src/HOL/Tools/Ctr_Sugar/ctr_sugar.ML
author blanchet
Wed May 21 14:09:42 2014 +0200 (2014-05-21)
changeset 57038 2114f3224b2c
parent 56858 0c3d0bc98abe
child 57090 0224caba67ca
permissions -rw-r--r--
move exhaust first, for technical reasons
     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_defs: thm list,
    25      disc_thmss: thm list list,
    26      discIs: thm list,
    27      sel_defs: thm list,
    28      sel_thmss: thm list list,
    29      disc_excludesss: thm list list list,
    30      disc_exhausts: thm list,
    31      sel_exhausts: thm list,
    32      collapses: thm list,
    33      expands: thm list,
    34      sel_splits: thm list,
    35      sel_split_asms: thm list,
    36      case_eq_ifs: thm list};
    37 
    38   val morph_ctr_sugar: morphism -> ctr_sugar -> ctr_sugar
    39   val transfer_ctr_sugar: Proof.context -> ctr_sugar -> ctr_sugar
    40   val ctr_sugar_of: Proof.context -> string -> ctr_sugar option
    41   val ctr_sugars_of: Proof.context -> ctr_sugar list
    42   val ctr_sugar_of_case: Proof.context -> string -> ctr_sugar option
    43   val ctr_sugar_interpretation: (ctr_sugar -> theory -> theory) -> theory -> theory
    44   val register_ctr_sugar: string -> ctr_sugar -> local_theory -> local_theory
    45   val default_register_ctr_sugar_global: string -> ctr_sugar -> theory -> theory
    46 
    47   val mk_half_pairss: 'a list * 'a list -> ('a * 'a) list list
    48   val join_halves: int -> 'a list list -> 'a list list -> 'a list * 'a list list list
    49 
    50   val mk_ctr: typ list -> term -> term
    51   val mk_case: typ list -> typ -> term -> term
    52   val mk_disc_or_sel: typ list -> term -> term
    53   val name_of_ctr: term -> string
    54   val name_of_disc: term -> string
    55   val dest_ctr: Proof.context -> string -> term -> term * term list
    56   val dest_case: Proof.context -> string -> typ list -> term ->
    57     (ctr_sugar * term list * term list) option
    58 
    59   type ('c, 'a, 'v) ctr_spec = ((binding * 'c) * 'a list) * (binding * 'v) list
    60 
    61   val disc_of_ctr_spec: ('c, 'a, 'v) ctr_spec -> binding
    62   val ctr_of_ctr_spec: ('c, 'a, 'v) ctr_spec -> 'c
    63   val args_of_ctr_spec: ('c, 'a, 'v) ctr_spec -> 'a list
    64   val sel_defaults_of_ctr_spec: ('c, 'a, 'v) ctr_spec -> (binding * 'v) list
    65 
    66   val free_constructors: ({prems: thm list, context: Proof.context} -> tactic) list list ->
    67     ((bool * bool) * binding) * (term, binding, term) ctr_spec list -> local_theory ->
    68     ctr_sugar * local_theory
    69   val parse_bound_term: (binding * string) parser
    70   val parse_ctr_options: (bool * bool) parser
    71   val parse_ctr_spec: 'c parser -> 'a parser -> ('c, 'a, string) ctr_spec parser
    72 end;
    73 
    74 structure Ctr_Sugar : CTR_SUGAR =
    75 struct
    76 
    77 open Ctr_Sugar_Util
    78 open Ctr_Sugar_Tactics
    79 open Ctr_Sugar_Code
    80 
    81 type ctr_sugar =
    82   {ctrs: term list,
    83    casex: term,
    84    discs: term list,
    85    selss: term list list,
    86    exhaust: thm,
    87    nchotomy: thm,
    88    injects: thm list,
    89    distincts: thm list,
    90    case_thms: thm list,
    91    case_cong: thm,
    92    weak_case_cong: thm,
    93    split: thm,
    94    split_asm: thm,
    95    disc_defs: thm list,
    96    disc_thmss: thm list list,
    97    discIs: thm list,
    98    sel_defs: thm list,
    99    sel_thmss: thm list list,
   100    disc_excludesss: thm list list list,
   101    disc_exhausts: thm list,
   102    sel_exhausts: thm list,
   103    collapses: thm list,
   104    expands: thm list,
   105    sel_splits: thm list,
   106    sel_split_asms: thm list,
   107    case_eq_ifs: thm list};
   108 
   109 fun morph_ctr_sugar phi {ctrs, casex, discs, selss, exhaust, nchotomy, injects, distincts,
   110     case_thms, case_cong, weak_case_cong, split, split_asm, disc_defs, disc_thmss, discIs, sel_defs,
   111     sel_thmss, disc_excludesss, disc_exhausts, sel_exhausts, collapses, expands, sel_splits,
   112     sel_split_asms, case_eq_ifs} =
   113   {ctrs = map (Morphism.term phi) ctrs,
   114    casex = Morphism.term phi casex,
   115    discs = map (Morphism.term phi) discs,
   116    selss = map (map (Morphism.term phi)) selss,
   117    exhaust = Morphism.thm phi exhaust,
   118    nchotomy = Morphism.thm phi nchotomy,
   119    injects = map (Morphism.thm phi) injects,
   120    distincts = map (Morphism.thm phi) distincts,
   121    case_thms = map (Morphism.thm phi) case_thms,
   122    case_cong = Morphism.thm phi case_cong,
   123    weak_case_cong = Morphism.thm phi weak_case_cong,
   124    split = Morphism.thm phi split,
   125    split_asm = Morphism.thm phi split_asm,
   126    disc_defs = map (Morphism.thm phi) disc_defs,
   127    disc_thmss = map (map (Morphism.thm phi)) disc_thmss,
   128    discIs = map (Morphism.thm phi) discIs,
   129    sel_defs = map (Morphism.thm phi) sel_defs,
   130    sel_thmss = map (map (Morphism.thm phi)) sel_thmss,
   131    disc_excludesss = map (map (map (Morphism.thm phi))) disc_excludesss,
   132    disc_exhausts = map (Morphism.thm phi) disc_exhausts,
   133    sel_exhausts = map (Morphism.thm phi) sel_exhausts,
   134    collapses = map (Morphism.thm phi) collapses,
   135    expands = map (Morphism.thm phi) expands,
   136    sel_splits = map (Morphism.thm phi) sel_splits,
   137    sel_split_asms = map (Morphism.thm phi) sel_split_asms,
   138    case_eq_ifs = map (Morphism.thm phi) case_eq_ifs};
   139 
   140 val transfer_ctr_sugar =
   141   morph_ctr_sugar o Morphism.transfer_morphism o Proof_Context.theory_of;
   142 
   143 structure Data = Generic_Data
   144 (
   145   type T = ctr_sugar Symtab.table;
   146   val empty = Symtab.empty;
   147   val extend = I;
   148   fun merge data : T = Symtab.merge (K true) data;
   149 );
   150 
   151 fun ctr_sugar_of ctxt =
   152   Symtab.lookup (Data.get (Context.Proof ctxt))
   153   #> Option.map (transfer_ctr_sugar ctxt);
