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 list * thm list * thm list * thm list *
14 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 list * thm list * thm list * thm list *
22 thm list) * local_theory) ->
23 (local_theory -> local_theory) parser
26 structure BNF_FP_Sugar : BNF_FP_SUGAR =
33 open BNF_FP_Sugar_Tactics
36 val coitersN = "coiters";
37 val corecsN = "corecs";
38 val disc_coitersN = "disc_coiters";
39 val disc_corecsN = "disc_corecs";
42 val sel_coitersN = "sel_coiters";
43 val sel_corecsN = "sel_corecs";
45 val simp_attrs = @{attributes [simp]};
48 (map #1 xs, map #2 xs, map #3 xs, map #4 xs, map #5 xs, map #6 xs, map #7 xs, map #8 xs,
49 map #9 xs, map #10 xs, map #11 xs);
51 fun strip_map_type (Type (@{type_name fun}, [T as Type _, T'])) = strip_map_type T' |>> cons T
52 | strip_map_type T = ([], T);
54 fun typ_subst inst (T as Type (s, Ts)) =
55 (case AList.lookup (op =) inst T of
56 NONE => Type (s, map (typ_subst inst) Ts)
58 | typ_subst inst T = the_default T (AList.lookup (op =) inst T);
60 fun resort_tfree S (TFree (s, _)) = TFree (s, S);
62 val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
64 fun mk_id T = Const (@{const_name id}, T --> T);
66 fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
67 fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
68 fun mk_uncurried2_fun f xss =
69 mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss);
71 fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v));
73 fun tack z_name (c, v) f =
74 let val z = Free (z_name, mk_sumT (fastype_of v, fastype_of c)) in
75 Term.lambda z (mk_sum_case (Term.lambda v v, Term.lambda c (f $ c)) $ z)
78 fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
80 fun merge_type_arg T T' = if T = T' then T else cannot_merge_types ();
82 fun merge_type_args (As, As') =
83 if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types ();
85 fun type_args_constrained_of (((cAs, _), _), _) = cAs;
86 fun type_binder_of (((_, b), _), _) = b;
87 fun mixfix_of ((_, mx), _) = mx;
88 fun ctr_specs_of (_, ctr_specs) = ctr_specs;
90 fun disc_of ((((disc, _), _), _), _) = disc;
91 fun ctr_of ((((_, ctr), _), _), _) = ctr;
92 fun args_of (((_, args), _), _) = args;
93 fun defaults_of ((_, ds), _) = ds;
94 fun ctr_mixfix_of (_, mx) = mx;
96 fun define_datatype prepare_constraint prepare_typ prepare_term lfp construct (no_dests, specs)
99 (* TODO: sanity checks on arguments *)
101 val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes"
104 val N = length specs;
106 fun prepare_type_arg (ty, c) =
107 let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
108 TFree (s, prepare_constraint no_defs_lthy0 c)
111 val Ass0 = map (map prepare_type_arg o type_args_constrained_of) specs;
112 val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
113 val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
115 val ((Bs, Cs), no_defs_lthy) =
117 |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
121 (* TODO: cleaner handling of fake contexts, without "background_theory" *)
122 (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
123 locale and shadows an existing global type*)
125 Theory.copy #> fold (fn spec => perhaps (try (Sign.add_type no_defs_lthy
126 (type_binder_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
127 val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
130 Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
133 val fp_bs = map type_binder_of specs;
134 val fake_Ts = map mk_fake_T fp_bs;
136 val mixfixes = map mixfix_of specs;
138 val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
139 | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
141 val ctr_specss = map ctr_specs_of specs;
143 val disc_binderss = map (map disc_of) ctr_specss;
145 map2 (fn fp_b => map (Binding.qualify false (Binding.name_of fp_b) o ctr_of))
147 val ctr_argsss = map (map args_of) ctr_specss;
148 val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
150 val sel_bindersss = map (map (map fst)) ctr_argsss;
151 val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
152 val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
154 val (As :: _) :: fake_ctr_Tsss =
155 burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
157 val _ = (case duplicates (op =) unsorted_As of [] => ()
158 | A :: _ => error ("Duplicate type parameter " ^
159 quote (Syntax.string_of_typ no_defs_lthy A)));
161 val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
162 val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
164 | A' :: _ => error ("Extra type variables on rhs: " ^
165 quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
167 fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) =
168 s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
169 quote (Syntax.string_of_typ fake_lthy T)))
170 | eq_fpT _ _ = false;
172 fun freeze_fp (T as Type (s, Us)) =
173 (case find_index (eq_fpT T) fake_Ts of ~1 => Type (s, map freeze_fp Us) | j => nth Bs j)
176 val ctr_TsssBs = map (map (map freeze_fp)) fake_ctr_Tsss;
177 val ctr_sum_prod_TsBs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssBs;
180 map dest_TFree Bs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsBs;
182 val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, unf_flds, fld_unfs, fld_injects,
