src/HOL/HOLCF/Tools/Domain/domain_induction.ML

       binding list ->
       Domain_Take_Proofs.take_induct_info ->
       Domain_Constructors.constr_info list ->
       theory -> thm list * theory
 
-  val quiet_mode: bool Unsynchronized.ref;
-  val trace_domain: bool Unsynchronized.ref;
-end;
+  val quiet_mode: bool Unsynchronized.ref
+  val trace_domain: bool Unsynchronized.ref
+end
 
 structure Domain_Induction :> DOMAIN_INDUCTION =
 struct
 
-val quiet_mode = Unsynchronized.ref false;
-val trace_domain = Unsynchronized.ref false;
-
-fun message s = if !quiet_mode then () else writeln s;
-fun trace s = if !trace_domain then tracing s else ();
-
-open HOLCF_Library;
+val quiet_mode = Unsynchronized.ref false
+val trace_domain = Unsynchronized.ref false
+
+fun message s = if !quiet_mode then () else writeln s
+fun trace s = if !trace_domain then tracing s else ()
+
+open HOLCF_Library
 
 (******************************************************************************)
 (***************************** proofs about take ******************************)
 (******************************************************************************)
 

     (dbinds : binding list)
     (take_info : Domain_Take_Proofs.take_induct_info)
     (constr_infos : Domain_Constructors.constr_info list)
     (thy : theory) : thm list list * theory =
 let
-  val {take_consts, take_Suc_thms, deflation_take_thms, ...} = take_info;
-  val deflation_thms = Domain_Take_Proofs.get_deflation_thms thy;
-
-  val n = Free ("n", @{typ nat});
-  val n' = @{const Suc} $ n;
+  val {take_consts, take_Suc_thms, deflation_take_thms, ...} = take_info
+  val deflation_thms = Domain_Take_Proofs.get_deflation_thms thy
+
+  val n = Free ("n", @{typ nat})
+  val n' = @{const Suc} $ n
 
   local
-    val newTs = map (#absT o #iso_info) constr_infos;
-    val subs = newTs ~~ map (fn t => t $ n) take_consts;
+    val newTs = map (#absT o #iso_info) constr_infos
+    val subs = newTs ~~ map (fn t => t $ n) take_consts
     fun is_ID (Const (c, _)) = (c = @{const_name ID})
-      | is_ID _              = false;
+      | is_ID _              = false
   in
     fun map_of_arg thy v T =
-      let val m = Domain_Take_Proofs.map_of_typ thy subs T;
-      in if is_ID m then v else mk_capply (m, v) end;
+      let val m = Domain_Take_Proofs.map_of_typ thy subs T
+      in if is_ID m then v else mk_capply (m, v) end
   end
 
   fun prove_take_apps
       ((dbind, take_const), constr_info) thy =
     let
-      val {iso_info, con_specs, con_betas, ...} = constr_info;
-      val {abs_inverse, ...} = iso_info;
+      val {iso_info, con_specs, con_betas, ...} = constr_info
+      val {abs_inverse, ...} = iso_info
       fun prove_take_app (con_const, args) =
         let
-          val Ts = map snd args;
-          val ns = Name.variant_list ["n"] (Datatype_Prop.make_tnames Ts);
-          val vs = map Free (ns ~~ Ts);
-          val lhs = mk_capply (take_const $ n', list_ccomb (con_const, vs));
-          val rhs = list_ccomb (con_const, map2 (map_of_arg thy) vs Ts);
-          val goal = mk_trp (mk_eq (lhs, rhs));
+          val Ts = map snd args
+          val ns = Name.variant_list ["n"] (Datatype_Prop.make_tnames Ts)
+          val vs = map Free (ns ~~ Ts)
+          val lhs = mk_capply (take_const $ n', list_ccomb (con_const, vs))
+          val rhs = list_ccomb (con_const, map2 (map_of_arg thy) vs Ts)
+          val goal = mk_trp (mk_eq (lhs, rhs))
           val rules =
               [abs_inverse] @ con_betas @ @{thms take_con_rules}
-              @ take_Suc_thms @ deflation_thms @ deflation_take_thms;
-          val tac = simp_tac (HOL_basic_ss addsimps rules) 1;
+              @ take_Suc_thms @ deflation_thms @ deflation_take_thms
+          val tac = simp_tac (HOL_basic_ss addsimps rules) 1
         in
           Goal.prove_global thy [] [] goal (K tac)
-        end;
-      val take_apps = map prove_take_app con_specs;
+        end
+      val take_apps = map prove_take_app con_specs
     in
       yield_singleton Global_Theory.add_thmss
         ((Binding.qualified true "take_rews" dbind, take_apps),
         [Simplifier.simp_add]) thy
-    end;
+    end
 in
   fold_map prove_take_apps
     (dbinds ~~ take_consts ~~ constr_infos) thy
-end;
+end
 
