wneuper/isa: src/HOL/MicroJava/J/WellForm.ML@a466c687c726

     1 (*  Title:      HOL/MicroJava/J/WellForm.ML

     2     ID:         $Id$

     3     Author:     David von Oheimb

     4     Copyright   1999 Technische Universitaet Muenchen

     5 *)

     7 val class_wf = prove_goalw thy [wf_prog_def, Let_def, class_def]

     8  "\\<And>X. \\<lbrakk>class G C = Some c; wf_prog wf_mb G\\<rbrakk> \\<Longrightarrow> wf_cdecl wf_mb G (C,c)" (K [

     9 	Asm_full_simp_tac 1,

    10 	fast_tac (set_cs addDs [get_in_set]) 1]);

    12 val class_Object = prove_goalw thy [wf_prog_def, Let_def, ObjectC_def,class_def]

    13 	"\\<And>X. wf_prog wf_mb G \\<Longrightarrow> class G Object = Some (None, [], [])" (K [

    14 	safe_tac set_cs,

    15 	dtac in_set_get 1,

    16 	 Auto_tac]);

    17 Addsimps [class_Object];

    19 val is_class_Object = prove_goalw thy [is_class_def]

    20 	"\\<And>X. wf_prog wf_mb G \\<Longrightarrow> is_class G Object" (K [Asm_simp_tac 1]);

    21 Addsimps [is_class_Object];

    23 Goal "\\<lbrakk>G\\<turnstile>C\\<prec>C1D; wf_prog wf_mb G\\<rbrakk> \\<Longrightarrow> D \\<noteq> C \\<and> \\<not>(D,C)\\<in>(subcls1 G)^+";

    24 by( forward_tac [r_into_trancl] 1);

    25 by( dtac subcls1D 1);

    26 by( strip_tac1 1);

    27 by( datac class_wf 1 1);

    28 by( rewtac wf_cdecl_def);

    29 by(force_tac (claset(), simpset() addsimps [reflcl_trancl RS sym]

    30 				  delsimps [reflcl_trancl]) 1);

    31 qed "subcls1_wfD";

    33 val wf_cdecl_supD = prove_goalw thy [wf_cdecl_def]

    34 "\\<And>X. \\<lbrakk>wf_cdecl wf_mb G (C, sc, r); C \\<noteq> Object\\<rbrakk> \\<Longrightarrow> \\<exists>D. sc = Some D \\<and> is_class G D" (K [

    35 	pair_tac "r" 1,

    36 	asm_full_simp_tac (simpset() addsplits [option.split_asm]) 1]);

    38 Goal "\\<lbrakk>wf_prog wf_mb G; (C,D)\\<in>(subcls1 G)^+\\<rbrakk> \\<Longrightarrow> \\<not>(D,C)\\<in>(subcls1 G)^+";

    39 by(etac tranclE 1);

    40 by(TRYALL(fast_tac (HOL_cs addSDs [subcls1_wfD] addIs [trancl_trans])));

    41 qed "subcls_asym";

    43 val subcls_irrefl = prove_goal thy "\\<And>X. \\<lbrakk>wf_prog wf_mb G; (C,D)\\<in>(subcls1 G)^+\\<rbrakk> \\<Longrightarrow> C \\<noteq> D" (K [

    44 	etac trancl_trans_induct 1,

    45 	 fast_tac (HOL_cs addDs [subcls1_wfD]) 1,

    46 	fast_tac (HOL_cs addDs [subcls_asym]) 1]);

    48 val acyclic_subcls1 = prove_goalw thy [acyclic_def]

    49 	"\\<And>X. wf_prog wf_mb G \\<Longrightarrow> acyclic (subcls1 G)" (K [

    50 	strip_tac1 1,

    51 	fast_tac (HOL_cs addDs [subcls_irrefl]) 1]);

    53 val wf_subcls1 = prove_goal thy "\\<And>X. wf_prog wf_mb G \\<Longrightarrow> wf ((subcls1 G)^-1)" (K [

    54 	rtac finite_acyclic_wf 1,

    55 	 stac finite_converse 1,

    56 	 rtac finite_subcls1 1,

    57 	stac acyclic_converse 1,

    58 	etac acyclic_subcls1 1]);

    60 val major::prems = goal thy

    61   "\\<lbrakk>wf_prog wf_mb G; \\<And>C. \\<forall>D. (C,D)\\<in>(subcls1 G)^+ \\<longrightarrow> P D \\<Longrightarrow> P C\\<rbrakk> \\<Longrightarrow> P C";

