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 val mk_sumTN_balanced = Balanced_Tree.make mk_sumT;
54 val dest_sumTN_balanced = Balanced_Tree.dest dest_sumT;
56 fun mk_InN_balanced sum_T n t k =
58 fun repair_types T (Const (s as @{const_name Inl}, _) $ t) = repair_inj_types T s fst t
59 | repair_types T (Const (s as @{const_name Inr}, _) $ t) = repair_inj_types T s snd t
60 | repair_types _ t = t
61 and repair_inj_types T s get t =
62 let val T' = get (dest_sumT T) in
63 Const (s, T' --> T) $ repair_types T' t
66 Balanced_Tree.access {left = mk_Inl dummyT, right = mk_Inr dummyT, init = t} n k
70 val mk_sum_caseN_balanced = Balanced_Tree.make mk_sum_case;
72 fun mk_sumEN_balanced 1 = @{thm one_pointE}
73 | mk_sumEN_balanced 2 = @{thm sumE} (*optimization*)
74 | mk_sumEN_balanced n =
75 Balanced_Tree.make (fn (thm1, thm2) => thm1 RSN (1, thm2 RSN (2, @{thm obj_sumE_f})))
76 (replicate n asm_rl) OF (replicate n (impI RS allI)) RS @{thm obj_one_pointE};
78 fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v));
80 fun tack z_name (c, v) f =
81 let val z = Free (z_name, mk_sumT (fastype_of v, fastype_of c)) in
82 Term.lambda z (mk_sum_case (Term.lambda v v, Term.lambda c (f $ c)) $ z)
85 fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
87 fun merge_type_arg_constrained ctxt (T, c) (T', c') =
91 | (NONE, _) => (T, c')
96 error ("Inconsistent sort constraints for type variable " ^
97 quote (Syntax.string_of_typ ctxt T)))
99 cannot_merge_types ();
101 fun merge_type_args_constrained ctxt (cAs, cAs') =
102 if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs'
103 else cannot_merge_types ();
105 fun type_args_constrained_of (((cAs, _), _), _) = cAs;
106 val type_args_of = map fst o type_args_constrained_of;
107 fun type_binder_of (((_, b), _), _) = b;
108 fun mixfix_of ((_, mx), _) = mx;
109 fun ctr_specs_of (_, ctr_specs) = ctr_specs;
111 fun disc_of (((disc, _), _), _) = disc;
112 fun ctr_of (((_, ctr), _), _) = ctr;
113 fun args_of ((_, args), _) = args;
114 fun ctr_mixfix_of (_, mx) = mx;
116 fun prepare_datatype prepare_typ lfp specs fake_lthy no_defs_lthy =
119 map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs
120 |> Library.foldr1 (merge_type_args_constrained no_defs_lthy);
121 val As = map fst constrained_As;
122 val As' = map dest_TFree As;
124 val _ = (case duplicates (op =) As of [] => ()
125 | A :: _ => error ("Duplicate type parameter " ^
126 quote (Syntax.string_of_typ no_defs_lthy A)));
128 (* TODO: use sort constraints on type args *)
130 val N = length specs;
133 Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
136 val bs = map type_binder_of specs;
137 val fakeTs = map mk_fake_T bs;
139 val mixfixes = map mixfix_of specs;
141 val _ = (case duplicates Binding.eq_name bs of [] => ()
142 | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
144 val ctr_specss = map ctr_specs_of specs;
146 val disc_binderss = map (map disc_of) ctr_specss;
147 val ctr_binderss = map (map ctr_of) ctr_specss;
148 val ctr_argsss = map (map args_of) ctr_specss;
149 val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
151 val sel_bindersss = map (map (map fst)) ctr_argsss;
152 val fake_ctr_Tsss = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
154 val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
155 val _ = (case subtract (op =) As' rhs_As' of
157 | A' :: _ => error ("Extra type variables on rhs: " ^
158 quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
162 |> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs
166 fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) =
167 s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
168 quote (Syntax.string_of_typ fake_lthy T)))
169 | eq_fpT _ _ = false;
171 fun freeze_fp (T as Type (s, Us)) =
172 (case find_index (eq_fpT T) fakeTs of ~1 => Type (s, map freeze_fp Us) | j => nth Xs j)
175 val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss;
176 val ctr_sum_prod_TsXs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssXs;
178 val eqs = map dest_TFree Xs ~~ ctr_sum_prod_TsXs;
180 val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, unf_flds, fld_unfs, fld_injects,
181 fp_iter_thms, fp_rec_thms), lthy)) =
182 fp_bnf (if lfp then bnf_lfp else bnf_gfp) bs mixfixes As' eqs no_defs_lthy;
184 val add_nested_bnf_names =
186 fun add (Type (s, Ts)) ss =
187 let val (needs, ss') = fold_map add Ts ss in
188 if exists I needs then (true, insert (op =) s ss') else (false, ss')
190 | add T ss = (member (op =) As T, ss);
194 map_filter (bnf_of lthy) (fold (fold (fold add_nested_bnf_names)) ctr_TsssXs []);
196 val timer = time (Timer.startRealTimer ());
198 fun mk_unf_or_fld get_T Ts t =
199 let val Type (_, Ts0) = get_T (fastype_of t) in
200 Term.subst_atomic_types (Ts0 ~~ Ts) t
