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_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
47 fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
48 fun mk_uncurried2_fun f xss =
49 mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss);
51 fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v))
53 fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
55 fun merge_type_arg_constrained ctxt (T, c) (T', c') =
59 | (NONE, _) => (T, c')
64 error ("Inconsistent sort constraints for type variable " ^
65 quote (Syntax.string_of_typ ctxt T)))
67 cannot_merge_types ();
69 fun merge_type_args_constrained ctxt (cAs, cAs') =
70 if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs'
71 else cannot_merge_types ();
73 fun type_args_constrained_of (((cAs, _), _), _) = cAs;
74 val type_args_of = map fst o type_args_constrained_of;
75 fun type_binder_of (((_, b), _), _) = b;
76 fun mixfix_of ((_, mx), _) = mx;
77 fun ctr_specs_of (_, ctr_specs) = ctr_specs;
79 fun disc_of (((disc, _), _), _) = disc;
80 fun ctr_of (((_, ctr), _), _) = ctr;
81 fun args_of ((_, args), _) = args;
82 fun ctr_mixfix_of (_, mx) = mx;
84 fun prepare_datatype prepare_typ lfp specs fake_lthy no_defs_lthy =
87 map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs
88 |> Library.foldr1 (merge_type_args_constrained no_defs_lthy);
89 val As = map fst constrained_As;
90 val As' = map dest_TFree As;
92 val _ = (case duplicates (op =) As of [] => ()
93 | A :: _ => error ("Duplicate type parameter " ^
94 quote (Syntax.string_of_typ no_defs_lthy A)));
96 (* TODO: use sort constraints on type args *)
101 Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
104 val bs = map type_binder_of specs;
105 val fakeTs = map mk_fake_T bs;
107 val mixfixes = map mixfix_of specs;
109 val _ = (case duplicates Binding.eq_name bs of [] => ()
110 | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
112 val ctr_specss = map ctr_specs_of specs;
114 val disc_binderss = map (map disc_of) ctr_specss;
115 val ctr_binderss = map (map ctr_of) ctr_specss;
116 val ctr_argsss = map (map args_of) ctr_specss;
117 val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
119 val sel_bindersss = map (map (map fst)) ctr_argsss;
120 val fake_ctr_Tsss = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
122 val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
123 val _ = (case subtract (op =) As' rhs_As' of
125 | A' :: _ => error ("Extra type variables on rhs: " ^
126 quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
130 |> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs
134 fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) =
135 s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
136 quote (Syntax.string_of_typ fake_lthy T)))
137 | eq_fpT _ _ = false;
139 fun freeze_fp (T as Type (s, Us)) =
140 (case find_index (eq_fpT T) fakeTs of ~1 => Type (s, map freeze_fp Us) | j => nth Xs j)
143 val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss;
144 val sum_prod_TsXs = map (mk_sumTN o map HOLogic.mk_tupleT) ctr_TsssXs;
146 val eqs = map dest_TFree Xs ~~ sum_prod_TsXs;
148 val (pre_map_defs, ((unfs0, flds0, fp_iters0, fp_recs0, unf_flds, fld_unfs, fld_injects,
149 fp_iter_thms, fp_rec_thms), lthy)) =
150 fp_bnf (if lfp then bnf_lfp else bnf_gfp) bs mixfixes As' eqs no_defs_lthy;
152 val timer = time (Timer.startRealTimer ());
154 fun mk_unf_or_fld get_T Ts t =
155 let val Type (_, Ts0) = get_T (fastype_of t) in
156 Term.subst_atomic_types (Ts0 ~~ Ts) t
159 val mk_unf = mk_unf_or_fld domain_type;
160 val mk_fld = mk_unf_or_fld range_type;
162 val unfs = map (mk_unf As) unfs0;
163 val flds = map (mk_fld As) flds0;
165 val fpTs = map (domain_type o fastype_of) unfs;
167 val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs;
168 val ns = map length ctr_Tsss;
169 val kss = map (fn n => 1 upto n) ns;
170 val mss = map (map length) ctr_Tsss;
171 val Css = map2 replicate ns Cs;
173 fun mk_iter_like Ts Us t =
175 val (binders, body) = strip_type (fastype_of t);
176 val (f_Us, prebody) = split_last binders;
177 val Type (_, Ts0) = if lfp then prebody else body;
178 val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
180 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
183 val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
184 val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
