src/HOL/Tools/Ctr_Sugar/ctr_sugar.ML
author blanchet
Thu Jan 02 09:50:22 2014 +0100 (2014-01-02)
changeset 54900 136fe16e726a
parent 54740 91f54d386680
child 54970 891141de5672
permissions -rw-r--r--
generate 'disc_iff' property in 'primcorec'
     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 -> (term list * term list) option
    56 
    57   val wrap_free_constructors: ({prems: thm list, context: Proof.context} -> tactic) list list ->
    58     (((bool * (bool * bool)) * term list) * binding) *
    59       (binding list * (binding list list * (binding * term) list list)) -> local_theory ->
    60     ctr_sugar * local_theory
    61   val parse_wrap_free_constructors_options: (bool * (bool * bool)) parser
    62   val parse_bound_term: (binding * string) parser
    63 end;
    64 
    65 structure Ctr_Sugar : CTR_SUGAR =
    66 struct
    67 
    68 open Ctr_Sugar_Util
    69 open Ctr_Sugar_Tactics
    70 open Ctr_Sugar_Code
    71 
    72 type ctr_sugar =
    73   {ctrs: term list,
    74    casex: term,
    75    discs: term list,
    76    selss: term list list,
    77    exhaust: thm,
    78    nchotomy: thm,
    79    injects: thm list,
    80    distincts: thm list,
    81    case_thms: thm list,
    82    case_cong: thm,
    83    weak_case_cong: thm,
    84    split: thm,
    85    split_asm: thm,
    86    disc_thmss: thm list list,
    87    discIs: thm list,
    88    sel_thmss: thm list list,
    89    disc_excludesss: thm list list list,
    90    disc_exhausts: thm list,
    91    sel_exhausts: thm list,
    92    collapses: thm list,
    93    expands: thm list,
    94    sel_splits: thm list,
    95    sel_split_asms: thm list,
    96    case_eq_ifs: thm list};
    97 
    98 fun eq_ctr_sugar ({ctrs = ctrs1, casex = case1, discs = discs1, selss = selss1, ...} : ctr_sugar,
    99     {ctrs = ctrs2, casex = case2, discs = discs2, selss = selss2, ...} : ctr_sugar) =
   100   ctrs1 = ctrs2 andalso case1 = case2 andalso discs1 = discs2 andalso selss1 = selss2;
   101 
   102 fun morph_ctr_sugar phi {ctrs, casex, discs, selss, exhaust, nchotomy, injects, distincts,
   103     case_thms, case_cong, weak_case_cong, split, split_asm, disc_thmss, discIs, sel_thmss,
   104     disc_excludesss, disc_exhausts, sel_exhausts, collapses, expands, sel_splits, sel_split_asms,
   105     case_eq_ifs} =
   106   {ctrs = map (Morphism.term phi) ctrs,
   107    casex = Morphism.term phi casex,
   108    discs = map (Morphism.term phi) discs,
   109    selss = map (map (Morphism.term phi)) selss,
   110    exhaust = Morphism.thm phi exhaust,
   111    nchotomy = Morphism.thm phi nchotomy,
   112    injects = map (Morphism.thm phi) injects,
   113    distincts = map (Morphism.thm phi) distincts,
   114    case_thms = map (Morphism.thm phi) case_thms,
   115    case_cong = Morphism.thm phi case_cong,
   116    weak_case_cong = Morphism.thm phi weak_case_cong,
   117    split = Morphism.thm phi split,
   118    split_asm = Morphism.thm phi split_asm,
   119    disc_thmss = map (map (Morphism.thm phi)) disc_thmss,
   120    discIs = map (Morphism.thm phi) discIs,
   121    sel_thmss = map (map (Morphism.thm phi)) sel_thmss,
   122    disc_excludesss = map (map (map (Morphism.thm phi))) disc_excludesss,
   123    disc_exhausts = map (Morphism.thm phi) disc_exhausts,
   124    sel_exhausts = map (Morphism.thm phi) sel_exhausts,
   125    collapses = map (Morphism.thm phi) collapses,
   126    expands = map (Morphism.thm phi) expands,
   127    sel_splits = map (Morphism.thm phi) sel_splits,
   128    sel_split_asms = map (Morphism.thm phi) sel_split_asms,
   129    case_eq_ifs = map (Morphism.thm phi) case_eq_ifs};
   130 
   131 val transfer_ctr_sugar =
   132   morph_ctr_sugar o Morphism.transfer_morphism o Proof_Context.theory_of;
   133 
   134 structure Data = Generic_Data
   135 (
   136   type T = ctr_sugar Symtab.table;
   137   val empty = Symtab.empty;
   138   val extend = I;
   139   val merge = Symtab.merge eq_ctr_sugar;
   140 );
   141 
   142 fun ctr_sugar_of ctxt =
   143   Symtab.lookup (Data.get (Context.Proof ctxt))
   144   #> Option.map (transfer_ctr_sugar ctxt);
   145 
   146 fun ctr_sugars_of ctxt =
   147   Symtab.fold (cons o transfer_ctr_sugar ctxt o snd) (Data.get (Context.Proof ctxt)) [];
   148 
   149 fun ctr_sugar_of_case ctxt s =
   150   find_first (fn {casex = Const (s', _), ...} => s' = s | _ => false) (ctr_sugars_of ctxt);
   151 
   152 fun register_ctr_sugar key ctr_sugar =
   153   Local_Theory.declaration {syntax = false, pervasive = true}
   154     (fn phi => Data.map (Symtab.default (key, morph_ctr_sugar phi ctr_sugar)));
   155 
   156 fun register_ctr_sugar_global key ctr_sugar =
   157   Context.theory_map (Data.map (Symtab.default (key, ctr_sugar)));
   158 
   159 val rep_compat_prefix = "new";
   160 
   161 val isN = "is_";
   162 val unN = "un_";
   163 fun mk_unN 1 1 suf = unN ^ suf
   164   | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
   165 
   166 val caseN = "case";
   167 val case_congN = "case_cong";
   168 val case_eq_ifN = "case_eq_if";
   169 val collapseN = "collapse";
   170 val disc_excludeN = "disc_exclude";
   171 val disc_exhaustN = "disc_exhaust";
   172 val discN = "disc";
   173 val discIN = "discI";
   174 val distinctN = "distinct";
   175 val exhaustN = "exhaust";
   176 val expandN = "expand";
   177 val injectN = "inject";
   178 val nchotomyN = "nchotomy";
   179 val selN = "sel";
   180 val sel_exhaustN = "sel_exhaust";
   181 val sel_splitN = "sel_split";
   182 val sel_split_asmN = "sel_split_asm";
