1(* Title: HOL/Tools/BNF/bnf_fp_util.ML 2 Author: Dmitriy Traytel, TU Muenchen 3 Author: Jasmin Blanchette, TU Muenchen 4 Author: Martin Desharnais, TU Muenchen 5 Author: Stefan Berghofer, TU Muenchen 6 Copyright 2012, 2013, 2014 7 8Shared library for the datatype and codatatype constructions. 9*) 10 11signature BNF_FP_UTIL = 12sig 13 exception EMPTY_DATATYPE of string 14 15 type fp_result = 16 {Ts: typ list, 17 bnfs: BNF_Def.bnf list, 18 pre_bnfs: BNF_Def.bnf list, 19 absT_infos: BNF_Comp.absT_info list, 20 ctors: term list, 21 dtors: term list, 22 xtor_un_folds: term list, 23 xtor_co_recs: term list, 24 xtor_co_induct: thm, 25 dtor_ctors: thm list, 26 ctor_dtors: thm list, 27 ctor_injects: thm list, 28 dtor_injects: thm list, 29 xtor_maps: thm list, 30 xtor_map_unique: thm, 31 xtor_setss: thm list list, 32 xtor_rels: thm list, 33 xtor_un_fold_thms: thm list, 34 xtor_co_rec_thms: thm list, 35 xtor_un_fold_unique: thm, 36 xtor_co_rec_unique: thm, 37 xtor_un_fold_o_maps: thm list, 38 xtor_co_rec_o_maps: thm list, 39 xtor_un_fold_transfers: thm list, 40 xtor_co_rec_transfers: thm list, 41 xtor_rel_co_induct: thm, 42 dtor_set_inducts: thm list} 43 44 val morph_fp_result: morphism -> fp_result -> fp_result 45 46 val time: Proof.context -> Timer.real_timer -> string -> Timer.real_timer 47 48 val fixpoint: ('a * 'a -> bool) -> ('a list -> 'a list) -> 'a list -> 'a list 49 50 val IITN: string 51 val LevN: string 52 val algN: string 53 val behN: string 54 val bisN: string 55 val carTN: string 56 val caseN: string 57 val coN: string 58 val coinductN: string 59 val coinduct_strongN: string 60 val corecN: string 61 val corec_discN: string 62 val corec_disc_iffN: string 63 val ctorN: string 64 val ctor_dtorN: string 65 val ctor_exhaustN: string 66 val ctor_induct2N: string 67 val ctor_inductN: string 68 val ctor_injectN: string 69 val ctor_foldN: string 70 val ctor_fold_o_mapN: string 71 val ctor_fold_transferN: string 72 val ctor_fold_uniqueN: string 73 val ctor_mapN: string 74 val ctor_map_uniqueN: string 75 val ctor_recN: string 76 val ctor_rec_o_mapN: string 77 val ctor_rec_transferN: string 78 val ctor_rec_uniqueN: string 79 val ctor_relN: string 80 val ctor_rel_inductN: string 81 val ctor_set_inclN: string 82 val ctor_set_set_inclN: string 83 val dtorN: string 84 val dtor_coinductN: string 85 val dtor_corecN: string 86 val dtor_corec_o_mapN: string 87 val dtor_corec_transferN: string 88 val dtor_corec_uniqueN: string 89 val dtor_ctorN: string 90 val dtor_exhaustN: string 91 val dtor_injectN: string 92 val dtor_mapN: string 93 val dtor_map_coinductN: string 94 val dtor_map_coinduct_strongN: string 95 val dtor_map_uniqueN: string 96 val dtor_relN: string 97 val dtor_rel_coinductN: string 98 val dtor_set_inclN: string 99 val dtor_set_set_inclN: string 100 val dtor_coinduct_strongN: string 101 val dtor_unfoldN: string 102 val dtor_unfold_o_mapN: string 103 val dtor_unfold_transferN: string 104 val dtor_unfold_uniqueN: string 105 val exhaustN: string 106 val colN: string 107 val inductN: string 108 val injectN: string 109 val isNodeN: string 110 val lsbisN: string 111 val mapN: string 112 val map_uniqueN: string 113 val min_algN: string 114 val morN: string 115 val nchotomyN: string 116 val recN: string 117 val rel_casesN: string 118 val rel_coinductN: string 119 val rel_inductN: string 120 val rel_injectN: string 121 val rel_introsN: string 122 val rel_distinctN: string 123 val rel_selN: string 124 val rvN: string 125 val corec_selN: string 126 val set_inclN: string 127 val set_set_inclN: string 128 val setN: string 129 val simpsN: string 130 val strTN: string 131 val str_initN: string 132 val sum_bdN: string 133 val sum_bdTN: string 134 val uniqueN: string 135 136 (* TODO: Don't index set facts. Isabelle packages traditionally generate uniform names. *) 137 val mk_ctor_setN: int -> string 138 val mk_dtor_setN: int -> string 139 val mk_dtor_set_inductN: int -> string 140 val mk_set_inductN: int -> string 141 142 val co_prefix: BNF_Util.fp_kind -> string 143 144 val split_conj_thm: thm -> thm list 145 val split_conj_prems: int -> thm -> thm 146 147 val mk_sumTN: typ list -> typ 148 val mk_sumTN_balanced: typ list -> typ 149 val mk_tupleT_balanced: typ list -> typ 150 val mk_sumprodT_balanced: typ list list -> typ 151 152 val mk_proj: typ -> int -> int -> term 153 154 val mk_convol: term * term -> term 155 val mk_rel_prod: term -> term -> term 156 val mk_rel_sum: term -> term -> term 157 158 val Inl_const: typ -> typ -> term 159 val Inr_const: typ -> typ -> term 160 val mk_tuple_balanced: term list -> term 161 val mk_tuple1_balanced: typ list -> term list -> term 162 val abs_curried_balanced: typ list -> term -> term 163 val mk_tupled_fun: term -> term -> term list -> term 164 165 val mk_case_sum: term * term -> term 166 val mk_case_sumN: term list -> term 167 val mk_case_absumprod: typ -> term -> term