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_cmd: (binding * string option * mixfix) list ->
11 (Attrib.binding * string) list -> local_theory -> local_theory;
12 val add_primcorec_cmd: bool ->
13 (binding * string option * mixfix) list * (Attrib.binding * string) list -> Proof.context ->
17 structure BNF_FP_Rec_Sugar : BNF_FP_REC_SUGAR =
22 open BNF_FP_Rec_Sugar_Util
23 open BNF_FP_Rec_Sugar_Tactics
25 exception Primrec_Error of string * term list;
27 fun primrec_error str = raise Primrec_Error (str, []);
28 fun primrec_error_eqn str eqn = raise Primrec_Error (str, [eqn]);
29 fun primrec_error_eqns str eqns = raise Primrec_Error (str, eqns);
31 fun finds eq = fold_map (fn x => List.partition (curry eq x) #>> pair x);
33 val free_name = try (fn Free (v, _) => v);
34 val const_name = try (fn Const (v, _) => v);
35 val undef_const = Const (@{const_name undefined}, dummyT);
37 fun permute_args n t = list_comb (t, map Bound (0 :: (n downto 1)))
38 |> fold (K (fn u => Abs (Name.uu, dummyT, u))) (0 upto n);
39 val abs_tuple = HOLogic.tupled_lambda o HOLogic.mk_tuple;
40 fun drop_All t = subst_bounds (strip_qnt_vars @{const_name all} t |> map Free |> rev,
41 strip_qnt_body @{const_name all} t)
42 fun mk_not @{const True} = @{const False}
43 | mk_not @{const False} = @{const True}
44 | mk_not (@{const Not} $ t) = t
45 | mk_not (@{const Trueprop} $ t) = @{const Trueprop} $ mk_not t
46 | mk_not t = HOLogic.mk_not t
47 val mk_conjs = try (foldr1 HOLogic.mk_conj) #> the_default @{const True};
48 val mk_disjs = try (foldr1 HOLogic.mk_disj) #> the_default @{const False};
50 fun invert_prems [t] = map mk_not (HOLogic.disjuncts t)
51 | invert_prems ts = [mk_disjs (map mk_not ts)];
53 val simp_attrs = @{attributes [simp]};
55 fun abstract n vs (t $ u) = abstract n vs t $ abstract n vs u
56 | abstract n vs (Abs (v, T, b)) = Abs (v, T, abstract (n + 1) vs b)
57 | abstract n vs t = let val idx = find_index (equal t) vs in
58 if idx < 0 then t else Bound (n + idx) end;
69 right_args: term list,
75 fun dissect_eqn lthy fun_names eqn' =
77 val eqn = drop_All eqn' |> HOLogic.dest_Trueprop
79 primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn';
80 val (lhs, rhs) = HOLogic.dest_eq eqn
82 primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn';
83 val (fun_name, args) = strip_comb lhs
84 |>> (fn x => if is_Free x then fst (dest_Free x)
85 else primrec_error_eqn "malformed function equation (does not start with free)" eqn);
86 val (left_args, rest) = take_prefix is_Free args;
87 val (nonfrees, right_args) = take_suffix is_Free rest;
88 val _ = length nonfrees = 1 orelse if length nonfrees = 0 then
89 primrec_error_eqn "constructor pattern missing in left-hand side" eqn else
90 primrec_error_eqn "more than one non-variable argument in left-hand side" eqn;
91 val _ = member (op =) fun_names fun_name orelse
92 primrec_error_eqn "malformed function equation (does not start with function name)" eqn
94 val (ctr, ctr_args) = strip_comb (the_single nonfrees);
95 val _ = try (num_binder_types o fastype_of) ctr = SOME (length ctr_args) orelse
96 primrec_error_eqn "partially applied constructor in pattern" eqn;
97 val _ = let val d = duplicates (op =) (left_args @ ctr_args @ right_args) in null d orelse
98 primrec_error_eqn ("duplicate variable \"" ^ Syntax.string_of_term lthy (hd d) ^
99 "\" in left-hand side") eqn end;
100 val _ = forall is_Free ctr_args orelse
101 primrec_error_eqn "non-primitive pattern in left-hand side" eqn;
103 let val b = fold_aterms (fn x as Free (v, _) =>
104 if (not (member (op =) (left_args @ ctr_args @ right_args) x) andalso
105 not (member (op =) fun_names v) andalso
106 not (Variable.is_fixed lthy v)) then cons x else I | _ => I) rhs []
