prove user-supplied equations for ctr and code reductions, preserving "let"s, "case"s etc.;
generate code-style theorems (currently commented out since this still fails for many cases);
filter tautologies (False ==> ...) out of generated theorems;
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 nitpick_attrs = @{attributes [nitpick_simp]};
43 val simp_attrs = @{attributes [simp]};
44 val code_nitpick_attrs = Code.add_default_eqn_attrib :: nitpick_attrs;
45 val code_nitpick_simp_attrs = Code.add_default_eqn_attrib :: nitpick_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
162 else if d = SOME ~1 andalso const_name u = SOME @{const_name comp} then
163 list_comb (map_types (K dummyT) u, map2 subst [NONE, d] vs)
165 list_comb (u, map (subst (d |> d = SOME ~1 ? K NONE)) vs)
171 fun subst_rec_calls lthy get_ctr_pos has_call ctr_args direct_calls indirect_calls t =
173 fun subst bound_Ts (Abs (v, T, b)) = Abs (v, T, subst (T :: bound_Ts) b)
174 | subst bound_Ts (t as g' $ y) =
176 val maybe_direct_y' = AList.lookup (op =) direct_calls y;
177 val maybe_indirect_y' = AList.lookup (op =) indirect_calls y;
178 val (g, g_args) = strip_comb g';
179 val ctr_pos = try (get_ctr_pos o the) (free_name g) |> the_default ~1;
180 val _ = ctr_pos < 0 orelse length g_args >= ctr_pos orelse
181 primrec_error_eqn "too few arguments in recursive call" t;
183 if not (member (op =) ctr_args y) then
184 pairself (subst bound_Ts) (g', y) |> (op $)
185 else if ctr_pos >= 0 then
186 list_comb (the maybe_direct_y', g_args)
187 else if is_some maybe_indirect_y' then
188 (if has_call g' then t else y)
189 |> massage_indirect_rec_call lthy has_call
190 (rewrite_map_arg get_ctr_pos) bound_Ts y (the maybe_indirect_y')
191 |> (if has_call g' then I else curry (op $) g')
198 |> tap (fn u => has_call u andalso (* FIXME detect this case earlier *)
199 primrec_error_eqn "recursive call not directly applied to constructor argument" t)
202 fun build_rec_arg lthy (funs_data : eqn_data list list) has_call (ctr_spec : rec_ctr_spec)
203 (maybe_eqn_data : eqn_data option) =
204 if is_none maybe_eqn_data then undef_const else
206 val eqn_data = the maybe_eqn_data;
207 val t = #rhs_term eqn_data;
208 val ctr_args = #ctr_args eqn_data;
210 val calls = #calls ctr_spec;
211 val n_args = fold (curry (op +) o (fn Direct_Rec _ => 2 | _ => 1)) calls 0;
213 val no_calls' = tag_list 0 calls
214 |> map_filter (try (apsnd (fn No_Rec n => n | Direct_Rec (n, _) => n)));
215 val direct_calls' = tag_list 0 calls
216 |> map_filter (try (apsnd (fn Direct_Rec (_, n) => n)));
217 val indirect_calls' = tag_list 0 calls
218 |> map_filter (try (apsnd (fn Indirect_Rec n => n)));
220 fun make_direct_type _ = dummyT; (* FIXME? *)
222 val rec_res_type_list = map (fn (x :: _) => (#rec_type x, #res_type x)) funs_data;
224 fun make_indirect_type (Type (Tname, Ts)) = Type (Tname, Ts |> map (fn T =>
225 let val maybe_res_type = AList.lookup (op =) rec_res_type_list T in
226 if is_some maybe_res_type
227 then HOLogic.mk_prodT (T, the maybe_res_type)
228 else make_indirect_type T end))
229 | make_indirect_type T = T;
231 val args = replicate n_args ("", dummyT)
232 |> Term.rename_wrt_term t
234 |> fold (fn (ctr_arg_idx, arg_idx) =>
235 nth_map arg_idx (K (nth ctr_args ctr_arg_idx)))
237 |> fold (fn (ctr_arg_idx, arg_idx) =>
238 nth_map arg_idx (K (nth ctr_args ctr_arg_idx |> map_types make_direct_type)))
240 |> fold (fn (ctr_arg_idx, arg_idx) =>
241 nth_map arg_idx (K (nth ctr_args ctr_arg_idx |> map_types make_indirect_type)))
244 val fun_name_ctr_pos_list =
245 map (fn (x :: _) => (#fun_name x, length (#left_args x))) funs_data;
246 val get_ctr_pos = try (the o AList.lookup (op =) fun_name_ctr_pos_list) #> the_default ~1;
247 val direct_calls = map (apfst (nth ctr_args) o apsnd (nth args)) direct_calls';
248 val indirect_calls = map (apfst (nth ctr_args) o apsnd (nth args)) indirect_calls';
250 val abstractions = args @ #left_args eqn_data @ #right_args eqn_data;
253 |> subst_rec_calls lthy get_ctr_pos has_call ctr_args direct_calls indirect_calls
254 |> fold_rev lambda abstractions
257 fun build_defs lthy bs mxs (funs_data : eqn_data list list) (rec_specs : rec_spec list) has_call =
259 val n_funs = length funs_data;
261 val ctr_spec_eqn_data_list' =
262 (take n_funs rec_specs |> map #ctr_specs) ~~ funs_data
263 |> maps (uncurry (finds (fn (x, y) => #ctr x = #ctr y))
