(*  Title:      HOL/Codatatype/Tools/bnf_wrap.ML

     Author:     Jasmin Blanchette, TU Muenchen

     Copyright   2012

 Wrapping existing datatypes.

 *)

 signature BNF_WRAP =

 sig

   val mk_half_pairss: 'a list -> ('a * 'a) list list

   val mk_ctr: typ list -> term -> term

   val base_name_of_ctr: term -> string

   val wrap_datatype: ({prems: thm list, context: Proof.context} -> tactic) list list ->

     ((bool * term list) * term) *

       (binding list * (binding list list * (binding * term) list list)) -> local_theory ->

     (term list list * thm list * thm list * thm list * thm list * thm list list) * local_theory

   val parse_wrap_options: bool parser

   val parse_bound_term: (binding * string) parser

 end;

 structure BNF_Wrap : BNF_WRAP =

 struct

 open BNF_Util

 open BNF_Wrap_Tactics

 val isN = "is_";

 val unN = "un_";

 fun mk_unN 1 1 suf = unN ^ suf

   | mk_unN _ l suf = unN ^ suf ^ string_of_int l;

 val case_congN = "case_cong";

 val case_eqN = "case_eq";

 val casesN = "cases";

 val collapseN = "collapse";

 val disc_excludeN = "disc_exclude";

 val disc_exhaustN = "disc_exhaust";

 val discsN = "discs";

 val distinctN = "distinct";

 val exhaustN = "exhaust";

 val injectN = "inject";

 val nchotomyN = "nchotomy";

 val selsN = "sels";

 val splitN = "split";

 val split_asmN = "split_asm";

 val weak_case_cong_thmsN = "weak_case_cong";

 val std_binding = @{binding _};

 val induct_simp_attrs = @{attributes [induct_simp]};

 val cong_attrs = @{attributes [cong]};

 val iff_attrs = @{attributes [iff]};

 val safe_elim_attrs = @{attributes [elim!]};

 val simp_attrs = @{attributes [simp]};

 fun pad_list x n xs = xs @ replicate (n - length xs) x;

 fun unflat_lookup eq ys zs = map (map (fn x => nth zs (find_index (curry eq x) ys)));

 fun mk_half_pairss' _ [] = []

   | mk_half_pairss' indent (y :: ys) =

     indent @ fold_rev (cons o single o pair y) ys (mk_half_pairss' ([] :: indent) ys);

 fun mk_half_pairss ys = mk_half_pairss' [[]] ys;

 fun mk_undefined T = Const (@{const_name undefined}, T);

 fun mk_ctr Ts ctr =

   let val Type (_, Ts0) = body_type (fastype_of ctr) in

     Term.subst_atomic_types (Ts0 ~~ Ts) ctr

   end;

 fun base_name_of_ctr c =

   Long_Name.base_name (case head_of c of

       Const (s, _) => s

     | Free (s, _) => s

     | _ => error "Cannot extract name of constructor");

 fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;

 fun prepare_wrap_datatype prep_term (((no_dests, raw_ctrs), raw_case),

     (raw_disc_bindings, (raw_sel_bindingss, raw_sel_defaultss))) no_defs_lthy =

   let

     (* TODO: sanity checks on arguments *)

     (* TODO: attributes (simp, case_names, etc.) *)

     (* TODO: case syntax *)

     (* TODO: integration with function package ("size") *)

     val n = length raw_ctrs;

     val ks = 1 upto n;

     val _ = if n > 0 then () else error "No constructors specified";

     val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;

     val case0 = prep_term no_defs_lthy raw_case;

     val sel_defaultss =

       pad_list [] n (map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss);

     val Type (dataT_name, As0) = body_type (fastype_of (hd ctrs0));

     val data_b = Binding.qualified_name dataT_name;

     val (As, B) =

       no_defs_lthy

       |> mk_TFrees' (map Type.sort_of_atyp As0)

       ||> the_single o fst o mk_TFrees 1;

     val dataT = Type (dataT_name, As);

     val ctrs = map (mk_ctr As) ctrs0;