109 primrec_error_eqn ("extra variable(s) in right-hand side: " ^
110 commas (map (Syntax.string_of_term lthy) b)) eqn
113 {fun_name = fun_name,
114 rec_type = body_type (type_of ctr),
117 left_args = left_args,
118 right_args = right_args,
119 res_type = map fastype_of (left_args @ right_args) ---> fastype_of rhs,
124 fun rewrite_map_arg get_ctr_pos rec_type res_type =
126 val pT = HOLogic.mk_prodT (rec_type, res_type);
128 val maybe_suc = Option.map (fn x => x + 1);
129 fun subst d (t as Bound d') = t |> d = SOME d' ? curry (op $) (fst_const pT)
130 | subst d (Abs (v, T, b)) = Abs (v, if d = SOME ~1 then pT else T, subst (maybe_suc d) b)
133 val (u, vs) = strip_comb t;
134 val ctr_pos = try (get_ctr_pos o the) (free_name u) |> the_default ~1;
137 if d = SOME ~1 andalso length vs = ctr_pos then
138 list_comb (permute_args ctr_pos (snd_const pT), vs)
139 else if length vs > ctr_pos andalso is_some d
140 andalso d = try (fn Bound n => n) (nth vs ctr_pos) then
141 list_comb (snd_const pT $ nth vs ctr_pos, map (subst d) (nth_drop ctr_pos vs))
143 primrec_error_eqn ("recursive call not directly applied to constructor argument") t
144 else if d = SOME ~1 andalso const_name u = SOME @{const_name comp} then
145 list_comb (map_types (K dummyT) u, map2 subst [NONE, d] vs)
147 list_comb (u, map (subst (d |> d = SOME ~1 ? K NONE)) vs)
153 fun subst_rec_calls lthy get_ctr_pos has_call ctr_args direct_calls indirect_calls t =
155 fun subst bound_Ts (Abs (v, T, b)) = Abs (v, T, subst (T :: bound_Ts) b)
156 | subst bound_Ts (t as g' $ y) =
158 val maybe_direct_y' = AList.lookup (op =) direct_calls y;
159 val maybe_indirect_y' = AList.lookup (op =) indirect_calls y;
160 val (g, g_args) = strip_comb g';
161 val ctr_pos = try (get_ctr_pos o the) (free_name g) |> the_default ~1;
162 val _ = ctr_pos < 0 orelse length g_args >= ctr_pos orelse
163 primrec_error_eqn "too few arguments in recursive call" t;
165 if not (member (op =) ctr_args y) then
166 pairself (subst bound_Ts) (g', y) |> (op $)
167 else if ctr_pos >= 0 then
168 list_comb (the maybe_direct_y', g_args)
169 else if is_some maybe_indirect_y' then
170 (if has_call g' then t else y)
171 |> massage_indirect_rec_call lthy has_call
172 (rewrite_map_arg get_ctr_pos) bound_Ts y (the maybe_indirect_y')
173 |> (if has_call g' then I else curry (op $) g')
180 |> tap (fn u => has_call u andalso (* FIXME detect this case earlier *)
181 primrec_error_eqn "recursive call not directly applied to constructor argument" t)
184 fun build_rec_arg lthy funs_data has_call ctr_spec maybe_eqn_data =
185 if is_none maybe_eqn_data then undef_const else
187 val eqn_data = the maybe_eqn_data;
188 val t = #rhs_term eqn_data;
189 val ctr_args = #ctr_args eqn_data;
191 val calls = #calls ctr_spec;
192 val n_args = fold (curry (op +) o (fn Direct_Rec _ => 2 | _ => 1)) calls 0;
194 val no_calls' = tag_list 0 calls
195 |> map_filter (try (apsnd (fn No_Rec n => n | Direct_Rec (n, _) => n)));
196 val direct_calls' = tag_list 0 calls
197 |> map_filter (try (apsnd (fn Direct_Rec (_, n) => n)));
198 val indirect_calls' = tag_list 0 calls
199 |> map_filter (try (apsnd (fn Indirect_Rec n => n)));
201 fun make_direct_type T = dummyT; (* FIXME? *)
203 val rec_res_type_list = map (fn (x :: _) => (#rec_type x, #res_type x)) funs_data;
205 fun make_indirect_type (Type (Tname, Ts)) = Type (Tname, Ts |> map (fn T =>
206 let val maybe_res_type = AList.lookup (op =) rec_res_type_list T in
207 if is_some maybe_res_type
208 then HOLogic.mk_prodT (T, the maybe_res_type)
209 else make_indirect_type T end))
210 | make_indirect_type T = T;
212 val args = replicate n_args ("", dummyT)
213 |> Term.rename_wrt_term t