264 ##> (fn x => null x orelse
265 primrec_error_eqns "excess equations in definition" (map #rhs_term x)) #> fst);
266 val _ = ctr_spec_eqn_data_list' |> map (fn (_, x) => length x <= 1 orelse
267 primrec_error_eqns ("multiple equations for constructor") (map #user_eqn x));
269 val ctr_spec_eqn_data_list =
270 ctr_spec_eqn_data_list' @ (drop n_funs rec_specs |> maps #ctr_specs |> map (rpair []));
272 val recs = take n_funs rec_specs |> map #recx;
273 val rec_args = ctr_spec_eqn_data_list
274 |> sort ((op <) o pairself (#offset o fst) |> make_ord)
275 |> map (uncurry (build_rec_arg lthy funs_data has_call) o apsnd (try the_single));
276 val ctr_poss = map (fn x =>
277 if length (distinct ((op =) o pairself (length o #left_args)) x) <> 1 then
278 primrec_error ("inconstant constructor pattern position for function " ^
279 quote (#fun_name (hd x)))
281 hd x |> #left_args |> length) funs_data;
284 |-> map2 (fn recx => fn ctr_pos => list_comb (recx, rec_args) |> permute_args ctr_pos)
285 |> Syntax.check_terms lthy
286 |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.map_name Thm.def_name b, []), t))) bs mxs
289 fun find_rec_calls has_call (eqn_data : eqn_data) =
291 fun find (Abs (_, _, b)) ctr_arg = find b ctr_arg
292 | find (t as _ $ _) ctr_arg =
294 val (f', args') = strip_comb t;
295 val n = find_index (equal ctr_arg) args';
298 find f' ctr_arg @ maps (fn x => find x ctr_arg) args'
300 let val (f, args) = chop n args' |>> curry list_comb f' in
302 f :: maps (fn x => find x ctr_arg) args
304 find f ctr_arg @ maps (fn x => find x ctr_arg) args
309 map (find (#rhs_term eqn_data)) (#ctr_args eqn_data)
310 |> (fn [] => NONE | callss => SOME (#ctr eqn_data, callss))
313 fun prepare_primrec fixes specs lthy =
315 val (bs, mxs) = map_split (apfst fst) fixes;
316 val fun_names = map Binding.name_of bs;
317 val eqns_data = map (dissect_eqn lthy fun_names) specs;
318 val funs_data = eqns_data
319 |> partition_eq ((op =) o pairself #fun_name)
320 |> finds (fn (x, y) => x = #fun_name (hd y)) fun_names |> fst
321 |> map (fn (x, y) => the_single y handle List.Empty =>
322 primrec_error ("missing equations for function " ^ quote x));
324 val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
325 val arg_Ts = map (#rec_type o hd) funs_data;
326 val res_Ts = map (#res_type o hd) funs_data;
327 val callssss = funs_data
328 |> map (partition_eq ((op =) o pairself #ctr))
329 |> map (maps (map_filter (find_rec_calls has_call)));
331 val ((n2m, rec_specs, _, induct_thm, induct_thms), lthy') =
332 rec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;
334 val actual_nn = length funs_data;
336 val _ = let val ctrs = (maps (map #ctr o #ctr_specs) rec_specs) in
337 map (fn {ctr, user_eqn, ...} => member (op =) ctrs ctr orelse
338 primrec_error_eqn ("argument " ^ quote (Syntax.string_of_term lthy' ctr) ^
339 " is not a constructor in left-hand side") user_eqn) eqns_data end;
341 val defs = build_defs lthy' bs mxs funs_data rec_specs has_call;
343 fun prove lthy def_thms' ({ctr_specs, nested_map_idents, nested_map_comps, ...} : rec_spec)
344 (fun_data : eqn_data list) =
346 val def_thms = map (snd o snd) def_thms';
347 val simp_thmss = finds (fn (x, y) => #ctr x = #ctr y) fun_data ctr_specs
349 |> map_filter (try (fn (x, [y]) =>
350 (#user_eqn x, length (#left_args x) + length (#right_args x), #rec_thm y)))
351 |> map (fn (user_eqn, num_extra_args, rec_thm) =>
352 mk_primrec_tac lthy num_extra_args nested_map_idents nested_map_comps def_thms rec_thm
353 |> K |> Goal.prove lthy [] [] user_eqn);
354 val poss = find_indices (fn (x, y) => #ctr x = #ctr y) fun_data eqns_data;
360 (if n2m then map2 (fn name => fn thm =>
361 (name, inductN, [thm], [])) fun_names (take actual_nn induct_thms) else [])
362 |> map (fn (prefix, thmN, thms, attrs) =>
363 ((Binding.qualify true prefix (Binding.name thmN), attrs), [(thms, [])]));
365 val common_name = mk_common_name fun_names;
368 (if n2m then [(inductN, [induct_thm], [])] else [])
369 |> map (fn (thmN, thms, attrs) =>
370 ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
373 fn lthy => fn defs =>
374 split_list (map2 (prove lthy defs) (take actual_nn rec_specs) funs_data)),
375 lthy' |> Local_Theory.notes (notes @ common_notes) |> snd)
378 (* primrec definition *)
380 fun add_primrec_simple fixes ts lthy =
382 val (((names, defs), prove), lthy) = prepare_primrec fixes ts lthy
