src/HOL/Nominal/nominal_atoms.ML
author urbanc
Mon Jan 09 15:55:15 2006 +0100 (2006-01-09)
changeset 18626 b6596f579e40
parent 18600 20ad06db427b
child 18651 0cb5a8f501aa
permissions -rw-r--r--
added some lemmas to the collection "abs_fresh"

the lemmas are of the form

finite (supp x) ==> (b # [a].x) = (b=a \/ b # x)

previously only lemmas of the form

(b # [a].x) = (b=a \/ b # x)

with the type-constraint that x is finitely supported
were included.
     1 (* $Id$ *)
     2 
     3 signature NOMINAL_ATOMS =
     4 sig
     5   val create_nom_typedecls : string list -> theory -> theory
     6   val atoms_of : theory -> string list
     7   val mk_permT : typ -> typ
     8   val setup : (theory -> theory) list
     9 end
    10 
    11 structure NominalAtoms : NOMINAL_ATOMS =
    12 struct
    13 
    14 (* data kind 'HOL/nominal' *)
    15 
    16 structure NominalArgs =
    17 struct
    18   val name = "HOL/nominal";
    19   type T = unit Symtab.table;
    20 
    21   val empty = Symtab.empty;
    22   val copy = I;
    23   val extend = I;
    24   fun merge _ x = Symtab.merge (K true) x;
    25 
    26   fun print sg tab = ();
    27 end;
    28 
    29 structure NominalData = TheoryDataFun(NominalArgs);
    30 
    31 fun atoms_of thy = map fst (Symtab.dest (NominalData.get thy));
    32 
    33 (* FIXME: add to hologic.ML ? *)
    34 fun mk_listT T = Type ("List.list", [T]);
    35 fun mk_permT T = mk_listT (HOLogic.mk_prodT (T, T));
    36 
    37 fun mk_Cons x xs =
    38   let val T = fastype_of x
    39   in Const ("List.list.Cons", T --> mk_listT T --> mk_listT T) $ x $ xs end;
    40 
    41 
    42 (* this function sets up all matters related to atom-  *)
    43 (* kinds; the user specifies a list of atom-kind names *)
    44 (* atom_decl <ak1> ... <akn>                           *)
    45 fun create_nom_typedecls ak_names thy =
    46   let
    47     (* declares a type-decl for every atom-kind: *) 
    48     (* that is typedecl <ak>                     *)
    49     val thy1 = TypedefPackage.add_typedecls (map (fn x => (x,[],NoSyn)) ak_names) thy;
    50     
    51     (* produces a list consisting of pairs:         *)
    52     (*  fst component is the atom-kind name         *)
    53     (*  snd component is its type                   *)
    54     val full_ak_names = map (Sign.intern_type (sign_of thy1)) ak_names;
    55     val ak_names_types = ak_names ~~ map (Type o rpair []) full_ak_names;
    56      
    57     (* adds for every atom-kind an axiom             *)
    58     (* <ak>_infinite: infinite (UNIV::<ak_type> set) *)
    59     val (inf_axs,thy2) = PureThy.add_axioms_i (map (fn (ak_name, T) =>
    60       let 
    61 	val name = ak_name ^ "_infinite"
    62         val axiom = HOLogic.mk_Trueprop (HOLogic.mk_not
    63                     (HOLogic.mk_mem (HOLogic.mk_UNIV T,
    64                      Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT T)))))
    65       in
    66 	((name, axiom), []) 
    67       end) ak_names_types) thy1;
    68     
    69     (* declares a swapping function for every atom-kind, it is         *)
    70     (* const swap_<ak> :: <akT> * <akT> => <akT> => <akT>              *)
    71     (* swap_<ak> (a,b) c = (if a=c then b (else if b=c then a else c)) *)
    72     (* overloades then the general swap-function                       *) 
    73     val (thy3, swap_eqs) = foldl_map (fn (thy, (ak_name, T)) =>
    74       let
    75         val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
    76         val swap_name = Sign.full_name (sign_of thy) ("swap_" ^ ak_name);
    77         val a = Free ("a", T);
    78         val b = Free ("b", T);
    79         val c = Free ("c", T);
    80         val ab = Free ("ab", HOLogic.mk_prodT (T, T))
    81         val cif = Const ("HOL.If", HOLogic.boolT --> T --> T --> T);
    82         val cswap_akname = Const (swap_name, swapT);
    83         val cswap = Const ("nominal.swap", swapT)
    84 
    85         val name = "swap_"^ak_name^"_def";
    86         val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq
    87 		   (cswap_akname $ HOLogic.mk_prod (a,b) $ c,
    88                     cif $ HOLogic.mk_eq (a,c) $ b $ (cif $ HOLogic.mk_eq (b,c) $ a $ c)))
    89         val def2 = Logic.mk_equals (cswap $ ab $ c, cswap_akname $ ab $ c)
    90       in
    91         thy |> Theory.add_consts_i [("swap_" ^ ak_name, swapT, NoSyn)] 
    92             |> (#2 o PureThy.add_defs_i true [((name, def2),[])])
    93             |> PrimrecPackage.add_primrec_i "" [(("", def1),[])]            
    94       end) (thy2, ak_names_types);
    95     
    96     (* declares a permutation function for every atom-kind acting  *)
    97     (* on such atoms                                               *)
    98     (* const <ak>_prm_<ak> :: (<akT> * <akT>)list => akT => akT    *)
    99     (* <ak>_prm_<ak> []     a = a                                  *)
   100     (* <ak>_prm_<ak> (x#xs) a = swap_<ak> x (perm xs a)            *)
   101     val (thy4, prm_eqs) = foldl_map (fn (thy, (ak_name, T)) =>
   102       let
   103         val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
   104         val swap_name = Sign.full_name (sign_of thy) ("swap_" ^ ak_name)
   105         val prmT = mk_permT T --> T --> T;
   106         val prm_name = ak_name ^ "_prm_" ^ ak_name;
   107         val qu_prm_name = Sign.full_name (sign_of thy) prm_name;
   108         val x  = Free ("x", HOLogic.mk_prodT (T, T));
   109         val xs = Free ("xs", mk_permT T);
   110         val a  = Free ("a", T) ;
   111 
   112         val cnil  = Const ("List.list.Nil", mk_permT T);
