src/HOL/Tools/Ctr_Sugar/ctr_sugar.ML
author blanchet
Thu Sep 04 11:20:59 2014 +0200 (2014-09-04)
changeset 58182 82478e6c60cb
parent 58177 166131276380
child 58185 e6e3b20340be
permissions -rw-r--r--
tweaked setup for datatype realizer
     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      case_cong_weak: 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      distinct_discsss: thm list list list,
    30      exhaust_discs: thm list,
    31      exhaust_sels: thm list,
    32      collapses: thm list,
    33      expands: thm list,
    34      split_sels: thm list,
    35      split_sel_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: theory -> ctr_sugar -> ctr_sugar
    40   val ctr_sugar_of: Proof.context -> string -> ctr_sugar option
    41   val ctr_sugar_of_global: theory -> string -> ctr_sugar option
    42   val ctr_sugars_of: Proof.context -> ctr_sugar list
    43   val ctr_sugars_of_global: theory -> ctr_sugar list
    44   val ctr_sugar_of_case: Proof.context -> string -> ctr_sugar option
    45   val ctr_sugar_of_case_global: theory -> string -> ctr_sugar option
    46   val ctr_sugar_interpretation: (ctr_sugar -> theory -> theory) ->
    47     (ctr_sugar -> local_theory -> local_theory) -> theory -> theory
    48   val register_ctr_sugar: string -> ctr_sugar -> local_theory -> local_theory
    49   val default_register_ctr_sugar_global: string -> ctr_sugar -> theory -> theory
    50 
    51   val mk_half_pairss: 'a list * 'a list -> ('a * 'a) list list
    52   val join_halves: int -> 'a list list -> 'a list list -> 'a list * 'a list list list
    53 
    54   val mk_ctr: typ list -> term -> term
    55   val mk_case: typ list -> typ -> term -> term
    56   val mk_disc_or_sel: typ list -> term -> term
    57   val name_of_ctr: term -> string
    58   val name_of_disc: term -> string
    59   val dest_ctr: Proof.context -> string -> term -> term * term list
    60   val dest_case: Proof.context -> string -> typ list -> term ->
    61     (ctr_sugar * term list * term list) option
    62 
    63   type ('c, 'a) ctr_spec = (binding * 'c) * 'a list
    64 
    65   val disc_of_ctr_spec: ('c, 'a) ctr_spec -> binding
    66   val ctr_of_ctr_spec: ('c, 'a) ctr_spec -> 'c
    67   val args_of_ctr_spec: ('c, 'a) ctr_spec -> 'a list
    68 
    69   val fake_local_theory_for_sel_defaults: (binding * typ) list -> Proof.context -> Proof.context
    70   val free_constructors: ({prems: thm list, context: Proof.context} -> tactic) list list ->
    71     (((bool * bool) * binding) * (term, binding) ctr_spec list) * term list -> local_theory ->
    72     ctr_sugar * local_theory
    73   val parse_bound_term: (binding * string) parser
    74   val parse_ctr_options: (bool * bool) parser
    75   val parse_ctr_spec: 'c parser -> 'a parser -> ('c, 'a) ctr_spec parser
    76   val parse_sel_default_eqs: string list parser
    77 end;
    78 
    79 structure Ctr_Sugar : CTR_SUGAR =
    80 struct
    81 
    82 open Ctr_Sugar_Util
    83 open Ctr_Sugar_Tactics
    84 open Ctr_Sugar_Code
    85 
    86 type ctr_sugar =
    87   {ctrs: term list,
    88    casex: term,
    89    discs: term list,
    90    selss: term list list,
    91    exhaust: thm,
    92    nchotomy: thm,
    93    injects: thm list,
    94    distincts: thm list,
    95    case_thms: thm list,
    96    case_cong: thm,
    97    case_cong_weak: thm,
    98    split: thm,
    99    split_asm: thm,
   100    disc_defs: thm list,
   101    disc_thmss: thm list list,
   102    discIs: thm list,
   103    sel_defs: thm list,
   104    sel_thmss: thm list list,
   105    distinct_discsss: thm list list list,
   106    exhaust_discs: thm list,
   107    exhaust_sels: thm list,
   108    collapses: thm list,
   109    expands: thm list,
   110    split_sels: thm list,
   111    split_sel_asms: thm list,
   112    case_eq_ifs: thm list};
   113 
   114 fun morph_ctr_sugar phi {ctrs, casex, discs, selss, exhaust, nchotomy, injects, distincts,
   115     case_thms, case_cong, case_cong_weak, split, split_asm, disc_defs, disc_thmss, discIs, sel_defs,
   116     sel_thmss, distinct_discsss, exhaust_discs, exhaust_sels, collapses, expands, split_sels,
   117     split_sel_asms, case_eq_ifs} =
   118   {ctrs = map (Morphism.term phi) ctrs,
   119    casex = Morphism.term phi casex,
   120    discs = map (Morphism.term phi) discs,
   121    selss = map (map (Morphism.term phi)) selss,
   122    exhaust = Morphism.thm phi exhaust,
   123    nchotomy = Morphism.thm phi nchotomy,
   124    injects = map (Morphism.thm phi) injects,
   125    distincts = map (Morphism.thm phi) distincts,
   126    case_thms = map (Morphism.thm phi) case_thms,
   127    case_cong = Morphism.thm phi case_cong,
   128    case_cong_weak = Morphism.thm phi case_cong_weak,
   129    split = Morphism.thm phi split,
   130    split_asm = Morphism.thm phi split_asm,
   131    disc_defs = map (Morphism.thm phi) disc_defs,
   132    disc_thmss = map (map (Morphism.thm phi)) disc_thmss,
   133    discIs = map (Morphism.thm phi) discIs,
   134    sel_defs = map (Morphism.thm phi) sel_defs,
   135    sel_thmss = map (map (Morphism.thm phi)) sel_thmss,
   136    distinct_discsss = map (map (map (Morphism.thm phi))) distinct_discsss,
   137    exhaust_discs = map (Morphism.thm phi) exhaust_discs,
   138    exhaust_sels = map (Morphism.thm phi) exhaust_sels,
   139    collapses = map (Morphism.thm phi) collapses,
   140    expands = map (Morphism.thm phi) expands,
   141    split_sels = map (Morphism.thm phi) split_sels,
   142    split_sel_asms = map (Morphism.thm phi) split_sel_asms,
   143    case_eq_ifs = map (Morphism.thm phi) case_eq_ifs};
   144 
   145 val transfer_ctr_sugar = morph_ctr_sugar o Morphism.transfer_morphism;
   146 
   147 structure Data = Generic_Data
   148 (
   149   type T = ctr_sugar Symtab.table;
   150   val empty = Symtab.empty;
   151   val extend = I;
   152   fun merge data : T = Symtab.merge (K true) data;
   153 );
   154 
   155 fun ctr_sugar_of_generic context =
   156   Option.map (transfer_ctr_sugar (Context.theory_of context)) o Symtab.lookup (Data.get context);
   157 
   158 fun ctr_sugars_of_generic context =
   159   Symtab.fold (cons o transfer_ctr_sugar (Context.theory_of context) o snd) (Data.get context) [];
   160 
