select the right premise in "mk_induct_discharge_prem_prems_tac" instead of relying on backtracking
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);
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), no_defs_lthy) =
107 |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
111 (* TODO: cleaner handling of fake contexts, without "background_theory" *)
112 (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
113 locale and shadows an existing global type*)
115 Theory.copy #> fold (fn spec => perhaps (try (Sign.add_type no_defs_lthy
116 (type_binding_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
117 val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
120 Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
123 val fake_Ts = map mk_fake_T fp_bs;
125 val mixfixes = map mixfix_of specs;
127 val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
128 | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
130 val ctr_specss = map ctr_specs_of specs;
132 val disc_bindingss = map (map disc_of) ctr_specss;
134 map2 (fn fp_b => map (Binding.qualify false (Binding.name_of fp_b) o ctr_of))
136 val ctr_argsss = map (map args_of) ctr_specss;
137 val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
139 val sel_bindingsss = map (map (map fst)) ctr_argsss;
140 val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
141 val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
143 val (As :: _) :: fake_ctr_Tsss =
144 burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
146 val _ = (case duplicates (op =) unsorted_As of [] => ()
147 | A :: _ => error ("Duplicate type parameter " ^
148 quote (Syntax.string_of_typ no_defs_lthy A)));
150 val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
151 val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
153 | A' :: _ => error ("Extra type variable on right-hand side: " ^
154 quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
156 fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) =
157 s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
158 quote (Syntax.string_of_typ fake_lthy T)))
159 | eq_fpT _ _ = false;
161 fun freeze_fp (T as Type (s, Us)) =
162 (case find_index (eq_fpT T) fake_Ts of ~1 => Type (s, map freeze_fp Us) | j => nth Bs j)
165 val ctr_TsssBs = map (map (map freeze_fp)) fake_ctr_Tsss;
166 val ctr_sum_prod_TsBs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssBs;
169 map dest_TFree Bs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsBs;
171 val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, fp_induct, unf_flds, fld_unfs, fld_injects,
172 fp_iter_thms, fp_rec_thms), lthy)) =
173 fp_bnf construct fp_bs mixfixes (map dest_TFree unsorted_As) fp_eqs no_defs_lthy0;
175 fun add_nesty_bnf_names Us =
177 fun add (Type (s, Ts)) ss =
178 let val (needs, ss') = fold_map add Ts ss in
179 if exists I needs then (true, insert (op =) s ss') else (false, ss')
181 | add T ss = (member (op =) Us T, ss);
185 map_filter (bnf_of lthy) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_TsssBs []);
187 val nesting_bnfs = nesty_bnfs As;
188 val nested_bnfs = nesty_bnfs Bs;
190 val timer = time (Timer.startRealTimer ());
192 fun mk_unf_or_fld get_T Ts t =
193 let val Type (_, Ts0) = get_T (fastype_of t) in
194 Term.subst_atomic_types (Ts0 ~~ Ts) t
197 val mk_unf = mk_unf_or_fld domain_type;
198 val mk_fld = mk_unf_or_fld range_type;
200 val unfs = map (mk_unf As) unfs0;
201 val flds = map (mk_fld As) flds0;
203 val fpTs = map (domain_type o fastype_of) unfs;
205 val exists_fp_subtype = exists_subtype (member (op =) fpTs);
207 val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Bs ~~ fpTs)))) ctr_TsssBs;
208 val ns = map length ctr_Tsss;
209 val kss = map (fn n => 1 upto n) ns;
210 val mss = map (map length) ctr_Tsss;
211 val Css = map2 replicate ns Cs;
213 fun mk_iter_like Ts Us t =
215 val (bindings, body) = strip_type (fastype_of t);
216 val (f_Us, prebody) = split_last bindings;
217 val Type (_, Ts0) = if lfp then prebody else body;
218 val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
220 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
223 val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
224 val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
226 val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
227 val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
229 val ((iter_only as (gss, _, _), rec_only as (hss, _, _)),
230 (zs, cs, cpss, coiter_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))) =
234 map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
235 ns mss fp_iter_fun_Ts;
236 val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
238 val ((gss, ysss), _) =
240 |> mk_Freess "f" g_Tss
241 ||>> mk_Freesss "x" y_Tsss;
242 val yssss = map (map (map single)) ysss;
244 fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) =
