src/HOL/BNF/Tools/bnf_fp_rec_sugar.ML
author blanchet
Thu Sep 26 16:10:57 2013 +0200 (2013-09-26)
changeset 53923 7b43d22accc3
parent 53918 0fc622be0185
child 53925 9008c4806198
permissions -rw-r--r--
tuning
     1 (*  Title:      HOL/BNF/Tools/bnf_fp_rec_sugar.ML
     2     Author:     Lorenz Panny, TU Muenchen
     3     Copyright   2013
     4 
     5 Recursor and corecursor sugar.
     6 *)
     7 
     8 signature BNF_FP_REC_SUGAR =
     9 sig
    10   val add_primrec_cmd: (binding * string option * mixfix) list ->
    11     (Attrib.binding * string) list -> local_theory -> local_theory;
    12   val add_primcorecursive_cmd: bool ->
    13     (binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list ->
    14     Proof.context -> Proof.state
    15   val add_primcorec_cmd: bool ->
    16     (binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list ->
    17     local_theory -> local_theory
    18 end;
    19 
    20 structure BNF_FP_Rec_Sugar : BNF_FP_REC_SUGAR =
    21 struct
    22 
    23 open BNF_Util
    24 open BNF_FP_Util
    25 open BNF_FP_Rec_Sugar_Util
    26 open BNF_FP_Rec_Sugar_Tactics
    27 
    28 val codeN = "code"
    29 val ctrN = "ctr"
    30 val discN = "disc"
    31 val selN = "sel"
    32 
    33 val nitpick_attrs = @{attributes [nitpick_simp]};
    34 val code_nitpick_simp_attrs = Code.add_default_eqn_attrib :: nitpick_attrs;
    35 val simp_attrs = @{attributes [simp]};
    36 
    37 exception Primrec_Error of string * term list;
    38 
    39 fun primrec_error str = raise Primrec_Error (str, []);
    40 fun primrec_error_eqn str eqn = raise Primrec_Error (str, [eqn]);
    41 fun primrec_error_eqns str eqns = raise Primrec_Error (str, eqns);
    42 
    43 fun finds eq = fold_map (fn x => List.partition (curry eq x) #>> pair x);
    44 
    45 val free_name = try (fn Free (v, _) => v);
    46 val const_name = try (fn Const (v, _) => v);
    47 val undef_const = Const (@{const_name undefined}, dummyT);
    48 
    49 fun permute_args n t = list_comb (t, map Bound (0 :: (n downto 1)))
    50   |> fold (K (Term.abs (Name.uu, dummyT))) (0 upto n);
    51 val abs_tuple = HOLogic.tupled_lambda o HOLogic.mk_tuple;
    52 fun drop_All t = subst_bounds (strip_qnt_vars @{const_name all} t |> map Free |> rev,
    53   strip_qnt_body @{const_name all} t)
    54 fun abstract vs =
    55   let fun a n (t $ u) = a n t $ a n u
    56         | a n (Abs (v, T, b)) = Abs (v, T, a (n + 1) b)
    57         | a n t = let val idx = find_index (equal t) vs in
    58             if idx < 0 then t else Bound (n + idx) end
    59   in a 0 end;
    60 fun mk_prod1 Ts (t, u) = HOLogic.pair_const (fastype_of1 (Ts, t)) (fastype_of1 (Ts, u)) $ t $ u;
    61 fun mk_tuple1 Ts = the_default HOLogic.unit o try (foldr1 (mk_prod1 Ts));
    62 
    63 fun get_indices fixes t = map (fst #>> Binding.name_of #> Free) fixes
    64   |> map_index (fn (i, v) => if exists_subterm (equal v) t then SOME i else NONE)
    65   |> map_filter I;
    66 
    67 
    68 (* Primrec *)
    69 
    70 type eqn_data = {
    71   fun_name: string,
    72   rec_type: typ,
    73   ctr: term,
    74   ctr_args: term list,
    75   left_args: term list,
    76   right_args: term list,
    77   res_type: typ,
    78   rhs_term: term,
    79   user_eqn: term
    80 };
    81 
    82 fun dissect_eqn lthy fun_names eqn' =
    83   let
    84     val eqn = drop_All eqn' |> HOLogic.dest_Trueprop
    85       handle TERM _ =>
    86         primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn';
    87     val (lhs, rhs) = HOLogic.dest_eq eqn
    88         handle TERM _ =>
    89           primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn';
    90     val (fun_name, args) = strip_comb lhs
    91       |>> (fn x => if is_Free x then fst (dest_Free x)
    92           else primrec_error_eqn "malformed function equation (does not start with free)" eqn);
    93     val (left_args, rest) = take_prefix is_Free args;
    94     val (nonfrees, right_args) = take_suffix is_Free rest;
    95     val num_nonfrees = length nonfrees;
    96     val _ = num_nonfrees = 1 orelse if num_nonfrees = 0 then
    97       primrec_error_eqn "constructor pattern missing in left-hand side" eqn else
    98       primrec_error_eqn "more than one non-variable argument in left-hand side" eqn;
    99     val _ = member (op =) fun_names fun_name orelse
   100       primrec_error_eqn "malformed function equation (does not start with function name)" eqn
   101 
   102     val (ctr, ctr_args) = strip_comb (the_single nonfrees);
   103     val _ = try (num_binder_types o fastype_of) ctr = SOME (length ctr_args) orelse
   104       primrec_error_eqn "partially applied constructor in pattern" eqn;
   105     val _ = let val d = duplicates (op =) (left_args @ ctr_args @ right_args) in null d orelse
   106       primrec_error_eqn ("duplicate variable \"" ^ Syntax.string_of_term lthy (hd d) ^
   107         "\" in left-hand side") eqn end;
   108     val _ = forall is_Free ctr_args orelse
   109       primrec_error_eqn "non-primitive pattern in left-hand side" eqn;
   110     val _ =
   111       let val b = fold_aterms (fn x as Free (v, _) =>
   112         if (not (member (op =) (left_args @ ctr_args @ right_args) x) andalso
   113         not (member (op =) fun_names v) andalso
   114         not (Variable.is_fixed lthy v)) then cons x else I | _ => I) rhs []
   115       in
   116         null b orelse
   117         primrec_error_eqn ("extra variable(s) in right-hand side: " ^
   118           commas (map (Syntax.string_of_term lthy) b)) eqn
   119       end;
   120   in
   121     {fun_name = fun_name,
