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 (mixfix list -> (string * sort) list option -> binding list -> typ list * typ list list ->
12 BNF_Def.BNF list -> local_theory ->
13 (term list * term list * term list * term list * thm * thm list * thm list * thm list *
14 thm list * thm list) * local_theory) ->
15 bool * ((((typ * sort) list * binding) * mixfix) * ((((binding * binding) *
16 (binding * typ) list) * (binding * term) list) * mixfix) list) list ->
17 local_theory -> local_theory
18 val parse_datatype_cmd: bool ->
19 (mixfix list -> (string * sort) list option -> binding list -> typ list * typ list list ->
20 BNF_Def.BNF list -> local_theory ->
21 (term list * term list * term list * term list * thm * thm list * thm list * thm list *
22 thm list * thm list) * local_theory) ->
23 (local_theory -> local_theory) parser
26 structure BNF_FP_Sugar : BNF_FP_SUGAR =
33 open BNF_FP_Sugar_Tactics
35 val simp_attrs = @{attributes [simp]};
38 (map #1 xs, map #2 xs, map #3 xs, map #4 xs, map #5 xs, map #6 xs, map #7 xs, map #8 xs,
39 map #9 xs, map #10 xs, map #11 xs);
41 fun strip_map_type (Type (@{type_name fun}, [T as Type _, T'])) = strip_map_type T' |>> cons T
42 | strip_map_type T = ([], T);
44 fun resort_tfree S (TFree (s, _)) = TFree (s, S);
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 val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
54 fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
55 fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
56 fun mk_uncurried2_fun f xss =
57 mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss);
59 fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v));
61 fun tack z_name (c, v) f =
62 let val z = Free (z_name, mk_sumT (fastype_of v, fastype_of c)) in
63 Term.lambda z (mk_sum_case (Term.lambda v v, Term.lambda c (f $ c)) $ z)
66 fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
68 fun merge_type_arg T T' = if T = T' then T else cannot_merge_types ();
70 fun merge_type_args (As, As') =
71 if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types ();
73 fun type_args_constrained_of (((cAs, _), _), _) = cAs;
74 fun type_binding_of (((_, b), _), _) = b;
75 fun mixfix_of ((_, mx), _) = mx;
76 fun ctr_specs_of (_, ctr_specs) = ctr_specs;
78 fun disc_of ((((disc, _), _), _), _) = disc;
79 fun ctr_of ((((_, ctr), _), _), _) = ctr;
80 fun args_of (((_, args), _), _) = args;
81 fun defaults_of ((_, ds), _) = ds;
82 fun ctr_mixfix_of (_, mx) = mx;
84 fun define_datatype prepare_constraint prepare_typ prepare_term lfp construct (no_dests, specs)
87 (* TODO: sanity checks on arguments *)
89 val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes"
92 val nn = length specs;
93 val fp_bs = map type_binding_of specs;
94 val fp_common_name = mk_common_name fp_bs;
96 fun prepare_type_arg (ty, c) =
97 let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
98 TFree (s, prepare_constraint no_defs_lthy0 c)
101 val Ass0 = map (map prepare_type_arg o type_args_constrained_of) specs;
102 val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
103 val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
105 val (((Bs, Cs), vs'), no_defs_lthy) =
107 |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
110 ||>> Variable.variant_fixes (map Binding.name_of fp_bs);
112 (* TODO: cleaner handling of fake contexts, without "background_theory" *)
113 (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
114 locale and shadows an existing global type*)
116 Theory.copy #> fold (fn spec => perhaps (try (Sign.add_type no_defs_lthy
117 (type_binding_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
118 val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
121 Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
124 val fake_Ts = map mk_fake_T fp_bs;
126 val mixfixes = map mixfix_of specs;
128 val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
129 | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
131 val ctr_specss = map ctr_specs_of specs;
133 val disc_bindingss = map (map disc_of) ctr_specss;
135 map2 (fn fp_b => map (Binding.qualify false (Binding.name_of fp_b) o ctr_of))
137 val ctr_argsss = map (map args_of) ctr_specss;
138 val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
140 val sel_bindingsss = map (map (map fst)) ctr_argsss;
141 val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
