src/HOL/Tools/record_package.ML

HOL-Real -> HOL-Complex

(*  Title:      HOL/Tools/record_package.ML
    ID:         $Id$
    Author:     Wolfgang Naraschewski and Markus Wenzel, TU Muenchen
    License:    GPL (GNU GENERAL PUBLIC LICENSE)

Extensible records with structural subtyping in HOL.
*)

signature BASIC_RECORD_PACKAGE =
sig
  val record_simproc: simproc
  val record_split_tac: int -> tactic
  val record_split_name: string
  val record_split_wrapper: string * wrapper
end;

signature RECORD_PACKAGE =
sig
  include BASIC_RECORD_PACKAGE
  val quiet_mode: bool ref
  val updateN: string
  val mk_fieldT: (string * typ) * typ -> typ
  val dest_fieldT: typ -> (string * typ) * typ
  val mk_field: (string * term) * term -> term
  val mk_fst: term -> term
  val mk_snd: term -> term
  val mk_recordT: (string * typ) list * typ -> typ
  val dest_recordT: typ -> (string * typ) list * typ
  val mk_record: (string * term) list * term -> term
  val mk_sel: term -> string -> term
  val mk_update: term -> string * term -> term
  val print_records: theory -> unit
  val add_record: (string list * bstring) -> string option
    -> (bstring * string * mixfix) list -> theory -> theory * {simps: thm list, iffs: thm list}
  val add_record_i: (string list * bstring) -> (typ list * string) option
    -> (bstring * typ * mixfix) list -> theory -> theory * {simps: thm list, iffs: thm list}
  val setup: (theory -> theory) list
end;

structure RecordPackage: RECORD_PACKAGE =
struct


(*** theory context references ***)

val product_typeN = "Record.product_type";

val product_type_intro = thm "product_type.intro";
val product_type_inject = thm "product_type.inject";
val product_type_conv1 = thm "product_type.conv1";
val product_type_conv2 = thm "product_type.conv2";
val product_type_induct = thm "product_type.induct";
val product_type_cases = thm "product_type.cases";
val product_type_split_paired_all = thm "product_type.split_paired_all";



(*** utilities ***)

(* messages *)

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


(* 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;


(* 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 on last parameter of ith subgoal (or s) *)

fun try_param_tac s rule i st =
  let
    val cert = cterm_of (#sign (rep_thm st));
    val g = nth_elem (i - 1, prems_of st);
    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')));
    val (x, ca) = (case rev (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 assoc (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;



(*** code generator data ***)

val [prod_code, fst_code, snd_code] =
  map (Codegen.parse_mixfix (K (Bound 0))) ["(_,/ _)", "fst", "snd"];
val prodT_code = Codegen.parse_mixfix (K dummyT) "(_ */ _)";



(*** syntax operations ***)

(** name components **)

val rN = "r";
val moreN = "more";
val schemeN = "_scheme";
val field_typeN = "_field_type";
val fieldN = "_field";
val fstN = "_val";
val sndN = "_more";
val updateN = "_update";
val makeN = "make";
val fieldsN = "fields";
val extendN = "extend";
val truncateN = "truncate";


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



(** tuple operations **)

(* types *)

fun mk_fieldT ((c, T), U) = Type (suffix field_typeN c, [T, U]);

fun dest_fieldT (typ as Type (c_field_type, [T, U])) =
      (case try (unsuffix field_typeN) c_field_type of
        None => raise TYPE ("dest_fieldT", [typ], [])
      | Some c => ((c, T), U))
  | dest_fieldT typ = raise TYPE ("dest_fieldT", [typ], []);


(* morphisms *)

fun mk_Rep U (c, T) =
  Const (suffix field_typeN (prefix_base RepN c),
    mk_fieldT ((c, T), U) --> HOLogic.mk_prodT (T, U));

fun mk_Abs U (c, T) =
  Const (suffix field_typeN (prefix_base AbsN c),
    HOLogic.mk_prodT (T, U) --> mk_fieldT ((c, T), U));


