src/HOL/Tools/Ctr_Sugar/ctr_sugar.ML
author blanchet
Wed Feb 12 08:35:56 2014 +0100 (2014-02-12)
changeset 55409 b74248961819
parent 55407 81f7e60755c3
child 55410 54b09e82b9e1
permissions -rw-r--r--
made 'ctr_sugar' more friendly to the 'datatype_realizer'
* * *
reverted changes to 'datatype_realizer.ML'
     1 (*  Title:      HOL/Tools/Ctr_Sugar/ctr_sugar.ML
     2     Author:     Jasmin Blanchette, TU Muenchen
     3     Copyright   2012, 2013
     4 
     5 Wrapping existing freely generated type's constructors.
     6 *)
     7 
     8 signature CTR_SUGAR =
     9 sig
    10   type ctr_sugar =
    11     {ctrs: term list,
    12      casex: term,
    13      discs: term list,
    14      selss: term list list,
    15      exhaust: thm,
    16      nchotomy: thm,
    17      injects: thm list,
    18      distincts: thm list,
    19      case_thms: thm list,
    20      case_cong: thm,
    21      weak_case_cong: thm,
    22      split: thm,
    23      split_asm: thm,
    24      disc_thmss: thm list list,
    25      discIs: thm list,
    26      sel_thmss: thm list list,
    27      disc_excludesss: thm list list list,
    28      disc_exhausts: thm list,
    29      sel_exhausts: thm list,
    30      collapses: thm list,
    31      expands: thm list,
    32      sel_splits: thm list,
    33      sel_split_asms: thm list,
    34      case_eq_ifs: thm list};
    35 
    36   val morph_ctr_sugar: morphism -> ctr_sugar -> ctr_sugar
    37   val transfer_ctr_sugar: Proof.context -> ctr_sugar -> ctr_sugar
    38   val ctr_sugar_of: Proof.context -> string -> ctr_sugar option
    39   val ctr_sugars_of: Proof.context -> ctr_sugar list
    40   val ctr_sugar_of_case: Proof.context -> string -> ctr_sugar option
    41   val register_ctr_sugar: string -> ctr_sugar -> local_theory -> local_theory
    42   val register_ctr_sugar_global: string -> ctr_sugar -> theory -> theory
    43 
    44   val rep_compat_prefix: string
    45 
    46   val mk_half_pairss: 'a list * 'a list -> ('a * 'a) list list
    47   val join_halves: int -> 'a list list -> 'a list list -> 'a list * 'a list list list
    48 
    49   val mk_ctr: typ list -> term -> term
    50   val mk_case: typ list -> typ -> term -> term
    51   val mk_disc_or_sel: typ list -> term -> term
    52   val name_of_ctr: term -> string
    53   val name_of_disc: term -> string
    54   val dest_ctr: Proof.context -> string -> term -> term * term list
    55   val dest_case: Proof.context -> string -> typ list -> term ->
    56     (ctr_sugar * term list * term list) option
    57 
    58   val wrap_free_constructors: ({prems: thm list, context: Proof.context} -> tactic) list list ->
    59     (((bool * (bool * bool)) * term list) * binding) *
    60       (binding list * (binding list list * (binding * term) list list)) -> local_theory ->
    61     ctr_sugar * local_theory
    62   val parse_wrap_free_constructors_options: (bool * (bool * bool)) parser
    63   val parse_bound_term: (binding * string) parser
    64 end;
    65 
    66 structure Ctr_Sugar : CTR_SUGAR =
    67 struct
    68 
    69 open Ctr_Sugar_Util
    70 open Ctr_Sugar_Tactics
    71 open Ctr_Sugar_Code
    72 
    73 type ctr_sugar =
    74   {ctrs: term list,
    75    casex: term,
    76    discs: term list,
    77    selss: term list list,
    78    exhaust: thm,
    79    nchotomy: thm,
    80    injects: thm list,
    81    distincts: thm list,
    82    case_thms: thm list,
    83    case_cong: thm,
    84    weak_case_cong: thm,
    85    split: thm,
    86    split_asm: thm,
    87    disc_thmss: thm list list,
    88    discIs: thm list,
    89    sel_thmss: thm list list,
    90    disc_excludesss: thm list list list,
    91    disc_exhausts: thm list,
    92    sel_exhausts: thm list,
    93    collapses: thm list,
    94    expands: thm list,
    95    sel_splits: thm list,
    96    sel_split_asms: thm list,
    97    case_eq_ifs: thm list};
    98 
    99 fun morph_ctr_sugar phi {ctrs, casex, discs, selss, exhaust, nchotomy, injects, distincts,
   100     case_thms, case_cong, weak_case_cong, split, split_asm, disc_thmss, discIs, sel_thmss,
   101     disc_excludesss, disc_exhausts, sel_exhausts, collapses, expands, sel_splits, sel_split_asms,
   102     case_eq_ifs} =
   103   {ctrs = map (Morphism.term phi) ctrs,
   104    casex = Morphism.term phi casex,
   105    discs = map (Morphism.term phi) discs,
   106    selss = map (map (Morphism.term phi)) selss,
   107    exhaust = Morphism.thm phi exhaust,
   108    nchotomy = Morphism.thm phi nchotomy,
   109    injects = map (Morphism.thm phi) injects,
   110    distincts = map (Morphism.thm phi) distincts,
   111    case_thms = map (Morphism.thm phi) case_thms,
   112    case_cong = Morphism.thm phi case_cong,
   113    weak_case_cong = Morphism.thm phi weak_case_cong,
   114    split = Morphism.thm phi split,
   115    split_asm = Morphism.thm phi split_asm,
   116    disc_thmss = map (map (Morphism.thm phi)) disc_thmss,
   117    discIs = map (Morphism.thm phi) discIs,
   118    sel_thmss = map (map (Morphism.thm phi)) sel_thmss,
   119    disc_excludesss = map (map (map (Morphism.thm phi))) disc_excludesss,
   120    disc_exhausts = map (Morphism.thm phi) disc_exhausts,
   121    sel_exhausts = map (Morphism.thm phi) sel_exhausts,
   122    collapses = map (Morphism.thm phi) collapses,
   123    expands = map (Morphism.thm phi) expands,
   124    sel_splits = map (Morphism.thm phi) sel_splits,
   125    sel_split_asms = map (Morphism.thm phi) sel_split_asms,
   126    case_eq_ifs = map (Morphism.thm phi) case_eq_ifs};
   127 
   128 val transfer_ctr_sugar =
   129   morph_ctr_sugar o Morphism.transfer_morphism o Proof_Context.theory_of;
   130 
   131 structure Data = Generic_Data
   132 (
   133   type T = ctr_sugar Symtab.table;
   134   val empty = Symtab.empty;