203 val mk_unf = mk_unf_or_fld domain_type;
204 val mk_fld = mk_unf_or_fld range_type;
206 val unfs = map (mk_unf As) unfs0;
207 val flds = map (mk_fld As) flds0;
209 val fpTs = map (domain_type o fastype_of) unfs;
211 val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs;
212 val ns = map length ctr_Tsss;
213 val kss = map (fn n => 1 upto n) ns;
214 val mss = map (map length) ctr_Tsss;
215 val Css = map2 replicate ns Cs;
217 fun mk_iter_like Ts Us t =
219 val (binders, body) = strip_type (fastype_of t);
220 val (f_Us, prebody) = split_last binders;
221 val Type (_, Ts0) = if lfp then prebody else body;
222 val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
224 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
227 val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
228 val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
230 val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
231 val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
233 fun dest_rec_pair (T as Type (@{type_name prod}, Us as [_, U])) =
234 if member (op =) Cs U then Us else [T]
235 | dest_rec_pair T = [T];
237 val ((iter_only as (gss, _, _), rec_only as (hss, _, _)),
238 (zs, cs, cpss, coiter_only as ((pgss, cgsss), _), corec_only as ((phss, chsss), _))) =
242 map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
243 ns mss fp_iter_fun_Ts;
244 val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
246 val ((gss, ysss), _) =
248 |> mk_Freess "f" g_Tss
249 ||>> mk_Freesss "x" y_Tsss;
252 map3 (fn n => fn ms => map2 (map dest_rec_pair oo dest_tupleT) ms o
253 dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts;
254 val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
256 val hss = map2 (map2 retype_free) gss h_Tss;
259 |> mk_Freessss "x" z_Tssss;
261 (((gss, g_Tss, map (map (map single)) ysss), (hss, h_Tss, zssss)),
262 ([], [], [], (([], []), ([], [])), (([], []), ([], []))))
266 (*avoid "'a itself" arguments in coiterators and corecursors*)
267 val mss' = map (fn [0] => [1] | ms => ms) mss;
270 map2 (fn C => fn n => replicate (Int.max (0, n - 1)) (C --> HOLogic.boolT)) Cs ns;
272 fun zip_preds_getters [] [fs] = fs
273 | zip_preds_getters (p :: ps) (fs :: fss) = p :: fs @ zip_preds_getters ps fss;
275 fun mk_types fun_Ts =
277 val f_sum_prod_Ts = map range_type fun_Ts;
278 val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
280 map3 (fn C => map2 (map (curry (op -->) C) oo dest_tupleT)) Cs mss' f_prod_Tss;
281 val pf_Tss = map2 zip_preds_getters p_Tss f_Tsss
282 in (f_sum_prod_Ts, f_Tsss, pf_Tss) end;
284 val (g_sum_prod_Ts, g_Tsss, pg_Tss) = mk_types fp_iter_fun_Ts;
285 val (h_sum_prod_Ts, h_Tsss, ph_Tss) = mk_types fp_rec_fun_Ts;
287 val ((((Free (z, _), cs), pss), gsss), _) =
289 |> yield_singleton (mk_Frees "z") dummyT
291 ||>> mk_Freess "p" p_Tss
292 ||>> mk_Freesss "g" g_Tsss;
294 val hsss = map2 (map2 (map2 retype_free)) gsss h_Tsss;
296 val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
300 val pfss = map2 zip_preds_getters pss fsss;
301 val cfsss = map2 (fn c => map (map (fn f => f $ c))) cs fsss
302 in (pfss, cfsss) end;
304 ((([], [], []), ([], [], [])),
305 ([z], cs, cpss, (mk_terms gsss, (g_sum_prod_Ts, pg_Tss)),
306 (mk_terms hsss, (h_sum_prod_Ts, ph_Tss))))
309 fun pour_some_sugar_on_type (((((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec),
310 fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss),
311 disc_binders), sel_binderss) no_defs_lthy =
313 val unfT = domain_type (fastype_of fld);
314 val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
315 val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
316 val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
318 val ((((u, v), fs), xss), _) =
320 |> yield_singleton (mk_Frees "u") unfT
321 ||>> yield_singleton (mk_Frees "v") fpT
322 ||>> mk_Frees "f" case_Ts
323 ||>> mk_Freess "x" ctr_Tss;
326 map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $
327 mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
329 val case_binder = Binding.suffix_name ("_" ^ caseN) b;
332 fold_rev Term.lambda (fs @ [v])
333 (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v));
335 val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
336 |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
337 Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
338 (case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
339 ||> `Local_Theory.restore;
341 (*transforms defined frees into consts (and more)*)
342 val phi = Proof_Context.export_morphism lthy lthy';
344 val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
345 val case_def = Morphism.thm phi raw_case_def;
347 val ctrs0 = map (Morphism.term phi) raw_ctrs;
348 val casex0 = Morphism.term phi raw_case;