   161 fun ctr_sugar_of_case_generic context s =
   162   find_first (fn {casex = Const (s', _), ...} => s' = s | _ => false)
   163     (ctr_sugars_of_generic context);
   164 
   165 val ctr_sugar_of = ctr_sugar_of_generic o Context.Proof;
   166 val ctr_sugar_of_global = ctr_sugar_of_generic o Context.Theory;
   167 
   168 val ctr_sugars_of = ctr_sugars_of_generic o Context.Proof;
   169 val ctr_sugars_of_global = ctr_sugars_of_generic o Context.Theory;
   170 
   171 val ctr_sugar_of_case = ctr_sugar_of_case_generic o Context.Proof;
   172 val ctr_sugar_of_case_global = ctr_sugar_of_case_generic o Context.Theory;
   173 
   174 structure Ctr_Sugar_Interpretation = Local_Interpretation
   175 (
   176   type T = ctr_sugar;
   177   val eq: T * T -> bool = op = o pairself #ctrs;
   178 );
   179 
   180 fun with_repaired_path g (ctr_sugar as {ctrs = ctr1 :: _, ...} : ctr_sugar) thy =
   181   thy
   182   |> Sign.root_path
   183   |> Sign.add_path (Long_Name.qualifier (fst (dest_Type (body_type (fastype_of ctr1)))))
   184   |> (fn thy => g (transfer_ctr_sugar thy ctr_sugar) thy)
   185   |> Sign.restore_naming thy;
   186 
   187 val ctr_sugar_interpretation = Ctr_Sugar_Interpretation.interpretation o with_repaired_path;
   188 
   189 fun register_ctr_sugar key ctr_sugar =
   190   Local_Theory.declaration {syntax = false, pervasive = true}
   191     (fn phi => Data.map (Symtab.update (key, morph_ctr_sugar phi ctr_sugar)))
   192   #> Ctr_Sugar_Interpretation.data ctr_sugar;
   193 
   194 fun default_register_ctr_sugar_global key ctr_sugar thy =
   195   let val tab = Data.get (Context.Theory thy) in
   196     if Symtab.defined tab key then
   197       thy
   198     else
   199       thy
   200       |> Context.theory_map (Data.put (Symtab.update_new (key, ctr_sugar) tab))
   201       |> Ctr_Sugar_Interpretation.data_global ctr_sugar
   202   end;
   203 
   204 val isN = "is_";
   205 val unN = "un_";
   206 val notN = "not_";
   207 
   208 fun mk_unN 1 1 suf = unN ^ suf
   209   | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
   210 
   211 val caseN = "case";
   212 val case_congN = "case_cong";
   213 val case_eq_ifN = "case_eq_if";
   214 val collapseN = "collapse";
   215 val discN = "disc";
   216 val discIN = "discI";
   217 val distinctN = "distinct";
   218 val distinct_discN = "distinct_disc";
   219 val exhaustN = "exhaust";
   220 val exhaust_discN = "exhaust_disc";
   221 val expandN = "expand";
   222 val injectN = "inject";
   223 val nchotomyN = "nchotomy";
   224 val selN = "sel";
   225 val exhaust_selN = "exhaust_sel";
   226 val splitN = "split";
   227 val split_asmN = "split_asm";
   228 val split_selN = "split_sel";
   229 val split_sel_asmN = "split_sel_asm";
   230 val splitsN = "splits";
   231 val split_selsN = "split_sels";
   232 val case_cong_weak_thmsN = "case_cong_weak";
   233 
   234 val cong_attrs = @{attributes [cong]};
   235 val dest_attrs = @{attributes [dest]};
   236 val safe_elim_attrs = @{attributes [elim!]};
   237 val iff_attrs = @{attributes [iff]};
   238 val inductsimp_attrs = @{attributes [induct_simp]};
   239 val nitpicksimp_attrs = @{attributes [nitpick_simp]};
   240 val simp_attrs = @{attributes [simp]};
   241 val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
   242 val code_nitpicksimp_simp_attrs = code_nitpicksimp_attrs @ simp_attrs;
   243 
   244 fun unflat_lookup eq xs ys = map (fn xs' => permute_like_unique eq xs xs' ys);
   245 
   246 fun mk_half_pairss' _ ([], []) = []
   247   | mk_half_pairss' indent (x :: xs, _ :: ys) =
   248     indent @ fold_rev (cons o single o pair x) ys (mk_half_pairss' ([] :: indent) (xs, ys));
   249 
   250 fun mk_half_pairss p = mk_half_pairss' [[]] p;
   251 
   252 fun join_halves n half_xss other_half_xss =
   253   (splice (flat half_xss) (flat other_half_xss),
   254    map2 (map2 append) (Library.chop_groups n half_xss)
   255      (transpose (Library.chop_groups n other_half_xss)));
   256 
   257 fun mk_undefined T = Const (@{const_name undefined}, T);
   258 
   259 fun mk_ctr Ts t =
   260   let val Type (_, Ts0) = body_type (fastype_of t) in
   261     subst_nonatomic_types (Ts0 ~~ Ts) t
   262   end;
   263 
   264 fun mk_case Ts T t =
   265   let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
   266     subst_nonatomic_types ((body, T) :: (Ts0 ~~ Ts)) t
   267   end;
   268 
   269 fun mk_disc_or_sel Ts t =
   270   subst_nonatomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
   271 
   272 val name_of_ctr = name_of_const "constructor";
   273 
   274 fun name_of_disc t =
   275   (case head_of t of
   276     Abs (_, _, @{const Not} $ (t' $ Bound 0)) =>
   277     Long_Name.map_base_name (prefix notN) (name_of_disc t')
   278   | Abs (_, _, Const (@{const_name HOL.eq}, _) $ Bound 0 $ t') =>
   279     Long_Name.map_base_name (prefix isN) (name_of_disc t')
   280   | Abs (_, _, @{const Not} $ (Const (@{const_name HOL.eq}, _) $ Bound 0 $ t')) =>
   281     Long_Name.map_base_name (prefix (notN ^ isN)) (name_of_disc t')
   282   | t' => name_of_const "destructor" t');
   283 
   284 val base_name_of_ctr = Long_Name.base_name o name_of_ctr;
   285 
   286 fun dest_ctr ctxt s t =
   287   let val (f, args) = Term.strip_comb t in
   288     (case ctr_sugar_of ctxt s of
   289       SOME {ctrs, ...} =>
   290       (case find_first (can (fo_match ctxt f)) ctrs of
   291         SOME f' => (f', args)
   292       | NONE => raise Fail "dest_ctr")
   293     | NONE => raise Fail "dest_ctr")
   294   end;
   295 
   296 fun dest_case ctxt s Ts t =
   297   (case Term.strip_comb t of
   298     (Const (c, _), args as _ :: _) =>
   299     (case ctr_sugar_of ctxt s of
   300       SOME (ctr_sugar as {casex = Const (case_name, _), discs = discs0, selss = selss0, ...}) =>
   301       if case_name = c then
   302         let val n = length discs0 in
   303           if n < length args then
   304             let
   305               val (branches, obj :: leftovers) = chop n args;
   306               val discs = map (mk_disc_or_sel Ts) discs0;
   307               val selss = map (map (mk_disc_or_sel Ts)) selss0;
   308               val conds = map (rapp obj) discs;
   309               val branch_argss = map (fn sels => map (rapp obj) sels @ leftovers) selss;