   122      rec_type = body_type (type_of ctr),
   123      ctr = ctr,
   124      ctr_args = ctr_args,
   125      left_args = left_args,
   126      right_args = right_args,
   127      res_type = map fastype_of (left_args @ right_args) ---> fastype_of rhs,
   128      rhs_term = rhs,
   129      user_eqn = eqn'}
   130   end;
   131 
   132 fun rewrite_map_arg get_ctr_pos rec_type res_type =
   133   let
   134     val pT = HOLogic.mk_prodT (rec_type, res_type);
   135 
   136     val maybe_suc = Option.map (fn x => x + 1);
   137     fun subst d (t as Bound d') = t |> d = SOME d' ? curry (op $) (fst_const pT)
   138       | subst d (Abs (v, T, b)) = Abs (v, if d = SOME ~1 then pT else T, subst (maybe_suc d) b)
   139       | subst d t =
   140         let
   141           val (u, vs) = strip_comb t;
   142           val ctr_pos = try (get_ctr_pos o the) (free_name u) |> the_default ~1;
   143         in
   144           if ctr_pos >= 0 then
   145             if d = SOME ~1 andalso length vs = ctr_pos then
   146               list_comb (permute_args ctr_pos (snd_const pT), vs)
   147             else if length vs > ctr_pos andalso is_some d
   148                 andalso d = try (fn Bound n => n) (nth vs ctr_pos) then
   149               list_comb (snd_const pT $ nth vs ctr_pos, map (subst d) (nth_drop ctr_pos vs))
   150             else
   151               primrec_error_eqn ("recursive call not directly applied to constructor argument") t
   152           else if d = SOME ~1 andalso const_name u = SOME @{const_name comp} then
   153             list_comb (map_types (K dummyT) u, map2 subst [NONE, d] vs)
   154           else
   155             list_comb (u, map (subst (d |> d = SOME ~1 ? K NONE)) vs)
   156         end
   157   in
   158     subst (SOME ~1)
   159   end;
   160 
   161 fun subst_rec_calls lthy get_ctr_pos has_call ctr_args direct_calls indirect_calls t =
   162   let
   163     fun subst bound_Ts (Abs (v, T, b)) = Abs (v, T, subst (T :: bound_Ts) b)
   164       | subst bound_Ts (t as g' $ y) =
   165         let
   166           val maybe_direct_y' = AList.lookup (op =) direct_calls y;
   167           val maybe_indirect_y' = AList.lookup (op =) indirect_calls y;
   168           val (g, g_args) = strip_comb g';
   169           val ctr_pos = try (get_ctr_pos o the) (free_name g) |> the_default ~1;
   170           val _ = ctr_pos < 0 orelse length g_args >= ctr_pos orelse
   171             primrec_error_eqn "too few arguments in recursive call" t;
   172         in
   173           if not (member (op =) ctr_args y) then
   174             pairself (subst bound_Ts) (g', y) |> (op $)
   175           else if ctr_pos >= 0 then
   176             list_comb (the maybe_direct_y', g_args)
   177           else if is_some maybe_indirect_y' then
   178             (if has_call g' then t else y)
   179             |> massage_indirect_rec_call lthy has_call
   180               (rewrite_map_arg get_ctr_pos) bound_Ts y (the maybe_indirect_y')
   181             |> (if has_call g' then I else curry (op $) g')
   182           else
   183             t
   184         end
   185       | subst _ t = t
   186   in
   187     subst [] t
   188     |> tap (fn u => has_call u andalso (* FIXME detect this case earlier *)
   189       primrec_error_eqn "recursive call not directly applied to constructor argument" t)
   190   end;
   191 
   192 fun build_rec_arg lthy funs_data has_call ctr_spec maybe_eqn_data =
   193   if is_none maybe_eqn_data then undef_const else
   194     let
   195       val eqn_data = the maybe_eqn_data;
   196       val t = #rhs_term eqn_data;
   197       val ctr_args = #ctr_args eqn_data;
   198 
   199       val calls = #calls ctr_spec;
   200       val n_args = fold (curry (op +) o (fn Direct_Rec _ => 2 | _ => 1)) calls 0;
   201 
   202       val no_calls' = tag_list 0 calls
   203         |> map_filter (try (apsnd (fn No_Rec n => n | Direct_Rec (n, _) => n)));
   204       val direct_calls' = tag_list 0 calls
   205         |> map_filter (try (apsnd (fn Direct_Rec (_, n) => n)));
   206       val indirect_calls' = tag_list 0 calls
   207         |> map_filter (try (apsnd (fn Indirect_Rec n => n)));
   208 
   209       fun make_direct_type _ = dummyT; (* FIXME? *)
   210 
   211       val rec_res_type_list = map (fn (x :: _) => (#rec_type x, #res_type x)) funs_data;
   212 
   213       fun make_indirect_type (Type (Tname, Ts)) = Type (Tname, Ts |> map (fn T =>
   214         let val maybe_res_type = AList.lookup (op =) rec_res_type_list T in
   215           if is_some maybe_res_type
   216           then HOLogic.mk_prodT (T, the maybe_res_type)
   217           else make_indirect_type T end))
   218         | make_indirect_type T = T;
   219 
   220       val args = replicate n_args ("", dummyT)
   221         |> Term.rename_wrt_term t
   222         |> map Free
   223         |> fold (fn (ctr_arg_idx, arg_idx) =>
   224             nth_map arg_idx (K (nth ctr_args ctr_arg_idx)))
   225           no_calls'
   226         |> fold (fn (ctr_arg_idx, arg_idx) =>
   227             nth_map arg_idx (K (nth ctr_args ctr_arg_idx |> map_types make_direct_type)))
   228           direct_calls'
   229         |> fold (fn (ctr_arg_idx, arg_idx) =>
   230             nth_map arg_idx (K (nth ctr_args ctr_arg_idx |> map_types make_indirect_type)))
   231           indirect_calls';
   232 
   233       val fun_name_ctr_pos_list =
   234         map (fn (x :: _) => (#fun_name x, length (#left_args x))) funs_data;
   235       val get_ctr_pos = try (the o AList.lookup (op =) fun_name_ctr_pos_list) #> the_default ~1;
   236       val direct_calls = map (apfst (nth ctr_args) o apsnd (nth args)) direct_calls';
