1(* Title: HOL/Tools/BNF/bnf_lfp.ML 2 Author: Dmitriy Traytel, TU Muenchen 3 Author: Andrei Popescu, TU Muenchen 4 Copyright 2012 5 6Datatype construction. 7*) 8 9signature BNF_LFP = 10sig 11 val construct_lfp: mixfix list -> binding list -> binding list -> binding list -> 12 binding list list -> binding list -> (string * sort) list -> typ list * typ list list -> 13 BNF_Def.bnf list -> BNF_Comp.absT_info list -> local_theory -> 14 BNF_FP_Util.fp_result * local_theory 15end; 16 17structure BNF_LFP : BNF_LFP = 18struct 19 20open BNF_Def 21open BNF_Util 22open BNF_Tactics 23open BNF_Comp 24open BNF_FP_Util 25open BNF_FP_Def_Sugar 26open BNF_LFP_Util 27open BNF_LFP_Tactics 28 29(*all BNFs have the same lives*) 30fun construct_lfp mixfixes map_bs rel_bs pred_bs set_bss0 bs resBs (resDs, Dss) bnfs absT_infos 31 lthy = 32 let 33 val time = time lthy; 34 val timer = time (Timer.startRealTimer ()); 35 36 val live = live_of_bnf (hd bnfs); 37 val n = length bnfs; (*active*) 38 val ks = 1 upto n; 39 val m = live - n; (*passive, if 0 don't generate a new BNF*) 40 41 val internals = Config.get lthy bnf_internals; 42 val b_names = map Binding.name_of bs; 43 val b_name = mk_common_name b_names; 44 val b = Binding.name b_name; 45 46 fun mk_internal_of_b name = 47 Binding.prefix_name (name ^ "_") #> Binding.prefix true b_name #> Binding.concealed; 48 fun mk_internal_b name = mk_internal_of_b name b; 49 fun mk_internal_bs name = map (mk_internal_of_b name) bs; 50 val external_bs = map2 (Binding.prefix false) b_names bs 51 |> not internals ? map Binding.concealed; 52 53 val deads = fold (union (op =)) Dss resDs; 54 val names_lthy = fold Variable.declare_typ deads lthy; 55 val passives = map fst (subtract (op = o apsnd TFree) deads resBs); 56 57 (* tvars *) 58 val (((((passiveAs, activeAs), passiveBs), activeBs), passiveCs), activeCs) = 59 names_lthy 60 |> variant_tfrees passives 61 ||>> mk_TFrees n 62 ||>> variant_tfrees passives 63 ||>> mk_TFrees n 64 ||>> variant_tfrees passives 65 ||>> mk_TFrees n 66 |> fst; 67 68 val allAs = passiveAs @ activeAs; 69 val allBs' = passiveBs @ activeBs; 70 val Ass = replicate n allAs; 71 val allBs = passiveAs @ activeBs; 72 val Bss = replicate n allBs; 73 val allCs = passiveAs @ activeCs; 74 val allCs' = passiveBs @ activeCs; 75 val Css' = replicate n allCs'; 76 77 (* types *) 78 val dead_poss = 79 map (fn x => if member (op =) deads (TFree x) then SOME (TFree x) else NONE) resBs; 80 fun mk_param NONE passive = (hd passive, tl passive) 81 | mk_param (SOME a) passive = (a, passive); 82 val mk_params = fold_map mk_param dead_poss #> fst; 83 84 fun mk_FTs Ts = map2 (fn Ds => mk_T_of_bnf Ds Ts) Dss bnfs; 85 val (params, params') = `(map Term.dest_TFree) (mk_params passiveAs); 86 val FTsAs = mk_FTs allAs; 87 val FTsBs = mk_FTs allBs; 88 val FTsCs = mk_FTs allCs; 89 val BTs = map HOLogic.mk_setT activeAs; 90 val B'Ts = map HOLogic.mk_setT activeBs; 91 val B''Ts = map HOLogic.mk_setT activeCs; 92 val sTs = map2 (curry op -->) FTsAs activeAs; 93 val s'Ts = map2 (curry op -->) FTsBs activeBs; 94 val s''Ts = map2 (curry op -->) FTsCs activeCs; 95 val fTs = map2 (curry op -->) activeAs activeBs; 96 val inv_fTs = map2 (curry op -->) activeBs activeAs; 97 val self_fTs = map2 (curry op -->) activeAs activeAs; 98 val gTs = map2 (curry op -->) activeBs activeCs; 99 val all_gTs = map2 (curry op -->) allBs allCs'; 100 101 (* terms *) 102 val mapsAsAs = @{map 4} mk_map_of_bnf Dss Ass Ass bnfs; 103 val mapsAsBs = @{map 4} mk_map_of_bnf Dss Ass Bss bnfs; 104 val mapsBsCs' = @{map 4} mk_map_of_bnf Dss Bss Css' bnfs; 105 val mapsAsCs' = @{map 4} mk_map_of_bnf Dss Ass Css' bnfs; 106 fun mk_setss Ts = @{map 3} mk_sets_of_bnf (map (replicate live) Dss) 107 (map (replicate live) (replicate n Ts)) bnfs; 108 val setssAs = mk_setss allAs; 109 val bd0s = @{map 3} mk_bd_of_bnf Dss Ass bnfs; 110 val bds = 111 @{map 3} (fn bd0 => fn Ds => fn bnf => mk_csum bd0 112 (mk_card_of (HOLogic.mk_UNIV 113 (mk_T_of_bnf Ds (replicate live (fst (dest_relT (fastype_of bd0)))) bnf)))) 114 bd0s Dss bnfs; 115 val witss = map wits_of_bnf bnfs; 116 117 val ((((((((zs, zs'), Bs), ss), fs), self_fs), all_gs), (xFs, xFs')), _) = 118 lthy 119 |> mk_Frees' "z" activeAs 120 ||>> mk_Frees "B" BTs 121 ||>> mk_Frees "s" sTs 122 ||>> mk_Frees "f" fTs 123 ||>> mk_Frees "f" self_fTs 124 ||>> mk_Frees "g" all_gTs 125 ||>> mk_Frees' "x" FTsAs; 126 127 val passive_UNIVs = map HOLogic.mk_UNIV passiveAs; 128 val active_UNIVs = map HOLogic.mk_UNIV activeAs; 129 val passive_ids = map HOLogic.id_const passiveAs; 130 val active_ids = map HOLogic.id_const activeAs; 131 132 (* thms *) 133 val bd0_card_orders = map bd_card_order_of_bnf bnfs; 134 val bd0_Card_orders = map bd_Card_order_of_bnf bnfs; 135 val bd0_Cinfinites = map bd_Cinfinite_of_bnf bnfs; 136 val set_bd0ss = map set_bd_of_bnf bnfs; 137 138 val bd_Card_order = @{thm Card_order_csum}; 139 val bd_Card_orders = replicate n bd_Card_order; 140 val bd_Cinfinites = map (fn thm => thm RS @{thm Cinfinite_csum1}) bd0_Cinfinites; 141 val bd_Cnotzeros = map (fn thm => thm RS @{thm Cinfinite_Cnotzero}) bd_Cinfinites; 142 val bd_Cinfinite = hd bd_Cinfinites; 143 val set_bdss = 144 map2 (fn set_bd0s => fn bd0_Card_order => 145 map (fn thm => ctrans OF [thm, bd0_Card_order RS @{thm ordLeq_csum1}]) set_bd0s) 146 set_bd0ss bd0_Card_orders; 147 val in_bds = map in_bd_of_bnf bnfs; 148 val sym_map_comps = map (fn bnf => map_comp0_of_bnf bnf RS sym) bnfs; 149 val map_comps = map map_comp_of_bnf bnfs; 150 val map_cong0s = map map_cong0_of_bnf bnfs; 151 val map_id0s = map map_id0_of_bnf bnfs; 152 val map_ids = map map_id_of_bnf bnfs; 153 val set_mapss = map set_map_of_bnf bnfs; 154 val rel_mono_strong0s = map rel_mono_strong0_of_bnf bnfs; 155 val le_rel_OOs = map le_rel_OO_of_bnf bnfs; 156 157 val timer = time (timer "Extracted terms & thms"); 158 159 (* nonemptiness check *) 160 fun new_wit X (wit: nonemptiness_witness) = subset (op =) (#I wit, (0 upto m - 1) @ map snd X); 161 162 val all = m upto m + n - 1; 163 164 fun enrich X = map_filter (fn i => 165 (case find_first (fn (_, i') => i = i') X of 166 NONE => 167 (case find_index (new_wit X) (nth witss (i - m)) of 168 ~1 => NONE 169 | j => SOME (j, i)) 170 | SOME ji => SOME ji)) all; 171 val reachable = fixpoint (op =) enrich []; 172 val _ = (case subtract (op =) (map snd reachable) all of 173 [] => () 174 | i :: _ => raise EMPTY_DATATYPE (Binding.name_of (nth bs (i - m)))); 175 176 val wit_thms = flat (map2 (fn bnf => fn (j, _) => nth (wit_thmss_of_bnf bnf) j) bnfs reachable); 177 178 val timer = time (timer "Checked nonemptiness"); 179 180 (* derived thms *) 181 182 (*map g1 ... gm g(m+1) ... g(m+n) (map id ... id f(m+1) ... f(m+n) x) = 183 map g1 ... gm (g(m+1) o f(m+1)) ... (g(m+n) o f(m+n)) x*) 184 fun mk_map_comp_id x mapAsBs mapBsCs mapAsCs map_comp0 = 185 let 186 val lhs = Term.list_comb (mapBsCs, all_gs) $ 187 (Term.list_comb (mapAsBs, passive_ids @ fs) $ x); 188 val rhs = Term.list_comb (mapAsCs, 189 take m all_gs @ map HOLogic.mk_comp (drop m all_gs ~~ fs)) $ x; 190 val vars = fold (Variable.add_free_names lthy) [lhs, rhs] []; 191 in 192 Goal.prove_sorry lthy vars [] (mk_Trueprop_eq (lhs, rhs)) 193 (fn {context = ctxt, prems = _} => mk_map_comp_id_tac ctxt map_comp0) 194 |> Thm.close_derivation \<^here> 195 end; 196 197 val map_comp_id_thms = @{map 5} mk_map_comp_id xFs mapsAsBs mapsBsCs' mapsAsCs' map_comps; 198 199 (*forall a : set(m+1) x. f(m+1) a = a; ...; forall a : set(m+n) x. f(m+n) a = a ==> 200 map id ... id f(m+1) ... f(m+n) x = x*) 201 fun mk_map_cong0L x mapAsAs sets map_cong0 map_id = 202 let 203 fun mk_prem set f z z' = HOLogic.mk_Trueprop 204 (mk_Ball (set $ x) (Term.absfree z' (HOLogic.mk_eq (f $ z, z)))); 205 val prems = @{map 4} mk_prem (drop m sets) self_fs zs zs'; 206 val goal = mk_Trueprop_eq (Term.list_comb (mapAsAs, passive_ids @ self_fs) $ x, x); 207 val vars = fold (Variable.add_free_names lthy) (goal :: prems) []; 208 in 209 Goal.prove_sorry lthy vars [] (Logic.list_implies (prems, goal)) 210 (fn {context = ctxt, prems = _} => mk_map_cong0L_tac ctxt m map_cong0 map_id) 211 |> Thm.close_derivation \<^here> 212 end; 213 214 val map_cong0L_thms = @{map 5} mk_map_cong0L xFs mapsAsAs setssAs map_cong0s map_ids; 215 val in_mono'_thms = map (fn bnf => in_mono_of_bnf bnf OF (replicate m subset_refl)) bnfs; 216 val in_cong'_thms = map (fn bnf => in_cong_of_bnf bnf OF (replicate m refl)) bnfs; 217 218 val timer = time (timer "Derived simple theorems"); 219 220 (* algebra *) 221 222 val alg_bind = mk_internal_b algN; 223 val alg_def_bind = (Thm.def_binding alg_bind, []); 224 225 (*forall i = 1 ... n: (\<forall>x \<in> Fi_in UNIV .. UNIV B1 ... Bn. si x \<in> Bi)*) 226 val alg_spec = 227 let 228 val ins = @{map 3} mk_in (replicate n (passive_UNIVs @ Bs)) setssAs FTsAs; 229 fun mk_alg_conjunct B s X x x' = 230 mk_Ball X (Term.absfree x' (HOLogic.mk_mem (s $ x, B))); 231 232 val rhs = Library.foldr1 HOLogic.mk_conj (@{map 5} mk_alg_conjunct Bs ss ins xFs xFs') 233 in 234 fold_rev (Term.absfree o Term.dest_Free) (Bs @ ss) rhs 235 end; 236 237 val ((alg_free, (_, alg_def_free)), (lthy, lthy_old)) = 238 lthy 239 |> Local_Theory.open_target |> snd 240 |> Local_Theory.define ((alg_bind, NoSyn), (alg_def_bind, alg_spec)) 241 ||> `Local_Theory.close_target; 242 243 val phi = Proof_Context.export_morphism lthy_old lthy; 244 val alg = fst (Term.dest_Const (Morphism.term phi alg_free)); 245 val alg_def = mk_unabs_def (2 * n) (HOLogic.mk_obj_eq (Morphism.thm phi alg_def_free)); 246 247 fun mk_alg Bs ss = 248 let 249 val args = Bs @ ss; 250 