142 val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
144 val (As :: _) :: fake_ctr_Tsss =
145 burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
147 val _ = (case duplicates (op =) unsorted_As of [] => ()
148 | A :: _ => error ("Duplicate type parameter " ^
149 quote (Syntax.string_of_typ no_defs_lthy A)));
151 val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
152 val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
154 | A' :: _ => error ("Extra type variable on right-hand side: " ^
155 quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
157 fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) =
158 s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
159 quote (Syntax.string_of_typ fake_lthy T)))
160 | eq_fpT _ _ = false;
162 fun freeze_fp (T as Type (s, Us)) =
163 (case find_index (eq_fpT T) fake_Ts of ~1 => Type (s, map freeze_fp Us) | j => nth Bs j)
166 val ctr_TsssBs = map (map (map freeze_fp)) fake_ctr_Tsss;
167 val ctr_sum_prod_TsBs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssBs;
170 map dest_TFree Bs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsBs;
172 val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, fp_induct, unf_flds, fld_unfs, fld_injects,
173 fp_iter_thms, fp_rec_thms), lthy)) =
174 fp_bnf construct fp_bs mixfixes (map dest_TFree unsorted_As) fp_eqs no_defs_lthy0;
176 fun add_nesty_bnf_names Us =
178 fun add (Type (s, Ts)) ss =
179 let val (needs, ss') = fold_map add Ts ss in
180 if exists I needs then (true, insert (op =) s ss') else (false, ss')
182 | add T ss = (member (op =) Us T, ss);
186 map_filter (bnf_of lthy) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_TsssBs []);
188 val nesting_bnfs = nesty_bnfs As;
189 val nested_bnfs = nesty_bnfs Bs;
191 val timer = time (Timer.startRealTimer ());
193 fun mk_unf_or_fld get_T Ts t =
194 let val Type (_, Ts0) = get_T (fastype_of t) in
195 Term.subst_atomic_types (Ts0 ~~ Ts) t
198 val mk_unf = mk_unf_or_fld domain_type;
199 val mk_fld = mk_unf_or_fld range_type;
201 val unfs = map (mk_unf As) unfs0;
202 val flds = map (mk_fld As) flds0;
204 val fpTs = map (domain_type o fastype_of) unfs;
206 val exists_fp_subtype = exists_subtype (member (op =) fpTs);
208 val vs = map2 (curry Free) vs' fpTs;
210 val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Bs ~~ fpTs)))) ctr_TsssBs;
211 val ns = map length ctr_Tsss;
212 val kss = map (fn n => 1 upto n) ns;
213 val mss = map (map length) ctr_Tsss;
214 val Css = map2 replicate ns Cs;
216 fun mk_iter_like Ts Us t =
218 val (bindings, body) = strip_type (fastype_of t);
219 val (f_Us, prebody) = split_last bindings;
220 val Type (_, Ts0) = if lfp then prebody else body;
221 val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
223 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
226 val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
227 val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
229 val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
230 val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
232 val ((iter_only as (gss, _, _), rec_only as (hss, _, _)),
233 (zs, cs, cpss, coiter_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))) =
237 map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
238 ns mss fp_iter_fun_Ts;
239 val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
241 val ((gss, ysss), _) =
243 |> mk_Freess "f" g_Tss
244 ||>> mk_Freesss "x" y_Tsss;
245 val yssss = map (map (map single)) ysss;
247 fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) =
248 if member (op =) Cs U then Us else [T]
249 | dest_rec_prodT T = [T];
252 map3 (fn n => fn ms => map2 (map dest_rec_prodT 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) h_Tss gss;
257 val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
260 |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
261 val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
263 (((gss, g_Tss, yssss), (hss, h_Tss, zssss)),
264 ([], [], [], (([], []), ([], [])), (([], []), ([], []))))
268 (*avoid "'a itself" arguments in coiterators and corecursors*)
269 val mss' = map (fn [0] => [1] | ms => ms) mss;
271 val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_predT) ns Cs;
273 fun zip_predss_getterss qss fss = maps (op @) (qss ~~ fss);
