src/HOL/Tools/Ctr_Sugar/ctr_sugar.ML
author blanchet
Mon Aug 18 17:19:58 2014 +0200 (2014-08-18)
changeset 57983 6edc3529bb4e
parent 57882 38bf4de248a6
child 57984 cbe9a16f8e11
permissions -rw-r--r--
reordered some (co)datatype property names for more consistency
     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: 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) ctr_spec = (binding * 'c) * 'a list
    60 
    61   val disc_of_ctr_spec: ('c, 'a) ctr_spec -> binding
    62   val ctr_of_ctr_spec: ('c, 'a) ctr_spec -> 'c
    63   val args_of_ctr_spec: ('c, 'a) ctr_spec -> 'a list
    64 
    65   val fake_local_theory_for_sel_defaults: (binding * typ) list -> Proof.context -> Proof.context
    66   val free_constructors: ({prems: thm list, context: Proof.context} -> tactic) list list ->
    67     (((bool * bool) * binding) * (term, binding) ctr_spec list) * term 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) ctr_spec parser
    72   val parse_sel_default_eqs: string list parser
    73 end;
    74 
    75 structure Ctr_Sugar : CTR_SUGAR =
    76 struct
    77 
    78 open Ctr_Sugar_Util
    79 open Ctr_Sugar_Tactics
    80 open Ctr_Sugar_Code
    81 
    82 type ctr_sugar =
    83   {ctrs: term list,
    84    casex: term,
    85    discs: term list,
    86    selss: term list list,
    87    exhaust: thm,
    88    nchotomy: thm,
    89    injects: thm list,
    90    distincts: thm list,
    91    case_thms: thm list,
    92    case_cong: thm,
    93    case_cong_weak: thm,
    94    split: thm,
    95    split_asm: thm,
    96    disc_defs: thm list,
    97    disc_thmss: thm list list,
    98    discIs: thm list,
    99    sel_defs: thm list,
   100    sel_thmss: thm list list,
   101    distinct_discsss: thm list list list,
   102    exhaust_discs: thm list,
   103    exhaust_sels: thm list,
   104    collapses: thm list,
   105    expands: thm list,
   106    split_sels: thm list,
   107    split_sel_asms: thm list,
   108    case_eq_ifs: thm list};
   109 
   110 fun morph_ctr_sugar phi {ctrs, casex, discs, selss, exhaust, nchotomy, injects, distincts,
   111     case_thms, case_cong, case_cong_weak, split, split_asm, disc_defs, disc_thmss, discIs, sel_defs,
   112     sel_thmss, distinct_discsss, exhaust_discs, exhaust_sels, collapses, expands, split_sels,
   113     split_sel_asms, case_eq_ifs} =
   114   {ctrs = map (Morphism.term phi) ctrs,
   115    casex = Morphism.term phi casex,
   116    discs = map (Morphism.term phi) discs,
   117    selss = map (map (Morphism.term phi)) selss,
   118    exhaust = Morphism.thm phi exhaust,
   119    nchotomy = Morphism.thm phi nchotomy,
   120    injects = map (Morphism.thm phi) injects,
   121    distincts = map (Morphism.thm phi) distincts,
   122    case_thms = map (Morphism.thm phi) case_thms,
   123    case_cong = Morphism.thm phi case_cong,
   124    case_cong_weak = Morphism.thm phi case_cong_weak,
   125    split = Morphism.thm phi split,
   126    split_asm = Morphism.thm phi split_asm,
   127    disc_defs = map (Morphism.thm phi) disc_defs,
   128    disc_thmss = map (map (Morphism.thm phi)) disc_thmss,
   129    discIs = map (Morphism.thm phi) discIs,
   130    sel_defs = map (Morphism.thm phi) sel_defs,
   131    sel_thmss = map (map (Morphism.thm phi)) sel_thmss,
   132    distinct_discsss = map (map (map (Morphism.thm phi))) distinct_discsss,
   133    exhaust_discs = map (Morphism.thm phi) exhaust_discs,
   134    exhaust_sels = map (Morphism.thm phi) exhaust_sels,
   135    collapses = map (Morphism.thm phi) collapses,
   136    expands = map (Morphism.thm phi) expands,
   137    split_sels = map (Morphism.thm phi) split_sels,
   138    split_sel_asms = map (Morphism.thm phi) split_sel_asms,
   139    case_eq_ifs = map (Morphism.thm phi) case_eq_ifs};
   140 
   141 val transfer_ctr_sugar =
   142   morph_ctr_sugar o Morphism.transfer_morphism o Proof_Context.theory_of;
   143 
   144 structure Data = Generic_Data
   145 (
   146   type T = ctr_sugar Symtab.table;
   147   val empty = Symtab.empty;
   148   val extend = I;
   149   fun merge data : T = Symtab.merge (K true) data;
   150 );
   151 
   152 fun ctr_sugar_of ctxt =
   153   Symtab.lookup (Data.get (Context.Proof ctxt))
   154   #> Option.map (transfer_ctr_sugar ctxt);
   155 
   156 fun ctr_sugars_of ctxt =
   157   Symtab.fold (cons o transfer_ctr_sugar ctxt o snd) (Data.get (Context.Proof ctxt)) [];
   158 
   159 fun ctr_sugar_of_case ctxt s =
   160   find_first (fn {casex = Const (s', _), ...} => s' = s | _ => false) (ctr_sugars_of ctxt);
   161 
   162 structure Ctr_Sugar_Interpretation = Interpretation
   163 (
   164   type T = ctr_sugar;
   165   val eq: T * T -> bool = op = o pairself #ctrs;
   166 );
   167 
   168 fun with_repaired_path f (ctr_sugar as {ctrs = ctr1 :: _, ...} : ctr_sugar) thy =
   169   thy
   170   |> Sign.root_path
   171   |> Sign.add_path (Long_Name.qualifier (fst (dest_Type (body_type (fastype_of ctr1)))))
   172   |> (fn thy => f (morph_ctr_sugar (Morphism.transfer_morphism thy) ctr_sugar) thy)
   173   |> Sign.restore_naming thy;
   174 
   175 fun ctr_sugar_interpretation f = Ctr_Sugar_Interpretation.interpretation (with_repaired_path f);
   176 
   177 fun register_ctr_sugar key ctr_sugar =
   178   Local_Theory.declaration {syntax = false, pervasive = true}
   179     (fn phi => Data.map (Symtab.update (key, morph_ctr_sugar phi ctr_sugar)))
   180   #> Local_Theory.background_theory (Ctr_Sugar_Interpretation.data ctr_sugar);
   181 
   182 fun default_register_ctr_sugar_global key ctr_sugar thy =
   183   let val tab = Data.get (Context.Theory thy) in
   184     if Symtab.defined tab key then
   185       thy
   186     else
   187       thy
   188       |> Context.theory_map (Data.put (Symtab.update_new (key, ctr_sugar) tab))
   189       |> Ctr_Sugar_Interpretation.data ctr_sugar
   190   end;
   191 
   192 val isN = "is_";
   193 val unN = "un_";
   194 val notN = "not_";
   195 
   196 fun mk_unN 1 1 suf = unN ^ suf
