(*  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 RECORD =

 sig

   val type_abbr: bool Config.T

   val type_as_fields: bool Config.T

   val timing: bool Config.T

   type info =

    {args: (string * sort) list,

     parent: (typ list * string) option,

     fields: (string * typ) list,

     extension: (string * typ list),

     ext_induct: thm, ext_inject: thm, ext_surjective: thm, ext_split: thm, ext_def: thm,

     select_convs: thm list, update_convs: thm list, select_defs: thm list, update_defs: thm list,

     fold_congs: thm list, unfold_congs: thm list, splits: thm list, defs: thm list,

     surjective: thm, equality: thm, induct_scheme: thm, induct: thm, cases_scheme: thm,

     cases: thm, simps: thm list, iffs: thm list}

   val get_info: theory -> string -> info option

   val the_info: theory -> string -> info

   val get_hierarchy: theory -> (string * typ list) -> (string * ((string * sort) * typ) list) list

   val add_record: (string * sort) list * binding -> (typ list * string) option ->

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

   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 simproc: simproc

   val eq_simproc: simproc

   val upd_simproc: simproc

   val split_simproc: (term -> int) -> simproc

   val ex_sel_eq_simproc: simproc

   val split_tac: int -> tactic

   val split_simp_tac: thm list -> (term -> int) -> int -> tactic

   val split_wrapper: string * (Proof.context -> wrapper)

   val updateN: string

   val ext_typeN: string

   val extN: string

   val setup: theory -> theory

 end;

 signature ISO_TUPLE_SUPPORT =

 sig

   val add_iso_tuple_type: binding * (string * sort) list ->

     typ * typ -> theory -> (term * term) * theory

   val mk_cons_tuple: term * term -> term

   val dest_cons_tuple: term -> term * term

   val iso_tuple_intros_tac: int -> tactic

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

 end;

 structure Iso_Tuple_Support: ISO_TUPLE_SUPPORT =

 struct

 val isoN = "_Tuple_Iso";

 val iso_tuple_intro = @{thm isomorphic_tuple_intro};

 val iso_tuple_intros = Tactic.build_net @{thms isomorphic_tuple.intros};

 val tuple_iso_tuple = (@{const_name Record.tuple_iso_tuple}, @{thm tuple_iso_tuple});

 fun named_cterm_instantiate values thm =  (* FIXME eliminate *)

   let

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

     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 Iso_Tuple_Thms = Theory_Data

 (

   type T = thm Symtab.table;

   val empty = Symtab.make [tuple_iso_tuple];

   val extend = I;

   fun merge data = Symtab.merge Thm.eq_thm_prop data;   (* FIXME handle Symtab.DUP ?? *)

 );

 fun get_typedef_info tyco vs

     (({rep_type, Abs_name, ...}, {Rep_inject, Abs_inverse, ... }) : Typedef.info) thy =

   let

     val exists_thm =

       UNIV_I

       |> Drule.instantiate' [SOME (ctyp_of thy (Logic.varifyT_global rep_type))] [];

     val proj_constr = Abs_inverse OF [exists_thm];

     val absT = Type (tyco, map TFree vs);

   in

     thy

     |> pair (tyco, ((Rep_inject, proj_constr), Const (Abs_name, rep_type --> absT), absT))

   end

 fun do_typedef raw_tyco repT raw_vs thy =

   let

     val ctxt = Proof_Context.init_global thy |> Variable.declare_typ repT;

     val vs = map (Proof_Context.check_tfree ctxt) raw_vs;

   in

     thy

     |> Typedef.add_typedef_global false (SOME raw_tyco) (raw_tyco, vs, NoSyn)

         (HOLogic.mk_UNIV repT) NONE (rtac UNIV_witness 1)

     |-> (fn (tyco, info) => get_typedef_info tyco vs info)

   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 (@{type_name tuple_isomorphism}, [prodT, leftT, rightT]);

   in

     Const (@{const_name Record.iso_tuple_cons}, isomT --> leftT --> rightT --> prodT) $

       Const (fst tuple_iso_tuple, isomT) $ left $ right

   end;

 fun dest_cons_tuple (Const (@{const_name Record.iso_tuple_cons}, _) $ Const _ $ t $ u) = (t, u)

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

 fun add_iso_tuple_type (b, alphas) (leftT, rightT) thy =

   let

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

     val ((_, ((rep_inject, abs_inverse), absC, absT)), typ_thy) =

       thy

       |> do_typedef b repT alphas

       ||> Sign.add_path (Binding.name_of b); (*FIXME proper prefixing instead*)

     (*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)] iso_tuple_intro;

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

     val isomT = fastype_of body;

     val isom_binding = Binding.suffix_name isoN b;

     val isom_name = Sign.full_name typ_thy isom_binding;

     val isom = Const (isom_name, isomT);

     val ([isom_def], cdef_thy) =

       typ_thy

       |> Sign.declare_const_global ((isom_binding, isomT), NoSyn) |> snd

       |> Global_Theory.add_defs false

         [((Binding.conceal (Thm.def_binding isom_binding), Logic.mk_equals (isom, body)), [])];

     val iso_tuple = isom_def RS (abs_inverse RS (rep_inject RS iso_tuple_intro));

     val cons = Const (@{const_name Record.iso_tuple_cons}, isomT --> leftT --> rightT --> absT);

     val thm_thy =

       cdef_thy

       |> Iso_Tuple_Thms.map (Symtab.insert Thm.eq_thm_prop (isom_name, iso_tuple))

       |> Sign.restore_naming thy

   in

     ((isom, cons $ isom), thm_thy)

   end;

 val iso_tuple_intros_tac =

   resolve_from_net_tac iso_tuple_intros THEN'

   CSUBGOAL (fn (cgoal, i) =>

     let

       val thy = Thm.theory_of_cterm cgoal;

       val goal = Thm.term_of cgoal;

       val isthms = Iso_Tuple_Thms.get thy;

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

       val goal' = Envir.beta_eta_contract goal;

       val is =

         (case goal' of

           Const (@{const_name Trueprop}, _) $

             (Const (@{const_name isomorphic_tuple}, _) $ Const is) => is

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

       val isthm =

         (case Symtab.lookup isthms (#1 is) of

           SOME isthm => isthm

         | NONE => err "no thm found for constant" (Const is));

     in rtac isthm i end);

 end;

 structure Record: RECORD =

 struct

 val surject_assistI = @{thm iso_tuple_surjective_proof_assistI};

 val surject_assist_idE = @{thm iso_tuple_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 iso_tuple_update_accessor_eq_assist_idI};

 val updacc_eq_triv = @{thm iso_tuple_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 iso_tuple_update_accessor_cong_from_eq};

 (** name components **)

 val rN = "r";

 val wN = "w";

 val moreN = "more";

 val schemeN = "_scheme";

 val ext_typeN = "_ext";

 val inner_typeN = "_inner";

 val extN ="_ext";

 val updateN = "_update";

 val makeN = "make";

 val fields_selN = "fields";

 val extendN = "extend";

 val truncateN = "truncate";

 (*** utilities ***)

 fun varifyT idx = map_type_tfree (fn (a, S) => TVar ((a, idx), S));

 (* timing *)

 val timing = Attrib.setup_config_bool @{binding record_timing} (K false);

 fun timeit_msg ctxt s x = if Config.get ctxt timing then (warning s; timeit x) else x ();

 fun timing_msg ctxt s = if Config.get ctxt timing then warning s else ();

 (* syntax *)

 val Trueprop = HOLogic.mk_Trueprop;

 infix 0 :== ===;

 infixr 0 ==>;

 val op :== = Misc_Legacy.mk_defpair;

 val op === = Trueprop o HOLogic.mk_eq;

 val op ==> = Logic.mk_implies;

 (* constructor *)

 fun mk_ext (name, T) ts =

   let val Ts = map fastype_of ts

   in list_comb (Const (suffix extN name, Ts ---> T), ts) 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 (_ :: _))) =

       (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], []);

 val is_recT = can dest_recT;

 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 take i rTs;

   in implode (map #1 rTs') end;

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

 (** record info **)

 (* type info and parent_info *)

 type info =

  {args: (string * sort) list,

   parent: (typ list * string) option,

   fields: (string * typ) list,

   extension: (string * typ list),

   ext_induct: thm,

   ext_inject: thm,

   ext_surjective: thm,

   ext_split: thm,

   ext_def: thm,

   select_convs: thm list,

   update_convs: thm list,

   select_defs: thm list,

   update_defs: thm list,

   fold_congs: thm list,  (* FIXME unused!? *)

   unfold_congs: thm list,  (* FIXME unused!? *)

   splits: thm list,

   defs: thm list,

   surjective: thm,

   equality: thm,

   induct_scheme: thm,

   induct: thm,

   cases_scheme: thm,

   cases: thm,

   simps: thm list,

   iffs: thm list};

 fun make_info args parent fields extension

     ext_induct ext_inject ext_surjective ext_split ext_def

     select_convs update_convs select_defs update_defs fold_congs unfold_congs splits defs

     surjective equality induct_scheme induct cases_scheme cases

     simps iffs : info =

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

   ext_induct = ext_induct, ext_inject = ext_inject, ext_surjective = ext_surjective,

   ext_split = ext_split, ext_def = ext_def, select_convs = select_convs,

   update_convs = update_convs, select_defs = select_defs, update_defs = update_defs,

   fold_congs = fold_congs, unfold_congs = unfold_congs, splits = splits, defs = defs,

   surjective = surjective, equality = equality, induct_scheme = induct_scheme,

   induct = induct, cases_scheme = cases_scheme, cases = cases, simps = simps, iffs = iffs};

 type parent_info =

  {name: string,

   fields: (string * typ) list,

   extension: (string * typ list),

   induct_scheme: thm,

   ext_def: thm};

 fun make_parent_info name fields extension ext_def induct_scheme : parent_info =

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

   ext_def = ext_def, induct_scheme = induct_scheme};

 (* theory data *)

 type data =

  {records: info Symtab.table,

   sel_upd:

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

     updates: string Symtab.table,

     simpset: simpset,

     defset: 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,  (*!!, ALL, 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_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 }: data;

 structure Data = Theory_Data

 (

   type T = data;

   val empty =

     make_data Symtab.empty

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

         simpset = HOL_basic_ss, defset = HOL_basic_ss}

        Symtab.empty [] Symtab.empty Symtab.empty Symtab.empty Symtab.empty;

   val extend = I;

   fun merge

    ({records = recs1,

      sel_upd = {selectors = sels1, updates = upds1, simpset = ss1, defset = ds1},

      equalities = equalities1,

      extinjects = extinjects1,

      extsplit = extsplit1,

      splits = splits1,

      extfields = extfields1,

      fieldext = fieldext1},

     {records = recs2,

      sel_upd = {selectors = sels2, updates = upds2, simpset = ss2, defset = ds2},

      equalities = equalities2,

      extinjects = extinjects2,

      extsplit = extsplit2,

      splits = splits2,

      extfields = extfields2,

      fieldext = fieldext2}) =

     make_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)}

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

       (Thm.merge_thms (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));

