author | oheimb |
Mon, 03 Jan 2000 14:07:08 +0100 | |
changeset 8082 | 381716a86fcb |
parent 8034 | 6fc37b5c5e98 |
child 8085 | dce06445aafd |
permissions | -rw-r--r-- |
8011 | 1 |
(* Title: HOL/MicroJava/J/JTypeSafe.ML |
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ID: $Id$ |
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Author: David von Oheimb |
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4 |
Copyright 1999 Technische Universitaet Muenchen |
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Type safety proof |
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*) |
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8 |
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Addsimps [split_beta]; |
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8082 | 11 |
Goal "\\<lbrakk>h a = None; (h, l)\\<Colon>\\<preceq>(G, lT); wf_prog wf_mb G; is_class G C\\<rbrakk> \\<Longrightarrow> \ |
8011 | 12 |
\ (h(a\\<mapsto>(C,(init_vars (fields (G,C))))), l)\\<Colon>\\<preceq>(G, lT)"; |
13 |
by( etac conforms_upd_obj 1); |
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by( rewtac oconf_def); |
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by( auto_tac (claset() addSDs [is_type_fields, map_of_SomeD], simpset())); |
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qed "NewC_conforms"; |
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Goalw [cast_ok_def] |
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8082 | 19 |
"\\<lbrakk> wf_prog wf_mb G; G,h\\<turnstile>v\\<Colon>\\<preceq>Tb; G\\<turnstile>Tb\\<Rightarrow>? T'; cast_ok G T' h v\\<rbrakk> \ |
8011 | 20 |
\ \\<Longrightarrow> G,h\\<turnstile>v\\<Colon>\\<preceq>T'"; |
21 |
by( case_tac1 "v = Null" 1); |
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by( Asm_full_simp_tac 1); |
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by( dtac widen_RefT 1); |
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by( Clarify_tac 1); |
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by( forward_tac [cast_RefT] 1); |
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by( Clarify_tac 1); |
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by( rtac widen.null 1); |
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by( case_tac1 "\\<exists>pt. T' = PrimT pt" 1); |
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by( strip_tac1 1); |
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by( dtac cast_PrimT2 1); |
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by( etac conf_widen 1); |
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by( atac 1); |
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by( atac 1); |
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by( Asm_full_simp_tac 1); |
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by( dtac (non_PrimT RS iffD1) 1); |
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by( strip_tac1 1); |
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by( forward_tac [cast_RefT2] 1); |
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by( strip_tac1 1); |
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by( dtac non_npD 1); |
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by( atac 1); |
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by( rewrite_goals_tac [the_Addr_def,obj_ty_def]); |
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by Auto_tac ; |
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by( ALLGOALS (rtac conf_AddrI)); |
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by Auto_tac; |
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qed "Cast_conf"; |
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8082 | 47 |
Goal "\\<lbrakk> wf_prog wf_mb G; field (G,C) fn = Some (fd, ft); (h,l)\\<Colon>\\<preceq>(G,lT); \ |
8011 | 48 |
\ x' = None \\<longrightarrow> G,h\\<turnstile>a'\\<Colon>\\<preceq>Class C; np a' x' = None \\<rbrakk> \\<Longrightarrow> \ |
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\ G,h\\<turnstile>the (snd (the (h (the_Addr a'))) (fn, fd))\\<Colon>\\<preceq>ft"; |
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by( dtac np_NoneD 1); |
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by( etac conjE 1); |
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by( mp_tac 1); |
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by( dtac non_np_objD 1); |
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by Auto_tac; |
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by( dtac (conforms_heapD RS hconfD) 1); |
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by( atac 1); |
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by( dtac widen_cfs_fields 1); |
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by( atac 1); |
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by( atac 1); |
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by( dtac oconf_objD 1); |
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by( atac 1); |
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by Auto_tac; |
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8082 | 63 |
qed "FAcc_type_sound"; |
8011 | 64 |
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Goal |
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8082 | 66 |
"\\<lbrakk> wf_prog wf_mb G; a = the_Addr a'; (c, fs) = the (h a); \ |
8011 | 67 |
\ (G, lT)\\<turnstile>v\\<Colon>T'; G\\<turnstile>T'\\<preceq>ft; \ |
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\ (G, lT)\\<turnstile>aa\\<Colon>Class C; \ |
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8034
6fc37b5c5e98
Various little changes like cmethd -> method and cfield -> field.