list -> term list list -> term list list -> term 168 169 val mk_Inl: typ -> term -> term 170 val mk_Inr: typ -> term -> term 171 val mk_sumprod_balanced: typ -> int -> int -> term list -> term 172 val mk_absumprod: typ -> term -> int -> int -> term list -> term 173 174 val dest_sumT: typ -> typ * typ 175 val dest_sumTN_balanced: int -> typ -> typ list 176 val dest_tupleT_balanced: int -> typ -> typ list 177 val dest_absumprodT: typ -> typ -> int -> int list -> typ -> typ list list 178 179 val If_const: typ -> term 180 181 val mk_Field: term -> term 182 val mk_If: term -> term -> term -> term 183 184 val mk_absumprodE: thm -> int list -> thm 185 186 val mk_sum_caseN: int -> int -> thm 187 val mk_sum_caseN_balanced: int -> int -> thm 188 189 val mk_sum_Cinfinite: thm list -> thm 190 val mk_sum_card_order: thm list -> thm 191 192 val force_typ: Proof.context -> typ -> term -> term 193 194 val mk_xtor_rel_co_induct_thm: BNF_Util.fp_kind -> term list -> term list -> term list -> 195 term list -> term list -> term list -> term list -> term list -> 196 ({prems: thm list, context: Proof.context} -> tactic) -> Proof.context -> thm 197 val mk_xtor_co_iter_transfer_thms: BNF_Util.fp_kind -> term list -> term list -> term list -> 198 term list -> term list -> term list -> term list -> 199 ({prems: thm list, context: Proof.context} -> tactic) -> Proof.context -> thm list 200 val mk_xtor_co_iter_o_map_thms: BNF_Util.fp_kind -> bool -> int -> thm -> thm list -> thm list -> 201 thm list -> thm list -> thm list 202 val derive_xtor_co_recs: BNF_Util.fp_kind -> binding list -> (typ list -> typ list) -> 203 (typ list list * typ list) -> BNF_Def.bnf list -> term list -> term list -> 204 thm -> thm list -> thm list -> thm list -> thm list -> 205 (BNF_Comp.absT_info * BNF_Comp.absT_info) option list -> 206 local_theory -> 207 (term list * (thm list * thm * thm list * thm list)) * local_theory 208 val raw_qualify: (binding -> binding) -> binding -> binding -> binding 209 210 val fixpoint_bnf: bool -> (binding -> binding) -> 211 (binding list -> (string * sort) list -> typ list * typ list list -> BNF_Def.bnf list -> 212 BNF_Comp.absT_info list -> local_theory -> 'a) -> 213 binding list -> (string * sort) list -> (string * sort) list -> (string * sort) list -> 214 typ list -> BNF_Comp.comp_cache -> local_theory -> 215 ((BNF_Def.bnf list * BNF_Comp.absT_info list) * BNF_Comp.comp_cache) * 'a 216end; 217 218structure BNF_FP_Util : BNF_FP_UTIL = 219struct 220 221open Ctr_Sugar 222open BNF_Comp 223open BNF_Def 224open BNF_Util 225open BNF_FP_Util_Tactics 226 227exception EMPTY_DATATYPE of string; 228 229type fp_result = 230 {Ts: typ list, 231 bnfs: bnf list, 232 pre_bnfs: BNF_Def.bnf list, 233 absT_infos: BNF_Comp.absT_info list, 234 ctors: term list, 235 dtors: term list, 236 xtor_un_folds: term list, 237 xtor_co_recs: term list, 238 xtor_co_induct: thm, 239 dtor_ctors: thm list, 240 ctor_dtors: thm list, 241 ctor_injects: thm list, 242 dtor_injects: thm list, 243 xtor_maps: thm list, 244 xtor_map_unique: thm, 245 xtor_setss: thm list list, 246 xtor_rels: thm list, 247 xtor_un_fold_thms: thm list, 248 xtor_co_rec_thms: thm list, 249 xtor_un_fold_unique: thm, 250 xtor_co_rec_unique: thm, 251 xtor_un_fold_o_maps: thm list, 252 xtor_co_rec_o_maps: thm list, 253 xtor_un_fold_transfers: thm list, 254 xtor_co_rec_transfers: thm list, 255 xtor_rel_co_induct: thm, 256 dtor_set_inducts: thm list}; 257 258fun morph_fp_result phi {Ts, bnfs, pre_bnfs, absT_infos, ctors, dtors, xtor_un_folds, 259 xtor_co_recs, xtor_co_induct, dtor_ctors, ctor_dtors, ctor_injects, dtor_injects, xtor_maps, 260 xtor_map_unique, xtor_setss, xtor_rels, xtor_un_fold_thms, xtor_co_rec_thms, 261 xtor_un_fold_unique, xtor_co_rec_unique, xtor_un_fold_o_maps, 262 xtor_co_rec_o_maps, xtor_un_fold_transfers, xtor_co_rec_transfers, xtor_rel_co_induct, 263 dtor_set_inducts} = 264 {Ts = map (Morphism.typ phi) Ts, 265 bnfs = map (morph_bnf phi) bnfs, 266 pre_bnfs = map (morph_bnf phi) pre_bnfs, 267 absT_infos = map (morph_absT_info phi) absT_infos, 268 ctors = map (Morphism.term phi) ctors, 269 dtors = map (Morphism.term phi) dtors, 270 xtor_un_folds = map (Morphism.term phi) xtor_un_folds, 271 xtor_co_recs = map (Morphism.term phi) xtor_co_recs, 272 xtor_co_induct = Morphism.thm phi xtor_co_induct, 273 dtor_ctors = map (Morphism.thm phi) dtor_ctors, 274 ctor_dtors = map (Morphism.thm phi) ctor_dtors, 275 ctor_injects = map (Morphism.thm phi) ctor_injects, 276 dtor_injects = map (Morphism.thm phi) dtor_injects, 277 xtor_maps = map (Morphism.thm phi) xtor_maps, 278 xtor_map_unique = Morphism.thm phi xtor_map_unique, 279 xtor_setss = map (map (Morphism.thm phi)) xtor_setss, 280 xtor_rels = map (Morphism.thm phi) xtor_rels, 281 xtor_un_fold_thms = map (Morphism.thm phi) xtor_un_fold_thms, 282 xtor_co_rec_thms = map (Morphism.thm phi) xtor_co_rec_thms, 283 