     val ctr_Tss = map (binder_types o fastype_of) ctrs;

     val ms = map length ctr_Tss;

     val raw_disc_bindings' = pad_list Binding.empty n raw_disc_bindings;

     fun can_really_rely_on_disc k =

       not (Binding.eq_name (nth raw_disc_bindings' (k - 1), Binding.empty)) orelse

       nth ms (k - 1) = 0;

     fun can_rely_on_disc k =

       can_really_rely_on_disc k orelse (k = 1 andalso not (can_really_rely_on_disc 2));

     fun can_omit_disc_binding k m =

       n = 1 orelse m = 0 orelse (n = 2 andalso can_rely_on_disc (3 - k));

     val std_disc_binding =

       Binding.qualify false (Binding.name_of data_b) o Binding.name o prefix isN o base_name_of_ctr;

     val disc_bindings =

       raw_disc_bindings'

       |> map4 (fn k => fn m => fn ctr => fn disc =>

         Option.map (Binding.qualify false (Binding.name_of data_b))

           (if Binding.eq_name (disc, Binding.empty) then

              if can_omit_disc_binding k m then NONE else SOME (std_disc_binding ctr)

            else if Binding.eq_name (disc, std_binding) then

              SOME (std_disc_binding ctr)

            else

              SOME disc)) ks ms ctrs0;

     val no_discs = map is_none disc_bindings;

     val no_discs_at_all = forall I no_discs;

     fun std_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;

     val sel_bindingss =

       pad_list [] n raw_sel_bindingss

       |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>

         Binding.qualify false (Binding.name_of data_b)

           (if Binding.eq_name (sel, Binding.empty) orelse Binding.eq_name (sel, std_binding) then

             std_sel_binding m l ctr

           else

             sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms;

     fun mk_case Ts T =

       let

         val (bindings, body) = strip_type (fastype_of case0)

         val Type (_, Ts0) = List.last bindings

       in Term.subst_atomic_types ((body, T) :: (Ts0 ~~ Ts)) case0 end;

     val casex = mk_case As B;

     val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;

     val ((((((((xss, xss'), yss), fs), gs), (v, v')), w), (p, p')), names_lthy) = no_defs_lthy |>

       mk_Freess' "x" ctr_Tss

       ||>> mk_Freess "y" ctr_Tss

       ||>> mk_Frees "f" case_Ts

       ||>> mk_Frees "g" case_Ts

       ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "v") dataT

       ||>> yield_singleton (mk_Frees "w") dataT

       ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;

     val q = Free (fst p', B --> HOLogic.boolT);

     fun ap_v t = t $ v;

     fun mk_v_eq_v () = HOLogic.mk_eq (v, v);

     val xctrs = map2 (curry Term.list_comb) ctrs xss;

     val yctrs = map2 (curry Term.list_comb) ctrs yss;

     val xfs = map2 (curry Term.list_comb) fs xss;

     val xgs = map2 (curry Term.list_comb) gs xss;

     val eta_fs = map2 eta_expand_arg xss xfs;

     val eta_gs = map2 eta_expand_arg xss xgs;

     val fcase = Term.list_comb (casex, eta_fs);

     val gcase = Term.list_comb (casex, eta_gs);

     val exist_xs_v_eq_ctrs =

       map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (v, xctr))) xctrs xss;

     val unique_disc_no_def = TrueI; (*arbitrary marker*)

     val alternate_disc_no_def = FalseE; (*arbitrary marker*)

     fun alternate_disc_lhs get_disc k =

       HOLogic.mk_not

         (case nth disc_bindings (k - 1) of

           NONE => nth exist_xs_v_eq_ctrs (k - 1)

         | SOME b => get_disc b (k - 1) $ v);

     val (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy') =

       if no_dests then

         (true, [], [], [], [], [], no_defs_lthy)

       else

         let

           fun disc_free b = Free (Binding.name_of b, dataT --> HOLogic.boolT);

           fun disc_spec b exist_xs_v_eq_ctr = mk_Trueprop_eq (disc_free b $ v, exist_xs_v_eq_ctr);

