1 (* Title: HOL/Codatatype/Tools/bnf_fp_sugar.ML
2 Author: Jasmin Blanchette, TU Muenchen
5 Sugar for constructing LFPs and GFPs.
8 signature BNF_FP_SUGAR =
10 (* TODO: programmatic interface *)
13 structure BNF_FP_Sugar : BNF_FP_SUGAR =
22 open BNF_FP_Sugar_Tactics
25 val coitersN = "coiters";
26 val corecsN = "corecs";
31 (map #1 xs, map #2 xs, map #3 xs, map #4 xs, map #5 xs, map #6 xs, map #7 xs, map #8 xs);
33 fun strip_map_type (Type (@{type_name fun}, [T as Type _, T'])) = strip_map_type T' |>> cons T
34 | strip_map_type T = ([], T);
36 fun typ_subst inst (T as Type (s, Ts)) =
37 (case AList.lookup (op =) inst T of
38 NONE => Type (s, map (typ_subst inst) Ts)
40 | typ_subst inst T = the_default T (AList.lookup (op =) inst T);
42 fun retype_free (Free (s, _)) T = Free (s, T);
44 val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs))
46 fun mk_id T = Const (@{const_name id}, T --> T);
48 fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
49 fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
50 fun mk_uncurried2_fun f xss =
51 mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss);
53 fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v));
55 fun tack z_name (c, v) f =
56 let val z = Free (z_name, mk_sumT (fastype_of v, fastype_of c)) in
57 Term.lambda z (mk_sum_case (Term.lambda v v) (Term.lambda c (f $ c)) $ z)
60 fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
62 fun merge_type_arg_constrained ctxt (T, c) (T', c') =
66 | (NONE, _) => (T, c')
71 error ("Inconsistent sort constraints for type variable " ^
72 quote (Syntax.string_of_typ ctxt T)))
74 cannot_merge_types ();
76 fun merge_type_args_constrained ctxt (cAs, cAs') =
77 if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs'
78 else cannot_merge_types ();
80 fun type_args_constrained_of (((cAs, _), _), _) = cAs;
81 val type_args_of = map fst o type_args_constrained_of;
82 fun type_binder_of (((_, b), _), _) = b;
83 fun mixfix_of ((_, mx), _) = mx;
84 fun ctr_specs_of (_, ctr_specs) = ctr_specs;
86 fun disc_of (((disc, _), _), _) = disc;
87 fun ctr_of (((_, ctr), _), _) = ctr;
88 fun args_of ((_, args), _) = args;
89 fun ctr_mixfix_of (_, mx) = mx;
91 fun prepare_datatype prepare_typ lfp specs fake_lthy no_defs_lthy =
94 map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs
95 |> Library.foldr1 (merge_type_args_constrained no_defs_lthy);
96 val As = map fst constrained_As;
97 val As' = map dest_TFree As;
99 val _ = (case duplicates (op =) As of [] => ()
100 | A :: _ => error ("Duplicate type parameter " ^
101 quote (Syntax.string_of_typ no_defs_lthy A)));
103 (* TODO: use sort constraints on type args *)
105 val N = length specs;
108 Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
111 val bs = map type_binder_of specs;
112 val fakeTs = map mk_fake_T bs;
114 val mixfixes = map mixfix_of specs;
116 val _ = (case duplicates Binding.eq_name bs of [] => ()
117 | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
119 val ctr_specss = map ctr_specs_of specs;
121 val disc_binderss = map (map disc_of) ctr_specss;
122 val ctr_binderss = map (map ctr_of) ctr_specss;
123 val ctr_argsss = map (map args_of) ctr_specss;
124 val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
126 val sel_bindersss = map (map (map fst)) ctr_argsss;
127 val fake_ctr_Tsss = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
129 val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
130 val _ = (case subtract (op =) As' rhs_As' of
132 | A' :: _ => error ("Extra type variables on rhs: " ^
133 quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
137 |> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs
141 fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) =
142 s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
143 quote (Syntax.string_of_typ fake_lthy T)))
144 | eq_fpT _ _ = false;
