src/HOL/Nominal/nominal_atoms.ML
author urbanc
Tue Jul 04 17:26:02 2006 +0200 (2006-07-04)
changeset 19993 e0a5783d708f
parent 19992 bb383dcec3d8
child 20046 9c8909fc5865
permissions -rw-r--r--
added simplification rules to the fresh_guess tactic
     1 (*  Title:      HOL/Nominal/nominal_atoms.ML
     2     ID:         $Id$
     3     Author:     Christian Urban and Stefan Berghofer, TU Muenchen
     4 
     5 Declaration of atom types to be used in nominal datatypes.
     6 *)
     7 
     8 signature NOMINAL_ATOMS =
     9 sig
    10   val create_nom_typedecls : string list -> theory -> theory
    11   val atoms_of : theory -> string list
    12   val mk_permT : typ -> typ
    13   val setup : theory -> theory
    14 end
    15 
    16 structure NominalAtoms : NOMINAL_ATOMS =
    17 struct
    18 
    19 (* data kind 'HOL/nominal' *)
    20 
    21 structure NominalArgs =
    22 struct
    23   val name = "HOL/nominal";
    24   type T = unit Symtab.table;
    25 
    26   val empty = Symtab.empty;
    27   val copy = I;
    28   val extend = I;
    29   fun merge _ x = Symtab.merge (K true) x;
    30 
    31   fun print sg tab = ();
    32 end;
    33 
    34 structure NominalData = TheoryDataFun(NominalArgs);
    35 
    36 fun atoms_of thy = map fst (Symtab.dest (NominalData.get thy));
    37 
    38 (* FIXME: add to hologic.ML ? *)
    39 fun mk_listT T = Type ("List.list", [T]);
    40 fun mk_permT T = mk_listT (HOLogic.mk_prodT (T, T));
    41 
    42 fun mk_Cons x xs =
    43   let val T = fastype_of x
    44   in Const ("List.list.Cons", T --> mk_listT T --> mk_listT T) $ x $ xs end;
    45 
    46 
    47 (* this function sets up all matters related to atom-  *)
    48 (* kinds; the user specifies a list of atom-kind names *)
    49 (* atom_decl <ak1> ... <akn>                           *)
    50 fun create_nom_typedecls ak_names thy =
    51   let
    52     (* declares a type-decl for every atom-kind: *) 
    53     (* that is typedecl <ak>                     *)
    54     val thy1 = TypedefPackage.add_typedecls (map (fn x => (x,[],NoSyn)) ak_names) thy;
    55     
    56     (* produces a list consisting of pairs:         *)
    57     (*  fst component is the atom-kind name         *)
    58     (*  snd component is its type                   *)
    59     val full_ak_names = map (Sign.intern_type (sign_of thy1)) ak_names;
    60     val ak_names_types = ak_names ~~ map (Type o rpair []) full_ak_names;
    61      
    62     (* adds for every atom-kind an axiom             *)
    63     (* <ak>_infinite: infinite (UNIV::<ak_type> set) *)
    64     val (inf_axs,thy2) = PureThy.add_axioms_i (map (fn (ak_name, T) =>
    65       let 
    66 	val name = ak_name ^ "_infinite"
    67         val axiom = HOLogic.mk_Trueprop (HOLogic.mk_not
    68                     (HOLogic.mk_mem (HOLogic.mk_UNIV T,
    69                      Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT T)))))
    70       in
    71 	((name, axiom), []) 
    72       end) ak_names_types) thy1;
    73     
    74     (* declares a swapping function for every atom-kind, it is         *)
    75     (* const swap_<ak> :: <akT> * <akT> => <akT> => <akT>              *)
    76     (* swap_<ak> (a,b) c = (if a=c then b (else if b=c then a else c)) *)
    77     (* overloades then the general swap-function                       *) 
    78     val (thy3, swap_eqs) = foldl_map (fn (thy, (ak_name, T)) =>
    79       let
    80         val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
    81         val swap_name = Sign.full_name (sign_of thy) ("swap_" ^ ak_name);
    82         val a = Free ("a", T);
    83         val b = Free ("b", T);
    84         val c = Free ("c", T);
    85         val ab = Free ("ab", HOLogic.mk_prodT (T, T))
    86         val cif = Const ("HOL.If", HOLogic.boolT --> T --> T --> T);
    87         val cswap_akname = Const (swap_name, swapT);
    88         val cswap = Const ("Nominal.swap", swapT)
    89 
    90         val name = "swap_"^ak_name^"_def";
    91         val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq
    92 		   (cswap_akname $ HOLogic.mk_prod (a,b) $ c,
    93                     cif $ HOLogic.mk_eq (a,c) $ b $ (cif $ HOLogic.mk_eq (b,c) $ a $ c)))
    94         val def2 = Logic.mk_equals (cswap $ ab $ c, cswap_akname $ ab $ c)
    95       in
    96         thy |> Theory.add_consts_i [("swap_" ^ ak_name, swapT, NoSyn)] 
    97             |> (#2 o PureThy.add_defs_unchecked_i true [((name, def2),[])])
    98             |> PrimrecPackage.add_primrec_unchecked_i "" [(("", def1),[])]            
    99       end) (thy2, ak_names_types);
   100     
   101     (* declares a permutation function for every atom-kind acting  *)
   102     (* on such atoms                                               *)
   103     (* const <ak>_prm_<ak> :: (<akT> * <akT>)list => akT => akT    *)
   104     (* <ak>_prm_<ak> []     a = a                                  *)
   105     (* <ak>_prm_<ak> (x#xs) a = swap_<ak> x (perm xs a)            *)
   106     val (thy4, prm_eqs) = foldl_map (fn (thy, (ak_name, T)) =>
   107       let
   108         val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
   109         val swap_name = Sign.full_name (sign_of thy) ("swap_" ^ ak_name)
   110         val prmT = mk_permT T --> T --> T;
   111         val prm_name = ak_name ^ "_prm_" ^ ak_name;
   112         val qu_prm_name = Sign.full_name (sign_of thy) prm_name;
   113         val x  = Free ("x", HOLogic.mk_prodT (T, T));
   114         val xs = Free ("xs", mk_permT T);
   115         val a  = Free ("a", T) ;
   116 
   117         val cnil  = Const ("List.list.Nil", mk_permT T);
   118         
   119         val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq (Const (qu_prm_name, prmT) $ cnil $ a, a));
   120 
   121         val def2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