350 val ctrs = map (mk_ctr As) ctrs0;
352 fun exhaust_tac {context = ctxt, ...} =
354 val fld_iff_unf_thm =
357 fold_rev Logic.all [u, v]
358 (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
360 Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
361 mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
362 (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
363 |> Thm.close_derivation
368 Local_Defs.unfold lthy @{thms all_unit_eq}
369 (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
370 (mk_sumEN_balanced n))
373 mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
377 map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
378 mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
380 val half_distinct_tacss =
381 map (map (fn (def, def') => fn {context = ctxt, ...} =>
382 mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
385 map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
386 mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
388 val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
390 fun some_lfp_sugar no_defs_lthy =
392 val fpT_to_C = fpT --> C;
394 fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
396 val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
398 val binder = Binding.suffix_name ("_" ^ suf) b;
401 mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)),
402 Term.list_comb (fp_iter_like,
403 map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
404 in (binder, spec) end;
407 [(iterN, fp_iter, iter_only),
408 (recN, fp_rec, rec_only)];
410 val (binders, specs) = map generate_iter_like iter_likes |> split_list;
412 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
413 |> apfst split_list o fold_map2 (fn b => fn spec =>
414 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
415 #>> apsnd snd) binders specs
416 ||> `Local_Theory.restore;
418 (*transforms defined frees into consts (and more)*)
419 val phi = Proof_Context.export_morphism lthy lthy';
421 val [iter_def, rec_def] = map (Morphism.thm phi) defs;
423 val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
425 ((ctrs, iter, recx, v, xss, ctr_defs, iter_def, rec_def), lthy)
428 fun some_gfp_sugar no_defs_lthy =
430 val B_to_fpT = C --> fpT;
432 fun generate_coiter_like (suf, fp_iter_like, ((pfss, cfsss), (f_sum_prod_Ts, pf_Tss))) =
434 val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
436 val binder = Binding.suffix_name ("_" ^ suf) b;
438 fun mk_preds_getters_join c n cps sum_prod_T cfss =
439 Term.lambda c (mk_IfN sum_prod_T cps
440 (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cfss) (1 upto n)));
443 mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binder, res_T)),
444 Term.list_comb (fp_iter_like,
445 map5 mk_preds_getters_join cs ns cpss f_sum_prod_Ts cfsss));
446 in (binder, spec) end;
449 [(coiterN, fp_iter, coiter_only),
450 (corecN, fp_rec, corec_only)];
452 val (binders, specs) = map generate_coiter_like coiter_likes |> split_list;
454 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
455 |> apfst split_list o fold_map2 (fn b => fn spec =>
456 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
457 #>> apsnd snd) binders specs
458 ||> `Local_Theory.restore;
460 (*transforms defined frees into consts (and more)*)
461 val phi = Proof_Context.export_morphism lthy lthy';
463 val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
465 val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
467 ((ctrs, coiter, corec, v, xss, ctr_defs, coiter_def, corec_def), lthy)
470 wrap_datatype tacss ((ctrs0, casex0), (disc_binders, sel_binderss)) lthy'
471 |> (if lfp then some_lfp_sugar else some_gfp_sugar)
474 val pre_map_defs = map map_def_of_bnf pre_bnfs;
475 val map_ids = map map_id_of_bnf nested_bnfs;
478 let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in
479 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
482 fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
484 val map0 = map_of_bnf (the (bnf_of lthy s));
485 val mapx = mk_map Ts Us map0;
486 val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx)))));
487 val args = map build_arg TUs;
488 in Term.list_comb (mapx, args) end;
490 fun pour_more_sugar_on_lfps ((ctrss, iters, recs, vs, xsss, ctr_defss, iter_defs, rec_defs),
493 val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
494 val giters = map (lists_bmoc gss) iters;
495 val hrecs = map (lists_bmoc hss) recs;
497 val (iter_thmss, rec_thmss) =
499 fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
500 fold_rev (fold_rev Logic.all) (xs :: fss)
501 (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
503 fun build_call fiter_likes maybe_tick (T, U) =
507 (case find_index (curry (op =) T) fpTs of
508 ~1 => build_map (build_call fiter_likes maybe_tick) T U
