src/HOL/MicroJava/J/Eval.thy

splitted Loop rule

(*  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 + WellType +
consts
  eval  :: "java_mb prog => (xstate \\<times> expr      \\<times> val      \\<times> xstate) set"
  evals :: "java_mb prog => (xstate \\<times> expr list \\<times> val list \\<times> xstate) set"
  exec  :: "java_mb prog => (xstate \\<times> stmt                 \\<times> xstate) set"

syntax
  eval :: "[java_mb prog,xstate,expr,val,xstate] => bool "
          ("_ \\<turnstile> _ -_\\<succ>_-> _" [51,82,60,82,82] 81)
  evals:: "[java_mb prog,xstate,expr list,
                        val list,xstate] => bool "
          ("_ \\<turnstile> _ -_[\\<succ>]_-> _" [51,82,60,51,82] 81)
  exec :: "[java_mb prog,xstate,stmt,    xstate] => bool "
          ("_ \\<turnstile> _ -_-> _" [51,82,60,82] 81)

syntax (HTML)
  eval :: "[java_mb prog,xstate,expr,val,xstate] => bool "
          ("_ |- _ -_>_-> _" [51,82,60,82,82] 81)
  evals:: "[java_mb prog,xstate,expr list,
                        val list,xstate] => bool "
          ("_ |- _ -_[>]_-> _" [51,82,60,51,82] 81)
  exec :: "[java_mb prog,xstate,stmt,    xstate] => bool "
          ("_ |- _ -_-> _" [51,82,60,82] 81)


translations
  "G\\<turnstile>s -e \\<succ> v-> (x,s')" <= "(s, e, v, x, s') \\<in> eval  G"
  "G\\<turnstile>s -e \\<succ> v->    s' " == "(s, e, v,    s') \\<in> eval  G"
  "G\\<turnstile>s -e[\\<succ>]v-> (x,s')" <= "(s, e, v, x, s') \\<in> evals G"
  "G\\<turnstile>s -e[\\<succ>]v->    s' " == "(s, e, v,    s') \\<in> evals G"
  "G\\<turnstile>s -c    -> (x,s')" <= "(s, c, x, s') \\<in> exec G"
  "G\\<turnstile>s -c    ->    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-> (Some xc,s)"

  (* cf. 15.8.1 *)
  NewC  "[| h = heap s; (a,x) = new_Addr h;
            h'= h(a\\<mapsto>(C,init_vars (fields (G,C)))) |] ==>
         G\\<turnstile>Norm s -NewC C\\<succ>Addr a-> c_hupd h' (x,s)"

  (* cf. 15.15 *)
  Cast  "[| G\\<turnstile>Norm s0 -e\\<succ>v-> (x1,s1);
            x2 = raise_if (\\<not> cast_ok G C (heap s1) v) ClassCast x1 |] ==>
         G\\<turnstile>Norm s0 -Cast C e\\<succ>v-> (x2,s1)"

  (* cf. 15.7.1 *)
  Lit   "G\\<turnstile>Norm s -Lit v\\<succ>v-> Norm s"

  BinOp "[| G\\<turnstile>Norm s -e1\\<succ>v1-> s1;
            G\\<turnstile>s1     -e2\\<succ>v2-> s2;
            v = (case bop of Eq  => Bool (v1 = v2)
                           | Add => Intg (the_Intg v1 + the_Intg v2)) |] ==>
         G\\<turnstile>Norm s -BinOp bop e1 e2\\<succ>v-> s2"

  (* cf. 15.13.1, 15.2 *)
  LAcc  "G\\<turnstile>Norm s -LAcc v\\<succ>the (locals s v)-> Norm s"

  (* cf. 15.25.1 *)
  LAss  "[| G\\<turnstile>Norm s -e\\<succ>v-> (x,(h,l));
            l' = (if x = None then l(va\\<mapsto>v) else l) |] ==>
         G\\<turnstile>Norm s -va::=e\\<succ>v-> (x,(h,l'))"


  (* cf. 15.10.1, 15.2 *)
  FAcc  "[| G\\<turnstile>Norm s0 -e\\<succ>a'-> (x1,s1); 
            v = the (snd (the (heap s1 (the_Addr a'))) (fn,T)) |] ==>
         G\\<turnstile>Norm s0 -{T}e..fn\\<succ>v-> (np a' x1,s1)"

  (* cf. 15.25.1 *)
  FAss  "[| G\\<turnstile>     Norm s0  -e1\\<succ>a'-> (x1,s1); a = the_Addr a';
            G\\<turnstile>(np a' x1,s1) -e2\\<succ>v -> (x2,s2);
            h  = heap s2; (c,fs) = the (h a);
            h' = h(a\\<mapsto>(c,(fs((fn,T)\\<mapsto>v)))) |] ==>
         G\\<turnstile>Norm s0 -{T}e1..fn:=e2\\<succ>v-> 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  "[| G\\<turnstile>Norm s0 -e\\<succ>a'-> s1; a = the_Addr a';
            G\\<turnstile>s1 -ps[\\<succ>]pvs-> (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-> s3;
            G\\<turnstile> s3 -res\\<succ>v -> (x4,s4) |] ==>
         G\\<turnstile>Norm s0 -{C}e..mn({pTs}ps)\\<succ>v-> (x4,(heap s4,l))"


(* evaluation of expression lists *)

  (* cf. 15.5 *)
  XcptEs "G\\<turnstile>(Some xc,s) -e[\\<succ>]arbitrary-> (Some xc,s)"

  (* cf. 15.11.??? *)
  Nil   "G\\<turnstile>Norm s0 -[][\\<succ>][]-> Norm s0"

  (* cf. 15.6.4 *)
  Cons  "[| G\\<turnstile>Norm s0 -e  \\<succ> v -> s1;
            G\\<turnstile>     s1 -es[\\<succ>]vs-> s2 |] ==>
         G\\<turnstile>Norm s0 -e#es[\\<succ>]v#vs-> s2"

(* execution of statements *)

  (* cf. 14.1 *)
  XcptS "G\\<turnstile>(Some xc,s) -c-> (Some xc,s)"

  (* cf. 14.5 *)
  Skip  "G\\<turnstile>Norm s -Skip-> Norm s"

  (* cf. 14.7 *)
  Expr  "[| G\\<turnstile>Norm s0 -e\\<succ>v-> s1 |] ==>
         G\\<turnstile>Norm s0 -Expr e-> s1"

  (* cf. 14.2 *)
  Comp  "[| G\\<turnstile>Norm s0 -c1-> s1;
            G\\<turnstile>     s1 -c2-> s2|] ==>
         G\\<turnstile>Norm s0 -c1;; c2-> s2"

  (* cf. 14.8.2 *)
  Cond  "[| G\\<turnstile>Norm s0  -e\\<succ>v-> s1;
            G\\<turnstile> s1 -(if the_Bool v then c1 else c2)-> s2|] ==>
         G\\<turnstile>Norm s0 -If(e) c1 Else c2-> s2"

  (* cf. 14.10, 14.10.1 *)
  LoopF "[| G\\<turnstile>Norm s0 -e\\<succ>v-> s1; \\<not>the_Bool v |] ==>
         G\\<turnstile>Norm s0 -While(e) c-> s1"
  LoopT "[| G\\<turnstile>Norm s0 -e\\<succ>v-> s1;  the_Bool v;
	    G\\<turnstile>s1 -c-> s2; G\\<turnstile>s2 -While(e) c-> s3 |] ==>
         G\\<turnstile>Norm s0 -While(e) c-> s3"

monos
  if_def2

end