(* constructors *)

fun mk_fieldC U (c, T) = (suffix fieldN c, T --> U --> mk_fieldT ((c, T), U));

fun mk_field ((c, t), u) =
  let val T = fastype_of t and U = fastype_of u
  in Const (suffix fieldN c, [T, U] ---> mk_fieldT ((c, T), U)) $ t $ u end;


(* destructors *)

fun mk_fstC U (c, T) = (suffix fstN c, mk_fieldT ((c, T), U) --> T);
fun mk_sndC U (c, T) = (suffix sndN c, mk_fieldT ((c, T), U) --> U);

fun dest_field fst_or_snd p =
  let
    val pT = fastype_of p;
    val ((c, T), U) = dest_fieldT pT;
    val (destN, destT) = if fst_or_snd then (fstN, T) else (sndN, U);
  in Const (suffix destN c, pT --> destT) $ p end;

val mk_fst = dest_field true;
val mk_snd = dest_field false;



(** record operations **)

(* types *)

val mk_recordT = foldr mk_fieldT;

fun dest_recordT T =
  (case try dest_fieldT T of
    None => ([], T)
  | Some (c_T, U) => apfst (cons c_T) (dest_recordT U));

fun find_fieldT c rT =
  (case assoc (fst (dest_recordT rT), c) of
    None => raise TYPE ("find_field: " ^ c, [rT], [])
  | Some T => T);


(* constructors *)

val mk_record = foldr mk_field;


(* selectors *)

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

fun mk_sel r c =
  let val rT = fastype_of r
  in Const (mk_selC rT (c, find_fieldT c rT)) $ r end;

fun mk_named_sels names r = names ~~ map (mk_sel r) names;

val mk_moreC = mk_selC;

fun mk_more r c =
  let val rT = fastype_of r
  in Const (mk_moreC rT (c, snd (dest_recordT rT))) $ r end;


(* updates *)

fun mk_updateC rT (c, T) = (suffix updateN c, T --> rT --> rT);

fun mk_update r (c, x) =
  let val rT = fastype_of r
  in Const (mk_updateC rT (c, find_fieldT c rT)) $ x $ r end;

val mk_more_updateC = mk_updateC;

fun mk_more_update r (c, x) =
  let val rT = fastype_of r
  in Const (mk_more_updateC rT (c, snd (dest_recordT rT))) $ x $ r 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 gen_record_tr sep mark sfx unit [t] = foldr (op $) (gen_fields_tr sep mark sfx t, unit)
  | gen_record_tr _ _ _ _ ts = raise TERM ("gen_record_tr", ts);

fun gen_record_scheme_tr sep mark sfx [t, more] = foldr (op $) (gen_fields_tr sep mark sfx t, more)
  | gen_record_scheme_tr _ _ _ ts = raise TERM ("gen_record_scheme_tr", ts);


val record_type_tr = gen_record_tr "_field_types" "_field_type" field_typeN (Syntax.const "unit");
val record_type_scheme_tr = gen_record_scheme_tr "_field_types" "_field_type" field_typeN;

val record_tr = gen_record_tr "_fields" "_field" fieldN HOLogic.unit;
val record_scheme_tr = gen_record_scheme_tr "_fields" "_field" fieldN;

fun record_update_tr [t, u] =
      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);


val parse_translation =
 [("_record_type", record_type_tr),
  ("_record_type_scheme", record_type_scheme_tr),
  ("_record", record_tr),
  ("_record_scheme", record_scheme_tr),
  ("_record_update", record_update_tr),
  ("_update_name", update_name_tr)];


(* print translations *)

fun gen_fields_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_fields_tr' mark sfx u)
      | None => ([], tm))
  | gen_fields_tr' _ _ tm = ([], tm);

fun gen_record_tr' sep mark sfx is_unit record record_scheme tm =
  let
    val (ts, u) = gen_fields_tr' mark sfx tm;
    val t' = foldr1 (fn (v, w) => Syntax.const sep $ v $ w) ts;
  in
    if is_unit u then Syntax.const record $ t'
    else Syntax.const record_scheme $ t' $ u
  end;


val record_type_tr' =
  gen_record_tr' "_field_types" "_field_type" field_typeN
    (fn Const ("unit", _) => true | _ => false) "_record_type" "_record_type_scheme";

val record_tr' =
  gen_record_tr' "_fields" "_field" fieldN
    (fn Const ("Unity", _) => true | _ => false) "_record" "_record_scheme";

fun record_update_tr' tm =
  let val (ts, u) = gen_fields_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 print_translation names =
  map (gen_field_tr' field_typeN record_type_tr') names @
  map (gen_field_tr' fieldN record_tr') names @
  map (gen_field_tr' updateN record_update_tr') names;



