src/HOL/Nominal/nominal_atoms.ML
author berghofe
Thu Sep 13 18:08:08 2007 +0200 (2007-09-13 ago)
changeset 24569 c80e1871098b
parent 24527 888d56a8d9d3
child 24677 c6295d2dce48
permissions -rw-r--r--
Added equivariance lemmas for induct_forall.
     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   type atom_info
    12   val get_atom_infos : theory -> atom_info Symtab.table
    13   val get_atom_info : theory -> string -> atom_info option
    14   val atoms_of : theory -> string list
    15   val mk_permT : typ -> typ
    16 end
    17 
    18 structure NominalAtoms : NOMINAL_ATOMS =
    19 struct
    20 
    21 val finite_emptyI = @{thm "finite.emptyI"};
    22 val Collect_const = @{thm "Collect_const"};
    23 
    24 val inductive_forall_def = @{thm "induct_forall_def"};
    25 
    26 
    27 (* theory data *)
    28 
    29 type atom_info =
    30   {pt_class : string,
    31    fs_class : string,
    32    cp_classes : (string * string) list};
    33 
    34 structure NominalData = TheoryDataFun
    35 (
    36   type T = atom_info Symtab.table;
    37   val empty = Symtab.empty;
    38   val copy = I;
    39   val extend = I;
    40   fun merge _ x = Symtab.merge (K true) x;
    41 );
    42 
    43 fun make_atom_info ((pt_class, fs_class), cp_classes) =
    44   {pt_class = pt_class,
    45    fs_class = fs_class,
    46    cp_classes = cp_classes};
    47 
    48 val get_atom_infos = NominalData.get;
    49 val get_atom_info = Symtab.lookup o NominalData.get;
    50 
    51 fun atoms_of thy = map fst (Symtab.dest (NominalData.get thy));
    52 
    53 fun mk_permT T = HOLogic.listT (HOLogic.mk_prodT (T, T));
    54 
    55 fun mk_Cons x xs =
    56   let val T = fastype_of x
    57   in Const ("List.list.Cons", T --> HOLogic.listT T --> HOLogic.listT T) $ x $ xs end;
    58 
    59 
    60 (* this function sets up all matters related to atom-  *)
    61 (* kinds; the user specifies a list of atom-kind names *)
    62 (* atom_decl <ak1> ... <akn>                           *)
    63 fun create_nom_typedecls ak_names thy =
    64   let
    65     
    66     (* declares a type-decl for every atom-kind: *) 
    67     (* that is typedecl <ak>                     *)
    68     val thy1 = TypedefPackage.add_typedecls (map (fn x => (x,[],NoSyn)) ak_names) thy;
    69     
    70     (* produces a list consisting of pairs:         *)
    71     (*  fst component is the atom-kind name         *)
    72     (*  snd component is its type                   *)
    73     val full_ak_names = map (Sign.intern_type thy1) ak_names;
    74     val ak_names_types = ak_names ~~ map (Type o rpair []) full_ak_names;
    75      
    76     (* adds for every atom-kind an axiom             *)
    77     (* <ak>_infinite: infinite (UNIV::<ak_type> set) *)
    78     val (inf_axs,thy2) = PureThy.add_axioms_i (map (fn (ak_name, T) =>
    79       let 
    80     val name = ak_name ^ "_infinite"
    81         val axiom = HOLogic.mk_Trueprop (HOLogic.mk_not
    82                     (Const ("Finite_Set.finite", HOLogic.mk_setT T --> HOLogic.boolT) $
    83                        HOLogic.mk_UNIV T))
    84       in
    85         ((name, axiom), []) 
    86       end) ak_names_types) thy1;
    87     
    88     (* declares a swapping function for every atom-kind, it is         *)
    89     (* const swap_<ak> :: <akT> * <akT> => <akT> => <akT>              *)
    90     (* swap_<ak> (a,b) c = (if a=c then b (else if b=c then a else c)) *)
    91     (* overloades then the general swap-function                       *) 
    92     val (swap_eqs, thy3) = fold_map (fn (ak_name, T) => fn thy =>
    93       let
    94         val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
    95         val swap_name = Sign.full_name thy ("swap_" ^ ak_name);
    96         val a = Free ("a", T);
    97         val b = Free ("b", T);
    98         val c = Free ("c", T);
    99         val ab = Free ("ab", HOLogic.mk_prodT (T, T))
   100         val cif = Const ("HOL.If", HOLogic.boolT --> T --> T --> T);
   101         val cswap_akname = Const (swap_name, swapT);
   102         val cswap = Const ("Nominal.swap", swapT)
   103 
   104         val name = "swap_"^ak_name^"_def";
   105         val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq
   106                 (cswap_akname $ HOLogic.mk_prod (a,b) $ c,
