allow defaults for one datatype to involve the constructor of another one in the mutually recursive case
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";
27 val disc_coitersN = "disc_coiters";
28 val disc_corecsN = "disc_corecs";
31 val sel_coitersN = "sel_coiters";
32 val sel_corecsN = "sel_corecs";
35 (map #1 xs, map #2 xs, map #3 xs, map #4 xs, map #5 xs, map #6 xs, map #7 xs, map #8 xs,
36 map #9 xs, map #10 xs, map #11 xs);
38 fun strip_map_type (Type (@{type_name fun}, [T as Type _, T'])) = strip_map_type T' |>> cons T
39 | strip_map_type T = ([], T);
41 fun typ_subst inst (T as Type (s, Ts)) =
42 (case AList.lookup (op =) inst T of
43 NONE => Type (s, map (typ_subst inst) Ts)
45 | typ_subst inst T = the_default T (AList.lookup (op =) inst T);
47 fun retype_free (Free (s, _)) T = Free (s, T);
49 val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs))
51 fun mk_predT T = T --> HOLogic.boolT;
53 fun mk_id T = Const (@{const_name id}, T --> T);
55 fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
56 fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
57 fun mk_uncurried2_fun f xss =
58 mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss);
60 fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v));
62 fun tack z_name (c, v) f =
63 let val z = Free (z_name, mk_sumT (fastype_of v, fastype_of c)) in
64 Term.lambda z (mk_sum_case (Term.lambda v v, Term.lambda c (f $ c)) $ z)
67 fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
69 fun merge_type_arg_constrained ctxt (T, c) (T', c') =
73 | (NONE, _) => (T, c')
78 error ("Inconsistent sort constraints for type variable " ^
79 quote (Syntax.string_of_typ ctxt T)))
81 cannot_merge_types ();
83 fun merge_type_args_constrained ctxt (cAs, cAs') =
84 if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs'
85 else cannot_merge_types ();
87 fun type_args_constrained_of (((cAs, _), _), _) = cAs;
88 val type_args_of = map fst o type_args_constrained_of;
89 fun type_binder_of (((_, b), _), _) = b;
90 fun mixfix_of ((_, mx), _) = mx;
91 fun ctr_specs_of (_, ctr_specs) = ctr_specs;
93 fun disc_of ((((disc, _), _), _), _) = disc;
94 fun ctr_of ((((_, ctr), _), _), _) = ctr;
95 fun args_of (((_, args), _), _) = args;
96 fun defaults_of ((_, ds), _) = ds;
97 fun ctr_mixfix_of (_, mx) = mx;
99 fun prepare_datatype prepare_typ prepare_term lfp (no_dests, specs) fake_lthy no_defs_lthy =
101 val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes"
105 map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs
106 |> Library.foldr1 (merge_type_args_constrained no_defs_lthy);
107 val As = map fst constrained_As;
108 val As' = map dest_TFree As;
110 val _ = (case duplicates (op =) As of [] => ()
111 | A :: _ => error ("Duplicate type parameter " ^
112 quote (Syntax.string_of_typ no_defs_lthy A)));
114 (* TODO: use sort constraints on type args *)
116 val N = length specs;
119 Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
122 val bs = map type_binder_of specs;
123 val fakeTs = map mk_fake_T bs;
125 val mixfixes = map mixfix_of specs;
127 val _ = (case duplicates Binding.eq_name bs of [] => ()
128 | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
130 val ctr_specss = map ctr_specs_of specs;
132 val disc_binderss = map (map disc_of) ctr_specss;
133 val ctr_binderss = map (map ctr_of) ctr_specss;
134 val ctr_argsss = map (map args_of) ctr_specss;
135 val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
137 val sel_bindersss = map (map (map fst)) ctr_argsss;
138 val fake_ctr_Tsss = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
140 val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
142 val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
143 val _ = (case subtract (op =) As' rhs_As' of
145 | A' :: _ => error ("Extra type variables on rhs: " ^
146 quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
150 |> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs
154 fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) =
155 s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
156 quote (Syntax.string_of_typ fake_lthy T)))
157 | eq_fpT _ _ = false;
159 fun freeze_fp (T as Type (s, Us)) =
160 (case find_index (eq_fpT T) fakeTs of ~1 => Type (s, map freeze_fp Us) | j => nth Xs j)
163 val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss;
164 val ctr_sum_prod_TsXs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssXs;
166 val eqs = map dest_TFree Xs ~~ ctr_sum_prod_TsXs;
168 val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, unf_flds, fld_unfs, fld_injects,