186 val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
187 val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
189 fun dest_rec_pair (T as Type (@{type_name prod}, Us as [_, U])) =
190 if member (op =) Cs U then Us else [T]
191 | dest_rec_pair T = [T];
193 val ((iter_only as (gss, g_Tss, yssss), rec_only as (hss, h_Tss, zssss)),
194 (cs, cpss, p_Tss, coiter_only as ((pgss, cgsss), g_sum_prod_Ts, g_prod_Tss, g_Tsss),
195 corec_only as ((phss, chsss), h_sum_prod_Ts, h_prod_Tss, h_Tsss))) =
199 map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN n o domain_type)
200 ns mss fp_iter_fun_Ts;
201 val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
203 val ((gss, ysss), _) =
205 |> mk_Freess "f" g_Tss
206 ||>> mk_Freesss "x" y_Tsss;
209 map3 (fn n => fn ms => map2 (map dest_rec_pair oo dest_tupleT) ms o dest_sumTN n
210 o domain_type) ns mss fp_rec_fun_Ts;
211 val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
213 val hss = map2 (map2 retype_free) gss h_Tss;
216 |> mk_Freessss "x" z_Tssss;
218 (((gss, g_Tss, map (map (map single)) ysss), (hss, h_Tss, zssss)),
219 ([], [], [], (([], []), [], [], []), (([], []), [], [], [])))
223 (*avoid "'a itself" arguments in coiterators and corecursors*)
224 val mss' = map (fn [0] => [1] | ms => ms) mss;
227 map2 (fn C => fn n => replicate (Int.max (0, n - 1)) (C --> HOLogic.boolT)) Cs ns;
229 fun popescu_zip [] [fs] = fs
230 | popescu_zip (p :: ps) (fs :: fss) = p :: fs @ popescu_zip ps fss;
232 fun mk_types fun_Ts =
234 val f_sum_prod_Ts = map range_type fun_Ts;
235 val f_prod_Tss = map2 dest_sumTN ns f_sum_prod_Ts;
237 map3 (fn C => map2 (map (curry (op -->) C) oo dest_tupleT)) Cs mss' f_prod_Tss;
238 val pf_Tss = map2 popescu_zip p_Tss f_Tsss
239 in (f_sum_prod_Ts, f_prod_Tss, f_Tsss, pf_Tss) end;
241 val (g_sum_prod_Ts, g_prod_Tss, g_Tsss, pg_Tss) = mk_types fp_iter_fun_Ts;
242 val (h_sum_prod_Ts, h_prod_Tss, h_Tsss, ph_Tss) = mk_types fp_rec_fun_Ts;
244 val (((c, pss), gsss), _) =
246 |> yield_singleton (mk_Frees "c") dummyT
247 ||>> mk_Freess "p" p_Tss
248 ||>> mk_Freesss "g" g_Tsss;
250 val hsss = map2 (map2 (map2 retype_free)) gsss h_Tsss;
252 val cs = map (retype_free c) Cs;
253 val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
257 val pfss = map2 popescu_zip pss fsss;
258 val cfsss = map2 (fn c => map (map (fn f => f $ c))) cs fsss
259 in (pfss, cfsss) end;
261 ((([], [], []), ([], [], [])),
262 (cs, cpss, p_Tss, (mk_terms gsss, g_sum_prod_Ts, g_prod_Tss, pg_Tss),
263 (mk_terms hsss, h_sum_prod_Ts, h_prod_Tss, ph_Tss)))
266 fun pour_some_sugar_on_type (((((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec),
267 fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss),
268 disc_binders), sel_binderss) no_defs_lthy =
270 val unfT = domain_type (fastype_of fld);
271 val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
272 val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
274 val ((((u, v), fs), xss), _) =
276 |> yield_singleton (mk_Frees "u") unfT
277 ||>> yield_singleton (mk_Frees "v") fpT
278 ||>> mk_Frees "f" case_Ts
279 ||>> mk_Freess "x" ctr_Tss;
282 map2 (fn k => fn xs =>
283 fold_rev Term.lambda xs (fld $ mk_InN ctr_prod_Ts (HOLogic.mk_tuple xs) k)) ks xss;
285 val case_binder = Binding.suffix_name ("_" ^ caseN) b;
288 fold_rev Term.lambda (fs @ [v]) (mk_sum_caseN (map2 mk_uncurried_fun fs xss) $ (unf $ v));
290 val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
291 |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
292 Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
293 (case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
294 ||> `Local_Theory.restore;
296 (*transforms defined frees into consts (and more)*)
297 val phi = Proof_Context.export_morphism lthy lthy';
299 val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
300 val case_def = Morphism.thm phi raw_case_def;
302 val ctrs0 = map (Morphism.term phi) raw_ctrs;
303 val casex0 = Morphism.term phi raw_case;
305 val ctrs = map (mk_ctr As) ctrs0;
307 fun exhaust_tac {context = ctxt, ...} =
309 val fld_iff_unf_thm =
312 fold_rev Logic.all [u, v]
313 (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
315 Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
316 mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
317 (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