nipkow
parents:
8011
diff
changeset
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69 |
\ field (G,C) fn = Some (fd, ft); h''\\<le>|h'; \ |
8011 | 70 |
\ x' = None \\<longrightarrow> G,h'\\<turnstile>a'\\<Colon>\\<preceq>Class C; h'\\<le>|h; \ |
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\ (h, l)\\<Colon>\\<preceq>(G, lT); G,h\\<turnstile>x\\<Colon>\\<preceq>T'; np a' x' = None\\<rbrakk> \\<Longrightarrow> \ |
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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)\\<Colon>\\<preceq>(G, lT) \\<and> \ |
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\ G,h(a\\<mapsto>(c,(fs((fn,fd)\\<mapsto>x))))\\<turnstile>x\\<Colon>\\<preceq>T'"; |
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by( dtac np_NoneD 1); |
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by( etac conjE 1); |
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by( Asm_full_simp_tac 1); |
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by( dtac non_np_objD 1); |
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by( atac 1); |
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by( SELECT_GOAL Auto_tac 1); |
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by( strip_tac1 1); |
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by( Full_simp_tac 1); |
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by( EVERY [forward_tac [hext_objD] 1, atac 1]); |
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by( etac exE 1); |
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by( Asm_full_simp_tac 1); |
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by( strip_tac1 1); |
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by( rtac conjI 1); |
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by( fast_tac (HOL_cs addEs [hext_trans, hext_upd_obj]) 1); |
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by( rtac conjI 1); |
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by( fast_tac (HOL_cs addEs [conf_upd_obj RS iffD2]) 2); |
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by( rtac conforms_upd_obj 1); |
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by Auto_tac; |
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by( rtac hextI 2); |
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by( Force_tac 2); |
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by( rtac oconf_hext 1); |
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by( etac hext_upd_obj 2); |
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by( dtac widen_cfs_fields 1); |
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by( atac 1); |
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by( atac 1); |
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by( rtac (oconf_obj RS iffD2) 1); |
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by( Simp_tac 1); |
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by( strip_tac 1); |
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by( case_tac1 "(aaa, b) = (fn, fd)" 1); |
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by( Asm_full_simp_tac 1); |
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by( fast_tac (HOL_cs addIs [conf_widen]) 1); |
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by( fast_tac (HOL_cs addDs [conforms_heapD RS hconfD, oconf_objD]) 1); |
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8082 | 108 |
qed "FAss_type_sound"; |
8011 | 109 |
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8082 | 110 |
Goalw [wf_mhead_def] "\\<lbrakk> wf_prog wf_mb G; list_all2 (conf G h) pvs pTs; \ |
8011 | 111 |
\ 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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\ \\<rbrakk> \\<Longrightarrow> G,h\\<turnstile>init_vars lvars(pns[\\<mapsto>]pvs)[\\<Colon>\\<preceq>]map_of lvars(pns[\\<mapsto>]pTs')"; |
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by( Clarsimp_tac 1); |
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by( rtac lconf_ext_list 1); |
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by( rtac (Ball_set_table RS lconf_init_vars) 1); |
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by( Force_tac 1); |
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by( atac 1); |
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by( atac 1); |
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by( (etac conf_list_gext_widen THEN_ALL_NEW atac) 1); |
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qed "Call_lemma2"; |
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Goalw [wf_java_prog_def] |
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"\\<lbrakk> wf_java_prog G; a' \\<noteq> Null; (h, l)\\<Colon>\\<preceq>(G, lT); \ |
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\ max_spec G T (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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8034
6fc37b5c5e98
Various little changes like cmethd -> method and cfield -> field.
