File record_package.ML (Isabelle2005: October 2005)

# File record_package.ML

    (*  Title:      HOL/Tools/record_package.ML
        ID:         $Id: record_package.ML,v 1.123 2005/09/23 20:31:22 wenzelm Exp $
        Author:     Wolfgang Naraschewski, Norbert Schirmer and Markus Wenzel, TU Muenchen

    Extensible records with structural subtyping in HOL.
    *)

    signature BASIC_RECORD_PACKAGE =
    sig
      val record_simproc: simproc
      val record_eq_simproc: simproc
      val record_upd_simproc: simproc
      val record_split_simproc: (term -> int) -> simproc
      val record_ex_sel_eq_simproc: simproc
      val record_split_tac: int -> tactic
      val record_split_simp_tac: thm list -> (term -> int) -> int -> tactic
      val record_split_name: string
      val record_split_wrapper: string * wrapper
      val print_record_type_abbr: bool ref
      val print_record_type_as_fields: bool ref
    end;

    signature RECORD_PACKAGE =
    sig
      include BASIC_RECORD_PACKAGE
      val quiet_mode: bool ref
      val record_quick_and_dirty_sensitive: bool ref
      val updateN: string
      val ext_typeN: string
      val last_extT: typ -> (string * typ list) option
      val dest_recTs : typ -> (string * typ list) list
      val get_extT_fields:  theory -> typ -> ((string * typ) list * (string * typ))
      val get_recT_fields:  theory -> typ -> ((string * typ) list * (string * typ))
      val get_extension: theory -> Symtab.key -> (string * typ list) option
      val get_extinjects: theory -> thm list
      val get_simpset: theory -> simpset
      val print_records: theory -> unit
      val add_record: string list * string -> string option -> (string * string * mixfix) list
        -> theory -> theory
      val add_record_i: string list * string -> (typ list * string) option
        -> (string * typ * mixfix) list -> theory -> theory
      val setup: (theory -> theory) list
    end;

    structure RecordPackage:RECORD_PACKAGE =
    struct

    val rec_UNIV_I = thm "rec_UNIV_I";
    val rec_True_simp = thm "rec_True_simp";
    val Pair_eq = thm "Product_Type.Pair_eq";
    val atomize_all = thm "HOL.atomize_all";
    val atomize_imp = thm "HOL.atomize_imp";
    val triv_goal   = thm "triv_goal";
    val prop_subst  = thm "prop_subst";
    val Pair_sel_convs = [fst_conv,snd_conv];

    (** name components **)

    val rN = "r";
    val wN = "w";
    val moreN = "more";
    val schemeN = "_scheme";
    val ext_typeN = "_ext_type";
    val extN ="_ext";
    val casesN = "_cases";
    val ext_dest = "_sel";
    val updateN = "_update";
    val updN = "_upd";
    val schemeN = "_scheme";
    val makeN = "make";
    val fields_selN = "fields";
    val extendN = "extend";
    val truncateN = "truncate";

    (*see typedef_package.ML*)
    val RepN = "Rep_";
    val AbsN = "Abs_";

    (*** utilities ***)

    fun but_last xs = fst (split_last xs);

    (* messages *)

    val quiet_mode = ref false;
    fun message s = if ! quiet_mode then () else writeln s;

    (* timing *)

    fun timeit_msg s x = if !timing then (warning s; timeit x) else x ();
    fun timing_msg s = if !timing then warning s else ();

    (* syntax *)

    fun prune n xs = Library.drop (n, xs);
    fun prefix_base s = NameSpace.map_base (fn bname => s ^ bname);

    val Trueprop = HOLogic.mk_Trueprop;
    fun All xs t = Term.list_all_free (xs, t);

    infix 9 $$;
    infix 0 :== ===;
    infixr 0 ==>;

    val (op $$) = Term.list_comb;
    val (op :==) = Logic.mk_defpair;
    val (op ===) = Trueprop o HOLogic.mk_eq;
    val (op ==>) = Logic.mk_implies;

    (* morphisms *)

    fun mk_RepN name = suffix ext_typeN (prefix_base RepN name);
    fun mk_AbsN name = suffix ext_typeN (prefix_base AbsN name);

    fun mk_Rep name repT absT  =
      Const (suffix ext_typeN (prefix_base RepN name),absT --> repT);

    fun mk_Abs name repT absT =
      Const (mk_AbsN name,repT --> absT);

    (* constructor *)

    fun mk_extC (name,T) Ts  = (suffix extN name, Ts ---> T);

    fun mk_ext (name,T) ts =
      let val Ts = map fastype_of ts
      in list_comb (Const (mk_extC (name,T) Ts),ts) end;

    (* cases *)

    fun mk_casesC (name,T,vT) Ts = (suffix casesN name, (Ts ---> vT) --> T --> vT)

    fun mk_cases (name,T,vT) f =
      let val Ts = binder_types (fastype_of f)
      in Const (mk_casesC (name,T,vT) Ts) $ f end;

    (* selector *)

    fun mk_selC sT (c,T) = (c,sT --> T);

    fun mk_sel s (c,T) =
      let val sT = fastype_of s
      in Const (mk_selC sT (c,T)) $ s end;

    (* updates *)

    fun mk_updC sfx sT (c,T) = (suffix sfx c, T --> sT --> sT);

    fun mk_upd sfx c v s =
      let val sT = fastype_of s;
          val vT = fastype_of v;
      in Const (mk_updC sfx sT (c, vT)) $ v $ s end;

    (* types *)

    fun dest_recT (typ as Type (c_ext_type, Ts as (T::_))) =
          (case try (unsuffix ext_typeN) c_ext_type of
            NONE => raise TYPE ("RecordPackage.dest_recT", [typ], [])
          | SOME c => ((c, Ts), List.last Ts))
      | dest_recT typ = raise TYPE ("RecordPackage.dest_recT", [typ], []);

    fun is_recT T =
      (case try dest_recT T of NONE => false | SOME _ => true);

    fun dest_recTs T =
      let val ((c, Ts), U) = dest_recT T
      in (c, Ts) :: dest_recTs U
      end handle TYPE _ => [];

    fun last_extT T =
      let val ((c, Ts), U) = dest_recT T
      in (case last_extT U of
            NONE => SOME (c,Ts)
          | SOME l => SOME l)
      end handle TYPE _ => NONE

    fun rec_id i T =
      let val rTs = dest_recTs T
          val rTs' = if i < 0 then rTs else Library.take (i,rTs)
      in Library.foldl (fn (s,(c,T)) => s ^ c) ("",rTs') end;

    (*** extend theory by record definition ***)

    (** record info **)

    (* type record_info and parent_info  *)

    type record_info =
     {args: (string * sort) list,
      parent: (typ list * string) option,
      fields: (string * typ) list,
      extension: (string * typ list),
      induct: thm
     };

    fun make_record_info args parent fields extension induct =
     {args = args, parent = parent, fields = fields, extension = extension,
      induct = induct}: record_info;

    type parent_info =
     {name: string,
      fields: (string * typ) list,
      extension: (string * typ list),
      induct: thm
    };

    fun make_parent_info name fields extension induct =
     {name = name, fields = fields, extension = extension, induct = induct}: parent_info;

    (* data kind 'HOL/record' *)

    type record_data =
     {records: record_info Symtab.table,
      sel_upd:
       {selectors: unit Symtab.table,
        updates: string Symtab.table,
        simpset: Simplifier.simpset},
      equalities: thm Symtab.table,
      extinjects: thm list,
      extsplit: thm Symtab.table, (* maps extension name to split rule *)
      splits: (thm*thm*thm*thm) Symtab.table,    (* !!,!,EX - split-equalities,induct rule *)
      extfields: (string*typ) list Symtab.table, (* maps extension to its fields *)
      fieldext: (string*typ list) Symtab.table   (* maps field to its extension *)
    };

    fun make_record_data
          records sel_upd equalities extinjects extsplit splits extfields fieldext =
     {records = records, sel_upd = sel_upd,
      equalities = equalities, extinjects=extinjects, extsplit = extsplit, splits = splits,
      extfields = extfields, fieldext = fieldext }: record_data;

    structure RecordsData = TheoryDataFun
    (struct
      val name = "HOL/records";
      type T = record_data;

      val empty =
        make_record_data Symtab.empty
          {selectors = Symtab.empty, updates = Symtab.empty, simpset = HOL_basic_ss}
           Symtab.empty [] Symtab.empty Symtab.empty Symtab.empty Symtab.empty;

      val copy = I;
      val extend = I;
      fun merge _
       ({records = recs1,
         sel_upd = {selectors = sels1, updates = upds1, simpset = ss1},
         equalities = equalities1,
         extinjects = extinjects1,
         extsplit = extsplit1,
         splits = splits1,
         extfields = extfields1,
         fieldext = fieldext1},
        {records = recs2,
         sel_upd = {selectors = sels2, updates = upds2, simpset = ss2},
         equalities = equalities2,
         extinjects = extinjects2,
         extsplit = extsplit2,
         splits = splits2,
         extfields = extfields2,
         fieldext = fieldext2}) =
        make_record_data
          (Symtab.merge (K true) (recs1, recs2))
          {selectors = Symtab.merge (K true) (sels1, sels2),
            updates = Symtab.merge (K true) (upds1, upds2),
            simpset = Simplifier.merge_ss (ss1, ss2)}
          (Symtab.merge Thm.eq_thm (equalities1, equalities2))
          (gen_merge_lists Thm.eq_thm extinjects1 extinjects2)
          (Symtab.merge Thm.eq_thm (extsplit1,extsplit2))
          (Symtab.merge (fn ((a,b,c,d),(w,x,y,z))
                         => Thm.eq_thm (a,w) andalso Thm.eq_thm (b,x) andalso
                            Thm.eq_thm (c,y) andalso Thm.eq_thm (d,z))
                        (splits1, splits2))
          (Symtab.merge (K true) (extfields1,extfields2))
          (Symtab.merge (K true) (fieldext1,fieldext2));

      fun print sg ({records = recs, ...}: record_data) =
        let
          val prt_typ = Sign.pretty_typ sg;

          fun pretty_parent NONE = []
            | pretty_parent (SOME (Ts, name)) =
                [Pretty.block [prt_typ (Type (name, Ts)), Pretty.str " +"]];

          fun pretty_field (c, T) = Pretty.block
            [Pretty.str (Sign.extern_const sg c), Pretty.str " ::",
              Pretty.brk 1, Pretty.quote (prt_typ T)];

          fun pretty_record (name, {args, parent, fields, ...}: record_info) =
            Pretty.block (Pretty.fbreaks (Pretty.block
              [prt_typ (Type (name, map TFree args)), Pretty.str " = "] ::
              pretty_parent parent @ map pretty_field fields));
        in map pretty_record (Symtab.dest recs) |> Pretty.chunks |> Pretty.writeln end;
    end);

    val print_records = RecordsData.print;

    (* access 'records' *)

    val get_record = Symtab.lookup o #records o RecordsData.get;

    fun put_record name info thy =
      let
        val {records, sel_upd, equalities, extinjects,extsplit,splits,extfields,fieldext} =
              RecordsData.get thy;
        val data = make_record_data (Symtab.update (name, info) records)
          sel_upd equalities extinjects extsplit splits extfields fieldext;
      in RecordsData.put data thy end;

