1 (* Title: HOL/BNF/Tools/bnf_fp_def_sugar.ML
2 Author: Jasmin Blanchette, TU Muenchen
5 Sugared datatype and codatatype constructions.
8 signature BNF_FP_DEF_SUGAR =
12 fp: BNF_FP_Util.fp_kind,
14 pre_bnfs: BNF_Def.bnf list,
15 nested_bnfs: BNF_Def.bnf list,
16 nesting_bnfs: BNF_Def.bnf list,
17 fp_res: BNF_FP_Util.fp_result,
18 ctr_defss: thm list list,
19 ctr_sugars: BNF_Ctr_Sugar.ctr_sugar list,
20 co_iterss: term list list,
23 co_iter_thmsss: thm list list list,
24 disc_co_itersss: thm list list list,
25 sel_co_iterssss: thm list list list list};
27 val of_fp_sugar: (fp_sugar -> 'a list) -> fp_sugar -> 'a
28 val morph_fp_sugar: morphism -> fp_sugar -> fp_sugar
29 val fp_sugar_of: Proof.context -> string -> fp_sugar option
31 val co_induct_of: 'a list -> 'a
32 val strong_co_induct_of: 'a list -> 'a
34 val tvar_subst: theory -> typ list -> typ list -> ((string * int) * typ) list
35 val exists_subtype_in: typ list -> typ -> bool
36 val flat_rec_arg_args: 'a list list -> 'a list
37 val flat_corec_preds_predsss_gettersss: 'a list -> 'a list list list -> 'a list list list ->
39 val mk_co_iter: theory -> BNF_FP_Util.fp_kind -> typ -> typ list -> term -> term
40 val nesty_bnfs: Proof.context -> typ list list list -> typ list -> BNF_Def.bnf list
41 val mk_map: int -> typ list -> typ list -> term -> term
42 val mk_rel: int -> typ list -> typ list -> term -> term
43 val build_map: local_theory -> (typ * typ -> term) -> typ * typ -> term
44 val build_rel: local_theory -> (typ * typ -> term) -> typ * typ -> term
45 val dest_map: Proof.context -> string -> term -> term * term list
46 val dest_ctr: Proof.context -> string -> term -> term * term list
47 val mk_co_iters_prelims: BNF_FP_Util.fp_kind -> typ list list list -> typ list -> typ list ->
48 int list -> int list list -> term list list -> Proof.context ->
50 * (typ list list * typ list list list list * term list list
51 * term list list list list) list option
52 * (string * term list * term list list
53 * ((term list list * term list list list) * (typ list * typ list list)) list) option)
56 val mk_iter_fun_arg_types: typ list list list -> int list -> int list list -> term ->
57 typ list list list list
58 val mk_coiter_fun_arg_types: typ list list list -> typ list -> int list -> term ->
60 * (typ list list list list * typ list list list * typ list list list list * typ list)
61 val define_iters: string list ->
62 (typ list list * typ list list list list * term list list * term list list list list) list ->
63 (string -> binding) -> typ list -> typ list -> term list -> Proof.context ->
64 (term list * thm list) * Proof.context
65 val define_coiters: string list -> string * term list * term list list
66 * ((term list list * term list list list) * (typ list * typ list list)) list ->
67 (string -> binding) -> typ list -> typ list -> term list -> Proof.context ->
68 (term list * thm list) * Proof.context
69 val derive_induct_iters_thms_for_types: BNF_Def.bnf list ->
70 (typ list list * typ list list list list * term list list * term list list list list) list ->
71 thm -> thm list list -> BNF_Def.bnf list -> BNF_Def.bnf list -> typ list -> typ list ->
72 typ list -> typ list list list -> term list list -> thm list list -> term list list ->
73 thm list list -> local_theory ->
74 (thm list * thm * Args.src list) * (thm list list * Args.src list)
75 * (thm list list * Args.src list)
76 val derive_coinduct_coiters_thms_for_types: BNF_Def.bnf list ->
77 string * term list * term list list * ((term list list * term list list list)
78 * (typ list * typ list list)) list ->
79 thm -> thm list -> thm list -> thm list list -> BNF_Def.bnf list -> typ list -> typ list ->
80 int list list -> int list list -> int list -> thm list list -> BNF_Ctr_Sugar.ctr_sugar list ->
81 term list list -> thm list list -> (thm list -> thm list) -> local_theory ->
82 ((thm list * thm) list * Args.src list)
83 * (thm list list * thm list list * Args.src list)
84 * (thm list list * thm list list) * (thm list list * thm list list * Args.src list)
85 * (thm list list * thm list list * Args.src list)
86 * (thm list list list * thm list list list * Args.src list)
88 val co_datatypes: BNF_FP_Util.fp_kind -> (mixfix list -> binding list -> binding list ->
89 binding list list -> binding list -> (string * sort) list -> typ list * typ list list ->
90 BNF_Def.bnf list -> local_theory -> BNF_FP_Util.fp_result * local_theory) ->
91 (bool * bool) * (((((binding * (typ * sort)) list * binding) * (binding * binding)) * mixfix) *
92 ((((binding * binding) * (binding * typ) list) * (binding * term) list) *
94 local_theory -> local_theory
95 val parse_co_datatype_cmd: BNF_FP_Util.fp_kind -> (mixfix list -> binding list -> binding list ->
96 binding list list -> binding list -> (string * sort) list -> typ list * typ list list ->
97 BNF_Def.bnf list -> local_theory -> BNF_FP_Util.fp_result * local_theory) ->
98 (local_theory -> local_theory) parser
101 structure BNF_FP_Def_Sugar : BNF_FP_DEF_SUGAR =
109 open BNF_FP_Def_Sugar_Tactics
118 nested_bnfs: bnf list,
119 nesting_bnfs: bnf list,
121 ctr_defss: thm list list,
122 ctr_sugars: ctr_sugar list,
123 co_iterss: term list list,
124 mapss: thm list list,
125 co_inducts: thm list,
126 co_iter_thmsss: thm list list list,
127 disc_co_itersss: thm list list list,
128 sel_co_iterssss: thm list list list list};
130 fun of_fp_sugar f (fp_sugar as {index, ...}) = nth (f fp_sugar) index;
132 fun eq_fp_sugar ({T = T1, fp = fp1, index = index1, fp_res = fp_res1, ...} : fp_sugar,
133 {T = T2, fp = fp2, index = index2, fp_res = fp_res2, ...} : fp_sugar) =
134 T1 = T2 andalso fp1 = fp2 andalso index1 = index2 andalso eq_fp_result (fp_res1, fp_res2);
136 fun morph_fp_sugar phi {T, fp, index, pre_bnfs, nested_bnfs, nesting_bnfs, fp_res, ctr_defss,
137 ctr_sugars, co_iterss, mapss, co_inducts, co_iter_thmsss, disc_co_itersss, sel_co_iterssss} =
138 {T = Morphism.typ phi T, fp = fp, index = index, pre_bnfs = map (morph_bnf phi) pre_bnfs,
139 nested_bnfs = map (morph_bnf phi) nested_bnfs, nesting_bnfs = map (morph_bnf phi) nesting_bnfs,
140 fp_res = morph_fp_result phi fp_res,
141 ctr_defss = map (map (Morphism.thm phi)) ctr_defss,
142 ctr_sugars = map (morph_ctr_sugar phi) ctr_sugars,
143 co_iterss = map (map (Morphism.term phi)) co_iterss,
144 mapss = map (map (Morphism.thm phi)) mapss,
145 co_inducts = map (Morphism.thm phi) co_inducts,
146 co_iter_thmsss = map (map (map (Morphism.thm phi))) co_iter_thmsss,
147 disc_co_itersss = map (map (map (Morphism.thm phi))) disc_co_itersss,
148 sel_co_iterssss = map (map (map (map (Morphism.thm phi)))) sel_co_iterssss};
150 structure Data = Generic_Data
152 type T = fp_sugar Symtab.table;
153 val empty = Symtab.empty;
155 val merge = Symtab.merge eq_fp_sugar;
158 fun fp_sugar_of ctxt =
159 Symtab.lookup (Data.get (Context.Proof ctxt))
160 #> Option.map (morph_fp_sugar
161 (Morphism.thm_morphism (Thm.transfer (Proof_Context.theory_of ctxt))));
163 fun co_induct_of (i :: _) = i;
164 fun strong_co_induct_of [_, s] = s;
166 (* TODO: register "sum" and "prod" as datatypes to enable N2M reduction for them *)