383 handle ERROR str => primrec_error str;
386 |> fold_map Local_Theory.define defs
387 |-> (fn defs => `(fn lthy => (names, (map fst defs, prove lthy defs))))
389 handle Primrec_Error (str, eqns) =>
391 then error ("primrec_new error:\n " ^ str)
392 else error ("primrec_new error:\n " ^ str ^ "\nin\n " ^
393 space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns));
397 fun gen_primrec prep_spec (raw_fixes : (binding * 'a option * mixfix) list) raw_spec lthy =
399 val d = duplicates (op =) (map (Binding.name_of o #1) raw_fixes)
400 val _ = null d orelse primrec_error ("duplicate function name(s): " ^ commas d);
402 val (fixes, specs) = fst (prep_spec raw_fixes raw_spec lthy);
405 flat ooo map3 (fn poss => fn prefix => fn thms =>
407 val (bs, attrss) = map_split (fst o nth specs) poss;
409 map3 (fn b => fn attrs => fn thm =>
410 ((Binding.qualify false prefix b, code_nitpick_simp_attrs @ attrs), [([thm], [])]))
413 ((Binding.qualify true prefix (Binding.name simpsN), []), [(thms, [])]) :: notes
417 |> add_primrec_simple fixes (map snd specs)
418 |-> (fn (names, (ts, (posss, simpss))) =>
419 Spec_Rules.add Spec_Rules.Equational (ts, flat simpss)
420 #> Local_Theory.notes (mk_notes posss names simpss)
421 #>> pair ts o map snd)
426 val add_primrec = gen_primrec Specification.check_spec;
427 val add_primrec_cmd = gen_primrec Specification.read_spec;
431 fun add_primrec_global fixes specs thy =
433 val lthy = Named_Target.theory_init thy;
434 val ((ts, simps), lthy') = add_primrec fixes specs lthy;
435 val simps' = burrow (Proof_Context.export lthy' lthy) simps;
436 in ((ts, simps'), Local_Theory.exit_global lthy') end;
438 fun add_primrec_overloaded ops fixes specs thy =
440 val lthy = Overloading.overloading ops thy;
441 val ((ts, simps), lthy') = add_primrec fixes specs lthy;
442 val simps' = burrow (Proof_Context.export lthy' lthy) simps;
443 in ((ts, simps'), Local_Theory.exit_global lthy') end;
449 type co_eqn_data_disc = {
458 maybe_ctr_rhs: term option,
459 maybe_code_rhs: term option,
463 type co_eqn_data_sel = {
473 datatype co_eqn_data =
474 Disc of co_eqn_data_disc |
475 Sel of co_eqn_data_sel;
477 fun co_dissect_eqn_disc seq fun_names (corec_specs : corec_spec list) maybe_ctr_rhs maybe_code_rhs
478 prems' concl matchedsss =
480 fun find_subterm p = let (* FIXME \<exists>? *)
481 fun f (t as u $ v) = if p t then SOME t else merge_options (f u, f v)
482 | f t = if p t then SOME t else NONE
485 val applied_fun = concl
486 |> find_subterm (member ((op =) o apsnd SOME) fun_names o try (fst o dest_Free o head_of))
488 handle Option.Option => primrec_error_eqn "malformed discriminator equation" concl;
489 val ((fun_name, fun_T), fun_args) = strip_comb applied_fun |>> dest_Free;
490 val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
492 val discs = map #disc ctr_specs;
493 val ctrs = map #ctr ctr_specs;
494 val not_disc = head_of concl = @{term Not};
495 val _ = not_disc andalso length ctrs <> 2 andalso
496 primrec_error_eqn "\<not>ed discriminator for a type with \<noteq> 2 constructors" concl;
497 val disc = find_subterm (member (op =) discs o head_of) concl;
498 val eq_ctr0 = concl |> perhaps (try (HOLogic.dest_not)) |> try (HOLogic.dest_eq #> snd)
499 |> (fn SOME t => let val n = find_index (equal t) ctrs in
500 if n >= 0 then SOME n else NONE end | _ => NONE);
501 val _ = is_some disc orelse is_some eq_ctr0 orelse
502 primrec_error_eqn "no discriminator in equation" concl;
504 if is_none disc then the eq_ctr0 else find_index (equal (head_of (the disc))) discs;
505 val ctr_no = if not_disc then 1 - ctr_no' else ctr_no';
506 val ctr = #ctr (nth ctr_specs ctr_no);
508 val catch_all = try (fst o dest_Free o the_single) prems' = SOME Name.uu_;
509 val matchedss = AList.lookup (op =) matchedsss fun_name |> the_default [];
510 val prems = map (abstract (List.rev fun_args)) prems';
512 (if catch_all orelse seq then maps s_not_conj matchedss else []) @
513 (if catch_all then [] else prems);
515 val matchedsss' = AList.delete (op =) fun_name matchedsss
516 |> cons (fun_name, if seq then matchedss @ [prems] else matchedss @ [real_prems]);
520 |>> map HOLogic.mk_Trueprop ||> HOLogic.mk_Trueprop o abstract (List.rev fun_args)
521 |> curry Logic.list_all (map dest_Free fun_args) o Logic.list_implies;
529 disc = #disc (nth ctr_specs ctr_no),
531 auto_gen = catch_all,
532 maybe_ctr_rhs = maybe_ctr_rhs,