val Ts = map fastype_of args; 251 val algT = Library.foldr (op -->) (Ts, HOLogic.boolT); 252 in 253 Term.list_comb (Const (alg, algT), args) 254 end; 255 256 val ((((((((zs, zs'), Bs), B's), ss), s's), fs), (xFs, xFs')), _) = 257 lthy 258 |> mk_Frees' "z" activeAs 259 ||>> mk_Frees "B" BTs 260 ||>> mk_Frees "B'" B'Ts 261 ||>> mk_Frees "s" sTs 262 ||>> mk_Frees "s'" s'Ts 263 ||>> mk_Frees "f" fTs 264 ||>> mk_Frees' "x" FTsAs; 265 266 val alg_set_thms = 267 let 268 val alg_prem = HOLogic.mk_Trueprop (mk_alg Bs ss); 269 fun mk_prem x set B = HOLogic.mk_Trueprop (mk_leq (set $ x) B); 270 fun mk_concl s x B = mk_Trueprop_mem (s $ x, B); 271 val premss = map2 ((fn x => fn sets => map2 (mk_prem x) (drop m sets) Bs)) xFs setssAs; 272 val concls = @{map 3} mk_concl ss xFs Bs; 273 val goals = map2 (fn prems => fn concl => 274 Logic.list_implies (alg_prem :: prems, concl)) premss concls; 275 in 276 map (fn goal => 277 Variable.add_free_names lthy goal [] 278 |> (fn vars => Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => 279 mk_alg_set_tac ctxt alg_def)) 280 |> Thm.close_derivation \<^here>) 281 goals 282 end; 283 284 val timer = time (timer "Algebra definition & thms"); 285 286 val alg_not_empty_thms = 287 let 288 val alg_prem = 289 HOLogic.mk_Trueprop (mk_alg Bs ss); 290 val concls = map (HOLogic.mk_Trueprop o mk_not_empty) Bs; 291 val goals = 292 map (fn concl => Logic.mk_implies (alg_prem, concl)) concls; 293 in 294 map2 (fn goal => fn alg_set => 295 Variable.add_free_names lthy goal [] 296 |> (fn vars => Goal.prove_sorry lthy vars [] goal 297 (fn {context = ctxt, prems = _} => 298 mk_alg_not_empty_tac ctxt alg_set alg_set_thms wit_thms)) 299 |> Thm.close_derivation \<^here>) 300 goals alg_set_thms 301 end; 302 303 val timer = time (timer "Proved nonemptiness"); 304 305 (* morphism *) 306 307 val mor_bind = mk_internal_b morN; 308 val mor_def_bind = (Thm.def_binding mor_bind, []); 309 310 (*fbetw) forall i = 1 ... n: (\<forall>x \<in> Bi. f x \<in> B'i)*) 311 (*mor) forall i = 1 ... n: (\<forall>x \<in> Fi_in UNIV ... UNIV B1 ... Bn. 312 f (s1 x) = s1' (Fi_map id ... id f1 ... fn x))*) 313 val mor_spec = 314 let 315 fun mk_fbetw f B1 B2 z z' = 316 mk_Ball B1 (Term.absfree z' (HOLogic.mk_mem (f $ z, B2))); 317 fun mk_mor sets mapAsBs f s s' T x x' = 318 mk_Ball (mk_in (passive_UNIVs @ Bs) sets T) 319 (Term.absfree x' (HOLogic.mk_eq (f $ (s $ x), s' $ 320 (Term.list_comb (mapAsBs, passive_ids @ fs) $ x)))); 321 val rhs = HOLogic.mk_conj 322 (Library.foldr1 HOLogic.mk_conj (@{map 5} mk_fbetw fs Bs B's zs zs'), 323 Library.foldr1 HOLogic.mk_conj 324 (@{map 8} mk_mor setssAs mapsAsBs fs ss s's FTsAs xFs xFs')) 325 in 326 fold_rev (Term.absfree o Term.dest_Free) (Bs @ ss @ B's @ s's @ fs) rhs 327 end; 328 329 val ((mor_free, (_, mor_def_free)), (lthy, lthy_old)) = 330 lthy 331 |> Local_Theory.open_target |> snd 332 |> Local_Theory.define ((mor_bind, NoSyn), (mor_def_bind, mor_spec)) 333 ||> `Local_Theory.close_target; 334 335 val phi = Proof_Context.export_morphism lthy_old lthy; 336 val mor = fst (Term.dest_Const (Morphism.term phi mor_free)); 337 val mor_def = mk_unabs_def (5 * n) (HOLogic.mk_obj_eq (Morphism.thm phi mor_def_free)); 338 339 fun mk_mor Bs1 ss1 Bs2 ss2 fs = 340 let 341 val args = Bs1 @ ss1 @ Bs2 @ ss2 @ fs; 342 val Ts = map fastype_of (Bs1 @ ss1 @ Bs2 @ ss2 @ fs); 343 val morT = Library.foldr (op -->) (Ts, HOLogic.boolT); 344 in 345 Term.list_comb (Const (mor, morT), args) 346 end; 347 348 val (((((((((((Bs, Bs_copy), B's), B''s), ss), s's), s''s), fs), fs_copy), gs), xFs), _) = 349 lthy 350 |> mk_Frees "B" BTs 351 ||>> mk_Frees "B" BTs 352 ||>> mk_Frees "B'" B'Ts 353 ||>> mk_Frees "B''" B''Ts 354 ||>> mk_Frees "s" sTs 355 ||>> mk_Frees "s'" s'Ts 356 ||>> mk_Frees "s''" s''Ts 357 ||>> mk_Frees "f" fTs 358 ||>> mk_Frees "f" fTs 359 ||>> mk_Frees "g" gTs 360 ||>> mk_Frees "x" FTsAs; 361 362 val morE_thms = 363 let 364 val prem = HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs); 365 fun mk_elim_prem sets x T = HOLogic.mk_Trueprop 366 (HOLogic.mk_mem (x, mk_in (passive_UNIVs @ Bs) sets T)); 367 fun mk_elim_goal sets mapAsBs f s s' x T = 368 Logic.list_implies ([prem, mk_elim_prem sets x T], 369 mk_Trueprop_eq (f $ (s $ x), s' $ Term.list_comb (mapAsBs, passive_ids @ fs @ [x]))); 370 val elim_goals = @{map 7} mk_elim_goal setssAs mapsAsBs fs ss s's xFs FTsAs; 371 fun prove goal = 372 Variable.add_free_names lthy goal [] 373 |> (fn vars => Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => 374 mk_mor_elim_tac ctxt mor_def)) 375 |> Thm.close_derivation \<^here>; 376 in 377 map prove elim_goals 378 end; 379 380 val mor_incl_thm = 381 let 382 val prems = map2 (HOLogic.mk_Trueprop oo mk_leq) Bs Bs_copy; 383 val concl = HOLogic.mk_Trueprop (mk_mor Bs ss Bs_copy ss active_ids); 384 val vars = fold (Variable.add_free_names lthy) (concl :: prems) []; 385 in 386 Goal.prove_sorry lthy vars [] (Logic.list_implies (prems, concl)) 387 (fn {context = ctxt, prems = _} => mk_mor_incl_tac ctxt mor_def map_ids) 388 |> Thm.close_derivation \<^here> 389 end; 390 391 val mor_comp_thm = 392 let 393 val prems = 394 [HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs), 395 HOLogic.mk_Trueprop (mk_mor B's s's B''s s''s gs)]; 396 val concl = 397 HOLogic.mk_Trueprop (mk_mor Bs ss B''s s''s (map2 (curry HOLogic.mk_comp) gs fs)); 398 val vars = fold (Variable.add_free_names lthy) (concl :: prems) []; 399 in 400 Goal.prove_sorry lthy vars [] (Logic.list_implies (prems, concl)) 401 (fn {context = ctxt, prems = _} => mk_mor_comp_tac ctxt mor_def set_mapss map_comp_id_thms) 402 |> Thm.close_derivation \<^here> 403 end; 404 405 val mor_cong_thm = 406 let 407 val prems = map HOLogic.mk_Trueprop 408 (map2 (curry HOLogic.mk_eq) fs_copy fs @ [mk_mor Bs ss B's s's fs]) 409 val concl = HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs_copy); 410 val vars = fold (Variable.add_free_names lthy) (concl :: prems) []; 411 in 412 Goal.prove_sorry lthy vars [] (Logic.list_implies (prems, concl)) 413 (fn {context = ctxt, prems = _} => (hyp_subst_tac ctxt THEN' assume_tac ctxt) 1) 414 |> Thm.close_derivation \<^here> 415 end; 416 417 val mor_str_thm = 418 let 419 val maps = map2 (fn Ds => fn bnf => Term.list_comb 420 (mk_map_of_bnf Ds (passiveAs @ FTsAs) allAs bnf, passive_ids @ ss)) Dss bnfs; 421 val goal = HOLogic.mk_Trueprop 422 (mk_mor (map HOLogic.mk_UNIV FTsAs) maps active_UNIVs ss ss); 423 val vars = Variable.add_free_names lthy goal []; 424 in 425 Goal.prove_sorry lthy vars [] goal 426 (fn {context = ctxt, prems = _} => mk_mor_str_tac ctxt ks mor_def) 427 |> Thm.close_derivation \<^here> 428 end; 429 430 val mor_UNIV_thm = 431 let 432 fun mk_conjunct mapAsBs f s s' = HOLogic.mk_eq 433 (HOLogic.mk_comp (f, s), 434 HOLogic.mk_comp (s', Term.list_comb (mapAsBs, passive_ids @ fs))); 435 val lhs = mk_mor active_UNIVs ss (map HOLogic.mk_UNIV activeBs) s's fs; 436 val rhs = Library.foldr1 HOLogic.mk_conj (@{map 4} mk_conjunct mapsAsBs fs ss s's); 437 val vars = fold (Variable.add_free_names lthy) [lhs, rhs] []; 438 in 439 Goal.prove_sorry lthy vars [] (mk_Trueprop_eq (lhs, rhs)) 440 (fn {context = ctxt, prems = _} => mk_mor_UNIV_tac ctxt m morE_thms mor_def) 441 |> Thm.close_derivation \<^here> 442 end; 443 444 val timer = time (timer "Morphism definition & thms"); 445 446 (* bounds *) 447 448 val sum_bd = Library.foldr1 (uncurry mk_csum) bds; 449 val sum_bdT = fst (dest_relT (fastype_of sum_bd)); 450 val (sum_bdT_params, sum_bdT_params') = `(map TFree) (Term.add_tfreesT sum_bdT []); 451 452 val (lthy, sbd, sbd_Cinfinite, sbd_Card_order, set_sbdss, in_sbds) = 453 if n = 1 454 then (lthy, sum_bd, bd_Cinfinite, bd_Card_order, set_bdss, in_bds) 455 else 456 let 457 val sbdT_bind = mk_internal_b sum_bdTN; 458 459 val ((sbdT_name, (sbdT_glob_info, sbdT_loc_info)), lthy) = 460 typedef (sbdT_bind, sum_bdT_params', NoSyn) 461 (HOLogic.mk_UNIV sum_bdT) NONE (fn ctxt => 462 EVERY' [rtac ctxt exI, rtac ctxt UNIV_I] 1) lthy; 463 464 val sbdT = Type (sbdT_name, sum_bdT_params); 465 val Abs_sbdT = Const (#Abs_name sbdT_glob_info, sum_bdT --> sbdT); 466 467 val sbd_bind = mk_internal_b sum_bdN; 468 val sbd_def_bind = (Thm.def_binding sbd_bind, []); 469 470 val sbd_spec = mk_dir_image sum_bd Abs_sbdT; 471 472 val ((sbd_free, (_, sbd_def_free)), (lthy, lthy_old)) = 473 lthy 474 |> Local_Theory.open_target |> snd 475 |> Local_Theory.define ((sbd_bind, NoSyn), (sbd_def_bind, sbd_spec)) 476 ||> `Local_Theory.close_target; 477 478 val phi = Proof_Context.export_morphism lthy_old lthy; 479 480 val sbd_def = HOLogic.mk_obj_eq (Morphism.thm phi sbd_def_free); 481 val sbd = Const (fst (Term.dest_Const (Morphism.term phi sbd_free)), mk_relT (`I sbdT)); 482 483 val Abs_sbdT_inj = mk_Abs_inj_thm (#Abs_inject sbdT_loc_info); 484 485 val sum_Cinfinite = mk_sum_Cinfinite bd_Cinfinites; 486 val sum_Card_order = sum_Cinfinite RS conjunct2; 487 488 val sbd_ordIso = @{thm ssubst_Pair_rhs} OF 489 [@{thm dir_image} OF [Abs_sbdT_inj, sum_Card_order], sbd_def]; 490 val sbd_Cinfinite = @{thm Cinfinite_cong} OF [sbd_ordIso, sum_Cinfinite]; 491 val sbd_Card_order = sbd_Cinfinite RS conjunct2; 492 493 fun mk_set_sbd i bd_Card_order bds = 494 map (fn thm => @{thm ordLeq_ordIso_trans} OF 495 [bd_Card_order RS mk_ordLeq_csum n i thm, sbd_ordIso]) bds; 496 val set_sbdss = @{map 3} mk_set_sbd ks bd_Card_orders set_bdss; 497 498 fun mk_in_bd_sum i Co Cnz bd = 499 Cnz RS ((@{thm ordLeq_ordIso_trans} OF 500 [Co RS mk_ordLeq_csum n i (Co RS @{thm ordLeq_refl}), sbd_ordIso]) RS 501 (bd RS @{thm ordLeq_transitive[OF _ cexp_mono2_Cnotzero[OF _ Card_order_csum]]})); 