183 fp_iter_thms, fp_rec_thms), lthy)) =
184 fp_bnf construct fp_bs mixfixes (map dest_TFree unsorted_As) fp_eqs no_defs_lthy0;
186 val add_nested_bnf_names =
188 fun add (Type (s, Ts)) ss =
189 let val (needs, ss') = fold_map add Ts ss in
190 if exists I needs then (true, insert (op =) s ss') else (false, ss')
192 | add T ss = (member (op =) As T, ss);
196 map_filter (bnf_of lthy) (fold (fold (fold add_nested_bnf_names)) ctr_TsssBs []);
198 val timer = time (Timer.startRealTimer ());
200 fun mk_unf_or_fld get_T Ts t =
201 let val Type (_, Ts0) = get_T (fastype_of t) in
202 Term.subst_atomic_types (Ts0 ~~ Ts) t
205 val mk_unf = mk_unf_or_fld domain_type;
206 val mk_fld = mk_unf_or_fld range_type;
208 val unfs = map (mk_unf As) unfs0;
209 val flds = map (mk_fld As) flds0;
211 val fpTs = map (domain_type o fastype_of) unfs;
213 val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Bs ~~ fpTs)))) ctr_TsssBs;
214 val ns = map length ctr_Tsss;
215 val kss = map (fn n => 1 upto n) ns;
216 val mss = map (map length) ctr_Tsss;
217 val Css = map2 replicate ns Cs;
219 fun mk_iter_like Ts Us t =
221 val (binders, body) = strip_type (fastype_of t);
222 val (f_Us, prebody) = split_last binders;
223 val Type (_, Ts0) = if lfp then prebody else body;
224 val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
226 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
229 val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
230 val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
232 val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
233 val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
235 val ((iter_only as (gss, _, _), rec_only as (hss, _, _)),
236 (zs, cs, cpss, coiter_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))) =
240 map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
241 ns mss fp_iter_fun_Ts;
242 val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
244 val ((gss, ysss), _) =
246 |> mk_Freess "f" g_Tss
247 ||>> mk_Freesss "x" y_Tsss;
248 val yssss = map (map (map single)) ysss;
250 fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) =
251 if member (op =) Cs U then Us else [T]
252 | dest_rec_prodT T = [T];
255 map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o
256 dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts;
257 val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
259 val hss = map2 (map2 retype_free) h_Tss gss;
260 val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
263 |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
264 val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
266 (((gss, g_Tss, yssss), (hss, h_Tss, zssss)),
267 ([], [], [], (([], []), ([], [])), (([], []), ([], []))))
271 (*avoid "'a itself" arguments in coiterators and corecursors*)
272 val mss' = map (fn [0] => [1] | ms => ms) mss;
274 val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_predT) ns Cs;
276 fun zip_predss_getterss qss fss = maps (op @) (qss ~~ fss);
278 fun zip_preds_predsss_gettersss [] [qss] [fss] = zip_predss_getterss qss fss
279 | zip_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
280 p :: zip_predss_getterss qss fss @ zip_preds_predsss_gettersss ps qsss fsss;
282 fun mk_types maybe_dest_sumT fun_Ts =
284 val f_sum_prod_Ts = map range_type fun_Ts;
285 val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
287 map3 (fn C => map2 (map (map (curry (op -->) C) o maybe_dest_sumT) oo dest_tupleT))
290 map (map (map (fn [_] => [] | [_, C] => [mk_predT (domain_type C)]))) f_Tssss;
291 val pf_Tss = map3 zip_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
292 in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end;
294 val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_iter_fun_Ts;
296 val ((((Free (z, _), cs), pss), gssss), _) =
298 |> yield_singleton (mk_Frees "z") dummyT
300 ||>> mk_Freess "p" p_Tss
301 ||>> mk_Freessss "g" g_Tssss;
302 val rssss = map (map (map (fn [] => []))) r_Tssss;
304 fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) =
305 if member (op =) Cs U then Us else [T]
306 | dest_corec_sumT T = [T];
308 val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts;
310 val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
311 val ((sssss, hssss_tl), _) =
313 |> mk_Freessss "q" s_Tssss
314 ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
315 val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
317 val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
319 fun mk_preds_getters_join [] [cf] = cf
320 | mk_preds_getters_join [cq] [cf, cf'] =
321 mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf');
323 fun mk_terms qssss fssss =
325 val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss;
326 val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss;
327 val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss;
328 val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss;
329 in (pfss, cqfsss) end;
331 ((([], [], []), ([], [], [])),
332 ([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)),
333 (mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss))))
336 fun define_ctrs_case_for_type ((((((((((((((((((fp_b, fpT), C), fld), unf), fp_iter), fp_rec),
337 fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss),
338 disc_binders), sel_binderss), raw_sel_defaultss) no_defs_lthy =
