src/HOL/BNF/Tools/bnf_ctr_sugar.ML
author blanchet
Thu Jun 06 15:56:17 2013 +0200 (2013-06-06)
changeset 52322 74315fe137ba
parent 52280 c3f837d92537
child 52375 bae65fd74633
permissions -rw-r--r--
too much qualification is like too little
     1 (*  Title:      HOL/BNF/Tools/bnf_ctr_sugar.ML
     2     Author:     Jasmin Blanchette, TU Muenchen
     3     Copyright   2012
     4 
     5 Wrapping existing freely generated type's constructors.
     6 *)
     7 
     8 signature BNF_CTR_SUGAR =
     9 sig
    10   type ctr_sugar =
    11     {ctrs: term list,
    12      discs: term list,
    13      selss: term list list,
    14      exhaust: thm,
    15      injects: thm list,
    16      distincts: thm list,
    17      case_thms: thm list,
    18      disc_thmss: thm list list,
    19      discIs: thm list,
    20      sel_thmss: thm list list};
    21 
    22   val morph_ctr_sugar: morphism -> ctr_sugar -> ctr_sugar
    23 
    24   val rep_compat_prefix: string
    25 
    26   val mk_half_pairss: 'a list * 'a list -> ('a * 'a) list list
    27   val join_halves: int -> 'a list list -> 'a list list -> 'a list * 'a list list list
    28 
    29   val mk_ctr: typ list -> term -> term
    30   val mk_disc_or_sel: typ list -> term -> term
    31 
    32   val name_of_ctr: term -> string
    33   val name_of_disc: term -> string
    34 
    35   val wrap_free_constructors: ({prems: thm list, context: Proof.context} -> tactic) list list ->
    36     (((bool * bool) * term list) * term) *
    37       (binding list * (binding list list * (binding * term) list list)) -> local_theory ->
    38     ctr_sugar * local_theory
    39   val parse_wrap_options: (bool * bool) parser
    40   val parse_bound_term: (binding * string) parser
    41 end;
    42 
    43 structure BNF_Ctr_Sugar : BNF_CTR_SUGAR =
    44 struct
    45 
    46 open BNF_Util
    47 open BNF_Ctr_Sugar_Tactics
    48 
    49 type ctr_sugar =
    50   {ctrs: term list,
    51    discs: term list,
    52    selss: term list list,
    53    exhaust: thm,
    54    injects: thm list,
    55    distincts: thm list,
    56    case_thms: thm list,
    57    disc_thmss: thm list list,
    58    discIs: thm list,
    59    sel_thmss: thm list list};
    60 
    61 fun morph_ctr_sugar phi {ctrs, discs, selss, exhaust, injects, distincts, case_thms, disc_thmss,
    62     discIs, sel_thmss} =
    63   {ctrs = map (Morphism.term phi) ctrs,
    64    discs = map (Morphism.term phi) discs,
    65    selss = map (map (Morphism.term phi)) selss,
    66    exhaust = Morphism.thm phi exhaust,
    67    injects = map (Morphism.thm phi) injects,
    68    distincts = map (Morphism.thm phi) distincts,
    69    case_thms = map (Morphism.thm phi) case_thms,
    70    disc_thmss = map (map (Morphism.thm phi)) disc_thmss,
    71    discIs = map (Morphism.thm phi) discIs,
    72    sel_thmss = map (map (Morphism.thm phi)) sel_thmss};
    73 
    74 val rep_compat_prefix = "new";
    75 
    76 val isN = "is_";
    77 val unN = "un_";
    78 fun mk_unN 1 1 suf = unN ^ suf
    79   | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
    80 
    81 val caseN = "case";
    82 val case_congN = "case_cong";
    83 val case_convN = "case_conv";
    84 val collapseN = "collapse";
    85 val disc_excludeN = "disc_exclude";
    86 val disc_exhaustN = "disc_exhaust";
    87 val discsN = "discs";
    88 val distinctN = "distinct";
    89 val exhaustN = "exhaust";
    90 val expandN = "expand";
    91 val injectN = "inject";
    92 val nchotomyN = "nchotomy";
    93 val selsN = "sels";
    94 val splitN = "split";
    95 val splitsN = "splits";
    96 val split_asmN = "split_asm";
    97 val weak_case_cong_thmsN = "weak_case_cong";
    98 
    99 val induct_simp_attrs = @{attributes [induct_simp]};
   100 val cong_attrs = @{attributes [cong]};
   101 val iff_attrs = @{attributes [iff]};
   102 val safe_elim_attrs = @{attributes [elim!]};
   103 val simp_attrs = @{attributes [simp]};
   104 
   105 fun unflat_lookup eq = map oo sort_like eq;
   106 
   107 fun mk_half_pairss' _ ([], []) = []
   108   | mk_half_pairss' indent (x :: xs, _ :: ys) =
   109     indent @ fold_rev (cons o single o pair x) ys (mk_half_pairss' ([] :: indent) (xs, ys));
   110 
   111 fun mk_half_pairss p = mk_half_pairss' [[]] p;
   112 
   113 fun join_halves n half_xss other_half_xss =
   114   let
   115     val xsss =
   116       map2 (map2 append) (Library.chop_groups n half_xss)
   117         (transpose (Library.chop_groups n other_half_xss))
   118     val xs = splice (flat half_xss) (flat other_half_xss);
   119   in (xs, xsss) end;
   120 
   121 fun mk_undefined T = Const (@{const_name undefined}, T);
   122 
   123 fun mk_ctr Ts t =
   124   let val Type (_, Ts0) = body_type (fastype_of t) in
   125     Term.subst_atomic_types (Ts0 ~~ Ts) t
   126   end;
   127 
   128 fun mk_disc_or_sel Ts t =
   129   Term.subst_atomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
   130 