509 | j => maybe_tick (nth vs j) (nth fiter_likes j));
511 fun mk_U maybe_prodT =
512 typ_subst (map2 (fn fpT => fn C => (fpT, maybe_prodT fpT C)) fpTs Cs);
514 fun repair_calls fiter_likes maybe_cons maybe_tick maybe_prodT (x as Free (_, T)) =
515 if member (op =) fpTs T then
516 maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
517 else if exists_subtype (member (op =) fpTs) T then
518 [build_call fiter_likes maybe_tick (T, mk_U maybe_prodT T) $ x]
522 val gxsss = map (map (maps (repair_calls giters (K I) (K I) (K I)))) xsss;
524 map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
526 val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
527 val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
530 map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss;
532 map2 (map o mk_iter_like_tac pre_map_defs map_ids rec_defs) fp_rec_thms ctr_defss;
534 (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
535 goal_iterss iter_tacss,
536 map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
537 goal_recss rec_tacss)
541 [(itersN, iter_thmss),
543 |> maps (fn (thmN, thmss) =>
544 map2 (fn b => fn thms =>
545 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
548 lthy |> Local_Theory.notes notes |> snd
551 fun pour_more_sugar_on_gfps ((ctrss, coiters, corecs, vs, _, ctr_defss, coiter_defs,
554 val z = the_single zs;
556 val gcoiters = map (lists_bmoc pgss) coiters;
557 val hcorecs = map (lists_bmoc phss) corecs;
559 val (coiter_thmss, corec_thmss) =
561 fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
563 fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' =
564 fold_rev (fold_rev Logic.all) ([c] :: pfss)
565 (Logic.list_implies (seq_conds mk_goal_cond n k cps,
566 mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
568 fun build_call fiter_likes maybe_tack (T, U) =
572 (case find_index (curry (op =) U) fpTs of
573 ~1 => build_map (build_call fiter_likes maybe_tack) T U
574 | j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
576 fun mk_U maybe_sumT =
577 typ_subst (map2 (fn C => fn fpT => (maybe_sumT fpT C, fpT)) Cs fpTs);
579 fun repair_calls fiter_likes maybe_sumT maybe_tack
580 (cf as Free (_, Type (_, [_, T])) $ _) =
581 if exists_subtype (member (op =) Cs) T then
582 build_call fiter_likes maybe_tack (T, mk_U maybe_sumT T) $ cf
586 val cgsss' = map (map (map (repair_calls gcoiters (K I) (K I)))) cgsss;
587 val chsss' = map (map (map (repair_calls hcorecs (curry mk_sumT) (tack z)))) chsss;
590 map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss cgsss';
592 map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss chsss';
595 map3 (map oo mk_coiter_like_tac coiter_defs map_ids) fp_iter_thms pre_map_defs
598 map3 (map oo mk_coiter_like_tac corec_defs map_ids) fp_rec_thms pre_map_defs
601 (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
602 goal_coiterss coiter_tacss,
603 map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
604 goal_corecss corec_tacss)
608 [(coitersN, coiter_thmss),
609 (corecsN, corec_thmss)]
610 |> maps (fn (thmN, thmss) =>
611 map2 (fn b => fn thms =>
612 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
615 lthy |> Local_Theory.notes notes |> snd
619 |> fold_map pour_some_sugar_on_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
620 fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~
621 ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss)
623 |> (if lfp then pour_more_sugar_on_lfps else pour_more_sugar_on_gfps);
625 val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
626 (if lfp then "" else "co") ^ "datatype"));
631 fun datatype_cmd info specs lthy =
633 (* TODO: cleaner handling of fake contexts, without "background_theory" *)
634 (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
635 locale and shadows an existing global type*)
636 val fake_thy = Theory.copy
637 #> fold (fn spec => perhaps (try (Sign.add_type lthy
638 (type_binder_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
639 val fake_lthy = Proof_Context.background_theory fake_thy lthy;
641 prepare_datatype Syntax.read_typ info specs fake_lthy lthy
644 val parse_opt_binding_colon = Scan.optional (Parse.binding --| Parse.$$$ ":") no_binder
647 Parse.$$$ "(" |-- parse_opt_binding_colon -- Parse.typ --| Parse.$$$ ")" ||
648 (Parse.typ >> pair no_binder);
650 val parse_single_spec =
651 Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
652 (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
653 Scan.repeat parse_ctr_arg -- Parse.opt_mixfix));
656 Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes"
657 (Parse.and_list1 parse_single_spec >> datatype_cmd true);
660 Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes"
661 (Parse.and_list1 parse_single_spec >> datatype_cmd false);