275 fun zip_preds_predsss_gettersss [] [qss] [fss] = zip_predss_getterss qss fss
276 | zip_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
277 p :: zip_predss_getterss qss fss @ zip_preds_predsss_gettersss ps qsss fsss;
279 fun mk_types maybe_dest_sumT fun_Ts =
281 val f_sum_prod_Ts = map range_type fun_Ts;
282 val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
284 map3 (fn C => map2 (map (map (curry (op -->) C) o maybe_dest_sumT) oo dest_tupleT))
287 map (map (map (fn [_] => [] | [_, C] => [mk_predT (domain_type C)]))) f_Tssss;
288 val pf_Tss = map3 zip_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
289 in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end;
291 val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_iter_fun_Ts;
293 val ((((Free (z, _), cs), pss), gssss), _) =
295 |> yield_singleton (mk_Frees "z") dummyT
297 ||>> mk_Freess "p" p_Tss
298 ||>> mk_Freessss "g" g_Tssss;
299 val rssss = map (map (map (fn [] => []))) r_Tssss;
301 fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) =
302 if member (op =) Cs U then Us else [T]
303 | dest_corec_sumT T = [T];
305 val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts;
307 val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
308 val ((sssss, hssss_tl), _) =
310 |> mk_Freessss "q" s_Tssss
311 ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
312 val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
314 val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
316 fun mk_preds_getters_join [] [cf] = cf
317 | mk_preds_getters_join [cq] [cf, cf'] =
318 mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf');
320 fun mk_terms qssss fssss =
322 val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss;
323 val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss;
324 val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss;
325 val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss;
326 in (pfss, cqfsss) end;
328 ((([], [], []), ([], [], [])),
329 ([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)),
330 (mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss))))
333 fun define_ctrs_case_for_type (((((((((((((((((((fp_b, fpT), C), v), fld), unf), fp_iter),
334 fp_rec), fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_bindings), ctr_mixfixes),
335 ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
337 val unfT = domain_type (fastype_of fld);
338 val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
339 val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
340 val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
342 val (((u, fs), xss), _) =
344 |> yield_singleton (mk_Frees "u") unfT
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_binding = Binding.suffix_name ("_" ^ caseN) fp_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_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
362 ||> `Local_Theory.restore;
364 val phi = Proof_Context.export_morphism lthy lthy';
366 val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
367 val case_def = Morphism.thm phi raw_case_def;
369 val ctrs0 = map (Morphism.term phi) raw_ctrs;
370 val casex0 = Morphism.term phi raw_case;
372 val ctrs = map (mk_ctr As) ctrs0;
374 fun exhaust_tac {context = ctxt, ...} =
376 val fld_iff_unf_thm =
379 fold_rev Logic.all [u, v]
380 (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
382 Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
383 mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
384 (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
385 |> Thm.close_derivation
390 Local_Defs.unfold lthy @{thms all_unit_eq}
391 (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
392 (mk_sumEN_balanced n))
395 mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
399 map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
400 mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
402 val half_distinct_tacss =
403 map (map (fn (def, def') => fn {context = ctxt, ...} =>
404 mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
407 map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
408 mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
410 val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
412 fun define_iter_rec ((selss0, discIs, sel_thmss), no_defs_lthy) =
414 val fpT_to_C = fpT --> C;
416 fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