   310               val branches' = map2 (curry Term.betapplys) branches branch_argss;
   311             in
   312               SOME (ctr_sugar, conds, branches')
   313             end
   314           else
   315             NONE
   316         end
   317       else
   318         NONE
   319     | _ => NONE)
   320   | _ => NONE);
   321 
   322 fun const_or_free_name (Const (s, _)) = Long_Name.base_name s
   323   | const_or_free_name (Free (s, _)) = s
   324   | const_or_free_name t = raise TERM ("const_or_free_name", [t])
   325 
   326 fun extract_sel_default ctxt t =
   327   let
   328     fun malformed () =
   329       error ("Malformed selector default value equation: " ^ Syntax.string_of_term ctxt t);
   330 
   331     val ((sel, (ctr, vars)), rhs) =
   332       fst (Term.replace_dummy_patterns (Syntax.check_term ctxt t) 0)
   333       |> HOLogic.dest_eq
   334       |>> (Term.dest_comb
   335         #>> const_or_free_name
   336         ##> (Term.strip_comb #>> (Term.dest_Const #> fst)))
   337       handle TERM _ => malformed ();
   338   in
   339     if forall (is_Free orf is_Var) vars andalso not (has_duplicates (op aconv) vars) then
   340       ((ctr, sel), fold_rev Term.lambda vars rhs)
   341     else
   342       malformed ()
   343   end;
   344 
   345 (* Ideally, we would enrich the context with constants rather than free variables. *)
   346 fun fake_local_theory_for_sel_defaults sel_bTs =
   347   Proof_Context.allow_dummies
   348   #> Proof_Context.add_fixes (map (fn (b, T) => (b, SOME T, NoSyn)) sel_bTs)
   349   #> snd;
   350 
   351 type ('c, 'a) ctr_spec = (binding * 'c) * 'a list;
   352 
   353 fun disc_of_ctr_spec ((disc, _), _) = disc;
   354 fun ctr_of_ctr_spec ((_, ctr), _) = ctr;
   355 fun args_of_ctr_spec (_, args) = args;
   356 
   357 fun prepare_free_constructors prep_term
   358     ((((discs_sels, no_code), raw_case_binding), ctr_specs), sel_default_eqs) no_defs_lthy =
   359   let
   360     (* TODO: sanity checks on arguments *)
   361 
   362     val raw_ctrs = map ctr_of_ctr_spec ctr_specs;
   363     val raw_disc_bindings = map disc_of_ctr_spec ctr_specs;
   364     val raw_sel_bindingss = map args_of_ctr_spec ctr_specs;
   365 
   366     val n = length raw_ctrs;
   367     val ks = 1 upto n;
   368 
   369     val _ = if n > 0 then () else error "No constructors specified";
   370 
   371     val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
   372 
   373     val Type (fcT_name, As0) = body_type (fastype_of (hd ctrs0));
   374     val fc_b_name = Long_Name.base_name fcT_name;
   375     val fc_b = Binding.name fc_b_name;
   376 
   377     fun qualify mandatory = Binding.qualify mandatory fc_b_name;
   378 
   379     fun dest_TFree_or_TVar (TFree sS) = sS
   380       | dest_TFree_or_TVar (TVar ((s, _), S)) = (s, S)
   381       | dest_TFree_or_TVar _ = error "Invalid type argument";
   382 
   383     val (unsorted_As, B) =
   384       no_defs_lthy
   385       |> variant_tfrees (map (fst o dest_TFree_or_TVar) As0)
   386       ||> the_single o fst o mk_TFrees 1;
   387 
   388     val As = map2 (resort_tfree o snd o dest_TFree_or_TVar) As0 unsorted_As;
   389 
   390     val fcT = Type (fcT_name, As);
   391     val ctrs = map (mk_ctr As) ctrs0;
   392     val ctr_Tss = map (binder_types o fastype_of) ctrs;
   393 
   394     val ms = map length ctr_Tss;
   395 
   396     fun can_definitely_rely_on_disc k =
   397       not (Binding.is_empty (nth raw_disc_bindings (k - 1))) orelse nth ms (k - 1) = 0;
   398     fun can_rely_on_disc k =
   399       can_definitely_rely_on_disc k orelse (k = 1 andalso not (can_definitely_rely_on_disc 2));
   400     fun should_omit_disc_binding k = n = 1 orelse (n = 2 andalso can_rely_on_disc (3 - k));
   401 
   402     val equal_binding = @{binding "="};
   403 
   404     fun is_disc_binding_valid b =
   405       not (Binding.is_empty b orelse Binding.eq_name (b, equal_binding));
   406 
   407     val standard_disc_binding = Binding.name o prefix isN o base_name_of_ctr;
   408 
   409     val disc_bindings =
   410       raw_disc_bindings
   411       |> map4 (fn k => fn m => fn ctr => fn disc =>
   412         qualify false
   413           (if Binding.is_empty disc then
   414              if m = 0 then equal_binding
   415              else if should_omit_disc_binding k then disc
   416              else standard_disc_binding ctr
   417            else if Binding.eq_name (disc, standard_binding) then
   418              standard_disc_binding ctr
   419            else
   420              disc)) ks ms ctrs0;
   421 
   422     fun standard_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
   423 
   424     val sel_bindingss =
   425       map3 (fn ctr => fn m => map2 (fn l => fn sel =>
   426         qualify false
   427           (if Binding.is_empty sel orelse Binding.eq_name (sel, standard_binding) then
   428             standard_sel_binding m l ctr
   429           else
   430             sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms raw_sel_bindingss;
   431 
   432     val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
   433 
   434     val (((((((([exh_y], (xss, xss')), yss), fs), gs), [u', v']), [w]), (p, p')), names_lthy) =
   435       no_defs_lthy
   436       |> mk_Frees "y" [fcT] (* for compatibility with "datatype_realizer.ML" *)
   437       ||>> mk_Freess' "x" ctr_Tss
   438       ||>> mk_Freess "y" ctr_Tss
   439       ||>> mk_Frees "f" case_Ts
   440       ||>> mk_Frees "g" case_Ts
   441       ||>> (apfst (map (rpair fcT)) oo Variable.variant_fixes) [fc_b_name, fc_b_name ^ "'"]
   442       ||>> mk_Frees "z" [B]
   443       ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
   444 
   445     val u = Free u';
   446     val v = Free v';
   447     val q = Free (fst p', mk_pred1T B);
   448 
   449     val xctrs = map2 (curry Term.list_comb) ctrs xss;
   450     val yctrs = map2 (curry Term.list_comb) ctrs yss;
   451 
   452     val xfs = map2 (curry Term.list_comb) fs xss;
   453     val xgs = map2 (curry Term.list_comb) gs xss;
   454 
   455     (* TODO: Eta-expension is for compatibility with the old datatype package (but it also provides
   456        nicer names). Consider removing. *)
   457     val eta_fs = map2 (fold_rev Term.lambda) xss xfs;
   458     val eta_gs = map2 (fold_rev Term.lambda) xss xgs;
