fn,None,s) è1 (Lit v,np a' None,s)"
(* cf. 15.25.1 *)
FAss1 "ËGÉ(e1,None,s) è1 (e1',s')Ì êë
GÉ(f ({T}e1..fn):=e2,None,s) è1 (f({T}e1'..fn):=e2,s')"
FAss2 "ËGÉ(e2,np a' None,s) è1 (e2',s')Ì êë
GÉ(f({T}Lit a'..fn):=e2,None,s) è1 (f({T}Lit a'..fn):=e2',s')"
FAss "Ëa = the_Addr a'; (c,fs) = the_Obj (heap s a);
s'= assign (hupd[aíObj c (fs[(fn,T)ív])]s) (None,s)Ì êë
GÉ(f({T}Lit a'..fn):=Lit v,None,s) è1 (Lit v,s')"
(* cf. 15.12.1 *)
AAcc1 "ËGÉ(e1,None,s) è1 (e1',s')Ì êë
GÉ(e1[e2],None,s) è1 (e1'[e2],s')"
AAcc2 "ËGÉ(e2,None,s) è1 (e2',s')Ì êë
GÉ(Lit a'[e2],None,s) è1 (Lit a'[e2'],s')"
AAcc "Ëvo = snd (the_Arr (heap s (the_Addr a'))) (the_Intg i');
x' = raise_if (vo = None) IndOutBound (np a' None)Ì êë
GÉ(Lit a'[Lit i'],None,s) è1 (Lit (the vo),x',s)"
(* cf. 15.11.4.1, 15.11.4.2, 15.11.4.4, 15.11.4.5, 14.15 *)
Call1 "ËGÉ(e,None,s) è1 (e',s')Ì êë
GÉ(e..mn({pT}p),None,s) è1 (e'..mn({pT}p),s')"
Call2 "ËGÉ(p,None,s) è1 (p',s')Ì êë
GÉ(Lit a'..mn({pT}p),None,s) è1 (Lit a'..mn({pT}p'),s')"
Call "Ëa = the_Addr a'; (md,(pn,rT),lvars,blk,res) =
the (cmethd G (fst (the_Obj (h a))) (mn,pT))Ì êë
GÉ(Lit a'..mn({pT}Lit pv),None,(h,l)) è1
(Body blk res l,np a' x,(h,init_vals lvars[Thisía'][Supería'][pnípv]))"
Body1 "ËGÉ(s0,None,s) í1 (s0',s')Ì êë
GÉ(Body s0 e l,None,s) è1 (Body s0' e l,s')"
Body2 "ËGÉ(e ,None,s) è1 (e',s')Ì êë
GÉ(Body Skip e l,None,s) è1 (Body Skip e' l,s')"
Body "GÉ(Body Skip (Lit v) l,None,s) è1 (Lit v,None,(heap s,l))"
(* execution of statements *)
(* cf. 14.1 *)
XcptS "Ës0 Û SkipÌ êë
GÉ(s0,Some xc,s) í1 (Skip,Some xc,s)"
(* cf. 14.5 *)
(*Skip "GÉ(Skip,None,s) í1 (Skip,None,s)"*)
(* cf. 14.2 *)
Comp1 "ËGÉ(s1,None,s) í1 (s1',s')Ì êë
GÉ(s1;; s2,None,s) í1 (s1';; s2,s')"
Comp "GÉ(Skip;; s2,None,s) í1 (s2,None,s)"
(* cf. 14.7 *)
Expr1 "ËGÉ(e ,None,s) è1 (e',s')Ì êë
GÉ(Expr e,None,s) í1 (Expr e',s')"
Expr "GÉ(Expr (Lit v),None,s) í1 (Skip,None,s)"
(* cf. 14.8.2 *)
If1 "ËGÉ(e ,None,s) è1 (e',s')Ì êë
GÉ(If(e) s1 Else s2,None,s) í1 (If(e') s1 Else s2,s')"
If "GÉ(If(Lit v) s1 Else s2,None,s) í1
(if the_Bool v then s1 else s2,None,s)"
(* cf. 14.10, 14.10.1 *)
Loop "GÉ(While(e) s0,None,s) í1
(If(e) (s0;; While(e) s0) Else Skip,None,s)"
*)
con_defs "[sub_expr_expr_def]"
end