 (******************************************************************************)
 (****************************** induction rules *******************************)
 (******************************************************************************)
 
 val case_UU_allI =
-    @{lemma "(!!x. x ~= UU ==> P x) ==> P UU ==> ALL x. P x" by metis};
+    @{lemma "(!!x. x ~= UU ==> P x) ==> P UU ==> ALL x. P x" by metis}
 
 fun prove_induction
     (comp_dbind : binding)
     (constr_infos : Domain_Constructors.constr_info list)
     (take_info : Domain_Take_Proofs.take_induct_info)
     (take_rews : thm list)
     (thy : theory) =
 let
-  val comp_dname = Binding.name_of comp_dbind;
-
-  val iso_infos = map #iso_info constr_infos;
-  val exhausts = map #exhaust constr_infos;
-  val con_rews = maps #con_rews constr_infos;
-  val {take_consts, take_induct_thms, ...} = take_info;
-
-  val newTs = map #absT iso_infos;
-  val P_names = Datatype_Prop.indexify_names (map (K "P") newTs);
-  val x_names = Datatype_Prop.indexify_names (map (K "x") newTs);
-  val P_types = map (fn T => T --> HOLogic.boolT) newTs;
-  val Ps = map Free (P_names ~~ P_types);
-  val xs = map Free (x_names ~~ newTs);
-  val n = Free ("n", HOLogic.natT);
+  val comp_dname = Binding.name_of comp_dbind
+
+  val iso_infos = map #iso_info constr_infos
+  val exhausts = map #exhaust constr_infos
+  val con_rews = maps #con_rews constr_infos
+  val {take_consts, take_induct_thms, ...} = take_info
+
+  val newTs = map #absT iso_infos
+  val P_names = Datatype_Prop.indexify_names (map (K "P") newTs)
+  val x_names = Datatype_Prop.indexify_names (map (K "x") newTs)
+  val P_types = map (fn T => T --> HOLogic.boolT) newTs
+  val Ps = map Free (P_names ~~ P_types)
+  val xs = map Free (x_names ~~ newTs)
+  val n = Free ("n", HOLogic.natT)
 
   fun con_assm defined p (con, args) =
     let
-      val Ts = map snd args;
-      val ns = Name.variant_list P_names (Datatype_Prop.make_tnames Ts);
-      val vs = map Free (ns ~~ Ts);
-      val nonlazy = map snd (filter_out (fst o fst) (args ~~ vs));
+      val Ts = map snd args
+      val ns = Name.variant_list P_names (Datatype_Prop.make_tnames Ts)
+      val vs = map Free (ns ~~ Ts)
+      val nonlazy = map snd (filter_out (fst o fst) (args ~~ vs))
       fun ind_hyp (v, T) t =
           case AList.lookup (op =) (newTs ~~ Ps) T of NONE => t
-          | SOME p' => Logic.mk_implies (mk_trp (p' $ v), t);
-      val t1 = mk_trp (p $ list_ccomb (con, vs));
-      val t2 = fold_rev ind_hyp (vs ~~ Ts) t1;
-      val t3 = Logic.list_implies (map (mk_trp o mk_defined) nonlazy, t2);
-    in fold_rev Logic.all vs (if defined then t3 else t2) end;
+          | SOME p' => Logic.mk_implies (mk_trp (p' $ v), t)
+      val t1 = mk_trp (p $ list_ccomb (con, vs))
+      val t2 = fold_rev ind_hyp (vs ~~ Ts) t1
+      val t3 = Logic.list_implies (map (mk_trp o mk_defined) nonlazy, t2)
+    in fold_rev Logic.all vs (if defined then t3 else t2) end
   fun eq_assms ((p, T), cons) =
-      mk_trp (p $ HOLCF_Library.mk_bottom T) :: map (con_assm true p) cons;
-  val assms = maps eq_assms (Ps ~~ newTs ~~ map #con_specs constr_infos);
-
-  val take_ss = HOL_ss addsimps (@{thm Rep_cfun_strict1} :: take_rews);
+      mk_trp (p $ HOLCF_Library.mk_bottom T) :: map (con_assm true p) cons
+  val assms = maps eq_assms (Ps ~~ newTs ~~ map #con_specs constr_infos)
+
+  val take_ss = HOL_ss addsimps (@{thm Rep_cfun_strict1} :: take_rews)
   fun quant_tac ctxt i = EVERY
-    (map (fn name => res_inst_tac ctxt [(("x", 0), name)] spec i) x_names);
+    (map (fn name => res_inst_tac ctxt [(("x", 0), name)] spec i) x_names)
 