(*** 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,
  field_inducts: thm list,
  field_cases: thm list,
  simps: thm list};

fun make_record_info args parent fields field_inducts field_cases simps =
 {args = args, parent = parent, fields = fields, field_inducts = field_inducts,
  field_cases = field_cases, simps = simps}: record_info;

type parent_info =
 {name: string,
  fields: (string * typ) list,
  field_inducts: thm list,
  field_cases: thm list,
  simps: thm list};

fun make_parent_info name fields field_inducts field_cases simps =
 {name = name, fields = fields, field_inducts = field_inducts,
  field_cases = field_cases, simps = simps}: parent_info;


(* data kind 'HOL/records' *)

type record_data =
 {records: record_info Symtab.table,
  sel_upd:
   {selectors: unit Symtab.table,
    updates: string Symtab.table,
    simpset: Simplifier.simpset},
  field_splits:
   {fields: unit Symtab.table,
    simpset: Simplifier.simpset}};

fun make_record_data records sel_upd field_splits =
 {records = records, sel_upd = sel_upd, field_splits = field_splits}: record_data;

structure RecordsArgs =
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}
      {fields = Symtab.empty, simpset = HOL_basic_ss};

  val copy = I;
  val prep_ext = I;
  fun merge
   ({records = recs1,
     sel_upd = {selectors = sels1, updates = upds1, simpset = ss1},
     field_splits = {fields = flds1, simpset = fld_ss1}},
    {records = recs2,
     sel_upd = {selectors = sels2, updates = upds2, simpset = ss2},
     field_splits = {fields = flds2, simpset = fld_ss2}}) =
    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)}
      {fields = Symtab.merge (K true) (flds1, flds2),
        simpset = Simplifier.merge_ss (fld_ss1, fld_ss2)};

  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.cond_extern sg Sign.constK 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;

structure RecordsData = TheoryDataFun(RecordsArgs);
val print_records = RecordsData.print;


(* access 'records' *)

fun get_record thy name = Symtab.lookup (#records (RecordsData.get thy), name);

fun put_record name info thy =
  let
    val {records, sel_upd, field_splits} = RecordsData.get thy;
    val data = make_record_data (Symtab.update ((name, info), records)) sel_upd field_splits;
  in RecordsData.put data thy end;


(* access 'sel_upd' *)

fun get_sel_upd sg = #sel_upd (RecordsData.get_sg sg);

fun get_selectors sg name = Symtab.lookup (#selectors (get_sel_upd sg), name);
fun get_updates sg name = Symtab.lookup (#updates (get_sel_upd sg), name);
fun get_simpset sg = #simpset (get_sel_upd sg);


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}, field_splits} = RecordsData.get thy;
    val data = make_record_data records
      {selectors = Symtab.extend (selectors, sels),
        updates = Symtab.extend (updates, upds),
        simpset = Simplifier.addsimps (simpset, simps)}
      field_splits;
  in RecordsData.put data thy end;


(* access 'field_splits' *)

fun add_record_splits splits thy =
  let
    val {records, sel_upd, field_splits = {fields, simpset}} = RecordsData.get thy;
    val flds = map (rpair () o fst) splits;
    val simps = map snd splits;
    val data = make_record_data records sel_upd
      {fields = Symtab.extend (fields, flds), simpset = Simplifier.addsimps (simpset, simps)};
  in RecordsData.put data thy end;