169 fp_iter_thms, fp_rec_thms), lthy)) =
170 fp_bnf (if lfp then bnf_lfp else bnf_gfp) bs mixfixes As' eqs no_defs_lthy;
172 val add_nested_bnf_names =
174 fun add (Type (s, Ts)) ss =
175 let val (needs, ss') = fold_map add Ts ss in
176 if exists I needs then (true, insert (op =) s ss') else (false, ss')
178 | add T ss = (member (op =) As T, ss);
182 map_filter (bnf_of lthy) (fold (fold (fold add_nested_bnf_names)) ctr_TsssXs []);
184 val timer = time (Timer.startRealTimer ());
186 fun mk_unf_or_fld get_T Ts t =
187 let val Type (_, Ts0) = get_T (fastype_of t) in
188 Term.subst_atomic_types (Ts0 ~~ Ts) t
191 val mk_unf = mk_unf_or_fld domain_type;
192 val mk_fld = mk_unf_or_fld range_type;
194 val unfs = map (mk_unf As) unfs0;
195 val flds = map (mk_fld As) flds0;
197 val fpTs = map (domain_type o fastype_of) unfs;
199 val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs;
200 val ns = map length ctr_Tsss;
201 val kss = map (fn n => 1 upto n) ns;
202 val mss = map (map length) ctr_Tsss;
203 val Css = map2 replicate ns Cs;
205 fun mk_iter_like Ts Us t =
207 val (binders, body) = strip_type (fastype_of t);
208 val (f_Us, prebody) = split_last binders;
209 val Type (_, Ts0) = if lfp then prebody else body;
210 val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
212 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
215 val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
216 val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
218 val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
219 val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
221 val ((iter_only as (gss, _, _), rec_only as (hss, _, _)),
222 (zs, cs, cpss, coiter_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))) =
226 map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
227 ns mss fp_iter_fun_Ts;
228 val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
230 val ((gss, ysss), _) =
232 |> mk_Freess "f" g_Tss
233 ||>> mk_Freesss "x" y_Tsss;
234 val yssss = map (map (map single)) ysss;
236 fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) =
237 if member (op =) Cs U then Us else [T]
238 | dest_rec_prodT T = [T];
241 map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o
242 dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts;
243 val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
245 val hss = map2 (map2 retype_free) gss h_Tss;
246 val zssss_hd = map2 (map2 (map2 (fn y => fn T :: _ => retype_free y T))) ysss z_Tssss;
249 |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
250 val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
252 (((gss, g_Tss, yssss), (hss, h_Tss, zssss)),
253 ([], [], [], (([], []), ([], [])), (([], []), ([], []))))
257 (*avoid "'a itself" arguments in coiterators and corecursors*)
258 val mss' = map (fn [0] => [1] | ms => ms) mss;
260 val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_predT) ns Cs;
262 fun zip_predss_getterss qss fss = maps (op @) (qss ~~ fss);
264 fun zip_preds_predsss_gettersss [] [qss] [fss] = zip_predss_getterss qss fss
265 | zip_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
266 p :: zip_predss_getterss qss fss @ zip_preds_predsss_gettersss ps qsss fsss;
268 fun mk_types maybe_dest_sumT fun_Ts =
270 val f_sum_prod_Ts = map range_type fun_Ts;
271 val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
273 map3 (fn C => map2 (map (map (curry (op -->) C) o maybe_dest_sumT) oo dest_tupleT))
276 map (map (map (fn [_] => [] | [_, C] => [mk_predT (domain_type C)]))) f_Tssss;
277 val pf_Tss = map3 zip_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
278 in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end;
280 val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_iter_fun_Ts;
282 val ((((Free (z, _), cs), pss), gssss), _) =
284 |> yield_singleton (mk_Frees "z") dummyT
286 ||>> mk_Freess "p" p_Tss
287 ||>> mk_Freessss "g" g_Tssss;
288 val rssss = map (map (map (fn [] => []))) r_Tssss;
290 fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) =
291 if member (op =) Cs U then Us else [T]
292 | dest_corec_sumT T = [T];
294 val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts;
296 val hssss_hd = map2 (map2 (map2 (fn [g] => fn T :: _ => retype_free g T))) gssss h_Tssss;
297 val ((sssss, hssss_tl), _) =
299 |> mk_Freessss "q" s_Tssss
300 ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
301 val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
303 val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