502 val in_sbds = @{map 4} mk_in_bd_sum ks bd_Card_orders bd_Cnotzeros in_bds; 503 in 504 (lthy, sbd, sbd_Cinfinite, sbd_Card_order, set_sbdss, in_sbds) 505 end; 506 507 val sbd_Cnotzero = sbd_Cinfinite RS @{thm Cinfinite_Cnotzero}; 508 val suc_bd = mk_cardSuc sbd; 509 510 val field_suc_bd = mk_Field suc_bd; 511 val suc_bdT = fst (dest_relT (fastype_of suc_bd)); 512 fun mk_Asuc_bd [] = mk_cexp ctwo suc_bd 513 | mk_Asuc_bd As = 514 mk_cexp (mk_csum (Library.foldr1 (uncurry mk_csum) (map mk_card_of As)) ctwo) suc_bd; 515 516 val suc_bd_Card_order = sbd_Card_order RS @{thm cardSuc_Card_order}; 517 val suc_bd_Cinfinite = sbd_Cinfinite RS @{thm Cinfinite_cardSuc}; 518 val suc_bd_Cnotzero = suc_bd_Cinfinite RS @{thm Cinfinite_Cnotzero}; 519 val suc_bd_worel = suc_bd_Card_order RS @{thm Card_order_wo_rel} 520 val basis_Asuc = if m = 0 then @{thm ordLeq_refl[OF Card_order_ctwo]} 521 else @{thm ordLeq_csum2[OF Card_order_ctwo]}; 522 val Asuc_bd_Cinfinite = suc_bd_Cinfinite RS (basis_Asuc RS @{thm Cinfinite_cexp}); 523 524 val suc_bd_Asuc_bd = @{thm ordLess_ordLeq_trans[OF ordLess_ctwo_cexp cexp_mono1]} OF 525 [suc_bd_Card_order, basis_Asuc, suc_bd_Card_order]; 526 527 528 val Asuc_bd = mk_Asuc_bd passive_UNIVs; 529 val Asuc_bdT = fst (dest_relT (fastype_of Asuc_bd)); 530 val II_BTs = replicate n (HOLogic.mk_setT Asuc_bdT); 531 val II_sTs = map2 (fn Ds => fn bnf => 532 mk_T_of_bnf Ds (passiveAs @ replicate n Asuc_bdT) bnf --> Asuc_bdT) Dss bnfs; 533 534 val ((((((Bs, ss), idxs), Asi_name), (idx, idx')), (jdx, jdx')), _) = 535 lthy 536 |> mk_Frees "B" BTs 537 ||>> mk_Frees "s" sTs 538 ||>> mk_Frees "i" (replicate n suc_bdT) 539 ||>> (fn ctxt => apfst the_single (mk_fresh_names ctxt 1 "Asi")) 540 ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "i") suc_bdT 541 ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "j") suc_bdT; 542 543 val suc_bd_limit_thm = 544 let 545 val prem = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj 546 (map (fn idx => HOLogic.mk_mem (idx, field_suc_bd)) idxs)); 547 fun mk_conjunct idx = HOLogic.mk_conj (mk_not_eq idx jdx, 548 HOLogic.mk_mem (HOLogic.mk_prod (idx, jdx), suc_bd)); 549 val concl = HOLogic.mk_Trueprop (mk_Bex field_suc_bd 550 (Term.absfree jdx' (Library.foldr1 HOLogic.mk_conj (map mk_conjunct idxs)))); 551 val vars = fold (Variable.add_free_names lthy) [prem, concl] []; 552 in 553 Goal.prove_sorry lthy vars [] (Logic.list_implies ([prem], concl)) 554 (fn {context = ctxt, prems = _} => mk_bd_limit_tac ctxt n suc_bd_Cinfinite) 555 |> Thm.close_derivation \<^here> 556 end; 557 558 val timer = time (timer "Bounds"); 559 560 (* minimal algebra *) 561 562 fun mk_minG Asi i k = mk_UNION (mk_underS suc_bd $ i) 563 (Term.absfree jdx' (mk_nthN n (Asi $ jdx) k)); 564 565 fun mk_minH_component Asi i sets Ts s k = 566 HOLogic.mk_binop \<^const_name>\<open>sup\<close> 567 (mk_minG Asi i k, mk_image s $ mk_in (passive_UNIVs @ map (mk_minG Asi i) ks) sets Ts); 568 569 fun mk_min_algs ss = 570 let 571 val BTs = map (range_type o fastype_of) ss; 572 val Ts = passiveAs @ BTs; 573 val (Asi, Asi') = `Free (Asi_name, suc_bdT --> 574 Library.foldr1 HOLogic.mk_prodT (map HOLogic.mk_setT BTs)); 575 in 576 mk_worec suc_bd (Term.absfree Asi' (Term.absfree idx' (HOLogic.mk_tuple 577 (@{map 4} (mk_minH_component Asi idx) (mk_setss Ts) (mk_FTs Ts) ss ks)))) 578 end; 579 580 val (min_algs_thms, min_algs_mono_thms, card_of_min_algs_thm, least_min_algs_thm) = 581 let 582 val i_field = HOLogic.mk_mem (idx, field_suc_bd); 583 val min_algs = mk_min_algs ss; 584 585 val min_algss = map (fn k => mk_nthN n (min_algs $ idx) k) ks; 586 587 val concl = HOLogic.mk_Trueprop 588 (HOLogic.mk_eq (min_algs $ idx, HOLogic.mk_tuple 589 (@{map 4} (mk_minH_component min_algs idx) setssAs FTsAs ss ks))); 590 val goal = Logic.mk_implies (HOLogic.mk_Trueprop i_field, concl); 591 val vars = Variable.add_free_names lthy goal []; 592 593 val min_algs_thm = Goal.prove_sorry lthy vars [] goal 594 (fn {context = ctxt, prems = _} => mk_min_algs_tac ctxt suc_bd_worel in_cong'_thms) 595 |> Thm.close_derivation \<^here>; 596 597 val min_algs_thms = map (fn k => min_algs_thm RS mk_nthI n k) ks; 598 599 fun mk_mono_goal min_alg = 600 HOLogic.mk_Trueprop (mk_relChain suc_bd (Term.absfree idx' min_alg)); 601 602 val monos = 603 map2 (fn goal => fn min_algs => 604 Variable.add_free_names lthy goal [] 605 |> (fn vars => Goal.prove_sorry lthy vars [] goal 606 (fn {context = ctxt, prems = _} => mk_min_algs_mono_tac ctxt min_algs)) 607 |> Thm.close_derivation \<^here>) 608 (map mk_mono_goal min_algss) min_algs_thms; 609 610 fun mk_card_conjunct min_alg = mk_ordLeq (mk_card_of min_alg) Asuc_bd; 611 val card_conjunction = Library.foldr1 HOLogic.mk_conj (map mk_card_conjunct min_algss); 612 val card_cT = Thm.ctyp_of lthy suc_bdT; 613 val card_ct = Thm.cterm_of lthy (Term.absfree idx' card_conjunction); 614 615 val card_of = 616 let 617 val goal = HOLogic.mk_Trueprop (HOLogic.mk_imp (i_field, card_conjunction)); 618 val vars = Variable.add_free_names lthy goal []; 619 in 620 Goal.prove_sorry lthy vars [] goal 621 (fn {context = ctxt, prems = _} => mk_min_algs_card_of_tac ctxt card_cT card_ct 622 m suc_bd_worel min_algs_thms in_sbds 623 sbd_Card_order sbd_Cnotzero suc_bd_Card_order suc_bd_Cinfinite suc_bd_Cnotzero 624 suc_bd_Asuc_bd Asuc_bd_Cinfinite) 625 |> Thm.close_derivation \<^here> 626 end; 627 628 val least_prem = HOLogic.mk_Trueprop (mk_alg Bs ss); 629 val least_conjunction = Library.foldr1 HOLogic.mk_conj (map2 mk_leq min_algss Bs); 630 val least_cT = Thm.ctyp_of lthy suc_bdT; 631 val least_ct = Thm.cterm_of lthy (Term.absfree idx' least_conjunction); 632 633 val least = 634 let 635 val goal = Logic.mk_implies (least_prem, 636 HOLogic.mk_Trueprop (HOLogic.mk_imp (i_field, least_conjunction))); 637 val vars = Variable.add_free_names lthy goal []; 638 in 639 Goal.prove_sorry lthy vars [] goal 640 (fn {context = ctxt, prems = _} => mk_min_algs_least_tac ctxt least_cT least_ct 641 suc_bd_worel min_algs_thms alg_set_thms) 642 |> Thm.close_derivation \<^here> 643 end; 644 in 645 (min_algs_thms, monos, card_of, least) 646 end; 647 648 val timer = time (timer "min_algs definition & thms"); 649 650 val min_alg_binds = mk_internal_bs min_algN; 651 fun min_alg_bind i = nth min_alg_binds (i - 1); 652 val min_alg_def_bind = rpair [] o Thm.def_binding o min_alg_bind; 653 654 fun min_alg_spec i = 655 let 656 val rhs = mk_UNION (field_suc_bd) 657 (Term.absfree idx' (mk_nthN n (mk_min_algs ss $ idx) i)); 658 in 659 fold_rev (Term.absfree o Term.dest_Free) ss rhs 660 end; 661 662 val ((min_alg_frees, (_, min_alg_def_frees)), (lthy, lthy_old)) = 663 lthy 664 |> Local_Theory.open_target |> snd 665 |> fold_map (fn i => Local_Theory.define 666 ((min_alg_bind i, NoSyn), (min_alg_def_bind i, min_alg_spec i))) ks 667 |>> apsnd split_list o split_list 668 ||> `Local_Theory.close_target; 669 670 val phi = Proof_Context.export_morphism lthy_old lthy; 671 val min_algs = map (fst o Term.dest_Const o Morphism.term phi) min_alg_frees; 672 val min_alg_defs = map (fn def => 673 mk_unabs_def n (HOLogic.mk_obj_eq (Morphism.thm phi def))) min_alg_def_frees; 674 675 fun mk_min_alg ss i = 676 let 677 val T = HOLogic.mk_setT (range_type (fastype_of (nth ss (i - 1)))) 678 val Ts = map fastype_of ss; 679 val min_algT = Library.foldr (op -->) (Ts, T); 680 in 681 Term.list_comb (Const (nth min_algs (i - 1), min_algT), ss) 682 end; 683 684 val min_algs = map (mk_min_alg ss) ks; 685 686 val ((Bs, ss), _) = 687 lthy 688 |> mk_Frees "B" BTs 689 ||>> mk_Frees "s" sTs; 690 691 val (alg_min_alg_thm, card_of_min_alg_thms, least_min_alg_thms, mor_incl_min_alg_thm) = 692 let 693 val alg_min_alg = 694 let 695 val goal = HOLogic.mk_Trueprop (mk_alg min_algs ss); 696 val vars = Variable.add_free_names lthy goal []; 697 in 698 Goal.prove_sorry lthy vars [] goal 699 (fn {context = ctxt, prems = _} => mk_alg_min_alg_tac ctxt m alg_def min_alg_defs 700 suc_bd_limit_thm sbd_Cinfinite set_sbdss min_algs_thms min_algs_mono_thms) 701 |> Thm.close_derivation \<^here> 702 end; 703 704 fun mk_card_of_thm min_alg def = 705 let 706 val goal = HOLogic.mk_Trueprop (mk_ordLeq (mk_card_of min_alg) Asuc_bd); 707 val vars = Variable.add_free_names lthy goal []; 708 in 709 Goal.prove_sorry lthy vars [] goal 710 (fn {context = ctxt, prems = _} => mk_card_of_min_alg_tac ctxt def card_of_min_algs_thm 711 suc_bd_Card_order suc_bd_Asuc_bd Asuc_bd_Cinfinite) 712 |> Thm.close_derivation \<^here> 713 end; 714 715 fun mk_least_thm min_alg B def = 716 let 717 val prem = HOLogic.mk_Trueprop (mk_alg Bs ss); 718 val goal = Logic.mk_implies (prem, HOLogic.mk_Trueprop (mk_leq min_alg B)); 719 val vars = Variable.add_free_names lthy goal []; 720 in 721 Goal.prove_sorry lthy vars [] goal 722 (fn {context = ctxt, prems = _} => mk_least_min_alg_tac ctxt def least_min_algs_thm) 723 |> Thm.close_derivation \<^here> 724 end; 725 726 val leasts = @{map 3} mk_least_thm min_algs Bs min_alg_defs; 727 728 val incl = 729 let 730 val prem = HOLogic.mk_Trueprop (mk_alg Bs ss); 731 val goal = Logic.mk_implies (prem, 732 HOLogic.mk_Trueprop (mk_mor min_algs ss Bs ss active_ids)); 733 val vars = Variable.add_free_names lthy goal []; 734 in 735 Goal.prove_sorry lthy vars [] goal 736 (fn {context = ctxt, prems = _} => 737 EVERY' (rtac ctxt mor_incl_thm :: map (etac ctxt) leasts) 1) 738 |> Thm.close_derivation \<^here> 739 end; 740 in 741 (alg_min_alg, map2 mk_card_of_thm min_algs min_alg_defs, leasts, incl) 742 end; 743 744 val timer = time (timer "Minimal algebra definition & thms"); 745 746 val II_repT = HOLogic.mk_prodT (HOLogic.mk_tupleT II_BTs, HOLogic.mk_tupleT II_sTs); 747 val IIT_bind = mk_internal_b IITN; 748 749 val ((IIT_name, (IIT_glob_info, IIT_loc_info)), lthy) = 750 typedef (IIT_bind, params, NoSyn) 751 (HOLogic.mk_UNIV II_repT) NONE (fn ctxt => EVERY' [rtac ctxt exI, rtac ctxt UNIV_I] 1) lthy; 752 753 val IIT = Type (IIT_name, params'); 754 val Abs_IIT = Const (#Abs_name IIT_glob_info, II_repT --> IIT); 755 val Rep_IIT = Const (#Rep_name IIT_glob_info, IIT --> II_repT); 756 val Abs_IIT_inverse_thm = UNIV_I RS #Abs_inverse IIT_loc_info; 757 758 val initT = IIT --> Asuc_bdT; 759 val active_initTs = replicate n initT; 760 val init_FTs = map2 (fn Ds => mk_T_of_bnf Ds (passiveAs @ active_initTs)) Dss bnfs; 761 val init_fTs = map (fn T => initT --> T) activeAs; 762 763 val ((((II_Bs, II_ss), (iidx, iidx')), init_xFs), _) = 764 lthy 765 |> mk_Frees "IIB" II_BTs 766 ||>> mk_Frees "IIs" II_sTs 767 ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "i") IIT 768 ||>> mk_Frees "x" init_FTs; 769 770 val II = HOLogic.mk_Collect (fst iidx', IIT, list_exists_free (II_Bs @ II_ss) 771 (HOLogic.mk_conj (HOLogic.mk_eq (iidx, 772 Abs_IIT $ (HOLogic.mk_prod (HOLogic.mk_tuple II_Bs, HOLogic.mk_tuple II_ss))), 773 mk_alg II_Bs II_ss))); 774 775 val select_Bs = map (mk_nthN n (HOLogic.mk_fst (Rep_IIT $ iidx))) ks; 776 val select_ss = map (mk_nthN n (HOLogic.mk_snd (Rep_IIT $ iidx))) ks; 777 778 val str_init_binds = mk_internal_bs str_initN; 779 fun str_init_bind i = nth str_init_binds (i - 1); 780 val str_init_def_bind = rpair [] o Thm.def_binding o str_init_bind; 781 782 fun str_init_spec i = 783 let 784 val init_xF = nth init_xFs (i - 1) 785 val select_s = nth select_ss (i - 1); 786 val map = mk_map_of_bnf (nth Dss (i - 1)) 787 (passiveAs @ active_initTs) (passiveAs @ replicate n Asuc_bdT) 788 (nth bnfs (i - 1)); 789 val map_args = passive_ids @ replicate n (mk_rapp iidx Asuc_bdT); 790 val rhs = select_s $ (Term.list_comb (map, map_args) $ init_xF); 791 in 792 fold_rev (Term.absfree o Term.dest_Free) [init_xF, iidx] rhs 793 end; 794 795 val ((str_init_frees, (_, str_init_def_frees)), (lthy, lthy_old)) = 796 lthy 797 |> Local_Theory.open_target |> snd 798 |> fold_map (fn i => Local_Theory.define 799 ((str_init_bind i, NoSyn), (str_init_def_bind i, str_init_spec i))) ks 800 |>> apsnd split_list o split_list 801 ||> `Local_Theory.close_target; 802 803 val phi = Proof_Context.export_morphism lthy_old lthy; 804 val str_inits = 805 map (Term.subst_atomic_types (map (`(Morphism.typ phi)) params') o Morphism.term phi) 806 str_init_frees; 807 808 val str_init_defs = map (fn def => 809 mk_unabs_def 2 (HOLogic.mk_obj_eq (Morphism.thm phi def))) str_init_def_frees; 810 811 val car_inits = map (mk_min_alg str_inits) ks; 812 813 val (((((((((Bs, ss), Asuc_fs), (iidx, iidx')), init_xs), (init_xFs, init_xFs')), init_fs), 814 init_fs_copy), init_phis), _) = 815 lthy 816 |> mk_Frees "B" BTs 817 ||>> mk_Frees "s" sTs 818 ||>> mk_Frees "f" (map (fn T => Asuc_bdT --> T) activeAs) 819 ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "i") IIT 820 ||>> mk_Frees "ix" active_initTs 821 ||>> mk_Frees' "x" init_FTs 822 ||>> mk_Frees "f" init_fTs 823 ||>> mk_Frees "f" init_fTs 824 ||>> mk_Frees "P" (replicate n (mk_pred1T initT)); 825 826 val alg_init_thm = 827 infer_instantiate' lthy (map (SOME o Thm.cterm_of lthy) str_inits) alg_min_alg_thm; 828 829 val alg_select_thm = Goal.prove_sorry lthy [] [] 830 (HOLogic.mk_Trueprop (mk_Ball II 831 (Term.absfree iidx' (mk_alg select_Bs select_ss)))) 832 (fn {context = ctxt, prems = _} => mk_alg_select_tac ctxt Abs_IIT_inverse_thm) 833 |> Thm.close_derivation \<^here>; 834 835 val mor_select_thm = 836 let 837 val i_prem = mk_Trueprop_mem (iidx, II); 838 val mor_prem = HOLogic.mk_Trueprop (mk_mor select_Bs select_ss active_UNIVs ss Asuc_fs); 839 val prems = [i_prem, mor_prem]; 840 val concl = HOLogic.mk_Trueprop 841 (mk_mor car_inits str_inits active_UNIVs ss 842 (map (fn f => HOLogic.mk_comp (f, mk_rapp iidx Asuc_bdT)) Asuc_fs)); 843 val vars = fold (Variable.add_free_names lthy) (concl :: prems) []; 844 in 845 Goal.prove_sorry lthy vars [] (Logic.list_implies (prems, concl)) 846 (fn {context = ctxt, prems = _} => mk_mor_select_tac ctxt mor_def mor_cong_thm 847 mor_comp_thm mor_incl_min_alg_thm alg_def alg_select_thm alg_set_thms set_mapss 848 str_init_defs) 849 |> Thm.close_derivation \<^here> 850 end; 851 852 val init_unique_mor_thms = 853 let 854 val prems = map2 (HOLogic.mk_Trueprop oo curry HOLogic.mk_mem) init_xs car_inits 855 val mor_prems = map HOLogic.mk_Trueprop 856 [mk_mor car_inits str_inits Bs ss init_fs, 857 mk_mor car_inits str_inits Bs ss init_fs_copy]; 858 fun mk_fun_eq f g x = HOLogic.mk_eq (f $ x, g $ x); 859 val unique = HOLogic.mk_Trueprop 860 (Library.foldr1 HOLogic.mk_conj (@{map 3} mk_fun_eq init_fs init_fs_copy init_xs)); 861 val cts = map (Thm.cterm_of lthy) ss; 862 val all_prems = prems @ mor_prems; 863 val vars = fold (Variable.add_free_names lthy) (unique :: all_prems) []; 864 val unique_mor = 865 Goal.prove_sorry lthy vars [] (Logic.list_implies (all_prems, unique)) 866 (fn {context = ctxt, prems = _} => mk_init_unique_mor_tac ctxt cts m alg_def 867 alg_init_thm least_min_alg_thms in_mono'_thms alg_set_thms morE_thms map_cong0s) 868 |> Thm.close_derivation \<^here>; 869 in 870 split_conj_thm unique_mor 871 end; 872 873 val init_setss = mk_setss (passiveAs @ active_initTs); 874 val active_init_setss = map (drop m) init_setss; 875 val init_ins = map2 (fn sets => mk_in (passive_UNIVs @ car_inits) sets) init_setss init_FTs; 876 877 fun mk_closed phis = 878 let 879 fun mk_conjunct phi str_init init_sets init_in x x' = 880 let 881 val prem = Library.foldr1 HOLogic.mk_conj 882 (map2 (fn set => mk_Ball (set $ x)) init_sets phis); 883 val concl = phi $ (str_init $ x); 884 in 885 mk_Ball init_in (Term.absfree x' (HOLogic.mk_imp (prem, concl))) 886 end; 887 in 888 Library.foldr1 HOLogic.mk_conj 889 (@{map 6} mk_conjunct phis str_inits active_init_setss init_ins init_xFs init_xFs') 890 end; 891 892 val init_induct_thm = 893 let 894 val prem = HOLogic.mk_Trueprop (mk_closed init_phis); 895 val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj 896 (map2 mk_Ball car_inits init_phis)); 897 val vars = fold (Variable.add_free_names lthy) [concl, prem] []; 898 in 899 Goal.prove_sorry lthy vars [] (Logic.mk_implies (prem, concl)) 900 (fn {context = ctxt, prems = _} => mk_init_induct_tac ctxt m alg_def alg_init_thm 901 least_min_alg_thms alg_set_thms) 902 |> Thm.close_derivation \<^here> 903 end; 904 905 val timer = time (timer "Initiality definition & thms"); 906 907 val ((T_names, (T_glob_infos, T_loc_infos)), lthy) = 908 lthy 909 |> @{fold_map 3} (fn b => fn mx => fn car_init => 910 typedef (b, params, mx) car_init NONE 911 (fn ctxt => 912 EVERY' [rtac ctxt iffD2, rtac ctxt @{thm ex_in_conv}, resolve_tac ctxt alg_not_empty_thms, 913 rtac ctxt alg_init_thm] 1)) bs mixfixes car_inits 914 |>> apsnd split_list o split_list; 915 916 val Ts = map (fn name => Type (name, params')) T_names; 917 fun mk_Ts passive = map (Term.typ_subst_atomic (passiveAs ~~ passive)) Ts; 918 val Ts' = mk_Ts passiveBs; 919 val Rep_Ts = map2 (fn info => fn T => Const (#Rep_name info, T --> initT)) T_glob_infos Ts; 920 val Abs_Ts = map2 (fn info => fn T => Const (#Abs_name info, initT --> T)) T_glob_infos Ts; 921 922 val type_defs = map #type_definition T_loc_infos; 923 val Reps = map #Rep T_loc_infos; 924 val Rep_inverses = map #Rep_inverse T_loc_infos; 925 val Abs_inverses = map #Abs_inverse T_loc_infos; 926 927 val timer = time (timer "THE TYPEDEFs & Rep/Abs thms"); 928 929 val UNIVs = map HOLogic.mk_UNIV Ts; 930 val FTs = mk_FTs (passiveAs @ Ts); 931 val FTs' = mk_FTs (passiveBs @ Ts'); 932 fun mk_set_Ts T = passiveAs @ replicate n (HOLogic.mk_setT T); 933 val setFTss = map (mk_FTs o mk_set_Ts) passiveAs; 934 val FTs_setss = mk_setss (passiveAs @ Ts); 935 val FTs'_setss = mk_setss (passiveBs @ Ts'); 936 val map_FT_inits = map2 (fn Ds => 937 mk_map_of_bnf Ds (passiveAs @ Ts) (passiveAs @ active_initTs)) Dss bnfs; 938 val fTs = map2 (curry op -->) Ts activeAs; 939 val foldT = Library.foldr1 HOLogic.mk_prodT (map2 (curry op -->) Ts activeAs); 940 941 val ((ss, (fold_f, fold_f')), _) = 942 lthy 943 |> mk_Frees "s" sTs 944 ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "f") foldT; 945 946 fun ctor_bind i = nth external_bs (i - 1) |> Binding.prefix_name (ctorN ^ "_"); 947 val ctor_def_bind = rpair [] o Binding.concealed o Thm.def_binding o ctor_bind; 948 949 fun ctor_spec abs str map_FT_init = 950 Library.foldl1 HOLogic.mk_comp [abs, str, 951 Term.list_comb (map_FT_init, map HOLogic.id_const passiveAs @ Rep_Ts)]; 952 953 val ((ctor_frees, (_, ctor_def_frees)), (lthy, lthy_old)) = 954 lthy 955 |> Local_Theory.open_target |> snd 956 |> @{fold_map 4} (fn i => fn abs => fn str => fn mapx => 957 Local_Theory.define 958 ((ctor_bind i, NoSyn), (ctor_def_bind i, ctor_spec abs str mapx))) 959 ks Abs_Ts str_inits map_FT_inits 960 |>> apsnd split_list o split_list 961 ||> `Local_Theory.close_target; 962 963 val phi = Proof_Context.export_morphism lthy_old lthy; 964 fun mk_ctors passive = 965 map (Term.subst_atomic_types (map (Morphism.typ phi) params' ~~ (mk_params passive)) o 966 Morphism.term phi) ctor_frees; 967 val ctors = mk_ctors passiveAs; 968 val ctor's = mk_ctors passiveBs; 969 val ctor_defs = map (fn def => HOLogic.mk_obj_eq (Morphism.thm phi def)) ctor_def_frees; 970 971 val (mor_Rep_thm, mor_Abs_thm) = 972 let 973 val defs = mor_def :: ctor_defs; 974 975 val mor_Rep = 976 Goal.prove_sorry lthy [] [] 977 (HOLogic.mk_Trueprop (mk_mor UNIVs ctors car_inits str_inits Rep_Ts)) 978 (fn {context = ctxt, prems = _} => mk_mor_Rep_tac ctxt m defs Reps Abs_inverses 979 alg_min_alg_thm alg_set_thms set_mapss) 980 |> Thm.close_derivation \<^here>; 981 982 fun mk_ct initFT str abs = Term.absdummy initFT (abs $ (str $ Bound 0)) 983 val cts = @{map 3} (Thm.cterm_of lthy ooo mk_ct) init_FTs str_inits Abs_Ts; 984 985 val mor_Abs = 986 Goal.prove_sorry lthy [] [] 987 (HOLogic.mk_Trueprop (mk_mor car_inits str_inits UNIVs ctors Abs_Ts)) 988 (fn {context = ctxt, prems = _} => mk_mor_Abs_tac ctxt cts defs Abs_inverses 989 map_comp_id_thms map_cong0L_thms) 990 |> Thm.close_derivation \<^here>; 991 in 992 (mor_Rep, mor_Abs) 993 end; 994 995 val timer = time (timer "ctor definitions & thms"); 996 997 val fold_fun = Term.absfree fold_f' 998 (mk_mor UNIVs ctors active_UNIVs ss (map (mk_nthN n fold_f) ks)); 999 val foldx = HOLogic.choice_const foldT $ fold_fun; 1000 1001 fun fold_bind i = nth external_bs (i - 1) |> Binding.prefix_name (ctor_foldN ^ "_"); 1002 val fold_def_bind = rpair [] o Binding.concealed o Thm.def_binding o fold_bind; 1003 1004 fun fold_spec i = fold_rev (Term.absfree o Term.dest_Free) ss (mk_nthN n foldx i); 1005 1006 val ((fold_frees, (_, fold_def_frees)), (lthy, lthy_old)) = 1007 lthy 1008 |> Local_Theory.open_target |> snd 1009 |> fold_map (fn i => 1010 Local_Theory.define ((fold_bind i, NoSyn), (fold_def_bind i, fold_spec i))) ks 1011 |>> apsnd split_list o split_list 1012 ||> `Local_Theory.close_target; 1013 1014 val phi = Proof_Context.export_morphism lthy_old lthy; 1015 val folds = map (Morphism.term phi) fold_frees; 1016 val fold_names = map (fst o dest_Const) folds; 1017 fun mk_folds passives actives = 1018 @{map 3} (fn name => fn T => fn active => 1019 Const (name, Library.foldr (op -->) 1020 (map2 (curry op -->) (mk_FTs (passives @ actives)) actives, T --> active))) 1021 fold_names (mk_Ts passives) actives; 1022 fun mk_fold Ts ss i = Term.list_comb (Const (nth fold_names (i - 1), Library.foldr (op -->) 1023 (map fastype_of ss, nth Ts (i - 1) --> range_type (fastype_of (nth ss (i - 1))))), ss); 1024 val fold_defs = map (fn def => 1025 mk_unabs_def n (HOLogic.mk_obj_eq (Morphism.thm phi def))) fold_def_frees; 1026 1027 (* algebra copies *) 1028 1029 val ((((((Bs, B's), ss), s's), inv_fs), fs), _) = 1030 lthy 1031 |> mk_Frees "B" BTs 1032 ||>> mk_Frees "B'" B'Ts 1033 ||>> mk_Frees "s" sTs 1034 ||>> mk_Frees "s'" s'Ts 1035 ||>> mk_Frees "f" inv_fTs 1036 ||>> mk_Frees "f" fTs; 1037 1038 val copy_thm = 1039 let 1040 val prems = HOLogic.mk_Trueprop (mk_alg Bs ss) :: 1041 @{map 3} (HOLogic.mk_Trueprop ooo mk_bij_betw) inv_fs B's Bs; 1042 val concl = HOLogic.mk_Trueprop (list_exists_free s's 1043 (HOLogic.mk_conj (mk_alg B's s's, mk_mor B's s's Bs ss inv_fs))); 1044 val vars = fold (Variable.add_free_names lthy) (concl :: prems) []; 1045 in 1046 Goal.prove_sorry lthy vars [] (Logic.list_implies (prems, concl)) 1047 (fn {context = ctxt, prems = _} => mk_copy_tac ctxt m alg_def mor_def alg_set_thms 1048 set_mapss) 1049 |> Thm.close_derivation \<^here> 1050 end; 1051 1052 val init_ex_mor_thm = 1053 let 1054 val goal = HOLogic.mk_Trueprop 1055 (list_exists_free fs (mk_mor UNIVs ctors active_UNIVs ss fs)); 1056 val vars = Variable.add_free_names lthy goal []; 1057 in 1058 Goal.prove_sorry lthy vars [] goal 1059 (fn {context = ctxt, prems = _} => 1060 mk_init_ex_mor_tac ctxt Abs_IIT_inverse_thm (alg_min_alg_thm RS copy_thm) 1061 card_of_min_alg_thms mor_Rep_thm mor_comp_thm mor_select_thm mor_incl_thm) 1062 |> Thm.close_derivation \<^here> 1063 end; 1064 1065 val mor_fold_thm = 1066 let 1067 val mor_cong = mor_cong_thm OF (map (mk_nth_conv n) ks); 1068 val cT = Thm.ctyp_of lthy foldT; 1069 val ct = Thm.cterm_of lthy fold_fun 1070 val goal = HOLogic.mk_Trueprop (mk_mor UNIVs ctors active_UNIVs ss (map (mk_fold Ts ss) ks)); 1071 val vars = Variable.add_free_names lthy goal []; 1072 in 1073 Goal.prove_sorry lthy vars [] goal 1074 (fn {context = ctxt, ...} => 1075 mk_mor_fold_tac ctxt cT ct fold_defs init_ex_mor_thm mor_cong) 1076 |> Thm.close_derivation \<^here> 1077 end; 1078 1079 val ctor_fold_thms = map (fn morE => rule_by_tactic lthy 1080 ((rtac lthy CollectI THEN' CONJ_WRAP' (K (rtac lthy @{thm subset_UNIV})) (1 upto m + n)) 1) 1081 (mor_fold_thm RS morE)) morE_thms; 1082 1083 val (fold_unique_mor_thms, fold_unique_mor_thm) = 1084 let 1085 val prem = HOLogic.mk_Trueprop (mk_mor UNIVs ctors active_UNIVs ss fs); 1086 fun mk_fun_eq f i = HOLogic.mk_eq (f, mk_fold Ts ss i); 1087 val unique = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 mk_fun_eq fs ks)); 1088 val vars = fold (Variable.add_free_names lthy) [prem, unique] []; 1089 val unique_mor = Goal.prove_sorry lthy vars [] (Logic.mk_implies (prem, unique)) 1090 (fn {context = ctxt, prems = _} => mk_fold_unique_mor_tac ctxt type_defs 1091 init_unique_mor_thms Reps mor_comp_thm mor_Abs_thm mor_fold_thm) 1092 |> Thm.close_derivation \<^here>; 1093 in 1094 `split_conj_thm unique_mor 1095 end; 1096 1097 val (ctor_fold_unique_thms, ctor_fold_unique_thm) = 1098 `split_conj_thm (mk_conjIN n RS 1099 (mor_UNIV_thm RS iffD2 RS fold_unique_mor_thm)) 1100 1101 val fold_ctor_thms = 1102 map (fn thm => (mor_incl_thm OF replicate n @{thm subset_UNIV}) RS thm RS sym) 1103 fold_unique_mor_thms; 1104 1105 val ctor_o_fold_thms = 1106 let 1107 val mor = mor_comp_thm OF [mor_fold_thm, mor_str_thm]; 1108 in 1109 map2 (fn unique => fn fold_ctor => 1110 trans OF [mor RS unique, fold_ctor]) fold_unique_mor_thms fold_ctor_thms 1111 end; 1112 1113 val timer = time (timer "fold definitions & thms"); 1114 1115 val map_ctors = map2 (fn Ds => fn bnf => 1116 Term.list_comb (mk_map_of_bnf Ds (passiveAs @ FTs) (passiveAs @ Ts) bnf, 1117 map HOLogic.id_const passiveAs @ ctors)) Dss bnfs; 1118 1119 fun dtor_bind i = nth external_bs (i - 1) |> Binding.prefix_name (dtorN ^ "_"); 1120 val dtor_def_bind = rpair [] o Binding.concealed o Thm.def_binding o dtor_bind; 1121 1122 fun dtor_spec i = mk_fold Ts map_ctors i; 1123 1124 val ((dtor_frees, (_, dtor_def_frees)), (lthy, lthy_old)) = 1125 lthy 1126 |> Local_Theory.open_target |> snd 1127 |> fold_map (fn i => 1128 Local_Theory.define ((dtor_bind i, NoSyn), (dtor_def_bind i, dtor_spec i))) ks 1129 |>> apsnd split_list o split_list 1130 ||> `Local_Theory.close_target; 1131 1132 val phi = Proof_Context.export_morphism lthy_old lthy; 1133 fun mk_dtors params = 1134 map (Term.subst_atomic_types (map (Morphism.typ phi) params' ~~ params) o Morphism.term phi) 1135 dtor_frees; 1136 val dtors = mk_dtors params'; 1137 val dtor_defs = map (fn def => HOLogic.mk_obj_eq (Morphism.thm phi def)) dtor_def_frees; 1138 1139 val ctor_o_dtor_thms = map2 (Local_Defs.fold lthy o single) dtor_defs ctor_o_fold_thms; 1140 1141 val dtor_o_ctor_thms = 1142 let 1143 fun mk_goal dtor ctor FT = 1144 mk_Trueprop_eq (HOLogic.mk_comp (dtor, ctor), HOLogic.id_const FT); 1145 val goals = @{map 3} mk_goal dtors ctors FTs; 1146 in 1147 @{map 5} (fn goal => fn dtor_def => fn foldx => fn map_comp_id => fn map_cong0L => 1148 Goal.prove_sorry lthy [] [] goal 1149 (fn {context = ctxt, prems = _} => mk_dtor_o_ctor_tac ctxt dtor_def foldx map_comp_id 1150 map_cong0L ctor_o_fold_thms) 1151 |> Thm.close_derivation \<^here>) 1152 goals dtor_defs ctor_fold_thms map_comp_id_thms map_cong0L_thms 1153 end; 1154 1155 val dtor_ctor_thms = map (fn thm => thm RS @{thm pointfree_idE}) dtor_o_ctor_thms; 1156 val ctor_dtor_thms = map (fn thm => thm RS @{thm pointfree_idE}) ctor_o_dtor_thms; 1157 1158 val bij_dtor_thms = 1159 map2 (fn thm1 => fn thm2 => @{thm o_bij} OF [thm1, thm2]) ctor_o_dtor_thms dtor_o_ctor_thms; 1160 val inj_dtor_thms = map (fn thm => thm RS @{thm bij_is_inj}) bij_dtor_thms; 1161 val surj_dtor_thms = map (fn thm => thm RS @{thm bij_is_surj}) bij_dtor_thms; 1162 val dtor_nchotomy_thms = map (fn thm => thm RS @{thm surjD}) surj_dtor_thms; 1163 val dtor_inject_thms = map (fn thm => thm RS @{thm inj_eq}) inj_dtor_thms; 1164 val dtor_exhaust_thms = map (fn thm => thm RS exE) dtor_nchotomy_thms; 1165 1166 val bij_ctor_thms = 1167 map2 (fn thm1 => fn thm2 => @{thm o_bij} OF [thm1, thm2]) dtor_o_ctor_thms ctor_o_dtor_thms; 1168 val inj_ctor_thms = map (fn thm => thm RS @{thm bij_is_inj}) bij_ctor_thms; 1169 val surj_ctor_thms = map (fn thm => thm RS @{thm bij_is_surj}) bij_ctor_thms; 1170 val ctor_nchotomy_thms = map (fn thm => thm RS @{thm surjD}) surj_ctor_thms; 1171 val ctor_inject_thms = map (fn thm => thm RS @{thm inj_eq}) inj_ctor_thms; 1172 val ctor_exhaust_thms = map (fn thm => thm RS exE) ctor_nchotomy_thms; 1173 1174 val timer = time (timer "dtor definitions & thms"); 1175 1176 val (((((((Izs, (Izs1, Izs1'))), (Izs2, Izs2')), xFs), yFs), init_phis), _) = 1177 lthy 1178 |> mk_Frees "z" Ts 1179 ||>> mk_Frees' "z1" Ts 1180 ||>> mk_Frees' "z2" Ts' 1181 ||>> mk_Frees "x" FTs 1182 ||>> mk_Frees "y" FTs' 1183 ||>> mk_Frees "P" (replicate n (mk_pred1T initT)); 1184 1185 val phis = map2 retype_const_or_free (map mk_pred1T Ts) init_phis; 1186 val phi2s = map2 retype_const_or_free (map2 mk_pred2T Ts Ts') init_phis; 1187 1188 val (ctor_induct_thm, induct_params) = 1189 let 1190 fun mk_prem phi ctor sets x = 1191 let 1192 fun mk_IH phi set z = 1193 let 1194 val prem = mk_Trueprop_mem (z, set $ x); 1195 val concl = HOLogic.mk_Trueprop (phi $ z); 1196 in 1197 Logic.all z (Logic.mk_implies (prem, concl)) 1198 end; 1199 1200 val IHs = @{map 3} mk_IH phis (drop m sets) Izs; 1201 val concl = HOLogic.mk_Trueprop (phi $ (ctor $ x)); 1202 in 1203 Logic.all x (Logic.list_implies (IHs, concl)) 1204 end; 1205 1206 val prems = @{map 4} mk_prem phis ctors FTs_setss xFs; 1207 1208 fun mk_concl phi z = phi $ z; 1209 val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 mk_concl phis Izs)); 1210 1211 val goal = Logic.list_implies (prems, concl); 1212 val vars = Variable.add_free_names lthy goal []; 1213 in 1214 (Goal.prove_sorry lthy vars [] goal 1215 (fn {context = ctxt, prems = _} => 1216 mk_ctor_induct_tac ctxt m set_mapss init_induct_thm morE_thms mor_Abs_thm 1217 Rep_inverses Abs_inverses Reps) 1218 |> Thm.close_derivation \<^here>, 1219 rev (Term.add_tfrees goal [])) 1220 end; 1221 1222 val cTs = map (SOME o Thm.ctyp_of lthy o TFree) induct_params; 1223 1224 val weak_ctor_induct_thms = 1225 let fun insts i = (replicate (i - 1) TrueI) @ (asm_rl :: replicate (n - i) TrueI); 1226 in map (fn i => (ctor_induct_thm OF insts i) RS mk_conjunctN n i) ks end; 1227 1228 val (ctor_induct2_thm, induct2_params) = 1229 let 1230 fun mk_prem phi ctor ctor' sets sets' x y = 1231 let 1232 fun mk_IH phi set set' z1 z2 = 1233 let 1234 val prem1 = mk_Trueprop_mem (z1, (set $ x)); 1235 val prem2 = mk_Trueprop_mem (z2, (set' $ y)); 1236 val concl = HOLogic.mk_Trueprop (phi $ z1 $ z2); 1237 in 1238 fold_rev Logic.all [z1, z2] (Logic.list_implies ([prem1, prem2], concl)) 1239 end; 1240 1241 val IHs = @{map 5} mk_IH phi2s (drop m sets) (drop m sets') Izs1 Izs2; 1242 val concl = HOLogic.mk_Trueprop (phi $ (ctor $ x) $ (ctor' $ y)); 1243 in 1244 fold_rev Logic.all [x, y] (Logic.list_implies (IHs, concl)) 1245 end; 1246 1247 val prems = @{map 7} mk_prem phi2s ctors ctor's FTs_setss FTs'_setss xFs yFs; 1248 1249 fun mk_concl phi z1 z2 = phi $ z1 $ z2; 1250 val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj 1251 (@{map 3} mk_concl phi2s Izs1 Izs2)); 1252 fun mk_t phi (z1, z1') (z2, z2') = 1253 Term.absfree z1' (HOLogic.mk_all (fst z2', snd z2', phi $ z1 $ z2)); 1254 val cts = @{map 3} (SOME o Thm.cterm_of lthy ooo mk_t) phi2s (Izs1 ~~ Izs1') (Izs2 ~~ Izs2'); 1255 val goal = Logic.list_implies (prems, concl); 1256 val vars = Variable.add_free_names lthy goal []; 1257 in 1258 (Goal.prove_sorry lthy vars [] goal 1259 (fn {context = ctxt, prems = _} => mk_ctor_induct2_tac ctxt cTs cts ctor_induct_thm 1260 weak_ctor_induct_thms) 1261 |> Thm.close_derivation \<^here>, 1262 rev (Term.add_tfrees goal [])) 1263 end; 1264 1265 val timer = time (timer "induction"); 1266 1267 fun mk_ctor_map_DEADID_thm ctor_inject map_id0 = 1268 trans OF [id_apply, iffD2 OF [ctor_inject, map_id0 RS sym]]; 1269 1270 fun mk_ctor_map_unique_DEADID_thm () = 1271 let 1272 val (funs, algs) = 1273 HOLogic.conjuncts (HOLogic.dest_Trueprop (Thm.concl_of ctor_fold_unique_thm)) 1274 |> map_split HOLogic.dest_eq 1275 ||> snd o strip_comb o hd 1276 |> @{apply 2} (map (fst o dest_Var)); 1277 fun mk_fun_insts T ix = Thm.cterm_of lthy (Var (ix, T --> T)); 1278 val theta = 1279 (funs ~~ @{map 2} mk_fun_insts Ts funs) @ (algs ~~ map (Thm.cterm_of lthy) ctors); 1280 val ctor_fold_ctors = (ctor_fold_unique_thm OF 1281 map (fn thm => mk_trans @{thm id_o} (mk_sym (thm RS 1282 @{thm trans[OF arg_cong2[of _ _ _ _ "(\<circ>)", OF refl] o_id]}))) map_id0s) 1283 |> split_conj_thm |> map mk_sym; 1284 in 1285 infer_instantiate lthy theta ctor_fold_unique_thm 1286 |> unfold_thms lthy ctor_fold_ctors 1287 |> Morphism.thm (Local_Theory.target_morphism lthy) 1288 end; 1289 1290 fun mk_ctor_Irel_DEADID_thm ctor_inject bnf = 1291 trans OF [ctor_inject, rel_eq_of_bnf bnf RS @{thm predicate2_eqD} RS sym]; 1292 1293 val IphiTs = map2 mk_pred2T passiveAs passiveBs; 1294 val Ipsi1Ts = map2 mk_pred2T passiveAs passiveCs; 1295 val Ipsi2Ts = map2 mk_pred2T passiveCs passiveBs; 1296 val activephiTs = map2 mk_pred2T activeAs activeBs; 1297 val activeIphiTs = map2 mk_pred2T Ts Ts'; 1298 1299 val rels = map2 (fn Ds => mk_rel_of_bnf Ds (passiveAs @ Ts) (passiveBs @ Ts')) Dss bnfs; 1300 1301 (*register new datatypes as BNFs*) 1302 val (timer, Ibnfs, (ctor_Imap_o_thms, ctor_Imap_thms), ctor_Imap_unique_thm, ctor_Iset_thmss', 1303 ctor_Irel_thms, Ibnf_notes, lthy) = 1304 if m = 0 then 1305 (timer, replicate n DEADID_bnf, 1306 map_split (`(mk_pointfree2 lthy)) (map2 mk_ctor_map_DEADID_thm ctor_inject_thms map_ids), 1307 mk_ctor_map_unique_DEADID_thm (), 1308 replicate n [], map2 mk_ctor_Irel_DEADID_thm ctor_inject_thms bnfs, [], lthy) 1309 else let 1310 val fTs = map2 (curry op -->) passiveAs passiveBs; 1311 val uTs = map2 (curry op -->) Ts Ts'; 1312 1313 val ((((fs, fs'), (AFss, AFss')), (ys, ys')), _) = 1314 lthy 1315 |> mk_Frees' "f" fTs 1316 ||>> mk_Freess' "z" setFTss 1317 ||>> mk_Frees' "y" passiveAs; 1318 1319 val map_FTFT's = map2 (fn Ds => 1320 mk_map_of_bnf Ds (passiveAs @ Ts) (passiveBs @ Ts')) Dss bnfs; 1321 fun mk_passive_maps ATs BTs Ts = 1322 map2 (fn Ds => mk_map_of_bnf Ds (ATs @ Ts) (BTs @ Ts)) Dss bnfs; 1323 fun mk_map_fold_arg fs Ts ctor fmap = 1324 HOLogic.mk_comp (ctor, Term.list_comb (fmap, fs @ map HOLogic.id_const Ts)); 1325 fun mk_map Ts fs Ts' ctors mk_maps = 1326 mk_fold Ts (map2 (mk_map_fold_arg fs Ts') ctors (mk_maps Ts')); 1327 val pmapsABT' = mk_passive_maps passiveAs passiveBs; 1328 val fs_maps = map (mk_map Ts fs Ts' ctor's pmapsABT') ks; 1329 1330 val ls = 1 upto m; 1331 val setsss = map (mk_setss o mk_set_Ts) passiveAs; 1332 1333 fun mk_col l T z z' sets = 1334 let 1335 fun mk_UN set = mk_Union T $ (set $ z); 1336 in 1337 Term.absfree z' 1338 (mk_union (nth sets (l - 1) $ z, 1339 Library.foldl1 mk_union (map mk_UN (drop m sets)))) 1340 end; 1341 1342 val colss = @{map 5} (fn l => fn T => @{map 3} (mk_col l T)) ls passiveAs AFss AFss' setsss; 1343 val setss_by_range = map (fn cols => map (mk_fold Ts cols) ks) colss; 1344 val setss_by_bnf = transpose setss_by_range; 1345 1346 val set_bss = 1347 map (flat o map2 (fn B => fn b => 1348 if member (op =) deads (TFree B) then [] else [b]) resBs) set_bss0; 1349 1350 val ctor_witss = 1351 let 1352 val witss = map2 (fn Ds => fn bnf => mk_wits_of_bnf 1353 (replicate (nwits_of_bnf bnf) Ds) 1354 (replicate (nwits_of_bnf bnf) (passiveAs @ Ts)) bnf) Dss bnfs; 1355 fun close_wit (I, wit) = fold_rev Term.absfree (map (nth ys') I) wit; 1356 fun wit_apply (arg_I, arg_wit) (fun_I, fun_wit) = 1357 (union (op =) arg_I fun_I, fun_wit $ arg_wit); 1358 1359 fun gen_arg support i = 1360 if i < m then [([i], nth ys i)] 1361 else maps (mk_wit support (nth ctors (i - m)) (i - m)) (nth support (i - m)) 1362 and mk_wit support ctor i (I, wit) = 1363 let val args = map (gen_arg (nth_map i (remove (op =) (I, wit)) support)) I; 1364 in 1365 (args, [([], wit)]) 1366 |-> fold (map_product wit_apply) 1367 |> map (apsnd (fn t => ctor $ t)) 1368 |> minimize_wits 1369 end; 1370 in 1371 @{map 3} (fn ctor => fn i => map close_wit o minimize_wits o maps (mk_wit witss ctor i)) 1372 ctors (0 upto n - 1) witss 1373 end; 1374 1375 val (lthy, sbd0, sbd0_card_order, sbd0_Cinfinite, set_sbd0ss) = 1376 if n = 1 1377 then (lthy, hd bd0s, hd bd0_card_orders, hd bd0_Cinfinites, set_bd0ss) 1378 else 1379 let 1380 val sum_bd0 = Library.foldr1 (uncurry mk_csum) bd0s; 1381 val sum_bd0T = fst (dest_relT (fastype_of sum_bd0)); 1382 val (sum_bd0T_params, sum_bd0T_params') = `(map TFree) (Term.add_tfreesT sum_bd0T []); 1383 1384 val sbd0T_bind = mk_internal_b (sum_bdTN ^ "0"); 1385 1386 val ((sbd0T_name, (sbd0T_glob_info, sbd0T_loc_info)), lthy) = 1387 typedef (sbd0T_bind, sum_bd0T_params', NoSyn) 1388 (HOLogic.mk_UNIV sum_bd0T) NONE (fn ctxt => 1389 EVERY' [rtac ctxt exI, rtac ctxt UNIV_I] 1) lthy; 1390 1391 val sbd0T = Type (sbd0T_name, sum_bd0T_params); 1392 val Abs_sbd0T = Const (#Abs_name sbd0T_glob_info, sum_bd0T --> sbd0T); 1393 1394 val sbd0_bind = mk_internal_b (sum_bdN ^ "0"); 1395 val sbd0_def_bind = (Thm.def_binding sbd0_bind, []); 1396 1397 val sbd0_spec = mk_dir_image sum_bd0 Abs_sbd0T; 1398 1399 val ((sbd0_free, (_, sbd0_def_free)), (lthy, lthy_old)) = 1400 lthy 1401 |> Local_Theory.open_target |> snd 1402 |> Local_Theory.define ((sbd0_bind, NoSyn), (sbd0_def_bind, sbd0_spec)) 1403 ||> `Local_Theory.close_target; 1404 1405 val phi = Proof_Context.export_morphism lthy_old lthy; 1406 1407 val sbd0_def = HOLogic.mk_obj_eq (Morphism.thm phi sbd0_def_free); 1408 val sbd0 = Const (fst (Term.dest_Const (Morphism.term phi sbd0_free)), 1409 mk_relT (`I sbd0T)); 1410 1411 val Abs_sbd0T_inj = mk_Abs_inj_thm (#Abs_inject sbd0T_loc_info); 1412 val Abs_sbd0T_bij = mk_Abs_bij_thm lthy Abs_sbd0T_inj (#Abs_cases sbd0T_loc_info); 1413 1414 val sum_Cinfinite = mk_sum_Cinfinite bd0_Cinfinites; 1415 val sum_Card_order = sum_Cinfinite RS conjunct2; 1416 val sum_card_order = mk_sum_card_order bd0_card_orders; 1417 1418 val sbd0_ordIso = @{thm ssubst_Pair_rhs} OF 1419 [@{thm dir_image} OF [Abs_sbd0T_inj, sum_Card_order], sbd0_def]; 1420 val sbd0_Cinfinite = @{thm Cinfinite_cong} OF [sbd0_ordIso, sum_Cinfinite]; 1421 1422 val sbd0_card_order = @{thm iffD2[OF arg_cong[of _ _ card_order]]} OF 1423 [sbd0_def, @{thm card_order_dir_image} OF [Abs_sbd0T_bij, sum_card_order]]; 1424 1425 fun mk_set_sbd0 i bd0_Card_order bd0s = 1426 map (fn thm => @{thm ordLeq_ordIso_trans} OF 1427 [bd0_Card_order RS mk_ordLeq_csum n i thm, sbd0_ordIso]) bd0s; 1428 val set_sbd0ss = @{map 3} mk_set_sbd0 ks bd0_Card_orders set_bd0ss; 1429 in 1430 (lthy, sbd0, sbd0_card_order, sbd0_Cinfinite, set_sbd0ss) 1431 end; 1432 1433 val (Ibnf_consts, lthy) = 1434 @{fold_map 9} (fn b => fn map_b => fn rel_b => fn pred_b => fn set_bs => fn mapx => 1435 fn sets => fn wits => fn T => fn lthy => 1436 define_bnf_consts Hardly_Inline (user_policy Note_Some lthy) false (SOME deads) 1437 