src/HOL/Tools/record.ML

tuned whitespace -- recover basic Isabelle conventions;

(*  Title:      HOL/Tools/record.ML
    Authors:    Wolfgang Naraschewski, Norbert Schirmer and Markus Wenzel, TU Muenchen
                Thomas Sewell, NICTA

Extensible records with structural subtyping in HOL.
*)

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)
      | fixT T = T;

    val T = fixT (decode_type thy tm);
    val midx = maxidx_of_typ T;
    val varifyT = varifyT midx;

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

    fun match rT T = Sign.typ_match thy (varifyT rT, T) Vartab.empty;
  in
    if ! print_record_type_abbr then
      (case last_extT T of
        SOME (name, _) =>
          if name = lastExt then
           (let val subst = match schemeT T in
              if HOLogic.is_unitT (Envir.norm_type subst (varifyT (TFree (zeta, Sign.defaultS thy))))
              then mk_type_abbr subst abbr alphas
              else mk_type_abbr subst (suffix schemeN abbr) (alphas @ [zeta])
            end handle TYPE_MATCH => default_tr' ctxt tm)
          else raise Match (*give print translation of specialised record a chance*)
      | _ => raise Match)
    else default_tr' ctxt tm
  end;

fun record_type_tr' sep mark record record_scheme ctxt t =
  let
    val thy = ProofContext.theory_of ctxt;

    val T = decode_type thy t;
    val varifyT = varifyT (Term.maxidx_of_typ T);

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

    fun field_lst T =
      (case T of
        Type (ext, args) =>
          (case try (unsuffix ext_typeN) ext of
            SOME ext' =>
              (case get_extfields thy ext' of
                SOME flds =>
                  (case get_fieldext thy (fst (hd flds)) of
                    SOME (_, alphas) =>
                     (let
                        val f :: fs = but_last flds;
                        val flds' = apfst (Sign.extern_const thy) f ::
                          map (apfst Long_Name.base_name) fs;
                        val (args', more) = split_last args;
                        val alphavars = map varifyT (but_last alphas);
                        val subst = fold2 (curry (Sign.typ_match thy)) alphavars args' Vartab.empty;
                        val flds'' = (map o apsnd) (Envir.norm_type subst o varifyT) flds';
                      in flds'' @ field_lst more end
                      handle TYPE_MATCH => [("", T)]
                        | Library.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'
        handle Empty => raise Match;
  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' ctxt ts =
      record_type_tr' "_field_types" "_field_type" "_record_type" "_record_type_scheme"
        ctxt (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' ctxt ts =
      record_type_abbr_tr' default_tr' abbr alphas zeta lastExt schemeT ctxt
        (list_comb (Syntax.const name_sfx, ts));
  in (name_sfx, tr') end;



(** record simprocs **)

val record_quick_and_dirty_sensitive = Unsynchronized.ref false;


fun quick_and_dirty_prove stndrd thy asms prop tac =
  if ! record_quick_and_dirty_sensitive andalso ! quick_and_dirty then
    Goal.prove (ProofContext.init thy) [] []
      (Logic.list_implies (map Logic.varify asms, Logic.varify prop))
      (K (SkipProof.cheat_tac @{theory HOL}))
      (*Drule.standard can take quite a while for large records, thats why
        we varify the proposition manually here.*)
  else
    let val prf = Goal.prove (ProofContext.init thy) [] 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 is_sel_upd_pair thy (Const (s, t)) (Const (u, t')) =
  (case get_updates thy u of
    SOME u_name => u_name = s
  | NONE => raise TERM ("is_sel_upd_pair: not update", [Const (u, t')]));

fun mk_comp f g =
  let
    val x = fastype_of g;
    val a = domain_type x;
    val b = range_type x;
    val c = range_type (fastype_of f);
    val T = (b --> c) --> ((a --> b) --> (a --> c))
  in Const ("Fun.comp", T) $ f $ g end;