215 |> fold (fn (ctr_arg_idx, arg_idx) =>
216 nth_map arg_idx (K (nth ctr_args ctr_arg_idx)))
218 |> fold (fn (ctr_arg_idx, arg_idx) =>
219 nth_map arg_idx (K (nth ctr_args ctr_arg_idx |> map_types make_direct_type)))
221 |> fold (fn (ctr_arg_idx, arg_idx) =>
222 nth_map arg_idx (K (nth ctr_args ctr_arg_idx |> map_types make_indirect_type)))
225 val fun_name_ctr_pos_list =
226 map (fn (x :: _) => (#fun_name x, length (#left_args x))) funs_data;
227 val get_ctr_pos = try (the o AList.lookup (op =) fun_name_ctr_pos_list) #> the_default ~1;
228 val direct_calls = map (apfst (nth ctr_args) o apsnd (nth args)) direct_calls';
229 val indirect_calls = map (apfst (nth ctr_args) o apsnd (nth args)) indirect_calls';
231 val abstractions = args @ #left_args eqn_data @ #right_args eqn_data;
234 |> subst_rec_calls lthy get_ctr_pos has_call ctr_args direct_calls indirect_calls
235 |> fold_rev lambda abstractions
238 fun build_defs lthy bs mxs funs_data rec_specs has_call =
240 val n_funs = length funs_data;
242 val ctr_spec_eqn_data_list' =
243 (take n_funs rec_specs |> map #ctr_specs) ~~ funs_data
244 |> maps (uncurry (finds (fn (x, y) => #ctr x = #ctr y))
245 ##> (fn x => null x orelse
246 primrec_error_eqns "excess equations in definition" (map #rhs_term x)) #> fst);
247 val _ = ctr_spec_eqn_data_list' |> map (fn (_, x) => length x <= 1 orelse
248 primrec_error_eqns ("multiple equations for constructor") (map #user_eqn x));
250 val ctr_spec_eqn_data_list =
251 ctr_spec_eqn_data_list' @ (drop n_funs rec_specs |> maps #ctr_specs |> map (rpair []));
253 val recs = take n_funs rec_specs |> map #recx;
254 val rec_args = ctr_spec_eqn_data_list
255 |> sort ((op <) o pairself (#offset o fst) |> make_ord)
256 |> map (uncurry (build_rec_arg lthy funs_data has_call) o apsnd (try the_single));
257 val ctr_poss = map (fn x =>
258 if length (distinct ((op =) o pairself (length o #left_args)) x) <> 1 then
259 primrec_error ("inconstant constructor pattern position for function " ^
260 quote (#fun_name (hd x)))
262 hd x |> #left_args |> length) funs_data;
265 |-> map2 (fn recx => fn ctr_pos => list_comb (recx, rec_args) |> permute_args ctr_pos)
266 |> Syntax.check_terms lthy
267 |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.map_name Thm.def_name b, []), t))) bs mxs
270 fun find_rec_calls has_call eqn_data =
272 fun find (Abs (_, _, b)) ctr_arg = find b ctr_arg
273 | find (t as _ $ _) ctr_arg =
275 val (f', args') = strip_comb t;
276 val n = find_index (equal ctr_arg) args';
279 find f' ctr_arg @ maps (fn x => find x ctr_arg) args'
281 let val (f, args) = chop n args' |>> curry list_comb f' in
283 f :: maps (fn x => find x ctr_arg) args
285 find f ctr_arg @ maps (fn x => find x ctr_arg) args
290 map (find (#rhs_term eqn_data)) (#ctr_args eqn_data)
291 |> (fn [] => NONE | callss => SOME (#ctr eqn_data, callss))
294 fun add_primrec fixes specs lthy =
296 val (bs, mxs) = map_split (apfst fst) fixes;
297 val fun_names = map Binding.name_of bs;
298 val eqns_data = map (snd #> dissect_eqn lthy fun_names) specs;
299 val funs_data = eqns_data
300 |> partition_eq ((op =) o pairself #fun_name)
301 |> finds (fn (x, y) => x = #fun_name (hd y)) fun_names |> fst
302 |> map (fn (x, y) => the_single y handle List.Empty =>
303 primrec_error ("missing equations for function " ^ quote x));
305 val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
306 val arg_Ts = map (#rec_type o hd) funs_data;
307 val res_Ts = map (#res_type o hd) funs_data;
308 val callssss = funs_data
309 |> map (partition_eq ((op =) o pairself #ctr))
310 |> map (maps (map_filter (find_rec_calls has_call)));
312 fun get_indices t = map (fst #>> Binding.name_of #> Free) fixes
313 |> map_index (fn (i, v) => if exists_subterm (equal v) t then SOME i else NONE)