   183 val splitN = "split";
   184 val splitsN = "splits";
   185 val split_asmN = "split_asm";
   186 val weak_case_cong_thmsN = "weak_case_cong";
   187 
   188 val cong_attrs = @{attributes [cong]};
   189 val dest_attrs = @{attributes [dest]};
   190 val safe_elim_attrs = @{attributes [elim!]};
   191 val iff_attrs = @{attributes [iff]};
   192 val inductsimp_attrs = @{attributes [induct_simp]};
   193 val nitpicksimp_attrs = @{attributes [nitpick_simp]};
   194 val simp_attrs = @{attributes [simp]};
   195 val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
   196 val code_nitpicksimp_simp_attrs = code_nitpicksimp_attrs @ simp_attrs;
   197 
   198 fun unflat_lookup eq xs ys = map (fn xs' => permute_like eq xs xs' ys);
   199 
   200 fun mk_half_pairss' _ ([], []) = []
   201   | mk_half_pairss' indent (x :: xs, _ :: ys) =
   202     indent @ fold_rev (cons o single o pair x) ys (mk_half_pairss' ([] :: indent) (xs, ys));
   203 
   204 fun mk_half_pairss p = mk_half_pairss' [[]] p;
   205 
   206 fun join_halves n half_xss other_half_xss =
   207   let
   208     val xsss =
   209       map2 (map2 append) (Library.chop_groups n half_xss)
   210         (transpose (Library.chop_groups n other_half_xss))
   211     val xs = splice (flat half_xss) (flat other_half_xss);
   212   in (xs, xsss) end;
   213 
   214 fun mk_undefined T = Const (@{const_name undefined}, T);
   215 
   216 fun mk_ctr Ts t =
   217   let val Type (_, Ts0) = body_type (fastype_of t) in
   218     subst_nonatomic_types (Ts0 ~~ Ts) t
   219   end;
   220 
   221 fun mk_case Ts T t =
   222   let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
   223     subst_nonatomic_types ((body, T) :: (Ts0 ~~ Ts)) t
   224   end;
   225 
   226 fun mk_disc_or_sel Ts t =
   227   subst_nonatomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
   228 
   229 fun name_of_const what t =
   230   (case head_of t of
   231     Const (s, _) => s
   232   | Free (s, _) => s
   233   | _ => error ("Cannot extract name of " ^ what));
   234 
   235 val name_of_ctr = name_of_const "constructor";
   236 
   237 val notN = "not_";
   238 val eqN = "eq_";
   239 val neqN = "neq_";
   240 
   241 fun name_of_disc t =
   242   (case head_of t of
   243     Abs (_, _, @{const Not} $ (t' $ Bound 0)) =>
   244     Long_Name.map_base_name (prefix notN) (name_of_disc t')
   245   | Abs (_, _, Const (@{const_name HOL.eq}, _) $ Bound 0 $ t') =>
   246     Long_Name.map_base_name (prefix eqN) (name_of_disc t')
   247   | Abs (_, _, @{const Not} $ (Const (@{const_name HOL.eq}, _) $ Bound 0 $ t')) =>
   248     Long_Name.map_base_name (prefix neqN) (name_of_disc t')
   249   | t' => name_of_const "destructor" t');
   250 
   251 val base_name_of_ctr = Long_Name.base_name o name_of_ctr;
   252 
   253 fun dest_ctr ctxt s t =
   254   let
   255     val (f, args) = Term.strip_comb t;
   256   in
   257     (case ctr_sugar_of ctxt s of
   258       SOME {ctrs, ...} =>
   259       (case find_first (can (fo_match ctxt f)) ctrs of
   260         SOME f' => (f', args)
   261       | NONE => raise Fail "dest_ctr")
   262     | NONE => raise Fail "dest_ctr")
   263   end;
   264 
   265 fun dest_case ctxt s Ts t =
   266   (case Term.strip_comb t of
   267     (Const (c, _), args as _ :: _) =>
   268     (case ctr_sugar_of ctxt s of
   269       SOME {casex = Const (case_name, _), discs = discs0, selss = selss0, ...} =>
   270       if case_name = c then
   271         let val n = length discs0 in
   272           if n < length args then
   273             let
   274               val (branches, obj :: leftovers) = chop n args;
   275               val discs = map (mk_disc_or_sel Ts) discs0;
   276               val selss = map (map (mk_disc_or_sel Ts)) selss0;
   277               val conds = map (rapp obj) discs;
   278               val branch_argss = map (fn sels => map (rapp obj) sels @ leftovers) selss;
   279               val branches' = map2 (curry Term.betapplys) branches branch_argss;
   280             in
   281               SOME (conds, branches')
   282             end
   283           else
   284             NONE
   285         end
   286       else
   287         NONE
   288     | _ => NONE)
   289   | _ => NONE);
   290 
   291 fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
   292 
   293 fun prepare_wrap_free_constructors prep_term ((((no_discs_sels, (no_code, rep_compat)), raw_ctrs),
   294     raw_case_binding), (raw_disc_bindings, (raw_sel_bindingss, raw_sel_defaultss))) no_defs_lthy =
   295   let
   296     (* TODO: sanity checks on arguments *)
   297 
   298     val n = length raw_ctrs;
   299     val ks = 1 upto n;
   300 
   301     val _ = if n > 0 then () else error "No constructors specified";
   302 
   303     val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
   304     val sel_defaultss =
   305       pad_list [] n (map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss);
   306 
   307     val Type (fcT_name, As0) = body_type (fastype_of (hd ctrs0));
   308     val fc_b_name = Long_Name.base_name fcT_name;
   309     val fc_b = Binding.name fc_b_name;
   310 
   311     fun qualify mandatory =
   312       Binding.qualify mandatory fc_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
   313 
   314     fun dest_TFree_or_TVar (TFree sS) = sS
   315       | dest_TFree_or_TVar (TVar ((s, _), S)) = (s, S)
   316       | dest_TFree_or_TVar _ = error "Invalid type argument";
   317 
   318     val (unsorted_As, B) =
   319       no_defs_lthy
