1 (* Title: HOL/BNF/Tools/bnf_fp_rec_sugar.ML
2 Author: Lorenz Panny, TU Muenchen
5 Recursor and corecursor sugar.
8 signature BNF_FP_REC_SUGAR =
10 val add_primrec: (binding * typ option * mixfix) list ->
11 (Attrib.binding * term) list -> local_theory -> (term list * thm list list) * local_theory
12 val add_primrec_cmd: (binding * string option * mixfix) list ->
13 (Attrib.binding * string) list -> local_theory -> (term list * thm list list) * local_theory
14 val add_primrec_global: (binding * typ option * mixfix) list ->
15 (Attrib.binding * term) list -> theory -> (term list * thm list list) * theory
16 val add_primrec_overloaded: (string * (string * typ) * bool) list ->
17 (binding * typ option * mixfix) list ->
18 (Attrib.binding * term) list -> theory -> (term list * thm list list) * theory
19 val add_primrec_simple: ((binding * typ) * mixfix) list -> term list ->
20 local_theory -> (string list * (term list * (int list list * thm list list))) * local_theory
21 val add_primcorecursive_cmd: bool ->
22 (binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list ->
23 Proof.context -> Proof.state
24 val add_primcorec_cmd: bool ->
25 (binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list ->
26 local_theory -> local_theory
29 structure BNF_FP_Rec_Sugar : BNF_FP_REC_SUGAR =
34 open BNF_FP_Rec_Sugar_Util
35 open BNF_FP_Rec_Sugar_Tactics
42 val nitpicksimp_attrs = @{attributes [nitpick_simp]};
43 val simp_attrs = @{attributes [simp]};
44 val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
45 val code_nitpicksimp_simp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs @ simp_attrs;
47 exception Primrec_Error of string * term list;
49 fun primrec_error str = raise Primrec_Error (str, []);
50 fun primrec_error_eqn str eqn = raise Primrec_Error (str, [eqn]);
51 fun primrec_error_eqns str eqns = raise Primrec_Error (str, eqns);
53 fun finds eq = fold_map (fn x => List.partition (curry eq x) #>> pair x);
55 val free_name = try (fn Free (v, _) => v);
56 val const_name = try (fn Const (v, _) => v);
57 val undef_const = Const (@{const_name undefined}, dummyT);
59 fun permute_args n t = list_comb (t, map Bound (0 :: (n downto 1)))
60 |> fold (K (Term.abs (Name.uu, dummyT))) (0 upto n);
61 val abs_tuple = HOLogic.tupled_lambda o HOLogic.mk_tuple;
62 fun drop_All t = subst_bounds (strip_qnt_vars @{const_name all} t |> map Free |> rev,
63 strip_qnt_body @{const_name all} t)
65 let fun a n (t $ u) = a n t $ a n u
66 | a n (Abs (v, T, b)) = Abs (v, T, a (n + 1) b)
67 | a n t = let val idx = find_index (equal t) vs in
68 if idx < 0 then t else Bound (n + idx) end
70 fun mk_prod1 Ts (t, u) = HOLogic.pair_const (fastype_of1 (Ts, t)) (fastype_of1 (Ts, u)) $ t $ u;
71 fun mk_tuple1 Ts = the_default HOLogic.unit o try (foldr1 (mk_prod1 Ts));
73 fun get_indices fixes t = map (fst #>> Binding.name_of #> Free) fixes
74 |> map_index (fn (i, v) => if exists_subterm (equal v) t then SOME i else NONE)
86 right_args: term list,
92 fun dissect_eqn lthy fun_names eqn' =
94 val eqn = drop_All eqn' |> HOLogic.dest_Trueprop
96 primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn';
97 val (lhs, rhs) = HOLogic.dest_eq eqn
99 primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn';
100 val (fun_name, args) = strip_comb lhs
101 |>> (fn x => if is_Free x then fst (dest_Free x)
102 else primrec_error_eqn "malformed function equation (does not start with free)" eqn);
103 val (left_args, rest) = take_prefix is_Free args;
104 val (nonfrees, right_args) = take_suffix is_Free rest;
105 val num_nonfrees = length nonfrees;
106 val _ = num_nonfrees = 1 orelse if num_nonfrees = 0 then
107 primrec_error_eqn "constructor pattern missing in left-hand side" eqn else
108 primrec_error_eqn "more than one non-variable argument in left-hand side" eqn;
109 val _ = member (op =) fun_names fun_name orelse
110 primrec_error_eqn "malformed function equation (does not start with function name)" eqn
112 val (ctr, ctr_args) = strip_comb (the_single nonfrees);
113 val _ = try (num_binder_types o fastype_of) ctr = SOME (length ctr_args) orelse
114 primrec_error_eqn "partially applied constructor in pattern" eqn;
115 val _ = let val d = duplicates (op =) (left_args @ ctr_args @ right_args) in null d orelse
116 primrec_error_eqn ("duplicate variable \"" ^ Syntax.string_of_term lthy (hd d) ^
117 "\" in left-hand side") eqn end;
118 val _ = forall is_Free ctr_args orelse
119 primrec_error_eqn "non-primitive pattern in left-hand side" eqn;
121 let val b = fold_aterms (fn x as Free (v, _) =>
122 if (not (member (op =) (left_args @ ctr_args @ right_args) x) andalso
123 not (member (op =) fun_names v) andalso
124 not (Variable.is_fixed lthy v)) then cons x else I | _ => I) rhs []
127 primrec_error_eqn ("extra variable(s) in right-hand side: " ^
128 commas (map (Syntax.string_of_term lthy) b)) eqn
131 {fun_name = fun_name,
132 rec_type = body_type (type_of ctr),
135 left_args = left_args,
136 right_args = right_args,
137 res_type = map fastype_of (left_args @ right_args) ---> fastype_of rhs,
142 fun rewrite_map_arg get_ctr_pos rec_type res_type =