315 val ((nontriv, rec_specs, _, induct_thm, induct_thms), lthy') =
316 rec_specs_of bs arg_Ts res_Ts get_indices callssss lthy;
318 val actual_nn = length funs_data;
320 val _ = let val ctrs = (maps (map #ctr o #ctr_specs) rec_specs) in
321 map (fn {ctr, user_eqn, ...} => member (op =) ctrs ctr orelse
322 primrec_error_eqn ("argument " ^ quote (Syntax.string_of_term lthy' ctr) ^
323 " is not a constructor in left-hand side") user_eqn) eqns_data end;
325 val defs = build_defs lthy' bs mxs funs_data rec_specs has_call;
327 fun prove def_thms' {ctr_specs, nested_map_idents, nested_map_comps, ...} induct_thm fun_data
330 val fun_name = #fun_name (hd fun_data);
331 val def_thms = map (snd o snd) def_thms';
332 val simp_thms = finds (fn (x, y) => #ctr x = #ctr y) fun_data ctr_specs
334 |> map_filter (try (fn (x, [y]) =>
335 (#user_eqn x, length (#left_args x) + length (#right_args x), #rec_thm y)))
336 |> map (fn (user_eqn, num_extra_args, rec_thm) =>
337 mk_primrec_tac lthy num_extra_args nested_map_idents nested_map_comps def_thms rec_thm
338 |> K |> Goal.prove lthy [] [] user_eqn)
341 [(inductN, if actual_nn > 1 then [induct_thm] else [], []),
342 (simpsN, simp_thms, simp_attrs)]
343 |> filter_out (null o #2)
344 |> map (fn (thmN, thms, attrs) =>
345 ((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])]));
347 lthy |> Local_Theory.notes notes
350 val common_name = mk_common_name fun_names;
353 [(inductN, if nontriv andalso actual_nn > 1 then [induct_thm] else [], [])]
354 |> filter_out (null o #2)
355 |> map (fn (thmN, thms, attrs) =>
356 ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
359 |> fold_map Local_Theory.define defs
360 |-> snd oo (fn def_thms' => fold_map3 (prove def_thms') (take actual_nn rec_specs)
361 (take actual_nn induct_thms) funs_data)
362 |> snd o Local_Theory.notes common_notes
365 fun add_primrec_cmd raw_fixes raw_specs lthy =
367 val _ = let val d = duplicates (op =) (map (Binding.name_of o #1) raw_fixes) in null d orelse
368 primrec_error ("duplicate function name(s): " ^ commas d) end;
369 val (fixes, specs) = fst (Specification.read_spec raw_fixes raw_specs lthy);
371 add_primrec fixes specs lthy
372 handle ERROR str => primrec_error str
374 handle Primrec_Error (str, eqns) =>
376 then error ("primrec_new error:\n " ^ str)
377 else error ("primrec_new error:\n " ^ str ^ "\nin\n " ^
378 space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns))
384 type co_eqn_data_disc = {
391 type co_eqn_data_sel = {
399 datatype co_eqn_data =
400 Disc of co_eqn_data_disc |
401 Sel of co_eqn_data_sel;
403 fun co_dissect_eqn_disc sequential fun_names corec_specs prems' concl matchedss =
405 fun find_subterm p = let (* FIXME \<exists>? *)
406 fun f (t as u $ v) = if p t then SOME t else merge_options (f u, f v)
407 | f t = if p t then SOME t else NONE
410 val applied_fun = concl
411 |> find_subterm (member ((op =) o apsnd SOME) fun_names o try (fst o dest_Free o head_of))
413 handle Option.Option => primrec_error_eqn "malformed discriminator equation" concl;
414 val (fun_name, fun_args) = strip_comb applied_fun |>> fst o dest_Free;
415 val corec_spec = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
417 val discs = #ctr_specs corec_spec |> map #disc;
418 val ctrs = #ctr_specs corec_spec |> map #ctr;
419 val not_disc = head_of concl = @{term Not};
420 val _ = not_disc andalso length ctrs <> 2 andalso
421 primrec_error_eqn "\<not>ed discriminator for a type with \<noteq> 2 constructors" concl;
422 val disc = find_subterm (member (op =) discs o head_of) concl;
423 val eq_ctr0 = concl |> perhaps (try (HOLogic.dest_not)) |> try (HOLogic.dest_eq #> snd)