   154 
   155 fun ctr_sugars_of ctxt =
   156   Symtab.fold (cons o transfer_ctr_sugar ctxt o snd) (Data.get (Context.Proof ctxt)) [];
   157 
   158 fun ctr_sugar_of_case ctxt s =
   159   find_first (fn {casex = Const (s', _), ...} => s' = s | _ => false) (ctr_sugars_of ctxt);
   160 
   161 structure Ctr_Sugar_Interpretation = Interpretation
   162 (
   163   type T = ctr_sugar;
   164   val eq: T * T -> bool = op = o pairself #ctrs;
   165 );
   166 
   167 fun with_repaired_path f (ctr_sugar as {ctrs = ctr1 :: _, ...} : ctr_sugar) thy =
   168   thy
   169   |> Sign.root_path
   170   |> Sign.add_path (Long_Name.qualifier (fst (dest_Type (body_type (fastype_of ctr1)))))
   171   |> (fn thy => f (morph_ctr_sugar (Morphism.transfer_morphism thy) ctr_sugar) thy)
   172   |> Sign.restore_naming thy;
   173 
   174 fun ctr_sugar_interpretation f = Ctr_Sugar_Interpretation.interpretation (with_repaired_path f);
   175 
   176 fun register_ctr_sugar key ctr_sugar =
   177   Local_Theory.declaration {syntax = false, pervasive = true}
   178     (fn phi => Data.map (Symtab.update (key, morph_ctr_sugar phi ctr_sugar)))
   179   #> Local_Theory.background_theory (Ctr_Sugar_Interpretation.data ctr_sugar);
   180 
   181 fun default_register_ctr_sugar_global key ctr_sugar thy =
   182   let val tab = Data.get (Context.Theory thy) in
   183     if Symtab.defined tab key then
   184       thy
   185     else
   186       thy
   187       |> Context.theory_map (Data.put (Symtab.update_new (key, ctr_sugar) tab))
   188       |> Ctr_Sugar_Interpretation.data ctr_sugar
   189   end;
   190 
   191 val isN = "is_";
   192 val unN = "un_";
   193 fun mk_unN 1 1 suf = unN ^ suf
   194   | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
   195 
   196 val caseN = "case";
   197 val case_congN = "case_cong";
   198 val case_eq_ifN = "case_eq_if";
   199 val collapseN = "collapse";
   200 val disc_excludeN = "disc_exclude";
   201 val disc_exhaustN = "disc_exhaust";
   202 val discN = "disc";
   203 val discIN = "discI";
   204 val distinctN = "distinct";
   205 val exhaustN = "exhaust";
   206 val expandN = "expand";
   207 val injectN = "inject";
   208 val nchotomyN = "nchotomy";
   209 val selN = "sel";
   210 val sel_exhaustN = "sel_exhaust";
   211 val sel_splitN = "sel_split";
   212 val sel_split_asmN = "sel_split_asm";
   213 val splitN = "split";
   214 val splitsN = "splits";
   215 val split_asmN = "split_asm";
   216 val weak_case_cong_thmsN = "weak_case_cong";
   217 
   218 val cong_attrs = @{attributes [cong]};
   219 val dest_attrs = @{attributes [dest]};
   220 val safe_elim_attrs = @{attributes [elim!]};
   221 val iff_attrs = @{attributes [iff]};
   222 val inductsimp_attrs = @{attributes [induct_simp]};
   223 val nitpicksimp_attrs = @{attributes [nitpick_simp]};
   224 val simp_attrs = @{attributes [simp]};
   225 val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
   226 val code_nitpicksimp_simp_attrs = code_nitpicksimp_attrs @ simp_attrs;
   227 
   228 fun unflat_lookup eq xs ys = map (fn xs' => permute_like_unique eq xs xs' ys);
   229 
   230 fun mk_half_pairss' _ ([], []) = []
   231   | mk_half_pairss' indent (x :: xs, _ :: ys) =
   232     indent @ fold_rev (cons o single o pair x) ys (mk_half_pairss' ([] :: indent) (xs, ys));
   233 
   234 fun mk_half_pairss p = mk_half_pairss' [[]] p;
   235 
   236 fun join_halves n half_xss other_half_xss =
   237   (splice (flat half_xss) (flat other_half_xss),
   238    map2 (map2 append) (Library.chop_groups n half_xss)
   239      (transpose (Library.chop_groups n other_half_xss)));
   240 
   241 fun mk_undefined T = Const (@{const_name undefined}, T);
   242 
   243 fun mk_ctr Ts t =
   244   let val Type (_, Ts0) = body_type (fastype_of t) in
   245     subst_nonatomic_types (Ts0 ~~ Ts) t
   246   end;
   247 
   248 fun mk_case Ts T t =
   249   let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
   250     subst_nonatomic_types ((body, T) :: (Ts0 ~~ Ts)) t
   251   end;
   252 
   253 fun mk_disc_or_sel Ts t =
   254   subst_nonatomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
   255 
   256 fun name_of_const what t =
   257   (case head_of t of
   258     Const (s, _) => s
   259   | Free (s, _) => s
   260   | _ => error ("Cannot extract name of " ^ what));
   261 
   262 val name_of_ctr = name_of_const "constructor";
   263 
   264 val notN = "not_";
   265 val eqN = "eq_";
   266 val neqN = "neq_";
   267 
   268 fun name_of_disc t =
   269   (case head_of t of
   270     Abs (_, _, @{const Not} $ (t' $ Bound 0)) =>
   271     Long_Name.map_base_name (prefix notN) (name_of_disc t')
   272   | Abs (_, _, Const (@{const_name HOL.eq}, _) $ Bound 0 $ t') =>
   273     Long_Name.map_base_name (prefix eqN) (name_of_disc t')
   274   | Abs (_, _, @{const Not} $ (Const (@{const_name HOL.eq}, _) $ Bound 0 $ t')) =>
   275     Long_Name.map_base_name (prefix neqN) (name_of_disc t')
   276   | t' => name_of_const "destructor" t');
   277 
   278 val base_name_of_ctr = Long_Name.base_name o name_of_ctr;
   279 
   280 fun dest_ctr ctxt s t =
   281   let val (f, args) = Term.strip_comb t in
   282     (case ctr_sugar_of ctxt s of
   283       SOME {ctrs, ...} =>
   284       (case find_first (can (fo_match ctxt f)) ctrs of
   285         SOME f' => (f', args)
   286       | NONE => raise Fail "dest_ctr")
   287     | NONE => raise Fail "dest_ctr")
   288   end;
   289 
   290 fun dest_case ctxt s Ts t =
   291   (case Term.strip_comb t of
   292     (Const (c, _), args as _ :: _) =>
   293     (case ctr_sugar_of ctxt s of
   294       SOME (ctr_sugar as {casex = Const (case_name, _), discs = discs0, selss = selss0, ...}) =>
   295       if case_name = c then
   296         let val n = length discs0 in
   297           if n < length args then
   298             let
   299               val (branches, obj :: leftovers) = chop n args;
   300               val discs = map (mk_disc_or_sel Ts) discs0;
   301               val selss = map (map (mk_disc_or_sel Ts)) selss0;