144 val pT = HOLogic.mk_prodT (rec_type, res_type);
146 val maybe_suc = Option.map (fn x => x + 1);
147 fun subst d (t as Bound d') = t |> d = SOME d' ? curry (op $) (fst_const pT)
148 | subst d (Abs (v, T, b)) = Abs (v, if d = SOME ~1 then pT else T, subst (maybe_suc d) b)
151 val (u, vs) = strip_comb t;
152 val ctr_pos = try (get_ctr_pos o the) (free_name u) |> the_default ~1;
155 if d = SOME ~1 andalso length vs = ctr_pos then
156 list_comb (permute_args ctr_pos (snd_const pT), vs)
157 else if length vs > ctr_pos andalso is_some d
158 andalso d = try (fn Bound n => n) (nth vs ctr_pos) then
159 list_comb (snd_const pT $ nth vs ctr_pos, map (subst d) (nth_drop ctr_pos vs))
161 primrec_error_eqn ("recursive call not directly applied to constructor argument") t
163 list_comb (u, map (subst (d |> d = SOME ~1 ? K NONE)) vs)
169 fun subst_rec_calls lthy get_ctr_pos has_call ctr_args mutual_calls nested_calls =
171 fun try_nested_rec bound_Ts y t =
172 AList.lookup (op =) nested_calls y
173 |> Option.map (fn y' =>
174 massage_nested_rec_call lthy has_call (rewrite_map_arg get_ctr_pos) bound_Ts y y' t);
176 fun subst bound_Ts (t as g' $ y) =
178 fun subst_rec () = subst bound_Ts g' $ subst bound_Ts y;
179 val y_head = head_of y;
181 if not (member (op =) ctr_args y_head) then
184 (case try_nested_rec bound_Ts y_head t of
187 let val (g, g_args) = strip_comb g' in
188 (case try (get_ctr_pos o the) (free_name g) of
190 (length g_args >= ctr_pos orelse
191 primrec_error_eqn "too few arguments in recursive call" t;
192 (case AList.lookup (op =) mutual_calls y of
193 SOME y' => list_comb (y', g_args)
194 | NONE => subst_rec ()))
195 | NONE => subst_rec ())
198 | subst bound_Ts (Abs (v, T, b)) = Abs (v, T, subst (T :: bound_Ts) b)
203 (* FIXME detect this case earlier? *)
204 primrec_error_eqn "recursive call not directly applied to constructor argument" t
206 try_nested_rec [] (head_of t) t |> the_default t
211 fun build_rec_arg lthy (funs_data : eqn_data list list) has_call (ctr_spec : rec_ctr_spec)
212 (maybe_eqn_data : eqn_data option) =
213 (case maybe_eqn_data of
215 | SOME {ctr_args, left_args, right_args, rhs_term = t, ...} =>
217 val calls = #calls ctr_spec;
218 val n_args = fold (Integer.add o (fn Mutual_Rec _ => 2 | _ => 1)) calls 0;
220 val no_calls' = tag_list 0 calls
221 |> map_filter (try (apsnd (fn No_Rec p => p | Mutual_Rec (p, _) => p)));
222 val mutual_calls' = tag_list 0 calls
223 |> map_filter (try (apsnd (fn Mutual_Rec (_, p) => p)));
224 val nested_calls' = tag_list 0 calls
225 |> map_filter (try (apsnd (fn Nested_Rec p => p)));
227 val args = replicate n_args ("", dummyT)
228 |> Term.rename_wrt_term t
230 |> fold (fn (ctr_arg_idx, (arg_idx, _)) =>
231 nth_map arg_idx (K (nth ctr_args ctr_arg_idx)))
233 |> fold (fn (ctr_arg_idx, (arg_idx, T)) =>
234 nth_map arg_idx (K (retype_free T (nth ctr_args ctr_arg_idx))))
236 |> fold (fn (ctr_arg_idx, (arg_idx, T)) =>
237 nth_map arg_idx (K (retype_free T (nth ctr_args ctr_arg_idx))))
240 val fun_name_ctr_pos_list =
241 map (fn (x :: _) => (#fun_name x, length (#left_args x))) funs_data;
242 val get_ctr_pos = try (the o AList.lookup (op =) fun_name_ctr_pos_list) #> the_default ~1;
243 val mutual_calls = map (apfst (nth ctr_args) o apsnd (nth args o fst)) mutual_calls';
244 val nested_calls = map (apfst (nth ctr_args) o apsnd (nth args o fst)) nested_calls';
247 |> subst_rec_calls lthy get_ctr_pos has_call ctr_args mutual_calls nested_calls
248 |> fold_rev lambda (args @ left_args @ right_args)
251 fun build_defs lthy bs mxs (funs_data : eqn_data list list) (rec_specs : rec_spec list) has_call =
253 val n_funs = length funs_data;
255 val ctr_spec_eqn_data_list' =
256 (take n_funs rec_specs |> map #ctr_specs) ~~ funs_data
257 |> maps (uncurry (finds (fn (x, y) => #ctr x = #ctr y))
258 ##> (fn x => null x orelse
259 primrec_error_eqns "excess equations in definition" (map #rhs_term x)) #> fst);
260 val _ = ctr_spec_eqn_data_list' |> map (fn (_, x) => length x <= 1 orelse
261 primrec_error_eqns ("multiple equations for constructor") (map #user_eqn x));
263 val ctr_spec_eqn_data_list =
264 ctr_spec_eqn_data_list' @ (drop n_funs rec_specs |> maps #ctr_specs |> map (rpair []));
266 val recs = take n_funs rec_specs |> map #recx;
267 val rec_args = ctr_spec_eqn_data_list
268 |> sort ((op <) o pairself (#offset o fst) |> make_ord)
269 |> map (uncurry (build_rec_arg lthy funs_data has_call) o apsnd (try the_single));
270 val ctr_poss = map (fn x =>
271 if length (distinct ((op =) o pairself (length o #left_args)) x) <> 1 then
272 primrec_error ("inconstant constructor pattern position for function " ^
273 quote (#fun_name (hd x)))
275 hd x |> #left_args |> length) funs_data;
278 |-> map2 (fn recx => fn ctr_pos => list_comb (recx, rec_args) |> permute_args ctr_pos)
279 |> Syntax.check_terms lthy
280 |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.conceal (Thm.def_binding b), []), t)))
284 fun massage_comp ctxt has_call bound_Ts t = (* FIXME unused *)
285 massage_nested_corec_call ctxt has_call (K (K (K I))) bound_Ts (fastype_of1 (bound_Ts, t)) t;
287 fun find_rec_calls ctxt has_call ({ctr, ctr_args, rhs_term, ...} : eqn_data) =
