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 ctr_mixfix_of (_, mx) = mx;
98 fun prepare_datatype prepare_typ lfp (no_dests, specs) fake_lthy no_defs_lthy =
100 val _ = if not lfp andalso no_dests then error "Cannot use \"no_dests\" option for codatatypes"
104 map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs
105 |> Library.foldr1 (merge_type_args_constrained no_defs_lthy);
106 val As = map fst constrained_As;
107 val As' = map dest_TFree As;
109 val _ = (case duplicates (op =) As of [] => ()
110 | A :: _ => error ("Duplicate type parameter " ^
111 quote (Syntax.string_of_typ no_defs_lthy A)));
113 (* TODO: use sort constraints on type args *)
115 val N = length specs;
118 Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
121 val bs = map type_binder_of specs;
122 val fakeTs = map mk_fake_T bs;
124 val mixfixes = map mixfix_of specs;
126 val _ = (case duplicates Binding.eq_name bs of [] => ()
127 | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
129 val ctr_specss = map ctr_specs_of specs;
131 val disc_binderss = map (map disc_of) ctr_specss;
132 val ctr_binderss = map (map ctr_of) ctr_specss;
133 val ctr_argsss = map (map args_of) ctr_specss;
134 val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
136 val sel_bindersss = map (map (map fst)) ctr_argsss;
137 val fake_ctr_Tsss = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
139 val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
140 val _ = (case subtract (op =) As' rhs_As' of
142 | A' :: _ => error ("Extra type variables on rhs: " ^
143 quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
147 |> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs
151 fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) =
152 s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
153 quote (Syntax.string_of_typ fake_lthy T)))
154 | eq_fpT _ _ = false;
156 fun freeze_fp (T as Type (s, Us)) =
157 (case find_index (eq_fpT T) fakeTs of ~1 => Type (s, map freeze_fp Us) | j => nth Xs j)
160 val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss;
161 val ctr_sum_prod_TsXs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssXs;
163 val eqs = map dest_TFree Xs ~~ ctr_sum_prod_TsXs;
165 val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, unf_flds, fld_unfs, fld_injects,
166 fp_iter_thms, fp_rec_thms), lthy)) =
167 fp_bnf (if lfp then bnf_lfp else bnf_gfp) bs mixfixes As' eqs no_defs_lthy;
169 val add_nested_bnf_names =
171 fun add (Type (s, Ts)) ss =
172 let val (needs, ss') = fold_map add Ts ss in
173 if exists I needs then (true, insert (op =) s ss') else (false, ss')
175 | add T ss = (member (op =) As T, ss);
179 map_filter (bnf_of lthy) (fold (fold (fold add_nested_bnf_names)) ctr_TsssXs []);
181 val timer = time (Timer.startRealTimer ());
183 fun mk_unf_or_fld get_T Ts t =
184 let val Type (_, Ts0) = get_T (fastype_of t) in
185 Term.subst_atomic_types (Ts0 ~~ Ts) t
188 val mk_unf = mk_unf_or_fld domain_type;
189 val mk_fld = mk_unf_or_fld range_type;
191 val unfs = map (mk_unf As) unfs0;
192 val flds = map (mk_fld As) flds0;
194 val fpTs = map (domain_type o fastype_of) unfs;
196 val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs;
197 val ns = map length ctr_Tsss;
198 val kss = map (fn n => 1 upto n) ns;
199 val mss = map (map length) ctr_Tsss;
200 val Css = map2 replicate ns Cs;
202 fun mk_iter_like Ts Us t =
204 val (binders, body) = strip_type (fastype_of t);
205 val (f_Us, prebody) = split_last binders;
206 val Type (_, Ts0) = if lfp then prebody else body;
207 val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
209 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
212 val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
213 val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
215 val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
216 val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
218 val ((iter_only as (gss, _, _), rec_only as (hss, _, _)),
219 (zs, cs, cpss, coiter_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))) =
223 map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
224 ns mss fp_iter_fun_Ts;
225 val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
227 val ((gss, ysss), _) =
229 |> mk_Freess "f" g_Tss
230 ||>> mk_Freesss "x" y_Tsss;
231 val yssss = map (map (map single)) ysss;
233 fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) =
234 if member (op =) Cs U then Us else [T]
235 | dest_rec_prodT T = [T];
238 map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o
239 dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts;
240 val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
242 val hss = map2 (map2 retype_free) gss h_Tss;
243 val zssss_hd = map2 (map2 (map2 (fn y => fn T :: _ => retype_free y T))) ysss z_Tssss;
246 |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
247 val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
249 (((gss, g_Tss, yssss), (hss, h_Tss, zssss)),