   135   val extend = I;
   136   fun merge data : T = Symtab.merge (K true) data;
   137 );
   138 
   139 fun ctr_sugar_of ctxt =
   140   Symtab.lookup (Data.get (Context.Proof ctxt))
   141   #> Option.map (transfer_ctr_sugar ctxt);
   142 
   143 fun ctr_sugars_of ctxt =
   144   Symtab.fold (cons o transfer_ctr_sugar ctxt o snd) (Data.get (Context.Proof ctxt)) [];
   145 
   146 fun ctr_sugar_of_case ctxt s =
   147   find_first (fn {casex = Const (s', _), ...} => s' = s | _ => false) (ctr_sugars_of ctxt);
   148 
   149 fun register_ctr_sugar key ctr_sugar =
   150   Local_Theory.declaration {syntax = false, pervasive = true}
   151     (fn phi => Data.map (Symtab.default (key, morph_ctr_sugar phi ctr_sugar)));
   152 
   153 fun register_ctr_sugar_global key ctr_sugar =
   154   Context.theory_map (Data.map (Symtab.default (key, ctr_sugar)));
   155 
   156 val rep_compat_prefix = "new";
   157 
   158 val isN = "is_";
   159 val unN = "un_";
   160 fun mk_unN 1 1 suf = unN ^ suf
   161   | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
   162 
   163 val caseN = "case";
   164 val case_congN = "case_cong";
   165 val case_eq_ifN = "case_eq_if";
   166 val collapseN = "collapse";
   167 val disc_excludeN = "disc_exclude";
   168 val disc_exhaustN = "disc_exhaust";
   169 val discN = "disc";
   170 val discIN = "discI";
   171 val distinctN = "distinct";
   172 val exhaustN = "exhaust";
   173 val expandN = "expand";
   174 val injectN = "inject";
   175 val nchotomyN = "nchotomy";
   176 val selN = "sel";
   177 val sel_exhaustN = "sel_exhaust";
   178 val sel_splitN = "sel_split";
   179 val sel_split_asmN = "sel_split_asm";
   180 val splitN = "split";
   181 val splitsN = "splits";
   182 val split_asmN = "split_asm";
   183 val weak_case_cong_thmsN = "weak_case_cong";
   184 
   185 val cong_attrs = @{attributes [cong]};
   186 val dest_attrs = @{attributes [dest]};
   187 val safe_elim_attrs = @{attributes [elim!]};
   188 val iff_attrs = @{attributes [iff]};
   189 val inductsimp_attrs = @{attributes [induct_simp]};
   190 val nitpicksimp_attrs = @{attributes [nitpick_simp]};
   191 val simp_attrs = @{attributes [simp]};
   192 val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
   193 val code_nitpicksimp_simp_attrs = code_nitpicksimp_attrs @ simp_attrs;
   194 
   195 fun unflat_lookup eq xs ys = map (fn xs' => permute_like eq xs xs' ys);
   196 
   197 fun mk_half_pairss' _ ([], []) = []
   198   | mk_half_pairss' indent (x :: xs, _ :: ys) =
   199     indent @ fold_rev (cons o single o pair x) ys (mk_half_pairss' ([] :: indent) (xs, ys));
   200 
   201 fun mk_half_pairss p = mk_half_pairss' [[]] p;
   202 
   203 fun join_halves n half_xss other_half_xss =
   204   (splice (flat half_xss) (flat other_half_xss),
   205    map2 (map2 append) (Library.chop_groups n half_xss)
   206      (transpose (Library.chop_groups n other_half_xss)));
   207 
   208 fun mk_undefined T = Const (@{const_name undefined}, T);
   209 
   210 fun mk_ctr Ts t =
   211   let val Type (_, Ts0) = body_type (fastype_of t) in
   212     subst_nonatomic_types (Ts0 ~~ Ts) t
   213   end;
   214 
   215 fun mk_case Ts T t =
   216   let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
   217     subst_nonatomic_types ((body, T) :: (Ts0 ~~ Ts)) t
   218   end;
   219 
   220 fun mk_disc_or_sel Ts t =
   221   subst_nonatomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
   222 
   223 fun name_of_const what t =
   224   (case head_of t of
   225     Const (s, _) => s
   226   | Free (s, _) => s
   227   | _ => error ("Cannot extract name of " ^ what));
   228 
   229 val name_of_ctr = name_of_const "constructor";
   230 
   231 val notN = "not_";
   232 val eqN = "eq_";
   233 val neqN = "neq_";
   234 
   235 fun name_of_disc t =
   236   (case head_of t of
   237     Abs (_, _, @{const Not} $ (t' $ Bound 0)) =>
   238     Long_Name.map_base_name (prefix notN) (name_of_disc t')
   239   | Abs (_, _, Const (@{const_name HOL.eq}, _) $ Bound 0 $ t') =>
   240     Long_Name.map_base_name (prefix eqN) (name_of_disc t')
   241   | Abs (_, _, @{const Not} $ (Const (@{const_name HOL.eq}, _) $ Bound 0 $ t')) =>
   242     Long_Name.map_base_name (prefix neqN) (name_of_disc t')
   243   | t' => name_of_const "destructor" t');
   244 
   245 val base_name_of_ctr = Long_Name.base_name o name_of_ctr;
   246 
   247 fun dest_ctr ctxt s t =
   248   let val (f, args) = Term.strip_comb t in
   249     (case ctr_sugar_of ctxt s of
   250       SOME {ctrs, ...} =>
   251       (case find_first (can (fo_match ctxt f)) ctrs of
   252         SOME f' => (f', args)
   253       | NONE => raise Fail "dest_ctr")
   254     | NONE => raise Fail "dest_ctr")
   255   end;
   256 
   257 fun dest_case ctxt s Ts t =
   258   (case Term.strip_comb t of
   259     (Const (c, _), args as _ :: _) =>
   260     (case ctr_sugar_of ctxt s of
   261       SOME (ctr_sugar as {casex = Const (case_name, _), discs = discs0, selss = selss0, ...}) =>
   262       if case_name = c then
   263         let val n = length discs0 in
   264           if n < length args then
   265             let
   266               val (branches, obj :: leftovers) = chop n args;
   267               val discs = map (mk_disc_or_sel Ts) discs0;
   268               val selss = map (map (mk_disc_or_sel Ts)) selss0;
   269               val conds = map (rapp obj) discs;
   270               val branch_argss = map (fn sels => map (rapp obj) sels @ leftovers) selss;
   271               val branches' = map2 (curry Term.betapplys) branches branch_argss;
   272             in
   273               SOME (ctr_sugar, conds, branches')
   274             end
   275           else
   276             NONE
   277         end
   278       else
   279         NONE
   280     | _ => NONE)