   237       val indirect_calls = map (apfst (nth ctr_args) o apsnd (nth args)) indirect_calls';
   238 
   239       val abstractions = args @ #left_args eqn_data @ #right_args eqn_data;
   240     in
   241       t
   242       |> subst_rec_calls lthy get_ctr_pos has_call ctr_args direct_calls indirect_calls
   243       |> fold_rev lambda abstractions
   244     end;
   245 
   246 fun build_defs lthy bs mxs funs_data rec_specs has_call =
   247   let
   248     val n_funs = length funs_data;
   249 
   250     val ctr_spec_eqn_data_list' =
   251       (take n_funs rec_specs |> map #ctr_specs) ~~ funs_data
   252       |> maps (uncurry (finds (fn (x, y) => #ctr x = #ctr y))
   253           ##> (fn x => null x orelse
   254             primrec_error_eqns "excess equations in definition" (map #rhs_term x)) #> fst);
   255     val _ = ctr_spec_eqn_data_list' |> map (fn (_, x) => length x <= 1 orelse
   256       primrec_error_eqns ("multiple equations for constructor") (map #user_eqn x));
   257 
   258     val ctr_spec_eqn_data_list =
   259       ctr_spec_eqn_data_list' @ (drop n_funs rec_specs |> maps #ctr_specs |> map (rpair []));
   260 
   261     val recs = take n_funs rec_specs |> map #recx;
   262     val rec_args = ctr_spec_eqn_data_list
   263       |> sort ((op <) o pairself (#offset o fst) |> make_ord)
   264       |> map (uncurry (build_rec_arg lthy funs_data has_call) o apsnd (try the_single));
   265     val ctr_poss = map (fn x =>
   266       if length (distinct ((op =) o pairself (length o #left_args)) x) <> 1 then
   267         primrec_error ("inconstant constructor pattern position for function " ^
   268           quote (#fun_name (hd x)))
   269       else
   270         hd x |> #left_args |> length) funs_data;
   271   in
   272     (recs, ctr_poss)
   273     |-> map2 (fn recx => fn ctr_pos => list_comb (recx, rec_args) |> permute_args ctr_pos)
   274     |> Syntax.check_terms lthy
   275     |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.map_name Thm.def_name b, []), t))) bs mxs
   276   end;
   277 
   278 fun find_rec_calls has_call eqn_data =
   279   let
   280     fun find (Abs (_, _, b)) ctr_arg = find b ctr_arg
   281       | find (t as _ $ _) ctr_arg =
   282         let
   283           val (f', args') = strip_comb t;
   284           val n = find_index (equal ctr_arg) args';
   285         in
   286           if n < 0 then
   287             find f' ctr_arg @ maps (fn x => find x ctr_arg) args'
   288           else
   289             let val (f, args) = chop n args' |>> curry list_comb f' in
   290               if has_call f then
   291                 f :: maps (fn x => find x ctr_arg) args
   292               else
   293                 find f ctr_arg @ maps (fn x => find x ctr_arg) args
   294             end
   295         end
   296       | find _ _ = [];
   297   in
   298     map (find (#rhs_term eqn_data)) (#ctr_args eqn_data)
   299     |> (fn [] => NONE | callss => SOME (#ctr eqn_data, callss))
   300   end;
   301 
   302 fun add_primrec fixes specs lthy =
   303   let
   304     val (bs, mxs) = map_split (apfst fst) fixes;
   305     val fun_names = map Binding.name_of bs;
   306     val eqns_data = map (snd #> dissect_eqn lthy fun_names) specs;
   307     val funs_data = eqns_data
   308       |> partition_eq ((op =) o pairself #fun_name)
   309       |> finds (fn (x, y) => x = #fun_name (hd y)) fun_names |> fst
   310       |> map (fn (x, y) => the_single y handle List.Empty =>
   311           primrec_error ("missing equations for function " ^ quote x));
   312 
   313     val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
   314     val arg_Ts = map (#rec_type o hd) funs_data;
   315     val res_Ts = map (#res_type o hd) funs_data;
   316     val callssss = funs_data
   317       |> map (partition_eq ((op =) o pairself #ctr))
   318       |> map (maps (map_filter (find_rec_calls has_call)));
   319 
   320     val ((n2m, rec_specs, _, induct_thm, induct_thms), lthy') =
   321       rec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;
   322 
   323     val actual_nn = length funs_data;
   324 
   325     val _ = let val ctrs = (maps (map #ctr o #ctr_specs) rec_specs) in
   326       map (fn {ctr, user_eqn, ...} => member (op =) ctrs ctr orelse
   327         primrec_error_eqn ("argument " ^ quote (Syntax.string_of_term lthy' ctr) ^
   328           " is not a constructor in left-hand side") user_eqn) eqns_data end;
   329 
   330     val defs = build_defs lthy' bs mxs funs_data rec_specs has_call;
   331 
   332     fun prove def_thms' {ctr_specs, nested_map_idents, nested_map_comps, ...} induct_thm fun_data
   333         lthy =
   334       let
   335         val fun_name = #fun_name (hd fun_data);
   336         val def_thms = map (snd o snd) def_thms';
   337         val simp_thms = finds (fn (x, y) => #ctr x = #ctr y) fun_data ctr_specs
   338           |> fst
   339           |> map_filter (try (fn (x, [y]) =>
   340             (#user_eqn x, length (#left_args x) + length (#right_args x), #rec_thm y)))
   341           |> map (fn (user_eqn, num_extra_args, rec_thm) =>
   342             mk_primrec_tac lthy num_extra_args nested_map_idents nested_map_comps def_thms rec_thm
   343             |> K |> Goal.prove lthy [] [] user_eqn)
   344 
   345         val notes =
   346           [(inductN, if n2m then [induct_thm] else [], []),
   347            (simpsN, simp_thms, code_nitpick_simp_attrs @ simp_attrs)]
   348           |> filter_out (null o #2)
   349           |> map (fn (thmN, thms, attrs) =>
   350             ((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])]));
