src/HOL/Tools/Ctr_Sugar/ctr_sugar.ML
author blanchet
Fri Feb 14 07:53:45 2014 +0100 (2014-02-14)
changeset 55464 56fa33537869
parent 55444 ec73f81e49e7
child 55468 98b25c51e9e5
permissions -rw-r--r--
have 'Ctr_Sugar' register its 'Spec_Rules'
     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 default_register_ctr_sugar_global: string -> ctr_sugar -> theory -> theory
    43 
    44   val mk_half_pairss: 'a list * 'a list -> ('a * 'a) list list
    45   val join_halves: int -> 'a list list -> 'a list list -> 'a list * 'a list list list
    46 
    47   val mk_ctr: typ list -> term -> term
    48   val mk_case: typ list -> typ -> term -> term
    49   val mk_disc_or_sel: typ list -> term -> term
    50   val name_of_ctr: term -> string
    51   val name_of_disc: term -> string
    52   val dest_ctr: Proof.context -> string -> term -> term * term list
    53   val dest_case: Proof.context -> string -> typ list -> term ->
    54     (ctr_sugar * term list * term list) option
    55 
    56   val wrap_free_constructors: ({prems: thm list, context: Proof.context} -> tactic) list list ->
    57     (((bool * bool) * term list) * binding) *
    58       (binding list * (binding list list * (binding * term) list list)) -> local_theory ->
    59     ctr_sugar * local_theory
    60   val parse_wrap_free_constructors_options: (bool * bool) parser
    61   val parse_bound_term: (binding * string) parser
    62 end;
    63 
    64 structure Ctr_Sugar : CTR_SUGAR =
    65 struct
    66 
    67 open Ctr_Sugar_Util
    68 open Ctr_Sugar_Tactics
    69 open Ctr_Sugar_Code
    70 
    71 type ctr_sugar =
    72   {ctrs: term list,
    73    casex: term,
    74    discs: term list,
    75    selss: term list list,
    76    exhaust: thm,
    77    nchotomy: thm,
    78    injects: thm list,
    79    distincts: thm list,
    80    case_thms: thm list,
    81    case_cong: thm,
    82    weak_case_cong: thm,
    83    split: thm,
    84    split_asm: thm,
    85    disc_thmss: thm list list,
    86    discIs: thm list,
    87    sel_thmss: thm list list,
    88    disc_excludesss: thm list list list,
    89    disc_exhausts: thm list,
    90    sel_exhausts: thm list,
    91    collapses: thm list,
    92    expands: thm list,
    93    sel_splits: thm list,
    94    sel_split_asms: thm list,
    95    case_eq_ifs: thm list};
    96 
    97 fun morph_ctr_sugar phi {ctrs, casex, discs, selss, exhaust, nchotomy, injects, distincts,
    98     case_thms, case_cong, weak_case_cong, split, split_asm, disc_thmss, discIs, sel_thmss,
    99     disc_excludesss, disc_exhausts, sel_exhausts, collapses, expands, sel_splits, sel_split_asms,
   100     case_eq_ifs} =
   101   {ctrs = map (Morphism.term phi) ctrs,
   102    casex = Morphism.term phi casex,
   103    discs = map (Morphism.term phi) discs,
   104    selss = map (map (Morphism.term phi)) selss,
   105    exhaust = Morphism.thm phi exhaust,
   106    nchotomy = Morphism.thm phi nchotomy,
   107    injects = map (Morphism.thm phi) injects,
   108    distincts = map (Morphism.thm phi) distincts,
   109    case_thms = map (Morphism.thm phi) case_thms,
   110    case_cong = Morphism.thm phi case_cong,
   111    weak_case_cong = Morphism.thm phi weak_case_cong,
   112    split = Morphism.thm phi split,
   113    split_asm = Morphism.thm phi split_asm,
   114    disc_thmss = map (map (Morphism.thm phi)) disc_thmss,
   115    discIs = map (Morphism.thm phi) discIs,
   116    sel_thmss = map (map (Morphism.thm phi)) sel_thmss,
   117    disc_excludesss = map (map (map (Morphism.thm phi))) disc_excludesss,
   118    disc_exhausts = map (Morphism.thm phi) disc_exhausts,
   119    sel_exhausts = map (Morphism.thm phi) sel_exhausts,
   120    collapses = map (Morphism.thm phi) collapses,
   121    expands = map (Morphism.thm phi) expands,
   122    sel_splits = map (Morphism.thm phi) sel_splits,
   123    sel_split_asms = map (Morphism.thm phi) sel_split_asms,
   124    case_eq_ifs = map (Morphism.thm phi) case_eq_ifs};
   125 
   126 val transfer_ctr_sugar =
   127   morph_ctr_sugar o Morphism.transfer_morphism o Proof_Context.theory_of;
   128 
   129 structure Data = Generic_Data
   130 (
   131   type T = ctr_sugar Symtab.table;
   132   val empty = Symtab.empty;
   133   val extend = I;
   134   fun merge data : T = Symtab.merge (K true) data;
   135 );
   136 
   137 fun ctr_sugar_of ctxt =
   138   Symtab.lookup (Data.get (Context.Proof ctxt))
   139   #> Option.map (transfer_ctr_sugar ctxt);
   140 
   141 fun ctr_sugars_of ctxt =
   142   Symtab.fold (cons o transfer_ctr_sugar ctxt o snd) (Data.get (Context.Proof ctxt)) [];
   143 
   144 fun ctr_sugar_of_case ctxt s =
   145   find_first (fn {casex = Const (s', _), ...} => s' = s | _ => false) (ctr_sugars_of ctxt);
   146 
   147 fun register_ctr_sugar key ctr_sugar =
   148   Local_Theory.declaration {syntax = false, pervasive = true}
   149     (fn phi => Data.map (Symtab.update (key, morph_ctr_sugar phi ctr_sugar)));
   150 
   151 fun default_register_ctr_sugar_global key ctr_sugar =
   152   Context.theory_map (Data.map (Symtab.default (key, ctr_sugar)));
   153 
   154 val isN = "is_";
   155 val unN = "un_";
   156 fun mk_unN 1 1 suf = unN ^ suf
   157   | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
   158 
   159 val caseN = "case";
