--- a/Nominal/Fv.thy	Wed Apr 14 18:46:59 2010 +0200
+++ b/Nominal/Fv.thy	Wed Apr 14 18:47:20 2010 +0200
@@ -416,7 +416,7 @@
 *}
 
 ML {*
-fun define_fv_alpha (dt_info : Datatype_Aux.info) bindsall bns lthy =
+fun define_fv (dt_info : Datatype_Aux.info) bindsall bns lthy =
 let
   val thy = ProofContext.theory_of lthy;
   val {descr, sorts, ...} = dt_info;
@@ -434,18 +434,8 @@
   val (bn_fv_bns, fv_bn_names_eqs) = fv_bns thy dt_info fv_frees rel_bns;
   val fvbns = map snd bn_fv_bns;
   val (fv_bn_names, fv_bn_eqs) = split_list fv_bn_names_eqs;
-  val alpha_names = Datatype_Prop.indexify_names (map (fn (i, _) =>
-    "alpha_" ^ name_of_typ (nth_dtyp i)) descr);
-  val alpha_types = map (fn (i, _) => nth_dtyp i --> nth_dtyp i --> @{typ bool}) descr;
-  val alpha_frees = map Free (alpha_names ~~ alpha_types);
-  (* We assume that a bn is either recursive or not *)
-  val bns_rec = map (fn (bn, _, _) => not (bn mem nr_bns)) bns;
-  val (alpha_bn_names, (bn_alpha_bns, alpha_bn_eqs)) =
-    alpha_bns dt_info alpha_frees bns bns_rec
-  val alpha_bn_frees = map snd bn_alpha_bns;
-  val alpha_bn_types = map fastype_of alpha_bn_frees;
 
-  fun fv_alpha_constr ith_dtyp (cname, dts) bindcs =
+  fun fv_constr ith_dtyp (cname, dts) bindcs =
     let
       val Ts = map (typ_of_dtyp descr sorts) dts;
       val bindslen = length bindcs
@@ -457,11 +447,8 @@
       val bindcs = map fst bind_pis;
       val names = Name.variant_list pi_strs (Datatype_Prop.make_tnames Ts);
       val args = map Free (names ~~ Ts);
-      val names2 = Name.variant_list (pi_strs @ names) (Datatype_Prop.make_tnames Ts);
-      val args2 = map Free (names2 ~~ Ts);
       val c = Const (cname, Ts ---> (nth_dtyp ith_dtyp));
       val fv_c = nth fv_frees ith_dtyp;
-      val alpha = nth alpha_frees ith_dtyp;
       val arg_nos = 0 upto (length dts - 1)
       fun fv_bind args (NONE, i, _, _) =
             if is_rec_type (nth dts i) then (nth fv_frees (body_index (nth dts i))) $ (nth args i) else
@@ -471,7 +458,6 @@
             (* TODO goes the code for preiously defined nominal datatypes *)
             @{term "{} :: atom set"}
         | fv_bind args (SOME (f, _), i, _, _) = f $ (nth args i)
-      fun fv_binds args relevant = mk_union (map (fv_bind args) relevant)
       fun fv_binds_as_set args relevant = mk_union (map (setify o fv_bind args) relevant)
       fun find_nonrec_binder j (SOME (f, false), i, _, _) = if i = j then SOME f else NONE
         | find_nonrec_binder _ _ = NONE
@@ -498,6 +484,81 @@
             end;
       val fv_eq = HOLogic.mk_Trueprop (HOLogic.mk_eq
         (fv_c $ list_comb (c, args), mk_union (map fv_arg  (dts ~~ args ~~ arg_nos))))
+    in
+      fv_eq
+    end;
+  fun fv_eq (i, (_, _, constrs)) binds = map2i (fv_constr i) constrs binds;
+  val fveqs = map2i fv_eq descr (gather_binds bindsall)
+  val fv_eqs_perfv = fveqs
+  val rel_bns_nos = map (fn (_, i, _) => i) rel_bns;
+  fun filter_fun (_, b) = b mem rel_bns_nos;
+  val all_fvs = (fv_names ~~ fv_eqs_perfv) ~~ (0 upto (length fv_names - 1))
+  val (fv_names_fst, fv_eqs_fst) = apsnd flat (split_list (map fst (filter_out filter_fun all_fvs)))
+  val (fv_names_snd, fv_eqs_snd) = apsnd flat (split_list (map fst (filter filter_fun all_fvs)))
+  val fv_eqs_all = fv_eqs_fst @ (flat fv_bn_eqs);
+  val fv_names_all = fv_names_fst @ fv_bn_names;
+  val add_binds = map (fn x => (Attrib.empty_binding, x))
+(* Function_Fun.add_fun Function_Common.default_config ... true *)
+  val (fvs, lthy') = (Primrec.add_primrec