168 fun register_fp_sugar key fp_sugar =
169 Local_Theory.declaration {syntax = false, pervasive = true}
170 (fn phi => Data.map (Symtab.default (key, morph_fp_sugar phi fp_sugar)));
172 fun register_fp_sugars fp pre_bnfs nested_bnfs nesting_bnfs (fp_res as {Ts, ...}) ctr_defss
173 ctr_sugars co_iterss mapss co_inducts co_iter_thmsss disc_co_itersss sel_co_iterssss lthy =
175 |> fold (fn T as Type (s, _) => fn (kk, lthy) => (kk + 1,
176 register_fp_sugar s {T = T, fp = fp, index = kk, pre_bnfs = pre_bnfs,
177 nested_bnfs = nested_bnfs, nesting_bnfs = nesting_bnfs, fp_res = fp_res,
178 ctr_defss = ctr_defss, ctr_sugars = ctr_sugars, co_iterss = co_iterss, mapss = mapss,
179 co_inducts = co_inducts, co_iter_thmsss = co_iter_thmsss, disc_co_itersss = disc_co_itersss,
180 sel_co_iterssss = sel_co_iterssss}
184 (* This function could produce clashes in contrived examples (e.g., "x.A", "x.x_A", "y.A"). *)
185 fun quasi_unambiguous_case_names names =
187 val ps = map (`Long_Name.base_name) names;
188 val dups = Library.duplicates (op =) (map fst ps);
190 let val ss = space_explode Long_Name.separator s in
191 space_implode "_" (drop (length ss - 2) ss)
194 map (fn (base, full) => if member (op =) dups base then underscore full else base) ps
197 val id_def = @{thm id_def};
198 val mp_conj = @{thm mp_conj};
200 val simp_attrs = @{attributes [simp]};
201 val code_simp_attrs = Code.add_default_eqn_attrib :: simp_attrs;
203 fun tvar_subst thy Ts Us =
204 Vartab.fold (cons o apsnd snd) (fold (Sign.typ_match thy) (Ts ~~ Us) Vartab.empty) [];
206 val exists_subtype_in = Term.exists_subtype o member (op =);
208 val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
210 fun flat_rec_arg_args xss =
211 (* FIXME (once the old datatype package is phased out): The first line below gives the preferred
212 order. The second line is for compatibility with the old datatype package. *)
216 map hd xss @ maps tl xss;
218 fun flat_corec_predss_getterss qss fss = maps (op @) (qss ~~ fss);
220 fun flat_corec_preds_predsss_gettersss [] [qss] [fss] = flat_corec_predss_getterss qss fss
221 | flat_corec_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
222 p :: flat_corec_predss_getterss qss fss @ flat_corec_preds_predsss_gettersss ps qsss fsss;
224 fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
225 fun mk_uncurried2_fun f xss =
226 mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat_rec_arg_args xss);
228 fun mk_flip (x, Type (_, [T1, Type (_, [T2, T3])])) =
229 Abs ("x", T1, Abs ("y", T2, Var (x, T2 --> T1 --> T3) $ Bound 0 $ Bound 1));
231 fun flip_rels lthy n thm =
233 val Rs = Term.add_vars (prop_of thm) [];
234 val Rs' = rev (drop (length Rs - n) Rs);
235 val cRs = map (fn f => (certify lthy (Var f), certify lthy (mk_flip f))) Rs';
237 Drule.cterm_instantiate cRs thm
240 fun mk_ctor_or_dtor get_T Ts t =
241 let val Type (_, Ts0) = get_T (fastype_of t) in
242 Term.subst_atomic_types (Ts0 ~~ Ts) t
245 val mk_ctor = mk_ctor_or_dtor range_type;
246 val mk_dtor = mk_ctor_or_dtor domain_type;
248 fun mk_co_iter thy fp fpT Cs t =
250 val (f_Cs, Type (_, [prebody, body])) = strip_fun_type (fastype_of t);
251 val fpT0 = fp_case fp prebody body;
252 val Cs0 = distinct (op =) (map (fp_case fp body_type domain_type) f_Cs);
253 val rho = tvar_subst thy (fpT0 :: Cs0) (fpT :: Cs);
255 Term.subst_TVars rho t
258 fun mk_co_iters thy fp fpTs Cs ts0 =
260 val nn = length fpTs;
262 map ((fp = Greatest_FP ? swap) o dest_funT o snd o strip_typeN nn o fastype_of) ts0
264 val rho = tvar_subst thy (fpTs0 @ Cs0) (fpTs @ Cs);
266 map (Term.subst_TVars rho) ts0
269 val mk_fp_iter_fun_types = binder_fun_types o fastype_of;
271 fun unzip_recT (Type (@{type_name prod}, _)) T = [T]
272 | unzip_recT _ (T as Type (@{type_name prod}, Ts)) = Ts
273 | unzip_recT _ T = [T];
275 fun unzip_corecT (Type (@{type_name sum}, _)) T = [T]
276 | unzip_corecT _ (T as Type (@{type_name sum}, Ts)) = Ts
277 | unzip_corecT _ T = [T];
279 fun mk_map live Ts Us t =
280 let val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) |>> List.last in
281 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
284 fun mk_rel live Ts Us t =
285 let val [Type (_, Ts0), Type (_, Us0)] = binder_types (snd (strip_typeN live (fastype_of t))) in
286 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
291 fun build_map_or_rel mk const of_bnf dest lthy build_simple =
293 fun build (TU as (T, U)) =
298 (Type (s, Ts), Type (s', Us)) =>
301 val bnf = the (bnf_of lthy s);
302 val live = live_of_bnf bnf;
303 val mapx = mk live Ts Us (of_bnf bnf);
304 val TUs' = map dest (fst (strip_typeN live (fastype_of mapx)));
305 in Term.list_comb (mapx, map build TUs') end
308 | _ => build_simple TU);
313 val build_map = build_map_or_rel mk_map HOLogic.id_const map_of_bnf dest_funT;
314 val build_rel = build_map_or_rel mk_rel HOLogic.eq_const rel_of_bnf dest_pred2T;
318 fun fo_match ctxt t pat =
319 let val thy = Proof_Context.theory_of ctxt in
320 Pattern.first_order_match thy (pat, t) (Vartab.empty, Vartab.empty)
323 val dummy_var_name = "?f"
325 fun mk_map_pattern ctxt s =
327 val bnf = the (bnf_of ctxt s);
328 val mapx = map_of_bnf bnf;
329 val live = live_of_bnf bnf;
330 val (f_Ts, _) = strip_typeN live (fastype_of mapx);
331 val fs = map_index (fn (i, T) => Var ((dummy_var_name, i), T)) f_Ts;
333 (mapx, betapplys (mapx, fs))
336 fun dest_map ctxt s call =
338 val (map0, pat) = mk_map_pattern ctxt s;
339 val (_, tenv) = fo_match ctxt call pat;
341 (map0, Vartab.fold_rev (fn (_, (_, f)) => cons f) tenv [])
344 fun dest_ctr ctxt s t =
346 val (f, args) = Term.strip_comb t;
348 (case fp_sugar_of ctxt s of
350 (case find_first (can (fo_match ctxt f)) (#ctrs (of_fp_sugar #ctr_sugars fp_sugar)) of
351 SOME f' => (f', args)
352 | NONE => raise Fail "dest_ctr")
353 | NONE => raise Fail "dest_ctr")
356 fun liveness_of_fp_bnf n bnf =
357 (case T_of_bnf bnf of
358 Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts
359 | _ => replicate n false);
361 fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
363 fun merge_type_arg T T' = if T = T' then T else cannot_merge_types ();
365 fun merge_type_args (As, As') =
366 if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types ();
368 fun reassoc_conjs thm =
369 reassoc_conjs (thm RS @{thm conj_assoc[THEN iffD1]})
372 fun type_args_named_constrained_of ((((ncAs, _), _), _), _) = ncAs;
373 fun type_binding_of ((((_, b), _), _), _) = b;
374 fun map_binding_of (((_, (b, _)), _), _) = b;
375 fun rel_binding_of (((_, (_, b)), _), _) = b;
376 fun mixfix_of ((_, mx), _) = mx;
377 fun ctr_specs_of (_, ctr_specs) = ctr_specs;
379 fun disc_of ((((disc, _), _), _), _) = disc;
380 fun ctr_of ((((_, ctr), _), _), _) = ctr;
381 fun args_of (((_, args), _), _) = args;
382 fun defaults_of ((_, ds), _) = ds;
383 fun ctr_mixfix_of (_, mx) = mx;
385 fun add_nesty_bnf_names Us =
387 fun add (Type (s, Ts)) ss =
388 let val (needs, ss') = fold_map add Ts ss in
389 if exists I needs then (true, insert (op =) s ss') else (false, ss')
391 | add T ss = (member (op =) Us T, ss);
394 fun nesty_bnfs ctxt ctr_Tsss Us =