   (* FIXME: move this message to domain_take_proofs.ML *)
-  val is_finite = #is_finite take_info;
+  val is_finite = #is_finite take_info
   val _ = if is_finite
           then message ("Proving finiteness rule for domain "^comp_dname^" ...")
-          else ();
-
-  val _ = trace " Proving finite_ind...";
+          else ()
+
+  val _ = trace " Proving finite_ind..."
   val finite_ind =
     let
       val concls =
           map (fn ((P, t), x) => P $ mk_capply (t $ n, x))
-              (Ps ~~ take_consts ~~ xs);
-      val goal = mk_trp (foldr1 mk_conj concls);
+              (Ps ~~ take_consts ~~ xs)
+      val goal = mk_trp (foldr1 mk_conj concls)
 
       fun tacf {prems, context} =
         let
           (* Prove stronger prems, without definedness side conditions *)
           fun con_thm p (con, args) =
             let
-              val subgoal = con_assm false p (con, args);
-              val rules = prems @ con_rews @ simp_thms;
-              val simplify = asm_simp_tac (HOL_basic_ss addsimps rules);
+              val subgoal = con_assm false p (con, args)
+              val rules = prems @ con_rews @ simp_thms
+              val simplify = asm_simp_tac (HOL_basic_ss addsimps rules)
               fun arg_tac (lazy, _) =
-                  rtac (if lazy then allI else case_UU_allI) 1;
+                  rtac (if lazy then allI else case_UU_allI) 1
               val tacs =
                   rewrite_goals_tac @{thms atomize_all atomize_imp} ::
                   map arg_tac args @
-                  [REPEAT (rtac impI 1), ALLGOALS simplify];
+                  [REPEAT (rtac impI 1), ALLGOALS simplify]
             in
               Goal.prove context [] [] subgoal (K (EVERY tacs))
-            end;
-          fun eq_thms (p, cons) = map (con_thm p) cons;
-          val conss = map #con_specs constr_infos;
-          val prems' = maps eq_thms (Ps ~~ conss);
+            end
+          fun eq_thms (p, cons) = map (con_thm p) cons
+          val conss = map #con_specs constr_infos
+          val prems' = maps eq_thms (Ps ~~ conss)
 