   281   | _ => NONE);
   282 
   283 fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
   284 
   285 fun prepare_wrap_free_constructors prep_term ((((no_discs_sels, (no_code, rep_compat)), raw_ctrs),
   286     raw_case_binding), (raw_disc_bindings, (raw_sel_bindingss, raw_sel_defaultss))) no_defs_lthy =
   287   let
   288     (* TODO: sanity checks on arguments *)
   289 
   290     val n = length raw_ctrs;
   291     val ks = 1 upto n;
   292 
   293     val _ = if n > 0 then () else error "No constructors specified";
   294 
   295     val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
   296     val sel_defaultss =
   297       pad_list [] n (map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss);
   298 
   299     val Type (fcT_name, As0) = body_type (fastype_of (hd ctrs0));
   300     val fc_b_name = Long_Name.base_name fcT_name;
   301     val fc_b = Binding.name fc_b_name;
   302 
   303     fun qualify mandatory =
   304       Binding.qualify mandatory fc_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
   305 
   306     fun dest_TFree_or_TVar (TFree sS) = sS
   307       | dest_TFree_or_TVar (TVar ((s, _), S)) = (s, S)
   308       | dest_TFree_or_TVar _ = error "Invalid type argument";
   309 
   310     val (unsorted_As, B) =
   311       no_defs_lthy
   312       |> variant_tfrees (map (fst o dest_TFree_or_TVar) As0)
   313       ||> the_single o fst o mk_TFrees 1;
   314 
   315     val As = map2 (resort_tfree o snd o dest_TFree_or_TVar) As0 unsorted_As;
   316 
   317     val fcT = Type (fcT_name, As);
   318     val ctrs = map (mk_ctr As) ctrs0;
   319     val ctr_Tss = map (binder_types o fastype_of) ctrs;
   320 
   321     val ms = map length ctr_Tss;
   322 
   323     val raw_disc_bindings' = pad_list Binding.empty n raw_disc_bindings;
   324 
   325     fun can_definitely_rely_on_disc k = not (Binding.is_empty (nth raw_disc_bindings' (k - 1)));
   326     fun can_rely_on_disc k =
   327       can_definitely_rely_on_disc k orelse (k = 1 andalso not (can_definitely_rely_on_disc 2));
   328     fun should_omit_disc_binding k = n = 1 orelse (n = 2 andalso can_rely_on_disc (3 - k));
   329 
   330     fun is_disc_binding_valid b =
   331       not (Binding.is_empty b orelse Binding.eq_name (b, equal_binding));
   332 
   333     val standard_disc_binding = Binding.name o prefix isN o base_name_of_ctr;
   334 
   335     val disc_bindings =
   336       raw_disc_bindings'
   337       |> map4 (fn k => fn m => fn ctr => fn disc =>
   338         qualify false
   339           (if Binding.is_empty disc then
   340              if should_omit_disc_binding k then disc else standard_disc_binding ctr
   341            else if Binding.eq_name (disc, equal_binding) then
   342              if m = 0 then disc
   343              else error "Cannot use \"=\" syntax for discriminating nonnullary constructor"
   344            else if Binding.eq_name (disc, standard_binding) then
   345              standard_disc_binding ctr
   346            else
   347              disc)) ks ms ctrs0;
   348 
   349     fun standard_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
   350 
   351     val sel_bindingss =
   352       pad_list [] n raw_sel_bindingss
   353       |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
   354         qualify false
   355           (if Binding.is_empty sel orelse Binding.eq_name (sel, standard_binding) then
   356             standard_sel_binding m l ctr
   357           else
   358             sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms;
   359 
   360     val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
   361 
   362     val (((((((([exh_y], (xss, xss')), yss), fs), gs), [u', v']), [w]), (p, p')), names_lthy) =
   363       no_defs_lthy
   364       |> mk_Frees "y" [fcT] (* for compatibility with "datatype_realizer.ML" *)
   365       ||>> mk_Freess' "x" ctr_Tss
   366       ||>> mk_Freess "y" ctr_Tss
   367       ||>> mk_Frees "f" case_Ts
   368       ||>> mk_Frees "g" case_Ts
   369       ||>> (apfst (map (rpair fcT)) oo Variable.variant_fixes) [fc_b_name, fc_b_name ^ "'"]
   370       ||>> mk_Frees "z" [B]
   371       ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
   372 
   373     val u = Free u';
   374     val v = Free v';
   375     val q = Free (fst p', mk_pred1T B);
   376 
   377     val xctrs = map2 (curry Term.list_comb) ctrs xss;
   378     val yctrs = map2 (curry Term.list_comb) ctrs yss;
   379 
   380     val xfs = map2 (curry Term.list_comb) fs xss;
   381     val xgs = map2 (curry Term.list_comb) gs xss;
   382 
   383     (* TODO: Eta-expension is for compatibility with the old datatype package (but it also provides
   384        nicer names). Consider removing. *)
   385     val eta_fs = map2 eta_expand_arg xss xfs;
   386     val eta_gs = map2 eta_expand_arg xss xgs;
   387 
   388     val case_binding =
   389       qualify false
   390         (if Binding.is_empty raw_case_binding orelse
   391             Binding.eq_name (raw_case_binding, standard_binding) then
   392            Binding.prefix_name (caseN ^ "_") fc_b
   393          else
   394            raw_case_binding);
   395 
   396     fun mk_case_disj xctr xf xs =
   397       list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr), HOLogic.mk_eq (w, xf)));
   398 
   399     val case_rhs = fold_rev (fold_rev Term.lambda) [fs, [u]]
   400       (Const (@{const_name The}, (B --> HOLogic.boolT) --> B) $
   401          Term.lambda w (Library.foldr1 HOLogic.mk_disj (map3 mk_case_disj xctrs xfs xss)));
   402 
   403     val ((raw_case, (_, raw_case_def)), (lthy', lthy)) = no_defs_lthy
   404       |> Local_Theory.define ((case_binding, NoSyn),
   405         ((Binding.conceal (Thm.def_binding case_binding), []), case_rhs))
   406       ||> `Local_Theory.restore;
   407 
