1 (* Title: HOL/Codatatype/Tools/bnf_fp_sugar.ML
2 Author: Jasmin Blanchette, TU Muenchen
5 Sugared datatype and codatatype constructions.
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);
41 fun resort_tfree S (TFree (s, _)) = TFree (s, S);
43 fun typ_subst inst (T as Type (s, Ts)) =
44 (case AList.lookup (op =) inst T of
45 NONE => Type (s, map (typ_subst inst) Ts)
47 | typ_subst inst T = the_default T (AList.lookup (op =) inst T);
49 val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
51 fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
52 fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
53 fun mk_uncurried2_fun f xss =
54 mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss);
56 fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v));
58 fun tack z_name (c, v) f =
59 let val z = Free (z_name, mk_sumT (fastype_of v, fastype_of c)) in
60 Term.lambda z (mk_sum_case (Term.lambda v v, Term.lambda c (f $ c)) $ z)
63 fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
65 fun merge_type_arg T T' = if T = T' then T else cannot_merge_types ();
67 fun merge_type_args (As, As') =
68 if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types ();
70 fun type_args_constrained_of (((cAs, _), _), _) = cAs;
71 fun type_binding_of (((_, b), _), _) = b;
72 fun mixfix_of ((_, mx), _) = mx;
73 fun ctr_specs_of (_, ctr_specs) = ctr_specs;
75 fun disc_of ((((disc, _), _), _), _) = disc;
76 fun ctr_of ((((_, ctr), _), _), _) = ctr;
77 fun args_of (((_, args), _), _) = args;
78 fun defaults_of ((_, ds), _) = ds;
79 fun ctr_mixfix_of (_, mx) = mx;
81 fun define_datatype prepare_constraint prepare_typ prepare_term lfp construct (no_dests, specs)
84 (* TODO: sanity checks on arguments *)
86 val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes"
89 val nn = length specs;
90 val fp_bs = map type_binding_of specs;
91 val fp_common_name = mk_common_name fp_bs;
93 fun prepare_type_arg (ty, c) =
94 let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
95 TFree (s, prepare_constraint no_defs_lthy0 c)
98 val Ass0 = map (map prepare_type_arg o type_args_constrained_of) specs;
99 val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
100 val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
102 val ((Bs, Cs), no_defs_lthy) =
104 |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
108 (* TODO: cleaner handling of fake contexts, without "background_theory" *)
109 (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
110 locale and shadows an existing global type*)
112 Theory.copy #> fold (fn spec => perhaps (try (Sign.add_type no_defs_lthy
113 (type_binding_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
114 val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
117 Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
120 val fake_Ts = map mk_fake_T fp_bs;
122 val mixfixes = map mixfix_of specs;
124 val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
125 | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
127 val ctr_specss = map ctr_specs_of specs;
129 val disc_bindingss = map (map disc_of) ctr_specss;
131 map2 (fn fp_b => map (Binding.qualify false (Binding.name_of fp_b) o ctr_of))
133 val ctr_argsss = map (map args_of) ctr_specss;
134 val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
136 val sel_bindingsss = map (map (map fst)) ctr_argsss;
137 val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
138 val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
140 val (As :: _) :: fake_ctr_Tsss =
141 burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
143 val _ = (case duplicates (op =) unsorted_As of [] => ()
144 | A :: _ => error ("Duplicate type parameter " ^
145 quote (Syntax.string_of_typ no_defs_lthy A)));
147 val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
148 val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
150 | A' :: _ => error ("Extra type variable on right-hand side: " ^
151 quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
153 fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) =
154 s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
155 quote (Syntax.string_of_typ fake_lthy T)))
156 | eq_fpT _ _ = false;
158 fun freeze_fp (T as Type (s, Us)) =
159 (case find_index (eq_fpT T) fake_Ts of ~1 => Type (s, map freeze_fp Us) | j => nth Bs j)