   122                    (Const (qu_prm_name, prmT) $ mk_Cons x xs $ a,
   123                     Const (swap_name, swapT) $ x $ (Const (qu_prm_name, prmT) $ xs $ a)));
   124       in
   125         thy |> Theory.add_consts_i [(prm_name, mk_permT T --> T --> T, NoSyn)] 
   126             |> PrimrecPackage.add_primrec_unchecked_i "" [(("", def1), []),(("", def2), [])]
   127       end) (thy3, ak_names_types);
   128     
   129     (* defines permutation functions for all combinations of atom-kinds; *)
   130     (* there are a trivial cases and non-trivial cases                   *)
   131     (* non-trivial case:                                                 *)
   132     (* <ak>_prm_<ak>_def:  perm pi a == <ak>_prm_<ak> pi a               *)
   133     (* trivial case with <ak> != <ak'>                                   *)
   134     (* <ak>_prm<ak'>_def[simp]:  perm pi a == a                          *)
   135     (*                                                                   *)
   136     (* the trivial cases are added to the simplifier, while the non-     *)
   137     (* have their own rules proved below                                 *)  
   138     val (perm_defs, thy5) = fold_map (fn (ak_name, T) => fn thy =>
   139       fold_map (fn (ak_name', T') => fn thy' =>
   140         let
   141           val perm_def_name = ak_name ^ "_prm_" ^ ak_name';
   142           val pi = Free ("pi", mk_permT T);
   143           val a  = Free ("a", T');
   144           val cperm = Const ("Nominal.perm", mk_permT T --> T' --> T');
   145           val cperm_def = Const (Sign.full_name (sign_of thy') perm_def_name, mk_permT T --> T' --> T');
   146 
   147           val name = ak_name ^ "_prm_" ^ ak_name' ^ "_def";
   148           val def = Logic.mk_equals
   149                     (cperm $ pi $ a, if ak_name = ak_name' then cperm_def $ pi $ a else a)
   150         in
   151           PureThy.add_defs_unchecked_i true [((name, def),[])] thy'
   152         end) ak_names_types thy) ak_names_types thy4;
   153     
   154     (* proves that every atom-kind is an instance of at *)
   155     (* lemma at_<ak>_inst:                              *)
   156     (* at TYPE(<ak>)                                    *)
   157     val (prm_cons_thms,thy6) = 
   158       thy5 |> PureThy.add_thms (map (fn (ak_name, T) =>
   159       let
   160         val ak_name_qu = Sign.full_name (sign_of thy5) (ak_name);
   161         val i_type = Type(ak_name_qu,[]);
   162 	val cat = Const ("Nominal.at",(Term.itselfT i_type)  --> HOLogic.boolT);
   163         val at_type = Logic.mk_type i_type;
   164         val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy5
   165                                   [Name "at_def",
   166                                    Name (ak_name ^ "_prm_" ^ ak_name ^ "_def"),
   167                                    Name (ak_name ^ "_prm_" ^ ak_name ^ ".simps"),
   168                                    Name ("swap_" ^ ak_name ^ "_def"),
   169                                    Name ("swap_" ^ ak_name ^ ".simps"),
   170                                    Name (ak_name ^ "_infinite")]
   171 	    
   172 	val name = "at_"^ak_name^ "_inst";
   173         val statement = HOLogic.mk_Trueprop (cat $ at_type);
   174 
   175         val proof = fn _ => auto_tac (claset(),simp_s);
   176 
   177       in 
   178         ((name, standard (Goal.prove thy5 [] [] statement proof)), []) 
   179       end) ak_names_types);
   180 
   181     (* declares a perm-axclass for every atom-kind               *)
   182     (* axclass pt_<ak>                                           *)
   183     (* pt_<ak>1[simp]: perm [] x = x                             *)
   184     (* pt_<ak>2:       perm (pi1@pi2) x = perm pi1 (perm pi2 x)  *)
   185     (* pt_<ak>3:       pi1 ~ pi2 ==> perm pi1 x = perm pi2 x     *)
   186      val (pt_ax_classes,thy7) =  fold_map (fn (ak_name, T) => fn thy =>
   187       let 
   188 	  val cl_name = "pt_"^ak_name;
   189           val ty = TFree("'a",["HOL.type"]);
   190           val x   = Free ("x", ty);
   191           val pi1 = Free ("pi1", mk_permT T);
   192           val pi2 = Free ("pi2", mk_permT T);
   193           val cperm = Const ("Nominal.perm", mk_permT T --> ty --> ty);
   194           val cnil  = Const ("List.list.Nil", mk_permT T);
   195           val cappend = Const ("List.op @",mk_permT T --> mk_permT T --> mk_permT T);
   196           val cprm_eq = Const ("Nominal.prm_eq",mk_permT T --> mk_permT T --> HOLogic.boolT);
   197           (* nil axiom *)
   198           val axiom1 = HOLogic.mk_Trueprop (HOLogic.mk_eq 
   199                        (cperm $ cnil $ x, x));
   200           (* append axiom *)
   201           val axiom2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
   202                        (cperm $ (cappend $ pi1 $ pi2) $ x, cperm $ pi1 $ (cperm $ pi2 $ x)));
   203           (* perm-eq axiom *)
   204           val axiom3 = Logic.mk_implies
   205                        (HOLogic.mk_Trueprop (cprm_eq $ pi1 $ pi2),
   206                         HOLogic.mk_Trueprop (HOLogic.mk_eq (cperm $ pi1 $ x, cperm $ pi2 $ x)));
   207       in
   208           AxClass.define_class_i (cl_name, ["HOL.type"]) []
   209                 [((cl_name ^ "1", [Simplifier.simp_add]), [axiom1]),
   210                  ((cl_name ^ "2", []), [axiom2]),                           
   211                  ((cl_name ^ "3", []), [axiom3])] thy                          
   212       end) ak_names_types thy6;
   213 
   214     (* proves that every pt_<ak>-type together with <ak>-type *)
   215     (* instance of pt                                         *)
   216     (* lemma pt_<ak>_inst:                                    *)
   217     (* pt TYPE('x::pt_<ak>) TYPE(<ak>)                        *)
   218     val (prm_inst_thms,thy8) = 
   219       thy7 |> PureThy.add_thms (map (fn (ak_name, T) =>
   220       let