+    (map (fn s => (Binding.name s, NONE, NoSyn)) fv_names_all) (add_binds fv_eqs_all) lthy)
+  val (fvs2, lthy'') =
+    if fv_eqs_snd = [] then (([], []), lthy') else
+   (Primrec.add_primrec
+    (map (fn s => (Binding.name s, NONE, NoSyn)) fv_names_snd) (add_binds fv_eqs_snd) lthy')
+  val ordered_fvs = fv_frees @ fvbns;
+  val all_fvs = (fst fvs @ fst fvs2, snd fvs @ snd fvs2)
+in
+  ((all_fvs, ordered_fvs), lthy'')
+end
+*}
+
+ML {*
+fun define_alpha (dt_info : Datatype_Aux.info) bindsall bns fv_frees lthy =
+let
+  val thy = ProofContext.theory_of lthy;
+  val {descr, sorts, ...} = dt_info;
+  fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);
+(* TODO: We need a transitive closure, but instead we do this hack considering
+   all binding functions as recursive or not *)
+  val nr_bns =
+    if (non_rec_binds bindsall) = [] then []
+    else map (fn (bn, _, _) => bn) bns;
+  val alpha_names = Datatype_Prop.indexify_names (map (fn (i, _) =>
+    "alpha_" ^ name_of_typ (nth_dtyp i)) descr);
+  val alpha_types = map (fn (i, _) => nth_dtyp i --> nth_dtyp i --> @{typ bool}) descr;
+  val alpha_frees = map Free (alpha_names ~~ alpha_types);
+  (* We assume that a bn is either recursive or not *)
+  val bns_rec = map (fn (bn, _, _) => not (bn mem nr_bns)) bns;
+  val (alpha_bn_names, (bn_alpha_bns, alpha_bn_eqs)) =
+    alpha_bns dt_info alpha_frees bns bns_rec
+  val alpha_bn_frees = map snd bn_alpha_bns;
+  val alpha_bn_types = map fastype_of alpha_bn_frees;
+
+  fun alpha_constr ith_dtyp (cname, dts) bindcs =
+    let
+      val Ts = map (typ_of_dtyp descr sorts) dts;
+      val bindslen = length bindcs
+      val pi_strs_same = replicate bindslen "pi"
+      val pi_strs = Name.variant_list [] pi_strs_same;
+      val pis = map (fn ps => Free (ps, @{typ perm})) pi_strs;
+      val bind_pis_gath = bindcs ~~ pis;
+      val bind_pis = un_gather_binds_cons bind_pis_gath;
+      val names = Name.variant_list pi_strs (Datatype_Prop.make_tnames Ts);
+      val args = map Free (names ~~ Ts);
+      val names2 = Name.variant_list (pi_strs @ names) (Datatype_Prop.make_tnames Ts);
+      val args2 = map Free (names2 ~~ Ts);
+      val c = Const (cname, Ts ---> (nth_dtyp ith_dtyp));
+      val alpha = nth alpha_frees ith_dtyp;
+      val arg_nos = 0 upto (length dts - 1)
+      fun fv_bind args (NONE, i, _, _) =
+            if is_rec_type (nth dts i) then (nth fv_frees (body_index (nth dts i))) $ (nth args i) else
+            if ((is_atom thy) o fastype_of) (nth args i) then mk_single_atom (nth args i) else
+            if ((is_atom_set thy) o fastype_of) (nth args i) then mk_atom_set (nth args i) else
+            if ((is_atom_fset thy) o fastype_of) (nth args i) then mk_atom_fset (nth args i) else
+            (* TODO goes the code for preiously defined nominal datatypes *)
+            @{term "{} :: atom set"}
+        | fv_bind args (SOME (f, _), i, _, _) = f $ (nth args i)
+      fun fv_binds args relevant = mk_union (map (fv_bind args) relevant)
       val alpha_rhs =
         HOLogic.mk_Trueprop (alpha $ (list_comb (c, args)) $ (list_comb (c, args2)));
       fun alpha_arg ((dt, arg_no), (arg, arg2)) =
@@ -572,36 +633,20 @@
         fold (fn pi_str => fn t => HOLogic.mk_exists (pi_str, @{typ perm}, t)) pi_strs alpha_lhss
       val alpha_eq = Logic.mk_implies (HOLogic.mk_Trueprop alpha_lhss_ex, alpha_rhs)
     in
-      (fv_eq, alpha_eq)
+      alpha_eq
     end;
-  fun fv_alpha_eq (i, (_, _, constrs)) binds = map2i (fv_alpha_constr i) constrs binds;