map_b rel_b pred_b set_bs 1438 (((((((b, T), fold_rev Term.absfree fs' mapx), sets), sbd0), wits), NONE), NONE) lthy) 1439 bs map_bs rel_bs pred_bs set_bss fs_maps setss_by_bnf ctor_witss Ts lthy; 1440 1441 val ((((((((((((((Izs, (Izs1, Izs1')), (Izs2, Izs2')), xFs), yFs))), Iphis), Ipsi1s), 1442 Ipsi2s), fs), fs_copy), us), (ys, ys')), _) = 1443 lthy 1444 |> mk_Frees "z" Ts 1445 ||>> mk_Frees' "z1" Ts 1446 ||>> mk_Frees' "z2" Ts' 1447 ||>> mk_Frees "x" FTs 1448 ||>> mk_Frees "y" FTs' 1449 ||>> mk_Frees "R" IphiTs 1450 ||>> mk_Frees "R" Ipsi1Ts 1451 ||>> mk_Frees "Q" Ipsi2Ts 1452 ||>> mk_Frees "f" fTs 1453 ||>> mk_Frees "f" fTs 1454 ||>> mk_Frees "u" uTs 1455 ||>> mk_Frees' "y" passiveAs; 1456 1457 val (_, Iconsts, Iconst_defs, mk_Iconsts) = @{split_list 4} Ibnf_consts; 1458 val (_, Isetss, Ibds_Ds, Iwitss_Ds, _, _) = @{split_list 6} Iconsts; 1459 val (Imap_defs, Iset_defss, Ibd_defs, Iwit_defss, Irel_defs, Ipred_defs) = 1460 @{split_list 6} Iconst_defs; 1461 val (mk_Imaps_Ds, mk_It_Ds, _, mk_Irels_Ds, mk_Ipreds_Ds, _, _) = 1462 @{split_list 7} mk_Iconsts; 1463 1464 val Irel_unabs_defs = map (fn def => mk_unabs_def m (HOLogic.mk_obj_eq def)) Irel_defs; 1465 val Ipred_unabs_defs = map (fn def => mk_unabs_def m (HOLogic.mk_obj_eq def)) Ipred_defs; 1466 val Iset_defs = flat Iset_defss; 1467 1468 fun mk_Imaps As Bs = map (fn mk => mk deads As Bs) mk_Imaps_Ds; 1469 fun mk_Isetss As = map2 (fn mk => fn Isets => map (mk deads As) Isets) mk_It_Ds Isetss; 1470 val Ibds = map2 (fn mk => mk deads passiveAs) mk_It_Ds Ibds_Ds; 1471 val Iwitss = 1472 map2 (fn mk => fn Iwits => map (mk deads passiveAs o snd) Iwits) mk_It_Ds Iwitss_Ds; 1473 fun mk_Irels As Bs = map (fn mk => mk deads As Bs) mk_Irels_Ds; 1474 fun mk_Ipreds As = map (fn mk => mk deads As) mk_Ipreds_Ds; 1475 1476 val Imaps = mk_Imaps passiveAs passiveBs; 1477 val fs_Imaps = map (fn m => Term.list_comb (m, fs)) Imaps; 1478 val fs_copy_Imaps = map (fn m => Term.list_comb (m, fs_copy)) Imaps; 1479 val (Isetss_by_range, Isetss_by_bnf) = `transpose (mk_Isetss passiveAs); 1480 1481 val map_setss = map (fn T => map2 (fn Ds => 1482 mk_map_of_bnf Ds (passiveAs @ Ts) (mk_set_Ts T)) Dss bnfs) passiveAs; 1483 1484 val timer = time (timer "bnf constants for the new datatypes"); 1485 1486 val (ctor_Imap_thms, ctor_Imap_o_thms) = 1487 let 1488 fun mk_goal fs_map map ctor ctor' = 1489 mk_Trueprop_eq (HOLogic.mk_comp (fs_map, ctor), 1490 HOLogic.mk_comp (ctor', Term.list_comb (map, fs @ fs_Imaps))); 1491 val goals = @{map 4} mk_goal fs_Imaps map_FTFT's ctors ctor's; 1492 val maps = 1493 @{map 4} (fn goal => fn foldx => fn map_comp_id => fn map_cong0 => 1494 Variable.add_free_names lthy goal [] 1495 |> (fn vars => Goal.prove_sorry lthy vars [] goal 1496 (fn {context = ctxt, prems = _} => unfold_thms_tac ctxt Imap_defs THEN 1497 mk_map_tac ctxt m n foldx map_comp_id map_cong0)) 1498 |> Thm.close_derivation \<^here>) 1499 goals ctor_fold_thms map_comp_id_thms map_cong0s; 1500 in 1501 `(map (fn thm => thm RS @{thm comp_eq_dest})) maps 1502 end; 1503 1504 val (ctor_Imap_unique_thms, ctor_Imap_unique_thm) = 1505 let 1506 fun mk_prem u map ctor ctor' = 1507 mk_Trueprop_eq (HOLogic.mk_comp (u, ctor), 1508 HOLogic.mk_comp (ctor', Term.list_comb (map, fs @ us))); 1509 val prems = @{map 4} mk_prem us map_FTFT's ctors ctor's; 1510 val goal = 1511 HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj 1512 (map2 (curry HOLogic.mk_eq) us fs_Imaps)); 1513 val vars = fold (Variable.add_free_names lthy) (goal :: prems) []; 1514 val unique = Goal.prove_sorry lthy vars [] (Logic.list_implies (prems, goal)) 1515 (fn {context = ctxt, prems = _} => unfold_thms_tac ctxt Imap_defs THEN 1516 mk_ctor_map_unique_tac ctxt ctor_fold_unique_thm sym_map_comps) 1517 |> Thm.close_derivation \<^here>; 1518 in 1519 `split_conj_thm unique 1520 end; 1521 1522 val timer = time (timer "map functions for the new datatypes"); 1523 1524 val ctor_Iset_thmss = 1525 let 1526 fun mk_goal sets ctor set col map = 1527 mk_Trueprop_eq (HOLogic.mk_comp (set, ctor), 1528 HOLogic.mk_comp (col, Term.list_comb (map, passive_ids @ sets))); 1529 val goalss = 1530 @{map 3} (fn sets => @{map 4} (mk_goal sets) ctors sets) 1531 Isetss_by_range colss map_setss; 1532 val setss = map (map2 (fn foldx => fn goal => 1533 Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} => 1534 unfold_thms_tac ctxt Iset_defs THEN mk_set_tac ctxt foldx) 1535 |> Thm.close_derivation \<^here>) 1536 ctor_fold_thms) goalss; 1537 1538 fun mk_simp_goal pas_set act_sets sets ctor z set = 1539 mk_Trueprop_eq (set $ (ctor $ z), 1540 mk_union (pas_set $ z, 1541 Library.foldl1 mk_union (map2 (fn X => mk_UNION (X $ z)) act_sets sets))); 1542 val simp_goalss = 1543 map2 (fn i => fn sets => 1544 @{map 4} (fn Fsets => mk_simp_goal (nth Fsets (i - 1)) (drop m Fsets) sets) 1545 FTs_setss ctors xFs sets) 1546 ls Isetss_by_range; 1547 1548 val ctor_setss = @{map 3} (fn i => @{map 3} (fn set_nats => fn goal => fn set => 1549 Variable.add_free_names lthy goal [] 1550 |> (fn vars => Goal.prove_sorry lthy vars [] goal 1551 (fn {context = ctxt, prems = _} => 1552 mk_ctor_set_tac ctxt set (nth set_nats (i - 1)) (drop m set_nats))) 1553 |> Thm.close_derivation \<^here>) 1554 set_mapss) ls simp_goalss setss; 1555 in 1556 ctor_setss 1557 end; 1558 1559 fun mk_set_thms ctor_set = (@{thm xt1(3)} OF [ctor_set, @{thm Un_upper1}]) :: 1560 map (fn i => (@{thm xt1(3)} OF [ctor_set, @{thm Un_upper2}]) RS 1561 (mk_Un_upper n i RS subset_trans) RSN 1562 (2, @{thm UN_upper} RS subset_trans)) 1563 (1 upto n); 1564 val set_Iset_thmsss = transpose (map (map mk_set_thms) ctor_Iset_thmss); 1565 1566 val timer = time (timer "set functions for the new datatypes"); 1567 1568 val cxs = map (SOME o Thm.cterm_of lthy) Izs; 1569 val Isetss_by_range' = 1570 map (map (Term.subst_atomic_types (passiveAs ~~ passiveBs))) Isetss_by_range; 1571 1572 val Iset_Imap0_thmss = 1573 let 1574 fun mk_set_map0 f map z set set' = 1575 HOLogic.mk_eq (mk_image f $ (set $ z), set' $ (map $ z)); 1576 1577 fun mk_cphi f map z set set' = Thm.cterm_of lthy 1578 (Term.absfree (dest_Free z) (mk_set_map0 f map z set set')); 1579 1580 val csetss = map (map (Thm.cterm_of lthy)) Isetss_by_range'; 1581 1582 val cphiss = @{map 3} (fn f => fn sets => fn sets' => 1583 (@{map 4} (mk_cphi f) fs_Imaps Izs sets sets')) fs Isetss_by_range Isetss_by_range'; 1584 1585 val inducts = map (fn cphis => 1586 Thm.instantiate' cTs (map SOME cphis @ cxs) ctor_induct_thm) cphiss; 1587 1588 val goals = 1589 @{map 3} (fn f => fn sets => fn sets' => 1590 HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj 1591 (@{map 4} (mk_set_map0 f) fs_Imaps Izs sets sets'))) 1592 fs Isetss_by_range Isetss_by_range'; 1593 1594 fun mk_tac ctxt induct = mk_set_nat_tac ctxt m (rtac ctxt induct) set_mapss ctor_Imap_thms; 1595 val thms = 1596 @{map 5} (fn goal => fn csets => fn ctor_sets => fn induct => fn i => 1597 Variable.add_free_names lthy goal [] 1598 |> (fn vars => Goal.prove_sorry lthy vars [] goal 1599 (fn {context = ctxt, prems = _} => mk_tac ctxt induct csets ctor_sets i)) 1600 |> Thm.close_derivation \<^here>) 1601 goals csetss ctor_Iset_thmss inducts ls; 1602 in 1603 map split_conj_thm thms 1604 end; 1605 1606 val Iset_bd_thmss = 1607 let 1608 fun mk_set_bd z bd set = mk_ordLeq (mk_card_of (set $ z)) bd; 1609 1610 fun mk_cphi z set = Thm.cterm_of lthy (Term.absfree (dest_Free z) (mk_set_bd z sbd0 set)); 1611 1612 val cphiss = map (map2 mk_cphi Izs) Isetss_by_range; 1613 1614 val inducts = map (fn cphis => 1615 Thm.instantiate' cTs (map SOME cphis @ cxs) ctor_induct_thm) cphiss; 1616 1617 val goals = 1618 map (fn sets => 1619 HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj 1620 (@{map 3} mk_set_bd Izs Ibds sets))) Isetss_by_range; 1621 1622 fun mk_tac ctxt induct = mk_set_bd_tac ctxt m (rtac ctxt induct) sbd0_Cinfinite set_sbd0ss; 1623 val thms = 1624 @{map 4} (fn goal => fn ctor_sets => fn induct => fn i => 1625 Variable.add_free_names lthy goal [] 1626 |> (fn vars => Goal.prove_sorry lthy vars [] goal 1627 (fn {context = ctxt, prems = _} => unfold_thms_tac ctxt Ibd_defs THEN 1628 mk_tac ctxt induct ctor_sets i)) 1629 |> Thm.close_derivation \<^here>) 1630 goals ctor_Iset_thmss inducts ls; 1631 in 1632 map split_conj_thm thms 1633 end; 1634 1635 val Imap_cong0_thms = 1636 let 1637 fun mk_prem z set f g y y' = 1638 mk_Ball (set $ z) (Term.absfree y' (HOLogic.mk_eq (f $ y, g $ y))); 1639 1640 fun mk_map_cong0 sets z fmap gmap = 1641 HOLogic.mk_imp 1642 (Library.foldr1 HOLogic.mk_conj (@{map 5} (mk_prem z) sets fs fs_copy ys ys'), 1643 HOLogic.mk_eq (fmap $ z, gmap $ z)); 1644 1645 fun mk_cphi sets z fmap gmap = 1646 Thm.cterm_of lthy (Term.absfree (dest_Free z) (mk_map_cong0 sets z fmap gmap)); 1647 1648 val cphis = @{map 4} mk_cphi Isetss_by_bnf Izs fs_Imaps fs_copy_Imaps; 1649 1650 val induct = Thm.instantiate' cTs (map SOME cphis @ cxs) ctor_induct_thm; 1651 1652 val goal = 1653 HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj 1654 (@{map 4} mk_map_cong0 Isetss_by_bnf Izs fs_Imaps fs_copy_Imaps)); 1655 val vars = Variable.add_free_names lthy goal []; 1656 1657 val thm = Goal.prove_sorry lthy vars [] goal 1658 (fn {context = ctxt, prems = _} => mk_mcong_tac ctxt (rtac ctxt induct) set_Iset_thmsss 1659 map_cong0s ctor_Imap_thms) 1660 |> Thm.close_derivation \<^here>; 1661 in 1662 split_conj_thm thm 1663 end; 1664 1665 val in_rels = map in_rel_of_bnf bnfs; 1666 val in_Irels = map (fn def => trans OF [def, @{thm OO_Grp_alt}] RS @{thm predicate2_eqD}) 1667 Irel_unabs_defs; 1668 1669 val ctor_Iset_incl_thmss = map (map