   131 fun mk_case Ts T t =
   132   let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
   133     Term.subst_atomic_types ((body, T) :: (Ts0 ~~ Ts)) t
   134   end;
   135 
   136 fun name_of_const what t =
   137   (case head_of t of
   138     Const (s, _) => s
   139   | Free (s, _) => s
   140   | _ => error ("Cannot extract name of " ^ what));
   141 
   142 val name_of_ctr = name_of_const "constructor";
   143 
   144 val notN = "not_";
   145 val eqN = "eq_";
   146 val neqN = "neq_";
   147 
   148 fun name_of_disc t =
   149   (case head_of t of
   150     Abs (_, _, @{const Not} $ (t' $ Bound 0)) =>
   151     Long_Name.map_base_name (prefix notN) (name_of_disc t')
   152   | Abs (_, _, Const (@{const_name HOL.eq}, _) $ Bound 0 $ t') =>
   153     Long_Name.map_base_name (prefix eqN) (name_of_disc t')
   154   | Abs (_, _, @{const Not} $ (Const (@{const_name HOL.eq}, _) $ Bound 0 $ t')) =>
   155     Long_Name.map_base_name (prefix neqN) (name_of_disc t')
   156   | t' => name_of_const "destructor" t');
   157 
   158 val base_name_of_ctr = Long_Name.base_name o name_of_ctr;
   159 
   160 fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
   161 
   162 fun prepare_wrap_free_constructors prep_term ((((no_dests, rep_compat), raw_ctrs), raw_case),
   163     (raw_disc_bindings, (raw_sel_bindingss, raw_sel_defaultss))) no_defs_lthy =
   164   let
   165     (* TODO: sanity checks on arguments *)
   166 
   167     val n = length raw_ctrs;
   168     val ks = 1 upto n;
   169 
   170     val _ = if n > 0 then () else error "No constructors specified";
   171 
   172     val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
   173     val case0 = prep_term no_defs_lthy raw_case;
   174     val sel_defaultss =
   175       pad_list [] n (map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss);
   176 
   177     val case0T = fastype_of case0;
   178     val Type (dataT_name, As0) =
   179       domain_type (snd (strip_typeN (num_binder_types case0T - 1) case0T));
   180     val data_b = Binding.qualified_name dataT_name;
   181     val data_b_name = Binding.name_of data_b;
   182 
   183     fun qualify mandatory =
   184       Binding.qualify mandatory data_b_name o
   185       (rep_compat ? Binding.qualify false rep_compat_prefix);
   186 
   187     val (As, B) =
   188       no_defs_lthy
   189       |> mk_TFrees' (map Type.sort_of_atyp As0)
   190       ||> the_single o fst o mk_TFrees 1;
   191 
   192     val dataT = Type (dataT_name, As);
   193     val ctrs = map (mk_ctr As) ctrs0;
   194     val ctr_Tss = map (binder_types o fastype_of) ctrs;
   195 
   196     val ms = map length ctr_Tss;
   197 
   198     val raw_disc_bindings' = pad_list Binding.empty n raw_disc_bindings;
   199 
   200     fun can_definitely_rely_on_disc k =
   201       not (Binding.is_empty (nth raw_disc_bindings' (k - 1)));
   202     fun can_rely_on_disc k =
   203       can_definitely_rely_on_disc k orelse (k = 1 andalso not (can_definitely_rely_on_disc 2));
   204     fun should_omit_disc_binding k =
   205       n = 1 orelse (n = 2 andalso can_rely_on_disc (3 - k));
   206 
   207     fun is_disc_binding_valid b =
   208       not (Binding.is_empty b orelse Binding.eq_name (b, equal_binding));
   209 
   210     val standard_disc_binding = Binding.name o prefix isN o base_name_of_ctr;
   211 
   212     val disc_bindings =
   213       raw_disc_bindings'
   214       |> map4 (fn k => fn m => fn ctr => fn disc =>
   215         qualify false
   216           (if Binding.is_empty disc then
   217              if should_omit_disc_binding k then disc else standard_disc_binding ctr
   218            else if Binding.eq_name (disc, equal_binding) then
   219              if m = 0 then disc
   220              else error "Cannot use \"=\" syntax for discriminating nonnullary constructor"
   221            else if Binding.eq_name (disc, standard_binding) then
   222              standard_disc_binding ctr
   223            else
   224              disc)) ks ms ctrs0;
   225 
   226     fun standard_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
   227 
   228     val sel_bindingss =
   229       pad_list [] n raw_sel_bindingss
   230       |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
   231         qualify false
   232           (if Binding.is_empty sel orelse Binding.eq_name (sel, standard_binding) then
   233             standard_sel_binding m l ctr
   234           else
   235             sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms;
   236 
   237     val casex = mk_case As B case0;
   238     val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
   239 
   240     val (((((((xss, xss'), yss), fs), gs), [u', v']), (p, p')), names_lthy) = no_defs_lthy |>
   241       mk_Freess' "x" ctr_Tss
   242       ||>> mk_Freess "y" ctr_Tss
   243       ||>> mk_Frees "f" case_Ts
   244       ||>> mk_Frees "g" case_Ts
   245       ||>> (apfst (map (rpair dataT)) oo Variable.variant_fixes) [data_b_name, data_b_name ^ "'"]