   221         val ak_name_qu = Sign.full_name (sign_of thy7) (ak_name);
   222         val pt_name_qu = Sign.full_name (sign_of thy7) ("pt_"^ak_name);
   223         val i_type1 = TFree("'x",[pt_name_qu]);
   224         val i_type2 = Type(ak_name_qu,[]);
   225 	val cpt = Const ("Nominal.pt",(Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
   226         val pt_type = Logic.mk_type i_type1;
   227         val at_type = Logic.mk_type i_type2;
   228         val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy7
   229                                   [Name "pt_def",
   230                                    Name ("pt_" ^ ak_name ^ "1"),
   231                                    Name ("pt_" ^ ak_name ^ "2"),
   232                                    Name ("pt_" ^ ak_name ^ "3")];
   233 
   234 	val name = "pt_"^ak_name^ "_inst";
   235         val statement = HOLogic.mk_Trueprop (cpt $ pt_type $ at_type);
   236 
   237         val proof = fn _ => auto_tac (claset(),simp_s);
   238       in 
   239         ((name, standard (Goal.prove thy7 [] [] statement proof)), []) 
   240       end) ak_names_types);
   241 
   242      (* declares an fs-axclass for every atom-kind       *)
   243      (* axclass fs_<ak>                                  *)
   244      (* fs_<ak>1: finite ((supp x)::<ak> set)            *)
   245      val (fs_ax_classes,thy11) =  fold_map (fn (ak_name, T) => fn thy =>
   246        let 
   247 	  val cl_name = "fs_"^ak_name;
   248 	  val pt_name = Sign.full_name (sign_of thy) ("pt_"^ak_name);
   249           val ty = TFree("'a",["HOL.type"]);
   250           val x   = Free ("x", ty);
   251           val csupp    = Const ("Nominal.supp", ty --> HOLogic.mk_setT T);
   252           val cfinites = Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT T))
   253           
   254           val axiom1   = HOLogic.mk_Trueprop (HOLogic.mk_mem (csupp $ x, cfinites));
   255 
   256        in  
   257         AxClass.define_class_i (cl_name, [pt_name]) [] [((cl_name ^ "1", []), [axiom1])] thy            
   258        end) ak_names_types thy8; 
   259 
   260      (* proves that every fs_<ak>-type together with <ak>-type   *)
   261      (* instance of fs-type                                      *)
   262      (* lemma abst_<ak>_inst:                                    *)
   263      (* fs TYPE('x::pt_<ak>) TYPE (<ak>)                         *)
   264      val (fs_inst_thms,thy12) = 
   265        thy11 |> PureThy.add_thms (map (fn (ak_name, T) =>
   266        let
   267          val ak_name_qu = Sign.full_name (sign_of thy11) (ak_name);
   268          val fs_name_qu = Sign.full_name (sign_of thy11) ("fs_"^ak_name);
   269          val i_type1 = TFree("'x",[fs_name_qu]);
   270          val i_type2 = Type(ak_name_qu,[]);
   271  	 val cfs = Const ("Nominal.fs", 
   272                                  (Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
   273          val fs_type = Logic.mk_type i_type1;
   274          val at_type = Logic.mk_type i_type2;
   275 	 val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy11
   276                                    [Name "fs_def",
   277                                     Name ("fs_" ^ ak_name ^ "1")];
   278     
   279 	 val name = "fs_"^ak_name^ "_inst";
   280          val statement = HOLogic.mk_Trueprop (cfs $ fs_type $ at_type);
   281 
   282          val proof = fn _ => auto_tac (claset(),simp_s);
   283        in 
   284          ((name, standard (Goal.prove thy11 [] [] statement proof)), []) 
   285        end) ak_names_types);
   286 
   287        (* declares for every atom-kind combination an axclass            *)
   288        (* cp_<ak1>_<ak2> giving a composition property                   *)
   289        (* cp_<ak1>_<ak2>1: pi1 o pi2 o x = (pi1 o pi2) o (pi1 o x)       *)
   290         val (_,thy12b) = fold_map (fn (ak_name, T) => fn thy =>
   291 	 fold_map (fn (ak_name', T') => fn thy' =>
   292 	     let
   293 	       val cl_name = "cp_"^ak_name^"_"^ak_name';
   294 	       val ty = TFree("'a",["HOL.type"]);
   295                val x   = Free ("x", ty);
   296                val pi1 = Free ("pi1", mk_permT T);
   297 	       val pi2 = Free ("pi2", mk_permT T');                  
   298 	       val cperm1 = Const ("Nominal.perm", mk_permT T  --> ty --> ty);
   299                val cperm2 = Const ("Nominal.perm", mk_permT T' --> ty --> ty);
   300                val cperm3 = Const ("Nominal.perm", mk_permT T  --> mk_permT T' --> mk_permT T');
   301 
   302                val ax1   = HOLogic.mk_Trueprop 
   303 			   (HOLogic.mk_eq (cperm1 $ pi1 $ (cperm2 $ pi2 $ x), 
   304                                            cperm2 $ (cperm3 $ pi1 $ pi2) $ (cperm1 $ pi1 $ x)));
   305 	       in  
   306 		 AxClass.define_class_i (cl_name, ["HOL.type"]) [] [((cl_name ^ "1", []), [ax1])] thy'  
   307 	       end) ak_names_types thy) ak_names_types thy12;
   308 
   309         (* proves for every <ak>-combination a cp_<ak1>_<ak2>_inst theorem;     *)
   310         (* lemma cp_<ak1>_<ak2>_inst:                                           *)
   311         (* cp TYPE('a::cp_<ak1>_<ak2>) TYPE(<ak1>) TYPE(<ak2>)                  *)
   312         val (cp_thms,thy12c) = fold_map (fn (ak_name, T) => fn thy =>
   313 	 fold_map (fn (ak_name', T') => fn thy' =>
   314            let
   315              val ak_name_qu  = Sign.full_name (sign_of thy') (ak_name);
   316 	     val ak_name_qu' = Sign.full_name (sign_of thy') (ak_name');
   317              val cp_name_qu  = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
   318              val i_type0 = TFree("'a",[cp_name_qu]);
   319              val i_type1 = Type(ak_name_qu,[]);
   320              val i_type2 = Type(ak_name_qu',[]);
   321 	     val ccp = Const ("Nominal.cp",
   322                              (Term.itselfT i_type0)-->(Term.itselfT i_type1)-->