   408     val phi = Proof_Context.export_morphism lthy lthy';
   409 
   410     val case_def = Morphism.thm phi raw_case_def;
   411 
   412     val case0 = Morphism.term phi raw_case;
   413     val casex = mk_case As B case0;
   414 
   415     val fcase = Term.list_comb (casex, fs);
   416 
   417     val ufcase = fcase $ u;
   418     val vfcase = fcase $ v;
   419 
   420     val eta_fcase = Term.list_comb (casex, eta_fs);
   421     val eta_gcase = Term.list_comb (casex, eta_gs);
   422 
   423     val eta_ufcase = eta_fcase $ u;
   424     val eta_vgcase = eta_gcase $ v;
   425 
   426     fun mk_uu_eq () = HOLogic.mk_eq (u, u);
   427 
   428     val uv_eq = mk_Trueprop_eq (u, v);
   429 
   430     val exist_xs_u_eq_ctrs =
   431       map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
   432 
   433     val unique_disc_no_def = TrueI; (*arbitrary marker*)
   434     val alternate_disc_no_def = FalseE; (*arbitrary marker*)
   435 
   436     fun alternate_disc_lhs get_udisc k =
   437       HOLogic.mk_not
   438         (let val b = nth disc_bindings (k - 1) in
   439            if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
   440          end);
   441 
   442     val (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy') =
   443       if no_discs_sels then
   444         (true, [], [], [], [], [], lthy')
   445       else
   446         let
   447           fun disc_free b = Free (Binding.name_of b, mk_pred1T fcT);
   448 
   449           fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
   450 
   451           fun alternate_disc k =
   452             Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
   453 
   454           fun mk_sel_case_args b proto_sels T =
   455             map2 (fn Ts => fn k =>
   456               (case AList.lookup (op =) proto_sels k of
   457                 NONE =>
   458                 (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
   459                   NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
   460                 | SOME t => t |> Type.constraint (Ts ---> T) |> Syntax.check_term lthy)
   461               | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
   462 
   463           fun sel_spec b proto_sels =
   464             let
   465               val _ =
   466                 (case duplicates (op =) (map fst proto_sels) of
   467                    k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
   468                      " for constructor " ^
   469                      quote (Syntax.string_of_term lthy (nth ctrs (k - 1))))
   470                  | [] => ())
   471               val T =
   472                 (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
   473                   [T] => T
   474                 | T :: T' :: _ => error ("Inconsistent range type for selector " ^
   475                     quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ lthy T) ^ " vs. "
   476                     ^ quote (Syntax.string_of_typ lthy T')));
   477             in
   478               mk_Trueprop_eq (Free (Binding.name_of b, fcT --> T) $ u,
   479                 Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
   480             end;
   481 
   482           val sel_bindings = flat sel_bindingss;
   483           val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
   484           val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
   485 
   486           val sel_binding_index =
   487             if all_sels_distinct then 1 upto length sel_bindings
   488             else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
   489 
   490           val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
   491           val sel_infos =
   492             AList.group (op =) (sel_binding_index ~~ proto_sels)
   493             |> sort (int_ord o pairself fst)
   494             |> map snd |> curry (op ~~) uniq_sel_bindings;
   495           val sel_bindings = map fst sel_infos;
   496 
   497           fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
   498 
   499           val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
   500             lthy
   501             |> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
   502                 if Binding.is_empty b then
   503                   if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
   504                   else pair (alternate_disc k, alternate_disc_no_def)
   505                 else if Binding.eq_name (b, equal_binding) then
   506                   pair (Term.lambda u exist_xs_u_eq_ctr, refl)
   507                 else
   508                   Specification.definition (SOME (b, NONE, NoSyn),
   509                     ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
   510               ks exist_xs_u_eq_ctrs disc_bindings
   511             ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
   512               Specification.definition (SOME (b, NONE, NoSyn),
   513                 ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
   514             ||> `Local_Theory.restore;
   515 
   516           val phi = Proof_Context.export_morphism lthy lthy';
   517 
   518           val disc_defs = map (Morphism.thm phi) raw_disc_defs;
   519           val sel_defs = map (Morphism.thm phi) raw_sel_defs;
   520           val sel_defss = unflat_selss sel_defs;
   521 
   522           val discs0 = map (Morphism.term phi) raw_discs;
   523           val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
   524 
   525           val discs = map (mk_disc_or_sel As) discs0;
   526           val selss = map (map (mk_disc_or_sel As)) selss0;
   527         in
   528           (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy')
   529         end;
   530 
   531     fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