   459 
   460     val case_binding =
   461       qualify false
   462         (if Binding.is_empty raw_case_binding orelse
   463             Binding.eq_name (raw_case_binding, standard_binding) then
   464            Binding.prefix_name (caseN ^ "_") fc_b
   465          else
   466            raw_case_binding);
   467 
   468     fun mk_case_disj xctr xf xs =
   469       list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr), HOLogic.mk_eq (w, xf)));
   470 
   471     val case_rhs = fold_rev (fold_rev Term.lambda) [fs, [u]]
   472       (Const (@{const_name The}, (B --> HOLogic.boolT) --> B) $
   473          Term.lambda w (Library.foldr1 HOLogic.mk_disj (map3 mk_case_disj xctrs xfs xss)));
   474 
   475     val ((raw_case, (_, raw_case_def)), (lthy', lthy)) = no_defs_lthy
   476       |> Local_Theory.define ((case_binding, NoSyn),
   477         ((Binding.conceal (Thm.def_binding case_binding), []), case_rhs))
   478       ||> `Local_Theory.restore;
   479 
   480     val phi = Proof_Context.export_morphism lthy lthy';
   481 
   482     val case_def = Morphism.thm phi raw_case_def;
   483 
   484     val case0 = Morphism.term phi raw_case;
   485     val casex = mk_case As B case0;
   486 
   487     val fcase = Term.list_comb (casex, fs);
   488 
   489     val ufcase = fcase $ u;
   490     val vfcase = fcase $ v;
   491 
   492     val eta_fcase = Term.list_comb (casex, eta_fs);
   493     val eta_gcase = Term.list_comb (casex, eta_gs);
   494 
   495     val eta_ufcase = eta_fcase $ u;
   496     val eta_vgcase = eta_gcase $ v;
   497 
   498     fun mk_uu_eq () = HOLogic.mk_eq (u, u);
   499 
   500     val uv_eq = mk_Trueprop_eq (u, v);
   501 
   502     val exist_xs_u_eq_ctrs =
   503       map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
   504 
   505     val unique_disc_no_def = TrueI; (*arbitrary marker*)
   506     val alternate_disc_no_def = FalseE; (*arbitrary marker*)
   507 
   508     fun alternate_disc_lhs get_udisc k =
   509       HOLogic.mk_not
   510         (let val b = nth disc_bindings (k - 1) in
   511            if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
   512          end);
   513 
   514     val no_discs_sels =
   515       not discs_sels andalso
   516       forall (forall Binding.is_empty) (raw_disc_bindings :: raw_sel_bindingss) andalso
   517       null sel_default_eqs;
   518 
   519     val (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy') =
   520       if no_discs_sels then
   521         (true, [], [], [], [], [], lthy')
   522       else
   523         let
   524           val all_sel_bindings = flat sel_bindingss;
   525           val num_all_sel_bindings = length all_sel_bindings;
   526           val uniq_sel_bindings = distinct Binding.eq_name all_sel_bindings;
   527           val all_sels_distinct = (length uniq_sel_bindings = num_all_sel_bindings);
   528 
   529           val sel_binding_index =
   530             if all_sels_distinct then
   531               1 upto num_all_sel_bindings
   532             else
   533               map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) all_sel_bindings;
   534 
   535           val all_proto_sels = flat (map3 (fn k => fn xs => map (pair k o pair xs)) ks xss xss);
   536           val sel_infos =
   537             AList.group (op =) (sel_binding_index ~~ all_proto_sels)
   538             |> sort (int_ord o pairself fst)
   539             |> map snd |> curry (op ~~) uniq_sel_bindings;
   540           val sel_bindings = map fst sel_infos;
   541 
   542           val sel_defaults =
   543             if null sel_default_eqs then
   544               []
   545             else
   546               let
   547                 val sel_Ts = map (curry (op -->) fcT o fastype_of o snd o snd o hd o snd) sel_infos;
   548                 val fake_lthy =
   549                   fake_local_theory_for_sel_defaults (sel_bindings ~~ sel_Ts) no_defs_lthy;
   550               in
   551                 map (extract_sel_default fake_lthy o prep_term fake_lthy) sel_default_eqs
   552               end;
   553 
   554           fun disc_free b = Free (Binding.name_of b, mk_pred1T fcT);
   555 
   556           fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
   557 
   558           fun alternate_disc k =
   559             Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
   560 
   561           fun mk_sel_case_args b proto_sels T =
   562             map3 (fn Const (c, _) => fn Ts => fn k =>
   563               (case AList.lookup (op =) proto_sels k of
   564                 NONE =>
   565                 (case filter (curry (op =) (c, Binding.name_of b) o fst) sel_defaults of
   566                   [] => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
   567                 | [(_, t)] => t
   568                 | _ => error "Multiple default values for selector/constructor pair")
   569               | SOME (xs, x) => fold_rev Term.lambda xs x)) ctrs ctr_Tss ks;
   570 
   571           fun sel_spec b proto_sels =
   572             let
   573               val _ =
   574                 (case duplicates (op =) (map fst proto_sels) of
   575                    k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
   576                      " for constructor " ^ quote (Syntax.string_of_term lthy (nth ctrs (k - 1))))
   577                  | [] => ())
   578               val T =
   579                 (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
   580                   [T] => T
   581                 | T :: T' :: _ => error ("Inconsistent range type for selector " ^
   582                     quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ lthy T) ^
   583                     " vs. " ^ quote (Syntax.string_of_typ lthy T')));
   584             in
   585               mk_Trueprop_eq (Free (Binding.name_of b, fcT --> T) $ u,
   586                 Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
   587             end;
   588 
   589           fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
   590 
   591           val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
   592             lthy
   593             |> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
   594                 if Binding.is_empty b then