   323                                                       (Term.itselfT i_type2)-->HOLogic.boolT);
   324              val at_type  = Logic.mk_type i_type1;
   325              val at_type' = Logic.mk_type i_type2;
   326 	     val cp_type  = Logic.mk_type i_type0;
   327              val simp_s   = HOL_basic_ss addsimps PureThy.get_thmss thy' [(Name "cp_def")];
   328 	     val cp1      = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"1"));
   329 
   330 	     val name = "cp_"^ak_name^ "_"^ak_name'^"_inst";
   331              val statement = HOLogic.mk_Trueprop (ccp $ cp_type $ at_type $ at_type');
   332 
   333              val proof = fn _ => EVERY [auto_tac (claset(),simp_s), rtac cp1 1];
   334 	   in
   335 	     PureThy.add_thms [((name, standard (Goal.prove thy' [] [] statement proof)), [])] thy'
   336 	   end) 
   337            ak_names_types thy) ak_names_types thy12b;
   338        
   339         (* proves for every non-trivial <ak>-combination a disjointness   *)
   340         (* theorem; i.e. <ak1> != <ak2>                                   *)
   341         (* lemma ds_<ak1>_<ak2>:                                          *)
   342         (* dj TYPE(<ak1>) TYPE(<ak2>)                                     *)
   343         val (dj_thms, thy12d) = fold_map (fn (ak_name,T) => fn thy =>
   344 	  fold_map (fn (ak_name',T') => fn thy' =>
   345           (if not (ak_name = ak_name') 
   346            then 
   347 	       let
   348 		 val ak_name_qu  = Sign.full_name (sign_of thy') (ak_name);
   349 	         val ak_name_qu' = Sign.full_name (sign_of thy') (ak_name');
   350                  val i_type1 = Type(ak_name_qu,[]);
   351                  val i_type2 = Type(ak_name_qu',[]);
   352 	         val cdj = Const ("Nominal.disjoint",
   353                            (Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
   354                  val at_type  = Logic.mk_type i_type1;
   355                  val at_type' = Logic.mk_type i_type2;
   356                  val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy' 
   357 					   [Name "disjoint_def",
   358                                             Name (ak_name^"_prm_"^ak_name'^"_def"),
   359                                             Name (ak_name'^"_prm_"^ak_name^"_def")];
   360 
   361 	         val name = "dj_"^ak_name^"_"^ak_name';
   362                  val statement = HOLogic.mk_Trueprop (cdj $ at_type $ at_type');
   363 
   364                  val proof = fn _ => auto_tac (claset(),simp_s);
   365 	       in
   366 		PureThy.add_thms [((name, standard (Goal.prove thy' [] [] statement proof)), [])] thy'
   367 	       end
   368            else 
   369             ([],thy')))  (* do nothing branch, if ak_name = ak_name' *) 
   370 	    ak_names_types thy) ak_names_types thy12c;
   371 
   372      (*<<<<<<<  pt_<ak> class instances  >>>>>>>*)
   373      (*=========================================*)
   374      (* some abbreviations for theorems *)
   375       val pt1           = thm "pt1";
   376       val pt2           = thm "pt2";
   377       val pt3           = thm "pt3";
   378       val at_pt_inst    = thm "at_pt_inst";
   379       val pt_set_inst   = thm "pt_set_inst"; 
   380       val pt_unit_inst  = thm "pt_unit_inst";
   381       val pt_prod_inst  = thm "pt_prod_inst"; 
   382       val pt_nprod_inst = thm "pt_nprod_inst"; 
   383       val pt_list_inst  = thm "pt_list_inst";   
   384       val pt_optn_inst  = thm "pt_option_inst";   
   385       val pt_noptn_inst = thm "pt_noption_inst";   
   386       val pt_fun_inst   = thm "pt_fun_inst";     
   387 
   388      (* for all atom-kind combinations <ak>/<ak'> show that        *)
   389      (* every <ak> is an instance of pt_<ak'>; the proof for       *)
   390      (* ak!=ak' is by definition; the case ak=ak' uses at_pt_inst. *)
   391      val thy13 = fold (fn ak_name => fn thy =>
   392 	fold (fn ak_name' => fn thy' =>
   393          let
   394            val qu_name =  Sign.full_name (sign_of thy') ak_name';
   395            val cls_name = Sign.full_name (sign_of thy') ("pt_"^ak_name);
   396            val at_inst  = PureThy.get_thm thy' (Name ("at_"^ak_name'^"_inst")); 
   397 
   398            val proof1 = EVERY [ClassPackage.intro_classes_tac [],
   399                                  rtac ((at_inst RS at_pt_inst) RS pt1) 1,
   400                                  rtac ((at_inst RS at_pt_inst) RS pt2) 1,
   401                                  rtac ((at_inst RS at_pt_inst) RS pt3) 1,
   402                                  atac 1];
   403            val simp_s = HOL_basic_ss addsimps 
   404                         PureThy.get_thmss thy' [Name (ak_name^"_prm_"^ak_name'^"_def")];  
   405            val proof2 = EVERY [ClassPackage.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)];
   406 
   407          in
   408            thy'
   409            |> AxClass.prove_arity (qu_name,[],[cls_name])
   410               (if ak_name = ak_name' then proof1 else proof2)
   411          end) ak_names thy) ak_names thy12c;
   412 
   413      (* show that                       *)
   414      (*      fun(pt_<ak>,pt_<ak>)       *)
   415      (*      noption(pt_<ak>)           *)
   416      (*      option(pt_<ak>)            *)
   417      (*      list(pt_<ak>)              *)
   418      (*      *(pt_<ak>,pt_<ak>)         *)
   419      (*      nprod(pt_<ak>,pt_<ak>)     *)
   420      (*      unit                       *)
   421      (*      set(pt_<ak>)               *)
   422      (* are instances of pt_<ak>        *)
   423      val thy18 = fold (fn ak_name => fn thy =>
   424        let
   425           val cls_name = Sign.full_name (sign_of thy) ("pt_"^ak_name);
   426           val at_thm   = PureThy.get_thm thy (Name ("at_"^ak_name^"_inst"));
   427           val pt_inst  = PureThy.get_thm thy (Name ("pt_"^ak_name^"_inst"));
   428           
   429           fun pt_proof thm = 