   532 
   533     val exhaust_goal =
   534       let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (exh_y, xctr)]) in
   535         fold_rev Logic.all [p, exh_y] (mk_imp_p (map2 mk_prem xctrs xss))
   536       end;
   537 
   538     val inject_goalss =
   539       let
   540         fun mk_goal _ _ [] [] = []
   541           | mk_goal xctr yctr xs ys =
   542             [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
   543               Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
   544       in
   545         map4 mk_goal xctrs yctrs xss yss
   546       end;
   547 
   548     val half_distinct_goalss =
   549       let
   550         fun mk_goal ((xs, xc), (xs', xc')) =
   551           fold_rev Logic.all (xs @ xs')
   552             (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
   553       in
   554         map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
   555       end;
   556 
   557     val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss;
   558 
   559     fun after_qed thmss lthy =
   560       let
   561         val ([exhaust_thm0], (inject_thmss, half_distinct_thmss)) = (hd thmss, chop n (tl thmss));
   562         (* for "datatype_realizer.ML": *)
   563         val exhaust_thm =
   564           Thm.name_derivation (fcT_name ^ Long_Name.separator ^ exhaustN) exhaust_thm0;
   565 
   566         val inject_thms = flat inject_thmss;
   567 
   568         val rho_As = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
   569 
   570         fun inst_thm t thm =
   571           Drule.instantiate' [] [SOME (certify lthy t)]
   572             (Thm.instantiate (rho_As, []) (Drule.zero_var_indexes thm));
   573 
   574         val uexhaust_thm = inst_thm u exhaust_thm;
   575 
   576         val exhaust_cases = map base_name_of_ctr ctrs;
   577 
   578         val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
   579 
   580         val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
   581           join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
   582 
   583         val nchotomy_thm =
   584           let
   585             val goal =
   586               HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
   587                 Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
   588           in
   589             Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
   590             |> Thm.close_derivation
   591           end;
   592 
   593         val case_thms =
   594           let
   595             val goals =
   596               map3 (fn xctr => fn xf => fn xs =>
   597                 fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xctrs xfs xss;
   598           in
   599             map4 (fn k => fn goal => fn injects => fn distinctss =>
   600                 Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   601                   mk_case_tac ctxt n k case_def injects distinctss)
   602                 |> Thm.close_derivation)
   603               ks goals inject_thmss distinct_thmsss
   604           end;
   605 
   606         val (case_cong_thm, weak_case_cong_thm) =
   607           let
   608             fun mk_prem xctr xs xf xg =
   609               fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
   610                 mk_Trueprop_eq (xf, xg)));
   611 
   612             val goal =
   613               Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
   614                  mk_Trueprop_eq (eta_ufcase, eta_vgcase));
   615             val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
   616           in
   617             (Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
   618              Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
   619             |> pairself (singleton (Proof_Context.export names_lthy lthy) #>
   620               Thm.close_derivation)
   621           end;
   622 
   623         val split_lhs = q $ ufcase;
   624 
   625         fun mk_split_conjunct xctr xs f_xs =
   626           list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
   627         fun mk_split_disjunct xctr xs f_xs =
   628           list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
   629             HOLogic.mk_not (q $ f_xs)));
   630 
   631         fun mk_split_goal xctrs xss xfs =
   632           mk_Trueprop_eq (split_lhs, Library.foldr1 HOLogic.mk_conj
   633             (map3 mk_split_conjunct xctrs xss xfs));
   634         fun mk_split_asm_goal xctrs xss xfs =
   635           mk_Trueprop_eq (split_lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
   636             (map3 mk_split_disjunct xctrs xss xfs)));
   637 
   638         fun prove_split selss goal =
   639           Goal.prove_sorry lthy [] [] goal (fn _ =>
   640             mk_split_tac lthy uexhaust_thm case_thms selss inject_thmss distinct_thmsss)
   641           |> singleton (Proof_Context.export names_lthy lthy)
   642           |> Thm.close_derivation;
   643 
   644         fun prove_split_asm asm_goal split_thm =
   645           Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
   646             mk_split_asm_tac ctxt split_thm)
   647           |> singleton (Proof_Context.export names_lthy lthy)
   648           |> Thm.close_derivation;
   649 
   650         val (split_thm, split_asm_thm) =
   651           let
   652             val goal = mk_split_goal xctrs xss xfs;
   653             val asm_goal = mk_split_asm_goal xctrs xss xfs;
   654 
   655             val thm = prove_split (replicate n []) goal;
   656             val asm_thm = prove_split_asm asm_goal thm;
   657           in
   658             (thm, asm_thm)
   659           end;
   660 
   661         val (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thms, discI_thms, nontriv_discI_thms,
