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 =
11 bool * ((((typ * sort) list * binding) * mixfix) * ((((binding * binding) *
12 (binding * typ) list) * (binding * term) list) * mixfix) list) list ->
13 local_theory -> local_theory
16 structure BNF_FP_Sugar : BNF_FP_SUGAR =
25 open BNF_FP_Sugar_Tactics
28 val coitersN = "coiters";
29 val corecsN = "corecs";
30 val disc_coitersN = "disc_coiters";
31 val disc_corecsN = "disc_corecs";
34 val sel_coitersN = "sel_coiters";
35 val sel_corecsN = "sel_corecs";
37 val simp_attrs = @{attributes [simp]};
40 (map #1 xs, map #2 xs, map #3 xs, map #4 xs, map #5 xs, map #6 xs, map #7 xs, map #8 xs,
41 map #9 xs, map #10 xs, map #11 xs);
43 fun strip_map_type (Type (@{type_name fun}, [T as Type _, T'])) = strip_map_type T' |>> cons T
44 | strip_map_type T = ([], T);
46 fun typ_subst inst (T as Type (s, Ts)) =
47 (case AList.lookup (op =) inst T of
48 NONE => Type (s, map (typ_subst inst) Ts)
50 | typ_subst inst T = the_default T (AList.lookup (op =) inst T);
52 fun resort_tfree S (TFree (s, _)) = TFree (s, S);
54 fun retype_free T (Free (s, _)) = Free (s, T);
56 val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
58 fun mk_predT T = T --> HOLogic.boolT;
60 fun mk_id T = Const (@{const_name id}, T --> T);
62 fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
63 fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
64 fun mk_uncurried2_fun f xss =
65 mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss);
67 fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v));
69 fun tack z_name (c, v) f =
70 let val z = Free (z_name, mk_sumT (fastype_of v, fastype_of c)) in
71 Term.lambda z (mk_sum_case (Term.lambda v v, Term.lambda c (f $ c)) $ z)
74 fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
76 fun merge_type_arg T T' = if T = T' then T else cannot_merge_types ();
78 fun merge_type_args (As, As') =
79 if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types ();
81 fun type_args_constrained_of (((cAs, _), _), _) = cAs;
82 val type_args_of = map fst o type_args_constrained_of;
83 fun type_binder_of (((_, b), _), _) = b;
84 fun mixfix_of ((_, mx), _) = mx;
85 fun ctr_specs_of (_, ctr_specs) = ctr_specs;
87 fun disc_of ((((disc, _), _), _), _) = disc;
88 fun ctr_of ((((_, ctr), _), _), _) = ctr;
89 fun args_of (((_, args), _), _) = args;
90 fun defaults_of ((_, ds), _) = ds;
91 fun ctr_mixfix_of (_, mx) = mx;
93 fun define_datatype prepare_constraint prepare_typ prepare_term lfp (no_dests, specs)
96 (* TODO: sanity checks on arguments *)
98 val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes"
101 val N = length specs;
103 fun prepare_type_arg (ty, c) =
104 let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
105 TFree (s, prepare_constraint no_defs_lthy0 c)
108 val Ass0 = map (map prepare_type_arg o type_args_constrained_of) specs;
109 val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
110 val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
112 val ((Bs, Cs), no_defs_lthy) =
114 |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
118 (* TODO: cleaner handling of fake contexts, without "background_theory" *)
119 (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
120 locale and shadows an existing global type*)
122 Theory.copy #> fold (fn spec => perhaps (try (Sign.add_type no_defs_lthy
123 (type_binder_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
124 val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
127 Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
130 val bs = map type_binder_of specs;
131 val fake_Ts = map mk_fake_T bs;
133 val mixfixes = map mixfix_of specs;
135 val _ = (case duplicates Binding.eq_name bs of [] => ()
136 | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
138 val ctr_specss = map ctr_specs_of specs;
140 val disc_binderss = map (map disc_of) ctr_specss;
141 val ctr_binderss = map (map ctr_of) ctr_specss;
142 val ctr_argsss = map (map args_of) ctr_specss;
143 val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
145 val sel_bindersss = map (map (map fst)) ctr_argsss;
146 val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
147 val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
149 val (Ass as As :: _) :: fake_ctr_Tsss =
150 burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
152 val _ = (case duplicates (op =) unsorted_As of [] => ()
153 | A :: _ => error ("Duplicate type parameter " ^
154 quote (Syntax.string_of_typ no_defs_lthy A)));
156 val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
157 val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
159 | A' :: _ => error ("Extra type variables on rhs: " ^