 );

 (* access 'records' *)

 val get_info = Symtab.lookup o #records o Data.get;

 fun the_info thy name =

   (case get_info thy name of

     SOME info => info

   | NONE => error ("Unknown record type " ^ quote name));

 fun put_record name info =

   Data.map (fn {records, sel_upd, equalities, extinjects, extsplit, splits, extfields, fieldext} =>

     make_data (Symtab.update (name, info) records)

       sel_upd equalities extinjects extsplit splits extfields fieldext);

 (* access 'sel_upd' *)

 val get_sel_upd = #sel_upd o Data.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.global_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;

 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 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},

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

     val data =

       make_data records

         {selectors = fold Symtab.update_new sels selectors,

           updates = fold Symtab.update_new upds updates,

           simpset = simpset addsimps simps,

           defset = defset addsimps defs}

          equalities extinjects extsplit splits extfields fieldext;

   in Data.put data thy end;

 (* access 'equalities' *)

 fun add_equalities name thm =

   Data.map (fn {records, sel_upd, equalities, extinjects, extsplit, splits, extfields, fieldext} =>

     make_data records sel_upd

       (Symtab.update_new (name, thm) equalities) extinjects extsplit splits extfields fieldext);

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

 (* access 'extinjects' *)

 fun add_extinjects thm =

   Data.map (fn {records, sel_upd, equalities, extinjects, extsplit, splits, extfields, fieldext} =>

     make_data records sel_upd equalities (insert Thm.eq_thm_prop thm extinjects)

       extsplit splits extfields fieldext);

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

 (* access 'extsplit' *)

 fun add_extsplit name thm =

   Data.map (fn {records, sel_upd, equalities, extinjects, extsplit, splits, extfields, fieldext} =>

     make_data records sel_upd equalities extinjects

       (Symtab.update_new (name, thm) extsplit) splits extfields fieldext);

 (* access 'splits' *)

 fun add_splits name thmP =

   Data.map (fn {records, sel_upd, equalities, extinjects, extsplit, splits, extfields, fieldext} =>

     make_data records sel_upd equalities extinjects extsplit

       (Symtab.update_new (name, thmP) splits) extfields fieldext);

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

 (* parent/extension of named record *)

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

 val get_extension = Option.map #extension oo (Symtab.lookup o #records o Data.get);

 (* access 'extfields' *)

 fun add_extfields name fields =

   Data.map (fn {records, sel_upd, equalities, extinjects, extsplit, splits, extfields, fieldext} =>

     make_data records sel_upd equalities extinjects extsplit splits

       (Symtab.update_new (name, fields) extfields) fieldext);

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

 fun get_extT_fields thy T =

   let

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

     val recname =

       let val (nm :: _ :: rst) = rev (Long_Name.explode name)   (* FIXME !? *)

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

     val varifyT = varifyT (maxidx_of_typs (moreT :: Ts) + 1);

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

     val (fields, (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) (#1 (split_last args) ~~ #1 (split_last Ts)) Vartab.empty;

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

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

 fun get_recT_fields thy T =

   let

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

     val (rest_fields, rest_more) =

       if is_recT root_moreT then get_recT_fields thy root_moreT

       else ([], (root_more, root_moreT));

   in (root_fields @ rest_fields, rest_more) end;

 (* access 'fieldext' *)

 fun add_fieldext extname_types fields =

   Data.map (fn {records, sel_upd, equalities, extinjects, extsplit, splits, extfields, fieldext} =>

     let

       val fieldext' =

         fold (fn field => Symtab.update_new (field, extname_types)) fields fieldext;

     in make_data records sel_upd equalities extinjects extsplit splits extfields fieldext' end);

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

 (* parent records *)

 local

 fun add_parents _ NONE = I

   | add_parents thy (SOME (types, name)) =

       let

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

         val {args, parent, ...} =

           (case get_info 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 = map_filter bad_inst (args ~~ types);

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

         val inst = args ~~ types;

         val subst = Term.map_type_tfree (the o AList.lookup (op =) inst);

         val parent' = Option.map (apfst (map subst)) parent;

       in cons (name, inst) #> add_parents thy parent' end;

 in

 fun get_hierarchy thy (name, types) = add_parents thy (SOME (types, name)) [];

 fun get_parent_info thy parent =

   add_parents thy parent [] |> map (fn (name, inst) =>

     let

       val subst = Term.map_type_tfree (the o AList.lookup (op =) inst);

       val {fields, extension, induct_scheme, ext_def, ...} = the_info thy name;

       val fields' = map (apsnd subst) fields;

       val extension' = apsnd (map subst) extension;

     in make_parent_info name fields' extension' ext_def induct_scheme end);

 end;

 (** concrete syntax for records **)

 (* parse translations *)

 local

 fun split_args (field :: fields) ((name, arg) :: fargs) =

       if can (unsuffix name) field then

         let val (args, rest) = split_args fields fargs

         in (arg :: args, rest) end

       else raise Fail ("expecting field " ^ quote field ^ " but got " ^ quote name)

   | split_args [] (fargs as (_ :: _)) = ([], fargs)

   | split_args (_ :: _) [] = raise Fail "expecting more fields"

   | split_args _ _ = ([], []);

 fun field_type_tr ((Const (@{syntax_const "_field_type"}, _) $ Const (name, _) $ arg)) =

       (name, arg)

   | field_type_tr t = raise TERM ("field_type_tr", [t]);

 fun field_types_tr (Const (@{syntax_const "_field_types"}, _) $ t $ u) =

       field_type_tr t :: field_types_tr u

   | field_types_tr t = [field_type_tr t];

 fun record_field_types_tr more ctxt t =

   let

     val thy = Proof_Context.theory_of ctxt;

     fun err msg = raise TERM ("Error in record-type input: " ^ msg, [t]);

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

           (case get_fieldext thy (Proof_Context.intern_const ctxt name) of

             SOME (ext, alphas) =>

               (case get_extfields thy ext of

                 SOME fields =>

                   let

                     val (fields', _) = split_last fields;

                     val types = map snd fields';

                     val (args, rest) = split_args (map fst fields') fargs

                       handle Fail msg => err msg;

                     val argtypes = Syntax.check_typs ctxt (map Syntax_Phases.decode_typ args);

                     val varifyT = varifyT (fold Term.maxidx_typ argtypes ~1 + 1);

                     val vartypes = map varifyT types;

                     val subst = Type.raw_matches (vartypes, argtypes) Vartab.empty

                       handle Type.TYPE_MATCH => err "type is no proper record (extension)";

                     val alphas' =

                       map (Syntax_Phases.term_of_typ ctxt o Envir.norm_type subst o varifyT)

                         (#1 (split_last alphas));

                     val more' = mk_ext rest;

                   in

                     list_comb

                       (Syntax.const (Lexicon.mark_type (suffix ext_typeN ext)), alphas' @ [more'])

                   end

               | NONE => err ("no fields defined for " ^ quote ext))

           | NONE => err (quote name ^ " is no proper field"))

       | mk_ext [] = more;

   in

     mk_ext (field_types_tr t)

   end;

 fun record_type_tr ctxt [t] = record_field_types_tr (Syntax.const @{type_syntax unit}) ctxt t

   | record_type_tr _ ts = raise TERM ("record_type_tr", ts);

 fun record_type_scheme_tr ctxt [t, more] = record_field_types_tr more ctxt t

   | record_type_scheme_tr _ ts = raise TERM ("record_type_scheme_tr", ts);

 fun field_tr ((Const (@{syntax_const "_field"}, _) $ Const (name, _) $ arg)) = (name, arg)

   | field_tr t = raise TERM ("field_tr", [t]);

 fun fields_tr (Const (@{syntax_const "_fields"}, _) $ t $ u) = field_tr t :: fields_tr u

   | fields_tr t = [field_tr t];

 fun record_fields_tr more ctxt t =

   let

     val thy = Proof_Context.theory_of ctxt;

     fun err msg = raise TERM ("Error in record input: " ^ msg, [t]);

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

           (case get_fieldext thy (Proof_Context.intern_const ctxt name) of

             SOME (ext, _) =>

               (case get_extfields thy ext of

                 SOME fields =>

                   let

                     val (args, rest) = split_args (map fst (fst (split_last fields))) fargs

                       handle Fail msg => err msg;

                     val more' = mk_ext rest;

                   in list_comb (Syntax.const (Lexicon.mark_const (ext ^ extN)), args @ [more']) end

               | NONE => err ("no fields defined for " ^ quote ext))

           | NONE => err (quote name ^ " is no proper field"))

       | mk_ext [] = more;

   in mk_ext (fields_tr t) end;

 fun record_tr ctxt [t] = record_fields_tr (Syntax.const @{const_syntax Unity}) ctxt t

   | record_tr _ ts = raise TERM ("record_tr", ts);

 fun record_scheme_tr ctxt [t, more] = record_fields_tr more ctxt t

   | record_scheme_tr _ ts = raise TERM ("record_scheme_tr", ts);

 fun field_update_tr (Const (@{syntax_const "_field_update"}, _) $ Const (name, _) $ arg) =

       Syntax.const (suffix updateN name) $ Abs (Name.uu_, dummyT, arg)

   | field_update_tr t = raise TERM ("field_update_tr", [t]);

 fun field_updates_tr (Const (@{syntax_const "_field_updates"}, _) $ t $ u) =

       field_update_tr t :: field_updates_tr u

   | field_updates_tr t = [field_update_tr t];

 fun record_update_tr [t, u] = fold (curry op $) (field_updates_tr u) t

   | record_update_tr ts = raise TERM ("record_update_tr", ts);

 in

 val parse_translation =

  [(@{syntax_const "_record_update"}, record_update_tr)];

 val advanced_parse_translation =

  [(@{syntax_const "_record"}, record_tr),

   (@{syntax_const "_record_scheme"}, record_scheme_tr),

   (@{syntax_const "_record_type"}, record_type_tr),

   (@{syntax_const "_record_type_scheme"}, record_type_scheme_tr)];

 end;

 (* print translations *)

 val type_abbr = Attrib.setup_config_bool @{binding record_type_abbr} (K true);

 val type_as_fields = Attrib.setup_config_bool @{binding record_type_as_fields} (K true);

 local

 (* FIXME early extern (!??) *)

 (* FIXME Syntax.free (??) *)

 fun field_type_tr' (c, t) = Syntax.const @{syntax_const "_field_type"} $ Syntax.const c $ t;

 fun field_types_tr' (t, u) = Syntax.const @{syntax_const "_field_types"} $ t $ u;

 fun record_type_tr' ctxt t =

   let

     val thy = Proof_Context.theory_of ctxt;

     val T = Syntax_Phases.decode_typ t;

     val varifyT = varifyT (Term.maxidx_of_typ T + 1);

     fun strip_fields T =

       (case T of

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

           (case try (unsuffix ext_typeN) ext of

             SOME ext' =>

               (case get_extfields thy ext' of

                 SOME (fields as (x, _) :: _) =>

                   (case get_fieldext thy x of

                     SOME (_, alphas) =>

                      (let

                         val (f :: fs, _) = split_last fields;

