src/HOL/MicroJava/J/JTypeSafe.thy
author wenzelm
Tue Aug 07 20:19:55 2007 +0200 (2007-08-07)
changeset 24178 4ff1dc2aa18d
parent 23894 1a4167d761ac
child 27098 d89fb4ee7280
permissions -rw-r--r--
turned Unify flags into configuration options (global only);
     1 (*  Title:      HOL/MicroJava/J/JTypeSafe.thy
     2     ID:         $Id$
     3     Author:     David von Oheimb
     4     Copyright   1999 Technische Universitaet Muenchen
     5 *)
     6 
     7 header {* \isaheader{Type Safety Proof} *}
     8 
     9 theory JTypeSafe imports Eval Conform begin
    10 
    11 declare split_beta [simp]
    12 
    13 lemma NewC_conforms: 
    14 "[|h a = None; (x,(h, l))::\<preceq>(G, lT); wf_prog wf_mb G; is_class G C|] ==>  
    15   (x,(h(a\<mapsto>(C,(init_vars (fields (G,C))))), l))::\<preceq>(G, lT)"
    16 apply( erule conforms_upd_obj)
    17 apply(  unfold oconf_def)
    18 apply(  auto dest!: fields_is_type simp add: wf_prog_ws_prog)
    19 done
    20 
    21 
    22 lemma Cast_conf: 
    23  "[| wf_prog wf_mb G; G,h\<turnstile>v::\<preceq>CC; G\<turnstile>CC \<preceq>? Class D; cast_ok G D h v|]  
    24   ==> G,h\<turnstile>v::\<preceq>Class D"
    25 apply (case_tac "CC")
    26 apply simp
    27 apply (case_tac "ref_ty")
    28 apply (clarsimp simp add: conf_def)
    29 apply simp
    30 apply (ind_cases "G \<turnstile> Class cname \<preceq>? Class D" for cname, simp)
    31 apply (rule conf_widen, assumption+) apply (erule widen.subcls)
    32 
    33 apply (unfold cast_ok_def)
    34 apply( case_tac "v = Null")
    35 apply(  simp)
    36 apply(  clarify)
    37 apply( drule (1) non_npD)
    38 apply( auto intro!: conf_AddrI simp add: obj_ty_def)
    39 done
    40 
    41 
    42 lemma FAcc_type_sound: 
    43 "[| wf_prog wf_mb G; field (G,C) fn = Some (fd, ft); (x,(h,l))::\<preceq>(G,lT);  
    44   x' = None --> G,h\<turnstile>a'::\<preceq> Class C; np a' x' = None |] ==>  
    45   G,h\<turnstile>the (snd (the (h (the_Addr a'))) (fn, fd))::\<preceq>ft"
    46 apply( drule np_NoneD)
    47 apply( erule conjE)
    48 apply( erule (1) notE impE)
    49 apply( drule non_np_objD)
    50 apply   auto
    51 apply( drule conforms_heapD [THEN hconfD])
    52 apply(  assumption)
    53 apply (frule wf_prog_ws_prog)
    54 apply( drule (2) widen_cfs_fields)
    55 apply( drule (1) oconf_objD)
    56 apply auto
    57 done
    58 
    59 lemma FAss_type_sound: 
    60  "[| wf_prog wf_mb G; a = the_Addr a'; (c, fs) = the (h a);  
    61     (G, lT)\<turnstile>v::T'; G\<turnstile>T'\<preceq>ft;  
    62     (G, lT)\<turnstile>aa::Class C;  
    63     field (G,C) fn = Some (fd, ft); h''\<le>|h';  
    64     x' = None --> G,h'\<turnstile>a'::\<preceq> Class C; h'\<le>|h;  
    65     Norm (h, l)::\<preceq>(G, lT); G,h\<turnstile>x::\<preceq>T'; np a' x' = None|] ==>  
    66   h''\<le>|h(a\<mapsto>(c,(fs((fn,fd)\<mapsto>x)))) \<and>   
    67   Norm(h(a\<mapsto>(c,(fs((fn,fd)\<mapsto>x)))), l)::\<preceq>(G, lT) \<and>   
