src/HOL/Tools/Datatype/rep_datatype.ML

 (*  Title:      HOL/Tools/Datatype/rep_datatype.ML
     Author:     Stefan Berghofer, TU Muenchen
 
-Representation of existing types as datatypes.
+Representation of existing types as datatypes: proofs and definitions
+independent of concrete representation of datatypes (i.e. requiring
+only abstract properties: injectivity / distinctness of constructors
+and induction).
 *)
 
 signature REP_DATATYPE =
 sig
   val derive_datatype_props : Datatype_Aux.config -> string list -> Datatype_Aux.descr list ->

     string list -> theory -> Proof.state
 end;
 
 structure Rep_Datatype: REP_DATATYPE =
 struct
+
+type config = Datatype_Aux.config;
+type descr = Datatype_Aux.descr;
+
+
+
+(** derived definitions and proofs **)
+
+(* case distinction theorems *)
+
+fun prove_casedist_thms (config : config) new_type_names descr induct case_names_exhausts thy =
+  let
+    val _ = Datatype_Aux.message config "Proving case distinction theorems ...";
+
+    val descr' = flat descr;
+    val recTs = Datatype_Aux.get_rec_types descr';
+    val newTs = take (length (hd descr)) recTs;
+
+    val maxidx = Thm.maxidx_of induct;
+    val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
+
+    fun prove_casedist_thm (i, (T, t)) =
+      let
+        val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) =>
+          Abs ("z", T', Const (@{const_name True}, T''))) induct_Ps;
+        val P =
+          Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx + 1), T), Bound 0) $
+            Var (("P", 0), HOLogic.boolT));
+        val insts = take i dummyPs @ (P :: drop (i + 1) dummyPs);
+        val cert = cterm_of thy;
+        val insts' = map cert induct_Ps ~~ map cert insts;
+        val induct' =
+          refl RS
+            (nth (Datatype_Aux.split_conj_thm (cterm_instantiate insts' induct)) i RSN (2, rev_mp));
+      in
+        Skip_Proof.prove_global thy []
+          (Logic.strip_imp_prems t)
+          (Logic.strip_imp_concl t)
+          (fn {prems, ...} =>
+            EVERY
+              [rtac induct' 1,
+               REPEAT (rtac TrueI 1),
+               REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)),
+               REPEAT (rtac TrueI 1)])
+      end;
+
+    val casedist_thms =
+      map_index prove_casedist_thm (newTs ~~ Datatype_Prop.make_casedists descr);
+  in
+    thy
+    |> Datatype_Aux.store_thms_atts "exhaust" new_type_names
+        (map single case_names_exhausts) casedist_thms
+  end;
+
+
+(* primrec combinators *)
+
+fun prove_primrec_thms (config : config) new_type_names descr
+    injects_of constr_inject (dist_rewrites, other_dist_rewrites) induct thy =
+  let
+    val _ = Datatype_Aux.message config "Constructing primrec combinators ...";
+
+    val big_name = space_implode "_" new_type_names;
+    val thy0 = Sign.add_path big_name thy;
+
+    val descr' = flat descr;
+    val recTs = Datatype_Aux.get_rec_types descr';
+    val used = fold Term.add_tfree_namesT recTs [];
+    val newTs = take (length (hd descr)) recTs;
+
+    val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
+
+    val big_rec_name' = big_name ^ "_rec_set";
+    val rec_set_names' =
+      if length descr' = 1 then [big_rec_name']
+      else map (prefix (big_rec_name' ^ "_") o string_of_int) (1 upto length descr');
+    val rec_set_names = map (Sign.full_bname thy0) rec_set_names';
+
+    val (rec_result_Ts, reccomb_fn_Ts) = Datatype_Prop.make_primrec_Ts descr used;
+
+    val rec_set_Ts =
+      map (fn (T1, T2) => (reccomb_fn_Ts @ [T1, T2]) ---> HOLogic.boolT) (recTs ~~ rec_result_Ts);
+
+    val rec_fns =
+      map (uncurry (Datatype_Aux.mk_Free "f")) (reccomb_fn_Ts ~~ (1 upto length reccomb_fn_Ts));