   246       ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
   247 
   248     val u = Free u';
   249     val v = Free v';
   250     val q = Free (fst p', mk_pred1T B);
   251 
   252     val xctrs = map2 (curry Term.list_comb) ctrs xss;
   253     val yctrs = map2 (curry Term.list_comb) ctrs yss;
   254 
   255     val xfs = map2 (curry Term.list_comb) fs xss;
   256     val xgs = map2 (curry Term.list_comb) gs xss;
   257 
   258     val fcase = Term.list_comb (casex, fs);
   259 
   260     val ufcase = fcase $ u;
   261     val vfcase = fcase $ v;
   262 
   263     (* TODO: Eta-expension is for compatibility with the old datatype package (but it also provides
   264        nicer names). Consider removing. *)
   265     val eta_fs = map2 eta_expand_arg xss xfs;
   266     val eta_gs = map2 eta_expand_arg xss xgs;
   267 
   268     val eta_fcase = Term.list_comb (casex, eta_fs);
   269     val eta_gcase = Term.list_comb (casex, eta_gs);
   270 
   271     val eta_ufcase = eta_fcase $ u;
   272     val eta_vgcase = eta_gcase $ v;
   273 
   274     fun mk_uu_eq () = HOLogic.mk_eq (u, u);
   275 
   276     val uv_eq = mk_Trueprop_eq (u, v);
   277 
   278     val exist_xs_u_eq_ctrs =
   279       map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
   280 
   281     val unique_disc_no_def = TrueI; (*arbitrary marker*)
   282     val alternate_disc_no_def = FalseE; (*arbitrary marker*)
   283 
   284     fun alternate_disc_lhs get_udisc k =
   285       HOLogic.mk_not
   286         (let val b = nth disc_bindings (k - 1) in
   287            if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
   288          end);
   289 
   290     val (all_sels_distinct, discs, selss, udiscs, uselss, vdiscs, vselss, disc_defs, sel_defs,
   291          sel_defss, lthy') =
   292       if no_dests then
   293         (true, [], [], [], [], [], [], [], [], [], no_defs_lthy)
   294       else
   295         let
   296           fun disc_free b = Free (Binding.name_of b, mk_pred1T dataT);
   297 
   298           fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
   299 
   300           fun alternate_disc k =
   301             Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
   302 
   303           fun mk_sel_case_args b proto_sels T =
   304             map2 (fn Ts => fn k =>
   305               (case AList.lookup (op =) proto_sels k of
   306                 NONE =>
   307                 (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
   308                   NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
   309                 | SOME t => t |> Type.constraint (Ts ---> T) |> Syntax.check_term no_defs_lthy)
   310               | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
   311 
   312           fun sel_spec b proto_sels =
   313             let
   314               val _ =
   315                 (case duplicates (op =) (map fst proto_sels) of
   316                    k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
   317                      " for constructor " ^
   318                      quote (Syntax.string_of_term no_defs_lthy (nth ctrs (k - 1))))
   319                  | [] => ())
   320               val T =
   321                 (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
   322                   [T] => T
   323                 | T :: T' :: _ => error ("Inconsistent range type for selector " ^
   324                     quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ no_defs_lthy T) ^
   325                     " vs. " ^ quote (Syntax.string_of_typ no_defs_lthy T')));
   326             in
   327               mk_Trueprop_eq (Free (Binding.name_of b, dataT --> T) $ u,
   328                 Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
   329             end;
   330 
   331           val sel_bindings = flat sel_bindingss;
   332           val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
   333           val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
   334 
   335           val sel_binding_index =
   336             if all_sels_distinct then 1 upto length sel_bindings
   337             else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
   338 
   339           val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
   340           val sel_infos =
   341             AList.group (op =) (sel_binding_index ~~ proto_sels)
   342             |> sort (int_ord o pairself fst)
   343             |> map snd |> curry (op ~~) uniq_sel_bindings;
   344           val sel_bindings = map fst sel_infos;
   345 
   346           fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
   347 
   348           val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
   349             no_defs_lthy
   350             |> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
   351                 if Binding.is_empty b then
   352                   if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