   320       |> variant_tfrees (map (fst o dest_TFree_or_TVar) As0)
   321       ||> the_single o fst o mk_TFrees 1;
   322 
   323     val As = map2 (resort_tfree o snd o dest_TFree_or_TVar) As0 unsorted_As;
   324 
   325     val fcT = Type (fcT_name, As);
   326     val ctrs = map (mk_ctr As) ctrs0;
   327     val ctr_Tss = map (binder_types o fastype_of) ctrs;
   328 
   329     val ms = map length ctr_Tss;
   330 
   331     val raw_disc_bindings' = pad_list Binding.empty n raw_disc_bindings;
   332 
   333     fun can_definitely_rely_on_disc k = not (Binding.is_empty (nth raw_disc_bindings' (k - 1)));
   334     fun can_rely_on_disc k =
   335       can_definitely_rely_on_disc k orelse (k = 1 andalso not (can_definitely_rely_on_disc 2));
   336     fun should_omit_disc_binding k = n = 1 orelse (n = 2 andalso can_rely_on_disc (3 - k));
   337 
   338     fun is_disc_binding_valid b =
   339       not (Binding.is_empty b orelse Binding.eq_name (b, equal_binding));
   340 
   341     val standard_disc_binding = Binding.name o prefix isN o base_name_of_ctr;
   342 
   343     val disc_bindings =
   344       raw_disc_bindings'
   345       |> map4 (fn k => fn m => fn ctr => fn disc =>
   346         qualify false
   347           (if Binding.is_empty disc then
   348              if should_omit_disc_binding k then disc else standard_disc_binding ctr
   349            else if Binding.eq_name (disc, equal_binding) then
   350              if m = 0 then disc
   351              else error "Cannot use \"=\" syntax for discriminating nonnullary constructor"
   352            else if Binding.eq_name (disc, standard_binding) then
   353              standard_disc_binding ctr
   354            else
   355              disc)) ks ms ctrs0;
   356 
   357     fun standard_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
   358 
   359     val sel_bindingss =
   360       pad_list [] n raw_sel_bindingss
   361       |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
   362         qualify false
   363           (if Binding.is_empty sel orelse Binding.eq_name (sel, standard_binding) then
   364             standard_sel_binding m l ctr
   365           else
   366             sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms;
   367 
   368     val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
   369 
   370     val ((((((((xss, xss'), yss), fs), gs), [u', v']), [w]), (p, p')), names_lthy) = no_defs_lthy |>
   371       mk_Freess' "x" ctr_Tss
   372       ||>> mk_Freess "y" ctr_Tss
   373       ||>> mk_Frees "f" case_Ts
   374       ||>> mk_Frees "g" case_Ts
   375       ||>> (apfst (map (rpair fcT)) oo Variable.variant_fixes) [fc_b_name, fc_b_name ^ "'"]
   376       ||>> mk_Frees "z" [B]
   377       ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
   378 
   379     val u = Free u';
   380     val v = Free v';
   381     val q = Free (fst p', mk_pred1T B);
   382 
   383     val xctrs = map2 (curry Term.list_comb) ctrs xss;
   384     val yctrs = map2 (curry Term.list_comb) ctrs yss;
   385 
   386     val xfs = map2 (curry Term.list_comb) fs xss;
   387     val xgs = map2 (curry Term.list_comb) gs xss;
   388 
   389     (* TODO: Eta-expension is for compatibility with the old datatype package (but it also provides
   390        nicer names). Consider removing. *)
   391     val eta_fs = map2 eta_expand_arg xss xfs;
   392     val eta_gs = map2 eta_expand_arg xss xgs;
   393 
   394     val case_binding =
   395       qualify false
   396         (if Binding.is_empty raw_case_binding orelse
   397             Binding.eq_name (raw_case_binding, standard_binding) then
   398            Binding.prefix_name (caseN ^ "_") fc_b
   399          else
   400            raw_case_binding);
   401 
   402     fun mk_case_disj xctr xf xs =
   403       list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr), HOLogic.mk_eq (w, xf)));
   404 
   405     val case_rhs = fold_rev (fold_rev Term.lambda) [fs, [u]]
   406       (Const (@{const_name The}, (B --> HOLogic.boolT) --> B) $
   407          Term.lambda w (Library.foldr1 HOLogic.mk_disj (map3 mk_case_disj xctrs xfs xss)));
   408 
   409     val ((raw_case, (_, raw_case_def)), (lthy', lthy)) = no_defs_lthy
   410       |> Local_Theory.define ((case_binding, NoSyn),
   411         ((Binding.conceal (Thm.def_binding case_binding), []), case_rhs))
   412       ||> `Local_Theory.restore;
   413 
   414     val phi = Proof_Context.export_morphism lthy lthy';
   415 
   416     val case_def = Morphism.thm phi raw_case_def;
   417 
   418     val case0 = Morphism.term phi raw_case;
   419     val casex = mk_case As B case0;
   420 
   421     val fcase = Term.list_comb (casex, fs);
   422 
   423     val ufcase = fcase $ u;
   424     val vfcase = fcase $ v;
   425 
   426     val eta_fcase = Term.list_comb (casex, eta_fs);
   427     val eta_gcase = Term.list_comb (casex, eta_gs);
   428 
   429     val eta_ufcase = eta_fcase $ u;
   430     val eta_vgcase = eta_gcase $ v;
   431 
   432     fun mk_uu_eq () = HOLogic.mk_eq (u, u);
   433 
   434     val uv_eq = mk_Trueprop_eq (u, v);
   435 
   436     val exist_xs_u_eq_ctrs =
   437       map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
   438 
   439     val unique_disc_no_def = TrueI; (*arbitrary marker*)
   440     val alternate_disc_no_def = FalseE; (*arbitrary marker*)
   441 
   442     fun alternate_disc_lhs get_udisc k =
   443       HOLogic.mk_not
   444         (let val b = nth disc_bindings (k - 1) in
   445            if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