533 maybe_code_rhs = maybe_code_rhs,
538 fun co_dissect_eqn_sel fun_names (corec_specs : corec_spec list) eqn' of_spec eqn =
540 val (lhs, rhs) = HOLogic.dest_eq eqn
542 primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn;
543 val sel = head_of lhs;
544 val ((fun_name, fun_T), fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst dest_Free
546 primrec_error_eqn "malformed selector argument in left-hand side" eqn;
547 val corec_spec = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name)
548 handle Option.Option => primrec_error_eqn "malformed selector argument in left-hand side" eqn;
551 then the (find_first (equal (the of_spec) o #ctr) (#ctr_specs corec_spec))
552 else #ctr_specs corec_spec |> filter (exists (equal sel) o #sels) |> the_single
553 handle List.Empty => primrec_error_eqn "ambiguous selector - use \"of\"" eqn;
554 val user_eqn = drop_All eqn';
567 fun co_dissect_eqn_ctr seq fun_names (corec_specs : corec_spec list) eqn' maybe_code_rhs
568 prems concl matchedsss =
570 val (lhs, rhs) = HOLogic.dest_eq concl;
571 val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
572 val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
573 val (ctr, ctr_args) = strip_comb (unfold_let rhs);
574 val {disc, sels, ...} = the (find_first (equal ctr o #ctr) ctr_specs)
575 handle Option.Option => primrec_error_eqn "not a constructor" ctr;
577 val disc_concl = betapply (disc, lhs);
578 val (maybe_eqn_data_disc, matchedsss') = if length ctr_specs = 1
579 then (NONE, matchedsss)
580 else apfst SOME (co_dissect_eqn_disc seq fun_names corec_specs
581 (SOME (abstract (List.rev fun_args) rhs)) maybe_code_rhs prems disc_concl matchedsss);
583 val sel_concls = (sels ~~ ctr_args)
584 |> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg));
587 val _ = tracing ("reduced\n " ^ Syntax.string_of_term @{context} concl ^ "\nto\n \<cdot> " ^
588 (is_some maybe_eqn_data_disc ? K (Syntax.string_of_term @{context} disc_concl ^ "\n \<cdot> ")) "" ^
589 space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) sel_concls) ^
590 "\nfor premise(s)\n \<cdot> " ^
591 space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) prems));
594 val eqns_data_sel = map (co_dissect_eqn_sel fun_names corec_specs eqn' (SOME ctr)) sel_concls;
596 (the_list maybe_eqn_data_disc @ eqns_data_sel, matchedsss')
599 fun co_dissect_eqn_code lthy has_call fun_names corec_specs eqn' concl matchedsss =
601 val (lhs, (rhs', rhs)) = HOLogic.dest_eq concl ||> `(expand_corec_code_rhs lthy has_call []);
602 val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
603 val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
605 val cond_ctrs = fold_rev_corec_code_rhs lthy (fn cs => fn ctr => fn _ =>
606 if member ((op =) o apsnd #ctr) ctr_specs ctr
608 else primrec_error_eqn "not a constructor" ctr) [] rhs' []
609 |> AList.group (op =);
611 val ctr_premss = (case cond_ctrs of [_] => [[]] | _ => map (s_dnf o snd) cond_ctrs);
612 val ctr_concls = cond_ctrs |> map (fn (ctr, _) =>
613 binder_types (fastype_of ctr)
614 |> map_index (fn (n, T) => massage_corec_code_rhs lthy (fn _ => fn ctr' => fn args =>
615 if ctr' = ctr then nth args n else Const (@{const_name undefined}, T)) [] rhs')
616 |> curry list_comb ctr
617 |> curry HOLogic.mk_eq lhs);
619 fold_map2 (co_dissect_eqn_ctr false fun_names corec_specs eqn'
620 (SOME (abstract (List.rev fun_args) rhs)))
621 ctr_premss ctr_concls matchedsss
624 fun co_dissect_eqn lthy seq has_call fun_names (corec_specs : corec_spec list) eqn' of_spec
627 val eqn = drop_All eqn'
628 handle TERM _ => primrec_error_eqn "malformed function equation" eqn';
629 val (prems, concl) = Logic.strip_horn eqn
630 |> apfst (map HOLogic.dest_Trueprop) o apsnd HOLogic.dest_Trueprop;
633 |> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq))
636 val maybe_rhs = concl |> perhaps (try (HOLogic.dest_not)) |> try (snd o HOLogic.dest_eq);
638 val discs = maps #ctr_specs corec_specs |> map #disc;
639 val sels = maps #ctr_specs corec_specs |> maps #sels;
640 val ctrs = maps #ctr_specs corec_specs |> map #ctr;
642 if member (op =) discs head orelse
643 is_some maybe_rhs andalso
644 member (op =) (filter (null o binder_types o fastype_of) ctrs) (the maybe_rhs) then
645 co_dissect_eqn_disc seq fun_names corec_specs NONE NONE prems concl matchedsss
647 else if member (op =) sels head then