    (* access 'sel_upd' *)

    val get_sel_upd = #sel_upd o RecordsData.get;

    val is_selector = Symtab.defined o #selectors o get_sel_upd;
    val get_updates = Symtab.lookup o #updates o get_sel_upd;
    val get_simpset = #simpset o get_sel_upd;

    fun put_sel_upd names simps thy =
      let
        val sels = map (rpair ()) names;
        val upds = map (suffix updateN) names ~~ names;

        val {records, sel_upd = {selectors, updates, simpset},
          equalities, extinjects, extsplit, splits, extfields,fieldext} = RecordsData.get thy;
        val data = make_record_data records
          {selectors = Symtab.extend (selectors, sels),
            updates = Symtab.extend (updates, upds),
            simpset = Simplifier.addsimps (simpset, simps)}
           equalities extinjects extsplit splits extfields fieldext;
      in RecordsData.put data thy end;

    (* access 'equalities' *)

    fun add_record_equalities name thm thy =
      let
        val {records, sel_upd, equalities, extinjects, extsplit, splits, extfields,fieldext} =
              RecordsData.get thy;
        val data = make_record_data records sel_upd
               (Symtab.update_new (name, thm) equalities) extinjects extsplit
               splits extfields fieldext;
      in RecordsData.put data thy end;

    val get_equalities =Symtab.lookup o #equalities o RecordsData.get;

    (* access 'extinjects' *)

    fun add_extinjects thm thy =
      let
        val {records, sel_upd, equalities, extinjects, extsplit, splits, extfields,fieldext} =
              RecordsData.get thy;
        val data = make_record_data records sel_upd equalities (extinjects@[thm]) extsplit
                     splits extfields fieldext;
      in RecordsData.put data thy end;

    fun get_extinjects sg = #extinjects (RecordsData.get sg);

    (* access 'extsplit' *)

    fun add_extsplit name thm thy =
      let
        val {records, sel_upd, equalities, extinjects, extsplit, splits, extfields,fieldext} =
              RecordsData.get thy;
        val data = make_record_data records sel_upd
          equalities extinjects (Symtab.update_new (name, thm) extsplit) splits
          extfields fieldext;
      in RecordsData.put data thy end;

    val get_extsplit = Symtab.lookup o #extsplit o RecordsData.get;

    (* access 'splits' *)

    fun add_record_splits name thmP thy =
      let
        val {records, sel_upd, equalities, extinjects, extsplit, splits, extfields,fieldext} =
              RecordsData.get thy;
        val data = make_record_data records sel_upd
          equalities extinjects extsplit (Symtab.update_new (name, thmP) splits)
          extfields fieldext;
      in RecordsData.put data thy end;

    val get_splits = Symtab.lookup o #splits o RecordsData.get;

    (* extension of a record name *)
    val get_extension =
      Option.map #extension oo (Symtab.lookup o #records o RecordsData.get);

    (* access 'extfields' *)

    fun add_extfields name fields thy =
      let
        val {records, sel_upd, equalities, extinjects, extsplit,splits, extfields, fieldext} =
              RecordsData.get thy;
        val data = make_record_data records sel_upd
             equalities extinjects extsplit splits
             (Symtab.update_new (name, fields) extfields) fieldext;
      in RecordsData.put data thy end;

    val get_extfields = Symtab.lookup o #extfields o RecordsData.get;

    fun get_extT_fields sg T =
      let
        val ((name,Ts),moreT) = dest_recT T;
        val recname = let val (nm::recn::rst) = rev (NameSpace.unpack name)
                      in NameSpace.pack (rev (nm::rst)) end;
        val midx = maxidx_of_typs (moreT::Ts);
        fun varify (a, S) = TVar ((a, midx), S);
        val varifyT = map_type_tfree varify;
        val {records,extfields,...} = RecordsData.get sg;
        val (flds,(more,_)) = split_last (Symtab.lookup_multi extfields name);
        val args = map varifyT (snd (#extension (the (Symtab.lookup records recname))));

        val (subst,_) = fold (Sign.typ_unify sg) (but_last args ~~ but_last Ts) (Vartab.empty,0);
        val flds' = map (apsnd ((Envir.norm_type subst) o varifyT)) flds;
      in (flds',(more,moreT)) end;

    fun get_recT_fields sg T =
      let
        val (root_flds,(root_more,root_moreT)) = get_extT_fields sg T;
        val (rest_flds,rest_more) =
               if is_recT root_moreT then get_recT_fields sg root_moreT
               else ([],(root_more,root_moreT));
      in (root_flds@rest_flds,rest_more) end;

    (* access 'fieldext' *)

    fun add_fieldext extname_types fields thy =
      let
        val {records, sel_upd, equalities, extinjects, extsplit, splits, extfields, fieldext} =
               RecordsData.get thy;
        val fieldext' =
          fold (fn field => Symtab.update_new (field, extname_types)) fields fieldext;
        val data=make_record_data records sel_upd equalities extinjects extsplit
                  splits extfields fieldext';
      in RecordsData.put data thy end;

    val get_fieldext = Symtab.lookup o #fieldext o RecordsData.get;

    (* parent records *)

    fun add_parents thy NONE parents = parents
      | add_parents thy (SOME (types, name)) parents =
          let
            val sign = Theory.sign_of thy;
            fun err msg = error (msg ^ " parent record " ^ quote name);

            val {args, parent, fields, extension, induct} =
              (case get_record thy name of SOME info => info | NONE => err "Unknown");
            val _ = if length types <> length args then err "Bad number of arguments for" else ();

            fun bad_inst ((x, S), T) =
              if Sign.of_sort sign (T, S) then NONE else SOME x
            val bads = List.mapPartial bad_inst (args ~~ types);

            val inst = map fst args ~~ types;
            val subst = Term.map_type_tfree (the o AList.lookup (op =) inst o fst);
            val parent' = Option.map (apfst (map subst)) parent;
            val fields' = map (apsnd subst) fields;
            val extension' = apsnd (map subst) extension;
          in
            conditional (not (null bads)) (fn () =>
              err ("Ill-sorted instantiation of " ^ commas bads ^ " in"));
            add_parents thy parent'
              (make_parent_info name fields' extension' induct::parents)
          end;

    (** concrete syntax for records **)

    (* parse translations *)

    fun gen_field_tr mark sfx (t as Const (c, _) $ Const (name, _) $ arg) =
          if c = mark then Syntax.const (suffix sfx name) $ arg
          else raise TERM ("gen_field_tr: " ^ mark, [t])
      | gen_field_tr mark _ t = raise TERM ("gen_field_tr: " ^ mark, [t]);

    fun gen_fields_tr sep mark sfx (tm as Const (c, _) $ t $ u) =
          if c = sep then gen_field_tr mark sfx t :: gen_fields_tr sep mark sfx u
          else [gen_field_tr mark sfx tm]
      | gen_fields_tr _ mark sfx tm = [gen_field_tr mark sfx tm];

    fun record_update_tr [t, u] =
          foldr (op $) t (rev (gen_fields_tr "_updates" "_update" updateN u))
      | record_update_tr ts = raise TERM ("record_update_tr", ts);

    fun update_name_tr (Free (x, T) :: ts) = Free (suffix updateN x, T) $$ ts
      | update_name_tr (Const (x, T) :: ts) = Const (suffix updateN x, T) $$ ts
      | update_name_tr (((c as Const ("_constrain", _)) $ t $ ty) :: ts) =
          (c $ update_name_tr [t] $ (Syntax.const "fun" $ ty $ Syntax.const "dummy")) $$ ts
      | update_name_tr ts = raise TERM ("update_name_tr", ts);

    fun dest_ext_field mark (t as (Const (c,_) $ Const (name,_) $ arg)) =
         if c = mark then (name,arg) else raise TERM ("dest_ext_field: " ^ mark, [t])
      | dest_ext_field _ t = raise TERM ("dest_ext_field", [t])

    fun dest_ext_fields sep mark (trm as (Const (c,_) $ t $ u)) =
         if c = sep then dest_ext_field mark t::dest_ext_fields sep mark u
         else [dest_ext_field mark trm]
      | dest_ext_fields _ mark t = [dest_ext_field mark t]

    fun gen_ext_fields_tr sep mark sfx more sg t =
      let
        val msg = "error in record input: ";
        val fieldargs = dest_ext_fields sep mark t;
        fun splitargs (field::fields) ((name,arg)::fargs) =
              if can (unsuffix name) field
              then let val (args,rest) = splitargs fields fargs
                   in (arg::args,rest) end
              else raise TERM (msg ^ "expecting field " ^ field ^ " but got " ^ name, [t])
          | splitargs [] (fargs as (_::_)) = ([],fargs)
          | splitargs (_::_) [] = raise TERM (msg ^ "expecting more fields", [t])
          | splitargs _ _ = ([],[]);

        fun mk_ext (fargs as (name,arg)::_) =
             (case get_fieldext sg (Sign.intern_const sg name) of
                SOME (ext,_) => (case get_extfields sg ext of
                                   SOME flds
                                     => let val (args,rest) =
                                                   splitargs (map fst (but_last flds)) fargs;
                                            val more' = mk_ext rest;
                                        in list_comb (Syntax.const (suffix sfx ext),args@[more'])
                                        end
                                 | NONE => raise TERM(msg ^ "no fields defined for "
                                                       ^ ext,[t]))
              | NONE => raise TERM (msg ^ name ^" is no proper field",[t]))
          | mk_ext [] = more

      in mk_ext fieldargs end;

    fun gen_ext_type_tr sep mark sfx more sg t =
      let
        val msg = "error in record-type input: ";
        val fieldargs = dest_ext_fields sep mark t;
        fun splitargs (field::fields) ((name,arg)::fargs) =
              if can (unsuffix name) field
              then let val (args,rest) = splitargs fields fargs
                   in (arg::args,rest) end
              else raise TERM (msg ^ "expecting field " ^ field ^ " but got " ^ name, [t])
          | splitargs [] (fargs as (_::_)) = ([],fargs)
          | splitargs (_::_) [] = raise TERM (msg ^ "expecting more fields", [t])
          | splitargs _ _ = ([],[]);

        fun get_sort xs n = AList.lookup (op =) xs n |> the_default (Sign.defaultS sg);

        fun to_type t = Sign.certify_typ sg
                           (Sign.intern_typ sg
                             (Syntax.typ_of_term (get_sort (Syntax.raw_term_sorts t)) I t));

        fun mk_ext (fargs as (name,arg)::_) =
             (case get_fieldext sg (Sign.intern_const sg name) of
                SOME (ext,alphas) =>
                  (case get_extfields sg ext of
                     SOME flds
                      => (let
                           val flds' = but_last flds;
                           val types = map snd flds';
                           val (args,rest) = splitargs (map fst flds') fargs;
                           val vartypes = map Type.varifyT types;
                           val argtypes = map to_type args;
                           val (subst,_) = fold (Sign.typ_unify sg) (vartypes ~~ argtypes)
                                                (Vartab.empty,0);
                           val alphas' = map ((Syntax.term_of_typ (! Syntax.show_sorts)) o
                                              Envir.norm_type subst o Type.varifyT)
                                             (but_last alphas);