(* 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, field_inducts, field_cases, simps} =
          (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 = mapfilter bad_inst (args ~~ types);

        val inst = map fst args ~~ types;
        val subst = Term.map_type_tfree (fn (x, _) => the (assoc (inst, x)));
        val parent' = apsome (apfst (map subst)) parent;
        val fields' = map (apsnd subst) fields;
      in
        conditional (not (null bads)) (fn () =>
          err ("Ill-sorted instantiation of " ^ commas bads ^ " in"));
        add_parents thy parent'
          (make_parent_info name fields' field_inducts field_cases simps :: parents)
      end;



(** record simproc **)

val record_simproc =
  Simplifier.simproc (Theory.sign_of HOL.thy) "record_simp" ["s (u k r)"]
    (fn sg => fn _ => fn t =>
      (case t of (sel as Const (s, _)) $ ((upd as Const (u, _)) $ k $ r) =>
        (case get_selectors sg s of Some () =>
          (case get_updates sg u of Some u_name =>
            let
              fun mk_free x t = Free (x, fastype_of t);
              val k' = mk_free "k" k;
              val r' = mk_free "r" r;
              val t' = sel $ (upd $ k' $ r');
              fun prove prop =
                Tactic.prove sg ["k", "r"] [] prop (K (simp_all_tac (get_simpset sg) []));
            in
              if u_name = s then Some (prove (Logic.mk_equals (t', k')))
              else Some (prove (Logic.mk_equals (t', sel $ r')))
            end
          | None => None)
        | None => None)
      | _ => None));



(** record field splitting **)

(* tactic *)

fun record_split_tac i st =
  let
    val {field_splits = {fields, simpset}, ...} = RecordsData.get_sg (Thm.sign_of_thm st);

    fun is_fieldT (_, Type (a, [_, _])) = is_some (Symtab.lookup (fields, a))
      | is_fieldT _ = false;
    val params = Logic.strip_params (Library.nth_elem (i - 1, Thm.prems_of st));
  in
    if exists is_fieldT params then Simplifier.full_simp_tac simpset i st
    else Seq.empty
  end handle Library.LIST _ => Seq.empty;


(* wrapper *)

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


(* method *)

val record_split_method =
  ("record_split", Method.no_args (Method.SIMPLE_METHOD' HEADGOAL record_split_tac),
    "split record fields");



(** internal theory extenders **)

(* field_typedefs *)

fun field_typedefs zeta moreT names theory =
  let
    val alpha = "'a";
    val aT = TFree (alpha, HOLogic.typeS);
    val UNIV = HOLogic.mk_UNIV (HOLogic.mk_prodT (aT, moreT));

    fun type_def (thy, name) =
      let val (thy', {type_definition, set_def = Some def, ...}) =
        thy |> setmp TypedefPackage.quiet_mode true
          (TypedefPackage.add_typedef_i true None
            (suffix field_typeN (Sign.base_name name), [alpha, zeta], Syntax.NoSyn) UNIV None
          (Tactic.rtac UNIV_witness 1))
      in (thy', Tactic.rewrite_rule [def] type_definition) end
  in foldl_map type_def (theory, names) end;


(* field_definitions *)

fun field_definitions fields names xs alphas zeta moreT more vars named_vars thy =
  let
    val sign = Theory.sign_of thy;
    val base = Sign.base_name;

    val xT = TFree (variant alphas "'x", HOLogic.typeS);


    (* prepare declarations and definitions *)

    (*field constructors*)
    val field_decls = map (mk_fieldC moreT) fields;

    fun mk_field_spec ((c, T), v) =
      Term.head_of (mk_field ((c, v), more)) :==
        lambda v (lambda more (mk_Abs moreT (c, T) $ (HOLogic.mk_prod (v, more))));
    val field_specs = map mk_field_spec (fields ~~ vars);

    (*field destructors*)
    val dest_decls = map (mk_fstC moreT) fields @ map (mk_sndC moreT) fields;

    fun mk_dest_spec dest sel (c, T) =
      let val p = Free ("p", mk_fieldT ((c, T), moreT));
      in Term.head_of (dest p) :== lambda p (sel (mk_Rep moreT (c, T) $ p)) end;
    val dest_specs1 = map (mk_dest_spec mk_fst HOLogic.mk_fst) fields;
    val dest_specs2 = map (mk_dest_spec mk_snd HOLogic.mk_snd) fields;


