(*  Title:      HOL/Tools/record.ML

    Author:     Wolfgang Naraschewski, TU Muenchen

    Author:     Markus Wenzel, TU Muenchen

    Author:     Norbert Schirmer, TU Muenchen

    Author:     Thomas Sewell, NICTA

Extensible records with structural subtyping.

*)

signature BASIC_RECORD =

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 Unsynchronized.ref

  val print_record_type_as_fields: bool Unsynchronized.ref

end;

signature RECORD =

sig

  include BASIC_RECORD

  val timing: bool Unsynchronized.ref

  val record_quick_and_dirty_sensitive: bool Unsynchronized.ref

  val updateN: string

  val updN: string

  val ext_typeN: string

  val extN: string

  val makeN: string

  val moreN: string

  val ext_dest: 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_parent: theory -> string -> (typ list * string) option

  val get_extension: theory -> string -> (string * typ list) option

  val get_extinjects: theory -> thm list

  val get_simpset: theory -> simpset

  val print_records: theory -> unit

  val read_typ: Proof.context -> string -> (string * sort) list -> typ * (string * sort) list

  val cert_typ: Proof.context -> typ -> (string * sort) list -> typ * (string * sort) list

  val add_record: bool -> string list * string -> string option -> (string * string * mixfix) list

    -> theory -> theory

  val add_record_i: bool -> string list * string -> (typ list * string) option

    -> (string * typ * mixfix) list -> theory -> theory

  val setup: theory -> theory

end;

signature ISTUPLE_SUPPORT =

sig

  val add_istuple_type: bstring * string list -> (typ * typ) -> theory -> term * term * theory

  val mk_cons_tuple: term * term -> term

  val dest_cons_tuple: term -> term * term

  val istuple_intros_tac: theory -> int -> tactic

  val named_cterm_instantiate: (string * cterm) list -> thm -> thm

end;

structure IsTupleSupport: ISTUPLE_SUPPORT =

struct

val isomN = "_TupleIsom";

val defN = "_def";

val istuple_UNIV_I = @{thm "istuple_UNIV_I"};

val istuple_True_simp = @{thm "istuple_True_simp"};

val istuple_intro = @{thm "isomorphic_tuple_intro"};

val istuple_intros = build_net (@{thms "isomorphic_tuple.intros"});

val constname = fst o dest_Const;

val tuple_istuple = (constname @{term tuple_istuple}, @{thm tuple_istuple});

val istuple_constN = constname @{term isomorphic_tuple};

val istuple_consN = constname @{term istuple_cons};

val tup_isom_typeN = fst (dest_Type @{typ "('a, 'b, 'c) tuple_isomorphism"});

fun named_cterm_instantiate values thm =

  let

    fun match name ((name', _), _) = name = name'

      | match name _ = false;

    fun getvar name =

      (case find_first (match name) (Term.add_vars (prop_of thm) []) of

        SOME var => cterm_of (theory_of_thm thm) (Var var)

      | NONE => raise THM ("named_cterm_instantiate: " ^ name, 0, [thm]));

  in

    cterm_instantiate (map (apfst getvar) values) thm

  end;

structure IsTupleThms = TheoryDataFun

(

  type T = thm Symtab.table;

  val empty = Symtab.make [tuple_istuple];

  val copy = I;

  val extend = I;

  val merge = K (Symtab.merge Thm.eq_thm_prop);

);

fun do_typedef name repT alphas thy =

  let

    fun get_thms thy name =

      let

        val SOME { Rep_inject=rep_inject, Abs_name=absN, abs_type=absT,

          Abs_inverse=abs_inverse, ...} = Typedef.get_info thy name;

        val rewrite_rule = MetaSimplifier.rewrite_rule [istuple_UNIV_I, istuple_True_simp];

      in (map rewrite_rule [rep_inject, abs_inverse],

            Const (absN, repT --> absT), absT) end;

  in

    thy

    |> Typecopy.typecopy (Binding.name name, alphas) repT NONE

    |-> (fn (name, _) => `(fn thy => get_thms thy name))

  end;

fun mk_cons_tuple (left, right) =

  let

    val (leftT, rightT) = (fastype_of left, fastype_of right);

    val prodT = HOLogic.mk_prodT (leftT, rightT);

    val isomT = Type (tup_isom_typeN, [prodT, leftT, rightT]);

  in

    Const (istuple_consN, isomT --> leftT --> rightT --> prodT) $

      Const (fst tuple_istuple, isomT) $ left $ right

  end;

fun dest_cons_tuple (v as Const (ic, _) $ Const _ $ left $ right) =

      if ic = istuple_consN then (left, right)

      else raise TERM ("dest_cons_tuple", [v])

  | dest_cons_tuple v = raise TERM ("dest_cons_tuple", [v]);

fun add_istuple_type (name, alphas) (leftT, rightT) thy =

  let

    val repT = HOLogic.mk_prodT (leftT, rightT);

    val (([rep_inject, abs_inverse], absC, absT), typ_thy) =

      thy

      |> do_typedef name repT alphas

      ||> Sign.add_path name;