395 map_filter (bnf_of ctxt) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_Tsss []);
397 fun indexify proj xs f p = f (find_index (curry op = (proj p)) xs) p;
399 fun mk_iter_fun_arg_types0 n ms = map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type;
401 fun mk_iter_fun_arg_types ctr_Tsss ns mss =
403 #> map3 mk_iter_fun_arg_types0 ns mss
404 #> map2 (map2 (map2 unzip_recT)) ctr_Tsss;
406 fun mk_iters_args_types ctr_Tsss Cs ns mss ctor_iter_fun_Tss lthy =
408 val Css = map2 replicate ns Cs;
409 val y_Tsss = map3 mk_iter_fun_arg_types0 ns mss (map un_fold_of ctor_iter_fun_Tss);
410 val g_Tss = map2 (fn C => map (fn y_Ts => y_Ts ---> C)) Cs y_Tsss;
412 val ((gss, ysss), lthy) =
414 |> mk_Freess "f" g_Tss
415 ||>> mk_Freesss "x" y_Tsss;
417 val y_Tssss = map (map (map single)) y_Tsss;
418 val yssss = map (map (map single)) ysss;
421 map4 (fn n => fn ms => fn ctr_Tss => fn ctor_iter_fun_Ts =>
422 map3 (fn m => fn ctr_Ts => fn ctor_iter_fun_T =>
423 map2 unzip_recT ctr_Ts (dest_tupleT m ctor_iter_fun_T))
424 ms ctr_Tss (dest_sumTN_balanced n (domain_type (co_rec_of ctor_iter_fun_Ts))))
425 ns mss ctr_Tsss ctor_iter_fun_Tss;
427 val z_Tsss' = map (map flat_rec_arg_args) z_Tssss;
428 val h_Tss = map2 (map2 (curry op --->)) z_Tsss' Css;
430 val hss = map2 (map2 retype_free) h_Tss gss;
431 val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
432 val (zssss_tl, lthy) =
434 |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
435 val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
437 ([(g_Tss, y_Tssss, gss, yssss), (h_Tss, z_Tssss, hss, zssss)], lthy)
440 fun mk_coiter_fun_arg_types0 ctr_Tsss Cs ns fun_Ts =
442 (*avoid "'a itself" arguments in coiterators*)
443 fun repair_arity [[]] = [[@{typ unit}]]
444 | repair_arity Tss = Tss;
446 val ctr_Tsss' = map repair_arity ctr_Tsss;
447 val f_sum_prod_Ts = map range_type fun_Ts;
448 val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
449 val f_Tsss = map2 (map2 (dest_tupleT o length)) ctr_Tsss' f_prod_Tss;
450 val f_Tssss = map3 (fn C => map2 (map2 (map (curry op --> C) oo unzip_corecT)))
452 val q_Tssss = map (map (map (fn [_] => [] | [_, T] => [mk_pred1T (domain_type T)]))) f_Tssss;
454 (q_Tssss, f_Tsss, f_Tssss, f_sum_prod_Ts)
457 fun mk_coiter_p_pred_types Cs ns = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
459 fun mk_coiter_fun_arg_types ctr_Tsss Cs ns dtor_coiter =
460 (mk_coiter_p_pred_types Cs ns,
461 mk_fp_iter_fun_types dtor_coiter |> mk_coiter_fun_arg_types0 ctr_Tsss Cs ns);
463 fun mk_coiters_args_types ctr_Tsss Cs ns mss dtor_coiter_fun_Tss lthy =
465 val p_Tss = mk_coiter_p_pred_types Cs ns;
467 fun mk_types get_Ts =
469 val fun_Ts = map get_Ts dtor_coiter_fun_Tss;
470 val (q_Tssss, f_Tsss, f_Tssss, f_sum_prod_Ts) = mk_coiter_fun_arg_types0 ctr_Tsss Cs ns fun_Ts;
471 val pf_Tss = map3 flat_corec_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
473 (q_Tssss, f_Tsss, f_Tssss, (f_sum_prod_Ts, pf_Tss))
476 val (r_Tssss, g_Tsss, g_Tssss, unfold_types) = mk_types un_fold_of;
477 val (s_Tssss, h_Tsss, h_Tssss, corec_types) = mk_types co_rec_of;
479 val ((((Free (z, _), cs), pss), gssss), lthy) =
481 |> yield_singleton (mk_Frees "z") dummyT
483 ||>> mk_Freess "p" p_Tss
484 ||>> mk_Freessss "g" g_Tssss;
485 val rssss = map (map (map (fn [] => []))) r_Tssss;
487 val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
488 val ((sssss, hssss_tl), lthy) =
490 |> mk_Freessss "q" s_Tssss
491 ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
492 val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
494 val cpss = map2 (map o rapp) cs pss;
496 fun build_sum_inj mk_inj = build_map lthy (uncurry mk_inj o dest_sumT o snd);
498 fun build_dtor_coiter_arg _ [] [cf] = cf
499 | build_dtor_coiter_arg T [cq] [cf, cf'] =
500 mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf)
501 (build_sum_inj Inr_const (fastype_of cf', T) $ cf');
503 fun mk_args qssss fssss f_Tsss =
505 val pfss = map3 flat_corec_preds_predsss_gettersss pss qssss fssss;
506 val cqssss = map2 (map o map o map o rapp) cs qssss;
507 val cfssss = map2 (map o map o map o rapp) cs fssss;
508 val cqfsss = map3 (map3 (map3 build_dtor_coiter_arg)) f_Tsss cqssss cfssss;
509 in (pfss, cqfsss) end;
511 val unfold_args = mk_args rssss gssss g_Tsss;
512 val corec_args = mk_args sssss hssss h_Tsss;
514 ((z, cs, cpss, [(unfold_args, unfold_types), (corec_args, corec_types)]), lthy)
517 fun mk_co_iters_prelims fp ctr_Tsss fpTs Cs ns mss xtor_co_iterss0 lthy =
519 val thy = Proof_Context.theory_of lthy;
521 val (xtor_co_iter_fun_Tss, xtor_co_iterss) =
522 map (mk_co_iters thy fp fpTs Cs #> `(mk_fp_iter_fun_types o hd)) (transpose xtor_co_iterss0)
523 |> apsnd transpose o apfst transpose o split_list;
525 val ((iters_args_types, coiters_args_types), lthy') =
526 if fp = Least_FP then
527 mk_iters_args_types ctr_Tsss Cs ns mss xtor_co_iter_fun_Tss lthy |>> (rpair NONE o SOME)
529 mk_coiters_args_types ctr_Tsss Cs ns mss xtor_co_iter_fun_Tss lthy |>> (pair NONE o SOME)
531 ((xtor_co_iterss, iters_args_types, coiters_args_types), lthy')
534 fun mk_iter_body ctor_iter fss xssss =
535 Term.list_comb (ctor_iter, map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss);
537 fun mk_preds_getterss_join c cps sum_prod_T cqfss =
538 let val n = length cqfss in
539 Term.lambda c (mk_IfN sum_prod_T cps
540 (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)))
543 fun mk_coiter_body cs cpss f_sum_prod_Ts cqfsss dtor_coiter =
544 Term.list_comb (dtor_coiter, map4 mk_preds_getterss_join cs cpss f_sum_prod_Ts cqfsss);
546 fun define_co_iters fp fpT Cs binding_specs lthy0 =
548 val thy = Proof_Context.theory_of lthy0;
550 val maybe_conceal_def_binding = Thm.def_binding
551 #> Config.get lthy0 bnf_note_all = false ? Binding.conceal;
553 val ((csts, defs), (lthy', lthy)) = lthy0
554 |> apfst split_list o fold_map (fn (b, spec) =>
555 Specification.definition (SOME (b, NONE, NoSyn), ((maybe_conceal_def_binding b, []), spec))
556 #>> apsnd snd) binding_specs
557 ||> `Local_Theory.restore;
559 val phi = Proof_Context.export_morphism lthy lthy';
561 val csts' = map (mk_co_iter thy fp fpT Cs o Morphism.term phi) csts;
562 val defs' = map (Morphism.thm phi) defs;
564 ((csts', defs'), lthy')
567 fun define_iters iterNs iter_args_typess' mk_binding fpTs Cs ctor_iters lthy =
569 val nn = length fpTs;
571 val fpT_to_C as Type (_, [fpT, _]) = snd (strip_typeN nn (fastype_of (hd ctor_iters)));
573 fun generate_iter suf (f_Tss, _, fss, xssss) ctor_iter =
575 val res_T = fold_rev (curry op --->) f_Tss fpT_to_C;
576 val b = mk_binding suf;
578 mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of b, res_T)),
579 mk_iter_body ctor_iter fss xssss);
582 define_co_iters Least_FP fpT Cs (map3 generate_iter iterNs iter_args_typess' ctor_iters) lthy
585 fun define_coiters coiterNs (_, cs, cpss, coiter_args_typess') mk_binding fpTs Cs dtor_coiters
588 val nn = length fpTs;
590 val C_to_fpT as Type (_, [_, fpT]) = snd (strip_typeN nn (fastype_of (hd dtor_coiters)));
592 fun generate_coiter suf ((pfss, cqfsss), (f_sum_prod_Ts, pf_Tss)) dtor_coiter =