   302               val conds = map (rapp obj) discs;
   303               val branch_argss = map (fn sels => map (rapp obj) sels @ leftovers) selss;
   304               val branches' = map2 (curry Term.betapplys) branches branch_argss;
   305             in
   306               SOME (ctr_sugar, conds, branches')
   307             end
   308           else
   309             NONE
   310         end
   311       else
   312         NONE
   313     | _ => NONE)
   314   | _ => NONE);
   315 
   316 fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
   317 
   318 type ('c, 'a, 'v) ctr_spec = ((binding * 'c) * 'a list) * (binding * 'v) list;
   319 
   320 fun disc_of_ctr_spec (((disc, _), _), _) = disc;
   321 fun ctr_of_ctr_spec (((_, ctr), _), _) = ctr;
   322 fun args_of_ctr_spec ((_, args), _) = args;
   323 fun sel_defaults_of_ctr_spec (_, ds) = ds;
   324 
   325 fun prepare_free_constructors prep_term (((no_discs_sels, no_code), raw_case_binding), ctr_specs)
   326     no_defs_lthy =
   327   let
   328     (* TODO: sanity checks on arguments *)
   329 
   330     val raw_ctrs = map ctr_of_ctr_spec ctr_specs;
   331     val raw_disc_bindings = map disc_of_ctr_spec ctr_specs;
   332     val raw_sel_bindingss = map args_of_ctr_spec ctr_specs;
   333     val raw_sel_defaultss = map sel_defaults_of_ctr_spec ctr_specs;
   334 
   335     val n = length raw_ctrs;
   336     val ks = 1 upto n;
   337 
   338     val _ = if n > 0 then () else error "No constructors specified";
   339 
   340     val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
   341     val sel_defaultss = map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss;
   342 
   343     val Type (fcT_name, As0) = body_type (fastype_of (hd ctrs0));
   344     val fc_b_name = Long_Name.base_name fcT_name;
   345     val fc_b = Binding.name fc_b_name;
   346 
   347     fun qualify mandatory = Binding.qualify mandatory fc_b_name;
   348 
   349     fun dest_TFree_or_TVar (TFree sS) = sS
   350       | dest_TFree_or_TVar (TVar ((s, _), S)) = (s, S)
   351       | dest_TFree_or_TVar _ = error "Invalid type argument";
   352 
   353     val (unsorted_As, B) =
   354       no_defs_lthy
   355       |> variant_tfrees (map (fst o dest_TFree_or_TVar) As0)
   356       ||> the_single o fst o mk_TFrees 1;
   357 
   358     val As = map2 (resort_tfree o snd o dest_TFree_or_TVar) As0 unsorted_As;
   359 
   360     val fcT = Type (fcT_name, As);
   361     val ctrs = map (mk_ctr As) ctrs0;
   362     val ctr_Tss = map (binder_types o fastype_of) ctrs;
   363 
   364     val ms = map length ctr_Tss;
   365 
   366     fun can_definitely_rely_on_disc k = not (Binding.is_empty (nth raw_disc_bindings (k - 1)));
   367     fun can_rely_on_disc k =
   368       can_definitely_rely_on_disc k orelse (k = 1 andalso not (can_definitely_rely_on_disc 2));
   369     fun should_omit_disc_binding k = n = 1 orelse (n = 2 andalso can_rely_on_disc (3 - k));
   370 
   371     fun is_disc_binding_valid b =
   372       not (Binding.is_empty b orelse Binding.eq_name (b, equal_binding));
   373 
   374     val standard_disc_binding = Binding.name o prefix isN o base_name_of_ctr;
   375 
   376     val disc_bindings =
   377       raw_disc_bindings
   378       |> map4 (fn k => fn m => fn ctr => fn disc =>
   379         qualify false
   380           (if Binding.is_empty disc then
   381              if should_omit_disc_binding k then disc else standard_disc_binding ctr
   382            else if Binding.eq_name (disc, equal_binding) then
   383              if m = 0 then disc
   384              else error "Cannot use \"=\" syntax for discriminating nonnullary constructor"
   385            else if Binding.eq_name (disc, standard_binding) then
   386              standard_disc_binding ctr
   387            else
   388              disc)) ks ms ctrs0;
   389 
   390     fun standard_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
   391 
   392     val sel_bindingss =
   393       map3 (fn ctr => fn m => map2 (fn l => fn sel =>
   394         qualify false
   395           (if Binding.is_empty sel orelse Binding.eq_name (sel, standard_binding) then
   396             standard_sel_binding m l ctr
   397           else
   398             sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms raw_sel_bindingss;
   399 
   400     val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
   401 
   402     val (((((((([exh_y], (xss, xss')), yss), fs), gs), [u', v']), [w]), (p, p')), names_lthy) =
   403       no_defs_lthy
   404       |> mk_Frees "y" [fcT] (* for compatibility with "datatype_realizer.ML" *)
   405       ||>> mk_Freess' "x" ctr_Tss
   406       ||>> mk_Freess "y" ctr_Tss
   407       ||>> mk_Frees "f" case_Ts
   408       ||>> mk_Frees "g" case_Ts
   409       ||>> (apfst (map (rpair fcT)) oo Variable.variant_fixes) [fc_b_name, fc_b_name ^ "'"]
   410       ||>> mk_Frees "z" [B]
   411       ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
   412 
   413     val u = Free u';
   414     val v = Free v';
   415     val q = Free (fst p', mk_pred1T B);
   416 
   417     val xctrs = map2 (curry Term.list_comb) ctrs xss;
   418     val yctrs = map2 (curry Term.list_comb) ctrs yss;
   419 
   420     val xfs = map2 (curry Term.list_comb) fs xss;
   421     val xgs = map2 (curry Term.list_comb) gs xss;
   422 
   423     (* TODO: Eta-expension is for compatibility with the old datatype package (but it also provides
   424        nicer names). Consider removing. *)
   425     val eta_fs = map2 eta_expand_arg xss xfs;
   426     val eta_gs = map2 eta_expand_arg xss xgs;
   427 
   428     val case_binding =
   429       qualify false
   430         (if Binding.is_empty raw_case_binding orelse
   431             Binding.eq_name (raw_case_binding, standard_binding) then
   432            Binding.prefix_name (caseN ^ "_") fc_b
   433          else
   434            raw_case_binding);
   435 
   436     fun mk_case_disj xctr xf xs =