                           val more' = mk_ext rest;
                         in list_comb (Syntax.const (suffix sfx ext),alphas'@[more'])
                         end handle TUNIFY => raise
                               TERM (msg ^ "type is no proper record (extension)", [t]))
                   | NONE => raise TERM (msg ^ "no fields defined for " ^ ext,[t]))
              | NONE => raise TERM (msg ^ name ^" is no proper field",[t]))
          | mk_ext [] = more

      in mk_ext fieldargs end;

    fun gen_adv_record_tr sep mark sfx unit sg [t] =
          gen_ext_fields_tr sep mark sfx unit sg t
      | gen_adv_record_tr _ _ _ _ _ ts = raise TERM ("gen_record_tr", ts);

    fun gen_adv_record_scheme_tr sep mark sfx sg [t, more] =
          gen_ext_fields_tr sep mark sfx more sg t
      | gen_adv_record_scheme_tr _ _ _ _ ts = raise TERM ("gen_record_scheme_tr", ts);

    fun gen_adv_record_type_tr sep mark sfx unit sg [t] =
          gen_ext_type_tr sep mark sfx unit sg t
      | gen_adv_record_type_tr _ _ _ _ _ ts = raise TERM ("gen_record_tr", ts);

    fun gen_adv_record_type_scheme_tr sep mark sfx sg [t, more] =
          gen_ext_type_tr sep mark sfx more sg t
      | gen_adv_record_type_scheme_tr _ _ _ _ ts = raise TERM ("gen_record_scheme_tr", ts);

    val adv_record_tr = gen_adv_record_tr "_fields" "_field" extN HOLogic.unit;
    val adv_record_scheme_tr = gen_adv_record_scheme_tr "_fields" "_field" extN;

    val adv_record_type_tr =
          gen_adv_record_type_tr "_field_types" "_field_type" ext_typeN
            (Syntax.term_of_typ false (HOLogic.unitT));
    val adv_record_type_scheme_tr =
          gen_adv_record_type_scheme_tr "_field_types" "_field_type" ext_typeN;

    val parse_translation =
     [("_record_update", record_update_tr),
      ("_update_name", update_name_tr)];

    val adv_parse_translation =
     [("_record",adv_record_tr),
      ("_record_scheme",adv_record_scheme_tr),
      ("_record_type",adv_record_type_tr),
      ("_record_type_scheme",adv_record_type_scheme_tr)];

    (* print translations *)

    val print_record_type_abbr = ref true;
    val print_record_type_as_fields = ref true;

    fun gen_field_upds_tr' mark sfx (tm as Const (name_field, _) $ t $ u) =
        (case try (unsuffix sfx) name_field of
          SOME name =>
            apfst (cons (Syntax.const mark $ Syntax.free name $ t)) (gen_field_upds_tr' mark sfx u)
         | NONE => ([], tm))
      | gen_field_upds_tr' _ _ tm = ([], tm);

    fun record_update_tr' tm =
      let val (ts, u) = gen_field_upds_tr' "_update" updateN tm in
        Syntax.const "_record_update" $ u $
          foldr1 (fn (v, w) => Syntax.const "_updates" $ v $ w) (rev ts)
      end;

    fun gen_field_tr' sfx tr' name =
      let val name_sfx = suffix sfx name
      in (name_sfx, fn [t, u] => tr' (Syntax.const name_sfx $ t $ u) | _ => raise Match) end;

    fun record_tr' sep mark record record_scheme unit sg t =
      let
        fun field_lst t =
          (case strip_comb t of
            (Const (ext,_),args as (_::_))
             => (case try (unsuffix extN) (Sign.intern_const sg ext) of
                   SOME ext'
                   => (case get_extfields sg ext' of
                         SOME flds
                         => (let
                              val (f::fs) = but_last (map fst flds);
                              val flds' = Sign.extern_const sg f :: map NameSpace.base fs;
                              val (args',more) = split_last args;
                             in (flds'~~args')@field_lst more end
                             handle UnequalLengths => [("",t)])
                       | NONE => [("",t)])
                 | NONE => [("",t)])
           | _ => [("",t)])

        val (flds,(_,more)) = split_last (field_lst t);
        val flds' = map (fn (n,t)=>Syntax.const mark$Syntax.const n$t) flds;
        val flds'' = foldr1 (fn (x,y) => Syntax.const sep$x$y) flds';

      in if null flds then raise Match
         else if unit more
              then Syntax.const record$flds''
              else Syntax.const record_scheme$flds''$more
      end

    fun gen_record_tr' name =
      let val name_sfx = suffix extN name;
          val unit = (fn Const ("Unity",_) => true | _ => false);
          fun tr' sg ts = record_tr' "_fields" "_field" "_record" "_record_scheme" unit sg
                           (list_comb (Syntax.const name_sfx,ts))
      in (name_sfx,tr')
      end

    fun print_translation names =
      map (gen_field_tr' updateN record_update_tr') names;

    (* record_type_abbr_tr' tries to reconstruct the record name type abbreviation from *)
    (* the (nested) extension types.                                                    *)
    fun record_type_abbr_tr' default_tr' abbr alphas zeta lastExt schemeT sg tm =
      let
          (* tm is term representation of a (nested) field type. We first reconstruct the      *)
          (* type from tm so that we can continue on the type level rather then the term level.*)

          fun get_sort xs n = AList.lookup (op =) xs n |> the_default (Sign.defaultS sg);

          (* WORKAROUND:
           * If a record type occurs in an error message of type inference there
           * may be some internal frees donoted by ??:
           * (Const "_tfree",_)$Free ("??'a",_).

           * This will unfortunately be translated to Type ("??'a",[]) instead of
           * TFree ("??'a",_) by typ_of_term, which will confuse unify below.
           * fixT works around.
           *)
          fun fixT (T as Type (x,[])) =
                if String.isPrefix "??'" x then TFree (x,Sign.defaultS sg) else T
            | fixT (Type (x,xs)) = Type (x,map fixT xs)
            | fixT T = T;

          val T = fixT (Sign.intern_typ sg
                          (Syntax.typ_of_term (get_sort (Syntax.raw_term_sorts tm)) I tm));

          fun mk_type_abbr subst name alphas =
              let val abbrT = Type (name, map (fn a => TVar ((a, 0), Sign.defaultS sg)) alphas);
              in Syntax.term_of_typ (! Syntax.show_sorts)
                   (Sign.extern_typ sg (Envir.norm_type subst abbrT)) end;

          fun unify rT T = fst (Sign.typ_unify sg (Type.varifyT rT,T) (Vartab.empty,0));

       in if !print_record_type_abbr
          then (case last_extT T of
                 SOME (name,_)
                  => if name = lastExt
                     then
                      (let
                         val subst = unify schemeT T
                       in
                        if HOLogic.is_unitT (Envir.norm_type subst (TVar((zeta,0),Sign.defaultS sg)))
                        then mk_type_abbr subst abbr alphas
                        else mk_type_abbr subst (suffix schemeN abbr) (alphas@[zeta])
                       end handle TUNIFY => default_tr' sg tm)
                     else raise Match (* give print translation of specialised record a chance *)
                | _ => raise Match)
           else default_tr' sg tm
      end

    fun record_type_tr' sep mark record record_scheme sg t =
      let
        fun get_sort xs n = AList.lookup (op =) xs n |> the_default (Sign.defaultS sg);

        val T = Sign.intern_typ sg (Syntax.typ_of_term (get_sort (Syntax.raw_term_sorts t)) I t)

        fun term_of_type T = Syntax.term_of_typ (!Syntax.show_sorts) (Sign.extern_typ sg T);

        fun field_lst T =
          (case T of
            Type (ext,args)
             => (case try (unsuffix ext_typeN) ext of
                   SOME ext'
                   => (case get_extfields sg ext' of
                         SOME flds
                         => (case get_fieldext sg (fst (hd flds)) of
                               SOME (_,alphas)
                               => (let
                                    val (f::fs) = but_last flds;
                                    val flds' = apfst (Sign.extern_const sg) f
                                                ::map (apfst NameSpace.base) fs;
                                    val (args',more) = split_last args;
                                    val alphavars = map Type.varifyT (but_last alphas);
                                    val (subst,_)= fold (Sign.typ_unify sg) (alphavars~~args')
                                                        (Vartab.empty,0);
                                    val flds'' =map (apsnd (Envir.norm_type subst o Type.varifyT))
                                                    flds';
                                  in flds''@field_lst more end
                                  handle TUNIFY         => [("",T)]
                                       | UnequalLengths => [("",T)])
                             | NONE => [("",T)])
                       | NONE => [("",T)])
                 | NONE => [("",T)])
            | _ => [("",T)])

        val (flds,(_,moreT)) = split_last (field_lst T);
        val flds' = map (fn (n,T)=>Syntax.const mark$Syntax.const n$term_of_type T) flds;
        val flds'' = foldr1 (fn (x,y) => Syntax.const sep$x$y) flds';

      in if not (!print_record_type_as_fields) orelse null flds then raise Match
         else if moreT = HOLogic.unitT
              then Syntax.const record$flds''
              else Syntax.const record_scheme$flds''$term_of_type moreT
      end

    fun gen_record_type_tr' name =
      let val name_sfx = suffix ext_typeN name;
          fun tr' sg ts = record_type_tr' "_field_types" "_field_type"
                           "_record_type" "_record_type_scheme" sg
                           (list_comb (Syntax.const name_sfx,ts))
      in (name_sfx,tr')
      end

    fun gen_record_type_abbr_tr' abbr alphas zeta lastExt schemeT name =
      let val name_sfx = suffix ext_typeN name;
          val default_tr' = record_type_tr' "_field_types" "_field_type"
                                   "_record_type" "_record_type_scheme"
          fun tr' sg ts = record_type_abbr_tr' default_tr' abbr alphas zeta lastExt schemeT sg
                             (list_comb (Syntax.const name_sfx,ts))
      in (name_sfx, tr') end;