   446          end);
   447 
   448     val (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy') =
   449       if no_discs_sels then
   450         (true, [], [], [], [], [], lthy)
   451       else
   452         let
   453           fun disc_free b = Free (Binding.name_of b, mk_pred1T fcT);
   454 
   455           fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
   456 
   457           fun alternate_disc k =
   458             Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
   459 
   460           fun mk_sel_case_args b proto_sels T =
   461             map2 (fn Ts => fn k =>
   462               (case AList.lookup (op =) proto_sels k of
   463                 NONE =>
   464                 (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
   465                   NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
   466                 | SOME t => t |> Type.constraint (Ts ---> T) |> Syntax.check_term lthy)
   467               | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
   468 
   469           fun sel_spec b proto_sels =
   470             let
   471               val _ =
   472                 (case duplicates (op =) (map fst proto_sels) of
   473                    k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
   474                      " for constructor " ^
   475                      quote (Syntax.string_of_term lthy (nth ctrs (k - 1))))
   476                  | [] => ())
   477               val T =
   478                 (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
   479                   [T] => T
   480                 | T :: T' :: _ => error ("Inconsistent range type for selector " ^
   481                     quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ lthy T) ^ " vs. "
   482                     ^ quote (Syntax.string_of_typ lthy T')));
   483             in
   484               mk_Trueprop_eq (Free (Binding.name_of b, fcT --> T) $ u,
   485                 Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
   486             end;
   487 
   488           val sel_bindings = flat sel_bindingss;
   489           val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
   490           val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
   491 
   492           val sel_binding_index =
   493             if all_sels_distinct then 1 upto length sel_bindings
   494             else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
   495 
   496           val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
   497           val sel_infos =
   498             AList.group (op =) (sel_binding_index ~~ proto_sels)
   499             |> sort (int_ord o pairself fst)
   500             |> map snd |> curry (op ~~) uniq_sel_bindings;
   501           val sel_bindings = map fst sel_infos;
   502 
   503           fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
   504 
   505           val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
   506             lthy
   507             |> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
   508                 if Binding.is_empty b then
   509                   if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
   510                   else pair (alternate_disc k, alternate_disc_no_def)
   511                 else if Binding.eq_name (b, equal_binding) then
   512                   pair (Term.lambda u exist_xs_u_eq_ctr, refl)
   513                 else
   514                   Specification.definition (SOME (b, NONE, NoSyn),
   515                     ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
   516               ks exist_xs_u_eq_ctrs disc_bindings
   517             ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
   518               Specification.definition (SOME (b, NONE, NoSyn),
   519                 ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
   520             ||> `Local_Theory.restore;
   521 
   522           val phi = Proof_Context.export_morphism lthy lthy';
   523 
   524           val disc_defs = map (Morphism.thm phi) raw_disc_defs;
   525           val sel_defs = map (Morphism.thm phi) raw_sel_defs;
   526           val sel_defss = unflat_selss sel_defs;
   527 
   528           val discs0 = map (Morphism.term phi) raw_discs;
   529           val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
   530 
   531           val discs = map (mk_disc_or_sel As) discs0;
   532           val selss = map (map (mk_disc_or_sel As)) selss0;
   533         in
   534           (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy')
   535         end;
   536 
   537     fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
   538 
   539     val exhaust_goal =
   540       let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (u, xctr)]) in
   541         fold_rev Logic.all [p, u] (mk_imp_p (map2 mk_prem xctrs xss))
   542       end;
   543 
   544     val inject_goalss =
   545       let
   546         fun mk_goal _ _ [] [] = []
   547           | mk_goal xctr yctr xs ys =
   548             [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
   549               Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
   550       in
   551         map4 mk_goal xctrs yctrs xss yss
   552       end;
   553 
   554     val half_distinct_goalss =
   555       let
   556         fun mk_goal ((xs, xc), (xs', xc')) =
   557           fold_rev Logic.all (xs @ xs')
   558             (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
   559       in