xtor_un_fold_unique = Morphism.thm phi xtor_un_fold_unique, 284 xtor_co_rec_unique = Morphism.thm phi xtor_co_rec_unique, 285 xtor_un_fold_o_maps = map (Morphism.thm phi) xtor_un_fold_o_maps, 286 xtor_co_rec_o_maps = map (Morphism.thm phi) xtor_co_rec_o_maps, 287 xtor_un_fold_transfers = map (Morphism.thm phi) xtor_un_fold_transfers, 288 xtor_co_rec_transfers = map (Morphism.thm phi) xtor_co_rec_transfers, 289 xtor_rel_co_induct = Morphism.thm phi xtor_rel_co_induct, 290 dtor_set_inducts = map (Morphism.thm phi) dtor_set_inducts}; 291 292fun time ctxt timer msg = (if Config.get ctxt bnf_timing 293 then warning (msg ^ ": " ^ string_of_int (Time.toMilliseconds (Timer.checkRealTimer timer)) ^ 294 " ms") 295 else (); Timer.startRealTimer ()); 296 297val preN = "pre_" 298val rawN = "raw_" 299 300val coN = "co" 301val unN = "un" 302val algN = "alg" 303val IITN = "IITN" 304val foldN = "fold" 305val unfoldN = unN ^ foldN 306val uniqueN = "unique" 307val transferN = "transfer" 308val simpsN = "simps" 309val ctorN = "ctor" 310val dtorN = "dtor" 311val ctor_foldN = ctorN ^ "_" ^ foldN 312val dtor_unfoldN = dtorN ^ "_" ^ unfoldN 313val ctor_fold_uniqueN = ctor_foldN ^ "_" ^ uniqueN 314val ctor_fold_o_mapN = ctor_foldN ^ "_o_" ^ mapN 315val dtor_unfold_uniqueN = dtor_unfoldN ^ "_" ^ uniqueN 316val dtor_unfold_o_mapN = dtor_unfoldN ^ "_o_" ^ mapN 317val ctor_fold_transferN = ctor_foldN ^ "_" ^ transferN 318val dtor_unfold_transferN = dtor_unfoldN ^ "_" ^ transferN 319val ctor_mapN = ctorN ^ "_" ^ mapN 320val dtor_mapN = dtorN ^ "_" ^ mapN 321val map_uniqueN = mapN ^ "_" ^ uniqueN 322val ctor_map_uniqueN = ctorN ^ "_" ^ map_uniqueN 323val dtor_map_uniqueN = dtorN ^ "_" ^ map_uniqueN 324val min_algN = "min_alg" 325val morN = "mor" 326val bisN = "bis" 327val lsbisN = "lsbis" 328val sum_bdTN = "sbdT" 329val sum_bdN = "sbd" 330val carTN = "carT" 331val strTN = "strT" 332val isNodeN = "isNode" 333val LevN = "Lev" 334val rvN = "recover" 335val behN = "beh" 336val setN = "set" 337val mk_ctor_setN = prefix (ctorN ^ "_") o mk_setN 338val mk_dtor_setN = prefix (dtorN ^ "_") o mk_setN 339fun mk_set_inductN i = mk_setN i ^ "_induct" 340val mk_dtor_set_inductN = prefix (dtorN ^ "_") o mk_set_inductN 341 342val str_initN = "str_init" 343val recN = "rec" 344val corecN = coN ^ recN 345val ctor_recN = ctorN ^ "_" ^ recN 346val ctor_rec_o_mapN = ctor_recN ^ "_o_" ^ mapN 347val ctor_rec_transferN = ctor_recN ^ "_" ^ transferN 348val ctor_rec_uniqueN = ctor_recN ^ "_" ^ uniqueN 349val dtor_corecN = dtorN ^ "_" ^ corecN 350val dtor_corec_o_mapN = dtor_corecN ^ "_o_" ^ mapN 351val dtor_corec_transferN = dtor_corecN ^ "_" ^ transferN 352val dtor_corec_uniqueN = dtor_corecN ^ "_" ^ uniqueN 353 354val ctor_dtorN = ctorN ^ "_" ^ dtorN 355val dtor_ctorN = dtorN ^ "_" ^ ctorN 356val nchotomyN = "nchotomy" 357val injectN = "inject" 358val exhaustN = "exhaust" 359val ctor_injectN = ctorN ^ "_" ^ injectN 360val ctor_exhaustN = ctorN ^ "_" ^ exhaustN 361val dtor_injectN = dtorN ^ "_" ^ injectN 362val dtor_exhaustN = dtorN ^ "_" ^ exhaustN 363val ctor_relN = ctorN ^ "_" ^ relN 364val dtor_relN = dtorN ^ "_" ^ relN 365val inductN = "induct" 366val coinductN = coN ^ inductN 367val ctor_inductN = ctorN ^ "_" ^ inductN 368val ctor_induct2N = ctor_inductN ^ "2" 369val dtor_map_coinductN = dtor_mapN ^ "_" ^ coinductN 370val dtor_coinductN = dtorN ^ "_" ^ coinductN 371val coinduct_strongN = coinductN ^ "_strong" 372val dtor_map_coinduct_strongN = dtor_mapN ^ "_" ^ coinduct_strongN 373val dtor_coinduct_strongN = dtorN ^ "_" ^ coinduct_strongN 374val colN = "col" 375val set_inclN = "set_incl" 376val ctor_set_inclN = ctorN ^ "_" ^ set_inclN 377val dtor_set_inclN = dtorN ^ "_" ^ set_inclN 378val set_set_inclN = "set_set_incl" 379val ctor_set_set_inclN = ctorN ^ "_" ^ set_set_inclN 380val dtor_set_set_inclN = dtorN ^ "_" ^ set_set_inclN 381 382val caseN = "case" 383val discN = "disc" 384val corec_discN = corecN ^ "_" ^ discN 385val iffN = "_iff" 386val corec_disc_iffN = corec_discN ^ iffN 387val distinctN = "distinct" 388val rel_distinctN = relN ^ "_" ^ distinctN 389val injectN = "inject" 390val rel_casesN = relN ^ "_cases" 391val rel_injectN = relN ^ "_" ^ injectN 392val rel_introsN = relN ^ "_intros" 393val rel_coinductN = relN ^ "_" ^ coinductN 394val rel_selN = relN ^ "_sel" 395val dtor_rel_coinductN = dtorN ^ "_" ^ rel_coinductN 396val rel_inductN = relN ^ "_" ^ inductN 397val ctor_rel_inductN = ctorN ^ "_" ^ rel_inductN 398val selN = "sel" 399val corec_selN = corecN ^ "_" ^ selN 400 401fun co_prefix fp = case_fp fp "" "co"; 402 403fun dest_sumT (Type (\<^type_name>\<open>sum\<close>, [T, T'])) = (T, T'); 404 405val dest_sumTN_balanced = Balanced_Tree.dest dest_sumT; 406 407fun dest_tupleT_balanced 0 \<^typ>\<open>unit\<close> = [] 408 | dest_tupleT_balanced n T = Balanced_Tree.dest HOLogic.dest_prodT n T; 409 410fun dest_absumprodT absT repT n ms = 411 