src/HOL/MicroJava/J/JTypeSafe.thy
author kleing
Sun Dec 16 00:18:17 2001 +0100 (2001-12-16)
changeset 12517 360e3215f029
parent 11644 3dfde687f0d7
child 12888 f6c1e7306c40
permissions -rw-r--r--
exception merge, cleanup, tuned
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(*  Title:      HOL/MicroJava/J/JTypeSafe.thy
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    ID:         $Id$
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    Author:     David von Oheimb
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    Copyright   1999 Technische Universitaet Muenchen
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*)
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header "Type Safety Proof"
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theory JTypeSafe = Eval + Conform:
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declare split_beta [simp]
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lemma NewC_conforms: 
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"[|h a = None; (h, l)::\<preceq>(G, lT); wf_prog wf_mb G; is_class G C|] ==>  
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  (h(a\<mapsto>(C,(init_vars (fields (G,C))))), l)::\<preceq>(G, lT)"
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apply( erule conforms_upd_obj)
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apply(  unfold oconf_def)
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apply(  auto dest!: fields_is_type)
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done
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lemma Cast_conf: 
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 "[| wf_prog wf_mb G; G,h\<turnstile>v::\<preceq>Class C; G\<turnstile>C\<preceq>? D; cast_ok G D h v|]  
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  ==> G,h\<turnstile>v::\<preceq>Class D" 
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apply (unfold cast_ok_def)
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apply( case_tac "v = Null")
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apply(  simp)
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apply(  drule widen_RefT)
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apply(  clarify)
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apply( drule (1) non_npD)
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apply( auto intro!: conf_AddrI simp add: obj_ty_def)
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done
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lemma FAcc_type_sound: 
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"[| wf_prog wf_mb G; field (G,C) fn = Some (fd, ft); (h,l)::\<preceq>(G,lT);  
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  x' = None --> G,h\<turnstile>a'::\<preceq> Class C; np a' x' = None |] ==>  
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  G,h\<turnstile>the (snd (the (h (the_Addr a'))) (fn, fd))::\<preceq>ft"
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apply( drule np_NoneD)
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apply( erule conjE)
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apply( erule (1) notE impE)
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apply( drule non_np_objD)
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apply   auto
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apply( drule conforms_heapD [THEN hconfD])
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apply(  assumption)
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apply( drule (2) widen_cfs_fields)
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apply( drule (1) oconf_objD)
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apply auto
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done
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lemma FAss_type_sound: 
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 "[| wf_prog wf_mb G; a = the_Addr a'; (c, fs) = the (h a);  
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    (G, lT)\<turnstile>v::T'; G\<turnstile>T'\<preceq>ft;  
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    (G, lT)\<turnstile>aa::Class C;  
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    field (G,C) fn = Some (fd, ft); h''\<le>|h';  
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    x' = None --> G,h'\<turnstile>a'::\<preceq> Class C; h'\<le>|h;  
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    (h, l)::\<preceq>(G, lT); G,h\<turnstile>x::\<preceq>T'; np a' x' = None|] ==>  
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  h''\<le>|h(a\<mapsto>(c,(fs((fn,fd)\<mapsto>x)))) \<and>   
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  (h(a\<mapsto>(c,(fs((fn,fd)\<mapsto>x)))), l)::\<preceq>(G, lT) \<and>   
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  G,h(a\<mapsto>(c,(fs((fn,fd)\<mapsto>x))))\<turnstile>x::\<preceq>T'"
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apply( drule np_NoneD)
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apply( erule conjE)
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apply( simp)
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apply( drule non_np_objD)
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apply(   assumption)
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apply(  force)
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apply( clarify)
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apply( simp (no_asm_use))
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apply( frule (1) hext_objD)
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apply( erule exE)
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apply( simp)
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apply( clarify)
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apply( rule conjI)
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apply(  fast elim: hext_trans hext_upd_obj)
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apply( rule conjI)
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prefer 2
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apply(  fast elim: conf_upd_obj [THEN iffD2])
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apply( rule conforms_upd_obj)
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apply   auto
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apply(  rule_tac [2] hextI)
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prefer 2
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apply(  force)
