src/HOL/Tools/Ctr_Sugar/ctr_sugar.ML
author blanchet
Thu Feb 06 00:03:12 2014 +0100 (2014-02-06)
changeset 55342 1bd9e637ac9f
parent 54970 891141de5672
child 55347 a87e49f4336d
permissions -rw-r--r--
tuning
     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 eq_ctr_sugar ({ctrs = ctrs1, casex = case1, discs = discs1, selss = selss1, ...} : ctr_sugar,
   100     {ctrs = ctrs2, casex = case2, discs = discs2, selss = selss2, ...} : ctr_sugar) =
   101   ctrs1 = ctrs2 andalso case1 = case2 andalso discs1 = discs2 andalso selss1 = selss2;
   102 
   103 fun morph_ctr_sugar phi {ctrs, casex, discs, selss, exhaust, nchotomy, injects, distincts,
   104     case_thms, case_cong, weak_case_cong, split, split_asm, disc_thmss, discIs, sel_thmss,
   105     disc_excludesss, disc_exhausts, sel_exhausts, collapses, expands, sel_splits, sel_split_asms,
   106     case_eq_ifs} =
   107   {ctrs = map (Morphism.term phi) ctrs,
   108    casex = Morphism.term phi casex,
   109    discs = map (Morphism.term phi) discs,
   110    selss = map (map (Morphism.term phi)) selss,
   111    exhaust = Morphism.thm phi exhaust,
   112    nchotomy = Morphism.thm phi nchotomy,
   113    injects = map (Morphism.thm phi) injects,
   114    distincts = map (Morphism.thm phi) distincts,
   115    case_thms = map (Morphism.thm phi) case_thms,
   116    case_cong = Morphism.thm phi case_cong,
   117    weak_case_cong = Morphism.thm phi weak_case_cong,
   118    split = Morphism.thm phi split,
   119    split_asm = Morphism.thm phi split_asm,
   120    disc_thmss = map (map (Morphism.thm phi)) disc_thmss,
   121    discIs = map (Morphism.thm phi) discIs,
   122    sel_thmss = map (map (Morphism.thm phi)) sel_thmss,
   123    disc_excludesss = map (map (map (Morphism.thm phi))) disc_excludesss,
   124    disc_exhausts = map (Morphism.thm phi) disc_exhausts,
   125    sel_exhausts = map (Morphism.thm phi) sel_exhausts,
   126    collapses = map (Morphism.thm phi) collapses,
   127    expands = map (Morphism.thm phi) expands,
   128    sel_splits = map (Morphism.thm phi) sel_splits,
   129    sel_split_asms = map (Morphism.thm phi) sel_split_asms,
   130    case_eq_ifs = map (Morphism.thm phi) case_eq_ifs};
   131 
   132 val transfer_ctr_sugar =
   133   morph_ctr_sugar o Morphism.transfer_morphism o Proof_Context.theory_of;
   134 
   135 structure Data = Generic_Data
   136 (
   137   type T = ctr_sugar Symtab.table;
   138   val empty = Symtab.empty;
   139   val extend = I;
   140   val merge = Symtab.merge eq_ctr_sugar;
   141 );
   142 
   143 fun ctr_sugar_of ctxt =
   144   Symtab.lookup (Data.get (Context.Proof ctxt))
   145   #> Option.map (transfer_ctr_sugar ctxt);
   146 
   147 fun ctr_sugars_of ctxt =
   148   Symtab.fold (cons o transfer_ctr_sugar ctxt o snd) (Data.get (Context.Proof ctxt)) [];
   149 
   150 fun ctr_sugar_of_case ctxt s =
   151   find_first (fn {casex = Const (s', _), ...} => s' = s | _ => false) (ctr_sugars_of ctxt);
   152 
   153 fun register_ctr_sugar key ctr_sugar =
   154   Local_Theory.declaration {syntax = false, pervasive = true}
   155     (fn phi => Data.map (Symtab.default (key, morph_ctr_sugar phi ctr_sugar)));
   156 
   157 fun register_ctr_sugar_global key ctr_sugar =
   158   Context.theory_map (Data.map (Symtab.default (key, ctr_sugar)));
   159 
   160 val rep_compat_prefix = "new";
   161 
   162 val isN = "is_";
   163 val unN = "un_";
   164 fun mk_unN 1 1 suf = unN ^ suf
   165   | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
   166 
   167 val caseN = "case";
   168 val case_congN = "case_cong";
   169 val case_eq_ifN = "case_eq_if";
   170 val collapseN = "collapse";
   171 val disc_excludeN = "disc_exclude";
   172 val disc_exhaustN = "disc_exhaust";
   173 val discN = "disc";
   174 val discIN = "discI";
   175 val distinctN = "distinct";
   176 val exhaustN = "exhaust";
   177 val expandN = "expand";
   178 val injectN = "inject";
   179 val nchotomyN = "nchotomy";
   180 val selN = "sel";
   181 val sel_exhaustN = "sel_exhaust";
   182 val sel_splitN = "sel_split";
   183 val sel_split_asmN = "sel_split_asm";
   184 val splitN = "split";
   185 val splitsN = "splits";
   186 val split_asmN = "split_asm";
   187 val weak_case_cong_thmsN = "weak_case_cong";
   188 
   189 val cong_attrs = @{attributes [cong]};
   190 val dest_attrs = @{attributes [dest]};
   191 val safe_elim_attrs = @{attributes [elim!]};
   192 val iff_attrs = @{attributes [iff]};
   193 val inductsimp_attrs = @{attributes [induct_simp]};
   194 val nitpicksimp_attrs = @{attributes [nitpick_simp]};
   195 val simp_attrs = @{attributes [simp]};
   196 val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
   197 val code_nitpicksimp_simp_attrs = code_nitpicksimp_attrs @ simp_attrs;
   198 
   199 fun unflat_lookup eq xs ys = map (fn xs' => permute_like eq xs xs' ys);
   200 
   201 fun mk_half_pairss' _ ([], []) = []
   202   | mk_half_pairss' indent (x :: xs, _ :: ys) =
   203     indent @ fold_rev (cons o single o pair x) ys (mk_half_pairss' ([] :: indent) (xs, ys));
   204 
   205 fun mk_half_pairss p = mk_half_pairss' [[]] p;
   206 
   207 fun join_halves n half_xss other_half_xss =
   208   (splice (flat half_xss) (flat other_half_xss),
   209    map2 (map2 append) (Library.chop_groups n half_xss)
   210      (transpose (Library.chop_groups n other_half_xss)));
   211 