nipkow
parents:
8011
diff
changeset
|
129 |
\ the (method (G,fst (the (h (the_Addr a')))) (mn, pTs'));\ |
8011 | 130 |
\ \\<forall>lT. (h, init_vars lvars(pns[\\<mapsto>]pvs)(This\\<mapsto>a'))\\<Colon>\\<preceq>(G, lT) \\<longrightarrow> \ |
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\ (G, lT)\\<turnstile>blk\\<surd> \\<longrightarrow> h\\<le>|xi \\<and> (xi, xl)\\<Colon>\\<preceq>(G, lT); \ |
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\ \\<forall>lT. (xi, xl)\\<Colon>\\<preceq>(G, lT) \\<longrightarrow> (\\<forall>T. (G, lT)\\<turnstile>res\\<Colon>T \\<longrightarrow> \ |
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\ xi\\<le>|h' \\<and> (h', xj)\\<Colon>\\<preceq>(G, lT) \\<and> (x' = None \\<longrightarrow> G,h'\\<turnstile>v\\<Colon>\\<preceq>T)); \ |
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\ G,xh\\<turnstile>a'\\<Colon>\\<preceq>RefT T \\<rbrakk> \\<Longrightarrow> \ |
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\ xc\\<le>|h' \\<and> (h', l)\\<Colon>\\<preceq>(G, lT) \\<and> (x' = None \\<longrightarrow> G,h'\\<turnstile>v\\<Colon>\\<preceq>rTa)"; |
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by( dtac (insertI1 RSN (2,(equalityD2 RS subsetD))) 1); |
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by( dtac (max_spec2appl_meths RS appl_methsD) 1); |
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by( etac conjE 1); |
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by( dtac non_np_objD' 1); |
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by( atac 1); |
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by( atac 1); |
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by( strip_tac1 1); |
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by( Asm_full_simp_tac 1); |
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by( Clarsimp_tac 1); |
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by( EVERY'[forward_tac [hext_objD], atac] 1); |
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by( Clarsimp_tac 1); |
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by( EVERY'[dtac Call_lemma, atac, atac] 1); |
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8082 | 148 |
by( clarsimp_tac (claset(),simpset() addsimps [wf_java_mdecl_def])1); |
8034
6fc37b5c5e98
Various little changes like cmethd -> method and cfield -> field.
nipkow
parents:
8011
diff
changeset
|
149 |
by( thin_tac "method ?sig ?x = ?y" 1); |
8011 | 150 |
by( EVERY'[dtac spec, etac impE] 1); |
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by( mp_tac 2); |
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by( rtac conformsI 1); |
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by( etac conforms_heapD 1); |
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by( rtac lconf_ext 1); |
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by( force_tac (claset() addSEs [Call_lemma2],simpset()) 1); |
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by( EVERY'[etac conf_hext, etac conf_obj_AddrI, atac] 1); |
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by( thin_tac "?E\\<turnstile>?blk\\<surd>" 1); |
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by( etac conjE 1); |
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by( EVERY'[dtac spec, mp_tac] 1); |
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(*by( thin_tac "?E\\<Colon>\\<preceq>(G, pT')" 1);*) |
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by( EVERY'[dtac spec, mp_tac] 1); |
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by( thin_tac "?E\\<turnstile>res\\<Colon>?rT" 1); |
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by( strip_tac1 1); |
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by( rtac conjI 1); |