424 |> (fn SOME t => let val n = find_index (equal t) ctrs in
425 if n >= 0 then SOME n else NONE end | _ => NONE);
426 val _ = is_some disc orelse is_some eq_ctr0 orelse
427 primrec_error_eqn "no discriminator in equation" concl;
429 if is_none disc then the eq_ctr0 else find_index (equal (head_of (the disc))) discs;
430 val ctr_no = if not_disc then 1 - ctr_no' else ctr_no';
432 val catch_all = try (fst o dest_Free o the_single) prems' = SOME Name.uu_;
433 val matcheds = AList.lookup (op =) matchedss fun_name |> the_default [];
434 val prems = map (abstract 0 (List.rev fun_args)) prems';
435 val real_prems = (if catch_all orelse sequential then invert_prems matcheds else []) @
436 (if catch_all then [] else prems);
438 val matchedss' = AList.delete (op =) fun_name matchedss
439 |> cons (fun_name, if sequential then prems @ matcheds else real_prems @ matcheds);
442 (real_prems, betapply (#disc (nth (#ctr_specs corec_spec) ctr_no), applied_fun))
443 |>> map HOLogic.mk_Trueprop ||> HOLogic.mk_Trueprop
444 |> Logic.list_implies;
455 fun co_dissect_eqn_sel fun_names corec_specs eqn' eqn =
457 val (lhs, rhs) = HOLogic.dest_eq eqn
459 primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn;
460 val sel = head_of lhs;
461 val (fun_name, fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst (fst o dest_Free)
463 primrec_error_eqn "malformed selector argument in left-hand side" eqn;
464 val corec_spec = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name)
465 handle Option.Option => primrec_error_eqn "malformed selector argument in left-hand side" eqn;
466 val (ctr_spec, sel) = #ctr_specs corec_spec
467 |> the o get_index (try (the o find_first (equal sel) o #sels))
468 |>> nth (#ctr_specs corec_spec);
469 val user_eqn = drop_All eqn';
481 fun co_dissect_eqn_ctr sequential fun_names corec_specs eqn' imp_prems imp_rhs matchedss =
483 val (lhs, rhs) = HOLogic.dest_eq imp_rhs;
484 val fun_name = head_of lhs |> fst o dest_Free;
485 val corec_spec = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
486 val (ctr, ctr_args) = strip_comb rhs;
487 val ctr_spec = the (find_first (equal ctr o #ctr) (#ctr_specs corec_spec))
488 handle Option.Option => primrec_error_eqn "not a constructor" ctr;
490 val disc_imp_rhs = betapply (#disc ctr_spec, lhs);
491 val (maybe_eqn_data_disc, matchedss') = if length (#ctr_specs corec_spec) = 1
492 then (NONE, matchedss)
493 else apfst SOME (co_dissect_eqn_disc
494 sequential fun_names corec_specs imp_prems disc_imp_rhs matchedss);
496 val sel_imp_rhss = (#sels ctr_spec ~~ ctr_args)
497 |> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg));
499 val _ = tracing ("reduced\n " ^ Syntax.string_of_term @{context} imp_rhs ^ "\nto\n \<cdot> " ^
500 (is_some maybe_eqn_data_disc ? K (Syntax.string_of_term @{context} disc_imp_rhs ^ "\n \<cdot> ")) "" ^
501 space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) sel_imp_rhss));
504 map (co_dissect_eqn_sel fun_names corec_specs eqn') sel_imp_rhss;
506 (the_list maybe_eqn_data_disc @ eqns_data_sel, matchedss')
509 fun co_dissect_eqn sequential fun_names corec_specs eqn' matchedss =
511 val eqn = drop_All eqn'
512 handle TERM _ => primrec_error_eqn "malformed function equation" eqn';
513 val (imp_prems, imp_rhs) = Logic.strip_horn eqn
514 |> apfst (map HOLogic.dest_Trueprop) o apsnd HOLogic.dest_Trueprop;
517 |> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq))
520 val maybe_rhs = imp_rhs |> perhaps (try (HOLogic.dest_not)) |> try (snd o HOLogic.dest_eq);
522 val discs = maps #ctr_specs corec_specs |> map #disc;
523 val sels = maps #ctr_specs corec_specs |> maps #sels;
524 val ctrs = maps #ctr_specs corec_specs |> map #ctr;
526 if member (op =) discs head orelse
527 is_some maybe_rhs andalso