   113         
   114         val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq (Const (qu_prm_name, prmT) $ cnil $ a, a));
   115 
   116         val def2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
   117                    (Const (qu_prm_name, prmT) $ mk_Cons x xs $ a,
   118                     Const (swap_name, swapT) $ x $ (Const (qu_prm_name, prmT) $ xs $ a)));
   119       in
   120         thy |> Theory.add_consts_i [(prm_name, mk_permT T --> T --> T, NoSyn)] 
   121             |> PrimrecPackage.add_primrec_i "" [(("", def1), []),(("", def2), [])]
   122       end) (thy3, ak_names_types);
   123     
   124     (* defines permutation functions for all combinations of atom-kinds; *)
   125     (* there are a trivial cases and non-trivial cases                   *)
   126     (* non-trivial case:                                                 *)
   127     (* <ak>_prm_<ak>_def:  perm pi a == <ak>_prm_<ak> pi a               *)
   128     (* trivial case with <ak> != <ak'>                                   *)
   129     (* <ak>_prm<ak'>_def[simp]:  perm pi a == a                          *)
   130     (*                                                                   *)
   131     (* the trivial cases are added to the simplifier, while the non-     *)
   132     (* have their own rules proved below                                 *)  
   133     val (perm_defs, thy5) = fold_map (fn (ak_name, T) => fn thy =>
   134       fold_map (fn (ak_name', T') => fn thy' =>
   135         let
   136           val perm_def_name = ak_name ^ "_prm_" ^ ak_name';
   137           val pi = Free ("pi", mk_permT T);
   138           val a  = Free ("a", T');
   139           val cperm = Const ("nominal.perm", mk_permT T --> T' --> T');
   140           val cperm_def = Const (Sign.full_name (sign_of thy') perm_def_name, mk_permT T --> T' --> T');
   141 
   142           val name = ak_name ^ "_prm_" ^ ak_name' ^ "_def";
   143           val def = Logic.mk_equals
   144                     (cperm $ pi $ a, if ak_name = ak_name' then cperm_def $ pi $ a else a)
   145         in
   146           PureThy.add_defs_i true [((name, def),[])] thy'
   147         end) ak_names_types thy) ak_names_types thy4;
   148     
   149     (* proves that every atom-kind is an instance of at *)
   150     (* lemma at_<ak>_inst:                              *)
   151     (* at TYPE(<ak>)                                    *)
   152     val (prm_cons_thms,thy6) = 
   153       thy5 |> PureThy.add_thms (map (fn (ak_name, T) =>
   154       let
   155         val ak_name_qu = Sign.full_name (sign_of thy5) (ak_name);
   156         val i_type = Type(ak_name_qu,[]);
   157 	val cat = Const ("nominal.at",(Term.itselfT i_type)  --> HOLogic.boolT);
   158         val at_type = Logic.mk_type i_type;
   159         val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy5
   160                                   [Name "at_def",
   161                                    Name (ak_name ^ "_prm_" ^ ak_name ^ "_def"),
   162                                    Name (ak_name ^ "_prm_" ^ ak_name ^ ".simps"),
   163                                    Name ("swap_" ^ ak_name ^ "_def"),
   164                                    Name ("swap_" ^ ak_name ^ ".simps"),
   165                                    Name (ak_name ^ "_infinite")]
   166 	    
   167 	val name = "at_"^ak_name^ "_inst";
   168         val statement = HOLogic.mk_Trueprop (cat $ at_type);
   169 
   170         val proof = fn _ => auto_tac (claset(),simp_s);
   171 
   172       in 
   173         ((name, standard (Goal.prove thy5 [] [] statement proof)), []) 
   174       end) ak_names_types);
   175 
   176     (* declares a perm-axclass for every atom-kind               *)
   177     (* axclass pt_<ak>                                           *)
   178     (* pt_<ak>1[simp]: perm [] x = x                             *)
   179     (* pt_<ak>2:       perm (pi1@pi2) x = perm pi1 (perm pi2 x)  *)
   180     (* pt_<ak>3:       pi1 ~ pi2 ==> perm pi1 x = perm pi2 x     *)
   181      val (pt_ax_classes,thy7) =  fold_map (fn (ak_name, T) => fn thy =>
   182       let 
   183 	  val cl_name = "pt_"^ak_name;
   184           val ty = TFree("'a",["HOL.type"]);
   185           val x   = Free ("x", ty);
   186           val pi1 = Free ("pi1", mk_permT T);
   187           val pi2 = Free ("pi2", mk_permT T);
   188           val cperm = Const ("nominal.perm", mk_permT T --> ty --> ty);
   189           val cnil  = Const ("List.list.Nil", mk_permT T);
   190           val cappend = Const ("List.op @",mk_permT T --> mk_permT T --> mk_permT T);
   191           val cprm_eq = Const ("nominal.prm_eq",mk_permT T --> mk_permT T --> HOLogic.boolT);
   192           (* nil axiom *)
   193           val axiom1 = HOLogic.mk_Trueprop (HOLogic.mk_eq 
   194                        (cperm $ cnil $ x, x));
   195           (* append axiom *)
   196           val axiom2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
   197                        (cperm $ (cappend $ pi1 $ pi2) $ x, cperm $ pi1 $ (cperm $ pi2 $ x)));
   198           (* perm-eq axiom *)
   199           val axiom3 = Logic.mk_implies
   200                        (HOLogic.mk_Trueprop (cprm_eq $ pi1 $ pi2),
   201                         HOLogic.mk_Trueprop (HOLogic.mk_eq (cperm $ pi1 $ x, cperm $ pi2 $ x)));
   202       in
   203           AxClass.add_axclass_i (cl_name, ["HOL.type"])
   204                 [((cl_name^"1", axiom1),[Simplifier.simp_add_global]), 
   205                  ((cl_name^"2", axiom2),[]),                           
   206                  ((cl_name^"3", axiom3),[])] thy                          