594 val res_T = fold_rev (curry op --->) pf_Tss C_to_fpT;
595 val b = mk_binding suf;
597 mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of b, res_T)),
598 mk_coiter_body cs cpss f_sum_prod_Ts cqfsss dtor_coiter);
601 define_co_iters Greatest_FP fpT Cs
602 (map3 generate_coiter coiterNs coiter_args_typess' dtor_coiters) lthy
605 fun derive_induct_iters_thms_for_types pre_bnfs [fold_args_types, rec_args_types] ctor_induct
606 ctor_iter_thmss nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss ctrss ctr_defss iterss iter_defss
609 val iterss' = transpose iterss;
610 val iter_defss' = transpose iter_defss;
612 val [folds, recs] = iterss';
613 val [fold_defs, rec_defs] = iter_defss';
615 val ctr_Tsss = map (map (binder_types o fastype_of)) ctrss;
617 val nn = length pre_bnfs;
618 val ns = map length ctr_Tsss;
619 val mss = map (map length) ctr_Tsss;
621 val pre_map_defs = map map_def_of_bnf pre_bnfs;
622 val pre_set_defss = map set_defs_of_bnf pre_bnfs;
623 val nesting_map_idents = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nesting_bnfs;
624 val nested_map_idents = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nested_bnfs;
625 val nested_set_maps = maps set_map_of_bnf nested_bnfs;
627 val fp_b_names = map base_name_of_typ fpTs;
629 val ((((ps, ps'), xsss), us'), names_lthy) =
631 |> mk_Frees' "P" (map mk_pred1T fpTs)
632 ||>> mk_Freesss "x" ctr_Tsss
633 ||>> Variable.variant_fixes fp_b_names;
635 val us = map2 (curry Free) us' fpTs;
637 fun mk_sets_nested bnf =
639 val Type (T_name, Us) = T_of_bnf bnf;
640 val lives = lives_of_bnf bnf;
641 val sets = sets_of_bnf bnf;
643 (case find_index (curry op = U) lives of
647 (T_name, map mk_set Us)
650 val setss_nested = map mk_sets_nested nested_bnfs;
652 val (induct_thms, induct_thm) =
655 let val Type (_, Ts0) = domain_type (fastype_of t) in
656 Term.subst_atomic_types (Ts0 ~~ Ts) t
659 fun mk_raw_prem_prems _ (x as Free (_, Type _)) (X as TFree _) =
660 [([], (find_index (curry op = X) Xs + 1, x))]
661 | mk_raw_prem_prems names_lthy (x as Free (s, Type (T_name, Ts0))) (Type (_, Xs_Ts0)) =
662 (case AList.lookup (op =) setss_nested T_name of
666 val (Xs_Ts, (Ts, raw_sets)) =
667 filter (exists_subtype_in Xs o fst) (Xs_Ts0 ~~ (Ts0 ~~ raw_sets0))
668 |> split_list ||> split_list;
669 val sets = map (mk_set Ts0) raw_sets;
670 val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
671 val xysets = map (pair x) (ys ~~ sets);
672 val ppremss = map2 (mk_raw_prem_prems names_lthy') ys Xs_Ts;
674 flat (map2 (map o apfst o cons) xysets ppremss)
676 | mk_raw_prem_prems _ _ _ = [];
678 fun close_prem_prem xs t =
679 fold_rev Logic.all (map Free (drop (nn + length xs)
680 (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
682 fun mk_prem_prem xs (xysets, (j, x)) =
683 close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
684 HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
685 HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
687 fun mk_raw_prem phi ctr ctr_Ts ctrXs_Ts =
689 val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
690 val pprems = flat (map2 (mk_raw_prem_prems names_lthy') xs ctrXs_Ts);
691 in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
693 fun mk_prem (xs, raw_pprems, concl) =
694 fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
696 val raw_premss = map4 (map3 o mk_raw_prem) ps ctrss ctr_Tsss ctrXs_Tsss;
699 Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
700 HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry op $) ps us)));
702 val kksss = map (map (map (fst o snd) o #2)) raw_premss;
704 val ctor_induct' = ctor_induct OF (map mk_sumEN_tupled_balanced mss);
707 Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
708 mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_maps
710 |> singleton (Proof_Context.export names_lthy lthy)
711 |> Thm.close_derivation;
716 val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
717 val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
719 val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
721 fun mk_iter_thmss (_, x_Tssss, fss, _) iters iter_defs ctor_iter_thms =
723 val fiters = map (lists_bmoc fss) iters;
725 fun mk_goal fss fiter xctr f xs fxs =
726 fold_rev (fold_rev Logic.all) (xs :: fss)
727 (mk_Trueprop_eq (fiter $ xctr, Term.list_comb (f, fxs)));
729 fun maybe_tick (T, U) u f =
730 if try (fst o HOLogic.dest_prodT) U = SOME T then
731 Term.lambda u (HOLogic.mk_prod (u, f $ u))
735 fun build_iter (x as Free (_, T)) U =
739 build_map lthy (indexify (perhaps (try (snd o HOLogic.dest_prodT)) o snd) Cs
740 (fn kk => fn TU => maybe_tick TU (nth us kk) (nth fiters kk))) (T, U) $ x;
742 val fxsss = map2 (map2 (flat_rec_arg_args oo map2 (map o build_iter))) xsss x_Tssss;
744 val goalss = map5 (map4 o mk_goal fss) fiters xctrss fss xsss fxsss;
747 map2 (map o mk_iter_tac pre_map_defs (nested_map_idents @ nesting_map_idents) iter_defs)
748 ctor_iter_thms ctr_defss;
751 Goal.prove_sorry lthy [] [] goal (tac o #context)
752 |> Thm.close_derivation;
754 map2 (map2 prove) goalss tacss
757 val fold_thmss = mk_iter_thmss fold_args_types folds fold_defs (map un_fold_of ctor_iter_thmss);
758 val rec_thmss = mk_iter_thmss rec_args_types recs rec_defs (map co_rec_of ctor_iter_thmss);
760 ((induct_thms, induct_thm, [induct_case_names_attr]),
761 (fold_thmss, code_simp_attrs), (rec_thmss, code_simp_attrs))
764 fun derive_coinduct_coiters_thms_for_types pre_bnfs (z, cs, cpss,
765 coiters_args_types as [((pgss, crgsss), _), ((phss, cshsss), _)])
766 dtor_coinduct dtor_injects dtor_ctors dtor_coiter_thmss nesting_bnfs fpTs Cs kss mss ns
767 ctr_defss ctr_sugars coiterss coiter_defss export_args lthy =
769 fun mk_ctor_dtor_coiter_thm dtor_inject dtor_ctor coiter =
770 iffD1 OF [dtor_inject, trans OF [coiter, dtor_ctor RS sym]];
772 val ctor_dtor_coiter_thmss =
773 map3 (map oo mk_ctor_dtor_coiter_thm) dtor_injects dtor_ctors dtor_coiter_thmss;
775 val coiterss' = transpose coiterss;
776 val coiter_defss' = transpose coiter_defss;
778 val [unfold_defs, corec_defs] = coiter_defss';
780 val nn = length pre_bnfs;
782 val pre_map_defs = map map_def_of_bnf pre_bnfs;
783 val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
784 val nesting_map_idents = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nesting_bnfs;
785 val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
787 val fp_b_names = map base_name_of_typ fpTs;
789 val ctrss = map #ctrs ctr_sugars;
790 val discss = map #discs ctr_sugars;
791 val selsss = map #selss ctr_sugars;
792 val exhausts = map #exhaust ctr_sugars;
793 val disc_thmsss = map #disc_thmss ctr_sugars;
794 val discIss = map #discIs ctr_sugars;
795 val sel_thmsss = map #sel_thmss ctr_sugars;
797 val (((rs, us'), vs'), names_lthy) =
799 |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
800 ||>> Variable.variant_fixes fp_b_names
801 ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
803 val us = map2 (curry Free) us' fpTs;
804 val udiscss = map2 (map o rapp) us discss;
805 val uselsss = map2 (map o map o rapp) us selsss;
807 val vs = map2 (curry Free) vs' fpTs;