305 fun mk_preds_getters_join [] [cf] = cf
306 | mk_preds_getters_join [cq] [cf, cf'] =
307 mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf');
309 fun mk_terms qssss fssss =
311 val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss;
312 val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss;
313 val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss;
314 val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss;
315 in (pfss, cqfsss) end;
317 ((([], [], []), ([], [], [])),
318 ([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)),
319 (mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss))))
322 fun define_ctrs_case_for_type ((((((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec),
323 fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss),
324 disc_binders), sel_binderss), raw_sel_defaultss) no_defs_lthy =
326 val unfT = domain_type (fastype_of fld);
327 val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
328 val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
329 val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
331 val ((((u, v), fs), xss), _) =
333 |> yield_singleton (mk_Frees "u") unfT
334 ||>> yield_singleton (mk_Frees "v") fpT
335 ||>> mk_Frees "f" case_Ts
336 ||>> mk_Freess "x" ctr_Tss;
339 map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $
340 mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
342 val case_binder = Binding.suffix_name ("_" ^ caseN) b;
345 fold_rev Term.lambda (fs @ [v])
346 (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v));
348 val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
349 |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
350 Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
351 (case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
352 ||> `Local_Theory.restore;
354 (*transforms defined frees into consts (and more)*)
355 val phi = Proof_Context.export_morphism lthy lthy';
357 val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
358 val case_def = Morphism.thm phi raw_case_def;
360 val ctrs0 = map (Morphism.term phi) raw_ctrs;
361 val casex0 = Morphism.term phi raw_case;
363 val ctrs = map (mk_ctr As) ctrs0;
365 fun exhaust_tac {context = ctxt, ...} =
367 val fld_iff_unf_thm =
370 fold_rev Logic.all [u, v]
371 (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
373 Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
374 mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
375 (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
376 |> Thm.close_derivation
381 Local_Defs.unfold lthy @{thms all_unit_eq}
382 (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
383 (mk_sumEN_balanced n))
386 mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
390 map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
391 mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
393 val half_distinct_tacss =
394 map (map (fn (def, def') => fn {context = ctxt, ...} =>
395 mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
398 map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
399 mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
401 val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
403 fun define_iter_rec ((selss0, discIs, sel_thmss), no_defs_lthy) =
405 val fpT_to_C = fpT --> C;
407 fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
409 val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
411 val binder = Binding.suffix_name ("_" ^ suf) b;
414 mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)),
415 Term.list_comb (fp_iter_like,
416 map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
417 in (binder, spec) end;
419 val iter_like_bundles =
420 [(iterN, fp_iter, iter_only),
421 (recN, fp_rec, rec_only)];
423 val (binders, specs) = map generate_iter_like iter_like_bundles |> split_list;
425 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
426 |> apfst split_list o fold_map2 (fn b => fn spec =>
427 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
428 #>> apsnd snd) binders specs
429 ||> `Local_Theory.restore;
431 (*transforms defined frees into consts (and more)*)
432 val phi = Proof_Context.export_morphism lthy lthy';
434 val [iter_def, rec_def] = map (Morphism.thm phi) defs;
436 val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
438 ((ctrs, selss0, iter, recx, v, xss, ctr_defs, discIs, sel_thmss, iter_def, rec_def),
442 fun define_coiter_corec ((selss0, discIs, sel_thmss), no_defs_lthy) =
444 val B_to_fpT = C --> fpT;
446 fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