   437       list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr), HOLogic.mk_eq (w, xf)));
   438 
   439     val case_rhs = fold_rev (fold_rev Term.lambda) [fs, [u]]
   440       (Const (@{const_name The}, (B --> HOLogic.boolT) --> B) $
   441          Term.lambda w (Library.foldr1 HOLogic.mk_disj (map3 mk_case_disj xctrs xfs xss)));
   442 
   443     val ((raw_case, (_, raw_case_def)), (lthy', lthy)) = no_defs_lthy
   444       |> Local_Theory.define ((case_binding, NoSyn),
   445         ((Binding.conceal (Thm.def_binding case_binding), []), case_rhs))
   446       ||> `Local_Theory.restore;
   447 
   448     val phi = Proof_Context.export_morphism lthy lthy';
   449 
   450     val case_def = Morphism.thm phi raw_case_def;
   451 
   452     val case0 = Morphism.term phi raw_case;
   453     val casex = mk_case As B case0;
   454 
   455     val fcase = Term.list_comb (casex, fs);
   456 
   457     val ufcase = fcase $ u;
   458     val vfcase = fcase $ v;
   459 
   460     val eta_fcase = Term.list_comb (casex, eta_fs);
   461     val eta_gcase = Term.list_comb (casex, eta_gs);
   462 
   463     val eta_ufcase = eta_fcase $ u;
   464     val eta_vgcase = eta_gcase $ v;
   465 
   466     fun mk_uu_eq () = HOLogic.mk_eq (u, u);
   467 
   468     val uv_eq = mk_Trueprop_eq (u, v);
   469 
   470     val exist_xs_u_eq_ctrs =
   471       map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
   472 
   473     val unique_disc_no_def = TrueI; (*arbitrary marker*)
   474     val alternate_disc_no_def = FalseE; (*arbitrary marker*)
   475 
   476     fun alternate_disc_lhs get_udisc k =
   477       HOLogic.mk_not
   478         (let val b = nth disc_bindings (k - 1) in
   479            if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
   480          end);
   481 
   482     val (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy') =
   483       if no_discs_sels then
   484         (true, [], [], [], [], [], lthy')
   485       else
   486         let
   487           fun disc_free b = Free (Binding.name_of b, mk_pred1T fcT);
   488 
   489           fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
   490 
   491           fun alternate_disc k =
   492             Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
   493 
   494           fun mk_sel_case_args b proto_sels T =
   495             map2 (fn Ts => fn k =>
   496               (case AList.lookup (op =) proto_sels k of
   497                 NONE =>
   498                 (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
   499                   NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
   500                 | SOME t => t |> Type.constraint (Ts ---> T) |> Syntax.check_term lthy)
   501               | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
   502 
   503           fun sel_spec b proto_sels =
   504             let
   505               val _ =
   506                 (case duplicates (op =) (map fst proto_sels) of
   507                    k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
   508                      " for constructor " ^
   509                      quote (Syntax.string_of_term lthy (nth ctrs (k - 1))))
   510                  | [] => ())
   511               val T =
   512                 (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
   513                   [T] => T
   514                 | T :: T' :: _ => error ("Inconsistent range type for selector " ^
   515                     quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ lthy T) ^ " vs. "
   516                     ^ quote (Syntax.string_of_typ lthy T')));
   517             in
   518               mk_Trueprop_eq (Free (Binding.name_of b, fcT --> T) $ u,
   519                 Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
   520             end;
   521 
   522           val sel_bindings = flat sel_bindingss;
   523           val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
   524           val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
   525 
   526           val sel_binding_index =
   527             if all_sels_distinct then 1 upto length sel_bindings
   528             else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
   529 
   530           val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
   531           val sel_infos =
   532             AList.group (op =) (sel_binding_index ~~ proto_sels)
   533             |> sort (int_ord o pairself fst)
   534             |> map snd |> curry (op ~~) uniq_sel_bindings;
   535           val sel_bindings = map fst sel_infos;
   536 
   537           fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
   538 
   539           val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
   540             lthy
   541             |> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
   542                 if Binding.is_empty b then
   543                   if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
   544                   else pair (alternate_disc k, alternate_disc_no_def)
   545                 else if Binding.eq_name (b, equal_binding) then
   546                   pair (Term.lambda u exist_xs_u_eq_ctr, refl)
   547                 else
   548                   Specification.definition (SOME (b, NONE, NoSyn),
   549                     ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
   550               ks exist_xs_u_eq_ctrs disc_bindings
   551             ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
   552               Specification.definition (SOME (b, NONE, NoSyn),
   553                 ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
   554             ||> `Local_Theory.restore;
   555 
   556           val phi = Proof_Context.export_morphism lthy lthy';
   557 
   558           val disc_defs = map (Morphism.thm phi) raw_disc_defs;
   559           val sel_defs = map (Morphism.thm phi) raw_sel_defs;
   560           val sel_defss = unflat_selss sel_defs;
   561 
   562           val discs0 = map (Morphism.term phi) raw_discs;
