1(* Title: HOL/Tools/Old_Datatype/old_rep_datatype.ML 2 Author: Stefan Berghofer, TU Muenchen 3 4Representation of existing types as datatypes: proofs and definitions 5independent of concrete representation of datatypes (i.e. requiring 6only abstract properties: injectivity / distinctness of constructors 7and induction). 8*) 9 10signature OLD_REP_DATATYPE = 11sig 12 val derive_datatype_props : Old_Datatype_Aux.config -> string list -> 13 Old_Datatype_Aux.descr list -> thm -> thm list list -> thm list list -> theory -> 14 string list * theory 15 val rep_datatype : Old_Datatype_Aux.config -> (string list -> Proof.context -> Proof.context) -> 16 term list -> theory -> Proof.state 17 val rep_datatype_cmd : Old_Datatype_Aux.config -> 18 (string list -> Proof.context -> Proof.context) -> string list -> theory -> Proof.state 19end; 20 21structure Old_Rep_Datatype: OLD_REP_DATATYPE = 22struct 23 24(** derived definitions and proofs **) 25 26(* case distinction theorems *) 27 28fun prove_casedist_thms (config : Old_Datatype_Aux.config) 29 new_type_names descr induct case_names_exhausts thy = 30 let 31 val _ = Old_Datatype_Aux.message config "Proving case distinction theorems ..."; 32 33 val descr' = flat descr; 34 val recTs = Old_Datatype_Aux.get_rec_types descr'; 35 val newTs = take (length (hd descr)) recTs; 36 37 val maxidx = Thm.maxidx_of induct; 38 val induct_Ps = 39 map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induct))); 40 41 fun prove_casedist_thm (i, (T, t)) = 42 let 43 val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) => 44 Abs ("z", T', Const (\<^const_name>\<open>True\<close>, T''))) induct_Ps; 45 val P = 46 Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx + 1), T), Bound 0) $ 47 Var (("P", 0), HOLogic.boolT)); 48 val insts = take i dummyPs @ (P :: drop (i + 1) dummyPs); 49 in 50 Goal.prove_sorry_global thy [] 51 (Logic.strip_imp_prems t) 52 (Logic.strip_imp_concl t) 53 (fn {context = ctxt, prems, ...} => 54 let 55 val insts' = map (#1 o dest_Var) induct_Ps ~~ map (Thm.cterm_of ctxt) insts; 56 val induct' = 57 refl RS 58 (nth (Old_Datatype_Aux.split_conj_thm (infer_instantiate ctxt insts' induct)) i 59 RSN (2, rev_mp)); 60 in 61 EVERY 62 [resolve_tac ctxt [induct'] 1, 63 REPEAT (resolve_tac ctxt [TrueI] 1), 64 REPEAT ((resolve_tac ctxt [impI] 1) THEN (eresolve_tac ctxt prems 1)), 65 REPEAT (resolve_tac ctxt [TrueI] 1)] 66 end) 67 end; 68 69 val casedist_thms = 70 map_index prove_casedist_thm (newTs ~~ Old_Datatype_Prop.make_casedists descr); 71 in 72 thy 73 |> Old_Datatype_Aux.store_thms_atts "exhaust" new_type_names 74 (map single case_names_exhausts) casedist_thms 75 end; 76 77 78(* primrec combinators *) 79 80fun prove_primrec_thms (config : Old_Datatype_Aux.config) new_type_names descr 81 injects_of constr_inject (dist_rewrites, other_dist_rewrites) induct thy = 82 let 83 val _ = Old_Datatype_Aux.message config "Constructing primrec combinators ..."; 84 85 val big_name = space_implode "_" new_type_names; 86 val thy0 = Sign.add_path big_name thy; 87 88 val descr' = flat descr; 89 val recTs = Old_Datatype_Aux.get_rec_types descr'; 90 val used = fold Term.add_tfree_namesT recTs []; 91 val newTs = take (length (hd descr)) recTs; 92 93 val induct_Ps = 94 map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induct))); 95 96 val big_rec_name' = "rec_set_" ^ big_name; 97 val rec_set_names' = 98 if length descr' = 1 then [big_rec_name'] 99 else map (prefix (big_rec_name' ^ "_") o string_of_int) (1 upto length descr'); 100 val rec_set_names = map (Sign.full_bname thy0) rec_set_names'; 101 102 val (rec_result_Ts, reccomb_fn_Ts) = Old_Datatype_Prop.make_primrec_Ts descr used; 103 104 val rec_set_Ts = 105 map (fn (T1, T2) => (reccomb_fn_Ts @ [T1, T2]) ---> HOLogic.boolT) (recTs ~~ rec_result_Ts); 106 107 val rec_fns = 108 map (uncurry (Old_Datatype_Aux.mk_Free "f")) (reccomb_fn_Ts ~~ (1 upto length reccomb_fn_Ts)); 109 val rec_sets' = 110 map (fn c => list_comb (Free c, rec_fns)) (rec_set_names' ~~ rec_set_Ts); 111 val rec_sets = 112 map (fn c => list_comb (Const c, rec_fns)) (rec_set_names ~~ rec_set_Ts); 113 114 (* introduction rules for graph of primrec function *) 115 116 fun make_rec_intr T rec_set (cname, cargs) (rec_intr_ts, l) = 117 let 118 fun mk_prem (dt, U) (j, k, prems, t1s, t2s) = 119 let val free1 = Old_Datatype_Aux.mk_Free "x" U j in 120 (case (Old_Datatype_Aux.strip_dtyp dt, strip_type U) of 121 ((_, Old_Datatype_Aux.DtRec m), (Us, _)) => 122 let 123 val free2 = Old_Datatype_Aux.mk_Free "y" (Us ---> nth rec_result_Ts m) k; 124 val i = length Us; 125 in 126 (j + 1, k + 1, 127 HOLogic.mk_Trueprop (HOLogic.list_all 128 (map (pair "x") Us, nth rec_sets' m $ 129 Old_Datatype_Aux.app_bnds free1 i $ 130 Old_Datatype_Aux.app_bnds free2 i)) :: prems, 131 free1 :: t1s, free2 :: t2s) 132 end 133 | _ => (j + 1, k, prems, free1 :: t1s, t2s)) 134 end; 135 136 val Ts = map (Old_Datatype_Aux.typ_of_dtyp descr') cargs; 137 val (_, _, prems, t1s, t2s) = fold_rev mk_prem (cargs ~~ Ts) (1, 1, [], [], []); 138 139 in 140 (rec_intr_ts @ 141 [Logic.list_implies (prems, HOLogic.mk_Trueprop 142 (rec_set $ list_comb (Const (cname, Ts ---> T), t1s) $ 143 list_comb (nth rec_fns l, t1s @ t2s)))], l + 1) 144 end; 145 146 val (rec_intr_ts, _) = 147 fold (fn ((d, T), set_name) => 148 fold (make_rec_intr T set_name) (#3 (snd d))) (descr' ~~ recTs ~~ rec_sets') ([], 0); 149 150 val ({intrs = rec_intrs, elims = rec_elims, ...}, thy1) = 151 thy0 152 |> Sign.concealed 153 |> Named_Target.theory_map_result Inductive.transform_result 154 (Inductive.add_inductive 155 {quiet_mode = #quiet config, verbose = false, alt_name = Binding.name big_rec_name', 156 coind = false, no_elim = false, no_ind = true, skip_mono = true} 157 (map (fn (s, T) => ((Binding.name s, T), NoSyn)) (rec_set_names' ~~ rec_set_Ts)) 158 (map dest_Free rec_fns) 159 (map (fn x => (Binding.empty_atts, x)) rec_intr_ts) []) 160 ||> Sign.restore_naming thy0; 161 162 (* prove uniqueness and termination of primrec combinators *) 163 164 val _ = Old_Datatype_Aux.message config 165 "Proving termination and uniqueness of primrec functions ..."; 166 167 fun mk_unique_tac ctxt ((((i, (tname, _, constrs)), elim), T), T') (tac, intrs) = 168 let 169 val distinct_tac = 170 if i < length newTs then 171 full_simp_tac (put_simpset HOL_ss ctxt addsimps (nth dist_rewrites i)) 1 172 else full_simp_tac (put_simpset HOL_ss ctxt addsimps (flat other_dist_rewrites)) 1; 173 174 val inject = 175 map (fn r => r RS iffD1) 176 (if i < length newTs then nth constr_inject i else injects_of tname); 177 178 fun mk_unique_constr_tac n (cname, cargs) (tac, intr :: intrs, j) = 179 let 180 val k = length (filter Old_Datatype_Aux.is_rec_type cargs); 181 in 182 (EVERY 183 [DETERM tac, 184 REPEAT (eresolve_tac ctxt @{thms ex1E} 1), resolve_tac ctxt @{thms ex1I} 