   351       in
   352         lthy |> Local_Theory.notes notes
   353       end;
   354 
   355     val common_name = mk_common_name fun_names;
   356 
   357     val common_notes =
   358       [(inductN, if n2m then [induct_thm] else [], [])]
   359       |> filter_out (null o #2)
   360       |> map (fn (thmN, thms, attrs) =>
   361         ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
   362   in
   363     lthy'
   364     |> fold_map Local_Theory.define defs
   365     |-> snd oo (fn def_thms' => fold_map3 (prove def_thms') (take actual_nn rec_specs)
   366       (take actual_nn induct_thms) funs_data)
   367     |> Local_Theory.notes common_notes |> snd
   368   end;
   369 
   370 fun add_primrec_cmd raw_fixes raw_specs lthy =
   371   let
   372     val _ = let val d = duplicates (op =) (map (Binding.name_of o #1) raw_fixes) in null d orelse
   373       primrec_error ("duplicate function name(s): " ^ commas d) end;
   374     val (fixes, specs) = fst (Specification.read_spec raw_fixes raw_specs lthy);
   375   in
   376     add_primrec fixes specs lthy
   377       handle ERROR str => primrec_error str
   378   end
   379   handle Primrec_Error (str, eqns) =>
   380     if null eqns
   381     then error ("primrec_new error:\n  " ^ str)
   382     else error ("primrec_new error:\n  " ^ str ^ "\nin\n  " ^
   383       space_implode "\n  " (map (quote o Syntax.string_of_term lthy) eqns));
   384 
   385 
   386 
   387 (* Primcorec *)
   388 
   389 type co_eqn_data_disc = {
   390   fun_name: string,
   391   fun_T: typ,
   392   fun_args: term list,
   393   ctr: term,
   394   ctr_no: int, (*###*)
   395   disc: term,
   396   prems: term list,
   397   auto_gen: bool,
   398   user_eqn: term
   399 };
   400 type co_eqn_data_sel = {
   401   fun_name: string,
   402   fun_T: typ,
   403   fun_args: term list,
   404   ctr: term,
   405   sel: term,
   406   rhs_term: term,
   407   user_eqn: term
   408 };
   409 datatype co_eqn_data =
   410   Disc of co_eqn_data_disc |
   411   Sel of co_eqn_data_sel;
   412 
   413 fun co_dissect_eqn_disc sequential fun_names corec_specs prems' concl matchedsss =
   414   let
   415     fun find_subterm p = let (* FIXME \<exists>? *)
   416       fun f (t as u $ v) = if p t then SOME t else merge_options (f u, f v)
   417         | f t = if p t then SOME t else NONE
   418       in f end;
   419 
   420     val applied_fun = concl
   421       |> find_subterm (member ((op =) o apsnd SOME) fun_names o try (fst o dest_Free o head_of))
   422       |> the
   423       handle Option.Option => primrec_error_eqn "malformed discriminator equation" concl;
   424     val ((fun_name, fun_T), fun_args) = strip_comb applied_fun |>> dest_Free;
   425     val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
   426 
   427     val discs = map #disc ctr_specs;
   428     val ctrs = map #ctr ctr_specs;
   429     val not_disc = head_of concl = @{term Not};
   430     val _ = not_disc andalso length ctrs <> 2 andalso
   431       primrec_error_eqn "\<not>ed discriminator for a type with \<noteq> 2 constructors" concl;
   432     val disc = find_subterm (member (op =) discs o head_of) concl;
   433     val eq_ctr0 = concl |> perhaps (try (HOLogic.dest_not)) |> try (HOLogic.dest_eq #> snd)
   434         |> (fn SOME t => let val n = find_index (equal t) ctrs in
   435           if n >= 0 then SOME n else NONE end | _ => NONE);
   436     val _ = is_some disc orelse is_some eq_ctr0 orelse
   437       primrec_error_eqn "no discriminator in equation" concl;
   438     val ctr_no' =
   439       if is_none disc then the eq_ctr0 else find_index (equal (head_of (the disc))) discs;
   440     val ctr_no = if not_disc then 1 - ctr_no' else ctr_no';
   441     val ctr = #ctr (nth ctr_specs ctr_no);
   442 
   443     val catch_all = try (fst o dest_Free o the_single) prems' = SOME Name.uu_;
   444     val matchedss = AList.lookup (op =) matchedsss fun_name |> the_default [];
   445     val prems = map (abstract (List.rev fun_args)) prems';
   446     val real_prems =
   447       (if catch_all orelse sequential then maps negate_disj matchedss else []) @
   448       (if catch_all then [] else prems);
   449 
   450     val matchedsss' = AList.delete (op =) fun_name matchedsss
   451       |> cons (fun_name, if sequential then matchedss @ [prems] else matchedss @ [real_prems]);
   452 
   453     val user_eqn =
   454       (real_prems, betapply (#disc (nth ctr_specs ctr_no), applied_fun))
   455       |>> map HOLogic.mk_Trueprop ||> HOLogic.mk_Trueprop
   456       |> Logic.list_implies;
   457   in
   458     (Disc {
   459       fun_name = fun_name,
   460       fun_T = fun_T,
   461       fun_args = fun_args,
   462       ctr = ctr,
   463       ctr_no = ctr_no,
   464       disc = #disc (nth ctr_specs ctr_no),
   465       prems = real_prems,
   466       auto_gen = catch_all,
   467       user_eqn = user_eqn
   468     }, matchedsss')
   469   end;
   470 
   471 fun co_dissect_eqn_sel fun_names corec_specs eqn' of_spec eqn =
   472   let
   473     val (lhs, rhs) = HOLogic.dest_eq eqn
   474       handle TERM _ =>
   475         primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn;
   476     val sel = head_of lhs;
   477     val ((fun_name, fun_T), fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst dest_Free
   478       handle TERM _ =>
   479         primrec_error_eqn "malformed selector argument in left-hand side" eqn;
   480     val corec_spec = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name)
   481       handle Option.Option => primrec_error_eqn "malformed selector argument in left-hand side" eqn;
   482     val ctr_spec =