+    val rec_sets' =
+      map (fn c => list_comb (Free c, rec_fns)) (rec_set_names' ~~ rec_set_Ts);
+    val rec_sets =
+      map (fn c => list_comb (Const c, rec_fns)) (rec_set_names ~~ rec_set_Ts);
+
+    (* introduction rules for graph of primrec function *)
+
+    fun make_rec_intr T rec_set (cname, cargs) (rec_intr_ts, l) =
+      let
+        fun mk_prem (dt, U) (j, k, prems, t1s, t2s) =
+          let val free1 = Datatype_Aux.mk_Free "x" U j in
+            (case (Datatype_Aux.strip_dtyp dt, strip_type U) of
+              ((_, Datatype_Aux.DtRec m), (Us, _)) =>
+                let
+                  val free2 = Datatype_Aux.mk_Free "y" (Us ---> nth rec_result_Ts m) k;
+                  val i = length Us;
+                in
+                  (j + 1, k + 1,
+                    HOLogic.mk_Trueprop (HOLogic.list_all
+                      (map (pair "x") Us, nth rec_sets' m $
+                        Datatype_Aux.app_bnds free1 i $ Datatype_Aux.app_bnds free2 i)) :: prems,
+                    free1 :: t1s, free2 :: t2s)
+                end
+            | _ => (j + 1, k, prems, free1 :: t1s, t2s))
+          end;
+
+        val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs;
+        val (_, _, prems, t1s, t2s) = fold_rev mk_prem (cargs ~~ Ts) (1, 1, [], [], []);
+
+      in
+        (rec_intr_ts @
+          [Logic.list_implies (prems, HOLogic.mk_Trueprop
+            (rec_set $ list_comb (Const (cname, Ts ---> T), t1s) $
+              list_comb (nth rec_fns l, t1s @ t2s)))], l + 1)
+      end;
+
+    val (rec_intr_ts, _) =
+      fold (fn ((d, T), set_name) =>
+        fold (make_rec_intr T set_name) (#3 (snd d))) (descr' ~~ recTs ~~ rec_sets') ([], 0);
+
+    val ({intrs = rec_intrs, elims = rec_elims, ...}, thy1) =
+      thy0
+      |> Sign.map_naming Name_Space.conceal
+      |> Inductive.add_inductive_global
+          {quiet_mode = #quiet config, verbose = false, alt_name = Binding.name big_rec_name',
+            coind = false, no_elim = false, no_ind = true, skip_mono = true, fork_mono = false}
+          (map (fn (s, T) => ((Binding.name s, T), NoSyn)) (rec_set_names' ~~ rec_set_Ts))
+          (map dest_Free rec_fns)
+          (map (fn x => (Attrib.empty_binding, x)) rec_intr_ts) []
+      ||> Sign.restore_naming thy0
+      ||> Theory.checkpoint;
+
+    (* prove uniqueness and termination of primrec combinators *)
+
+    val _ = Datatype_Aux.message config "Proving termination and uniqueness of primrec functions ...";
+
+    fun mk_unique_tac ((((i, (tname, _, constrs)), elim), T), T') (tac, intrs) =
+      let
+        val distinct_tac =
+          if i < length newTs then
+            full_simp_tac (HOL_ss addsimps (nth dist_rewrites i)) 1
+          else full_simp_tac (HOL_ss addsimps (flat other_dist_rewrites)) 1;
+
+        val inject =
+          map (fn r => r RS iffD1)
+            (if i < length newTs then nth constr_inject i else injects_of tname);
+
+        fun mk_unique_constr_tac n (cname, cargs) (tac, intr :: intrs, j) =
+          let
+            val k = length (filter Datatype_Aux.is_rec_type cargs);
+          in
+            (EVERY
+              [DETERM tac,
+                REPEAT (etac ex1E 1), rtac ex1I 1,
+                DEPTH_SOLVE_1 (ares_tac [intr] 1),
+                REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1),
+                etac elim 1,
+                REPEAT_DETERM_N j distinct_tac,
+                TRY (dresolve_tac inject 1),
+                REPEAT (etac conjE 1), hyp_subst_tac 1,
+                REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]),
+                TRY (hyp_subst_tac 1),
+                rtac refl 1,