    (*construct a type and body for the isomorphism constant by

      instantiating the theorem to which the definition will be applied*)

    val intro_inst =

      rep_inject RS named_cterm_instantiate [("abst", cterm_of typ_thy absC)] istuple_intro;

    val (_, body) = Logic.dest_equals (List.last (prems_of intro_inst));

    val isomT = fastype_of body;

    val isom_bind = Binding.name (name ^ isomN);

    val isom = Const (Sign.full_name typ_thy isom_bind, isomT);

    val isom_spec = (name ^ isomN ^ defN, Logic.mk_equals (isom, body));

    val ([isom_def], cdef_thy) =

      typ_thy

      |> Sign.add_consts_i [Syntax.no_syn (isom_bind, isomT)]

      |> PureThy.add_defs false [Thm.no_attributes (apfst Binding.name isom_spec)];

    val istuple = isom_def RS (abs_inverse RS (rep_inject RS istuple_intro));

    val cons = Const (istuple_consN, isomT --> leftT --> rightT --> absT);

    val thm_thy =

      cdef_thy

      |> IsTupleThms.map (Symtab.insert Thm.eq_thm_prop (constname isom, istuple))

      |> Sign.parent_path;

  in

    (isom, cons $ isom, thm_thy)

  end;

fun istuple_intros_tac thy =

  let

    val isthms = IsTupleThms.get thy;

    fun err s t = raise TERM ("istuple_intros_tac: " ^ s, [t]);

    val use_istuple_thm_tac = SUBGOAL (fn (goal, n) =>

      let

        val goal' = Envir.beta_eta_contract goal;

        val isom =

          (case goal' of

            Const tp $ (Const pr $ Const is) =>

              if fst tp = "Trueprop" andalso fst pr = istuple_constN

              then Const is

              else err "unexpected goal predicate" goal'

          | _ => err "unexpected goal format" goal');

        val isthm =

          (case Symtab.lookup isthms (constname isom) of

            SOME isthm => isthm

          | NONE => err "no thm found for constant" isom);

      in rtac isthm n end);

  in

    fn n => resolve_from_net_tac istuple_intros n THEN use_istuple_thm_tac n

  end;

end;

structure Record: RECORD =

struct

val eq_reflection = thm "eq_reflection";

val Pair_eq = thm "Product_Type.prod.inject";

val atomize_all = thm "HOL.atomize_all";

val atomize_imp = thm "HOL.atomize_imp";

val meta_allE = thm "Pure.meta_allE";

val prop_subst = thm "prop_subst";

val Pair_sel_convs = [fst_conv, snd_conv];

val K_record_comp = @{thm "K_record_comp"};

val K_comp_convs = [@{thm o_apply}, K_record_comp]

val transitive_thm = thm "transitive";

val o_assoc = @{thm "o_assoc"};

val id_apply = @{thm id_apply};

val id_o_apps = [@{thm id_apply}, @{thm id_o}, @{thm o_id}];

val Not_eq_iff = @{thm Not_eq_iff};

val refl_conj_eq = thm "refl_conj_eq";

val meta_all_sameI = thm "meta_all_sameI";

val meta_iffD2 = thm "meta_iffD2";

val surject_assistI = @{thm "istuple_surjective_proof_assistI"};

val surject_assist_idE = @{thm "istuple_surjective_proof_assist_idE"};

val updacc_accessor_eqE = @{thm "update_accessor_accessor_eqE"};

val updacc_updator_eqE = @{thm "update_accessor_updator_eqE"};

val updacc_eq_idI = @{thm "istuple_update_accessor_eq_assist_idI"};

val updacc_eq_triv = @{thm "istuple_update_accessor_eq_assist_triv"};

val updacc_foldE = @{thm "update_accessor_congruence_foldE"};

val updacc_unfoldE = @{thm "update_accessor_congruence_unfoldE"};

val updacc_noopE = @{thm "update_accessor_noopE"};

val updacc_noop_compE = @{thm "update_accessor_noop_compE"};

val updacc_cong_idI = @{thm "update_accessor_cong_assist_idI"};

val updacc_cong_triv = @{thm "update_accessor_cong_assist_triv"};

val updacc_cong_from_eq = @{thm "istuple_update_accessor_cong_from_eq"};

val o_eq_dest = thm "o_eq_dest";

val o_eq_id_dest = thm "o_eq_id_dest";

val o_eq_dest_lhs = thm "o_eq_dest_lhs";