162 val ctr_TsssBs = map (map (map freeze_fp)) fake_ctr_Tsss;
163 val ctr_sum_prod_TsBs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssBs;
166 map dest_TFree Bs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsBs;
168 val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, fp_induct, unf_flds, fld_unfs, fld_injects,
169 fp_iter_thms, fp_rec_thms), lthy)) =
170 fp_bnf construct fp_bs mixfixes (map dest_TFree unsorted_As) fp_eqs no_defs_lthy0;
172 fun add_nesty_bnf_names Us =
174 fun add (Type (s, Ts)) ss =
175 let val (needs, ss') = fold_map add Ts ss in
176 if exists I needs then (true, insert (op =) s ss') else (false, ss')
178 | add T ss = (member (op =) Us T, ss);
182 map_filter (bnf_of lthy) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_TsssBs []);
184 val nesting_bnfs = nesty_bnfs As;
185 val nested_bnfs = nesty_bnfs Bs;
187 val timer = time (Timer.startRealTimer ());
189 fun mk_unf_or_fld get_T Ts t =
190 let val Type (_, Ts0) = get_T (fastype_of t) in
191 Term.subst_atomic_types (Ts0 ~~ Ts) t
194 val mk_unf = mk_unf_or_fld domain_type;
195 val mk_fld = mk_unf_or_fld range_type;
197 val unfs = map (mk_unf As) unfs0;
198 val flds = map (mk_fld As) flds0;
200 val fpTs = map (domain_type o fastype_of) unfs;
202 val exists_fp_subtype = exists_subtype (member (op =) fpTs);
204 val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Bs ~~ fpTs)))) ctr_TsssBs;
205 val ns = map length ctr_Tsss;
206 val kss = map (fn n => 1 upto n) ns;
207 val mss = map (map length) ctr_Tsss;
208 val Css = map2 replicate ns Cs;
210 fun mk_iter_like Ts Us t =
212 val (bindings, body) = strip_type (fastype_of t);
213 val (f_Us, prebody) = split_last bindings;
214 val Type (_, Ts0) = if lfp then prebody else body;
215 val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
217 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
220 val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
221 val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
223 val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
224 val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
226 val ((iter_only as (gss, _, _), rec_only as (hss, _, _)),
227 (zs, cs, cpss, coiter_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))) =
231 map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
232 ns mss fp_iter_fun_Ts;
233 val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
235 val ((gss, ysss), _) =
237 |> mk_Freess "f" g_Tss
238 ||>> mk_Freesss "x" y_Tsss;
239 val yssss = map (map (map single)) ysss;
241 fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) =
242 if member (op =) Cs U then Us else [T]
243 | dest_rec_prodT T = [T];
246 map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o
247 dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts;
248 val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
250 val hss = map2 (map2 retype_free) h_Tss gss;
251 val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
254 |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
255 val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
257 (((gss, g_Tss, yssss), (hss, h_Tss, zssss)),
258 ([], [], [], (([], []), ([], [])), (([], []), ([], []))))
262 (*avoid "'a itself" arguments in coiterators and corecursors*)
263 val mss' = map (fn [0] => [1] | ms => ms) mss;
265 val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_predT) ns Cs;
267 fun zip_predss_getterss qss fss = maps (op @) (qss ~~ fss);
269 fun zip_preds_predsss_gettersss [] [qss] [fss] = zip_predss_getterss qss fss
270 | zip_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
271 p :: zip_predss_getterss qss fss @ zip_preds_predsss_gettersss ps qsss fsss;
273 fun mk_types maybe_dest_sumT fun_Ts =
275 val f_sum_prod_Ts = map range_type fun_Ts;
276 val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
278 map3 (fn C => map2 (map (map (curry (op -->) C) o maybe_dest_sumT) oo dest_tupleT))
281 map (map (map (fn [_] => [] | [_, C] => [mk_predT (domain_type C)]))) f_Tssss;
282 val pf_Tss = map3 zip_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
283 in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end;
285 val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_iter_fun_Ts;
287 val ((((Free (z, _), cs), pss), gssss), _) =
289 |> yield_singleton (mk_Frees "z") dummyT
