(*  Title:      HOL/BNF/Tools/bnf_lfp_rec_sugar.ML

     Author:     Lorenz Panny, TU Muenchen

     Author:     Jasmin Blanchette, TU Muenchen

     Copyright   2013

 Recursor sugar.

 *)

 signature BNF_LFP_REC_SUGAR =

 sig

   val add_primrec: (binding * typ option * mixfix) list ->

     (Attrib.binding * term) list -> local_theory -> (term list * thm list list) * local_theory

   val add_primrec_cmd: (binding * string option * mixfix) list ->

     (Attrib.binding * string) list -> local_theory -> (term list * thm list list) * local_theory

   val add_primrec_global: (binding * typ option * mixfix) list ->

     (Attrib.binding * term) list -> theory -> (term list * thm list list) * theory

   val add_primrec_overloaded: (string * (string * typ) * bool) list ->

     (binding * typ option * mixfix) list ->

     (Attrib.binding * term) list -> theory -> (term list * thm list list) * theory

   val add_primrec_simple: ((binding * typ) * mixfix) list -> term list ->

     local_theory -> (string list * (term list * (int list list * thm list list))) * local_theory

 end;

 structure BNF_LFP_Rec_Sugar : BNF_LFP_REC_SUGAR =

 struct

 open Ctr_Sugar

 open BNF_Util

 open BNF_Tactics

 open BNF_Def

 open BNF_FP_Util

 open BNF_FP_Def_Sugar

 open BNF_FP_N2M_Sugar

 open BNF_FP_Rec_Sugar_Util

 val nitpicksimp_attrs = @{attributes [nitpick_simp]};

 val simp_attrs = @{attributes [simp]};

 val code_nitpicksimp_simp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs @ simp_attrs;

 exception Primrec_Error of string * term list;

 fun primrec_error str = raise Primrec_Error (str, []);

 fun primrec_error_eqn str eqn = raise Primrec_Error (str, [eqn]);

 fun primrec_error_eqns str eqns = raise Primrec_Error (str, eqns);

 datatype rec_call =

   No_Rec of int * typ |

   Mutual_Rec of (int * typ) * (int * typ) |

   Nested_Rec of int * typ;

 type rec_ctr_spec =

   {ctr: term,

    offset: int,

    calls: rec_call list,

    rec_thm: thm};

 type rec_spec =

   {recx: term,

    nested_map_idents: thm list,

    nested_map_comps: thm list,

    ctr_specs: rec_ctr_spec list};

 exception AINT_NO_MAP of term;

 fun ill_formed_rec_call ctxt t =

   error ("Ill-formed recursive call: " ^ quote (Syntax.string_of_term ctxt t));

 fun invalid_map ctxt t =

   error ("Invalid map function in " ^ quote (Syntax.string_of_term ctxt t));

 fun unexpected_rec_call ctxt t =

   error ("Unexpected recursive call: " ^ quote (Syntax.string_of_term ctxt t));

 fun massage_nested_rec_call ctxt has_call raw_massage_fun bound_Ts y y' =

   let

     fun check_no_call t = if has_call t then unexpected_rec_call ctxt t else ();

     val typof = curry fastype_of1 bound_Ts;

     val build_map_fst = build_map ctxt (fst_const o fst);

     val yT = typof y;

     val yU = typof y';

     fun y_of_y' () = build_map_fst (yU, yT) $ y';

     val elim_y = Term.map_aterms (fn t => if t = y then y_of_y' () else t);

     fun massage_mutual_fun U T t =

       (case t of

         Const (@{const_name comp}, _) $ t1 $ t2 =>

         mk_comp bound_Ts (tap check_no_call t1, massage_mutual_fun U T t2)

       | _ =>

         if has_call t then

           (case try HOLogic.dest_prodT U of

             SOME (U1, U2) => if U1 = T then raw_massage_fun T U2 t else invalid_map ctxt t

           | NONE => invalid_map ctxt t)