   430 	      EVERY [ClassPackage.intro_classes_tac [],
   431                      rtac (thm RS pt1) 1, rtac (thm RS pt2) 1, rtac (thm RS pt3) 1, atac 1];
   432 
   433           val pt_thm_fun   = at_thm RS (pt_inst RS (pt_inst RS pt_fun_inst));
   434           val pt_thm_noptn = pt_inst RS pt_noptn_inst; 
   435           val pt_thm_optn  = pt_inst RS pt_optn_inst; 
   436           val pt_thm_list  = pt_inst RS pt_list_inst;
   437           val pt_thm_prod  = pt_inst RS (pt_inst RS pt_prod_inst);
   438           val pt_thm_nprod = pt_inst RS (pt_inst RS pt_nprod_inst);
   439           val pt_thm_unit  = pt_unit_inst;
   440           val pt_thm_set   = pt_inst RS pt_set_inst
   441        in 
   442 	thy
   443 	|> AxClass.prove_arity ("fun",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_fun)
   444         |> AxClass.prove_arity ("Nominal.noption",[[cls_name]],[cls_name]) (pt_proof pt_thm_noptn) 
   445         |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (pt_proof pt_thm_optn)
   446         |> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (pt_proof pt_thm_list)
   447         |> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_prod)
   448         |> AxClass.prove_arity ("Nominal.nprod",[[cls_name],[cls_name]],[cls_name]) 
   449                                     (pt_proof pt_thm_nprod)
   450         |> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (pt_proof pt_thm_unit)
   451         |> AxClass.prove_arity ("set",[[cls_name]],[cls_name]) (pt_proof pt_thm_set)
   452      end) ak_names thy13; 
   453 
   454        (*<<<<<<<  fs_<ak> class instances  >>>>>>>*)
   455        (*=========================================*)
   456        (* abbreviations for some lemmas *)
   457        val fs1            = thm "fs1";
   458        val fs_at_inst     = thm "fs_at_inst";
   459        val fs_unit_inst   = thm "fs_unit_inst";
   460        val fs_prod_inst   = thm "fs_prod_inst";
   461        val fs_nprod_inst  = thm "fs_nprod_inst";
   462        val fs_list_inst   = thm "fs_list_inst";
   463        val fs_option_inst = thm "fs_option_inst";
   464        val dj_supp        = thm "dj_supp"
   465 
   466        (* shows that <ak> is an instance of fs_<ak>     *)
   467        (* uses the theorem at_<ak>_inst                 *)
   468        val thy20 = fold (fn ak_name => fn thy =>
   469 	fold (fn ak_name' => fn thy' => 
   470         let
   471            val qu_name =  Sign.full_name (sign_of thy') ak_name';
   472            val qu_class = Sign.full_name (sign_of thy') ("fs_"^ak_name);
   473            val proof = 
   474 	       (if ak_name = ak_name'
   475 	        then
   476 	          let val at_thm = PureThy.get_thm thy' (Name ("at_"^ak_name^"_inst"));
   477                   in  EVERY [ClassPackage.intro_classes_tac [],
   478                              rtac ((at_thm RS fs_at_inst) RS fs1) 1] end
   479                 else
   480 		  let val dj_inst = PureThy.get_thm thy' (Name ("dj_"^ak_name'^"_"^ak_name));
   481                       val simp_s = HOL_basic_ss addsimps [dj_inst RS dj_supp, Finites.emptyI]; 
   482                   in EVERY [ClassPackage.intro_classes_tac [], asm_simp_tac simp_s 1] end)      
   483         in 
   484 	 AxClass.prove_arity (qu_name,[],[qu_class]) proof thy' 
   485         end) ak_names thy) ak_names thy18;
   486 
   487        (* shows that                  *)
   488        (*    unit                     *)
   489        (*    *(fs_<ak>,fs_<ak>)       *)
   490        (*    nprod(fs_<ak>,fs_<ak>)   *)
   491        (*    list(fs_<ak>)            *)
   492        (*    option(fs_<ak>)          *) 
   493        (* are instances of fs_<ak>    *)
   494 
   495        val thy24 = fold (fn ak_name => fn thy => 
   496         let
   497           val cls_name = Sign.full_name (sign_of thy) ("fs_"^ak_name);
   498           val fs_inst  = PureThy.get_thm thy (Name ("fs_"^ak_name^"_inst"));
   499           fun fs_proof thm = EVERY [ClassPackage.intro_classes_tac [], rtac (thm RS fs1) 1];      
   500 
   501           val fs_thm_unit  = fs_unit_inst;
   502           val fs_thm_prod  = fs_inst RS (fs_inst RS fs_prod_inst);
   503           val fs_thm_nprod = fs_inst RS (fs_inst RS fs_nprod_inst);
   504           val fs_thm_list  = fs_inst RS fs_list_inst;
   505           val fs_thm_optn  = fs_inst RS fs_option_inst;
   506         in 
   507          thy 
   508          |> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (fs_proof fs_thm_unit) 
   509          |> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (fs_proof fs_thm_prod) 
   510          |> AxClass.prove_arity ("Nominal.nprod",[[cls_name],[cls_name]],[cls_name]) 
   511                                      (fs_proof fs_thm_nprod) 
   512          |> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (fs_proof fs_thm_list)
   513          |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (fs_proof fs_thm_optn)
   514         end) ak_names thy20; 
   515 
   516        (*<<<<<<<  cp_<ak>_<ai> class instances  >>>>>>>*)
   517        (*==============================================*)
   518        (* abbreviations for some lemmas *)
   519        val cp1             = thm "cp1";
   520        val cp_unit_inst    = thm "cp_unit_inst";
   521        val cp_bool_inst    = thm "cp_bool_inst";
   522        val cp_prod_inst    = thm "cp_prod_inst";
   523        val cp_list_inst    = thm "cp_list_inst";
   524        val cp_fun_inst     = thm "cp_fun_inst";
   525        val cp_option_inst  = thm "cp_option_inst";
   526        val cp_noption_inst = thm "cp_noption_inst";
   527        val pt_perm_compose = thm "pt_perm_compose";
   528        
   529        val dj_pp_forget    = thm "dj_perm_perm_forget";
   530 
   531        (* shows that <aj> is an instance of cp_<ak>_<ai>  *)
   532        (* for every  <ak>/<ai>-combination                *)