   207       end) ak_names_types thy6;
   208 
   209     (* proves that every pt_<ak>-type together with <ak>-type *)
   210     (* instance of pt                                         *)
   211     (* lemma pt_<ak>_inst:                                    *)
   212     (* pt TYPE('x::pt_<ak>) TYPE(<ak>)                        *)
   213     val (prm_inst_thms,thy8) = 
   214       thy7 |> PureThy.add_thms (map (fn (ak_name, T) =>
   215       let
   216         val ak_name_qu = Sign.full_name (sign_of thy7) (ak_name);
   217         val pt_name_qu = Sign.full_name (sign_of thy7) ("pt_"^ak_name);
   218         val i_type1 = TFree("'x",[pt_name_qu]);
   219         val i_type2 = Type(ak_name_qu,[]);
   220 	val cpt = Const ("nominal.pt",(Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
   221         val pt_type = Logic.mk_type i_type1;
   222         val at_type = Logic.mk_type i_type2;
   223         val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy7
   224                                   [Name "pt_def",
   225                                    Name ("pt_" ^ ak_name ^ "1"),
   226                                    Name ("pt_" ^ ak_name ^ "2"),
   227                                    Name ("pt_" ^ ak_name ^ "3")];
   228 
   229 	val name = "pt_"^ak_name^ "_inst";
   230         val statement = HOLogic.mk_Trueprop (cpt $ pt_type $ at_type);
   231 
   232         val proof = fn _ => auto_tac (claset(),simp_s);
   233       in 
   234         ((name, standard (Goal.prove thy7 [] [] statement proof)), []) 
   235       end) ak_names_types);
   236 
   237      (* declares an fs-axclass for every atom-kind       *)
   238      (* axclass fs_<ak>                                  *)
   239      (* fs_<ak>1: finite ((supp x)::<ak> set)            *)
   240      val (fs_ax_classes,thy11) =  fold_map (fn (ak_name, T) => fn thy =>
   241        let 
   242 	  val cl_name = "fs_"^ak_name;
   243 	  val pt_name = Sign.full_name (sign_of thy) ("pt_"^ak_name);
   244           val ty = TFree("'a",["HOL.type"]);
   245           val x   = Free ("x", ty);
   246           val csupp    = Const ("nominal.supp", ty --> HOLogic.mk_setT T);
   247           val cfinites = Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT T))
   248           
   249           val axiom1   = HOLogic.mk_Trueprop (HOLogic.mk_mem (csupp $ x, cfinites));
   250 
   251        in  
   252         AxClass.add_axclass_i (cl_name, [pt_name]) [((cl_name^"1", axiom1),[])] thy            
   253        end) ak_names_types thy8; 
   254 
   255      (* proves that every fs_<ak>-type together with <ak>-type   *)
   256      (* instance of fs-type                                      *)
   257      (* lemma abst_<ak>_inst:                                    *)
   258      (* fs TYPE('x::pt_<ak>) TYPE (<ak>)                         *)
   259      val (fs_inst_thms,thy12) = 
   260        thy11 |> PureThy.add_thms (map (fn (ak_name, T) =>
   261        let
   262          val ak_name_qu = Sign.full_name (sign_of thy11) (ak_name);
   263          val fs_name_qu = Sign.full_name (sign_of thy11) ("fs_"^ak_name);
   264          val i_type1 = TFree("'x",[fs_name_qu]);
   265          val i_type2 = Type(ak_name_qu,[]);
   266  	 val cfs = Const ("nominal.fs", 
   267                                  (Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
   268          val fs_type = Logic.mk_type i_type1;
   269          val at_type = Logic.mk_type i_type2;
   270 	 val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy11
   271                                    [Name "fs_def",
   272                                     Name ("fs_" ^ ak_name ^ "1")];
   273     
   274 	 val name = "fs_"^ak_name^ "_inst";
   275          val statement = HOLogic.mk_Trueprop (cfs $ fs_type $ at_type);
   276 
   277          val proof = fn _ => auto_tac (claset(),simp_s);
   278        in 
   279          ((name, standard (Goal.prove thy11 [] [] statement proof)), []) 
   280        end) ak_names_types);
   281 
   282        (* declares for every atom-kind combination an axclass            *)
   283        (* cp_<ak1>_<ak2> giving a composition property                   *)
   284        (* cp_<ak1>_<ak2>1: pi1 o pi2 o x = (pi1 o pi2) o (pi1 o x)       *)
   285         val (_,thy12b) = fold_map (fn (ak_name, T) => fn thy =>
   286 	 fold_map (fn (ak_name', T') => fn thy' =>
   287 	     let
   288 	       val cl_name = "cp_"^ak_name^"_"^ak_name';
   289 	       val ty = TFree("'a",["HOL.type"]);
   290                val x   = Free ("x", ty);
   291                val pi1 = Free ("pi1", mk_permT T);
   292 	       val pi2 = Free ("pi2", mk_permT T');                  
   293 	       val cperm1 = Const ("nominal.perm", mk_permT T  --> ty --> ty);
   294                val cperm2 = Const ("nominal.perm", mk_permT T' --> ty --> ty);
   295                val cperm3 = Const ("nominal.perm", mk_permT T  --> mk_permT T' --> mk_permT T');
   296 
   297                val ax1   = HOLogic.mk_Trueprop 
   298 			   (HOLogic.mk_eq (cperm1 $ pi1 $ (cperm2 $ pi2 $ x), 
   299                                            cperm2 $ (cperm3 $ pi1 $ pi2) $ (cperm1 $ pi1 $ x)));
   300 	       in  
   301 		 AxClass.add_axclass_i (cl_name, ["HOL.type"]) [((cl_name^"1", ax1),[])] thy'  
   302 	       end) ak_names_types thy) ak_names_types thy12;
   303 
   304         (* proves for every <ak>-combination a cp_<ak1>_<ak2>_inst theorem;     *)
   305         (* lemma cp_<ak1>_<ak2>_inst:                                           *)
   306         (* cp TYPE('a::cp_<ak1>_<ak2>) TYPE(<ak1>) TYPE(<ak2>)                  *)