   662              disc_exclude_thms, disc_exclude_thmsss, disc_exhaust_thms, sel_exhaust_thms,
   663              all_collapse_thms, safe_collapse_thms, expand_thms, sel_split_thms, sel_split_asm_thms,
   664              case_eq_if_thms) =
   665           if no_discs_sels then
   666             ([], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [])
   667           else
   668             let
   669               val udiscs = map (rapp u) discs;
   670               val uselss = map (map (rapp u)) selss;
   671               val usel_ctrs = map2 (curry Term.list_comb) ctrs uselss;
   672               val usel_fs = map2 (curry Term.list_comb) fs uselss;
   673 
   674               val vdiscs = map (rapp v) discs;
   675               val vselss = map (map (rapp v)) selss;
   676 
   677               fun make_sel_thm xs' case_thm sel_def =
   678                 zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
   679                     (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
   680 
   681               val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
   682 
   683               fun has_undefined_rhs thm =
   684                 (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
   685                   Const (@{const_name undefined}, _) => true
   686                 | _ => false);
   687 
   688               val all_sel_thms =
   689                 (if all_sels_distinct andalso forall null sel_defaultss then
   690                    flat sel_thmss
   691                  else
   692                    map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
   693                      (xss' ~~ case_thms))
   694                 |> filter_out has_undefined_rhs;
   695 
   696               fun mk_unique_disc_def () =
   697                 let
   698                   val m = the_single ms;
   699                   val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
   700                 in
   701                   Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
   702                   |> singleton (Proof_Context.export names_lthy lthy)
   703                   |> Thm.close_derivation
   704                 end;
   705 
   706               fun mk_alternate_disc_def k =
   707                 let
   708                   val goal =
   709                     mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
   710                       nth exist_xs_u_eq_ctrs (k - 1));
   711                 in
   712                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   713                     mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
   714                       (nth distinct_thms (2 - k)) uexhaust_thm)
   715                   |> singleton (Proof_Context.export names_lthy lthy)
   716                   |> Thm.close_derivation
   717                 end;
   718 
   719               val has_alternate_disc_def =
   720                 exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
   721 
   722               val disc_defs' =
   723                 map2 (fn k => fn def =>
   724                   if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
   725                   else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
   726                   else def) ks disc_defs;
   727 
   728               val discD_thms = map (fn def => def RS iffD1) disc_defs';
   729               val discI_thms =
   730                 map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
   731                   disc_defs';
   732               val not_discI_thms =
   733                 map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
   734                     (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
   735                   ms disc_defs';
   736 
   737               val (disc_thmss', disc_thmss) =
   738                 let
   739                   fun mk_thm discI _ [] = refl RS discI
   740                     | mk_thm _ not_discI [distinct] = distinct RS not_discI;
   741                   fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
   742                 in
   743                   map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
   744                 end;
   745 
   746               val nontriv_disc_thms =
   747                 flat (map2 (fn b => if is_disc_binding_valid b then I else K [])
   748                   disc_bindings disc_thmss);
   749 
   750               fun is_discI_boring b =
   751                 (n = 1 andalso Binding.is_empty b) orelse Binding.eq_name (b, equal_binding);
   752 
   753               val nontriv_discI_thms =
   754                 flat (map2 (fn b => if is_discI_boring b then K [] else single) disc_bindings
   755                   discI_thms);
   756 
   757               val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
   758                 let
   759                   fun mk_goal [] = []
   760                     | mk_goal [((_, udisc), (_, udisc'))] =
   761                       [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
   762                          HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
   763 
   764                   fun prove tac goal =
   765                     Goal.prove_sorry lthy [] [] goal (K tac)
   766                     |> Thm.close_derivation;
   767 
   768                   val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
   769 
   770                   val half_goalss = map mk_goal half_pairss;
   771                   val half_thmss =
   772                     map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
   773                         fn disc_thm => [prove (mk_half_disc_exclude_tac lthy m discD disc_thm) goal])
   774                       half_goalss half_pairss (flat disc_thmss');