160 quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
162 fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) =
163 s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
164 quote (Syntax.string_of_typ fake_lthy T)))
165 | eq_fpT _ _ = false;
167 fun freeze_fp (T as Type (s, Us)) =
168 (case find_index (eq_fpT T) fake_Ts of ~1 => Type (s, map freeze_fp Us) | j => nth Bs j)
171 val ctr_TsssBs = map (map (map freeze_fp)) fake_ctr_Tsss;
172 val ctr_sum_prod_TsBs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssBs;
175 map dest_TFree Bs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsBs;
177 val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, unf_flds, fld_unfs, fld_injects,
178 fp_iter_thms, fp_rec_thms), lthy)) =
179 fp_bnf (if lfp then bnf_lfp else bnf_gfp) bs mixfixes (map dest_TFree unsorted_As) fp_eqs
182 val add_nested_bnf_names =
184 fun add (Type (s, Ts)) ss =
185 let val (needs, ss') = fold_map add Ts ss in
186 if exists I needs then (true, insert (op =) s ss') else (false, ss')
188 | add T ss = (member (op =) As T, ss);
192 map_filter (bnf_of lthy) (fold (fold (fold add_nested_bnf_names)) ctr_TsssBs []);
194 val timer = time (Timer.startRealTimer ());
196 fun mk_unf_or_fld get_T Ts t =
197 let val Type (_, Ts0) = get_T (fastype_of t) in
198 Term.subst_atomic_types (Ts0 ~~ Ts) t
201 val mk_unf = mk_unf_or_fld domain_type;
202 val mk_fld = mk_unf_or_fld range_type;
204 val unfs = map (mk_unf As) unfs0;
205 val flds = map (mk_fld As) flds0;
207 val fpTs = map (domain_type o fastype_of) unfs;
209 val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Bs ~~ fpTs)))) ctr_TsssBs;
210 val ns = map length ctr_Tsss;
211 val kss = map (fn n => 1 upto n) ns;
212 val mss = map (map length) ctr_Tsss;
213 val Css = map2 replicate ns Cs;
215 fun mk_iter_like Ts Us t =
217 val (binders, body) = strip_type (fastype_of t);
218 val (f_Us, prebody) = split_last binders;
219 val Type (_, Ts0) = if lfp then prebody else body;
220 val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
222 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
225 val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
226 val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
228 val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
229 val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
231 val ((iter_only as (gss, _, _), rec_only as (hss, _, _)),
232 (zs, cs, cpss, coiter_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))) =
236 map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
237 ns mss fp_iter_fun_Ts;
238 val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
240 val ((gss, ysss), _) =
242 |> mk_Freess "f" g_Tss
243 ||>> mk_Freesss "x" y_Tsss;
244 val yssss = map (map (map single)) ysss;
246 fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) =
247 if member (op =) Cs U then Us else [T]
248 | dest_rec_prodT T = [T];
251 map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o
252 dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts;
253 val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
255 val hss = map2 (map2 retype_free) h_Tss gss;
256 val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
259 |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
260 val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
262 (((gss, g_Tss, yssss), (hss, h_Tss, zssss)),
263 ([], [], [], (([], []), ([], [])), (([], []), ([], []))))
267 (*avoid "'a itself" arguments in coiterators and corecursors*)
268 val mss' = map (fn [0] => [1] | ms => ms) mss;
270 val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_predT) ns Cs;
272 fun zip_predss_getterss qss fss = maps (op @) (qss ~~ fss);
274 fun zip_preds_predsss_gettersss [] [qss] [fss] = zip_predss_getterss qss fss
275 | zip_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
276 p :: zip_predss_getterss qss fss @ zip_preds_predsss_gettersss ps qsss fsss;
278 fun mk_types maybe_dest_sumT fun_Ts =
280 val f_sum_prod_Ts = map range_type fun_Ts;
281 val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
283 map3 (fn C => map2 (map (map (curry (op -->) C) o maybe_dest_sumT) oo dest_tupleT))
286 map (map (map (fn [_] => [] | [_, C] => [mk_predT (domain_type C)]))) f_Tssss;
287 val pf_Tss = map3 zip_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
288 in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end;
290 val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_iter_fun_Ts;
292 val ((((Free (z, _), cs), pss), gssss), _) =
294 |> yield_singleton (mk_Frees "z") dummyT
296 ||>> mk_Freess "p" p_Tss
297 ||>> mk_Freessss "g" g_Tssss;
298 val rssss = map (map (map (fn [] => []))) r_Tssss;