   307         val (cp_thms,thy12c) = fold_map (fn (ak_name, T) => fn thy =>
   308 	 fold_map (fn (ak_name', T') => fn thy' =>
   309            let
   310              val ak_name_qu  = Sign.full_name (sign_of thy') (ak_name);
   311 	     val ak_name_qu' = Sign.full_name (sign_of thy') (ak_name');
   312              val cp_name_qu  = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
   313              val i_type0 = TFree("'a",[cp_name_qu]);
   314              val i_type1 = Type(ak_name_qu,[]);
   315              val i_type2 = Type(ak_name_qu',[]);
   316 	     val ccp = Const ("nominal.cp",
   317                              (Term.itselfT i_type0)-->(Term.itselfT i_type1)-->
   318                                                       (Term.itselfT i_type2)-->HOLogic.boolT);
   319              val at_type  = Logic.mk_type i_type1;
   320              val at_type' = Logic.mk_type i_type2;
   321 	     val cp_type  = Logic.mk_type i_type0;
   322              val simp_s   = HOL_basic_ss addsimps PureThy.get_thmss thy' [(Name "cp_def")];
   323 	     val cp1      = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"1"));
   324 
   325 	     val name = "cp_"^ak_name^ "_"^ak_name'^"_inst";
   326              val statement = HOLogic.mk_Trueprop (ccp $ cp_type $ at_type $ at_type');
   327 
   328              val proof = fn _ => EVERY [auto_tac (claset(),simp_s), rtac cp1 1];
   329 	   in
   330 	     PureThy.add_thms [((name, standard (Goal.prove thy' [] [] statement proof)), [])] thy'
   331 	   end) 
   332            ak_names_types thy) ak_names_types thy12b;
   333        
   334         (* proves for every non-trivial <ak>-combination a disjointness   *)
   335         (* theorem; i.e. <ak1> != <ak2>                                   *)
   336         (* lemma ds_<ak1>_<ak2>:                                          *)
   337         (* dj TYPE(<ak1>) TYPE(<ak2>)                                     *)
   338         val (dj_thms, thy12d) = fold_map (fn (ak_name,T) => fn thy =>
   339 	  fold_map (fn (ak_name',T') => fn thy' =>
   340           (if not (ak_name = ak_name') 
   341            then 
   342 	       let
   343 		 val ak_name_qu  = Sign.full_name (sign_of thy') (ak_name);
   344 	         val ak_name_qu' = Sign.full_name (sign_of thy') (ak_name');
   345                  val i_type1 = Type(ak_name_qu,[]);
   346                  val i_type2 = Type(ak_name_qu',[]);
   347 	         val cdj = Const ("nominal.disjoint",
   348                            (Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
   349                  val at_type  = Logic.mk_type i_type1;
   350                  val at_type' = Logic.mk_type i_type2;
   351                  val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy' 
   352 					   [Name "disjoint_def",
   353                                             Name (ak_name^"_prm_"^ak_name'^"_def"),
   354                                             Name (ak_name'^"_prm_"^ak_name^"_def")];
   355 
   356 	         val name = "dj_"^ak_name^"_"^ak_name';
   357                  val statement = HOLogic.mk_Trueprop (cdj $ at_type $ at_type');
   358 
   359                  val proof = fn _ => auto_tac (claset(),simp_s);
   360 	       in
   361 		PureThy.add_thms [((name, standard (Goal.prove thy' [] [] statement proof)), [])] thy'
   362 	       end
   363            else 
   364             ([],thy')))  (* do nothing branch, if ak_name = ak_name' *) 
   365 	    ak_names_types thy) ak_names_types thy12c;
   366 
   367      (*<<<<<<<  pt_<ak> class instances  >>>>>>>*)
   368      (*=========================================*)
   369      (* some abbreviations for theorems *)
   370       val pt1           = thm "pt1";
   371       val pt2           = thm "pt2";
   372       val pt3           = thm "pt3";
   373       val at_pt_inst    = thm "at_pt_inst";
   374       val pt_set_inst   = thm "pt_set_inst"; 
   375       val pt_unit_inst  = thm "pt_unit_inst";
   376       val pt_prod_inst  = thm "pt_prod_inst"; 
   377       val pt_nprod_inst = thm "pt_nprod_inst"; 
   378       val pt_list_inst  = thm "pt_list_inst";   
   379       val pt_optn_inst  = thm "pt_option_inst";   
   380       val pt_noptn_inst = thm "pt_noption_inst";   
   381       val pt_fun_inst   = thm "pt_fun_inst";     
   382 
   383      (* for all atom-kind combinations <ak>/<ak'> show that        *)
   384      (* every <ak> is an instance of pt_<ak'>; the proof for       *)
   385      (* ak!=ak' is by definition; the case ak=ak' uses at_pt_inst. *)
   386      val thy13 = fold (fn ak_name => fn thy =>
   387 	fold (fn ak_name' => fn thy' =>
   388          let
   389            val qu_name =  Sign.full_name (sign_of thy') ak_name';
   390            val cls_name = Sign.full_name (sign_of thy') ("pt_"^ak_name);
   391            val at_inst  = PureThy.get_thm thy' (Name ("at_"^ak_name'^"_inst")); 
   392 
   393            val proof1 = EVERY [AxClass.intro_classes_tac [],
   394                                  rtac ((at_inst RS at_pt_inst) RS pt1) 1,
   395                                  rtac ((at_inst RS at_pt_inst) RS pt2) 1,
   396                                  rtac ((at_inst RS at_pt_inst) RS pt3) 1,
   397                                  atac 1];
   398            val simp_s = HOL_basic_ss addsimps 
   399                         PureThy.get_thmss thy' [Name (ak_name^"_prm_"^ak_name'^"_def")];  
   400            val proof2 = EVERY [AxClass.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)];
   401 
   402          in
   403            thy'
   404            |> AxClass.add_inst_arity_i (qu_name,[],[cls_name])