289 fun find bound_Ts (Abs (_, T, b)) ctr_arg = find (T :: bound_Ts) b ctr_arg
290 | find bound_Ts (t as _ $ _) ctr_arg =
292 val typof = curry fastype_of1 bound_Ts;
293 val (f', args') = strip_comb t;
294 val n = find_index (equal ctr_arg o head_of) args';
297 find bound_Ts f' ctr_arg @ maps (fn x => find bound_Ts x ctr_arg) args'
300 val (f, args as arg :: _) = chop n args' |>> curry list_comb f'
301 val (arg_head, arg_args) = Term.strip_comb arg;
304 mk_partial_compN (length arg_args) (typof f) (typof arg_head) f ::
305 maps (fn x => find bound_Ts x ctr_arg) args
307 find bound_Ts f ctr_arg @ maps (fn x => find bound_Ts x ctr_arg) args
312 map (find [] rhs_term) ctr_args
313 |> (fn [] => NONE | callss => SOME (ctr, callss))
316 fun prepare_primrec fixes specs lthy =
318 val (bs, mxs) = map_split (apfst fst) fixes;
319 val fun_names = map Binding.name_of bs;
320 val eqns_data = map (dissect_eqn lthy fun_names) specs;
321 val funs_data = eqns_data
322 |> partition_eq ((op =) o pairself #fun_name)
323 |> finds (fn (x, y) => x = #fun_name (hd y)) fun_names |> fst
324 |> map (fn (x, y) => the_single y handle List.Empty =>
325 primrec_error ("missing equations for function " ^ quote x));
327 val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
328 val arg_Ts = map (#rec_type o hd) funs_data;
329 val res_Ts = map (#res_type o hd) funs_data;
330 val callssss = funs_data
331 |> map (partition_eq ((op =) o pairself #ctr))
332 |> map (maps (map_filter (find_rec_calls lthy has_call)));
334 val ((n2m, rec_specs, _, induct_thm, induct_thms), lthy') =
335 rec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;
337 val actual_nn = length funs_data;
339 val _ = let val ctrs = (maps (map #ctr o #ctr_specs) rec_specs) in
340 map (fn {ctr, user_eqn, ...} => member (op =) ctrs ctr orelse
341 primrec_error_eqn ("argument " ^ quote (Syntax.string_of_term lthy' ctr) ^
342 " is not a constructor in left-hand side") user_eqn) eqns_data end;
344 val defs = build_defs lthy' bs mxs funs_data rec_specs has_call;
346 fun prove lthy def_thms' ({ctr_specs, nested_map_idents, nested_map_comps, ...} : rec_spec)
347 (fun_data : eqn_data list) =
349 val def_thms = map (snd o snd) def_thms';
350 val simp_thmss = finds (fn (x, y) => #ctr x = #ctr y) fun_data ctr_specs
352 |> map_filter (try (fn (x, [y]) =>
353 (#user_eqn x, length (#left_args x) + length (#right_args x), #rec_thm y)))
354 |> map (fn (user_eqn, num_extra_args, rec_thm) =>
355 mk_primrec_tac lthy num_extra_args nested_map_idents nested_map_comps def_thms rec_thm
356 |> K |> Goal.prove lthy [] [] user_eqn
357 |> Thm.close_derivation);
358 val poss = find_indices (fn (x, y) => #ctr x = #ctr y) fun_data eqns_data;
364 (if n2m then map2 (fn name => fn thm =>
365 (name, inductN, [thm], [])) fun_names (take actual_nn induct_thms) else [])
366 |> map (fn (prefix, thmN, thms, attrs) =>
367 ((Binding.qualify true prefix (Binding.name thmN), attrs), [(thms, [])]));
369 val common_name = mk_common_name fun_names;
372 (if n2m then [(inductN, [induct_thm], [])] else [])
373 |> map (fn (thmN, thms, attrs) =>
374 ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
377 fn lthy => fn defs =>
378 split_list (map2 (prove lthy defs) (take actual_nn rec_specs) funs_data)),
379 lthy' |> Local_Theory.notes (notes @ common_notes) |> snd)
382 (* primrec definition *)
384 fun add_primrec_simple fixes ts lthy =
386 val (((names, defs), prove), lthy) = prepare_primrec fixes ts lthy
387 handle ERROR str => primrec_error str;
390 |> fold_map Local_Theory.define defs
391 |-> (fn defs => `(fn lthy => (names, (map fst defs, prove lthy defs))))
393 handle Primrec_Error (str, eqns) =>
395 then error ("primrec_new error:\n " ^ str)
396 else error ("primrec_new error:\n " ^ str ^ "\nin\n " ^
397 space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns));
401 fun gen_primrec prep_spec (raw_fixes : (binding * 'a option * mixfix) list) raw_spec lthy =
403 val d = duplicates (op =) (map (Binding.name_of o #1) raw_fixes)
404 val _ = null d orelse primrec_error ("duplicate function name(s): " ^ commas d);
406 val (fixes, specs) = fst (prep_spec raw_fixes raw_spec lthy);
409 flat ooo map3 (fn poss => fn prefix => fn thms =>
411 val (bs, attrss) = map_split (fst o nth specs) poss;
413 map3 (fn b => fn attrs => fn thm =>
414 ((Binding.qualify false prefix b, code_nitpicksimp_simp_attrs @ attrs), [([thm], [])]))
417 ((Binding.qualify true prefix (Binding.name simpsN), []), [(thms, [])]) :: notes
421 |> add_primrec_simple fixes (map snd specs)
422 |-> (fn (names, (ts, (posss, simpss))) =>
423 Spec_Rules.add Spec_Rules.Equational (ts, flat simpss)
424 #> Local_Theory.notes (mk_notes posss names simpss)
425 #>> pair ts o map snd)
430 val add_primrec = gen_primrec Specification.check_spec;
431 val add_primrec_cmd = gen_primrec Specification.read_spec;
435 fun add_primrec_global fixes specs thy =
437 val lthy = Named_Target.theory_init thy;
438 val ((ts, simps), lthy') = add_primrec fixes specs lthy;
439 val simps' = burrow (Proof_Context.export lthy' lthy) simps;
440 in ((ts, simps'), Local_Theory.exit_global lthy') end;