           fun alternate_disc k = Term.lambda v (alternate_disc_lhs (K o disc_free) (3 - k));

           fun mk_default T t =

             let

               val Ts0 = map TFree (Term.add_tfreesT (fastype_of t) []);

               val Ts = map TFree (Term.add_tfreesT T []);

             in Term.subst_atomic_types (Ts0 ~~ Ts) t end;

           fun mk_sel_case_args b proto_sels T =

             map2 (fn Ts => fn k =>

               (case AList.lookup (op =) proto_sels k of

                 NONE =>

                 (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of

                   NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)

                 | SOME t => mk_default (Ts ---> T) t)

               | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;

           fun sel_spec b proto_sels =

             let

               val _ =

                 (case duplicates (op =) (map fst proto_sels) of

                    k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^

                      " for constructor " ^

                      quote (Syntax.string_of_term no_defs_lthy (nth ctrs (k - 1))))

                  | [] => ())

               val T =

                 (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of

                   [T] => T

                 | T :: T' :: _ => error ("Inconsistent range type for selector " ^

                     quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ no_defs_lthy T) ^

                     " vs. " ^ quote (Syntax.string_of_typ no_defs_lthy T')));

             in

               mk_Trueprop_eq (Free (Binding.name_of b, dataT --> T) $ v,

                 Term.list_comb (mk_case As T, mk_sel_case_args b proto_sels T) $ v)

             end;

           val sel_bindings = flat sel_bindingss;

           val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;

           val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);

           val sel_binding_index =

             if all_sels_distinct then 1 upto length sel_bindings

             else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;

           val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);

           val sel_infos =

             AList.group (op =) (sel_binding_index ~~ proto_sels)

             |> sort (int_ord o pairself fst)

             |> map snd |> curry (op ~~) uniq_sel_bindings;

           val sel_bindings = map fst sel_infos;

           fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;

           val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =

             no_defs_lthy

             |> apfst split_list o fold_map4 (fn k => fn m => fn exist_xs_v_eq_ctr =>

               fn NONE =>

                  if n = 1 then pair (Term.lambda v (mk_v_eq_v ()), unique_disc_no_def)

                  else if m = 0 then pair (Term.lambda v exist_xs_v_eq_ctr, refl)

                  else pair (alternate_disc k, alternate_disc_no_def)

                | SOME b => Specification.definition (SOME (b, NONE, NoSyn),

                    ((Thm.def_binding b, []), disc_spec b exist_xs_v_eq_ctr)) #>> apsnd snd)

               ks ms exist_xs_v_eq_ctrs disc_bindings

             ||>> apfst split_list o fold_map (fn (b, proto_sels) =>

               Specification.definition (SOME (b, NONE, NoSyn),

                 ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos

             ||> `Local_Theory.restore;

           val phi = Proof_Context.export_morphism lthy lthy';

           val disc_defs = map (Morphism.thm phi) raw_disc_defs;

           val sel_defs = map (Morphism.thm phi) raw_sel_defs;

           val sel_defss = unflat_selss sel_defs;

           val discs0 = map (Morphism.term phi) raw_discs;

           val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);

           fun mk_disc_or_sel Ts c =

             Term.subst_atomic_types (snd (Term.dest_Type (domain_type (fastype_of c))) ~~ Ts) c;

           val discs = map (mk_disc_or_sel As) discs0;

           val selss = map (map (mk_disc_or_sel As)) selss0;

         in

           (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy')

         end;

     fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);

     val goal_exhaust =

       let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (v, xctr)]) in

         fold_rev Logic.all [p, v] (mk_imp_p (map2 mk_prem xctrs xss))

       end;

     val goal_injectss =

       let

         fun mk_goal _ _ [] [] = []

           | mk_goal xctr yctr xs ys =

             [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),

               Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];

       in

         map4 mk_goal xctrs yctrs xss yss

       end;

     val goal_half_distinctss =

       let

         fun mk_goal ((xs, xc), (xs', xc')) =

           fold_rev Logic.all (xs @ xs')