    68   G,h(a\<mapsto>(c,(fs((fn,fd)\<mapsto>x))))\<turnstile>x::\<preceq>T'"
    69 apply( drule np_NoneD)
    70 apply( erule conjE)
    71 apply( simp)
    72 apply( drule non_np_objD)
    73 apply(  assumption)
    74 apply( clarify)
    75 apply( simp (no_asm_use))
    76 apply( frule (1) hext_objD)
    77 apply( erule exE)
    78 apply( simp)
    79 apply( clarify)
    80 apply( rule conjI)
    81 apply(  fast elim: hext_trans hext_upd_obj)
    82 apply( rule conjI)
    83 prefer 2
    84 apply(  fast elim: conf_upd_obj [THEN iffD2])
    85 
    86 apply( rule conforms_upd_obj)
    87 apply   auto
    88 apply(  rule_tac [2] hextI)
    89 prefer 2
    90 apply(  force)
    91 apply( rule oconf_hext)
    92 apply(  erule_tac [2] hext_upd_obj)
    93 apply (frule wf_prog_ws_prog)
    94 apply( drule (2) widen_cfs_fields)
    95 apply( rule oconf_obj [THEN iffD2])
    96 apply( simp (no_asm))
    97 apply( intro strip)
    98 apply( case_tac "(aaa, b) = (fn, fd)")
    99 apply(  simp)
   100 apply(  fast intro: conf_widen)
   101 apply( fast dest: conforms_heapD [THEN hconfD] oconf_objD)
   102 done
   103 
   104 
   105 
   106 lemma Call_lemma2: "[| wf_prog wf_mb G; list_all2 (conf G h) pvs pTs;  
   107    list_all2 (\<lambda>T T'. G\<turnstile>T\<preceq>T') pTs pTs'; wf_mhead G (mn,pTs') rT;  
   108   length pTs' = length pns; distinct pns;  
   109   Ball (set lvars) (split (\<lambda>vn. is_type G))  
   110   |] ==> G,h\<turnstile>init_vars lvars(pns[\<mapsto>]pvs)[::\<preceq>]map_of lvars(pns[\<mapsto>]pTs')"
   111 apply (unfold wf_mhead_def)
   112 apply( clarsimp)
   113 apply( rule lconf_ext_list)
   114 apply(    rule Ball_set_table [THEN lconf_init_vars])
   115 apply(    force)
   116 apply(   assumption)
   117 apply(  assumption)
   118 apply( erule (2) conf_list_gext_widen)
   119 done
   120 
   121 lemma Call_type_sound: 
   122  "[| wf_java_prog G; a' \<noteq> Null; Norm (h, l)::\<preceq>(G, lT); class G C = Some y;  
   123      max_spec G C (mn,pTsa) = {((mda,rTa),pTs')}; xc\<le>|xh; xh\<le>|h;  
   124      list_all2 (conf G h) pvs pTsa; 
   125      (md, rT, pns, lvars, blk, res) =  
   126                the (method (G,fst (the (h (the_Addr a')))) (mn, pTs')); 
   127   \<forall>lT. (np a' None, h, init_vars lvars(pns[\<mapsto>]pvs)(This\<mapsto>a'))::\<preceq>(G, lT) -->  
   128   (G, lT)\<turnstile>blk\<surd> -->  h\<le>|xi \<and>  (xcptb, xi, xl)::\<preceq>(G, lT);  
   129   \<forall>lT. (xcptb,xi, xl)::\<preceq>(G, lT) --> (\<forall>T. (G, lT)\<turnstile>res::T -->  
   130           xi\<le>|h' \<and> (x',h', xj)::\<preceq>(G, lT) \<and> (x' = None --> G,h'\<turnstile>v::\<preceq>T));  
   131   G,xh\<turnstile>a'::\<preceq> Class C
   132   |] ==>  
   133   xc\<le>|h' \<and> (x',(h', l))::\<preceq>(G, lT) \<and>  (x' = None --> G,h'\<turnstile>v::\<preceq>rTa)"
   134 apply( drule max_spec2mheads)
   135 apply( clarify)
   136 apply( drule (2) non_np_objD')