808 val vdiscss = map2 (map o rapp) vs discss;
809 val vselsss = map2 (map o map o rapp) vs selsss;
811 val coinduct_thms_pairs =
813 val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
814 val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
816 map4 (fn u => fn v => fn uvr => fn uv_eq =>
817 fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
819 (* TODO: generalize (cf. "build_map") *)
820 fun build_rel rs' T =
821 (case find_index (curry op = T) fpTs of
823 if exists_subtype_in fpTs T then
826 val bnf = the (bnf_of lthy s);
827 val live = live_of_bnf bnf;
828 val rel = mk_rel live Ts Ts (rel_of_bnf bnf);
829 val Ts' = map domain_type (fst (strip_typeN live (fastype_of rel)));
830 in Term.list_comb (rel, map (build_rel rs') Ts') end
835 fun build_rel_app rs' usel vsel = fold rapp [usel, vsel] (build_rel rs' (fastype_of usel));
837 fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels =
838 (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
842 [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
843 Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]);
845 fun mk_prem_concl rs' n udiscs uselss vdiscs vselss =
846 Library.foldr1 HOLogic.mk_conj
847 (flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss))
848 handle List.Empty => @{term True};
850 fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss =
851 fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
852 HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss)));
855 HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
856 (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
860 Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss,
863 val goals = map mk_goal [rs, strong_rs];
865 fun prove dtor_coinduct' goal =
866 Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
867 mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors
868 exhausts ctr_defss disc_thmsss sel_thmsss)
869 |> singleton (Proof_Context.export names_lthy lthy)
870 |> Thm.close_derivation;
872 fun postproc nn thm =
873 Thm.permute_prems 0 nn
874 (if nn = 1 then thm RS mp else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
875 |> Drule.zero_var_indexes
878 val rel_eqs = map rel_eq_of_bnf pre_bnfs;
879 val rel_monos = map rel_mono_of_bnf pre_bnfs;
881 [dtor_coinduct, mk_strong_coinduct_thm dtor_coinduct rel_eqs rel_monos lthy];
883 map2 (postproc nn oo prove) dtor_coinducts goals
886 fun mk_coinduct_concls ms discs ctrs =
888 fun mk_disc_concl disc = [name_of_disc disc];
889 fun mk_ctr_concl 0 _ = []
890 | mk_ctr_concl _ ctor = [name_of_ctr ctor];
891 val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
892 val ctr_concls = map2 mk_ctr_concl ms ctrs;
894 flat (map2 append disc_concls ctr_concls)
897 val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
898 val coinduct_conclss =
899 map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
901 fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
903 val fcoiterss' as [gunfolds, hcorecs] =
904 map2 (fn (pfss, _) => map (lists_bmoc pfss)) (map fst coiters_args_types) coiterss';
906 val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) =
908 fun mk_goal pfss c cps fcoiter n k ctr m cfs' =
909 fold_rev (fold_rev Logic.all) ([c] :: pfss)
910 (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
911 mk_Trueprop_eq (fcoiter $ c, Term.list_comb (ctr, take m cfs'))));
913 fun mk_U maybe_mk_sumT =
914 typ_subst_nonatomic (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
916 fun tack z_name (c, u) f =
917 let val z = Free (z_name, mk_sumT (fastype_of u, fastype_of c)) in
918 Term.lambda z (mk_sum_case (Term.lambda u u, Term.lambda c (f $ c)) $ z)
921 fun build_coiter fcoiters maybe_mk_sumT maybe_tack cqf =
922 let val T = fastype_of cqf in
923 if exists_subtype_in Cs T then
924 let val U = mk_U maybe_mk_sumT T in
925 build_map lthy (indexify snd fpTs (fn kk => fn _ =>
926 maybe_tack (nth cs kk, nth us kk) (nth fcoiters kk))) (T, U) $ cqf
932 val crgsss' = map (map (map (build_coiter (un_fold_of fcoiterss') (K I) (K I)))) crgsss;
933 val cshsss' = map (map (map (build_coiter (co_rec_of fcoiterss') (curry mk_sumT) (tack z))))
936 val unfold_goalss = map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss';
937 val corec_goalss = map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss';
940 map3 (map oo mk_coiter_tac unfold_defs nesting_map_idents)
941 (map un_fold_of ctor_dtor_coiter_thmss) pre_map_defs ctr_defss;
943 map3 (map oo mk_coiter_tac corec_defs nesting_map_idents)
944 (map co_rec_of ctor_dtor_coiter_thmss) pre_map_defs ctr_defss;
947 Goal.prove_sorry lthy [] [] goal (tac o #context)
948 |> Thm.close_derivation;
950 val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
952 map2 (map2 prove) corec_goalss corec_tacss
953 |> map (map (unfold_thms lthy @{thms sum_case_if}));
955 val unfold_safesss = map2 (map2 (map2 (curry op =))) crgsss' crgsss;
956 val corec_safesss = map2 (map2 (map2 (curry op =))) cshsss' cshsss;
959 map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
962 val safe_unfold_thmss = filter_safesss unfold_safesss unfold_thmss;
963 val safe_corec_thmss = filter_safesss corec_safesss corec_thmss;
965 (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss)
968 val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
970 fun mk_goal c cps fcoiter n k disc =
971 mk_Trueprop_eq (disc $ (fcoiter $ c),
972 if n = 1 then @{const True}
973 else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
975 val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss;
976 val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
978 fun mk_case_split' cp = Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
980 val case_splitss' = map (map mk_case_split') cpss;
983 map3 (map oo mk_disc_coiter_iff_tac) case_splitss' unfold_thmss disc_thmsss;
985 map3 (map oo mk_disc_coiter_iff_tac) case_splitss' corec_thmss disc_thmsss;
988 Goal.prove_sorry lthy [] [] goal (tac o #context)
989 |> singleton export_args
990 |> singleton (Proof_Context.export names_lthy lthy)
991 |> Thm.close_derivation;
993 fun proves [_] [_] = []
994 | proves goals tacs = map2 prove goals tacs;
996 (map2 proves unfold_goalss unfold_tacss, map2 proves corec_goalss corec_tacss)
999 val is_triv_discI = is_triv_implies orf is_concl_refl;
1001 fun mk_disc_coiter_thms coiters discIs =
1002 map (op RS) (filter_out (is_triv_discI o snd) (coiters ~~ discIs));
1004 val disc_unfold_thmss = map2 mk_disc_coiter_thms unfold_thmss discIss;
1005 val disc_corec_thmss = map2 mk_disc_coiter_thms corec_thmss discIss;
1007 fun mk_sel_coiter_thm coiter_thm sel sel_thm =
1009 val (domT, ranT) = dest_funT (fastype_of sel);
1011 Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
1012 [NONE, NONE, SOME (certify lthy sel)] arg_cong
1013 |> Thm.varifyT_global;
1014 val sel_thm' = sel_thm RSN (2, trans);
1016 coiter_thm RS arg_cong' RS sel_thm'
1019 fun mk_sel_coiter_thms coiter_thmss =
1020 map3 (map3 (map2 o mk_sel_coiter_thm)) coiter_thmss selsss sel_thmsss;
1022 val sel_unfold_thmsss = mk_sel_coiter_thms unfold_thmss;