250 ([], [], [], (([], []), ([], [])), (([], []), ([], []))))
254 (*avoid "'a itself" arguments in coiterators and corecursors*)
255 val mss' = map (fn [0] => [1] | ms => ms) mss;
257 val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_predT) ns Cs;
259 fun zip_predss_getterss qss fss = maps (op @) (qss ~~ fss);
261 fun zip_preds_predsss_gettersss [] [qss] [fss] = zip_predss_getterss qss fss
262 | zip_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
263 p :: zip_predss_getterss qss fss @ zip_preds_predsss_gettersss ps qsss fsss;
265 fun mk_types maybe_dest_sumT fun_Ts =
267 val f_sum_prod_Ts = map range_type fun_Ts;
268 val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
270 map3 (fn C => map2 (map (map (curry (op -->) C) o maybe_dest_sumT) oo dest_tupleT))
273 map (map (map (fn [_] => [] | [_, C] => [mk_predT (domain_type C)]))) f_Tssss;
274 val pf_Tss = map3 zip_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
275 in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end;
277 val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_iter_fun_Ts;
279 val ((((Free (z, _), cs), pss), gssss), _) =
281 |> yield_singleton (mk_Frees "z") dummyT
283 ||>> mk_Freess "p" p_Tss
284 ||>> mk_Freessss "g" g_Tssss;
285 val rssss = map (map (map (fn [] => []))) r_Tssss;
287 fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) =
288 if member (op =) Cs U then Us else [T]
289 | dest_corec_sumT T = [T];
291 val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts;
293 val hssss_hd = map2 (map2 (map2 (fn [g] => fn T :: _ => retype_free g T))) gssss h_Tssss;
294 val ((sssss, hssss_tl), _) =
296 |> mk_Freessss "q" s_Tssss
297 ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
298 val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
300 val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
302 fun mk_preds_getters_join [] [cf] = cf
303 | mk_preds_getters_join [cq] [cf, cf'] =
304 mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf');
306 fun mk_terms qssss fssss =
308 val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss;
309 val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss;
310 val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss;
311 val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss;
312 in (pfss, cqfsss) end;
314 ((([], [], []), ([], [], [])),
315 ([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)),
316 (mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss))))
319 fun pour_some_sugar_on_type (((((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec),
320 fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss),
321 disc_binders), sel_binderss) no_defs_lthy =
323 val unfT = domain_type (fastype_of fld);
324 val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
325 val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
326 val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
328 val ((((u, v), fs), xss), _) =
330 |> yield_singleton (mk_Frees "u") unfT
331 ||>> yield_singleton (mk_Frees "v") fpT
332 ||>> mk_Frees "f" case_Ts
333 ||>> mk_Freess "x" ctr_Tss;
336 map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $
337 mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
339 val case_binder = Binding.suffix_name ("_" ^ caseN) b;
342 fold_rev Term.lambda (fs @ [v])
343 (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v));
345 val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
346 |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
347 Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
348 (case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
349 ||> `Local_Theory.restore;
351 (*transforms defined frees into consts (and more)*)
352 val phi = Proof_Context.export_morphism lthy lthy';
354 val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
355 val case_def = Morphism.thm phi raw_case_def;
357 val ctrs0 = map (Morphism.term phi) raw_ctrs;
358 val casex0 = Morphism.term phi raw_case;
360 val ctrs = map (mk_ctr As) ctrs0;
362 fun exhaust_tac {context = ctxt, ...} =
364 val fld_iff_unf_thm =
367 fold_rev Logic.all [u, v]
368 (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
370 Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
371 mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
372 (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
373 |> Thm.close_derivation
378 Local_Defs.unfold lthy @{thms all_unit_eq}
379 (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
380 (mk_sumEN_balanced n))
383 mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
387 map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
388 mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
390 val half_distinct_tacss =
391 map (map (fn (def, def') => fn {context = ctxt, ...} =>
392 mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
395 map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
396 mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