447 Term.lambda c (mk_IfN sum_prod_T cps
448 (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
450 fun generate_coiter_like (suf, fp_iter_like, ((pfss, cqfsss), (f_sum_prod_Ts,
453 val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
455 val binder = Binding.suffix_name ("_" ^ suf) b;
458 mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binder, res_T)),
459 Term.list_comb (fp_iter_like,
460 map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
461 in (binder, spec) end;
463 val coiter_like_bundles =
464 [(coiterN, fp_iter, coiter_only),
465 (corecN, fp_rec, corec_only)];
467 val (binders, specs) = map generate_coiter_like coiter_like_bundles |> split_list;
469 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
470 |> apfst split_list o fold_map2 (fn b => fn spec =>
471 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
472 #>> apsnd snd) binders specs
473 ||> `Local_Theory.restore;
475 (*transforms defined frees into consts (and more)*)
476 val phi = Proof_Context.export_morphism lthy lthy';
478 val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
480 val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
482 ((ctrs, selss0, coiter, corec, v, xss, ctr_defs, discIs, sel_thmss, coiter_def,
487 let val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss in
488 wrap_datatype tacss (((no_dests, ctrs0), casex0), (disc_binders, (sel_binderss,
489 sel_defaultss))) lthy
492 val define_iter_likes = if lfp then define_iter_rec else define_coiter_corec;
494 ((wrap, define_iter_likes), lthy')
497 val pre_map_defs = map map_def_of_bnf pre_bnfs;
498 val map_ids = map map_id_of_bnf nested_bnfs;
501 let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in
502 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
505 fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
507 val map0 = map_of_bnf (the (bnf_of lthy s));
508 val mapx = mk_map Ts Us map0;
509 val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx)))));
510 val args = map build_arg TUs;
511 in Term.list_comb (mapx, args) end;
513 fun derive_iter_rec_thms_for_types ((ctrss, _, iters, recs, vs, xsss, ctr_defss, _, _, iter_defs,
516 val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
517 val giters = map (lists_bmoc gss) iters;
518 val hrecs = map (lists_bmoc hss) recs;
520 val (iter_thmss, rec_thmss) =
522 fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
523 fold_rev (fold_rev Logic.all) (xs :: fss)
524 (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
526 fun build_call fiter_likes maybe_tick (T, U) =
530 (case find_index (curry (op =) T) fpTs of
531 ~1 => build_map (build_call fiter_likes maybe_tick) T U
532 | j => maybe_tick (nth vs j) (nth fiter_likes j));
534 fun mk_U maybe_mk_prodT =
535 typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
537 fun repair_calls fiter_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) =
538 if member (op =) fpTs T then
539 maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
540 else if exists_subtype (member (op =) fpTs) T then
541 [build_call fiter_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x]
545 val gxsss = map (map (maps (repair_calls giters (K I) (K I) (K I)))) xsss;
547 map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
549 val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
550 val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
553 map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss;
555 map2 (map o mk_iter_like_tac pre_map_defs map_ids rec_defs) fp_rec_thms ctr_defss;
557 (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
558 goal_iterss iter_tacss,
559 map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
560 goal_recss rec_tacss)
564 [(itersN, iter_thmss),
566 |> maps (fn (thmN, thmss) =>
567 map2 (fn b => fn thms =>
568 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
571 lthy |> Local_Theory.notes notes |> snd
574 fun derive_coiter_corec_thms_for_types ((ctrss, selsss, coiters, corecs, vs, _, ctr_defss,
575 discIss, sel_thmsss, coiter_defs, corec_defs), lthy) =
577 val z = the_single zs;
579 val gcoiters = map (lists_bmoc pgss) coiters;
580 val hcorecs = map (lists_bmoc phss) corecs;
582 val (coiter_thmss, corec_thmss) =
584 fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
586 fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' =
587 fold_rev (fold_rev Logic.all) ([c] :: pfss)
588 (Logic.list_implies (seq_conds mk_goal_cond n k cps,
589 mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