1, 185 DEPTH_SOLVE_1 (ares_tac ctxt [intr] 1), 186 REPEAT_DETERM_N k (eresolve_tac ctxt [thin_rl] 1 THEN rotate_tac 1 1), 187 eresolve_tac ctxt [elim] 1, 188 REPEAT_DETERM_N j distinct_tac, 189 TRY (dresolve_tac ctxt inject 1), 190 REPEAT (eresolve_tac ctxt [conjE] 1), hyp_subst_tac ctxt 1, 191 REPEAT 192 (EVERY [eresolve_tac ctxt [allE] 1, dresolve_tac ctxt [mp] 1, assume_tac ctxt 1]), 193 TRY (hyp_subst_tac ctxt 1), 194 resolve_tac ctxt [refl] 1, 195 REPEAT_DETERM_N (n - j - 1) distinct_tac], 196 intrs, j + 1) 197 end; 198 199 val (tac', intrs', _) = 200 fold (mk_unique_constr_tac (length constrs)) constrs (tac, intrs, 0); 201 in (tac', intrs') end; 202 203 val rec_unique_thms = 204 let 205 val rec_unique_ts = 206 map (fn (((set_t, T1), T2), i) => 207 Const (\<^const_name>\<open>Ex1\<close>, (T2 --> HOLogic.boolT) --> HOLogic.boolT) $ 208 absfree ("y", T2) (set_t $ Old_Datatype_Aux.mk_Free "x" T1 i $ Free ("y", T2))) 209 (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs)); 210 val insts = 211 map (fn ((i, T), t) => absfree ("x" ^ string_of_int i, T) t) 212 ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts); 213 in 214 Old_Datatype_Aux.split_conj_thm (Goal.prove_sorry_global thy1 [] [] 215 (HOLogic.mk_Trueprop (Old_Datatype_Aux.mk_conj rec_unique_ts)) 216 (fn {context = ctxt, ...} => 217 let 218 val induct' = 219 infer_instantiate ctxt 220 (map (#1 o dest_Var) induct_Ps ~~ map (Thm.cterm_of ctxt) insts) induct; 221 in 222 #1 (fold (mk_unique_tac ctxt) (descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts) 223 (((resolve_tac ctxt [induct'] THEN_ALL_NEW Object_Logic.atomize_prems_tac ctxt) 1 THEN 224 rewrite_goals_tac ctxt [mk_meta_eq @{thm choice_eq}], rec_intrs))) 225 end)) 226 end; 227 228 val rec_total_thms = map (fn r => r RS @{thm theI'}) rec_unique_thms; 229 230 (* define primrec combinators *) 231 232 val big_reccomb_name = "rec_" ^ space_implode "_" new_type_names; 233 val reccomb_names = 234 map (Sign.full_bname thy1) 235 (if length descr' = 1 then [big_reccomb_name] 236 else map (prefix (big_reccomb_name ^ "_") o string_of_int) (1 upto length descr')); 237 val reccombs = 238 map (fn ((name, T), T') => Const (name, reccomb_fn_Ts @ [T] ---> T')) 239 (reccomb_names ~~ recTs ~~ rec_result_Ts); 240 241 val (reccomb_defs, thy2) = 242 thy1 243 |> Sign.add_consts (map (fn ((name, T), T') => 244 (Binding.name (Long_Name.base_name name), reccomb_fn_Ts @ [T] ---> T', NoSyn)) 245 (reccomb_names ~~ recTs ~~ rec_result_Ts)) 246 |> (Global_Theory.add_defs false o map Thm.no_attributes) 247 (map 248 (fn ((((name, comb), set), T), T') => 249 (Binding.name (Thm.def_name (Long_Name.base_name name)), 250 Logic.mk_equals (comb, fold_rev lambda rec_fns (absfree ("x", T) 251 (Const (\<^const_name>\<open>The\<close>, (T' --> HOLogic.boolT) --> T') $ absfree ("y", T') 252 (set $ Free ("x", T) $ Free ("y", T'))))))) 253 (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts)) 254 ||> Sign.parent_path; 255 256 257 (* prove characteristic equations for primrec combinators *) 258 259 val _ = Old_Datatype_Aux.message config 260 "Proving characteristic theorems for primrec combinators ..."; 261 262 val rec_thms = 263 map (fn t => 264 Goal.prove_sorry_global thy2 [] [] t 265 (fn {context = ctxt, ...