   560         map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
   561       end;
   562 
   563     val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss;
   564 
   565     fun after_qed thmss lthy =
   566       let
   567         val ([exhaust_thm], (inject_thmss, half_distinct_thmss)) = (hd thmss, chop n (tl thmss));
   568 
   569         val inject_thms = flat inject_thmss;
   570 
   571         val rho_As = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
   572 
   573         fun inst_thm t thm =
   574           Drule.instantiate' [] [SOME (certify lthy t)]
   575             (Thm.instantiate (rho_As, []) (Drule.zero_var_indexes thm));
   576 
   577         val uexhaust_thm = inst_thm u exhaust_thm;
   578 
   579         val exhaust_cases = map base_name_of_ctr ctrs;
   580 
   581         val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
   582 
   583         val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
   584           join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
   585 
   586         val nchotomy_thm =
   587           let
   588             val goal =
   589               HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
   590                 Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
   591           in
   592             Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
   593             |> Thm.close_derivation
   594           end;
   595 
   596         val case_thms =
   597           let
   598             val goals =
   599               map3 (fn xctr => fn xf => fn xs =>
   600                 fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xctrs xfs xss;
   601           in
   602             map4 (fn k => fn goal => fn injects => fn distinctss =>
   603                 Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   604                   mk_case_tac ctxt n k case_def injects distinctss)
   605                 |> Thm.close_derivation)
   606               ks goals inject_thmss distinct_thmsss
   607           end;
   608 
   609         val (case_cong_thm, weak_case_cong_thm) =
   610           let
   611             fun mk_prem xctr xs xf xg =
   612               fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
   613                 mk_Trueprop_eq (xf, xg)));
   614 
   615             val goal =
   616               Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
   617                  mk_Trueprop_eq (eta_ufcase, eta_vgcase));
   618             val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
   619           in
   620             (Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
   621              Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
   622             |> pairself (Thm.close_derivation #> singleton (Proof_Context.export names_lthy lthy))
   623           end;
   624 
   625         val split_lhs = q $ ufcase;
   626 
   627         fun mk_split_conjunct xctr xs f_xs =
   628           list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
   629         fun mk_split_disjunct xctr xs f_xs =
   630           list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
   631             HOLogic.mk_not (q $ f_xs)));
   632 
   633         fun mk_split_goal xctrs xss xfs =
   634           mk_Trueprop_eq (split_lhs, Library.foldr1 HOLogic.mk_conj
   635             (map3 mk_split_conjunct xctrs xss xfs));
   636         fun mk_split_asm_goal xctrs xss xfs =
   637           mk_Trueprop_eq (split_lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
   638             (map3 mk_split_disjunct xctrs xss xfs)));
   639 
   640         fun prove_split selss goal =
   641           Goal.prove_sorry lthy [] [] goal (fn _ =>
   642             mk_split_tac lthy uexhaust_thm case_thms selss inject_thmss distinct_thmsss)
   643           |> Thm.close_derivation
   644           |> singleton (Proof_Context.export names_lthy lthy);
   645 
   646         fun prove_split_asm asm_goal split_thm =
   647           Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
   648             mk_split_asm_tac ctxt split_thm)
   649           |> Thm.close_derivation
   650           |> singleton (Proof_Context.export names_lthy lthy);
   651 
   652         val (split_thm, split_asm_thm) =
   653           let
   654             val goal = mk_split_goal xctrs xss xfs;
   655             val asm_goal = mk_split_asm_goal xctrs xss xfs;
   656 
   657             val thm = prove_split (replicate n []) goal;
   658             val asm_thm = prove_split_asm asm_goal thm;
   659           in
   660             (thm, asm_thm)
   661           end;
   662 
   663         val (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thms, discI_thms, nontriv_discI_thms,
   664              disc_exclude_thms, disc_exclude_thmsss, disc_exhaust_thms, sel_exhaust_thms,
   665              all_collapse_thms, safe_collapse_thms, expand_thms, sel_split_thms, sel_split_asm_thms,
   666              case_eq_if_thms) =
   667           if no_discs_sels then
   668             ([], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [])
   669           else
   670             let
   671               val udiscs = map (rapp u) discs;
   672               val uselss = map (map (rapp u)) selss;
   673               val usel_ctrs = map2 (curry Term.list_comb) ctrs uselss;
   674               val usel_fs = map2 (curry Term.list_comb) fs uselss;
   675 
   676               val vdiscs = map (rapp v) discs;
   677               val vselss = map (map (rapp v)) selss;
   678 