291 ||>> mk_Freess "p" p_Tss
292 ||>> mk_Freessss "g" g_Tssss;
293 val rssss = map (map (map (fn [] => []))) r_Tssss;
295 fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) =
296 if member (op =) Cs U then Us else [T]
297 | dest_corec_sumT T = [T];
299 val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts;
301 val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
302 val ((sssss, hssss_tl), _) =
304 |> mk_Freessss "q" s_Tssss
305 ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
306 val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
308 val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
310 fun mk_preds_getters_join [] [cf] = cf
311 | mk_preds_getters_join [cq] [cf, cf'] =
312 mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf');
314 fun mk_terms qssss fssss =
316 val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss;
317 val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss;
318 val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss;
319 val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss;
320 in (pfss, cqfsss) end;
322 ((([], [], []), ([], [], [])),
323 ([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)),
324 (mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss))))
327 fun define_ctrs_case_for_type ((((((((((((((((((fp_b, fpT), C), fld), unf), fp_iter), fp_rec),
328 fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_bindings), ctr_mixfixes), ctr_Tss),
329 disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
331 val unfT = domain_type (fastype_of fld);
332 val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
333 val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
334 val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
336 val ((((u, fs), xss), v'), _) =
338 |> yield_singleton (mk_Frees "u") unfT
339 ||>> mk_Frees "f" case_Ts
340 ||>> mk_Freess "x" ctr_Tss
341 ||>> yield_singleton (Variable.variant_fixes) (Binding.name_of fp_b);
343 val v = Free (v', fpT);
346 map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $
347 mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
349 val case_binding = Binding.suffix_name ("_" ^ caseN) fp_b;
352 fold_rev Term.lambda (fs @ [v])
353 (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v));
355 val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
356 |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
357 Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
358 (case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
359 ||> `Local_Theory.restore;
361 val phi = Proof_Context.export_morphism lthy lthy';
363 val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
364 val case_def = Morphism.thm phi raw_case_def;
366 val ctrs0 = map (Morphism.term phi) raw_ctrs;
367 val casex0 = Morphism.term phi raw_case;
369 val ctrs = map (mk_ctr As) ctrs0;
371 fun exhaust_tac {context = ctxt, ...} =
373 val fld_iff_unf_thm =
376 fold_rev Logic.all [u, v]
377 (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
379 Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
380 mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
381 (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
382 |> Thm.close_derivation
387 Local_Defs.unfold lthy @{thms all_unit_eq}
388 (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
389 (mk_sumEN_balanced n))
392 mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
396 map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
397 mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
399 val half_distinct_tacss =
400 map (map (fn (def, def') => fn {context = ctxt, ...} =>
401 mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
404 map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
405 mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
407 val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
409 fun define_iter_rec ((selss0, discIs, sel_thmss), no_defs_lthy) =
411 val fpT_to_C = fpT --> C;
413 fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
415 val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
416 val binding = Binding.suffix_name ("_" ^ suf) fp_b;
418 mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
419 Term.list_comb (fp_iter_like,
420 map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
421 in (binding, spec) end;
423 val iter_like_infos =