   137 apply( clarsimp)
   138 apply( frule (1) hext_objD)
   139 apply( clarsimp)
   140 apply( drule (3) Call_lemma)
   141 apply( clarsimp simp add: wf_java_mdecl_def)
   142 apply( erule_tac V = "method ?sig ?x = ?y" in thin_rl)
   143 apply( drule spec, erule impE,  erule_tac [2] notE impE, tactic "assume_tac 2")
   144 apply(  rule conformsI)
   145 apply(   erule conforms_heapD)
   146 apply(  rule lconf_ext)
   147 apply(   force elim!: Call_lemma2)
   148 apply(  erule conf_hext, erule (1) conf_obj_AddrI)
   149 apply( erule_tac V = "?E\<turnstile>?blk\<surd>" in thin_rl) 
   150 apply (simp add: conforms_def)
   151 
   152 apply( erule conjE)
   153 apply( drule spec, erule (1) impE)
   154 apply( drule spec, erule (1) impE)
   155 apply( erule_tac V = "?E\<turnstile>res::?rT" in thin_rl)
   156 apply( clarify)
   157 apply( rule conjI)
   158 apply(  fast intro: hext_trans)
   159 apply( rule conjI)
   160 apply(  rule_tac [2] impI)
   161 apply(  erule_tac [2] notE impE, tactic "assume_tac 2")
   162 apply(  frule_tac [2] conf_widen)
   163 apply(    tactic "assume_tac 4")
   164 apply(   tactic "assume_tac 2")
   165 prefer 2
   166 apply(  fast elim!: widen_trans)
   167 apply (rule conforms_xcpt_change)
   168 apply( rule conforms_hext) apply assumption
   169 apply(  erule (1) hext_trans)
   170 apply( erule conforms_heapD)
   171 apply (simp add: conforms_def)
   172 done
   173 
   174 
   175 
   176 declare split_if [split del]
   177 declare fun_upd_apply [simp del]
   178 declare fun_upd_same [simp]
   179 declare wf_prog_ws_prog [simp]
   180 
   181 ML{*
   182 val forward_hyp_tac = ALLGOALS (TRY o (EVERY' [dtac spec, mp_tac,
   183   (mp_tac ORELSE' (dtac spec THEN' mp_tac)), REPEAT o (etac conjE)]))
   184 *}
   185 
   186 declare [[unify_search_bound = 40, unify_trace_bound = 40]]
   187 
   188 
   189 theorem eval_evals_exec_type_sound: 
   190 "wf_java_prog G ==>  
   191   (G\<turnstile>(x,(h,l)) -e  \<succ>v  -> (x', (h',l')) -->  
   192       (\<forall>lT.   (x,(h ,l ))::\<preceq>(G,lT) --> (\<forall>T . (G,lT)\<turnstile>e  :: T -->  
   193       h\<le>|h' \<and> (x',(h',l'))::\<preceq>(G,lT) \<and> (x'=None --> G,h'\<turnstile>v  ::\<preceq> T )))) \<and>  
   194   (G\<turnstile>(x,(h,l)) -es[\<succ>]vs-> (x', (h',l')) -->  
   195       (\<forall>lT.   (x,(h ,l ))::\<preceq>(G,lT) --> (\<forall>Ts. (G,lT)\<turnstile>es[::]Ts -->  
   196       h\<le>|h' \<and> (x',(h',l'))::\<preceq>(G,lT) \<and> (x'=None --> list_all2 (\<lambda>v T. G,h'\<turnstile>v::\<preceq>T) vs Ts)))) \<and>  
   197   (G\<turnstile>(x,(h,l)) -c       -> (x', (h',l')) -->  
   198       (\<forall>lT.   (x,(h ,l ))::\<preceq>(G,lT) -->       (G,lT)\<turnstile>c  \<surd> -->  
   199       h\<le>|h' \<and> (x',(h',l'))::\<preceq>(G,lT)))"
   200 apply( rule eval_evals_exec_induct)
   201 apply( unfold c_hupd_def)
   202 
   203 -- "several simplifications, XcptE, XcptEs, XcptS, Skip, Nil??"
