(* 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 :: "java_mb prog \\<Rightarrow> (xstate \\<times> expr \\<times> val \\<times> xstate) set"
evals :: "java_mb prog \\<Rightarrow> (xstate \\<times> expr list \\<times> val list \\<times> xstate) set"
exec :: "java_mb prog \\<Rightarrow> (xstate \\<times> stmt \\<times> xstate) set"
syntax
eval :: "[java_mb prog,xstate,expr,val,xstate] \\<Rightarrow> bool "("_\\<turnstile>_ -_\\<succ>_\\<rightarrow> _"[51,82,82,82,82]81)
evals:: "[java_mb prog,xstate,expr list,
val list,xstate] \\<Rightarrow> bool "("_\\<turnstile>_ -_[\\<succ>]_\\<rightarrow> _"[51,82,51,51,82]81)
exec :: "[java_mb 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"
BinOp "\\<lbrakk>G\\<turnstile>Norm s -e1\\<succ>v1\\<rightarrow> s1;
G\\<turnstile>s1 -e1\\<succ>v2\\<rightarrow> s2;
v = (case bop of Eq \\<Rightarrow> Bool (v1 = v2)
| Add \\<Rightarrow> Intg (the_Intg v1 + the_Intg v2))\\<rbrakk> \\<Longrightarrow>
G\\<turnstile>Norm s -BinOp bop e1 e2\\<succ>v\\<rightarrow> s2"
(* 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 (method (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