   197   | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
   198 
   199 val caseN = "case";
   200 val case_congN = "case_cong";
   201 val case_eq_ifN = "case_eq_if";
   202 val collapseN = "collapse";
   203 val discN = "disc";
   204 val discIN = "discI";
   205 val distinctN = "distinct";
   206 val distinct_discN = "distinct_disc";
   207 val exhaustN = "exhaust";
   208 val exhaust_discN = "exhaust_disc";
   209 val expandN = "expand";
   210 val injectN = "inject";
   211 val nchotomyN = "nchotomy";
   212 val selN = "sel";
   213 val exhaust_selN = "exhaust_sel";
   214 val splitN = "split";
   215 val split_asmN = "split_asm";
   216 val split_selN = "split_sel";
   217 val split_sel_asmN = "split_sel_asm";
   218 val splitsN = "splits";
   219 val case_cong_weak_thmsN = "case_cong_weak";
   220 
   221 val cong_attrs = @{attributes [cong]};
   222 val dest_attrs = @{attributes [dest]};
   223 val safe_elim_attrs = @{attributes [elim!]};
   224 val iff_attrs = @{attributes [iff]};
   225 val inductsimp_attrs = @{attributes [induct_simp]};
   226 val nitpicksimp_attrs = @{attributes [nitpick_simp]};
   227 val simp_attrs = @{attributes [simp]};
   228 val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
   229 val code_nitpicksimp_simp_attrs = code_nitpicksimp_attrs @ simp_attrs;
   230 
   231 fun unflat_lookup eq xs ys = map (fn xs' => permute_like_unique eq xs xs' ys);
   232 
   233 fun mk_half_pairss' _ ([], []) = []
   234   | mk_half_pairss' indent (x :: xs, _ :: ys) =
   235     indent @ fold_rev (cons o single o pair x) ys (mk_half_pairss' ([] :: indent) (xs, ys));
   236 
   237 fun mk_half_pairss p = mk_half_pairss' [[]] p;
   238 
   239 fun join_halves n half_xss other_half_xss =
   240   (splice (flat half_xss) (flat other_half_xss),
   241    map2 (map2 append) (Library.chop_groups n half_xss)
   242      (transpose (Library.chop_groups n other_half_xss)));
   243 
   244 fun mk_undefined T = Const (@{const_name undefined}, T);
   245 
   246 fun mk_ctr Ts t =
   247   let val Type (_, Ts0) = body_type (fastype_of t) in
   248     subst_nonatomic_types (Ts0 ~~ Ts) t
   249   end;
   250 
   251 fun mk_case Ts T t =
   252   let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
   253     subst_nonatomic_types ((body, T) :: (Ts0 ~~ Ts)) t
   254   end;
   255 
   256 fun mk_disc_or_sel Ts t =
   257   subst_nonatomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
   258 
   259 val name_of_ctr = name_of_const "constructor";
   260 
   261 fun name_of_disc t =
   262   (case head_of t of
   263     Abs (_, _, @{const Not} $ (t' $ Bound 0)) =>
   264     Long_Name.map_base_name (prefix notN) (name_of_disc t')
   265   | Abs (_, _, Const (@{const_name HOL.eq}, _) $ Bound 0 $ t') =>
   266     Long_Name.map_base_name (prefix isN) (name_of_disc t')
   267   | Abs (_, _, @{const Not} $ (Const (@{const_name HOL.eq}, _) $ Bound 0 $ t')) =>
   268     Long_Name.map_base_name (prefix (notN ^ isN)) (name_of_disc t')
   269   | t' => name_of_const "destructor" t');
   270 
   271 val base_name_of_ctr = Long_Name.base_name o name_of_ctr;
   272 
   273 fun dest_ctr ctxt s t =
   274   let val (f, args) = Term.strip_comb t in
   275     (case ctr_sugar_of ctxt s of
   276       SOME {ctrs, ...} =>
   277       (case find_first (can (fo_match ctxt f)) ctrs of
   278         SOME f' => (f', args)
   279       | NONE => raise Fail "dest_ctr")
   280     | NONE => raise Fail "dest_ctr")
   281   end;
   282 
   283 fun dest_case ctxt s Ts t =
   284   (case Term.strip_comb t of
   285     (Const (c, _), args as _ :: _) =>
   286     (case ctr_sugar_of ctxt s of
   287       SOME (ctr_sugar as {casex = Const (case_name, _), discs = discs0, selss = selss0, ...}) =>
   288       if case_name = c then
   289         let val n = length discs0 in
   290           if n < length args then
   291             let
   292               val (branches, obj :: leftovers) = chop n args;
   293               val discs = map (mk_disc_or_sel Ts) discs0;
   294               val selss = map (map (mk_disc_or_sel Ts)) selss0;
   295               val conds = map (rapp obj) discs;
   296               val branch_argss = map (fn sels => map (rapp obj) sels @ leftovers) selss;
   297               val branches' = map2 (curry Term.betapplys) branches branch_argss;
   298             in
   299               SOME (ctr_sugar, conds, branches')
   300             end
   301           else
   302             NONE
   303         end
   304       else
   305         NONE
   306     | _ => NONE)
   307   | _ => NONE);
   308 
   309 fun const_or_free_name (Const (s, _)) = Long_Name.base_name s
   310   | const_or_free_name (Free (s, _)) = s
   311   | const_or_free_name t = raise TERM ("const_or_free_name", [t])
   312 
   313 fun extract_sel_default ctxt t =
   314   let
   315     fun malformed () =
   316       error ("Malformed selector default value equation: " ^ Syntax.string_of_term ctxt t);
   317 
   318     val ((sel, (ctr, vars)), rhs) =
   319       fst (Term.replace_dummy_patterns (Syntax.check_term ctxt t) 0)
   320       |> HOLogic.dest_eq
   321       |>> (Term.dest_comb
   322         #>> const_or_free_name
   323         ##> (Term.strip_comb #>> (Term.dest_Const #> fst)))
   324       handle TERM _ => malformed ();
   325   in
   326     if forall (is_Free orf is_Var) vars andalso not (has_duplicates (op aconv) vars) then
   327       ((ctr, sel), fold_rev Term.lambda vars rhs)
   328     else
   329       malformed ()
   330   end;
   331 
   332 (* Ideally, we would enrich the context with constants rather than free variables. *)
   333 fun fake_local_theory_for_sel_defaults sel_bTs =
   334   Proof_Context.allow_dummies
   335   #> Proof_Context.add_fixes (map (fn (b, T) => (b, SOME T, NoSyn)) sel_bTs)
   336   #> snd;
   337 
   338 type ('c, 'a) ctr_spec = (binding * 'c) * 'a list;
   339 
   340 fun disc_of_ctr_spec ((disc, _), _) = disc;
   341 fun ctr_of_ctr_spec ((_, ctr), _) = ctr;