   563           val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
   564 
   565           val discs = map (mk_disc_or_sel As) discs0;
   566           val selss = map (map (mk_disc_or_sel As)) selss0;
   567         in
   568           (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy')
   569         end;
   570 
   571     fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
   572 
   573     val exhaust_goal =
   574       let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (exh_y, xctr)]) in
   575         fold_rev Logic.all [p, exh_y] (mk_imp_p (map2 mk_prem xctrs xss))
   576       end;
   577 
   578     val inject_goalss =
   579       let
   580         fun mk_goal _ _ [] [] = []
   581           | mk_goal xctr yctr xs ys =
   582             [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
   583               Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
   584       in
   585         map4 mk_goal xctrs yctrs xss yss
   586       end;
   587 
   588     val half_distinct_goalss =
   589       let
   590         fun mk_goal ((xs, xc), (xs', xc')) =
   591           fold_rev Logic.all (xs @ xs')
   592             (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
   593       in
   594         map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
   595       end;
   596 
   597     val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss;
   598 
   599     fun after_qed thmss lthy =
   600       let
   601         val ([exhaust_thm0], (inject_thmss, half_distinct_thmss)) = (hd thmss, chop n (tl thmss));
   602         (* for "datatype_realizer.ML": *)
   603         val exhaust_thm =
   604           Thm.name_derivation (fcT_name ^ Long_Name.separator ^ exhaustN) exhaust_thm0;
   605 
   606         val inject_thms = flat inject_thmss;
   607 
   608         val rho_As = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
   609 
   610         fun inst_thm t thm =
   611           Drule.instantiate' [] [SOME (certify lthy t)]
   612             (Thm.instantiate (rho_As, []) (Drule.zero_var_indexes thm));
   613 
   614         val uexhaust_thm = inst_thm u exhaust_thm;
   615 
   616         val exhaust_cases = map base_name_of_ctr ctrs;
   617 
   618         val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
   619 
   620         val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
   621           join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
   622 
   623         val nchotomy_thm =
   624           let
   625             val goal =
   626               HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
   627                 Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
   628           in
   629             Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
   630             |> Thm.close_derivation
   631           end;
   632 
   633         val case_thms =
   634           let
   635             val goals =
   636               map3 (fn xctr => fn xf => fn xs =>
   637                 fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xctrs xfs xss;
   638           in
   639             map4 (fn k => fn goal => fn injects => fn distinctss =>
   640                 Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   641                   mk_case_tac ctxt n k case_def injects distinctss)
   642                 |> Thm.close_derivation)
   643               ks goals inject_thmss distinct_thmsss
   644           end;
   645 
   646         val (case_cong_thm, weak_case_cong_thm) =
   647           let
   648             fun mk_prem xctr xs xf xg =
   649               fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
   650                 mk_Trueprop_eq (xf, xg)));
   651 
   652             val goal =
   653               Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
   654                  mk_Trueprop_eq (eta_ufcase, eta_vgcase));
   655             val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
   656           in
   657             (Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
   658              Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
   659             |> pairself (singleton (Proof_Context.export names_lthy lthy) #>
   660               Thm.close_derivation)
   661           end;
   662 
   663         val split_lhs = q $ ufcase;
   664 
   665         fun mk_split_conjunct xctr xs f_xs =
   666           list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
   667         fun mk_split_disjunct xctr xs f_xs =
   668           list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
   669             HOLogic.mk_not (q $ f_xs)));
   670 
   671         fun mk_split_goal xctrs xss xfs =
   672           mk_Trueprop_eq (split_lhs, Library.foldr1 HOLogic.mk_conj
   673             (map3 mk_split_conjunct xctrs xss xfs));
   674         fun mk_split_asm_goal xctrs xss xfs =
   675           mk_Trueprop_eq (split_lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
   676             (map3 mk_split_disjunct xctrs xss xfs)));
   677 
   678         fun prove_split selss goal =
   679           Goal.prove_sorry lthy [] [] goal (fn _ =>
   680             mk_split_tac lthy uexhaust_thm case_thms selss inject_thmss distinct_thmsss)
   681           |> singleton (Proof_Context.export names_lthy lthy)
   682           |> Thm.close_derivation;
   683 
   684         fun prove_split_asm asm_goal split_thm =
   685           Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
   686             mk_split_asm_tac ctxt split_thm)
   687           |> singleton (Proof_Context.export names_lthy lthy)
   688           |> Thm.close_derivation;
   689 
   690         val (split_thm, split_asm_thm) =
   691           let
   692             val goal = mk_split_goal xctrs xss xfs;
   693             val asm_goal = mk_split_asm_goal xctrs xss xfs;
   694 
   695             val thm = prove_split (replicate n []) goal;
   696             val asm_thm = prove_split_asm asm_goal thm;
   697           in
   698             (thm, asm_thm)