                         val fields' =

                           apfst (Proof_Context.extern_const ctxt) f ::

                             map (apfst Long_Name.base_name) fs;

                         val (args', more) = split_last args;

                         val alphavars = map varifyT (#1 (split_last alphas));

                         val subst = Type.raw_matches (alphavars, args') Vartab.empty;

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

                       in fields'' @ strip_fields more end

                       handle Type.TYPE_MATCH => [("", T)])

                   | _ => [("", T)])

               | _ => [("", T)])

           | _ => [("", T)])

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

     val (fields, (_, moreT)) = split_last (strip_fields T);

     val _ = null fields andalso raise Match;

     val u =

       foldr1 field_types_tr'

         (map (field_type_tr' o apsnd (Syntax_Phases.term_of_typ ctxt)) fields);

   in

     if not (Config.get ctxt type_as_fields) orelse null fields then raise Match

     else if moreT = HOLogic.unitT then Syntax.const @{syntax_const "_record_type"} $ u

     else

       Syntax.const @{syntax_const "_record_type_scheme"} $ u $

         Syntax_Phases.term_of_typ ctxt moreT

   end;

 (*try to reconstruct the record name type abbreviation from

   the (nested) extension types*)

 fun record_type_abbr_tr' abbr alphas zeta last_ext schemeT ctxt tm =

   let

     val T = Syntax_Phases.decode_typ tm;

     val varifyT = varifyT (maxidx_of_typ T + 1);

     fun mk_type_abbr subst name args =

       let val abbrT = Type (name, map (varifyT o TFree) args)

       in Syntax_Phases.term_of_typ ctxt (Envir.norm_type subst abbrT) end;

     fun match rT T = Type.raw_match (varifyT rT, T) Vartab.empty;

   in

     if Config.get ctxt type_abbr then

       (case last_extT T of

         SOME (name, _) =>

           if name = last_ext then

             let val subst = match schemeT T in

               if HOLogic.is_unitT (Envir.norm_type subst (varifyT (TFree zeta)))

               then mk_type_abbr subst abbr alphas

               else mk_type_abbr subst (suffix schemeN abbr) (alphas @ [zeta])

             end handle Type.TYPE_MATCH => record_type_tr' ctxt tm

           else raise Match (*give print translation of specialised record a chance*)

       | _ => raise Match)

     else record_type_tr' ctxt tm

   end;

 in

 fun record_ext_type_tr' name =

   let

     val ext_type_name = Lexicon.mark_type (suffix ext_typeN name);

     fun tr' ctxt ts =

       record_type_tr' ctxt (list_comb (Syntax.const ext_type_name, ts));

   in (ext_type_name, tr') end;

 fun record_ext_type_abbr_tr' abbr alphas zeta last_ext schemeT name =

   let

     val ext_type_name = Lexicon.mark_type (suffix ext_typeN name);

     fun tr' ctxt ts =

       record_type_abbr_tr' abbr alphas zeta last_ext schemeT ctxt

         (list_comb (Syntax.const ext_type_name, ts));

   in (ext_type_name, tr') end;

 end;

 local

 (* FIXME Syntax.free (??) *)

 fun field_tr' (c, t) = Syntax.const @{syntax_const "_field"} $ Syntax.const c $ t;

 fun fields_tr' (t, u) = Syntax.const @{syntax_const "_fields"} $ t $ u;

 fun record_tr' ctxt t =

   let

     val thy = Proof_Context.theory_of ctxt;

     fun strip_fields t =

       (case strip_comb t of

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

           (case try (Lexicon.unmark_const o unsuffix extN) ext of

             SOME ext' =>

               (case get_extfields thy ext' of

                 SOME fields =>

                  (let

                     val (f :: fs, _) = split_last (map fst fields);

                     val fields' = Proof_Context.extern_const ctxt f :: map Long_Name.base_name fs;

                     val (args', more) = split_last args;

                   in (fields' ~~ args') @ strip_fields more end

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

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

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

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

     val (fields, (_, more)) = split_last (strip_fields t);

     val _ = null fields andalso raise Match;

     val u = foldr1 fields_tr' (map field_tr' fields);

   in

     (case more of

       Const (@{const_syntax Unity}, _) => Syntax.const @{syntax_const "_record"} $ u

     | _ => Syntax.const @{syntax_const "_record_scheme"} $ u $ more)

   end;

 in

 fun record_ext_tr' name =

   let

     val ext_name = Lexicon.mark_const (name ^ extN);

     fun tr' ctxt ts = record_tr' ctxt (list_comb (Syntax.const ext_name, ts));

   in (ext_name, tr') end;

 end;

 local

 fun dest_update ctxt c =

   (case try Lexicon.unmark_const c of

     SOME d => try (unsuffix updateN) (Proof_Context.extern_const ctxt d)

   | NONE => NONE);

 fun field_updates_tr' ctxt (tm as Const (c, _) $ k $ u) =

       (case dest_update ctxt c of

         SOME name =>

           (case try Syntax_Trans.const_abs_tr' k of

             SOME t =>

               apfst (cons (Syntax.const @{syntax_const "_field_update"} $ Syntax.free name $ t))

                 (field_updates_tr' ctxt u)

           | NONE => ([], tm))

       | NONE => ([], tm))

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

 fun record_update_tr' ctxt tm =

   (case field_updates_tr' ctxt tm of

     ([], _) => raise Match

   | (ts, u) =>

       Syntax.const @{syntax_const "_record_update"} $ u $

         foldr1 (fn (v, w) => Syntax.const @{syntax_const "_field_updates"} $ v $ w) (rev ts));

 in

 fun field_update_tr' name =

   let

     val update_name = Lexicon.mark_const (name ^ updateN);

     fun tr' ctxt [t, u] = record_update_tr' ctxt (Syntax.const update_name $ t $ u)

       | tr' _ _ = raise Match;

   in (update_name, tr') end;

 end;

 (** record simprocs **)

 fun is_sel_upd_pair thy (Const (s, _)) (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_id f =

   let val T = range_type (fastype_of f)

   in HOLogic.mk_comp (Const (@{const_name 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 =

   let

     val (acc, [body]) = strip_comb term;

     val upd_funs = sort_distinct Term_Ord.fast_term_ord (get_upd_funs body);

     fun get_simp upd =

       let

         (* FIXME fresh "f" (!?) *)

         val T = domain_type (fastype_of upd);

         val lhs = HOLogic.mk_comp (acc, upd $ Free ("f", T));

         val rhs =

           if is_sel_upd_pair thy acc upd

           then HOLogic.mk_comp (Free ("f", T), acc)

           else mk_comp_id acc;

         val prop = lhs === rhs;

         val othm =

           Goal.prove (Proof_Context.init_global thy) [] [] prop

             (fn _ =>

               simp_tac defset 1 THEN

               REPEAT_DETERM (Iso_Tuple_Support.iso_tuple_intros_tac 1) THEN

               TRY (simp_tac (HOL_ss addsimps @{thms id_apply id_o o_id}) 1));

         val dest =

           if is_sel_upd_pair thy acc upd

           then @{thm o_eq_dest}

           else @{thm o_eq_id_dest};

       in Drule.export_without_context (othm RS dest) end;

   in map get_simp upd_funs end;

 fun get_updupd_simp thy defset u u' comp =

   let

     (* FIXME fresh "f" (!?) *)

     val f = Free ("f", domain_type (fastype_of u));

     val f' = Free ("f'", domain_type (fastype_of u'));

     val lhs = HOLogic.mk_comp (u $ f, u' $ f');

     val rhs =

       if comp

       then u $ HOLogic.mk_comp (f, f')

       else HOLogic.mk_comp (u' $ f', u $ f);

     val prop = lhs === rhs;

     val othm =

       Goal.prove (Proof_Context.init_global thy) [] [] prop

         (fn _ =>

           simp_tac defset 1 THEN

           REPEAT_DETERM (Iso_Tuple_Support.iso_tuple_intros_tac 1) THEN

           TRY (simp_tac (HOL_ss addsimps @{thms id_apply}) 1));

     val dest = if comp then @{thm o_eq_dest_lhs} else @{thm o_eq_dest};

   in Drule.export_without_context (othm RS dest) end;

 fun get_updupd_simps thy term defset =

   let

     val upd_funs = get_upd_funs term;

     val cname = fst o dest_Const;

     fun getswap u u' = get_updupd_simp thy defset u u' (cname u = cname u');

     fun build_swaps_to_eq _ [] swaps = swaps

       | build_swaps_to_eq upd (u :: us) swaps =

           let

             val key = (cname u, cname upd);

             val newswaps =

               if Symreltab.defined swaps key then swaps

               else Symreltab.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 [] _ _ swaps = map snd (Symreltab.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 Symreltab.empty end;

 val named_cterm_instantiate = Iso_Tuple_Support.named_cterm_instantiate;

 fun prove_unfold_defs thy ex_simps ex_simprs prop =

   let

     val defset = get_sel_upd_defs thy;

     val prop' = Envir.beta_eta_contract prop;

     val (lhs, _) = Logic.dest_equals (Logic.strip_assums_concl prop');

     val (_, args) = strip_comb lhs;

     val simps = (if length args = 1 then get_accupd_simps else get_updupd_simps) thy lhs defset;

   in

     Goal.prove (Proof_Context.init_global thy) [] [] prop'

       (fn _ =>

         simp_tac (HOL_basic_ss addsimps (simps @ @{thms K_record_comp})) 1 THEN

         TRY (simp_tac (HOL_basic_ss addsimps ex_simps addsimprocs ex_simprs) 1))

   end;

 local

 fun eq (s1: string) (s2: string) = (s1 = s2);

 fun has_field extfields f T =

   exists (fn (eN, _) => exists (eq f o fst) (Symtab.lookup_list extfields eN)) (dest_recTs T);

 fun K_skeleton n (T as Type (_, [_, kT])) (b as Bound i) (Abs (x, xT, t)) =

       if null (loose_bnos t) then ((n, kT), (Abs (x, xT, Bound (i + 1)))) else ((n, T), b)

   | K_skeleton n T b _ = ((n, T), b);

 in

 (* simproc *)

 (*

   Simplify selections of an record update:

     (1)  S (S_update k r) = k (S r)

     (2)  S (X_update k r) = S r

   The simproc skips multiple updates at once, eg:

    S (X_update x (Y_update y (S_update k r))) = k (S r)

   But be careful in (2) because of the extensibility of records.

   - If S is a more-selector we have to make sure that the update on component

     X does not affect the selected subrecord.

   - If X is a more-selector we have to make sure that S is not in the updated

     subrecord.