} => EVERY 266 [rewrite_goals_tac ctxt reccomb_defs, 267 resolve_tac ctxt @{thms the1_equality} 1, 268 resolve_tac ctxt rec_unique_thms 1, 269 resolve_tac ctxt rec_intrs 1, 270 REPEAT (resolve_tac ctxt [allI] 1 ORELSE resolve_tac ctxt rec_total_thms 1)])) 271 (Old_Datatype_Prop.make_primrecs reccomb_names descr thy2); 272 in 273 thy2 274 |> Sign.add_path (space_implode "_" new_type_names) 275 |> Global_Theory.note_thms "" 276 ((Binding.name "rec", [Named_Theorems.add \<^named_theorems>\<open>nitpick_simp\<close>]), [(rec_thms, [])]) 277 ||> Sign.parent_path 278 |-> (fn (_, thms) => pair (reccomb_names, thms)) 279 end; 280 281 282(* case combinators *) 283 284fun prove_case_thms (config : Old_Datatype_Aux.config) 285 new_type_names descr reccomb_names primrec_thms thy = 286 let 287 val _ = Old_Datatype_Aux.message config 288 "Proving characteristic theorems for case combinators ..."; 289 290 val ctxt = Proof_Context.init_global thy; 291 val thy1 = Sign.add_path (space_implode "_" new_type_names) thy; 292 293 val descr' = flat descr; 294 val recTs = Old_Datatype_Aux.get_rec_types descr'; 295 val used = fold Term.add_tfree_namesT recTs []; 296 val newTs = take (length (hd descr)) recTs; 297 val T' = TFree (singleton (Name.variant_list used) "'t", \<^sort>\<open>type\<close>); 298 299 fun mk_dummyT dt = binder_types (Old_Datatype_Aux.typ_of_dtyp descr' dt) ---> T'; 300 301 val case_dummy_fns = 302 map (fn (_, (_, _, constrs)) => map (fn (_, cargs) => 303 let 304 val Ts = map (Old_Datatype_Aux.typ_of_dtyp descr') cargs; 305 val Ts' = map mk_dummyT (filter Old_Datatype_Aux.is_rec_type cargs) 306 in Const (\<^const_name>\<open>undefined\<close>, Ts @ Ts' ---> T') end) constrs) descr'; 307 308 val case_names0 = map (fn s => Sign.full_bname thy1 ("case_" ^ s)) new_type_names; 309 310 (* define case combinators via primrec combinators *) 311 312 fun def_case ((((i, (_, _, constrs)), T as Type (Tcon, _)), name), recname) (defs, thy) = 313 if is_some (Ctr_Sugar.ctr_sugar_of ctxt Tcon) then 314 (defs, thy) 315 else 316 let 317 val (fns1, fns2) = split_list (map (fn ((_, cargs), j) => 318 let 319 val Ts = map (Old_Datatype_Aux.typ_of_dtyp descr') cargs; 320 val Ts' = Ts @ map mk_dummyT (filter Old_Datatype_Aux.is_rec_type cargs); 321 val frees' = map2 (Old_Datatype_Aux.mk_Free "x") Ts' (1 upto length Ts'); 322 val frees = take (length cargs) frees'; 323 val free = Old_Datatype_Aux.mk_Free "f" (Ts ---> T') j; 324 in 325 (free, fold_rev (absfree o dest_Free) frees' (list_comb (free, frees))) 326 end) (constrs ~~ (1 upto length constrs))); 327 328 val caseT = map (snd o dest_Free) fns1 @ [T] ---> T'; 329 val fns = flat (take i case_dummy_fns) @ fns2 @ flat (drop (i + 1) case_dummy_fns); 330 val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T'); 331 val decl = ((Binding.name (Long_Name.base_name name), caseT), NoSyn); 332 val def = 333 (Binding.name (Thm.def_name (Long_Name.base_name name)), 334 Logic.mk_equals (Const (name, caseT), 335 fold_rev lambda fns1 336 (list_comb (reccomb, 337 flat (take i case_dummy_fns) @ fns2 @ flat (drop (i + 1) case_dummy_fns))))); 338 val ([def_thm], thy') = 339 thy 340 |> Sign.declare_const_global decl |> snd 341 |> (Global_Theory.add_defs false o map Thm.no_attributes) [def]; 342 in (defs @ [def_thm], thy') end; 343 344 val (case_defs, thy2) = 345 fold def_case (hd descr ~~ newTs ~~ case_names0 ~~ take (length newTs) reccomb_names) 346 ([], thy1); 347 348 fun prove_case t = 349 Goal.prove_sorry_global thy2 [] [] t (fn {context = ctxt, ...