   775 
   776                   val other_half_goalss = map (mk_goal o map swap) half_pairss;
   777                   val other_half_thmss =
   778                     map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
   779                       other_half_goalss;
   780                 in
   781                   join_halves n half_thmss other_half_thmss ||> `transpose
   782                   |>> has_alternate_disc_def ? K []
   783                 end;
   784 
   785               val disc_exhaust_thm =
   786                 let
   787                   fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
   788                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
   789                 in
   790                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   791                     mk_disc_exhaust_tac n exhaust_thm discI_thms)
   792                   |> Thm.close_derivation
   793                 end;
   794 
   795               val (safe_collapse_thms, all_collapse_thms) =
   796                 let
   797                   fun mk_goal m udisc usel_ctr =
   798                     let
   799                       val prem = HOLogic.mk_Trueprop udisc;
   800                       val concl = mk_Trueprop_eq ((usel_ctr, u) |> m = 0 ? swap);
   801                     in
   802                       (prem aconv concl, Logic.all u (Logic.mk_implies (prem, concl)))
   803                     end;
   804                   val (trivs, goals) = map3 mk_goal ms udiscs usel_ctrs |> split_list;
   805                   val thms =
   806                     map5 (fn m => fn discD => fn sel_thms => fn triv => fn goal =>
   807                         Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   808                           mk_collapse_tac ctxt m discD sel_thms ORELSE HEADGOAL atac)
   809                         |> Thm.close_derivation
   810                         |> not triv ? perhaps (try (fn thm => refl RS thm)))
   811                       ms discD_thms sel_thmss trivs goals;
   812                 in
   813                   (map_filter (fn (true, _) => NONE | (false, thm) => SOME thm) (trivs ~~ thms),
   814                    thms)
   815                 end;
   816 
   817               val swapped_all_collapse_thms =
   818                 map2 (fn m => fn thm => if m = 0 then thm else thm RS sym) ms all_collapse_thms;
   819 
   820               val sel_exhaust_thm =
   821                 let
   822                   fun mk_prem usel_ctr = mk_imp_p [mk_Trueprop_eq (u, usel_ctr)];
   823                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem usel_ctrs));
   824                 in
   825                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   826                     mk_sel_exhaust_tac n disc_exhaust_thm swapped_all_collapse_thms)
   827                   |> Thm.close_derivation
   828                 end;
   829 
   830               val expand_thm =
   831                 let
   832                   fun mk_prems k udisc usels vdisc vsels =
   833                     (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
   834                     (if null usels then
   835                        []
   836                      else
   837                        [Logic.list_implies
   838                           (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
   839                              HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
   840                                (map2 (curry HOLogic.mk_eq) usels vsels)))]);
   841 
   842                   val goal =
   843                     Library.foldr Logic.list_implies
   844                       (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
   845                   val uncollapse_thms =
   846                     map2 (fn thm => fn [] => thm | _ => thm RS sym) all_collapse_thms uselss;
   847                 in
   848                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   849                     mk_expand_tac lthy n ms (inst_thm u disc_exhaust_thm)
   850                       (inst_thm v disc_exhaust_thm) uncollapse_thms disc_exclude_thmsss
   851                       disc_exclude_thmsss')
   852                   |> singleton (Proof_Context.export names_lthy lthy)
   853                   |> Thm.close_derivation
   854                 end;
   855 
   856               val (sel_split_thm, sel_split_asm_thm) =
   857                 let
   858                   val zss = map (K []) xss;
   859                   val goal = mk_split_goal usel_ctrs zss usel_fs;
   860                   val asm_goal = mk_split_asm_goal usel_ctrs zss usel_fs;
   861 
   862                   val thm = prove_split sel_thmss goal;
   863                   val asm_thm = prove_split_asm asm_goal thm;
   864                 in
   865                   (thm, asm_thm)
   866                 end;
   867 
   868               val case_eq_if_thm =
   869                 let
   870                   val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs usel_fs);
   871                 in
   872                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   873                     mk_case_eq_if_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)
   874                   |> singleton (Proof_Context.export names_lthy lthy)
   875                   |> Thm.close_derivation
   876                 end;
   877             in
   878               (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thms, discI_thms,
   879                nontriv_discI_thms, disc_exclude_thms, disc_exclude_thmsss, [disc_exhaust_thm],
   880                [sel_exhaust_thm], all_collapse_thms, safe_collapse_thms, [expand_thm],
   881                [sel_split_thm], [sel_split_asm_thm], [case_eq_if_thm])