648 ([co_dissect_eqn_sel fun_names corec_specs eqn' of_spec concl], matchedsss)
649 else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso
650 member (op =) ctrs (head_of (unfold_let (the maybe_rhs))) then
651 co_dissect_eqn_ctr seq fun_names corec_specs eqn' NONE prems concl matchedsss
652 else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso
654 co_dissect_eqn_code lthy has_call fun_names corec_specs eqn' concl matchedsss
657 primrec_error_eqn "malformed function equation" eqn
660 fun build_corec_arg_disc (ctr_specs : corec_ctr_spec list)
661 ({fun_args, ctr_no, prems, ...} : co_eqn_data_disc) =
662 if is_none (#pred (nth ctr_specs ctr_no)) then I else
664 |> curry subst_bounds (List.rev fun_args)
665 |> HOLogic.tupled_lambda (HOLogic.mk_tuple fun_args)
666 |> K |> nth_map (the (#pred (nth ctr_specs ctr_no)));
668 fun build_corec_arg_no_call (sel_eqns : co_eqn_data_sel list) sel =
669 find_first (equal sel o #sel) sel_eqns
670 |> try (fn SOME {fun_args, rhs_term, ...} => abs_tuple fun_args rhs_term)
671 |> the_default undef_const
674 fun build_corec_args_direct_call lthy has_call (sel_eqns : co_eqn_data_sel list) sel =
676 val maybe_sel_eqn = find_first (equal sel o #sel) sel_eqns;
678 if is_none maybe_sel_eqn then (I, I, I) else
680 val {fun_args, rhs_term, ... } = the maybe_sel_eqn;
681 val bound_Ts = List.rev (map fastype_of fun_args);
682 fun rewrite_q _ t = if has_call t then @{term False} else @{term True};
683 fun rewrite_g _ t = if has_call t then undef_const else t;
684 fun rewrite_h bound_Ts t =
685 if has_call t then mk_tuple1 bound_Ts (snd (strip_comb t)) else undef_const;
686 fun massage f _ = massage_direct_corec_call lthy has_call f bound_Ts rhs_term
687 |> abs_tuple fun_args;
695 fun build_corec_arg_indirect_call lthy has_call (sel_eqns : co_eqn_data_sel list) sel =
697 val maybe_sel_eqn = find_first (equal sel o #sel) sel_eqns;
699 if is_none maybe_sel_eqn then I else
701 val {fun_args, rhs_term, ...} = the maybe_sel_eqn;
702 val bound_Ts = List.rev (map fastype_of fun_args);
703 fun rewrite bound_Ts U T (Abs (v, V, b)) = Abs (v, V, rewrite (V :: bound_Ts) U T b)
704 | rewrite bound_Ts U T (t as _ $ _) =
705 let val (u, vs) = strip_comb t in
706 if is_Free u andalso has_call u then
707 Inr_const U T $ mk_tuple1 bound_Ts vs
708 else if try (fst o dest_Const) u = SOME @{const_name prod_case} then
709 map (rewrite bound_Ts U T) vs |> chop 1 |>> HOLogic.mk_split o the_single |> list_comb
711 list_comb (rewrite bound_Ts U T u, map (rewrite bound_Ts U T) vs)
714 if is_Free t andalso has_call t then Inr_const U T $ HOLogic.unit else t;
717 |> massage_indirect_corec_call lthy has_call rewrite bound_Ts (range_type (fastype_of t))
718 |> abs_tuple fun_args;
724 fun build_corec_args_sel lthy has_call (all_sel_eqns : co_eqn_data_sel list)
725 (ctr_spec : corec_ctr_spec) =
726 let val sel_eqns = filter (equal (#ctr ctr_spec) o #ctr) all_sel_eqns in
727 if null sel_eqns then I else
729 val sel_call_list = #sels ctr_spec ~~ #calls ctr_spec;
731 val no_calls' = map_filter (try (apsnd (fn No_Corec n => n))) sel_call_list;
732 val direct_calls' = map_filter (try (apsnd (fn Direct_Corec n => n))) sel_call_list;
733 val indirect_calls' = map_filter (try (apsnd (fn Indirect_Corec n => n))) sel_call_list;
736 #> fold (fn (sel, n) => nth_map n (build_corec_arg_no_call sel_eqns sel)) no_calls'
737 #> fold (fn (sel, (q, g, h)) =>
738 let val (fq, fg, fh) = build_corec_args_direct_call lthy has_call sel_eqns sel in
739 nth_map q fq o nth_map g fg o nth_map h fh end) direct_calls'
740 #> fold (fn (sel, n) => nth_map n
741 (build_corec_arg_indirect_call lthy has_call sel_eqns sel)) indirect_calls'
745 fun co_build_defs lthy bs mxs has_call arg_Tss (corec_specs : corec_spec list)
746 (disc_eqnss : co_eqn_data_disc list list) (sel_eqnss : co_eqn_data_sel list list) =
748 val corec_specs' = take (length bs) corec_specs;
749 val corecs = map #corec corec_specs';
750 val ctr_specss = map #ctr_specs corec_specs';
751 val corec_args = hd corecs
752 |> fst o split_last o binder_types o fastype_of
753 |> map (Const o pair @{const_name undefined})
754 |> fold2 (fold o build_corec_arg_disc) ctr_specss disc_eqnss
755 |> fold2 (fold o build_corec_args_sel lthy has_call) sel_eqnss ctr_specss;
757 | currys Ts t = t $ mk_tuple1 (List.rev Ts) (map Bound (length Ts - 1 downto 0))
758 |> fold_rev (Term.abs o pair Name.uu) Ts;