   342 fun args_of_ctr_spec (_, args) = args;
   343 
   344 fun prepare_free_constructors prep_term
   345     ((((discs_sels, no_code), raw_case_binding), ctr_specs), sel_default_eqs) no_defs_lthy =
   346   let
   347     (* TODO: sanity checks on arguments *)
   348 
   349     val raw_ctrs = map ctr_of_ctr_spec ctr_specs;
   350     val raw_disc_bindings = map disc_of_ctr_spec ctr_specs;
   351     val raw_sel_bindingss = map args_of_ctr_spec ctr_specs;
   352 
   353     val n = length raw_ctrs;
   354     val ks = 1 upto n;
   355 
   356     val _ = if n > 0 then () else error "No constructors specified";
   357 
   358     val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
   359 
   360     val Type (fcT_name, As0) = body_type (fastype_of (hd ctrs0));
   361     val fc_b_name = Long_Name.base_name fcT_name;
   362     val fc_b = Binding.name fc_b_name;
   363 
   364     fun qualify mandatory = Binding.qualify mandatory fc_b_name;
   365 
   366     fun dest_TFree_or_TVar (TFree sS) = sS
   367       | dest_TFree_or_TVar (TVar ((s, _), S)) = (s, S)
   368       | dest_TFree_or_TVar _ = error "Invalid type argument";
   369 
   370     val (unsorted_As, B) =
   371       no_defs_lthy
   372       |> variant_tfrees (map (fst o dest_TFree_or_TVar) As0)
   373       ||> the_single o fst o mk_TFrees 1;
   374 
   375     val As = map2 (resort_tfree o snd o dest_TFree_or_TVar) As0 unsorted_As;
   376 
   377     val fcT = Type (fcT_name, As);
   378     val ctrs = map (mk_ctr As) ctrs0;
   379     val ctr_Tss = map (binder_types o fastype_of) ctrs;
   380 
   381     val ms = map length ctr_Tss;
   382 
   383     fun can_definitely_rely_on_disc k =
   384       not (Binding.is_empty (nth raw_disc_bindings (k - 1))) orelse nth ms (k - 1) = 0;
   385     fun can_rely_on_disc k =
   386       can_definitely_rely_on_disc k orelse (k = 1 andalso not (can_definitely_rely_on_disc 2));
   387     fun should_omit_disc_binding k = n = 1 orelse (n = 2 andalso can_rely_on_disc (3 - k));
   388 
   389     val equal_binding = @{binding "="};
   390 
   391     fun is_disc_binding_valid b =
   392       not (Binding.is_empty b orelse Binding.eq_name (b, equal_binding));
   393 
   394     val standard_disc_binding = Binding.name o prefix isN o base_name_of_ctr;
   395 
   396     val disc_bindings =
   397       raw_disc_bindings
   398       |> map4 (fn k => fn m => fn ctr => fn disc =>
   399         qualify false
   400           (if Binding.is_empty disc then
   401              if m = 0 then equal_binding
   402              else if should_omit_disc_binding k then disc
   403              else standard_disc_binding ctr
   404            else if Binding.eq_name (disc, standard_binding) then
   405              standard_disc_binding ctr
   406            else
   407              disc)) ks ms ctrs0;
   408 
   409     fun standard_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
   410 
   411     val sel_bindingss =
   412       map3 (fn ctr => fn m => map2 (fn l => fn sel =>
   413         qualify false
   414           (if Binding.is_empty sel orelse Binding.eq_name (sel, standard_binding) then
   415             standard_sel_binding m l ctr
   416           else
   417             sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms raw_sel_bindingss;
   418 
   419     val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
   420 
   421     val (((((((([exh_y], (xss, xss')), yss), fs), gs), [u', v']), [w]), (p, p')), names_lthy) =
   422       no_defs_lthy
   423       |> mk_Frees "y" [fcT] (* for compatibility with "datatype_realizer.ML" *)
   424       ||>> mk_Freess' "x" ctr_Tss
   425       ||>> mk_Freess "y" ctr_Tss
   426       ||>> mk_Frees "f" case_Ts
   427       ||>> mk_Frees "g" case_Ts
   428       ||>> (apfst (map (rpair fcT)) oo Variable.variant_fixes) [fc_b_name, fc_b_name ^ "'"]
   429       ||>> mk_Frees "z" [B]
   430       ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
   431 
   432     val u = Free u';
   433     val v = Free v';
   434     val q = Free (fst p', mk_pred1T B);
   435 
   436     val xctrs = map2 (curry Term.list_comb) ctrs xss;
   437     val yctrs = map2 (curry Term.list_comb) ctrs yss;
   438 
   439     val xfs = map2 (curry Term.list_comb) fs xss;
   440     val xgs = map2 (curry Term.list_comb) gs xss;
   441 
   442     (* TODO: Eta-expension is for compatibility with the old datatype package (but it also provides
   443        nicer names). Consider removing. *)
   444     val eta_fs = map2 (fold_rev Term.lambda) xss xfs;
   445     val eta_gs = map2 (fold_rev Term.lambda) xss xgs;
   446 
   447     val case_binding =
   448       qualify false
   449         (if Binding.is_empty raw_case_binding orelse
   450             Binding.eq_name (raw_case_binding, standard_binding) then
   451            Binding.prefix_name (caseN ^ "_") fc_b
   452          else
   453            raw_case_binding);
   454 
   455     fun mk_case_disj xctr xf xs =
   456       list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr), HOLogic.mk_eq (w, xf)));
   457 
   458     val case_rhs = fold_rev (fold_rev Term.lambda) [fs, [u]]
   459       (Const (@{const_name The}, (B --> HOLogic.boolT) --> B) $
   460          Term.lambda w (Library.foldr1 HOLogic.mk_disj (map3 mk_case_disj xctrs xfs xss)));
   461 
   462     val ((raw_case, (_, raw_case_def)), (lthy', lthy)) = no_defs_lthy
   463       |> Local_Theory.define ((case_binding, NoSyn),
   464         ((Binding.conceal (Thm.def_binding case_binding), []), case_rhs))
   465       ||> `Local_Theory.restore;
   466 
   467     val phi = Proof_Context.export_morphism lthy lthy';
   468 
   469     val case_def = Morphism.thm phi raw_case_def;
   470 
   471     val case0 = Morphism.term phi raw_case;
   472     val casex = mk_case As B case0;
   473 
   474     val fcase = Term.list_comb (casex, fs);
   475 
   476     val ufcase = fcase $ u;
   477     val vfcase = fcase $ v;
   478 
   479     val eta_fcase = Term.list_comb (casex, eta_fs);