 *)

 val simproc =

   Simplifier.simproc_global @{theory HOL} "record_simp" ["x"]

     (fn thy => fn _ => fn t =>

       (case t of

         (sel as Const (s, Type (_, [_, rangeS]))) $

             ((upd as Const (u, Type (_, [_, Type (_, [rT, _])]))) $ k $ r) =>

           if is_selector thy s andalso is_some (get_updates thy u) then

             let

               val {sel_upd = {updates, ...}, extfields, ...} = Data.get thy;

               fun mk_eq_terms ((upd as Const (u, Type(_, [kT, _]))) $ k $ r) =

                     (case Symtab.lookup updates u of

                       NONE => NONE

                     | SOME u_name =>

                         if u_name = s then

                           (case mk_eq_terms r of

                             NONE =>

                               let

                                 val rv = ("r", rT);

                                 val rb = Bound 0;

                                 val (kv, kb) = K_skeleton "k" kT (Bound 1) k;

                               in SOME (upd $ kb $ rb, kb $ (sel $ rb), [kv, rv]) end

                           | SOME (trm, trm', vars) =>

                               let

                                 val (kv, kb) = K_skeleton "k" kT (Bound (length vars)) k;

                               in SOME (upd $ kb $ trm, kb $ trm', kv :: vars) end)

                         else if has_field extfields u_name rangeS orelse

                           has_field extfields s (domain_type kT) then NONE

                         else

                           (case mk_eq_terms r of

                             SOME (trm, trm', vars) =>

                               let val (kv, kb) = K_skeleton "k" kT (Bound (length vars)) k

                               in SOME (upd $ kb $ trm, trm', kv :: vars) end

                           | NONE =>

                               let

                                 val rv = ("r", rT);

                                 val rb = Bound 0;

                                 val (kv, kb) = K_skeleton "k" kT (Bound 1) k;

                               in SOME (upd $ kb $ rb, sel $ rb, [kv, rv]) end))

                 | mk_eq_terms _ = NONE;

             in

               (case mk_eq_terms (upd $ k $ r) of

                 SOME (trm, trm', vars) =>

                   SOME

                     (prove_unfold_defs thy [] []

                       (Logic.list_all (vars, Logic.mk_equals (sel $ trm, trm'))))

               | NONE => NONE)

             end

           else NONE

       | _ => NONE));

 fun get_upd_acc_cong_thm upd acc thy simpset =

   let

     val insts = [("upd", cterm_of thy upd), ("ac", cterm_of thy acc)];

     val prop = Thm.concl_of (named_cterm_instantiate insts updacc_cong_triv);

   in

     Goal.prove (Proof_Context.init_global thy) [] [] prop

       (fn _ =>

         simp_tac simpset 1 THEN

         REPEAT_DETERM (Iso_Tuple_Support.iso_tuple_intros_tac 1) THEN

         TRY (resolve_tac [updacc_cong_idI] 1))

   end;

 (* upd_simproc *)

 (*Simplify multiple updates:

     (1) "N_update y (M_update g (N_update x (M_update f r))) =

           (N_update (y o x) (M_update (g o f) r))"

     (2)  "r(|M:= M r|) = r"

   In both cases "more" updates complicate matters: for this reason

   we omit considering further updates if doing so would introduce

   both a more update and an update to a field within it.*)

 val upd_simproc =

   Simplifier.simproc_global @{theory HOL} "record_upd_simp" ["x"]

     (fn thy => fn _ => fn t =>

       let

         (*We can use more-updators with other updators as long

           as none of the other updators go deeper than any more

           updator. min here is the depth of the deepest other

           updator, max the depth of the shallowest more updator.*)

         fun include_depth (dep, true) (min, max) =

               if min <= dep

               then SOME (min, if dep <= max orelse max = ~1 then dep else max)

               else NONE

           | include_depth (dep, false) (min, max) =

               if dep <= max orelse max = ~1

               then SOME (if min <= dep then dep else min, max)

               else NONE;

         fun getupdseq (term as (upd as Const (u, _)) $ f $ tm) min max =

               (case get_update_details u thy of

                 SOME (s, dep, ismore) =>

                   (case include_depth (dep, ismore) (min, max) of

                     SOME (min', max') =>

                       let val (us, bs, _) = getupdseq tm min' max'

                       in ((upd, s, f) :: us, bs, fastype_of term) end

                   | NONE => ([], term, HOLogic.unitT))

               | NONE => ([], term, HOLogic.unitT))

           | getupdseq term _ _ = ([], term, HOLogic.unitT);

         val (upds, base, baseT) = getupdseq t 0 ~1;

         fun is_upd_noop s (Abs (n, T, Const (s', T') $ tm')) tm =

               if s = s' andalso null (loose_bnos tm')

                 andalso subst_bound (HOLogic.unit, tm') = tm

               then (true, Abs (n, T, Const (s', T') $ Bound 1))

               else (false, HOLogic.unit)

           | is_upd_noop _ _ _ = (false, HOLogic.unit);

         fun get_noop_simps (upd as Const _) (Abs (_, _, (acc as Const _) $ _)) =

           let

             val ss = get_sel_upd_defs thy;

             val uathm = get_upd_acc_cong_thm upd acc thy ss;

           in

            [Drule.export_without_context (uathm RS updacc_noopE),

             Drule.export_without_context (uathm RS updacc_noop_compE)]

           end;

         (*If f is constant then (f o g) = f.  We know that K_skeleton

           only returns constant abstractions thus when we see an

           abstraction we can discard inner updates.*)

         fun add_upd (f as Abs _) fs = [f]

           | add_upd f fs = (f :: fs);

         (*mk_updterm returns

           (orig-term-skeleton, simplified-skeleton,

             variables, duplicate-updates, simp-flag, noop-simps)

           where duplicate-updates is a table used to pass upward

           the list of update functions which can be composed

           into an update above them, simp-flag indicates whether

           any simplification was achieved, and noop-simps are

           used for eliminating case (2) defined above*)

         fun mk_updterm ((upd as Const (u, T), s, f) :: upds) above term =

               let

                 val (lhs, rhs, vars, dups, simp, noops) =

                   mk_updterm upds (Symtab.update (u, ()) above) term;

                 val (fvar, skelf) =

                   K_skeleton (Long_Name.base_name s) (domain_type T) (Bound (length vars)) f;

                 val (isnoop, skelf') = is_upd_noop s f term;

                 val funT = domain_type T;

                 fun mk_comp_local (f, f') =

                   Const (@{const_name Fun.comp}, funT --> funT --> funT) $ f $ f';

               in

                 if isnoop then

                   (upd $ skelf' $ lhs, rhs, vars,

                     Symtab.update (u, []) dups, true,

                     if Symtab.defined noops u then noops

                     else Symtab.update (u, get_noop_simps upd skelf') noops)

                 else if Symtab.defined above u then

                   (upd $ skelf $ lhs, rhs, fvar :: vars,

                     Symtab.map_default (u, []) (add_upd skelf) dups,

                     true, noops)

                 else

                   (case Symtab.lookup dups u of

                     SOME fs =>

                      (upd $ skelf $ lhs,

                       upd $ foldr1 mk_comp_local (add_upd skelf fs) $ rhs,

                       fvar :: vars, dups, true, noops)

                   | NONE => (upd $ skelf $ lhs, upd $ skelf $ rhs, fvar :: vars, dups, simp, noops))

               end

           | mk_updterm [] _ _ =

               (Bound 0, Bound 0, [("r", baseT)], Symtab.empty, false, Symtab.empty)

           | mk_updterm us _ _ = raise TERM ("mk_updterm match", map (fn (x, _, _) => x) us);

         val (lhs, rhs, vars, _, simp, noops) = mk_updterm upds Symtab.empty base;

         val noops' = maps snd (Symtab.dest noops);

       in

         if simp then

           SOME

             (prove_unfold_defs thy noops' [simproc]

               (Logic.list_all (vars, Logic.mk_equals (lhs, rhs))))

         else NONE

       end);

 end;

 (* eq_simproc *)

 (*Look up the most specific record-equality.

  Note on efficiency:

  Testing equality of records boils down to the test of equality of all components.

  Therefore the complexity is: #components * complexity for single component.

  Especially if a record has a lot of components it may be better to split up

  the record first and do simplification on that (split_simp_tac).

  e.g. r(|lots of updates|) = x

              eq_simproc          split_simp_tac

  Complexity: #components * #updates     #updates

 *)

 val eq_simproc =

   Simplifier.simproc_global @{theory HOL} "record_eq_simp" ["r = s"]

     (fn thy => fn _ => fn t =>

       (case t of Const (@{const_name HOL.eq}, Type (_, [T, _])) $ _ $ _ =>

         (case rec_id ~1 T of

           "" => NONE

         | name =>

             (case get_equalities thy name of

               NONE => NONE

             | SOME thm => SOME (thm RS @{thm Eq_TrueI})))

       | _ => NONE));

 (* split_simproc *)

 (*Split quantified occurrences of records, for which P holds.  P can peek on the

   subterm starting at the quantified occurrence of the record (including the quantifier):

     P t = 0: do not split

     P t = ~1: completely split

     P t > 0: split up to given bound of record extensions.*)

 fun split_simproc P =

   Simplifier.simproc_global @{theory HOL} "record_split_simp" ["x"]

     (fn thy => fn _ => fn t =>

       (case t of

         Const (quantifier, Type (_, [Type (_, [T, _]), _])) $ _ =>

           if quantifier = @{const_name all} orelse

             quantifier = @{const_name All} orelse

             quantifier = @{const_name Ex}

           then

             (case rec_id ~1 T of

               "" => NONE

             | _ =>

                 let val split = P t in

                   if split <> 0 then

                     (case get_splits thy (rec_id split T) of

                       NONE => NONE

                     | SOME (all_thm, All_thm, Ex_thm, _) =>

                         SOME

                           (case quantifier of

                             @{const_name all} => all_thm

                           | @{const_name All} => All_thm RS @{thm eq_reflection}

                           | @{const_name Ex} => Ex_thm RS @{thm eq_reflection}

                           | _ => raise Fail "split_simproc"))

                   else NONE

                 end)

           else NONE

       | _ => NONE));

 val ex_sel_eq_simproc =

   Simplifier.simproc_global @{theory HOL} "ex_sel_eq_simproc" ["Ex t"]

     (fn thy => fn ss => fn t =>

       let

         fun mkeq (lr, Teq, (sel, Tsel), x) i =

           if is_selector thy sel then

             let

               val x' =

                 if not (loose_bvar1 (x, 0))

                 then Free ("x" ^ string_of_int i, range_type Tsel)

                 else raise TERM ("", [x]);

               val sel' = Const (sel, Tsel) $ Bound 0;

               val (l, r) = if lr then (sel', x') else (x', sel');

             in Const (@{const_name HOL.eq}, Teq) $ l $ r end

           else raise TERM ("", [Const (sel, Tsel)]);

         fun dest_sel_eq (Const (@{const_name HOL.eq}, Teq) $ (Const (sel, Tsel) $ Bound 0) $ X) =

               (true, Teq, (sel, Tsel), X)

           | dest_sel_eq (Const (@{const_name HOL.eq}, Teq) $ X $ (Const (sel, Tsel) $ Bound 0)) =

               (false, Teq, (sel, Tsel), X)

           | dest_sel_eq _ = raise TERM ("", []);

       in

         (case t of

           Const (@{const_name Ex}, Tex) $ Abs (s, T, t) =>

            (let

              val eq = mkeq (dest_sel_eq t) 0;

              val prop =

                Logic.list_all ([("r", T)],

                  Logic.mk_equals

                   (Const (@{const_name Ex}, Tex) $ Abs (s, T, eq), @{term True}));

             in

               SOME (Skip_Proof.prove_global thy [] [] prop

                 (fn _ => simp_tac (Simplifier.inherit_context ss (get_simpset thy)

                     addsimps @{thms simp_thms} addsimprocs [split_simproc (K ~1)]) 1))

             end handle TERM _ => NONE)

         | _ => NONE)

       end);

 (* split_simp_tac *)

 (*Split (and simplify) all records in the goal for which P holds.