   353                   else pair (alternate_disc k, alternate_disc_no_def)
   354                 else if Binding.eq_name (b, equal_binding) then
   355                   pair (Term.lambda u exist_xs_u_eq_ctr, refl)
   356                 else
   357                   Specification.definition (SOME (b, NONE, NoSyn),
   358                     ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
   359               ks exist_xs_u_eq_ctrs disc_bindings
   360             ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
   361               Specification.definition (SOME (b, NONE, NoSyn),
   362                 ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
   363             ||> `Local_Theory.restore;
   364 
   365           val phi = Proof_Context.export_morphism lthy lthy';
   366 
   367           val disc_defs = map (Morphism.thm phi) raw_disc_defs;
   368           val sel_defs = map (Morphism.thm phi) raw_sel_defs;
   369           val sel_defss = unflat_selss sel_defs;
   370 
   371           val discs0 = map (Morphism.term phi) raw_discs;
   372           val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
   373 
   374           val discs = map (mk_disc_or_sel As) discs0;
   375           val selss = map (map (mk_disc_or_sel As)) selss0;
   376 
   377           val udiscs = map (rapp u) discs;
   378           val uselss = map (map (rapp u)) selss;
   379 
   380           val vdiscs = map (rapp v) discs;
   381           val vselss = map (map (rapp v)) selss;
   382         in
   383           (all_sels_distinct, discs, selss, udiscs, uselss, vdiscs, vselss, disc_defs, sel_defs,
   384            sel_defss, lthy')
   385         end;
   386 
   387     fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
   388 
   389     val exhaust_goal =
   390       let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (u, xctr)]) in
   391         fold_rev Logic.all [p, u] (mk_imp_p (map2 mk_prem xctrs xss))
   392       end;
   393 
   394     val inject_goalss =
   395       let
   396         fun mk_goal _ _ [] [] = []
   397           | mk_goal xctr yctr xs ys =
   398             [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
   399               Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
   400       in
   401         map4 mk_goal xctrs yctrs xss yss
   402       end;
   403 
   404     val half_distinct_goalss =
   405       let
   406         fun mk_goal ((xs, xc), (xs', xc')) =
   407           fold_rev Logic.all (xs @ xs')
   408             (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
   409       in
   410         map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
   411       end;
   412 
   413     val cases_goal =
   414       map3 (fn xs => fn xctr => fn xf =>
   415         fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xss xctrs xfs;
   416 
   417     val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss @ [cases_goal];
   418 
   419     fun after_qed thmss lthy =
   420       let
   421         val ([exhaust_thm], (inject_thmss, (half_distinct_thmss, [case_thms]))) =
   422           (hd thmss, apsnd (chop (n * n)) (chop n (tl thmss)));
   423 
   424         val inject_thms = flat inject_thmss;
   425 
   426         val Tinst = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
   427 
   428         fun inst_thm t thm =
   429           Drule.instantiate' [] [SOME (certify lthy t)]
   430             (Thm.instantiate (Tinst, []) (Drule.zero_var_indexes thm));
   431 
   432         val uexhaust_thm = inst_thm u exhaust_thm;
   433 
   434         val exhaust_cases = map base_name_of_ctr ctrs;
   435 
   436         val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
   437 
   438         val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
   439           join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
   440 
   441         val nchotomy_thm =
   442           let
   443             val goal =
   444               HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
   445                 Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
   446           in
   447             Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
   448             |> Thm.close_derivation
   449           end;
   450 
   451         val (all_sel_thms, sel_thmss, disc_thmss, disc_thms, discI_thms, disc_exclude_thms,
   452              disc_exhaust_thms, collapse_thms, expand_thms, case_conv_thms) =
   453           if no_dests then
   454             ([], [], [], [], [], [], [], [], [], [])
   455           else
   456             let
   457               fun make_sel_thm xs' case_thm sel_def =
   458                 zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
   459                     (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
   460 
   461               fun has_undefined_rhs thm =
   462                 (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
