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
36 val coinductsN = "coinducts";
37 val coitersN = "coiters";
38 val corecsN = "corecs";
39 val disc_coitersN = "disc_coiters";
40 val disc_corecsN = "disc_corecs";
41 val inductsN = "inducts";
44 val sel_coitersN = "sel_coiters";
45 val sel_corecsN = "sel_corecs";
47 val simp_attrs = @{attributes [simp]};
50 (map #1 xs, map #2 xs, map #3 xs, map #4 xs, map #5 xs, map #6 xs, map #7 xs, map #8 xs,
51 map #9 xs, map #10 xs, map #11 xs);
53 fun strip_map_type (Type (@{type_name fun}, [T as Type _, T'])) = strip_map_type T' |>> cons T
54 | strip_map_type T = ([], T);
56 fun typ_subst inst (T as Type (s, Ts)) =
57 (case AList.lookup (op =) inst T of
58 NONE => Type (s, map (typ_subst inst) Ts)
60 | typ_subst inst T = the_default T (AList.lookup (op =) inst T);
62 fun resort_tfree S (TFree (s, _)) = TFree (s, S);
64 val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
66 fun mk_id T = Const (@{const_name id}, T --> T);
68 fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
69 fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
70 fun mk_uncurried2_fun f xss =
71 mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss);
73 fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v));
75 fun tack z_name (c, v) f =
76 let val z = Free (z_name, mk_sumT (fastype_of v, fastype_of c)) in
77 Term.lambda z (mk_sum_case (Term.lambda v v, Term.lambda c (f $ c)) $ z)
80 fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
82 fun merge_type_arg T T' = if T = T' then T else cannot_merge_types ();
84 fun merge_type_args (As, As') =
85 if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types ();
87 fun type_args_constrained_of (((cAs, _), _), _) = cAs;
88 fun type_binding_of (((_, b), _), _) = b;
89 fun mixfix_of ((_, mx), _) = mx;
90 fun ctr_specs_of (_, ctr_specs) = ctr_specs;
92 fun disc_of ((((disc, _), _), _), _) = disc;
93 fun ctr_of ((((_, ctr), _), _), _) = ctr;
94 fun args_of (((_, args), _), _) = args;
95 fun defaults_of ((_, ds), _) = ds;
96 fun ctr_mixfix_of (_, mx) = mx;
98 fun define_datatype prepare_constraint prepare_typ prepare_term lfp construct (no_dests, specs)
101 (* TODO: sanity checks on arguments *)
103 val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes"
106 val N = length specs;
108 fun prepare_type_arg (ty, c) =
109 let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
110 TFree (s, prepare_constraint no_defs_lthy0 c)
113 val Ass0 = map (map prepare_type_arg o type_args_constrained_of) specs;
114 val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
115 val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
117 val ((Bs, Cs), no_defs_lthy) =
119 |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
123 (* TODO: cleaner handling of fake contexts, without "background_theory" *)
124 (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
125 locale and shadows an existing global type*)
127 Theory.copy #> fold (fn spec => perhaps (try (Sign.add_type no_defs_lthy
128 (type_binding_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
129 val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
132 Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
135 val fp_bs = map type_binding_of specs;
136 val fp_common_name = mk_common_name fp_bs;
138 val fake_Ts = map mk_fake_T fp_bs;
140 val mixfixes = map mixfix_of specs;
142 val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
143 | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
145 val ctr_specss = map ctr_specs_of specs;
147 val disc_bindingss = map (map disc_of) ctr_specss;
149 map2 (fn fp_b => map (Binding.qualify false (Binding.name_of fp_b) o ctr_of))
151 val ctr_argsss = map (map args_of) ctr_specss;
152 val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
154 val sel_bindingsss = map (map (map fst)) ctr_argsss;
155 val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
156 val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
158 val (As :: _) :: fake_ctr_Tsss =
159 burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
161 val _ = (case duplicates (op =) unsorted_As of [] => ()
162 | A :: _ => error ("Duplicate type parameter " ^
163 quote (Syntax.string_of_typ no_defs_lthy A)));
165 val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
166 val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
168 | A' :: _ => error ("Extra type variables on rhs: " ^
