src/HOL/Tools/BNF/bnf_lfp_compat.ML

 open BNF_Util
 open BNF_FP_Util
 open BNF_FP_Def_Sugar
 open BNF_FP_N2M_Sugar
 
-fun dtyp_of_typ _ (TFree a) = Datatype_Aux.DtTFree a
-  | dtyp_of_typ recTs (T as Type (s, Ts)) =
-    (case find_index (curry (op =) T) recTs of
-      ~1 => Datatype_Aux.DtType (s, map (dtyp_of_typ recTs) Ts)
-    | kk => Datatype_Aux.DtRec kk);
-
 val compatN = "compat_";
 
 val code_nitpicksimp_simp_attrs = Code.add_default_eqn_attrib :: @{attributes [nitpick_simp, simp]};
 
 (* TODO: graceful failure for local datatypes -- perhaps by making the command global *)

 
     val (unsorted_As, _) = lthy |> mk_TFrees (length var_As);
     val As = map2 (resort_tfree o Type.sort_of_atyp) var_As unsorted_As;
     val fpTs as fpT1 :: _ = map (fn s => Type (s, As)) fpT_names';
 
-    fun nested_Tindicessss_of parent_Tkks (T as Type (s, _)) kk =
+    fun nested_Tparentss_indicessss_of parent_Tkks (T as Type (s, _)) kk =
       (case try lfp_sugar_of s of
         SOME ({T = T0, fp_res = {Ts = mutual_Ts0, ...}, ctr_sugars, ...}) =>
         let
           val rho = Vartab.fold (cons o apsnd snd) (Sign.typ_match thy (T0, T) Vartab.empty) [];
           val substT = Term.typ_subst_TVars rho;
           val mutual_Ts = map substT mutual_Ts0;
           val mutual_nn = length mutual_Ts;
           val mutual_kks = kk upto kk + mutual_nn - 1;
           val mutual_Tkks = mutual_Ts ~~ mutual_kks;
 
-          fun Tindices_of_ctr_arg parent_Tkks (U as Type (s, _)) (accum as (Tkssss, kk')) =
+          fun indices_of_ctr_arg parent_Tkks (U as Type (s, Us)) (accum as (Tparents_ksss, kk')) =
               if s = @{type_name fun} then
                 if exists_subtype_in mutual_Ts U then
                   (warning "Incomplete support for recursion through functions -- \
                      \the old 'primrec' will fail";
-                   Tindices_of_ctr_arg parent_Tkks (range_type U) accum)
+                   indices_of_ctr_arg parent_Tkks (range_type U) accum)
                 else
                   ([], accum)
               else
                 (case AList.lookup (op =) (parent_Tkks @ mutual_Tkks) U of
                   SOME kk => ([kk], accum)
                 | NONE =>
-                  if exists_subtype_in mutual_Ts U then
-                    ([kk'], nested_Tindicessss_of parent_Tkks U kk' |>> append Tkssss)
+                  if exists (exists_strict_subtype_in mutual_Ts) Us then
+                    error "Deeply nested recursion not supported"
+                  else if exists (member (op =) mutual_Ts) Us then
+                    ([kk'],
+                     nested_Tparentss_indicessss_of parent_Tkks U kk' |>> append Tparents_ksss)
                   else
                     ([], accum))
-            | Tindices_of_ctr_arg _ _ accum = ([], accum);
-
-          fun Tindicesss_of_mutual_type T kk ctr_Tss =
-            fold_map (fold_map (Tindices_of_ctr_arg ((T, kk) :: parent_Tkks))) ctr_Tss
-            #>> pair T;
+            | indices_of_ctr_arg _ _ accum = ([], accum);
+
+          fun Tparents_indicesss_of_mutual_type T kk ctr_Tss =
+            let val parent_Tkks' = (T, kk) :: parent_Tkks in
+              fold_map (fold_map (indices_of_ctr_arg parent_Tkks')) ctr_Tss
+              #>> pair parent_Tkks'
+            end;
 
           val ctrss = map #ctrs ctr_sugars;
           val ctr_Tsss = map (map (binder_types o substT o fastype_of)) ctrss;
         in
           ([], kk + mutual_nn)
-          |> fold_map3 Tindicesss_of_mutual_type mutual_Ts mutual_kks ctr_Tsss
-          |> (fn (Tkkssss, (Tkkssss', kk)) => (Tkkssss @ Tkkssss', kk))
+          |> fold_map3 Tparents_indicesss_of_mutual_type mutual_Ts mutual_kks ctr_Tsss
+          |> (fn (Tparentss_kkssss, (Tparentss_kkssss', kk)) =>
+            (Tparentss_kkssss @ Tparentss_kkssss', kk))
         end
       | NONE => error ("Unsupported recursion via type constructor " ^ quote s ^
           " not corresponding to new-style datatype (cf. \"datatype_new\")"));
 
     fun get_indices (Var ((_, kk), _)) = [kk];
 