   595                   if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
   596                   else pair (alternate_disc k, alternate_disc_no_def)
   597                 else if Binding.eq_name (b, equal_binding) then
   598                   pair (Term.lambda u exist_xs_u_eq_ctr, refl)
   599                 else
   600                   Specification.definition (SOME (b, NONE, NoSyn),
   601                     ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
   602               ks exist_xs_u_eq_ctrs disc_bindings
   603             ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
   604               Specification.definition (SOME (b, NONE, NoSyn),
   605                 ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
   606             ||> `Local_Theory.restore;
   607 
   608           val phi = Proof_Context.export_morphism lthy lthy';
   609 
   610           val disc_defs = map (Morphism.thm phi) raw_disc_defs;
   611           val sel_defs = map (Morphism.thm phi) raw_sel_defs;
   612           val sel_defss = unflat_selss sel_defs;
   613 
   614           val discs0 = map (Morphism.term phi) raw_discs;
   615           val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
   616 
   617           val discs = map (mk_disc_or_sel As) discs0;
   618           val selss = map (map (mk_disc_or_sel As)) selss0;
   619         in
   620           (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy')
   621         end;
   622 
   623     fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
   624 
   625     val exhaust_goal =
   626       let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (exh_y, xctr)]) in
   627         fold_rev Logic.all [p, exh_y] (mk_imp_p (map2 mk_prem xctrs xss))
   628       end;
   629 
   630     val inject_goalss =
   631       let
   632         fun mk_goal _ _ [] [] = []
   633           | mk_goal xctr yctr xs ys =
   634             [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
   635               Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
   636       in
   637         map4 mk_goal xctrs yctrs xss yss
   638       end;
   639 
   640     val half_distinct_goalss =
   641       let
   642         fun mk_goal ((xs, xc), (xs', xc')) =
   643           fold_rev Logic.all (xs @ xs')
   644             (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
   645       in
   646         map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
   647       end;
   648 
   649     val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss;
   650 
   651     fun after_qed ([exhaust_thm] :: thmss) lthy =
   652       let
   653         val ((inject_thms, inject_thmss), half_distinct_thmss) = chop n thmss |>> `flat;
   654 
   655         val rho_As = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
   656 
   657         fun inst_thm t thm =
   658           Drule.instantiate' [] [SOME (certify lthy t)]
   659             (Thm.instantiate (rho_As, []) (Drule.zero_var_indexes thm));
   660 
   661         val uexhaust_thm = inst_thm u exhaust_thm;
   662 
   663         val exhaust_cases = map base_name_of_ctr ctrs;
   664 
   665         val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
   666 
   667         val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
   668           join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
   669 
   670         val nchotomy_thm =
   671           let
   672             val goal =
   673               HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
   674                 Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
   675           in
   676             Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
   677             |> Thm.close_derivation
   678           end;
   679 
   680         val case_thms =
   681           let
   682             val goals =
   683               map3 (fn xctr => fn xf => fn xs =>
   684                 fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xctrs xfs xss;
   685           in
   686             map4 (fn k => fn goal => fn injects => fn distinctss =>
   687                 Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   688                   mk_case_tac ctxt n k case_def injects distinctss)
   689                 |> Thm.close_derivation)
   690               ks goals inject_thmss distinct_thmsss
   691           end;
   692 
   693         val (case_cong_thm, case_cong_weak_thm) =
   694           let
   695             fun mk_prem xctr xs xf xg =
   696               fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
   697                 mk_Trueprop_eq (xf, xg)));
   698 
   699             val goal =
   700               Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
   701                  mk_Trueprop_eq (eta_ufcase, eta_vgcase));
   702             val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
   703           in
   704             (Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
   705              Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
   706             |> pairself (singleton (Proof_Context.export names_lthy lthy) #>
   707               Thm.close_derivation)
   708           end;
   709 
   710         val split_lhs = q $ ufcase;
   711 
   712         fun mk_split_conjunct xctr xs f_xs =
   713           list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
   714         fun mk_split_disjunct xctr xs f_xs =
   715           list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
   716             HOLogic.mk_not (q $ f_xs)));
   717 
   718         fun mk_split_goal xctrs xss xfs =
   719           mk_Trueprop_eq (split_lhs, Library.foldr1 HOLogic.mk_conj
   720             (map3 mk_split_conjunct xctrs xss xfs));
   721         fun mk_split_asm_goal xctrs xss xfs =
   722           mk_Trueprop_eq (split_lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
   723             (map3 mk_split_disjunct xctrs xss xfs)));
   724 
   725         fun prove_split selss goal =
   726           Goal.prove_sorry lthy [] [] goal (fn _ =>
   727             mk_split_tac lthy uexhaust_thm case_thms selss inject_thmss distinct_thmsss)
   728           |> singleton (Proof_Context.export names_lthy lthy)
   729           |> Thm.close_derivation;
