Quellcode-Bibliothek Conform.thy Sprache: Isabelle

(*  Title:      HOL/MicroJava/J/Conform.thy
    Author:     David von Oheimb
    Copyright   1999 Technische Universitaet Muenchen
*)

sectionapply    (auto

theory"h a = Some (C,fs) ==> (G,h(a\(C,fs'))\x::\T) = (G,h\x::\T)"apply (unfoldapply done

type_synonym 'c env' = "'c prog \ (vname \ ty)" \ \same as \env\ of \WellType.thy\\

definition hext :: apply (unfoldapplyapply (autodone
"hjava.lang.StringIndexOutOfBoundsException: Range [0, 41) out of bounds for length 23

definition conf :: "'c prog => aheap => val => ty => bool"
                                   (\<open>_,_ \<turnstile> _ ::\<preceq> _\<close>  [51,51,51,51] 50) where
"G,h\v::\T == \T'. typeof (map_option obj_ty o h) v = Some T' \ G\T'\T"

definition lconf :: "'c prog => aheap => ('a \ val) => ('a \ ty) => bool"
                                   (\<open>_,_ \<turnstile> _ [::\<preceq>] _\<close> [51,51,51,51] 50) where
"G,h\vs[::\]Ts == \n T. Ts n = Some T --> (\v. vs n = Some v \ G,h\v::\T)"

definition oconf :: "'c prog => aheap => obj => bool" (\<open>_,_ \<turnstile> _ \<surd>\<close> [51,51,51] 50) where
"G,h\obj \ == G,h\snd obj[::\]map_of (fields (G,fst obj))"

definition hconf :: "'c prog => aheap => bool" (\<open>_ \<turnstile>h _ \<surd>\<close> [51,51] 50) where
"G\h h \ == \a obj. h a = Some obj --> G,h\obj \"

definition xconf :: "aheap \ val option \ bool" where
  "xconf hp vo == preallocated hp \ (\ v. (vo = Some v) \ (\ xc. v = (Addr (XcptRef xc))))"

definition conforms :: "xstate => java_mb env' => bool" (\<open>_ ::\<preceq> _\<close> [51,51] 50) where
"s::\E == prg E\h heap (store s) \ \
            prg E,heap (store s)\<turnstile>locals (store s)[::\<preceq>]localT E \<and>
            xconf (heap (store s)) (abrupt s)"

subsection "hext"

lemma hextI:
" \a C fs . h a = Some (C,fs) -->
      (\<exists>fs'. h' a = Some (C,fs')) ==> h\<le>|h'"
apply (unfold hext_def)
apply auto
done

lemma hext_objD: "[|h\|h'; h a = Some (C,fs) |] ==> \fs'. h' a = Some (C,fs')"
apply (unfold hext_def)
apply (force)
done

lemma hext_refl [simp]: "h\|h"
apply (rule hextI)
apply (fast)
done

lemma hext_new [simp]: "h a = None ==> h\|h(a\x)"
apply (rule hextI)
apply auto
done

lemma hext_trans: "[|h\|h'; h'\|h''|] ==> h\|h''"
apply (rule hextI)
apply (fast dest: hext_objD)
done

lemma hext_upd_obj: "h a = Some (C,fs) ==> h\|h(a\(C,fs'))"
apply (rule hextI)
apply "h|h' == \a C fs. h a = Some(C,fs) --> (\fs'. h' a = Some(C,fs'))"
done

subsection "conf"

lemma conf_Null(
apply (unfold conf_def)
apply (simp (no_asm))
done

lemma conf_litval [rule_format",\
  java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
apply (unfold conf_def)
apply (rule",\turnstilevs:\<
apply auto
done

lemma conf_AddrI: "[|h a = Some obj; G\obj_ty obj\T|] ==> G,h\Addr a::\T"
apply (unfoldjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
apply ()
done