   For quantified occurrences of a record

   P can peek on the whole subterm (including the quantifier); for free variables P

   can only peek on the variable itself.

   P t = 0: do not split

   P t = ~1: completely split

   P t > 0: split up to given bound of record extensions.*)

 fun split_simp_tac thms P = CSUBGOAL (fn (cgoal, i) =>

   let

     val thy = Thm.theory_of_cterm cgoal;

     val goal = term_of cgoal;

     val frees = filter (is_recT o #2) (Term.add_frees goal []);

     val has_rec = exists_Const

       (fn (s, Type (_, [Type (_, [T, _]), _])) =>

           (s = @{const_name all} orelse s = @{const_name All} orelse s = @{const_name Ex}) andalso

           is_recT T

         | _ => false);

     fun mk_split_free_tac free induct_thm i =

       let

         val cfree = cterm_of thy free;

         val _$ (_ $ r) = concl_of induct_thm;

         val crec = cterm_of thy r;

         val thm = cterm_instantiate [(crec, cfree)] induct_thm;

       in

         simp_tac (HOL_basic_ss addsimps @{thms induct_atomize}) i THEN

         rtac thm i THEN

         simp_tac (HOL_basic_ss addsimps @{thms induct_rulify}) i

       end;

     val split_frees_tacs =

       frees |> map_filter (fn (x, T) =>

         (case rec_id ~1 T of

           "" => NONE

         | _ =>

             let

               val free = Free (x, T);

               val split = P free;

             in

               if split <> 0 then

                 (case get_splits thy (rec_id split T) of

                   NONE => NONE

                 | SOME (_, _, _, induct_thm) =>

                     SOME (mk_split_free_tac free induct_thm i))

               else NONE

             end));

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

     val thms' = @{thms o_apply K_record_comp} @ thms;

   in

     EVERY split_frees_tacs THEN

     full_simp_tac (get_simpset thy addsimps thms' addsimprocs simprocs) i

   end);

 (* split_tac *)

 (*Split all records in the goal, which are quantified by !! or ALL.*)

 val split_tac = CSUBGOAL (fn (cgoal, i) =>

   let

     val goal = term_of cgoal;

     val has_rec = exists_Const

       (fn (s, Type (_, [Type (_, [T, _]), _])) =>

           (s = @{const_name all} orelse s = @{const_name All}) andalso is_recT T

         | _ => false);

     fun is_all (Const (@{const_name all}, _) $ _) = ~1

       | is_all (Const (@{const_name All}, _) $ _) = ~1

       | is_all _ = 0;

   in

     if has_rec goal then

       full_simp_tac (HOL_basic_ss addsimprocs [split_simproc is_all]) i

     else no_tac

   end);

 (* wrapper *)

 val split_name = "record_split_tac";

 val split_wrapper = (split_name, fn _ => fn tac => split_tac ORELSE' tac);

 (** theory extender interface **)

 (* attributes *)

 fun case_names_fields x = Rule_Cases.case_names ["fields"] x;

 fun induct_type_global name = [case_names_fields, Induct.induct_type name];

 fun cases_type_global name = [case_names_fields, Induct.cases_type name];

 (* tactics *)

 (*Do case analysis / induction according to rule on last parameter of ith subgoal

   (or on s if there are no parameters).

   Instatiation of record variable (and predicate) in rule is calculated to

   avoid problems with higher order unification.*)

 fun try_param_tac s rule = CSUBGOAL (fn (cgoal, i) =>

   let

     val cert = Thm.cterm_of (Thm.theory_of_cterm cgoal);

     val g = Thm.term_of cgoal;

     val params = Logic.strip_params g;

     val concl = HOLogic.dest_Trueprop (Logic.strip_assums_concl g);

     val rule' = Thm.lift_rule cgoal rule;

     val (P, ys) = strip_comb (HOLogic.dest_Trueprop (Logic.strip_assums_concl (prop_of rule')));

     (*ca indicates if rule is a case analysis or induction rule*)

     val (x, ca) =

       (case rev (drop (length params) ys) of

         [] => (head_of (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop

           (hd (rev (Logic.strip_assums_hyp (hd (prems_of rule')))))))), true)

       | [x] => (head_of x, false));

     val rule'' =

       cterm_instantiate

         (map (pairself cert)

           (case rev params of

             [] =>

               (case AList.lookup (op =) (Term.add_frees g []) s of

                 NONE => 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, fold_rev Term.abs params (if ca then concl else incr_boundvars 1 (Abs (s, T, concl)))),

                 (x, fold_rev Term.abs params (Bound 0))])) rule';

   in compose_tac (false, rule'', nprems_of rule) i end);

 fun extension_definition name fields alphas zeta moreT more vars thy =

   let

     val ctxt = Proof_Context.init_global thy;

     val base_name = Long_Name.base_name name;

     val fieldTs = map snd fields;

     val fields_moreTs = fieldTs @ [moreT];

     val alphas_zeta = alphas @ [zeta];

     val ext_binding = Binding.name (suffix extN base_name);

     val ext_name = suffix extN name;

     val ext_tyco = suffix ext_typeN name

     val extT = Type (ext_tyco, map TFree alphas_zeta);

     val ext_type = fields_moreTs ---> extT;

     (* the tree of new types that will back the record extension *)

     val mktreeV = Balanced_Tree.make Iso_Tuple_Support.mk_cons_tuple;

     fun mk_iso_tuple (left, right) (thy, i) =

       let

         val suff = if i = 0 then ext_typeN else inner_typeN ^ string_of_int i;

         val ((_, cons), thy') = thy

           |> Iso_Tuple_Support.add_iso_tuple_type

             (Binding.suffix_name suff (Binding.name base_name), alphas_zeta)

               (fastype_of left, fastype_of right);

       in

         (cons $ left $ right, (thy', i + 1))

       end;

     (*trying to create a 1-element iso_tuple will fail, and is pointless anyway*)

     fun mk_even_iso_tuple [arg] = pair arg

       | mk_even_iso_tuple args = mk_iso_tuple (Iso_Tuple_Support.dest_cons_tuple (mktreeV args));

     fun build_meta_tree_type i thy vars more =

       let val len = length vars in

         if len < 1 then raise TYPE ("meta_tree_type args too short", [], vars)

         else if len > 16 then

           let

             fun group16 [] = []

               | group16 xs = take 16 xs :: group16 (drop 16 xs);

             val vars' = group16 vars;

             val (composites, (thy', i')) = fold_map mk_even_iso_tuple vars' (thy, i);

           in

             build_meta_tree_type i' thy' composites more

           end

         else

           let val (term, (thy', _)) = mk_iso_tuple (mktreeV vars, more) (thy, 0)

           in (term, thy') end

       end;

     val _ = timing_msg ctxt "record extension preparing definitions";

     (* 1st stage part 1: introduce the tree of new types *)

     val (ext_body, typ_thy) = timeit_msg ctxt "record extension nested type def:" (fn () =>

       build_meta_tree_type 1 thy vars more);

     (* prepare declarations and definitions *)

     (* 1st stage part 2: define the ext constant *)

     fun mk_ext args = list_comb (Const (ext_name, ext_type), args);

     val ext_spec = Logic.mk_equals (mk_ext (vars @ [more]), ext_body);

     val ([ext_def], defs_thy) = timeit_msg ctxt "record extension constructor def:" (fn () =>

       typ_thy

       |> Sign.declare_const_global ((ext_binding, ext_type), NoSyn) |> snd

       |> Global_Theory.add_defs false [((Thm.def_binding ext_binding, ext_spec), [])]

       ||> Theory.checkpoint);

     (* prepare propositions *)

     val _ = timing_msg ctxt "record extension preparing propositions";

     val vars_more = vars @ [more];

     val variants = map (fn Free (x, _) => x) vars_more;

     val ext = mk_ext vars_more;

     val s = Free (rN, extT);

     val P = Free (singleton (Name.variant_list variants) "P", extT --> HOLogic.boolT);

     val inject_prop =  (* FIXME local x x' *)

       let val vars_more' = map (fn (Free (x, T)) => Free (x ^ "'", T)) vars_more in

         HOLogic.mk_conj (HOLogic.eq_const extT $

           mk_ext vars_more $ mk_ext vars_more', @{term True})

         ===

         foldr1 HOLogic.mk_conj

           (map HOLogic.mk_eq (vars_more ~~ vars_more') @ [@{term True}])

       end;

     val induct_prop = (fold_rev Logic.all vars_more (Trueprop (P $ ext)), Trueprop (P $ s));

     val split_meta_prop =  (* FIXME local P *)

       let val P = Free (singleton (Name.variant_list variants) "P", extT --> propT)

       in Logic.mk_equals (Logic.all s (P $ s), fold_rev Logic.all vars_more (P $ ext)) end;

     val inject = timeit_msg ctxt "record extension inject proof:" (fn () =>

       simplify HOL_ss

         (Skip_Proof.prove_global defs_thy [] [] inject_prop

           (fn _ =>

             simp_tac (HOL_basic_ss addsimps [ext_def]) 1 THEN

             REPEAT_DETERM

               (rtac @{thm refl_conj_eq} 1 ORELSE

                 Iso_Tuple_Support.iso_tuple_intros_tac 1 ORELSE

                 rtac refl 1))));

     (*We need a surjection property r = (| f = f r, g = g r ... |)

       to prove other theorems. We haven't given names to the accessors

       f, g etc yet however, so we generate an ext structure with

       free variables as all arguments and allow the introduction tactic to

       operate on it as far as it can. We then use Drule.export_without_context

       to convert the free variables into unifiable variables and unify them with

       (roughly) the definition of the accessor.*)

     val surject = timeit_msg ctxt "record extension surjective proof:" (fn () =>

       let

         val cterm_ext = cterm_of defs_thy ext;

         val start = named_cterm_instantiate [("y", cterm_ext)] surject_assist_idE;

         val tactic1 =

           simp_tac (HOL_basic_ss addsimps [ext_def]) 1 THEN

           REPEAT_ALL_NEW Iso_Tuple_Support.iso_tuple_intros_tac 1;

         val tactic2 = REPEAT (rtac surject_assistI 1 THEN rtac refl 1);

         val [halfway] = Seq.list_of (tactic1 start);

         val [surject] = Seq.list_of (tactic2 (Drule.export_without_context halfway));

       in

         surject

       end);

     val split_meta = timeit_msg ctxt "record extension split_meta proof:" (fn () =>

       Skip_Proof.prove_global defs_thy [] [] split_meta_prop

         (fn _ =>

           EVERY1

            [rtac @{thm equal_intr_rule}, Goal.norm_hhf_tac,

             etac @{thm meta_allE}, atac,

             rtac (@{thm prop_subst} OF [surject]),

             REPEAT o etac @{thm meta_allE}, atac]));

     val induct = timeit_msg ctxt "record extension induct proof:" (fn () =>

       let val (assm, concl) = induct_prop in

         Skip_Proof.prove_global defs_thy [] [assm] concl

           (fn {prems, ...} =>

             cut_tac (split_meta RS Drule.equal_elim_rule2) 1 THEN

             resolve_tac prems 2 THEN

             asm_simp_tac HOL_ss 1)

       end);

     val ([(_, [induct']), (_, [inject']), (_, [surjective']), (_, [split_meta'])], thm_thy) =

       defs_thy

       |> Global_Theory.note_thmss ""