318 |> Thm.close_derivation
323 Local_Defs.unfold lthy @{thms all_unit_eq}
324 (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) [] (mk_sumEN n))
327 mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
331 map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
332 mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
334 val half_distinct_tacss =
335 map (map (fn (def, def') => fn {context = ctxt, ...} =>
336 mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
339 map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
340 mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
342 val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
344 fun some_lfp_sugar no_defs_lthy =
346 val fpT_to_C = fpT --> C;
348 fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
350 val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
352 val binder = Binding.suffix_name ("_" ^ suf) b;
355 mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)),
356 Term.list_comb (fp_iter_like,
357 map2 (mk_sum_caseN oo map2 mk_uncurried2_fun) fss xssss));
358 in (binder, spec) end;
361 [(iterN, fp_iter, iter_only),
362 (recN, fp_rec, rec_only)];
364 val (binders, specs) = map generate_iter_like iter_likes |> split_list;
366 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
367 |> apfst split_list o fold_map2 (fn b => fn spec =>
368 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
369 #>> apsnd snd) binders specs
370 ||> `Local_Theory.restore;
372 (*transforms defined frees into consts (and more)*)
373 val phi = Proof_Context.export_morphism lthy lthy';
375 val [iter_def, rec_def] = map (Morphism.thm phi) defs;
377 val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
379 ((ctrs, iter, recx, v, xss, ctr_defs, iter_def, rec_def), lthy)
382 fun some_gfp_sugar no_defs_lthy =
384 val B_to_fpT = C --> fpT;
386 fun generate_coiter_like (suf, fp_iter_like, ((pfss, cfsss), f_sum_prod_Ts, f_prod_Tss,
389 val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
391 val binder = Binding.suffix_name ("_" ^ suf) b;
393 fun mk_popescu_join c n cps sum_prod_T prod_Ts cfss =
394 Term.lambda c (mk_IfN sum_prod_T cps
395 (map2 (mk_InN prod_Ts) (map HOLogic.mk_tuple cfss) (1 upto n)));
398 mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binder, res_T)),
399 Term.list_comb (fp_iter_like,
400 map6 mk_popescu_join cs ns cpss f_sum_prod_Ts f_prod_Tss cfsss));
401 in (binder, spec) end;
404 [(coiterN, fp_iter, coiter_only),
405 (corecN, fp_rec, corec_only)];
407 val (binders, specs) = map generate_coiter_like coiter_likes |> split_list;
409 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
410 |> apfst split_list o fold_map2 (fn b => fn spec =>
411 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
412 #>> apsnd snd) binders specs
413 ||> `Local_Theory.restore;
415 (*transforms defined frees into consts (and more)*)
416 val phi = Proof_Context.export_morphism lthy lthy';
418 val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
420 val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
422 ((ctrs, coiter, corec, v, xss, ctr_defs, coiter_def, corec_def), lthy)
425 wrap_datatype tacss ((ctrs0, casex0), (disc_binders, sel_binderss)) lthy'
426 |> (if lfp then some_lfp_sugar else some_gfp_sugar)
430 let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in
431 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
434 fun pour_more_sugar_on_lfps ((ctrss, iters, recs, vs, xsss, ctr_defss, iter_defs, rec_defs),
437 val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
438 val giters = map (lists_bmoc gss) iters;
439 val hrecs = map (lists_bmoc hss) recs;
441 val (iter_thmss, rec_thmss) =
443 fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
444 fold_rev (fold_rev Logic.all) (xs :: fss)
445 (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
447 fun build_call fiter_likes maybe_tick =
451 Const (@{const_name id}, T --> T)
453 (case (find_index (curry (op =) T) fpTs, (T, U)) of
454 (~1, (Type (s, Ts), Type (_, Us))) =>
456 val map0 = map_of_bnf (the (bnf_of lthy (Long_Name.base_name s)));
457 val mapx = mk_map Ts Us map0;
459 map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx)))));
460 val args = map build TUs;
461 in Term.list_comb (mapx, args) end
462 | (j, _) => maybe_tick (nth vs j) (nth fiter_likes j))
465 fun mk_U maybe_prodT =