(** name components **)

val rN = "r";

val wN = "w";

val moreN = "more";

val schemeN = "_scheme";

val ext_typeN = "_ext_type";

val inner_typeN = "_inner_type";

val extN ="_ext";

val casesN = "_cases";

val ext_dest = "_sel";

val updateN = "_update";

val updN = "_upd";

val makeN = "make";

val fields_selN = "fields";

val extendN = "extend";

val truncateN = "truncate";

(*see typedef.ML*)

val RepN = "Rep_";

val AbsN = "Abs_";

(*** utilities ***)

fun but_last xs = fst (split_last xs);

fun varifyT midx =

  let fun varify (a, S) = TVar ((a, midx + 1), S);

  in map_type_tfree varify end;

fun domain_type' T =

  domain_type T handle Match => T;

fun range_type' T =

  range_type T handle Match => T;

(* messages *)  (* FIXME proper context *)

fun trace_thm str thm =

  tracing (str ^ Pretty.string_of (Display.pretty_thm_without_context thm));

fun trace_thms str thms =

  (tracing str; map (trace_thm "") thms);

fun trace_term str t =

  tracing (str ^ Syntax.string_of_term_global Pure.thy t);

(* timing *)

val timing = Unsynchronized.ref false;

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 = Long_Name.map_base_name (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 :==) = PrimitiveDefs.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 --> T) --> sT --> sT);

fun mk_upd' sfx c v sT =

  let val vT = domain_type (fastype_of v);

  in Const (mk_updC sfx sT (c, vT)) $ v end;

fun mk_upd sfx c v s = mk_upd' sfx c v (fastype_of s) $ s;

(* 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 ("Record.dest_recT", [typ], [])

      | SOME c => ((c, Ts), List.last Ts))

  | dest_recT typ = raise TYPE ("Record.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;   (* FIXME ? *)

(*** 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,

  extdef: thm};

fun make_record_info args parent fields extension induct extdef =

 {args = args, parent = parent, fields = fields, extension = extension,

  induct = induct, extdef = extdef}: record_info;

type parent_info =

 {name: string,

  fields: (string * typ) list,

  extension: (string * typ list),

  induct: thm,

  extdef: thm};

fun make_parent_info name fields extension induct extdef =

 {name = name, fields = fields, extension = extension,

  induct = induct, extdef = extdef}: parent_info;

(* theory data *)

type record_data =

 {records: record_info Symtab.table,

  sel_upd:

   {selectors: (int * bool) Symtab.table,

    updates: string Symtab.table,

    simpset: Simplifier.simpset,

    defset: Simplifier.simpset,

    foldcong: Simplifier.simpset,

    unfoldcong: 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

(

  type T = record_data;

  val empty =

    make_record_data Symtab.empty

      {selectors = Symtab.empty, updates = Symtab.empty,

          simpset = HOL_basic_ss, defset = HOL_basic_ss,

          foldcong = HOL_basic_ss, unfoldcong = 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, defset = ds1,

       foldcong = fc1, unfoldcong = uc1},

     equalities = equalities1,

     extinjects = extinjects1,

     extsplit = extsplit1,

     splits = splits1,

     extfields = extfields1,

     fieldext = fieldext1},

    {records = recs2,

     sel_upd =

      {selectors = sels2, updates = upds2,

       simpset = ss2, defset = ds2,

       foldcong = fc2, unfoldcong = uc2},

     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),

        defset = Simplifier.merge_ss (ds1, ds2),

        foldcong = Simplifier.merge_ss (fc1, fc2),

        unfoldcong = Simplifier.merge_ss (uc1, uc2)}

      (Symtab.merge Thm.eq_thm_prop (equalities1, equalities2))

      (Library.merge Thm.eq_thm_prop (extinjects1, extinjects2))