591 fun build_call fiter_likes maybe_tack (T, U) =
595 (case find_index (curry (op =) U) fpTs of
596 ~1 => build_map (build_call fiter_likes maybe_tack) T U
597 | j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
599 fun mk_U maybe_mk_sumT =
600 typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
602 fun repair_calls fiter_likes maybe_mk_sumT maybe_tack cqf =
603 let val T = fastype_of cqf in
604 if exists_subtype (member (op =) Cs) T then
605 build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf
610 val crgsss' = map (map (map (repair_calls gcoiters (K I) (K I)))) crgsss;
611 val cshsss' = map (map (map (repair_calls hcorecs (curry mk_sumT) (tack z)))) cshsss;
614 map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss crgsss';
616 map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss cshsss';
619 map3 (map oo mk_coiter_like_tac coiter_defs map_ids) fp_iter_thms pre_map_defs
622 map3 (map oo mk_coiter_like_tac corec_defs map_ids) fp_rec_thms pre_map_defs
625 (map2 (map2 (fn goal => fn tac =>
626 Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
627 goal_coiterss coiter_tacss,
628 map2 (map2 (fn goal => fn tac =>
629 Skip_Proof.prove lthy [] [] goal (tac o #context)
630 |> Local_Defs.unfold lthy @{thms sum_case_if} |> Thm.close_derivation))
631 goal_corecss corec_tacss)
634 fun mk_disc_coiter_like_thms [_] = K []
635 | mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms;
637 val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss;
638 val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss;
640 fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm =
642 val (domT, ranT) = dest_funT (fastype_of sel0);
644 Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
645 [NONE, NONE, SOME (certify lthy sel0)] arg_cong
646 |> Thm.varifyT_global;
647 val sel_thm' = sel_thm RSN (2, trans);
649 coiter_like_thm RS arg_cong' RS sel_thm'
652 val sel_coiter_thmsss =
653 map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss;
654 val sel_corec_thmsss =
655 map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss;
658 [(coitersN, coiter_thmss),
659 (disc_coitersN, disc_coiter_thmss),
660 (sel_coitersN, map flat sel_coiter_thmsss),
661 (corecsN, corec_thmss),
662 (disc_corecsN, disc_corec_thmss),
663 (sel_corecsN, map flat sel_corec_thmsss)]
664 |> maps (fn (thmN, thmss) =>
665 map_filter (fn (_, []) => NONE | (b, thms) =>
666 SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []),
667 [(thms, [])])) (bs ~~ thmss));
669 lthy |> Local_Theory.notes notes |> snd
672 fun wrap_types_and_define_iter_likes ((wraps, define_iter_likess), lthy) =
673 fold_map2 (curry (op o)) define_iter_likess wraps lthy |>> split_list11
676 |> fold_map define_ctrs_case_for_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
677 fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~
678 ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss ~~ raw_sel_defaultsss)
679 |>> split_list |> wrap_types_and_define_iter_likes
680 |> (if lfp then derive_iter_rec_thms_for_types else derive_coiter_corec_thms_for_types);
682 val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
683 (if lfp then "" else "co") ^ "datatype"));
688 fun datatype_cmd lfp (bundle as (_, specs)) lthy =
690 (* TODO: cleaner handling of fake contexts, without "background_theory" *)
691 (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
692 locale and shadows an existing global type*)
693 val fake_thy = Theory.copy
694 #> fold (fn spec => perhaps (try (Sign.add_type lthy
695 (type_binder_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
696 val fake_lthy = Proof_Context.background_theory fake_thy lthy;
698 prepare_datatype Syntax.read_typ Syntax.read_term lfp bundle fake_lthy lthy
701 val parse_opt_binding_colon = Scan.optional (Parse.binding --| @{keyword ":"}) no_binder
704 @{keyword "("} |-- parse_opt_binding_colon -- Parse.typ --| @{keyword ")"} ||
705 (Parse.typ >> pair no_binder);
708 @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
710 val parse_single_spec =
711 Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
712 (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
713 Scan.repeat parse_ctr_arg -- Scan.optional parse_defaults [] -- Parse.opt_mixfix));
715 val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_single_spec;
718 Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes"
719 (parse_datatype >> datatype_cmd true);
722 Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes"
723 (parse_datatype >> datatype_cmd false);