           [((Binding.name "ext_induct", []), [([induct], [])]),

            ((Binding.name "ext_inject", []), [([inject], [])]),

            ((Binding.name "ext_surjective", []), [([surject], [])]),

            ((Binding.name "ext_split", []), [([split_meta], [])])];

   in

     (((ext_name, ext_type), (ext_tyco, alphas_zeta),

       extT, induct', inject', surjective', split_meta', ext_def), thm_thy)

   end;

 fun chunks [] [] = []

   | chunks [] xs = [xs]

   | chunks (l :: ls) xs = take l xs :: chunks ls (drop l xs);

 fun chop_last [] = error "chop_last: list should not be empty"

   | chop_last [x] = ([], x)

   | chop_last (x :: xs) = let val (tl, l) = chop_last xs in (x :: tl, l) end;

 fun subst_last _ [] = error "subst_last: list should not be empty"

   | subst_last s [_] = [s]

   | subst_last s (x :: xs) = x :: subst_last s xs;

 (* mk_recordT *)

 (*build up the record type from the current extension tpye extT and a list

   of parent extensions, starting with the root of the record hierarchy*)

 fun mk_recordT extT =

   fold_rev (fn (parent, Ts) => fn T => Type (parent, subst_last T Ts)) extT;

 (* code generation *)

 fun mk_random_eq tyco vs extN Ts =

   let

     (* FIXME local i etc. *)

     val size = @{term "i::code_numeral"};

     fun termifyT T = HOLogic.mk_prodT (T, @{typ "unit => term"});

     val T = Type (tyco, map TFree vs);

     val Tm = termifyT T;

     val params = Name.invent_names Name.context "x" Ts;

     val lhs = HOLogic.mk_random T size;

     val tc = HOLogic.mk_return Tm @{typ Random.seed}

       (HOLogic.mk_valtermify_app extN params T);

     val rhs =

       HOLogic.mk_ST

         (map (fn (v, T') =>

           ((HOLogic.mk_random T' size, @{typ Random.seed}), SOME (v, termifyT T'))) params)

         tc @{typ Random.seed} (SOME Tm, @{typ Random.seed});

   in

     (lhs, rhs)

   end

 fun mk_full_exhaustive_eq tyco vs extN Ts =

   let

     (* FIXME local i etc. *)

     val size = @{term "i::code_numeral"};

     fun termifyT T = HOLogic.mk_prodT (T, @{typ "unit => term"});

     val T = Type (tyco, map TFree vs);

     val test_function = Free ("f", termifyT T --> @{typ "(bool * term list) option"});

     val params = Name.invent_names Name.context "x" Ts;

     fun full_exhaustiveT T =

       (termifyT T --> @{typ "(bool * Code_Evaluation.term list) option"}) -->

         @{typ code_numeral} --> @{typ "(bool * Code_Evaluation.term list) option"};

     fun mk_full_exhaustive T =

       Const (@{const_name "Quickcheck_Exhaustive.full_exhaustive_class.full_exhaustive"},

         full_exhaustiveT T);

     val lhs = mk_full_exhaustive T $ test_function $ size;

     val tc = test_function $ (HOLogic.mk_valtermify_app extN params T);

     val rhs = fold_rev (fn (v, T) => fn cont =>

         mk_full_exhaustive T $ (lambda (Free (v, termifyT T)) cont) $ size) params tc;

   in

     (lhs, rhs)

   end;

 fun instantiate_sort_record (sort, mk_eq) tyco vs extN Ts thy =

   let

     val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (mk_eq tyco vs extN Ts));

   in

     thy

     |> Class.instantiation ([tyco], vs, sort)

     |> `(fn lthy => Syntax.check_term lthy eq)

     |-> (fn eq => Specification.definition (NONE, (apfst Binding.conceal Attrib.empty_binding, eq)))

     |> snd

     |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))

   end;

 fun ensure_sort_record (sort, mk_eq) ext_tyco vs extN Ts thy =

   let

     val algebra = Sign.classes_of thy;

     val has_inst = can (Sorts.mg_domain algebra ext_tyco) sort;

   in

     if has_inst then thy

     else

       (case Quickcheck_Common.perhaps_constrain thy (map (rpair sort) Ts) vs of

         SOME constrain =>

           instantiate_sort_record (sort, mk_eq) ext_tyco (map constrain vs) extN

             ((map o map_atyps) (fn TFree v => TFree (constrain v)) Ts) thy

       | NONE => thy)

   end;

 fun add_code ext_tyco vs extT ext simps inject thy =

   let

     val eq =

       HOLogic.mk_Trueprop (HOLogic.mk_eq

         (Const (@{const_name HOL.equal}, extT --> extT --> HOLogic.boolT),

          Const (@{const_name HOL.eq}, extT --> extT --> HOLogic.boolT)));

     fun tac eq_def =

       Class.intro_classes_tac []

       THEN rewrite_goals_tac [Simpdata.mk_eq eq_def]

       THEN ALLGOALS (rtac @{thm refl});

     fun mk_eq thy eq_def =

       Simplifier.rewrite_rule

         [AxClass.unoverload thy (Thm.symmetric (Simpdata.mk_eq eq_def))] inject;

     fun mk_eq_refl thy =

       @{thm equal_refl}

       |> Thm.instantiate

         ([pairself (ctyp_of thy) (TVar (("'a", 0), @{sort equal}), Logic.varifyT_global extT)], [])

       |> AxClass.unoverload thy;

     val ensure_random_record = ensure_sort_record (@{sort random}, mk_random_eq);

     val ensure_exhaustive_record =

       ensure_sort_record (@{sort full_exhaustive}, mk_full_exhaustive_eq);

   in

     thy

     |> Code.add_datatype [ext]

     |> fold Code.add_default_eqn simps

     |> Class.instantiation ([ext_tyco], vs, [HOLogic.class_equal])

     |> `(fn lthy => Syntax.check_term lthy eq)

     |-> (fn eq => Specification.definition

           (NONE, (Attrib.empty_binding, eq)))

     |-> (fn (_, (_, eq_def)) =>

        Class.prove_instantiation_exit_result Morphism.thm

           (fn _ => fn eq_def => tac eq_def) eq_def)

     |-> (fn eq_def => fn thy =>

           thy |> Code.del_eqn eq_def |> Code.add_default_eqn (mk_eq thy eq_def))

     |> (fn thy => Code.add_nbe_default_eqn (mk_eq_refl thy) thy)

     |> ensure_random_record ext_tyco vs (fst ext) (binder_types (snd ext))

     |> ensure_exhaustive_record ext_tyco vs (fst ext) (binder_types (snd ext))

   end;

 (* definition *)

 fun definition (alphas, binding) parent (parents: parent_info list) raw_fields thy =

   let

     val ctxt = Proof_Context.init_global thy;

     val prefix = Binding.name_of binding;

     val name = Sign.full_name thy binding;

     val full = Sign.full_name_path thy prefix;

     val bfields = map (fn (x, T, _) => (x, T)) raw_fields;

     val field_syntax = map #3 raw_fields;

     val parent_fields = maps #fields parents;

     val parent_chunks = map (length o #fields) parents;

     val parent_names = map fst parent_fields;

     val parent_types = map snd parent_fields;

     val parent_fields_len = length parent_fields;

     val parent_variants =

       Name.variant_list [moreN, rN, rN ^ "'", wN] (map Long_Name.base_name parent_names);

     val parent_vars = map2 (curry Free) parent_variants parent_types;

     val parent_len = length parents;

     val fields = map (apfst full) bfields;

     val names = map fst fields;

     val types = map snd fields;

     val alphas_fields = fold Term.add_tfreesT types [];

     val alphas_ext = inter (op =) alphas_fields alphas;

     val len = length fields;

     val variants =

       Name.variant_list (moreN :: rN :: (rN ^ "'") :: wN :: parent_variants)

         (map (Binding.name_of o fst) bfields);

     val vars = map2 (curry Free) variants types;

     val named_vars = names ~~ vars;

     val idxms = 0 upto len;

     val all_fields = parent_fields @ fields;

     val all_types = parent_types @ types;

     val all_variants = parent_variants @ variants;

     val all_vars = parent_vars @ vars;

     val all_named_vars = (parent_names ~~ parent_vars) @ named_vars;

     val zeta = (singleton (Name.variant_list (map #1 alphas)) "'z", HOLogic.typeS);

     val moreT = TFree zeta;

     val more = Free (moreN, moreT);

     val full_moreN = full (Binding.name moreN);

     val bfields_more = bfields @ [(Binding.name moreN, moreT)];

     val fields_more = fields @ [(full_moreN, moreT)];

     val named_vars_more = named_vars @ [(full_moreN, more)];

     val all_vars_more = all_vars @ [more];

     val all_named_vars_more = all_named_vars @ [(full_moreN, more)];

     (* 1st stage: ext_thy *)

     val extension_name = full binding;

     val ((ext, (ext_tyco, vs),

         extT, ext_induct, ext_inject, ext_surjective, ext_split, ext_def), ext_thy) =

       thy

       |> Sign.qualified_path false binding

       |> extension_definition extension_name fields alphas_ext zeta moreT more vars;

     val _ = timing_msg ctxt "record preparing definitions";

     val Type extension_scheme = extT;

     val extension_name = unsuffix ext_typeN (fst extension_scheme);

     val extension = let val (n, Ts) = extension_scheme in (n, subst_last HOLogic.unitT Ts) end;

     val extension_names = map (unsuffix ext_typeN o fst o #extension) parents @ [extension_name];

     val extension_id = implode extension_names;

     fun rec_schemeT n = mk_recordT (map #extension (drop n parents)) extT;

     val rec_schemeT0 = rec_schemeT 0;

     fun recT n =

       let val (c, Ts) = extension in

         mk_recordT (map #extension (drop n parents))

           (Type (c, subst_last HOLogic.unitT Ts))

       end;

     val recT0 = recT 0;

     fun mk_rec args n =

       let

         val (args', more) = chop_last args;

         fun mk_ext' ((name, T), args) more = mk_ext (name, T) (args @ [more]);

         fun build Ts =

           fold_rev mk_ext' (drop n ((extension_names ~~ Ts) ~~ chunks parent_chunks args')) more;

       in

         if more = HOLogic.unit

         then build (map_range recT (parent_len + 1))

         else build (map_range rec_schemeT (parent_len + 1))

       end;

     val r_rec0 = mk_rec all_vars_more 0;