         else

           mk_comp bound_Ts (t, build_map_fst (U, T)));

     fun massage_map (Type (_, Us)) (Type (s, Ts)) t =

         (case try (dest_map ctxt s) t of

           SOME (map0, fs) =>

           let

             val Type (_, ran_Ts) = range_type (typof t);

             val map' = mk_map (length fs) Us ran_Ts map0;

             val fs' = map_flattened_map_args ctxt s (map3 massage_map_or_map_arg Us Ts) fs;

           in

             Term.list_comb (map', fs')

           end

         | NONE => raise AINT_NO_MAP t)

       | massage_map _ _ t = raise AINT_NO_MAP t

     and massage_map_or_map_arg U T t =

       if T = U then

         tap check_no_call t

       else

         massage_map U T t

         handle AINT_NO_MAP _ => massage_mutual_fun U T t;

     fun massage_call (t as t1 $ t2) =

         if has_call t then

           if t2 = y then

             massage_map yU yT (elim_y t1) $ y'

             handle AINT_NO_MAP t' => invalid_map ctxt t'

           else

             let val (g, xs) = Term.strip_comb t2 in

               if g = y then

                 if exists has_call xs then unexpected_rec_call ctxt t2

                 else Term.list_comb (massage_call (mk_compN (length xs) bound_Ts (t1, y)), xs)

               else

                 ill_formed_rec_call ctxt t

             end

         else

           elim_y t

       | massage_call t = if t = y then y_of_y' () else ill_formed_rec_call ctxt t;

   in

     massage_call

   end;

 fun rec_specs_of bs arg_Ts res_Ts get_indices callssss0 lthy =

   let

     val thy = Proof_Context.theory_of lthy;

     val ((missing_arg_Ts, perm0_kks,

           fp_sugars as {nested_bnfs, fp_res = {xtor_co_iterss = ctor_iters1 :: _, ...},

             co_inducts = [induct_thm], ...} :: _, (lfp_sugar_thms, _)), lthy') =

       nested_to_mutual_fps Least_FP bs arg_Ts get_indices callssss0 lthy;

     val perm_fp_sugars = sort (int_ord o pairself #index) fp_sugars;

     val indices = map #index fp_sugars;

     val perm_indices = map #index perm_fp_sugars;

     val perm_ctrss = map (#ctrs o of_fp_sugar #ctr_sugars) perm_fp_sugars;

     val perm_ctr_Tsss = map (map (binder_types o fastype_of)) perm_ctrss;

     val perm_lfpTs = map (body_type o fastype_of o hd) perm_ctrss;

     val nn0 = length arg_Ts;

     val nn = length perm_lfpTs;

     val kks = 0 upto nn - 1;

     val perm_ns = map length perm_ctr_Tsss;

     val perm_mss = map (map length) perm_ctr_Tsss;

     val perm_Cs = map (body_type o fastype_of o co_rec_of o of_fp_sugar (#xtor_co_iterss o #fp_res))

       perm_fp_sugars;

     val perm_fun_arg_Tssss =

       mk_iter_fun_arg_types perm_ctr_Tsss perm_ns perm_mss (co_rec_of ctor_iters1);

     fun unpermute0 perm0_xs = permute_like (op =) perm0_kks kks perm0_xs;

     fun unpermute perm_xs = permute_like (op =) perm_indices indices perm_xs;

     val induct_thms = unpermute0 (conj_dests nn induct_thm);

     val lfpTs = unpermute perm_lfpTs;

     val Cs = unpermute perm_Cs;

     val As_rho = tvar_subst thy (take nn0 lfpTs) arg_Ts;

     val Cs_rho = map (fst o dest_TVar) Cs ~~ pad_list HOLogic.unitT nn res_Ts;

     val substA = Term.subst_TVars As_rho;

     val substAT = Term.typ_subst_TVars As_rho;

     val substCT = Term.typ_subst_TVars Cs_rho;

     val substACT = substAT o substCT;