761 val _ = tracing ("corecursor arguments:\n \<cdot> " ^
762 space_implode "\n \<cdot> " (map (Syntax.string_of_term lthy) corec_args));
767 |> map (map (fn x => (#fun_args x, #ctr_no x, #prems x, #auto_gen x))
768 #> fst o (fn xs => fold_map (fn x => fn ys => ((x, ys), ys @ [x])) xs [])
769 #> maps (uncurry (map o pair)
770 #> map (fn ((fun_args, c, x, a), (_, c', y, a')) =>
771 ((c, c', a orelse a'), (x, s_not (s_conjs y)))
772 ||> apfst (map HOLogic.mk_Trueprop) o apsnd HOLogic.mk_Trueprop
773 ||> Logic.list_implies
774 ||> curry Logic.list_all (map dest_Free fun_args))))
776 map (list_comb o rpair corec_args) corecs
777 |> map2 (fn Ts => fn t => if length Ts = 0 then t $ HOLogic.unit else t) arg_Tss
778 |> map2 currys arg_Tss
779 |> Syntax.check_terms lthy
780 |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.map_name Thm.def_name b, []), t))) bs mxs
784 fun mk_real_disc_eqns fun_binding arg_Ts ({ctr_specs, ...} : corec_spec)
785 (sel_eqns : co_eqn_data_sel list) (disc_eqns : co_eqn_data_disc list) =
786 if length disc_eqns <> length ctr_specs - 1 then disc_eqns else
788 val n = 0 upto length ctr_specs
789 |> the o find_first (fn idx => not (exists (equal idx o #ctr_no) disc_eqns));
790 val fun_args = (try (#fun_args o hd) disc_eqns, try (#fun_args o hd) sel_eqns)
791 |> the_default (map (curry Free Name.uu) arg_Ts) o merge_options;
792 val extra_disc_eqn = {
793 fun_name = Binding.name_of fun_binding,
794 fun_T = arg_Ts ---> body_type (fastype_of (#ctr (hd ctr_specs))),
796 ctr = #ctr (nth ctr_specs n),
798 disc = #disc (nth ctr_specs n),
799 prems = maps (s_not_conj o #prems) disc_eqns,
801 maybe_ctr_rhs = NONE,
802 maybe_code_rhs = NONE,
803 user_eqn = undef_const};
805 chop n disc_eqns ||> cons extra_disc_eqn |> (op @)
808 fun add_primcorec simple seq fixes specs of_specs lthy =
810 val (bs, mxs) = map_split (apfst fst) fixes;
811 val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> HOLogic.mk_tupleT) fixes |> split_list;
813 val callssss = []; (* FIXME *)
815 val ((n2m, corec_specs', _, coinduct_thm, strong_coinduct_thm, coinduct_thms,
816 strong_coinduct_thms), lthy') =
817 corec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;
819 val actual_nn = length bs;
820 val fun_names = map Binding.name_of bs;
821 val corec_specs = take actual_nn corec_specs'; (*###*)
823 val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
825 fold_map2 (co_dissect_eqn lthy seq has_call fun_names corec_specs)
826 (map snd specs) of_specs []
829 val disc_eqnss' = map_filter (try (fn Disc 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
832 |> map (sort ((op <) o pairself #ctr_no |> make_ord) o flat o snd);
833 val _ = disc_eqnss' |> map (fn x =>
834 let val d = duplicates ((op =) o pairself #ctr_no) x in null d orelse
835 primrec_error_eqns "excess discriminator equations in definition"
836 (maps (fn t => filter (equal (#ctr_no t) o #ctr_no) x) d |> map #user_eqn) end);
838 val sel_eqnss = map_filter (try (fn Sel x => x)) eqns_data
839 |> partition_eq ((op =) o pairself #fun_name)
840 |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
843 val arg_Tss = map (binder_types o snd o fst) fixes;
844 val disc_eqnss = map5 mk_real_disc_eqns bs arg_Tss corec_specs sel_eqnss disc_eqnss';
845 val (defs, exclss') =
846 co_build_defs lthy' bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss;
848 fun excl_tac (c, c', a) =
849 if a orelse c = c' orelse seq then
850 SOME (K (HEADGOAL (mk_primcorec_assumption_tac lthy [])))
852 SOME (K (auto_tac lthy))
857 val _ = tracing ("exclusiveness properties:\n \<cdot> " ^
858 space_implode "\n \<cdot> " (maps (map (Syntax.string_of_term lthy o snd)) exclss'));
861 val exclss'' = exclss' |> map (map (fn (idx, t) =>
862 (idx, (Option.map (Goal.prove lthy [] [] t) (excl_tac idx), t))));
863 val taut_thmss = map (map (apsnd (the o fst)) o filter (is_some o fst o snd)) exclss'';
864 val (obligation_idxss, obligationss) = exclss''
865 |> map (map (apsnd (rpair [] o snd)) o filter (is_none o fst o snd))
866 |> split_list o map split_list;
868 fun prove thmss' def_thms' lthy =
870 val def_thms = map (snd o snd) def_thms';
872 val exclss' = map (op ~~) (obligation_idxss ~~ thmss');
873 fun mk_exclsss excls n =
874 (excls, map (fn k => replicate k [TrueI] @ replicate (n - k) []) (0 upto n - 1))
875 |-> fold (fn ((c, c', _), thm) => nth_map c (nth_map c' (K [thm])));