   463                   Const (@{const_name undefined}, _) => true
   464                 | _ => false);
   465 
   466               val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
   467 
   468               val all_sel_thms =
   469                 (if all_sels_distinct andalso forall null sel_defaultss then
   470                    flat sel_thmss
   471                  else
   472                    map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
   473                      (xss' ~~ case_thms))
   474                 |> filter_out has_undefined_rhs;
   475 
   476               fun mk_unique_disc_def () =
   477                 let
   478                   val m = the_single ms;
   479                   val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
   480                 in
   481                   Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
   482                   |> Thm.close_derivation
   483                   |> singleton (Proof_Context.export names_lthy lthy)
   484                 end;
   485 
   486               fun mk_alternate_disc_def k =
   487                 let
   488                   val goal =
   489                     mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
   490                       nth exist_xs_u_eq_ctrs (k - 1));
   491                 in
   492                   Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   493                     mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
   494                       (nth distinct_thms (2 - k)) uexhaust_thm)
   495                   |> Thm.close_derivation
   496                   |> singleton (Proof_Context.export names_lthy lthy)
   497                 end;
   498 
   499               val has_alternate_disc_def =
   500                 exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
   501 
   502               val disc_defs' =
   503                 map2 (fn k => fn def =>
   504                   if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
   505                   else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
   506                   else def) ks disc_defs;
   507 
   508               val discD_thms = map (fn def => def RS iffD1) disc_defs';
   509               val discI_thms =
   510                 map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
   511                   disc_defs';
   512               val not_discI_thms =
   513                 map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
   514                     (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
   515                   ms disc_defs';
   516 
   517               val (disc_thmss', disc_thmss) =
   518                 let
   519                   fun mk_thm discI _ [] = refl RS discI
   520                     | mk_thm _ not_discI [distinct] = distinct RS not_discI;
   521                   fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
   522                 in
   523                   map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
   524                 end;
   525 
   526               val disc_thms = flat (map2 (fn b => if is_disc_binding_valid b then I else K [])
   527                 disc_bindings disc_thmss);
   528 
   529               val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
   530                 let
   531                   fun mk_goal [] = []
   532                     | mk_goal [((_, udisc), (_, udisc'))] =
   533                       [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
   534                          HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
   535 
   536                   fun prove tac goal =
   537                     Goal.prove_sorry lthy [] [] goal (K tac)
   538                     |> Thm.close_derivation;
   539 
   540                   val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
   541 
   542                   val half_goalss = map mk_goal half_pairss;
   543                   val half_thmss =
   544                     map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
   545                         fn disc_thm => [prove (mk_half_disc_exclude_tac lthy m discD disc_thm) goal])
   546                       half_goalss half_pairss (flat disc_thmss');
   547 
   548                   val other_half_goalss = map (mk_goal o map swap) half_pairss;
   549                   val other_half_thmss =
   550                     map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
   551                       other_half_goalss;
   552                 in
   553                   join_halves n half_thmss other_half_thmss ||> `transpose
   554                   |>> has_alternate_disc_def ? K []
   555                 end;
   556 
   557               val disc_exhaust_thm =
   558                 let
   559                   fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
   560                   val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