424 [(iterN, fp_iter, iter_only),
425 (recN, fp_rec, rec_only)];
427 val (bindings, specs) = map generate_iter_like iter_like_infos |> split_list;
429 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
430 |> apfst split_list o fold_map2 (fn b => fn spec =>
431 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
432 #>> apsnd snd) bindings specs
433 ||> `Local_Theory.restore;
435 val phi = Proof_Context.export_morphism lthy lthy';
437 val [iter_def, rec_def] = map (Morphism.thm phi) defs;
439 val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
441 ((ctrs, selss0, iter, recx, xss, ctr_defs, discIs, sel_thmss, iter_def, rec_def), lthy)
444 fun define_coiter_corec ((selss0, discIs, sel_thmss), no_defs_lthy) =
446 val B_to_fpT = C --> fpT;
448 fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
449 Term.lambda c (mk_IfN sum_prod_T cps
450 (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
452 fun generate_coiter_like (suf, fp_iter_like, ((pfss, cqfsss), (f_sum_prod_Ts,
455 val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
456 val binding = Binding.suffix_name ("_" ^ suf) fp_b;
458 mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
459 Term.list_comb (fp_iter_like,
460 map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
461 in (binding, spec) end;
463 val coiter_like_infos =
464 [(coiterN, fp_iter, coiter_only),
465 (corecN, fp_rec, corec_only)];
467 val (bindings, specs) = map generate_coiter_like coiter_like_infos |> split_list;
469 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
470 |> apfst split_list o fold_map2 (fn b => fn spec =>
471 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
472 #>> apsnd snd) bindings specs
473 ||> `Local_Theory.restore;
475 val phi = Proof_Context.export_morphism lthy lthy';
477 val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
479 val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
481 ((ctrs, selss0, coiter, corec, xss, ctr_defs, discIs, sel_thmss, coiter_def, corec_def),
486 let val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss in
487 wrap_datatype tacss (((no_dests, ctrs0), casex0), (disc_bindings, (sel_bindingss,
488 sel_defaultss))) lthy
491 val define_iter_likes = if lfp then define_iter_rec else define_coiter_corec;
493 ((wrap, define_iter_likes), lthy')
496 val pre_map_defs = map map_def_of_bnf pre_bnfs;
497 val pre_set_defss = map set_defs_of_bnf pre_bnfs;
498 val nested_set_natural's = maps set_natural'_of_bnf nested_bnfs;
499 val nesting_map_ids = map map_id_of_bnf nesting_bnfs;
501 fun mk_map live Ts Us t =
503 val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) |>> List.last
505 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
508 fun build_map build_arg (T as Type (s, Ts)) (U as Type (_, Us)) =
510 val bnf = the (bnf_of lthy s);
511 val live = live_of_bnf bnf;
512 val mapx = mk_map live Ts Us (map_of_bnf bnf);
513 val TUs = map dest_funT (fst (strip_typeN live (fastype_of mapx)));
514 val args = map build_arg TUs;
515 in Term.list_comb (mapx, args) end;
517 fun derive_induct_iter_rec_thms_for_types ((ctrss, _, iters, recs, xsss, ctr_defss, _, _,
518 iter_defs, rec_defs), lthy) =
520 val (((phis, phis'), vs'), names_lthy) =
522 |> mk_Frees' "P" (map mk_predT fpTs)
523 ||>> Variable.variant_fixes (map Binding.name_of fp_bs);
525 val vs = map2 (curry Free) vs' fpTs;
527 fun mk_sets_nested bnf =
529 val Type (T_name, Us) = T_of_bnf bnf;
530 val lives = lives_of_bnf bnf;
531 val sets = sets_of_bnf bnf;
533 (case find_index (curry (op =) U) lives of
537 (T_name, map mk_set Us)
540 val setss_nested = map mk_sets_nested nested_bnfs;
542 val (induct_thms, induct_thm) =
545 let val Type (_, Ts0) = domain_type (fastype_of t) in
546 Term.subst_atomic_types (Ts0 ~~ Ts) t
549 fun mk_raw_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) =
550 (case find_index (curry (op =) T) fpTs of
552 (case AList.lookup (op =) setss_nested T_name of
557 split_list (filter (exists_fp_subtype o fst) (Ts0 ~~ raw_sets0));
558 val sets = map (mk_set Ts0) raw_sets;
559 val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
560 val xysets = map (pair x) (ys ~~ sets);
561 val ppremss = map (mk_raw_prem_prems names_lthy') ys;
563 flat (map2 (map o apfst o cons) xysets ppremss)
565 | i => [([], (i + 1, x))])
566 | mk_raw_prem_prems _ _ = [];