+                REPEAT_DETERM_N (n - j - 1) distinct_tac],
+              intrs, j + 1)
+          end;
+
+        val (tac', intrs', _) =
+          fold (mk_unique_constr_tac (length constrs)) constrs (tac, intrs, 0);
+      in (tac', intrs') end;
+
+    val rec_unique_thms =
+      let
+        val rec_unique_ts =
+          map (fn (((set_t, T1), T2), i) =>
+            Const (@{const_name Ex1}, (T2 --> HOLogic.boolT) --> HOLogic.boolT) $
+              absfree ("y", T2) (set_t $ Datatype_Aux.mk_Free "x" T1 i $ Free ("y", T2)))
+                (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs));
+        val cert = cterm_of thy1;
+        val insts =
+          map (fn ((i, T), t) => absfree ("x" ^ string_of_int i, T) t)
+            ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts);
+        val induct' = cterm_instantiate (map cert induct_Ps ~~ map cert insts) induct;
+        val (tac, _) =
+          fold mk_unique_tac (descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts)
+            (((rtac induct' THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1 THEN
+                rewrite_goals_tac [mk_meta_eq @{thm choice_eq}], rec_intrs));
+      in
+        Datatype_Aux.split_conj_thm (Skip_Proof.prove_global thy1 [] []
+          (HOLogic.mk_Trueprop (Datatype_Aux.mk_conj rec_unique_ts)) (K tac))
+      end;
+
+    val rec_total_thms = map (fn r => r RS @{thm theI'}) rec_unique_thms;
+
+    (* define primrec combinators *)
+
+    val big_reccomb_name = space_implode "_" new_type_names ^ "_rec";
+    val reccomb_names =
+      map (Sign.full_bname thy1)
+        (if length descr' = 1 then [big_reccomb_name]
+         else map (prefix (big_reccomb_name ^ "_") o string_of_int) (1 upto length descr'));
+    val reccombs =
+      map (fn ((name, T), T') => Const (name, reccomb_fn_Ts @ [T] ---> T'))
+        (reccomb_names ~~ recTs ~~ rec_result_Ts);
+
+    val (reccomb_defs, thy2) =
+      thy1
+      |> Sign.add_consts_i (map (fn ((name, T), T') =>
+            (Binding.name (Long_Name.base_name name), reccomb_fn_Ts @ [T] ---> T', NoSyn))
+            (reccomb_names ~~ recTs ~~ rec_result_Ts))
+      |> (Global_Theory.add_defs false o map Thm.no_attributes)
+          (map
+            (fn ((((name, comb), set), T), T') =>
+              (Binding.name (Long_Name.base_name name ^ "_def"),
+                Logic.mk_equals (comb, fold_rev lambda rec_fns (absfree ("x", T)
+                 (Const (@{const_name The}, (T' --> HOLogic.boolT) --> T') $ absfree ("y", T')
+                   (set $ Free ("x", T) $ Free ("y", T')))))))
+            (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts))
+      ||> Sign.parent_path
+      ||> Theory.checkpoint;
+
+
+    (* prove characteristic equations for primrec combinators *)
+
+    val _ = Datatype_Aux.message config "Proving characteristic theorems for primrec combinators ...";
+
+    val rec_thms =
+      map (fn t =>
+        Skip_Proof.prove_global thy2 [] [] t
+          (fn _ => EVERY
+            [rewrite_goals_tac reccomb_defs,
+             rtac @{thm the1_equality} 1,
+             resolve_tac rec_unique_thms 1,
+             resolve_tac rec_intrs 1,
+             REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)]))
+       (Datatype_Prop.make_primrecs reccomb_names descr thy2);
+  in
+    thy2
+    |> Sign.add_path (space_implode "_" new_type_names)
+    |> Global_Theory.note_thmss ""
+      [((Binding.name "recs", [Nitpick_Simps.add]), [(rec_thms, [])])]
+    ||> Sign.parent_path
+    ||> Theory.checkpoint
+    |-> (fn thms => pair (reccomb_names, maps #2 thms))
+  end;
+
+
+(* case combinators *)
+
+fun prove_case_thms (config : config) new_type_names descr reccomb_names primrec_thms thy =