442 fun add_primrec_overloaded ops fixes specs thy =
444 val lthy = Overloading.overloading ops thy;
445 val ((ts, simps), lthy') = add_primrec fixes specs lthy;
446 val simps' = burrow (Proof_Context.export lthy' lthy) simps;
447 in ((ts, simps'), Local_Theory.exit_global lthy') end;
453 type coeqn_data_disc = {
462 maybe_ctr_rhs: term option,
463 maybe_code_rhs: term option,
467 type coeqn_data_sel = {
477 datatype coeqn_data =
478 Disc of coeqn_data_disc |
479 Sel of coeqn_data_sel;
481 fun dissect_coeqn_disc seq fun_names (basic_ctr_specss : basic_corec_ctr_spec list list)
482 maybe_ctr_rhs maybe_code_rhs prems' concl matchedsss =
484 fun find_subterm p = let (* FIXME \<exists>? *)
485 fun f (t as u $ v) = if p t then SOME t else merge_options (f u, f v)
486 | f t = if p t then SOME t else NONE
489 val applied_fun = concl
490 |> find_subterm (member ((op =) o apsnd SOME) fun_names o try (fst o dest_Free o head_of))
492 handle Option.Option => primrec_error_eqn "malformed discriminator formula" concl;
493 val ((fun_name, fun_T), fun_args) = strip_comb applied_fun |>> dest_Free;
494 val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name;
496 val discs = map #disc basic_ctr_specs;
497 val ctrs = map #ctr basic_ctr_specs;
498 val not_disc = head_of concl = @{term Not};
499 val _ = not_disc andalso length ctrs <> 2 andalso
500 primrec_error_eqn "negated discriminator for a type with \<noteq> 2 constructors" concl;
501 val disc' = find_subterm (member (op =) discs o head_of) concl;
502 val eq_ctr0 = concl |> perhaps (try HOLogic.dest_not) |> try (HOLogic.dest_eq #> snd)
503 |> (fn SOME t => let val n = find_index (equal t) ctrs in
504 if n >= 0 then SOME n else NONE end | _ => NONE);
505 val _ = is_some disc' orelse is_some eq_ctr0 orelse
506 primrec_error_eqn "no discriminator in equation" concl;
508 if is_none disc' then the eq_ctr0 else find_index (equal (head_of (the disc'))) discs;
509 val ctr_no = if not_disc then 1 - ctr_no' else ctr_no';
510 val {ctr, disc, ...} = nth basic_ctr_specs ctr_no;
512 val catch_all = try (fst o dest_Free o the_single) prems' = SOME Name.uu_;
513 val matchedss = AList.lookup (op =) matchedsss fun_name |> the_default [];
514 val prems = map (abstract (List.rev fun_args)) prems';
516 (if catch_all orelse seq then maps s_not_conj matchedss else []) @
517 (if catch_all then [] else prems);
519 val matchedsss' = AList.delete (op =) fun_name matchedsss
520 |> cons (fun_name, if seq then matchedss @ [prems] else matchedss @ [real_prems]);
524 |>> map HOLogic.mk_Trueprop ||> HOLogic.mk_Trueprop o abstract (List.rev fun_args)
525 |> curry Logic.list_all (map dest_Free fun_args) o Logic.list_implies;
535 auto_gen = catch_all,
536 maybe_ctr_rhs = maybe_ctr_rhs,
537 maybe_code_rhs = maybe_code_rhs,
542 fun dissect_coeqn_sel fun_names (basic_ctr_specss : basic_corec_ctr_spec list list) eqn'
545 val (lhs, rhs) = HOLogic.dest_eq eqn
547 primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn;
548 val sel = head_of lhs;
549 val ((fun_name, fun_T), fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst dest_Free
551 primrec_error_eqn "malformed selector argument in left-hand side" eqn;
552 val basic_ctr_specs = the (AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name)
553 handle Option.Option => primrec_error_eqn "malformed selector argument in left-hand side" eqn;
555 (case maybe_of_spec of
556 SOME of_spec => the (find_first (equal of_spec o #ctr) basic_ctr_specs)
557 | NONE => filter (exists (equal sel) o #sels) basic_ctr_specs |> the_single
558 handle List.Empty => primrec_error_eqn "ambiguous selector - use \"of\"" eqn);
559 val user_eqn = drop_All eqn';
572 fun dissect_coeqn_ctr seq fun_names (basic_ctr_specss : basic_corec_ctr_spec list list) eqn'
573 maybe_code_rhs prems concl matchedsss =
575 val (lhs, rhs) = HOLogic.dest_eq concl;
576 val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
577 val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name;
578 val (ctr, ctr_args) = strip_comb (unfold_let rhs);
579 val {disc, sels, ...} = the (find_first (equal ctr o #ctr) basic_ctr_specs)
580 handle Option.Option => primrec_error_eqn "not a constructor" ctr;
582 val disc_concl = betapply (disc, lhs);
583 val (maybe_eqn_data_disc, matchedsss') = if length basic_ctr_specs = 1
584 then (NONE, matchedsss)
585 else apfst SOME (dissect_coeqn_disc seq fun_names basic_ctr_specss
586 (SOME (abstract (List.rev fun_args) rhs)) maybe_code_rhs prems disc_concl matchedsss);
588 val sel_concls = sels ~~ ctr_args
589 |> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg));
592 val _ = tracing ("reduced\n " ^ Syntax.string_of_term @{context} concl ^ "\nto\n \<cdot> " ^
593 (is_some maybe_eqn_data_disc ? K (Syntax.string_of_term @{context} disc_concl ^ "\n \<cdot> ")) "" ^
594 space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) sel_concls) ^
595 "\nfor premise(s)\n \<cdot> " ^
596 space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) prems));
600 map (dissect_coeqn_sel fun_names basic_ctr_specss eqn' (SOME ctr)) sel_concls;
602 (the_list maybe_eqn_data_disc @ eqns_data_sel, matchedsss')