169 quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
171 fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) =
172 s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
173 quote (Syntax.string_of_typ fake_lthy T)))
174 | eq_fpT _ _ = false;
176 fun freeze_fp (T as Type (s, Us)) =
177 (case find_index (eq_fpT T) fake_Ts of ~1 => Type (s, map freeze_fp Us) | j => nth Bs j)
180 val ctr_TsssBs = map (map (map freeze_fp)) fake_ctr_Tsss;
181 val ctr_sum_prod_TsBs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssBs;
184 map dest_TFree Bs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsBs;
186 val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, fp_induct, unf_flds, fld_unfs, fld_injects,
187 fp_iter_thms, fp_rec_thms), lthy)) =
188 fp_bnf construct fp_bs mixfixes (map dest_TFree unsorted_As) fp_eqs no_defs_lthy0;
190 val add_nested_bnf_names =
192 fun add (Type (s, Ts)) ss =
193 let val (needs, ss') = fold_map add Ts ss in
194 if exists I needs then (true, insert (op =) s ss') else (false, ss')
196 | add T ss = (member (op =) As T, ss);
200 map_filter (bnf_of lthy) (fold (fold (fold add_nested_bnf_names)) ctr_TsssBs []);
202 val timer = time (Timer.startRealTimer ());
204 fun mk_unf_or_fld get_T Ts t =
205 let val Type (_, Ts0) = get_T (fastype_of t) in
206 Term.subst_atomic_types (Ts0 ~~ Ts) t
209 val mk_unf = mk_unf_or_fld domain_type;
210 val mk_fld = mk_unf_or_fld range_type;
212 val unfs = map (mk_unf As) unfs0;
213 val flds = map (mk_fld As) flds0;
215 val fpTs = map (domain_type o fastype_of) unfs;
217 val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Bs ~~ fpTs)))) ctr_TsssBs;
218 val ns = map length ctr_Tsss;
219 val kss = map (fn n => 1 upto n) ns;
220 val mss = map (map length) ctr_Tsss;
221 val Css = map2 replicate ns Cs;
223 fun mk_iter_like Ts Us t =
225 val (bindings, body) = strip_type (fastype_of t);
226 val (f_Us, prebody) = split_last bindings;
227 val Type (_, Ts0) = if lfp then prebody else body;
228 val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
230 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
233 val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
234 val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
236 val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
237 val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
239 val ((iter_only as (gss, _, _), rec_only as (hss, _, _)),
240 (zs, cs, cpss, coiter_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))) =
244 map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
245 ns mss fp_iter_fun_Ts;
246 val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
248 val ((gss, ysss), _) =
250 |> mk_Freess "f" g_Tss
251 ||>> mk_Freesss "x" y_Tsss;
252 val yssss = map (map (map single)) ysss;
254 fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) =
255 if member (op =) Cs U then Us else [T]
256 | dest_rec_prodT T = [T];
259 map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o
260 dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts;
261 val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
263 val hss = map2 (map2 retype_free) h_Tss gss;
264 val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
267 |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
268 val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
270 (((gss, g_Tss, yssss), (hss, h_Tss, zssss)),
271 ([], [], [], (([], []), ([], [])), (([], []), ([], []))))
275 (*avoid "'a itself" arguments in coiterators and corecursors*)
276 val mss' = map (fn [0] => [1] | ms => ms) mss;
278 val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_predT) ns Cs;
280 fun zip_predss_getterss qss fss = maps (op @) (qss ~~ fss);
282 fun zip_preds_predsss_gettersss [] [qss] [fss] = zip_predss_getterss qss fss
283 | zip_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
284 p :: zip_predss_getterss qss fss @ zip_preds_predsss_gettersss ps qsss fsss;
286 fun mk_types maybe_dest_sumT fun_Ts =
288 val f_sum_prod_Ts = map range_type fun_Ts;
289 val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
291 map3 (fn C => map2 (map (map (curry (op -->) C) o maybe_dest_sumT) oo dest_tupleT))
294 map (map (map (fn [_] => [] | [_, C] => [mk_predT (domain_type C)]))) f_Tssss;
295 val pf_Tss = map3 zip_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
296 in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end;
298 val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_iter_fun_Ts;
300 val ((((Free (z, _), cs), pss), gssss), _) =
302 |> yield_singleton (mk_Frees "z") dummyT
304 ||>> mk_Freess "p" p_Tss
305 ||>> mk_Freessss "g" g_Tssss;
306 val rssss = map (map (map (fn [] => []))) r_Tssss;
308 fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) =
309 if member (op =) Cs U then Us else [T]
310 | dest_corec_sumT T = [T];
312 val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts;
314 val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
315 val ((sssss, hssss_tl), _) =
317 |> mk_Freessss "q" s_Tssss
318 ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
319 val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
321 val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
323 fun mk_preds_getters_join [] [cf] = cf
324 | mk_preds_getters_join [cq] [cf, cf'] =
325 mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf');
327 fun mk_terms qssss fssss =
329 val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss;
330 val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss;
331 val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss;
332 val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss;
333 in (pfss, cqfsss) end;
335 ((([], [], []), ([], [], [])),
336 ([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)),
337 (mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss))))
340 fun define_ctrs_case_for_type ((((((((((((((((((fp_b, fpT), C), fld), unf), fp_iter), fp_rec),
341 fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_bindings), ctr_mixfixes), ctr_Tss),
342 disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
344 val unfT = domain_type (fastype_of fld);
345 val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
346 val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
347 val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
349 val ((((u, v), fs), xss), _) =
351 |> yield_singleton (mk_Frees "u") unfT
352 ||>> yield_singleton (mk_Frees "v") fpT
353 ||>> mk_Frees "f" case_Ts
354 ||>> mk_Freess "x" ctr_Tss;
357 map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $
358 mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
360 val case_binding = Binding.suffix_name ("_" ^ caseN) fp_b;
363 fold_rev Term.lambda (fs @ [v])
364 (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v));
366 val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
367 |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
368 Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
369 (case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
370 ||> `Local_Theory.restore;
372 val phi = Proof_Context.export_morphism lthy lthy';
374 val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
375 val case_def = Morphism.thm phi raw_case_def;
377 val ctrs0 = map (Morphism.term phi) raw_ctrs;
378 val casex0 = Morphism.term phi raw_case;
380 val ctrs = map (mk_ctr As) ctrs0;
382 fun exhaust_tac {context = ctxt, ...} =
384 val fld_iff_unf_thm =
387 fold_rev Logic.all [u, v]
388 (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
390 Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
391 mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
392 (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
393 |> Thm.close_derivation
398 Local_Defs.unfold lthy @{thms all_unit_eq}
399 (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
400 (mk_sumEN_balanced n))
403 mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
407 map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
408 mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
410 val half_distinct_tacss =
411 map (map (fn (def, def') => fn {context = ctxt, ...} =>
412 mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
415 map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
416 mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
418 val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
420 fun define_iter_rec ((selss0, discIs, sel_thmss), no_defs_lthy) =
422 val fpT_to_C = fpT --> C;
424 fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
426 val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
427 val binding = Binding.suffix_name ("_" ^ suf) fp_b;
429 mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
430 Term.list_comb (fp_iter_like,
431 map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
432 in (binding, spec) end;
434 val iter_like_infos =
435 [(iterN, fp_iter, iter_only),
436 (recN, fp_rec, rec_only)];
438 val (bindings, specs) = map generate_iter_like iter_like_infos |> split_list;
440 val ((csts, defs), (lthy', lthy)) = no_defs_lthy
441 |> apfst split_list o fold_map2 (fn b => fn spec =>
442 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
443 #>> apsnd snd) bindings specs
444 ||> `Local_Theory.restore;
446 val phi = Proof_Context.export_morphism lthy lthy';
448 val [iter_def, rec_def] = map (Morphism.thm phi) defs;
450 val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
452 ((ctrs, selss0, iter, recx, v, xss, ctr_defs, discIs, sel_thmss, iter_def, rec_def),
456 fun define_coiter_corec ((selss0, discIs, sel_thmss), no_defs_lthy) =
458 val B_to_fpT = C --> fpT;
460 fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
461 Term.lambda c (mk_IfN sum_prod_T cps
462 (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
464 fun generate_coiter_like (suf, fp_iter_like, ((pfss, cqfsss), (f_sum_prod_Ts,
467 val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
468 val binding = Binding.suffix_name ("_" ^ suf) fp_b;
470 mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, 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 (binding, spec) end;
475 val coiter_like_infos =
476 [(coiterN, fp_iter, coiter_only),
477 (corecN, fp_rec, corec_only)];
479 val (bindings, 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) bindings 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_bindings, (sel_bindingss,
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_induct_iter_rec_thms_for_types ((ctrss, _, iters, recs, vs, xsss, ctr_defss, _, _,
525 iter_defs, rec_defs), lthy) =
527 val (induct_thms, induct_thm) =
529 val induct_thm = fp_induct;
531 `(conj_dests N) induct_thm
534 val (iter_thmss, rec_thmss) =
536 val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
537 val giters = map (lists_bmoc gss) iters;
538 val hrecs = map (lists_bmoc hss) recs;
540 fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
541 fold_rev (fold_rev Logic.all) (xs :: fss)
542 (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
544 fun build_call fiter_likes maybe_tick (T, U) =
548 (case find_index (curry (op =) T) fpTs of
549 ~1 => build_map (build_call fiter_likes maybe_tick) T U
550 | j => maybe_tick (nth vs j) (nth fiter_likes j));
552 fun mk_U maybe_mk_prodT =
553 typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
555 fun repair_calls fiter_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) =
556 if member (op =) fpTs T then
557 maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
558 else if exists_subtype (member (op =) fpTs) T then
559 [build_call fiter_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x]
563 val gxsss = map (map (maps (repair_calls giters (K I) (K I) (K I)))) xsss;
565 map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
567 val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
568 val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
571 map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss;
573 map2 (map o mk_iter_like_tac pre_map_defs map_ids rec_defs) fp_rec_thms ctr_defss;
575 (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
576 goal_iterss iter_tacss,
577 map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
578 goal_recss rec_tacss)
582 [(inductN, [induct_thm], []), (*### attribs *)
583 (inductsN, induct_thms, [])] (*### attribs *)
584 |> map (fn (thmN, thms, attrs) =>
585 ((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
588 [(itersN, iter_thmss, simp_attrs),
589 (recsN, rec_thmss, Code.add_default_eqn_attrib :: simp_attrs)]
590 |> maps (fn (thmN, thmss, attrs) =>
591 map2 (fn b => fn thms =>
592 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
593 [(thms, [])])) fp_bs thmss);
595 lthy |> Local_Theory.notes (common_notes @ notes) |> snd
598 fun derive_coinduct_coiter_corec_thms_for_types ((ctrss, selsss, coiters, corecs, vs, _,
599 ctr_defss, discIss, sel_thmsss, coiter_defs, corec_defs), lthy) =
601 val (coinduct_thms, coinduct_thm) =
603 val coinduct_thm = fp_induct;
605 `(conj_dests N) coinduct_thm
608 val (coiter_thmss, corec_thmss) =
610 val z = the_single zs;
611 val gcoiters = map (lists_bmoc pgss) coiters;
612 val hcorecs = map (lists_bmoc phss) corecs;
614 fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
616 fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' =
617 fold_rev (fold_rev Logic.all) ([c] :: pfss)
618 (Logic.list_implies (seq_conds mk_goal_cond n k cps,
619 mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
621 fun build_call fiter_likes maybe_tack (T, U) =
625 (case find_index (curry (op =) U) fpTs of
626 ~1 => build_map (build_call fiter_likes maybe_tack) T U
627 | j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
629 fun mk_U maybe_mk_sumT =
630 typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
632 fun repair_calls fiter_likes maybe_mk_sumT maybe_tack cqf =
633 let val T = fastype_of cqf in
634 if exists_subtype (member (op =) Cs) T then
635 build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf
640 val crgsss' = map (map (map (repair_calls gcoiters (K I) (K I)))) crgsss;
641 val cshsss' = map (map (map (repair_calls hcorecs (curry mk_sumT) (tack z)))) cshsss;
644 map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss crgsss';
646 map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss cshsss';
649 map3 (map oo mk_coiter_like_tac coiter_defs map_ids) fp_iter_thms pre_map_defs
652 map3 (map oo mk_coiter_like_tac corec_defs map_ids) fp_rec_thms pre_map_defs
655 (map2 (map2 (fn goal => fn tac =>
656 Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
657 goal_coiterss coiter_tacss,
658 map2 (map2 (fn goal => fn tac =>
659 Skip_Proof.prove lthy [] [] goal (tac o #context)
660 |> Local_Defs.unfold lthy @{thms sum_case_if} |> Thm.close_derivation))
661 goal_corecss corec_tacss)
664 fun mk_disc_coiter_like_thms [_] = K []
665 | mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms;
667 val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss;
668 val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss;
670 fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm =
672 val (domT, ranT) = dest_funT (fastype_of sel0);
674 Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
675 [NONE, NONE, SOME (certify lthy sel0)] arg_cong
676 |> Thm.varifyT_global;
677 val sel_thm' = sel_thm RSN (2, trans);
679 coiter_like_thm RS arg_cong' RS sel_thm'
682 val sel_coiter_thmsss =
683 map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss;
684 val sel_corec_thmsss =
685 map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss;
688 [(coitersN, coiter_thmss, []),
689 (disc_coitersN, disc_coiter_thmss, []),
690 (sel_coitersN, map flat sel_coiter_thmsss, []),
691 (corecsN, corec_thmss, []),
692 (disc_corecsN, disc_corec_thmss, []),
693 (sel_corecsN, map flat sel_corec_thmsss, [])]
694 |> maps (fn (thmN, thmss, attrs) =>
695 map_filter (fn (_, []) => NONE | (b, thms) =>
696 SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
697 [(thms, [])])) (fp_bs ~~ thmss));
699 lthy |> Local_Theory.notes notes |> snd
702 fun wrap_types_and_define_iter_likes ((wraps, define_iter_likess), lthy) =
703 fold_map2 (curry (op o)) define_iter_likess wraps lthy |>> split_list11
706 |> fold_map define_ctrs_case_for_type (fp_bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
707 fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_bindingss ~~
708 ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~ raw_sel_defaultsss)
709 |>> split_list |> wrap_types_and_define_iter_likes
710 |> (if lfp then derive_induct_iter_rec_thms_for_types
711 else derive_coinduct_coiter_corec_thms_for_types);
713 val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
714 (if lfp then "" else "co") ^ "datatype"));
719 val datatyp = define_datatype (K I) (K I) (K I);
721 val datatype_cmd = define_datatype Typedecl.read_constraint Syntax.parse_typ Syntax.read_term;
723 val parse_binding_colon = Parse.binding --| @{keyword ":"};
724 val parse_opt_binding_colon = Scan.optional parse_binding_colon no_binding;
727 @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
728 (Parse.typ >> pair no_binding);
731 @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
733 val parse_single_spec =
734 Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
735 (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
736 Scan.repeat parse_ctr_arg -- Scan.optional parse_defaults [] -- Parse.opt_mixfix));
738 val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_single_spec;
740 fun parse_datatype_cmd lfp construct = parse_datatype >> datatype_cmd lfp construct;