528 member (op =) (filter (null o binder_types o fastype_of) ctrs) (the maybe_rhs) then
529 co_dissect_eqn_disc sequential fun_names corec_specs imp_prems imp_rhs matchedss
531 else if member (op =) sels head then
532 ([co_dissect_eqn_sel fun_names corec_specs eqn' imp_rhs], matchedss)
533 else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) then
534 co_dissect_eqn_ctr sequential fun_names corec_specs eqn' imp_prems imp_rhs matchedss
536 primrec_error_eqn "malformed function equation" eqn
539 fun build_corec_arg_disc ctr_specs {fun_args, ctr_no, prems, ...} =
540 if is_none (#pred (nth ctr_specs ctr_no)) then I else
542 |> curry subst_bounds (List.rev fun_args)
543 |> HOLogic.tupled_lambda (HOLogic.mk_tuple fun_args)
544 |> K |> nth_map (the (#pred (nth ctr_specs ctr_no)));
546 fun build_corec_arg_no_call sel_eqns sel = find_first (equal sel o #sel) sel_eqns
547 |> try (fn SOME sel_eqn => (#fun_args sel_eqn, #rhs_term sel_eqn))
548 |> the_default ([], undef_const)
552 fun build_corec_arg_direct_call lthy has_call sel_eqns sel =
554 val maybe_sel_eqn = find_first (equal sel o #sel) sel_eqns;
555 fun rewrite is_end U _ t =
556 if U = @{typ bool} then @{term True} |> has_call t ? K @{term False} (* stop? *)
557 else if is_end = has_call t then undef_const
558 else if is_end then t (* end *)
559 else HOLogic.mk_tuple (snd (strip_comb t)); (* continue *)
560 fun massage rhs_term is_end t = massage_direct_corec_call
561 lthy has_call (rewrite is_end) [] (range_type (fastype_of t)) rhs_term;
563 if is_none maybe_sel_eqn then K I else
564 abs_tuple (#fun_args (the maybe_sel_eqn)) oo massage (#rhs_term (the maybe_sel_eqn))
567 fun build_corec_arg_indirect_call lthy has_call sel_eqns sel =
569 val maybe_sel_eqn = find_first (equal sel o #sel) sel_eqns;
572 fun subst (Abs (v, T, b)) = Abs (v, T, subst b)
573 | subst (t as _ $ _) =
574 let val (u, vs) = strip_comb t in
575 if is_Free u andalso has_call u then
576 Const (@{const_name Inr}, dummyT) $ (*HOLogic.mk_tuple vs*)
577 (try (foldr1 (fn (x, y) => Const (@{const_name Pair}, dummyT) $ x $ y)) vs
578 |> the_default (hd vs))
579 else if try (fst o dest_Const) u = SOME @{const_name prod_case} then
580 list_comb (u |> map_types (K dummyT), map subst vs)
582 list_comb (subst u, map subst vs)
588 fun massage rhs_term t = massage_indirect_corec_call
589 lthy has_call rewrite [] (fastype_of t |> range_type) rhs_term;
591 if is_none maybe_sel_eqn then I else
592 abs_tuple (#fun_args (the maybe_sel_eqn)) o massage (#rhs_term (the maybe_sel_eqn))
595 fun build_corec_args_sel lthy has_call all_sel_eqns ctr_spec =
596 let val sel_eqns = filter (equal (#ctr ctr_spec) o #ctr) all_sel_eqns in
597 if null sel_eqns then I else
599 val sel_call_list = #sels ctr_spec ~~ #calls ctr_spec;
601 val no_calls' = map_filter (try (apsnd (fn No_Corec n => n))) sel_call_list;
602 val direct_calls' = map_filter (try (apsnd (fn Direct_Corec n => n))) sel_call_list;
603 val indirect_calls' = map_filter (try (apsnd (fn Indirect_Corec n => n))) sel_call_list;
606 #> fold (fn (sel, n) => nth_map n
607 (build_corec_arg_no_call sel_eqns sel)) no_calls'
608 #> fold (fn (sel, (q, g, h)) =>
609 let val f = build_corec_arg_direct_call lthy has_call sel_eqns sel in
610 nth_map h (f false) o nth_map g (f true) o nth_map q (f true) end) direct_calls'
611 #> fold (fn (sel, n) => nth_map n
612 (build_corec_arg_indirect_call lthy has_call sel_eqns sel)) indirect_calls'
616 fun mk_real_disc_eqns ctr_specs disc_eqns =
619 if length disc_eqns = 0 then disc_eqns
620 else if length disc_eqns = length ctr_specs - 1 then
622 val n = 0 upto length ctr_specs
623 |> the(*###*) o find_first (fn idx => not (exists (equal idx o #ctr_no) disc_eqns));