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apply( rule oconf_hext)
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apply(  erule_tac [2] hext_upd_obj)
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apply( drule (2) widen_cfs_fields)
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apply( rule oconf_obj [THEN iffD2])
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apply( simp (no_asm))
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apply( intro strip)
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apply( case_tac "(aaa, b) = (fn, fd)")
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apply(  simp)
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apply(  fast intro: conf_widen)
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apply( fast dest: conforms_heapD [THEN hconfD] oconf_objD)
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done
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lemma Call_lemma2: "[| wf_prog wf_mb G; list_all2 (conf G h) pvs pTs;  
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   list_all2 (\<lambda>T T'. G\<turnstile>T\<preceq>T') pTs pTs'; wf_mhead G (mn,pTs') rT;  
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  length pTs' = length pns; nodups pns;  
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  Ball (set lvars) (split (\<lambda>vn. is_type G))  
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  |] ==> G,h\<turnstile>init_vars lvars(pns[\<mapsto>]pvs)[::\<preceq>]map_of lvars(pns[\<mapsto>]pTs')"
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apply (unfold wf_mhead_def)
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apply( clarsimp)
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apply( rule lconf_ext_list)
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apply(    rule Ball_set_table [THEN lconf_init_vars])
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apply(    force)
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apply(   assumption)
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apply(  assumption)
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apply( erule (2) conf_list_gext_widen)
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done
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lemma Call_type_sound: 
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 "[| wf_java_prog G; a' \<noteq> Null; (h, l)::\<preceq>(G, lT); class G C = Some y;  
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     max_spec G C (mn,pTsa) = {((mda,rTa),pTs')}; xc\<le>|xh; xh\<le>|h;  
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     list_all2 (conf G h) pvs pTsa; 
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     (md, rT, pns, lvars, blk, res) =  
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               the (method (G,fst (the (h (the_Addr a')))) (mn, pTs')); 
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  \<forall>lT. (h, init_vars lvars(pns[\<mapsto>]pvs)(This\<mapsto>a'))::\<preceq>(G, lT) -->  
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  (G, lT)\<turnstile>blk\<surd> -->  h\<le>|xi \<and>  (xi, xl)::\<preceq>(G, lT);  
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  \<forall>lT. (xi, xl)::\<preceq>(G, lT) --> (\<forall>T. (G, lT)\<turnstile>res::T -->  
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          xi\<le>|h' \<and> (h', xj)::\<preceq>(G, lT) \<and> (x' = None --> G,h'\<turnstile>v::\<preceq>T));  
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  G,xh\<turnstile>a'::\<preceq> Class C |] ==>  
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  xc\<le>|h' \<and> (h', l)::\<preceq>(G, lT) \<and>  (x' = None --> G,h'\<turnstile>v::\<preceq>rTa)"
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apply( drule max_spec2mheads)
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apply( clarify)
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apply( drule (2) non_np_objD')
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apply(  clarsimp)
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apply( clarsimp)
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apply( frule (1) hext_objD)
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apply( clarsimp)
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apply( drule (3) Call_lemma)
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apply( clarsimp simp add: wf_java_mdecl_def)
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apply( erule_tac V = "method ?sig ?x = ?y" in thin_rl)
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apply( drule spec, erule impE)
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apply(  erule_tac [2] notE impE, tactic "assume_tac 2")
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apply(  rule conformsI)
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apply(   erule conforms_heapD)
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apply(  rule lconf_ext)
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apply(   force elim!: Call_lemma2)
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apply(  erule conf_hext, erule (1) conf_obj_AddrI)
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apply( erule_tac V = "?E\<turnstile>?blk\<surd>" in thin_rl)
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apply( erule conjE)
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apply( drule spec, erule (1) impE)
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apply( drule spec, erule (1) impE)
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apply( erule_tac V = "?E\<turnstile>res::?rT" in thin_rl)
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apply( clarify)
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apply( rule conjI)
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apply(  fast intro: hext_trans)
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apply( rule conjI)
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apply(  rule_tac [2] impI)
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apply(  erule_tac [2] notE impE, tactic "assume_tac 2")
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apply(  frule_tac [2] conf_widen)
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apply(    tactic "assume_tac 4")
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apply(   tactic "assume_tac 2")
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prefer 2
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apply(  fast elim!: widen_trans)
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apply( erule conforms_hext)