   679               fun make_sel_thm xs' case_thm sel_def =
   680                 zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
   681                     (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
   682 
   683               val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
   684 
   685               fun has_undefined_rhs thm =
   686                 (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
   687                   Const (@{const_name undefined}, _) => true
   688                 | _ => false);
   689 
   690               val all_sel_thms =
   691                 (if all_sels_distinct andalso forall null sel_defaultss then
   692                    flat sel_thmss
   693                  else
   694                    map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
   695                      (xss' ~~ case_thms))
   696                 |> filter_out has_undefined_rhs;
   697 
   698               fun mk_unique_disc_def () =
   699                 let
   700                   val m = the_single ms;
   701                   val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
   702                 in
   703                   Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
   704                   |> Thm.close_derivation
   705                   |> singleton (Proof_Context.export names_lthy lthy)
   706                 end;
   707 
   708               fun mk_alternate_disc_def k =
   709                 let
   710                   val goal =
   711                     mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
   712                       nth exist_xs_u_eq_ctrs (k - 1));
   713                 in
   714                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   715                     mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
   716                       (nth distinct_thms (2 - k)) uexhaust_thm)
   717                   |> Thm.close_derivation
   718                   |> singleton (Proof_Context.export names_lthy lthy)
   719                 end;
   720 
   721               val has_alternate_disc_def =
   722                 exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
   723 
   724               val disc_defs' =
   725                 map2 (fn k => fn def =>
   726                   if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
   727                   else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
   728                   else def) ks disc_defs;
   729 
   730               val discD_thms = map (fn def => def RS iffD1) disc_defs';
   731               val discI_thms =
   732                 map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
   733                   disc_defs';
   734               val not_discI_thms =
   735                 map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
   736                     (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
   737                   ms disc_defs';
   738 
   739               val (disc_thmss', disc_thmss) =
   740                 let
   741                   fun mk_thm discI _ [] = refl RS discI
   742                     | mk_thm _ not_discI [distinct] = distinct RS not_discI;
   743                   fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
   744                 in
   745                   map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
   746                 end;
   747 
   748               val nontriv_disc_thms =
   749                 flat (map2 (fn b => if is_disc_binding_valid b then I else K [])
   750                   disc_bindings disc_thmss);
   751 
   752               fun is_discI_boring b =
   753                 (n = 1 andalso Binding.is_empty b) orelse Binding.eq_name (b, equal_binding);
   754 
   755               val nontriv_discI_thms =
   756                 flat (map2 (fn b => if is_discI_boring b then K [] else single) disc_bindings
   757                   discI_thms);
   758 
   759               val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
   760                 let
   761                   fun mk_goal [] = []
   762                     | mk_goal [((_, udisc), (_, udisc'))] =
   763                       [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
   764                          HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
   765 
   766                   fun prove tac goal =
   767                     Goal.prove_sorry lthy [] [] goal (K tac)
   768                     |> Thm.close_derivation;
   769 
   770                   val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
   771 
   772                   val half_goalss = map mk_goal half_pairss;
   773                   val half_thmss =
   774                     map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
   775                         fn disc_thm => [prove (mk_half_disc_exclude_tac lthy m discD disc_thm) goal])
   776                       half_goalss half_pairss (flat disc_thmss');
   777 
   778                   val other_half_goalss = map (mk_goal o map swap) half_pairss;
   779                   val other_half_thmss =
   780                     map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
   781                       other_half_goalss;
   782                 in
   783                   join_halves n half_thmss other_half_thmss ||> `transpose
   784                   |>> has_alternate_disc_def ? K []
   785                 end;
   786 
   787               val disc_exhaust_thm =
   788                 let