} => 350 EVERY [rewrite_goals_tac ctxt (case_defs @ map mk_meta_eq primrec_thms), 351 resolve_tac ctxt [refl] 1]); 352 353 fun prove_cases (Type (Tcon, _)) ts = 354 (case Ctr_Sugar.ctr_sugar_of ctxt Tcon of 355 SOME {case_thms, ...} => case_thms 356 | NONE => map prove_case ts); 357 358 val case_thms = 359 map2 prove_cases newTs (Old_Datatype_Prop.make_cases case_names0 descr thy2); 360 361 fun case_name_of (th :: _) = 362 fst (dest_Const (head_of (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop (Thm.prop_of th)))))); 363 364 val case_names = map case_name_of case_thms; 365 in 366 thy2 367 |> Context.theory_map 368 ((fold o fold) (Named_Theorems.add_thm \<^named_theorems>\<open>nitpick_simp\<close>) case_thms) 369 |> Sign.parent_path 370 |> Old_Datatype_Aux.store_thmss "case" new_type_names case_thms 371 |-> (fn thmss => pair (thmss, case_names)) 372 end; 373 374 375(* case splitting *) 376 377fun prove_split_thms (config : Old_Datatype_Aux.config) 378 new_type_names case_names descr constr_inject dist_rewrites casedist_thms case_thms thy = 379 let 380 val _ = Old_Datatype_Aux.message config "Proving equations for case splitting ..."; 381 382 val descr' = flat descr; 383 val recTs = Old_Datatype_Aux.get_rec_types descr'; 384 val newTs = take (length (hd descr)) recTs; 385 386 fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'), exhaustion), case_thms'), T) = 387 let 388 val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (Thm.prems_of exhaustion))); 389 val ctxt = Proof_Context.init_global thy; 390 val exhaustion' = exhaustion 391 |> infer_instantiate ctxt [(#1 (dest_Var lhs), Thm.cterm_of ctxt (Free ("x", T)))]; 392 val tac = 393 EVERY [resolve_tac ctxt [exhaustion'] 1, 394 ALLGOALS (asm_simp_tac 395 (put_simpset HOL_ss ctxt addsimps (dist_rewrites' @ inject @ case_thms')))]; 396 in 397 (Goal.prove_sorry_global thy [] [] t1 (K tac), 398 Goal.prove_sorry_global thy [] [] t2 (K tac)) 399 end; 400 401 val split_thm_pairs = 402 map prove_split_thms 403 (Old_Datatype_Prop.make_splits case_names descr thy ~~ constr_inject ~~ 404 dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs); 405 406 val (split_thms, split_asm_thms) = split_list split_thm_pairs 407 408 in 409 thy 410 |> Old_Datatype_Aux.store_thms "split" new_type_names split_thms 411 ||>> Old_Datatype_Aux.store_thms "split_asm" new_type_names split_asm_thms 412 |-> (fn (thms1, thms2) => pair (thms1 ~~ thms2)) 413 end; 414 415fun prove_case_cong_weaks new_type_names case_names descr thy = 416 let 417 fun prove_case_cong_weak t = 418 Goal.prove_sorry_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) 419 (fn {context = ctxt, prems, ...} => 420 EVERY [resolve_tac ctxt [hd prems RS arg_cong] 1]); 421 422 val case_cong_weaks = 423 map prove_case_cong_weak (Old_Datatype_Prop.make_case_cong_weaks case_names descr thy); 424 425 in thy |> Old_Datatype_Aux.store_thms "case_cong_weak" new_type_names case_cong_weaks end; 426 427 428(* additional theorems for TFL *) 429 430fun prove_nchotomys (config : Old_Datatype_Aux.config) new_type_names descr casedist_thms thy = 431 let 432 val _ = Old_Datatype_Aux.message config "Proving additional theorems for TFL ..."; 433 434 fun prove_nchotomy (t, exhaustion) = 435 let 436 (* For goal i, select the correct disjunct to attack, then prove it *) 437 fun tac ctxt i 0 = 438 EVERY [TRY (resolve_tac ctxt [disjI1] i), hyp_subst_tac ctxt i, 439 REPEAT (resolve_tac ctxt [exI] i), resolve_tac ctxt [refl] i] 440 | tac ctxt i n = resolve_tac ctxt [disjI2] i THEN tac ctxt i (n - 1); 441 in 442 Goal.prove_sorry_global thy [] [] t 443 (fn {context = ctxt, ...