    62 by(cut_facts_tac [major RS wf_subcls1] 1);

    63 by(dtac wf_trancl 1);

    64 by(asm_full_simp_tac (HOL_ss addsimps [trancl_converse]) 1);

    65 by(eres_inst_tac [("a","C")] wf_induct 1);

    66 by(resolve_tac prems 1);

    67 by(Auto_tac);

    68 qed "subcls_induct";

    70 val prems = goal thy "\\<lbrakk>is_class G C; wf_prog wf_mb G; P Object; \

    71 \\\<And>C D fs ms. \\<lbrakk>C \\<noteq> Object; is_class G C; class G C = Some (Some D,fs,ms) \\<and> \

    72 \   wf_cdecl wf_mb G (C, Some D,fs,ms) \\<and> G\\<turnstile>C\\<prec>C1D \\<and> is_class G D \\<and> P D\\<rbrakk> \\<Longrightarrow> P C\

    73 \ \\<rbrakk> \\<Longrightarrow> P C";

    74 by( cut_facts_tac prems 1);

    75 by( rtac impE 1);

    76 by(   atac 2);

    77 by(  atac 2);

    78 by( etac thin_rl 1);

    79 by( rtac subcls_induct 1);

    80 by(  atac 1);

    81 by( rtac impI 1);

    82 by( case_tac "C = Object" 1);

    83 by(  Fast_tac 1);

    84 by( ex_ftac is_classD 1);

    85 by( forward_tac [class_wf] 1);

    86 by(  atac 1);

    87 by( forward_tac [wf_cdecl_supD] 1);

    88 by(  atac 1);

    89 by( strip_tac1 1);

    90 by( rtac (hd (tl (tl (tl prems)))) 1);

    91 by(   atac 1);

    92 by(  atac 1);

    93 by( subgoal_tac "G\\<turnstile>C\\<prec>C1D" 1);

    94 by(  fast_tac (HOL_cs addIs [r_into_trancl]) 1);

    95 by( etac subcls1I 1);

    96 qed "subcls1_induct";

    98 Goal "wf_prog wf_mb G \\<Longrightarrow> method (G,C) = \

    99 \ (case class G C of None \\<Rightarrow> empty | Some (sc,fs,ms) \\<Rightarrow> \

   100 \ (case sc of None \\<Rightarrow> empty | Some D \\<Rightarrow> method (G,D)) \\<oplus> \

   101 \ map_of (map (\\<lambda>(s,m). (s,(C,m))) ms))";

   102 by( stac (method_TC RS (wf_subcls1_rel RS (hd method.rules))) 1);

   103 by( clarsimp_tac (claset(), simpset() addsimps [wf_subcls1,empty_def]

   104 		addsplits [option.split]) 1);

   105 by( case_tac "C = Object" 1);

   106 by(  Asm_full_simp_tac 1);

   107 by( dtac class_wf 1);

   108 by(  atac 1);

   109 by( dtac wf_cdecl_supD 1);

   110 by(  atac 1);

   111 by( Asm_full_simp_tac 1);

   112 qed "method_rec";

   114 Goal "\\<lbrakk>class G C = Some (sc,fs,ms); wf_prog wf_mb G\\<rbrakk> \\<Longrightarrow> fields (G,C) = \

   115 \ map (\\<lambda>(fn,ft). ((fn,C),ft)) fs @ \

   116 \ (case sc of None \\<Rightarrow> [] | Some D \\<Rightarrow> fields (G,D))";

   117 by( stac (fields_TC RS (wf_subcls1_rel RS (hd fields.rules))) 1);

   118 by( asm_simp_tac (simpset() addsimps [wf_subcls1,empty_def]) 1);

   119 by( option_case_tac2 "sc" 1);

   120 by(  Asm_simp_tac 1);

   121 by( case_tac "C = Object" 1);

   122 by(  rotate_tac 2 1);

   123 by(  Asm_full_simp_tac 1);

   124 by( dtac class_wf 1);

   125 by(  atac 1);

   126 by( dtac wf_cdecl_supD 1);

   127 by(  atac 1);

   128 by( Asm_full_simp_tac 1);

   129 qed "fields_rec";

   131 val method_Object = prove_goal thy "\\<And>X. wf_prog wf_mb G \\<Longrightarrow> method (G,Object) = empty"

   132 	(K [stac method_rec 1,Auto_tac]);