    (* 1st stage: defs_thy *)

    val (defs_thy, (((typedefs, field_defs), dest_defs1), dest_defs2)) =
      thy
      |> field_typedefs zeta moreT names
      |>> (Theory.add_consts_i o map (Syntax.no_syn o apfst base)) (field_decls @ dest_decls)
      |>>> (PureThy.add_defs_i false o map Thm.no_attributes) field_specs
      |>>> (PureThy.add_defs_i false o map Thm.no_attributes) dest_specs1
      |>>> (PureThy.add_defs_i false o map Thm.no_attributes) dest_specs2;

    val prod_types = map (fn (((a, b), c), d) => product_type_intro OF [a, b, c, d])
      (typedefs ~~ field_defs ~~ dest_defs1 ~~ dest_defs2);


    (* 2nd stage: thms_thy *)

    fun make th = map (fn prod_type => Drule.standard (th OF [prod_type])) prod_types;

    val dest_convs = make product_type_conv1 @ make product_type_conv2;
    val field_injects = make product_type_inject;
    val field_inducts = make product_type_induct;
    val field_cases = make product_type_cases;
    val field_splits = make product_type_split_paired_all;

    val (thms_thy, [field_defs', dest_defs', dest_convs', field_injects',
        field_splits', field_inducts', field_cases']) = defs_thy
      |> Codegen.assoc_consts_i (flat (map (fn (s, _) =>
           [(suffix fieldN s, None, prod_code),
            (suffix fstN s, None, fst_code),
            (suffix sndN s, None, snd_code)]) fields))
      |> Codegen.assoc_types (map (fn (s, _) =>
           (suffix field_typeN s, prodT_code)) fields)
      |> (PureThy.add_thmss o map Thm.no_attributes)
       [("field_defs", field_defs),
        ("dest_defs", dest_defs1 @ dest_defs2),
        ("dest_convs", dest_convs),
        ("field_injects", field_injects),
        ("field_splits", field_splits),
        ("field_inducts", field_inducts),
        ("field_cases", field_cases)];

  in (thms_thy, dest_convs', field_injects', field_splits', field_inducts', field_cases') end;


(* record_definition *)

fun record_definition (args, bname) parent (parents: parent_info list) raw_fields thy =
  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);


    (* basic components *)

    val ancestry = map (length o flat o map #fields) (Library.prefixes1 parents);

    val parent_fields = flat (map #fields parents);
    val parent_names = map fst parent_fields;
    val parent_types = map snd parent_fields;
    val parent_len = length parent_fields;
    val parent_xs = variantlist (map (base o fst) parent_fields, [moreN, rN]);
    val parent_vars = ListPair.map Free (parent_xs, parent_types);
    val parent_named_vars = parent_names ~~ parent_vars;

    val fields = map (apfst full) bfields;
    val names = map fst fields;
    val types = map snd fields;
    val len = length fields;
    val xs = variantlist (map fst bfields, moreN :: rN :: parent_xs);
    val vars = ListPair.map Free (xs, types);
    val named_vars = names ~~ vars;

    val all_fields = parent_fields @ fields;
    val all_names = parent_names @ names;
    val all_types = parent_types @ types;
    val all_len = parent_len + len;
    val all_xs = parent_xs @ xs;
    val all_vars = parent_vars @ vars;
    val all_named_vars = parent_named_vars @ named_vars;

    val zeta = variant alphas "'z";
    val moreT = TFree (zeta, HOLogic.typeS);
    val more = Free (moreN, moreT);
    val full_moreN = full moreN;
    fun more_part t = mk_more t full_moreN;
    fun more_part_update t x = mk_more_update t (full_moreN, x);
    val all_types_more = all_types @ [moreT];
    val all_xs_more = all_xs @ [moreN];

    val parent_more = funpow parent_len mk_snd;
    val idxs = 0 upto (len - 1);

    val fieldsT = mk_recordT (fields, HOLogic.unitT);
    fun rec_schemeT n = mk_recordT (prune n all_fields, moreT);
    fun rec_scheme n = mk_record (prune n all_named_vars, more);
    fun recT n = mk_recordT (prune n all_fields, HOLogic.unitT);
    fun rec_ n = mk_record (prune n all_named_vars, HOLogic.unit);
    fun r_scheme n = Free (rN, rec_schemeT n);
    fun r n = Free (rN, recT n);