-    val (Tkkssss, _) = nested_Tindicessss_of [] fpT1 0;
-    val Ts = map fst Tkkssss;
+    val (Tparentss_kkssss, _) = nested_Tparentss_indicessss_of [] fpT1 0;
+    val Tparentss = map fst Tparentss_kkssss;
+    val Ts = map (fst o hd) Tparentss;
+    val kkssss = map snd Tparentss_kkssss;
 
     val fp_sugars0 = map (lfp_sugar_of o fst o dest_Type) Ts;
     val ctrss0 = map (#ctrs o of_fp_sugar #ctr_sugars) fp_sugars0;
     val ctr_Tsss0 = map (map (binder_types o fastype_of)) ctrss0;
 
     fun apply_comps n kk =
       mk_partial_compN n (replicate n @{typ unit} ---> @{typ unit})
         (Var ((Name.uu, kk), @{typ "unit => unit"}));
 
     val callssss =
-      map2 (map2 (map2 (fn kks => fn ctr_T =>
-          map (apply_comps (num_binder_types ctr_T)) kks)) o snd)
-        Tkkssss ctr_Tsss0;
+      map2 (map2 (map2 (fn kks => fn ctr_T => map (apply_comps (num_binder_types ctr_T)) kks)))
+        kkssss ctr_Tsss0;
 
     val b_names = Name.variant_list [] (map base_name_of_typ Ts);
     val compat_b_names = map (prefix compatN) b_names;
     val compat_bs = map Binding.name compat_b_names;
     val common_name = compatN ^ mk_common_name b_names;
+
     val nn_fp = length fpTs;
     val nn = length Ts;
 
     val ((fp_sugars, (lfp_sugar_thms, _)), lthy) =
       if nn > nn_fp then

 
     val {ctr_sugars, co_inducts = [induct], co_inductss = inductss, co_iterss,
       co_iter_thmsss = iter_thmsss, ...} :: _ = fp_sugars;
     val inducts = map the_single inductss;
 
-    val mk_dtyp = dtyp_of_typ Ts;
-
-    fun mk_ctr_descr Ts = mk_ctr Ts #> dest_Const ##> (binder_types #> map mk_dtyp);
-    fun mk_typ_descr index (Type (T_name, Ts)) ({ctrs, ...} : ctr_sugar) =
-      (index, (T_name, map mk_dtyp Ts, map (mk_ctr_descr Ts) ctrs));
-
-    val descr = map3 mk_typ_descr (0 upto nn - 1) Ts ctr_sugars;
+    fun mk_dtyp [] (TFree a) = Datatype_Aux.DtTFree a
+      | mk_dtyp [] (Type (s, Ts)) = Datatype_Aux.DtType (s, map (mk_dtyp []) Ts)
+      | mk_dtyp [kk] (Type (@{type_name fun}, [T, T'])) =
+        Datatype_Aux.DtType (@{type_name fun}, [mk_dtyp [] T, mk_dtyp [kk] T'])
+      | mk_dtyp [kk] T = if nth Ts kk = T then Datatype_Aux.DtRec kk else mk_dtyp [] T;
+
+    fun mk_ctr_descr Ts kkss ctr0 =
+      mk_ctr Ts ctr0 |> (fn Const (s, T) => (s, map2 mk_dtyp kkss (binder_types T)));
+    fun mk_typ_descr kksss ((Type (T_name, Ts), kk) :: parents) ctrs0 =
+      (kk, (T_name, map (mk_dtyp (map snd (take 1 parents))) Ts, map2 (mk_ctr_descr Ts) kksss ctrs0));
+
+    val descr = map3 mk_typ_descr kkssss Tparentss ctrss0;
     val recs = map (fst o dest_Const o co_rec_of) co_iterss;
     val rec_thms = flat (map co_rec_of iter_thmsss);
 
     fun mk_info ({T = Type (T_name0, _), index, ...} : fp_sugar) =
       let