   212 fun mk_undefined T = Const (@{const_name undefined}, T);
   213 
   214 fun mk_ctr Ts t =
   215   let val Type (_, Ts0) = body_type (fastype_of t) in
   216     subst_nonatomic_types (Ts0 ~~ Ts) t
   217   end;
   218 
   219 fun mk_case Ts T t =
   220   let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
   221     subst_nonatomic_types ((body, T) :: (Ts0 ~~ Ts)) t
   222   end;
   223 
   224 fun mk_disc_or_sel Ts t =
   225   subst_nonatomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
   226 
   227 fun name_of_const what t =
   228   (case head_of t of
   229     Const (s, _) => s
   230   | Free (s, _) => s
   231   | _ => error ("Cannot extract name of " ^ what));
   232 
   233 val name_of_ctr = name_of_const "constructor";
   234 
   235 val notN = "not_";
   236 val eqN = "eq_";
   237 val neqN = "neq_";
   238 
   239 fun name_of_disc t =
   240   (case head_of t of
   241     Abs (_, _, @{const Not} $ (t' $ Bound 0)) =>
   242     Long_Name.map_base_name (prefix notN) (name_of_disc t')
   243   | Abs (_, _, Const (@{const_name HOL.eq}, _) $ Bound 0 $ t') =>
   244     Long_Name.map_base_name (prefix eqN) (name_of_disc t')
   245   | Abs (_, _, @{const Not} $ (Const (@{const_name HOL.eq}, _) $ Bound 0 $ t')) =>
   246     Long_Name.map_base_name (prefix neqN) (name_of_disc t')
   247   | t' => name_of_const "destructor" t');
   248 
   249 val base_name_of_ctr = Long_Name.base_name o name_of_ctr;
   250 
   251 fun dest_ctr ctxt s t =
   252   let val (f, args) = Term.strip_comb t in
   253     (case ctr_sugar_of ctxt s of
   254       SOME {ctrs, ...} =>
   255       (case find_first (can (fo_match ctxt f)) ctrs of
   256         SOME f' => (f', args)
   257       | NONE => raise Fail "dest_ctr")
   258     | NONE => raise Fail "dest_ctr")
   259   end;
   260 
   261 fun dest_case ctxt s Ts t =
   262   (case Term.strip_comb t of
   263     (Const (c, _), args as _ :: _) =>
   264     (case ctr_sugar_of ctxt s of
   265       SOME (ctr_sugar as {casex = Const (case_name, _), discs = discs0, selss = selss0, ...}) =>
   266       if case_name = c then
   267         let val n = length discs0 in
   268           if n < length args then
   269             let
   270               val (branches, obj :: leftovers) = chop n args;
   271               val discs = map (mk_disc_or_sel Ts) discs0;
   272               val selss = map (map (mk_disc_or_sel Ts)) selss0;
   273               val conds = map (rapp obj) discs;
   274               val branch_argss = map (fn sels => map (rapp obj) sels @ leftovers) selss;
   275               val branches' = map2 (curry Term.betapplys) branches branch_argss;
   276             in
   277               SOME (ctr_sugar, conds, branches')
   278             end
   279           else
   280             NONE
   281         end
   282       else
   283         NONE
   284     | _ => NONE)
   285   | _ => NONE);
   286 
   287 fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
   288 
   289 fun prepare_wrap_free_constructors prep_term ((((no_discs_sels, (no_code, rep_compat)), raw_ctrs),
   290     raw_case_binding), (raw_disc_bindings, (raw_sel_bindingss, raw_sel_defaultss))) no_defs_lthy =
   291   let
   292     (* TODO: sanity checks on arguments *)
   293 
   294     val n = length raw_ctrs;
   295     val ks = 1 upto n;
   296 
   297     val _ = if n > 0 then () else error "No constructors specified";
   298 
   299     val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
   300     val sel_defaultss =
   301       pad_list [] n (map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss);
   302 
   303     val Type (fcT_name, As0) = body_type (fastype_of (hd ctrs0));
   304     val fc_b_name = Long_Name.base_name fcT_name;
   305     val fc_b = Binding.name fc_b_name;
   306 
   307     fun qualify mandatory =
   308       Binding.qualify mandatory fc_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
   309 
   310     fun dest_TFree_or_TVar (TFree sS) = sS
   311       | dest_TFree_or_TVar (TVar ((s, _), S)) = (s, S)
   312       | dest_TFree_or_TVar _ = error "Invalid type argument";
   313 
   314     val (unsorted_As, B) =
   315       no_defs_lthy
   316       |> variant_tfrees (map (fst o dest_TFree_or_TVar) As0)
   317       ||> the_single o fst o mk_TFrees 1;
   318 
   319     val As = map2 (resort_tfree o snd o dest_TFree_or_TVar) As0 unsorted_As;
   320 
   321     val fcT = Type (fcT_name, As);
   322     val ctrs = map (mk_ctr As) ctrs0;
   323     val ctr_Tss = map (binder_types o fastype_of) ctrs;
   324 
   325     val ms = map length ctr_Tss;
   326 
   327     val raw_disc_bindings' = pad_list Binding.empty n raw_disc_bindings;
   328 
   329     fun can_definitely_rely_on_disc k = not (Binding.is_empty (nth raw_disc_bindings' (k - 1)));
   330     fun can_rely_on_disc k =
   331       can_definitely_rely_on_disc k orelse (k = 1 andalso not (can_definitely_rely_on_disc 2));
   332     fun should_omit_disc_binding k = n = 1 orelse (n = 2 andalso can_rely_on_disc (3 - k));
   333 
   334     fun is_disc_binding_valid b =
   335       not (Binding.is_empty b orelse Binding.eq_name (b, equal_binding));
   336 
   337     val standard_disc_binding = Binding.name o prefix isN o base_name_of_ctr;
   338 
   339     val disc_bindings =
   340       raw_disc_bindings'
   341       |> map4 (fn k => fn m => fn ctr => fn disc =>