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apply(  erule (1) hext_trans)
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apply( erule conforms_heapD)
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done
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declare split_if [split del]
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declare fun_upd_apply [simp del]
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declare fun_upd_same [simp]
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ML{*
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val forward_hyp_tac = ALLGOALS (TRY o (EVERY' [dtac spec, mp_tac,
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  (mp_tac ORELSE' (dtac spec THEN' mp_tac)), REPEAT o (etac conjE)]))
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*}
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ML{*
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Unify.search_bound := 40;
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Unify.trace_bound  := 40
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*}
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theorem eval_evals_exec_type_sound: 
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"wf_java_prog G ==>  
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  (G\<turnstile>(x,(h,l)) -e  \<succ>v  -> (x', (h',l')) -->  
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      (\<forall>lT.   (h ,l )::\<preceq>(G,lT) --> (\<forall>T . (G,lT)\<turnstile>e  :: T -->  
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      h\<le>|h' \<and> (h',l')::\<preceq>(G,lT) \<and> (x'=None --> G,h'\<turnstile>v  ::\<preceq> T )))) \<and>  
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  (G\<turnstile>(x,(h,l)) -es[\<succ>]vs-> (x', (h',l')) -->  
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      (\<forall>lT.   (h ,l )::\<preceq>(G,lT) --> (\<forall>Ts. (G,lT)\<turnstile>es[::]Ts -->  
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      h\<le>|h' \<and> (h',l')::\<preceq>(G,lT) \<and> (x'=None --> list_all2 (\<lambda>v T. G,h'\<turnstile>v::\<preceq>T) vs Ts)))) \<and>  
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  (G\<turnstile>(x,(h,l)) -c       -> (x', (h',l')) -->  
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      (\<forall>lT.   (h ,l )::\<preceq>(G,lT) -->       (G,lT)\<turnstile>c  \<surd> -->  
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      h\<le>|h' \<and> (h',l')::\<preceq>(G,lT)))"
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apply( rule eval_evals_exec_induct)
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apply( unfold c_hupd_def)
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-- "several simplifications, XcptE, XcptEs, XcptS, Skip, Nil??"
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apply( simp_all)
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apply( tactic "ALLGOALS strip_tac")
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apply( tactic {* ALLGOALS (eresolve_tac (thms "ty_expr_ty_exprs_wt_stmt.elims") 
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                 THEN_ALL_NEW Full_simp_tac) *})
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apply(tactic "ALLGOALS (EVERY' [REPEAT o (etac conjE), REPEAT o hyp_subst_tac])")
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-- "Level 7"
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-- "15 NewC"
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apply( drule new_AddrD)
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apply( erule disjE)
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prefer 2
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apply(  simp (no_asm_simp))
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apply( clarsimp)
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apply( rule conjI)
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apply(  force elim!: NewC_conforms)
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apply( rule conf_obj_AddrI)
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apply(  rule_tac [2] rtrancl_refl)
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apply( simp (no_asm))
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-- "for Cast"
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defer 1
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-- "14 Lit"
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apply( erule conf_litval)
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-- "13 BinOp"
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apply (tactic "forward_hyp_tac")
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apply (tactic "forward_hyp_tac")
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apply( rule conjI, erule (1) hext_trans)
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apply( erule conjI)
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apply( clarsimp)
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apply( drule eval_no_xcpt)
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apply( simp split add: binop.split)
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-- "12 LAcc"
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apply( fast elim: conforms_localD [THEN lconfD])
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-- "for FAss"
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apply( tactic {* EVERY'[eresolve_tac (thms "ty_expr_ty_exprs_wt_stmt.elims") 
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       THEN_ALL_NEW Full_simp_tac, REPEAT o (etac conjE), hyp_subst_tac] 3*})
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-- "for if"
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apply( tactic {* (case_tac "the_Bool v" THEN_ALL_NEW Asm_full_simp_tac) 8*})
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apply (tactic "forward_hyp_tac")
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-- "11+1 if"
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prefer 8
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apply(  fast intro: hext_trans)
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prefer 8
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apply(  fast intro: hext_trans)
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-- "10 Expr"
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prefer 6
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apply( fast)
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-- "9 ???"