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by( fast_tac (HOL_cs addIs [hext_trans]) 1); |
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by( rtac conjI 1); |
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by( rtac impI 2); |
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by( mp_tac 2); |
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by( forward_tac [conf_widen] 2); |
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by( atac 4); |
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by( atac 2); |
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by( fast_tac (HOL_cs addSEs [widen_trans]) 2); |
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by( etac conforms_hext 1); |
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by( etac hext_trans 1); |
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by( atac 1); |
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by( etac conforms_heapD 1); |
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qed "Call_type_sound"; |
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||
179 |
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180 |
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Unify.search_bound := 40; |
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Unify.trace_bound := 40; |
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Delsplits[split_if]; |
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Delsimps[fun_upd_apply];(*###*) |
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Goal |
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"wf_java_prog G \\<Longrightarrow> \ |
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\ (G\\<turnstile>(x,(h,l)) -e \\<succ>v \\<rightarrow> (x', (h',l')) \\<longrightarrow> \ |
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\ (\\<forall>lT. (h ,l )\\<Colon>\\<preceq>(G,lT) \\<longrightarrow> (\\<forall>T . (G,lT)\\<turnstile>e \\<Colon> T \\<longrightarrow> \ |
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\ h\\<le>|h' \\<and> (h',l')\\<Colon>\\<preceq>(G,lT) \\<and> (x'=None \\<longrightarrow> G,h'\\<turnstile>v \\<Colon>\\<preceq> T )))) \\<and> \ |
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\ (G\\<turnstile>(x,(h,l)) -es[\\<succ>]vs\\<rightarrow> (x', (h',l')) \\<longrightarrow> \ |
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\ (\\<forall>lT. (h ,l )\\<Colon>\\<preceq>(G,lT) \\<longrightarrow> (\\<forall>Ts. (G,lT)\\<turnstile>es[\\<Colon>]Ts \\<longrightarrow> \ |
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\ h\\<le>|h' \\<and> (h',l')\\<Colon>\\<preceq>(G,lT) \\<and> (x'=None \\<longrightarrow> list_all2 (\\<lambda>v T. G,h'\\<turnstile>v\\<Colon>\\<preceq>T) vs Ts)))) \\<and> \ |
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\ (G\\<turnstile>(x,(h,l)) -c \\<rightarrow> (x', (h',l')) \\<longrightarrow> \ |
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\ (\\<forall>lT. (h ,l )\\<Colon>\\<preceq>(G,lT) \\<longrightarrow> (G,lT)\\<turnstile>c \\<surd> \\<longrightarrow> \ |
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\ h\\<le>|h' \\<and> (h',l')\\<Colon>\\<preceq>(G,lT)))"; |
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by( rtac eval_evals_exec.induct 1); |
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by( rewtac c_hupd_def); |
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198 |
||
199 |
(* several simplifications, XcptE, XcptEs, XcptS, Skip *) |
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by( ALLGOALS Asm_full_simp_tac); |
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by( ALLGOALS strip_tac); |
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by( ALLGOALS (eresolve_tac ty_expr_ty_exprs_wt_stmt.elims |
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THEN_ALL_NEW Full_simp_tac)); |