   882             end;
   883 
   884         val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
   885         val cases_type_attr = Attrib.internal (K (Induct.cases_type fcT_name));
   886 
   887         val anonymous_notes =
   888           [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs),
   889            (map (fn th => th RS @{thm eq_False[THEN iffD2]}
   890               handle THM _ => th RS @{thm eq_True[THEN iffD2]}) nontriv_disc_thms,
   891             code_nitpicksimp_attrs)]
   892           |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
   893 
   894         val notes =
   895           [(caseN, case_thms, code_nitpicksimp_simp_attrs),
   896            (case_congN, [case_cong_thm], []),
   897            (case_eq_ifN, case_eq_if_thms, []),
   898            (collapseN, safe_collapse_thms, simp_attrs),
   899            (discN, nontriv_disc_thms, simp_attrs),
   900            (discIN, nontriv_discI_thms, []),
   901            (disc_excludeN, disc_exclude_thms, dest_attrs),
   902            (disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
   903            (distinctN, distinct_thms, simp_attrs @ inductsimp_attrs),
   904            (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
   905            (expandN, expand_thms, []),
   906            (injectN, inject_thms, iff_attrs @ inductsimp_attrs),
   907            (nchotomyN, [nchotomy_thm], []),
   908            (selN, all_sel_thms, code_nitpicksimp_simp_attrs),
   909            (sel_exhaustN, sel_exhaust_thms, [exhaust_case_names_attr]),
   910            (sel_splitN, sel_split_thms, []),
   911            (sel_split_asmN, sel_split_asm_thms, []),
   912            (splitN, [split_thm], []),
   913            (split_asmN, [split_asm_thm], []),
   914            (splitsN, [split_thm, split_asm_thm], []),
   915            (weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
   916           |> filter_out (null o #2)
   917           |> map (fn (thmN, thms, attrs) =>
   918             ((qualify true (Binding.name thmN), attrs), [(thms, [])]));
   919 
   920         val ctr_sugar =
   921           {ctrs = ctrs, casex = casex, discs = discs, selss = selss, exhaust = exhaust_thm,
   922            nchotomy = nchotomy_thm, injects = inject_thms, distincts = distinct_thms,
   923            case_thms = case_thms, case_cong = case_cong_thm, weak_case_cong = weak_case_cong_thm,
   924            split = split_thm, split_asm = split_asm_thm, disc_thmss = disc_thmss,
   925            discIs = discI_thms, sel_thmss = sel_thmss, disc_excludesss = disc_exclude_thmsss,
   926            disc_exhausts = disc_exhaust_thms, sel_exhausts = sel_exhaust_thms,
   927            collapses = all_collapse_thms, expands = expand_thms, sel_splits = sel_split_thms,
   928            sel_split_asms = sel_split_asm_thms, case_eq_ifs = case_eq_if_thms};
   929       in
   930         (ctr_sugar,
   931          lthy
   932          |> not rep_compat ?
   933             Local_Theory.declaration {syntax = false, pervasive = true}
   934               (fn phi => Case_Translation.register
   935                  (Morphism.term phi casex) (map (Morphism.term phi) ctrs))
   936          |> Local_Theory.background_theory (fold (fold Code.del_eqn) [disc_defs, sel_defs])
   937          |> not no_code ?
   938             Local_Theory.declaration {syntax = false, pervasive = false}
   939               (fn phi => Context.mapping
   940                 (add_ctr_code fcT_name (map (Morphism.typ phi) As)
   941                   (map (dest_Const o Morphism.term phi) ctrs) (Morphism.fact phi inject_thms)
   942                   (Morphism.fact phi distinct_thms) (Morphism.fact phi case_thms))
   943                 I)
   944          |> Local_Theory.notes (anonymous_notes @ notes) |> snd
   945          |> register_ctr_sugar fcT_name ctr_sugar)
   946       end;
   947   in
   948     (goalss, after_qed, lthy')
   949   end;
   950 
   951 fun wrap_free_constructors tacss = (fn (goalss, after_qed, lthy) =>
   952   map2 (map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])) goalss tacss
   953   |> (fn thms => after_qed thms lthy)) oo prepare_wrap_free_constructors (K I);
   954 
   955 val wrap_free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
   956   Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
   957   prepare_wrap_free_constructors Syntax.read_term;
   958 
   959 fun parse_bracket_list parser = @{keyword "["} |-- Parse.list parser --|  @{keyword "]"};
   960 
   961 val parse_bindings = parse_bracket_list parse_binding;
   962 val parse_bindingss = parse_bracket_list parse_bindings;
   963 
   964 val parse_bound_term = (parse_binding --| @{keyword ":"}) -- Parse.term;
   965 val parse_bound_terms = parse_bracket_list parse_bound_term;
   966 val parse_bound_termss = parse_bracket_list parse_bound_terms;
   967 
   968 val parse_wrap_free_constructors_options =
   969   Scan.optional (@{keyword "("} |-- Parse.list1
   970         (Parse.reserved "no_discs_sels" >> K 0 || Parse.reserved "no_code" >> K 1 ||
   971          Parse.reserved "rep_compat" >> K 2) --| @{keyword ")"}
   972       >> (fn js => (member (op =) js 0, (member (op =) js 1, member (op =) js 2))))
   973     (false, (false, false));
   974 
   975 val _ =
   976   Outer_Syntax.local_theory_to_proof @{command_spec "wrap_free_constructors"}
   977     "wrap an existing freely generated type's constructors"
   978     ((parse_wrap_free_constructors_options -- (@{keyword "["} |-- Parse.list Parse.term --|
   979         @{keyword "]"}) --
   980       parse_binding -- Scan.optional (parse_bindings -- Scan.optional (parse_bindingss --
   981         Scan.optional parse_bound_termss []) ([], [])) ([], ([], [])))
   982      >> wrap_free_constructors_cmd);
   983 
   984 end;