416 *}

   417 

   418 ML {*

   419 fun define_fv (dt_info : Datatype_Aux.info) bindsall bns lthy =

   420 let

   421   val thy = ProofContext.theory_of lthy;

   422   val {descr, sorts, ...} = dt_info;

   423   fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);

   424   val fv_names = Datatype_Prop.indexify_names (map (fn (i, _) =>

   425     "fv_" ^ name_of_typ (nth_dtyp i)) descr);

   426   val fv_types = map (fn (i, _) => nth_dtyp i --> @{typ "atom set"}) descr;

   427   val fv_frees = map Free (fv_names ~~ fv_types);

   428 (* TODO: We need a transitive closure, but instead we do this hack considering

   429    all binding functions as recursive or not *)

   430   val nr_bns =

   431     if (non_rec_binds bindsall) = [] then []

   432     else map (fn (bn, _, _) => bn) bns;

   433   val rel_bns = filter (fn (bn, _, _) => bn mem nr_bns) bns;

   434   val (bn_fv_bns, fv_bn_names_eqs) = fv_bns thy dt_info fv_frees rel_bns;

   435   val fvbns = map snd bn_fv_bns;

   436   val (fv_bn_names, fv_bn_eqs) = split_list fv_bn_names_eqs;

   437 

   438   fun fv_constr ith_dtyp (cname, dts) bindcs =

   439     let

   440       val Ts = map (typ_of_dtyp descr sorts) dts;

   441       val bindslen = length bindcs

   442       val pi_strs_same = replicate bindslen "pi"

   443       val pi_strs = Name.variant_list [] pi_strs_same;

   444       val pis = map (fn ps => Free (ps, @{typ perm})) pi_strs;

   445       val bind_pis_gath = bindcs ~~ pis;

   446       val bind_pis = un_gather_binds_cons bind_pis_gath;

   447       val bindcs = map fst bind_pis;

   448       val names = Name.variant_list pi_strs (Datatype_Prop.make_tnames Ts);

   449       val args = map Free (names ~~ Ts);

   450       val c = Const (cname, Ts ---> (nth_dtyp ith_dtyp));

   451       val fv_c = nth fv_frees ith_dtyp;

   452       val arg_nos = 0 upto (length dts - 1)

   453       fun fv_bind args (NONE, i, _, _) =

   454             if is_rec_type (nth dts i) then (nth fv_frees (body_index (nth dts i))) $ (nth args i) else

   455             if ((is_atom thy) o fastype_of) (nth args i) then mk_single_atom (nth args i) else

   456             if ((is_atom_set thy) o fastype_of) (nth args i) then mk_atom_set (nth args i) else

   457             if ((is_atom_fset thy) o fastype_of) (nth args i) then mk_atom_fset (nth args i) else

   458             (* TODO goes the code for preiously defined nominal datatypes *)

   459             @{term "{} :: atom set"}

   460         | fv_bind args (SOME (f, _), i, _, _) = f $ (nth args i)

   461       fun fv_binds_as_set args relevant = mk_union (map (setify o fv_bind args) relevant)

   462       fun find_nonrec_binder j (SOME (f, false), i, _, _) = if i = j then SOME f else NONE

   463         | find_nonrec_binder _ _ = NONE

   464       fun fv_arg ((dt, x), arg_no) =

   465         case get_first (find_nonrec_binder arg_no) bindcs of

   466           SOME f =>

   467             (case get_first (fn (x, y) => if x = f then SOME y else NONE) bn_fv_bns of

   468                 SOME fv_bn => fv_bn $ x

   469               | NONE => error "bn specified in a non-rec binding but not in bn list")

   470         | NONE =>

   471             let

   472               val arg =

   473                 if is_rec_type dt then nth fv_frees (body_index dt) $ x else

   474                 if ((is_atom thy) o fastype_of) x then mk_single_atom x else

   475                 if ((is_atom_set thy) o fastype_of) x then mk_atom_set x else

   476                 if ((is_atom_fset thy) o fastype_of) x then mk_atom_fset x else

   477                 (* TODO goes the code for preiously defined nominal datatypes *)

   478                 @{term "{} :: atom set"};

   479               (* If i = j then we generate it only once *)

   480               val relevant = filter (fn (_, i, j, _) => ((i = arg_no) orelse (j = arg_no))) bindcs;

   481               val sub = fv_binds_as_set args relevant

   482             in

   483               mk_diff arg sub

   484             end;

   485       val fv_eq = HOLogic.mk_Trueprop (HOLogic.mk_eq

   486         (fv_c $ list_comb (c, args), mk_union (map fv_arg  (dts ~~ args ~~ arg_nos))))

   487     in

   488       fv_eq

   489     end;

   490   fun fv_eq (i, (_, _, constrs)) binds = map2i (fv_constr i) constrs binds;

   491   val fveqs = map2i fv_eq descr (gather_binds bindsall)

   492   val fv_eqs_perfv = fveqs

   493   val rel_bns_nos = map (fn (_, i, _) => i) rel_bns;

   494   fun filter_fun (_, b) = b mem rel_bns_nos;

   495   val all_fvs = (fv_names ~~ fv_eqs_perfv) ~~ (0 upto (length fv_names - 1))

   496   val (fv_names_fst, fv_eqs_fst) = apsnd flat (split_list (map fst (filter_out filter_fun all_fvs)))

   497   val (fv_names_snd, fv_eqs_snd) = apsnd flat (split_list (map fst (filter filter_fun all_fvs)))

   498   val fv_eqs_all = fv_eqs_fst @ (flat fv_bn_eqs);

   499   val fv_names_all = fv_names_fst @ fv_bn_names;

   500   val add_binds = map (fn x => (Attrib.empty_binding, x))

   501 (* Function_Fun.add_fun Function_Common.default_config ... true *)

   502   val (fvs, lthy') = (Primrec.add_primrec

   503     (map (fn s => (Binding.name s, NONE, NoSyn)) fv_names_all) (add_binds fv_eqs_all) lthy)

   504   val (fvs2, lthy'') =

   505     if fv_eqs_snd = [] then (([], []), lthy') else

   506    (Primrec.add_primrec

   507     (map (fn s => (Binding.name s, NONE, NoSyn)) fv_names_snd) (add_binds fv_eqs_snd) lthy')

   508   val ordered_fvs = fv_frees @ fvbns;

   509   val all_fvs = (fst fvs @ fst fvs2, snd fvs @ snd fvs2)

   510 in

   511   ((all_fvs, ordered_fvs), lthy'')

   512 end