      (Symtab.merge Thm.eq_thm_prop (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_records thy =

  let

    val {records = recs, ...} = RecordsData.get thy;

    val prt_typ = Syntax.pretty_typ_global thy;

    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 thy 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;

(* 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;

fun get_ss_with_context getss thy =

    Simplifier.theory_context thy (getss (get_sel_upd thy));

val get_simpset = get_ss_with_context (#simpset);

val get_sel_upd_defs = get_ss_with_context (#defset);

val get_foldcong_ss = get_ss_with_context (#foldcong);

val get_unfoldcong_ss = get_ss_with_context (#unfoldcong);

fun get_update_details u thy =

  let val sel_upd = get_sel_upd thy in

    (case Symtab.lookup (#updates sel_upd) u of

      SOME s =>

        let val SOME (dep, ismore) = Symtab.lookup (#selectors sel_upd) s

        in SOME (s, dep, ismore) end

    | NONE => NONE)

  end;

fun put_sel_upd names more depth simps defs (folds, unfolds) thy =

  let

    val all = names @ [more];

    val sels = map (rpair (depth, false)) names @ [(more, (depth, true))];

    val upds = map (suffix updateN) all ~~ all;

    val {records, sel_upd = {selectors, updates, simpset, defset, foldcong, unfoldcong},

      equalities, extinjects, extsplit, splits, extfields, fieldext} = RecordsData.get thy;

    val data = make_record_data records

      {selectors = fold Symtab.update_new sels selectors,

        updates = fold Symtab.update_new upds updates,

        simpset = Simplifier.addsimps (simpset, simps),

        defset = Simplifier.addsimps (defset, defs),

        foldcong = foldcong addcongs folds,

        unfoldcong = unfoldcong addcongs unfolds}

       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 (insert Thm.eq_thm_prop thm extinjects)

        extsplit splits extfields fieldext;

  in RecordsData.put data thy end;

val get_extinjects = rev o #extinjects o RecordsData.get;

(* 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;

(* parent/extension of named record *)

val get_parent = (Option.join o Option.map #parent) oo (Symtab.lookup o #records o RecordsData.get);

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 thy T =

  let

    val ((name, Ts), moreT) = dest_recT T;

    val recname =

      let val (nm :: recn :: rst) = rev (Long_Name.explode name)

      in Long_Name.implode (rev (nm :: rst)) end;

    val midx = maxidx_of_typs (moreT :: Ts);

    val varifyT = varifyT midx;

    val {records, extfields, ...} = RecordsData.get thy;

    val (flds, (more, _)) = split_last (Symtab.lookup_list extfields name);

    val args = map varifyT (snd (#extension (the (Symtab.lookup records recname))));

    val subst = fold (Sign.typ_match thy) (but_last args ~~ but_last Ts) (Vartab.empty);

    val flds' = map (apsnd ((Envir.norm_type subst) o varifyT)) flds;

  in (flds', (more, moreT)) end;

fun get_recT_fields thy T =

  let

    val (root_flds, (root_more, root_moreT)) = get_extT_fields thy T;

    val (rest_flds, rest_more) =

      if is_recT root_moreT then get_recT_fields thy 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

        fun err msg = error (msg ^ " parent record " ^ quote name);

        val {args, parent, fields, extension, induct, extdef} =

          (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 thy (T, S) then NONE else SOME x

        val bads = List.mapPartial bad_inst (args ~~ types);

        val _ = null bads orelse err ("Ill-sorted instantiation of " ^ commas bads ^ " in");

        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

        add_parents thy parent'

          (make_parent_info name fields' extension' induct extdef :: parents)

      end;

(** concrete syntax for records **)

(* decode type *)

fun decode_type thy t =

  let

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

    val map_sort = Sign.intern_sort thy;

  in

    Syntax.typ_of_term (get_sort (Syntax.term_sorts map_sort t)) map_sort t

    |> Sign.intern_tycons thy

  end;

(* parse translations *)

fun gen_field_tr mark sfx (t as Const (c, _) $ Const (name, _) $ arg) =

      if c = mark then Syntax.const (suffix sfx name) $ Abs ("_", dummyT, 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] =

      Library.foldr (op $) (rev (gen_fields_tr "_updates" "_update" updateN u), t)

  | 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 ctxt t =

  let

    val thy = ProofContext.theory_of ctxt;

    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 thy (Sign.intern_const thy name) of

            SOME (ext, _) =>

              (case get_extfields thy 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 ctxt t =

  let

    val thy = ProofContext.theory_of ctxt;