map2 dest_tupleT_balanced ms o dest_sumTN_balanced n o mk_repT absT repT; 412 413val mk_sumTN = Library.foldr1 mk_sumT; 414val mk_sumTN_balanced = Balanced_Tree.make mk_sumT; 415 416fun mk_tupleT_balanced [] = HOLogic.unitT 417 | mk_tupleT_balanced Ts = Balanced_Tree.make HOLogic.mk_prodT Ts; 418 419val mk_sumprodT_balanced = mk_sumTN_balanced o map mk_tupleT_balanced; 420 421fun mk_proj T n k = 422 let val (binders, _) = strip_typeN n T in 423 fold_rev (fn T => fn t => Abs (Name.uu, T, t)) binders (Bound (n - k - 1)) 424 end; 425 426fun mk_convol (f, g) = 427 let 428 val (fU, fTU) = `range_type (fastype_of f); 429 val ((gT, gU), gTU) = `dest_funT (fastype_of g); 430 val convolT = fTU --> gTU --> gT --> HOLogic.mk_prodT (fU, gU); 431 in Const (\<^const_name>\<open>convol\<close>, convolT) $ f $ g end; 432 433fun mk_rel_prod R S = 434 let 435 val ((A1, A2), RT) = `dest_pred2T (fastype_of R); 436 val ((B1, B2), ST) = `dest_pred2T (fastype_of S); 437 val rel_prodT = RT --> ST --> mk_pred2T (HOLogic.mk_prodT (A1, B1)) (HOLogic.mk_prodT (A2, B2)); 438 in Const (\<^const_name>\<open>rel_prod\<close>, rel_prodT) $ R $ S end; 439 440fun mk_rel_sum R S = 441 let 442 val ((A1, A2), RT) = `dest_pred2T (fastype_of R); 443 val ((B1, B2), ST) = `dest_pred2T (fastype_of S); 444 val rel_sumT = RT --> ST --> mk_pred2T (mk_sumT (A1, B1)) (mk_sumT (A2, B2)); 445 in Const (\<^const_name>\<open>rel_sum\<close>, rel_sumT) $ R $ S end; 446 447fun Inl_const LT RT = Const (\<^const_name>\<open>Inl\<close>, LT --> mk_sumT (LT, RT)); 448fun mk_Inl RT t = Inl_const (fastype_of t) RT $ t; 449 450fun Inr_const LT RT = Const (\<^const_name>\<open>Inr\<close>, RT --> mk_sumT (LT, RT)); 451fun mk_Inr LT t = Inr_const LT (fastype_of t) $ t; 452 453fun mk_prod1 bound_Ts (t, u) = 454 HOLogic.pair_const (fastype_of1 (bound_Ts, t)) (fastype_of1 (bound_Ts, u)) $ t $ u; 455 456fun mk_tuple1_balanced _ [] = HOLogic.unit 457 | mk_tuple1_balanced bound_Ts ts = Balanced_Tree.make (mk_prod1 bound_Ts) ts; 458 459val mk_tuple_balanced = mk_tuple1_balanced []; 460 461fun abs_curried_balanced Ts t = 462 t $ mk_tuple1_balanced (List.rev Ts) (map Bound (length Ts - 1 downto 0)) 463 |> fold_rev (Term.abs o pair Name.uu) Ts; 464 465fun mk_sumprod_balanced T n k ts = Sum_Tree.mk_inj T n k (mk_tuple_balanced ts); 466 467fun mk_absumprod absT abs0 n k ts = 468 let val abs = mk_abs absT abs0; 469 in abs $ mk_sumprod_balanced (domain_type (fastype_of abs)) n k ts end; 470 471fun mk_case_sum (f, g) = 472 let 473 val (fT, T') = dest_funT (fastype_of f); 474 val (gT, _) = dest_funT (fastype_of g); 475 in 476 Sum_Tree.mk_sumcase fT gT T' f g 477 end; 478 479val mk_case_sumN = Library.foldr1 mk_case_sum; 480val mk_case_sumN_balanced = Balanced_Tree.make mk_case_sum; 481 482fun mk_tupled_fun f x xs = 483 if xs = [x] then f else HOLogic.tupled_lambda x (Term.list_comb (f, xs)); 484 485fun mk_case_absumprod absT rep fs xss xss' = 486 HOLogic.mk_comp (mk_case_sumN_balanced 487 (@{map 3} mk_tupled_fun fs (map mk_tuple_balanced xss) xss'), mk_rep absT rep); 488 489fun If_const T = Const (\<^const_name>\<open>If\<close>, HOLogic.boolT --> T --> T --> T); 490fun mk_If p t f = let val T = fastype_of t in If_const T $ p $ t $ f end; 491 492fun mk_Field r = 493 let val T = fst (dest_relT (fastype_of r)); 494 in Const (\<^const_name>\<open>Field\<close>, mk_relT (T, T) --> HOLogic.mk_setT T) $ r end; 495 496(*dangerous; use with monotonic, converging functions only!*) 497fun fixpoint eq f X = if subset eq (f X, X) then X else fixpoint eq f (f X); 498 499(* stolen from "~~/src/HOL/Tools/Datatype/datatype_aux.ML" *) 500fun split_conj_thm th = 501 ((th RS conjunct1) :: split_conj_thm (th RS conjunct2)) handle THM _ => [th]; 502 503fun split_conj_prems limit th = 504 let 505 fun split n i th = 506 if i = n then th else split n (i + 1) (conjI RSN (i, th)) handle THM _ => th; 507 in split limit 1 th end; 508 509fun mk_obj_sumEN_balanced n = 510 Balanced_Tree.make (fn (thm1, thm2) => thm1 RSN (1, thm2 RSN (2, @{thm obj_sumE_f}))) 511 (replicate n asm_rl); 512 513fun mk_tupled_allIN_balanced 0 = @{thm unit_all_impI} 514 | mk_tupled_allIN_balanced n = 515 let 516 val (tfrees, _) = BNF_Util.mk_TFrees n \<^context>; 517 val T = mk_tupleT_balanced tfrees; 518 in 519 @{thm asm_rl[of "\<forall>x. P x \<longrightarrow> Q x" for P Q]} 520 |> Thm.instantiate' [SOME (Thm.ctyp_of \<^context> T)] [] 521 |> Raw_Simplifier.rewrite_goals_rule \<^context> @{thms split_paired_All[THEN eq_reflection]} 522 |> (fn thm => impI RS funpow n (fn th => allI RS th) thm) 523 |> Thm.varifyT_global 524 end; 525 526fun mk_absumprodE type_definition ms = 527 let val n = length ms in 528 mk_obj_sumEN_balanced n OF map mk_tupled_allIN_balanced ms RS 529 (type_definition RS @{thm type_copy_obj_one_point_absE}) 530 end; 531 532fun mk_sum_caseN 1 1 = refl 533 | mk_sum_caseN _ 1 = @{thm sum.case(1)} 534 | mk_sum_caseN 2 2 = @{thm sum.case(2)} 535 | mk_sum_caseN n k = trans OF [@{thm case_sum_step(2)}, mk_sum_caseN (n - 1) (k - 1)]; 536 537fun mk_sum_step base step thm = 538 if Thm.eq_thm_prop (thm, refl) then base else trans OF [step, thm]; 539 540fun mk_sum_caseN_balanced 1 1 = refl 541 | mk_sum_caseN_balanced n k = 542 Balanced_Tree.access {left = mk_sum_step @{thm sum.case(1)} @{thm case_sum_step(1)}, 543 right = mk_sum_step @{thm sum.case(2)} @{thm case_sum_step(2)}, init = refl} n k; 544 545fun mk_sum_Cinfinite [thm] = thm 546 | mk_sum_Cinfinite (thm :: thms) = @{thm Cinfinite_csum_weak} OF [thm, mk_sum_Cinfinite thms]; 547 548fun mk_sum_card_order [thm] = thm 549 | mk_sum_card_order (thm :: thms) = @{thm card_order_csum} OF [thm, mk_sum_card_order thms]; 550 551fun mk_xtor_rel_co_induct_thm fp pre_rels pre_phis rels phis xs ys xtors xtor's tac lthy = 552 let 553 val pre_relphis = map (fn rel => Term.list_comb (rel, phis @ pre_phis)) pre_rels; 554 val relphis = map (fn rel => Term.list_comb (rel, phis)) rels; 555 fun mk_xtor fp' xtor x = if fp = fp' then xtor $ x else x; 556 val dtor = mk_xtor Greatest_FP; 557 val ctor = mk_xtor Least_FP; 558 fun flip f x y = if fp = Greatest_FP then f y x else f x y; 559 560 fun mk_prem pre_relphi phi x y xtor xtor' = 561 HOLogic.mk_Trueprop (list_all_free [x, y] (flip (curry HOLogic.mk_imp) 562 (pre_relphi $ (dtor xtor x) $ (dtor xtor' y)) (phi $ (ctor xtor x) $ (ctor xtor' y)))); 563 val prems = @{map 6} mk_prem pre_relphis pre_phis xs ys xtors xtor's; 564 565 val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj 566 (map2 (flip mk_leq) relphis pre_phis)); 567 in 568 Goal.prove_sorry lthy (map (fst o dest_Free) (phis @ pre_phis)) prems concl tac 569 |> Thm.close_derivation \<^here> 570 |> (fn thm => thm OF (replicate (length pre_rels) @{thm allI[OF allI[OF impI]]})) 571 end; 572 573fun mk_xtor_co_iter_transfer_thms fp pre_rels pre_iphis pre_ophis rels phis un_folds un_folds' tac lthy = 574 let 575 val pre_relphis = map (fn rel => Term.list_comb (rel, phis @ pre_iphis)) pre_rels; 576 val relphis = map (fn rel => Term.list_comb (rel, phis)) rels; 577 fun flip f x y = if fp = Greatest_FP then f y x else f x y; 578 579 val arg_rels = map2 (flip mk_rel_fun) pre_relphis pre_ophis; 580 fun mk_transfer relphi pre_phi un_fold un_fold' = 581 fold_rev mk_rel_fun arg_rels (flip mk_rel_fun relphi pre_phi) $ un_fold $ un_fold'; 582 val transfers = @{map 4} mk_transfer relphis pre_ophis un_folds un_folds'; 583 584 val goal = fold_rev Logic.all (phis @ pre_ophis) 585 (HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj transfers)); 586 in 587 Goal.prove_sorry lthy [] [] goal tac 588 |> Thm.close_derivation \<^here> 589 |> split_conj_thm 590 end; 591 592fun mk_xtor_co_iter_o_map_thms fp is_rec m un_fold_unique xtor_maps xtor_un_folds sym_map_comps 593 map_cong0s = 594 let 595 val n = length sym_map_comps; 596 val rewrite_comp_comp2 = case_fp fp @{thm rewriteR_comp_comp2} @{thm rewriteL_comp_comp2}; 597 val rewrite_comp_comp = case_fp fp @{thm rewriteR_comp_comp} @{thm rewriteL_comp_comp}; 598 val map_cong_passive_args1 = replicate m (case_fp fp @{thm id_comp} @{thm comp_id} RS fun_cong); 599 val map_cong_active_args1 = replicate n (if is_rec 600 then case_fp fp @{thm convol_o} @{thm o_case_sum} RS fun_cong 601 else refl); 602 val map_cong_passive_args2 = replicate m (case_fp fp @{thm comp_id} @{thm id_comp} RS fun_cong); 603 val map_cong_active_args2 = replicate n (if is_rec 604 then case_fp fp @{thm map_prod_o_convol_id} @{thm case_sum_o_map_sum_id} 605 else case_fp fp @{thm id_comp} @{thm comp_id} RS fun_cong); 606 fun mk_map_congs passive active = 607 map (fn thm => thm OF (passive @ active) RS @{thm ext}) map_cong0s; 608 val map_cong1s = mk_map_congs map_cong_passive_args1 map_cong_active_args1; 609 val map_cong2s = mk_map_congs map_cong_passive_args2 map_cong_active_args2; 610 611 fun mk_rewrites map_congs = map2 (fn sym_map_comp => fn map_cong => 612 mk_trans sym_map_comp map_cong RS rewrite_comp_comp) sym_map_comps map_congs; 613 val rewrite1s = mk_rewrites map_cong1s; 614 val rewrite2s = mk_rewrites map_cong2s; 615 val unique_prems = 616 @{map 4} (fn xtor_map => fn un_fold => fn rewrite1 => fn rewrite2 => 617 mk_trans (rewrite_comp_comp2 OF [xtor_map, un_fold]) 618 (mk_trans rewrite1 (mk_sym rewrite2))) 619 xtor_maps xtor_un_folds rewrite1s rewrite2s; 620 in 621 split_conj_thm (un_fold_unique OF map (case_fp fp I mk_sym) unique_prems) 622 end; 623 624fun force_typ ctxt T = 625 Term.map_types Type_Infer.paramify_vars 626 #> Type.constraint T 627 #> Syntax.check_term ctxt 628 #> singleton (Variable.polymorphic ctxt); 629 630fun absT_info_encodeT thy (SOME (src : absT_info, dst : absT_info)) src_absT = 631 let 632 val src_repT = mk_repT (#absT src) (#repT src) src_absT; 633 val dst_absT = mk_absT thy (#repT dst) (#absT dst) src_repT; 634 in 635 dst_absT 