   561                 in
   562                   Goal.prove_sorry lthy [] [] goal (fn _ =>
   563                     mk_disc_exhaust_tac n exhaust_thm discI_thms)
   564                   |> Thm.close_derivation
   565                 end;
   566 
   567               val (collapse_thms, collapse_thm_opts) =
   568                 let
   569                   fun mk_goal ctr udisc usels =
   570                     let
   571                       val prem = HOLogic.mk_Trueprop udisc;
   572                       val concl =
   573                         mk_Trueprop_eq ((null usels ? swap) (Term.list_comb (ctr, usels), u));
   574                     in
   575                       if prem aconv concl then NONE
   576                       else SOME (Logic.all u (Logic.mk_implies (prem, concl)))
   577                     end;
   578                   val goals = map3 mk_goal ctrs udiscs uselss;
   579                 in
   580                   map4 (fn m => fn discD => fn sel_thms => Option.map (fn goal =>
   581                     Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   582                       mk_collapse_tac ctxt m discD sel_thms)
   583                     |> Thm.close_derivation
   584                     |> perhaps (try (fn thm => refl RS thm)))) ms discD_thms sel_thmss goals
   585                   |> `(map_filter I)
   586                 end;
   587 
   588               val expand_thms =
   589                 let
   590                   fun mk_prems k udisc usels vdisc vsels =
   591                     (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
   592                     (if null usels then
   593                        []
   594                      else
   595                        [Logic.list_implies
   596                           (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
   597                              HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
   598                                (map2 (curry HOLogic.mk_eq) usels vsels)))]);
   599 
   600                   val goal =
   601                     Library.foldr Logic.list_implies
   602                       (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
   603                   val uncollapse_thms =
   604                     map2 (fn NONE => K asm_rl | SOME thm => fn [] => thm | _ => thm RS sym)
   605                       collapse_thm_opts uselss;
   606                 in
   607                   [Goal.prove_sorry lthy [] [] goal (fn _ =>
   608                      mk_expand_tac lthy n ms (inst_thm u disc_exhaust_thm)
   609                        (inst_thm v disc_exhaust_thm) uncollapse_thms disc_exclude_thmsss
   610                        disc_exclude_thmsss')]
   611                   |> map Thm.close_derivation
   612                   |> Proof_Context.export names_lthy lthy
   613                 end;
   614 
   615               val case_conv_thms =
   616                 let
   617                   fun mk_body f usels = Term.list_comb (f, usels);
   618                   val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs (map2 mk_body fs uselss));
   619                 in
   620                   [Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
   621                      mk_case_conv_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)]
   622                   |> map Thm.close_derivation
   623                   |> Proof_Context.export names_lthy lthy
   624                 end;
   625             in
   626               (all_sel_thms, sel_thmss, disc_thmss, disc_thms, discI_thms, disc_exclude_thms,
   627                [disc_exhaust_thm], collapse_thms, expand_thms, case_conv_thms)
   628             end;
   629 
   630         val (case_cong_thm, weak_case_cong_thm) =
   631           let
   632             fun mk_prem xctr xs xf xg =
   633               fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
   634                 mk_Trueprop_eq (xf, xg)));
   635 
   636             val goal =
   637               Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
   638                  mk_Trueprop_eq (eta_ufcase, eta_vgcase));
   639             val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
   640           in
   641             (Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
   642              Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
   643             |> pairself (Thm.close_derivation #> singleton (Proof_Context.export names_lthy lthy))
   644           end;
   645 
   646         val (split_thm, split_asm_thm) =
   647           let
   648             fun mk_conjunct xctr xs f_xs =
   649               list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
   650             fun mk_disjunct xctr xs f_xs =
   651               list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
   652                 HOLogic.mk_not (q $ f_xs)));
   653 