   342         qualify false
   343           (if Binding.is_empty disc then
   344              if should_omit_disc_binding k then disc else standard_disc_binding ctr
   345            else if Binding.eq_name (disc, equal_binding) then
   346              if m = 0 then disc
   347              else error "Cannot use \"=\" syntax for discriminating nonnullary constructor"
   348            else if Binding.eq_name (disc, standard_binding) then
   349              standard_disc_binding ctr
   350            else
   351              disc)) ks ms ctrs0;
   352 
   353     fun standard_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
   354 
   355     val sel_bindingss =
   356       pad_list [] n raw_sel_bindingss
   357       |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
   358         qualify false
   359           (if Binding.is_empty sel orelse Binding.eq_name (sel, standard_binding) then
   360             standard_sel_binding m l ctr
   361           else
   362             sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms;
   363 
   364     val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
   365 
   366     val ((((((((xss, xss'), yss), fs), gs), [u', v']), [w]), (p, p')), names_lthy) = no_defs_lthy |>
   367       mk_Freess' "x" ctr_Tss
   368       ||>> mk_Freess "y" ctr_Tss
   369       ||>> mk_Frees "f" case_Ts
   370       ||>> mk_Frees "g" case_Ts
   371       ||>> (apfst (map (rpair fcT)) oo Variable.variant_fixes) [fc_b_name, fc_b_name ^ "'"]
   372       ||>> mk_Frees "z" [B]
   373       ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
   374 
   375     val u = Free u';
   376     val v = Free v';
   377     val q = Free (fst p', mk_pred1T B);
   378 
   379     val xctrs = map2 (curry Term.list_comb) ctrs xss;
   380     val yctrs = map2 (curry Term.list_comb) ctrs yss;
   381 
   382     val xfs = map2 (curry Term.list_comb) fs xss;
   383     val xgs = map2 (curry Term.list_comb) gs xss;
   384 
   385     (* TODO: Eta-expension is for compatibility with the old datatype package (but it also provides
   386        nicer names). Consider removing. *)
   387     val eta_fs = map2 eta_expand_arg xss xfs;
   388     val eta_gs = map2 eta_expand_arg xss xgs;
   389 
   390     val case_binding =
   391       qualify false
   392         (if Binding.is_empty raw_case_binding orelse
   393             Binding.eq_name (raw_case_binding, standard_binding) then
   394            Binding.prefix_name (caseN ^ "_") fc_b
   395          else
   396            raw_case_binding);
   397 
   398     fun mk_case_disj xctr xf xs =
   399       list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr), HOLogic.mk_eq (w, xf)));
   400 
   401     val case_rhs = fold_rev (fold_rev Term.lambda) [fs, [u]]
   402       (Const (@{const_name The}, (B --> HOLogic.boolT) --> B) $
   403          Term.lambda w (Library.foldr1 HOLogic.mk_disj (map3 mk_case_disj xctrs xfs xss)));
   404 
   405     val ((raw_case, (_, raw_case_def)), (lthy', lthy)) = no_defs_lthy
   406       |> Local_Theory.define ((case_binding, NoSyn),
   407         ((Binding.conceal (Thm.def_binding case_binding), []), case_rhs))
   408       ||> `Local_Theory.restore;
   409 
   410     val phi = Proof_Context.export_morphism lthy lthy';
   411 
   412     val case_def = Morphism.thm phi raw_case_def;
   413 
   414     val case0 = Morphism.term phi raw_case;
   415     val casex = mk_case As B case0;
   416 
   417     val fcase = Term.list_comb (casex, fs);
   418 
   419     val ufcase = fcase $ u;
   420     val vfcase = fcase $ v;
   421 
   422     val eta_fcase = Term.list_comb (casex, eta_fs);
   423     val eta_gcase = Term.list_comb (casex, eta_gs);
   424 
   425     val eta_ufcase = eta_fcase $ u;
   426     val eta_vgcase = eta_gcase $ v;
   427 
   428     fun mk_uu_eq () = HOLogic.mk_eq (u, u);
   429 
   430     val uv_eq = mk_Trueprop_eq (u, v);
   431 
   432     val exist_xs_u_eq_ctrs =
   433       map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
   434 
   435     val unique_disc_no_def = TrueI; (*arbitrary marker*)
   436     val alternate_disc_no_def = FalseE; (*arbitrary marker*)
   437 
   438     fun alternate_disc_lhs get_udisc k =
   439       HOLogic.mk_not
   440         (let val b = nth disc_bindings (k - 1) in
   441            if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
   442          end);
   443 
   444     val (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy') =
   445       if no_discs_sels then
   446         (true, [], [], [], [], [], lthy)
   447       else
   448         let
   449           fun disc_free b = Free (Binding.name_of b, mk_pred1T fcT);
   450 
   451           fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
   452 
   453           fun alternate_disc k =
   454             Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
   455 
   456           fun mk_sel_case_args b proto_sels T =
   457             map2 (fn Ts => fn k =>
   458               (case AList.lookup (op =) proto_sels k of
   459                 NONE =>
   460                 (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
   461                   NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
   462                 | SOME t => t |> Type.constraint (Ts ---> T) |> Syntax.check_term lthy)