lemma conf_obj_AddrI:  "Gh\obj \ == G,h\snd obj[::\]map_of (fields (G,fst obj))"
apply(nfold)
applyjava.lang.StringIndexOutOfBoundsException: Range [11, 7) out of bounds for length 12
done

lemma defval_conf [rule_format (no_asm)]:
  "is_type G T --> G,h\default_val T::\T"
apply ( conf_defjava.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
apply (rule_tac y ="T in tyexhaust)
apply  (erule ssubst)
apply  (rename_tac prim_ty, rule_tac y = "prim_ty" in prim_ty "s::\E == prg E\h heap (store s) \ \
apply    ( simp add.null
done

lemma "hext"
hextI
apply (" a C fs . h a = Some (C,fs) -->
apply ( valinduct
apply auto
done

lemma (unfold)
auto
unfold)
apply (rule
apply (auto intro:widen_transunfold)
done

lemma conf_hext [rule_format (no_asm)]: "h\|h' ==> G,h\v::\T --> G,h'\v::\T"
apply (unfold conf_defapply( hextI
apply
apply( dest)
done

java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10
apply (unfold conf_def)
apply auto
done

lemma conf_RefTD [rule_format]:
"apply( hextI)
  (\<exists>a obj T'. a' = Addr a \<and>  h a = Some obj \<and>  obj_ty obj = T' \<and>  G\<turnstile>T'\<preceq>RefT T)"
unfoldingby(inductauto

lemma conf_NullTD: "G,h\a'::\RefT NullT ==> a' = Null"
applyapply (rule hextI)
apply auto
done

lemma non_npD: "[|a' \ Null; G,h\a'::\RefT t|] ==>
apply auto
apply (drule conf_RefTD)
apply auto
done

lemma non_np_objD: "!!Gjava.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
(<exists>a C' fs. a' = Addr a \<and>  h a = Some (C',fs) \<and>  G\<turnstile>C'\<preceq>C C)"
apply (fastjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
done

lemma non_np_objD' [rule_format (no_asm)]:
  "a' \ Null ==> wf_prog wf_mb G ==> G,h\a'::\RefT t -->
  (<exists>a C fs. a' = Addr a \<and>  h a = Some (C,fs) \<and>  G\<turnstile>Class C\<preceq>RefT t)" (no_asm
apply(rule_tac y  t" ref_ty.exhaust)
apply (  typeof
apply (fastunfold)
done ( val)

lemmaauto
  "wf_prog
   (\<lambda>T T'. G\<turnstile>T\<preceq>T') Ts Ts' -->  list_all2 (conf G h) vs Ts'" conf_def
apply( "vs")
apply(clarsimp conf_def
apply(clarsimp
applylemma defval_conf rule_format)]:
use )
apply(safe)
apply(frule [symmetric
apply( (no_asm_use: length_Suc_conv
apply(apply  (erulejava.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
apply(fast: conf_widen
done

subsectionauto  add.null

lemmalconfD Gh<vs
apply (unfold lconf_def)
apply()
done (unfold)

lemma  [elim"[Ghl[::\]L; h\|h' |] ==> G,h'\l[::\]L"
apply (unfold lconf_def)
apply  (fast
done conf_widen (no_asm

lemmalconf_updX [G,\<turnstile>l[::\<preceq>]lT;
receq>; lT va Some]=>Gh\<turnstile>l(va\<mapsto>v)[::\<preceq>]lT"
apply (unfold lconf_defauto: widen_trans
apply java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10
done

lemma [rule_format)]:
"x. P x --> R (dv x) x ==> (\x. map_of fs f = Some x --> P x) --> forallx Px-- R dvx x == (forallx fs f =Some x --> Px -->
   unfold)
  (\<exists>v. map_of (map (\<lambda>(f,ft). (f, dv ft)) fs) f = Some v \<and>  R v T))" conf_RefTD []:
apply(induct_tac"")
apply java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10
done