   483       if is_some of_spec
   484       then the (find_first (equal (the of_spec) o #ctr) (#ctr_specs corec_spec))
   485       else #ctr_specs corec_spec |> filter (exists (equal sel) o #sels) |> the_single
   486         handle List.Empty => primrec_error_eqn "ambiguous selector - use \"of\"" eqn;
   487     val user_eqn = drop_All eqn';
   488   in
   489     Sel {
   490       fun_name = fun_name,
   491       fun_T = fun_T,
   492       fun_args = fun_args,
   493       ctr = #ctr ctr_spec,
   494       sel = sel,
   495       rhs_term = rhs,
   496       user_eqn = user_eqn
   497     }
   498   end;
   499 
   500 fun co_dissect_eqn_ctr sequential fun_names corec_specs eqn' imp_prems imp_rhs matchedsss =
   501   let
   502     val (lhs, rhs) = HOLogic.dest_eq imp_rhs;
   503     val fun_name = head_of lhs |> fst o dest_Free;
   504     val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
   505     val (ctr, ctr_args) = strip_comb rhs;
   506     val {disc, sels, ...} = the (find_first (equal ctr o #ctr) ctr_specs)
   507       handle Option.Option => primrec_error_eqn "not a constructor" ctr;
   508 
   509     val disc_imp_rhs = betapply (disc, lhs);
   510     val (maybe_eqn_data_disc, matchedsss') = if length ctr_specs = 1
   511       then (NONE, matchedsss)
   512       else apfst SOME (co_dissect_eqn_disc
   513           sequential fun_names corec_specs imp_prems disc_imp_rhs matchedsss);
   514 
   515     val sel_imp_rhss = (sels ~~ ctr_args)
   516       |> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg));
   517 
   518 (*
   519 val _ = tracing ("reduced\n    " ^ Syntax.string_of_term @{context} imp_rhs ^ "\nto\n    \<cdot> " ^
   520  (is_some maybe_eqn_data_disc ? K (Syntax.string_of_term @{context} disc_imp_rhs ^ "\n    \<cdot> ")) "" ^
   521  space_implode "\n    \<cdot> " (map (Syntax.string_of_term @{context}) sel_imp_rhss));
   522 *)
   523 
   524     val eqns_data_sel =
   525       map (co_dissect_eqn_sel fun_names corec_specs eqn' (SOME ctr)) sel_imp_rhss;
   526   in
   527     (the_list maybe_eqn_data_disc @ eqns_data_sel, matchedsss')
   528   end;
   529 
   530 fun co_dissect_eqn sequential fun_names corec_specs eqn' of_spec matchedsss =
   531   let
   532     val eqn = drop_All eqn'
   533       handle TERM _ => primrec_error_eqn "malformed function equation" eqn';
   534     val (imp_prems, imp_rhs) = Logic.strip_horn eqn
   535       |> apfst (map HOLogic.dest_Trueprop) o apsnd HOLogic.dest_Trueprop;
   536 
   537     val head = imp_rhs
   538       |> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq))
   539       |> head_of;
   540 
   541     val maybe_rhs = imp_rhs |> perhaps (try (HOLogic.dest_not)) |> try (snd o HOLogic.dest_eq);
   542 
   543     val discs = maps #ctr_specs corec_specs |> map #disc;
   544     val sels = maps #ctr_specs corec_specs |> maps #sels;
   545     val ctrs = maps #ctr_specs corec_specs |> map #ctr;
   546   in
   547     if member (op =) discs head orelse
   548       is_some maybe_rhs andalso
   549         member (op =) (filter (null o binder_types o fastype_of) ctrs) (the maybe_rhs) then
   550       co_dissect_eqn_disc sequential fun_names corec_specs imp_prems imp_rhs matchedsss
   551       |>> single
   552     else if member (op =) sels head then
   553       ([co_dissect_eqn_sel fun_names corec_specs eqn' of_spec imp_rhs], matchedsss)
   554     else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) then
   555       co_dissect_eqn_ctr sequential fun_names corec_specs eqn' imp_prems imp_rhs matchedsss
   556     else
   557       primrec_error_eqn "malformed function equation" eqn
   558   end;
   559 
   560 fun build_corec_arg_disc ctr_specs {fun_args, ctr_no, prems, ...} =
   561   if is_none (#pred (nth ctr_specs ctr_no)) then I else
   562     mk_conjs prems
   563     |> curry subst_bounds (List.rev fun_args)
   564     |> HOLogic.tupled_lambda (HOLogic.mk_tuple fun_args)
   565     |> K |> nth_map (the (#pred (nth ctr_specs ctr_no)));
   566 
   567 fun build_corec_arg_no_call sel_eqns sel =
   568   find_first (equal sel o #sel) sel_eqns
   569   |> try (fn SOME {fun_args, rhs_term, ...} => abs_tuple fun_args rhs_term)
   570   |> the_default undef_const
   571   |> K;
   572 
   573 fun build_corec_args_direct_call lthy has_call sel_eqns sel =
   574   let
   575     val maybe_sel_eqn = find_first (equal sel o #sel) sel_eqns;
   576   in
   577     if is_none maybe_sel_eqn then (I, I, I) else
   578     let
   579       val {fun_args, rhs_term, ... } = the maybe_sel_eqn;
   580       fun rewrite_q _ t = if has_call t then @{term False} else @{term True};
   581       fun rewrite_g _ t = if has_call t then undef_const else t;
   582       fun rewrite_h bound_Ts t =
   583         if has_call t then mk_tuple1 bound_Ts (snd (strip_comb t)) else undef_const;
   584       fun massage f t = massage_direct_corec_call lthy has_call f [] rhs_term |> abs_tuple fun_args;
   585     in
   586       (massage rewrite_q,
   587        massage rewrite_g,
   588        massage rewrite_h)
   589     end
   590   end;
   591 
   592 fun build_corec_arg_indirect_call lthy has_call sel_eqns sel =
   593   let
   594     val maybe_sel_eqn = find_first (equal sel o #sel) sel_eqns;
   595   in
   596     if is_none maybe_sel_eqn then I else
   597     let
   598       val {fun_args, rhs_term, ...} = the maybe_sel_eqn;
   599       fun rewrite bound_Ts U T (Abs (v, V, b)) = Abs (v, V, rewrite (V :: bound_Ts) U T b)
   600         | rewrite bound_Ts U T (t as _ $ _) =
   601           let val (u, vs) = strip_comb t in
   602             if is_Free u andalso has_call u then