   405               (if ak_name = ak_name' then proof1 else proof2)
   406          end) ak_names thy) ak_names thy12c;
   407 
   408      (* show that                       *)
   409      (*      fun(pt_<ak>,pt_<ak>)       *)
   410      (*      noption(pt_<ak>)           *)
   411      (*      option(pt_<ak>)            *)
   412      (*      list(pt_<ak>)              *)
   413      (*      *(pt_<ak>,pt_<ak>)         *)
   414      (*      nprod(pt_<ak>,pt_<ak>)     *)
   415      (*      unit                       *)
   416      (*      set(pt_<ak>)               *)
   417      (* are instances of pt_<ak>        *)
   418      val thy18 = fold (fn ak_name => fn thy =>
   419        let
   420           val cls_name = Sign.full_name (sign_of thy) ("pt_"^ak_name);
   421           val at_thm   = PureThy.get_thm thy (Name ("at_"^ak_name^"_inst"));
   422           val pt_inst  = PureThy.get_thm thy (Name ("pt_"^ak_name^"_inst"));
   423           
   424           fun pt_proof thm = 
   425 	      EVERY [AxClass.intro_classes_tac [],
   426                      rtac (thm RS pt1) 1, rtac (thm RS pt2) 1, rtac (thm RS pt3) 1, atac 1];
   427 
   428           val pt_thm_fun   = at_thm RS (pt_inst RS (pt_inst RS pt_fun_inst));
   429           val pt_thm_noptn = pt_inst RS pt_noptn_inst; 
   430           val pt_thm_optn  = pt_inst RS pt_optn_inst; 
   431           val pt_thm_list  = pt_inst RS pt_list_inst;
   432           val pt_thm_prod  = pt_inst RS (pt_inst RS pt_prod_inst);
   433           val pt_thm_nprod = pt_inst RS (pt_inst RS pt_nprod_inst);
   434           val pt_thm_unit  = pt_unit_inst;
   435           val pt_thm_set   = pt_inst RS pt_set_inst
   436        in 
   437 	thy
   438 	|> AxClass.add_inst_arity_i ("fun",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_fun)
   439         |> AxClass.add_inst_arity_i ("nominal.noption",[[cls_name]],[cls_name]) (pt_proof pt_thm_noptn) 
   440         |> AxClass.add_inst_arity_i ("Datatype.option",[[cls_name]],[cls_name]) (pt_proof pt_thm_optn)
   441         |> AxClass.add_inst_arity_i ("List.list",[[cls_name]],[cls_name]) (pt_proof pt_thm_list)
   442         |> AxClass.add_inst_arity_i ("*",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_prod)
   443         |> AxClass.add_inst_arity_i ("nominal.nprod",[[cls_name],[cls_name]],[cls_name]) 
   444                                     (pt_proof pt_thm_nprod)
   445         |> AxClass.add_inst_arity_i ("Product_Type.unit",[],[cls_name]) (pt_proof pt_thm_unit)
   446         |> AxClass.add_inst_arity_i ("set",[[cls_name]],[cls_name]) (pt_proof pt_thm_set)
   447      end) ak_names thy13; 
   448 
   449        (*<<<<<<<  fs_<ak> class instances  >>>>>>>*)
   450        (*=========================================*)
   451        (* abbreviations for some lemmas *)
   452        val fs1            = thm "fs1";
   453        val fs_at_inst     = thm "fs_at_inst";
   454        val fs_unit_inst   = thm "fs_unit_inst";
   455        val fs_prod_inst   = thm "fs_prod_inst";
   456        val fs_nprod_inst  = thm "fs_nprod_inst";
   457        val fs_list_inst   = thm "fs_list_inst";
   458        val fs_option_inst = thm "fs_option_inst";
   459        val dj_supp        = thm "dj_supp"
   460 
   461        (* shows that <ak> is an instance of fs_<ak>     *)
   462        (* uses the theorem at_<ak>_inst                 *)
   463        val thy20 = fold (fn ak_name => fn thy =>
   464 	fold (fn ak_name' => fn thy' => 
   465         let
   466            val qu_name =  Sign.full_name (sign_of thy') ak_name';
   467            val qu_class = Sign.full_name (sign_of thy') ("fs_"^ak_name);
   468            val proof = 
   469 	       (if ak_name = ak_name'
   470 	        then
   471 	          let val at_thm = PureThy.get_thm thy' (Name ("at_"^ak_name^"_inst"));
   472                   in  EVERY [AxClass.intro_classes_tac [],
   473                              rtac ((at_thm RS fs_at_inst) RS fs1) 1] end
   474                 else
   475 		  let val dj_inst = PureThy.get_thm thy' (Name ("dj_"^ak_name'^"_"^ak_name));
   476                       val simp_s = HOL_basic_ss addsimps [dj_inst RS dj_supp, Finites.emptyI]; 
   477                   in EVERY [AxClass.intro_classes_tac [], asm_simp_tac simp_s 1] end)      
   478         in 
   479 	 AxClass.add_inst_arity_i (qu_name,[],[qu_class]) proof thy' 
   480         end) ak_names thy) ak_names thy18;
   481 
   482        (* shows that                  *)
   483        (*    unit                     *)
   484        (*    *(fs_<ak>,fs_<ak>)       *)
   485        (*    nprod(fs_<ak>,fs_<ak>)   *)
   486        (*    list(fs_<ak>)            *)
   487        (*    option(fs_<ak>)          *) 
   488        (* are instances of fs_<ak>    *)
   489 
   490        val thy24 = fold (fn ak_name => fn thy => 
   491         let
   492           val cls_name = Sign.full_name (sign_of thy) ("fs_"^ak_name);
   493           val fs_inst  = PureThy.get_thm thy (Name ("fs_"^ak_name^"_inst"));
   494           fun fs_proof thm = EVERY [AxClass.intro_classes_tac [], rtac (thm RS fs1) 1];      
   495 
   496           val fs_thm_unit  = fs_unit_inst;
   497           val fs_thm_prod  = fs_inst RS (fs_inst RS fs_prod_inst);
   498           val fs_thm_nprod = fs_inst RS (fs_inst RS fs_nprod_inst);
   499           val fs_thm_list  = fs_inst RS fs_list_inst;
   500           val fs_thm_optn  = fs_inst RS fs_option_inst;
   501         in 
   502          thy 
   503          |> AxClass.add_inst_arity_i ("Product_Type.unit",[],[cls_name]) (fs_proof fs_thm_unit) 