340 val unfT = domain_type (fastype_of fld);
341 val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
342 val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
343 val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
345 val ((((u, v), fs), xss), _) =
347 |> yield_singleton (mk_Frees "u") unfT
348 ||>> yield_singleton (mk_Frees "v") fpT
349 ||>> mk_Frees "f" case_Ts
350 ||>> mk_Freess "x" ctr_Tss;
353 map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $
354 mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
356 val case_binder = Binding.suffix_name ("_" ^ caseN) fp_b;
359 fold_rev Term.lambda (fs @ [v])
360 (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v));
362 val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
363 |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
364 Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
365 (case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
366 ||> `Local_Theory.restore;
368 val phi = Proof_Context.export_morphism lthy lthy';
370 val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
371 val case_def = Morphism.thm phi raw_case_def;
373 val ctrs0 = map (Morphism.term phi) raw_ctrs;
374 val casex0 = Morphism.term phi raw_case;
376 val ctrs = map (mk_ctr As) ctrs0;
378 fun exhaust_tac {context = ctxt, ...} =
380 val fld_iff_unf_thm =
383 fold_rev Logic.all [u, v]
384 (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
386 Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
387 mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
388 (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
389 |> Thm.close_derivation
394 Local_Defs.unfold lthy @{thms all_unit_eq}
395 (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
396 (mk_sumEN_balanced n))
399 mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
403 map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
404 mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
406 val half_distinct_tacss =
407 map (map (fn (def, def') => fn {context = ctxt, ...} =>
408 mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
411 map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
412 mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
414 val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
416 fun define_iter_rec ((selss0, discIs, sel_thmss), no_defs_lthy) =
418 val fpT_to_C = fpT --> C;
420 fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
422 val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
424 val binder = Binding.suffix_name ("_" ^ suf) fp_b;
427 mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)),
428 Term.list_comb (fp_iter_like,
429 map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
430 in (binder, spec) end;
432 val iter_like_infos =
433 [(iterN, fp_iter, iter_only),
434 (recN, fp_rec, rec_only)];
436 val (binders, specs) = map generate_iter_like iter_like_infos |> split_list;
438 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
439 |> apfst split_list o fold_map2 (fn b => fn spec =>
440 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
441 #>> apsnd snd) binders specs
442 ||> `Local_Theory.restore;
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) fp_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 val phi = Proof_Context.export_morphism lthy lthy';
489 val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
491 val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
493 ((ctrs, selss0, coiter, corec, v, xss, ctr_defs, discIs, sel_thmss, coiter_def,
498 let val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss in
499 wrap_datatype tacss (((no_dests, ctrs0), casex0), (disc_binders, (sel_binderss,
500 sel_defaultss))) lthy
503 val define_iter_likes = if lfp then define_iter_rec else define_coiter_corec;
505 ((wrap, define_iter_likes), lthy')
508 val pre_map_defs = map map_def_of_bnf pre_bnfs;
509 val map_ids = map map_id_of_bnf nested_bnfs;
512 let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in
513 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
516 fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
518 val map0 = map_of_bnf (the (bnf_of lthy s));
519 val mapx = mk_map Ts Us map0;
520 val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx)))));
521 val args = map build_arg TUs;
522 in Term.list_comb (mapx, args) end;
524 fun derive_iter_rec_thms_for_types ((ctrss, _, iters, recs, vs, xsss, ctr_defss, _, _, iter_defs,
527 val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
528 val giters = map (lists_bmoc gss) iters;
529 val hrecs = map (lists_bmoc hss) recs;
531 val (iter_thmss, rec_thmss) =
533 fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
534 fold_rev (fold_rev Logic.all) (xs :: fss)
535 (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
537 fun build_call fiter_likes maybe_tick (T, U) =
541 (case find_index (curry (op =) T) fpTs of
542 ~1 => build_map (build_call fiter_likes maybe_tick) T U
543 | j => maybe_tick (nth vs j) (nth fiter_likes j));
545 fun mk_U maybe_mk_prodT =
546 typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
548 fun repair_calls fiter_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) =
549 if member (op =) fpTs T then
550 maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
551 else if exists_subtype (member (op =) fpTs) T then