    (* prepare print translation functions *)

    val field_tr's =
      print_translation (distinct (flat (map NameSpace.accesses' (full_moreN :: names))));


    (* prepare declarations *)

    val sel_decls = map (mk_selC (rec_schemeT 0)) bfields @
      [mk_moreC (rec_schemeT 0) (moreN, moreT)];
    val update_decls = map (mk_updateC (rec_schemeT 0)) bfields @
      [mk_more_updateC (rec_schemeT 0) (moreN, moreT)];
    val make_decl = (makeN, all_types ---> recT 0);
    val fields_decl = (fieldsN, types ---> fieldsT);
    val extend_decl = (extendN, recT 0 --> moreT --> rec_schemeT 0);
    val truncate_decl = (truncateN, rec_schemeT 0 --> recT 0);


    (* prepare definitions *)

    (*record (scheme) type abbreviation*)
    val recordT_specs =
      [(suffix schemeN bname, alphas @ [zeta], rec_schemeT 0, Syntax.NoSyn),
        (bname, alphas, recT 0, Syntax.NoSyn)];

    (*selectors*)
    fun mk_sel_spec (i, c) =
      mk_sel (r_scheme 0) c :== mk_fst (funpow i mk_snd (parent_more (r_scheme 0)));
    val sel_specs =
      ListPair.map mk_sel_spec (idxs, names) @
        [more_part (r_scheme 0) :== funpow len mk_snd (parent_more (r_scheme 0))];

    (*updates*)
    val all_sels = mk_named_sels all_names (r_scheme 0);
    fun mk_upd_spec (i, (c, x)) =
      mk_update (r_scheme 0) (c, x) :==
        mk_record (nth_update (c, x) (parent_len + i, all_sels), more_part (r_scheme 0))
    val update_specs =
      ListPair.map mk_upd_spec (idxs, named_vars) @
        [more_part_update (r_scheme 0) more :== mk_record (all_sels, more)];

    (*derived operations*)
    val make_spec = Const (full makeN, all_types ---> recT 0) $$ all_vars :==
      mk_record (all_named_vars, HOLogic.unit);
    val fields_spec = Const (full fieldsN, types ---> fieldsT) $$ vars :==
      mk_record (named_vars, HOLogic.unit);
    val extend_spec = Const (full extendN, recT 0 --> moreT --> rec_schemeT 0) $ r 0 $ more :==
      mk_record (mk_named_sels all_names (r 0), more);
    val truncate_spec = Const (full truncateN, rec_schemeT 0 --> recT 0) $ r_scheme 0 :==
      mk_record (all_sels, HOLogic.unit);


    (* prepare propositions *)

    (*selectors*)
    val sel_props =
      map (fn (c, x) => mk_sel (rec_scheme 0) c === x) named_vars @
        [more_part (rec_scheme 0) === more];

    (*updates*)
    fun mk_upd_prop (i, (c, T)) =
      let val x' = Free (variant all_xs (base c ^ "'"), T) in
        mk_update (rec_scheme 0) (c, x') ===
          mk_record (nth_update (c, x') (parent_len + i, all_named_vars), more)
      end;
    val update_props =
      ListPair.map mk_upd_prop (idxs, fields) @
        let val more' = Free (variant all_xs (moreN ^ "'"), moreT)
        in [more_part_update (rec_scheme 0) more' === mk_record (all_named_vars, more')] end;

