1 theory Fv

     2 imports "Nominal2_Atoms" "Nominal2_Eqvt" "Nominal2_Supp" "Abs"

     3 begin

     4 

     5 atom_decl name

     6 

     7 datatype rlam =

     8   rVar "name"

     9 | rApp "rlam" "rlam"

    10 | rLam "name" "rlam"

    11 

    12 ML {*

    13   open Datatype_Aux (* typ_of_dtyp, DtRec, ... *);

    14   fun mk_atom ty = Const (@{const_name atom}, ty --> @{typ atom})

    15 *}

    16 

    17 ML {* dest_Type @{typ rlam} *}

    18 

    19 ML {*

    20   val {descr, ...} = Datatype.the_info @{theory} "Fv.rlam";

    21   val sorts = [];

    22 

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

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

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

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

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

    28   (* TODO: should be optimized to avoid {}+{}+{} *)

    29   fun mk_union sets = foldr1 (HOLogic.mk_binop @{const_name union}) sets;

    30 

    31   fun fv_eq_constr i (cname, dts) =

    32     let

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

    34       val names = Name.variant_list ["pi"] (Datatype_Prop.make_tnames Ts);

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

    36       val c = Const (cname, Ts ---> (nth_dtyp i));

    37       val fv_c = Free (nth fv_names i, (nth_dtyp i) --> @{typ "atom set"});

    38       fun fv_arg (dt, x) =

    39         if is_rec_type dt then

    40           nth fv_frees (body_index dt) $ x

    41         (* TODO: we just assume everything is a 'name' *)

    42         else HOLogic.mk_set @{typ atom} [mk_atom (type_of x) $ x]

    43      in

    44       (Attrib.empty_binding, HOLogic.mk_Trueprop (HOLogic.mk_eq

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

    46     end;

    47   fun fv_eq (i, (_, _, constrs)) = map (fv_eq_constr i) constrs;

    48   val fv_eqs = maps fv_eq descr

    49 *}

    50 

    51 local_setup {*

    52 snd o (Primrec.add_primrec

    53   (map (fn s => (Binding.name s, NONE, NoSyn)) fv_names) fv_eqs)

    54 *}

    55 print_theorems

    56 

    57 fun

    58   fv_rlam :: "rlam \<Rightarrow> atom set"

    59 where

    60   "fv_rlam (rVar a) = {atom a}"

    61 | "fv_rlam (rApp t1 t2) = (fv_rlam t1) \<union> (fv_rlam t2)"

    62 | "fv_rlam (rLam a t) = (fv_rlam t) - {atom a}"

    63 

    64 end