245 if member (op =) Cs U then Us else [T]
246 | dest_rec_prodT T = [T];
249 map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o
250 dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts;
251 val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
253 val hss = map2 (map2 retype_free) h_Tss gss;
254 val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
257 |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
258 val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
260 (((gss, g_Tss, yssss), (hss, h_Tss, zssss)),
261 ([], [], [], (([], []), ([], [])), (([], []), ([], []))))
265 (*avoid "'a itself" arguments in coiterators and corecursors*)
266 val mss' = map (fn [0] => [1] | ms => ms) mss;
268 val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_predT) ns Cs;
270 fun zip_predss_getterss qss fss = maps (op @) (qss ~~ fss);
272 fun zip_preds_predsss_gettersss [] [qss] [fss] = zip_predss_getterss qss fss
273 | zip_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
274 p :: zip_predss_getterss qss fss @ zip_preds_predsss_gettersss ps qsss fsss;
276 fun mk_types maybe_dest_sumT fun_Ts =
278 val f_sum_prod_Ts = map range_type fun_Ts;
279 val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
281 map3 (fn C => map2 (map (map (curry (op -->) C) o maybe_dest_sumT) oo dest_tupleT))
284 map (map (map (fn [_] => [] | [_, C] => [mk_predT (domain_type C)]))) f_Tssss;
285 val pf_Tss = map3 zip_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
286 in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end;
288 val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_iter_fun_Ts;
290 val ((((Free (z, _), cs), pss), gssss), _) =
292 |> yield_singleton (mk_Frees "z") dummyT
294 ||>> mk_Freess "p" p_Tss
295 ||>> mk_Freessss "g" g_Tssss;
296 val rssss = map (map (map (fn [] => []))) r_Tssss;
298 fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) =
299 if member (op =) Cs U then Us else [T]
300 | dest_corec_sumT T = [T];
302 val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts;
304 val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
305 val ((sssss, hssss_tl), _) =
307 |> mk_Freessss "q" s_Tssss
308 ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
309 val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
311 val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
313 fun mk_preds_getters_join [] [cf] = cf
314 | mk_preds_getters_join [cq] [cf, cf'] =
315 mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf');
317 fun mk_terms qssss fssss =
319 val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss;
320 val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss;
321 val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss;
322 val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss;
323 in (pfss, cqfsss) end;
325 ((([], [], []), ([], [], [])),
326 ([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)),
327 (mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss))))
330 fun define_ctrs_case_for_type ((((((((((((((((((fp_b, fpT), C), fld), unf), fp_iter), fp_rec),
331 fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_bindings), ctr_mixfixes), ctr_Tss),
332 disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
334 val unfT = domain_type (fastype_of fld);
335 val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
336 val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
337 val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
339 val ((((u, fs), xss), v'), _) =
341 |> yield_singleton (mk_Frees "u") unfT
342 ||>> mk_Frees "f" case_Ts
343 ||>> mk_Freess "x" ctr_Tss
344 ||>> yield_singleton (Variable.variant_fixes) (Binding.name_of fp_b);
346 val v = Free (v', fpT);
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, xss, ctr_defs, discIs, sel_thmss, iter_def, rec_def), lthy)
447 fun define_coiter_corec ((selss0, discIs, sel_thmss), no_defs_lthy) =
449 val B_to_fpT = C --> fpT;
451 fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
452 Term.lambda c (mk_IfN sum_prod_T cps
453 (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
455 fun generate_coiter_like (suf, fp_iter_like, ((pfss, cqfsss), (f_sum_prod_Ts,
458 val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
459 val binding = Binding.suffix_name ("_" ^ suf) fp_b;
461 mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
462 Term.list_comb (fp_iter_like,
463 map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
464 in (binding, spec) end;
466 val coiter_like_infos =
467 [(coiterN, fp_iter, coiter_only),
468 (corecN, fp_rec, corec_only)];
470 val (bindings, specs) = map generate_coiter_like coiter_like_infos |> split_list;
472 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
473 |> apfst split_list o fold_map2 (fn b => fn spec =>
474 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