146 fun freeze_fp (T as Type (s, Us)) =
147 (case find_index (eq_fpT T) fakeTs of ~1 => Type (s, map freeze_fp Us) | j => nth Xs j)
150 val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss;
151 val sum_prod_TsXs = map (mk_sumTN o map HOLogic.mk_tupleT) ctr_TsssXs;
153 val eqs = map dest_TFree Xs ~~ sum_prod_TsXs;
155 val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, unf_flds, fld_unfs, fld_injects,
156 fp_iter_thms, fp_rec_thms), lthy)) =
157 fp_bnf (if lfp then bnf_lfp else bnf_gfp) bs mixfixes As' eqs no_defs_lthy;
159 val add_nested_bnf_names =
161 fun add (Type (s, Ts)) ss =
162 let val (needs, ss') = fold_map add Ts ss in
163 if exists I needs then (true, insert (op =) s ss') else (false, ss')
165 | add T ss = (member (op =) As T, ss);
169 map_filter (bnf_of lthy o Long_Name.base_name)
170 (fold (fold (fold add_nested_bnf_names)) ctr_TsssXs []);
172 val timer = time (Timer.startRealTimer ());
174 fun mk_unf_or_fld get_T Ts t =
175 let val Type (_, Ts0) = get_T (fastype_of t) in
176 Term.subst_atomic_types (Ts0 ~~ Ts) t
179 val mk_unf = mk_unf_or_fld domain_type;
180 val mk_fld = mk_unf_or_fld range_type;
182 val unfs = map (mk_unf As) unfs0;
183 val flds = map (mk_fld As) flds0;
185 val fpTs = map (domain_type o fastype_of) unfs;
187 val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs;
188 val ns = map length ctr_Tsss;
189 val kss = map (fn n => 1 upto n) ns;
190 val mss = map (map length) ctr_Tsss;
191 val Css = map2 replicate ns Cs;
193 fun mk_iter_like Ts Us t =
195 val (binders, body) = strip_type (fastype_of t);
196 val (f_Us, prebody) = split_last binders;
197 val Type (_, Ts0) = if lfp then prebody else body;
198 val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
200 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
203 val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
204 val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
206 val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
207 val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
209 fun dest_rec_pair (T as Type (@{type_name prod}, Us as [_, U])) =
210 if member (op =) Cs U then Us else [T]
211 | dest_rec_pair T = [T];
213 val ((iter_only as (gss, g_Tss, yssss), rec_only as (hss, h_Tss, zssss)),
214 (zs, cs, cpss, p_Tss, coiter_only as ((pgss, cgsss), g_sum_prod_Ts, g_prod_Tss, g_Tsss),
215 corec_only as ((phss, chsss), h_sum_prod_Ts, h_prod_Tss, h_Tsss))) =
219 map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN n o domain_type)
220 ns mss fp_iter_fun_Ts;
221 val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
223 val ((gss, ysss), _) =
225 |> mk_Freess "f" g_Tss
226 ||>> mk_Freesss "x" y_Tsss;
229 map3 (fn n => fn ms => map2 (map dest_rec_pair oo dest_tupleT) ms o dest_sumTN n
230 o domain_type) ns mss fp_rec_fun_Ts;
231 val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
233 val hss = map2 (map2 retype_free) gss h_Tss;
236 |> mk_Freessss "x" z_Tssss;
238 (((gss, g_Tss, map (map (map single)) ysss), (hss, h_Tss, zssss)),
239 ([], [], [], [], (([], []), [], [], []), (([], []), [], [], [])))
243 (*avoid "'a itself" arguments in coiterators and corecursors*)
244 val mss' = map (fn [0] => [1] | ms => ms) mss;
247 map2 (fn C => fn n => replicate (Int.max (0, n - 1)) (C --> HOLogic.boolT)) Cs ns;
249 fun popescu_zip [] [fs] = fs
250 | popescu_zip (p :: ps) (fs :: fss) = p :: fs @ popescu_zip ps fss;
252 fun mk_types fun_Ts =
254 val f_sum_prod_Ts = map range_type fun_Ts;
255 val f_prod_Tss = map2 dest_sumTN ns f_sum_prod_Ts;
257 map3 (fn C => map2 (map (curry (op -->) C) oo dest_tupleT)) Cs mss' f_prod_Tss;
258 val pf_Tss = map2 popescu_zip p_Tss f_Tsss
259 in (f_sum_prod_Ts, f_prod_Tss, f_Tsss, pf_Tss) end;
261 val (g_sum_prod_Ts, g_prod_Tss, g_Tsss, pg_Tss) = mk_types fp_iter_fun_Ts;
262 val (h_sum_prod_Ts, h_prod_Tss, h_Tsss, ph_Tss) = mk_types fp_rec_fun_Ts;