418 val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
419 val binding = Binding.suffix_name ("_" ^ suf) fp_b;
421 mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
422 Term.list_comb (fp_iter_like,
423 map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
424 in (binding, spec) end;
426 val iter_like_infos =
427 [(iterN, fp_iter, iter_only),
428 (recN, fp_rec, rec_only)];
430 val (bindings, specs) = map generate_iter_like iter_like_infos |> split_list;
432 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
433 |> apfst split_list o fold_map2 (fn b => fn spec =>
434 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
435 #>> apsnd snd) bindings specs
436 ||> `Local_Theory.restore;
438 val phi = Proof_Context.export_morphism lthy lthy';
440 val [iter_def, rec_def] = map (Morphism.thm phi) defs;
442 val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
444 ((ctrs, selss0, iter, recx, v, xss, ctr_defs, discIs, sel_thmss, iter_def, rec_def),
448 fun define_coiter_corec ((selss0, discIs, sel_thmss), no_defs_lthy) =
450 val B_to_fpT = C --> fpT;
452 fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
453 Term.lambda c (mk_IfN sum_prod_T cps
454 (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
456 fun generate_coiter_like (suf, fp_iter_like, ((pfss, cqfsss), (f_sum_prod_Ts,
459 val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
460 val binding = Binding.suffix_name ("_" ^ suf) fp_b;
462 mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
463 Term.list_comb (fp_iter_like,
464 map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
465 in (binding, spec) end;
467 val coiter_like_infos =
468 [(coiterN, fp_iter, coiter_only),
469 (corecN, fp_rec, corec_only)];
471 val (bindings, specs) = map generate_coiter_like coiter_like_infos |> split_list;
473 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
474 |> apfst split_list o fold_map2 (fn b => fn spec =>
475 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
476 #>> apsnd snd) bindings specs
477 ||> `Local_Theory.restore;
479 val phi = Proof_Context.export_morphism lthy lthy';
481 val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
483 val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
485 ((ctrs, selss0, coiter, corec, v, xss, ctr_defs, discIs, sel_thmss, coiter_def,
490 let val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss in
491 wrap_datatype tacss (((no_dests, ctrs0), casex0), (disc_bindings, (sel_bindingss,
492 sel_defaultss))) lthy
495 val define_iter_likes = if lfp then define_iter_rec else define_coiter_corec;
497 ((wrap, define_iter_likes), lthy')
500 (* TODO: remove all "nested" and "nesting" BNFs from pre_bnfs, if they're there ### *)
501 val pre_map_defs = map map_def_of_bnf pre_bnfs;
502 val pre_set_defss = map set_defs_of_bnf pre_bnfs;
503 val nested_set_natural's = maps set_natural'_of_bnf nested_bnfs;
504 val nesting_map_ids = map map_id_of_bnf nesting_bnfs;
507 let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in
508 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
511 fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
513 val map0 = map_of_bnf (the (bnf_of lthy s));
514 val mapx = mk_map Ts Us map0;
515 val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx)))));
516 val args = map build_arg TUs;
517 in Term.list_comb (mapx, args) end;
519 fun derive_induct_iter_rec_thms_for_types ((ctrss, _, iters, recs, vs, xsss, ctr_defss, _, _,
520 iter_defs, rec_defs), lthy) =
522 fun mk_sets_nested bnf =
524 val Type (T_name, Us) = T_of_bnf bnf;
525 val lives = lives_of_bnf bnf;
526 val sets = sets_of_bnf bnf;
528 (case find_index (curry (op =) U) lives of
532 (T_name, map mk_set Us)
535 val setss_nested = map mk_sets_nested nested_bnfs;
537 val (induct_thms, induct_thm) =
539 val ((phis, phis'), names_lthy) =
541 |> mk_Frees' "P" (map mk_predT fpTs);
544 let val Type (_, Ts0) = domain_type (fastype_of t) in
545 Term.subst_atomic_types (Ts0 ~~ Ts) t
548 fun mk_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) =
549 (case find_index (curry (op =) T) fpTs of
551 (case AList.lookup (op =) setss_nested T_name of
556 split_list (filter (exists_fp_subtype o fst) (Ts0 ~~ raw_sets0));
557 val sets = map (mk_set Ts0) raw_sets;
558 val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