+  let
+    val _ = Datatype_Aux.message config "Proving characteristic theorems for case combinators ...";
+
+    val thy1 = Sign.add_path (space_implode "_" new_type_names) thy;
+
+    val descr' = flat descr;
+    val recTs = Datatype_Aux.get_rec_types descr';
+    val used = fold Term.add_tfree_namesT recTs [];
+    val newTs = take (length (hd descr)) recTs;
+    val T' = TFree (singleton (Name.variant_list used) "'t", HOLogic.typeS);
+
+    fun mk_dummyT dt = binder_types (Datatype_Aux.typ_of_dtyp descr' dt) ---> T';
+
+    val case_dummy_fns =
+      map (fn (_, (_, _, constrs)) => map (fn (_, cargs) =>
+        let
+          val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs;
+          val Ts' = map mk_dummyT (filter Datatype_Aux.is_rec_type cargs)
+        in Const (@{const_name undefined}, Ts @ Ts' ---> T') end) constrs) descr';
+
+    val case_names = map (fn s => Sign.full_bname thy1 (s ^ "_case")) new_type_names;
+
+    (* define case combinators via primrec combinators *)
+
+    val (case_defs, thy2) =
+      fold (fn ((((i, (_, _, constrs)), T), name), recname) => fn (defs, thy) =>
+          let
+            val (fns1, fns2) = split_list (map (fn ((_, cargs), j) =>
+              let
+                val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs;
+                val Ts' = Ts @ map mk_dummyT (filter Datatype_Aux.is_rec_type cargs);
+                val frees' = map2 (Datatype_Aux.mk_Free "x") Ts' (1 upto length Ts');
+                val frees = take (length cargs) frees';
+                val free = Datatype_Aux.mk_Free "f" (Ts ---> T') j;
+              in
+                (free, fold_rev (absfree o dest_Free) frees' (list_comb (free, frees)))
+              end) (constrs ~~ (1 upto length constrs)));
+
+            val caseT = map (snd o dest_Free) fns1 @ [T] ---> T';
+            val fns = flat (take i case_dummy_fns) @ fns2 @ flat (drop (i + 1) case_dummy_fns);
+            val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T');
+            val decl = ((Binding.name (Long_Name.base_name name), caseT), NoSyn);
+            val def =
+              (Binding.name (Long_Name.base_name name ^ "_def"),
+                Logic.mk_equals (Const (name, caseT),
+                  fold_rev lambda fns1
+                    (list_comb (reccomb,
+                      flat (take i case_dummy_fns) @ fns2 @ flat (drop (i + 1) case_dummy_fns)))));
+            val ([def_thm], thy') =
+              thy
+              |> Sign.declare_const_global decl |> snd
+              |> (Global_Theory.add_defs false o map Thm.no_attributes) [def];
+
+          in (defs @ [def_thm], thy') end)
+        (hd descr ~~ newTs ~~ case_names ~~ take (length newTs) reccomb_names) ([], thy1)
+      ||> Theory.checkpoint;
+
+    val case_thms =
+      (map o map) (fn t =>
+          Skip_Proof.prove_global thy2 [] [] t
+            (fn _ =>
+              EVERY [rewrite_goals_tac (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1]))
+        (Datatype_Prop.make_cases case_names descr thy2);
+  in
+    thy2
+    |> Context.theory_map ((fold o fold) Nitpick_Simps.add_thm case_thms)
+    |> Sign.parent_path
+    |> Datatype_Aux.store_thmss "cases" new_type_names case_thms
+    |-> (fn thmss => pair (thmss, case_names))
+  end;
+
+
+(* case splitting *)
+
+fun prove_split_thms (config : config)
+    new_type_names case_names descr constr_inject dist_rewrites casedist_thms case_thms thy =
+  let
+    val _ = Datatype_Aux.message config "Proving equations for case splitting ...";
+
+    val descr' = flat descr;
+    val recTs = Datatype_Aux.get_rec_types descr';
+    val newTs = take (length (hd descr)) recTs;
+