hd) set_Iset_thmsss; 1670 val ctor_set_Iset_incl_thmsss = map (transpose o map tl) set_Iset_thmsss; 1671 val ctor_Iset_thmss' = transpose ctor_Iset_thmss; 1672 1673 val Irels = mk_Irels passiveAs passiveBs; 1674 val Ipreds = mk_Ipreds passiveAs; 1675 val Irelphis = map (fn rel => Term.list_comb (rel, Iphis)) Irels; 1676 val relphis = map (fn rel => Term.list_comb (rel, Iphis @ Irelphis)) rels; 1677 val Irelpsi1s = map (fn rel => Term.list_comb (rel, Ipsi1s)) (mk_Irels passiveAs passiveCs); 1678 val Irelpsi2s = map (fn rel => Term.list_comb (rel, Ipsi2s)) (mk_Irels passiveCs passiveBs); 1679 val Irelpsi12s = map (fn rel => 1680 Term.list_comb (rel, map2 (curry mk_rel_compp) Ipsi1s Ipsi2s)) Irels; 1681 1682 val ctor_Irel_thms = 1683 let 1684 fun mk_goal xF yF ctor ctor' Irelphi relphi = 1685 mk_Trueprop_eq (Irelphi $ (ctor $ xF) $ (ctor' $ yF), relphi $ xF $ yF); 1686 val goals = @{map 6} mk_goal xFs yFs ctors ctor's Irelphis relphis; 1687 in 1688 @{map 12} (fn i => fn goal => fn in_rel => fn map_comp0 => fn map_cong0 => 1689 fn ctor_map => fn ctor_sets => fn ctor_inject => fn ctor_dtor => 1690 fn set_map0s => fn ctor_set_incls => fn ctor_set_set_inclss => 1691 Variable.add_free_names lthy goal [] 1692 |> (fn vars => Goal.prove_sorry lthy vars [] goal 1693 (fn {context = ctxt, prems = _} => 1694 mk_ctor_rel_tac ctxt in_Irels i in_rel map_comp0 map_cong0 ctor_map ctor_sets 1695 ctor_inject ctor_dtor set_map0s ctor_set_incls ctor_set_set_inclss)) 1696 |> Thm.close_derivation \<^here>) 1697 ks goals in_rels map_comps map_cong0s ctor_Imap_thms ctor_Iset_thmss' 1698 ctor_inject_thms ctor_dtor_thms set_mapss ctor_Iset_incl_thmss 1699 ctor_set_Iset_incl_thmsss 1700 end; 1701 1702 val le_Irel_OO_thm = 1703 let 1704 fun mk_le_Irel_OO Irelpsi1 Irelpsi2 Irelpsi12 Iz1 Iz2 = 1705 HOLogic.mk_imp (mk_rel_compp (Irelpsi1, Irelpsi2) $ Iz1 $ Iz2, 1706 Irelpsi12 $ Iz1 $ Iz2); 1707 val goals = @{map 5} mk_le_Irel_OO Irelpsi1s Irelpsi2s Irelpsi12s Izs1 Izs2; 1708 1709 val cTs = map (SOME o Thm.ctyp_of lthy o TFree) induct2_params; 1710 val cxs = map (SOME o Thm.cterm_of lthy) (splice Izs1 Izs2); 1711 fun mk_cphi z1 z2 goal = SOME (Thm.cterm_of lthy (Term.absfree z1 (Term.absfree z2 goal))); 1712 val cphis = @{map 3} mk_cphi Izs1' Izs2' goals; 1713 val induct = Thm.instantiate' cTs (cphis @ cxs) ctor_induct2_thm; 1714 1715 val goal = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj goals); 1716 val vars = Variable.add_free_names lthy goal []; 1717 in 1718 Goal.prove_sorry lthy vars [] goal 1719 (fn {context = ctxt, prems = _} => mk_le_rel_OO_tac ctxt m induct ctor_nchotomy_thms 1720 ctor_Irel_thms rel_mono_strong0s le_rel_OOs) 1721 |> Thm.close_derivation \<^here> 1722 end; 1723 1724 val timer = time (timer "helpers for BNF properties"); 1725 1726 val map_id0_tacs = map (fn thm => fn ctxt => mk_map_id0_tac ctxt map_id0s thm) 1727 ctor_Imap_unique_thms; 1728 val map_comp0_tacs = 1729 map2 (fn thm => fn i => fn ctxt => 1730 mk_map_comp0_tac ctxt map_comps ctor_Imap_thms thm i) 1731 ctor_Imap_unique_thms ks; 1732 val map_cong0_tacs = map (fn thm => fn ctxt => mk_map_cong0_tac ctxt m thm) Imap_cong0_thms; 1733 val set_map0_tacss = map (map (fn thm => fn ctxt => mk_set_map0_tac ctxt thm)) 1734 (transpose Iset_Imap0_thmss); 1735 val bd_co_tacs = replicate n (fn ctxt => 1736 unfold_thms_tac ctxt Ibd_defs THEN rtac ctxt sbd0_card_order 1); 1737 val bd_cinf_tacs = replicate n (fn ctxt => 1738 unfold_thms_tac ctxt Ibd_defs THEN rtac ctxt (sbd0_Cinfinite RS conjunct1) 1); 1739 val set_bd_tacss = map (map (fn thm => fn ctxt => rtac ctxt thm 1)) (transpose Iset_bd_thmss); 1740 val le_rel_OO_tacs = map (fn i => fn ctxt => 1741 (rtac ctxt @{thm predicate2I} THEN' etac ctxt (le_Irel_OO_thm RS mk_conjunctN n i RS mp)) 1) ks; 1742 1743 val rel_OO_Grp_tacs = map (fn def => fn ctxt => rtac ctxt def 1) Irel_unabs_defs; 1744 1745 val pred_set_tacs = map (fn def => fn ctxt => rtac ctxt def 1) Ipred_unabs_defs; 1746 1747 val tacss = @{map 10} zip_axioms map_id0_tacs map_comp0_tacs map_cong0_tacs set_map0_tacss 1748 bd_co_tacs bd_cinf_tacs set_bd_tacss le_rel_OO_tacs rel_OO_Grp_tacs pred_set_tacs; 1749 1750 fun wit_tac ctxt = unfold_thms_tac ctxt (flat Iwit_defss) THEN 1751 mk_wit_tac ctxt n (flat ctor_Iset_thmss) (maps wit_thms_of_bnf bnfs); 1752 1753 val (Ibnfs, lthy) = 1754 @{fold_map 6} (fn tacs => fn map_b => fn rel_b => fn pred_b => fn set_bs => fn consts => 1755 bnf_def Do_Inline (user_policy Note_Some) false I tacs wit_tac (SOME deads) 1756 map_b rel_b pred_b set_bs consts) 1757 tacss map_bs rel_bs pred_bs set_bss 1758 (((((((replicate n Binding.empty ~~ Ts) ~~ Imaps) ~~ Isetss_by_bnf) ~~ Ibds) ~~ 1759 Iwitss) ~~ map SOME Irels) ~~ map SOME Ipreds) lthy; 1760 1761 val timer = time (timer "registered new datatypes as BNFs"); 1762 1763 val ls' = if m = 1 then [0] else ls 1764 1765 val Ibnf_common_notes = 1766 [(ctor_map_uniqueN, [ctor_Imap_unique_thm])] 1767 |> map (fn (thmN, thms) => 1768 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])); 1769 1770 val Ibnf_notes = 1771 [(ctor_mapN, map single ctor_Imap_thms), 1772 (ctor_relN, map single ctor_Irel_thms), 1773 (ctor_set_inclN, ctor_Iset_incl_thmss), 1774 (ctor_set_set_inclN, map flat ctor_set_Iset_incl_thmsss)] @ 1775 map2 (fn i => fn thms => (mk_ctor_setN i, map single thms)) ls' ctor_Iset_thmss 1776 |> maps (fn (thmN, thmss) => 1777 map2 (fn b => fn thms => 1778 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])) 1779 bs thmss) 1780 in 1781 (timer, Ibnfs, (ctor_Imap_o_thms, ctor_Imap_thms), ctor_Imap_unique_thm, ctor_Iset_thmss', 1782 ctor_Irel_thms, Ibnf_common_notes @ Ibnf_notes, lthy) 1783 end; 1784 1785 val ((((((xFs, yFs)), Iphis), activephis), activeIphis), _) = 1786 lthy 1787 |> mk_Frees "x" FTs 1788 ||>> mk_Frees "y" FTs' 1789 ||>> mk_Frees "R" IphiTs 1790 ||>> mk_Frees "S" activephiTs 1791 ||>> mk_Frees "IR" activeIphiTs; 1792 1793 val ctor_fold_o_Imap_thms = mk_xtor_co_iter_o_map_thms Least_FP false m ctor_fold_unique_thm 1794 ctor_Imap_o_thms (map (mk_pointfree2 lthy) ctor_fold_thms) sym_map_comps map_cong0s; 1795 1796 val Irels = if m = 0 then map HOLogic.eq_const Ts 1797 else map (mk_rel_of_bnf deads passiveAs passiveBs) Ibnfs; 1798 val Irel_induct_thm = 1799 mk_xtor_rel_co_induct_thm Least_FP rels activeIphis Irels Iphis xFs yFs ctors ctor's 1800 (fn {context = ctxt, prems = IHs} => mk_rel_induct_tac ctxt IHs m ctor_induct2_thm ks 1801 ctor_Irel_thms rel_mono_strong0s) lthy; 1802 1803 val rels = map2 (fn Ds => mk_rel_of_bnf Ds allAs allBs') Dss bnfs; 1804 val ctor_fold_transfer_thms = 1805 mk_xtor_co_iter_transfer_thms Least_FP rels activephis activephis Irels Iphis 1806 (mk_folds passiveAs activeAs) (mk_folds passiveBs activeBs) 1807 (fn {context = ctxt, prems = _} => mk_fold_transfer_tac ctxt m Irel_induct_thm 1808 (map map_transfer_of_bnf bnfs) ctor_fold_thms) 1809 lthy; 1810 1811 val timer = time (timer "relator induction"); 1812 1813 fun mk_Ts As = map (typ_subst_atomic (passiveAs ~~ As)) Ts; 1814 val export = map (Morphism.term (Local_Theory.target_morphism lthy)) 1815 val ((recs, (ctor_rec_thms, ctor_rec_unique_thm, ctor_rec_o_Imap_thms, ctor_rec_transfer_thms)), 1816 lthy) = lthy 1817 |> derive_xtor_co_recs Least_FP external_bs mk_Ts (Dss, resDs) bnfs 1818 (export ctors) (export folds) 1819 ctor_fold_unique_thm ctor_fold_thms ctor_fold_transfer_thms ctor_Imap_thms ctor_Irel_thms 1820 (replicate n NONE); 1821 1822 val timer = time (timer "recursor"); 1823 1824 val common_notes = 1825 [(ctor_inductN, [ctor_induct_thm]), 1826 (ctor_induct2N, [ctor_induct2_thm]), 1827 (ctor_rel_inductN, [Irel_induct_thm])] 1828 |> map (fn (thmN, thms) => 1829 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])); 1830 1831 val notes = 1832 [(ctor_dtorN, ctor_dtor_thms), 1833 (ctor_exhaustN, ctor_exhaust_thms), 1834 (ctor_foldN, ctor_fold_thms), 1835 (ctor_fold_o_mapN, ctor_fold_o_Imap_thms), 1836 (ctor_fold_transferN, ctor_fold_transfer_thms), 1837 (ctor_fold_uniqueN, ctor_fold_unique_thms), 1838 (ctor_injectN, ctor_inject_thms), 1839 (dtor_ctorN, dtor_ctor_thms), 1840 (dtor_exhaustN, dtor_exhaust_thms), 1841 (dtor_injectN, dtor_inject_thms)] 1842 |> map (apsnd (map single)) 1843 |> maps (fn (thmN, thmss) => 1844 map2 (fn b => fn thms => 1845 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])) 1846 bs thmss); 1847 1848 val lthy' = lthy |> internals ? snd o Local_Theory.notes (common_notes @ notes @ Ibnf_notes); 1849 1850 val fp_res = 1851 {Ts = Ts, bnfs = Ibnfs, pre_bnfs = bnfs, absT_infos = absT_infos, 1852 ctors = ctors, dtors = dtors, xtor_un_folds = folds, xtor_co_recs = export recs, 1853 xtor_co_induct = ctor_induct_thm, dtor_ctors = dtor_ctor_thms, 1854 ctor_dtors = ctor_dtor_thms, ctor_injects = ctor_inject_thms, 1855 dtor_injects = dtor_inject_thms, xtor_maps = ctor_Imap_thms, 1856 xtor_map_unique = ctor_Imap_unique_thm, xtor_setss = ctor_Iset_thmss', 1857 xtor_rels = ctor_Irel_thms, xtor_un_fold_thms = ctor_fold_thms, 1858 xtor_co_rec_thms = ctor_rec_thms, xtor_un_fold_unique = ctor_fold_unique_thm, 1859 xtor_co_rec_unique = ctor_rec_unique_thm, 1860 xtor_un_fold_o_maps = ctor_fold_o_Imap_thms, 1861 xtor_co_rec_o_maps = ctor_rec_o_Imap_thms, 1862 xtor_un_fold_transfers = ctor_fold_transfer_thms, 1863 xtor_co_rec_transfers = ctor_rec_transfer_thms, xtor_rel_co_induct = Irel_induct_thm, 1864 dtor_set_inducts = []}; 1865 in 1866 timer; (fp_res, lthy') 1867 end; 1868 1869val _ = 1870 Outer_Syntax.local_theory \<^command_keyword>\<open>datatype\<close> "define inductive datatypes" 1871 (parse_co_datatype_cmd Least_FP construct_lfp); 1872 1873end; 1874