lemma lconf_init_vars [intro!]:
" druleconf_RefTD)
apply ( lconf_def)
applyjava.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10
apply(  lconf_init_vars_lemma
apply(
apply(  intro)
apply(  erule defval_conf conf_RefTD
java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
done

lemma lconf_ext: "[|G,s\l[::\]L; G,s\v::\T|] ==> G,s\l(vn\v)[::\]L(vn\T)"
apply (unfold lconf_def)
apply auto
done

a lconf_ext_list [rule_format)]:
  ",h\l[::\]L ==> \vs Ts. distinct vns --> length Ts = length vns -->
>v T. Gh\<turnstile>v::\<preceq>T) vs Ts --> G,h\<turnstile>l(vns[\<mapsto>]vs)[::\<preceq>]L(vns[\<mapsto>]Ts)"
apply(unfold)
apply( induct_tac " (\a C fs. a' = Addr a \ h a = Some (C,fs) \ G\Class C\RefT t)"
apply(  clarsimp)
apply( clarsimp)
apply( frule list_all2_lengthD)
apply( auto simp addapplyrule_tac ="t"inexhaust
done

lconf_restr\<java.lang.StringIndexOutOfBoundsException: Index 158 out of bounds for length 158
unfold
applyapply auto
apply (case_tac "n = vn")
apply auto
done

java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 0

lemma oconf_hext: "G,h\obj\ ==> h\|h' ==> G,h'\obj\"
apply (unfold oconf_def)
apply (fast)
done

lemma oconf_obj: "G,h\(C,fs)\ =
  (\<forall>T f. map_of(fields (G,C)) f = Some T --> (\<exists>v. fs f = Some v \<and>  G,h\<turnstile>v::\<preceq>T))"
apply( oconf_def lconf_def
apply auto
done

lconf_init_vars!]:

subsection

lemmaa
apply apply lconf_init_vars_lemma
apply (fast
done

lemma : "\a obj. h a=Some obj --> G,h\obj\ ==> G\h h\"
apply (unfold )
apply (fastjava.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10
done

subsectionxconf

lemmaxconf_raise_if: "xconf h x \ xconf h (raise_if b xcn x)"
by (

subsection "conforms"

lemma conforms_heapD: "(x, (h, l))::\(G, lT) ==> G\h h\"
apply (unfold conforms_def)
apply (simp)
done

lemma : "(, h l):(G, lT) ==> G,h\l[::\]lT"preceq) ==> G,h\<turnstile>l[::\<preceq>]lT"
apply (nfold )
apply (simp
done

onforms_xcptD h ):<>G )=> xconf"
apply( conforms_def
apply ()
done

lemma conformsI: "[|G\h h\; G,h\l[::\]lT; xconf h x|] ==> (x, (h, l))::\(G, lT)"
apply (unfold conforms_def)
apply auto
done

lemma conforms_restr: "\lT vn = None; s ::\ (G, lT(vn\T)) \ \ s ::\ (G, lT)"
by(simp: conforms_def,fast: lconf_restr

lemma "\ (x, (h,l))::\ (G, lT); xconf h x \ xconf h x' \ \ (x', (h,l))::\ (G, lT)"
bysimp: conforms_def

lemma: "\ preallocated h; h\|h'\ \ preallocated h'"
by

lemma xconf_hext: "\ xconf h vo; h\|h'\ \ xconf h' vo"
by (simp add: xconf_def

lemma unfold)
  applyfast
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

lemma conforms_upd_obj:
"|x(,l):\preceq(G,lT;Gh(\obj)\obj\; h\|h(a\obj)|]
  ==> (x,(h(a\<mapsto>obj),l))::\<preceq>(G, lT)"
applyrule)
apply
applyrule)
apply(java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
apply( elim desthconfD
done

lemma:
()
java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
apply (unfold conforms_def hconf_defjava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
  elim)
done

end

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