    (** record simprocs **)

    val record_quick_and_dirty_sensitive = ref false;

    fun quick_and_dirty_prove stndrd sg asms prop tac =
      if !record_quick_and_dirty_sensitive andalso !quick_and_dirty
      then Tactic.prove sg [] [] (Logic.list_implies (map Logic.varify asms,Logic.varify prop))
            (K (SkipProof.cheat_tac HOL.thy))
            (* standard can take quite a while for large records, thats why
             * we varify the proposition manually here.*)
      else let val prf = Tactic.prove sg [] asms prop tac;
           in if stndrd then standard prf else prf end;

    fun quick_and_dirty_prf noopt opt () =
          if !record_quick_and_dirty_sensitive andalso !quick_and_dirty
          then noopt ()
          else opt ();

    fun prove_split_simp sg ss T prop =
      let
        val {sel_upd={simpset,...},extsplit,...} = RecordsData.get sg;
        val extsplits =
                Library.foldl (fn (thms,(n,_)) => the_list (Symtab.lookup extsplit n) @ thms)
                        ([],dest_recTs T);
        val thms = (case get_splits sg (rec_id (~1) T) of
                       SOME (all_thm,_,_,_) =>
                         all_thm::(case extsplits of [thm] => [] | _ => extsplits)
                                  (* [thm] is the same as all_thm *)
                     | NONE => extsplits)
      in
        quick_and_dirty_prove true sg [] prop
          (fn _ => simp_tac (Simplifier.inherit_bounds ss simpset addsimps thms) 1)
      end;

    local
    fun eq (s1:string) (s2:string) = (s1 = s2);
    fun has_field extfields f T =
         exists (fn (eN,_) => exists (eq f o fst) (Symtab.lookup_multi extfields eN))
           (dest_recTs T);
    in
    (* record_simproc *)
    (* Simplifies selections of an record update:
     *  (1)  S (r(|S:=k|)) = k respectively
     *  (2)  S (r(|X:=k|)) = S r
     * The simproc skips multiple updates at once, eg:
     *  S (r (|S:=k,X:=2,Y:=3|)) = k
     * But be careful in (2) because of the extendibility of records.
     * - If S is a more-selector we have to make sure that the update on component
     *   X does not affect the selected subrecord.
     * - If X is a more-selector we have to make sure that S is not in the updated
     *   subrecord.
     *)
    val record_simproc =
      Simplifier.simproc HOL.thy "record_simp" ["x"]
        (fn sg => fn ss => fn t =>
          (case t of (sel as Const (s, Type (_,[domS,rangeS])))$
                       ((upd as Const (u,Type(_,[_,Type (_,[rT,_])]))) $ k $ r)=>
            if is_selector sg s then
              (case get_updates sg u of SOME u_name =>
                let
                  val {sel_upd={updates,...},extfields,...} = RecordsData.get sg;

                  fun mk_eq_terms ((upd as Const (u,Type(_,[kT,_]))) $ k $ r) =
                      (case Symtab.lookup updates u of
                         NONE => NONE
                       | SOME u_name
                         => if u_name = s
                            then let
                                   val rv = ("r",rT)
                                   val rb = Bound 0
                                   val kv = ("k",kT)
                                   val kb = Bound 1
                                 in SOME (upd$kb$rb,kb,[kv,rv],true) end
                            else if has_field extfields u_name rangeS
                                 orelse has_field extfields s kT
                                 then NONE
                                 else (case mk_eq_terms r of
                                         SOME (trm,trm',vars,update_s)
                                         => let
                                              val kv = ("k",kT)
                                              val kb = Bound (length vars)
                                            in SOME (upd$kb$trm,trm',kv::vars,update_s) end
                                       | NONE
                                         => let
                                              val rv = ("r",rT)
                                              val rb = Bound 0
                                              val kv = ("k",kT)
                                              val kb = Bound 1
                                            in SOME (upd$kb$rb,rb,[kv,rv],false) end))
                    | mk_eq_terms r = NONE
                in
                  (case mk_eq_terms (upd$k$r) of
                     SOME (trm,trm',vars,update_s)
                     => if update_s
                        then SOME (prove_split_simp sg ss domS
                                     (list_all(vars,(equals rangeS$(sel$trm)$trm'))))
                        else SOME (prove_split_simp sg ss domS
                                     (list_all(vars,(equals rangeS$(sel$trm)$(sel$trm')))))
                   | NONE => NONE)
                end
              | NONE => NONE)
            else NONE
          | _ => NONE));

    (* record_upd_simproc *)
    (* simplify multiple updates:
     *  (1)  "r(|M:=3,N:=1,M:=2,N:=4|) == r(|M:=2,N:=4|)"
     *  (2)  "r(|M:= M r|) = r"
     * For (2) special care of "more" updates has to be taken:
     *    r(|more := m; A := A r|)
     * If A is contained in the fields of m we cannot remove the update A := A r!
     * (But r(|more := r; A := A (r(|more := r|))|) = r(|more := r|)
    *)
    val record_upd_simproc =
      Simplifier.simproc HOL.thy "record_upd_simp" ["x"]
        (fn sg => fn ss => fn t =>
          (case t of ((upd as Const (u, Type(_,[_,Type(_,[rT,_])]))) $ k $ r) =>
             let datatype ('a,'b) calc = Init of 'b | Inter of 'a
                 val {sel_upd={selectors,updates,...},extfields,...} = RecordsData.get sg;

                 (*fun mk_abs_var x t = (x, fastype_of t);*)
                 fun sel_name u = NameSpace.base (unsuffix updateN u);

                 fun seed s (upd as Const (more,Type(_,[mT,_]))$ k $ r) =
                      if has_field extfields s mT then upd else seed s r
                   | seed _ r = r;

                 fun grow u uT k kT vars (sprout,skeleton) =
                       if sel_name u = moreN
                       then let val kv = ("k", kT);
                                val kb = Bound (length vars);
                            in ((Const (u,uT)$k$sprout,Const (u,uT)$kb$skeleton),kv::vars) end
                       else ((sprout,skeleton),vars);

                 fun is_upd_same (sprout,skeleton) u ((sel as Const (s,_))$r) =
                       if (unsuffix updateN u) = s andalso (seed s sprout) = r
                       then SOME (sel,seed s skeleton)
                       else NONE
                   | is_upd_same _ _ _ = NONE

                 fun init_seed r = ((r,Bound 0), [("r", rT)]);

                 (* mk_updterm returns either
                  *  - Init (orig-term, orig-term-skeleton, vars) if no optimisation can be made,
                  *     where vars are the bound variables in the skeleton
                  *  - Inter (orig-term-skeleton,simplified-term-skeleton,
                  *           vars, (term-sprout, skeleton-sprout))
                  *     where "All vars. orig-term-skeleton = simplified-term-skeleton" is
                  *     the desired simplification rule,
                  *     the sprouts accumulate the "more-updates" on the way from the seed
                  *     to the outermost update. It is only relevant to calculate the
                  *     possible simplification for (2)
                  * The algorithm first walks down the updates to the seed-record while
                  * memorising the updates in the already-table. While walking up the
                  * updates again, the optimised term is constructed.
                  *)
                 fun mk_updterm upds already
                     (t as ((upd as Const (u,uT as (Type (_,[kT,_])))) $ k $ r)) =
                     if Symtab.defined upds u
                     then let
                             fun rest already = mk_updterm upds already
                          in if u mem_string already
                             then (case (rest already r) of
                                     Init ((sprout,skel),vars) =>
                                     let
                                       val kv = (sel_name u, kT);
                                       val kb = Bound (length vars);
                                       val (sprout',vars')= grow u uT k kT (kv::vars) (sprout,skel);
                                     in Inter (upd$kb$skel,skel,vars',sprout') end
                                   | Inter (trm,trm',vars,sprout) =>
                                     let
                                       val kv = (sel_name u, kT);
                                       val kb = Bound (length vars);
                                       val (sprout',vars') = grow u uT k kT (kv::vars) sprout;
                                     in Inter(upd$kb$trm,trm',kv::vars',sprout') end)
                             else
                              (case rest (u::already) r of
                                 Init ((sprout,skel),vars) =>
                                  (case is_upd_same (sprout,skel) u k of
                                     SOME (sel,skel') =>
                                     let
                                       val (sprout',vars') = grow u uT k kT vars (sprout,skel);
                                      in Inter(upd$(sel$skel')$skel,skel,vars',sprout') end
                                   | NONE =>
                                     let
                                       val kv = (sel_name u, kT);
                                       val kb = Bound (length vars);
                                     in Init ((upd$k$sprout,upd$kb$skel),kv::vars) end)
                               | Inter (trm,trm',vars,sprout) =>
                                   (case is_upd_same sprout u k of
                                      SOME (sel,skel) =>
                                      let
                                        val (sprout',vars') = grow u uT k kT vars sprout
                                      in Inter(upd$(sel$skel)$trm,trm',vars',sprout') end
                                    | NONE =>
                                      let
                                        val kv = (sel_name u, kT)
                                        val kb = Bound (length vars)
                                        val (sprout',vars') = grow u uT k kT (kv::vars) sprout
                                      in Inter (upd$kb$trm,upd$kb$trm',vars',sprout') end))
                          end
                     else Init (init_seed t)
                   | mk_updterm _ _ t = Init (init_seed t);

             in (case mk_updterm updates [] t of
                   Inter (trm,trm',vars,_)
                    => SOME (prove_split_simp sg ss rT
                              (list_all(vars,(equals rT$trm$trm'))))
                 | _ => NONE)
             end
           | _ => NONE));
    end

    (* record_eq_simproc *)
    (* looks up the most specific record-equality.
     * Note on efficiency:
     * Testing equality of records boils down to the test of equality of all components.
     * Therefore the complexity is: #components * complexity for single component.
     * Especially if a record has a lot of components it may be better to split up
     * the record first and do simplification on that (record_split_simp_tac).
     * e.g. r(|lots of updates|) = x
     *
     *               record_eq_simproc       record_split_simp_tac
     * Complexity: #components * #updates     #updates
     *
     *)
    val record_eq_simproc =
      Simplifier.simproc HOL.thy "record_eq_simp" ["r = s"]
        (fn sg => fn _ => fn t =>
          (case t of Const ("op =", Type (_, [T, _])) $ _ $ _ =>
            (case rec_id (~1) T of
               "" => NONE
             | name => (case get_equalities sg name of
                                    NONE => NONE
                                  | SOME thm => SOME (thm RS Eq_TrueI)))
           | _ => NONE));

    (* record_split_simproc *)
    (* splits quantified occurrences of records, for which P holds. P can peek on the
     * subterm starting at the quantified occurrence of the record (including the quantifier)
     * P t = 0: do not split
     * P t = ~1: completely split
     * P t > 0: split up to given bound of record extensions
     *)
    fun record_split_simproc P =
      Simplifier.simproc HOL.thy "record_split_simp" ["x"]
        (fn sg => fn _ => fn t =>
          (case t of (Const (quantifier, Type (_, [Type (_, [T, _]), _])))$trm =>
             if quantifier = "All" orelse quantifier = "all" orelse quantifier = "Ex"
             then (case rec_id (~1) T of
                     "" => NONE
                   | name
                      => let val split = P t
                         in if split <> 0 then
                            (case get_splits sg (rec_id split T) of
                                  NONE => NONE
                                | SOME (all_thm, All_thm, Ex_thm,_)
                                   => SOME (case quantifier of
                                              "all" => all_thm
                                            | "All" => All_thm RS HOL.eq_reflection
                                            | "Ex"  => Ex_thm RS HOL.eq_reflection
                                            | _     => error "record_split_simproc"))
                            else NONE
                          end)
             else NONE
           | _ => NONE))

    val record_ex_sel_eq_simproc =
      Simplifier.simproc HOL.thy "record_ex_sel_eq_simproc" ["Ex t"]
        (fn sg => fn ss => fn t =>
           let
             fun prove prop =
               quick_and_dirty_prove true sg [] prop
                 (fn _ => simp_tac (Simplifier.inherit_bounds ss (get_simpset sg)
                   addsimps simp_thms addsimprocs [record_split_simproc (K ~1)]) 1);

             fun mkeq (lr,Teq,(sel,Tsel),x) i =
                  if is_selector sg sel then
                     let val x' = if not (loose_bvar1 (x,0))
                                  then Free ("x" ^ string_of_int i, range_type Tsel)
                                  else raise TERM ("",[x]);
                         val sel' = Const (sel,Tsel)$Bound 0;
                         val (l,r) = if lr then (sel',x') else (x',sel');
                      in Const ("op =",Teq)$l$r end
                  else raise TERM ("",[Const (sel,Tsel)]);

             fun dest_sel_eq (Const ("op =",Teq)$(Const (sel,Tsel)$Bound 0)$X) =
                               (true,Teq,(sel,Tsel),X)
               | dest_sel_eq (Const ("op =",Teq)$X$(Const (sel,Tsel)$Bound 0)) =
                               (false,Teq,(sel,Tsel),X)
               | dest_sel_eq _ = raise TERM ("",[]);