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apply( simp_all)
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-- "8 Cast"
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prefer 8
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apply (rule impI)
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apply (drule raise_if_NoneD)
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apply (clarsimp)
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apply (fast elim: Cast_conf)
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-- "7 LAss"
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apply (fold fun_upd_def)
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apply( tactic {* (eresolve_tac (thms "ty_expr_ty_exprs_wt_stmt.elims") 
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                 THEN_ALL_NEW Full_simp_tac) 1 *})
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apply( blast intro: conforms_upd_local conf_widen)
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-- "6 FAcc"
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apply( fast elim!: FAcc_type_sound)
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-- "5 While"
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prefer 5
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apply(erule_tac V = "?a \<longrightarrow> ?b" in thin_rl)
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apply(drule (1) ty_expr_ty_exprs_wt_stmt.Loop)
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apply(force elim: hext_trans)
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apply (tactic "forward_hyp_tac")
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-- "4 Cons"
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prefer 3
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apply( fast dest: evals_no_xcpt intro: conf_hext hext_trans)
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-- "3 ;;"
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prefer 3
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apply( fast intro: hext_trans)
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-- "2 FAss"
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apply( case_tac "x2 = None")
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prefer 2
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apply(  simp (no_asm_simp))
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apply(  fast intro: hext_trans)
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apply( simp)
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apply( drule eval_no_xcpt)
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apply( erule FAss_type_sound, rule HOL.refl, assumption+)
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apply( tactic prune_params_tac)
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-- "Level 52"
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-- "1 Call"
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apply( case_tac "x")
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prefer 2
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apply(  clarsimp)
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apply(  drule exec_xcpt)
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apply(  simp)
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apply(  drule_tac eval_xcpt)
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apply(  simp)
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apply(  fast elim: hext_trans)
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apply( clarify)
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apply( drule evals_no_xcpt)
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apply( simp)
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apply( case_tac "a' = Null")
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apply(  simp)
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apply(  drule exec_xcpt)
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apply(  simp)
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apply(  drule eval_xcpt)
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apply(  simp)
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apply(  fast elim: hext_trans)
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apply( drule (1) ty_expr_is_type)
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apply(clarsimp)
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apply(unfold is_class_def)
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apply(clarsimp)
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apply(rule Call_type_sound);
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prefer 11
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apply blast
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apply (simp (no_asm_simp))+ 
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done
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ML{*
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Unify.search_bound := 20;
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Unify.trace_bound  := 20
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*}
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lemma eval_type_sound: "!!E s s'.  
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  [| G=prg E; wf_java_prog G; G\<turnstile>(x,s) -e\<succ>v -> (x',s'); s::\<preceq>E; E\<turnstile>e::T |]  
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  ==> s'::\<preceq>E \<and> (x'=None --> G,heap s'\<turnstile>v::\<preceq>T)"
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apply( simp (no_asm_simp) only: split_tupled_all)
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apply (drule eval_evals_exec_type_sound 
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             [THEN conjunct1, THEN mp, THEN spec, THEN mp])
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apply auto
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done
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lemma exec_type_sound: "!!E s s'.  
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  [| G=prg E; wf_java_prog G; G\<turnstile>(x,s) -s0-> (x',s'); s::\<preceq>E; E\<turnstile>s0\<surd> |]  
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  ==> s'::\<preceq>E"
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apply( simp (no_asm_simp) only: split_tupled_all)
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apply (drule eval_evals_exec_type_sound 
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             [THEN conjunct2, THEN conjunct2, THEN mp, THEN spec, THEN mp])
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apply   auto
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done
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theorem all_methods_understood: 
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"[|G=prg E; wf_java_prog G; G\<turnstile>(x,s) -e\<succ>a'-> Norm s'; a' \<noteq> Null; 
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          s::\<preceq>E; E\<turnstile>e::Class C; method (G,C) sig \<noteq> None|] ==>  
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  method (G,fst (the (heap s' (the_Addr a')))) sig \<noteq> None"
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apply( drule (4) eval_type_sound)
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apply(clarsimp)
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apply( frule widen_methd)
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apply(   assumption)
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prefer 2
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apply(  fast)
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apply( drule non_npD)
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apply auto
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done
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declare split_beta [simp del]
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declare fun_upd_apply [simp]
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end
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