    (*equality*)
    fun mk_sel_eq (t, T) =
      let val t' = Term.abstract_over (r_scheme 0, t)
      in Trueprop (HOLogic.eq_const T $ Term.incr_boundvars 1 t' $ t') end;
    val sel_eqs = map2 mk_sel_eq
      (map (mk_sel (r_scheme 0)) all_names @ [more_part (r_scheme 0)], all_types @ [moreT]);
    val equality_prop =
      Term.all (rec_schemeT 0) $ (Abs ("r", rec_schemeT 0,
        Term.all (rec_schemeT 0) $ (Abs ("r'", rec_schemeT 0,
          Logic.list_implies (sel_eqs,
            Trueprop (HOLogic.eq_const (rec_schemeT 0) $ Bound 1 $ Bound 0))))));

    (*induct*)
    fun induct_scheme_prop n =
      let val P = Free ("P", rec_schemeT n --> HOLogic.boolT) in
        (All (prune n all_xs_more ~~ prune n all_types_more)
          (Trueprop (P $ rec_scheme n)), Trueprop (P $ r_scheme n))
      end;
    fun induct_prop n =
      let val P = Free ("P", recT n --> HOLogic.boolT) in
        (All (prune n all_xs ~~ prune n all_types) (Trueprop (P $ rec_ n)), Trueprop (P $ r n))
      end;

    (*cases*)
    val C = Trueprop (Free (variant all_xs_more "C", HOLogic.boolT));
    fun cases_scheme_prop n =
      All (prune n all_xs_more ~~ prune n all_types_more)
        ((r_scheme n === rec_scheme n) ==> C) ==> C;
    fun cases_prop n = All (prune n all_xs ~~ prune n all_types) ((r n === rec_ n) ==> C) ==> C;


    (* 1st stage: fields_thy *)

    val (fields_thy, field_simps, field_injects, field_splits, field_inducts, field_cases) =
      thy
      |> Theory.add_path bname
      |> field_definitions fields names xs alphas zeta moreT more vars named_vars;

    val all_field_inducts = flat (map #field_inducts parents) @ field_inducts;
    val all_field_cases = flat (map #field_cases parents) @ field_cases;

    val named_splits = map2 (fn (c, th) => (suffix field_typeN c, th)) (names, field_splits);


    (* 2nd stage: defs_thy *)

    val (defs_thy, (((sel_defs, update_defs), derived_defs))) =
      fields_thy
      |> add_record_splits named_splits
      |> Theory.parent_path
      |> Theory.add_tyabbrs_i recordT_specs
      |> Theory.add_path bname
      |> Theory.add_trfuns ([], [], field_tr's, [])
      |> 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)
        (update_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) update_specs
      |>>> (PureThy.add_defs_i false o map Thm.no_attributes)
        [make_spec, fields_spec, extend_spec, truncate_spec]
      |>> Theory.hide_consts false [full makeN, full fieldsN, full extendN, full truncateN,
        full moreN, full (suffix updateN moreN)];


    (* 3rd stage: thms_thy *)

    val prove_standard = Tactic.prove_standard (Theory.sign_of defs_thy);
    fun prove_simp simps =
      let val tac = simp_all_tac HOL_basic_ss simps
      in fn prop => prove_standard [] [] prop (K tac) end;

    val parent_simps = flat (map #simps parents);
    val sel_convs = map (prove_simp (parent_simps @ sel_defs @ field_simps)) sel_props;
    val update_convs = map (prove_simp (parent_simps @ update_defs @ sel_convs)) update_props;

    fun induct_scheme n =
      let val (assm, concl) = induct_scheme_prop n in
        prove_standard [] [assm] concl (fn prems =>
          EVERY (map (fn rule => try_param_tac rN rule 1) (prune n all_field_inducts))
          THEN resolve_tac prems 1)
      end;

    fun cases_scheme n =
      prove_standard [] [] (cases_scheme_prop n) (fn _ =>
        EVERY (map (fn rule => try_param_tac rN rule 1) (prune n all_field_cases))
        THEN simp_all_tac HOL_basic_ss []);

    val induct_scheme0 = induct_scheme 0;
    val cases_scheme0 = cases_scheme 0;
    val more_induct_scheme = map induct_scheme ancestry;
    val more_cases_scheme = map cases_scheme ancestry;