           val tacs1 = [
             quant_tac context 1,
             simp_tac HOL_ss 1,
             InductTacs.induct_tac context [[SOME "n"]] 1,
             simp_tac (take_ss addsimps prems) 1,
-            TRY (safe_tac HOL_cs)];
+            TRY (safe_tac HOL_cs)]
           fun con_tac _ = 
             asm_simp_tac take_ss 1 THEN
-            (resolve_tac prems' THEN_ALL_NEW etac spec) 1;
+            (resolve_tac prems' THEN_ALL_NEW etac spec) 1
           fun cases_tacs (cons, exhaust) =
             res_inst_tac context [(("y", 0), "x")] exhaust 1 ::
             asm_simp_tac (take_ss addsimps prems) 1 ::
-            map con_tac cons;
+            map con_tac cons
           val tacs = tacs1 @ maps cases_tacs (conss ~~ exhausts)
         in
           EVERY (map DETERM tacs)
-        end;
-    in Goal.prove_global thy [] assms goal tacf end;
-
-  val _ = trace " Proving ind...";
+        end
+    in Goal.prove_global thy [] assms goal tacf end
+
+  val _ = trace " Proving ind..."
   val ind =
     let
-      val concls = map (op $) (Ps ~~ xs);
-      val goal = mk_trp (foldr1 mk_conj concls);
-      val adms = if is_finite then [] else map (mk_trp o mk_adm) Ps;
+      val concls = map (op $) (Ps ~~ xs)
+      val goal = mk_trp (foldr1 mk_conj concls)
+      val adms = if is_finite then [] else map (mk_trp o mk_adm) Ps
       fun tacf {prems, context} =
         let
           fun finite_tac (take_induct, fin_ind) =
               rtac take_induct 1 THEN
               (if is_finite then all_tac else resolve_tac prems 1) THEN
-              (rtac fin_ind THEN_ALL_NEW solve_tac prems) 1;
-          val fin_inds = Project_Rule.projections context finite_ind;
+              (rtac fin_ind THEN_ALL_NEW solve_tac prems) 1
+          val fin_inds = Project_Rule.projections context finite_ind
         in
           TRY (safe_tac HOL_cs) THEN
           EVERY (map finite_tac (take_induct_thms ~~ fin_inds))
-        end;
+        end
     in Goal.prove_global thy [] (adms @ assms) goal tacf end
 
   (* case names for induction rules *)
-  val dnames = map (fst o dest_Type) newTs;
+  val dnames = map (fst o dest_Type) newTs
   val case_ns =
     let
       val adms =
           if is_finite then [] else
           if length dnames = 1 then ["adm"] else
-          map (fn s => "adm_" ^ Long_Name.base_name s) dnames;
+          map (fn s => "adm_" ^ Long_Name.base_name s) dnames
       val bottoms =
           if length dnames = 1 then ["bottom"] else
-          map (fn s => "bottom_" ^ Long_Name.base_name s) dnames;
+          map (fn s => "bottom_" ^ Long_Name.base_name s) dnames
       fun one_eq bot constr_info =
-        let fun name_of (c, args) = Long_Name.base_name (fst (dest_Const c));
-        in bot :: map name_of (#con_specs constr_info) end;
-    in adms @ flat (map2 one_eq bottoms constr_infos) end;
-
-  val inducts = Project_Rule.projections (ProofContext.init_global thy) ind;
+        let fun name_of (c, args) = Long_Name.base_name (fst (dest_Const c))
+        in bot :: map name_of (#con_specs constr_info) end
+    in adms @ flat (map2 one_eq bottoms constr_infos) end
+
+  val inducts = Project_Rule.projections (ProofContext.init_global thy) ind
   fun ind_rule (dname, rule) =
       ((Binding.empty, rule),
-       [Rule_Cases.case_names case_ns, Induct.induct_type dname]);
+       [Rule_Cases.case_names case_ns, Induct.induct_type dname])
 
 in
   thy
   |> snd o Global_Theory.add_thms [
      ((Binding.qualified true "finite_induct" comp_dbind, finite_ind), []),
      ((Binding.qualified true "induct"        comp_dbind, ind       ), [])]
   |> (snd o Global_Theory.add_thms (map ind_rule (dnames ~~ inducts)))
-end; (* prove_induction *)
+end (* prove_induction *)
 
 (******************************************************************************)
 (************************ bisimulation and coinduction ************************)
 (******************************************************************************)
 

     (constr_infos : Domain_Constructors.constr_info list)
     (take_info : Domain_Take_Proofs.take_induct_info)
     (take_rews : thm list list)
     (thy : theory) : theory =
 let
-  val iso_infos = map #iso_info constr_infos;
-  val newTs = map #absT iso_infos;
-
-  val {take_consts, take_0_thms, take_lemma_thms, ...} = take_info;
-
-  val R_names = Datatype_Prop.indexify_names (map (K "R") newTs);
-  val R_types = map (fn T => T --> T --> boolT) newTs;
-  val Rs = map Free (R_names ~~ R_types);
-  val n = Free ("n", natT);
-  val reserved = "x" :: "y" :: R_names;
+  val iso_infos = map #iso_info constr_infos
+  val newTs = map #absT iso_infos
+
+  val {take_consts, take_0_thms, take_lemma_thms, ...} = take_info
+
+  val R_names = Datatype_Prop.indexify_names (map (K "R") newTs)
+  val R_types = map (fn T => T --> T --> boolT) newTs
+  val Rs = map Free (R_names ~~ R_types)
+  val n = Free ("n", natT)
+  val reserved = "x" :: "y" :: R_names
 