   463               | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
   464 
   465           fun sel_spec b proto_sels =
   466             let
   467               val _ =
   468                 (case duplicates (op =) (map fst proto_sels) of
   469                    k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
   470                      " for constructor " ^
   471                      quote (Syntax.string_of_term lthy (nth ctrs (k - 1))))
   472                  | [] => ())
   473               val T =
   474                 (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
   475                   [T] => T
   476                 | T :: T' :: _ => error ("Inconsistent range type for selector " ^
   477                     quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ lthy T) ^ " vs. "
   478                     ^ quote (Syntax.string_of_typ lthy T')));
   479             in
   480               mk_Trueprop_eq (Free (Binding.name_of b, fcT --> T) $ u,
   481                 Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
   482             end;
   483 
   484           val sel_bindings = flat sel_bindingss;
   485           val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
   486           val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
   487 
   488           val sel_binding_index =
   489             if all_sels_distinct then 1 upto length sel_bindings
   490             else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
   491 
   492           val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
   493           val sel_infos =
   494             AList.group (op =) (sel_binding_index ~~ proto_sels)
   495             |> sort (int_ord o pairself fst)
   496             |> map snd |> curry (op ~~) uniq_sel_bindings;
   497           val sel_bindings = map fst sel_infos;
   498 
   499           fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
   500 
   501           val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
   502             lthy
   503             |> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
   504                 if Binding.is_empty b then
   505                   if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
   506                   else pair (alternate_disc k, alternate_disc_no_def)
   507                 else if Binding.eq_name (b, equal_binding) then
   508                   pair (Term.lambda u exist_xs_u_eq_ctr, refl)
   509                 else
   510                   Specification.definition (SOME (b, NONE, NoSyn),
   511                     ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
   512               ks exist_xs_u_eq_ctrs disc_bindings
   513             ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
   514               Specification.definition (SOME (b, NONE, NoSyn),
   515                 ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
   516             ||> `Local_Theory.restore;
   517 
   518           val phi = Proof_Context.export_morphism lthy lthy';
   519 
   520           val disc_defs = map (Morphism.thm phi) raw_disc_defs;
   521           val sel_defs = map (Morphism.thm phi) raw_sel_defs;
   522           val sel_defss = unflat_selss sel_defs;
   523 
   524           val discs0 = map (Morphism.term phi) raw_discs;
   525           val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
   526 
   527           val discs = map (mk_disc_or_sel As) discs0;
   528           val selss = map (map (mk_disc_or_sel As)) selss0;
   529         in
   530           (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy')
   531         end;
   532 
   533     fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
   534 
   535     val exhaust_goal =
   536       let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (u, xctr)]) in
   537         fold_rev Logic.all [p, u] (mk_imp_p (map2 mk_prem xctrs xss))
   538       end;
   539 
   540     val inject_goalss =
   541       let
   542         fun mk_goal _ _ [] [] = []
   543           | mk_goal xctr yctr xs ys =
   544             [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
   545               Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
   546       in
   547         map4 mk_goal xctrs yctrs xss yss
   548       end;
   549 
   550     val half_distinct_goalss =
   551       let
   552         fun mk_goal ((xs, xc), (xs', xc')) =
   553           fold_rev Logic.all (xs @ xs')
   554             (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
   555       in
   556         map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
   557       end;
   558 
   559     val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss;
   560 
   561     fun after_qed thmss lthy =
   562       let
   563         val ([exhaust_thm], (inject_thmss, half_distinct_thmss)) = (hd thmss, chop n (tl thmss));
   564 
   565         val inject_thms = flat inject_thmss;
   566 
   567         val rho_As = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
   568 
   569         fun inst_thm t thm =
   570           Drule.instantiate' [] [SOME (certify lthy t)]
   571             (Thm.instantiate (rho_As, []) (Drule.zero_var_indexes thm));
   572 
   573         val uexhaust_thm = inst_thm u exhaust_thm;
   574 
   575         val exhaust_cases = map base_name_of_ctr ctrs;