     val perm_Cs' = map substCT perm_Cs;

     fun offset_of_ctr 0 _ = 0

       | offset_of_ctr n (({ctrs, ...} : ctr_sugar) :: ctr_sugars) =

         length ctrs + offset_of_ctr (n - 1) ctr_sugars;

     fun call_of [i] [T] = (if exists_subtype_in Cs T then Nested_Rec else No_Rec) (i, substACT T)

       | call_of [i, i'] [T, T'] = Mutual_Rec ((i, substACT T), (i', substACT T'));

     fun mk_ctr_spec ctr offset fun_arg_Tss rec_thm =

       let

         val (fun_arg_hss, _) = indexedd fun_arg_Tss 0;

         val fun_arg_hs = flat_rec_arg_args fun_arg_hss;

         val fun_arg_iss = map (map (find_index_eq fun_arg_hs)) fun_arg_hss;

       in

         {ctr = substA ctr, offset = offset, calls = map2 call_of fun_arg_iss fun_arg_Tss,

          rec_thm = rec_thm}

       end;

     fun mk_ctr_specs index (ctr_sugars : ctr_sugar list) iter_thmsss =

       let

         val ctrs = #ctrs (nth ctr_sugars index);

         val rec_thmss = co_rec_of (nth iter_thmsss index);

         val k = offset_of_ctr index ctr_sugars;

         val n = length ctrs;

       in

         map4 mk_ctr_spec ctrs (k upto k + n - 1) (nth perm_fun_arg_Tssss index) rec_thmss

       end;

     fun mk_spec ({T, index, ctr_sugars, co_iterss = iterss, co_iter_thmsss = iter_thmsss, ...}

       : fp_sugar) =

       {recx = mk_co_iter thy Least_FP (substAT T) perm_Cs' (co_rec_of (nth iterss index)),

        nested_map_idents = map (unfold_thms lthy @{thms id_def} o map_id0_of_bnf) nested_bnfs,

        nested_map_comps = map map_comp_of_bnf nested_bnfs,

        ctr_specs = mk_ctr_specs index ctr_sugars iter_thmsss};

   in

     ((is_some lfp_sugar_thms, map mk_spec fp_sugars, missing_arg_Ts, induct_thm, induct_thms),

      lthy')

   end;

 val undef_const = Const (@{const_name undefined}, dummyT);

 fun permute_args n t =

   list_comb (t, map Bound (0 :: (n downto 1))) |> fold (K (Term.abs (Name.uu, dummyT))) (0 upto n);

 type eqn_data = {

   fun_name: string,

   rec_type: typ,

   ctr: term,

   ctr_args: term list,

   left_args: term list,

   right_args: term list,

   res_type: typ,

   rhs_term: term,

   user_eqn: term

 };

 fun dissect_eqn lthy fun_names eqn' =

   let

     val eqn = drop_All eqn' |> HOLogic.dest_Trueprop

       handle TERM _ =>

         primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn';

     val (lhs, rhs) = HOLogic.dest_eq eqn

         handle TERM _ =>

           primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn';

     val (fun_name, args) = strip_comb lhs

       |>> (fn x => if is_Free x then fst (dest_Free x)

           else primrec_error_eqn "malformed function equation (does not start with free)" eqn);

     val (left_args, rest) = take_prefix is_Free args;

     val (nonfrees, right_args) = take_suffix is_Free rest;

     val num_nonfrees = length nonfrees;

     val _ = num_nonfrees = 1 orelse if num_nonfrees = 0 then

       primrec_error_eqn "constructor pattern missing in left-hand side" eqn else

       primrec_error_eqn "more than one non-variable argument in left-hand side" eqn;

     val _ = member (op =) fun_names fun_name orelse

       primrec_error_eqn "malformed function equation (does not start with function name)" eqn

     val (ctr, ctr_args) = strip_comb (the_single nonfrees);

     val _ = try (num_binder_types o fastype_of) ctr = SOME (length ctr_args) orelse

       primrec_error_eqn "partially applied constructor in pattern" eqn;