+    fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'), exhaustion), case_thms'), T) =
+      let
+        val cert = cterm_of thy;
+        val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion)));
+        val exhaustion' = cterm_instantiate [(cert lhs, cert (Free ("x", T)))] exhaustion;
+        val tac =
+          EVERY [rtac exhaustion' 1,
+            ALLGOALS (asm_simp_tac (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))];
+      in
+        (Skip_Proof.prove_global thy [] [] t1 (K tac),
+         Skip_Proof.prove_global thy [] [] t2 (K tac))
+      end;
+
+    val split_thm_pairs =
+      map prove_split_thms
+        (Datatype_Prop.make_splits case_names descr thy ~~ constr_inject ~~
+          dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs);
+
+    val (split_thms, split_asm_thms) = split_list split_thm_pairs
+
+  in
+    thy
+    |> Datatype_Aux.store_thms "split" new_type_names split_thms
+    ||>> Datatype_Aux.store_thms "split_asm" new_type_names split_asm_thms
+    |-> (fn (thms1, thms2) => pair (thms1 ~~ thms2))
+  end;
+
+fun prove_weak_case_congs new_type_names case_names descr thy =
+  let
+    fun prove_weak_case_cong t =
+     Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
+       (fn {prems, ...} => EVERY [rtac (hd prems RS arg_cong) 1]);
+
+    val weak_case_congs =
+      map prove_weak_case_cong (Datatype_Prop.make_weak_case_congs case_names descr thy);
+
+  in thy |> Datatype_Aux.store_thms "weak_case_cong" new_type_names weak_case_congs end;
+
+
+(* additional theorems for TFL *)
+
+fun prove_nchotomys (config : config) new_type_names descr casedist_thms thy =
+  let
+    val _ = Datatype_Aux.message config "Proving additional theorems for TFL ...";
+
+    fun prove_nchotomy (t, exhaustion) =
+      let
+        (* For goal i, select the correct disjunct to attack, then prove it *)
+        fun tac i 0 = EVERY [TRY (rtac disjI1 i), hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i]
+          | tac i n = rtac disjI2 i THEN tac i (n - 1);
+      in
+        Skip_Proof.prove_global thy [] [] t
+          (fn _ =>
+            EVERY [rtac allI 1,
+             Datatype_Aux.exh_tac (K exhaustion) 1,
+             ALLGOALS (fn i => tac i (i - 1))])
+      end;
+
+    val nchotomys =
+      map prove_nchotomy (Datatype_Prop.make_nchotomys descr ~~ casedist_thms);
+
+  in thy |> Datatype_Aux.store_thms "nchotomy" new_type_names nchotomys end;
+
+fun prove_case_congs new_type_names case_names descr nchotomys case_thms thy =
+  let
+    fun prove_case_cong ((t, nchotomy), case_rewrites) =
+      let
+        val Const ("==>", _) $ tm $ _ = t;
+        val Const (@{const_name Trueprop}, _) $ (Const (@{const_name HOL.eq}, _) $ _ $ Ma) = tm;
+        val cert = cterm_of thy;
+        val nchotomy' = nchotomy RS spec;
+        val [v] = Term.add_vars (concl_of nchotomy') [];
+        val nchotomy'' = cterm_instantiate [(cert (Var v), cert Ma)] nchotomy';
+      in
+        Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
+          (fn {prems, ...} =>
+            let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites)) in
+              EVERY [
+                simp_tac (HOL_ss addsimps [hd prems]) 1,
+                cut_facts_tac [nchotomy''] 1,
+                REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1),
+                REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)]
+            end)
+      end;
+
+    val case_congs =
+      map prove_case_cong
+        (Datatype_Prop.make_case_congs case_names descr thy ~~ nchotomys ~~ case_thms);
+
+  in thy |> Datatype_Aux.store_thms "case_cong" new_type_names case_congs end;
+
+
+
+(** derive datatype props **)
+
+local
 