   730 
   731         fun prove_split_asm asm_goal split_thm =
   732           Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
   733             mk_split_asm_tac ctxt split_thm)
   734           |> singleton (Proof_Context.export names_lthy lthy)
   735           |> Thm.close_derivation;
   736 
   737         val (split_thm, split_asm_thm) =
   738           let
   739             val goal = mk_split_goal xctrs xss xfs;
   740             val asm_goal = mk_split_asm_goal xctrs xss xfs;
   741 
   742             val thm = prove_split (replicate n []) goal;
   743             val asm_thm = prove_split_asm asm_goal thm;
   744           in
   745             (thm, asm_thm)
   746           end;
   747 
   748         val (sel_defs, all_sel_thms, sel_thmss, disc_defs, disc_thmss, nontriv_disc_thmss,
   749              discI_thms, nontriv_discI_thms, distinct_disc_thms, distinct_disc_thmsss,
   750              exhaust_disc_thms, exhaust_sel_thms, all_collapse_thms, safe_collapse_thms,
   751              expand_thms, split_sel_thms, split_sel_asm_thms, case_eq_if_thms) =
   752           if no_discs_sels then
   753             ([], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [])
   754           else
   755             let
   756               val udiscs = map (rapp u) discs;
   757               val uselss = map (map (rapp u)) selss;
   758               val usel_ctrs = map2 (curry Term.list_comb) ctrs uselss;
   759               val usel_fs = map2 (curry Term.list_comb) fs uselss;
   760 
   761               val vdiscs = map (rapp v) discs;
   762               val vselss = map (map (rapp v)) selss;
   763 
   764               fun make_sel_thm xs' case_thm sel_def =
   765                 zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
   766                     (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
   767 
   768               val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
   769 
   770               fun has_undefined_rhs thm =
   771                 (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
   772                   Const (@{const_name undefined}, _) => true
   773                 | _ => false);
   774 
   775               val all_sel_thms =
   776                 (if all_sels_distinct andalso null sel_default_eqs then
   777                    flat sel_thmss
   778                  else
   779                    map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
   780                      (xss' ~~ case_thms))
   781                 |> filter_out has_undefined_rhs;
   782 
   783               fun mk_unique_disc_def () =
   784                 let
   785                   val m = the_single ms;
   786                   val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
   787                 in
   788                   Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
   789                   |> singleton (Proof_Context.export names_lthy lthy)
   790                   |> Thm.close_derivation
   791                 end;
   792 
   793               fun mk_alternate_disc_def k =
   794                 let
   795                   val goal =
   796                     mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
   797                       nth exist_xs_u_eq_ctrs (k - 1));
   798                 in
   799                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   800                     mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
   801                       (nth distinct_thms (2 - k)) uexhaust_thm)
   802                   |> singleton (Proof_Context.export names_lthy lthy)
   803                   |> Thm.close_derivation
   804                 end;
   805 
   806               val has_alternate_disc_def =
   807                 exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
   808 
   809               val disc_defs' =
   810                 map2 (fn k => fn def =>
   811                   if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
   812                   else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
   813                   else def) ks disc_defs;
   814 
   815               val discD_thms = map (fn def => def RS iffD1) disc_defs';
   816               val discI_thms =
   817                 map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
   818                   disc_defs';
   819               val not_discI_thms =
   820                 map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
   821                     (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
   822                   ms disc_defs';
   823 
   824               val (disc_thmss', disc_thmss) =
   825                 let
   826                   fun mk_thm discI _ [] = refl RS discI
   827                     | mk_thm _ not_discI [distinct] = distinct RS not_discI;
   828                   fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
   829                 in
   830                   map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
   831                 end;
   832 
   833               val nontriv_disc_thmss =
   834                 map2 (fn b => if is_disc_binding_valid b then I else K []) disc_bindings disc_thmss;
   835 
   836               fun is_discI_boring b =
   837                 (n = 1 andalso Binding.is_empty b) orelse Binding.eq_name (b, equal_binding);
   838 
   839               val nontriv_discI_thms =
   840                 flat (map2 (fn b => if is_discI_boring b then K [] else single) disc_bindings
   841                   discI_thms);
   842 
   843               val (distinct_disc_thms, (distinct_disc_thmsss', distinct_disc_thmsss)) =
   844                 let
   845                   fun mk_goal [] = []
   846                     | mk_goal [((_, udisc), (_, udisc'))] =
   847                       [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
   848                          HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
   849 
   850                   fun prove tac goal =
   851                     Goal.prove_sorry lthy [] [] goal (K tac)
   852                     |> Thm.close_derivation;
   853 
   854                   val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
   855 