     val _ = let val d = duplicates (op =) (left_args @ ctr_args @ right_args) in null d orelse

       primrec_error_eqn ("duplicate variable \"" ^ Syntax.string_of_term lthy (hd d) ^

         "\" in left-hand side") eqn end;

     val _ = forall is_Free ctr_args orelse

       primrec_error_eqn "non-primitive pattern in left-hand side" eqn;

     val _ =

       let val b = fold_aterms (fn x as Free (v, _) =>

         if (not (member (op =) (left_args @ ctr_args @ right_args) x) andalso

         not (member (op =) fun_names v) andalso

         not (Variable.is_fixed lthy v)) then cons x else I | _ => I) rhs []

       in

         null b orelse

         primrec_error_eqn ("extra variable(s) in right-hand side: " ^

           commas (map (Syntax.string_of_term lthy) b)) eqn

       end;

   in

     {fun_name = fun_name,

      rec_type = body_type (type_of ctr),

      ctr = ctr,

      ctr_args = ctr_args,

      left_args = left_args,

      right_args = right_args,

      res_type = map fastype_of (left_args @ right_args) ---> fastype_of rhs,

      rhs_term = rhs,

      user_eqn = eqn'}

   end;

 fun rewrite_map_arg get_ctr_pos rec_type res_type =

   let

     val pT = HOLogic.mk_prodT (rec_type, res_type);

     val maybe_suc = Option.map (fn x => x + 1);

     fun subst d (t as Bound d') = t |> d = SOME d' ? curry (op $) (fst_const pT)

       | subst d (Abs (v, T, b)) = Abs (v, if d = SOME ~1 then pT else T, subst (maybe_suc d) b)

       | subst d t =

         let

           val (u, vs) = strip_comb t;

           val ctr_pos = try (get_ctr_pos o fst o dest_Free) u |> the_default ~1;

         in

           if ctr_pos >= 0 then

             if d = SOME ~1 andalso length vs = ctr_pos then

               list_comb (permute_args ctr_pos (snd_const pT), vs)

             else if length vs > ctr_pos andalso is_some d

                 andalso d = try (fn Bound n => n) (nth vs ctr_pos) then

               list_comb (snd_const pT $ nth vs ctr_pos, map (subst d) (nth_drop ctr_pos vs))

             else

               primrec_error_eqn ("recursive call not directly applied to constructor argument") t

           else

             list_comb (u, map (subst (d |> d = SOME ~1 ? K NONE)) vs)

         end

   in

     subst (SOME ~1)

   end;

 fun subst_rec_calls lthy get_ctr_pos has_call ctr_args mutual_calls nested_calls =

   let

     fun try_nested_rec bound_Ts y t =

       AList.lookup (op =) nested_calls y

       |> Option.map (fn y' =>

         massage_nested_rec_call lthy has_call (rewrite_map_arg get_ctr_pos) bound_Ts y y' t);

     fun subst bound_Ts (t as g' $ y) =

         let

           fun subst_rec () = subst bound_Ts g' $ subst bound_Ts y;

           val y_head = head_of y;

         in

           if not (member (op =) ctr_args y_head) then

             subst_rec ()

           else

             (case try_nested_rec bound_Ts y_head t of

               SOME t' => t'

             | NONE =>

               let val (g, g_args) = strip_comb g' in

                 (case try (get_ctr_pos o fst o dest_Free) g of

                   SOME ctr_pos =>

                   (length g_args >= ctr_pos orelse

                    primrec_error_eqn "too few arguments in recursive call" t;