   504          |> AxClass.add_inst_arity_i ("*",[[cls_name],[cls_name]],[cls_name]) (fs_proof fs_thm_prod) 
   505          |> AxClass.add_inst_arity_i ("nominal.nprod",[[cls_name],[cls_name]],[cls_name]) 
   506                                      (fs_proof fs_thm_nprod) 
   507          |> AxClass.add_inst_arity_i ("List.list",[[cls_name]],[cls_name]) (fs_proof fs_thm_list)
   508          |> AxClass.add_inst_arity_i ("Datatype.option",[[cls_name]],[cls_name]) (fs_proof fs_thm_optn)
   509         end) ak_names thy20; 
   510 
   511        (*<<<<<<<  cp_<ak>_<ai> class instances  >>>>>>>*)
   512        (*==============================================*)
   513        (* abbreviations for some lemmas *)
   514        val cp1             = thm "cp1";
   515        val cp_unit_inst    = thm "cp_unit_inst";
   516        val cp_bool_inst    = thm "cp_bool_inst";
   517        val cp_prod_inst    = thm "cp_prod_inst";
   518        val cp_list_inst    = thm "cp_list_inst";
   519        val cp_fun_inst     = thm "cp_fun_inst";
   520        val cp_option_inst  = thm "cp_option_inst";
   521        val cp_noption_inst = thm "cp_noption_inst";
   522        val pt_perm_compose = thm "pt_perm_compose";
   523        val dj_pp_forget    = thm "dj_perm_perm_forget";
   524 
   525        (* shows that <aj> is an instance of cp_<ak>_<ai>  *)
   526        (* for every  <ak>/<ai>-combination                *)
   527        val thy25 = fold (fn ak_name => fn thy => 
   528 	 fold (fn ak_name' => fn thy' => 
   529           fold (fn ak_name'' => fn thy'' => 
   530             let
   531               val name =  Sign.full_name (sign_of thy'') ak_name;
   532               val cls_name = Sign.full_name (sign_of thy'') ("cp_"^ak_name'^"_"^ak_name'');
   533               val proof =
   534                 (if (ak_name'=ak_name'') then 
   535 		  (let
   536                     val pt_inst  = PureThy.get_thm thy'' (Name ("pt_"^ak_name''^"_inst"));
   537 		    val at_inst  = PureThy.get_thm thy'' (Name ("at_"^ak_name''^"_inst"));
   538                   in 
   539 		   EVERY [AxClass.intro_classes_tac [], 
   540                           rtac (at_inst RS (pt_inst RS pt_perm_compose)) 1]
   541                   end)
   542 		else
   543 		  (let 
   544                      val dj_inst  = PureThy.get_thm thy'' (Name ("dj_"^ak_name''^"_"^ak_name'));
   545 		     val simp_s = HOL_basic_ss addsimps 
   546                                         ((dj_inst RS dj_pp_forget)::
   547                                          (PureThy.get_thmss thy'' 
   548 					   [Name (ak_name' ^"_prm_"^ak_name^"_def"),
   549                                             Name (ak_name''^"_prm_"^ak_name^"_def")]));  
   550 		  in 
   551                     EVERY [AxClass.intro_classes_tac [], simp_tac simp_s 1]
   552                   end))
   553 	      in
   554                 AxClass.add_inst_arity_i (name,[],[cls_name]) proof thy''
   555 	      end) ak_names thy') ak_names thy) ak_names thy24;
   556       
   557        (* shows that                                                    *) 
   558        (*      units                                                    *) 
   559        (*      products                                                 *)
   560        (*      lists                                                    *)
   561        (*      functions                                                *)
   562        (*      options                                                  *)
   563        (*      noptions                                                 *)
   564        (* are instances of cp_<ak>_<ai> for every <ak>/<ai>-combination *)
   565        val thy26 = fold (fn ak_name => fn thy =>
   566 	fold (fn ak_name' => fn thy' =>
   567         let
   568             val cls_name = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
   569             val cp_inst  = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
   570             val pt_inst  = PureThy.get_thm thy' (Name ("pt_"^ak_name^"_inst"));
   571             val at_inst  = PureThy.get_thm thy' (Name ("at_"^ak_name^"_inst"));
   572 
   573             fun cp_proof thm  = EVERY [AxClass.intro_classes_tac [],rtac (thm RS cp1) 1];     
   574 	  
   575             val cp_thm_unit = cp_unit_inst;
   576             val cp_thm_prod = cp_inst RS (cp_inst RS cp_prod_inst);
   577             val cp_thm_list = cp_inst RS cp_list_inst;
   578             val cp_thm_fun  = at_inst RS (pt_inst RS (cp_inst RS (cp_inst RS cp_fun_inst)));
   579             val cp_thm_optn = cp_inst RS cp_option_inst;
   580             val cp_thm_noptn = cp_inst RS cp_noption_inst;
   581         in
   582          thy'
   583          |> AxClass.add_inst_arity_i ("Product_Type.unit",[],[cls_name]) (cp_proof cp_thm_unit)
   584 	 |> AxClass.add_inst_arity_i ("*",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_prod)
   585          |> AxClass.add_inst_arity_i ("List.list",[[cls_name]],[cls_name]) (cp_proof cp_thm_list)
   586          |> AxClass.add_inst_arity_i ("fun",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_fun)
   587          |> AxClass.add_inst_arity_i ("Datatype.option",[[cls_name]],[cls_name]) (cp_proof cp_thm_optn)
   588          |> AxClass.add_inst_arity_i ("nominal.noption",[[cls_name]],[cls_name]) (cp_proof cp_thm_noptn)
   589         end) ak_names thy) ak_names thy25;
   590        
   591      (* show that discrete nominal types are permutation types, finitely     *) 
   592      (* supported and have the commutation property                          *)
   593      (* discrete types have a permutation operation defined as pi o x = x;   *)
