(*  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;