                    (case AList.lookup (op =) mutual_calls y of

                      SOME y' => list_comb (y', g_args)

                    | NONE => subst_rec ()))

                 | NONE => subst_rec ())

               end)

         end

       | subst bound_Ts (Abs (v, T, b)) = Abs (v, T, subst (T :: bound_Ts) b)

       | subst _ t = t

     fun subst' t =

       if has_call t then

         (* FIXME detect this case earlier? *)

         primrec_error_eqn "recursive call not directly applied to constructor argument" t

       else

         try_nested_rec [] (head_of t) t |> the_default t

   in

     subst' o subst []

   end;

 fun build_rec_arg lthy (funs_data : eqn_data list list) has_call (ctr_spec : rec_ctr_spec)

     (maybe_eqn_data : eqn_data option) =

   (case maybe_eqn_data of

     NONE => undef_const

   | SOME {ctr_args, left_args, right_args, rhs_term = t, ...} =>

     let

       val calls = #calls ctr_spec;

       val n_args = fold (Integer.add o (fn Mutual_Rec _ => 2 | _ => 1)) calls 0;

       val no_calls' = tag_list 0 calls

         |> map_filter (try (apsnd (fn No_Rec p => p | Mutual_Rec (p, _) => p)));

       val mutual_calls' = tag_list 0 calls

         |> map_filter (try (apsnd (fn Mutual_Rec (_, p) => p)));

       val nested_calls' = tag_list 0 calls

         |> map_filter (try (apsnd (fn Nested_Rec p => p)));

       val args = replicate n_args ("", dummyT)

         |> Term.rename_wrt_term t

         |> map Free

         |> fold (fn (ctr_arg_idx, (arg_idx, _)) =>

             nth_map arg_idx (K (nth ctr_args ctr_arg_idx)))

           no_calls'

         |> fold (fn (ctr_arg_idx, (arg_idx, T)) =>

             nth_map arg_idx (K (retype_free T (nth ctr_args ctr_arg_idx))))

           mutual_calls'

         |> fold (fn (ctr_arg_idx, (arg_idx, T)) =>

             nth_map arg_idx (K (retype_free T (nth ctr_args ctr_arg_idx))))

           nested_calls';

       val fun_name_ctr_pos_list =

         map (fn (x :: _) => (#fun_name x, length (#left_args x))) funs_data;

       val get_ctr_pos = try (the o AList.lookup (op =) fun_name_ctr_pos_list) #> the_default ~1;

       val mutual_calls = map (apfst (nth ctr_args) o apsnd (nth args o fst)) mutual_calls';

       val nested_calls = map (apfst (nth ctr_args) o apsnd (nth args o fst)) nested_calls';

     in

       t

       |> subst_rec_calls lthy get_ctr_pos has_call ctr_args mutual_calls nested_calls

       |> fold_rev lambda (args @ left_args @ right_args)

     end);

 fun build_defs lthy bs mxs (funs_data : eqn_data list list) (rec_specs : rec_spec list) has_call =

   let

     val n_funs = length funs_data;

     val ctr_spec_eqn_data_list' =

       (take n_funs rec_specs |> map #ctr_specs) ~~ funs_data

       |> maps (uncurry (finds (fn (x, y) => #ctr x = #ctr y))

           ##> (fn x => null x orelse

             primrec_error_eqns "excess equations in definition" (map #rhs_term x)) #> fst);

     val _ = ctr_spec_eqn_data_list' |> map (fn (_, x) => length x <= 1 orelse

       primrec_error_eqns ("multiple equations for constructor") (map #user_eqn x));

     val ctr_spec_eqn_data_list =

       ctr_spec_eqn_data_list' @ (drop n_funs rec_specs |> maps #ctr_specs |> map (rpair []));

     val recs = take n_funs rec_specs |> map #recx;

     val rec_args = ctr_spec_eqn_data_list

       |> sort ((op <) o pairself (#offset o fst) |> make_ord)

       |> map (uncurry (build_rec_arg lthy funs_data has_call) o apsnd (try the_single));

     val ctr_poss = map (fn x =>

       if length (distinct ((op =) o pairself (length o #left_args)) x) <> 1 then

         primrec_error ("inconstant constructor pattern position for function " ^

           quote (#fun_name (hd x)))

       else

         hd x |> #left_args |> length) funs_data;