   789                   fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
   790                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
   791                 in
   792                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   793                     mk_disc_exhaust_tac n exhaust_thm discI_thms)
   794                   |> Thm.close_derivation
   795                 end;
   796 
   797               val (safe_collapse_thms, all_collapse_thms) =
   798                 let
   799                   fun mk_goal m udisc usel_ctr =
   800                     let
   801                       val prem = HOLogic.mk_Trueprop udisc;
   802                       val concl = mk_Trueprop_eq ((usel_ctr, u) |> m = 0 ? swap);
   803                     in
   804                       (prem aconv concl, Logic.all u (Logic.mk_implies (prem, concl)))
   805                     end;
   806                   val (trivs, goals) = map3 mk_goal ms udiscs usel_ctrs |> split_list;
   807                   val thms =
   808                     map5 (fn m => fn discD => fn sel_thms => fn triv => fn goal =>
   809                         Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   810                           mk_collapse_tac ctxt m discD sel_thms ORELSE HEADGOAL atac)
   811                         |> Thm.close_derivation
   812                         |> not triv ? perhaps (try (fn thm => refl RS thm)))
   813                       ms discD_thms sel_thmss trivs goals;
   814                 in
   815                   (map_filter (fn (true, _) => NONE | (false, thm) => SOME thm) (trivs ~~ thms),
   816                    thms)
   817                 end;
   818 
   819               val swapped_all_collapse_thms =
   820                 map2 (fn m => fn thm => if m = 0 then thm else thm RS sym) ms all_collapse_thms;
   821 
   822               val sel_exhaust_thm =
   823                 let
   824                   fun mk_prem usel_ctr = mk_imp_p [mk_Trueprop_eq (u, usel_ctr)];
   825                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem usel_ctrs));
   826                 in
   827                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   828                     mk_sel_exhaust_tac n disc_exhaust_thm swapped_all_collapse_thms)
   829                   |> Thm.close_derivation
   830                 end;
   831 
   832               val expand_thm =
   833                 let
   834                   fun mk_prems k udisc usels vdisc vsels =
   835                     (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
   836                     (if null usels then
   837                        []
   838                      else
   839                        [Logic.list_implies
   840                           (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
   841                              HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
   842                                (map2 (curry HOLogic.mk_eq) usels vsels)))]);
   843 
   844                   val goal =
   845                     Library.foldr Logic.list_implies
   846                       (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
   847                   val uncollapse_thms =
   848                     map2 (fn thm => fn [] => thm | _ => thm RS sym) all_collapse_thms uselss;
   849                 in
   850                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   851                     mk_expand_tac lthy n ms (inst_thm u disc_exhaust_thm)
   852                       (inst_thm v disc_exhaust_thm) uncollapse_thms disc_exclude_thmsss
   853                       disc_exclude_thmsss')
   854                   |> Thm.close_derivation
   855                   |> singleton (Proof_Context.export names_lthy lthy)
   856                 end;
   857 
   858               val (sel_split_thm, sel_split_asm_thm) =
   859                 let
   860                   val zss = map (K []) xss;
   861                   val goal = mk_split_goal usel_ctrs zss usel_fs;
   862                   val asm_goal = mk_split_asm_goal usel_ctrs zss usel_fs;
   863 
   864                   val thm = prove_split sel_thmss goal;
   865                   val asm_thm = prove_split_asm asm_goal thm;
   866                 in
   867                   (thm, asm_thm)
   868                 end;
   869 
   870               val case_eq_if_thm =
   871                 let
   872                   val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs usel_fs);
   873                 in
   874                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   875                     mk_case_eq_if_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)
   876                   |> Thm.close_derivation
   877                   |> singleton (Proof_Context.export names_lthy lthy)
   878                 end;
   879             in
   880               (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thms, discI_thms,
   881                nontriv_discI_thms, disc_exclude_thms, disc_exclude_thmsss, [disc_exhaust_thm],
   882                [sel_exhaust_thm], all_collapse_thms, safe_collapse_thms, [expand_thm],
   883                [sel_split_thm], [sel_split_asm_thm], [case_eq_if_thm])
   884             end;
   885 
   886         val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
   887         val cases_type_attr = Attrib.internal (K (Induct.cases_type fcT_name));
   888 
   889         val anonymous_notes =
   890           [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs),