   603               Inr_const U T $ mk_tuple1 bound_Ts vs
   604             else if try (fst o dest_Const) u = SOME @{const_name prod_case} then
   605               map (rewrite bound_Ts U T) vs |> chop 1 |>> HOLogic.mk_split o the_single |> list_comb
   606             else
   607               list_comb (rewrite bound_Ts U T u, map (rewrite bound_Ts U T) vs)
   608           end
   609         | rewrite _ U T t =
   610           if is_Free t andalso has_call t then Inr_const U T $ HOLogic.unit else t;
   611       fun massage t =
   612         massage_indirect_corec_call lthy has_call rewrite [] (range_type (fastype_of t)) rhs_term
   613         |> abs_tuple fun_args;
   614     in
   615       massage
   616     end
   617   end;
   618 
   619 fun build_corec_args_sel lthy has_call all_sel_eqns ctr_spec =
   620   let val sel_eqns = filter (equal (#ctr ctr_spec) o #ctr) all_sel_eqns in
   621     if null sel_eqns then I else
   622       let
   623         val sel_call_list = #sels ctr_spec ~~ #calls ctr_spec;
   624 
   625         val no_calls' = map_filter (try (apsnd (fn No_Corec n => n))) sel_call_list;
   626         val direct_calls' = map_filter (try (apsnd (fn Direct_Corec n => n))) sel_call_list;
   627         val indirect_calls' = map_filter (try (apsnd (fn Indirect_Corec n => n))) sel_call_list;
   628       in
   629         I
   630         #> fold (fn (sel, n) => nth_map n (build_corec_arg_no_call sel_eqns sel)) no_calls'
   631         #> fold (fn (sel, (q, g, h)) =>
   632           let val (fq, fg, fh) = build_corec_args_direct_call lthy has_call sel_eqns sel in
   633             nth_map q fq o nth_map g fg o nth_map h fh end) direct_calls'
   634         #> fold (fn (sel, n) => nth_map n
   635           (build_corec_arg_indirect_call lthy has_call sel_eqns sel)) indirect_calls'
   636       end
   637   end;
   638 
   639 fun co_build_defs lthy bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss =
   640   let
   641     val corec_specs' = take (length bs) corec_specs;
   642     val corecs = map #corec corec_specs';
   643     val ctr_specss = map #ctr_specs corec_specs';
   644     val corec_args = hd corecs
   645       |> fst o split_last o binder_types o fastype_of
   646       |> map (Const o pair @{const_name undefined})
   647       |> fold2 (fold o build_corec_arg_disc) ctr_specss disc_eqnss
   648       |> fold2 (fold o build_corec_args_sel lthy has_call) sel_eqnss ctr_specss;
   649     fun currys [] t = t
   650       | currys Ts t = t $ mk_tuple1 (List.rev Ts) (map Bound (length Ts - 1 downto 0))
   651           |> fold_rev (Term.abs o pair Name.uu) Ts;
   652 
   653 (*
   654 val _ = tracing ("corecursor arguments:\n    \<cdot> " ^
   655  space_implode "\n    \<cdot> " (map (Syntax.string_of_term lthy) corec_args));
   656 *)
   657 
   658     val exclss' =
   659       disc_eqnss
   660       |> map (map (fn x => (#fun_args x, #ctr_no x, #prems x, #auto_gen x))
   661         #> fst o (fn xs => fold_map (fn x => fn ys => ((x, ys), ys @ [x])) xs [])
   662         #> maps (uncurry (map o pair)
   663           #> map (fn ((fun_args, c, x, a), (_, c', y, a')) =>
   664               ((c, c', a orelse a'), (x, s_not (mk_conjs y)))
   665             ||> apfst (map HOLogic.mk_Trueprop) o apsnd HOLogic.mk_Trueprop
   666             ||> Logic.list_implies
   667             ||> curry Logic.list_all (map dest_Free fun_args))))
   668   in
   669     map (list_comb o rpair corec_args) corecs
   670     |> map2 (fn Ts => fn t => if length Ts = 0 then t $ HOLogic.unit else t) arg_Tss
   671     |> map2 currys arg_Tss
   672     |> Syntax.check_terms lthy
   673     |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.map_name Thm.def_name b, []), t))) bs mxs
   674     |> rpair exclss'
   675   end;
   676 
   677 fun mk_real_disc_eqns fun_binding arg_Ts {ctr_specs, ...} sel_eqns disc_eqns =
   678   if length disc_eqns <> length ctr_specs - 1 then disc_eqns else
   679     let
   680       val n = 0 upto length ctr_specs
   681         |> the o find_first (fn idx => not (exists (equal idx o #ctr_no) disc_eqns));
   682       val fun_args = (try (#fun_args o hd) disc_eqns, try (#fun_args o hd) sel_eqns)
   683         |> the_default (map (curry Free Name.uu) arg_Ts) o merge_options;
   684       val extra_disc_eqn = {
   685         fun_name = Binding.name_of fun_binding,
   686         fun_T = arg_Ts ---> body_type (fastype_of (#ctr (hd ctr_specs))),
   687         fun_args = fun_args,
   688         ctr = #ctr (nth ctr_specs n),
   689         ctr_no = n,
   690         disc = #disc (nth ctr_specs n),
   691         prems = maps (negate_conj o #prems) disc_eqns,
   692         auto_gen = true,
   693         user_eqn = undef_const};
   694     in
   695       chop n disc_eqns ||> cons extra_disc_eqn |> (op @)
   696     end;
   697 
   698 fun add_primcorec simple sequential fixes specs of_specs lthy =
   699   let
   700     val (bs, mxs) = map_split (apfst fst) fixes;
   701     val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> HOLogic.mk_tupleT) fixes |> split_list;
   702 
   703     val callssss = []; (* FIXME *)
   704 
   705     val ((n2m, corec_specs', _, coinduct_thm, strong_coinduct_thm, coinduct_thms,
   706           strong_coinduct_thms), lthy') =
   707       corec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;
   708 
   709     val actual_nn = length bs;
   710     val fun_names = map Binding.name_of bs;
   711     val corec_specs = take actual_nn corec_specs'; (*###*)
   712 
   713     val eqns_data =
   714       fold_map2 (co_dissect_eqn sequential fun_names corec_specs) (map snd specs) of_specs []