560 map2 (fn y => fn set => HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x)))
562 val bodies = flat (map (mk_prem_prems names_lthy') ys);
564 map2 (curry Logic.mk_implies) heads bodies
566 | i => [HOLogic.mk_Trueprop (nth phis i $ x)])
567 | mk_prem_prems _ _ = [];
569 fun close_prem_prem (Free x') t =
571 (map Free (drop (nn + 1) (rev (Term.add_frees t (x' :: phis'))))) t;
573 fun mk_prem_triple phi ctr ctr_Ts =
575 val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
577 maps (fn x => map (close_prem_prem x) (mk_prem_prems names_lthy' x)) xs;
579 (xs, prem_prems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs)))
582 val prem_tripless = map3 (map2 o mk_prem_triple) phis ctrss ctr_Tsss;
584 fun mk_prem (xs, prem_prems, concl) =
585 fold_rev Logic.all xs (Logic.list_implies (prem_prems, concl));
588 Library.foldr (Logic.list_implies o apfst (map mk_prem)) (prem_tripless,
589 HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
590 (map2 (curry (op $)) phis vs)));
592 val rss = map (map (length o #2)) prem_tripless;
594 val fld_induct' = fp_induct OF (map mk_sumEN_tupled_balanced mss);
597 Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
598 mk_induct_tac ctxt ns mss rss (flat ctr_defss) fld_induct' pre_set_defss
599 nested_set_natural's)
600 (* TODO: thread name context properly ### *)
601 |> singleton (Proof_Context.export names_lthy lthy)
602 |> singleton (Proof_Context.export no_defs_lthy no_defs_lthy0)
604 `(conj_dests nn) induct_thm
607 val (iter_thmss, rec_thmss) =
609 val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
610 val giters = map (lists_bmoc gss) iters;
611 val hrecs = map (lists_bmoc hss) recs;
613 fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
614 fold_rev (fold_rev Logic.all) (xs :: fss)
615 (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
617 fun build_call fiter_likes maybe_tick (T, U) =
621 (case find_index (curry (op =) T) fpTs of
622 ~1 => build_map (build_call fiter_likes maybe_tick) T U
623 | j => maybe_tick (nth vs j) (nth fiter_likes j));
625 fun mk_U maybe_mk_prodT =
626 typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
628 fun intr_calls fiter_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) =
629 if member (op =) fpTs T then
630 maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
631 else if exists_fp_subtype T then
632 [build_call fiter_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x]
636 val gxsss = map (map (maps (intr_calls giters (K I) (K I) (K I)))) xsss;
637 val hxsss = map (map (maps (intr_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
639 val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
640 val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
643 map2 (map o mk_iter_like_tac pre_map_defs nesting_map_ids iter_defs) fp_iter_thms
646 map2 (map o mk_iter_like_tac pre_map_defs nesting_map_ids rec_defs) fp_rec_thms
649 (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
650 goal_iterss iter_tacss,
651 map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
652 goal_recss rec_tacss)
656 (if nn > 1 then [(inductN, [induct_thm], [])] (* FIXME: attribs *) else [])
657 |> map (fn (thmN, thms, attrs) =>
658 ((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
661 [(inductN, map single induct_thms, []), (* FIXME: attribs *)
662 (itersN, iter_thmss, simp_attrs),
663 (recsN, rec_thmss, Code.add_default_eqn_attrib :: simp_attrs)]
664 |> maps (fn (thmN, thmss, attrs) =>
665 map2 (fn b => fn thms =>
666 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
667 [(thms, [])])) fp_bs thmss);
669 lthy |> Local_Theory.notes (common_notes @ notes) |> snd
672 fun derive_coinduct_coiter_corec_thms_for_types ((ctrss, selsss, coiters, corecs, vs, _,
673 ctr_defss, discIss, sel_thmsss, coiter_defs, corec_defs), lthy) =
675 val (coinduct_thms, coinduct_thm) =
677 val coinduct_thm = fp_induct;
679 `(conj_dests nn) coinduct_thm
682 val (coiter_thmss, corec_thmss) =
684 val z = the_single zs;
685 val gcoiters = map (lists_bmoc pgss) coiters;
686 val hcorecs = map (lists_bmoc phss) corecs;
688 fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
690 fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' =
691 fold_rev (fold_rev Logic.all) ([c] :: pfss)
692 (Logic.list_implies (seq_conds mk_goal_cond n k cps,
693 mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