             (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));

       in

         map (map mk_goal) (mk_half_pairss (xss ~~ xctrs))

       end;

     val goal_cases =

       map3 (fn xs => fn xctr => fn xf =>

         fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xss xctrs xfs;

     val goalss = [goal_exhaust] :: goal_injectss @ goal_half_distinctss @ [goal_cases];

     fun after_qed thmss lthy =

       let

         val ([exhaust_thm], (inject_thmss, (half_distinct_thmss, [case_thms]))) =

           (hd thmss, apsnd (chop (n * n)) (chop n (tl thmss)));

         val inject_thms = flat inject_thmss;

         val exhaust_thm' =

           let val Tinst = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As) in

             Drule.instantiate' [] [SOME (certify lthy v)]

               (Thm.instantiate (Tinst, []) (Drule.zero_var_indexes exhaust_thm))

           end;

         val exhaust_cases = map base_name_of_ctr ctrs;

         val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;

         val (distinct_thmsss', distinct_thmsss) =

           map2 (map2 append) (Library.chop_groups n half_distinct_thmss)

             (transpose (Library.chop_groups n other_half_distinct_thmss))

           |> `transpose;

         val distinct_thms = interleave (flat half_distinct_thmss) (flat other_half_distinct_thmss);

         val nchotomy_thm =

           let

             val goal =

               HOLogic.mk_Trueprop (HOLogic.mk_all (fst v', snd v',

                 Library.foldr1 HOLogic.mk_disj exist_xs_v_eq_ctrs));

           in

             Skip_Proof.prove lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)

           end;

         val (all_sel_thms, sel_thmss, disc_thms, discI_thms, disc_exclude_thms, disc_exhaust_thms,

              collapse_thms, case_eq_thms) =

           if no_dests then

             ([], [], [], [], [], [], [], [])

           else

             let

               fun make_sel_thm xs' case_thm sel_def =

                 zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')

                     (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));

               fun has_undefined_rhs thm =

                 (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of

                   Const (@{const_name undefined}, _) => true

                 | _ => false);

               val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;

               val all_sel_thms =

                 (if all_sels_distinct andalso forall null sel_defaultss then

                    flat sel_thmss

                  else

                    map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs

                      (xss' ~~ case_thms))

                 |> filter_out has_undefined_rhs;

               fun mk_unique_disc_def () =

                 let

                   val m = the_single ms;

                   val goal = mk_Trueprop_eq (mk_v_eq_v (), the_single exist_xs_v_eq_ctrs);

                 in

                   Skip_Proof.prove lthy [] [] goal (fn _ => mk_unique_disc_def_tac m exhaust_thm')

                   |> singleton (Proof_Context.export names_lthy lthy)

                   |> Thm.close_derivation

                 end;

               fun mk_alternate_disc_def k =

                 let

                   val goal =

                     mk_Trueprop_eq (alternate_disc_lhs (K (nth discs)) (3 - k),

                       nth exist_xs_v_eq_ctrs (k - 1));

                 in

                   Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>

                     mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))

                       (nth distinct_thms (2 - k)) exhaust_thm')

                   |> singleton (Proof_Context.export names_lthy lthy)

                   |> Thm.close_derivation

                 end;

               val has_alternate_disc_def =

                 exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;

               val disc_defs' =

                 map2 (fn k => fn def =>

                   if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()

                   else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k

                   else def) ks disc_defs;

               val discD_thms = map (fn def => def RS iffD1) disc_defs';

               val discI_thms =

                 map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms

                   disc_defs';

               val not_discI_thms =

                 map2 (fn m => fn def => funpow m (fn thm => allI RS thm)