           in
             (case t of
               (Const ("Ex",Tex)$Abs(s,T,t)) =>
                 (let val eq = mkeq (dest_sel_eq t) 0;
                     val prop = list_all ([("r",T)],
                                  Logic.mk_equals (Const ("Ex",Tex)$Abs(s,T,eq),
                                                   HOLogic.true_const));
                 in SOME (prove prop) end
                 handle TERM _ => NONE)
              | _ => NONE)
             end)

    local
    val inductive_atomize = thms "induct_atomize";
    val inductive_rulify1 = thms "induct_rulify1";
    in
    (* record_split_simp_tac *)
    (* splits (and simplifies) all records in the goal for which P holds.
     * For quantified occurrences of a record
     * P can peek on the whole subterm (including the quantifier); for free variables P
     * can only peek on the variable itself.
     * P t = 0: do not split
     * P t = ~1: completely split
     * P t > 0: split up to given bound of record extensions
     *)
    fun record_split_simp_tac thms P i st =
      let
        val sg = Thm.sign_of_thm st;
        val {sel_upd={simpset,...},...}
                = RecordsData.get sg;

        val has_rec = exists_Const
          (fn (s, Type (_, [Type (_, [T, _]), _])) =>
              (s = "all" orelse s = "All" orelse s = "Ex") andalso is_recT T
            | _ => false);

        val goal = List.nth (Thm.prems_of st, i - 1);
        val frees = List.filter (is_recT o type_of) (term_frees goal);

        fun mk_split_free_tac free induct_thm i =
            let val cfree = cterm_of sg free;
                val (_$(_$r)) = concl_of induct_thm;
                val crec = cterm_of sg r;
                val thm  = cterm_instantiate [(crec,cfree)] induct_thm;
            in EVERY [simp_tac (HOL_basic_ss addsimps inductive_atomize) i,
                      rtac thm i,
                      simp_tac (HOL_basic_ss addsimps inductive_rulify1) i]
            end;

        fun split_free_tac P i (free as Free (n,T)) =
            (case rec_id (~1) T of
               "" => NONE
             | name => let val split = P free
                       in if split <> 0 then
                          (case get_splits sg (rec_id split T) of
                                 NONE => NONE
                               | SOME (_,_,_,induct_thm)
                                   => SOME (mk_split_free_tac free induct_thm i))
                          else NONE
                       end)
         | split_free_tac _ _ _ = NONE;

        val split_frees_tacs = List.mapPartial (split_free_tac P i) frees;

        val simprocs = if has_rec goal then [record_split_simproc P] else [];

      in st |> ((EVERY split_frees_tacs)
               THEN (Simplifier.full_simp_tac (simpset addsimps thms addsimprocs simprocs) i))
      end handle Empty => Seq.empty;
    end;

    (* record_split_tac *)
    (* splits all records in the goal, which are quantified by ! or !!. *)
    fun record_split_tac i st =
      let
        val sg = Thm.sign_of_thm st;

        val has_rec = exists_Const
          (fn (s, Type (_, [Type (_, [T, _]), _])) =>
              (s = "all" orelse s = "All") andalso is_recT T
            | _ => false);

        val goal = List.nth (Thm.prems_of st, i - 1);

        fun is_all t =
          (case t of (Const (quantifier, _)$_) =>
             if quantifier = "All" orelse quantifier = "all" then ~1 else 0
           | _ => 0);

      in if has_rec goal
         then Simplifier.full_simp_tac
               (HOL_basic_ss addsimprocs [record_split_simproc is_all]) i st
         else Seq.empty
      end handle Subscript => Seq.empty;

    (* wrapper *)

    val record_split_name = "record_split_tac";
    val record_split_wrapper = (record_split_name, fn tac => record_split_tac ORELSE' tac);

    (** theory extender interface **)

    (* prepare arguments *)

    fun read_raw_parent sign s =
      (case Sign.read_typ_abbrev (sign, K NONE) s handle TYPE (msg, _, _) => error msg of
        Type (name, Ts) => (Ts, name)
      | _ => error ("Bad parent record specification: " ^ quote s));

    fun read_typ sign (env, s) =
      let
        fun def_sort (x, ~1) = AList.lookup (op =) env x
          | def_sort _ = NONE;
        val T = Type.no_tvars (Sign.read_typ (sign, def_sort) s) handle TYPE (msg, _, _) => error msg;
      in (Term.add_typ_tfrees (T, env), T) end;

    fun cert_typ sign (env, raw_T) =
      let val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle TYPE (msg, _, _) => error msg
      in (Term.add_typ_tfrees (T, env), T) end;

    (* attributes *)

    fun case_names_fields x = RuleCases.case_names ["fields"] x;
    fun induct_type_global name = [case_names_fields, InductAttrib.induct_type_global name];
    fun cases_type_global name = [case_names_fields, InductAttrib.cases_type_global name];

    (* tactics *)

    fun simp_all_tac ss simps = ALLGOALS (Simplifier.asm_full_simp_tac (ss addsimps simps));

    (* do case analysis / induction according to rule on last parameter of ith subgoal
     * (or on s if there are no parameters);
     * Instatiation of record variable (and predicate) in rule is calculated to
     * avoid problems with higher order unification.
     *)

    fun try_param_tac s rule i st =
      let
        val cert = cterm_of (Thm.theory_of_thm st);
        val g = List.nth (prems_of st, i - 1);
        val params = Logic.strip_params g;
        val concl = HOLogic.dest_Trueprop (Logic.strip_assums_concl g);
        val rule' = Thm.lift_rule (st, i) rule;
        val (P, ys) = strip_comb (HOLogic.dest_Trueprop
          (Logic.strip_assums_concl (prop_of rule')));
        (* ca indicates if rule is a case analysis or induction rule *)
        val (x, ca) = (case rev (Library.drop (length params, ys)) of
            [] => (head_of (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop
              (hd (rev (Logic.strip_assums_hyp (hd (prems_of rule')))))))), true)
          | [x] => (head_of x, false));
        val rule'' = cterm_instantiate (map (pairself cert) (case (rev params) of
            [] => (case AList.lookup (op =) (map dest_Free (term_frees (prop_of st))) s of
              NONE => sys_error "try_param_tac: no such variable"
            | SOME T => [(P, if ca then concl else lambda (Free (s, T)) concl),
                (x, Free (s, T))])
          | (_, T) :: _ => [(P, list_abs (params, if ca then concl
              else incr_boundvars 1 (Abs (s, T, concl)))),
            (x, list_abs (params, Bound 0))])) rule'
      in compose_tac (false, rule'', nprems_of rule) i st end;

    (* !!x1 ... xn. ... ==> EX x1 ... xn. P x1 ... xn;
       instantiates x1 ... xn with parameters x1 ... xn *)
    fun ex_inst_tac i st =
      let
        val sg = sign_of_thm st;
        val g = List.nth (prems_of st, i - 1);
        val params = Logic.strip_params g;
        val exI' = Thm.lift_rule (st, i) exI;
        val (_$(_$x)) = Logic.strip_assums_concl (hd (prems_of exI'));
        val cx = cterm_of sg (fst (strip_comb x));

      in Seq.single (Library.foldl (fn (st,v) =>
            Seq.hd
            (compose_tac (false, cterm_instantiate
                                    [(cx,cterm_of sg (list_abs (params,Bound v)))] exI',1)
                    i st)) (st,((length params) - 1) downto 0))
      end;

    fun extension_typedef name repT alphas thy =
      let
        val UNIV = HOLogic.mk_UNIV repT;

        val (thy',{set_def=SOME def, Abs_induct = abs_induct,
                   Abs_inject=abs_inject, Abs_inverse = abs_inverse,...}) =
            thy |> setmp TypedefPackage.quiet_mode true
               (TypedefPackage.add_typedef_i true NONE
                 (suffix ext_typeN (Sign.base_name name), alphas, Syntax.NoSyn) UNIV NONE
                 (Tactic.rtac UNIV_witness 1))
        val rewrite_rule = Tactic.rewrite_rule [def, rec_UNIV_I, rec_True_simp];
      in (thy',map rewrite_rule [abs_inject, abs_inverse, abs_induct])
      end;

    fun mixit convs refls =
      let fun f ((res,lhs,rhs),refl) = ((refl,List.revAppend (lhs,refl::tl rhs))::res,hd rhs::lhs,tl rhs);
      in #1 (Library.foldl f (([],[],convs),refls)) end;

    fun extension_definition full name fields names alphas zeta moreT more vars thy =
      let
        val base = Sign.base_name;
        val fieldTs = (map snd fields);
        val alphas_zeta = alphas@[zeta];
        val alphas_zetaTs = map (fn n => TFree (n, HOLogic.typeS)) alphas_zeta;
        val vT = TFree (variant alphas_zeta "'v", HOLogic.typeS);
        val extT_name = suffix ext_typeN name
        val extT = Type (extT_name, alphas_zetaTs);
        val repT = foldr1 HOLogic.mk_prodT (fieldTs@[moreT]);
        val fields_more = fields@[(full moreN,moreT)];
        val fields_moreTs = fieldTs@[moreT];
        val bfields_more = map (apfst base) fields_more;
        val r = Free (rN,extT)
        val len = length fields;
        val idxms = 0 upto len;

        (* prepare declarations and definitions *)

        (*fields constructor*)
        val ext_decl = (mk_extC (name,extT) fields_moreTs);
        (*
        val ext_spec = Const ext_decl :==
             (foldr (uncurry lambda)
                (mk_Abs name repT extT $ (foldr1 HOLogic.mk_prod (vars@[more]))) (vars@[more]))
        *)
        val ext_spec = list_comb (Const ext_decl,vars@[more]) :==
             (mk_Abs name repT extT $ (foldr1 HOLogic.mk_prod (vars@[more])));

        fun mk_ext args = list_comb (Const ext_decl, args);

        (*destructors*)
        val _ = timing_msg "record extension preparing definitions";
        val dest_decls = map (mk_selC extT o (apfst (suffix ext_dest))) bfields_more;

        fun mk_dest_spec (i, (c,T)) =
          let val snds = (funpow i HOLogic.mk_snd (mk_Rep name repT extT $ r))
          in Const (mk_selC extT (suffix ext_dest c,T))
             :== (lambda r (if i=len then snds else HOLogic.mk_fst snds))
          end;
        val dest_specs =
          ListPair.map mk_dest_spec (idxms, fields_more);

        (*updates*)
        val upd_decls = map (mk_updC updN extT) bfields_more;
        fun mk_upd_spec (c,T) =
          let
            val args = map (fn (n,nT) => if n=c then Free (base c,T)
                                         else (mk_sel r (suffix ext_dest n,nT)))
                           fields_more;
          in Const (mk_updC updN extT (c,T))$(Free (base c,T))$r
              :== mk_ext args
          end;
        val upd_specs = map mk_upd_spec fields_more;

        (* 1st stage: defs_thy *)
        fun mk_defs () =
          thy
            |> extension_typedef name repT (alphas@[zeta])
            |>> Theory.add_consts_i
                  (map Syntax.no_syn ((apfst base ext_decl)::dest_decls@upd_decls))
            |>>> PureThy.add_defs_i false (map Thm.no_attributes (ext_spec::dest_specs))
            |>>> PureThy.add_defs_i false (map Thm.no_attributes upd_specs)
        val (defs_thy, (([abs_inject, abs_inverse, abs_induct],ext_def::dest_defs),upd_defs)) =
            timeit_msg "record extension type/selector/update defs:" mk_defs;