264 val ((((Free (z, _), cs), pss), gsss), _) =
266 |> yield_singleton (mk_Frees "z") dummyT
268 ||>> mk_Freess "p" p_Tss
269 ||>> mk_Freesss "g" g_Tsss;
271 val hsss = map2 (map2 (map2 retype_free)) gsss h_Tsss;
273 val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
277 val pfss = map2 popescu_zip pss fsss;
278 val cfsss = map2 (fn c => map (map (fn f => f $ c))) cs fsss
279 in (pfss, cfsss) end;
281 ((([], [], []), ([], [], [])),
282 ([z], cs, cpss, p_Tss, (mk_terms gsss, g_sum_prod_Ts, g_prod_Tss, pg_Tss),
283 (mk_terms hsss, h_sum_prod_Ts, h_prod_Tss, ph_Tss)))
286 fun pour_some_sugar_on_type (((((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec),
287 fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss),
288 disc_binders), sel_binderss) no_defs_lthy =
290 val unfT = domain_type (fastype_of fld);
291 val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
292 val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
294 val ((((u, v), fs), xss), _) =
296 |> yield_singleton (mk_Frees "u") unfT
297 ||>> yield_singleton (mk_Frees "v") fpT
298 ||>> mk_Frees "f" case_Ts
299 ||>> mk_Freess "x" ctr_Tss;
302 map2 (fn k => fn xs =>
303 fold_rev Term.lambda xs (fld $ mk_InN ctr_prod_Ts (HOLogic.mk_tuple xs) k)) ks xss;
305 val case_binder = Binding.suffix_name ("_" ^ caseN) b;
308 fold_rev Term.lambda (fs @ [v]) (mk_sum_caseN (map2 mk_uncurried_fun fs xss) $ (unf $ v));
310 val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
311 |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
312 Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
313 (case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
314 ||> `Local_Theory.restore;
316 (*transforms defined frees into consts (and more)*)
317 val phi = Proof_Context.export_morphism lthy lthy';
319 val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
320 val case_def = Morphism.thm phi raw_case_def;
322 val ctrs0 = map (Morphism.term phi) raw_ctrs;
323 val casex0 = Morphism.term phi raw_case;
325 val ctrs = map (mk_ctr As) ctrs0;
327 fun exhaust_tac {context = ctxt, ...} =
329 val fld_iff_unf_thm =
332 fold_rev Logic.all [u, v]
333 (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
335 Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
336 mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
337 (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
338 |> Thm.close_derivation
343 Local_Defs.unfold lthy @{thms all_unit_eq}
344 (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) [] (mk_sumEN n))
347 mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
351 map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
352 mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
354 val half_distinct_tacss =
355 map (map (fn (def, def') => fn {context = ctxt, ...} =>
356 mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
359 map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
360 mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
362 val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
364 fun some_lfp_sugar no_defs_lthy =
366 val fpT_to_C = fpT --> C;
368 fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
370 val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
372 val binder = Binding.suffix_name ("_" ^ suf) b;
375 mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)),
376 Term.list_comb (fp_iter_like,
377 map2 (mk_sum_caseN oo map2 mk_uncurried2_fun) fss xssss));
378 in (binder, spec) end;
381 [(iterN, fp_iter, iter_only),
382 (recN, fp_rec, rec_only)];
384 val (binders, specs) = map generate_iter_like iter_likes |> split_list;
386 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
387 |> apfst split_list o fold_map2 (fn b => fn spec =>
388 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
389 #>> apsnd snd) binders specs
390 ||> `Local_Theory.restore;