398 val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
400 fun some_lfp_sugar ((selss0, discIs, sel_thmss), no_defs_lthy) =
402 val fpT_to_C = fpT --> C;
404 fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
406 val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
408 val binder = Binding.suffix_name ("_" ^ suf) b;
411 mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)),
412 Term.list_comb (fp_iter_like,
413 map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
414 in (binder, spec) end;
416 val iter_like_bundles =
417 [(iterN, fp_iter, iter_only),
418 (recN, fp_rec, rec_only)];
420 val (binders, specs) = map generate_iter_like iter_like_bundles |> split_list;
422 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
423 |> apfst split_list o fold_map2 (fn b => fn spec =>
424 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
425 #>> apsnd snd) binders specs
426 ||> `Local_Theory.restore;
428 (*transforms defined frees into consts (and more)*)
429 val phi = Proof_Context.export_morphism lthy lthy';
431 val [iter_def, rec_def] = map (Morphism.thm phi) defs;
433 val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
435 ((ctrs, selss0, iter, recx, v, xss, ctr_defs, discIs, sel_thmss, iter_def, rec_def),
439 fun some_gfp_sugar ((selss0, discIs, sel_thmss), no_defs_lthy) =
441 val B_to_fpT = C --> fpT;
443 fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
444 Term.lambda c (mk_IfN sum_prod_T cps
445 (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
447 fun generate_coiter_like (suf, fp_iter_like, ((pfss, cqfsss), (f_sum_prod_Ts,
450 val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
452 val binder = Binding.suffix_name ("_" ^ suf) b;
455 mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binder, res_T)),
456 Term.list_comb (fp_iter_like,
457 map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
458 in (binder, spec) end;
460 val coiter_like_bundles =
461 [(coiterN, fp_iter, coiter_only),
462 (corecN, fp_rec, corec_only)];
464 val (binders, specs) = map generate_coiter_like coiter_like_bundles |> split_list;
466 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
467 |> apfst split_list o fold_map2 (fn b => fn spec =>
468 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
469 #>> apsnd snd) binders specs
470 ||> `Local_Theory.restore;
472 (*transforms defined frees into consts (and more)*)
473 val phi = Proof_Context.export_morphism lthy lthy';
475 val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
477 val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
479 ((ctrs, selss0, coiter, corec, v, xss, ctr_defs, discIs, sel_thmss, coiter_def,
483 wrap_datatype tacss (((no_dests, ctrs0), casex0), (disc_binders, (sel_binderss, []))) lthy'
484 |> (if lfp then some_lfp_sugar else some_gfp_sugar)
487 val pre_map_defs = map map_def_of_bnf pre_bnfs;
488 val map_ids = map map_id_of_bnf nested_bnfs;
491 let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in
492 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
495 fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
497 val map0 = map_of_bnf (the (bnf_of lthy s));
498 val mapx = mk_map Ts Us map0;
499 val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx)))));
500 val args = map build_arg TUs;
501 in Term.list_comb (mapx, args) end;
503 fun pour_more_sugar_on_lfps ((ctrss, _, iters, recs, vs, xsss, ctr_defss, _, _, iter_defs,
506 val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
507 val giters = map (lists_bmoc gss) iters;
508 val hrecs = map (lists_bmoc hss) recs;
510 val (iter_thmss, rec_thmss) =
512 fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
513 fold_rev (fold_rev Logic.all) (xs :: fss)
514 (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
516 fun build_call fiter_likes maybe_tick (T, U) =
520 (case find_index (curry (op =) T) fpTs of
521 ~1 => build_map (build_call fiter_likes maybe_tick) T U
522 | j => maybe_tick (nth vs j) (nth fiter_likes j));
524 fun mk_U maybe_mk_prodT =
525 typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
527 fun repair_calls fiter_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) =
528 if member (op =) fpTs T then
529 maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
530 else if exists_subtype (member (op =) fpTs) T then
531 [build_call fiter_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x]
535 val gxsss = map (map (maps (repair_calls giters (K I) (K I) (K I)))) xsss;
537 map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
539 val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
540 val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
543 map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss;
545 map2 (map o mk_iter_like_tac pre_map_defs map_ids rec_defs) fp_rec_thms ctr_defss;
547 (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
548 goal_iterss iter_tacss,
549 map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
550 goal_recss rec_tacss)