   160 val case_congN = "case_cong";
   161 val case_eq_ifN = "case_eq_if";
   162 val collapseN = "collapse";
   163 val disc_excludeN = "disc_exclude";
   164 val disc_exhaustN = "disc_exhaust";
   165 val discN = "disc";
   166 val discIN = "discI";
   167 val distinctN = "distinct";
   168 val exhaustN = "exhaust";
   169 val expandN = "expand";
   170 val injectN = "inject";
   171 val nchotomyN = "nchotomy";
   172 val selN = "sel";
   173 val sel_exhaustN = "sel_exhaust";
   174 val sel_splitN = "sel_split";
   175 val sel_split_asmN = "sel_split_asm";
   176 val splitN = "split";
   177 val splitsN = "splits";
   178 val split_asmN = "split_asm";
   179 val weak_case_cong_thmsN = "weak_case_cong";
   180 
   181 val cong_attrs = @{attributes [cong]};
   182 val dest_attrs = @{attributes [dest]};
   183 val safe_elim_attrs = @{attributes [elim!]};
   184 val iff_attrs = @{attributes [iff]};
   185 val inductsimp_attrs = @{attributes [induct_simp]};
   186 val nitpicksimp_attrs = @{attributes [nitpick_simp]};
   187 val simp_attrs = @{attributes [simp]};
   188 val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
   189 val code_nitpicksimp_simp_attrs = code_nitpicksimp_attrs @ simp_attrs;
   190 
   191 fun unflat_lookup eq xs ys = map (fn xs' => permute_like eq xs xs' ys);
   192 
   193 fun mk_half_pairss' _ ([], []) = []
   194   | mk_half_pairss' indent (x :: xs, _ :: ys) =
   195     indent @ fold_rev (cons o single o pair x) ys (mk_half_pairss' ([] :: indent) (xs, ys));
   196 
   197 fun mk_half_pairss p = mk_half_pairss' [[]] p;
   198 
   199 fun join_halves n half_xss other_half_xss =
   200   (splice (flat half_xss) (flat other_half_xss),
   201    map2 (map2 append) (Library.chop_groups n half_xss)
   202      (transpose (Library.chop_groups n other_half_xss)));
   203 
   204 fun mk_undefined T = Const (@{const_name undefined}, T);
   205 
   206 fun mk_ctr Ts t =
   207   let val Type (_, Ts0) = body_type (fastype_of t) in
   208     subst_nonatomic_types (Ts0 ~~ Ts) t
   209   end;
   210 
   211 fun mk_case Ts T t =
   212   let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
   213     subst_nonatomic_types ((body, T) :: (Ts0 ~~ Ts)) t
   214   end;
   215 
   216 fun mk_disc_or_sel Ts t =
   217   subst_nonatomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
   218 
   219 fun name_of_const what t =
   220   (case head_of t of
   221     Const (s, _) => s
   222   | Free (s, _) => s
   223   | _ => error ("Cannot extract name of " ^ what));
   224 
   225 val name_of_ctr = name_of_const "constructor";
   226 
   227 val notN = "not_";
   228 val eqN = "eq_";
   229 val neqN = "neq_";
   230 
   231 fun name_of_disc t =
   232   (case head_of t of
   233     Abs (_, _, @{const Not} $ (t' $ Bound 0)) =>
   234     Long_Name.map_base_name (prefix notN) (name_of_disc t')
   235   | Abs (_, _, Const (@{const_name HOL.eq}, _) $ Bound 0 $ t') =>
   236     Long_Name.map_base_name (prefix eqN) (name_of_disc t')
   237   | Abs (_, _, @{const Not} $ (Const (@{const_name HOL.eq}, _) $ Bound 0 $ t')) =>
   238     Long_Name.map_base_name (prefix neqN) (name_of_disc t')
   239   | t' => name_of_const "destructor" t');
   240 
   241 val base_name_of_ctr = Long_Name.base_name o name_of_ctr;
   242 
   243 fun dest_ctr ctxt s t =
   244   let val (f, args) = Term.strip_comb t in
   245     (case ctr_sugar_of ctxt s of
   246       SOME {ctrs, ...} =>
   247       (case find_first (can (fo_match ctxt f)) ctrs of
   248         SOME f' => (f', args)
   249       | NONE => raise Fail "dest_ctr")
   250     | NONE => raise Fail "dest_ctr")
   251   end;
   252 
   253 fun dest_case ctxt s Ts t =
   254   (case Term.strip_comb t of
   255     (Const (c, _), args as _ :: _) =>
   256     (case ctr_sugar_of ctxt s of
   257       SOME (ctr_sugar as {casex = Const (case_name, _), discs = discs0, selss = selss0, ...}) =>
   258       if case_name = c then
   259         let val n = length discs0 in
   260           if n < length args then
   261             let
   262               val (branches, obj :: leftovers) = chop n args;
   263               val discs = map (mk_disc_or_sel Ts) discs0;
   264               val selss = map (map (mk_disc_or_sel Ts)) selss0;
   265               val conds = map (rapp obj) discs;
   266               val branch_argss = map (fn sels => map (rapp obj) sels @ leftovers) selss;
   267               val branches' = map2 (curry Term.betapplys) branches branch_argss;
   268             in
   269               SOME (ctr_sugar, conds, branches')
   270             end
   271           else
   272             NONE
   273         end
   274       else
   275         NONE
   276     | _ => NONE)
   277   | _ => NONE);
   278 
   279 fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
   280 
   281 fun prepare_wrap_free_constructors prep_term ((((no_discs_sels, no_code), raw_ctrs),
   282     raw_case_binding), (raw_disc_bindings, (raw_sel_bindingss, raw_sel_defaultss))) no_defs_lthy =
   283   let
   284     (* TODO: sanity checks on arguments *)
   285 
   286     val n = length raw_ctrs;
   287     val ks = 1 upto n;
   288 
   289     val _ = if n > 0 then () else error "No constructors specified";
   290 
   291     val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
   292     val sel_defaultss =