    val (thms_thy, (([sel_convs', update_convs', sel_defs', update_defs', _],
        [induct_scheme', cases_scheme']), [more_induct_scheme', more_cases_scheme'])) =
      defs_thy
      |> (PureThy.add_thmss o map Thm.no_attributes)
       [("select_convs", sel_convs),
        ("update_convs", update_convs),
        ("select_defs", sel_defs),
        ("update_defs", update_defs),
        ("defs", derived_defs)]
      |>>> PureThy.add_thms
       [(("induct_scheme", induct_scheme0), induct_type_global (suffix schemeN name)),
        (("cases_scheme", cases_scheme0), cases_type_global (suffix schemeN name))]
      |>>> PureThy.add_thmss
        [(("more_induct_scheme", more_induct_scheme), induct_type_global ""),
         (("more_cases_scheme", more_cases_scheme), cases_type_global "")];


    (* 4th stage: more_thms_thy *)

    val prove_standard = Tactic.prove_standard (Theory.sign_of thms_thy);

    fun induct (n, scheme) =
      let val (assm, concl) = induct_prop n in
        prove_standard [] [assm] concl (fn prems =>
          res_inst_tac [(rN, rN)] scheme 1
          THEN try_param_tac "more" unit_induct 1
          THEN resolve_tac prems 1)
      end;

    fun cases (n, scheme) =
      prove_standard [] [] (cases_prop n) (fn _ =>
        res_inst_tac [(rN, rN)] scheme 1
        THEN simp_all_tac HOL_basic_ss [unit_all_eq1]);

    val induct0 = induct (0, induct_scheme');
    val cases0 = cases (0, cases_scheme');
    val more_induct = map induct (ancestry ~~ more_induct_scheme');
    val more_cases = map cases (ancestry ~~ more_cases_scheme');

    val equality = prove_standard [] [] equality_prop (fn _ =>
      fn st => let val [r, r'] = map #1 (rev (Tactic.innermost_params 1 st)) in
        st |> (res_inst_tac [(rN, r)] cases_scheme' 1
        THEN res_inst_tac [(rN, r')] cases_scheme' 1
        THEN simp_all_tac HOL_basic_ss (parent_simps @ sel_convs))
      end);

    val (more_thms_thy, [_, _, equality']) =
      thms_thy |> PureThy.add_thms
       [(("induct", induct0), induct_type_global name),
        (("cases", cases0), cases_type_global name),
        (("equality", equality), [ContextRules.intro_bang_global None])]
      |>> (#1 oo PureThy.add_thmss)
        [(("more_induct", more_induct), induct_type_global ""),
         (("more_cases", more_cases), cases_type_global "")];

    val simps = sel_convs' @ update_convs' @ [equality'];
    val iffs = field_injects;

    val more_thms_thy' =
      more_thms_thy |> (#1 oo PureThy.add_thmss)
        [(("simps", simps), [Simplifier.simp_add_global]),
         (("iffs", iffs), [iff_add_global])];


    (* 5th stage: final_thy *)

    val final_thy =
      more_thms_thy'
      |> put_record name (make_record_info args parent fields field_inducts field_cases
        (field_simps @ simps))
      |> put_sel_upd (names @ [full_moreN]) (field_simps @ sel_defs' @ update_defs')
      |> Theory.parent_path;

  in (final_thy, {simps = simps, iffs = iffs}) end;



(** theory extender interface **)

(* prepare arguments *)

(*note: read_raw_typ avoids expanding type abbreviations*)
fun read_raw_parent sign s =
  (case Sign.read_raw_typ (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) = assoc (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;


(* 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 = apsome (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, if_none (assoc (envir, x)) 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);



(** package setup **)

(* setup theory *)

val setup =
 [RecordsData.init,
  Theory.add_trfuns ([], parse_translation, [], []),
  Method.add_methods [record_split_method],
  Simplifier.change_simpset_of Simplifier.addsimprocs [record_simproc]];


(* outer syntax *)

local structure P = OuterParse and K = OuterSyntax.Keyword 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 (#1 o add_record x y z)));

val _ = OuterSyntax.add_parsers [recordP];

end;

end;

structure BasicRecordPackage: BASIC_RECORD_PACKAGE = RecordPackage;
open BasicRecordPackage;