   204 apply( simp_all)
   205 apply( tactic "ALLGOALS strip_tac")
   206 apply( tactic {* ALLGOALS (eresolve_tac [thm "ty_expr.cases", thm "ty_exprs.cases", thm "wt_stmt.cases"]
   207                  THEN_ALL_NEW (full_simp_tac (simpset_of @{theory Conform}))) *})
   208 apply(tactic "ALLGOALS (EVERY' [REPEAT o (etac conjE), REPEAT o hyp_subst_tac])")
   209 
   210 -- "Level 7"
   211 -- "15 NewC"
   212 apply (drule sym)
   213 apply( drule new_AddrD)
   214 apply( erule disjE)
   215 prefer 2
   216 apply(  simp (no_asm_simp))
   217 apply (rule conforms_xcpt_change, assumption) 
   218 apply (simp (no_asm_simp) add: xconf_def)
   219 apply( clarsimp)
   220 apply( rule conjI)
   221 apply(  force elim!: NewC_conforms)
   222 apply( rule conf_obj_AddrI)
   223 apply(  rule_tac [2] rtranclp.rtrancl_refl)
   224 apply( simp (no_asm))
   225 
   226 -- "for Cast"
   227 defer 1
   228 
   229 -- "14 Lit"
   230 apply( erule conf_litval)
   231 
   232 -- "13 BinOp"
   233 apply (tactic "forward_hyp_tac")
   234 apply (tactic "forward_hyp_tac")
   235 apply( rule conjI, erule (1) hext_trans)
   236 apply( erule conjI)
   237 apply( clarsimp)
   238 apply( drule eval_no_xcpt)
   239 apply( simp split add: binop.split)
   240 
   241 -- "12 LAcc"
   242 apply simp
   243 apply( fast elim: conforms_localD [THEN lconfD])
   244 
   245 -- "for FAss"
   246 apply( tactic {* EVERY'[eresolve_tac [thm "ty_expr.cases", thm "ty_exprs.cases", thm "wt_stmt.cases"] 
   247        THEN_ALL_NEW (full_simp_tac @{simpset}), REPEAT o (etac conjE), hyp_subst_tac] 3*})
   248 
   249 -- "for if"
   250 apply( tactic {* (case_tac "the_Bool v" THEN_ALL_NEW
   251   (asm_full_simp_tac @{simpset})) 7*})
   252 
   253 apply (tactic "forward_hyp_tac")
   254 
   255 -- "11+1 if"
   256 prefer 7
   257 apply(  fast intro: hext_trans)
   258 prefer 7
   259 apply(  fast intro: hext_trans)
   260 
   261 -- "10 Expr"
   262 prefer 6
   263 apply( fast)
   264 
   265 -- "9 ???"
   266 apply( simp_all)
   267 
   268 -- "8 Cast"
   269 prefer 8
   270 apply (rule conjI)
   271   apply (fast intro: conforms_xcpt_change xconf_raise_if)
   272 
   273   apply clarify
   274   apply (drule raise_if_NoneD)
   275   apply (clarsimp)
   276   apply (rule Cast_conf)
   277   apply assumption+
   278 
   279 
   280 -- "7 LAss"
   281 apply (fold fun_upd_def)
   282 apply( tactic {* (eresolve_tac [thm "ty_expr.cases", thm "ty_exprs.cases", thm "wt_stmt.cases"] 
   283                  THEN_ALL_NEW (full_simp_tac @{simpset})) 1 *})
   284 apply (intro strip)
   285 apply (case_tac E)
   286 apply (simp)
   287 apply( blast intro: conforms_upd_local conf_widen)
   288 
   289 -- "6 FAcc"
   290 apply (rule conjI) 
   291   apply (simp add: np_def)
   292   apply (fast intro: conforms_xcpt_change xconf_raise_if)
   293 apply( fast elim!: FAcc_type_sound)
   294 
   295 -- "5 While"
   296 prefer 5
   297 apply(erule_tac V = "?a \<longrightarrow> ?b" in thin_rl)
   298 apply(drule (1) ty_expr_ty_exprs_wt_stmt.Loop)
   299 apply(force elim: hext_trans)
   300 
   301 apply (tactic "forward_hyp_tac")
   302 
   303 -- "4 Cond"
   304 prefer 4
   305 apply (case_tac "the_Bool v")
   306 apply simp
   307 apply( fast dest: evals_no_xcpt intro: conf_hext hext_trans)
   308 apply simp
   309 apply( fast dest: evals_no_xcpt intro: conf_hext hext_trans)
   310 
   311 -- "3 ;;"
   312 prefer 3
   313 apply( fast dest: evals_no_xcpt intro: conf_hext hext_trans)
   314 
   315 
   316 -- "2 FAss"
   317 apply (subgoal_tac "(np a' x1, aa, ba) ::\<preceq> (G, lT)")
   318   prefer 2
   319   apply (simp add: np_def)