   293       pad_list [] n (map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss);
   294 
   295     val Type (fcT_name, As0) = body_type (fastype_of (hd ctrs0));
   296     val fc_b_name = Long_Name.base_name fcT_name;
   297     val fc_b = Binding.name fc_b_name;
   298 
   299     fun qualify mandatory = Binding.qualify mandatory fc_b_name;
   300 
   301     fun dest_TFree_or_TVar (TFree sS) = sS
   302       | dest_TFree_or_TVar (TVar ((s, _), S)) = (s, S)
   303       | dest_TFree_or_TVar _ = error "Invalid type argument";
   304 
   305     val (unsorted_As, B) =
   306       no_defs_lthy
   307       |> variant_tfrees (map (fst o dest_TFree_or_TVar) As0)
   308       ||> the_single o fst o mk_TFrees 1;
   309 
   310     val As = map2 (resort_tfree o snd o dest_TFree_or_TVar) As0 unsorted_As;
   311 
   312     val fcT = Type (fcT_name, As);
   313     val ctrs = map (mk_ctr As) ctrs0;
   314     val ctr_Tss = map (binder_types o fastype_of) ctrs;
   315 
   316     val ms = map length ctr_Tss;
   317 
   318     val raw_disc_bindings' = pad_list Binding.empty n raw_disc_bindings;
   319 
   320     fun can_definitely_rely_on_disc k = not (Binding.is_empty (nth raw_disc_bindings' (k - 1)));
   321     fun can_rely_on_disc k =
   322       can_definitely_rely_on_disc k orelse (k = 1 andalso not (can_definitely_rely_on_disc 2));
   323     fun should_omit_disc_binding k = n = 1 orelse (n = 2 andalso can_rely_on_disc (3 - k));
   324 
   325     fun is_disc_binding_valid b =
   326       not (Binding.is_empty b orelse Binding.eq_name (b, equal_binding));
   327 
   328     val standard_disc_binding = Binding.name o prefix isN o base_name_of_ctr;
   329 
   330     val disc_bindings =
   331       raw_disc_bindings'
   332       |> map4 (fn k => fn m => fn ctr => fn disc =>
   333         qualify false
   334           (if Binding.is_empty disc then
   335              if should_omit_disc_binding k then disc else standard_disc_binding ctr
   336            else if Binding.eq_name (disc, equal_binding) then
   337              if m = 0 then disc
   338              else error "Cannot use \"=\" syntax for discriminating nonnullary constructor"
   339            else if Binding.eq_name (disc, standard_binding) then
   340              standard_disc_binding ctr
   341            else
   342              disc)) ks ms ctrs0;
   343 
   344     fun standard_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
   345 
   346     val sel_bindingss =
   347       pad_list [] n raw_sel_bindingss
   348       |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
   349         qualify false
   350           (if Binding.is_empty sel orelse Binding.eq_name (sel, standard_binding) then
   351             standard_sel_binding m l ctr
   352           else
   353             sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms;
   354 
   355     val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
   356 
   357     val (((((((([exh_y], (xss, xss')), yss), fs), gs), [u', v']), [w]), (p, p')), names_lthy) =
   358       no_defs_lthy
   359       |> mk_Frees "y" [fcT] (* for compatibility with "datatype_realizer.ML" *)
   360       ||>> mk_Freess' "x" ctr_Tss
   361       ||>> mk_Freess "y" ctr_Tss
   362       ||>> mk_Frees "f" case_Ts
   363       ||>> mk_Frees "g" case_Ts
   364       ||>> (apfst (map (rpair fcT)) oo Variable.variant_fixes) [fc_b_name, fc_b_name ^ "'"]
   365       ||>> mk_Frees "z" [B]
   366       ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
   367 
   368     val u = Free u';
   369     val v = Free v';
   370     val q = Free (fst p', mk_pred1T B);
   371 
   372     val xctrs = map2 (curry Term.list_comb) ctrs xss;
   373     val yctrs = map2 (curry Term.list_comb) ctrs yss;
   374 
   375     val xfs = map2 (curry Term.list_comb) fs xss;
   376     val xgs = map2 (curry Term.list_comb) gs xss;
   377 
   378     (* TODO: Eta-expension is for compatibility with the old datatype package (but it also provides
   379        nicer names). Consider removing. *)
   380     val eta_fs = map2 eta_expand_arg xss xfs;
   381     val eta_gs = map2 eta_expand_arg xss xgs;
   382 
   383     val case_binding =
   384       qualify false
   385         (if Binding.is_empty raw_case_binding orelse
   386             Binding.eq_name (raw_case_binding, standard_binding) then
   387            Binding.prefix_name (caseN ^ "_") fc_b
   388          else
   389            raw_case_binding);
   390 
   391     fun mk_case_disj xctr xf xs =
   392       list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr), HOLogic.mk_eq (w, xf)));
   393 
   394     val case_rhs = fold_rev (fold_rev Term.lambda) [fs, [u]]
   395       (Const (@{const_name The}, (B --> HOLogic.boolT) --> B) $
   396          Term.lambda w (Library.foldr1 HOLogic.mk_disj (map3 mk_case_disj xctrs xfs xss)));
   397 
   398     val ((raw_case, (_, raw_case_def)), (lthy', lthy)) = no_defs_lthy
   399       |> Local_Theory.define ((case_binding, NoSyn),
   400         ((Binding.conceal (Thm.def_binding case_binding), []), case_rhs))
   401       ||> `Local_Theory.restore;
   402 
   403     val phi = Proof_Context.export_morphism lthy lthy';
   404 
   405     val case_def = Morphism.thm phi raw_case_def;
   406 
   407     val case0 = Morphism.term phi raw_case;