   480     val eta_gcase = Term.list_comb (casex, eta_gs);
   481 
   482     val eta_ufcase = eta_fcase $ u;
   483     val eta_vgcase = eta_gcase $ v;
   484 
   485     fun mk_uu_eq () = HOLogic.mk_eq (u, u);
   486 
   487     val uv_eq = mk_Trueprop_eq (u, v);
   488 
   489     val exist_xs_u_eq_ctrs =
   490       map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
   491 
   492     val unique_disc_no_def = TrueI; (*arbitrary marker*)
   493     val alternate_disc_no_def = FalseE; (*arbitrary marker*)
   494 
   495     fun alternate_disc_lhs get_udisc k =
   496       HOLogic.mk_not
   497         (let val b = nth disc_bindings (k - 1) in
   498            if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
   499          end);
   500 
   501     val no_discs_sels =
   502       not discs_sels andalso
   503       forall (forall Binding.is_empty) (raw_disc_bindings :: raw_sel_bindingss) andalso
   504       null sel_default_eqs;
   505 
   506     val (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy') =
   507       if no_discs_sels then
   508         (true, [], [], [], [], [], lthy')
   509       else
   510         let
   511           val all_sel_bindings = flat sel_bindingss;
   512           val num_all_sel_bindings = length all_sel_bindings;
   513           val uniq_sel_bindings = distinct Binding.eq_name all_sel_bindings;
   514           val all_sels_distinct = (length uniq_sel_bindings = num_all_sel_bindings);
   515 
   516           val sel_binding_index =
   517             if all_sels_distinct then
   518               1 upto num_all_sel_bindings
   519             else
   520               map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) all_sel_bindings;
   521 
   522           val all_proto_sels = flat (map3 (fn k => fn xs => map (pair k o pair xs)) ks xss xss);
   523           val sel_infos =
   524             AList.group (op =) (sel_binding_index ~~ all_proto_sels)
   525             |> sort (int_ord o pairself fst)
   526             |> map snd |> curry (op ~~) uniq_sel_bindings;
   527           val sel_bindings = map fst sel_infos;
   528 
   529           val sel_defaults =
   530             if null sel_default_eqs then
   531               []
   532             else
   533               let
   534                 val sel_Ts = map (curry (op -->) fcT o fastype_of o snd o snd o hd o snd) sel_infos;
   535                 val fake_lthy =
   536                   fake_local_theory_for_sel_defaults (sel_bindings ~~ sel_Ts) no_defs_lthy;
   537               in
   538                 map (extract_sel_default fake_lthy o prep_term fake_lthy) sel_default_eqs
   539               end;
   540 
   541           fun disc_free b = Free (Binding.name_of b, mk_pred1T fcT);
   542 
   543           fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
   544 
   545           fun alternate_disc k =
   546             Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
   547 
   548           fun mk_sel_case_args b proto_sels T =
   549             map3 (fn Const (c, _) => fn Ts => fn k =>
   550               (case AList.lookup (op =) proto_sels k of
   551                 NONE =>
   552                 (case filter (curry (op =) (c, Binding.name_of b) o fst) sel_defaults of
   553                   [] => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
   554                 | [(_, t)] => t
   555                 | _ => error "Multiple default values for selector/constructor pair")
   556               | SOME (xs, x) => fold_rev Term.lambda xs x)) ctrs ctr_Tss ks;
   557 
   558           fun sel_spec b proto_sels =
   559             let
   560               val _ =
   561                 (case duplicates (op =) (map fst proto_sels) of
   562                    k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
   563                      " for constructor " ^ quote (Syntax.string_of_term lthy (nth ctrs (k - 1))))
   564                  | [] => ())
   565               val T =
   566                 (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
   567                   [T] => T
   568                 | T :: T' :: _ => error ("Inconsistent range type for selector " ^
   569                     quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ lthy T) ^
   570                     " vs. " ^ quote (Syntax.string_of_typ lthy T')));
   571             in
   572               mk_Trueprop_eq (Free (Binding.name_of b, fcT --> T) $ u,
   573                 Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
   574             end;
   575 
   576           fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
   577 
   578           val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
   579             lthy
   580             |> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
   581                 if Binding.is_empty b then
   582                   if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
   583                   else pair (alternate_disc k, alternate_disc_no_def)
   584                 else if Binding.eq_name (b, equal_binding) then
   585                   pair (Term.lambda u exist_xs_u_eq_ctr, refl)
   586                 else
   587                   Specification.definition (SOME (b, NONE, NoSyn),
   588                     ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
   589               ks exist_xs_u_eq_ctrs disc_bindings
   590             ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
   591               Specification.definition (SOME (b, NONE, NoSyn),
   592                 ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
   593             ||> `Local_Theory.restore;
   594 
   595           val phi = Proof_Context.export_morphism lthy lthy';
   596 
   597           val disc_defs = map (Morphism.thm phi) raw_disc_defs;
   598           val sel_defs = map (Morphism.thm phi) raw_sel_defs;
   599           val sel_defss = unflat_selss sel_defs;
   600 