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

     fun r n = Free (rN, rec_schemeT n);

     val r0 = r 0;

     fun r_unit n = Free (rN, recT n);

     val r_unit0 = r_unit 0;

     val w = Free (wN, rec_schemeT 0);

     (* print translations *)

     val record_ext_type_abbr_tr's =

       let

         val trname = hd extension_names;

         val last_ext = unsuffix ext_typeN (fst extension);

       in [record_ext_type_abbr_tr' name alphas zeta last_ext rec_schemeT0 trname] end;

     val record_ext_type_tr's =

       let

         (*avoid conflict with record_type_abbr_tr's*)

         val trnames = if parent_len > 0 then [extension_name] else [];

       in map record_ext_type_tr' trnames end;

     val advanced_print_translation =

       map field_update_tr' (full_moreN :: names) @ [record_ext_tr' extension_name] @

       record_ext_type_tr's @ record_ext_type_abbr_tr's;

     (* prepare declarations *)

     val sel_decls = map (mk_selC rec_schemeT0 o apfst Binding.name_of) bfields_more;

     val upd_decls = map (mk_updC updateN rec_schemeT0 o apfst Binding.name_of) bfields_more;

     val make_decl = (makeN, all_types ---> recT0);

     val fields_decl = (fields_selN, types ---> Type extension);

     val extend_decl = (extendN, recT0 --> moreT --> rec_schemeT0);

     val truncate_decl = (truncateN, rec_schemeT0 --> recT0);

     (* prepare definitions *)

     val ext_defs = ext_def :: map #ext_def parents;

     (*Theorems from the iso_tuple intros.

       By unfolding ext_defs from r_rec0 we create a tree of constructor

       calls (many of them Pair, but others as well). The introduction

       rules for update_accessor_eq_assist can unify two different ways

       on these constructors. If we take the complete result sequence of

       running a the introduction tactic, we get one theorem for each upd/acc

       pair, from which we can derive the bodies of our selector and

       updator and their convs.*)

     val (accessor_thms, updator_thms, upd_acc_cong_assists) =

       timeit_msg ctxt "record getting tree access/updates:" (fn () =>

         let

           val r_rec0_Vars =

             let

               (*pick variable indices of 1 to avoid possible variable

                 collisions with existing variables in updacc_eq_triv*)

               fun to_Var (Free (c, T)) = Var ((c, 1), T);

             in mk_rec (map to_Var all_vars_more) 0 end;

           val cterm_rec = cterm_of ext_thy r_rec0;

           val cterm_vrs = cterm_of ext_thy r_rec0_Vars;

           val insts = [("v", cterm_rec), ("v'", cterm_vrs)];

           val init_thm = named_cterm_instantiate insts updacc_eq_triv;

           val terminal = rtac updacc_eq_idI 1 THEN rtac refl 1;

           val tactic =

             simp_tac (HOL_basic_ss addsimps ext_defs) 1 THEN

             REPEAT (Iso_Tuple_Support.iso_tuple_intros_tac 1 ORELSE terminal);

           val updaccs = Seq.list_of (tactic init_thm);

         in

           (updaccs RL [updacc_accessor_eqE],

            updaccs RL [updacc_updator_eqE],

            updaccs RL [updacc_cong_from_eq])

         end);

     fun lastN xs = drop parent_fields_len xs;

     (*selectors*)

     fun mk_sel_spec ((c, T), thm) =

       let

         val (acc $ arg, _) =

           HOLogic.dest_eq (HOLogic.dest_Trueprop (Envir.beta_eta_contract (Thm.concl_of thm)));

         val _ =

           if arg aconv r_rec0 then ()

           else raise TERM ("mk_sel_spec: different arg", [arg]);

       in

         Const (mk_selC rec_schemeT0 (c, T)) :== acc

       end;

     val sel_specs = map mk_sel_spec (fields_more ~~ lastN accessor_thms);

     (*updates*)

     fun mk_upd_spec ((c, T), thm) =

       let

         val (upd $ _ $ arg, _) =

           HOLogic.dest_eq (HOLogic.dest_Trueprop (Envir.beta_eta_contract (Thm.concl_of thm)));

         val _ =

           if arg aconv r_rec0 then ()

           else raise TERM ("mk_sel_spec: different arg", [arg]);

       in Const (mk_updC updateN rec_schemeT0 (c, T)) :== upd end;

     val upd_specs = map mk_upd_spec (fields_more ~~ lastN updator_thms);

     (*derived operations*)

     val make_spec =

       list_comb (Const (full (Binding.name makeN), all_types ---> recT0), all_vars) :==

         mk_rec (all_vars @ [HOLogic.unit]) 0;

     val fields_spec =

       list_comb (Const (full (Binding.name fields_selN), types ---> Type extension), vars) :==

         mk_rec (all_vars @ [HOLogic.unit]) parent_len;

     val extend_spec =

       Const (full (Binding.name extendN), recT0 --> moreT --> rec_schemeT0) $ r_unit0 $ more :==

         mk_rec ((map (mk_sel r_unit0) all_fields) @ [more]) 0;

     val truncate_spec =

       Const (full (Binding.name truncateN), rec_schemeT0 --> recT0) $ r0 :==

         mk_rec ((map (mk_sel r0) all_fields) @ [HOLogic.unit]) 0;

     (* 2st stage: defs_thy *)

     val (((sel_defs, upd_defs), derived_defs), defs_thy) =

       timeit_msg ctxt "record trfuns/tyabbrs/selectors/updates/make/fields/extend/truncate defs:"

         (fn () =>

           ext_thy

           |> Sign.add_advanced_trfuns ([], [], advanced_print_translation, [])

           |> Sign.restore_naming thy

           |> Typedecl.abbrev_global (binding, map #1 alphas, NoSyn) recT0 |> snd

           |> Typedecl.abbrev_global

             (Binding.suffix_name schemeN binding, map #1 (alphas @ [zeta]), NoSyn) rec_schemeT0

           |> snd

           |> Sign.qualified_path false binding

           |> fold (fn ((x, T), mx) => snd o Sign.declare_const_global ((Binding.name x, T), mx))

             (sel_decls ~~ (field_syntax @ [NoSyn]))

           |> fold (fn (x, T) => snd o Sign.declare_const_global ((Binding.name x, T), NoSyn))

             (upd_decls @ [make_decl, fields_decl, extend_decl, truncate_decl])

           |> (Global_Theory.add_defs false o

                 map (Thm.no_attributes o apfst (Binding.conceal o Binding.name))) sel_specs

           ||>> (Global_Theory.add_defs false o

                 map (Thm.no_attributes o apfst (Binding.conceal o Binding.name))) upd_specs

           ||>> (Global_Theory.add_defs false o

                 map (Thm.no_attributes o apfst (Binding.conceal o Binding.name)))

             [make_spec, fields_spec, extend_spec, truncate_spec]

           ||> Theory.checkpoint);

     (* prepare propositions *)

     val _ = timing_msg ctxt "record preparing propositions";

     val P = Free (singleton (Name.variant_list all_variants) "P", rec_schemeT0 --> HOLogic.boolT);

     val C = Free (singleton (Name.variant_list all_variants) "C", HOLogic.boolT);

     val P_unit = Free (singleton (Name.variant_list all_variants) "P", recT0 --> HOLogic.boolT);

     (*selectors*)

     val sel_conv_props =

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

     (*updates*)

     fun mk_upd_prop i (c, T) =

       let

         val x' =

           Free (singleton (Name.variant_list all_variants) (Long_Name.base_name c ^ "'"), T --> T);

         val n = parent_fields_len + i;

         val args' = nth_map n (K (x' $ nth all_vars_more n)) all_vars_more;

       in mk_upd updateN c x' r_rec0 === mk_rec args' 0 end;

     val upd_conv_props = map2 mk_upd_prop idxms fields_more;

     (*induct*)

     val induct_scheme_prop =

       fold_rev Logic.all all_vars_more (Trueprop (P $ r_rec0)) ==> Trueprop (P $ r0);

     val induct_prop =

       (fold_rev Logic.all all_vars (Trueprop (P_unit $ r_rec_unit0)), Trueprop (P_unit $ r_unit0));

     (*surjective*)

     val surjective_prop =

       let val args = map (fn (c, Free (_, T)) => mk_sel r0 (c, T)) all_named_vars_more

       in r0 === mk_rec args 0 end;

     (*cases*)

     val cases_scheme_prop =

       (fold_rev Logic.all all_vars_more ((r0 === r_rec0) ==> Trueprop C), Trueprop C);

     val cases_prop =

       fold_rev Logic.all all_vars ((r_unit0 === r_rec_unit0) ==> Trueprop C) ==> Trueprop C;

     (*split*)

     val split_meta_prop =

       let

         val P = Free (singleton (Name.variant_list all_variants) "P", rec_schemeT0 --> propT);

       in

         Logic.mk_equals (Logic.all r0 (P $ r0), fold_rev Logic.all all_vars_more (P $ r_rec0))

       end;

     val split_object_prop =

       let val ALL = fold_rev (fn (v, T) => fn t => HOLogic.mk_all (v, T, t))

       in ALL [dest_Free r0] (P $ r0) === ALL (map dest_Free all_vars_more) (P $ r_rec0) end;

     val split_ex_prop =

       let val EX = fold_rev (fn (v, T) => fn t => HOLogic.mk_exists (v, T, t))

       in EX [dest_Free r0] (P $ r0) === EX (map dest_Free all_vars_more) (P $ r_rec0) end;

     (*equality*)

     val equality_prop =

       let

         val s' = Free (rN ^ "'", rec_schemeT0);

         fun mk_sel_eq (c, Free (_, T)) = mk_sel r0 (c, T) === mk_sel s' (c, T);

         val seleqs = map mk_sel_eq all_named_vars_more;

       in Logic.all r0 (Logic.all s' (Logic.list_implies (seleqs, r0 === s'))) end;