695 fun build_call fiter_likes maybe_tack (T, U) =
699 (case find_index (curry (op =) U) fpTs of
700 ~1 => build_map (build_call fiter_likes maybe_tack) T U
701 | j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
703 fun mk_U maybe_mk_sumT =
704 typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
706 fun intr_calls fiter_likes maybe_mk_sumT maybe_tack cqf =
707 let val T = fastype_of cqf in
708 if exists_subtype (member (op =) Cs) T then
709 build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf
714 val crgsss' = map (map (map (intr_calls gcoiters (K I) (K I)))) crgsss;
715 val cshsss' = map (map (map (intr_calls hcorecs (curry mk_sumT) (tack z)))) cshsss;
718 map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss crgsss';
720 map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss cshsss';
723 map3 (map oo mk_coiter_like_tac coiter_defs nesting_map_ids) fp_iter_thms pre_map_defs
726 map3 (map oo mk_coiter_like_tac corec_defs nesting_map_ids) fp_rec_thms pre_map_defs
729 (map2 (map2 (fn goal => fn tac =>
730 Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
731 goal_coiterss coiter_tacss,
732 map2 (map2 (fn goal => fn tac =>
733 Skip_Proof.prove lthy [] [] goal (tac o #context)
734 |> Local_Defs.unfold lthy @{thms sum_case_if} |> Thm.close_derivation))
735 goal_corecss corec_tacss)
738 fun mk_disc_coiter_like_thms [_] = K []
739 | mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms;
741 val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss;
742 val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss;
744 fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm =
746 val (domT, ranT) = dest_funT (fastype_of sel0);
748 Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
749 [NONE, NONE, SOME (certify lthy sel0)] arg_cong
750 |> Thm.varifyT_global;
751 val sel_thm' = sel_thm RSN (2, trans);
753 coiter_like_thm RS arg_cong' RS sel_thm'
756 val sel_coiter_thmsss =
757 map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss;
758 val sel_corec_thmsss =
759 map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss;
762 (if nn > 1 then [(coinductN, [coinduct_thm], [])] (* FIXME: attribs *) else [])
763 |> map (fn (thmN, thms, attrs) =>
764 ((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
767 [(coinductN, map single coinduct_thms, []), (* FIXME: attribs *)
768 (coitersN, coiter_thmss, []),
769 (disc_coitersN, disc_coiter_thmss, []),
770 (sel_coitersN, map flat sel_coiter_thmsss, []),
771 (corecsN, corec_thmss, []),
772 (disc_corecsN, disc_corec_thmss, []),
773 (sel_corecsN, map flat sel_corec_thmsss, [])]
774 |> maps (fn (thmN, thmss, attrs) =>
775 map_filter (fn (_, []) => NONE | (b, thms) =>
776 SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
777 [(thms, [])])) (fp_bs ~~ thmss));
779 lthy |> Local_Theory.notes (common_notes @ notes) |> snd
782 fun wrap_types_and_define_iter_likes ((wraps, define_iter_likess), lthy) =
783 fold_map2 (curry (op o)) define_iter_likess wraps lthy |>> split_list11
786 |> fold_map define_ctrs_case_for_type (fp_bs ~~ fpTs ~~ Cs ~~ vs ~~ flds ~~ unfs ~~
787 fp_iters ~~ fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~
788 ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~
790 |>> split_list |> wrap_types_and_define_iter_likes
791 |> (if lfp then derive_induct_iter_rec_thms_for_types
792 else derive_coinduct_coiter_corec_thms_for_types);
794 val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
795 (if lfp then "" else "co") ^ "datatype"));
800 val datatyp = define_datatype (K I) (K I) (K I);
802 val datatype_cmd = define_datatype Typedecl.read_constraint Syntax.parse_typ Syntax.read_term;
804 val parse_binding_colon = Parse.binding --| @{keyword ":"};
805 val parse_opt_binding_colon = Scan.optional parse_binding_colon no_binding;
808 @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
809 (Parse.typ >> pair no_binding);
812 @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
814 val parse_single_spec =
815 Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
816 (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
817 Scan.repeat parse_ctr_arg -- Scan.optional parse_defaults [] -- Parse.opt_mixfix));
819 val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_single_spec;
821 fun parse_datatype_cmd lfp construct = parse_datatype >> datatype_cmd lfp construct;