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by( ALLGOALS (EVERY' [REPEAT o (etac conjE), REPEAT o hyp_subst_tac])); |
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by( rewtac wf_java_prog_def); |
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206 |
||
207 |
(* Level 7 *) |
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208 |
||
209 |
(* 14 NewC *) |
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by( dtac new_AddrD 1); |
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by( etac disjE 1); |
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by( Asm_simp_tac 2); |
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by( etac conjE 1); |
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by( Asm_simp_tac 1); |
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by( rtac conjI 1); |
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by( fast_tac (HOL_cs addSEs [NewC_conforms]) 1); |
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217 |
by( rtac conf_obj_AddrI 1); |
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218 |
by( rtac widen.refl 2); |
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by( Asm_simp_tac 2); |
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220 |
by( Simp_tac 1); |
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221 |
||
222 |
(* for Cast *) |
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by( defer_tac 1); |
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224 |
||
225 |
(* 13 Lit *) |
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by( etac conf_litval 1); |
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227 |
||
228 |
(* 12 LAcc *) |
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by( fast_tac (claset() addEs [conforms_localD RS lconfD]) 1); |
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230 |
||
231 |
(* 11 Nil *) |
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232 |
by( Simp_tac 5); |
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233 |
||
234 |
(* for FAss *) |
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235 |
by( EVERY'[eresolve_tac ty_expr_ty_exprs_wt_stmt.elims THEN_ALL_NEW Full_simp_tac, |
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REPEAT o (etac conjE), hyp_subst_tac] 3); |
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237 |
||
238 |
(* for if *) |
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239 |
by( (case_tac1 "the_Bool v" THEN_ALL_NEW Asm_full_simp_tac) 8); |
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240 |
||
241 |
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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243 |
by forward_hyp_tac; |
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244 |
||
245 |
(* 10+1 if *) |
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246 |
by( fast_tac (HOL_cs addIs [hext_trans]) 8); |
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247 |
by( fast_tac (HOL_cs addIs [hext_trans]) 8); |
|
248 |
||
249 |
(* 9 Expr *) |
|
250 |
by( Fast_tac 6); |
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251 |
||
252 |
by( ALLGOALS Asm_full_simp_tac); |
|
253 |
||
254 |
(* 8 Cast *) |
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255 |
by( EVERY'[rtac impI, dtac raise_if_NoneD, Clarsimp_tac, |
|
256 |
fast_tac (claset() addEs [Cast_conf])] 8); |
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257 |
||
258 |
(* 7 LAss *) |
|
259 |
by( asm_simp_tac (simpset() addsplits [expand_if]) 1); |
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260 |
by( EVERY'[eresolve_tac ty_expr_ty_exprs_wt_stmt.elims THEN_ALL_NEW Full_simp_tac] 1); |
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261 |
by( blast_tac (claset() addIs [conforms_upd_local, conf_widen]) 1); |
|
262 |
||
263 |