605 fun dissect_coeqn_code lthy has_call fun_names basic_ctr_specss eqn' concl matchedsss =
607 val (lhs, (rhs', rhs)) = HOLogic.dest_eq concl ||> `(expand_corec_code_rhs lthy has_call []);
608 val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
609 val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name;
611 val cond_ctrs = fold_rev_corec_code_rhs lthy (fn cs => fn ctr => fn _ =>
612 if member ((op =) o apsnd #ctr) basic_ctr_specs ctr
614 else primrec_error_eqn "not a constructor" ctr) [] rhs' []
615 |> AList.group (op =);
617 val ctr_premss = (case cond_ctrs of [_] => [[]] | _ => map (s_dnf o snd) cond_ctrs);
618 val ctr_concls = cond_ctrs |> map (fn (ctr, _) =>
619 binder_types (fastype_of ctr)
620 |> map_index (fn (n, T) => massage_corec_code_rhs lthy (fn _ => fn ctr' => fn args =>
621 if ctr' = ctr then nth args n else Const (@{const_name undefined}, T)) [] rhs')
622 |> curry list_comb ctr
623 |> curry HOLogic.mk_eq lhs);
625 fold_map2 (dissect_coeqn_ctr false fun_names basic_ctr_specss eqn'
626 (SOME (abstract (List.rev fun_args) rhs)))
627 ctr_premss ctr_concls matchedsss
630 fun dissect_coeqn lthy seq has_call fun_names (basic_ctr_specss : basic_corec_ctr_spec list list)
631 eqn' maybe_of_spec matchedsss =
633 val eqn = drop_All eqn'
634 handle TERM _ => primrec_error_eqn "malformed function equation" eqn';
635 val (prems, concl) = Logic.strip_horn eqn
636 |> apfst (map HOLogic.dest_Trueprop) o apsnd HOLogic.dest_Trueprop;
639 |> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq))
642 val maybe_rhs = concl |> perhaps (try HOLogic.dest_not) |> try (snd o HOLogic.dest_eq);
644 val discs = maps (map #disc) basic_ctr_specss;
645 val sels = maps (maps #sels) basic_ctr_specss;
646 val ctrs = maps (map #ctr) basic_ctr_specss;
648 if member (op =) discs head orelse
649 is_some maybe_rhs andalso
650 member (op =) (filter (null o binder_types o fastype_of) ctrs) (the maybe_rhs) then
651 dissect_coeqn_disc seq fun_names basic_ctr_specss NONE NONE prems concl matchedsss
653 else if member (op =) sels head then
654 ([dissect_coeqn_sel fun_names basic_ctr_specss eqn' maybe_of_spec concl], matchedsss)
655 else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso
656 member (op =) ctrs (head_of (unfold_let (the maybe_rhs))) then
657 dissect_coeqn_ctr seq fun_names basic_ctr_specss eqn' NONE prems concl matchedsss
658 else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso
660 dissect_coeqn_code lthy has_call fun_names basic_ctr_specss eqn' concl matchedsss
663 primrec_error_eqn "malformed function equation" eqn
666 fun build_corec_arg_disc (ctr_specs : corec_ctr_spec list)
667 ({fun_args, ctr_no, prems, ...} : coeqn_data_disc) =
668 if is_none (#pred (nth ctr_specs ctr_no)) then I else
670 |> curry subst_bounds (List.rev fun_args)
671 |> HOLogic.tupled_lambda (HOLogic.mk_tuple fun_args)
672 |> K |> nth_map (the (#pred (nth ctr_specs ctr_no)));
674 fun build_corec_arg_no_call (sel_eqns : coeqn_data_sel list) sel =
675 find_first (equal sel o #sel) sel_eqns
676 |> try (fn SOME {fun_args, rhs_term, ...} => abs_tuple fun_args rhs_term)
677 |> the_default undef_const
680 fun build_corec_args_mutual_call lthy has_call (sel_eqns : coeqn_data_sel list) sel =
681 (case find_first (equal sel o #sel) sel_eqns of
683 | SOME {fun_args, rhs_term, ... } =>
685 val bound_Ts = List.rev (map fastype_of fun_args);
686 fun rewrite_stop _ t = if has_call t then @{term False} else @{term True};
687 fun rewrite_end _ t = if has_call t then undef_const else t;
688 fun rewrite_cont bound_Ts t =
689 if has_call t then mk_tuple1 bound_Ts (snd (strip_comb t)) else undef_const;
690 fun massage f _ = massage_mutual_corec_call lthy has_call f bound_Ts rhs_term
691 |> abs_tuple fun_args;
693 (massage rewrite_stop, massage rewrite_end, massage rewrite_cont)
696 fun build_corec_arg_nested_call lthy has_call (sel_eqns : coeqn_data_sel list) sel =
697 (case find_first (equal sel o #sel) sel_eqns of
699 | SOME {fun_args, rhs_term, ...} =>
701 val bound_Ts = List.rev (map fastype_of fun_args);
702 fun rewrite bound_Ts U T (Abs (v, V, b)) = Abs (v, V, rewrite (V :: bound_Ts) U T b)
703 | rewrite bound_Ts U T (t as _ $ _) =
704 let val (u, vs) = strip_comb t in
705 if is_Free u andalso has_call u then
706 Inr_const U T $ mk_tuple1 bound_Ts vs
707 else if const_name u = SOME @{const_name prod_case} then
708 map (rewrite bound_Ts U T) vs |> chop 1 |>> HOLogic.mk_split o the_single |> list_comb
710 list_comb (rewrite bound_Ts U T u, map (rewrite bound_Ts U T) vs)
713 if is_Free t andalso has_call t then Inr_const U T $ HOLogic.unit else t;
716 |> massage_nested_corec_call lthy has_call rewrite bound_Ts (range_type (fastype_of t))
717 |> abs_tuple fun_args;
722 fun build_corec_args_sel lthy has_call (all_sel_eqns : coeqn_data_sel list)
723 (ctr_spec : corec_ctr_spec) =
724 (case filter (equal (#ctr ctr_spec) o #ctr) all_sel_eqns of
728 val sel_call_list = #sels ctr_spec ~~ #calls ctr_spec;
729 val no_calls' = map_filter (try (apsnd (fn No_Corec n => n))) sel_call_list;
730 val mutual_calls' = map_filter (try (apsnd (fn Mutual_Corec n => n))) sel_call_list;