   576 
   577         val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
   578 
   579         val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
   580           join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
   581 
   582         val nchotomy_thm =
   583           let
   584             val goal =
   585               HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
   586                 Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
   587           in
   588             Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
   589             |> Thm.close_derivation
   590           end;
   591 
   592         val case_thms =
   593           let
   594             val goals =
   595               map3 (fn xctr => fn xf => fn xs =>
   596                 fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xctrs xfs xss;
   597           in
   598             map4 (fn k => fn goal => fn injects => fn distinctss =>
   599                 Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   600                   mk_case_tac ctxt n k case_def injects distinctss)
   601                 |> Thm.close_derivation)
   602               ks goals inject_thmss distinct_thmsss
   603           end;
   604 
   605         val (case_cong_thm, weak_case_cong_thm) =
   606           let
   607             fun mk_prem xctr xs xf xg =
   608               fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
   609                 mk_Trueprop_eq (xf, xg)));
   610 
   611             val goal =
   612               Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
   613                  mk_Trueprop_eq (eta_ufcase, eta_vgcase));
   614             val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
   615           in
   616             (Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
   617              Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
   618             |> pairself (Thm.close_derivation #> singleton (Proof_Context.export names_lthy lthy))
   619           end;
   620 
   621         val split_lhs = q $ ufcase;
   622 
   623         fun mk_split_conjunct xctr xs f_xs =
   624           list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
   625         fun mk_split_disjunct xctr xs f_xs =
   626           list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
   627             HOLogic.mk_not (q $ f_xs)));
   628 
   629         fun mk_split_goal xctrs xss xfs =
   630           mk_Trueprop_eq (split_lhs, Library.foldr1 HOLogic.mk_conj
   631             (map3 mk_split_conjunct xctrs xss xfs));
   632         fun mk_split_asm_goal xctrs xss xfs =
   633           mk_Trueprop_eq (split_lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
   634             (map3 mk_split_disjunct xctrs xss xfs)));
   635 
   636         fun prove_split selss goal =
   637           Goal.prove_sorry lthy [] [] goal (fn _ =>
   638             mk_split_tac lthy uexhaust_thm case_thms selss inject_thmss distinct_thmsss)
   639           |> Thm.close_derivation
   640           |> singleton (Proof_Context.export names_lthy lthy);
   641 
   642         fun prove_split_asm asm_goal split_thm =
   643           Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
   644             mk_split_asm_tac ctxt split_thm)
   645           |> Thm.close_derivation
   646           |> singleton (Proof_Context.export names_lthy lthy);
   647 
   648         val (split_thm, split_asm_thm) =
   649           let
   650             val goal = mk_split_goal xctrs xss xfs;
   651             val asm_goal = mk_split_asm_goal xctrs xss xfs;
   652 
   653             val thm = prove_split (replicate n []) goal;
   654             val asm_thm = prove_split_asm asm_goal thm;
   655           in
   656             (thm, asm_thm)
   657           end;
   658 
   659         val (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thms, discI_thms, nontriv_discI_thms,
   660              disc_exclude_thms, disc_exclude_thmsss, disc_exhaust_thms, sel_exhaust_thms,
   661              all_collapse_thms, safe_collapse_thms, expand_thms, sel_split_thms, sel_split_asm_thms,
   662              case_eq_if_thms) =
   663           if no_discs_sels then
   664             ([], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [])
   665           else
   666             let
   667               val udiscs = map (rapp u) discs;
   668               val uselss = map (map (rapp u)) selss;
   669               val usel_ctrs = map2 (curry Term.list_comb) ctrs uselss;
   670               val usel_fs = map2 (curry Term.list_comb) fs uselss;
   671 
   672               val vdiscs = map (rapp v) discs;
   673               val vselss = map (map (rapp v)) selss;
   674 
   675               fun make_sel_thm xs' case_thm sel_def =
   676                 zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
   677                     (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
   678 
   679               val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
   680 
   681               fun has_undefined_rhs thm =
   682                 (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
   683                   Const (@{const_name undefined}, _) => true
   684                 | _ => false);
   685 
   686               val all_sel_thms =