   715       |> flat o fst;
   716 
   717     val disc_eqnss' = map_filter (try (fn Disc x => x)) eqns_data
   718       |> partition_eq ((op =) o pairself #fun_name)
   719       |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
   720       |> map (sort ((op <) o pairself #ctr_no |> make_ord) o flat o snd);
   721     val _ = disc_eqnss' |> map (fn x =>
   722       let val d = duplicates ((op =) o pairself #ctr_no) x in null d orelse
   723         primrec_error_eqns "excess discriminator equations in definition"
   724           (maps (fn t => filter (equal (#ctr_no t) o #ctr_no) x) d |> map #user_eqn) end);
   725 
   726     val sel_eqnss = map_filter (try (fn Sel x => x)) eqns_data
   727       |> partition_eq ((op =) o pairself #fun_name)
   728       |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
   729       |> map (flat o snd);
   730 
   731     val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
   732     val arg_Tss = map (binder_types o snd o fst) fixes;
   733     val disc_eqnss = map5 mk_real_disc_eqns bs arg_Tss corec_specs sel_eqnss disc_eqnss';
   734     val (defs, exclss') =
   735       co_build_defs lthy' bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss;
   736 
   737     fun excl_tac (c, c', a) =
   738       if a orelse c = c' orelse sequential then SOME (K (mk_primcorec_assumption_tac lthy []))
   739       else if simple then SOME (K (auto_tac lthy))
   740       else NONE;
   741 
   742 (*
   743 val _ = tracing ("exclusiveness properties:\n    \<cdot> " ^
   744  space_implode "\n    \<cdot> " (maps (map (Syntax.string_of_term lthy o snd)) exclss'));
   745 *)
   746 
   747     val exclss'' = exclss' |> map (map (fn (idx, t) =>
   748       (idx, (Option.map (Goal.prove lthy [] [] t) (excl_tac idx), t))));
   749     val taut_thmss = map (map (apsnd (the o fst)) o filter (is_some o fst o snd)) exclss'';
   750     val (obligation_idxss, obligationss) = exclss''
   751       |> map (map (apsnd (rpair [] o snd)) o filter (is_none o fst o snd))
   752       |> split_list o map split_list;
   753 
   754     fun prove thmss' def_thms' lthy =
   755       let
   756         val def_thms = map (snd o snd) def_thms';
   757 
   758         val exclss' = map (op ~~) (obligation_idxss ~~ thmss');
   759         fun mk_exclsss excls n =
   760           (excls, map (fn k => replicate k [TrueI] @ replicate (n - k) []) (0 upto n - 1))
   761           |-> fold (fn ((c, c', _), thm) => nth_map c (nth_map c' (K [thm])));
   762         val exclssss = (exclss' ~~ taut_thmss |> map (op @), fun_names ~~ corec_specs)
   763           |-> map2 (fn excls => fn (_, {ctr_specs, ...}) => mk_exclsss excls (length ctr_specs));
   764 
   765         fun prove_disc {ctr_specs, ...} exclsss
   766             {fun_name, fun_T, fun_args, ctr_no, prems, user_eqn, ...} =
   767           if Term.aconv_untyped (#disc (nth ctr_specs ctr_no), @{term "\<lambda>x. x = x"}) then [] else
   768             let
   769               val {disc_corec, ...} = nth ctr_specs ctr_no;
   770               val k = 1 + ctr_no;
   771               val m = length prems;
   772               val t =
   773                 list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
   774                 |> curry betapply (#disc (nth ctr_specs ctr_no)) (*###*)
   775                 |> HOLogic.mk_Trueprop
   776                 |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
   777                 |> curry Logic.list_all (map dest_Free fun_args);
   778             in
   779               mk_primcorec_disc_tac lthy def_thms disc_corec k m exclsss
   780               |> K |> Goal.prove lthy [] [] t
   781               |> pair (#disc (nth ctr_specs ctr_no))
   782               |> single
   783             end;
   784 
   785         fun prove_sel {ctr_specs, nested_maps, nested_map_idents, nested_map_comps, ...}
   786             disc_eqns exclsss {fun_name, fun_T, fun_args, ctr, sel, rhs_term, ...} =
   787           let
   788             val SOME ctr_spec = find_first (equal ctr o #ctr) ctr_specs;
   789             val ctr_no = find_index (equal ctr o #ctr) ctr_specs;
   790             val prems = the_default (maps (negate_conj o #prems) disc_eqns)
   791                 (find_first (equal ctr_no o #ctr_no) disc_eqns |> Option.map #prems);
   792             val sel_corec = find_index (equal sel) (#sels ctr_spec)
   793               |> nth (#sel_corecs ctr_spec);
   794             val k = 1 + ctr_no;
   795             val m = length prems;
   796             val t =
   797               list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
   798               |> curry betapply sel
   799               |> rpair (abstract (List.rev fun_args) rhs_term)
   800               |> HOLogic.mk_Trueprop o HOLogic.mk_eq
   801               |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
   802               |> curry Logic.list_all (map dest_Free fun_args);
   803             val (distincts, _, _, sel_splits, sel_split_asms) = case_thms_of_term lthy [] rhs_term;
   804           in
   805             mk_primcorec_sel_tac lthy def_thms distincts sel_splits sel_split_asms nested_maps
   806               nested_map_idents nested_map_comps sel_corec k m exclsss
   807             |> K |> Goal.prove lthy [] [] t
   808             |> pair sel
   809           end;
   810 
   811         fun prove_ctr disc_alist sel_alist disc_eqns sel_eqns {ctr, disc, sels, collapse, ...} =
   812           if not (exists (equal ctr o #ctr) disc_eqns)
   813               andalso not (exists (equal ctr o #ctr) sel_eqns)
   814             orelse (* don't try to prove theorems when some sel_eqns are missing *)