fun mk_comp_id f =
  let val T = range_type (fastype_of f)
  in mk_comp (Const ("Fun.id", T --> T)) f end;

fun get_upd_funs (upd $ _ $ t) = upd :: get_upd_funs t
  | get_upd_funs _ = [];

fun get_accupd_simps thy term defset intros_tac =
  let
    val (acc, [body]) = strip_comb term;
    val recT = domain_type (fastype_of acc);
    val upd_funs = sort_distinct TermOrd.fast_term_ord (get_upd_funs body);
    fun get_simp upd =
      let
        val T = domain_type (fastype_of upd);
        val lhs = mk_comp acc (upd $ Free ("f", T));
        val rhs =
          if is_sel_upd_pair thy acc upd
          then mk_comp (Free ("f", T)) acc
          else mk_comp_id acc;
        val prop = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs));
        val othm =
          Goal.prove (ProofContext.init thy) [] [] prop
            (fn prems =>
              EVERY
               [simp_tac defset 1,
                REPEAT_DETERM (intros_tac 1),
                TRY (simp_tac (HOL_ss addsimps id_o_apps) 1)]);
        val dest =
          if is_sel_upd_pair thy acc upd
          then o_eq_dest
          else o_eq_id_dest;
      in standard (othm RS dest) end;
  in map get_simp upd_funs end;

(* FIXME dup? *)
structure SymSymTab =
  Table(type key = string * string val ord = prod_ord fast_string_ord fast_string_ord);

fun get_updupd_simp thy defset intros_tac u u' comp =
  let
    val f = Free ("f", domain_type (fastype_of u));
    val f' = Free ("f'", domain_type (fastype_of u'));
    val lhs = mk_comp (u $ f) (u' $ f');
    val rhs =
      if comp
      then u $ mk_comp f f'
      else mk_comp (u' $ f') (u $ f);
    val prop = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs));
    val othm =
      Goal.prove (ProofContext.init thy) [] [] prop
        (fn prems =>
          EVERY
           [simp_tac defset 1,
            REPEAT_DETERM (intros_tac 1),
            TRY (simp_tac (HOL_ss addsimps [id_apply]) 1)]);
    val dest = if comp then o_eq_dest_lhs else o_eq_dest;
  in standard (othm RS dest) end;

fun get_updupd_simps thy term defset intros_tac =
  let
    val recT = fastype_of term;
    val upd_funs = get_upd_funs term;
    val cname = fst o dest_Const;
    fun getswap u u' = get_updupd_simp thy defset intros_tac u u' (cname u = cname u');
    fun build_swaps_to_eq upd [] swaps = swaps
      | build_swaps_to_eq upd (u :: us) swaps =
          let
            val key = (cname u, cname upd);
            val newswaps =
              if SymSymTab.defined swaps key then swaps
              else SymSymTab.insert (K true) (key, getswap u upd) swaps;
          in
            if cname u = cname upd then newswaps
            else build_swaps_to_eq upd us newswaps
          end;
    fun swaps_needed [] prev seen swaps = map snd (SymSymTab.dest swaps)
      | swaps_needed (u :: us) prev seen swaps =
          if Symtab.defined seen (cname u)
          then swaps_needed us prev seen (build_swaps_to_eq u prev swaps)
          else swaps_needed us (u :: prev) (Symtab.insert (K true) (cname u, ()) seen) swaps;
  in swaps_needed upd_funs [] Symtab.empty SymSymTab.empty end;

val named_cterm_instantiate = IsTupleSupport.named_cterm_instantiate;

fun prove_unfold_defs thy ss T ex_simps ex_simprs prop =
  let
    val defset = get_sel_upd_defs thy;
    val in_tac = IsTupleSupport.istuple_intros_tac thy;
    val prop' = Envir.beta_eta_contract prop;
    val (lhs, rhs) = Logic.dest_equals (Logic.strip_assums_concl prop');
    val (head, args) = strip_comb lhs;
    val simps =
      if length args = 1
      then get_accupd_simps thy lhs defset in_tac