   856                   val half_goalss = map mk_goal half_pairss;
   857                   val half_thmss =
   858                     map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
   859                         fn disc_thm => [prove (mk_half_distinct_disc_tac lthy m discD disc_thm) goal])
   860                       half_goalss half_pairss (flat disc_thmss');
   861 
   862                   val other_half_goalss = map (mk_goal o map swap) half_pairss;
   863                   val other_half_thmss =
   864                     map2 (map2 (prove o mk_other_half_distinct_disc_tac)) half_thmss
   865                       other_half_goalss;
   866                 in
   867                   join_halves n half_thmss other_half_thmss ||> `transpose
   868                   |>> has_alternate_disc_def ? K []
   869                 end;
   870 
   871               val exhaust_disc_thm =
   872                 let
   873                   fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
   874                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
   875                 in
   876                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   877                     mk_exhaust_disc_tac n exhaust_thm discI_thms)
   878                   |> Thm.close_derivation
   879                 end;
   880 
   881               val (safe_collapse_thms, all_collapse_thms) =
   882                 let
   883                   fun mk_goal m udisc usel_ctr =
   884                     let
   885                       val prem = HOLogic.mk_Trueprop udisc;
   886                       val concl = mk_Trueprop_eq ((usel_ctr, u) |> m = 0 ? swap);
   887                     in
   888                       (prem aconv concl, Logic.all u (Logic.mk_implies (prem, concl)))
   889                     end;
   890                   val (trivs, goals) = map3 mk_goal ms udiscs usel_ctrs |> split_list;
   891                   val thms =
   892                     map5 (fn m => fn discD => fn sel_thms => fn triv => fn goal =>
   893                         Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   894                           mk_collapse_tac ctxt m discD sel_thms ORELSE HEADGOAL atac)
   895                         |> Thm.close_derivation
   896                         |> not triv ? perhaps (try (fn thm => refl RS thm)))
   897                       ms discD_thms sel_thmss trivs goals;
   898                 in
   899                   (map_filter (fn (true, _) => NONE | (false, thm) => SOME thm) (trivs ~~ thms),
   900                    thms)
   901                 end;
   902 
   903               val swapped_all_collapse_thms =
   904                 map2 (fn m => fn thm => if m = 0 then thm else thm RS sym) ms all_collapse_thms;
   905 
   906               val exhaust_sel_thm =
   907                 let
   908                   fun mk_prem usel_ctr = mk_imp_p [mk_Trueprop_eq (u, usel_ctr)];
   909                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem usel_ctrs));
   910                 in
   911                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   912                     mk_exhaust_sel_tac n exhaust_disc_thm swapped_all_collapse_thms)
   913                   |> Thm.close_derivation
   914                 end;
   915 
   916               val expand_thm =
   917                 let
   918                   fun mk_prems k udisc usels vdisc vsels =
   919                     (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
   920                     (if null usels then
   921                        []
   922                      else
   923                        [Logic.list_implies
   924                           (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
   925                              HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
   926                                (map2 (curry HOLogic.mk_eq) usels vsels)))]);
   927 
   928                   val goal =
   929                     Library.foldr Logic.list_implies
   930                       (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
   931                   val uncollapse_thms =
   932                     map2 (fn thm => fn [] => thm | _ => thm RS sym) all_collapse_thms uselss;
   933                 in
   934                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   935                     mk_expand_tac lthy n ms (inst_thm u exhaust_disc_thm)
   936                       (inst_thm v exhaust_disc_thm) uncollapse_thms distinct_disc_thmsss
   937                       distinct_disc_thmsss')
   938                   |> singleton (Proof_Context.export names_lthy lthy)
   939                   |> Thm.close_derivation
   940                 end;
   941 
   942               val (split_sel_thm, split_sel_asm_thm) =
   943                 let
   944                   val zss = map (K []) xss;
   945                   val goal = mk_split_goal usel_ctrs zss usel_fs;
   946                   val asm_goal = mk_split_asm_goal usel_ctrs zss usel_fs;
   947 
   948                   val thm = prove_split sel_thmss goal;
   949                   val asm_thm = prove_split_asm asm_goal thm;
   950                 in
   951                   (thm, asm_thm)
   952                 end;
   953 
   954               val case_eq_if_thm =
   955                 let
   956                   val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs usel_fs);
   957                 in
   958                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   959                     mk_case_eq_if_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)
   960                   |> singleton (Proof_Context.export names_lthy lthy)
   961                   |> Thm.close_derivation
   962                 end;
   963             in
   964               (sel_defs, all_sel_thms, sel_thmss, disc_defs, disc_thmss, nontriv_disc_thmss,
   965                discI_thms, nontriv_discI_thms, distinct_disc_thms, distinct_disc_thmsss,
   966                [exhaust_disc_thm], [exhaust_sel_thm], all_collapse_thms, safe_collapse_thms,
   967                [expand_thm], [split_sel_thm], [split_sel_asm_thm], [case_eq_if_thm])
   968             end;
   969 
   970         val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