624 val extra_disc_eqn = {
625 fun_name = #fun_name (hd disc_eqns),
626 fun_args = #fun_args (hd disc_eqns),
628 prems = maps (invert_prems o #prems) disc_eqns,
629 user_eqn = Const (@{const_name undefined}, dummyT)};
631 chop n disc_eqns ||> cons extra_disc_eqn |> (op @)
638 fun co_build_defs lthy bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss =
640 val _ = disc_eqnss |> map (fn x =>
641 let val d = duplicates ((op =) o pairself #ctr_no) x in null d orelse
642 primrec_error_eqns "excess discriminator equations in definition"
643 (maps (fn t => filter (equal (#ctr_no t) o #ctr_no) x) d |> map #user_eqn) end);
644 val corec_specs' = take (length bs) corec_specs;
645 val corecs = map #corec corec_specs';
646 val ctr_specss = map #ctr_specs corec_specs';
647 val real_disc_eqnss = map2 mk_real_disc_eqns ctr_specss disc_eqnss;
648 val corec_args = hd corecs
649 |> fst o split_last o binder_types o fastype_of
650 |> map (Const o pair @{const_name undefined})
651 |> fold2 (fold o build_corec_arg_disc) ctr_specss real_disc_eqnss
652 |> fold2 (fold o build_corec_args_sel lthy has_call) sel_eqnss ctr_specss;
653 fun currys Ts t = if length Ts <= 1 then t else
654 t $ foldr1 (fn (u, v) => HOLogic.pair_const dummyT dummyT $ u $ v)
655 (length Ts - 1 downto 0 |> map Bound)
656 |> fold_rev (fn T => fn u => Abs (Name.uu, T, u)) Ts;
658 val _ = tracing ("corecursor arguments:\n \<cdot> " ^
659 space_implode "\n \<cdot> " (map (Syntax.string_of_term lthy) corec_args));
663 |> map (map (fn {fun_args, ctr_no, prems, ...} => (fun_args, ctr_no, prems))
664 #> fst o (fn xs => fold_map (fn x => fn ys => ((x, ys), ys @ [x])) xs [])
665 #> maps (uncurry (map o pair)
666 #> map (fn ((fun_args, c, x), (_, c', y)) => ((c, c'), (x, mk_not (mk_conjs y)))
667 ||> apfst (map HOLogic.mk_Trueprop) o apsnd HOLogic.mk_Trueprop
668 ||> Logic.list_implies
669 ||> curry Logic.list_all (map dest_Free fun_args))))
671 map (list_comb o rpair corec_args) corecs
672 |> map2 (fn Ts => fn t => if length Ts = 0 then t $ HOLogic.unit else t) arg_Tss
673 |> map2 currys arg_Tss
674 |> Syntax.check_terms lthy
675 |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.map_name Thm.def_name b, []), t))) bs mxs
679 fun add_primcorec sequential fixes specs lthy =
681 val (bs, mxs) = map_split (apfst fst) fixes;
682 val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> HOLogic.mk_tupleT) fixes |> split_list;
684 (* copied from primrec_new *)
685 fun get_indices t = map (fst #>> Binding.name_of #> Free) fixes
686 |> map_index (fn (i, v) => if exists_subterm (equal v) t then SOME i else NONE)
689 val callssss = []; (* FIXME *)
691 val ((nontriv, corec_specs', _, coinduct_thm, strong_co_induct_thm, coinduct_thmss,
692 strong_coinduct_thmss), lthy') =
693 corec_specs_of bs arg_Ts res_Ts get_indices callssss lthy;
695 val fun_names = map Binding.name_of bs;
696 val corec_specs = take (length fun_names) corec_specs'; (*###*)
699 fold_map (co_dissect_eqn sequential fun_names corec_specs) (map snd specs) []
702 val disc_eqnss = map_filter (try (fn Disc x => x)) eqns_data
703 |> partition_eq ((op =) o pairself #fun_name)
704 |> finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names |> fst
705 |> map (sort ((op <) o pairself #ctr_no |> make_ord) o flat o snd);
707 val sel_eqnss = map_filter (try (fn Sel x => x)) eqns_data
708 |> partition_eq ((op =) o pairself #fun_name)
709 |> finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names |> fst
712 val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
713 val arg_Tss = map (binder_types o snd o fst) fixes;
714 val (defs, exclss') =
715 co_build_defs lthy' bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss;