568 fun close_prem_prem xs t =
569 fold_rev Logic.all (map Free (drop (nn + length xs)
570 (rev (Term.add_frees t (map dest_Free xs @ phis'))))) t;
572 fun mk_prem_prem xs (xysets, (j, x)) =
573 close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
574 HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
575 HOLogic.mk_Trueprop (nth phis (j - 1) $ x)));
577 fun mk_raw_prem phi ctr ctr_Ts =
579 val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
580 val pprems = maps (mk_raw_prem_prems names_lthy') xs;
581 in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
583 fun mk_prem (xs, raw_pprems, concl) =
584 fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
586 val raw_premss = map3 (map2 o mk_raw_prem) phis ctrss ctr_Tsss;
589 Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
590 HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
591 (map2 (curry (op $)) phis vs)));
593 val kksss = map (map (map (fst o snd) o #2)) raw_premss;
595 val fld_induct' = fp_induct OF (map mk_sumEN_tupled_balanced mss);
598 Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
599 mk_induct_tac ctxt ns mss kksss (flat ctr_defss) fld_induct'
600 nested_set_natural's pre_set_defss)
601 |> singleton (Proof_Context.export names_lthy lthy)
603 `(conj_dests nn) induct_thm
606 val (iter_thmss, rec_thmss) =
608 val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
609 val giters = map (lists_bmoc gss) iters;
610 val hrecs = map (lists_bmoc hss) recs;
612 fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
613 fold_rev (fold_rev Logic.all) (xs :: fss)
614 (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
616 fun build_call fiter_likes maybe_tick (T, U) =
620 (case find_index (curry (op =) T) fpTs of
621 ~1 => build_map (build_call fiter_likes maybe_tick) T U
622 | j => maybe_tick (nth vs j) (nth fiter_likes j));
624 fun mk_U maybe_mk_prodT =
625 typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
627 fun intr_calls fiter_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) =
628 if member (op =) fpTs T then
629 maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
630 else if exists_fp_subtype T then
631 [build_call fiter_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x]
635 val gxsss = map (map (maps (intr_calls giters (K I) (K I) (K I)))) xsss;
636 val hxsss = map (map (maps (intr_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
638 val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
639 val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
642 map2 (map o mk_iter_like_tac pre_map_defs nesting_map_ids iter_defs) fp_iter_thms
645 map2 (map o mk_iter_like_tac pre_map_defs nesting_map_ids rec_defs) fp_rec_thms
648 (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
649 goal_iterss iter_tacss,
650 map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
651 goal_recss rec_tacss)
655 (if nn > 1 then [(inductN, [induct_thm], [])] (* FIXME: attribs *) else [])
656 |> map (fn (thmN, thms, attrs) =>
657 ((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
660 [(inductN, map single induct_thms, []), (* FIXME: attribs *)
661 (itersN, iter_thmss, simp_attrs),
662 (recsN, rec_thmss, Code.add_default_eqn_attrib :: simp_attrs)]
663 |> maps (fn (thmN, thmss, attrs) =>
664 map2 (fn b => fn thms =>
665 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
666 [(thms, [])])) fp_bs thmss);
668 lthy |> Local_Theory.notes (common_notes @ notes) |> snd
671 fun derive_coinduct_coiter_corec_thms_for_types ((ctrss, selsss, coiters, corecs, _, ctr_defss,
672 discIss, sel_thmsss, coiter_defs, corec_defs), lthy) =
676 |> Variable.variant_fixes (map Binding.name_of fp_bs);
678 val vs = map2 (curry Free) vs' fpTs;
680 val (coinduct_thms, coinduct_thm) =
682 val coinduct_thm = fp_induct;
684 `(conj_dests nn) coinduct_thm
687 val (coiter_thmss, corec_thmss) =
689 val z = the_single zs;
690 val gcoiters = map (lists_bmoc pgss) coiters;
691 val hcorecs = map (lists_bmoc phss) corecs;
693 fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
695 fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' =
696 fold_rev (fold_rev Logic.all) ([c] :: pfss)
697 (Logic.list_implies (seq_conds mk_goal_cond n k cps,
698 mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
700 fun build_call fiter_likes maybe_tack (T, U) =