   533        val thy25 = fold (fn ak_name => fn thy => 
   534 	 fold (fn ak_name' => fn thy' => 
   535           fold (fn ak_name'' => fn thy'' => 
   536             let
   537               val name =  Sign.full_name (sign_of thy'') ak_name;
   538               val cls_name = Sign.full_name (sign_of thy'') ("cp_"^ak_name'^"_"^ak_name'');
   539               val proof =
   540                 (if (ak_name'=ak_name'') then 
   541 		  (let
   542                     val pt_inst  = PureThy.get_thm thy'' (Name ("pt_"^ak_name''^"_inst"));
   543 		    val at_inst  = PureThy.get_thm thy'' (Name ("at_"^ak_name''^"_inst"));
   544                   in 
   545 		   EVERY [ClassPackage.intro_classes_tac [], 
   546                           rtac (at_inst RS (pt_inst RS pt_perm_compose)) 1]
   547                   end)
   548 		else
   549 		  (let 
   550                      val dj_inst  = PureThy.get_thm thy'' (Name ("dj_"^ak_name''^"_"^ak_name'));
   551 		     val simp_s = HOL_basic_ss addsimps 
   552                                         ((dj_inst RS dj_pp_forget)::
   553                                          (PureThy.get_thmss thy'' 
   554 					   [Name (ak_name' ^"_prm_"^ak_name^"_def"),
   555                                             Name (ak_name''^"_prm_"^ak_name^"_def")]));  
   556 		  in 
   557                     EVERY [ClassPackage.intro_classes_tac [], simp_tac simp_s 1]
   558                   end))
   559 	      in
   560                 AxClass.prove_arity (name,[],[cls_name]) proof thy''
   561 	      end) ak_names thy') ak_names thy) ak_names thy24;
   562       
   563        (* shows that                                                    *) 
   564        (*      units                                                    *) 
   565        (*      products                                                 *)
   566        (*      lists                                                    *)
   567        (*      functions                                                *)
   568        (*      options                                                  *)
   569        (*      noptions                                                 *)
   570        (* are instances of cp_<ak>_<ai> for every <ak>/<ai>-combination *)
   571        val thy26 = fold (fn ak_name => fn thy =>
   572 	fold (fn ak_name' => fn thy' =>
   573         let
   574             val cls_name = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
   575             val cp_inst  = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
   576             val pt_inst  = PureThy.get_thm thy' (Name ("pt_"^ak_name^"_inst"));
   577             val at_inst  = PureThy.get_thm thy' (Name ("at_"^ak_name^"_inst"));
   578 
   579             fun cp_proof thm  = EVERY [ClassPackage.intro_classes_tac [],rtac (thm RS cp1) 1];     
   580 	  
   581             val cp_thm_unit = cp_unit_inst;
   582             val cp_thm_prod = cp_inst RS (cp_inst RS cp_prod_inst);
   583             val cp_thm_list = cp_inst RS cp_list_inst;
   584             val cp_thm_fun  = at_inst RS (pt_inst RS (cp_inst RS (cp_inst RS cp_fun_inst)));
   585             val cp_thm_optn = cp_inst RS cp_option_inst;
   586             val cp_thm_noptn = cp_inst RS cp_noption_inst;
   587         in
   588          thy'
   589          |> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (cp_proof cp_thm_unit)
   590 	 |> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_prod)
   591          |> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (cp_proof cp_thm_list)
   592          |> AxClass.prove_arity ("fun",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_fun)
   593          |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (cp_proof cp_thm_optn)
   594          |> AxClass.prove_arity ("Nominal.noption",[[cls_name]],[cls_name]) (cp_proof cp_thm_noptn)
   595         end) ak_names thy) ak_names thy25;
   596        
   597      (* show that discrete nominal types are permutation types, finitely     *) 
   598      (* supported and have the commutation property                          *)
   599      (* discrete types have a permutation operation defined as pi o x = x;   *)
   600      (* which renders the proofs to be simple "simp_all"-proofs.             *)            
   601      val thy32 =
   602         let 
   603 	  fun discrete_pt_inst discrete_ty defn = 
   604 	     fold (fn ak_name => fn thy =>
   605 	     let
   606 	       val qu_class = Sign.full_name (sign_of thy) ("pt_"^ak_name);
   607 	       val simp_s = HOL_basic_ss addsimps [defn];
   608                val proof = EVERY [ClassPackage.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)];      
   609              in  
   610 	       AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
   611              end) ak_names;
   612 
   613           fun discrete_fs_inst discrete_ty defn = 
   614 	     fold (fn ak_name => fn thy =>
   615 	     let
   616 	       val qu_class = Sign.full_name (sign_of thy) ("fs_"^ak_name);
   617 	       val supp_def = thm "Nominal.supp_def";
   618                val simp_s = HOL_ss addsimps [supp_def,Collect_const,Finites.emptyI,defn];
   619                val proof = EVERY [ClassPackage.intro_classes_tac [], asm_simp_tac simp_s 1];      
   620              in  
   621 	       AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
   622              end) ak_names;  
   623 
   624           fun discrete_cp_inst discrete_ty defn = 
   625 	     fold (fn ak_name' => (fold (fn ak_name => fn thy =>
   626 	     let
   627 	       val qu_class = Sign.full_name (sign_of thy) ("cp_"^ak_name^"_"^ak_name');
   628 	       val supp_def = thm "Nominal.supp_def";
   629                val simp_s = HOL_ss addsimps [defn];
   630                val proof = EVERY [ClassPackage.intro_classes_tac [], asm_simp_tac simp_s 1];      
   631              in  
   632 	       AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