   408     val casex = mk_case As B case0;
   409 
   410     val fcase = Term.list_comb (casex, fs);
   411 
   412     val ufcase = fcase $ u;
   413     val vfcase = fcase $ v;
   414 
   415     val eta_fcase = Term.list_comb (casex, eta_fs);
   416     val eta_gcase = Term.list_comb (casex, eta_gs);
   417 
   418     val eta_ufcase = eta_fcase $ u;
   419     val eta_vgcase = eta_gcase $ v;
   420 
   421     fun mk_uu_eq () = HOLogic.mk_eq (u, u);
   422 
   423     val uv_eq = mk_Trueprop_eq (u, v);
   424 
   425     val exist_xs_u_eq_ctrs =
   426       map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
   427 
   428     val unique_disc_no_def = TrueI; (*arbitrary marker*)
   429     val alternate_disc_no_def = FalseE; (*arbitrary marker*)
   430 
   431     fun alternate_disc_lhs get_udisc k =
   432       HOLogic.mk_not
   433         (let val b = nth disc_bindings (k - 1) in
   434            if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
   435          end);
   436 
   437     val (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy') =
   438       if no_discs_sels then
   439         (true, [], [], [], [], [], lthy')
   440       else
   441         let
   442           fun disc_free b = Free (Binding.name_of b, mk_pred1T fcT);
   443 
   444           fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
   445 
   446           fun alternate_disc k =
   447             Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
   448 
   449           fun mk_sel_case_args b proto_sels T =
   450             map2 (fn Ts => fn k =>
   451               (case AList.lookup (op =) proto_sels k of
   452                 NONE =>
   453                 (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
   454                   NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
   455                 | SOME t => t |> Type.constraint (Ts ---> T) |> Syntax.check_term lthy)
   456               | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
   457 
   458           fun sel_spec b proto_sels =
   459             let
   460               val _ =
   461                 (case duplicates (op =) (map fst proto_sels) of
   462                    k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
   463                      " for constructor " ^
   464                      quote (Syntax.string_of_term lthy (nth ctrs (k - 1))))
   465                  | [] => ())
   466               val T =
   467                 (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
   468                   [T] => T
   469                 | T :: T' :: _ => error ("Inconsistent range type for selector " ^
   470                     quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ lthy T) ^ " vs. "
   471                     ^ quote (Syntax.string_of_typ lthy T')));
   472             in
   473               mk_Trueprop_eq (Free (Binding.name_of b, fcT --> T) $ u,
   474                 Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
   475             end;
   476 
   477           val sel_bindings = flat sel_bindingss;
   478           val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
   479           val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
   480 
   481           val sel_binding_index =
   482             if all_sels_distinct then 1 upto length sel_bindings
   483             else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
   484 
   485           val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
   486           val sel_infos =
   487             AList.group (op =) (sel_binding_index ~~ proto_sels)
   488             |> sort (int_ord o pairself fst)
   489             |> map snd |> curry (op ~~) uniq_sel_bindings;
   490           val sel_bindings = map fst sel_infos;
   491 
   492           fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
   493 
   494           val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
   495             lthy
   496             |> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
   497                 if Binding.is_empty b then
   498                   if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
   499                   else pair (alternate_disc k, alternate_disc_no_def)
   500                 else if Binding.eq_name (b, equal_binding) then
   501                   pair (Term.lambda u exist_xs_u_eq_ctr, refl)
   502                 else
   503                   Specification.definition (SOME (b, NONE, NoSyn),
   504                     ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
   505               ks exist_xs_u_eq_ctrs disc_bindings
   506             ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
   507               Specification.definition (SOME (b, NONE, NoSyn),
   508                 ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
   509             ||> `Local_Theory.restore;
   510 
   511           val phi = Proof_Context.export_morphism lthy lthy';
   512 
   513           val disc_defs = map (Morphism.thm phi) raw_disc_defs;
   514           val sel_defs = map (Morphism.thm phi) raw_sel_defs;
   515           val sel_defss = unflat_selss sel_defs;
   516 
   517           val discs0 = map (Morphism.term phi) raw_discs;
   518           val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