   (* declare bisimulation predicate *)
-  val bisim_bind = Binding.suffix_name "_bisim" comp_dbind;
-  val bisim_type = R_types ---> boolT;
+  val bisim_bind = Binding.suffix_name "_bisim" comp_dbind
+  val bisim_type = R_types ---> boolT
   val (bisim_const, thy) =
-      Sign.declare_const ((bisim_bind, bisim_type), NoSyn) thy;
+      Sign.declare_const ((bisim_bind, bisim_type), NoSyn) thy
 
   (* define bisimulation predicate *)
   local
     fun one_con T (con, args) =
       let
-        val Ts = map snd args;
-        val ns1 = Name.variant_list reserved (Datatype_Prop.make_tnames Ts);
-        val ns2 = map (fn n => n^"'") ns1;
-        val vs1 = map Free (ns1 ~~ Ts);
-        val vs2 = map Free (ns2 ~~ Ts);
-        val eq1 = mk_eq (Free ("x", T), list_ccomb (con, vs1));
-        val eq2 = mk_eq (Free ("y", T), list_ccomb (con, vs2));
+        val Ts = map snd args
+        val ns1 = Name.variant_list reserved (Datatype_Prop.make_tnames Ts)
+        val ns2 = map (fn n => n^"'") ns1
+        val vs1 = map Free (ns1 ~~ Ts)
+        val vs2 = map Free (ns2 ~~ Ts)
+        val eq1 = mk_eq (Free ("x", T), list_ccomb (con, vs1))
+        val eq2 = mk_eq (Free ("y", T), list_ccomb (con, vs2))
         fun rel ((v1, v2), T) =
             case AList.lookup (op =) (newTs ~~ Rs) T of
-              NONE => mk_eq (v1, v2) | SOME r => r $ v1 $ v2;
-        val eqs = foldr1 mk_conj (map rel (vs1 ~~ vs2 ~~ Ts) @ [eq1, eq2]);
+              NONE => mk_eq (v1, v2) | SOME r => r $ v1 $ v2
+        val eqs = foldr1 mk_conj (map rel (vs1 ~~ vs2 ~~ Ts) @ [eq1, eq2])
       in
         Library.foldr mk_ex (vs1 @ vs2, eqs)
-      end;
+      end
     fun one_eq ((T, R), cons) =
       let
-        val x = Free ("x", T);
-        val y = Free ("y", T);
-        val disj1 = mk_conj (mk_eq (x, mk_bottom T), mk_eq (y, mk_bottom T));
-        val disjs = disj1 :: map (one_con T) cons;
+        val x = Free ("x", T)
+        val y = Free ("y", T)
+        val disj1 = mk_conj (mk_eq (x, mk_bottom T), mk_eq (y, mk_bottom T))
+        val disjs = disj1 :: map (one_con T) cons
       in
         mk_all (x, mk_all (y, mk_imp (R $ x $ y, foldr1 mk_disj disjs)))
-      end;
-    val conjs = map one_eq (newTs ~~ Rs ~~ map #con_specs constr_infos);
-    val bisim_rhs = lambdas Rs (Library.foldr1 mk_conj conjs);
-    val bisim_eqn = Logic.mk_equals (bisim_const, bisim_rhs);
+      end
+    val conjs = map one_eq (newTs ~~ Rs ~~ map #con_specs constr_infos)
+    val bisim_rhs = lambdas Rs (Library.foldr1 mk_conj conjs)
+    val bisim_eqn = Logic.mk_equals (bisim_const, bisim_rhs)
   in
     val (bisim_def_thm, thy) = thy |>
         yield_singleton (Global_Theory.add_defs false)
-         ((Binding.qualified true "bisim_def" comp_dbind, bisim_eqn), []);
+         ((Binding.qualified true "bisim_def" comp_dbind, bisim_eqn), [])
   end (* local *)
 