   815               filter (equal ctr o #ctr) sel_eqns
   816               |> fst o finds ((op =) o apsnd #sel) sels
   817               |> exists (null o snd)
   818           then [] else
   819             let
   820               val (fun_name, fun_T, fun_args, prems) =
   821                 (find_first (equal ctr o #ctr) disc_eqns, find_first (equal ctr o #ctr) sel_eqns)
   822                 |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #prems x))
   823                 ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, []))
   824                 |> the o merge_options;
   825               val m = length prems;
   826               val t = filter (equal ctr o #ctr) sel_eqns
   827                 |> fst o finds ((op =) o apsnd #sel) sels
   828                 |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) #-> abstract)
   829                 |> curry list_comb ctr
   830                 |> curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
   831                   map Bound (length fun_args - 1 downto 0)))
   832                 |> HOLogic.mk_Trueprop
   833                 |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
   834                 |> curry Logic.list_all (map dest_Free fun_args);
   835               val maybe_disc_thm = AList.lookup (op =) disc_alist disc;
   836               val sel_thms = map snd (filter (member (op =) sels o fst) sel_alist);
   837             in
   838               mk_primcorec_ctr_of_dtr_tac lthy m collapse maybe_disc_thm sel_thms
   839               |> K |> Goal.prove lthy [] [] t
   840               |> single
   841             end;
   842 
   843         val disc_alists = map3 (maps oo prove_disc) corec_specs exclssss disc_eqnss;
   844         val sel_alists = map4 (map ooo prove_sel) corec_specs disc_eqnss exclssss sel_eqnss;
   845 
   846         val disc_thmss = map (map snd) disc_alists;
   847         val sel_thmss = map (map snd) sel_alists;
   848         val ctr_thmss = map5 (maps oooo prove_ctr) disc_alists sel_alists disc_eqnss sel_eqnss
   849           (map #ctr_specs corec_specs);
   850 
   851         val safess = map (map (not o exists_subterm (member (op =) (map SOME fun_names) o
   852           try (fst o dest_Free)) o snd o HOLogic.dest_eq o HOLogic.dest_Trueprop o
   853           Logic.strip_imp_concl o drop_All o prop_of)) ctr_thmss;
   854         val safe_ctr_thmss = map (map snd o filter fst o (op ~~)) (safess ~~ ctr_thmss);
   855 
   856         val simp_thmss =
   857           map3 (fn x => fn y => fn z => x @ y @ z) disc_thmss sel_thmss safe_ctr_thmss;
   858 
   859         val common_name = mk_common_name fun_names;
   860 
   861         val anonymous_notes =
   862           [(flat safe_ctr_thmss, simp_attrs)]
   863           |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
   864 
   865         val notes =
   866           [(coinductN, map (if n2m then single else K []) coinduct_thms, []),
   867            (codeN, ctr_thmss(*FIXME*), code_nitpick_simp_attrs),
   868            (ctrN, ctr_thmss, []),
   869            (discN, disc_thmss, simp_attrs),
   870            (selN, sel_thmss, simp_attrs),
   871            (simpsN, simp_thmss, []),
   872            (strong_coinductN, map (if n2m then single else K []) strong_coinduct_thms, [])]
   873           |> maps (fn (thmN, thmss, attrs) =>
   874             map2 (fn fun_name => fn thms =>
   875                 ((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])]))
   876               fun_names (take actual_nn thmss))
   877           |> filter_out (null o fst o hd o snd);
   878 
   879         val common_notes =
   880           [(coinductN, if n2m then [coinduct_thm] else [], []),
   881            (strong_coinductN, if n2m then [strong_coinduct_thm] else [], [])]
   882           |> filter_out (null o #2)
   883           |> map (fn (thmN, thms, attrs) =>
   884             ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
   885       in
   886         lthy |> Local_Theory.notes (anonymous_notes @ notes @ common_notes) |> snd
   887       end;
   888 
   889     fun after_qed thmss' = fold_map Local_Theory.define defs #-> prove thmss';
   890 
   891     val _ = if not simple orelse forall null obligationss then () else
   892       primrec_error "need exclusiveness proofs - use primcorecursive instead of primcorec";
   893   in
   894     if simple then
   895       lthy'
   896       |> after_qed (map (fn [] => []) obligationss)
   897       |> pair NONE o SOME
   898     else
   899       lthy'
   900       |> Proof.theorem NONE after_qed obligationss
   901       |> Proof.refine (Method.primitive_text I)
   902       |> Seq.hd
   903       |> rpair NONE o SOME
   904   end;
   905 
   906 fun add_primcorec_ursive_cmd simple seq (raw_fixes, raw_specs') lthy =
   907   let
   908     val (raw_specs, of_specs) = split_list raw_specs' ||> map (Option.map (Syntax.read_term lthy));
   909     val ((fixes, specs), _) = Specification.read_spec raw_fixes raw_specs lthy;
   910   in
   911     add_primcorec simple seq fixes specs of_specs lthy
   912     handle ERROR str => primrec_error str
   913   end
   914   handle Primrec_Error (str, eqns) =>
   915     if null eqns
   916     then error ("primcorec error:\n  " ^ str)
   917     else error ("primcorec error:\n  " ^ str ^ "\nin\n  " ^
   918       space_implode "\n  " (map (quote o Syntax.string_of_term lthy) eqns));
   919 
   920 val add_primcorecursive_cmd = (the o fst) ooo add_primcorec_ursive_cmd false;
   921 val add_primcorec_cmd = (the o snd) ooo add_primcorec_ursive_cmd true;
   922 
   923 end;