   519 
   520           val discs = map (mk_disc_or_sel As) discs0;
   521           val selss = map (map (mk_disc_or_sel As)) selss0;
   522         in
   523           (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy')
   524         end;
   525 
   526     fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
   527 
   528     val exhaust_goal =
   529       let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (exh_y, xctr)]) in
   530         fold_rev Logic.all [p, exh_y] (mk_imp_p (map2 mk_prem xctrs xss))
   531       end;
   532 
   533     val inject_goalss =
   534       let
   535         fun mk_goal _ _ [] [] = []
   536           | mk_goal xctr yctr xs ys =
   537             [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
   538               Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
   539       in
   540         map4 mk_goal xctrs yctrs xss yss
   541       end;
   542 
   543     val half_distinct_goalss =
   544       let
   545         fun mk_goal ((xs, xc), (xs', xc')) =
   546           fold_rev Logic.all (xs @ xs')
   547             (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
   548       in
   549         map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
   550       end;
   551 
   552     val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss;
   553 
   554     fun after_qed thmss lthy =
   555       let
   556         val ([exhaust_thm0], (inject_thmss, half_distinct_thmss)) = (hd thmss, chop n (tl thmss));
   557         (* for "datatype_realizer.ML": *)
   558         val exhaust_thm =
   559           Thm.name_derivation (fcT_name ^ Long_Name.separator ^ exhaustN) exhaust_thm0;
   560 
   561         val inject_thms = flat inject_thmss;
   562 
   563         val rho_As = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
   564 
   565         fun inst_thm t thm =
   566           Drule.instantiate' [] [SOME (certify lthy t)]
   567             (Thm.instantiate (rho_As, []) (Drule.zero_var_indexes thm));
   568 
   569         val uexhaust_thm = inst_thm u exhaust_thm;
   570 
   571         val exhaust_cases = map base_name_of_ctr ctrs;
   572 
   573         val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
   574 
   575         val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
   576           join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
   577 
   578         val nchotomy_thm =
   579           let
   580             val goal =
   581               HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
   582                 Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
   583           in
   584             Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
   585             |> Thm.close_derivation
   586           end;
   587 
   588         val case_thms =
   589           let
   590             val goals =
   591               map3 (fn xctr => fn xf => fn xs =>
   592                 fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xctrs xfs xss;
   593           in
   594             map4 (fn k => fn goal => fn injects => fn distinctss =>
   595                 Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   596                   mk_case_tac ctxt n k case_def injects distinctss)
   597                 |> Thm.close_derivation)
   598               ks goals inject_thmss distinct_thmsss
   599           end;
   600 
   601         val (case_cong_thm, weak_case_cong_thm) =
   602           let
   603             fun mk_prem xctr xs xf xg =
   604               fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
   605                 mk_Trueprop_eq (xf, xg)));
   606 
   607             val goal =
   608               Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
   609                  mk_Trueprop_eq (eta_ufcase, eta_vgcase));
   610             val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
   611           in
   612             (Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
   613              Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
   614             |> pairself (singleton (Proof_Context.export names_lthy lthy) #>
   615               Thm.close_derivation)
   616           end;
   617 
   618         val split_lhs = q $ ufcase;
   619 
   620         fun mk_split_conjunct xctr xs f_xs =
   621           list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
   622         fun mk_split_disjunct xctr xs f_xs =
   623           list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
   624             HOLogic.mk_not (q $ f_xs)));
   625 
   626         fun mk_split_goal xctrs xss xfs =
   627           mk_Trueprop_eq (split_lhs, Library.foldr1 HOLogic.mk_conj
   628             (map3 mk_split_conjunct xctrs xss xfs));
   629         fun mk_split_asm_goal xctrs xss xfs =
   630           mk_Trueprop_eq (split_lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
   631             (map3 mk_split_disjunct xctrs xss xfs)));
   632 
   633         fun prove_split selss goal =
   634           Goal.prove_sorry lthy [] [] goal (fn _ =>
   635             mk_split_tac lthy uexhaust_thm case_thms selss inject_thmss distinct_thmsss)
   636           |> singleton (Proof_Context.export names_lthy lthy)
   637           |> Thm.close_derivation;
   638 
   639         fun prove_split_asm asm_goal split_thm =
   640           Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
   641             mk_split_asm_tac ctxt split_thm)
   642           |> singleton (Proof_Context.export names_lthy lthy)
   643           |> Thm.close_derivation;
   644 
   645         val (split_thm, split_asm_thm) =
   646           let
   647             val goal = mk_split_goal xctrs xss xfs;
   648             val asm_goal = mk_split_asm_goal xctrs xss xfs;
   649 
   650             val thm = prove_split (replicate n []) goal;
   651             val asm_thm = prove_split_asm asm_goal thm;
   652           in
   653             (thm, asm_thm)
   654           end;
   655 
   656         val (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thmss, discI_thms,
   657              nontriv_discI_thms, disc_exclude_thms, disc_exclude_thmsss, disc_exhaust_thms,
   658              sel_exhaust_thms, all_collapse_thms, safe_collapse_thms, expand_thms, sel_split_thms,
   659              sel_split_asm_thms, case_eq_if_thms) =
   660           if no_discs_sels then
   661             ([], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [])
   662           else
   663             let
   664               val udiscs = map (rapp u) discs;
   665               val uselss = map (map (rapp u)) selss;
   666               val usel_ctrs = map2 (curry Term.list_comb) ctrs uselss;
   667               val usel_fs = map2 (curry Term.list_comb) fs uselss;
   668 
   669               val vdiscs = map (rapp v) discs;
   670               val vselss = map (map (rapp v)) selss;
   671 
   672               fun make_sel_thm xs' case_thm sel_def =
   673                 zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
   674                     (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
   675 
   676               val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
   677 
   678               fun has_undefined_rhs thm =
   679                 (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
   680                   Const (@{const_name undefined}, _) => true
   681                 | _ => false);
   682 
   683               val all_sel_thms =
   684                 (if all_sels_distinct andalso forall null sel_defaultss then
   685                    flat sel_thmss
   686                  else
   687                    map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
   688                      (xss' ~~ case_thms))
   689                 |> filter_out has_undefined_rhs;
   690 
   691               fun mk_unique_disc_def () =
   692                 let
   693                   val m = the_single ms;
   694                   val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
   695                 in
   696                   Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
   697                   |> singleton (Proof_Context.export names_lthy lthy)
   698                   |> Thm.close_derivation
   699                 end;
   700 
   701               fun mk_alternate_disc_def k =
   702                 let
   703                   val goal =
   704                     mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
   705                       nth exist_xs_u_eq_ctrs (k - 1));
   706                 in
   707                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   708                     mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
   709                       (nth distinct_thms (2 - k)) uexhaust_thm)
   710                   |> singleton (Proof_Context.export names_lthy lthy)
   711                   |> Thm.close_derivation
   712                 end;
   713 
   714               val has_alternate_disc_def =
   715                 exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
   716 
   717               val disc_defs' =
   718                 map2 (fn k => fn def =>
   719                   if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
   720                   else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
   721                   else def) ks disc_defs;
   722 
   723               val discD_thms = map (fn def => def RS iffD1) disc_defs';
   724               val discI_thms =
   725                 map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
   726                   disc_defs';
   727               val not_discI_thms =
   728                 map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
   729                     (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
   730                   ms disc_defs';
   731 
   732               val (disc_thmss', disc_thmss) =
   733                 let
   734                   fun mk_thm discI _ [] = refl RS discI
   735                     | mk_thm _ not_discI [distinct] = distinct RS not_discI;
   736                   fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
   737                 in
   738                   map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
   739                 end;
   740 
   741               val nontriv_disc_thmss =
   742                 map2 (fn b => if is_disc_binding_valid b then I else K []) disc_bindings disc_thmss;
   743 
   744               fun is_discI_boring b =
   745                 (n = 1 andalso Binding.is_empty b) orelse Binding.eq_name (b, equal_binding);
   746 
   747               val nontriv_discI_thms =
   748                 flat (map2 (fn b => if is_discI_boring b then K [] else single) disc_bindings
   749                   discI_thms);
   750 
   751               val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
   752                 let
   753                   fun mk_goal [] = []
   754                     | mk_goal [((_, udisc), (_, udisc'))] =
   755                       [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
   756                          HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
   757 
   758                   fun prove tac goal =
   759                     Goal.prove_sorry lthy [] [] goal (K tac)
   760                     |> Thm.close_derivation;
   761 
   762                   val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
   763 
   764                   val half_goalss = map mk_goal half_pairss;
   765                   val half_thmss =
   766                     map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
   767                         fn disc_thm => [prove (mk_half_disc_exclude_tac lthy m discD disc_thm) goal])
   768                       half_goalss half_pairss (flat disc_thmss');
   769 
   770                   val other_half_goalss = map (mk_goal o map swap) half_pairss;
   771                   val other_half_thmss =
   772                     map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
   773                       other_half_goalss;
   774                 in
   775                   join_halves n half_thmss other_half_thmss ||> `transpose
   776                   |>> has_alternate_disc_def ? K []
   777                 end;
   778 
   779               val disc_exhaust_thm =
   780                 let
   781                   fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
   782                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
   783                 in
   784                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   785                     mk_disc_exhaust_tac n exhaust_thm discI_thms)
   786                   |> Thm.close_derivation
   787                 end;
   788 
   789               val (safe_collapse_thms, all_collapse_thms) =
   790                 let
   791                   fun mk_goal m udisc usel_ctr =
   792                     let
   793                       val prem = HOLogic.mk_Trueprop udisc;
   794                       val concl = mk_Trueprop_eq ((usel_ctr, u) |> m = 0 ? swap);
   795                     in
   796                       (prem aconv concl, Logic.all u (Logic.mk_implies (prem, concl)))
   797                     end;
   798                   val (trivs, goals) = map3 mk_goal ms udiscs usel_ctrs |> split_list;
   799                   val thms =
   800                     map5 (fn m => fn discD => fn sel_thms => fn triv => fn goal =>
   801                         Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   802                           mk_collapse_tac ctxt m discD sel_thms ORELSE HEADGOAL atac)
   803                         |> Thm.close_derivation
   804                         |> not triv ? perhaps (try (fn thm => refl RS thm)))
   805                       ms discD_thms sel_thmss trivs goals;
   806                 in
   807                   (map_filter (fn (true, _) => NONE | (false, thm) => SOME thm) (trivs ~~ thms),
   808                    thms)
   809                 end;
   810 
   811               val swapped_all_collapse_thms =
   812                 map2 (fn m => fn thm => if m = 0 then thm else thm RS sym) ms all_collapse_thms;
   813 
   814               val sel_exhaust_thm =
   815                 let
   816                   fun mk_prem usel_ctr = mk_imp_p [mk_Trueprop_eq (u, usel_ctr)];
   817                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem usel_ctrs));
   818                 in
   819                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   820                     mk_sel_exhaust_tac n disc_exhaust_thm swapped_all_collapse_thms)
   821                   |> Thm.close_derivation
   822                 end;
   823 
   824               val expand_thm =
   825                 let
   826                   fun mk_prems k udisc usels vdisc vsels =
   827                     (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
   828                     (if null usels then
   829                        []
   830                      else
   831                        [Logic.list_implies
   832                           (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
   833                              HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
   834                                (map2 (curry HOLogic.mk_eq) usels vsels)))]);
   835 
   836                   val goal =
   837                     Library.foldr Logic.list_implies
   838                       (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
   839                   val uncollapse_thms =
   840                     map2 (fn thm => fn [] => thm | _ => thm RS sym) all_collapse_thms uselss;
   841                 in
   842                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   843                     mk_expand_tac lthy n ms (inst_thm u disc_exhaust_thm)
   844                       (inst_thm v disc_exhaust_thm) uncollapse_thms disc_exclude_thmsss
   845                       disc_exclude_thmsss')
   846                   |> singleton (Proof_Context.export names_lthy lthy)
   847                   |> Thm.close_derivation
   848                 end;
   849 
   850               val (sel_split_thm, sel_split_asm_thm) =
   851                 let
   852                   val zss = map (K []) xss;
   853                   val goal = mk_split_goal usel_ctrs zss usel_fs;
   854                   val asm_goal = mk_split_asm_goal usel_ctrs zss usel_fs;
   855 
   856                   val thm = prove_split sel_thmss goal;
   857                   val asm_thm = prove_split_asm asm_goal thm;
   858                 in
   859                   (thm, asm_thm)
   860                 end;
   861 
   862               val case_eq_if_thm =
   863                 let
   864                   val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs usel_fs);
   865                 in
   866                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   867                     mk_case_eq_if_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)
   868                   |> singleton (Proof_Context.export names_lthy lthy)
   869                   |> Thm.close_derivation
   870                 end;
   871             in
   872               (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thmss, discI_thms,
   873                nontriv_discI_thms, disc_exclude_thms, disc_exclude_thmsss, [disc_exhaust_thm],
   874                [sel_exhaust_thm], all_collapse_thms, safe_collapse_thms, [expand_thm],
   875                [sel_split_thm], [sel_split_asm_thm], [case_eq_if_thm])
   876             end;
   877 
   878         val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
   879         val cases_type_attr = Attrib.internal (K (Induct.cases_type fcT_name));
   880 
   881         val nontriv_disc_eq_thmss =
   882           map (map (fn th => th RS @{thm eq_False[THEN iffD2]}
   883             handle THM _ => th RS @{thm eq_True[THEN iffD2]})) nontriv_disc_thmss;
   884 
   885         val anonymous_notes =
   886           [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs),
   887            (flat nontriv_disc_eq_thmss, code_nitpicksimp_attrs)]
   888           |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
   889 
   890         val notes =
   891           [(caseN, case_thms, code_nitpicksimp_simp_attrs),
   892            (case_congN, [case_cong_thm], []),
   893            (case_eq_ifN, case_eq_if_thms, []),
   894            (collapseN, safe_collapse_thms, simp_attrs),
   895            (discN, flat nontriv_disc_thmss, simp_attrs),
   896            (discIN, nontriv_discI_thms, []),
   897            (disc_excludeN, disc_exclude_thms, dest_attrs),
   898            (disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
   899            (distinctN, distinct_thms, simp_attrs @ inductsimp_attrs),
   900            (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
   901            (expandN, expand_thms, []),
   902            (injectN, inject_thms, iff_attrs @ inductsimp_attrs),
   903            (nchotomyN, [nchotomy_thm], []),
   904            (selN, all_sel_thms, code_nitpicksimp_simp_attrs),
   905            (sel_exhaustN, sel_exhaust_thms, [exhaust_case_names_attr]),
   906            (sel_splitN, sel_split_thms, []),
   907            (sel_split_asmN, sel_split_asm_thms, []),
   908            (splitN, [split_thm], []),
   909            (split_asmN, [split_asm_thm], []),
   910            (splitsN, [split_thm, split_asm_thm], []),
   911            (weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
   912           |> filter_out (null o #2)
   913           |> map (fn (thmN, thms, attrs) =>
   914             ((qualify true (Binding.name thmN), attrs), [(thms, [])]));
   915 
   916         val ctr_sugar =
   917           {ctrs = ctrs, casex = casex, discs = discs, selss = selss, exhaust = exhaust_thm,
   918            nchotomy = nchotomy_thm, injects = inject_thms, distincts = distinct_thms,
   919            case_thms = case_thms, case_cong = case_cong_thm, weak_case_cong = weak_case_cong_thm,
   920            split = split_thm, split_asm = split_asm_thm, disc_thmss = disc_thmss,
   921            discIs = discI_thms, sel_thmss = sel_thmss, disc_excludesss = disc_exclude_thmsss,
   922            disc_exhausts = disc_exhaust_thms, sel_exhausts = sel_exhaust_thms,
   923            collapses = all_collapse_thms, expands = expand_thms, sel_splits = sel_split_thms,
   924            sel_split_asms = sel_split_asm_thms, case_eq_ifs = case_eq_if_thms};
   925       in
   926         (ctr_sugar,
   927          lthy
   928          |> Spec_Rules.add Spec_Rules.Equational ([casex], case_thms)
   929          |> Spec_Rules.add Spec_Rules.Equational (flat selss, all_sel_thms)
   930          |> fold (Spec_Rules.add Spec_Rules.Equational) (map single discs ~~ nontriv_disc_eq_thmss)
   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       @{keyword ")"}
   970       >> (fn js => (member (op =) js 0, member (op =) js 1)))
   971     (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;