    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 mk_ext (fargs as (name, arg) :: _) =

          (case get_fieldext thy (Sign.intern_const thy name) of

            SOME (ext, alphas) =>

              (case get_extfields thy ext of

                SOME flds =>

                 (let

                    val flds' = but_last flds;

                    val types = map snd flds';

                    val (args, rest) = splitargs (map fst flds') fargs;

                    val argtypes = map (Sign.certify_typ thy o decode_type thy) args;

                    val midx = fold (fn T => fn i => Int.max (maxidx_of_typ T, i)) argtypes 0;

                    val varifyT = varifyT midx;

                    val vartypes = map varifyT types;

                    val subst = fold (Sign.typ_match thy) (vartypes ~~ argtypes) Vartab.empty;

                    val alphas' =

                      map (Syntax.term_of_typ (! Syntax.show_sorts) o Envir.norm_type subst o varifyT)

                        (but_last alphas);

                    val more' = mk_ext rest;

                  in

                    list_comb (Syntax.const (suffix sfx ext), alphas' @ [more'])

                  end handle TYPE_MATCH =>

                    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 ctxt [t] =

      gen_ext_fields_tr sep mark sfx unit ctxt t

  | gen_adv_record_tr _ _ _ _ _ ts = raise TERM ("gen_record_tr", ts);

fun gen_adv_record_scheme_tr sep mark sfx ctxt [t, more] =

      gen_ext_fields_tr sep mark sfx more ctxt t

  | gen_adv_record_scheme_tr _ _ _ _ ts = raise TERM ("gen_record_scheme_tr", ts);

fun gen_adv_record_type_tr sep mark sfx unit ctxt [t] =

      gen_ext_type_tr sep mark sfx unit ctxt t

  | gen_adv_record_type_tr _ _ _ _ _ ts = raise TERM ("gen_record_tr", ts);

fun gen_adv_record_type_scheme_tr sep mark sfx ctxt [t, more] =

      gen_ext_type_tr sep mark sfx more ctxt 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 = Unsynchronized.ref true;

val print_record_type_as_fields = Unsynchronized.ref true;

fun gen_field_upds_tr' mark sfx (tm as Const (name_field, _) $ k $ u) =

      let

        val t =

          (case k of

            Abs (_, _, Abs (_, _, t) $ Bound 0) =>

              if null (loose_bnos t) then t else raise Match

          | Abs (x, _, t) =>

              if null (loose_bnos t) then t else raise Match

          | _ => raise Match);

          (* FIXME ? *)

          (* (case k of (Const ("K_record", _) $ t) => t

                   | Abs (x, _, Const ("K_record", _) $ t $ Bound 0) => t

                   | _ => raise Match)*)

      in

        (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))

      end

  | gen_field_upds_tr' _ _ tm = ([], tm);

fun record_update_tr' tm =

  let val (ts, u) = gen_field_upds_tr' "_update" updateN tm in

    if null ts then raise Match

    else

      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 ctxt t =

  let

    val thy = ProofContext.theory_of ctxt;

    fun field_lst t =

      (case strip_comb t of

        (Const (ext, _), args as (_ :: _)) =>

          (case try (unsuffix extN) (Sign.intern_const thy ext) of

            SOME ext' =>

              (case get_extfields thy ext' of

                SOME flds =>

                 (let

                    val f :: fs = but_last (map fst flds);

                    val flds' = Sign.extern_const thy f :: map Long_Name.base_name fs;

                    val (args', more) = split_last args;

                  in (flds' ~~ args') @ field_lst more end

                  handle Library.UnequalLengths => [("", t)])

              | NONE => [("", t)])

          | NONE => [("", t)])

       | _ => [("", t)]);

    val (flds, (_, more)) = split_last (field_lst t);

    val _ = if null flds then raise Match else ();

    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 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 (@{const_syntax "Product_Type.Unity"}, _) => true | _ => false);

    fun tr' ctxt ts =

      record_tr' "_fields" "_field" "_record" "_record_scheme" unit ctxt

        (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' *)

(*try to reconstruct the record name type abbreviation from

  the (nested) extension types*)

fun record_type_abbr_tr' default_tr' abbr alphas zeta lastExt schemeT ctxt tm =

  let

    val thy = ProofContext.theory_of ctxt;

    (*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*)

    (*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 thy) else T

      | fixT (Type (x, xs)) = Type (x, map fixT xs)