   633              end) ak_names)) ak_names;  
   634           
   635         in
   636          thy26
   637          |> discrete_pt_inst "nat"  (thm "perm_nat_def")
   638          |> discrete_fs_inst "nat"  (thm "perm_nat_def") 
   639          |> discrete_cp_inst "nat"  (thm "perm_nat_def") 
   640          |> discrete_pt_inst "bool" (thm "perm_bool")
   641          |> discrete_fs_inst "bool" (thm "perm_bool")
   642          |> discrete_cp_inst "bool" (thm "perm_bool")
   643          |> discrete_pt_inst "IntDef.int" (thm "perm_int_def")
   644          |> discrete_fs_inst "IntDef.int" (thm "perm_int_def") 
   645          |> discrete_cp_inst "IntDef.int" (thm "perm_int_def") 
   646          |> discrete_pt_inst "List.char" (thm "perm_char_def")
   647          |> discrete_fs_inst "List.char" (thm "perm_char_def")
   648          |> discrete_cp_inst "List.char" (thm "perm_char_def")
   649         end;
   650 
   651  
   652        (* abbreviations for some lemmas *)
   653        (*===============================*)
   654        val abs_fun_pi          = thm "Nominal.abs_fun_pi";
   655        val abs_fun_pi_ineq     = thm "Nominal.abs_fun_pi_ineq";
   656        val abs_fun_eq          = thm "Nominal.abs_fun_eq";
   657        val abs_fun_eq'         = thm "Nominal.abs_fun_eq'";
   658        val dj_perm_forget      = thm "Nominal.dj_perm_forget";
   659        val dj_pp_forget        = thm "Nominal.dj_perm_perm_forget";
   660        val fresh_iff           = thm "Nominal.fresh_abs_fun_iff";
   661        val fresh_iff_ineq      = thm "Nominal.fresh_abs_fun_iff_ineq";
   662        val abs_fun_supp        = thm "Nominal.abs_fun_supp";
   663        val abs_fun_supp_ineq   = thm "Nominal.abs_fun_supp_ineq";
   664        val pt_swap_bij         = thm "Nominal.pt_swap_bij";
   665        val pt_fresh_fresh      = thm "Nominal.pt_fresh_fresh";
   666        val pt_bij              = thm "Nominal.pt_bij";
   667        val pt_perm_compose     = thm "Nominal.pt_perm_compose";
   668        val pt_perm_compose'    = thm "Nominal.pt_perm_compose'";
   669        val perm_app            = thm "Nominal.pt_fun_app_eq";
   670        val at_fresh            = thm "Nominal.at_fresh";
   671        val at_fresh_ineq       = thm "Nominal.at_fresh_ineq";
   672        val at_calc             = thms "Nominal.at_calc";
   673        val at_supp             = thm "Nominal.at_supp";
   674        val dj_supp             = thm "Nominal.dj_supp";
   675        val fresh_left_ineq     = thm "Nominal.pt_fresh_left_ineq";
   676        val fresh_left          = thm "Nominal.pt_fresh_left";
   677        val fresh_right_ineq    = thm "Nominal.pt_fresh_right_ineq";
   678        val fresh_right         = thm "Nominal.pt_fresh_right";
   679        val fresh_bij_ineq      = thm "Nominal.pt_fresh_bij_ineq";
   680        val fresh_bij           = thm "Nominal.pt_fresh_bij";
   681        val fresh_aux_ineq      = thm "Nominal.pt_fresh_aux_ineq";
   682        val fresh_aux           = thm "Nominal.pt_fresh_aux";
   683        val fresh_eqvt          = thm "Nominal.pt_fresh_eqvt";
   684        val all_eqvt            = thm "Nominal.pt_all_eqvt";
   685        val pt_pi_rev           = thm "Nominal.pt_pi_rev";
   686        val pt_rev_pi           = thm "Nominal.pt_rev_pi";
   687        val at_exists_fresh     = thm "Nominal.at_exists_fresh";
   688   
   689 
   690        (* Now we collect and instantiate some lemmas w.r.t. all atom      *)
   691        (* types; this allows for example to use abs_perm (which is a      *)
   692        (* collection of theorems) instead of thm abs_fun_pi with explicit *)
   693        (* instantiations.                                                 *)
   694        val (_,thy33) = 
   695 	 let 
   696              
   697 
   698              (* takes a theorem thm and a list of theorems [t1,..,tn]            *)
   699              (* produces a list of theorems of the form [t1 RS thm,..,tn RS thm] *) 
   700              fun instR thm thms = map (fn ti => ti RS thm) thms;
   701 
   702              (* takes two theorem lists (hopefully of the same length ;o)                *)
   703              (* produces a list of theorems of the form                                  *)
   704              (* [t1 RS m1,..,tn RS mn] where [t1,..,tn] is thms1 and [m1,..,mn] is thms2 *) 
   705              fun inst_zip thms1 thms2 = map (fn (t1,t2) => t1 RS t2) (thms1 ~~ thms2);
   706 
   707              (* takes a theorem list of the form [l1,...,ln]              *)
   708              (* and a list of theorem lists of the form                   *)
   709              (* [[h11,...,h1m],....,[hk1,....,hkm]                        *)
   710              (* produces the list of theorem lists                        *)
   711              (* [[l1 RS h11,...,l1 RS h1m],...,[ln RS hk1,...,ln RS hkm]] *)
   712              fun inst_mult thms thmss = map (fn (t,ts) => instR t ts) (thms ~~ thmss);
   713 
   714              (* FIXME: these lists do not need to be created dynamically again *)
   715 
   716              (* list of all at_inst-theorems *)
   717              val ats = map (fn ak => PureThy.get_thm thy32 (Name ("at_"^ak^"_inst"))) ak_names
   718              (* list of all pt_inst-theorems *)
   719              val pts = map (fn ak => PureThy.get_thm thy32 (Name ("pt_"^ak^"_inst"))) ak_names
   720              (* list of all cp_inst-theorems as a collection of lists*)
   721              val cps = 
   722 		 let fun cps_fun ak1 ak2 = PureThy.get_thm thy32 (Name ("cp_"^ak1^"_"^ak2^"_inst"))
   723 		 in map (fn aki => (map (cps_fun aki) ak_names)) ak_names end; 
   724              (* list of all cp_inst-theorems that have different atom types *)
   725              val cps' = 
   726 		let fun cps'_fun ak1 ak2 = 
   727 		if ak1=ak2 then NONE else SOME(PureThy.get_thm thy32 (Name ("cp_"^ak1^"_"^ak2^"_inst")))