731 val nested_calls' = map_filter (try (apsnd (fn Nested_Corec n => n))) sel_call_list;
734 #> fold (fn (sel, n) => nth_map n (build_corec_arg_no_call sel_eqns sel)) no_calls'
735 #> fold (fn (sel, (q, g, h)) =>
736 let val (fq, fg, fh) = build_corec_args_mutual_call lthy has_call sel_eqns sel in
737 nth_map q fq o nth_map g fg o nth_map h fh end) mutual_calls'
738 #> fold (fn (sel, n) => nth_map n
739 (build_corec_arg_nested_call lthy has_call sel_eqns sel)) nested_calls'
742 fun build_codefs lthy bs mxs has_call arg_Tss (corec_specs : corec_spec list)
743 (disc_eqnss : coeqn_data_disc list list) (sel_eqnss : coeqn_data_sel list list) =
745 val corecs = map #corec corec_specs;
746 val ctr_specss = map #ctr_specs corec_specs;
747 val corec_args = hd corecs
748 |> fst o split_last o binder_types o fastype_of
749 |> map (Const o pair @{const_name undefined})
750 |> fold2 (fold o build_corec_arg_disc) ctr_specss disc_eqnss
751 |> fold2 (fold o build_corec_args_sel lthy has_call) sel_eqnss ctr_specss;
753 | currys Ts t = t $ mk_tuple1 (List.rev Ts) (map Bound (length Ts - 1 downto 0))
754 |> fold_rev (Term.abs o pair Name.uu) Ts;
757 val _ = tracing ("corecursor arguments:\n \<cdot> " ^
758 space_implode "\n \<cdot> " (map (Syntax.string_of_term lthy) corec_args));
763 |> map (map (fn x => (#fun_args x, #ctr_no x, #prems x, #auto_gen x))
764 #> fst o (fn xs => fold_map (fn x => fn ys => ((x, ys), ys @ [x])) xs [])
765 #> maps (uncurry (map o pair)
766 #> map (fn ((fun_args, c, x, a), (_, c', y, a')) =>
767 ((c, c', a orelse a'), (x, s_not (s_conjs y)))
768 ||> apfst (map HOLogic.mk_Trueprop) o apsnd HOLogic.mk_Trueprop
769 ||> Logic.list_implies
770 ||> curry Logic.list_all (map dest_Free fun_args))))
772 map (list_comb o rpair corec_args) corecs
773 |> map2 (fn Ts => fn t => if length Ts = 0 then t $ HOLogic.unit else t) arg_Tss
774 |> map2 currys arg_Tss
775 |> Syntax.check_terms lthy
776 |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.conceal (Thm.def_binding b), []), t)))
781 fun mk_real_disc_eqns fun_binding arg_Ts ({ctr_specs, ...} : corec_spec)
782 (sel_eqns : coeqn_data_sel list) (disc_eqns : coeqn_data_disc list) =
783 if length disc_eqns <> length ctr_specs - 1 then disc_eqns else
785 val n = 0 upto length ctr_specs
786 |> the o find_first (fn idx => not (exists (equal idx o #ctr_no) disc_eqns));
787 val fun_args = (try (#fun_args o hd) disc_eqns, try (#fun_args o hd) sel_eqns)
788 |> the_default (map (curry Free Name.uu) arg_Ts) o merge_options;
789 val extra_disc_eqn = {
790 fun_name = Binding.name_of fun_binding,
791 fun_T = arg_Ts ---> body_type (fastype_of (#ctr (hd ctr_specs))),
793 ctr = #ctr (nth ctr_specs n),
795 disc = #disc (nth ctr_specs n),
796 prems = maps (s_not_conj o #prems) disc_eqns,
798 maybe_ctr_rhs = NONE,
799 maybe_code_rhs = NONE,
800 user_eqn = undef_const};
802 chop n disc_eqns ||> cons extra_disc_eqn |> (op @)
805 fun find_corec_calls has_call basic_ctr_specs ({ctr, sel, rhs_term, ...} : coeqn_data_sel) =
807 val sel_no = find_first (equal ctr o #ctr) basic_ctr_specs
808 |> find_index (equal sel) o #sels o the;
809 fun find t = if has_call t then [t] else [];
812 |> K |> nth_map sel_no |> AList.map_entry (op =) ctr
815 fun add_primcorec_ursive maybe_tac seq fixes specs maybe_of_specs lthy =
817 val (bs, mxs) = map_split (apfst fst) fixes;
818 val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> HOLogic.mk_tupleT) fixes |> split_list;
820 val fun_names = map Binding.name_of bs;
821 val basic_ctr_specss = map (basic_corec_specs_of lthy) res_Ts;
822 val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
824 fold_map2 (dissect_coeqn lthy seq has_call fun_names basic_ctr_specss) (map snd specs)
829 map_filter (try (fn Sel x => x)) eqns_data
830 |> partition_eq ((op =) o pairself #fun_name)
831 |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
833 |> map2 (fold o find_corec_calls has_call) basic_ctr_specss
834 |> map2 (curry (op |>)) (map (map (fn {ctr, sels, ...} =>
835 (ctr, map (K []) sels))) basic_ctr_specss);
838 val _ = tracing ("callssss = " ^ @{make_string} callssss);
841 val ((n2m, corec_specs', _, coinduct_thm, strong_coinduct_thm, coinduct_thms,
842 strong_coinduct_thms), lthy') =
843 corec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;
844 val actual_nn = length bs;
845 val corec_specs = take actual_nn corec_specs'; (*###*)
846 val ctr_specss = map #ctr_specs corec_specs;
848 val disc_eqnss' = map_filter (try (fn Disc x => x)) eqns_data
849 |> partition_eq ((op =) o pairself #fun_name)
850 |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
851 |> map (sort ((op <) o pairself #ctr_no |> make_ord) o flat o snd);
852 val _ = disc_eqnss' |> map (fn x =>
853 let val d = duplicates ((op =) o pairself #ctr_no) x in null d orelse
854 primrec_error_eqns "excess discriminator formula in definition"
855 (maps (fn t => filter (equal (#ctr_no t) o #ctr_no) x) d |> map #user_eqn) end);
857 val sel_eqnss = map_filter (try (fn Sel x => x)) eqns_data
858 |> partition_eq ((op =) o pairself #fun_name)
859 |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