717 (* try to prove (automatically generated) tautologies by ourselves *)
718 val exclss'' = exclss'
720 (`(try (fn t => Goal.prove lthy [] [] t (mk_primcorec_taut_tac lthy |> K))))));
721 val taut_thmss = map (map (apsnd (the o fst)) o filter (is_some o fst o snd)) exclss'';
722 val (obligation_idxss, obligationss) = exclss''
723 |> map (map (apsnd (rpair [] o snd)) o filter (is_none o fst o snd))
724 |> split_list o map split_list;
726 fun prove thmss' def_thms' lthy =
728 val def_thms = map (snd o snd) def_thms';
730 val exclss' = map (op ~~) (obligation_idxss ~~ thmss');
731 fun mk_exclsss excls n =
732 (excls, map (fn k => replicate k [TrueI] @ replicate (n - k) []) (0 upto n - 1))
733 |-> fold (fn ((c, c'), thm) => nth_map c (nth_map c' (K [thm])));
734 val exclssss = (exclss' ~~ taut_thmss |> map (op @), fun_names ~~ corec_specs)
735 |-> map2 (fn excls => fn (_, {ctr_specs, ...}) => mk_exclsss excls (length ctr_specs));
737 fun prove_disc {ctr_specs, ...} exclsss
738 {fun_name, fun_args, ctr_no, prems, ...} =
740 val disc_corec = nth ctr_specs ctr_no |> #disc_corec;
742 val m = length prems;
744 (* FIXME use applied_fun from dissect_\<dots> instead? *)
745 list_comb (Free (fun_name, dummyT), map Bound (length fun_args - 1 downto 0))
746 |> curry betapply (#disc (nth ctr_specs ctr_no)) (*###*)
747 |> HOLogic.mk_Trueprop
748 |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
749 |> curry Logic.list_all (map dest_Free fun_args)
750 |> Syntax.check_term lthy(*###*);
752 mk_primcorec_disc_tac lthy def_thms disc_corec k m exclsss
753 |> K |> Goal.prove lthy [] [] t
756 (* FIXME don't use user_eqn (cf. constructor view reduction),
757 instead generate "sel" and "code" theorems ourselves *)
759 ((fun_name, {ctr_specs, nested_maps, nested_map_idents, nested_map_comps, ...}),
760 disc_eqns) exclsss sel_eqn =
762 val (SOME ctr_spec) = find_first (equal (#ctr sel_eqn) o #ctr) ctr_specs;
763 val ctr_no = find_index (equal (#ctr sel_eqn) o #ctr) ctr_specs;
764 val prems = the_default (maps (invert_prems o #prems) disc_eqns)
765 (find_first (equal ctr_no o #ctr_no) disc_eqns |> Option.map #prems);
766 val sel_corec = find_index (equal (#sel sel_eqn)) (#sels ctr_spec)
767 |> nth (#sel_corecs ctr_spec);
769 val m = length prems;
770 val t = #user_eqn sel_eqn
771 |> abstract 0 (List.rev (#fun_args sel_eqn)) (* FIXME do this in dissect_\<dots> *)
772 |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
773 |> curry Logic.list_all (map dest_Free (#fun_args sel_eqn));
775 mk_primcorec_eq_tac lthy def_thms sel_corec k m exclsss
776 nested_maps nested_map_idents nested_map_comps
777 |> K |> Goal.prove lthy [] [] t
782 map3 (map oo prove_disc) (take (length disc_eqnss) corec_specs) exclssss disc_eqnss
783 |> map (fn (fun_name, thms) =>
784 ((Binding.qualify true fun_name (@{binding disc}), simp_attrs), [(thms, [])]));
787 map3 (map oo prove_sel) (fun_names ~~ corec_specs ~~ disc_eqnss) exclssss sel_eqnss
788 |> map (fn (fun_name, thms) =>
789 ((Binding.qualify true fun_name (@{binding sel}), simp_attrs), [(thms, [])]));
791 lthy |> snd o Local_Theory.notes (disc_notes @ sel_notes)
795 |> Proof.theorem NONE (curry (op #->) (fold_map Local_Theory.define defs) o prove) obligationss
796 |> Proof.refine (Method.primitive_text I)
800 fun add_primcorec_cmd seq (raw_fixes, raw_specs) lthy =
802 val (fixes, specs) = fst (Specification.read_spec raw_fixes raw_specs lthy);
804 add_primcorec seq fixes specs lthy
805 handle ERROR str => primrec_error str
807 handle Primrec_Error (str, eqns) =>
809 then error ("primcorec error:\n " ^ str)
810 else error ("primcorec error:\n " ^ str ^ "\nin\n " ^
811 space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns))