src/HOL/Tools/Ctr_Sugar/ctr_sugar.ML
author blanchet
Mon Apr 28 00:54:31 2014 +0200 (2014-04-28)
changeset 56767 9b311dbd0f55
parent 56657 558afd429255
child 56858 0c3d0bc98abe
permissions -rw-r--r--
restored naming trick
     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 ctr_sugar_interpretation: (ctr_sugar -> theory -> theory) -> theory -> theory
    42   val register_ctr_sugar: string -> ctr_sugar -> local_theory -> local_theory
    43   val default_register_ctr_sugar_global: string -> ctr_sugar -> theory -> theory
    44 
    45   val mk_half_pairss: 'a list * 'a list -> ('a * 'a) list list
    46   val join_halves: int -> 'a list list -> 'a list list -> 'a list * 'a list list list
    47 
    48   val mk_ctr: typ list -> term -> term
    49   val mk_case: typ list -> typ -> term -> term
    50   val mk_disc_or_sel: typ list -> term -> term
    51   val name_of_ctr: term -> string
    52   val name_of_disc: term -> string
    53   val dest_ctr: Proof.context -> string -> term -> term * term list
    54   val dest_case: Proof.context -> string -> typ list -> term ->
    55     (ctr_sugar * term list * term list) option
    56 
    57   type ('c, 'a, 'v) ctr_spec = ((binding * 'c) * 'a list) * (binding * 'v) list
    58 
    59   val disc_of_ctr_spec: ('c, 'a, 'v) ctr_spec -> binding
    60   val ctr_of_ctr_spec: ('c, 'a, 'v) ctr_spec -> 'c
    61   val args_of_ctr_spec: ('c, 'a, 'v) ctr_spec -> 'a list
    62   val sel_defaults_of_ctr_spec: ('c, 'a, 'v) ctr_spec -> (binding * 'v) list
    63 
    64   val free_constructors: ({prems: thm list, context: Proof.context} -> tactic) list list ->
    65     ((bool * bool) * binding) * (term, binding, term) ctr_spec list -> local_theory ->
    66     ctr_sugar * local_theory
    67   val parse_bound_term: (binding * string) parser
    68   val parse_ctr_options: (bool * bool) parser
    69   val parse_ctr_spec: 'c parser -> 'a parser -> ('c, 'a, string) ctr_spec parser
    70 end;
    71 
    72 structure Ctr_Sugar : CTR_SUGAR =
    73 struct
    74 
    75 open Ctr_Sugar_Util
    76 open Ctr_Sugar_Tactics
    77 open Ctr_Sugar_Code
    78 
    79 type ctr_sugar =
    80   {ctrs: term list,
    81    casex: term,
    82    discs: term list,
    83    selss: term list list,
    84    exhaust: thm,
    85    nchotomy: thm,
    86    injects: thm list,
    87    distincts: thm list,
    88    case_thms: thm list,
    89    case_cong: thm,
    90    weak_case_cong: thm,
    91    split: thm,
    92    split_asm: thm,
    93    disc_thmss: thm list list,
    94    discIs: thm list,
    95    sel_thmss: thm list list,
    96    disc_excludesss: thm list list list,
    97    disc_exhausts: thm list,
    98    sel_exhausts: thm list,
    99    collapses: thm list,
   100    expands: thm list,
   101    sel_splits: thm list,
   102    sel_split_asms: thm list,
   103    case_eq_ifs: thm list};
   104 
   105 fun morph_ctr_sugar phi {ctrs, casex, discs, selss, exhaust, nchotomy, injects, distincts,
   106     case_thms, case_cong, weak_case_cong, split, split_asm, disc_thmss, discIs, sel_thmss,
   107     disc_excludesss, disc_exhausts, sel_exhausts, collapses, expands, sel_splits, sel_split_asms,
   108     case_eq_ifs} =
   109   {ctrs = map (Morphism.term phi) ctrs,
   110    casex = Morphism.term phi casex,
   111    discs = map (Morphism.term phi) discs,
   112    selss = map (map (Morphism.term phi)) selss,
   113    exhaust = Morphism.thm phi exhaust,
   114    nchotomy = Morphism.thm phi nchotomy,
   115    injects = map (Morphism.thm phi) injects,
   116    distincts = map (Morphism.thm phi) distincts,
   117    case_thms = map (Morphism.thm phi) case_thms,
   118    case_cong = Morphism.thm phi case_cong,
   119    weak_case_cong = Morphism.thm phi weak_case_cong,
   120    split = Morphism.thm phi split,
   121    split_asm = Morphism.thm phi split_asm,
   122    disc_thmss = map (map (Morphism.thm phi)) disc_thmss,
   123    discIs = map (Morphism.thm phi) discIs,
   124    sel_thmss = map (map (Morphism.thm phi)) sel_thmss,
   125    disc_excludesss = map (map (map (Morphism.thm phi))) disc_excludesss,
   126    disc_exhausts = map (Morphism.thm phi) disc_exhausts,
   127    sel_exhausts = map (Morphism.thm phi) sel_exhausts,
   128    collapses = map (Morphism.thm phi) collapses,
   129    expands = map (Morphism.thm phi) expands,
   130    sel_splits = map (Morphism.thm phi) sel_splits,
   131    sel_split_asms = map (Morphism.thm phi) sel_split_asms,
   132    case_eq_ifs = map (Morphism.thm phi) case_eq_ifs};
   133 
   134 val transfer_ctr_sugar =
   135   morph_ctr_sugar o Morphism.transfer_morphism o Proof_Context.theory_of;
   136 
   137 structure Data = Generic_Data
   138 (
   139   type T = ctr_sugar Symtab.table;
   140   val empty = Symtab.empty;
   141   val extend = I;
   142   fun merge data : T = Symtab.merge (K true) data;
   143 );
   144 
   145 fun ctr_sugar_of ctxt =
   146   Symtab.lookup (Data.get (Context.Proof ctxt))
   147   #> Option.map (transfer_ctr_sugar ctxt);
   148 
   149 fun ctr_sugars_of ctxt =
   150   Symtab.fold (cons o transfer_ctr_sugar ctxt o snd) (Data.get (Context.Proof ctxt)) [];
   151 
   152 fun ctr_sugar_of_case ctxt s =
   153   find_first (fn {casex = Const (s', _), ...} => s' = s | _ => false) (ctr_sugars_of ctxt);
   154 
   155 structure Ctr_Sugar_Interpretation = Interpretation
   156 (
   157   type T = ctr_sugar;
   158   val eq: T * T -> bool = op = o pairself #ctrs;
   159 );
   160 
   161 fun with_repaired_path f (ctr_sugar as {ctrs = ctr1 :: _, ...} : ctr_sugar) thy =
   162   thy
   163   |> Sign.root_path
   164   |> Sign.add_path (Long_Name.qualifier (fst (dest_Type (body_type (fastype_of ctr1)))))
   165   |> (fn thy => f (morph_ctr_sugar (Morphism.transfer_morphism thy) ctr_sugar) thy)
   166   |> Sign.restore_naming thy;
   167 
   168 fun ctr_sugar_interpretation f = Ctr_Sugar_Interpretation.interpretation (with_repaired_path f);
   169 
   170 fun register_ctr_sugar key ctr_sugar =
   171   Local_Theory.declaration {syntax = false, pervasive = true}
   172     (fn phi => Data.map (Symtab.update (key, morph_ctr_sugar phi ctr_sugar)))
   173   #> Local_Theory.background_theory (Ctr_Sugar_Interpretation.data ctr_sugar);
   174 
   175 fun default_register_ctr_sugar_global key ctr_sugar thy =
   176   let val tab = Data.get (Context.Theory thy) in
   177     if Symtab.defined tab key then
   178       thy
   179     else
   180       thy
   181       |> Context.theory_map (Data.put (Symtab.update_new (key, ctr_sugar) tab))
   182       |> Ctr_Sugar_Interpretation.data ctr_sugar
   183   end;
   184 
   185 val isN = "is_";
   186 val unN = "un_";
   187 fun mk_unN 1 1 suf = unN ^ suf
   188   | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
   189 
   190 val caseN = "case";
   191 val case_congN = "case_cong";
   192 val case_eq_ifN = "case_eq_if";
   193 val collapseN = "collapse";
   194 val disc_excludeN = "disc_exclude";
   195 val disc_exhaustN = "disc_exhaust";
   196 val discN = "disc";
   197 val discIN = "discI";
   198 val distinctN = "distinct";
   199 val exhaustN = "exhaust";
   200 val expandN = "expand";
   201 val injectN = "inject";
   202 val nchotomyN = "nchotomy";
   203 val selN = "sel";
   204 val sel_exhaustN = "sel_exhaust";
   205 val sel_splitN = "sel_split";
   206 val sel_split_asmN = "sel_split_asm";
   207 val splitN = "split";
   208 val splitsN = "splits";
   209 val split_asmN = "split_asm";
   210 val weak_case_cong_thmsN = "weak_case_cong";
   211 
   212 val cong_attrs = @{attributes [cong]};
   213 val dest_attrs = @{attributes [dest]};
   214 val safe_elim_attrs = @{attributes [elim!]};
   215 val iff_attrs = @{attributes [iff]};
   216 val inductsimp_attrs = @{attributes [induct_simp]};
   217 val nitpicksimp_attrs = @{attributes [nitpick_simp]};
   218 val simp_attrs = @{attributes [simp]};
   219 val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
   220 val code_nitpicksimp_simp_attrs = code_nitpicksimp_attrs @ simp_attrs;
   221 
   222 fun unflat_lookup eq xs ys = map (fn xs' => permute_like_unique eq xs xs' ys);
   223 
   224 fun mk_half_pairss' _ ([], []) = []
   225   | mk_half_pairss' indent (x :: xs, _ :: ys) =
   226     indent @ fold_rev (cons o single o pair x) ys (mk_half_pairss' ([] :: indent) (xs, ys));
   227 
   228 fun mk_half_pairss p = mk_half_pairss' [[]] p;
   229 
   230 fun join_halves n half_xss other_half_xss =
   231   (splice (flat half_xss) (flat other_half_xss),
   232    map2 (map2 append) (Library.chop_groups n half_xss)
   233      (transpose (Library.chop_groups n other_half_xss)));
   234 
   235 fun mk_undefined T = Const (@{const_name undefined}, T);
   236 
   237 fun mk_ctr Ts t =
   238   let val Type (_, Ts0) = body_type (fastype_of t) in
   239     subst_nonatomic_types (Ts0 ~~ Ts) t
   240   end;
   241 
   242 fun mk_case Ts T t =
   243   let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
   244     subst_nonatomic_types ((body, T) :: (Ts0 ~~ Ts)) t
   245   end;
   246 
   247 fun mk_disc_or_sel Ts t =
   248   subst_nonatomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
   249 
   250 fun name_of_const what t =
   251   (case head_of t of
   252     Const (s, _) => s
   253   | Free (s, _) => s
   254   | _ => error ("Cannot extract name of " ^ what));
   255 
   256 val name_of_ctr = name_of_const "constructor";
   257 
   258 val notN = "not_";
   259 val eqN = "eq_";
   260 val neqN = "neq_";
   261 
   262 fun name_of_disc t =
   263   (case head_of t of
   264     Abs (_, _, @{const Not} $ (t' $ Bound 0)) =>
   265     Long_Name.map_base_name (prefix notN) (name_of_disc t')
   266   | Abs (_, _, Const (@{const_name HOL.eq}, _) $ Bound 0 $ t') =>
   267     Long_Name.map_base_name (prefix eqN) (name_of_disc t')
   268   | Abs (_, _, @{const Not} $ (Const (@{const_name HOL.eq}, _) $ Bound 0 $ t')) =>
   269     Long_Name.map_base_name (prefix neqN) (name_of_disc t')
   270   | t' => name_of_const "destructor" t');
   271 
   272 val base_name_of_ctr = Long_Name.base_name o name_of_ctr;
   273 
   274 fun dest_ctr ctxt s t =
   275   let val (f, args) = Term.strip_comb t in
   276     (case ctr_sugar_of ctxt s of
   277       SOME {ctrs, ...} =>
   278       (case find_first (can (fo_match ctxt f)) ctrs of
   279         SOME f' => (f', args)
   280       | NONE => raise Fail "dest_ctr")
   281     | NONE => raise Fail "dest_ctr")
   282   end;
   283 
   284 fun dest_case ctxt s Ts t =
   285   (case Term.strip_comb t of
   286     (Const (c, _), args as _ :: _) =>
   287     (case ctr_sugar_of ctxt s of
   288       SOME (ctr_sugar as {casex = Const (case_name, _), discs = discs0, selss = selss0, ...}) =>
   289       if case_name = c then
   290         let val n = length discs0 in
   291           if n < length args then
   292             let
   293               val (branches, obj :: leftovers) = chop n args;
   294               val discs = map (mk_disc_or_sel Ts) discs0;
   295               val selss = map (map (mk_disc_or_sel Ts)) selss0;
   296               val conds = map (rapp obj) discs;
   297               val branch_argss = map (fn sels => map (rapp obj) sels @ leftovers) selss;
   298               val branches' = map2 (curry Term.betapplys) branches branch_argss;
   299             in
   300               SOME (ctr_sugar, conds, branches')
   301             end
   302           else
   303             NONE
   304         end
   305       else
   306         NONE
   307     | _ => NONE)
   308   | _ => NONE);
   309 
   310 fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
   311 
   312 type ('c, 'a, 'v) ctr_spec = ((binding * 'c) * 'a list) * (binding * 'v) list;
   313 
   314 fun disc_of_ctr_spec (((disc, _), _), _) = disc;
   315 fun ctr_of_ctr_spec (((_, ctr), _), _) = ctr;
   316 fun args_of_ctr_spec ((_, args), _) = args;
   317 fun sel_defaults_of_ctr_spec (_, ds) = ds;
   318 
   319 fun prepare_free_constructors prep_term (((no_discs_sels, no_code), raw_case_binding), ctr_specs)
   320     no_defs_lthy =
   321   let
   322     (* TODO: sanity checks on arguments *)
   323 
   324     val raw_ctrs = map ctr_of_ctr_spec ctr_specs;
   325     val raw_disc_bindings = map disc_of_ctr_spec ctr_specs;
   326     val raw_sel_bindingss = map args_of_ctr_spec ctr_specs;
   327     val raw_sel_defaultss = map sel_defaults_of_ctr_spec ctr_specs;
   328 
   329     val n = length raw_ctrs;
   330     val ks = 1 upto n;
   331 
   332     val _ = if n > 0 then () else error "No constructors specified";
   333 
   334     val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
   335     val sel_defaultss = map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss;
   336 
   337     val Type (fcT_name, As0) = body_type (fastype_of (hd ctrs0));
   338     val fc_b_name = Long_Name.base_name fcT_name;
   339     val fc_b = Binding.name fc_b_name;
   340 
   341     fun qualify mandatory = Binding.qualify mandatory fc_b_name;
   342 
   343     fun dest_TFree_or_TVar (TFree sS) = sS
   344       | dest_TFree_or_TVar (TVar ((s, _), S)) = (s, S)
   345       | dest_TFree_or_TVar _ = error "Invalid type argument";
   346 
   347     val (unsorted_As, B) =
   348       no_defs_lthy
   349       |> variant_tfrees (map (fst o dest_TFree_or_TVar) As0)
   350       ||> the_single o fst o mk_TFrees 1;
   351 
   352     val As = map2 (resort_tfree o snd o dest_TFree_or_TVar) As0 unsorted_As;
   353 
   354     val fcT = Type (fcT_name, As);
   355     val ctrs = map (mk_ctr As) ctrs0;
   356     val ctr_Tss = map (binder_types o fastype_of) ctrs;
   357 
   358     val ms = map length ctr_Tss;
   359 
   360     fun can_definitely_rely_on_disc k = not (Binding.is_empty (nth raw_disc_bindings (k - 1)));
   361     fun can_rely_on_disc k =
   362       can_definitely_rely_on_disc k orelse (k = 1 andalso not (can_definitely_rely_on_disc 2));
   363     fun should_omit_disc_binding k = n = 1 orelse (n = 2 andalso can_rely_on_disc (3 - k));
   364 
   365     fun is_disc_binding_valid b =
   366       not (Binding.is_empty b orelse Binding.eq_name (b, equal_binding));
   367 
   368     val standard_disc_binding = Binding.name o prefix isN o base_name_of_ctr;
   369 
   370     val disc_bindings =
   371       raw_disc_bindings
   372       |> map4 (fn k => fn m => fn ctr => fn disc =>
   373         qualify false
   374           (if Binding.is_empty disc then
   375              if should_omit_disc_binding k then disc else standard_disc_binding ctr
   376            else if Binding.eq_name (disc, equal_binding) then
   377              if m = 0 then disc
   378              else error "Cannot use \"=\" syntax for discriminating nonnullary constructor"
   379            else if Binding.eq_name (disc, standard_binding) then
   380              standard_disc_binding ctr
   381            else
   382              disc)) ks ms ctrs0;
   383 
   384     fun standard_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
   385 
   386     val sel_bindingss =
   387       map3 (fn ctr => fn m => map2 (fn l => fn sel =>
   388         qualify false
   389           (if Binding.is_empty sel orelse Binding.eq_name (sel, standard_binding) then
   390             standard_sel_binding m l ctr
   391           else
   392             sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms raw_sel_bindingss;
   393 
   394     val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
   395 
   396     val (((((((([exh_y], (xss, xss')), yss), fs), gs), [u', v']), [w]), (p, p')), names_lthy) =
   397       no_defs_lthy
   398       |> mk_Frees "y" [fcT] (* for compatibility with "datatype_realizer.ML" *)
   399       ||>> mk_Freess' "x" ctr_Tss
   400       ||>> mk_Freess "y" ctr_Tss
   401       ||>> mk_Frees "f" case_Ts
   402       ||>> mk_Frees "g" case_Ts
   403       ||>> (apfst (map (rpair fcT)) oo Variable.variant_fixes) [fc_b_name, fc_b_name ^ "'"]
   404       ||>> mk_Frees "z" [B]
   405       ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
   406 
   407     val u = Free u';
   408     val v = Free v';
   409     val q = Free (fst p', mk_pred1T B);
   410 
   411     val xctrs = map2 (curry Term.list_comb) ctrs xss;
   412     val yctrs = map2 (curry Term.list_comb) ctrs yss;
   413 
   414     val xfs = map2 (curry Term.list_comb) fs xss;
   415     val xgs = map2 (curry Term.list_comb) gs xss;
   416 
   417     (* TODO: Eta-expension is for compatibility with the old datatype package (but it also provides
   418        nicer names). Consider removing. *)
   419     val eta_fs = map2 eta_expand_arg xss xfs;
   420     val eta_gs = map2 eta_expand_arg xss xgs;
   421 
   422     val case_binding =
   423       qualify false
   424         (if Binding.is_empty raw_case_binding orelse
   425             Binding.eq_name (raw_case_binding, standard_binding) then
   426            Binding.prefix_name (caseN ^ "_") fc_b
   427          else
   428            raw_case_binding);
   429 
   430     fun mk_case_disj xctr xf xs =
   431       list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr), HOLogic.mk_eq (w, xf)));
   432 
   433     val case_rhs = fold_rev (fold_rev Term.lambda) [fs, [u]]
   434       (Const (@{const_name The}, (B --> HOLogic.boolT) --> B) $
   435          Term.lambda w (Library.foldr1 HOLogic.mk_disj (map3 mk_case_disj xctrs xfs xss)));
   436 
   437     val ((raw_case, (_, raw_case_def)), (lthy', lthy)) = no_defs_lthy
   438       |> Local_Theory.define ((case_binding, NoSyn),
   439         ((Binding.conceal (Thm.def_binding case_binding), []), case_rhs))
   440       ||> `Local_Theory.restore;
   441 
   442     val phi = Proof_Context.export_morphism lthy lthy';
   443 
   444     val case_def = Morphism.thm phi raw_case_def;
   445 
   446     val case0 = Morphism.term phi raw_case;
   447     val casex = mk_case As B case0;
   448 
   449     val fcase = Term.list_comb (casex, fs);
   450 
   451     val ufcase = fcase $ u;
   452     val vfcase = fcase $ v;
   453 
   454     val eta_fcase = Term.list_comb (casex, eta_fs);
   455     val eta_gcase = Term.list_comb (casex, eta_gs);
   456 
   457     val eta_ufcase = eta_fcase $ u;
   458     val eta_vgcase = eta_gcase $ v;
   459 
   460     fun mk_uu_eq () = HOLogic.mk_eq (u, u);
   461 
   462     val uv_eq = mk_Trueprop_eq (u, v);
   463 
   464     val exist_xs_u_eq_ctrs =
   465       map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
   466 
   467     val unique_disc_no_def = TrueI; (*arbitrary marker*)
   468     val alternate_disc_no_def = FalseE; (*arbitrary marker*)
   469 
   470     fun alternate_disc_lhs get_udisc k =
   471       HOLogic.mk_not
   472         (let val b = nth disc_bindings (k - 1) in
   473            if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
   474          end);
   475 
   476     val (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy') =
   477       if no_discs_sels then
   478         (true, [], [], [], [], [], lthy')
   479       else
   480         let
   481           fun disc_free b = Free (Binding.name_of b, mk_pred1T fcT);
   482 
   483           fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
   484 
   485           fun alternate_disc k =
   486             Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
   487 
   488           fun mk_sel_case_args b proto_sels T =
   489             map2 (fn Ts => fn k =>
   490               (case AList.lookup (op =) proto_sels k of
   491                 NONE =>
   492                 (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
   493                   NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
   494                 | SOME t => t |> Type.constraint (Ts ---> T) |> Syntax.check_term lthy)
   495               | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
   496 
   497           fun sel_spec b proto_sels =
   498             let
   499               val _ =
   500                 (case duplicates (op =) (map fst proto_sels) of
   501                    k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
   502                      " for constructor " ^
   503                      quote (Syntax.string_of_term lthy (nth ctrs (k - 1))))
   504                  | [] => ())
   505               val T =
   506                 (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
   507                   [T] => T
   508                 | T :: T' :: _ => error ("Inconsistent range type for selector " ^
   509                     quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ lthy T) ^ " vs. "
   510                     ^ quote (Syntax.string_of_typ lthy T')));
   511             in
   512               mk_Trueprop_eq (Free (Binding.name_of b, fcT --> T) $ u,
   513                 Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
   514             end;
   515 
   516           val sel_bindings = flat sel_bindingss;
   517           val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
   518           val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
   519 
   520           val sel_binding_index =
   521             if all_sels_distinct then 1 upto length sel_bindings
   522             else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
   523 
   524           val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
   525           val sel_infos =
   526             AList.group (op =) (sel_binding_index ~~ proto_sels)
   527             |> sort (int_ord o pairself fst)
   528             |> map snd |> curry (op ~~) uniq_sel_bindings;
   529           val sel_bindings = map fst sel_infos;
   530 
   531           fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
   532 
   533           val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
   534             lthy
   535             |> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
   536                 if Binding.is_empty b then
   537                   if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
   538                   else pair (alternate_disc k, alternate_disc_no_def)
   539                 else if Binding.eq_name (b, equal_binding) then
   540                   pair (Term.lambda u exist_xs_u_eq_ctr, refl)
   541                 else
   542                   Specification.definition (SOME (b, NONE, NoSyn),
   543                     ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
   544               ks exist_xs_u_eq_ctrs disc_bindings
   545             ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
   546               Specification.definition (SOME (b, NONE, NoSyn),
   547                 ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
   548             ||> `Local_Theory.restore;
   549 
   550           val phi = Proof_Context.export_morphism lthy lthy';
   551 
   552           val disc_defs = map (Morphism.thm phi) raw_disc_defs;
   553           val sel_defs = map (Morphism.thm phi) raw_sel_defs;
   554           val sel_defss = unflat_selss sel_defs;
   555 
   556           val discs0 = map (Morphism.term phi) raw_discs;
   557           val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
   558 
   559           val discs = map (mk_disc_or_sel As) discs0;
   560           val selss = map (map (mk_disc_or_sel As)) selss0;
   561         in
   562           (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy')
   563         end;
   564 
   565     fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
   566 
   567     val exhaust_goal =
   568       let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (exh_y, xctr)]) in
   569         fold_rev Logic.all [p, exh_y] (mk_imp_p (map2 mk_prem xctrs xss))
   570       end;
   571 
   572     val inject_goalss =
   573       let
   574         fun mk_goal _ _ [] [] = []
   575           | mk_goal xctr yctr xs ys =
   576             [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
   577               Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
   578       in
   579         map4 mk_goal xctrs yctrs xss yss
   580       end;
   581 
   582     val half_distinct_goalss =
   583       let
   584         fun mk_goal ((xs, xc), (xs', xc')) =
   585           fold_rev Logic.all (xs @ xs')
   586             (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
   587       in
   588         map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
   589       end;
   590 
   591     val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss;
   592 
   593     fun after_qed thmss lthy =
   594       let
   595         val ([exhaust_thm0], (inject_thmss, half_distinct_thmss)) = (hd thmss, chop n (tl thmss));
   596         (* for "datatype_realizer.ML": *)
   597         val exhaust_thm =
   598           Thm.name_derivation (fcT_name ^ Long_Name.separator ^ exhaustN) exhaust_thm0;
   599 
   600         val inject_thms = flat inject_thmss;
   601 
   602         val rho_As = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
   603 
   604         fun inst_thm t thm =
   605           Drule.instantiate' [] [SOME (certify lthy t)]
   606             (Thm.instantiate (rho_As, []) (Drule.zero_var_indexes thm));
   607 
   608         val uexhaust_thm = inst_thm u exhaust_thm;
   609 
   610         val exhaust_cases = map base_name_of_ctr ctrs;
   611 
   612         val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
   613 
   614         val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
   615           join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
   616 
   617         val nchotomy_thm =
   618           let
   619             val goal =
   620               HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
   621                 Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
   622           in
   623             Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
   624             |> Thm.close_derivation
   625           end;
   626 
   627         val case_thms =
   628           let
   629             val goals =
   630               map3 (fn xctr => fn xf => fn xs =>
   631                 fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xctrs xfs xss;
   632           in
   633             map4 (fn k => fn goal => fn injects => fn distinctss =>
   634                 Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   635                   mk_case_tac ctxt n k case_def injects distinctss)
   636                 |> Thm.close_derivation)
   637               ks goals inject_thmss distinct_thmsss
   638           end;
   639 
   640         val (case_cong_thm, weak_case_cong_thm) =
   641           let
   642             fun mk_prem xctr xs xf xg =
   643               fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
   644                 mk_Trueprop_eq (xf, xg)));
   645 
   646             val goal =
   647               Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
   648                  mk_Trueprop_eq (eta_ufcase, eta_vgcase));
   649             val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
   650           in
   651             (Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
   652              Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
   653             |> pairself (singleton (Proof_Context.export names_lthy lthy) #>
   654               Thm.close_derivation)
   655           end;
   656 
   657         val split_lhs = q $ ufcase;
   658 
   659         fun mk_split_conjunct xctr xs f_xs =
   660           list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
   661         fun mk_split_disjunct xctr xs f_xs =
   662           list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
   663             HOLogic.mk_not (q $ f_xs)));
   664 
   665         fun mk_split_goal xctrs xss xfs =
   666           mk_Trueprop_eq (split_lhs, Library.foldr1 HOLogic.mk_conj
   667             (map3 mk_split_conjunct xctrs xss xfs));
   668         fun mk_split_asm_goal xctrs xss xfs =
   669           mk_Trueprop_eq (split_lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
   670             (map3 mk_split_disjunct xctrs xss xfs)));
   671 
   672         fun prove_split selss goal =
   673           Goal.prove_sorry lthy [] [] goal (fn _ =>
   674             mk_split_tac lthy uexhaust_thm case_thms selss inject_thmss distinct_thmsss)
   675           |> singleton (Proof_Context.export names_lthy lthy)
   676           |> Thm.close_derivation;
   677 
   678         fun prove_split_asm asm_goal split_thm =
   679           Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
   680             mk_split_asm_tac ctxt split_thm)
   681           |> singleton (Proof_Context.export names_lthy lthy)
   682           |> Thm.close_derivation;
   683 
   684         val (split_thm, split_asm_thm) =
   685           let
   686             val goal = mk_split_goal xctrs xss xfs;
   687             val asm_goal = mk_split_asm_goal xctrs xss xfs;
   688 
   689             val thm = prove_split (replicate n []) goal;
   690             val asm_thm = prove_split_asm asm_goal thm;
   691           in
   692             (thm, asm_thm)
   693           end;
   694 
   695         val (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thmss, discI_thms,
   696              nontriv_discI_thms, disc_exclude_thms, disc_exclude_thmsss, disc_exhaust_thms,
   697              sel_exhaust_thms, all_collapse_thms, safe_collapse_thms, expand_thms, sel_split_thms,
   698              sel_split_asm_thms, case_eq_if_thms) =
   699           if no_discs_sels then
   700             ([], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [])
   701           else
   702             let
   703               val udiscs = map (rapp u) discs;
   704               val uselss = map (map (rapp u)) selss;
   705               val usel_ctrs = map2 (curry Term.list_comb) ctrs uselss;
   706               val usel_fs = map2 (curry Term.list_comb) fs uselss;
   707 
   708               val vdiscs = map (rapp v) discs;
   709               val vselss = map (map (rapp v)) selss;
   710 
   711               fun make_sel_thm xs' case_thm sel_def =
   712                 zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
   713                     (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
   714 
   715               val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
   716 
   717               fun has_undefined_rhs thm =
   718                 (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
   719                   Const (@{const_name undefined}, _) => true
   720                 | _ => false);
   721 
   722               val all_sel_thms =
   723                 (if all_sels_distinct andalso forall null sel_defaultss then
   724                    flat sel_thmss
   725                  else
   726                    map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
   727                      (xss' ~~ case_thms))
   728                 |> filter_out has_undefined_rhs;
   729 
   730               fun mk_unique_disc_def () =
   731                 let
   732                   val m = the_single ms;
   733                   val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
   734                 in
   735                   Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
   736                   |> singleton (Proof_Context.export names_lthy lthy)
   737                   |> Thm.close_derivation
   738                 end;
   739 
   740               fun mk_alternate_disc_def k =
   741                 let
   742                   val goal =
   743                     mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
   744                       nth exist_xs_u_eq_ctrs (k - 1));
   745                 in
   746                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   747                     mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
   748                       (nth distinct_thms (2 - k)) uexhaust_thm)
   749                   |> singleton (Proof_Context.export names_lthy lthy)
   750                   |> Thm.close_derivation
   751                 end;
   752 
   753               val has_alternate_disc_def =
   754                 exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
   755 
   756               val disc_defs' =
   757                 map2 (fn k => fn def =>
   758                   if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
   759                   else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
   760                   else def) ks disc_defs;
   761 
   762               val discD_thms = map (fn def => def RS iffD1) disc_defs';
   763               val discI_thms =
   764                 map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
   765                   disc_defs';
   766               val not_discI_thms =
   767                 map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
   768                     (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
   769                   ms disc_defs';
   770 
   771               val (disc_thmss', disc_thmss) =
   772                 let
   773                   fun mk_thm discI _ [] = refl RS discI
   774                     | mk_thm _ not_discI [distinct] = distinct RS not_discI;
   775                   fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
   776                 in
   777                   map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
   778                 end;
   779 
   780               val nontriv_disc_thmss =
   781                 map2 (fn b => if is_disc_binding_valid b then I else K []) disc_bindings disc_thmss;
   782 
   783               fun is_discI_boring b =
   784                 (n = 1 andalso Binding.is_empty b) orelse Binding.eq_name (b, equal_binding);
   785 
   786               val nontriv_discI_thms =
   787                 flat (map2 (fn b => if is_discI_boring b then K [] else single) disc_bindings
   788                   discI_thms);
   789 
   790               val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
   791                 let
   792                   fun mk_goal [] = []
   793                     | mk_goal [((_, udisc), (_, udisc'))] =
   794                       [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
   795                          HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
   796 
   797                   fun prove tac goal =
   798                     Goal.prove_sorry lthy [] [] goal (K tac)
   799                     |> Thm.close_derivation;
   800 
   801                   val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
   802 
   803                   val half_goalss = map mk_goal half_pairss;
   804                   val half_thmss =
   805                     map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
   806                         fn disc_thm => [prove (mk_half_disc_exclude_tac lthy m discD disc_thm) goal])
   807                       half_goalss half_pairss (flat disc_thmss');
   808 
   809                   val other_half_goalss = map (mk_goal o map swap) half_pairss;
   810                   val other_half_thmss =
   811                     map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
   812                       other_half_goalss;
   813                 in
   814                   join_halves n half_thmss other_half_thmss ||> `transpose
   815                   |>> has_alternate_disc_def ? K []
   816                 end;
   817 
   818               val disc_exhaust_thm =
   819                 let
   820                   fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
   821                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
   822                 in
   823                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   824                     mk_disc_exhaust_tac n exhaust_thm discI_thms)
   825                   |> Thm.close_derivation
   826                 end;
   827 
   828               val (safe_collapse_thms, all_collapse_thms) =
   829                 let
   830                   fun mk_goal m udisc usel_ctr =
   831                     let
   832                       val prem = HOLogic.mk_Trueprop udisc;
   833                       val concl = mk_Trueprop_eq ((usel_ctr, u) |> m = 0 ? swap);
   834                     in
   835                       (prem aconv concl, Logic.all u (Logic.mk_implies (prem, concl)))
   836                     end;
   837                   val (trivs, goals) = map3 mk_goal ms udiscs usel_ctrs |> split_list;
   838                   val thms =
   839                     map5 (fn m => fn discD => fn sel_thms => fn triv => fn goal =>
   840                         Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   841                           mk_collapse_tac ctxt m discD sel_thms ORELSE HEADGOAL atac)
   842                         |> Thm.close_derivation
   843                         |> not triv ? perhaps (try (fn thm => refl RS thm)))
   844                       ms discD_thms sel_thmss trivs goals;
   845                 in
   846                   (map_filter (fn (true, _) => NONE | (false, thm) => SOME thm) (trivs ~~ thms),
   847                    thms)
   848                 end;
   849 
   850               val swapped_all_collapse_thms =
   851                 map2 (fn m => fn thm => if m = 0 then thm else thm RS sym) ms all_collapse_thms;
   852 
   853               val sel_exhaust_thm =
   854                 let
   855                   fun mk_prem usel_ctr = mk_imp_p [mk_Trueprop_eq (u, usel_ctr)];
   856                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem usel_ctrs));
   857                 in
   858                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   859                     mk_sel_exhaust_tac n disc_exhaust_thm swapped_all_collapse_thms)
   860                   |> Thm.close_derivation
   861                 end;
   862 
   863               val expand_thm =
   864                 let
   865                   fun mk_prems k udisc usels vdisc vsels =
   866                     (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
   867                     (if null usels then
   868                        []
   869                      else
   870                        [Logic.list_implies
   871                           (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
   872                              HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
   873                                (map2 (curry HOLogic.mk_eq) usels vsels)))]);
   874 
   875                   val goal =
   876                     Library.foldr Logic.list_implies
   877                       (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
   878                   val uncollapse_thms =
   879                     map2 (fn thm => fn [] => thm | _ => thm RS sym) all_collapse_thms uselss;
   880                 in
   881                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   882                     mk_expand_tac lthy n ms (inst_thm u disc_exhaust_thm)
   883                       (inst_thm v disc_exhaust_thm) uncollapse_thms disc_exclude_thmsss
   884                       disc_exclude_thmsss')
   885                   |> singleton (Proof_Context.export names_lthy lthy)
   886                   |> Thm.close_derivation
   887                 end;
   888 
   889               val (sel_split_thm, sel_split_asm_thm) =
   890                 let
   891                   val zss = map (K []) xss;
   892                   val goal = mk_split_goal usel_ctrs zss usel_fs;
   893                   val asm_goal = mk_split_asm_goal usel_ctrs zss usel_fs;
   894 
   895                   val thm = prove_split sel_thmss goal;
   896                   val asm_thm = prove_split_asm asm_goal thm;
   897                 in
   898                   (thm, asm_thm)
   899                 end;
   900 
   901               val case_eq_if_thm =
   902                 let
   903                   val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs usel_fs);
   904                 in
   905                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   906                     mk_case_eq_if_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)
   907                   |> singleton (Proof_Context.export names_lthy lthy)
   908                   |> Thm.close_derivation
   909                 end;
   910             in
   911               (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thmss, discI_thms,
   912                nontriv_discI_thms, disc_exclude_thms, disc_exclude_thmsss, [disc_exhaust_thm],
   913                [sel_exhaust_thm], all_collapse_thms, safe_collapse_thms, [expand_thm],
   914                [sel_split_thm], [sel_split_asm_thm], [case_eq_if_thm])
   915             end;
   916 
   917         val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
   918         val cases_type_attr = Attrib.internal (K (Induct.cases_type fcT_name));
   919 
   920         val nontriv_disc_eq_thmss =
   921           map (map (fn th => th RS @{thm eq_False[THEN iffD2]}
   922             handle THM _ => th RS @{thm eq_True[THEN iffD2]})) nontriv_disc_thmss;
   923 
   924         val anonymous_notes =
   925           [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs),
   926            (flat nontriv_disc_eq_thmss, code_nitpicksimp_attrs)]
   927           |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
   928 
   929         val notes =
   930           [(caseN, case_thms, code_nitpicksimp_simp_attrs),
   931            (case_congN, [case_cong_thm], []),
   932            (case_eq_ifN, case_eq_if_thms, []),
   933            (collapseN, safe_collapse_thms, simp_attrs),
   934            (discN, flat nontriv_disc_thmss, simp_attrs),
   935            (discIN, nontriv_discI_thms, []),
   936            (disc_excludeN, disc_exclude_thms, dest_attrs),
   937            (disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
   938            (distinctN, distinct_thms, simp_attrs @ inductsimp_attrs),
   939            (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
   940            (expandN, expand_thms, []),
   941            (injectN, inject_thms, iff_attrs @ inductsimp_attrs),
   942            (nchotomyN, [nchotomy_thm], []),
   943            (selN, all_sel_thms, code_nitpicksimp_simp_attrs),
   944            (sel_exhaustN, sel_exhaust_thms, [exhaust_case_names_attr]),
   945            (sel_splitN, sel_split_thms, []),
   946            (sel_split_asmN, sel_split_asm_thms, []),
   947            (splitN, [split_thm], []),
   948            (split_asmN, [split_asm_thm], []),
   949            (splitsN, [split_thm, split_asm_thm], []),
   950            (weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
   951           |> filter_out (null o #2)
   952           |> map (fn (thmN, thms, attrs) =>
   953             ((qualify true (Binding.name thmN), attrs), [(thms, [])]));
   954 
   955         val ctr_sugar =
   956           {ctrs = ctrs, casex = casex, discs = discs, selss = selss, exhaust = exhaust_thm,
   957            nchotomy = nchotomy_thm, injects = inject_thms, distincts = distinct_thms,
   958            case_thms = case_thms, case_cong = case_cong_thm, weak_case_cong = weak_case_cong_thm,
   959            split = split_thm, split_asm = split_asm_thm, disc_thmss = disc_thmss,
   960            discIs = discI_thms, sel_thmss = sel_thmss, disc_excludesss = disc_exclude_thmsss,
   961            disc_exhausts = disc_exhaust_thms, sel_exhausts = sel_exhaust_thms,
   962            collapses = all_collapse_thms, expands = expand_thms, sel_splits = sel_split_thms,
   963            sel_split_asms = sel_split_asm_thms, case_eq_ifs = case_eq_if_thms};
   964       in
   965         (ctr_sugar,
   966          lthy
   967          |> Spec_Rules.add Spec_Rules.Equational ([casex], case_thms)
   968          |> fold (Spec_Rules.add Spec_Rules.Equational)
   969            (AList.group (eq_list (op aconv)) (map (`(single o lhs_head_of)) all_sel_thms))
   970          |> fold (Spec_Rules.add Spec_Rules.Equational)
   971            (filter_out (null o snd) (map single discs ~~ nontriv_disc_eq_thmss))
   972          |> Local_Theory.declaration {syntax = false, pervasive = true}
   973               (fn phi => Case_Translation.register
   974                  (Morphism.term phi casex) (map (Morphism.term phi) ctrs))
   975          |> Local_Theory.background_theory (fold (fold Code.del_eqn) [disc_defs, sel_defs])
   976          |> not no_code ?
   977             Local_Theory.declaration {syntax = false, pervasive = false}
   978               (fn phi => Context.mapping
   979                 (add_ctr_code fcT_name (map (Morphism.typ phi) As)
   980                   (map (dest_Const o Morphism.term phi) ctrs) (Morphism.fact phi inject_thms)
   981                   (Morphism.fact phi distinct_thms) (Morphism.fact phi case_thms))
   982                 I)
   983          |> Local_Theory.notes (anonymous_notes @ notes) |> snd
   984          |> register_ctr_sugar fcT_name ctr_sugar)
   985       end;
   986   in
   987     (goalss, after_qed, lthy')
   988   end;
   989 
   990 fun free_constructors tacss = (fn (goalss, after_qed, lthy) =>
   991   map2 (map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])) goalss tacss
   992   |> (fn thms => after_qed thms lthy)) oo prepare_free_constructors (K I);
   993 
   994 val free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
   995   Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
   996   prepare_free_constructors Syntax.read_term;
   997 
   998 val parse_bound_term = parse_binding --| @{keyword ":"} -- Parse.term;
   999 
  1000 val parse_ctr_options =
  1001   Scan.optional (@{keyword "("} |-- Parse.list1
  1002         (Parse.reserved "no_discs_sels" >> K 0 || Parse.reserved "no_code" >> K 1) --|
  1003       @{keyword ")"}
  1004       >> (fn js => (member (op =) js 0, member (op =) js 1)))
  1005     (false, false);
  1006 
  1007 val parse_defaults =
  1008   @{keyword "("} |-- Parse.reserved "defaults" |-- Scan.repeat parse_bound_term --| @{keyword ")"};
  1009 
  1010 fun parse_ctr_spec parse_ctr parse_arg =
  1011   parse_opt_binding_colon -- parse_ctr -- Scan.repeat parse_arg --
  1012   Scan.optional parse_defaults [];
  1013 
  1014 val parse_ctr_specs = Parse.enum1 "|" (parse_ctr_spec Parse.term parse_binding);
  1015 
  1016 val _ =
  1017   Outer_Syntax.local_theory_to_proof @{command_spec "free_constructors"}
  1018     "register an existing freely generated type's constructors"
  1019     (parse_ctr_options -- parse_binding --| @{keyword "for"} -- parse_ctr_specs
  1020      >> free_constructors_cmd);
  1021 
  1022 val _ = Context.>> (Context.map_theory Ctr_Sugar_Interpretation.init);
  1023 
  1024 end;