   654             val lhs = q $ ufcase;
   655 
   656             val goal =
   657               mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));
   658             val asm_goal =
   659               mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
   660                 (map3 mk_disjunct xctrs xss xfs)));
   661 
   662             val split_thm =
   663               Goal.prove_sorry lthy [] [] goal
   664                 (fn _ => mk_split_tac lthy uexhaust_thm case_thms inject_thmss distinct_thmsss)
   665               |> Thm.close_derivation
   666               |> singleton (Proof_Context.export names_lthy lthy);
   667             val split_asm_thm =
   668               Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
   669                 mk_split_asm_tac ctxt split_thm)
   670               |> Thm.close_derivation
   671               |> singleton (Proof_Context.export names_lthy lthy);
   672           in
   673             (split_thm, split_asm_thm)
   674           end;
   675 
   676         val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
   677         val cases_type_attr = Attrib.internal (K (Induct.cases_type dataT_name));
   678 
   679         val notes =
   680           [(caseN, case_thms, simp_attrs),
   681            (case_congN, [case_cong_thm], []),
   682            (case_convN, case_conv_thms, []),
   683            (collapseN, collapse_thms, simp_attrs),
   684            (discsN, disc_thms, simp_attrs),
   685            (disc_excludeN, disc_exclude_thms, []),
   686            (disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
   687            (distinctN, distinct_thms, simp_attrs @ induct_simp_attrs),
   688            (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
   689            (expandN, expand_thms, []),
   690            (injectN, inject_thms, iff_attrs @ induct_simp_attrs),
   691            (nchotomyN, [nchotomy_thm], []),
   692            (selsN, all_sel_thms, simp_attrs),
   693            (splitN, [split_thm], []),
   694            (split_asmN, [split_asm_thm], []),
   695            (splitsN, [split_thm, split_asm_thm], []),
   696            (weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
   697           |> filter_out (null o #2)
   698           |> map (fn (thmN, thms, attrs) =>
   699             ((qualify true (Binding.name thmN), attrs), [(thms, [])]));
   700 
   701         val notes' =
   702           [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs)]
   703           |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
   704       in
   705         ({ctrs = ctrs, discs = discs, selss = selss, exhaust = exhaust_thm, injects = inject_thms,
   706           distincts = distinct_thms, case_thms = case_thms, disc_thmss = disc_thmss,
   707           discIs = discI_thms, sel_thmss = sel_thmss},
   708          lthy
   709          |> not rep_compat ?
   710             (Local_Theory.declaration {syntax = false, pervasive = true}
   711                (fn phi => Case_Translation.register
   712                   (Morphism.term phi casex) (map (Morphism.term phi) ctrs)))
   713          |> Local_Theory.notes (notes' @ notes) |> snd)
   714       end;
   715   in
   716     (goalss, after_qed, lthy')
   717   end;
   718 
   719 fun wrap_free_constructors tacss = (fn (goalss, after_qed, lthy) =>
   720   map2 (map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])) goalss tacss
   721   |> (fn thms => after_qed thms lthy)) oo prepare_wrap_free_constructors (K I);
   722 
   723 val wrap_free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
   724   Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
   725   prepare_wrap_free_constructors Syntax.read_term;
   726 
   727 fun parse_bracket_list parser = @{keyword "["} |-- Parse.list parser --|  @{keyword "]"};
   728 
   729 val parse_bindings = parse_bracket_list parse_binding;
   730 val parse_bindingss = parse_bracket_list parse_bindings;
   731 
   732 val parse_bound_term = (parse_binding --| @{keyword ":"}) -- Parse.term;
   733 val parse_bound_terms = parse_bracket_list parse_bound_term;
   734 val parse_bound_termss = parse_bracket_list parse_bound_terms;
   735 
   736 val parse_wrap_options =
   737   Scan.optional (@{keyword "("} |-- Parse.list1 ((@{keyword "no_dests"} >> K (true, false)) ||
   738       (@{keyword "rep_compat"} >> K (false, true))) --| @{keyword ")"}
   739     >> (pairself (exists I) o split_list)) (false, false);
   740 
   741 val _ =
   742   Outer_Syntax.local_theory_to_proof @{command_spec "wrap_free_constructors"}
   743     "wrap an existing freely generated type's constructors"
   744     ((parse_wrap_options -- (@{keyword "["} |-- Parse.list Parse.term --| @{keyword "]"}) --
   745       Parse.term -- Scan.optional (parse_bindings -- Scan.optional (parse_bindingss --
   746         Scan.optional parse_bound_termss []) ([], [])) ([], ([], [])))
   747      >> wrap_free_constructors_cmd);
   748 
   749 end;