   601           val discs0 = map (Morphism.term phi) raw_discs;
   602           val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
   603 
   604           val discs = map (mk_disc_or_sel As) discs0;
   605           val selss = map (map (mk_disc_or_sel As)) selss0;
   606         in
   607           (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy')
   608         end;
   609 
   610     fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
   611 
   612     val exhaust_goal =
   613       let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (exh_y, xctr)]) in
   614         fold_rev Logic.all [p, exh_y] (mk_imp_p (map2 mk_prem xctrs xss))
   615       end;
   616 
   617     val inject_goalss =
   618       let
   619         fun mk_goal _ _ [] [] = []
   620           | mk_goal xctr yctr xs ys =
   621             [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
   622               Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
   623       in
   624         map4 mk_goal xctrs yctrs xss yss
   625       end;
   626 
   627     val half_distinct_goalss =
   628       let
   629         fun mk_goal ((xs, xc), (xs', xc')) =
   630           fold_rev Logic.all (xs @ xs')
   631             (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
   632       in
   633         map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
   634       end;
   635 
   636     val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss;
   637 
   638     fun after_qed ([exhaust_thm] :: thmss) lthy =
   639       let
   640         val ((inject_thms, inject_thmss), half_distinct_thmss) = chop n thmss |>> `flat;
   641 
   642         val rho_As = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
   643 
   644         fun inst_thm t thm =
   645           Drule.instantiate' [] [SOME (certify lthy t)]
   646             (Thm.instantiate (rho_As, []) (Drule.zero_var_indexes thm));
   647 
   648         val uexhaust_thm = inst_thm u exhaust_thm;
   649 
   650         val exhaust_cases = map base_name_of_ctr ctrs;
   651 
   652         val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
   653 
   654         val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
   655           join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
   656 
   657         val nchotomy_thm =
   658           let
   659             val goal =
   660               HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
   661                 Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
   662           in
   663             Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
   664             |> Thm.close_derivation
   665           end;
   666 
   667         val case_thms =
   668           let
   669             val goals =
   670               map3 (fn xctr => fn xf => fn xs =>
   671                 fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xctrs xfs xss;
   672           in
   673             map4 (fn k => fn goal => fn injects => fn distinctss =>
   674                 Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   675                   mk_case_tac ctxt n k case_def injects distinctss)
   676                 |> Thm.close_derivation)
   677               ks goals inject_thmss distinct_thmsss
   678           end;
   679 
   680         val (case_cong_thm, case_cong_weak_thm) =
   681           let
   682             fun mk_prem xctr xs xf xg =
   683               fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
   684                 mk_Trueprop_eq (xf, xg)));
   685 
   686             val goal =
   687               Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
   688                  mk_Trueprop_eq (eta_ufcase, eta_vgcase));
   689             val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
   690           in
   691             (Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
   692              Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
   693             |> pairself (singleton (Proof_Context.export names_lthy lthy) #>
   694               Thm.close_derivation)
   695           end;
   696 
   697         val split_lhs = q $ ufcase;
   698 
   699         fun mk_split_conjunct xctr xs f_xs =
   700           list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
   701         fun mk_split_disjunct xctr xs f_xs =
   702           list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
   703             HOLogic.mk_not (q $ f_xs)));
   704 
   705         fun mk_split_goal xctrs xss xfs =
   706           mk_Trueprop_eq (split_lhs, Library.foldr1 HOLogic.mk_conj
   707             (map3 mk_split_conjunct xctrs xss xfs));
   708         fun mk_split_asm_goal xctrs xss xfs =
   709           mk_Trueprop_eq (split_lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
   710             (map3 mk_split_disjunct xctrs xss xfs)));
   711 
   712         fun prove_split selss goal =
   713           Goal.prove_sorry lthy [] [] goal (fn _ =>
   714             mk_split_tac lthy uexhaust_thm case_thms selss inject_thmss distinct_thmsss)
   715           |> singleton (Proof_Context.export names_lthy lthy)
   716           |> Thm.close_derivation;
   717 
   718         fun prove_split_asm asm_goal split_thm =
   719           Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
   720             mk_split_asm_tac ctxt split_thm)
   721           |> singleton (Proof_Context.export names_lthy lthy)
   722           |> Thm.close_derivation;
   723 
   724         val (split_thm, split_asm_thm) =
   725           let
   726             val goal = mk_split_goal xctrs xss xfs;
   727             val asm_goal = mk_split_asm_goal xctrs xss xfs;
   728 
   729             val thm = prove_split (replicate n []) goal;
   730             val asm_thm = prove_split_asm asm_goal thm;
   731           in
   732             (thm, asm_thm)
   733           end;
   734 
   735         val (sel_defs, all_sel_thms, sel_thmss, disc_defs, disc_thmss, nontriv_disc_thmss,