     (* 3rd stage: thms_thy *)

     val record_ss = get_simpset defs_thy;

     val sel_upd_ss = record_ss addsimps (sel_defs @ accessor_thms @ upd_defs @ updator_thms);

     val (sel_convs, upd_convs) =

       timeit_msg ctxt "record sel_convs/upd_convs proof:" (fn () =>

         grouped 10 Par_List.map (fn prop =>

           Skip_Proof.prove_global defs_thy [] [] prop

             (K (ALLGOALS (asm_full_simp_tac sel_upd_ss)))) (sel_conv_props @ upd_conv_props))

       |> chop (length sel_conv_props);

     val (fold_congs, unfold_congs) = timeit_msg ctxt "record upd fold/unfold congs:" (fn () =>

       let

         val symdefs = map Thm.symmetric (sel_defs @ upd_defs);

         val fold_ss = HOL_basic_ss addsimps symdefs;

         val ua_congs = map (Drule.export_without_context o simplify fold_ss) upd_acc_cong_assists;

       in (ua_congs RL [updacc_foldE], ua_congs RL [updacc_unfoldE]) end);

     val parent_induct = Option.map #induct_scheme (try List.last parents);

     val induct_scheme = timeit_msg ctxt "record induct_scheme proof:" (fn () =>

       Skip_Proof.prove_global defs_thy [] [] induct_scheme_prop

         (fn _ =>

           EVERY

            [case parent_induct of NONE => all_tac | SOME ind => try_param_tac rN ind 1,

             try_param_tac rN ext_induct 1,

             asm_simp_tac HOL_basic_ss 1]));

     val induct = timeit_msg ctxt "record induct proof:" (fn () =>

       Skip_Proof.prove_global defs_thy [] [#1 induct_prop] (#2 induct_prop) (fn {prems, ...} =>

         try_param_tac rN induct_scheme 1

         THEN try_param_tac "more" @{thm unit.induct} 1

         THEN resolve_tac prems 1));

     val surjective = timeit_msg ctxt "record surjective proof:" (fn () =>

       let

         val leaf_ss =

           get_sel_upd_defs defs_thy addsimps (sel_defs @ @{thms o_assoc id_apply id_o o_id});

         val init_ss = HOL_basic_ss addsimps ext_defs;

       in

         Skip_Proof.prove_global defs_thy [] [] surjective_prop

           (fn _ =>

             EVERY

              [rtac surject_assist_idE 1,

               simp_tac init_ss 1,

               REPEAT

                 (Iso_Tuple_Support.iso_tuple_intros_tac 1 ORELSE

                   (rtac surject_assistI 1 THEN simp_tac leaf_ss 1))])

       end);

     val cases_scheme = timeit_msg ctxt "record cases_scheme proof:" (fn () =>

       Skip_Proof.prove_global defs_thy [] [#1 cases_scheme_prop] (#2 cases_scheme_prop)

         (fn {prems, ...} =>

           resolve_tac prems 1 THEN

           rtac surjective 1));

     val cases = timeit_msg ctxt "record cases proof:" (fn () =>

       Skip_Proof.prove_global defs_thy [] [] cases_prop

         (fn _ =>

           try_param_tac rN cases_scheme 1 THEN

           ALLGOALS (asm_full_simp_tac (HOL_basic_ss addsimps @{thms unit_all_eq1}))));

     val split_meta = timeit_msg ctxt "record split_meta proof:" (fn () =>

       Skip_Proof.prove_global defs_thy [] [] split_meta_prop

         (fn _ =>

           EVERY1

            [rtac @{thm equal_intr_rule}, Goal.norm_hhf_tac,

             etac @{thm meta_allE}, atac,

             rtac (@{thm prop_subst} OF [surjective]),

             REPEAT o etac @{thm meta_allE}, atac]));

     val split_object = timeit_msg ctxt "record split_object proof:" (fn () =>

       Skip_Proof.prove_global defs_thy [] [] split_object_prop

         (fn _ =>

           rtac @{lemma "Trueprop A == Trueprop B ==> A = B" by (rule iffI) unfold} 1 THEN

           rewrite_goals_tac @{thms atomize_all [symmetric]} THEN

           rtac split_meta 1));

     val split_ex = timeit_msg ctxt "record split_ex proof:" (fn () =>

       Skip_Proof.prove_global defs_thy [] [] split_ex_prop

         (fn _ =>

           simp_tac

             (HOL_basic_ss addsimps

               (@{lemma "EX x. P x == ~ (ALL x. ~ P x)" by simp} ::

                 @{thms not_not Not_eq_iff})) 1 THEN

           rtac split_object 1));

     val equality = timeit_msg ctxt "record equality proof:" (fn () =>

       Skip_Proof.prove_global defs_thy [] [] equality_prop

         (fn _ => asm_full_simp_tac (record_ss addsimps (split_meta :: sel_convs)) 1));

     val ([(_, sel_convs'), (_, upd_convs'), (_, sel_defs'), (_, upd_defs'),

           (_, fold_congs'), (_, unfold_congs'),

           (_, splits' as [split_meta', split_object', split_ex']), (_, derived_defs'),

           (_, [surjective']), (_, [equality']), (_, [induct_scheme']), (_, [induct']),

           (_, [cases_scheme']), (_, [cases'])], thms_thy) = defs_thy

       |> Global_Theory.note_thmss ""

        [((Binding.name "select_convs", []), [(sel_convs, [])]),

         ((Binding.name "update_convs", []), [(upd_convs, [])]),

         ((Binding.name "select_defs", []), [(sel_defs, [])]),

         ((Binding.name "update_defs", []), [(upd_defs, [])]),

         ((Binding.name "fold_congs", []), [(fold_congs, [])]),

         ((Binding.name "unfold_congs", []), [(unfold_congs, [])]),

         ((Binding.name "splits", []), [([split_meta, split_object, split_ex], [])]),

         ((Binding.name "defs", []), [(derived_defs, [])]),

         ((Binding.name "surjective", []), [([surjective], [])]),

         ((Binding.name "equality", []), [([equality], [])]),

         ((Binding.name "induct_scheme", induct_type_global (suffix schemeN name)),

           [([induct_scheme], [])]),

         ((Binding.name "induct", induct_type_global name), [([induct], [])]),

         ((Binding.name "cases_scheme", cases_type_global (suffix schemeN name)),

           [([cases_scheme], [])]),

         ((Binding.name "cases", cases_type_global name), [([cases], [])])];

     val sel_upd_simps = sel_convs' @ upd_convs';

     val sel_upd_defs = sel_defs' @ upd_defs';

     val depth = parent_len + 1;

     val ([(_, simps'), (_, iffs')], thms_thy') = thms_thy

       |> Global_Theory.note_thmss ""

           [((Binding.name "simps", [Simplifier.simp_add]), [(sel_upd_simps, [])]),

            ((Binding.name "iffs", [iff_add]), [([ext_inject], [])])];

     val info =

       make_info alphas parent fields extension

         ext_induct ext_inject ext_surjective ext_split ext_def

         sel_convs' upd_convs' sel_defs' upd_defs' fold_congs' unfold_congs' splits' derived_defs'

         surjective' equality' induct_scheme' induct' cases_scheme' cases' simps' iffs';

     val final_thy =

       thms_thy'

       |> put_record name info

       |> put_sel_upd names full_moreN depth sel_upd_simps sel_upd_defs

       |> add_equalities extension_id equality'

       |> add_extinjects ext_inject

       |> add_extsplit extension_name ext_split

       |> add_splits extension_id (split_meta', split_object', split_ex', induct_scheme')

       |> add_extfields extension_name (fields @ [(full_moreN, moreT)])

       |> add_fieldext (extension_name, snd extension) names

       |> add_code ext_tyco vs extT ext simps' ext_inject

       |> Sign.restore_naming thy;

   in final_thy end;

 (* add_record *)

 local

 fun read_parent NONE ctxt = (NONE, ctxt)

   | read_parent (SOME raw_T) ctxt =

       (case Proof_Context.read_typ_abbrev ctxt raw_T of

         Type (name, Ts) => (SOME (Ts, name), fold Variable.declare_typ Ts ctxt)

       | T => error ("Bad parent record specification: " ^ Syntax.string_of_typ ctxt T));

 fun read_fields raw_fields ctxt =

   let

     val Ts = Syntax.read_typs ctxt (map (fn (_, raw_T, _) => raw_T) raw_fields);

     val fields = map2 (fn (x, _, mx) => fn T => (x, T, mx)) raw_fields Ts;

     val ctxt' = fold Variable.declare_typ Ts ctxt;

   in (fields, ctxt') end;

 in

 fun add_record (params, binding) raw_parent raw_fields thy =

   let

     val _ = Theory.requires thy "Record" "record definitions";

     val ctxt = Proof_Context.init_global thy;

     fun cert_typ T = Type.no_tvars (Proof_Context.cert_typ ctxt T)

       handle TYPE (msg, _, _) => error msg;

     (* specification *)

     val parent = Option.map (apfst (map cert_typ)) raw_parent

       handle ERROR msg =>

         cat_error msg ("The error(s) above occurred in parent record specification");

     val parent_args = (case parent of SOME (Ts, _) => Ts | NONE => []);

     val parents = get_parent_info thy parent;

     val bfields =

       raw_fields |> map (fn (x, raw_T, mx) => (x, cert_typ raw_T, mx)

         handle ERROR msg =>

           cat_error msg ("The error(s) above occurred in record field " ^ Binding.print x));

     (* errors *)

     val name = Sign.full_name thy binding;

     val err_dup_record =

       if is_none (get_info thy name) then []

       else ["Duplicate definition of record " ^ quote name];

     val spec_frees = fold Term.add_tfreesT (parent_args @ map #2 bfields) [];

     val err_extra_frees =

       (case subtract (op =) params spec_frees of

         [] => []

       | extras => ["Extra free type variable(s) " ^

           commas (map (Syntax.string_of_typ ctxt o TFree) extras)]);

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

     val err_dup_fields =

       (case duplicates Binding.eq_name (map #1 bfields) of

         [] => []

       | dups => ["Duplicate field(s) " ^ commas (map Binding.print dups)]);

     val err_bad_fields =

       if forall (not_equal moreN o Binding.name_of o #1) bfields then []

       else ["Illegal field name " ^ quote moreN];

     val errs =

       err_dup_record @ err_extra_frees @ err_no_fields @ err_dup_fields @ err_bad_fields;

     val _ = if null errs then () else error (cat_lines errs);

   in

     thy |> definition (params, binding) parent parents bfields

   end

   handle ERROR msg => cat_error msg ("Failed to define record " ^ Binding.print binding);

 fun add_record_cmd (raw_params, binding) raw_parent raw_fields thy =

   let

     val ctxt = Proof_Context.init_global thy;

     val params = map (apsnd (Typedecl.read_constraint ctxt)) raw_params;

     val ctxt1 = fold (Variable.declare_typ o TFree) params ctxt;

     val (parent, ctxt2) = read_parent raw_parent ctxt1;

     val (fields, ctxt3) = read_fields raw_fields ctxt2;

     val params' = map (Proof_Context.check_tfree ctxt3) params;

   in thy |> add_record (params', binding) parent fields end;

 end;

 (* setup theory *)

 val setup =

   Sign.add_trfuns ([], parse_translation, [], []) #>

   Sign.add_advanced_trfuns ([], advanced_parse_translation, [], []) #>

   Simplifier.map_simpset_global (fn ss => ss addsimprocs [simproc, upd_simproc, eq_simproc]);

 (* outer syntax *)

 val _ =

   Outer_Syntax.command @{command_spec "record"} "define extensible record"

     (Parse.type_args_constrained -- Parse.binding --

       (@{keyword "="} |-- Scan.option (Parse.typ --| @{keyword "+"}) --

         Scan.repeat1 Parse.const_binding)

     >> (fn (x, (y, z)) => Toplevel.theory (add_record_cmd x y z)));

 end;