        (* prepare propositions *)
        val _ = timing_msg "record extension preparing propositions";
        val vars_more = vars@[more];
        val named_vars_more = (names@[full moreN])~~vars_more;
        val variants = map (fn (Free (x,_))=>x) vars_more;
        val ext = mk_ext vars_more;
        val s     = Free (rN, extT);
        val w     = Free (wN, extT);
        val P = Free (variant variants "P", extT-->HOLogic.boolT);
        val C = Free (variant variants "C", HOLogic.boolT);

        val inject_prop =
          let val vars_more' = map (fn (Free (x,T)) => Free (x ^ "'",T)) vars_more;
          in All (map dest_Free (vars_more@vars_more'))
              ((HOLogic.eq_const extT $
                mk_ext vars_more$mk_ext vars_more')
               ===
               foldr1 HOLogic.mk_conj (map HOLogic.mk_eq (vars_more ~~ vars_more')))
          end;

        val induct_prop =
          (All (map dest_Free vars_more) (Trueprop (P $ ext)), Trueprop (P $ s));

        val cases_prop =
          (All (map dest_Free vars_more)
            (Trueprop (HOLogic.mk_eq (s,ext)) ==> Trueprop C))
          ==> Trueprop C;

        (*destructors*)
        val dest_conv_props =
           map (fn (c, x as Free (_,T)) => mk_sel ext (suffix ext_dest c,T) === x) named_vars_more;

        (*updates*)
        fun mk_upd_prop (i,(c,T)) =
          let val x' = Free (variant variants (base c ^ "'"),T)
              val args' = nth_update x' (i, vars_more)
          in mk_upd updN c x' ext === mk_ext args'  end;
        val upd_conv_props = ListPair.map mk_upd_prop (idxms, fields_more);

        val surjective_prop =
          let val args =
               map (fn (c, Free (_,T)) => mk_sel s (suffix ext_dest c,T)) named_vars_more;
          in s === mk_ext args end;

        val split_meta_prop =
          let val P = Free (variant variants "P", extT-->Term.propT) in
            Logic.mk_equals
             (All [dest_Free s] (P $ s), All (map dest_Free vars_more) (P $ ext))
          end;

        fun prove stndrd = quick_and_dirty_prove stndrd defs_thy;
        val prove_standard = quick_and_dirty_prove true defs_thy;
        fun prove_simp stndrd simps =
          let val tac = simp_all_tac HOL_ss simps
          in fn prop => prove stndrd [] prop (K tac) end;

        fun inject_prf () = (prove_simp true [ext_def,abs_inject,Pair_eq] inject_prop);
        val inject = timeit_msg "record extension inject proof:" inject_prf;

        fun induct_prf () =
          let val (assm, concl) = induct_prop
          in prove_standard [assm] concl (fn prems =>
               EVERY [try_param_tac rN abs_induct 1,
                      simp_tac (HOL_ss addsimps [split_paired_all]) 1,
                      resolve_tac (map (rewrite_rule [ext_def]) prems) 1])
          end;
        val induct = timeit_msg "record extension induct proof:" induct_prf;

        fun cases_prf_opt () =
          let
            val sg = (sign_of defs_thy);
            val (_$(Pvar$_)) = concl_of induct;
            val ind = cterm_instantiate
                        [(cterm_of sg Pvar, cterm_of sg
                                (lambda w (HOLogic.imp$HOLogic.mk_eq(r,w)$C)))]
                        induct;
            in standard (ObjectLogic.rulify (mp OF [ind, refl])) end;

        fun cases_prf_noopt () =
            prove_standard [] cases_prop (fn prems =>
             EVERY [asm_full_simp_tac (HOL_basic_ss addsimps [atomize_all, atomize_imp]) 1,
                    try_param_tac rN induct 1,
                    rtac impI 1,
                    REPEAT (etac allE 1),
                    etac mp 1,
                    rtac refl 1])

        val cases_prf = quick_and_dirty_prf cases_prf_noopt cases_prf_opt;
        val cases = timeit_msg "record extension cases proof:" cases_prf;

        fun dest_convs_prf () = map (prove_simp false
                          ([ext_def,abs_inverse]@Pair_sel_convs@dest_defs)) dest_conv_props;
        val dest_convs = timeit_msg "record extension dest_convs proof:" dest_convs_prf;
        fun dest_convs_standard_prf () = map standard dest_convs;

        val dest_convs_standard =
            timeit_msg "record extension dest_convs_standard proof:" dest_convs_standard_prf;

        fun upd_convs_prf_noopt () = map (prove_simp true (dest_convs_standard@upd_defs))
                                           upd_conv_props;
        fun upd_convs_prf_opt () =
          let
            val sg = sign_of defs_thy;
            fun mkrefl (c,T) = Thm.reflexive
                                (cterm_of sg (Free (variant variants (base c ^ "'"),T)));
            val refls = map mkrefl fields_more;
            val constr_refl = Thm.reflexive (cterm_of sg (head_of ext));
            val dest_convs' = map mk_meta_eq dest_convs;

            fun mkthm (udef,(fld_refl,thms)) =
              let val bdyeq = Library.foldl (uncurry Thm.combination) (constr_refl,thms);
                   (* (|N=N (|N=N,M=M,K=K,more=more|)
                        M=M (|N=N,M=M,K=K,more=more|)
                        K=K'
                        more = more (|N=N,M=M,K=K,more=more|) =
                      (|N=N,M=M,K=K',more=more|)
                    *)
                  val (_$(_$v$r)$_) = prop_of udef;
                  val (_$v'$_) = prop_of fld_refl;
                  val udef' = cterm_instantiate
                                [(cterm_of sg v,cterm_of sg v'),
                                 (cterm_of sg r,cterm_of sg ext)] udef;
              in  standard (Thm.transitive udef' bdyeq) end;
          in map mkthm (rev upd_defs  ~~ (mixit dest_convs' refls))
             handle e => print_exn e end;

        val upd_convs_prf = quick_and_dirty_prf upd_convs_prf_noopt upd_convs_prf_opt;

        val upd_convs =
             timeit_msg "record extension upd_convs proof:" upd_convs_prf;

        fun surjective_prf () =
          prove_standard [] surjective_prop (fn prems =>
              (EVERY [try_param_tac rN induct 1,
                      simp_tac (HOL_basic_ss addsimps dest_convs_standard) 1]));
        val surjective = timeit_msg "record extension surjective proof:" surjective_prf;

        fun split_meta_prf () =
            prove_standard [] split_meta_prop (fn prems =>
             EVERY [rtac equal_intr_rule 1,
                      rtac meta_allE 1, etac triv_goal 1, atac 1,
                    rtac (prop_subst OF [surjective]) 1,
                    REPEAT (EVERY [rtac meta_allE 1, etac triv_goal 1, etac thin_rl 1]),
                    atac 1]);
        val split_meta = timeit_msg "record extension split_meta proof:" split_meta_prf;

        val (thm_thy,([inject',induct',cases',surjective',split_meta'],
                      [dest_convs',upd_convs'])) =
          defs_thy
          |> (PureThy.add_thms o map Thm.no_attributes)
               [("ext_inject", inject),
                ("ext_induct", induct),
                ("ext_cases", cases),
                ("ext_surjective", surjective),
                ("ext_split", split_meta)]
          |>>> (PureThy.add_thmss o map Thm.no_attributes)
                  [("dest_convs",dest_convs_standard),("upd_convs",upd_convs)]

      in (thm_thy,extT,induct',inject',dest_convs',split_meta',upd_convs')
      end;

    fun chunks []      []   = []
      | chunks []      xs   = [xs]
      | chunks (l::ls) xs  = Library.take (l,xs)::chunks ls (Library.drop (l,xs));

    fun chop_last [] = error "last: list should not be empty"
      | chop_last [x] = ([],x)
      | chop_last (x::xs) = let val (tl,l) = chop_last xs in (x::tl,l) end;

    fun subst_last s []      = error "subst_last: list should not be empty"
      | subst_last s ([x])   = [s]
      | subst_last s (x::xs) = (x::subst_last s xs);

    (* mk_recordT builds up the record type from the current extension tpye extT and a list
     * of parent extensions, starting with the root of the record hierarchy
    *)
    fun mk_recordT extT parent_exts =
        foldr (fn ((parent,Ts),T) => Type (parent, subst_last T Ts)) extT parent_exts;

    fun obj_to_meta_all thm =
      let
        fun E thm = case (SOME (spec OF [thm]) handle THM _ => NONE) of
                      SOME thm' => E thm'
                    | NONE => thm;
        val th1 = E thm;
        val th2 = Drule.forall_intr_vars th1;
      in th2 end;

    fun meta_to_obj_all thm =
      let
        val {sign, prop, ...} = rep_thm thm;
        val params = Logic.strip_params prop;
        val concl = HOLogic.dest_Trueprop (Logic.strip_assums_concl prop);
        val ct = cterm_of sign
          (HOLogic.mk_Trueprop (HOLogic.list_all (params, concl)));
        val thm' = Seq.hd (REPEAT (rtac allI 1) (Thm.trivial ct));
      in
        Thm.implies_elim thm' thm
      end;

    (* record_definition *)
    fun record_definition (args, bname) parent (parents: parent_info list) raw_fields thy =
      (* smlnj needs type annotation of parents *)
      let
        val sign = Theory.sign_of thy;

        val alphas = map fst args;
        val name = Sign.full_name sign bname;
        val full = Sign.full_name_path sign bname;
        val base = Sign.base_name;

        val (bfields, field_syntax) = split_list (map (fn (x, T, mx) => ((x, T), mx)) raw_fields);

        val parent_fields = List.concat (map #fields parents);
        val parent_chunks = map (length o #fields) parents;
        val parent_names = map fst parent_fields;
        val parent_types = map snd parent_fields;
        val parent_fields_len = length parent_fields;
        val parent_variants = variantlist (map base parent_names, [moreN, rN, rN ^ "'", wN]);
        val parent_vars = ListPair.map Free (parent_variants, parent_types);
        val parent_len = length parents;
        val parents_idx = (map #name parents) ~~ (0 upto (parent_len - 1));

        val fields = map (apfst full) bfields;
        val names = map fst fields;
        val extN = full bname;
        val types = map snd fields;
        val alphas_fields = foldr add_typ_tfree_names [] types;
        val alphas_ext = alphas inter alphas_fields;
        val len = length fields;
        val variants = variantlist (map fst bfields, moreN::rN::rN ^ "'"::wN::parent_variants);
        val vars = ListPair.map Free (variants, types);
        val named_vars = names ~~ vars;
        val idxs = 0 upto (len - 1);
        val idxms = 0 upto len;

        val all_fields = parent_fields @ fields;
        val all_names = parent_names @ names;
        val all_types = parent_types @ types;
        val all_len = parent_fields_len + len;
        val all_variants = parent_variants @ variants;
        val all_vars = parent_vars @ vars;
        val all_named_vars = (parent_names ~~ parent_vars) @ named_vars;

        val zeta = variant alphas "'z";
        val moreT = TFree (zeta, HOLogic.typeS);
        val more = Free (moreN, moreT);
        val full_moreN = full moreN;
        val bfields_more = bfields @ [(moreN,moreT)];
        val fields_more = fields @ [(full_moreN,moreT)];
        val vars_more = vars @ [more];
        val named_vars_more = named_vars @[(full_moreN,more)];
        val all_vars_more = all_vars @ [more];
        val all_named_vars_more = all_named_vars @ [(full_moreN,more)];