392 (*transforms defined frees into consts (and more)*)
393 val phi = Proof_Context.export_morphism lthy lthy';
395 val [iter_def, rec_def] = map (Morphism.thm phi) defs;
397 val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
399 ((ctrs, iter, recx, v, xss, ctr_defs, iter_def, rec_def), lthy)
402 fun some_gfp_sugar no_defs_lthy =
404 val B_to_fpT = C --> fpT;
406 fun generate_coiter_like (suf, fp_iter_like, ((pfss, cfsss), f_sum_prod_Ts, f_prod_Tss,
409 val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
411 val binder = Binding.suffix_name ("_" ^ suf) b;
413 fun mk_popescu_join c n cps sum_prod_T prod_Ts cfss =
414 Term.lambda c (mk_IfN sum_prod_T cps
415 (map2 (mk_InN prod_Ts) (map HOLogic.mk_tuple cfss) (1 upto n)));
418 mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binder, res_T)),
419 Term.list_comb (fp_iter_like,
420 map6 mk_popescu_join cs ns cpss f_sum_prod_Ts f_prod_Tss cfsss));
421 in (binder, spec) end;
424 [(coiterN, fp_iter, coiter_only),
425 (corecN, fp_rec, corec_only)];
427 val (binders, specs) = map generate_coiter_like coiter_likes |> split_list;
429 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
430 |> apfst split_list o fold_map2 (fn b => fn spec =>
431 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
432 #>> apsnd snd) binders specs
433 ||> `Local_Theory.restore;
435 (*transforms defined frees into consts (and more)*)
436 val phi = Proof_Context.export_morphism lthy lthy';
438 val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
440 val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
442 ((ctrs, coiter, corec, v, xss, ctr_defs, coiter_def, corec_def), lthy)
445 wrap_datatype tacss ((ctrs0, casex0), (disc_binders, sel_binderss)) lthy'
446 |> (if lfp then some_lfp_sugar else some_gfp_sugar)
449 val pre_map_defs = map map_def_of_bnf pre_bnfs;
450 val map_ids = map map_id_of_bnf nested_bnfs;
453 let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in
454 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
457 fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
459 val map0 = map_of_bnf (the (bnf_of lthy (Long_Name.base_name s)));
460 val mapx = mk_map Ts Us map0;
461 val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx)))));
462 val args = map build_arg TUs;
463 in Term.list_comb (mapx, args) end;
465 fun pour_more_sugar_on_lfps ((ctrss, iters, recs, vs, xsss, ctr_defss, iter_defs, rec_defs),
468 val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
469 val giters = map (lists_bmoc gss) iters;
470 val hrecs = map (lists_bmoc hss) recs;
472 val (iter_thmss, rec_thmss) =
474 fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
475 fold_rev (fold_rev Logic.all) (xs :: fss)
476 (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
478 fun build_call fiter_likes maybe_tick (T, U) =
482 (case find_index (curry (op =) T) fpTs of
483 ~1 => build_map (build_call fiter_likes maybe_tick) T U
484 | j => maybe_tick (nth vs j) (nth fiter_likes j));
486 fun mk_U maybe_prodT =
487 typ_subst (map2 (fn fpT => fn C => (fpT, maybe_prodT fpT C)) fpTs Cs);
489 fun repair_calls fiter_likes maybe_cons maybe_tick maybe_prodT (x as Free (_, T)) =
490 if member (op =) fpTs T then
491 maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
492 else if exists_subtype (member (op =) fpTs) T then
493 [build_call fiter_likes maybe_tick (T, mk_U maybe_prodT T) $ x]
497 val gxsss = map (map (maps (repair_calls giters (K I) (K I) (K I)))) xsss;
499 map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
501 val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
502 val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
505 map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss;
507 map2 (map o mk_iter_like_tac pre_map_defs map_ids rec_defs) fp_rec_thms ctr_defss;
509 (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
510 goal_iterss iter_tacss,
511 map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
512 goal_recss rec_tacss)
516 [(itersN, iter_thmss),
518 |> maps (fn (thmN, thmss) =>
519 map2 (fn b => fn thms =>
520 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
523 lthy |> Local_Theory.notes notes |> snd
526 fun pour_more_sugar_on_gfps ((ctrss, coiters, corecs, vs, xsss, ctr_defss, coiter_defs,
529 val z = the_single zs;
531 val gcoiters = map (lists_bmoc pgss) coiters;
532 val hcorecs = map (lists_bmoc phss) corecs;
534 val (coiter_thmss, corec_thmss) =
536 fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
538 fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr cfs' =
539 fold_rev (fold_rev Logic.all) ([c] :: pfss)
540 (Logic.list_implies (seq_conds mk_goal_cond n k cps,
541 mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, cfs'))));
543 fun build_call fiter_likes maybe_tack (T, U) =
547 (case find_index (curry (op =) U) fpTs of
548 ~1 => build_map (build_call fiter_likes maybe_tack) T U
549 | j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
551 fun mk_U maybe_sumT =
552 typ_subst (map2 (fn C => fn fpT => (maybe_sumT fpT C, fpT)) Cs fpTs);
554 fun repair_calls fiter_likes maybe_sumT maybe_tack
555 (cf as Free (_, Type (_, [_, T])) $ _) =
556 if exists_subtype (member (op =) Cs) T then
557 build_call fiter_likes maybe_tack (T, mk_U maybe_sumT T) $ cf
561 val cgsss = map (map (map (repair_calls gcoiters (K I) (K I)))) cgsss;
562 val chsss = map (map (map (repair_calls hcorecs (curry mk_sumT) (tack z)))) chsss;
565 map7 (map3 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss cgsss;
567 map7 (map3 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss chsss;
570 map3 (map oo mk_coiter_like_tac coiter_defs map_ids) fp_iter_thms pre_map_defs
573 map3 (map oo mk_coiter_like_tac corec_defs map_ids) fp_rec_thms pre_map_defs
576 (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
577 goal_coiterss coiter_tacss,
578 map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
579 goal_corecss corec_tacss)
583 [(coitersN, coiter_thmss),
584 (corecsN, corec_thmss)]
585 |> maps (fn (thmN, thmss) =>
586 map2 (fn b => fn thms =>
587 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
590 lthy |> Local_Theory.notes notes |> snd
594 |> fold_map pour_some_sugar_on_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
595 fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~
596 ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss)
598 |> (if lfp then pour_more_sugar_on_lfps else pour_more_sugar_on_gfps);
600 val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
601 (if lfp then "" else "co") ^ "datatype"));
606 fun datatype_cmd info specs lthy =
608 (* TODO: cleaner handling of fake contexts, without "background_theory" *)
609 (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
610 locale and shadows an existing global type*)
611 val fake_thy = Theory.copy
612 #> fold (fn spec => perhaps (try (Sign.add_type lthy
613 (type_binder_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
614 val fake_lthy = Proof_Context.background_theory fake_thy lthy;
616 prepare_datatype Syntax.read_typ info specs fake_lthy lthy
619 val parse_opt_binding_colon = Scan.optional (Parse.binding --| Parse.$$$ ":") no_binder
622 Parse.$$$ "(" |-- parse_opt_binding_colon -- Parse.typ --| Parse.$$$ ")" ||
623 (Parse.typ >> pair no_binder);
625 val parse_single_spec =
626 Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
627 (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
628 Scan.repeat parse_ctr_arg -- Parse.opt_mixfix));
631 Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes"
632 (Parse.and_list1 parse_single_spec >> datatype_cmd true);
635 Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes"
636 (Parse.and_list1 parse_single_spec >> datatype_cmd false);