   133 val fields_Object = prove_goal thy "\\<And>X. wf_prog wf_mb G \\<Longrightarrow> fields (G,Object) = []"(K [

   134 	stac fields_rec 1,Auto_tac]);

   135 Addsimps [method_Object, fields_Object];

   136 val field_Object = prove_goalw thy [field_def]

   137  "\\<And>X. wf_prog wf_mb G \\<Longrightarrow> field (G,Object) = empty" (K [Asm_simp_tac 1]);

   138 Addsimps [field_Object];

   140 Goal "\\<lbrakk>is_class G C; wf_prog wf_mb G\\<rbrakk> \\<Longrightarrow> G\\<turnstile>C\\<preceq>C Object";

   141 by(etac subcls1_induct 1);

   142 by(  atac 1);

   143 by( Fast_tac 1);

   144 by(auto_tac (HOL_cs addSDs [wf_cdecl_supD], simpset()));

   145 by(eatac rtrancl_into_rtrancl2 1 1);

   146 qed "subcls_C_Object";

   148 val is_type_rTI = prove_goalw thy [wf_mhead_def]

   149 	"\\<And>sig. wf_mhead G sig rT \\<Longrightarrow> is_type G rT"

   150 	(K [split_all_tac 1, Auto_tac]);

   152 Goal "\\<lbrakk>(C',C)\\<in>(subcls1 G)^+; wf_prog wf_mb G\\<rbrakk> \\<Longrightarrow> \

   153 \ x \\<in> set (fields (G,C)) \\<longrightarrow> x \\<in> set (fields (G,C'))";

   154 by(etac trancl_trans_induct 1);

   155 by( safe_tac (HOL_cs addSDs [subcls1D]));

   156 by(stac fields_rec 1);

   157 by(  Auto_tac);

   158 qed_spec_mp "fields_mono";

   160 Goal "\\<lbrakk>is_class G C; wf_prog wf_mb G\\<rbrakk> \\<Longrightarrow> \

   161 \ \\<forall>((fn,fd),fT)\\<in>set (fields (G,C)). G\\<turnstile>C\\<preceq>C fd";

   162 by( etac subcls1_induct 1);

   163 by(   atac 1);

   164 by(  Asm_simp_tac 1);

   165 by( safe_tac HOL_cs);

   166 by( stac fields_rec 1);

   167 by(   atac 1);

   168 by(  atac 1);

   169 by( Simp_tac 1);

   170 by( rtac ballI 1);

   171 by( split_all_tac 1);

   172 by( Simp_tac 1);

   173 by( etac UnE 1);

   174 by(  dtac split_Pair_eq 1);

   175 by(  SELECT_GOAL (Auto_tac) 1);

   176 by( etac (r_into_rtrancl RS rtrancl_trans) 1);

   177 by( etac BallE 1);

   178 by(  contr_tac 1);

   179 by( Asm_full_simp_tac 1);

   180 qed "widen_fields_defpl'";

   182 Goal "\\<lbrakk>is_class G C; wf_prog wf_mb G; ((fn,fd),fT) \\<in> set (fields (G,C))\\<rbrakk> \\<Longrightarrow> \

   183 \ G\\<turnstile>C\\<preceq>C fd";

   184 by( datac widen_fields_defpl' 1 1);

   185 (*###################*)

   186 by( dtac bspec 1);

   187 auto();

   188 qed "widen_fields_defpl";

   191 Goal "\\<lbrakk>is_class G C; wf_prog wf_mb G\\<rbrakk> \\<Longrightarrow> unique (fields (G,C))";

   192 by( etac subcls1_induct 1);

   193 by(   atac 1);

   194 by(  safe_tac (HOL_cs addSDs [wf_cdecl_supD]));

   195 by(  Asm_simp_tac 1);

   196 by( dtac subcls1_wfD 1);

   197 by(  atac 1);

   198 by( stac fields_rec 1);

   199 by   Auto_tac;

   200 by( rotate_tac ~1 1);

   201 by( ex_ftac is_classD 1);

   202 by( forward_tac [class_wf] 1);

   203 by  Auto_tac;

   204 by( asm_full_simp_tac (simpset() addsimps [wf_cdecl_def]) 1);

   205 by( etac unique_append 1);

   206 by(  rtac unique_map_Pair 1);

   207 by(  Step_tac 1);

   208 by (EVERY1[dtac widen_fields_defpl, atac, atac]);

   209 by( Asm_full_simp_tac 1);