876 val exclssss = (exclss' ~~ taut_thmss |> map (op @), fun_names ~~ corec_specs)
877 |-> map2 (fn excls => fn (_, {ctr_specs, ...}) => mk_exclsss excls (length ctr_specs));
879 fun prove_disc ({ctr_specs, ...} : corec_spec) exclsss
880 ({fun_name, fun_T, fun_args, ctr_no, prems, ...} : co_eqn_data_disc) =
881 if Term.aconv_untyped (#disc (nth ctr_specs ctr_no), @{term "\<lambda>x. x = x"}) then [] else
883 val {disc_corec, ...} = nth ctr_specs ctr_no;
885 val m = length prems;
887 list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
888 |> curry betapply (#disc (nth ctr_specs ctr_no)) (*###*)
889 |> HOLogic.mk_Trueprop
890 |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
891 |> curry Logic.list_all (map dest_Free fun_args);
893 if prems = [@{term False}] then [] else
894 mk_primcorec_disc_tac lthy def_thms disc_corec k m exclsss
895 |> K |> Goal.prove lthy [] [] t
896 |> pair (#disc (nth ctr_specs ctr_no))
900 fun prove_sel ({nested_maps, nested_map_idents, nested_map_comps, ctr_specs, ...}
901 : corec_spec) (disc_eqns : co_eqn_data_disc list) exclsss
902 ({fun_name, fun_T, fun_args, ctr, sel, rhs_term, ...} : co_eqn_data_sel) =
904 val SOME ctr_spec = find_first (equal ctr o #ctr) ctr_specs;
905 val ctr_no = find_index (equal ctr o #ctr) ctr_specs;
906 val prems = the_default (maps (s_not_conj o #prems) disc_eqns)
907 (find_first (equal ctr_no o #ctr_no) disc_eqns |> Option.map #prems);
908 val sel_corec = find_index (equal sel) (#sels ctr_spec)
909 |> nth (#sel_corecs ctr_spec);
911 val m = length prems;
913 list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
914 |> curry betapply sel
915 |> rpair (abstract (List.rev fun_args) rhs_term)
916 |> HOLogic.mk_Trueprop o HOLogic.mk_eq
917 |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
918 |> curry Logic.list_all (map dest_Free fun_args);
919 val (distincts, _, sel_splits, sel_split_asms) = case_thms_of_term lthy [] rhs_term;
921 mk_primcorec_sel_tac lthy def_thms distincts sel_splits sel_split_asms nested_maps
922 nested_map_idents nested_map_comps sel_corec k m exclsss
923 |> K |> Goal.prove lthy [] [] t
927 fun prove_ctr disc_alist sel_alist (disc_eqns : co_eqn_data_disc list)
928 (sel_eqns : co_eqn_data_sel list) ({ctr, disc, sels, collapse, ...} : corec_ctr_spec) =
929 (* don't try to prove theorems when some sel_eqns are missing *)
930 if not (exists (equal ctr o #ctr) disc_eqns)
931 andalso not (exists (equal ctr o #ctr) sel_eqns)
933 filter (equal ctr o #ctr) sel_eqns
934 |> fst o finds ((op =) o apsnd #sel) sels
935 |> exists (null o snd)
938 val (fun_name, fun_T, fun_args, prems, maybe_rhs) =
939 (find_first (equal ctr o #ctr) disc_eqns, find_first (equal ctr o #ctr) sel_eqns)
940 |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #prems x,
942 ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, [], NONE))
943 |> the o merge_options;
944 val m = length prems;
945 val t = (if is_some maybe_rhs then the maybe_rhs else
946 filter (equal ctr o #ctr) sel_eqns
947 |> fst o finds ((op =) o apsnd #sel) sels
948 |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) #-> abstract)
949 |> curry list_comb ctr)
950 |> curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
951 map Bound (length fun_args - 1 downto 0)))
952 |> HOLogic.mk_Trueprop
953 |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
954 |> curry Logic.list_all (map dest_Free fun_args);
955 val maybe_disc_thm = AList.lookup (op =) disc_alist disc;
956 val sel_thms = map snd (filter (member (op =) sels o fst) sel_alist);
958 if prems = [@{term False}] then [] else
959 mk_primcorec_ctr_of_dtr_tac lthy m collapse maybe_disc_thm sel_thms
960 |> K |> Goal.prove lthy [] [] t
965 fun prove_code disc_eqns sel_eqns ctr_alist
966 {distincts, sel_splits, sel_split_asms, ctr_specs, ...} =
967 (* FIXME doesn't work reliably yet *)
969 val (fun_name, fun_T, fun_args, maybe_rhs) =
970 (find_first (member (op =) (map #ctr ctr_specs) o #ctr) disc_eqns,
971 find_first (member (op =) (map #ctr ctr_specs) o #ctr) sel_eqns)
972 |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #maybe_code_rhs x))
973 ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, NONE))
974 |> the o merge_options;
976 val maybe_rhs' = if is_some maybe_rhs then maybe_rhs else
978 fun prove_code_ctr {ctr, disc, sels, ...} =
979 if not (exists (equal ctr o fst) ctr_alist) then NONE else