636 end 637 | absT_info_encodeT _ NONE T = T; 638 639fun absT_info_decodeT thy = absT_info_encodeT thy o Option.map swap; 640 641fun absT_info_encode thy fp (opt as SOME (src : absT_info, dst : absT_info)) t = 642 let 643 val co_alg_funT = case_fp fp domain_type range_type; 644 fun co_swap pair = case_fp fp I swap pair; 645 val mk_co_comp = curry (HOLogic.mk_comp o co_swap); 646 val mk_co_abs = case_fp fp mk_abs mk_rep; 647 val mk_co_rep = case_fp fp mk_rep mk_abs; 648 val co_abs = case_fp fp #abs #rep; 649 val co_rep = case_fp fp #rep #abs; 650 val src_absT = co_alg_funT (fastype_of t); 651 val dst_absT = absT_info_encodeT thy opt src_absT; 652 val co_src_abs = mk_co_abs src_absT (co_abs src); 653 val co_dst_rep = mk_co_rep dst_absT (co_rep dst); 654 in 655 mk_co_comp (mk_co_comp t co_src_abs) co_dst_rep 656 end 657 | absT_info_encode _ _ NONE t = t; 658 659fun absT_info_decode thy fp = absT_info_encode thy fp o Option.map swap; 660 661fun mk_xtor_un_fold_xtor_thms ctxt fp un_folds xtors xtor_un_fold_unique map_id0s 662 absT_info_opts = 663 let 664 val thy = Proof_Context.theory_of ctxt; 665 fun mk_goal un_fold = 666 let 667 val rhs = list_comb (un_fold, @{map 2} (absT_info_encode thy fp) absT_info_opts xtors); 668 val T = range_type (fastype_of rhs); 669 in 670 HOLogic.mk_eq (HOLogic.id_const T, rhs) 671 end; 672 val goal = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map mk_goal un_folds)); 673 fun mk_inverses NONE = [] 674 | mk_inverses (SOME (src, dst)) = 675 [#type_definition dst RS @{thm type_definition.Abs_inverse[OF _ UNIV_I]}, 676 #type_definition src RS @{thm type_definition.Rep_inverse}]; 677 val inverses = maps mk_inverses absT_info_opts; 678 in 679 Goal.prove_sorry ctxt [] [] goal (fn {context = ctxt, prems = _} => 680 mk_xtor_un_fold_xtor_tac ctxt xtor_un_fold_unique map_id0s inverses) 681 |> split_conj_thm |> map mk_sym 682 end; 683 684fun derive_xtor_co_recs fp bs mk_Ts (Dss, resDs) pre_bnfs xtors0 un_folds0 685 xtor_un_fold_unique xtor_un_folds xtor_un_fold_transfers xtor_maps xtor_rels 686 absT_info_opts lthy = 687 let 688 val thy = Proof_Context.theory_of lthy; 689 fun co_swap pair = case_fp fp I swap pair; 690 val mk_co_comp = curry (HOLogic.mk_comp o co_swap); 691 fun mk_co_algT T U = case_fp fp (T --> U) (U --> T); 692 val co_alg_funT = case_fp fp domain_type range_type; 693 val mk_co_product = curry (case_fp fp mk_convol mk_case_sum); 694 val co_proj1_const = case_fp fp fst_const (uncurry Inl_const o dest_sumT) o co_alg_funT; 695 val co_proj2_const = case_fp fp snd_const (uncurry Inr_const o dest_sumT) o co_alg_funT; 696 val mk_co_productT = curry (case_fp fp HOLogic.mk_prodT mk_sumT); 697 val rewrite_comp_comp = case_fp fp @{thm rewriteL_comp_comp} @{thm rewriteR_comp_comp}; 698 699 val n = length pre_bnfs; 700 val live = live_of_bnf (hd pre_bnfs); 701 val m = live - n; 702 val ks = 1 upto n; 703 704 val map_id0s = map map_id0_of_bnf pre_bnfs; 705 val map_comps = map map_comp_of_bnf pre_bnfs; 706 val map_cong0s = map map_cong0_of_bnf pre_bnfs; 707 val map_transfers = map map_transfer_of_bnf pre_bnfs; 708 val sym_map_comp0s = map (mk_sym o map_comp0_of_bnf) pre_bnfs; 709 710 val deads = fold (union (op =)) Dss resDs; 711 val ((((As, Bs), Xs), Ys), names_lthy) = lthy 712 |> fold Variable.declare_typ deads 713 |> mk_TFrees m 714 ||>> mk_TFrees m 715 ||>> mk_TFrees n 716 ||>> mk_TFrees n; 717 718 val XFTs = @{map 2} (fn Ds => mk_T_of_bnf Ds (As @ Xs)) Dss pre_bnfs; 719 val co_algXFTs = @{map 2} mk_co_algT XFTs Xs; 720 val Ts = mk_Ts As; 721 val un_foldTs = @{map 2} (fn T => fn X => co_algXFTs ---> mk_co_algT T X) Ts Xs; 722 val un_folds = @{map 2} (force_typ names_lthy) un_foldTs un_folds0; 723 val ABs = As ~~ Bs; 724 val XYs = Xs ~~ Ys; 725 726 val Us = map (typ_subst_atomic ABs) Ts; 727 728 val TFTs = @{map 2} (fn Ds => mk_T_of_bnf Ds (As @ Ts)) Dss pre_bnfs; 729 730 val TFTs' = @{map 2} (absT_info_decodeT thy) absT_info_opts TFTs; 731 val xtors = @{map 3} (force_typ names_lthy oo mk_co_algT) TFTs' Ts xtors0; 732 733 val ids = map HOLogic.id_const As; 734 val co_rec_Xs = @{map 2} mk_co_productT Ts Xs; 735 val co_rec_Ys = @{map 2} mk_co_productT Us Ys; 736 val co_rec_algXs = @{map 2} mk_co_algT co_rec_Xs Xs; 737 val co_proj1s = map co_proj1_const co_rec_algXs; 738 val co_rec_maps = @{map 2} (fn Ds => 739 mk_map_of_bnf Ds (As @ case_fp fp co_rec_Xs Ts) (As @ case_fp fp Ts co_rec_Xs)) Dss pre_bnfs; 740 val co_rec_Ts = @{map 2} (fn Ds => mk_T_of_bnf Ds (As @ co_rec_Xs)) Dss pre_bnfs 741 val co_rec_argTs = @{map 2} mk_co_algT co_rec_Ts Xs; 742 val co_rec_resTs = @{map 2} mk_co_algT Ts Xs; 743 744 val (((co_rec_ss, fs), xs), names_lthy) = names_lthy 745 |> mk_Frees "s" co_rec_argTs 746 ||>> mk_Frees "f" co_rec_resTs 747 ||>> mk_Frees "x" (case_fp fp TFTs' Xs); 748 749 val co_rec_strs = 750 @{map 4} (fn xtor => fn s => fn mapx => fn absT_info_opt => 751 mk_co_product (mk_co_comp (absT_info_encode thy fp absT_info_opt xtor) 752 (list_comb (mapx, ids @ co_proj1s))) s) 753 xtors co_rec_ss co_rec_maps absT_info_opts; 754 755 val theta = Xs ~~ co_rec_Xs; 756 val co_rec_un_folds = map (subst_atomic_types theta) un_folds; 757 758 val co_rec_spec0s = map (fn un_fold => list_comb (un_fold, co_rec_strs)) co_rec_un_folds; 759 760 val co_rec_ids = @{map 2} (mk_co_comp o co_proj1_const) co_rec_algXs co_rec_spec0s; 761 val co_rec_specs = @{map 2} (mk_co_comp o co_proj2_const) co_rec_algXs co_rec_spec0s; 762 763 val co_recN = case_fp fp ctor_recN dtor_corecN; 764 fun co_rec_bind i = nth bs (i - 1) |> Binding.prefix_name (co_recN ^ "_"); 765 val co_rec_def_bind = rpair [] o Binding.concealed o Thm.def_binding o co_rec_bind; 766 767 fun co_rec_spec i = 768 fold_rev (Term.absfree o Term.dest_Free) co_rec_ss (nth co_rec_specs (i - 1)); 769 770 val ((co_rec_frees, (_, co_rec_def_frees)), (lthy, lthy_old)) = 771 lthy 772 |> Local_Theory.open_target |> snd 773 |> fold_map (fn i => 774 Local_Theory.define ((co_rec_bind i, NoSyn), (co_rec_def_bind i, co_rec_spec i))) ks 775 |>> apsnd split_list o split_list 776 ||> `Local_Theory.close_target; 777 778 val phi = Proof_Context.export_morphism lthy_old lthy; 779 val co_rec_names = map (fst o dest_Const o Morphism.term phi) co_rec_frees; 780 val co_recs = @{map 2} (fn name => fn resT => 781 Const (name, co_rec_argTs ---> resT)) co_rec_names co_rec_resTs; 782 val co_rec_defs = map (fn def => 783 mk_unabs_def n (HOLogic.mk_obj_eq (Morphism.thm phi def))) co_rec_def_frees; 784 785 val xtor_un_fold_xtor_thms = 786 mk_xtor_un_fold_xtor_thms lthy fp (map (Term.subst_atomic_types (Xs ~~ Ts)) un_folds) 787 xtors xtor_un_fold_unique map_id0s absT_info_opts; 788 789 val co_rec_id_thms = 790 let 791 val goal = @{map 2} (fn T => fn t => HOLogic.mk_eq (t, HOLogic.id_const T)) Ts co_rec_ids 792 |> Library.foldr1 HOLogic.mk_conj |> HOLogic.mk_Trueprop; 793 val vars = Variable.add_free_names lthy goal []; 794 in 795 Goal.prove_sorry lthy vars [] goal 796 (fn {context = ctxt, prems = _} => mk_xtor_co_rec_id_tac ctxt xtor_un_fold_xtor_thms 797 xtor_un_fold_unique xtor_un_folds map_comps) 798 |> Thm.close_derivation \<^here> 799 |> split_conj_thm 800 end; 801 802 val co_rec_app_ss = map (fn co_rec => list_comb (co_rec, co_rec_ss)) co_recs; 803 val co_products = @{map 2} (fn T => mk_co_product (HOLogic.id_const T)) Ts co_rec_app_ss; 804 val co_rec_maps_rev = @{map 2} (fn Ds => 805 mk_map_of_bnf Ds (As @ case_fp fp Ts co_rec_Xs) (As @ case_fp fp co_rec_Xs Ts)) Dss pre_bnfs; 806 fun mk_co_app f g x = case_fp fp (f $ (g $ x)) (g $ (f $ x)); 807 val co_rec_expand_thms = map (fn thm => thm RS 808 case_fp fp @{thm convol_expand_snd} @{thm case_sum_expand_Inr_pointfree}) co_rec_id_thms; 809 val xtor_co_rec_thms = 810 let 811 fun mk_goal co_rec s mapx xtor x absT_info_opt = 812 let 813 val lhs = mk_co_app co_rec xtor x; 814 val rhs = mk_co_app s 815 (list_comb (mapx, ids @ co_products) |> absT_info_decode thy fp absT_info_opt) x; 816 in 817 mk_Trueprop_eq (lhs, rhs) 818 end; 819 val goals = 820 @{map 6} mk_goal co_rec_app_ss co_rec_ss co_rec_maps_rev xtors xs absT_info_opts; 821 in 822 map2 (fn goal => fn un_fold => 823 Variable.add_free_names lthy goal [] 824 |> (fn vars => Goal.prove_sorry lthy vars [] goal 825 (fn {context = ctxt, prems = _} => 826 mk_xtor_co_rec_tac ctxt un_fold co_rec_defs co_rec_expand_thms)) 827 |> Thm.close_derivation \<^here>) 828 goals xtor_un_folds 829 end; 830 831 val co_product_fs = @{map 2} (fn T => mk_co_product (HOLogic.id_const T)) Ts fs; 832 val co_rec_expand'_thms = map (fn thm => 833 thm RS case_fp fp @{thm convol_expand_snd'} @{thm case_sum_expand_Inr'}) co_rec_id_thms; 834 val xtor_co_rec_unique_thm = 835 let 836 fun mk_prem f s mapx xtor absT_info_opt = 837 let 838 val lhs = mk_co_comp f xtor; 839 val rhs = mk_co_comp s (list_comb (mapx, ids @ co_product_fs)) 840 |> absT_info_decode thy fp absT_info_opt; 841 in 842 mk_Trueprop_eq (co_swap (lhs, rhs)) 843 end; 844 val prems = @{map 5} mk_prem fs co_rec_ss co_rec_maps_rev xtors absT_info_opts; 845 val concl = @{map 2} (curry HOLogic.mk_eq) fs co_rec_app_ss 846 |> Library.foldr1 HOLogic.mk_conj |> HOLogic.mk_Trueprop; 847 val goal = Logic.list_implies (prems, concl); 848 val vars = Variable.add_free_names lthy goal []; 849 fun mk_inverses NONE = [] 850 | mk_inverses (SOME (src, dst)) = 851 [#type_definition dst RS @{thm type_copy_Rep_o_Abs} RS rewrite_comp_comp, 852 #type_definition src RS @{thm type_copy_Abs_o_Rep}]; 853 val inverses = maps mk_inverses absT_info_opts; 854 in 855 Goal.prove_sorry lthy vars [] goal 856 (fn {context = ctxt, prems = _} => mk_xtor_co_rec_unique_tac ctxt fp co_rec_defs 857 co_rec_expand'_thms xtor_un_fold_unique map_id0s sym_map_comp0s inverses) 858 |> Thm.close_derivation \<^here> 859 end; 860 861 val xtor_co_rec_o_map_thms = if forall is_none