862 val arg_Tss = map (binder_types o snd o fst) fixes;
863 val disc_eqnss = map5 mk_real_disc_eqns bs arg_Tss corec_specs sel_eqnss disc_eqnss';
864 val (defs, exclss') =
865 build_codefs lthy' bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss;
867 fun excl_tac (c, c', a) =
868 if a orelse c = c' orelse seq then SOME (K (HEADGOAL (mk_primcorec_assumption_tac lthy [])))
872 val _ = tracing ("exclusiveness properties:\n \<cdot> " ^
873 space_implode "\n \<cdot> " (maps (map (Syntax.string_of_term lthy o snd)) exclss'));
876 val exclss'' = exclss' |> map (map (fn (idx, t) =>
877 (idx, (Option.map (Goal.prove lthy [] [] t #> Thm.close_derivation) (excl_tac idx), t))));
878 val taut_thmss = map (map (apsnd (the o fst)) o filter (is_some o fst o snd)) exclss'';
879 val (goal_idxss, goalss) = exclss''
880 |> map (map (apsnd (rpair [] o snd)) o filter (is_none o fst o snd))
881 |> split_list o map split_list;
883 fun prove thmss' def_thms' lthy =
885 val def_thms = map (snd o snd) def_thms';
887 val exclss' = map (op ~~) (goal_idxss ~~ thmss');
888 fun mk_exclsss excls n =
889 (excls, map (fn k => replicate k [TrueI] @ replicate (n - k) []) (0 upto n - 1))
890 |-> fold (fn ((c, c', _), thm) => nth_map c (nth_map c' (K [thm])));
891 val exclssss = (exclss' ~~ taut_thmss |> map (op @), fun_names ~~ corec_specs)
892 |-> map2 (fn excls => fn (_, {ctr_specs, ...}) => mk_exclsss excls (length ctr_specs));
894 fun prove_disc ({ctr_specs, ...} : corec_spec) exclsss
895 ({fun_name, fun_T, fun_args, ctr_no, prems, ...} : coeqn_data_disc) =
896 if Term.aconv_untyped (#disc (nth ctr_specs ctr_no), @{term "\<lambda>x. x = x"}) then [] else
898 val {disc_corec, ...} = nth ctr_specs ctr_no;
900 val m = length prems;
902 list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
903 |> curry betapply (#disc (nth ctr_specs ctr_no)) (*###*)
904 |> HOLogic.mk_Trueprop
905 |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
906 |> curry Logic.list_all (map dest_Free fun_args);
908 if prems = [@{term False}] then [] else
909 mk_primcorec_disc_tac lthy def_thms disc_corec k m exclsss
910 |> K |> Goal.prove lthy [] [] t
911 |> Thm.close_derivation
912 |> pair (#disc (nth ctr_specs ctr_no))
916 fun prove_sel ({nested_maps, nested_map_idents, nested_map_comps, ctr_specs, ...}
917 : corec_spec) (disc_eqns : coeqn_data_disc list) exclsss
918 ({fun_name, fun_T, fun_args, ctr, sel, rhs_term, ...} : coeqn_data_sel) =
920 val SOME ctr_spec = find_first (equal ctr o #ctr) ctr_specs;
921 val ctr_no = find_index (equal ctr o #ctr) ctr_specs;
922 val prems = the_default (maps (s_not_conj o #prems) disc_eqns)
923 (find_first (equal ctr_no o #ctr_no) disc_eqns |> Option.map #prems);
924 val sel_corec = find_index (equal sel) (#sels ctr_spec)
925 |> nth (#sel_corecs ctr_spec);
927 val m = length prems;
929 list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
930 |> curry betapply sel
931 |> rpair (abstract (List.rev fun_args) rhs_term)
932 |> HOLogic.mk_Trueprop o HOLogic.mk_eq
933 |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
934 |> curry Logic.list_all (map dest_Free fun_args);
935 val (distincts, _, sel_splits, sel_split_asms) = case_thms_of_term lthy [] rhs_term;
937 mk_primcorec_sel_tac lthy def_thms distincts sel_splits sel_split_asms nested_maps
938 nested_map_idents nested_map_comps sel_corec k m exclsss
939 |> K |> Goal.prove lthy [] [] t
940 |> Thm.close_derivation
944 fun prove_ctr disc_alist sel_alist (disc_eqns : coeqn_data_disc list)
945 (sel_eqns : coeqn_data_sel list) ({ctr, disc, sels, collapse, ...} : corec_ctr_spec) =
946 (* don't try to prove theorems when some sel_eqns are missing *)
947 if not (exists (equal ctr o #ctr) disc_eqns)
948 andalso not (exists (equal ctr o #ctr) sel_eqns)
950 filter (equal ctr o #ctr) sel_eqns
951 |> fst o finds ((op =) o apsnd #sel) sels
952 |> exists (null o snd)
955 val (fun_name, fun_T, fun_args, prems, maybe_rhs) =
956 (find_first (equal ctr o #ctr) disc_eqns, find_first (equal ctr o #ctr) sel_eqns)
957 |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #prems x,
959 ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, [], NONE))
960 |> the o merge_options;
961 val m = length prems;
962 val t = (if is_some maybe_rhs then the maybe_rhs else
963 filter (equal ctr o #ctr) sel_eqns
964 |> fst o finds ((op =) o apsnd #sel) sels
965 |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) #-> abstract)
966 |> curry list_comb ctr)
967 |> curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
968 map Bound (length fun_args - 1 downto 0)))
969 |> HOLogic.mk_Trueprop
970 |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
971 |> curry Logic.list_all (map dest_Free fun_args);
972 val maybe_disc_thm = AList.lookup (op =) disc_alist disc;
973 val sel_thms = map snd (filter (member (op =) sels o fst) sel_alist);
975 if prems = [@{term False}] then [] else
976 mk_primcorec_ctr_of_dtr_tac lthy m collapse maybe_disc_thm sel_thms
977 |> K |> Goal.prove lthy [] [] t
978 |> Thm.close_derivation
983 fun prove_code disc_eqns sel_eqns ctr_alist ctr_specs =