(* 6 FAcc *) |
|
264 |
by( fast_tac (claset() addSEs [FAcc_type_sound]) 1); |
|
265 |
||
266 |
(* 5 While *) |
|
267 |
by( fast_tac (claset() addIs [ty_expr_ty_exprs_wt_stmt.Cond, ty_expr_ty_exprs_wt_stmt.Comp, ty_expr_ty_exprs_wt_stmt.Skip] |
|
268 |
addEs [ty_expr_ty_exprs_wt_stmt.Loop]) 5); |
|
269 |
||
270 |
by forward_hyp_tac; |
|
271 |
||
272 |
(* 4 Cons *) |
|
273 |
by( fast_tac (claset() addDs [evals_no_xcpt] addIs [conf_hext,hext_trans]) 3); |
|
274 |
||
275 |
(* 3 ;; *) |
|
276 |
by( fast_tac (claset() addIs [hext_trans]) 3); |
|
277 |
||
278 |
(* 2 FAss *) |
|
279 |
by( case_tac1 "x2 = None" 1); |
|
280 |
by( Asm_simp_tac 2); |
|
281 |
by( fast_tac (claset() addIs [hext_trans]) 2); |
|
282 |
by( Asm_full_simp_tac 1); |
|
283 |
by( dtac eval_no_xcpt 1); |
|
284 |
by( SELECT_GOAL (etac FAss_type_sound 1 THEN rtac refl 1 THEN ALLGOALS atac) 1); |
|
285 |
||
286 |
by prune_params_tac; |
|
287 |
(* Level 45 *) |
|
288 |
||
289 |
(* 1 Call *) |
|
290 |
by( case_tac1 "x = None" 1); |
|
291 |
by( dtac (not_None_eq RS iffD1) 2); |
|
292 |
by( Clarsimp_tac 2); |
|
293 |
by( dtac exec_xcpt 2); |
|
294 |
by( Asm_full_simp_tac 2); |
|
295 |
by( dtac eval_xcpt 2); |
|
296 |
by( Asm_full_simp_tac 2); |
|
297 |
by( fast_tac (HOL_cs addEs [hext_trans]) 2); |
|
298 |
by( Clarify_tac 1); |
|
299 |
by( dtac evals_no_xcpt 1); |
|
300 |
by( Asm_full_simp_tac 1); |
|
301 |
by( case_tac1 "a' = Null" 1); |
|
302 |
by( Asm_full_simp_tac 1); |
|
303 |
by( dtac exec_xcpt 1); |
|
304 |
by( Asm_full_simp_tac 1); |
|
305 |
by( dtac eval_xcpt 1); |
|
306 |
by( Asm_full_simp_tac 1); |
|
307 |
by( fast_tac (HOL_cs addEs [hext_trans]) 1); |
|
308 |
by( (rtac (rewrite_rule[wf_java_prog_def]Call_type_sound) THEN_ALL_NEW Asm_simp_tac) 1); |
|
309 |
qed "eval_evals_exec_type_sound"; |
|
310 |
||
311 |
Goal "\\<And>E s s'. \ |
|
312 |
\ \\<lbrakk> G=prg E; wf_java_prog G; G\\<turnstile>(x,s) -e\\<succ>v \\<rightarrow> (x',s'); s\\<Colon>\\<preceq>E; E\\<turnstile>e\\<Colon>T \\<rbrakk> \ |
|
313 |
\ \\<Longrightarrow> s'\\<Colon>\\<preceq>E \\<and> (x'=None \\<longrightarrow> G,heap s'\\<turnstile>v\\<Colon>\\<preceq>T)"; |
|
314 |
by( split_all_tac 1); |
|
315 |
bd (eval_evals_exec_type_sound RS conjunct1 RS mp RS spec RS mp) 1; |
|
316 |
by Auto_tac; |
|
317 |
qed "eval_type_sound"; |
|
318 |
||
319 |
Goal "\\<And>E s s'. \ |
|
320 |
\ \\<lbrakk> G=prg E; wf_java_prog G; G\\<turnstile>(x,s) -s0\\<rightarrow> (x',s'); s\\<Colon>\\<preceq>E; E\\<turnstile>s0\\<surd> \\<rbrakk> \ |
|
321 |
\ \\<Longrightarrow> s'\\<Colon>\\<preceq>E"; |
|
322 |
by( split_all_tac 1); |
|
323 |
bd (eval_evals_exec_type_sound RS conjunct2 RS conjunct2 RS mp RS spec RS mp) 1; |
|
324 |
by Auto_tac; |
|
325 |
qed "exec_type_sound"; |
|
326 |
||
327 |
Goal "\\<lbrakk>G=prg E; wf_java_prog G; G\\<turnstile>(x,s) -e\\<succ>a'\\<rightarrow> Norm s'; a' \\<noteq> Null;\ |
|
328 |
\ s\\<Colon>\\<preceq>E; E\\<turnstile>e\\<Colon>RefT T; m_head G T sig \\<noteq> None\\<rbrakk> \\<Longrightarrow> \ |
|
8034
6fc37b5c5e98
Various little changes like cmethd -> method and cfield -> field.
nipkow
parents:
8011
diff
changeset
|
329 |
\ method (G,fst (the (heap s' (the_Addr a')))) sig \\<noteq> None"; |
8011 | 330 |
by( dtac eval_type_sound 1); |
331 |
by( atac 1); |
|
332 |
by( atac 1); |
|
333 |
by( atac 1); |
|
334 |
by( atac 1); |
|
335 |
by( not_None_tac 1); |
|
336 |
by( split_all_tac 1); |
|
337 |
by(rewtac wf_java_prog_def); |
|
338 |
by( forward_tac [widen_methd] 1); |
|
339 |
by( atac 1); |
|
340 |
by( rtac (not_None_eq RS iffD1) 2); |
|
341 |
by( Fast_tac 2); |
|
342 |
by( etac conjE 1); |
|
343 |
by( dtac non_npD 1); |
|
344 |
by Auto_tac; |
|
345 |
qed "all_methods_understood"; |
|
346 |
||
347 |
Delsimps [split_beta]; |
|
348 |
Addsimps[fun_upd_apply];(*###*) |
|
349 |