554 [(itersN, iter_thmss),
556 |> maps (fn (thmN, thmss) =>
557 map2 (fn b => fn thms =>
558 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
561 lthy |> Local_Theory.notes notes |> snd
564 fun pour_more_sugar_on_gfps ((ctrss, selsss, coiters, corecs, vs, _, ctr_defss, discIss,
565 sel_thmsss, coiter_defs, corec_defs), lthy) =
567 val z = the_single zs;
569 val gcoiters = map (lists_bmoc pgss) coiters;
570 val hcorecs = map (lists_bmoc phss) corecs;
572 val (coiter_thmss, corec_thmss) =
574 fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
576 fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' =
577 fold_rev (fold_rev Logic.all) ([c] :: pfss)
578 (Logic.list_implies (seq_conds mk_goal_cond n k cps,
579 mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
581 fun build_call fiter_likes maybe_tack (T, U) =
585 (case find_index (curry (op =) U) fpTs of
586 ~1 => build_map (build_call fiter_likes maybe_tack) T U
587 | j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
589 fun mk_U maybe_mk_sumT =
590 typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
592 fun repair_calls fiter_likes maybe_mk_sumT maybe_tack cqf =
593 let val T = fastype_of cqf in
594 if exists_subtype (member (op =) Cs) T then
595 build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf
600 val crgsss' = map (map (map (repair_calls gcoiters (K I) (K I)))) crgsss;
601 val cshsss' = map (map (map (repair_calls hcorecs (curry mk_sumT) (tack z)))) cshsss;
604 map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss crgsss';
606 map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss cshsss';
609 map3 (map oo mk_coiter_like_tac coiter_defs map_ids) fp_iter_thms pre_map_defs
612 map3 (map oo mk_coiter_like_tac corec_defs map_ids) fp_rec_thms pre_map_defs
615 (map2 (map2 (fn goal => fn tac =>
616 Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
617 goal_coiterss coiter_tacss,
618 map2 (map2 (fn goal => fn tac =>
619 Skip_Proof.prove lthy [] [] goal (tac o #context)
620 |> Local_Defs.unfold lthy @{thms sum_case_if} |> Thm.close_derivation))
621 goal_corecss corec_tacss)
624 fun mk_disc_coiter_like_thms [_] = K []
625 | mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms;
627 val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss;
628 val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss;
630 fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm =
632 val (domT, ranT) = dest_funT (fastype_of sel0);
634 Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
635 [NONE, NONE, SOME (certify lthy sel0)] arg_cong
636 |> Thm.varifyT_global;
637 val sel_thm' = sel_thm RSN (2, trans);
639 coiter_like_thm RS arg_cong' RS sel_thm'
642 val sel_coiter_thmsss =
643 map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss;
644 val sel_corec_thmsss =
645 map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss;
648 [(coitersN, coiter_thmss),
649 (disc_coitersN, disc_coiter_thmss),
650 (sel_coitersN, map flat sel_coiter_thmsss),
651 (corecsN, corec_thmss),
652 (disc_corecsN, disc_corec_thmss),
653 (sel_corecsN, map flat sel_corec_thmsss)]
654 |> maps (fn (thmN, thmss) =>
655 map_filter (fn (_, []) => NONE | (b, thms) =>
656 SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []),
657 [(thms, [])])) (bs ~~ thmss));
659 lthy |> Local_Theory.notes notes |> snd
663 |> fold_map pour_some_sugar_on_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
664 fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~
665 ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss)
667 |> (if lfp then pour_more_sugar_on_lfps else pour_more_sugar_on_gfps);
669 val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
670 (if lfp then "" else "co") ^ "datatype"));
675 fun datatype_cmd lfp (bundle as (_, specs)) lthy =
677 (* TODO: cleaner handling of fake contexts, without "background_theory" *)
678 (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
679 locale and shadows an existing global type*)
680 val fake_thy = Theory.copy
681 #> fold (fn spec => perhaps (try (Sign.add_type lthy
682 (type_binder_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
683 val fake_lthy = Proof_Context.background_theory fake_thy lthy;
685 prepare_datatype Syntax.read_typ lfp bundle fake_lthy lthy
688 val parse_opt_binding_colon = Scan.optional (Parse.binding --| @{keyword ":"}) no_binder
691 @{keyword "("} |-- parse_opt_binding_colon -- Parse.typ --| @{keyword ")"} ||
692 (Parse.typ >> pair no_binder);
694 val parse_single_spec =
695 Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
696 (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
697 Scan.repeat parse_ctr_arg -- Parse.opt_mixfix));
699 val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_single_spec;
702 Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes"
703 (parse_datatype >> datatype_cmd true);
706 Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes"
707 (parse_datatype >> datatype_cmd false);