absT_info_opts 862 then 863 mk_xtor_co_iter_o_map_thms fp true m xtor_co_rec_unique_thm 864 (map (mk_pointfree2 lthy) xtor_maps) (map (mk_pointfree2 lthy) xtor_co_rec_thms) 865 sym_map_comp0s map_cong0s 866 else 867 replicate n refl (* FIXME *); 868 869 val ABphiTs = @{map 2} mk_pred2T As Bs; 870 val XYphiTs = @{map 2} mk_pred2T Xs Ys; 871 872 val ((ABphis, XYphis), names_lthy) = names_lthy 873 |> mk_Frees "R" ABphiTs 874 ||>> mk_Frees "S" XYphiTs; 875 876 val xtor_co_rec_transfer_thms = if forall is_none absT_info_opts 877 then 878 let 879 val pre_rels = 880 @{map 2} (fn Ds => mk_rel_of_bnf Ds (As @ co_rec_Xs) (Bs @ co_rec_Ys)) Dss pre_bnfs; 881 val rels = @{map 3} (fn T => fn T' => Thm.prop_of #> HOLogic.dest_Trueprop 882 #> fst o dest_comb #> fst o dest_comb #> funpow n (snd o dest_comb) 883 #> case_fp fp (fst o dest_comb #> snd o dest_comb) (snd o dest_comb) #> head_of 884 #> force_typ names_lthy (ABphiTs ---> mk_pred2T T T')) 885 Ts Us xtor_un_fold_transfers; 886 887 fun tac {context = ctxt, prems = _} = mk_xtor_co_rec_transfer_tac ctxt fp n m co_rec_defs 888 xtor_un_fold_transfers map_transfers xtor_rels; 889 890 val mk_rel_co_product = case_fp fp mk_rel_prod mk_rel_sum; 891 val rec_phis = 892 map2 (fn rel => mk_rel_co_product (Term.list_comb (rel, ABphis))) rels XYphis; 893 in 894 mk_xtor_co_iter_transfer_thms fp pre_rels rec_phis XYphis rels ABphis 895 co_recs (map (subst_atomic_types (ABs @ XYs)) co_recs) tac lthy 896 end 897 else 898 replicate n TrueI (* FIXME *); 899 900 val notes = 901 [(case_fp fp ctor_recN dtor_corecN, xtor_co_rec_thms), 902 (case_fp fp ctor_rec_uniqueN dtor_corec_uniqueN, split_conj_thm xtor_co_rec_unique_thm), 903 (case_fp fp ctor_rec_o_mapN dtor_corec_o_mapN, xtor_co_rec_o_map_thms), 904 (case_fp fp ctor_rec_transferN dtor_corec_transferN, xtor_co_rec_transfer_thms)] 905 |> map (apsnd (map single)) 906 |> maps (fn (thmN, thmss) => 907 map2 (fn b => fn thms => 908 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])) 909 bs thmss); 910 911 val lthy = lthy |> Config.get lthy bnf_internals ? snd o Local_Theory.notes notes; 912 in 913 ((co_recs, 914 (xtor_co_rec_thms, xtor_co_rec_unique_thm, xtor_co_rec_o_map_thms, xtor_co_rec_transfer_thms)), 915 lthy) 916 end; 917 918fun raw_qualify extra_qualify base_b = 919 let 920 val qs = Binding.path_of base_b; 921 val n = Binding.name_of base_b; 922 in 923 Binding.prefix_name rawN 924 #> fold_rev (fn (s, mand) => Binding.qualify mand s) (qs @ [(n, true)]) 925 #> extra_qualify #> Binding.concealed 926 end; 927 928fun fixpoint_bnf force_out_of_line extra_qualify construct_fp bs resBs Ds0 Xs rhsXs comp_cache0 929 lthy = 930 let 931 val time = time lthy; 932 val timer = time (Timer.startRealTimer ()); 933 934 fun flatten_tyargs Ass = 935 subtract (op =) Xs (filter (fn T => exists (fn Ts => member (op =) Ts T) Ass) resBs) @ Xs; 936 937 val ((bnfs, (deadss, livess)), (comp_cache_unfold_set, lthy')) = 938 apfst (apsnd split_list o split_list) 939 (@{fold_map 2} 940 (fn b => bnf_of_typ true Smart_Inline (raw_qualify extra_qualify b) flatten_tyargs Xs Ds0) 941 bs rhsXs ((comp_cache0, empty_unfolds), lthy)); 942 943 fun norm_qualify i = 944 Binding.qualify true (Binding.name_of (nth bs (Int.max (0, i - 1)))) 945 #> extra_qualify #> Binding.concealed; 946 947 val Ass = map (map dest_TFree) livess; 948 val Ds' = fold (fold Term.add_tfreesT) deadss []; 949 val Ds = union (op =) Ds' Ds0; 950 val missing = resBs |> fold (subtract (op =)) (Ds' :: Ass); 951 val (dead_phantoms, live_phantoms) = List.partition (member (op =) Ds0) missing; 952 val resBs' = resBs |> fold (subtract (op =)) [dead_phantoms, Ds]; 953 954 val timer = time (timer "Construction of BNFs"); 955 956 val ((kill_posss, _), (bnfs', ((comp_cache', unfold_set'), lthy''))) = 957 normalize_bnfs norm_qualify Ass Ds (K (resBs' @ Xs)) bnfs (comp_cache_unfold_set, lthy'); 958 959 val Dss = @{map 3} (fn lives => fn kill_posss => fn deads => deads @ map (nth lives) kill_posss) 960 livess kill_posss deadss; 961 val all_Dss = Dss |> force_out_of_line ? map (fn Ds' => union (op =) Ds' (map TFree Ds0)); 962 963 fun pre_qualify b = 964 Binding.qualify false (Binding.name_of b) 965 #> extra_qualify 966 #> not (Config.get lthy'' bnf_internals) ? Binding.concealed; 967 968 val ((pre_bnfs, (deadss, absT_infos)), lthy''') = lthy'' 969 |> @{fold_map 5} (fn b => seal_bnf (pre_qualify b) unfold_set' (Binding.prefix_name preN b)) 970 bs (replicate (length rhsXs) (force_out_of_line orelse not (null live_phantoms))) Dss 971 all_Dss bnfs' 972 |>> split_list 973 |>> apsnd split_list; 974 975 val timer = time (timer "Normalization & sealing of BNFs"); 976 977 val res = construct_fp bs resBs (map TFree dead_phantoms, deadss) pre_bnfs absT_infos lthy'''; 978 979 val timer = time (timer "FP construction in total"); 980 in 981 (((pre_bnfs, absT_infos), comp_cache'), res) 982 end; 983 984end; 985