 fun make_dt_info descr induct inducts rec_names rec_rewrites
     (index, (((((((((((_, (tname, _, _))), inject), distinct),
       exhaust), nchotomy), case_name), case_rewrites), case_cong), weak_case_cong),
         (split, split_asm))) =

     case_cong = case_cong,
     weak_case_cong = weak_case_cong,
     split = split,
     split_asm = split_asm});
 
+in
+
 fun derive_datatype_props config dt_names descr induct inject distinct thy1 =
   let
     val thy2 = thy1 |> Theory.checkpoint;
     val flat_descr = flat descr;
     val new_type_names = map Long_Name.base_name dt_names;
     val _ =
       Datatype_Aux.message config
         ("Deriving properties for datatype(s) " ^ commas_quote new_type_names);
 
     val (exhaust, thy3) = thy2
-      |> Datatype_Abs_Proofs.prove_casedist_thms config new_type_names
-        descr induct (Datatype_Data.mk_case_names_exhausts flat_descr dt_names);
+      |> prove_casedist_thms config new_type_names descr induct
+        (Datatype_Data.mk_case_names_exhausts flat_descr dt_names);
     val (nchotomys, thy4) = thy3
-      |> Datatype_Abs_Proofs.prove_nchotomys config new_type_names descr exhaust;
+      |> prove_nchotomys config new_type_names descr exhaust;
     val ((rec_names, rec_rewrites), thy5) = thy4
-      |> Datatype_Abs_Proofs.prove_primrec_thms
-        config new_type_names descr (#inject o the o Symtab.lookup (Datatype_Data.get_all thy4))
-        inject (distinct, Datatype_Data.all_distincts thy2 (Datatype_Aux.get_rec_types flat_descr))
-        induct;
+      |> prove_primrec_thms config new_type_names descr
+        (#inject o the o Symtab.lookup (Datatype_Data.get_all thy4)) inject
+        (distinct, Datatype_Data.all_distincts thy2 (Datatype_Aux.get_rec_types flat_descr)) induct;
     val ((case_rewrites, case_names), thy6) = thy5
-      |> Datatype_Abs_Proofs.prove_case_thms config new_type_names descr rec_names rec_rewrites;
+      |> prove_case_thms config new_type_names descr rec_names rec_rewrites;
     val (case_congs, thy7) = thy6
-      |> Datatype_Abs_Proofs.prove_case_congs new_type_names case_names descr
-        nchotomys case_rewrites;
+      |> prove_case_congs new_type_names case_names descr nchotomys case_rewrites;
     val (weak_case_congs, thy8) = thy7
-      |> Datatype_Abs_Proofs.prove_weak_case_congs new_type_names case_names descr;
+      |> prove_weak_case_congs new_type_names case_names descr;
     val (splits, thy9) = thy8
-      |> Datatype_Abs_Proofs.prove_split_thms
-        config new_type_names case_names descr inject distinct exhaust case_rewrites;
+      |> prove_split_thms config new_type_names case_names descr
+        inject distinct exhaust case_rewrites;
 
     val inducts = Project_Rule.projections (Proof_Context.init_global thy2) induct;
     val dt_infos =
       map_index
         (make_dt_info flat_descr induct inducts rec_names rec_rewrites)

     |> Datatype_Data.interpretation_data (config, dt_names)
     |> Datatype_Case.add_case_tr' case_names
     |> pair dt_names
   end;
 
+end;
+
 
 
 (** declare existing type as datatype **)
 
 local