   687                 (if all_sels_distinct andalso forall null sel_defaultss then
   688                    flat sel_thmss
   689                  else
   690                    map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
   691                      (xss' ~~ case_thms))
   692                 |> filter_out has_undefined_rhs;
   693 
   694               fun mk_unique_disc_def () =
   695                 let
   696                   val m = the_single ms;
   697                   val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
   698                 in
   699                   Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
   700                   |> Thm.close_derivation
   701                   |> singleton (Proof_Context.export names_lthy lthy)
   702                 end;
   703 
   704               fun mk_alternate_disc_def k =
   705                 let
   706                   val goal =
   707                     mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
   708                       nth exist_xs_u_eq_ctrs (k - 1));
   709                 in
   710                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   711                     mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
   712                       (nth distinct_thms (2 - k)) uexhaust_thm)
   713                   |> Thm.close_derivation
   714                   |> singleton (Proof_Context.export names_lthy lthy)
   715                 end;
   716 
   717               val has_alternate_disc_def =
   718                 exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
   719 
   720               val disc_defs' =
   721                 map2 (fn k => fn def =>
   722                   if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
   723                   else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
   724                   else def) ks disc_defs;
   725 
   726               val discD_thms = map (fn def => def RS iffD1) disc_defs';
   727               val discI_thms =
   728                 map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
   729                   disc_defs';
   730               val not_discI_thms =
   731                 map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
   732                     (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
   733                   ms disc_defs';
   734 
   735               val (disc_thmss', disc_thmss) =
   736                 let
   737                   fun mk_thm discI _ [] = refl RS discI
   738                     | mk_thm _ not_discI [distinct] = distinct RS not_discI;
   739                   fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
   740                 in
   741                   map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
   742                 end;
   743 
   744               val nontriv_disc_thms =
   745                 flat (map2 (fn b => if is_disc_binding_valid b then I else K [])
   746                   disc_bindings disc_thmss);
   747 
   748               fun is_discI_boring b =
   749                 (n = 1 andalso Binding.is_empty b) orelse Binding.eq_name (b, equal_binding);
   750 
   751               val nontriv_discI_thms =
   752                 flat (map2 (fn b => if is_discI_boring b then K [] else single) disc_bindings
   753                   discI_thms);
   754 
   755               val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
   756                 let
   757                   fun mk_goal [] = []
   758                     | mk_goal [((_, udisc), (_, udisc'))] =
   759                       [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
   760                          HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
   761 
   762                   fun prove tac goal =
   763                     Goal.prove_sorry lthy [] [] goal (K tac)
   764                     |> Thm.close_derivation;
   765 
   766                   val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
   767 
   768                   val half_goalss = map mk_goal half_pairss;
   769                   val half_thmss =
   770                     map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
   771                         fn disc_thm => [prove (mk_half_disc_exclude_tac lthy m discD disc_thm) goal])
   772                       half_goalss half_pairss (flat disc_thmss');
   773 
   774                   val other_half_goalss = map (mk_goal o map swap) half_pairss;
   775                   val other_half_thmss =
   776                     map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
   777                       other_half_goalss;
   778                 in
   779                   join_halves n half_thmss other_half_thmss ||> `transpose
   780                   |>> has_alternate_disc_def ? K []
   781                 end;
   782 
   783               val disc_exhaust_thm =
   784                 let
   785                   fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
   786                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
   787                 in
   788                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   789                     mk_disc_exhaust_tac n exhaust_thm discI_thms)
   790                   |> Thm.close_derivation