   736              discI_thms, nontriv_discI_thms, distinct_disc_thms, distinct_disc_thmsss,
   737              exhaust_disc_thms, exhaust_sel_thms, all_collapse_thms, safe_collapse_thms,
   738              expand_thms, split_sel_thms, split_sel_asm_thms, case_eq_if_thms) =
   739           if no_discs_sels then
   740             ([], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [])
   741           else
   742             let
   743               val udiscs = map (rapp u) discs;
   744               val uselss = map (map (rapp u)) selss;
   745               val usel_ctrs = map2 (curry Term.list_comb) ctrs uselss;
   746               val usel_fs = map2 (curry Term.list_comb) fs uselss;
   747 
   748               val vdiscs = map (rapp v) discs;
   749               val vselss = map (map (rapp v)) selss;
   750 
   751               fun make_sel_thm xs' case_thm sel_def =
   752                 zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
   753                     (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
   754 
   755               val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
   756 
   757               fun has_undefined_rhs thm =
   758                 (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
   759                   Const (@{const_name undefined}, _) => true
   760                 | _ => false);
   761 
   762               val all_sel_thms =
   763                 (if all_sels_distinct andalso null sel_default_eqs then
   764                    flat sel_thmss
   765                  else
   766                    map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
   767                      (xss' ~~ case_thms))
   768                 |> filter_out has_undefined_rhs;
   769 
   770               fun mk_unique_disc_def () =
   771                 let
   772                   val m = the_single ms;
   773                   val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
   774                 in
   775                   Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
   776                   |> singleton (Proof_Context.export names_lthy lthy)
   777                   |> Thm.close_derivation
   778                 end;
   779 
   780               fun mk_alternate_disc_def k =
   781                 let
   782                   val goal =
   783                     mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
   784                       nth exist_xs_u_eq_ctrs (k - 1));
   785                 in
   786                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   787                     mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
   788                       (nth distinct_thms (2 - k)) uexhaust_thm)
   789                   |> singleton (Proof_Context.export names_lthy lthy)
   790                   |> Thm.close_derivation
   791                 end;
   792 
   793               val has_alternate_disc_def =
   794                 exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
   795 
   796               val disc_defs' =
   797                 map2 (fn k => fn def =>
   798                   if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
   799                   else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
   800                   else def) ks disc_defs;
   801 
   802               val discD_thms = map (fn def => def RS iffD1) disc_defs';
   803               val discI_thms =
   804                 map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
   805                   disc_defs';
   806               val not_discI_thms =
   807                 map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
   808                     (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
   809                   ms disc_defs';
   810 
   811               val (disc_thmss', disc_thmss) =
   812                 let
   813                   fun mk_thm discI _ [] = refl RS discI
   814                     | mk_thm _ not_discI [distinct] = distinct RS not_discI;
   815                   fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
   816                 in
   817                   map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
   818                 end;
   819 
   820               val nontriv_disc_thmss =
   821                 map2 (fn b => if is_disc_binding_valid b then I else K []) disc_bindings disc_thmss;
   822 
   823               fun is_discI_boring b =
   824                 (n = 1 andalso Binding.is_empty b) orelse Binding.eq_name (b, equal_binding);
   825 
   826               val nontriv_discI_thms =
   827                 flat (map2 (fn b => if is_discI_boring b then K [] else single) disc_bindings
   828                   discI_thms);
   829 
   830               val (distinct_disc_thms, (distinct_disc_thmsss', distinct_disc_thmsss)) =
   831                 let
   832                   fun mk_goal [] = []
   833                     | mk_goal [((_, udisc), (_, udisc'))] =
   834                       [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
   835                          HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
   836 
   837                   fun prove tac goal =
   838                     Goal.prove_sorry lthy [] [] goal (K tac)
   839                     |> Thm.close_derivation;
   840 
   841                   val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
   842 
   843                   val half_goalss = map mk_goal half_pairss;
   844                   val half_thmss =
   845                     map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
   846                         fn disc_thm => [prove (mk_half_distinct_disc_tac lthy m discD disc_thm) goal])
   847                       half_goalss half_pairss (flat disc_thmss');
   848 
   849                   val other_half_goalss = map (mk_goal o map swap) half_pairss;
   850                   val other_half_thmss =