1023 val sel_corec_thmsss = mk_sel_coiter_thms corec_thmss;
1025 val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
1026 val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
1027 val coinduct_case_concl_attrs =
1028 map2 (fn casex => fn concls =>
1029 Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
1030 coinduct_cases coinduct_conclss;
1031 val coinduct_case_attrs =
1032 coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
1034 ((coinduct_thms_pairs, coinduct_case_attrs),
1035 (unfold_thmss, corec_thmss, []),
1036 (safe_unfold_thmss, safe_corec_thmss),
1037 (disc_unfold_thmss, disc_corec_thmss, []),
1038 (disc_unfold_iff_thmss, disc_corec_iff_thmss, simp_attrs),
1039 (sel_unfold_thmsss, sel_corec_thmsss, simp_attrs))
1042 fun define_co_datatypes prepare_constraint prepare_typ prepare_term fp construct_fp
1043 (wrap_opts as (no_discs_sels, rep_compat), specs) no_defs_lthy0 =
1045 (* TODO: sanity checks on arguments *)
1047 val _ = if fp = Greatest_FP andalso no_discs_sels then
1048 error "Cannot define codatatypes without discriminators and selectors"
1052 fun qualify mandatory fp_b_name =
1053 Binding.qualify mandatory fp_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
1055 val nn = length specs;
1056 val fp_bs = map type_binding_of specs;
1057 val fp_b_names = map Binding.name_of fp_bs;
1058 val fp_common_name = mk_common_name fp_b_names;
1059 val map_bs = map map_binding_of specs;
1060 val rel_bs = map rel_binding_of specs;
1062 fun prepare_type_arg (_, (ty, c)) =
1063 let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
1064 TFree (s, prepare_constraint no_defs_lthy0 c)
1067 val Ass0 = map (map prepare_type_arg o type_args_named_constrained_of) specs;
1068 val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
1069 val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
1070 val num_As = length unsorted_As;
1071 val set_bss = map (map fst o type_args_named_constrained_of) specs;
1073 val (((Bs0, Cs), Xs), no_defs_lthy) =
1075 |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
1078 ||>> variant_tfrees fp_b_names;
1080 fun add_fake_type spec = Typedecl.basic_typedecl (type_binding_of spec, num_As, mixfix_of spec);
1082 val (fake_T_names, fake_lthy) = fold_map add_fake_type specs no_defs_lthy0;
1084 val qsoty = quote o Syntax.string_of_typ fake_lthy;
1086 val _ = (case duplicates (op =) unsorted_As of [] => ()
1087 | A :: _ => error ("Duplicate type parameter " ^ qsoty A ^ " in " ^ co_prefix fp ^
1088 "datatype specification"));
1091 map (Logic.type_map (singleton (Variable.polymorphic no_defs_lthy0))) unsorted_As
1092 |> filter_out Term.is_TVar;
1093 val _ = null bad_args orelse
1094 error ("Locally fixed type argument " ^ qsoty (hd bad_args) ^ " in " ^ co_prefix fp ^
1095 "datatype specification");
1097 val mixfixes = map mixfix_of specs;
1099 val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
1100 | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
1102 val ctr_specss = map ctr_specs_of specs;
1104 val disc_bindingss = map (map disc_of) ctr_specss;
1106 map2 (fn fp_b_name => map (qualify false fp_b_name o ctr_of)) fp_b_names ctr_specss;
1107 val ctr_argsss = map (map args_of) ctr_specss;
1108 val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
1110 val sel_bindingsss = map (map (map fst)) ctr_argsss;
1111 val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
1112 val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
1114 val (As :: _) :: fake_ctr_Tsss =
1115 burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
1116 val As' = map dest_TFree As;
1118 val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
1119 val _ = (case subtract (op =) As' rhs_As' of [] => ()
1120 | extras => error ("Extra type variables on right-hand side: " ^
1121 commas (map (qsoty o TFree) extras)));
1123 val fake_Ts = map (fn s => Type (s, As)) fake_T_names;
1125 fun eq_fpT_check (T as Type (s, Ts)) (T' as Type (s', Ts')) =
1126 s = s' andalso (Ts = Ts' orelse
1127 error ("Wrong type arguments in " ^ co_prefix fp ^ "recursive type " ^ qsoty T ^
1128 " (expected " ^ qsoty T' ^ ")"))
1129 | eq_fpT_check _ _ = false;
1131 fun freeze_fp (T as Type (s, Ts)) =
1132 (case find_index (eq_fpT_check T) fake_Ts of
1133 ~1 => Type (s, map freeze_fp Ts)
1137 val unfreeze_fp = Term.typ_subst_atomic (Xs ~~ fake_Ts);
1139 val ctrXs_Tsss = map (map (map freeze_fp)) fake_ctr_Tsss;
1140 val ctrXs_sum_prod_Ts = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctrXs_Tsss;
1143 map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctrXs_sum_prod_Ts;
1145 val rhsXs_As' = fold (fold (fold Term.add_tfreesT)) ctrXs_Tsss [];
1146 val _ = (case subtract (op =) rhsXs_As' As' of [] => ()
1147 | extras => List.app (fn extra => warning ("Unused type variable on right-hand side of " ^
1148 co_prefix fp ^ "datatype definition: " ^ qsoty (TFree extra))) extras);
1150 val (pre_bnfs, (fp_res as {bnfs = fp_bnfs as any_fp_bnf :: _, ctors = ctors0, dtors = dtors0,
1151 xtor_co_iterss = xtor_co_iterss0, xtor_co_induct, dtor_ctors, ctor_dtors, ctor_injects,
1152 dtor_injects, xtor_map_thms, xtor_set_thmss, xtor_rel_thms, xtor_co_iter_thmss, ...},
1154 fp_bnf (construct_fp mixfixes map_bs rel_bs set_bss) fp_bs (map dest_TFree unsorted_As) fp_eqs
1156 handle BAD_DEAD (X, X_backdrop) =>
1160 val fake_T = qsoty (unfreeze_fp X);
1161 val fake_T_backdrop = qsoty (unfreeze_fp X_backdrop);
1162 fun register_hint () =
1163 "\nUse the " ^ quote (fst (fst @{command_spec "bnf"})) ^ " command to register " ^
1164 quote bad_tc ^ " as a bounded natural functor to allow nested (co)recursion through \
1167 if is_some (bnf_of no_defs_lthy bad_tc) orelse
1168 is_some (fp_sugar_of no_defs_lthy bad_tc) then
1169 error ("Inadmissible " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
1170 " in type expression " ^ fake_T_backdrop)
1171 else if is_some (Datatype_Data.get_info (Proof_Context.theory_of no_defs_lthy)
1173 error ("Unsupported " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
1174 " via the old-style datatype " ^ quote bad_tc ^ " in type expression " ^
1175 fake_T_backdrop ^ register_hint ())
1177 error ("Unsupported " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
1178 " via type constructor " ^ quote bad_tc ^ " in type expression " ^ fake_T_backdrop ^
1182 val time = time lthy;
1183 val timer = time (Timer.startRealTimer ());
1185 val nesting_bnfs = nesty_bnfs lthy ctrXs_Tsss As;
1186 val nested_bnfs = nesty_bnfs lthy ctrXs_Tsss Xs;
1188 val pre_map_defs = map map_def_of_bnf pre_bnfs;
1189 val pre_set_defss = map set_defs_of_bnf pre_bnfs;
1190 val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
1191 val nesting_set_maps = maps set_map_of_bnf nesting_bnfs;
1192 val nested_set_maps = maps set_map_of_bnf nested_bnfs;
1194 val live = live_of_bnf any_fp_bnf;
1196 if live = 0 andalso exists (not o Binding.is_empty) (map_bs @ rel_bs) then
1197 warning "Map function and relator names ignored"
1202 map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
1203 (liveness_of_fp_bnf num_As any_fp_bnf) As Bs0;
1205 val B_ify = Term.typ_subst_atomic (As ~~ Bs);