   971         val cases_type_attr = Attrib.internal (K (Induct.cases_type fcT_name));
   972 
   973         val nontriv_disc_eq_thmss =
   974           map (map (fn th => th RS @{thm eq_False[THEN iffD2]}
   975             handle THM _ => th RS @{thm eq_True[THEN iffD2]})) nontriv_disc_thmss;
   976 
   977         val anonymous_notes =
   978           [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs),
   979            (flat nontriv_disc_eq_thmss, code_nitpicksimp_attrs)]
   980           |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
   981 
   982         val notes =
   983           [(caseN, case_thms, code_nitpicksimp_simp_attrs),
   984            (case_congN, [case_cong_thm], []),
   985            (case_cong_weak_thmsN, [case_cong_weak_thm], cong_attrs),
   986            (case_eq_ifN, case_eq_if_thms, []),
   987            (collapseN, safe_collapse_thms, if ms = [0] then [] else simp_attrs),
   988            (discN, flat nontriv_disc_thmss, simp_attrs),
   989            (discIN, nontriv_discI_thms, []),
   990            (distinctN, distinct_thms, simp_attrs @ inductsimp_attrs),
   991            (distinct_discN, distinct_disc_thms, dest_attrs),
   992            (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
   993            (exhaust_discN, exhaust_disc_thms, [exhaust_case_names_attr]),
   994            (exhaust_selN, exhaust_sel_thms, [exhaust_case_names_attr]),
   995            (expandN, expand_thms, []),
   996            (injectN, inject_thms, iff_attrs @ inductsimp_attrs),
   997            (nchotomyN, [nchotomy_thm], []),
   998            (selN, all_sel_thms, code_nitpicksimp_simp_attrs),
   999            (splitN, [split_thm], []),
  1000            (split_asmN, [split_asm_thm], []),
  1001            (split_selN, split_sel_thms, []),
  1002            (split_sel_asmN, split_sel_asm_thms, []),
  1003            (split_selsN, split_sel_thms @ split_sel_asm_thms, []),
  1004            (splitsN, [split_thm, split_asm_thm], [])]
  1005           |> filter_out (null o #2)
  1006           |> map (fn (thmN, thms, attrs) =>
  1007             ((qualify true (Binding.name thmN), attrs), [(thms, [])]));
  1008 
  1009         val (noted, lthy') =
  1010           lthy
  1011           |> Spec_Rules.add Spec_Rules.Equational ([casex], case_thms)
  1012           |> fold (Spec_Rules.add Spec_Rules.Equational)
  1013             (AList.group (eq_list (op aconv)) (map (`(single o lhs_head_of)) all_sel_thms))
  1014           |> fold (Spec_Rules.add Spec_Rules.Equational)
  1015             (filter_out (null o snd) (map single discs ~~ nontriv_disc_eq_thmss))
  1016           |> Local_Theory.declaration {syntax = false, pervasive = true}
  1017                (fn phi => Case_Translation.register
  1018                   (Morphism.term phi casex) (map (Morphism.term phi) ctrs))
  1019           |> Local_Theory.background_theory (fold (fold Code.del_eqn) [disc_defs, sel_defs])
  1020           |> not no_code ?
  1021              Local_Theory.declaration {syntax = false, pervasive = false}
  1022                (fn phi => Context.mapping
  1023                   (add_ctr_code fcT_name (map (Morphism.typ phi) As)
  1024                      (map (dest_Const o Morphism.term phi) ctrs) (Morphism.fact phi inject_thms)
  1025                      (Morphism.fact phi distinct_thms) (Morphism.fact phi case_thms))
  1026                   I)
  1027           |> Local_Theory.notes (anonymous_notes @ notes)
  1028           (* for "old_datatype_realizer.ML": *)
  1029           |>> name_noted_thms fcT_name exhaustN;
  1030 
  1031         val ctr_sugar =
  1032           {ctrs = ctrs, casex = casex, discs = discs, selss = selss, exhaust = exhaust_thm,
  1033            nchotomy = nchotomy_thm, injects = inject_thms, distincts = distinct_thms,
  1034            case_thms = case_thms, case_cong = case_cong_thm, case_cong_weak = case_cong_weak_thm,
  1035            split = split_thm, split_asm = split_asm_thm, disc_defs = disc_defs,
  1036            disc_thmss = disc_thmss, discIs = discI_thms, sel_defs = sel_defs, sel_thmss = sel_thmss,
  1037            distinct_discsss = distinct_disc_thmsss, exhaust_discs = exhaust_disc_thms,
  1038            exhaust_sels = exhaust_sel_thms, collapses = all_collapse_thms, expands = expand_thms,
  1039            split_sels = split_sel_thms, split_sel_asms = split_sel_asm_thms,
  1040            case_eq_ifs = case_eq_if_thms}
  1041           |> morph_ctr_sugar (substitute_noted_thm noted);
  1042       in
  1043         (ctr_sugar, lthy' |> register_ctr_sugar fcT_name ctr_sugar)
  1044       end;
  1045   in
  1046     (goalss, after_qed, lthy')
  1047   end;
  1048 
  1049 fun free_constructors tacss = (fn (goalss, after_qed, lthy) =>
  1050   map2 (map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])) goalss tacss
  1051   |> (fn thms => after_qed thms lthy)) oo prepare_free_constructors (K I);
  1052 
  1053 val free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
  1054   Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
  1055   prepare_free_constructors Syntax.read_term;
  1056 
  1057 val parse_bound_term = Parse.binding --| @{keyword ":"} -- Parse.term;
  1058 
  1059 val parse_ctr_options =
  1060   Scan.optional (@{keyword "("} |-- Parse.list1
  1061         (Parse.reserved "discs_sels" >> K 0 || Parse.reserved "no_code" >> K 1) --|
  1062       @{keyword ")"}
  1063       >> (fn js => (member (op =) js 0, member (op =) js 1)))
  1064     (false, false);
  1065 
  1066 fun parse_ctr_spec parse_ctr parse_arg =
  1067   parse_opt_binding_colon -- parse_ctr -- Scan.repeat parse_arg;
  1068 
  1069 val parse_ctr_specs = Parse.enum1 "|" (parse_ctr_spec Parse.term Parse.binding);
  1070 val parse_sel_default_eqs = Scan.optional (@{keyword "where"} |-- Parse.enum1 "|" Parse.prop) [];
  1071 
  1072 val _ =
  1073   Outer_Syntax.local_theory_to_proof @{command_spec "free_constructors"}
  1074     "register an existing freely generated type's constructors"
  1075     (parse_ctr_options -- Parse.binding --| @{keyword "for"} -- parse_ctr_specs
  1076        -- parse_sel_default_eqs
  1077      >> free_constructors_cmd);
  1078 
  1079 val _ = Context.>> (Context.map_theory Ctr_Sugar_Interpretation.init);
  1080 
  1081 end;