   791                 end;
   792 
   793               val (safe_collapse_thms, all_collapse_thms) =
   794                 let
   795                   fun mk_goal m udisc usel_ctr =
   796                     let
   797                       val prem = HOLogic.mk_Trueprop udisc;
   798                       val concl = mk_Trueprop_eq ((usel_ctr, u) |> m = 0 ? swap);
   799                     in
   800                       (prem aconv concl, Logic.all u (Logic.mk_implies (prem, concl)))
   801                     end;
   802                   val (trivs, goals) = map3 mk_goal ms udiscs usel_ctrs |> split_list;
   803                   val thms =
   804                     map5 (fn m => fn discD => fn sel_thms => fn triv => fn goal =>
   805                         Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   806                           mk_collapse_tac ctxt m discD sel_thms ORELSE HEADGOAL atac)
   807                         |> Thm.close_derivation
   808                         |> not triv ? perhaps (try (fn thm => refl RS thm)))
   809                       ms discD_thms sel_thmss trivs goals;
   810                 in
   811                   (map_filter (fn (true, _) => NONE | (false, thm) => SOME thm) (trivs ~~ thms),
   812                    thms)
   813                 end;
   814 
   815               val swapped_all_collapse_thms =
   816                 map2 (fn m => fn thm => if m = 0 then thm else thm RS sym) ms all_collapse_thms;
   817 
   818               val sel_exhaust_thm =
   819                 let
   820                   fun mk_prem usel_ctr = mk_imp_p [mk_Trueprop_eq (u, usel_ctr)];
   821                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem usel_ctrs));
   822                 in
   823                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   824                     mk_sel_exhaust_tac n disc_exhaust_thm swapped_all_collapse_thms)
   825                   |> Thm.close_derivation
   826                 end;
   827 
   828               val expand_thm =
   829                 let
   830                   fun mk_prems k udisc usels vdisc vsels =
   831                     (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
   832                     (if null usels then
   833                        []
   834                      else
   835                        [Logic.list_implies
   836                           (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
   837                              HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
   838                                (map2 (curry HOLogic.mk_eq) usels vsels)))]);
   839 
   840                   val goal =
   841                     Library.foldr Logic.list_implies
   842                       (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
   843                   val uncollapse_thms =
   844                     map2 (fn thm => fn [] => thm | _ => thm RS sym) all_collapse_thms uselss;
   845                 in
   846                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   847                     mk_expand_tac lthy n ms (inst_thm u disc_exhaust_thm)
   848                       (inst_thm v disc_exhaust_thm) uncollapse_thms disc_exclude_thmsss
   849                       disc_exclude_thmsss')
   850                   |> Thm.close_derivation
   851                   |> singleton (Proof_Context.export names_lthy lthy)
   852                 end;
   853 
   854               val (sel_split_thm, sel_split_asm_thm) =
   855                 let
   856                   val zss = map (K []) xss;
   857                   val goal = mk_split_goal usel_ctrs zss usel_fs;
   858                   val asm_goal = mk_split_asm_goal usel_ctrs zss usel_fs;
   859 
   860                   val thm = prove_split sel_thmss goal;
   861                   val asm_thm = prove_split_asm asm_goal thm;
   862                 in
   863                   (thm, asm_thm)
   864                 end;
   865 
   866               val case_eq_if_thm =
   867                 let
   868                   val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs usel_fs);
   869                 in
   870                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   871                     mk_case_eq_if_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)
   872                   |> Thm.close_derivation
   873                   |> singleton (Proof_Context.export names_lthy lthy)
   874                 end;
   875             in
   876               (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thms, discI_thms,
   877                nontriv_discI_thms, disc_exclude_thms, disc_exclude_thmsss, [disc_exhaust_thm],
   878                [sel_exhaust_thm], all_collapse_thms, safe_collapse_thms, [expand_thm],
   879                [sel_split_thm], [sel_split_asm_thm], [case_eq_if_thm])
   880             end;
   881 
   882         val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
   883         val cases_type_attr = Attrib.internal (K (Induct.cases_type fcT_name));
   884 
   885         val anonymous_notes =
   886           [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs),
   887            (map (fn th => th RS @{thm eq_False[THEN iffD2]}
   888               handle THM _ => th RS @{thm eq_True[THEN iffD2]}) nontriv_disc_thms,
   889             code_nitpicksimp_attrs)]
   890           |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
   891 
   892         val notes =
   893           [(caseN, case_thms, code_nitpicksimp_simp_attrs),
   894            (case_congN, [case_cong_thm], []),
   895            (case_eq_ifN, case_eq_if_thms, []),
   896            (collapseN, safe_collapse_thms, simp_attrs),
   897            (discN, nontriv_disc_thms, simp_attrs),
   898            (discIN, nontriv_discI_thms, []),
   899            (disc_excludeN, disc_exclude_thms, dest_attrs),
   900            (disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
   901            (distinctN, distinct_thms, simp_attrs @ inductsimp_attrs),
   902            (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
   903            (expandN, expand_thms, []),
   904            (injectN, inject_thms, iff_attrs @ inductsimp_attrs),
   905            (nchotomyN, [nchotomy_thm], []),
   906            (selN, all_sel_thms, code_nitpicksimp_simp_attrs),
   907            (sel_exhaustN, sel_exhaust_thms, [exhaust_case_names_attr]),
   908            (sel_splitN, sel_split_thms, []),
   909            (sel_split_asmN, sel_split_asm_thms, []),
   910            (splitN, [split_thm], []),
   911            (split_asmN, [split_asm_thm], []),
   912            (splitsN, [split_thm, split_asm_thm], []),
   913            (weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
   914           |> filter_out (null o #2)
   915           |> map (fn (thmN, thms, attrs) =>
   916             ((qualify true (Binding.name thmN), attrs), [(thms, [])]));
   917 
   918         val ctr_sugar =
   919           {ctrs = ctrs, casex = casex, discs = discs, selss = selss, exhaust = exhaust_thm,
   920            nchotomy = nchotomy_thm, injects = inject_thms, distincts = distinct_thms,
   921            case_thms = case_thms, case_cong = case_cong_thm, weak_case_cong = weak_case_cong_thm,
   922            split = split_thm, split_asm = split_asm_thm, disc_thmss = disc_thmss,
   923            discIs = discI_thms, sel_thmss = sel_thmss, disc_excludesss = disc_exclude_thmsss,
   924            disc_exhausts = disc_exhaust_thms, sel_exhausts = sel_exhaust_thms,
   925            collapses = all_collapse_thms, expands = expand_thms, sel_splits = sel_split_thms,
   926            sel_split_asms = sel_split_asm_thms, case_eq_ifs = case_eq_if_thms};
   927       in
   928         (ctr_sugar,
   929          lthy
   930          |> not rep_compat ?
   931             Local_Theory.declaration {syntax = false, pervasive = true}
   932               (fn phi => Case_Translation.register
   933                  (Morphism.term phi casex) (map (Morphism.term phi) ctrs))
   934          |> Local_Theory.background_theory (fold (fold Code.del_eqn) [disc_defs, sel_defs])
   935          |> not no_code ?
   936             Local_Theory.declaration {syntax = false, pervasive = false}
   937               (fn phi => Context.mapping
   938                 (add_ctr_code fcT_name (map (Morphism.typ phi) As)
   939                   (map (dest_Const o Morphism.term phi) ctrs) (Morphism.fact phi inject_thms)
   940                   (Morphism.fact phi distinct_thms) (Morphism.fact phi case_thms))
   941                 I)
   942          |> Local_Theory.notes (anonymous_notes @ notes) |> snd
   943          |> register_ctr_sugar fcT_name ctr_sugar)
   944       end;
   945   in
   946     (goalss, after_qed, lthy')
   947   end;
   948 
   949 fun wrap_free_constructors tacss = (fn (goalss, after_qed, lthy) =>
   950   map2 (map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])) goalss tacss
   951   |> (fn thms => after_qed thms lthy)) oo prepare_wrap_free_constructors (K I);
   952 
   953 val wrap_free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
   954   Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
   955   prepare_wrap_free_constructors Syntax.read_term;
   956 
   957 fun parse_bracket_list parser = @{keyword "["} |-- Parse.list parser --|  @{keyword "]"};
   958 
   959 val parse_bindings = parse_bracket_list parse_binding;
   960 val parse_bindingss = parse_bracket_list parse_bindings;
   961 
   962 val parse_bound_term = (parse_binding --| @{keyword ":"}) -- Parse.term;
   963 val parse_bound_terms = parse_bracket_list parse_bound_term;
   964 val parse_bound_termss = parse_bracket_list parse_bound_terms;
   965 
   966 val parse_wrap_free_constructors_options =
   967   Scan.optional (@{keyword "("} |-- Parse.list1
   968         (Parse.reserved "no_discs_sels" >> K 0 || Parse.reserved "no_code" >> K 1 ||
   969          Parse.reserved "rep_compat" >> K 2) --| @{keyword ")"}
   970       >> (fn js => (member (op =) js 0, (member (op =) js 1, member (op =) js 2))))
   971     (false, (false, false));
   972 
   973 val _ =
   974   Outer_Syntax.local_theory_to_proof @{command_spec "wrap_free_constructors"}
   975     "wrap an existing freely generated type's constructors"
   976     ((parse_wrap_free_constructors_options -- (@{keyword "["} |-- Parse.list Parse.term --|
   977         @{keyword "]"}) --
   978       parse_binding -- Scan.optional (parse_bindings -- Scan.optional (parse_bindingss --
   979         Scan.optional parse_bound_termss []) ([], [])) ([], ([], [])))
   980      >> wrap_free_constructors_cmd);
   981 
   982 end;