300 fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) =
301 if member (op =) Cs U then Us else [T]
302 | dest_corec_sumT T = [T];
304 val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts;
306 val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
307 val ((sssss, hssss_tl), _) =
309 |> mk_Freessss "q" s_Tssss
310 ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
311 val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
313 val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
315 fun mk_preds_getters_join [] [cf] = cf
316 | mk_preds_getters_join [cq] [cf, cf'] =
317 mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf');
319 fun mk_terms qssss fssss =
321 val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss;
322 val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss;
323 val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss;
324 val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss;
325 in (pfss, cqfsss) end;
327 ((([], [], []), ([], [], [])),
328 ([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)),
329 (mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss))))
332 fun define_ctrs_case_for_type ((((((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec),
333 fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss),
334 disc_binders), sel_binderss), raw_sel_defaultss) no_defs_lthy =
336 val unfT = domain_type (fastype_of fld);
337 val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
338 val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
339 val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
341 val ((((u, v), fs), xss), _) =
343 |> yield_singleton (mk_Frees "u") unfT
344 ||>> yield_singleton (mk_Frees "v") fpT
345 ||>> mk_Frees "f" case_Ts
346 ||>> mk_Freess "x" ctr_Tss;
349 map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $
350 mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
352 val case_binder = Binding.suffix_name ("_" ^ caseN) b;
355 fold_rev Term.lambda (fs @ [v])
356 (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v));
358 val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
359 |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
360 Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
361 (case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
362 ||> `Local_Theory.restore;
364 (*transforms defined frees into consts (and more)*)
365 val phi = Proof_Context.export_morphism lthy lthy';
367 val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
368 val case_def = Morphism.thm phi raw_case_def;
370 val ctrs0 = map (Morphism.term phi) raw_ctrs;
371 val casex0 = Morphism.term phi raw_case;
373 val ctrs = map (mk_ctr As) ctrs0;
375 fun exhaust_tac {context = ctxt, ...} =
377 val fld_iff_unf_thm =
380 fold_rev Logic.all [u, v]
381 (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
383 Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
384 mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
385 (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
386 |> Thm.close_derivation
391 Local_Defs.unfold lthy @{thms all_unit_eq}
392 (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
393 (mk_sumEN_balanced n))
396 mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
400 map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
401 mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
403 val half_distinct_tacss =
404 map (map (fn (def, def') => fn {context = ctxt, ...} =>
405 mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
408 map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
409 mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
411 val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
413 fun define_iter_rec ((selss0, discIs, sel_thmss), no_defs_lthy) =
415 val fpT_to_C = fpT --> C;
417 fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
419 val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
421 val binder = Binding.suffix_name ("_" ^ suf) b;
424 mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)),
425 Term.list_comb (fp_iter_like,
426 map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
427 in (binder, spec) end;
429 val iter_like_infos =
430 [(iterN, fp_iter, iter_only),
431 (recN, fp_rec, rec_only)];
433 val (binders, specs) = map generate_iter_like iter_like_infos |> split_list;
435 (* TODO: Allow same constructor (and selector/discriminator) names for different
436 types (cf. old "datatype" package) *)
437 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
438 |> apfst split_list o fold_map2 (fn b => fn spec =>
439 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