1207 val ctors = map (mk_ctor As) ctors0;
1208 val dtors = map (mk_dtor As) dtors0;
1210 val fpTs = map (domain_type o fastype_of) dtors;
1212 fun massage_simple_notes base =
1213 filter_out (null o #2)
1214 #> map (fn (thmN, thms, attrs) =>
1215 ((qualify true base (Binding.name thmN), attrs), [(thms, [])]));
1217 val massage_multi_notes =
1218 maps (fn (thmN, thmss, attrs) =>
1219 if forall null thmss then
1222 map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
1223 ((qualify true fp_b_name (Binding.name thmN), attrs T_name), [(thms, [])]))
1224 fp_b_names fpTs thmss);
1226 val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctrXs_Tsss;
1227 val ns = map length ctr_Tsss;
1228 val kss = map (fn n => 1 upto n) ns;
1229 val mss = map (map length) ctr_Tsss;
1231 val ((xtor_co_iterss, iters_args_types, coiters_args_types), lthy') =
1232 mk_co_iters_prelims fp ctr_Tsss fpTs Cs ns mss xtor_co_iterss0 lthy;
1234 fun define_ctrs_dtrs_for_type (((((((((((((((((((((((fp_bnf, fp_b), fpT), ctor), dtor),
1235 xtor_co_iters), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs),
1236 pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), ctr_bindings),
1237 ctr_mixfixes), ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
1239 val fp_b_name = Binding.name_of fp_b;
1241 val dtorT = domain_type (fastype_of ctor);
1242 val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
1243 val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
1245 val ((((w, xss), yss), u'), names_lthy) =
1247 |> yield_singleton (mk_Frees "w") dtorT
1248 ||>> mk_Freess "x" ctr_Tss
1249 ||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
1250 ||>> yield_singleton Variable.variant_fixes fp_b_name;
1252 val u = Free (u', fpT);
1254 val tuple_xs = map HOLogic.mk_tuple xss;
1255 val tuple_ys = map HOLogic.mk_tuple yss;
1258 map3 (fn k => fn xs => fn tuple_x => fold_rev Term.lambda xs (ctor $
1259 mk_InN_balanced ctr_sum_prod_T n tuple_x k)) ks xss tuple_xs;
1261 val maybe_conceal_def_binding = Thm.def_binding
1262 #> Config.get no_defs_lthy bnf_note_all = false ? Binding.conceal;
1264 val ((raw_ctrs, raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
1265 |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
1266 Local_Theory.define ((b, mx), ((maybe_conceal_def_binding b, []), rhs)) #>> apsnd snd)
1267 ctr_bindings ctr_mixfixes ctr_rhss
1268 ||> `Local_Theory.restore;
1270 val phi = Proof_Context.export_morphism lthy lthy';
1272 val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
1274 map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs;
1276 val ctrs0 = map (Morphism.term phi) raw_ctrs;
1277 val ctrs = map (mk_ctr As) ctrs0;
1279 fun wrap_ctrs lthy =
1281 fun exhaust_tac {context = ctxt, prems = _} =
1283 val ctor_iff_dtor_thm =
1286 fold_rev Logic.all [w, u]
1287 (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
1289 Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
1290 mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT])
1291 (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
1292 |> Thm.close_derivation
1297 unfold_thms lthy @{thms unit_all_eq1}
1298 (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
1299 (mk_sumEN_balanced n))
1300 |> Morphism.thm phi;
1302 mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
1306 map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
1307 mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs;
1309 val half_distinct_tacss =
1310 map (map (fn (def, def') => fn {context = ctxt, ...} =>
1311 mk_half_distinct_tac ctxt ctor_inject [def, def'])) (mk_half_pairss (`I ctr_defs));
1313 val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss;
1315 val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
1317 wrap_free_constructors tacss (((wrap_opts, ctrs0), standard_binding), (disc_bindings,
1318 (sel_bindingss, sel_defaultss))) lthy
1321 fun derive_maps_sets_rels (ctr_sugar, lthy) =
1323 ((([], [], [], []), ctr_sugar), lthy)
1326 val rel_flip = rel_flip_of_bnf fp_bnf;
1327 val nones = replicate live NONE;
1330 if fp = Least_FP then
1333 let val ctor' = mk_ctor Bs ctor in
1334 cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong
1338 certify lthy o (fp = Greatest_FP ? curry (op $) (map_types ify ctor)) oo
1339 mk_InN_balanced (ify ctr_sum_prod_T) n;
1341 val cxIns = map2 (mk_cIn I) tuple_xs ks;
1342 val cyIns = map2 (mk_cIn B_ify) tuple_ys ks;
1344 fun mk_map_thm ctr_def' cxIn =
1345 fold_thms lthy [ctr_def']
1346 (unfold_thms lthy (pre_map_def ::
1347 (if fp = Least_FP then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map)
1348 (cterm_instantiate_pos (nones @ [SOME cxIn])
1349 (if fp = Least_FP then fp_map_thm else fp_map_thm RS ctor_cong)))
1350 |> singleton (Proof_Context.export names_lthy no_defs_lthy);
1352 fun mk_set_thm fp_set_thm ctr_def' cxIn =
1353 fold_thms lthy [ctr_def']
1354 (unfold_thms lthy (pre_set_defs @ nested_set_maps @ nesting_set_maps @
1355 (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_set)
1356 (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
1357 |> singleton (Proof_Context.export names_lthy no_defs_lthy);
1359 fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns;
1361 val map_thms = map2 mk_map_thm ctr_defs' cxIns;
1362 val set_thmss = map mk_set_thms fp_set_thms;
1364 val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns);
1366 fun mk_rel_thm postproc ctr_defs' cxIn cyIn =
1367 fold_thms lthy ctr_defs'
1368 (unfold_thms lthy (@{thm Inl_Inr_False} :: pre_rel_def ::
1369 (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_rel)
1370 (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
1372 |> singleton (Proof_Context.export names_lthy no_defs_lthy);
1374 fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) =
1375 mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn;
1377 val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
1379 fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) =
1380 mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
1383 fun mk_other_half_rel_distinct_thm thm =
1384 flip_rels lthy live thm
1385 RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
1387 val half_rel_distinct_thmss =
1388 map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
1389 val other_half_rel_distinct_thmss =
1390 map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
1391 val (rel_distinct_thms, _) =
1392 join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
1395 [(mapN, map_thms, code_simp_attrs),
1396 (rel_distinctN, rel_distinct_thms, code_simp_attrs),
1397 (rel_injectN, rel_inject_thms, code_simp_attrs),
1398 (setN, flat set_thmss, code_simp_attrs)]
1399 |> massage_simple_notes fp_b_name;
1401 (((map_thms, rel_inject_thms, rel_distinct_thms, set_thmss), ctr_sugar),
1402 lthy |> Local_Theory.notes notes |> snd)
1405 fun mk_binding suf = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
1407 fun massage_res (((maps_sets_rels, ctr_sugar), co_iter_res), lthy) =
1408 (((maps_sets_rels, (ctrs, xss, ctr_defs, ctr_sugar)), co_iter_res), lthy);
1411 #> derive_maps_sets_rels
1413 (if fp = Least_FP then define_iters [foldN, recN] (the iters_args_types)