-  val fveqs_alphaeqs = map2i fv_alpha_eq descr (gather_binds bindsall)
-  val (fv_eqs_perfv, alpha_eqs) = apsnd flat (split_list (map split_list fveqs_alphaeqs))
-  val rel_bns_nos = map (fn (_, i, _) => i) rel_bns;
-  fun filter_fun (_, b) = b mem rel_bns_nos;
-  val all_fvs = (fv_names ~~ fv_eqs_perfv) ~~ (0 upto (length fv_names - 1))
-  val (fv_names_fst, fv_eqs_fst) = apsnd flat (split_list (map fst (filter_out filter_fun all_fvs)))
-  val (fv_names_snd, fv_eqs_snd) = apsnd flat (split_list (map fst (filter filter_fun all_fvs)))
-  val fv_eqs_all = fv_eqs_fst @ (flat fv_bn_eqs);
-  val fv_names_all = fv_names_fst @ fv_bn_names;
+  fun alpha_eq (i, (_, _, constrs)) binds = map2i (alpha_constr i) constrs binds;
+  val alphaeqs = map2i alpha_eq descr (gather_binds bindsall)
+  val alpha_eqs = flat alphaeqs
   val add_binds = map (fn x => (Attrib.empty_binding, x))
-(* Function_Fun.add_fun Function_Common.default_config ... true *)
-  val (fvs, lthy') = (Primrec.add_primrec
-    (map (fn s => (Binding.name s, NONE, NoSyn)) fv_names_all) (add_binds fv_eqs_all) lthy)
-  val (fvs2, lthy'') =
-    if fv_eqs_snd = [] then (([], []), lthy') else
-   (Primrec.add_primrec
-    (map (fn s => (Binding.name s, NONE, NoSyn)) fv_names_snd) (add_binds fv_eqs_snd) lthy')
-  val (alphas, lthy''') = (Inductive.add_inductive_i
+  val (alphas, lthy') = (Inductive.add_inductive_i
      {quiet_mode = true, verbose = false, alt_name = Binding.empty,
       coind = false, no_elim = false, no_ind = false, skip_mono = true, fork_mono = false}
      (map2 (fn x => fn y => ((Binding.name x, y), NoSyn)) (alpha_names @ alpha_bn_names)
      (alpha_types @ alpha_bn_types)) []
-     (add_binds (alpha_eqs @ flat alpha_bn_eqs)) [] lthy'')
-  val ordered_fvs = fv_frees @ fvbns;
-  val all_fvs = (fst fvs @ fst fvs2, snd fvs @ snd fvs2)
+     (add_binds (alpha_eqs @ flat alpha_bn_eqs)) [] lthy)
 in
-  (((all_fvs, ordered_fvs), alphas), lthy''')
+  (alphas, lthy')
 end
 *}
 

--- a/Nominal/Lift.thy	Wed Apr 14 18:46:59 2010 +0200
+++ b/Nominal/Lift.thy	Wed Apr 14 18:47:20 2010 +0200
@@ -1,7 +1,7 @@
 theory Lift
 imports "../Nominal-General/Nominal2_Atoms" 
         "../Nominal-General/Nominal2_Eqvt" 
-        "../Nominal_General/Nominal2_Supp" 
+        "../Nominal-General/Nominal2_Supp" 
         "Abs" "Perm" "Equivp" "Rsp"
 begin
 
@@ -69,13 +69,16 @@
 ML {*
 fun define_fv_alpha_export dt binds bns ctxt =
 let
-  val ((((fv_ts_loc, fv_def_loc), ord_fv_ts_loc), alpha), ctxt') =
-    define_fv_alpha dt binds bns ctxt;
+  val (((fv_ts_loc, fv_def_loc), ord_fv_ts_loc), ctxt') =
+    define_fv dt binds bns ctxt;
+  val fv_ts_nobn = take (length bns) fv_ts_loc
+  val (alpha, ctxt'') =
+    define_alpha dt binds bns fv_ts_nobn ctxt';
   val alpha_ts_loc = #preds alpha
   val alpha_induct_loc = #induct alpha
   val alpha_intros_loc = #intrs alpha;
   val alpha_cases_loc = #elims alpha
-  val morphism = ProofContext.export_morphism ctxt' ctxt;
+  val morphism = ProofContext.export_morphism ctxt'' ctxt;
   val fv_ts = map (Morphism.term morphism) fv_ts_loc;
   val ord_fv_ts = map (Morphism.term morphism) ord_fv_ts_loc;
   val fv_def = Morphism.fact morphism fv_def_loc;
@@ -84,7 +87,7 @@
   val alpha_intros = Morphism.fact morphism alpha_intros_loc
   val alpha_cases = Morphism.fact morphism alpha_cases_loc
 in
-  ((((fv_ts, ord_fv_ts), fv_def), ((alpha_ts, alpha_intros), (alpha_cases, alpha_induct))), ctxt')
+  ((((fv_ts, ord_fv_ts), fv_def), ((alpha_ts, alpha_intros), (alpha_cases, alpha_induct))), ctxt'')
 end;
 *}