466 typ_subst (map2 (fn fpT => fn C => (fpT, maybe_prodT fpT C)) fpTs Cs);
468 fun repair_calls fiter_likes maybe_cons maybe_tick maybe_prodT (x as Free (_, T)) =
469 if member (op =) fpTs T then
470 maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
471 else if exists_subtype (member (op =) fpTs) T then
472 [build_call fiter_likes maybe_tick (T, mk_U maybe_prodT T) $ x]
476 fun repair_rec_call (x as Free (_, T)) =
477 (case find_index (curry (op =) T) fpTs of ~1 => [x] | j => [x, nth hrecs j $ x]);
479 val gxsss = map (map (maps (repair_calls giters (K I) (K I) (K I)))) xsss;
481 map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
483 val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
484 val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
487 map2 (map o mk_iter_like_tac pre_map_defs iter_defs) fp_iter_thms ctr_defss;
489 map2 (map o mk_iter_like_tac pre_map_defs rec_defs) fp_rec_thms ctr_defss;
493 (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
494 goal_iterss iter_tacss,
495 map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
496 goal_recss rec_tacss)
502 [(itersN, iter_thmss),
504 |> maps (fn (thmN, thmss) =>
505 map2 (fn b => fn thms =>
506 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
510 lthy |> Local_Theory.notes notes |> snd
513 fun pour_more_sugar_on_gfps ((ctrss, coiters, corecs, vs, xsss, ctr_defss, coiter_defs,
517 val gcoiters = map (lists_bmoc pgss) coiters;
518 val hcorecs = map (lists_bmoc phss) corecs;
520 val (coiter_thmss, corec_thmss) =
522 fun mk_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
524 fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr cfs' =
525 fold_rev (fold_rev Logic.all) ([c] :: pfss)
526 (Logic.list_implies (seq_conds mk_cond n k cps,
527 mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, cfs'))));
529 fun repair_call fcoiter_likes (cf as Free (_, Type (_, [_, T])) $ _) =
530 (case find_index (curry (op =) T) Cs of ~1 => cf | j => nth fcoiter_likes j $ cf);
532 val cgsss = map (map (map (repair_call gcoiters))) cgsss;
533 val chsss = map (map (map (repair_call hcorecs))) chsss;
536 map7 (map3 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss cgsss;
538 map7 (map3 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss chsss;
541 map3 (map oo mk_coiter_like_tac coiter_defs) fp_iter_thms pre_map_defs ctr_defss;
543 (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
544 goal_coiterss coiter_tacss,
545 map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
546 goal_coiterss coiter_tacss (* TODO: should be corecs *))
550 [(coitersN, coiter_thmss),
551 (corecsN, corec_thmss)]
552 |> maps (fn (thmN, thmss) =>
553 map2 (fn b => fn thms =>
554 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
558 lthy (* NOTYET |> Local_Theory.notes notes |> snd *)
562 |> fold_map pour_some_sugar_on_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
563 fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~
564 ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss)
566 |> (if lfp then pour_more_sugar_on_lfps else pour_more_sugar_on_gfps);
568 val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
569 (if lfp then "" else "co") ^ "datatype"));
574 fun datatype_cmd info specs lthy =
576 (* TODO: cleaner handling of fake contexts, without "background_theory" *)
577 (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
578 locale and shadows an existing global type*)
579 val fake_thy = Theory.copy
580 #> fold (fn spec => perhaps (try (Sign.add_type lthy
581 (type_binder_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
582 val fake_lthy = Proof_Context.background_theory fake_thy lthy;
584 prepare_datatype Syntax.read_typ info specs fake_lthy lthy
587 val parse_opt_binding_colon = Scan.optional (Parse.binding --| Parse.$$$ ":") no_binder
590 Parse.$$$ "(" |-- parse_opt_binding_colon -- Parse.typ --| Parse.$$$ ")" ||
591 (Parse.typ >> pair no_binder);
593 val parse_single_spec =
594 Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
595 (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
596 Scan.repeat parse_ctr_arg -- Parse.opt_mixfix));
599 Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes"
600 (Parse.and_list1 parse_single_spec >> datatype_cmd true);
603 Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes"
604 (Parse.and_list1 parse_single_spec >> datatype_cmd false);