   (* prove coinduction lemma *)
   val coind_lemma =
     let
-      val assm = mk_trp (list_comb (bisim_const, Rs));
+      val assm = mk_trp (list_comb (bisim_const, Rs))
       fun one ((T, R), take_const) =
         let
-          val x = Free ("x", T);
-          val y = Free ("y", T);
-          val lhs = mk_capply (take_const $ n, x);
-          val rhs = mk_capply (take_const $ n, y);
+          val x = Free ("x", T)
+          val y = Free ("y", T)
+          val lhs = mk_capply (take_const $ n, x)
+          val rhs = mk_capply (take_const $ n, y)
         in
           mk_all (x, mk_all (y, mk_imp (R $ x $ y, mk_eq (lhs, rhs))))
-        end;
+        end
       val goal =
-          mk_trp (foldr1 mk_conj (map one (newTs ~~ Rs ~~ take_consts)));
-      val rules = @{thm Rep_cfun_strict1} :: take_0_thms;
+          mk_trp (foldr1 mk_conj (map one (newTs ~~ Rs ~~ take_consts)))
+      val rules = @{thm Rep_cfun_strict1} :: take_0_thms
       fun tacf {prems, context} =
         let
-          val prem' = rewrite_rule [bisim_def_thm] (hd prems);
-          val prems' = Project_Rule.projections context prem';
-          val dests = map (fn th => th RS spec RS spec RS mp) prems';
+          val prem' = rewrite_rule [bisim_def_thm] (hd prems)
+          val prems' = Project_Rule.projections context prem'
+          val dests = map (fn th => th RS spec RS spec RS mp) prems'
           fun one_tac (dest, rews) =
               dtac dest 1 THEN safe_tac HOL_cs THEN
-              ALLGOALS (asm_simp_tac (HOL_basic_ss addsimps rews));
+              ALLGOALS (asm_simp_tac (HOL_basic_ss addsimps rews))
         in
           rtac @{thm nat.induct} 1 THEN
           simp_tac (HOL_ss addsimps rules) 1 THEN
           safe_tac HOL_cs THEN
           EVERY (map one_tac (dests ~~ take_rews))
         end
     in
       Goal.prove_global thy [] [assm] goal tacf
-    end;
+    end
 
   (* prove individual coinduction rules *)
   fun prove_coind ((T, R), take_lemma) =
     let
-      val x = Free ("x", T);
-      val y = Free ("y", T);
-      val assm1 = mk_trp (list_comb (bisim_const, Rs));
-      val assm2 = mk_trp (R $ x $ y);
-      val goal = mk_trp (mk_eq (x, y));
+      val x = Free ("x", T)
+      val y = Free ("y", T)
+      val assm1 = mk_trp (list_comb (bisim_const, Rs))
+      val assm2 = mk_trp (R $ x $ y)
+      val goal = mk_trp (mk_eq (x, y))
       fun tacf {prems, context} =
         let
-          val rule = hd prems RS coind_lemma;
+          val rule = hd prems RS coind_lemma
         in
           rtac take_lemma 1 THEN
           asm_simp_tac (HOL_basic_ss addsimps (rule :: prems)) 1
-        end;
+        end
     in
       Goal.prove_global thy [] [assm1, assm2] goal tacf
-    end;
-  val coinds = map prove_coind (newTs ~~ Rs ~~ take_lemma_thms);
-  val coind_binds = map (Binding.qualified true "coinduct") dbinds;
+    end
+  val coinds = map prove_coind (newTs ~~ Rs ~~ take_lemma_thms)
+  val coind_binds = map (Binding.qualified true "coinduct") dbinds
 
 in
   thy |> snd o Global_Theory.add_thms
     (map Thm.no_attributes (coind_binds ~~ coinds))
-end; (* let *)
+end (* let *)
 
 (******************************************************************************)
 (******************************* main function ********************************)
 (******************************************************************************)
 