} => 444 EVERY [resolve_tac ctxt [allI] 1, 445 Old_Datatype_Aux.exh_tac ctxt (K exhaustion) 1, 446 ALLGOALS (fn i => tac ctxt i (i - 1))]) 447 end; 448 449 val nchotomys = 450 map prove_nchotomy (Old_Datatype_Prop.make_nchotomys descr ~~ casedist_thms); 451 452 in thy |> Old_Datatype_Aux.store_thms "nchotomy" new_type_names nchotomys end; 453 454fun prove_case_congs new_type_names case_names descr nchotomys case_thms thy = 455 let 456 fun prove_case_cong ((t, nchotomy), case_rewrites) = 457 let 458 val Const (\<^const_name>\<open>Pure.imp\<close>, _) $ tm $ _ = t; 459 val Const (\<^const_name>\<open>Trueprop\<close>, _) $ (Const (\<^const_name>\<open>HOL.eq\<close>, _) $ _ $ Ma) = tm; 460 val nchotomy' = nchotomy RS spec; 461 val [v] = Term.add_var_names (Thm.concl_of nchotomy') []; 462 in 463 Goal.prove_sorry_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) 464 (fn {context = ctxt, prems, ...} => 465 let 466 val nchotomy'' = 467 infer_instantiate ctxt [(v, Thm.cterm_of ctxt Ma)] nchotomy'; 468 val simplify = asm_simp_tac (put_simpset HOL_ss ctxt addsimps (prems @ case_rewrites)) 469 in 470 EVERY [ 471 simp_tac (put_simpset HOL_ss ctxt addsimps [hd prems]) 1, 472 cut_tac nchotomy'' 1, 473 REPEAT (eresolve_tac ctxt [disjE] 1 THEN 474 REPEAT (eresolve_tac ctxt [exE] 1) THEN simplify 1), 475 REPEAT (eresolve_tac ctxt [exE] 1) THEN simplify 1 (* Get last disjunct *)] 476 end) 477 end; 478 479 val case_congs = 480 map prove_case_cong 481 (Old_Datatype_Prop.make_case_congs case_names descr thy ~~ nchotomys ~~ case_thms); 482 483 in thy |> Old_Datatype_Aux.store_thms "case_cong" new_type_names case_congs end; 484 485 486 487(** derive datatype props **) 488 489local 490 491fun make_dt_info descr induct inducts rec_names rec_rewrites 492 (index, (((((((((((_, (tname, _, _))), inject), distinct), 493 exhaust), nchotomy), case_name), case_rewrites), case_cong), case_cong_weak), 494 (split, split_asm))) = 495 (tname, 496 {index = index, 497 descr = descr, 498 inject = inject, 499 distinct = distinct, 500 induct = induct, 501 inducts = inducts, 502 exhaust = exhaust, 503 nchotomy = nchotomy, 504 rec_names = rec_names, 505 rec_rewrites = rec_rewrites, 506 case_name = case_name, 507 case_rewrites = case_rewrites, 508 case_cong = case_cong, 509 case_cong_weak = case_cong_weak, 510 split = split, 511 split_asm = split_asm}); 512 513in 514 515fun derive_datatype_props config dt_names descr induct inject distinct thy2 = 516 let 517 val flat_descr = flat descr; 518 val new_type_names = map Long_Name.base_name dt_names; 519 val _ = 520 Old_Datatype_Aux.message config 521 ("Deriving properties for datatype(s) " ^ commas_quote new_type_names); 522 523 val (exhaust, thy3) = thy2 524 |> prove_casedist_thms config new_type_names descr induct 525 (Old_Datatype_Data.mk_case_names_exhausts flat_descr dt_names); 526 val (nchotomys, thy4) = thy3 527 |> prove_nchotomys config new_type_names descr exhaust; 528 val ((rec_names, rec_rewrites), thy5) = thy4 529 |> prove_primrec_thms config new_type_names descr 530 (#inject o the o Symtab.lookup (Old_Datatype_Data.get_all thy4)) inject 531 (distinct, 532 Old_Datatype_Data.all_distincts thy2 (Old_Datatype_Aux.get_rec_types flat_descr)) induct; 533 val ((case_rewrites, case_names), thy6) = thy5 534 |> prove_case_thms config new_type_names descr rec_names rec_rewrites; 535 val (case_congs, thy7) = thy6 536 |> prove_case_congs new_type_names case_names descr nchotomys case_rewrites; 537 val (case_cong_weaks, thy8) = thy7 538 |> prove_case_cong_weaks new_type_names case_names descr; 539 val (splits, thy9) = thy8 540 |> prove_split_thms config new_type_names case_names descr 541 inject distinct exhaust case_rewrites; 542 543 val inducts = Project_Rule.projections (Proof_Context.init_global thy2) induct; 544 val dt_infos = 545 map_index 546 (make_dt_info flat_descr induct inducts rec_names rec_rewrites) 547 (hd descr ~~ inject ~~ distinct ~~ exhaust ~~ nchotomys ~~ 548 case_names ~~ case_rewrites ~~ case_congs ~~ case_cong_weaks ~~ splits); 549 val dt_names = map fst dt_infos; 550 val prfx = Binding.qualify true (space_implode "_" new_type_names); 551 val simps = flat (inject @ distinct @ case_rewrites) @ rec_rewrites; 552 val named_rules = flat (map_index (fn (i, tname) => 553 [((Binding.empty, [Induct.induct_type tname]), [([nth inducts i], [])]), 554 ((Binding.empty, [Induct.cases_type tname]), [([nth exhaust i], [])])]) dt_names); 555 val unnamed_rules = map (fn induct => 556 ((Binding.empty, [Rule_Cases.inner_rule, Induct.induct_type ""]), [([induct], [])])) 557 (drop (length dt_names) inducts); 558 559 val ctxt = Proof_Context.init_global thy9; 560 val case_combs = 561 map (Proof_Context.read_const {proper = true, strict = true} ctxt) case_names; 562 val constrss = map (fn (dtname, {descr, index, ...}) => 563 map (Proof_Context.read_const {proper = true, strict = true} ctxt o fst) 564 (#3 (the (AList.lookup op = descr index)))) dt_infos; 565 in 566 thy9 567 |> Global_Theory.note_thmss "" 568 ([((prfx (Binding.name "simps"), []), [(simps, [])]), 569 ((prfx (Binding.name "inducts"), []), [(inducts, [])]), 570 ((prfx (Binding.name "splits"), []), [(maps (fn (x, y) => [x, y]) splits, [])]), 571 ((Binding.empty, [Simplifier.simp_add]), 572 [(flat case_rewrites @ flat distinct @ rec_rewrites, [])]), 573 ((Binding.empty, [iff_add]), [(flat inject, [])]), 574 ((Binding.empty, [Classical.safe_elim NONE]), 575 [(map (fn th => th RS notE) (flat distinct), [])]), 576 ((Binding.empty, [Simplifier.cong_add]), [(case_cong_weaks, [])]), 577 ((Binding.empty, [Induct.induct_simp_add]), [(flat (distinct @ inject), [])])] @ 578 named_rules @ unnamed_rules) 579 |> snd 580 |> Code.declare_default_eqns_global (map (rpair true) rec_rewrites) 581 |> Old_Datatype_Data.register dt_infos 582 |> Context.theory_map (fold2 Case_Translation.register case_combs constrss) 583 |> Old_Datatype_Data.interpretation_data (config, dt_names) 584 |> pair dt_names 585 end; 586 587end; 588 589 590 591(** declare existing type as datatype **) 592 593local 594 595fun prove_rep_datatype config dt_names descr raw_inject half_distinct raw_induct thy1 = 596 let 597 val raw_distinct = (map o maps) (fn thm => [thm, thm RS not_sym]) half_distinct; 598 val new_type_names = map Long_Name.base_name dt_names; 599 val prfx = Binding.qualify true (space_implode "_" new_type_names); 600 val (((inject, distinct), [(_, [induct])]), thy2) = 601 thy1 602 |> Old_Datatype_Aux.store_thmss "inject" new_type_names raw_inject 603 ||>> Old_Datatype_Aux.store_thmss "distinct" new_type_names raw_distinct 604 ||>> Global_Theory.note_thmss "" 605 [((prfx (Binding.name "induct"), [Old_Datatype_Data.mk_case_names_induct descr]), 606 [([raw_induct], [])])]; 607 in 608 thy2 609 |> derive_datatype_props config dt_names [descr] induct inject distinct 610 end; 611 612fun gen_rep_datatype prep_term config after_qed raw_ts thy = 613 let 614 val ctxt = Proof_Context.init_global thy; 615 616 fun constr_of_term (Const (c, T)) = (c, T) 617 | constr_of_term t = error ("Not a constant: " ^ Syntax.string_of_term ctxt t); 618 fun no_constr (c, T) = 619 error ("Bad constructor: " ^ Proof_Context.markup_const ctxt c ^ "::" ^ 620 Syntax.string_of_typ ctxt T); 621 fun type_of_constr (cT as (_, T)) = 622 let 623 val frees = Term.add_tfreesT T []; 624 val (tyco, vs) = (apsnd o map) dest_TFree (dest_Type (body_type T)) 625 handle TYPE _ => no_constr cT 626 val _ = if has_duplicates (eq_fst (op =)) vs then no_constr cT else (); 627 val _ = if length frees <> length vs then no_constr cT else (); 628 in (tyco, (vs, cT)) end; 629 630 val raw_cs = 631 AList.group (op =) (map (type_of_constr o constr_of_term o prep_term thy) raw_ts); 632 val _ = 633 (case map_filter (fn (tyco, _) => 634 if Symtab.defined (Old_Datatype_Data.get_all thy) tyco then SOME tyco else NONE) raw_cs of 635 [] => () 636 | tycos => error ("Type(s) " ^ commas_quote tycos ^ " already represented inductively")); 637 val raw_vss = maps (map (map snd o fst) o snd) raw_cs; 638 val ms = 639 (case distinct (op =) (map length raw_vss) of 640 [n] => 0 upto n - 1 641 | _ => error "Different types in given constructors"); 642 fun inter_sort m = 643 map (fn xs => nth xs m) raw_vss 644 |> foldr1 (Sorts.inter_sort (Sign.classes_of thy)); 645 val sorts = map inter_sort ms; 646 val vs = Name.invent_names Name.context Name.aT sorts; 647 648 fun norm_constr (raw_vs, (c, T)) = 649 (c, map_atyps 650 (TFree o (the o AList.lookup (op =) (map fst raw_vs ~~ vs)) o fst o dest_TFree) T); 651 652 val cs = map (apsnd (map norm_constr)) raw_cs; 653 val dtyps_of_typ = map (Old_Datatype_Aux.dtyp_of_typ (map (rpair vs o fst) cs)) o binder_types; 654 val dt_names = map fst cs; 655 656 fun mk_spec (i, (tyco, constr)) = 657 (i, (tyco, map Old_Datatype_Aux.DtTFree vs, (map o apsnd) dtyps_of_typ constr)); 658 val descr = map_index mk_spec cs; 659 val injs = Old_Datatype_Prop.make_injs [descr]; 660 val half_distincts = Old_Datatype_Prop.make_distincts [descr]; 661 val ind = Old_Datatype_Prop.make_ind [descr]; 662 val rules = (map o map o map) Logic.close_form [[[ind]], injs, half_distincts]; 663 664 fun after_qed' raw_thms = 665 let 666 val [[[raw_induct]], raw_inject, half_distinct] = 667 unflat rules (map Drule.zero_var_indexes_list raw_thms); 668 (*FIXME somehow dubious*) 669 in 670 Proof_Context.background_theory_result (* FIXME !? *) 671 (prove_rep_datatype config dt_names descr raw_inject half_distinct raw_induct) 672 #-> after_qed 673 end; 674 in 675 ctxt 676 |> Proof.theorem NONE after_qed' ((map o map) (rpair []) (flat rules)) 677 end; 678 679in 680 681val rep_datatype = gen_rep_datatype Sign.cert_term; 682val rep_datatype_cmd = gen_rep_datatype Syntax.read_term_global; 683 684end; 685 686 687(* outer syntax *) 688 689val _ = 690 Outer_Syntax.command \<^command_keyword>\<open>old_rep_datatype\<close> 691 "register existing types as old-style datatypes" 692 (Scan.repeat1 Parse.term >> (fn ts => 693 Toplevel.theory_to_proof (rep_datatype_cmd Old_Datatype_Aux.default_config (K I) ts))); 694 695end; 696