   210 by( dtac split_Pair_eq 1);

   211 by( Asm_full_simp_tac 1);

   212 qed "unique_fields";

   214 (*####TO Trancl.ML*)

   215 Goal "(a,b):r^* ==> a=b | a~=b & (a,b):r^+";

   216 by(force_tac (claset(), simpset() addsimps [reflcl_trancl RS sym]

   217 				  delsimps [reflcl_trancl]) 1);

   218 qed "rtranclD";

   220 Goal

   221 "\\<lbrakk>wf_prog wf_mb G; G\\<turnstile>C'\\<preceq>C C; map_of(fields (G,C )) f = Some ft\\<rbrakk> \\<Longrightarrow> \

   222 \                          map_of (fields (G,C')) f = Some ft";

   223 by( dtac rtranclD 1);

   224 by( Auto_tac);

   225 by( rtac table_mono 1);

   226 by(   atac 3);

   227 by(  rtac unique_fields 1);

   228 by(   etac subcls_is_class 1);

   229 by(  atac 1);

   230 by( fast_tac (HOL_cs addEs [fields_mono]) 1);

   231 qed "widen_fields_mono";

   234 val cfs_fields_lemma = prove_goalw thy [field_def]

   235 "\\<And>X. field (G,C) fn = Some (fd, fT) \\<Longrightarrow> map_of(fields (G,C)) (fn, fd) = Some fT"

   236 (K [rtac table_map_Some 1, Asm_full_simp_tac 1]);

   238 val widen_cfs_fields = prove_goal thy "\\<And>X. \\<lbrakk>field (G,C) fn = Some (fd, fT);\

   239 \  G\\<turnstile>C'\\<preceq>C C; wf_prog wf_mb G\\<rbrakk> \\<Longrightarrow> map_of (fields (G,C')) (fn, fd) = Some fT" (K[

   240 fast_tac (HOL_cs addIs [widen_fields_mono, cfs_fields_lemma]) 1]);

   242 Goal "wf_prog wf_mb G \\<Longrightarrow> method (G,C) sig = Some (md,mh,m)\

   243 \  \\<longrightarrow> G\\<turnstile>C\\<preceq>C md \\<and> wf_mdecl wf_mb G md (sig,(mh,m))";

   244 by( case_tac "is_class G C" 1);

   245 by(  forw_inst_tac [("C","C")] method_rec 2);

   246 by(    asm_full_simp_tac (simpset() addsimps [is_class_def]

   247 	delsimps [not_None_eq]) 2);

   248 by( etac subcls1_induct 1);

   249 by(   atac 1);

   250 by(  Force_tac 1);

   251 by( forw_inst_tac [("C","C")] method_rec 1);

   252 by( strip_tac1 1);

   253 by( rotate_tac ~1 1);

   254 by( Asm_full_simp_tac 1);

   255 by( dtac override_SomeD 1);

   256 by( etac disjE 1);

   257 by(  thin_tac "?P \\<longrightarrow> ?Q" 1);

   258 by(  Clarify_tac 2);

   259 by(  rtac rtrancl_trans 2);

   260 by(   atac 3);

   261 by(  rtac r_into_rtrancl 2);

   262 by(  fast_tac (HOL_cs addIs [subcls1I]) 2);

   263 by( forward_tac [table_mapf_SomeD] 1);

   264 by( strip_tac1 1);

   265 by( Asm_full_simp_tac 1);

   266 by( rewtac wf_cdecl_def);

   267 by( Asm_full_simp_tac 1);

   268 qed_spec_mp "method_wf_mdecl";

   270 Goal "\\<lbrakk>G\\<turnstile>T\\<preceq>C T'; wf_prog wf_mb G\\<rbrakk> \\<Longrightarrow> \

   271 \  \\<forall>D rT b. method (G,T') sig = Some (D,rT ,b) \\<longrightarrow>\

   272 \ (\\<exists>D' rT' b'. method (G,T) sig = Some (D',rT',b') \\<and> G\\<turnstile>rT'\\<preceq>rT)";

   273 by( dtac rtranclD 1);

   274 by( etac disjE 1);

   275 by(  Fast_tac 1);

   276 by( etac conjE 1);

   277 by( etac trancl_trans_induct 1);

   278 by(  strip_tac1 2);

   279 by(  EVERY[dtac spec 2, dtac spec 2, dtac spec 2, mp_tac 2]);

   280 by(  fast_tac (HOL_cs addEs [widen_trans]) 2);