   851                     map2 (map2 (prove o mk_other_half_distinct_disc_tac)) half_thmss
   852                       other_half_goalss;
   853                 in
   854                   join_halves n half_thmss other_half_thmss ||> `transpose
   855                   |>> has_alternate_disc_def ? K []
   856                 end;
   857 
   858               val exhaust_disc_thm =
   859                 let
   860                   fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
   861                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
   862                 in
   863                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   864                     mk_exhaust_disc_tac n exhaust_thm discI_thms)
   865                   |> Thm.close_derivation
   866                 end;
   867 
   868               val (safe_collapse_thms, all_collapse_thms) =
   869                 let
   870                   fun mk_goal m udisc usel_ctr =
   871                     let
   872                       val prem = HOLogic.mk_Trueprop udisc;
   873                       val concl = mk_Trueprop_eq ((usel_ctr, u) |> m = 0 ? swap);
   874                     in
   875                       (prem aconv concl, Logic.all u (Logic.mk_implies (prem, concl)))
   876                     end;
   877                   val (trivs, goals) = map3 mk_goal ms udiscs usel_ctrs |> split_list;
   878                   val thms =
   879                     map5 (fn m => fn discD => fn sel_thms => fn triv => fn goal =>
   880                         Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   881                           mk_collapse_tac ctxt m discD sel_thms ORELSE HEADGOAL atac)
   882                         |> Thm.close_derivation
   883                         |> not triv ? perhaps (try (fn thm => refl RS thm)))
   884                       ms discD_thms sel_thmss trivs goals;
   885                 in
   886                   (map_filter (fn (true, _) => NONE | (false, thm) => SOME thm) (trivs ~~ thms),
   887                    thms)
   888                 end;
   889 
   890               val swapped_all_collapse_thms =
   891                 map2 (fn m => fn thm => if m = 0 then thm else thm RS sym) ms all_collapse_thms;
   892 
   893               val exhaust_sel_thm =
   894                 let
   895                   fun mk_prem usel_ctr = mk_imp_p [mk_Trueprop_eq (u, usel_ctr)];
   896                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem usel_ctrs));
   897                 in
   898                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   899                     mk_exhaust_sel_tac n exhaust_disc_thm swapped_all_collapse_thms)
   900                   |> Thm.close_derivation
   901                 end;
   902 
   903               val expand_thm =
   904                 let
   905                   fun mk_prems k udisc usels vdisc vsels =
   906                     (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
   907                     (if null usels then
   908                        []
   909                      else
   910                        [Logic.list_implies
   911                           (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
   912                              HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
   913                                (map2 (curry HOLogic.mk_eq) usels vsels)))]);
   914 
   915                   val goal =
   916                     Library.foldr Logic.list_implies
   917                       (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
   918                   val uncollapse_thms =
   919                     map2 (fn thm => fn [] => thm | _ => thm RS sym) all_collapse_thms uselss;
   920                 in
   921                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   922                     mk_expand_tac lthy n ms (inst_thm u exhaust_disc_thm)
   923                       (inst_thm v exhaust_disc_thm) uncollapse_thms distinct_disc_thmsss
   924                       distinct_disc_thmsss')
   925                   |> singleton (Proof_Context.export names_lthy lthy)
   926                   |> Thm.close_derivation
   927                 end;
   928 
   929               val (split_sel_thm, split_sel_asm_thm) =
   930                 let
   931                   val zss = map (K []) xss;
   932                   val goal = mk_split_goal usel_ctrs zss usel_fs;
   933                   val asm_goal = mk_split_asm_goal usel_ctrs zss usel_fs;
   934 
   935                   val thm = prove_split sel_thmss goal;
   936                   val asm_thm = prove_split_asm asm_goal thm;
   937                 in
   938                   (thm, asm_thm)
   939                 end;
   940 
   941               val case_eq_if_thm =
   942                 let
   943                   val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs usel_fs);
   944                 in
   945                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   946                     mk_case_eq_if_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)
   947                   |> singleton (Proof_Context.export names_lthy lthy)
   948                   |> Thm.close_derivation
   949                 end;
   950             in
   951               (sel_defs, all_sel_thms, sel_thmss, disc_defs, disc_thmss, nontriv_disc_thmss,
   952                discI_thms, nontriv_discI_thms, distinct_disc_thms, distinct_disc_thmsss,
   953                [exhaust_disc_thm], [exhaust_sel_thm], all_collapse_thms, safe_collapse_thms,
   954                [expand_thm], [split_sel_thm], [split_sel_asm_thm], [case_eq_if_thm])
   955             end;
   956 
   957         val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
   958         val cases_type_attr = Attrib.internal (K (Induct.cases_type fcT_name));
   959 
   960         val nontriv_disc_eq_thmss =
   961           map (map (fn th => th RS @{thm eq_False[THEN iffD2]}