     (take_info : Domain_Take_Proofs.take_induct_info)
     (constr_infos : Domain_Constructors.constr_info list)
     (thy : theory) =
 let
 
-val comp_dname = space_implode "_" (map Binding.name_of dbinds);
-val comp_dbind = Binding.name comp_dname;
+val comp_dname = space_implode "_" (map Binding.name_of dbinds)
+val comp_dbind = Binding.name comp_dname
 
 (* Test for emptiness *)
 (* FIXME: reimplement emptiness test
 local
-  open Domain_Library;
-  val dnames = map (fst o fst) eqs;
-  val conss = map snd eqs;
+  open Domain_Library
+  val dnames = map (fst o fst) eqs
+  val conss = map snd eqs
   fun rec_to ns lazy_rec (n,cons) = forall (exists (fn arg => 
         is_rec arg andalso not (member (op =) ns (rec_of arg)) andalso
         ((rec_of arg =  n andalso not (lazy_rec orelse is_lazy arg)) orelse 
           rec_of arg <> n andalso rec_to (rec_of arg::ns) 
             (lazy_rec orelse is_lazy arg) (n, (List.nth(conss,rec_of arg))))
-        ) o snd) cons;
+        ) o snd) cons
   fun warn (n,cons) =
     if rec_to [] false (n,cons)
-    then (warning ("domain "^List.nth(dnames,n)^" is empty!"); true)
-    else false;
-in
-  val n__eqs = mapn (fn n => fn (_,cons) => (n,cons)) 0 eqs;
-  val is_emptys = map warn n__eqs;
-end;
+    then (warning ("domain "^List.nth(dnames,n)^" is empty!") true)
+    else false
+in
+  val n__eqs = mapn (fn n => fn (_,cons) => (n,cons)) 0 eqs
+  val is_emptys = map warn n__eqs
+end
 *)
 
 (* Test for indirect recursion *)
 local
-  val newTs = map (#absT o #iso_info) constr_infos;
+  val newTs = map (#absT o #iso_info) constr_infos
   fun indirect_typ (Type (_, Ts)) =
       exists (fn T => member (op =) newTs T orelse indirect_typ T) Ts
-    | indirect_typ _ = false;
-  fun indirect_arg (_, T) = indirect_typ T;
-  fun indirect_con (_, args) = exists indirect_arg args;
-  fun indirect_eq cons = exists indirect_con cons;
-in
-  val is_indirect = exists indirect_eq (map #con_specs constr_infos);
+    | indirect_typ _ = false
+  fun indirect_arg (_, T) = indirect_typ T
+  fun indirect_con (_, args) = exists indirect_arg args
+  fun indirect_eq cons = exists indirect_con cons
+in
+  val is_indirect = exists indirect_eq (map #con_specs constr_infos)
   val _ =
       if is_indirect
       then message "Indirect recursion detected, skipping proofs of (co)induction rules"
-      else message ("Proving induction properties of domain "^comp_dname^" ...");
-end;
+      else message ("Proving induction properties of domain "^comp_dname^" ...")
+end
 
 (* theorems about take *)
 
 val (take_rewss, thy) =
-    take_theorems dbinds take_info constr_infos thy;
-
-val {take_lemma_thms, take_0_thms, take_strict_thms, ...} = take_info;
-
-val take_rews = take_0_thms @ take_strict_thms @ flat take_rewss;
+    take_theorems dbinds take_info constr_infos thy
+
+val {take_lemma_thms, take_0_thms, take_strict_thms, ...} = take_info
+
+val take_rews = take_0_thms @ take_strict_thms @ flat take_rewss
 
 (* prove induction rules, unless definition is indirect recursive *)
 val thy =
     if is_indirect then thy else
-    prove_induction comp_dbind constr_infos take_info take_rews thy;
+    prove_induction comp_dbind constr_infos take_info take_rews thy
 
 val thy =
     if is_indirect then thy else
-    prove_coinduction (comp_dbind, dbinds) constr_infos take_info take_rewss thy;
+    prove_coinduction (comp_dbind, dbinds) constr_infos take_info take_rewss thy
 
 in
   (take_rews, thy)
-end; (* let *)
-end; (* struct *)
+end (* let *)
+end (* struct *)