   891            (map (fn th => th RS @{thm eq_False[THEN iffD2]}
   892               handle THM _ => th RS @{thm eq_True[THEN iffD2]}) nontriv_disc_thms,
   893             code_nitpicksimp_attrs)]
   894           |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
   895 
   896         val notes =
   897           [(caseN, case_thms, code_nitpicksimp_simp_attrs),
   898            (case_congN, [case_cong_thm], []),
   899            (case_eq_ifN, case_eq_if_thms, []),
   900            (collapseN, safe_collapse_thms, simp_attrs),
   901            (discN, nontriv_disc_thms, simp_attrs),
   902            (discIN, nontriv_discI_thms, []),
   903            (disc_excludeN, disc_exclude_thms, dest_attrs),
   904            (disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
   905            (distinctN, distinct_thms, simp_attrs @ inductsimp_attrs),
   906            (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
   907            (expandN, expand_thms, []),
   908            (injectN, inject_thms, iff_attrs @ inductsimp_attrs),
   909            (nchotomyN, [nchotomy_thm], []),
   910            (selN, all_sel_thms, code_nitpicksimp_simp_attrs),
   911            (sel_exhaustN, sel_exhaust_thms, [exhaust_case_names_attr]),
   912            (sel_splitN, sel_split_thms, []),
   913            (sel_split_asmN, sel_split_asm_thms, []),
   914            (splitN, [split_thm], []),
   915            (split_asmN, [split_asm_thm], []),
   916            (splitsN, [split_thm, split_asm_thm], []),
   917            (weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
   918           |> filter_out (null o #2)
   919           |> map (fn (thmN, thms, attrs) =>
   920             ((qualify true (Binding.name thmN), attrs), [(thms, [])]));
   921 
   922         val ctr_sugar =
   923           {ctrs = ctrs, casex = casex, discs = discs, selss = selss, exhaust = exhaust_thm,
   924            nchotomy = nchotomy_thm, injects = inject_thms, distincts = distinct_thms,
   925            case_thms = case_thms, case_cong = case_cong_thm, weak_case_cong = weak_case_cong_thm,
   926            split = split_thm, split_asm = split_asm_thm, disc_thmss = disc_thmss,
   927            discIs = discI_thms, sel_thmss = sel_thmss, disc_excludesss = disc_exclude_thmsss,
   928            disc_exhausts = disc_exhaust_thms, sel_exhausts = sel_exhaust_thms,
   929            collapses = all_collapse_thms, expands = expand_thms, sel_splits = sel_split_thms,
   930            sel_split_asms = sel_split_asm_thms, case_eq_ifs = case_eq_if_thms};
   931       in
   932         (ctr_sugar,
   933          lthy
   934          |> not rep_compat ?
   935             Local_Theory.declaration {syntax = false, pervasive = true}
   936               (fn phi => Case_Translation.register
   937                  (Morphism.term phi casex) (map (Morphism.term phi) ctrs))
   938          |> Local_Theory.background_theory (fold (fold Code.del_eqn) [disc_defs, sel_defs])
   939          |> not no_code ?
   940             Local_Theory.declaration {syntax = false, pervasive = false}
   941               (fn phi => Context.mapping
   942                 (add_ctr_code fcT_name (map (Morphism.typ phi) As)
   943                   (map (dest_Const o Morphism.term phi) ctrs) (Morphism.fact phi inject_thms)
   944                   (Morphism.fact phi distinct_thms) (Morphism.fact phi case_thms))
   945                 I)
   946          |> Local_Theory.notes (anonymous_notes @ notes) |> snd
   947          |> register_ctr_sugar fcT_name ctr_sugar)
   948       end;
   949   in
   950     (goalss, after_qed, lthy')
   951   end;
   952 
   953 fun wrap_free_constructors tacss = (fn (goalss, after_qed, lthy) =>
   954   map2 (map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])) goalss tacss
   955   |> (fn thms => after_qed thms lthy)) oo prepare_wrap_free_constructors (K I);
   956 
   957 val wrap_free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
   958   Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
   959   prepare_wrap_free_constructors Syntax.read_term;
   960 
   961 fun parse_bracket_list parser = @{keyword "["} |-- Parse.list parser --|  @{keyword "]"};
   962 
   963 val parse_bindings = parse_bracket_list parse_binding;
   964 val parse_bindingss = parse_bracket_list parse_bindings;
   965 
   966 val parse_bound_term = (parse_binding --| @{keyword ":"}) -- Parse.term;
   967 val parse_bound_terms = parse_bracket_list parse_bound_term;
   968 val parse_bound_termss = parse_bracket_list parse_bound_terms;
   969 
   970 val parse_wrap_free_constructors_options =
   971   Scan.optional (@{keyword "("} |-- Parse.list1
   972         (Parse.reserved "no_discs_sels" >> K 0 || Parse.reserved "no_code" >> K 1 ||
   973          Parse.reserved "rep_compat" >> K 2) --| @{keyword ")"}
   974       >> (fn js => (member (op =) js 0, (member (op =) js 1, member (op =) js 2))))
   975     (false, (false, false));
   976 
   977 val _ =
   978   Outer_Syntax.local_theory_to_proof @{command_spec "wrap_free_constructors"}
   979     "wrap an existing freely generated type's constructors"
   980     ((parse_wrap_free_constructors_options -- (@{keyword "["} |-- Parse.list Parse.term --|
   981         @{keyword "]"}) --
   982       parse_binding -- Scan.optional (parse_bindings -- Scan.optional (parse_bindingss --
   983         Scan.optional parse_bound_termss []) ([], [])) ([], ([], [])))
   984      >> wrap_free_constructors_cmd);
   985 
   986 end;