440 #>> apsnd snd) binders specs
441 ||> `Local_Theory.restore;
443 (*transforms defined frees into consts (and more)*)
444 val phi = Proof_Context.export_morphism lthy lthy';
446 val [iter_def, rec_def] = map (Morphism.thm phi) defs;
448 val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
450 ((ctrs, selss0, iter, recx, v, xss, ctr_defs, discIs, sel_thmss, iter_def, rec_def),
454 fun define_coiter_corec ((selss0, discIs, sel_thmss), no_defs_lthy) =
456 val B_to_fpT = C --> fpT;
458 fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
459 Term.lambda c (mk_IfN sum_prod_T cps
460 (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
462 fun generate_coiter_like (suf, fp_iter_like, ((pfss, cqfsss), (f_sum_prod_Ts,
465 val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
467 val binder = Binding.suffix_name ("_" ^ suf) b;
470 mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binder, res_T)),
471 Term.list_comb (fp_iter_like,
472 map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
473 in (binder, spec) end;
475 val coiter_like_infos =
476 [(coiterN, fp_iter, coiter_only),
477 (corecN, fp_rec, corec_only)];
479 val (binders, specs) = map generate_coiter_like coiter_like_infos |> split_list;
481 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
482 |> apfst split_list o fold_map2 (fn b => fn spec =>
483 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
484 #>> apsnd snd) binders specs
485 ||> `Local_Theory.restore;
487 (*transforms defined frees into consts (and more)*)
488 val phi = Proof_Context.export_morphism lthy lthy';
490 val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
492 val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
494 ((ctrs, selss0, coiter, corec, v, xss, ctr_defs, discIs, sel_thmss, coiter_def,
499 let val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss in
500 wrap_datatype tacss (((no_dests, ctrs0), casex0), (disc_binders, (sel_binderss,
501 sel_defaultss))) lthy
504 val define_iter_likes = if lfp then define_iter_rec else define_coiter_corec;
506 ((wrap, define_iter_likes), lthy')
509 val pre_map_defs = map map_def_of_bnf pre_bnfs;
510 val map_ids = map map_id_of_bnf nested_bnfs;
513 let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in
514 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
517 fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
519 val map0 = map_of_bnf (the (bnf_of lthy s));
520 val mapx = mk_map Ts Us map0;
521 val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx)))));
522 val args = map build_arg TUs;
523 in Term.list_comb (mapx, args) end;
525 fun derive_iter_rec_thms_for_types ((ctrss, _, iters, recs, vs, xsss, ctr_defss, _, _, iter_defs,
528 val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
529 val giters = map (lists_bmoc gss) iters;
530 val hrecs = map (lists_bmoc hss) recs;
532 val (iter_thmss, rec_thmss) =
534 fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
535 fold_rev (fold_rev Logic.all) (xs :: fss)
536 (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
538 fun build_call fiter_likes maybe_tick (T, U) =
542 (case find_index (curry (op =) T) fpTs of
543 ~1 => build_map (build_call fiter_likes maybe_tick) T U
544 | j => maybe_tick (nth vs j) (nth fiter_likes j));
546 fun mk_U maybe_mk_prodT =
547 typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
549 fun repair_calls fiter_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) =
550 if member (op =) fpTs T then
551 maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
552 else if exists_subtype (member (op =) fpTs) T then
553 [build_call fiter_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x]
557 val gxsss = map (map (maps (repair_calls giters (K I) (K I) (K I)))) xsss;
559 map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
561 val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
562 val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
565 map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss;
567 map2 (map o mk_iter_like_tac pre_map_defs map_ids rec_defs) fp_rec_thms ctr_defss;
569 (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
570 goal_iterss iter_tacss,
571 map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
572 goal_recss rec_tacss)
576 [(itersN, iter_thmss, simp_attrs),
577 (recsN, rec_thmss, Code.add_default_eqn_attrib :: simp_attrs)]
578 |> maps (fn (thmN, thmss, attrs) =>
579 map2 (fn b => fn thms =>
580 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
581 [(thms, [])])) bs thmss);
583 lthy |> Local_Theory.notes notes |> snd
586 fun derive_coiter_corec_thms_for_types ((ctrss, selsss, coiters, corecs, vs, _, ctr_defss,