   962             handle THM _ => th RS @{thm eq_True[THEN iffD2]})) nontriv_disc_thmss;
   963 
   964         val anonymous_notes =
   965           [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs),
   966            (flat nontriv_disc_eq_thmss, code_nitpicksimp_attrs)]
   967           |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
   968 
   969         val notes =
   970           [(caseN, case_thms, code_nitpicksimp_simp_attrs),
   971            (case_congN, [case_cong_thm], []),
   972            (case_cong_weak_thmsN, [case_cong_weak_thm], cong_attrs),
   973            (case_eq_ifN, case_eq_if_thms, []),
   974            (collapseN, safe_collapse_thms, simp_attrs),
   975            (discN, flat nontriv_disc_thmss, simp_attrs),
   976            (discIN, nontriv_discI_thms, []),
   977            (distinctN, distinct_thms, simp_attrs @ inductsimp_attrs),
   978            (distinct_discN, distinct_disc_thms, dest_attrs),
   979            (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
   980            (exhaust_discN, exhaust_disc_thms, [exhaust_case_names_attr]),
   981            (exhaust_selN, exhaust_sel_thms, [exhaust_case_names_attr]),
   982            (expandN, expand_thms, []),
   983            (injectN, inject_thms, iff_attrs @ inductsimp_attrs),
   984            (nchotomyN, [nchotomy_thm], []),
   985            (selN, all_sel_thms, code_nitpicksimp_simp_attrs),
   986            (split_selN, split_sel_thms, []),
   987            (split_sel_asmN, split_sel_asm_thms, []),
   988            (splitN, [split_thm], []),
   989            (split_asmN, [split_asm_thm], []),
   990            (splitsN, [split_thm, split_asm_thm], [])]
   991           |> filter_out (null o #2)
   992           |> map (fn (thmN, thms, attrs) =>
   993             ((qualify true (Binding.name thmN), attrs), [(thms, [])]));
   994 
   995         val (noted, lthy') =
   996           lthy
   997           |> Spec_Rules.add Spec_Rules.Equational ([casex], case_thms)
   998           |> fold (Spec_Rules.add Spec_Rules.Equational)
   999             (AList.group (eq_list (op aconv)) (map (`(single o lhs_head_of)) all_sel_thms))
  1000           |> fold (Spec_Rules.add Spec_Rules.Equational)
  1001             (filter_out (null o snd) (map single discs ~~ nontriv_disc_eq_thmss))
  1002           |> Local_Theory.declaration {syntax = false, pervasive = true}
  1003                (fn phi => Case_Translation.register
  1004                   (Morphism.term phi casex) (map (Morphism.term phi) ctrs))
  1005           |> Local_Theory.background_theory (fold (fold Code.del_eqn) [disc_defs, sel_defs])
  1006           |> not no_code ?
  1007              Local_Theory.declaration {syntax = false, pervasive = false}
  1008                (fn phi => Context.mapping
  1009                   (add_ctr_code fcT_name (map (Morphism.typ phi) As)
  1010                      (map (dest_Const o Morphism.term phi) ctrs) (Morphism.fact phi inject_thms)
  1011                      (Morphism.fact phi distinct_thms) (Morphism.fact phi case_thms))
  1012                   I)
  1013           |> Local_Theory.notes (anonymous_notes @ notes)
  1014           (* for "datatype_realizer.ML": *)
  1015           |>> name_noted_thms fcT_name exhaustN;
  1016 
  1017         val ctr_sugar =
  1018           {ctrs = ctrs, casex = casex, discs = discs, selss = selss, exhaust = exhaust_thm,
  1019            nchotomy = nchotomy_thm, injects = inject_thms, distincts = distinct_thms,
  1020            case_thms = case_thms, case_cong = case_cong_thm, case_cong_weak = case_cong_weak_thm,
  1021            split = split_thm, split_asm = split_asm_thm, disc_defs = disc_defs,
  1022            disc_thmss = disc_thmss, discIs = discI_thms, sel_defs = sel_defs, sel_thmss = sel_thmss,
  1023            distinct_discsss = distinct_disc_thmsss, exhaust_discs = exhaust_disc_thms,
  1024            exhaust_sels = exhaust_sel_thms, collapses = all_collapse_thms, expands = expand_thms,
  1025            split_sels = split_sel_thms, split_sel_asms = split_sel_asm_thms,
  1026            case_eq_ifs = case_eq_if_thms}
  1027           |> morph_ctr_sugar (substitute_noted_thm noted);
  1028       in
  1029         (ctr_sugar, lthy' |> register_ctr_sugar fcT_name ctr_sugar)
  1030       end;
  1031   in
  1032     (goalss, after_qed, lthy')
  1033   end;
  1034 
  1035 fun free_constructors tacss = (fn (goalss, after_qed, lthy) =>
  1036   map2 (map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])) goalss tacss
  1037   |> (fn thms => after_qed thms lthy)) oo prepare_free_constructors (K I);
  1038 
  1039 val free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
  1040   Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
  1041   prepare_free_constructors Syntax.read_term;
  1042 
  1043 val parse_bound_term = Parse.binding --| @{keyword ":"} -- Parse.term;
  1044 
  1045 val parse_ctr_options =
  1046   Scan.optional (@{keyword "("} |-- Parse.list1
  1047         (Parse.reserved "discs_sels" >> K 0 || Parse.reserved "no_code" >> K 1) --|
  1048       @{keyword ")"}
  1049       >> (fn js => (member (op =) js 0, member (op =) js 1)))
  1050     (false, false);
  1051 
  1052 fun parse_ctr_spec parse_ctr parse_arg =
  1053   parse_opt_binding_colon -- parse_ctr -- Scan.repeat parse_arg;
  1054 
  1055 val parse_ctr_specs = Parse.enum1 "|" (parse_ctr_spec Parse.term Parse.binding);
  1056 val parse_sel_default_eqs = Scan.optional (@{keyword "where"} |-- Parse.enum1 "|" Parse.prop) [];
  1057 
  1058 val _ =
  1059   Outer_Syntax.local_theory_to_proof @{command_spec "free_constructors"}
  1060     "register an existing freely generated type's constructors"
  1061     (parse_ctr_options -- Parse.binding --| @{keyword "for"} -- parse_ctr_specs
  1062        -- parse_sel_default_eqs
  1063      >> free_constructors_cmd);
  1064 
  1065 val _ = Context.>> (Context.map_theory Ctr_Sugar_Interpretation.init);
  1066 
  1067 end;