   in

     (recs, ctr_poss)

     |-> map2 (fn recx => fn ctr_pos => list_comb (recx, rec_args) |> permute_args ctr_pos)

     |> Syntax.check_terms lthy

     |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.conceal (Thm.def_binding b), []), t)))

       bs mxs

   end;

 fun find_rec_calls has_call ({ctr, ctr_args, rhs_term, ...} : eqn_data) =

   let

     fun find bound_Ts (Abs (_, T, b)) ctr_arg = find (T :: bound_Ts) b ctr_arg

       | find bound_Ts (t as _ $ _) ctr_arg =

         let

           val typof = curry fastype_of1 bound_Ts;

           val (f', args') = strip_comb t;

           val n = find_index (equal ctr_arg o head_of) args';

         in

           if n < 0 then

             find bound_Ts f' ctr_arg @ maps (fn x => find bound_Ts x ctr_arg) args'

           else

             let

               val (f, args as arg :: _) = chop n args' |>> curry list_comb f'

               val (arg_head, arg_args) = Term.strip_comb arg;

             in

               if has_call f then

                 mk_partial_compN (length arg_args) (typof arg_head) f ::

                 maps (fn x => find bound_Ts x ctr_arg) args

               else

                 find bound_Ts f ctr_arg @ maps (fn x => find bound_Ts x ctr_arg) args

             end

         end

       | find _ _ _ = [];

   in

     map (find [] rhs_term) ctr_args

     |> (fn [] => NONE | callss => SOME (ctr, callss))

   end;

 fun mk_primrec_tac ctxt num_extra_args map_idents map_comps fun_defs recx =

   unfold_thms_tac ctxt fun_defs THEN

   HEADGOAL (rtac (funpow num_extra_args (fn thm => thm RS fun_cong) recx RS trans)) THEN

   unfold_thms_tac ctxt (@{thms id_def split o_def fst_conv snd_conv} @ map_comps @ map_idents) THEN

   HEADGOAL (rtac refl);

 fun prepare_primrec fixes specs lthy =

   let

     val (bs, mxs) = map_split (apfst fst) fixes;

     val fun_names = map Binding.name_of bs;

     val eqns_data = map (dissect_eqn lthy fun_names) specs;

     val funs_data = eqns_data

       |> partition_eq ((op =) o pairself #fun_name)

       |> finds (fn (x, y) => x = #fun_name (hd y)) fun_names |> fst

       |> map (fn (x, y) => the_single y handle List.Empty =>

           primrec_error ("missing equations for function " ^ quote x));

     val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));

     val arg_Ts = map (#rec_type o hd) funs_data;

     val res_Ts = map (#res_type o hd) funs_data;

     val callssss = funs_data

       |> map (partition_eq ((op =) o pairself #ctr))

       |> map (maps (map_filter (find_rec_calls has_call)));

     val ((n2m, rec_specs, _, induct_thm, induct_thms), lthy') =

       rec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;

     val actual_nn = length funs_data;

     val _ = let val ctrs = (maps (map #ctr o #ctr_specs) rec_specs) in

       map (fn {ctr, user_eqn, ...} => member (op =) ctrs ctr orelse

         primrec_error_eqn ("argument " ^ quote (Syntax.string_of_term lthy' ctr) ^

           " is not a constructor in left-hand side") user_eqn) eqns_data end;

     val defs = build_defs lthy' bs mxs funs_data rec_specs has_call;

     fun prove lthy def_thms' ({ctr_specs, nested_map_idents, nested_map_comps, ...} : rec_spec)