   699           end;
   700 
   701         val (sel_defs, all_sel_thms, sel_thmss, disc_defs, disc_thmss, nontriv_disc_thmss,
   702              discI_thms, nontriv_discI_thms, disc_exclude_thms, disc_exclude_thmsss,
   703              disc_exhaust_thms, sel_exhaust_thms, all_collapse_thms, safe_collapse_thms,
   704              expand_thms, sel_split_thms, sel_split_asm_thms, case_eq_if_thms) =
   705           if no_discs_sels then
   706             ([], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [])
   707           else
   708             let
   709               val udiscs = map (rapp u) discs;
   710               val uselss = map (map (rapp u)) selss;
   711               val usel_ctrs = map2 (curry Term.list_comb) ctrs uselss;
   712               val usel_fs = map2 (curry Term.list_comb) fs uselss;
   713 
   714               val vdiscs = map (rapp v) discs;
   715               val vselss = map (map (rapp v)) selss;
   716 
   717               fun make_sel_thm xs' case_thm sel_def =
   718                 zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
   719                     (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
   720 
   721               val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
   722 
   723               fun has_undefined_rhs thm =
   724                 (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
   725                   Const (@{const_name undefined}, _) => true
   726                 | _ => false);
   727 
   728               val all_sel_thms =
   729                 (if all_sels_distinct andalso forall null sel_defaultss then
   730                    flat sel_thmss
   731                  else
   732                    map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
   733                      (xss' ~~ case_thms))
   734                 |> filter_out has_undefined_rhs;
   735 
   736               fun mk_unique_disc_def () =
   737                 let
   738                   val m = the_single ms;
   739                   val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
   740                 in
   741                   Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
   742                   |> singleton (Proof_Context.export names_lthy lthy)
   743                   |> Thm.close_derivation
   744                 end;
   745 
   746               fun mk_alternate_disc_def k =
   747                 let
   748                   val goal =
   749                     mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
   750                       nth exist_xs_u_eq_ctrs (k - 1));
   751                 in
   752                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   753                     mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
   754                       (nth distinct_thms (2 - k)) uexhaust_thm)
   755                   |> singleton (Proof_Context.export names_lthy lthy)
   756                   |> Thm.close_derivation
   757                 end;
   758 
   759               val has_alternate_disc_def =
   760                 exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
   761 
   762               val disc_defs' =
   763                 map2 (fn k => fn def =>
   764                   if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
   765                   else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
   766                   else def) ks disc_defs;
   767 
   768               val discD_thms = map (fn def => def RS iffD1) disc_defs';
   769               val discI_thms =
   770                 map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
   771                   disc_defs';
   772               val not_discI_thms =
   773                 map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
   774                     (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
   775                   ms disc_defs';
   776 
   777               val (disc_thmss', disc_thmss) =
   778                 let
   779                   fun mk_thm discI _ [] = refl RS discI
   780                     | mk_thm _ not_discI [distinct] = distinct RS not_discI;
   781                   fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
   782                 in
   783                   map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
   784                 end;
   785 
   786               val nontriv_disc_thmss =
   787                 map2 (fn b => if is_disc_binding_valid b then I else K []) disc_bindings disc_thmss;
   788 
   789               fun is_discI_boring b =
   790                 (n = 1 andalso Binding.is_empty b) orelse Binding.eq_name (b, equal_binding);
   791 
   792               val nontriv_discI_thms =
   793                 flat (map2 (fn b => if is_discI_boring b then K [] else single) disc_bindings
   794                   discI_thms);
   795 
   796               val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
   797                 let
   798                   fun mk_goal [] = []
   799                     | mk_goal [((_, udisc), (_, udisc'))] =
   800                       [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
   801                          HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
   802 
   803                   fun prove tac goal =
   804                     Goal.prove_sorry lthy [] [] goal (K tac)
   805                     |> Thm.close_derivation;
   806 
   807                   val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
   808 
   809                   val half_goalss = map mk_goal half_pairss;
   810                   val half_thmss =
   811                     map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
   812                         fn disc_thm => [prove (mk_half_disc_exclude_tac lthy m discD disc_thm) goal])
   813                       half_goalss half_pairss (flat disc_thmss');
   814 
   815                   val other_half_goalss = map (mk_goal o map swap) half_pairss;