   281 by( strip_tac1 1);

   282 by( dtac subcls1D 1);

   283 by( strip_tac1 1);

   284 by( stac method_rec 1);

   285 by(  atac 1);

   286 by( rewtac override_def);

   287 by( asm_simp_tac (simpset() delsimps [split_paired_Ex]) 1);

   288 by( case_tac "\\<exists>z. map_of(map (\\<lambda>(s,m). (s, ?C, m)) ms) sig = Some z" 1);

   289 by(  etac exE 1);

   290 by(  asm_full_simp_tac (HOL_ss addsimps [not_None_eq RS sym]) 2);

   291 by(  ALLGOALS (rotate_tac ~1 THEN' forward_tac[ssubst] THEN' (fn n=>atac(n+1))));

   292 by(  ALLGOALS (asm_simp_tac (simpset() delsimps [split_paired_Ex])));

   293 by( dtac class_wf 1);

   294 by(  atac 1);

   295 by( split_all_tac 1);

   296 by( rewtac wf_cdecl_def);

   297 by( dtac table_mapf_Some2 1);

   298 by( Clarsimp_tac 1);

   299 by( dres_inst_tac [("xys1","ms")] get_in_set 1);

   300 by Auto_tac;

   301 qed_spec_mp "subcls_widen_methd";

   304 Goal

   305  "\\<lbrakk> G\\<turnstile> C\\<preceq>C D; wf_prog wf_mb G; \

   306 \    method (G,D) sig = Some (md, rT, b) \\<rbrakk> \

   307 \ \\<Longrightarrow> \\<exists>mD' rT' b'. method (G,C) sig= Some(mD',rT',b') \\<and> G\\<turnstile>rT'\\<preceq>rT";

   308 by(auto_tac (claset() addDs [subcls_widen_methd,method_wf_mdecl],

   309              simpset() addsimps [wf_mdecl_def,wf_mhead_def,split_def]));

   310 qed "subtype_widen_methd";

   313 Goal "wf_prog wf_mb G \\<Longrightarrow> \\<forall>D. method (G,C) sig = Some(D,mh,code) \\<longrightarrow> is_class G D \\<and> method (G,D) sig = Some(D,mh,code)";

   314 by( case_tac "is_class G C" 1);

   315 by(  forw_inst_tac [("C","C")] method_rec 2);

   316 by(    asm_full_simp_tac (simpset() addsimps [is_class_def]

   317 	delsimps [not_None_eq]) 2);

   318 by (etac subcls1_induct 1);

   319   ba 1;

   320  by (Asm_full_simp_tac 1);

   321 by (stac method_rec 1);

   322  ba 1;

   323 by (Clarify_tac 1);

   324 by (eres_inst_tac [("x","Da")] allE 1);

   325 by (Clarsimp_tac 1);

   326  by (asm_full_simp_tac (simpset() addsimps [map_of_map]) 1);

   327  by (Clarify_tac 1);

   328  by (stac method_rec 1);

   329   ba 1;

   330  by (asm_full_simp_tac (simpset() addsimps [override_def,map_of_map] addsplits [option.split]) 1);

   331 qed_spec_mp "method_in_md";

   334 Goal "\\<lbrakk>is_class G C; wf_prog wf_mb G\\<rbrakk> \\<Longrightarrow> \

   335 \ \\<forall>f\\<in>set (fields (G,C)). is_type G (snd f)";

   336 by( etac subcls1_induct 1);

   337 by(   atac 1);

   338 by(  Asm_simp_tac 1);

   339 by( strip_tac1 1);

   340 by( stac fields_rec 1);

   341 by(   atac 1);

   342 by(  atac 1);

   343 by( Asm_simp_tac 1);

   344 by( safe_tac set_cs);

   345 by(  Fast_tac 2);

   346 by( dtac class_wf 1);

   347 by(  atac 1);

   348 by( rewtac wf_cdecl_def);

   349 by( Asm_full_simp_tac 1);

   350 by( strip_tac1 1);

   351 by( EVERY[dtac bspec 1, atac 1]);

   352 by( rewtac wf_fdecl_def);

   353 by( split_all_tac 1);

   354 by( Asm_full_simp_tac 1);

   355 bind_thm ("is_type_fields", result() RS bspec);

author	nipkow
	Tue, 28 Mar 2000 17:31:36 +0200
changeset 8600	a466c687c726
parent 8185	59b62e8804b4
child 8624	69619f870939
permissions	-rw-r--r--