   320   apply (fast intro: conforms_xcpt_change xconf_raise_if)
   321 apply( case_tac "x2")
   322   -- "x2 = None"
   323   apply (simp)
   324   apply (tactic forward_hyp_tac, clarify)
   325   apply( drule eval_no_xcpt)
   326   apply( erule FAss_type_sound, rule HOL.refl, assumption+)
   327   -- "x2 = Some a"
   328   apply (  simp (no_asm_simp))
   329   apply(  fast intro: hext_trans)
   330 
   331 
   332 apply( tactic prune_params_tac)
   333 -- "Level 52"
   334 
   335 -- "1 Call"
   336 apply( case_tac "x")
   337 prefer 2
   338 apply(  clarsimp)
   339 apply(  drule exec_xcpt)
   340 apply(  simp)
   341 apply(  drule_tac eval_xcpt)
   342 apply(  simp)
   343 apply(  fast elim: hext_trans)
   344 apply( clarify)
   345 apply( drule evals_no_xcpt)
   346 apply( simp)
   347 apply( case_tac "a' = Null")
   348 apply(  simp)
   349 apply(  drule exec_xcpt)
   350 apply(  simp)
   351 apply(  drule eval_xcpt)
   352 apply(  simp)
   353 apply (rule conjI)
   354   apply(  fast elim: hext_trans)
   355   apply (rule conforms_xcpt_change, assumption) 
   356   apply (simp (no_asm_simp) add: xconf_def)
   357 apply(clarsimp)
   358 
   359 apply( drule ty_expr_is_type, simp)
   360 apply(clarsimp)
   361 apply(unfold is_class_def)
   362 apply(clarsimp)
   363 
   364 apply(rule Call_type_sound);
   365 prefer 11
   366 apply blast
   367 apply (simp (no_asm_simp))+ 
   368 
   369 done
   370 
   371 declare [[unify_search_bound = 20, unify_trace_bound = 20]]
   372 
   373 
   374 lemma eval_type_sound: "!!E s s'.  
   375   [| wf_java_prog G; G\<turnstile>(x,s) -e\<succ>v -> (x',s'); (x,s)::\<preceq>E; E\<turnstile>e::T; G=prg E |]  
   376   ==> (x',s')::\<preceq>E \<and> (x'=None --> G,heap s'\<turnstile>v::\<preceq>T) \<and> heap s \<le>| heap s'"
   377 apply (simp (no_asm_simp) only: split_tupled_all)
   378 apply (drule eval_evals_exec_type_sound [THEN conjunct1, THEN mp, THEN spec, THEN mp])
   379 apply auto
   380 done
   381 
   382 
   383 lemma evals_type_sound: "!!E s s'.  
   384   [| wf_java_prog G; G\<turnstile>(x,s) -es[\<succ>]vs -> (x',s'); (x,s)::\<preceq>E; E\<turnstile>es[::]Ts; G=prg E |]  
   385   ==> (x',s')::\<preceq>E \<and> (x'=None --> (list_all2 (\<lambda>v T. G,heap s'\<turnstile>v::\<preceq>T) vs Ts)) \<and> heap s \<le>| heap s'"
   386 apply (simp (no_asm_simp) only: split_tupled_all)
   387 apply (drule eval_evals_exec_type_sound [THEN conjunct2, THEN conjunct1, THEN mp, THEN spec, THEN mp])
   388 apply auto
   389 done
   390 
   391 lemma exec_type_sound: "!!E s s'.  
   392   \<lbrakk> wf_java_prog G; G\<turnstile>(x,s) -s0-> (x',s'); (x,s)::\<preceq>E; E\<turnstile>s0\<surd>; G=prg E \<rbrakk>
   393   \<Longrightarrow> (x',s')::\<preceq>E \<and> heap s \<le>| heap s'"
   394 apply( simp (no_asm_simp) only: split_tupled_all)
   395 apply (drule eval_evals_exec_type_sound 
   396              [THEN conjunct2, THEN conjunct2, THEN mp, THEN spec, THEN mp])
   397 apply   auto
   398 done
   399 
   400 theorem all_methods_understood: 
   401 "[|G=prg E; wf_java_prog G; G\<turnstile>(x,s) -e\<succ>a'-> Norm s'; a' \<noteq> Null; 
   402           (x,s)::\<preceq>E; E\<turnstile>e::Class C; method (G,C) sig \<noteq> None|] ==>  
   403   method (G,fst (the (heap s' (the_Addr a')))) sig \<noteq> None"
   404 apply (frule eval_type_sound, assumption+)
   405 apply(clarsimp)
   406 apply( frule widen_methd)
   407 apply assumption
   408 prefer 2
   409 apply(  fast)
   410 apply( drule non_npD)
   411 apply auto
   412 done
   413 
   414 declare split_beta [simp del]
   415 declare fun_upd_apply [simp]
   416 declare wf_prog_ws_prog [simp del]
   417 
   418 end
   419