1414 else define_coiters [unfoldN, corecN] (the coiters_args_types))
1415 mk_binding fpTs Cs xtor_co_iters
1416 #> massage_res, lthy')
1419 fun wrap_types_etc (wrap_types_etcs, lthy) =
1420 fold_map I wrap_types_etcs lthy
1421 |>> apsnd split_list o apfst (apsnd split_list4 o apfst split_list4 o split_list)
1425 map7 (fn {injects, distincts, case_thms, ...} => fn un_folds => fn co_recs =>
1426 fn mapsx => fn rel_injects => fn rel_distincts => fn setss =>
1427 injects @ distincts @ case_thms @ co_recs @ un_folds @ mapsx @ rel_injects
1428 @ rel_distincts @ flat setss);
1430 fun derive_and_note_induct_iters_thms_for_types
1431 ((((mapss, rel_injects, rel_distincts, setss), (ctrss, _, ctr_defss, ctr_sugars)),
1432 (iterss, iter_defss)), lthy) =
1434 val ((induct_thms, induct_thm, induct_attrs), (fold_thmss, fold_attrs),
1435 (rec_thmss, rec_attrs)) =
1436 derive_induct_iters_thms_for_types pre_bnfs (the iters_args_types) xtor_co_induct
1437 xtor_co_iter_thmss nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss ctrss ctr_defss iterss
1440 val induct_type_attr = Attrib.internal o K o Induct.induct_type;
1443 mk_simp_thmss ctr_sugars fold_thmss rec_thmss mapss rel_injects rel_distincts setss;
1446 (if nn > 1 then [(inductN, [induct_thm], induct_attrs)] else [])
1447 |> massage_simple_notes fp_common_name;
1450 [(foldN, fold_thmss, K fold_attrs),
1451 (inductN, map single induct_thms, fn T_name => induct_attrs @ [induct_type_attr T_name]),
1452 (recN, rec_thmss, K rec_attrs),
1453 (simpsN, simp_thmss, K [])]
1454 |> massage_multi_notes;
1457 |> Local_Theory.notes (common_notes @ notes) |> snd
1458 |> register_fp_sugars Least_FP pre_bnfs nested_bnfs nesting_bnfs fp_res ctr_defss ctr_sugars
1459 iterss mapss [induct_thm] (transpose [fold_thmss, rec_thmss]) [] []
1462 fun derive_and_note_coinduct_coiters_thms_for_types
1463 ((((mapss, rel_injects, rel_distincts, setss), (_, _, ctr_defss, ctr_sugars)),
1464 (coiterss, coiter_defss)), lthy) =
1466 val (([(coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)],
1468 (unfold_thmss, corec_thmss, coiter_attrs),
1469 (safe_unfold_thmss, safe_corec_thmss),
1470 (disc_unfold_thmss, disc_corec_thmss, disc_coiter_attrs),
1471 (disc_unfold_iff_thmss, disc_corec_iff_thmss, disc_coiter_iff_attrs),
1472 (sel_unfold_thmsss, sel_corec_thmsss, sel_coiter_attrs)) =
1473 derive_coinduct_coiters_thms_for_types pre_bnfs (the coiters_args_types) xtor_co_induct
1474 dtor_injects dtor_ctors xtor_co_iter_thmss nesting_bnfs fpTs Cs kss mss ns ctr_defss
1475 ctr_sugars coiterss coiter_defss (Proof_Context.export lthy' no_defs_lthy) lthy;
1477 val sel_unfold_thmss = map flat sel_unfold_thmsss;
1478 val sel_corec_thmss = map flat sel_corec_thmsss;
1480 val coinduct_type_attr = Attrib.internal o K o Induct.coinduct_type;
1482 fun flat_coiter_thms coiters disc_coiters disc_coiter_iffs sel_coiters =
1483 coiters @ disc_coiters @ disc_coiter_iffs @ sel_coiters;
1486 mk_simp_thmss ctr_sugars
1487 (map4 flat_coiter_thms safe_unfold_thmss disc_unfold_thmss disc_unfold_iff_thmss
1489 (map4 flat_coiter_thms safe_corec_thmss disc_corec_thmss disc_corec_iff_thmss
1491 mapss rel_injects rel_distincts setss;
1493 val anonymous_notes =
1494 [(flat safe_unfold_thmss @ flat safe_corec_thmss, simp_attrs)]
1495 |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
1499 [(coinductN, [coinduct_thm], coinduct_attrs),
1500 (strong_coinductN, [strong_coinduct_thm], coinduct_attrs)]
1503 |> massage_simple_notes fp_common_name;
1506 [(coinductN, map single coinduct_thms,
1507 fn T_name => coinduct_attrs @ [coinduct_type_attr T_name]),
1508 (corecN, corec_thmss, K coiter_attrs),
1509 (disc_corecN, disc_corec_thmss, K disc_coiter_attrs),
1510 (disc_corec_iffN, disc_corec_iff_thmss, K disc_coiter_iff_attrs),
1511 (disc_unfoldN, disc_unfold_thmss, K disc_coiter_attrs),
1512 (disc_unfold_iffN, disc_unfold_iff_thmss, K disc_coiter_iff_attrs),
1513 (sel_corecN, sel_corec_thmss, K sel_coiter_attrs),
1514 (sel_unfoldN, sel_unfold_thmss, K sel_coiter_attrs),
1515 (simpsN, simp_thmss, K []),
1516 (strong_coinductN, map single strong_coinduct_thms, K coinduct_attrs),
1517 (unfoldN, unfold_thmss, K coiter_attrs)]
1518 |> massage_multi_notes;
1521 |> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd
1522 |> register_fp_sugars Greatest_FP pre_bnfs nested_bnfs nesting_bnfs fp_res ctr_defss
1523 ctr_sugars coiterss mapss [coinduct_thm, strong_coinduct_thm]
1524 (transpose [unfold_thmss, corec_thmss]) (transpose [disc_unfold_thmss, disc_corec_thmss])
1525 (transpose [sel_unfold_thmsss, sel_corec_thmsss])
1529 |> fold_map define_ctrs_dtrs_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ ctors ~~ dtors ~~
1530 xtor_co_iterss ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~
1531 pre_set_defss ~~ pre_rel_defs ~~ xtor_map_thms ~~ xtor_set_thmss ~~ xtor_rel_thms ~~ ns ~~
1532 kss ~~ mss ~~ ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~
1533 sel_bindingsss ~~ raw_sel_defaultsss)
1535 |> fp_case fp derive_and_note_induct_iters_thms_for_types
1536 derive_and_note_coinduct_coiters_thms_for_types;
1538 val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
1539 co_prefix fp ^ "datatype"));
1544 val co_datatypes = define_co_datatypes (K I) (K I) (K I);
1546 val co_datatype_cmd =
1547 define_co_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.parse_term;
1550 @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
1551 (Parse.typ >> pair Binding.empty);
1553 val parse_defaults =
1554 @{keyword "("} |-- Parse.reserved "defaults" |-- Scan.repeat parse_bound_term --| @{keyword ")"};
1556 val parse_type_arg_constrained =
1557 Parse.type_ident -- Scan.option (@{keyword "::"} |-- Parse.!!! Parse.sort);
1559 val parse_type_arg_named_constrained = parse_opt_binding_colon -- parse_type_arg_constrained;
1561 val parse_type_args_named_constrained =
1562 parse_type_arg_constrained >> (single o pair Binding.empty) ||
1563 @{keyword "("} |-- Parse.!!! (Parse.list1 parse_type_arg_named_constrained --| @{keyword ")"}) ||
1566 val parse_map_rel_binding = Parse.short_ident --| @{keyword ":"} -- parse_binding;
1568 val no_map_rel = (Binding.empty, Binding.empty);
1570 fun extract_map_rel ("map", b) = apfst (K b)
1571 | extract_map_rel ("rel", b) = apsnd (K b)
1572 | extract_map_rel (s, _) = error ("Unknown label " ^ quote s ^ " (expected \"map\" or \"rel\")");
1574 val parse_map_rel_bindings =
1575 @{keyword "("} |-- Scan.repeat parse_map_rel_binding --| @{keyword ")"}
1576 >> (fn ps => fold extract_map_rel ps no_map_rel) ||
1577 Scan.succeed no_map_rel;
1579 val parse_ctr_spec =
1580 parse_opt_binding_colon -- parse_binding -- Scan.repeat parse_ctr_arg --
1581 Scan.optional parse_defaults [] -- Parse.opt_mixfix;
1584 parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
1585 Parse.opt_mixfix -- (@{keyword "="} |-- Parse.enum1 "|" parse_ctr_spec);
1587 val parse_co_datatype = parse_wrap_free_constructors_options -- Parse.and_list1 parse_spec;
1589 fun parse_co_datatype_cmd fp construct_fp = parse_co_datatype >> co_datatype_cmd fp construct_fp;