981 val (fun_name, fun_T, fun_args, prems) =
982 (find_first (equal ctr o #ctr) disc_eqns,
983 find_first (equal ctr o #ctr) sel_eqns)
984 |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #prems x))
985 ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, []))
986 |> the o merge_options;
987 val m = length prems;
989 filter (equal ctr o #ctr) sel_eqns
990 |> fst o finds ((op =) o apsnd #sel) sels
991 |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) #-> abstract)
992 |> curry list_comb ctr;
996 val maybe_ctr_conds_argss = map prove_code_ctr ctr_specs;
998 if exists is_none maybe_ctr_conds_argss then NONE else
999 fold_rev (fn SOME (prems, u) => fn t => mk_If (s_conjs prems) u t)
1000 maybe_ctr_conds_argss (Const (@{const_name undefined}, body_type fun_T))
1004 if is_none maybe_rhs' then [] else
1006 val rhs = the maybe_rhs';
1007 val bound_Ts = List.rev (map fastype_of fun_args);
1008 val rhs' = expand_corec_code_rhs lthy has_call bound_Ts rhs;
1009 val cond_ctrs = fold_rev_corec_code_rhs lthy (K oo (cons oo pair)) bound_Ts rhs' [];
1010 val ctr_thms = map (the o AList.lookup (op =) ctr_alist o snd) cond_ctrs;
1011 val ms = map (Logic.count_prems o prop_of) ctr_thms;
1012 val (t', t) = (rhs', rhs)
1014 (curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
1015 map Bound (length fun_args - 1 downto 0)))
1016 #> HOLogic.mk_Trueprop
1017 #> curry Logic.list_all (map dest_Free fun_args));
1018 val discIs = map #discI ctr_specs;
1019 val raw_code = mk_primcorec_raw_code_of_ctr_tac lthy distincts discIs sel_splits
1020 sel_split_asms ms ctr_thms
1021 |> K |> Goal.prove lthy [] [] t';
1023 mk_primcorec_code_of_raw_code_tac sel_splits raw_code
1024 |> K |> Goal.prove lthy [] [] t
1029 val disc_alists = map3 (maps oo prove_disc) corec_specs exclssss disc_eqnss;
1030 val sel_alists = map4 (map ooo prove_sel) corec_specs disc_eqnss exclssss sel_eqnss;
1031 val disc_thmss = map (map snd) disc_alists;
1032 val sel_thmss = map (map snd) sel_alists;
1034 val ctr_alists = map5 (maps oooo prove_ctr) disc_alists sel_alists disc_eqnss sel_eqnss
1035 (map #ctr_specs corec_specs);
1036 val ctr_thmss = map (map snd) ctr_alists;
1038 val code_thmss = map4 prove_code disc_eqnss sel_eqnss ctr_alists corec_specs;
1040 val simp_thmss = map2 append disc_thmss sel_thmss
1042 val common_name = mk_common_name fun_names;
1045 [(coinductN, map (if n2m then single else K []) coinduct_thms, []),
1046 (codeN, code_thmss, code_nitpick_attrs),
1047 (ctrN, ctr_thmss, []),
1048 (discN, disc_thmss, simp_attrs),
1049 (selN, sel_thmss, simp_attrs),
1050 (simpsN, simp_thmss, []),
1051 (strong_coinductN, map (if n2m then single else K []) strong_coinduct_thms, [])]
1052 |> maps (fn (thmN, thmss, attrs) =>
1053 map2 (fn fun_name => fn thms =>
1054 ((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])]))
1055 fun_names (take actual_nn thmss))
1056 |> filter_out (null o fst o hd o snd);
1059 [(coinductN, if n2m then [coinduct_thm] else [], []),
1060 (strong_coinductN, if n2m then [strong_coinduct_thm] else [], [])]
1061 |> filter_out (null o #2)
1062 |> map (fn (thmN, thms, attrs) =>
1063 ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
1065 lthy |> Local_Theory.notes (notes @ common_notes) |> snd
1068 fun after_qed thmss' = fold_map Local_Theory.define defs #-> prove thmss';
1070 val _ = if not simple orelse forall null obligationss then () else
1071 primrec_error "need exclusiveness proofs - use primcorecursive instead of primcorec";
1075 |> after_qed (map (fn [] => []) obligationss)
1079 |> Proof.theorem NONE after_qed obligationss
1080 |> Proof.refine (Method.primitive_text I)
1082 |> rpair NONE o SOME
1085 fun add_primcorec_ursive_cmd simple seq (raw_fixes, raw_specs') lthy =
1087 val (raw_specs, of_specs) = split_list raw_specs' ||> map (Option.map (Syntax.read_term lthy));
1088 val ((fixes, specs), _) = Specification.read_spec raw_fixes raw_specs lthy;
1090 add_primcorec simple seq fixes specs of_specs lthy
1091 handle ERROR str => primrec_error str
1093 handle Primrec_Error (str, eqns) =>
1095 then error ("primcorec error:\n " ^ str)
1096 else error ("primcorec error:\n " ^ str ^ "\nin\n " ^
1097 space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns));
1099 val add_primcorecursive_cmd = (the o fst) ooo add_primcorec_ursive_cmd false;
1100 val add_primcorec_cmd = (the o snd) ooo add_primcorec_ursive_cmd true;