        (* 1st stage: extension_thy *)
        val (extension_thy,extT,ext_induct,ext_inject,ext_dest_convs,ext_split,u_convs) =
          thy
          |> Theory.add_path bname
          |> extension_definition full extN fields names alphas_ext zeta moreT more vars;

        val _ = timing_msg "record preparing definitions";
        val Type extension_scheme = extT;
        val extension_name = unsuffix ext_typeN (fst extension_scheme);
        val extension = let val (n,Ts) = extension_scheme in (n,subst_last HOLogic.unitT Ts) end;
        val extension_names =
             (map ((unsuffix ext_typeN) o fst o #extension) parents) @ [extN];
        val extension_id = Library.foldl (op ^) ("",extension_names);

        fun rec_schemeT n = mk_recordT extT (map #extension (prune n parents));
        val rec_schemeT0 = rec_schemeT 0;

        fun recT n =
          let val (c,Ts) = extension
          in mk_recordT (Type (c,subst_last HOLogic.unitT Ts))(map #extension (prune n parents))
          end;
        val recT0 = recT 0;

        fun mk_rec args n =
          let val (args',more) = chop_last args;
              fun mk_ext' (((name,T),args),more) = mk_ext (name,T) (args@[more]);
              fun build Ts =
               foldr mk_ext' more (prune n (extension_names ~~ Ts ~~ (chunks parent_chunks args')))
          in
            if more = HOLogic.unit
            then build (map recT (0 upto parent_len))
            else build (map rec_schemeT (0 upto parent_len))
          end;

        val r_rec0 = mk_rec all_vars_more 0;
        val r_rec_unit0 = mk_rec (all_vars@[HOLogic.unit]) 0;

        fun r n = Free (rN, rec_schemeT n)
        val r0 = r 0;
        fun r_unit n = Free (rN, recT n)
        val r_unit0 = r_unit 0;
        val w = Free (wN, rec_schemeT 0)

        (* prepare print translation functions *)
        val field_tr's =
          print_translation (distinct (List.concat (map NameSpace.accesses' (full_moreN :: names))));

        val adv_ext_tr's =
        let
          val trnames = NameSpace.accesses' extN;
        in map (gen_record_tr') trnames end;

        val adv_record_type_abbr_tr's =
          let val trnames = NameSpace.accesses' (hd extension_names);
              val lastExt = (unsuffix ext_typeN (fst extension));
          in map (gen_record_type_abbr_tr' name alphas zeta lastExt rec_schemeT0) trnames
          end;

        val adv_record_type_tr's =
          let val trnames = if parent_len > 0 then NameSpace.accesses' extN else [];
                            (* avoid conflict with adv_record_type_abbr_tr's *)
          in map (gen_record_type_tr') trnames
          end;

        (* prepare declarations *)

        val sel_decls = map (mk_selC rec_schemeT0) bfields_more;
        val upd_decls = map (mk_updC updateN rec_schemeT0) bfields_more;
        val make_decl = (makeN, all_types ---> recT0);
        val fields_decl = (fields_selN, types ---> Type extension);
        val extend_decl = (extendN, recT0 --> moreT --> rec_schemeT0);
        val truncate_decl = (truncateN, rec_schemeT0 --> recT0);

        (* prepare definitions *)

        fun parent_more s =
             if null parents then s
             else mk_sel s (NameSpace.qualified (#name (List.last parents)) moreN, extT);

        fun parent_more_upd v s =
          if null parents then v
          else let val mp = NameSpace.qualified (#name (List.last parents)) moreN;
               in mk_upd updateN mp v s end;

        (*record (scheme) type abbreviation*)
        val recordT_specs =
          [(suffix schemeN bname, alphas @ [zeta], rec_schemeT0, Syntax.NoSyn),
            (bname, alphas, recT0, Syntax.NoSyn)];

        (*selectors*)
        fun mk_sel_spec (c,T) =
             Const (mk_selC rec_schemeT0 (c,T))
              :== (lambda r0 (Const (mk_selC extT (suffix ext_dest c,T))$parent_more r0));
        val sel_specs = map mk_sel_spec fields_more;

        (*updates*)

        fun mk_upd_spec (c,T) =
          let
            val new = mk_upd updN c (Free (base c,T)) (parent_more r0);
          in Const (mk_updC updateN rec_schemeT0 (c,T))$(Free (base c,T))$r0
              :== (parent_more_upd new r0)
          end;
        val upd_specs = map mk_upd_spec fields_more;

        (*derived operations*)
        val make_spec = Const (full makeN, all_types ---> recT0) $$ all_vars :==
          mk_rec (all_vars @ [HOLogic.unit]) 0;
        val fields_spec = Const (full fields_selN, types ---> Type extension) $$ vars :==
          mk_rec (all_vars @ [HOLogic.unit]) parent_len;
        val extend_spec =
          Const (full extendN, recT0-->moreT-->rec_schemeT0) $ r_unit0 $ more :==
          mk_rec ((map (mk_sel r_unit0) all_fields) @ [more]) 0;
        val truncate_spec = Const (full truncateN, rec_schemeT0 --> recT0) $ r0 :==
          mk_rec ((map (mk_sel r0) all_fields) @ [HOLogic.unit]) 0;

        (* 2st stage: defs_thy *)

        fun mk_defs () =
          extension_thy
            |> Theory.add_trfuns
                ([],[],field_tr's, [])
            |> Theory.add_advanced_trfuns
                ([],[],adv_ext_tr's @ adv_record_type_tr's @ adv_record_type_abbr_tr's,[])

            |> Theory.parent_path
            |> Theory.add_tyabbrs_i recordT_specs
            |> Theory.add_path bname
            |> Theory.add_consts_i
                (map2 (fn ((x, T), mx) => (x, T, mx)) (sel_decls, field_syntax @ [Syntax.NoSyn]))
            |> (Theory.add_consts_i o map Syntax.no_syn)
                (upd_decls @ [make_decl, fields_decl, extend_decl, truncate_decl])
            |> (PureThy.add_defs_i false o map Thm.no_attributes) sel_specs
            |>>> (PureThy.add_defs_i false o map Thm.no_attributes) upd_specs
            |>>> (PureThy.add_defs_i false o map Thm.no_attributes)
                   [make_spec, fields_spec, extend_spec, truncate_spec]
        val (defs_thy,((sel_defs,upd_defs),derived_defs)) =
            timeit_msg "record trfuns/tyabbrs/selectors/updates/make/fields/extend/truncate defs:"
             mk_defs;

        (* prepare propositions *)
        val _ = timing_msg "record preparing propositions";
        val P = Free (variant all_variants "P", rec_schemeT0-->HOLogic.boolT);
        val C = Free (variant all_variants "C", HOLogic.boolT);
        val P_unit = Free (variant all_variants "P", recT0-->HOLogic.boolT);

        (*selectors*)
        val sel_conv_props =
           map (fn (c, x as Free (_,T)) => mk_sel r_rec0 (c,T) === x) named_vars_more;

        (*updates*)
        fun mk_upd_prop (i,(c,T)) =
          let val x' = Free (variant all_variants (base c ^ "'"),T)
              val args' = nth_update x' (parent_fields_len + i, all_vars_more)
          in mk_upd updateN c x' r_rec0 === mk_rec args' 0  end;
        val upd_conv_props = ListPair.map mk_upd_prop (idxms, fields_more);

        (*induct*)
        val induct_scheme_prop =
          All (map dest_Free all_vars_more) (Trueprop (P $ r_rec0)) ==> Trueprop (P $ r0);
        val induct_prop =
          (All (map dest_Free all_vars) (Trueprop (P_unit $ r_rec_unit0)),
           Trueprop (P_unit $ r_unit0));

        (*surjective*)
        val surjective_prop =
          let val args = map (fn (c,Free (_,T)) => mk_sel r0 (c,T)) all_named_vars_more
          in r0 === mk_rec args 0 end;

        (*cases*)
        val cases_scheme_prop =
          (All (map dest_Free all_vars_more)
            (Trueprop (HOLogic.mk_eq (r0,r_rec0)) ==> Trueprop C))
          ==> Trueprop C;

        val cases_prop =
          (All (map dest_Free all_vars)
            (Trueprop (HOLogic.mk_eq (r_unit0,r_rec_unit0)) ==> Trueprop C))
           ==> Trueprop C;

        (*split*)
        val split_meta_prop =
          let val P = Free (variant all_variants "P", rec_schemeT0-->Term.propT) in
            Logic.mk_equals
             (All [dest_Free r0] (P $ r0), All (map dest_Free all_vars_more) (P $ r_rec0))
          end;

        val split_object_prop =
          let fun ALL vs t = foldr (fn ((v,T),t) => HOLogic.mk_all (v,T,t)) t vs
          in (ALL [dest_Free r0] (P $ r0)) === (ALL (map dest_Free all_vars_more) (P $ r_rec0))
          end;

        val split_ex_prop =
          let fun EX vs t = foldr (fn ((v,T),t) => HOLogic.mk_exists (v,T,t)) t vs
          in (EX [dest_Free r0] (P $ r0)) === (EX (map dest_Free all_vars_more) (P $ r_rec0))
          end;

        (*equality*)
        val equality_prop =
          let
            val s' = Free (rN ^ "'", rec_schemeT0)
            fun mk_sel_eq (c,Free (_,T)) =  mk_sel r0 (c,T) === mk_sel s' (c,T)
            val seleqs = map mk_sel_eq all_named_vars_more
          in All (map dest_Free [r0,s']) (Logic.list_implies (seleqs,r0 === s')) end;