704 (case find_index (curry (op =) U) fpTs of
705 ~1 => build_map (build_call fiter_likes maybe_tack) T U
706 | j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
708 fun mk_U maybe_mk_sumT =
709 typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
711 fun intr_calls fiter_likes maybe_mk_sumT maybe_tack cqf =
712 let val T = fastype_of cqf in
713 if exists_subtype (member (op =) Cs) T then
714 build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf
719 val crgsss' = map (map (map (intr_calls gcoiters (K I) (K I)))) crgsss;
720 val cshsss' = map (map (map (intr_calls hcorecs (curry mk_sumT) (tack z)))) cshsss;
723 map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss crgsss';
725 map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss cshsss';
728 map3 (map oo mk_coiter_like_tac coiter_defs nesting_map_ids) fp_iter_thms pre_map_defs
731 map3 (map oo mk_coiter_like_tac corec_defs nesting_map_ids) fp_rec_thms pre_map_defs
734 (map2 (map2 (fn goal => fn tac =>
735 Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
736 goal_coiterss coiter_tacss,
737 map2 (map2 (fn goal => fn tac =>
738 Skip_Proof.prove lthy [] [] goal (tac o #context)
739 |> Local_Defs.unfold lthy @{thms sum_case_if} |> Thm.close_derivation))
740 goal_corecss corec_tacss)
743 fun mk_disc_coiter_like_thms [_] = K []
744 | mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms;
746 val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss;
747 val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss;
749 fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm =
751 val (domT, ranT) = dest_funT (fastype_of sel0);
753 Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
754 [NONE, NONE, SOME (certify lthy sel0)] arg_cong
755 |> Thm.varifyT_global;
756 val sel_thm' = sel_thm RSN (2, trans);
758 coiter_like_thm RS arg_cong' RS sel_thm'
761 val sel_coiter_thmsss =
762 map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss;
763 val sel_corec_thmsss =
764 map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss;
767 (if nn > 1 then [(coinductN, [coinduct_thm], [])] (* FIXME: attribs *) else [])
768 |> map (fn (thmN, thms, attrs) =>
769 ((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
772 [(coinductN, map single coinduct_thms, []), (* FIXME: attribs *)
773 (coitersN, coiter_thmss, []),
774 (disc_coitersN, disc_coiter_thmss, []),
775 (sel_coitersN, map flat sel_coiter_thmsss, []),
776 (corecsN, corec_thmss, []),
777 (disc_corecsN, disc_corec_thmss, []),
778 (sel_corecsN, map flat sel_corec_thmsss, [])]
779 |> maps (fn (thmN, thmss, attrs) =>
780 map_filter (fn (_, []) => NONE | (b, thms) =>
781 SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
782 [(thms, [])])) (fp_bs ~~ thmss));
784 lthy |> Local_Theory.notes (common_notes @ notes) |> snd
787 fun wrap_types_and_define_iter_likes ((wraps, define_iter_likess), lthy) =
788 fold_map2 (curry (op o)) define_iter_likess wraps lthy |>> split_list10
791 |> fold_map define_ctrs_case_for_type (fp_bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
792 fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_bindingss ~~
793 ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~ raw_sel_defaultsss)
794 |>> split_list |> wrap_types_and_define_iter_likes
795 |> (if lfp then derive_induct_iter_rec_thms_for_types
796 else derive_coinduct_coiter_corec_thms_for_types);
798 val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
799 (if lfp then "" else "co") ^ "datatype"));
804 val datatyp = define_datatype (K I) (K I) (K I);
806 val datatype_cmd = define_datatype Typedecl.read_constraint Syntax.parse_typ Syntax.read_term;
808 val parse_binding_colon = Parse.binding --| @{keyword ":"};
809 val parse_opt_binding_colon = Scan.optional parse_binding_colon no_binding;
812 @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
813 (Parse.typ >> pair no_binding);
816 @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
818 val parse_single_spec =
819 Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
820 (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
821 Scan.repeat parse_ctr_arg -- Scan.optional parse_defaults [] -- Parse.opt_mixfix));
823 val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_single_spec;
825 fun parse_datatype_cmd lfp construct = parse_datatype >> datatype_cmd lfp construct;