985 val (fun_name, fun_T, fun_args, maybe_rhs) =
986 (find_first (member (op =) (map #ctr ctr_specs) o #ctr) disc_eqns,
987 find_first (member (op =) (map #ctr ctr_specs) o #ctr) sel_eqns)
988 |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #maybe_code_rhs x))
989 ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, NONE))
990 |> the o merge_options;
992 val bound_Ts = List.rev (map fastype_of fun_args);
994 val lhs = list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0));
999 val raw_rhs = expand_corec_code_rhs lthy has_call bound_Ts rhs;
1001 fold_rev_corec_code_rhs lthy (K oo (cons oo pair)) bound_Ts raw_rhs [];
1002 val ctr_thms = map (the o AList.lookup (op =) ctr_alist o snd) cond_ctrs;
1003 in SOME (rhs, raw_rhs, ctr_thms) end
1006 fun prove_code_ctr {ctr, sels, ...} =
1007 if not (exists (equal ctr o fst) ctr_alist) then NONE else
1009 val prems = find_first (equal ctr o #ctr) disc_eqns
1010 |> Option.map #prems |> the_default [];
1012 filter (equal ctr o #ctr) sel_eqns
1013 |> fst o finds ((op =) o apsnd #sel) sels
1014 |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x))
1016 |> curry list_comb ctr;
1020 val maybe_ctr_conds_argss = map prove_code_ctr ctr_specs;
1022 if exists is_none maybe_ctr_conds_argss then NONE else
1024 val rhs = fold_rev (fn SOME (prems, u) => fn t => mk_If (s_conjs prems) u t)
1025 maybe_ctr_conds_argss
1026 (Const (@{const_name Code.abort}, @{typ String.literal} -->
1027 (@{typ unit} --> body_type fun_T) --> body_type fun_T) $
1028 HOLogic.mk_literal fun_name $
1029 absdummy @{typ unit} (incr_boundvars 1 lhs));
1030 in SOME (rhs, rhs, map snd ctr_alist) end
1033 (case maybe_rhs_info of
1035 | SOME (rhs, raw_rhs, ctr_thms) =>
1037 val ms = map (Logic.count_prems o prop_of) ctr_thms;
1038 val (raw_t, t) = (raw_rhs, rhs)
1040 (curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
1041 map Bound (length fun_args - 1 downto 0)))
1042 #> HOLogic.mk_Trueprop
1043 #> curry Logic.list_all (map dest_Free fun_args));
1044 val (distincts, discIs, sel_splits, sel_split_asms) =
1045 case_thms_of_term lthy bound_Ts raw_rhs;
1047 val raw_code_thm = mk_primcorec_raw_code_of_ctr_tac lthy distincts discIs sel_splits
1048 sel_split_asms ms ctr_thms
1049 |> K |> Goal.prove lthy [] [] raw_t
1050 |> Thm.close_derivation;
1052 mk_primcorec_code_of_raw_code_tac lthy distincts sel_splits raw_code_thm
1053 |> K |> Goal.prove lthy [] [] t
1054 |> Thm.close_derivation
1059 val disc_alists = map3 (maps oo prove_disc) corec_specs exclssss disc_eqnss;
1060 val sel_alists = map4 (map ooo prove_sel) corec_specs disc_eqnss exclssss sel_eqnss;
1061 val disc_thmss = map (map snd) disc_alists;
1062 val sel_thmss = map (map snd) sel_alists;
1064 val ctr_alists = map5 (maps oooo prove_ctr) disc_alists sel_alists disc_eqnss sel_eqnss
1066 val ctr_thmss = map (map snd) ctr_alists;
1068 val code_thmss = map4 prove_code disc_eqnss sel_eqnss ctr_alists ctr_specss;
1070 val simp_thmss = map2 append disc_thmss sel_thmss
1072 val common_name = mk_common_name fun_names;
1075 [(coinductN, map (if n2m then single else K []) coinduct_thms, []),
1076 (codeN, code_thmss, code_nitpicksimp_attrs),
1077 (ctrN, ctr_thmss, []),
1078 (discN, disc_thmss, simp_attrs),
1079 (selN, sel_thmss, simp_attrs),
1080 (simpsN, simp_thmss, []),
1081 (strong_coinductN, map (if n2m then single else K []) strong_coinduct_thms, [])]
1082 |> maps (fn (thmN, thmss, attrs) =>
1083 map2 (fn fun_name => fn thms =>
1084 ((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])]))
1085 fun_names (take actual_nn thmss))
1086 |> filter_out (null o fst o hd o snd);
1089 [(coinductN, if n2m then [coinduct_thm] else [], []),
1090 (strong_coinductN, if n2m then [strong_coinduct_thm] else [], [])]
1091 |> filter_out (null o #2)
1092 |> map (fn (thmN, thms, attrs) =>
1093 ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
1095 lthy |> Local_Theory.notes (notes @ common_notes) |> snd
1098 fun after_qed thmss' = fold_map Local_Theory.define defs #-> prove thmss';
1100 (goalss, after_qed, lthy')
1103 fun add_primcorec_ursive_cmd maybe_tac seq (raw_fixes, raw_specs') lthy =
1105 val (raw_specs, maybe_of_specs) =
1106 split_list raw_specs' ||> map (Option.map (Syntax.read_term lthy));
1107 val ((fixes, specs), _) = Specification.read_spec raw_fixes raw_specs lthy;
1109 add_primcorec_ursive maybe_tac seq fixes specs maybe_of_specs lthy
1110 handle ERROR str => primrec_error str
1112 handle Primrec_Error (str, eqns) =>
1114 then error ("primcorec error:\n " ^ str)
1115 else error ("primcorec error:\n " ^ str ^ "\nin\n " ^
1116 space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns));
1118 val add_primcorecursive_cmd = (fn (goalss, after_qed, lthy) =>
1120 |> Proof.theorem NONE after_qed goalss
1121 |> Proof.refine (Method.primitive_text I)
1122 |> Seq.hd) ooo add_primcorec_ursive_cmd NONE;
1124 val add_primcorec_cmd = (fn (goalss, after_qed, lthy) =>
1126 |> after_qed (map (fn [] => []
1127 | _ => primrec_error "need exclusiveness proofs - use primcorecursive instead of primcorec")
1128 goalss)) ooo add_primcorec_ursive_cmd (SOME (fn {context = ctxt, ...} => auto_tac ctxt));