   594      (* which renders the proofs to be simple "simp_all"-proofs.             *)            
   595      val thy32 =
   596         let 
   597 	  fun discrete_pt_inst discrete_ty defn = 
   598 	     fold (fn ak_name => fn thy =>
   599 	     let
   600 	       val qu_class = Sign.full_name (sign_of thy) ("pt_"^ak_name);
   601 	       val simp_s = HOL_basic_ss addsimps [defn];
   602                val proof = EVERY [AxClass.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)];      
   603              in  
   604 	       AxClass.add_inst_arity_i (discrete_ty,[],[qu_class]) proof thy
   605              end) ak_names;
   606 
   607           fun discrete_fs_inst discrete_ty defn = 
   608 	     fold (fn ak_name => fn thy =>
   609 	     let
   610 	       val qu_class = Sign.full_name (sign_of thy) ("fs_"^ak_name);
   611 	       val supp_def = thm "nominal.supp_def";
   612                val simp_s = HOL_ss addsimps [supp_def,Collect_const,Finites.emptyI,defn];
   613                val proof = EVERY [AxClass.intro_classes_tac [], asm_simp_tac simp_s 1];      
   614              in  
   615 	       AxClass.add_inst_arity_i (discrete_ty,[],[qu_class]) proof thy
   616              end) ak_names;  
   617 
   618           fun discrete_cp_inst discrete_ty defn = 
   619 	     fold (fn ak_name' => (fold (fn ak_name => fn thy =>
   620 	     let
   621 	       val qu_class = Sign.full_name (sign_of thy) ("cp_"^ak_name^"_"^ak_name');
   622 	       val supp_def = thm "nominal.supp_def";
   623                val simp_s = HOL_ss addsimps [defn];
   624                val proof = EVERY [AxClass.intro_classes_tac [], asm_simp_tac simp_s 1];      
   625              in  
   626 	       AxClass.add_inst_arity_i (discrete_ty,[],[qu_class]) proof thy
   627              end) ak_names)) ak_names;  
   628           
   629         in
   630          thy26
   631          |> discrete_pt_inst "nat"  (thm "perm_nat_def")
   632          |> discrete_fs_inst "nat"  (thm "perm_nat_def") 
   633          |> discrete_cp_inst "nat"  (thm "perm_nat_def") 
   634          |> discrete_pt_inst "bool" (thm "perm_bool")
   635          |> discrete_fs_inst "bool" (thm "perm_bool")
   636          |> discrete_cp_inst "bool" (thm "perm_bool")
   637          |> discrete_pt_inst "IntDef.int" (thm "perm_int_def")
   638          |> discrete_fs_inst "IntDef.int" (thm "perm_int_def") 
   639          |> discrete_cp_inst "IntDef.int" (thm "perm_int_def") 
   640          |> discrete_pt_inst "List.char" (thm "perm_char_def")
   641          |> discrete_fs_inst "List.char" (thm "perm_char_def")
   642          |> discrete_cp_inst "List.char" (thm "perm_char_def")
   643         end;
   644 
   645 
   646        (* abbreviations for some lemmas *)
   647        (*===============================*)
   648        val abs_fun_pi        = thm "nominal.abs_fun_pi";
   649        val abs_fun_pi_ineq   = thm "nominal.abs_fun_pi_ineq";
   650        val abs_fun_eq        = thm "nominal.abs_fun_eq";
   651        val dj_perm_forget    = thm "nominal.dj_perm_forget";
   652        val dj_pp_forget      = thm "nominal.dj_perm_perm_forget";
   653        val fresh_iff         = thm "nominal.fresh_abs_fun_iff";
   654        val fresh_iff_ineq    = thm "nominal.fresh_abs_fun_iff_ineq";
   655        val abs_fun_supp      = thm "nominal.abs_fun_supp";
   656        val abs_fun_supp_ineq = thm "nominal.abs_fun_supp_ineq";
   657        val pt_swap_bij       = thm "nominal.pt_swap_bij";
   658        val pt_fresh_fresh    = thm "nominal.pt_fresh_fresh";
   659        val pt_bij            = thm "nominal.pt_bij";
   660        val pt_perm_compose   = thm "nominal.pt_perm_compose";
   661        val perm_eq_app       = thm "nominal.perm_eq_app";
   662        val at_fresh          = thm "nominal.at_fresh";
   663        val at_calc           = thms "nominal.at_calc";
   664        val at_supp           = thm "nominal.at_supp";
   665        val dj_supp           = thm "nominal.dj_supp";
   666        val fresh_left_ineq   = thm "nominal.pt_fresh_left_ineq";
   667        val fresh_left        = thm "nominal.pt_fresh_left";
   668        val fresh_bij_ineq    = thm "nominal.pt_fresh_bij_ineq";
   669        val fresh_bij         = thm "nominal.pt_fresh_bij";
   670 
   671        (* Now we collect and instantiate some lemmas w.r.t. all atom      *)
   672        (* types; this allows for example to use abs_perm (which is a      *)
   673        (* collection of theorems) instead of thm abs_fun_pi with explicit *)
   674        (* instantiations.                                                 *)
   675        val (_,thy33) = 
   676 	 let 
   677              (* takes a theorem thm and a list of theorems [t1,..,tn]            *)
   678              (* produces a list of theorems of the form [t1 RS thm,..,tn RS thm] *) 
   679              fun instR thm thms = map (fn ti => ti RS thm) thms;
   680 
   681              (* takes two theorem lists (hopefully of the same length ;o)                *)
   682              (* produces a list of theorems of the form                                  *)
   683              (* [t1 RS m1,..,tn RS mn] where [t1,..,tn] is thms1 and [m1,..,mn] is thms2 *) 
   684              fun inst_zip thms1 thms2 = map (fn (t1,t2) => t1 RS t2) (thms1 ~~ thms2);
   685 
   686              (* takes a theorem list of the form [l1,...,ln]              *)
   687              (* and a list of theorem lists of the form                   *)
   688              (* [[h11,...,h1m],....,[hk1,....,hkm]                        *)
   689              (* produces the list of theorem lists                        *)