587 discIss, sel_thmsss, coiter_defs, corec_defs), lthy) =
589 val z = the_single zs;
591 val gcoiters = map (lists_bmoc pgss) coiters;
592 val hcorecs = map (lists_bmoc phss) corecs;
594 val (coiter_thmss, corec_thmss) =
596 fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
598 fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' =
599 fold_rev (fold_rev Logic.all) ([c] :: pfss)
600 (Logic.list_implies (seq_conds mk_goal_cond n k cps,
601 mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
603 fun build_call fiter_likes maybe_tack (T, U) =
607 (case find_index (curry (op =) U) fpTs of
608 ~1 => build_map (build_call fiter_likes maybe_tack) T U
609 | j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
611 fun mk_U maybe_mk_sumT =
612 typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
614 fun repair_calls fiter_likes maybe_mk_sumT maybe_tack cqf =
615 let val T = fastype_of cqf in
616 if exists_subtype (member (op =) Cs) T then
617 build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf
622 val crgsss' = map (map (map (repair_calls gcoiters (K I) (K I)))) crgsss;
623 val cshsss' = map (map (map (repair_calls hcorecs (curry mk_sumT) (tack z)))) cshsss;
626 map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss crgsss';
628 map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss cshsss';
631 map3 (map oo mk_coiter_like_tac coiter_defs map_ids) fp_iter_thms pre_map_defs
634 map3 (map oo mk_coiter_like_tac corec_defs map_ids) fp_rec_thms pre_map_defs
637 (map2 (map2 (fn goal => fn tac =>
638 Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
639 goal_coiterss coiter_tacss,
640 map2 (map2 (fn goal => fn tac =>
641 Skip_Proof.prove lthy [] [] goal (tac o #context)
642 |> Local_Defs.unfold lthy @{thms sum_case_if} |> Thm.close_derivation))
643 goal_corecss corec_tacss)
646 fun mk_disc_coiter_like_thms [_] = K []
647 | mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms;
649 val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss;
650 val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss;
652 fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm =
654 val (domT, ranT) = dest_funT (fastype_of sel0);
656 Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
657 [NONE, NONE, SOME (certify lthy sel0)] arg_cong
658 |> Thm.varifyT_global;
659 val sel_thm' = sel_thm RSN (2, trans);
661 coiter_like_thm RS arg_cong' RS sel_thm'
664 val sel_coiter_thmsss =
665 map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss;
666 val sel_corec_thmsss =
667 map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss;
670 [(coitersN, coiter_thmss, []),
671 (disc_coitersN, disc_coiter_thmss, []),
672 (sel_coitersN, map flat sel_coiter_thmsss, []),
673 (corecsN, corec_thmss, []),
674 (disc_corecsN, disc_corec_thmss, []),
675 (sel_corecsN, map flat sel_corec_thmsss, [])]
676 |> maps (fn (thmN, thmss, attrs) =>
677 map_filter (fn (_, []) => NONE | (b, thms) =>
678 SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
679 [(thms, [])])) (bs ~~ thmss));
681 lthy |> Local_Theory.notes notes |> snd
684 fun wrap_types_and_define_iter_likes ((wraps, define_iter_likess), lthy) =
685 fold_map2 (curry (op o)) define_iter_likess wraps lthy |>> split_list11
688 |> fold_map define_ctrs_case_for_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
689 fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~
690 ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss ~~ raw_sel_defaultsss)
691 |>> split_list |> wrap_types_and_define_iter_likes
692 |> (if lfp then derive_iter_rec_thms_for_types else derive_coiter_corec_thms_for_types);
694 val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
695 (if lfp then "" else "co") ^ "datatype"));
700 val datatyp = define_datatype (K I) (K I) (K I);
702 val datatype_cmd = define_datatype Typedecl.read_constraint Syntax.parse_typ Syntax.read_term;
704 val parse_opt_binding_colon = Scan.optional (Parse.binding --| @{keyword ":"}) no_binder
707 @{keyword "("} |-- parse_opt_binding_colon -- Parse.typ --| @{keyword ")"} ||
708 (Parse.typ >> pair no_binder);
711 @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
713 val parse_single_spec =
714 Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
715 (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
716 Scan.repeat parse_ctr_arg -- Scan.optional parse_defaults [] -- Parse.opt_mixfix));
718 val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_single_spec;
721 Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes"
722 (parse_datatype >> datatype_cmd true);
725 Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes"
726 (parse_datatype >> datatype_cmd false);