   816                   val other_half_thmss =
   817                     map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
   818                       other_half_goalss;
   819                 in
   820                   join_halves n half_thmss other_half_thmss ||> `transpose
   821                   |>> has_alternate_disc_def ? K []
   822                 end;
   823 
   824               val disc_exhaust_thm =
   825                 let
   826                   fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
   827                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
   828                 in
   829                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   830                     mk_disc_exhaust_tac n exhaust_thm discI_thms)
   831                   |> Thm.close_derivation
   832                 end;
   833 
   834               val (safe_collapse_thms, all_collapse_thms) =
   835                 let
   836                   fun mk_goal m udisc usel_ctr =
   837                     let
   838                       val prem = HOLogic.mk_Trueprop udisc;
   839                       val concl = mk_Trueprop_eq ((usel_ctr, u) |> m = 0 ? swap);
   840                     in
   841                       (prem aconv concl, Logic.all u (Logic.mk_implies (prem, concl)))
   842                     end;
   843                   val (trivs, goals) = map3 mk_goal ms udiscs usel_ctrs |> split_list;
   844                   val thms =
   845                     map5 (fn m => fn discD => fn sel_thms => fn triv => fn goal =>
   846                         Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   847                           mk_collapse_tac ctxt m discD sel_thms ORELSE HEADGOAL atac)
   848                         |> Thm.close_derivation
   849                         |> not triv ? perhaps (try (fn thm => refl RS thm)))
   850                       ms discD_thms sel_thmss trivs goals;
   851                 in
   852                   (map_filter (fn (true, _) => NONE | (false, thm) => SOME thm) (trivs ~~ thms),
   853                    thms)
   854                 end;
   855 
   856               val swapped_all_collapse_thms =
   857                 map2 (fn m => fn thm => if m = 0 then thm else thm RS sym) ms all_collapse_thms;
   858 
   859               val sel_exhaust_thm =
   860                 let
   861                   fun mk_prem usel_ctr = mk_imp_p [mk_Trueprop_eq (u, usel_ctr)];
   862                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem usel_ctrs));
   863                 in
   864                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   865                     mk_sel_exhaust_tac n disc_exhaust_thm swapped_all_collapse_thms)
   866                   |> Thm.close_derivation
   867                 end;
   868 
   869               val expand_thm =
   870                 let
   871                   fun mk_prems k udisc usels vdisc vsels =
   872                     (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
   873                     (if null usels then
   874                        []
   875                      else
   876                        [Logic.list_implies
   877                           (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
   878                              HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
   879                                (map2 (curry HOLogic.mk_eq) usels vsels)))]);
   880 
   881                   val goal =
   882                     Library.foldr Logic.list_implies
   883                       (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
   884                   val uncollapse_thms =
   885                     map2 (fn thm => fn [] => thm | _ => thm RS sym) all_collapse_thms uselss;
   886                 in
   887                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   888                     mk_expand_tac lthy n ms (inst_thm u disc_exhaust_thm)
   889                       (inst_thm v disc_exhaust_thm) uncollapse_thms disc_exclude_thmsss
   890                       disc_exclude_thmsss')
   891                   |> singleton (Proof_Context.export names_lthy lthy)
   892                   |> Thm.close_derivation
   893                 end;
   894 
   895               val (sel_split_thm, sel_split_asm_thm) =
   896                 let
   897                   val zss = map (K []) xss;
   898                   val goal = mk_split_goal usel_ctrs zss usel_fs;
   899                   val asm_goal = mk_split_asm_goal usel_ctrs zss usel_fs;
   900 
   901                   val thm = prove_split sel_thmss goal;
   902                   val asm_thm = prove_split_asm asm_goal thm;
   903                 in
   904                   (thm, asm_thm)
   905                 end;
   906 
   907               val case_eq_if_thm =
   908                 let
   909                   val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs usel_fs);
   910                 in
   911                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   912                     mk_case_eq_if_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)
   913                   |> singleton (Proof_Context.export names_lthy lthy)
   914                   |> Thm.close_derivation
   915                 end;
   916             in
   917               (sel_defs, all_sel_thms, sel_thmss, disc_defs, disc_thmss, nontriv_disc_thmss,
   918                discI_thms, nontriv_discI_thms, disc_exclude_thms, disc_exclude_thmsss,
   919                [disc_exhaust_thm], [sel_exhaust_thm], all_collapse_thms, safe_collapse_thms,
   920                [expand_thm], [sel_split_thm], [sel_split_asm_thm], [case_eq_if_thm])
   921             end;
   922 
   923         val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
   924         val cases_type_attr = Attrib.internal (K (Induct.cases_type fcT_name));
   925 
   926         val nontriv_disc_eq_thmss =