                     (Local_Defs.unfold lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))

                   ms disc_defs';

               val (disc_thmss', disc_thmss) =

                 let

                   fun mk_thm discI _ [] = refl RS discI

                     | mk_thm _ not_discI [distinct] = distinct RS not_discI;

                   fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;

                 in

                   map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose

                 end;

               val disc_thms = flat (map2 (fn true => K [] | false => I) no_discs disc_thmss);

               val disc_exclude_thms =

                 if has_alternate_disc_def then

                   []

                 else

                   let

                     fun mk_goal [] = []

                       | mk_goal [((_, true), (_, true))] = []

                       | mk_goal [(((_, disc), _), ((_, disc'), _))] =

                         [Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (betapply (disc, v)),

                            HOLogic.mk_Trueprop (HOLogic.mk_not (betapply (disc', v)))))];

                     fun prove tac goal = Skip_Proof.prove lthy [] [] goal (K tac);

                     val infos = ms ~~ discD_thms ~~ discs ~~ no_discs;

                     val half_pairss = mk_half_pairss infos;

                     val goal_halvess = map mk_goal half_pairss;

                     val half_thmss =

                       map3 (fn [] => K (K []) | [goal] => fn [((((m, discD), _), _), _)] =>

                           fn disc_thm => [prove (mk_half_disc_exclude_tac m discD disc_thm) goal])

                         goal_halvess half_pairss (flat disc_thmss');

                     val goal_other_halvess = map (mk_goal o map swap) half_pairss;

                     val other_half_thmss =

                       map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss

                         goal_other_halvess;

                   in

                     interleave (flat half_thmss) (flat other_half_thmss)

                   end;

               val disc_exhaust_thms =

                 if has_alternate_disc_def orelse no_discs_at_all then

                   []

                 else

                   let

                     fun mk_prem disc = mk_imp_p [HOLogic.mk_Trueprop (betapply (disc, v))];

                     val goal = fold_rev Logic.all [p, v] (mk_imp_p (map mk_prem discs));

                   in

                     [Skip_Proof.prove lthy [] [] goal (fn _ =>

                        mk_disc_exhaust_tac n exhaust_thm discI_thms)]

                   end;

               val collapse_thms =

                 if no_dests then

                   []

                 else

                   let

                     fun mk_goal ctr disc sels =

                       let

                         val prem = HOLogic.mk_Trueprop (betapply (disc, v));

                         val concl =

                           mk_Trueprop_eq ((null sels ? swap)

                             (Term.list_comb (ctr, map ap_v sels), v));

                       in

                         if prem aconv concl then NONE

                         else SOME (Logic.all v (Logic.mk_implies (prem, concl)))

                       end;

                     val goals = map3 mk_goal ctrs discs selss;

                   in

                     map4 (fn m => fn discD => fn sel_thms => Option.map (fn goal =>

                       Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>

                         mk_collapse_tac ctxt m discD sel_thms)

                       |> perhaps (try (fn thm => refl RS thm)))) ms discD_thms sel_thmss goals

                     |> map_filter I

                   end;

               val case_eq_thms =

                 if no_dests then

                   []

                 else

                   let

                     fun mk_body f sels = Term.list_comb (f, map ap_v sels);

                     val goal =

                       mk_Trueprop_eq (fcase $ v, mk_IfN B (map ap_v discs) (map2 mk_body fs selss));

                   in

                     [Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>

                       mk_case_eq_tac ctxt n exhaust_thm' case_thms disc_thmss' sel_thmss)]

                     |> Proof_Context.export names_lthy lthy

                   end;

             in

               (all_sel_thms, sel_thmss, disc_thms, discI_thms, disc_exclude_thms, disc_exhaust_thms,

                collapse_thms, case_eq_thms)

             end;

         val (case_cong_thm, weak_case_cong_thm) =

           let

             fun mk_prem xctr xs f g =

               fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (w, xctr),

                 mk_Trueprop_eq (f, g)));

             val v_eq_w = mk_Trueprop_eq (v, w);

             val goal =

               Logic.list_implies (v_eq_w :: map4 mk_prem xctrs xss fs gs,

                  mk_Trueprop_eq (fcase $ v, gcase $ w));

             val goal_weak = Logic.mk_implies (v_eq_w, mk_Trueprop_eq (fcase $ v, fcase $ w));

           in

             (Skip_Proof.prove lthy [] [] goal (fn _ => mk_case_cong_tac exhaust_thm' case_thms),