         (fun_data : eqn_data list) =

       let

         val def_thms = map (snd o snd) def_thms';

         val simp_thmss = finds (fn (x, y) => #ctr x = #ctr y) fun_data ctr_specs

           |> fst

           |> map_filter (try (fn (x, [y]) =>

             (#user_eqn x, length (#left_args x) + length (#right_args x), #rec_thm y)))

           |> map (fn (user_eqn, num_extra_args, rec_thm) =>

             mk_primrec_tac lthy num_extra_args nested_map_idents nested_map_comps def_thms rec_thm

             |> K |> Goal.prove lthy [] [] user_eqn

             |> Thm.close_derivation);

         val poss = find_indices (fn (x, y) => #ctr x = #ctr y) fun_data eqns_data;

       in

         (poss, simp_thmss)

       end;

     val notes =

       (if n2m then map2 (fn name => fn thm =>

         (name, inductN, [thm], [])) fun_names (take actual_nn induct_thms) else [])

       |> map (fn (prefix, thmN, thms, attrs) =>

         ((Binding.qualify true prefix (Binding.name thmN), attrs), [(thms, [])]));

     val common_name = mk_common_name fun_names;

     val common_notes =

       (if n2m then [(inductN, [induct_thm], [])] else [])

       |> map (fn (thmN, thms, attrs) =>

         ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));

   in

     (((fun_names, defs),

       fn lthy => fn defs =>

         split_list (map2 (prove lthy defs) (take actual_nn rec_specs) funs_data)),

       lthy' |> Local_Theory.notes (notes @ common_notes) |> snd)

   end;

 (* primrec definition *)

 fun add_primrec_simple fixes ts lthy =

   let

     val (((names, defs), prove), lthy) = prepare_primrec fixes ts lthy

       handle ERROR str => primrec_error str;

   in

     lthy

     |> fold_map Local_Theory.define defs

     |-> (fn defs => `(fn lthy => (names, (map fst defs, prove lthy defs))))

   end

   handle Primrec_Error (str, eqns) =>

     if null eqns

     then error ("primrec_new error:\n  " ^ str)

     else error ("primrec_new error:\n  " ^ str ^ "\nin\n  " ^

       space_implode "\n  " (map (quote o Syntax.string_of_term lthy) eqns));

 local

 fun gen_primrec prep_spec (raw_fixes : (binding * 'a option * mixfix) list) raw_spec lthy =

   let

     val d = duplicates (op =) (map (Binding.name_of o #1) raw_fixes)

     val _ = null d orelse primrec_error ("duplicate function name(s): " ^ commas d);

     val (fixes, specs) = fst (prep_spec raw_fixes raw_spec lthy);

     val mk_notes =

       flat ooo map3 (fn poss => fn prefix => fn thms =>

         let

           val (bs, attrss) = map_split (fst o nth specs) poss;

           val notes =

             map3 (fn b => fn attrs => fn thm =>

               ((Binding.qualify false prefix b, code_nitpicksimp_simp_attrs @ attrs), [([thm], [])]))

             bs attrss thms;

         in

           ((Binding.qualify true prefix (Binding.name simpsN), []), [(thms, [])]) :: notes

         end);

   in

     lthy

     |> add_primrec_simple fixes (map snd specs)

     |-> (fn (names, (ts, (posss, simpss))) =>

       Spec_Rules.add Spec_Rules.Equational (ts, flat simpss)

       #> Local_Theory.notes (mk_notes posss names simpss)

       #>> pair ts o map snd)

   end;

 in

 val add_primrec = gen_primrec Specification.check_spec;

 val add_primrec_cmd = gen_primrec Specification.read_spec;

 end;

 fun add_primrec_global fixes specs thy =

   let

     val lthy = Named_Target.theory_init thy;

     val ((ts, simps), lthy') = add_primrec fixes specs lthy;

     val simps' = burrow (Proof_Context.export lthy' lthy) simps;

   in ((ts, simps'), Local_Theory.exit_global lthy') end;

 fun add_primrec_overloaded ops fixes specs thy =

   let

     val lthy = Overloading.overloading ops thy;

     val ((ts, simps), lthy') = add_primrec fixes specs lthy;

     val simps' = burrow (Proof_Context.export lthy' lthy) simps;

   in ((ts, simps'), Local_Theory.exit_global lthy') end;

 end;