   927           map (map (fn th => th RS @{thm eq_False[THEN iffD2]}
   928             handle THM _ => th RS @{thm eq_True[THEN iffD2]})) nontriv_disc_thmss;
   929 
   930         val anonymous_notes =
   931           [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs),
   932            (flat nontriv_disc_eq_thmss, code_nitpicksimp_attrs)]
   933           |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
   934 
   935         (* "exhaust" is deliberately put first to avoid apparent circular dependencies in the proof
   936            objects, which would confuse MaSh. *)
   937         val notes =
   938           [(exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
   939            (caseN, case_thms, code_nitpicksimp_simp_attrs),
   940            (case_congN, [case_cong_thm], []),
   941            (case_eq_ifN, case_eq_if_thms, []),
   942            (collapseN, safe_collapse_thms, simp_attrs),
   943            (discN, flat nontriv_disc_thmss, simp_attrs),
   944            (discIN, nontriv_discI_thms, []),
   945            (disc_excludeN, disc_exclude_thms, dest_attrs),
   946            (disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
   947            (distinctN, distinct_thms, simp_attrs @ inductsimp_attrs),
   948            (expandN, expand_thms, []),
   949            (injectN, inject_thms, iff_attrs @ inductsimp_attrs),
   950            (nchotomyN, [nchotomy_thm], []),
   951            (selN, all_sel_thms, code_nitpicksimp_simp_attrs),
   952            (sel_exhaustN, sel_exhaust_thms, [exhaust_case_names_attr]),
   953            (sel_splitN, sel_split_thms, []),
   954            (sel_split_asmN, sel_split_asm_thms, []),
   955            (splitN, [split_thm], []),
   956            (split_asmN, [split_asm_thm], []),
   957            (splitsN, [split_thm, split_asm_thm], []),
   958            (weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
   959           |> filter_out (null o #2)
   960           |> map (fn (thmN, thms, attrs) =>
   961             ((qualify true (Binding.name thmN), attrs), [(thms, [])]));
   962 
   963         val ctr_sugar =
   964           {ctrs = ctrs, casex = casex, discs = discs, selss = selss, exhaust = exhaust_thm,
   965            nchotomy = nchotomy_thm, injects = inject_thms, distincts = distinct_thms,
   966            case_thms = case_thms, case_cong = case_cong_thm, weak_case_cong = weak_case_cong_thm,
   967            split = split_thm, split_asm = split_asm_thm, disc_defs = disc_defs,
   968            disc_thmss = disc_thmss, discIs = discI_thms, sel_defs = sel_defs, sel_thmss = sel_thmss,
   969            disc_excludesss = disc_exclude_thmsss, disc_exhausts = disc_exhaust_thms,
   970            sel_exhausts = sel_exhaust_thms, collapses = all_collapse_thms, expands = expand_thms,
   971            sel_splits = sel_split_thms, sel_split_asms = sel_split_asm_thms,
   972            case_eq_ifs = case_eq_if_thms};
   973       in
   974         (ctr_sugar,
   975          lthy
   976          |> Spec_Rules.add Spec_Rules.Equational ([casex], case_thms)
   977          |> fold (Spec_Rules.add Spec_Rules.Equational)
   978            (AList.group (eq_list (op aconv)) (map (`(single o lhs_head_of)) all_sel_thms))
   979          |> fold (Spec_Rules.add Spec_Rules.Equational)
   980            (filter_out (null o snd) (map single discs ~~ nontriv_disc_eq_thmss))
   981          |> Local_Theory.declaration {syntax = false, pervasive = true}
   982               (fn phi => Case_Translation.register
   983                  (Morphism.term phi casex) (map (Morphism.term phi) ctrs))
   984          |> Local_Theory.background_theory (fold (fold Code.del_eqn) [disc_defs, sel_defs])
   985          |> not no_code ?
   986             Local_Theory.declaration {syntax = false, pervasive = false}
   987               (fn phi => Context.mapping
   988                 (add_ctr_code fcT_name (map (Morphism.typ phi) As)
   989                   (map (dest_Const o Morphism.term phi) ctrs) (Morphism.fact phi inject_thms)
   990                   (Morphism.fact phi distinct_thms) (Morphism.fact phi case_thms))
   991                 I)
   992          |> Local_Theory.notes (anonymous_notes @ notes) |> snd
   993          |> register_ctr_sugar fcT_name ctr_sugar)
   994       end;
   995   in
   996     (goalss, after_qed, lthy')
   997   end;
   998 
   999 fun free_constructors tacss = (fn (goalss, after_qed, lthy) =>
  1000   map2 (map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])) goalss tacss
  1001   |> (fn thms => after_qed thms lthy)) oo prepare_free_constructors (K I);
  1002 
  1003 val free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
  1004   Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
  1005   prepare_free_constructors Syntax.read_term;
  1006 
  1007 val parse_bound_term = parse_binding --| @{keyword ":"} -- Parse.term;
  1008 
  1009 val parse_ctr_options =
  1010   Scan.optional (@{keyword "("} |-- Parse.list1
  1011         (Parse.reserved "no_discs_sels" >> K 0 || Parse.reserved "no_code" >> K 1) --|
  1012       @{keyword ")"}
  1013       >> (fn js => (member (op =) js 0, member (op =) js 1)))
  1014     (false, false);
  1015 
  1016 val parse_defaults =
  1017   @{keyword "("} |-- Parse.reserved "defaults" |-- Scan.repeat parse_bound_term --| @{keyword ")"};
  1018 
  1019 fun parse_ctr_spec parse_ctr parse_arg =
  1020   parse_opt_binding_colon -- parse_ctr -- Scan.repeat parse_arg --
  1021   Scan.optional parse_defaults [];
  1022 
  1023 val parse_ctr_specs = Parse.enum1 "|" (parse_ctr_spec Parse.term parse_binding);
  1024 
  1025 val _ =
  1026   Outer_Syntax.local_theory_to_proof @{command_spec "free_constructors"}
  1027     "register an existing freely generated type's constructors"
  1028     (parse_ctr_options -- parse_binding --| @{keyword "for"} -- parse_ctr_specs
  1029      >> free_constructors_cmd);
  1030 
  1031 val _ = Context.>> (Context.map_theory Ctr_Sugar_Interpretation.init);
  1032 
  1033 end;