              Skip_Proof.prove lthy [] [] goal_weak (K (etac arg_cong 1)))

             |> pairself (singleton (Proof_Context.export names_lthy lthy))

           end;

         val (split_thm, split_asm_thm) =

           let

             fun mk_conjunct xctr xs f_xs =

               list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (v, xctr), q $ f_xs));

             fun mk_disjunct xctr xs f_xs =

               list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (v, xctr),

                 HOLogic.mk_not (q $ f_xs)));

             val lhs = q $ (fcase $ v);

             val goal =

               mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));

             val goal_asm =

               mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj

                 (map3 mk_disjunct xctrs xss xfs)));

             val split_thm =

               Skip_Proof.prove lthy [] [] goal

                 (fn _ => mk_split_tac exhaust_thm' case_thms inject_thmss distinct_thmsss)

               |> singleton (Proof_Context.export names_lthy lthy)

             val split_asm_thm =

               Skip_Proof.prove lthy [] [] goal_asm (fn {context = ctxt, ...} =>

                 mk_split_asm_tac ctxt split_thm)

               |> singleton (Proof_Context.export names_lthy lthy)

           in

             (split_thm, split_asm_thm)

           end;

         val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));

         val cases_type_attr = Attrib.internal (K (Induct.cases_type dataT_name));

         val notes =

           [(case_congN, [case_cong_thm], []),

            (case_eqN, case_eq_thms, []),

            (casesN, case_thms, simp_attrs),

            (collapseN, collapse_thms, simp_attrs),

            (discsN, disc_thms, simp_attrs),

            (disc_excludeN, disc_exclude_thms, []),

            (disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),

            (distinctN, distinct_thms, simp_attrs @ induct_simp_attrs),

            (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),

            (injectN, inject_thms, iff_attrs @ induct_simp_attrs),

            (nchotomyN, [nchotomy_thm], []),

            (selsN, all_sel_thms, simp_attrs),

            (splitN, [split_thm], []),

            (split_asmN, [split_asm_thm], []),

            (weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]

           |> filter_out (null o #2)

           |> map (fn (thmN, thms, attrs) =>

             ((Binding.qualify true (Binding.name_of data_b) (Binding.name thmN), attrs),

              [(thms, [])]));

         val notes' =

           [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs)]

           |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));

       in

         ((selss, inject_thms, distinct_thms, case_thms, discI_thms, sel_thmss),

          lthy |> Local_Theory.notes (notes' @ notes) |> snd)

       end;

   in

     (goalss, after_qed, lthy')

   end;

 fun wrap_datatype tacss = (fn (goalss, after_qed, lthy) =>

   map2 (map2 (Skip_Proof.prove lthy [] [])) goalss tacss

   |> (fn thms => after_qed thms lthy)) oo prepare_wrap_datatype (K I);

 val wrap_datatype_cmd = (fn (goalss, after_qed, lthy) =>

   Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo

   prepare_wrap_datatype Syntax.read_term;

 fun parse_bracket_list parser = @{keyword "["} |-- Parse.list parser --|  @{keyword "]"};

 val parse_bindings = parse_bracket_list Parse.binding;

 val parse_bindingss = parse_bracket_list parse_bindings;

 val parse_bound_term = (Parse.binding --| @{keyword ":"}) -- Parse.term;

 val parse_bound_terms = parse_bracket_list parse_bound_term;

 val parse_bound_termss = parse_bracket_list parse_bound_terms;

 val parse_wrap_options =

   Scan.optional (@{keyword "("} |-- (@{keyword "no_dests"} >> K true) --| @{keyword ")"}) false;

 val _ =

   Outer_Syntax.local_theory_to_proof @{command_spec "wrap_data"} "wraps an existing datatype"

     ((parse_wrap_options -- (@{keyword "["} |-- Parse.list Parse.term --| @{keyword "]"}) --

       Parse.term -- Scan.optional (parse_bindings -- Scan.optional (parse_bindingss --

         Scan.optional parse_bound_termss []) ([], [])) ([], ([], [])))

      >> wrap_datatype_cmd);

 end;