475 #>> apsnd snd) bindings specs
476 ||> `Local_Theory.restore;
478 val phi = Proof_Context.export_morphism lthy lthy';
480 val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
482 val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
484 ((ctrs, selss0, coiter, corec, xss, ctr_defs, discIs, sel_thmss, coiter_def, corec_def),
489 let val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss in
490 wrap_datatype tacss (((no_dests, ctrs0), casex0), (disc_bindings, (sel_bindingss,
491 sel_defaultss))) lthy
494 val define_iter_likes = if lfp then define_iter_rec else define_coiter_corec;
496 ((wrap, define_iter_likes), lthy')
499 val pre_map_defs = map map_def_of_bnf pre_bnfs;
500 val pre_set_defss = map set_defs_of_bnf pre_bnfs;
501 val nested_set_natural's = maps set_natural'_of_bnf nested_bnfs;
502 val nesting_map_ids = map map_id_of_bnf nesting_bnfs;
505 let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in
506 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
509 fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
511 val map0 = map_of_bnf (the (bnf_of lthy s));
512 val mapx = mk_map Ts Us map0;
513 val TUs = map dest_funT (fst (split_last (fst (strip_map_type (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 =
570 (map Free (drop (2 * nn) (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;
582 (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs)))
585 val raw_premss = map3 (map2 o mk_raw_prem) phis ctrss ctr_Tsss;
587 fun mk_prem (xs, raw_pprems, concl) =
588 fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
591 Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
592 HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
593 (map2 (curry (op $)) phis vs)));
595 fun mk_prem_prems_indices raw_pprems =
597 val rr = length raw_pprems;
599 map2 (fn pp => fn (xysets, (i, _)) => ((rr, pp), i)) (1 upto rr) raw_pprems
602 val ppjjkksss = map (map (mk_prem_prems_indices o #2)) raw_premss;
604 val _ = tracing ("PPJJISSS:\n" ^ PolyML.makestring (ppjjkksss)) (*###*)
606 val fld_induct' = fp_induct OF (map mk_sumEN_tupled_balanced mss);
609 Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
610 mk_induct_tac ctxt ns mss ppjjkksss (flat ctr_defss) fld_induct'
611 nested_set_natural's pre_set_defss)
612 |> singleton (Proof_Context.export names_lthy lthy)
614 `(conj_dests nn) induct_thm
617 val (iter_thmss, rec_thmss) =
619 val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
620 val giters = map (lists_bmoc gss) iters;
621 val hrecs = map (lists_bmoc hss) recs;
623 fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
624 fold_rev (fold_rev Logic.all) (xs :: fss)
625 (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
627 fun build_call fiter_likes maybe_tick (T, U) =
631 (case find_index (curry (op =) T) fpTs of
632 ~1 => build_map (build_call fiter_likes maybe_tick) T U
633 | j => maybe_tick (nth vs j) (nth fiter_likes j));
635 fun mk_U maybe_mk_prodT =
636 typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
638 fun intr_calls fiter_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) =
639 if member (op =) fpTs T then
640 maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
641 else if exists_fp_subtype T then
642 [build_call fiter_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x]
646 val gxsss = map (map (maps (intr_calls giters (K I) (K I) (K I)))) xsss;
647 val hxsss = map (map (maps (intr_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
649 val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
650 val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
653 map2 (map o mk_iter_like_tac pre_map_defs nesting_map_ids iter_defs) fp_iter_thms
656 map2 (map o mk_iter_like_tac pre_map_defs nesting_map_ids rec_defs) fp_rec_thms
659 (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
660 goal_iterss iter_tacss,
661 map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
662 goal_recss rec_tacss)
666 (if nn > 1 then [(inductN, [induct_thm], [])] (* FIXME: attribs *) else [])
667 |> map (fn (thmN, thms, attrs) =>
668 ((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
671 [(inductN, map single induct_thms, []), (* FIXME: attribs *)
672 (itersN, iter_thmss, simp_attrs),
673 (recsN, rec_thmss, Code.add_default_eqn_attrib :: simp_attrs)]
674 |> maps (fn (thmN, thmss, attrs) =>
675 map2 (fn b => fn thms =>
676 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
677 [(thms, [])])) fp_bs thmss);
679 lthy |> Local_Theory.notes (common_notes @ notes) |> snd
682 fun derive_coinduct_coiter_corec_thms_for_types ((ctrss, selsss, coiters, corecs, _, ctr_defss,
683 discIss, sel_thmsss, coiter_defs, corec_defs), lthy) =
687 |> Variable.variant_fixes (map Binding.name_of fp_bs);
689 val vs = map2 (curry Free) vs' fpTs;
691 val (coinduct_thms, coinduct_thm) =
693 val coinduct_thm = fp_induct;