552 [build_call fiter_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x]
556 val gxsss = map (map (maps (repair_calls giters (K I) (K I) (K I)))) xsss;
558 map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
560 val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
561 val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
564 map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss;
566 map2 (map o mk_iter_like_tac pre_map_defs map_ids rec_defs) fp_rec_thms ctr_defss;
568 (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
569 goal_iterss iter_tacss,
570 map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
571 goal_recss rec_tacss)
575 [(itersN, iter_thmss, simp_attrs),
576 (recsN, rec_thmss, Code.add_default_eqn_attrib :: simp_attrs)]
577 |> maps (fn (thmN, thmss, attrs) =>
578 map2 (fn b => fn thms =>
579 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
580 [(thms, [])])) fp_bs thmss);
582 lthy |> Local_Theory.notes notes |> snd
585 fun derive_coiter_corec_thms_for_types ((ctrss, selsss, coiters, corecs, vs, _, ctr_defss,
586 discIss, sel_thmsss, coiter_defs, corec_defs), lthy) =
588 val z = the_single zs;
590 val gcoiters = map (lists_bmoc pgss) coiters;
591 val hcorecs = map (lists_bmoc phss) corecs;
593 val (coiter_thmss, corec_thmss) =
595 fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
597 fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' =
598 fold_rev (fold_rev Logic.all) ([c] :: pfss)
599 (Logic.list_implies (seq_conds mk_goal_cond n k cps,
600 mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
602 fun build_call fiter_likes maybe_tack (T, U) =
606 (case find_index (curry (op =) U) fpTs of
607 ~1 => build_map (build_call fiter_likes maybe_tack) T U
608 | j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
610 fun mk_U maybe_mk_sumT =
611 typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
613 fun repair_calls fiter_likes maybe_mk_sumT maybe_tack cqf =
614 let val T = fastype_of cqf in
615 if exists_subtype (member (op =) Cs) T then
616 build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf
621 val crgsss' = map (map (map (repair_calls gcoiters (K I) (K I)))) crgsss;
622 val cshsss' = map (map (map (repair_calls hcorecs (curry mk_sumT) (tack z)))) cshsss;
625 map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss crgsss';
627 map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss cshsss';
630 map3 (map oo mk_coiter_like_tac coiter_defs map_ids) fp_iter_thms pre_map_defs
633 map3 (map oo mk_coiter_like_tac corec_defs map_ids) fp_rec_thms pre_map_defs
636 (map2 (map2 (fn goal => fn tac =>
637 Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
638 goal_coiterss coiter_tacss,
639 map2 (map2 (fn goal => fn tac =>
640 Skip_Proof.prove lthy [] [] goal (tac o #context)
641 |> Local_Defs.unfold lthy @{thms sum_case_if} |> Thm.close_derivation))
642 goal_corecss corec_tacss)
645 fun mk_disc_coiter_like_thms [_] = K []
646 | mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms;
648 val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss;
649 val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss;
651 fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm =
653 val (domT, ranT) = dest_funT (fastype_of sel0);
655 Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
656 [NONE, NONE, SOME (certify lthy sel0)] arg_cong
657 |> Thm.varifyT_global;
658 val sel_thm' = sel_thm RSN (2, trans);
660 coiter_like_thm RS arg_cong' RS sel_thm'
663 val sel_coiter_thmsss =
664 map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss;
665 val sel_corec_thmsss =
666 map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss;
669 [(coitersN, coiter_thmss, []),
670 (disc_coitersN, disc_coiter_thmss, []),
671 (sel_coitersN, map flat sel_coiter_thmsss, []),
672 (corecsN, corec_thmss, []),
673 (disc_corecsN, disc_corec_thmss, []),
674 (sel_corecsN, map flat sel_corec_thmsss, [])]
675 |> maps (fn (thmN, thmss, attrs) =>
676 map_filter (fn (_, []) => NONE | (b, thms) =>
677 SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
678 [(thms, [])])) (fp_bs ~~ thmss));
680 lthy |> Local_Theory.notes notes |> snd
683 fun wrap_types_and_define_iter_likes ((wraps, define_iter_likess), lthy) =
684 fold_map2 (curry (op o)) define_iter_likess wraps lthy |>> split_list11
687 |> fold_map define_ctrs_case_for_type (fp_bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
688 fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~
689 ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss ~~ raw_sel_defaultsss)
690 |>> split_list |> wrap_types_and_define_iter_likes
691 |> (if lfp then derive_iter_rec_thms_for_types else derive_coiter_corec_thms_for_types);
693 val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
694 (if lfp then "" else "co") ^ "datatype"));
699 val datatyp = define_datatype (K I) (K I) (K I);
701 val datatype_cmd = define_datatype Typedecl.read_constraint Syntax.parse_typ Syntax.read_term;
703 val parse_binding_colon = Parse.binding --| @{keyword ":"};
704 val parse_opt_binding_colon = Scan.optional parse_binding_colon no_binder;
707 @{keyword "("} |-- parse_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;
720 fun parse_datatype_cmd lfp construct = parse_datatype >> datatype_cmd lfp construct;