   728 		in map (fn aki => (List.mapPartial I (map (cps'_fun aki) ak_names))) ak_names end;
   729              (* list of all dj_inst-theorems *)
   730              val djs = 
   731 	       let fun djs_fun (ak1,ak2) = 
   732 		     if ak1=ak2 then NONE else SOME(PureThy.get_thm thy32 (Name ("dj_"^ak2^"_"^ak1)))
   733 	       in List.mapPartial I (map djs_fun (Library.product ak_names ak_names)) end;
   734              (* list of all fs_inst-theorems *)
   735              val fss = map (fn ak => PureThy.get_thm thy32 (Name ("fs_"^ak^"_inst"))) ak_names
   736               
   737              fun inst_pt thms = Library.flat (map (fn ti => instR ti pts) thms); 
   738              fun inst_at thms = Library.flat (map (fn ti => instR ti ats) thms);               
   739              fun inst_fs thms = Library.flat (map (fn ti => instR ti fss) thms);
   740              fun inst_cp thms cps = Library.flat (inst_mult thms cps); 
   741 	     fun inst_pt_at thms = inst_zip ats (inst_pt thms);			
   742              fun inst_dj thms = Library.flat (map (fn ti => instR ti djs) thms);  
   743 	     fun inst_pt_pt_at_cp thms = inst_cp (inst_zip ats (inst_zip pts (inst_pt thms))) cps;
   744              fun inst_pt_at_fs thms = inst_zip (inst_fs [fs1]) (inst_zip ats (inst_pt thms));
   745 	     fun inst_pt_pt_at_cp thms = 
   746 		 let val i_pt_pt_at = inst_zip ats (inst_zip pts (inst_pt thms));
   747                      val i_pt_pt_at_cp = inst_cp i_pt_pt_at cps';
   748 		 in i_pt_pt_at_cp end;
   749              fun inst_pt_pt_at_cp_dj thms = inst_zip djs (inst_pt_pt_at_cp thms);
   750            in
   751             thy32 
   752 	    |>   PureThy.add_thmss [(("alpha", inst_pt_at [abs_fun_eq]),[])]
   753             ||>> PureThy.add_thmss [(("alpha'", inst_pt_at [abs_fun_eq']),[])]
   754             ||>> PureThy.add_thmss [(("perm_swap", inst_pt_at [pt_swap_bij]),[])]
   755             ||>> PureThy.add_thmss 
   756 	      let val thms1 = inst_pt_at [pt_pi_rev];
   757 		  val thms2 = inst_pt_at [pt_rev_pi];
   758               in [(("perm_pi_simp",thms1 @ thms2),[])] end
   759             ||>> PureThy.add_thmss [(("perm_fresh_fresh", inst_pt_at [pt_fresh_fresh]),[])]
   760             ||>> PureThy.add_thmss [(("perm_bij", inst_pt_at [pt_bij]),[])]
   761             ||>> PureThy.add_thmss 
   762 	      let val thms1 = inst_pt_at [pt_perm_compose];
   763 		  val thms2 = instR cp1 (Library.flat cps');
   764               in [(("perm_compose",thms1 @ thms2),[])] end
   765             ||>> PureThy.add_thmss [(("perm_compose'",inst_pt_at [pt_perm_compose']),[])] 
   766             ||>> PureThy.add_thmss [(("perm_app", inst_pt_at [perm_app]),[])]
   767             ||>> PureThy.add_thmss [(("supp_atm", (inst_at [at_supp]) @ (inst_dj [dj_supp])),[])]
   768             ||>> PureThy.add_thmss [(("exists_fresh", inst_at [at_exists_fresh]),[])]
   769             ||>> PureThy.add_thmss [(("all_eqvt", inst_pt_at [all_eqvt]),[])]
   770             ||>> PureThy.add_thmss 
   771 	      let val thms1 = inst_at [at_fresh]
   772 		  val thms2 = inst_dj [at_fresh_ineq]
   773 	      in [(("fresh_atm", thms1 @ thms2),[])] end
   774             ||>> PureThy.add_thmss
   775 	      let val thms1 = List.concat (List.concat perm_defs)
   776               in [(("calc_atm", (inst_at at_calc) @ thms1),[])] end
   777             ||>> PureThy.add_thmss
   778 	      let val thms1 = inst_pt_at [abs_fun_pi]
   779 		  and thms2 = inst_pt_pt_at_cp [abs_fun_pi_ineq]
   780 	      in [(("abs_perm", thms1 @ thms2),[])] end
   781             ||>> PureThy.add_thmss
   782 	      let val thms1 = inst_dj [dj_perm_forget]
   783 		  and thms2 = inst_dj [dj_pp_forget]
   784               in [(("perm_dj", thms1 @ thms2),[])] end
   785             ||>> PureThy.add_thmss
   786 	      let val thms1 = inst_pt_at_fs [fresh_iff]
   787                   and thms2 = inst_pt_at [fresh_iff]
   788 		  and thms3 = inst_pt_pt_at_cp_dj [fresh_iff_ineq]
   789 	    in [(("abs_fresh", thms1 @ thms2 @ thms3),[])] end
   790 	    ||>> PureThy.add_thmss
   791 	      let val thms1 = inst_pt_at [abs_fun_supp]
   792 		  and thms2 = inst_pt_at_fs [abs_fun_supp]
   793 		  and thms3 = inst_pt_pt_at_cp_dj [abs_fun_supp_ineq]
   794 	      in [(("abs_supp", thms1 @ thms2 @ thms3),[])] end
   795             ||>> PureThy.add_thmss
   796 	      let val thms1 = inst_pt_at [fresh_left]
   797 		  and thms2 = inst_pt_pt_at_cp [fresh_left_ineq]
   798 	      in [(("fresh_left", thms1 @ thms2),[])] end
   799             ||>> PureThy.add_thmss
   800 	      let val thms1 = inst_pt_at [fresh_right]
   801 		  and thms2 = inst_pt_pt_at_cp [fresh_right_ineq]
   802 	      in [(("fresh_right", thms1 @ thms2),[])] end
   803             ||>> PureThy.add_thmss
   804 	      let val thms1 = inst_pt_at [fresh_bij]
   805 		  and thms2 = inst_pt_pt_at_cp [fresh_bij_ineq]
   806 	      in [(("fresh_bij", thms1 @ thms2),[])] end
   807             ||>> PureThy.add_thmss
   808 	      let val thms1 = inst_pt_at [fresh_eqvt]
   809 	      in [(("fresh_eqvt", thms1),[])] end
   810             ||>> PureThy.add_thmss
   811 	      let val thms1 = inst_pt_at [fresh_aux]
   812 		  and thms2 = inst_pt_pt_at_cp_dj [fresh_aux_ineq]
   813 	      in [(("fresh_aux", thms1 @ thms2),[])] end
   814 	   end;
   815 
   816     in NominalData.put (fold Symtab.update (map (rpair ()) full_ak_names)
   817       (NominalData.get thy11)) thy33
   818     end;
   819 
   820 
   821 (* syntax und parsing *)
   822 structure P = OuterParse and K = OuterKeyword;
   823 
   824 val atom_declP =
   825   OuterSyntax.command "atom_decl" "Declare new kinds of atoms" K.thy_decl
   826     (Scan.repeat1 P.name >> (Toplevel.theory o create_nom_typedecls));
   827 
   828 val _ = OuterSyntax.add_parsers [atom_declP];
   829 
   830 val setup = NominalData.init;
   831 
   832 end;