695 `(conj_dests nn) coinduct_thm
698 val (coiter_thmss, corec_thmss) =
700 val z = the_single zs;
701 val gcoiters = map (lists_bmoc pgss) coiters;
702 val hcorecs = map (lists_bmoc phss) corecs;
704 fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
706 fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' =
707 fold_rev (fold_rev Logic.all) ([c] :: pfss)
708 (Logic.list_implies (seq_conds mk_goal_cond n k cps,
709 mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
711 fun build_call fiter_likes maybe_tack (T, U) =
715 (case find_index (curry (op =) U) fpTs of
716 ~1 => build_map (build_call fiter_likes maybe_tack) T U
717 | j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
719 fun mk_U maybe_mk_sumT =
720 typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
722 fun intr_calls fiter_likes maybe_mk_sumT maybe_tack cqf =
723 let val T = fastype_of cqf in
724 if exists_subtype (member (op =) Cs) T then
725 build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf
730 val crgsss' = map (map (map (intr_calls gcoiters (K I) (K I)))) crgsss;
731 val cshsss' = map (map (map (intr_calls hcorecs (curry mk_sumT) (tack z)))) cshsss;
734 map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss crgsss';
736 map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss cshsss';
739 map3 (map oo mk_coiter_like_tac coiter_defs nesting_map_ids) fp_iter_thms pre_map_defs
742 map3 (map oo mk_coiter_like_tac corec_defs nesting_map_ids) fp_rec_thms pre_map_defs
745 (map2 (map2 (fn goal => fn tac =>
746 Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
747 goal_coiterss coiter_tacss,
748 map2 (map2 (fn goal => fn tac =>
749 Skip_Proof.prove lthy [] [] goal (tac o #context)
750 |> Local_Defs.unfold lthy @{thms sum_case_if} |> Thm.close_derivation))
751 goal_corecss corec_tacss)
754 fun mk_disc_coiter_like_thms [_] = K []
755 | mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms;
757 val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss;
758 val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss;
760 fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm =
762 val (domT, ranT) = dest_funT (fastype_of sel0);
764 Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
765 [NONE, NONE, SOME (certify lthy sel0)] arg_cong
766 |> Thm.varifyT_global;
767 val sel_thm' = sel_thm RSN (2, trans);
769 coiter_like_thm RS arg_cong' RS sel_thm'
772 val sel_coiter_thmsss =
773 map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss;
774 val sel_corec_thmsss =
775 map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss;
778 (if nn > 1 then [(coinductN, [coinduct_thm], [])] (* FIXME: attribs *) else [])
779 |> map (fn (thmN, thms, attrs) =>
780 ((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
783 [(coinductN, map single coinduct_thms, []), (* FIXME: attribs *)
784 (coitersN, coiter_thmss, []),
785 (disc_coitersN, disc_coiter_thmss, []),
786 (sel_coitersN, map flat sel_coiter_thmsss, []),
787 (corecsN, corec_thmss, []),
788 (disc_corecsN, disc_corec_thmss, []),
789 (sel_corecsN, map flat sel_corec_thmsss, [])]
790 |> maps (fn (thmN, thmss, attrs) =>
791 map_filter (fn (_, []) => NONE | (b, thms) =>
792 SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
793 [(thms, [])])) (fp_bs ~~ thmss));
795 lthy |> Local_Theory.notes (common_notes @ notes) |> snd
798 fun wrap_types_and_define_iter_likes ((wraps, define_iter_likess), lthy) =
799 fold_map2 (curry (op o)) define_iter_likess wraps lthy |>> split_list10
802 |> fold_map define_ctrs_case_for_type (fp_bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
803 fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_bindingss ~~
804 ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~ raw_sel_defaultsss)
805 |>> split_list |> wrap_types_and_define_iter_likes
806 |> (if lfp then derive_induct_iter_rec_thms_for_types
807 else derive_coinduct_coiter_corec_thms_for_types);
809 val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
810 (if lfp then "" else "co") ^ "datatype"));
815 val datatyp = define_datatype (K I) (K I) (K I);
817 val datatype_cmd = define_datatype Typedecl.read_constraint Syntax.parse_typ Syntax.read_term;
819 val parse_binding_colon = Parse.binding --| @{keyword ":"};
820 val parse_opt_binding_colon = Scan.optional parse_binding_colon no_binding;
823 @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
824 (Parse.typ >> pair no_binding);
827 @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
829 val parse_single_spec =
830 Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
831 (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
832 Scan.repeat parse_ctr_arg -- Scan.optional parse_defaults [] -- Parse.opt_mixfix));
834 val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_single_spec;
836 fun parse_datatype_cmd lfp construct = parse_datatype >> datatype_cmd lfp construct;