   690              (* [[l1 RS h11,...,l1 RS h1m],...,[ln RS hk1,...,ln RS hkm]] *)
   691              fun inst_mult thms thmss = map (fn (t,ts) => instR t ts) (thms ~~ thmss);
   692 
   693              (* FIXME: these lists do not need to be created dynamically again *)
   694 
   695              (* list of all at_inst-theorems *)
   696              val ats = map (fn ak => PureThy.get_thm thy32 (Name ("at_"^ak^"_inst"))) ak_names
   697              (* list of all pt_inst-theorems *)
   698              val pts = map (fn ak => PureThy.get_thm thy32 (Name ("pt_"^ak^"_inst"))) ak_names
   699              (* list of all cp_inst-theorems as a collection of lists*)
   700              val cps = 
   701 		 let fun cps_fun ak1 ak2 = PureThy.get_thm thy32 (Name ("cp_"^ak1^"_"^ak2^"_inst"))
   702 		 in map (fn aki => (map (cps_fun aki) ak_names)) ak_names end; 
   703              (* list of all cp_inst-theorems that have different atom types *)
   704              val cps' = 
   705 		let fun cps'_fun ak1 ak2 = 
   706 		if ak1=ak2 then NONE else SOME(PureThy.get_thm thy32 (Name ("cp_"^ak1^"_"^ak2^"_inst")))
   707 		in map (fn aki => (List.mapPartial I (map (cps'_fun aki) ak_names))) ak_names end;
   708              (* list of all dj_inst-theorems *)
   709              val djs = 
   710 	       let fun djs_fun (ak1,ak2) = 
   711 		     if ak1=ak2 then NONE else SOME(PureThy.get_thm thy32 (Name ("dj_"^ak2^"_"^ak1)))
   712 	       in List.mapPartial I (map djs_fun (Library.product ak_names ak_names)) end;
   713              (* list of all fs_inst-theorems *)
   714              val fss = map (fn ak => PureThy.get_thm thy32 (Name ("fs_"^ak^"_inst"))) ak_names
   715 
   716              fun inst_pt thms = Library.flat (map (fn ti => instR ti pts) thms); 
   717              fun inst_at thms = Library.flat (map (fn ti => instR ti ats) thms);               
   718              fun inst_fs thms = Library.flat (map (fn ti => instR ti fss) thms);
   719              fun inst_cp thms cps = Library.flat (inst_mult thms cps); 
   720 	     fun inst_pt_at thms = inst_zip ats (inst_pt thms);			
   721              fun inst_dj thms = Library.flat (map (fn ti => instR ti djs) thms);  
   722 	     fun inst_pt_pt_at_cp thms = inst_cp (inst_zip ats (inst_zip pts (inst_pt thms))) cps;
   723              fun inst_pt_at_fs thms = inst_zip (inst_fs [fs1]) (inst_zip ats (inst_pt thms));
   724 	     fun inst_pt_pt_at_cp thms = 
   725 		 let val i_pt_pt_at = inst_zip ats (inst_zip pts (inst_pt thms));
   726                      val i_pt_pt_at_cp = inst_cp i_pt_pt_at cps';
   727 		 in i_pt_pt_at_cp end;
   728              fun inst_pt_pt_at_cp_dj thms = inst_zip djs (inst_pt_pt_at_cp thms);
   729            in
   730             thy32 
   731 	    |>   PureThy.add_thmss [(("alpha", inst_pt_at [abs_fun_eq]),[])]
   732             ||>> PureThy.add_thmss [(("perm_swap", inst_pt_at [pt_swap_bij]),[])]
   733             ||>> PureThy.add_thmss [(("perm_fresh_fresh", inst_pt_at [pt_fresh_fresh]),[])]
   734             ||>> PureThy.add_thmss [(("perm_bij", inst_pt_at [pt_bij]),[])]
   735             ||>> PureThy.add_thmss 
   736 	      let val thms1 = inst_pt_at [pt_perm_compose];
   737 		  val thms2 = instR cp1 (Library.flat cps');
   738               in [(("perm_compose",thms1 @ thms2),[])] end
   739             ||>> PureThy.add_thmss [(("perm_app_eq", inst_pt_at [perm_eq_app]),[])]
   740             ||>> PureThy.add_thmss [(("supp_atm", (inst_at [at_supp]) @ (inst_dj [dj_supp])),[])]
   741             ||>> PureThy.add_thmss [(("fresh_atm", inst_at [at_fresh]),[])]
   742             ||>> PureThy.add_thmss [(("calc_atm", inst_at at_calc),[])]
   743             ||>> PureThy.add_thmss
   744 	      let val thms1 = inst_pt_at [abs_fun_pi]
   745 		  and thms2 = inst_pt_pt_at_cp [abs_fun_pi_ineq]
   746 	      in [(("abs_perm", thms1 @ thms2),[])] end
   747             ||>> PureThy.add_thmss
   748 	      let val thms1 = inst_dj [dj_perm_forget]
   749 		  and thms2 = inst_dj [dj_pp_forget]
   750               in [(("perm_dj", thms1 @ thms2),[])] end
   751             ||>> PureThy.add_thmss
   752 	      let val thms1 = inst_pt_at_fs [fresh_iff]
   753                   and thms2 = inst_pt_at [fresh_iff]
   754 		  and thms3 = inst_pt_pt_at_cp_dj [fresh_iff_ineq]
   755 	    in [(("abs_fresh", thms1 @ thms2 @ thms3),[])] end
   756 	    ||>> PureThy.add_thmss
   757 	      let val thms1 = inst_pt_at [abs_fun_supp]
   758 		  and thms2 = inst_pt_at_fs [abs_fun_supp]
   759 		  and thms3 = inst_pt_pt_at_cp_dj [abs_fun_supp_ineq]
   760 	      in [(("abs_supp", thms1 @ thms2 @ thms3),[])] end
   761             ||>> PureThy.add_thmss
   762 	      let val thms1 = inst_pt_at [fresh_left]
   763 		  and thms2 = inst_pt_pt_at_cp [fresh_left_ineq]
   764 	      in [(("fresh_left", thms1 @ thms2),[])] end
   765             ||>> PureThy.add_thmss
   766 	      let val thms1 = inst_pt_at [fresh_bij]
   767 		  and thms2 = inst_pt_pt_at_cp [fresh_bij_ineq]
   768 	      in [(("fresh_eqvt", thms1 @ thms2),[])] end
   769 	   end;
   770 
   771     in NominalData.put (fold Symtab.update (map (rpair ()) full_ak_names)
   772       (NominalData.get thy11)) thy33
   773     end;
   774 
   775 
   776 (* syntax und parsing *)
   777 structure P = OuterParse and K = OuterKeyword;
   778 
   779 val atom_declP =
   780   OuterSyntax.command "atom_decl" "Declare new kinds of atoms" K.thy_decl
   781     (Scan.repeat1 P.name >> (Toplevel.theory o create_nom_typedecls));
   782 
   783 val _ = OuterSyntax.add_parsers [atom_declP];
   784 
   785 val setup = [NominalData.init];
   786 
   787 end;