        (* 3rd stage: thms_thy *)

        fun prove stndrd = quick_and_dirty_prove stndrd defs_thy;
        val prove_standard = quick_and_dirty_prove true defs_thy;

        fun prove_simp stndrd ss simps =
          let val tac = simp_all_tac ss simps
          in fn prop => prove stndrd [] prop (K tac) end;

        val ss = get_simpset defs_thy;

        fun sel_convs_prf () = map (prove_simp false ss
                               (sel_defs@ext_dest_convs)) sel_conv_props;
        val sel_convs = timeit_msg "record sel_convs proof:" sel_convs_prf;
        fun sel_convs_standard_prf () = map standard sel_convs
        val sel_convs_standard =
              timeit_msg "record sel_convs_standard proof:" sel_convs_standard_prf;

        fun upd_convs_prf () =
              map (prove_simp true ss (upd_defs@u_convs)) upd_conv_props;

        val upd_convs = timeit_msg "record upd_convs proof:" upd_convs_prf;

        val parent_induct = if null parents then [] else [#induct (hd (rev parents))];

        fun induct_scheme_prf () = prove_standard [] induct_scheme_prop (fn prems =>
              (EVERY [if null parent_induct
                      then all_tac else try_param_tac rN (hd parent_induct) 1,
                      try_param_tac rN ext_induct 1,
                      asm_simp_tac HOL_basic_ss 1]));
        val induct_scheme = timeit_msg "record induct_scheme proof:" induct_scheme_prf;

        fun induct_prf () =
          let val (assm, concl) = induct_prop;
          in
            prove_standard [assm] concl (fn prems =>
              try_param_tac rN induct_scheme 1
              THEN try_param_tac "more" unit_induct 1
              THEN resolve_tac prems 1)
          end;
        val induct = timeit_msg "record induct proof:" induct_prf;

        fun surjective_prf () =
          prove_standard [] surjective_prop (fn prems =>
              (EVERY [try_param_tac rN induct_scheme 1,
                      simp_tac (ss addsimps sel_convs_standard) 1]))
        val surjective = timeit_msg "record surjective proof:" surjective_prf;

        fun cases_scheme_prf_opt () =
          let
            val sg = (sign_of defs_thy);
            val (_$(Pvar$_)) = concl_of induct_scheme;
            val ind = cterm_instantiate
                        [(cterm_of sg Pvar, cterm_of sg
                                (lambda w (HOLogic.imp$HOLogic.mk_eq(r0,w)$C)))]
                        induct_scheme;
            in standard (ObjectLogic.rulify (mp OF [ind, refl])) end;

        fun cases_scheme_prf_noopt () =
            prove_standard [] cases_scheme_prop (fn prems =>
             EVERY [asm_full_simp_tac (HOL_basic_ss addsimps [atomize_all, atomize_imp]) 1,
                   try_param_tac rN induct_scheme 1,
                   rtac impI 1,
                   REPEAT (etac allE 1),
                   etac mp 1,
                   rtac refl 1])
        val cases_scheme_prf = quick_and_dirty_prf cases_scheme_prf_noopt cases_scheme_prf_opt;
        val cases_scheme = timeit_msg "record cases_scheme proof:" cases_scheme_prf;

        fun cases_prf () =
          prove_standard [] cases_prop  (fn _ =>
            try_param_tac rN cases_scheme 1
            THEN simp_all_tac HOL_basic_ss [unit_all_eq1]);
        val cases = timeit_msg "record cases proof:" cases_prf;

        fun split_meta_prf () =
            prove false [] split_meta_prop (fn prems =>
             EVERY [rtac equal_intr_rule 1,
                      rtac meta_allE 1, etac triv_goal 1, atac 1,
                    rtac (prop_subst OF [surjective]) 1,
                    REPEAT (EVERY [rtac meta_allE 1, etac triv_goal 1, etac thin_rl 1]),
                    atac 1]);
        val split_meta = timeit_msg "record split_meta proof:" split_meta_prf;
        val split_meta_standard = standard split_meta;

        fun split_object_prf_opt () =
          let
            val sg = sign_of defs_thy;
            val cPI= cterm_of sg (lambda r0 (Trueprop (P$r0)));
            val (_$Abs(_,_,P$_)) = fst (Logic.dest_equals (concl_of split_meta_standard));
            val cP = cterm_of sg P;
            val split_meta' = cterm_instantiate [(cP,cPI)] split_meta_standard;
            val (l,r) = HOLogic.dest_eq (HOLogic.dest_Trueprop split_object_prop);
            val cl = cterm_of sg (HOLogic.mk_Trueprop l);
            val cr = cterm_of sg (HOLogic.mk_Trueprop r);
            val thl = assume cl                 (*All r. P r*) (* 1 *)
                    |> obj_to_meta_all          (*!!r. P r*)
                    |> equal_elim split_meta'   (*!!n m more. P (ext n m more)*)
                    |> meta_to_obj_all          (*All n m more. P (ext n m more)*) (* 2*)
                    |> implies_intr cl          (* 1 ==> 2 *)
            val thr = assume cr                           (*All n m more. P (ext n m more)*)
                    |> obj_to_meta_all                    (*!!n m more. P (ext n m more)*)
                    |> equal_elim (symmetric split_meta') (*!!r. P r*)
                    |> meta_to_obj_all                    (*All r. P r*)
                    |> implies_intr cr                    (* 2 ==> 1 *)
         in standard (thr COMP (thl COMP iffI)) end;

        fun split_object_prf_noopt () =
            prove_standard [] split_object_prop (fn prems =>
             EVERY [rtac iffI 1,
                    REPEAT (rtac allI 1), etac allE 1, atac 1,
                    rtac allI 1, rtac induct_scheme 1,REPEAT (etac allE 1),atac 1]);

        val split_object_prf = quick_and_dirty_prf split_object_prf_noopt split_object_prf_opt;
        val split_object = timeit_msg "record split_object proof:" split_object_prf;

        fun split_ex_prf () =
            prove_standard [] split_ex_prop (fn prems =>
              EVERY [rtac iffI 1,
                       etac exE 1,
                       simp_tac (HOL_basic_ss addsimps [split_meta_standard]) 1,
                       ex_inst_tac 1,
                       (*REPEAT (rtac exI 1),*)
                       atac 1,
                     REPEAT (etac exE 1),
                     rtac exI 1,
                     atac 1]);
        val split_ex = timeit_msg "record split_ex proof:" split_ex_prf;

        fun equality_tac thms =
          let val (s'::s::eqs) = rev thms;
              val ss' = ss addsimps (s'::s::sel_convs_standard);
              val eqs' = map (simplify ss') eqs;
          in simp_tac (HOL_basic_ss addsimps (s'::s::eqs')) 1 end;

       fun equality_prf () = prove_standard [] equality_prop (fn _ =>
          fn st => let val [s, s'] = map #1 (rev (Tactic.innermost_params 1 st)) in
            st |> (res_inst_tac [(rN, s)] cases_scheme 1
            THEN res_inst_tac [(rN, s')] cases_scheme 1
            THEN (METAHYPS equality_tac 1))
                 (* simp_all_tac ss (sel_convs) would also work but is less efficient *)
          end);
         val equality = timeit_msg "record equality proof:" equality_prf;

        val (thms_thy,(([sel_convs',upd_convs',sel_defs',upd_defs',[split_meta',split_object',split_ex'],
                        derived_defs'],
                       [surjective',equality']),[induct_scheme',induct',cases_scheme',cases'])) =
          defs_thy
          |> (PureThy.add_thmss o map Thm.no_attributes)
             [("select_convs", sel_convs_standard),
              ("update_convs", upd_convs),
              ("select_defs", sel_defs),
              ("update_defs", upd_defs),
              ("splits", [split_meta_standard,split_object,split_ex]),
              ("defs", derived_defs)]
          |>>> (PureThy.add_thms o map Thm.no_attributes)
              [("surjective", surjective),
               ("equality", equality)]
          |>>> PureThy.add_thms
            [(("induct_scheme", induct_scheme), induct_type_global (suffix schemeN name)),
             (("induct", induct), induct_type_global name),
             (("cases_scheme", cases_scheme), cases_type_global (suffix schemeN name)),
             (("cases", cases), cases_type_global name)];

        val sel_upd_simps = sel_convs' @ upd_convs';
        val iffs = [ext_inject]
        val final_thy =
          thms_thy
          |> (#1 oo PureThy.add_thmss)
              [(("simps", sel_upd_simps), [Simplifier.simp_add_global]),
               (("iffs",iffs), [iff_add_global])]
          |> put_record name (make_record_info args parent fields extension induct_scheme')
          |> put_sel_upd (names @ [full_moreN]) sel_upd_simps
          |> add_record_equalities extension_id equality'
          |> add_extinjects ext_inject
          |> add_extsplit extension_name ext_split
          |> add_record_splits extension_id (split_meta',split_object',split_ex',induct_scheme')
          |> add_extfields extension_name (fields @ [(full_moreN,moreT)])
          |> add_fieldext (extension_name,snd extension) (names @ [full_moreN])
          |> Theory.parent_path;

      in final_thy
      end;

    (* add_record *)

    (*we do all preparations and error checks here, deferring the real
      work to record_definition*)
    fun gen_add_record prep_typ prep_raw_parent (params, bname) raw_parent raw_fields thy =
      let
        val _ = Theory.requires thy "Record" "record definitions";
        val sign = Theory.sign_of thy;
        val _ = message ("Defining record " ^ quote bname ^ " ...");

        (* parents *)

        fun prep_inst T = snd (cert_typ sign ([], T));

        val parent = Option.map (apfst (map prep_inst) o prep_raw_parent sign) raw_parent
          handle ERROR => error ("The error(s) above in parent record specification");
        val parents = add_parents thy parent [];

        val init_env =
          (case parent of
            NONE => []
          | SOME (types, _) => foldr Term.add_typ_tfrees [] types);

        (* fields *)

        fun prep_field (env, (c, raw_T, mx)) =
          let val (env', T) = prep_typ sign (env, raw_T) handle ERROR =>
            error ("The error(s) above occured in field " ^ quote c)
          in (env', (c, T, mx)) end;

        val (envir, bfields) = foldl_map prep_field (init_env, raw_fields);
        val envir_names = map fst envir;

        (* args *)

        val defaultS = Sign.defaultS sign;
        val args = map (fn x => (x, AList.lookup (op =) envir x |> the_default defaultS)) params;

        (* errors *)

        val name = Sign.full_name sign bname;
        val err_dup_record =
          if is_none (get_record thy name) then []
          else ["Duplicate definition of record " ^ quote name];

        val err_dup_parms =
          (case duplicates params of
            [] => []
          | dups => ["Duplicate parameter(s) " ^ commas dups]);

        val err_extra_frees =
          (case gen_rems (op =) (envir_names, params) of
            [] => []
          | extras => ["Extra free type variable(s) " ^ commas extras]);

        val err_no_fields = if null bfields then ["No fields present"] else [];

        val err_dup_fields =
          (case duplicates (map #1 bfields) of
            [] => []
          | dups => ["Duplicate field(s) " ^ commas_quote dups]);

        val err_bad_fields =
          if forall (not_equal moreN o #1) bfields then []
          else ["Illegal field name " ^ quote moreN];

        val err_dup_sorts =
          (case duplicates envir_names of
            [] => []
          | dups => ["Inconsistent sort constraints for " ^ commas dups]);

        val errs =
          err_dup_record @ err_dup_parms @ err_extra_frees @ err_no_fields @
          err_dup_fields @ err_bad_fields @ err_dup_sorts;
      in
        if null errs then () else error (cat_lines errs)  ;
        thy |> record_definition (args, bname) parent parents bfields
      end
      handle ERROR => error ("Failed to define record " ^ quote bname);

    val add_record = gen_add_record read_typ read_raw_parent;
    val add_record_i = gen_add_record cert_typ (K I);

    (* setup theory *)

    val setup =
     [RecordsData.init,
      Theory.add_trfuns ([], parse_translation, [], []),
      Theory.add_advanced_trfuns ([], adv_parse_translation, [], []),
      Simplifier.change_simpset_of Simplifier.addsimprocs
        [record_simproc, record_upd_simproc, record_eq_simproc]];

    (* outer syntax *)

    local structure P = OuterParse and K = OuterKeyword in

    val record_decl =
      P.type_args -- P.name --
        (P.$$$ "=" |-- Scan.option (P.typ --| P.$$$ "+") -- Scan.repeat1 P.const);

    val recordP =
      OuterSyntax.command "record" "define extensible record" K.thy_decl
        (record_decl >> (fn (x, (y, z)) => Toplevel.theory (add_record x y z)));

    val _ = OuterSyntax.add_parsers [recordP];

    end;

    end;

    structure BasicRecordPackage: BASIC_RECORD_PACKAGE = RecordPackage;
    open BasicRecordPackage;