   107                     cif $ HOLogic.mk_eq (a,c) $ b $ (cif $ HOLogic.mk_eq (b,c) $ a $ c)))
   108         val def2 = Logic.mk_equals (cswap $ ab $ c, cswap_akname $ ab $ c)
   109       in
   110         thy |> Theory.add_consts_i [("swap_" ^ ak_name, swapT, NoSyn)] 
   111             |> PureThy.add_defs_unchecked_i true [((name, def2),[])]
   112             |> snd
   113             |> PrimrecPackage.add_primrec_unchecked_i "" [(("", def1),[])]
   114       end) ak_names_types thy2;
   115     
   116     (* declares a permutation function for every atom-kind acting  *)
   117     (* on such atoms                                               *)
   118     (* const <ak>_prm_<ak> :: (<akT> * <akT>)list => akT => akT    *)
   119     (* <ak>_prm_<ak> []     a = a                                  *)
   120     (* <ak>_prm_<ak> (x#xs) a = swap_<ak> x (perm xs a)            *)
   121     val (prm_eqs, thy4) = fold_map (fn (ak_name, T) => fn thy =>
   122       let
   123         val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
   124         val swap_name = Sign.full_name thy ("swap_" ^ ak_name)
   125         val prmT = mk_permT T --> T --> T;
   126         val prm_name = ak_name ^ "_prm_" ^ ak_name;
   127         val qu_prm_name = Sign.full_name thy prm_name;
   128         val x  = Free ("x", HOLogic.mk_prodT (T, T));
   129         val xs = Free ("xs", mk_permT T);
   130         val a  = Free ("a", T) ;
   131 
   132         val cnil  = Const ("List.list.Nil", mk_permT T);
   133         
   134         val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq (Const (qu_prm_name, prmT) $ cnil $ a, a));
   135 
   136         val def2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
   137                    (Const (qu_prm_name, prmT) $ mk_Cons x xs $ a,
   138                     Const (swap_name, swapT) $ x $ (Const (qu_prm_name, prmT) $ xs $ a)));
   139       in
   140         thy |> Theory.add_consts_i [(prm_name, mk_permT T --> T --> T, NoSyn)] 
   141             |> PrimrecPackage.add_primrec_unchecked_i "" [(("", def1), []),(("", def2), [])]
   142       end) ak_names_types thy3;
   143     
   144     (* defines permutation functions for all combinations of atom-kinds; *)
   145     (* there are a trivial cases and non-trivial cases                   *)
   146     (* non-trivial case:                                                 *)
   147     (* <ak>_prm_<ak>_def:  perm pi a == <ak>_prm_<ak> pi a               *)
   148     (* trivial case with <ak> != <ak'>                                   *)
   149     (* <ak>_prm<ak'>_def[simp]:  perm pi a == a                          *)
   150     (*                                                                   *)
   151     (* the trivial cases are added to the simplifier, while the non-     *)
   152     (* have their own rules proved below                                 *)  
   153     val (perm_defs, thy5) = fold_map (fn (ak_name, T) => fn thy =>
   154       fold_map (fn (ak_name', T') => fn thy' =>
   155         let
   156           val perm_def_name = ak_name ^ "_prm_" ^ ak_name';
   157           val pi = Free ("pi", mk_permT T);
   158           val a  = Free ("a", T');
   159           val cperm = Const ("Nominal.perm", mk_permT T --> T' --> T');
   160           val cperm_def = Const (Sign.full_name thy' perm_def_name, mk_permT T --> T' --> T');
   161 
   162           val name = ak_name ^ "_prm_" ^ ak_name' ^ "_def";
   163           val def = Logic.mk_equals
   164                     (cperm $ pi $ a, if ak_name = ak_name' then cperm_def $ pi $ a else a)
   165         in
   166           PureThy.add_defs_unchecked_i true [((name, def),[])] thy'
   167         end) ak_names_types thy) ak_names_types thy4;
   168     
   169     (* proves that every atom-kind is an instance of at *)
   170     (* lemma at_<ak>_inst:                              *)
   171     (* at TYPE(<ak>)                                    *)
   172     val (prm_cons_thms,thy6) = 
   173       thy5 |> PureThy.add_thms (map (fn (ak_name, T) =>
   174       let
   175         val ak_name_qu = Sign.full_name thy5 (ak_name);
   176         val i_type = Type(ak_name_qu,[]);
   177 	val cat = Const ("Nominal.at",(Term.itselfT i_type)  --> HOLogic.boolT);
   178         val at_type = Logic.mk_type i_type;
   179         val simp_s = HOL_ss addsimps PureThy.get_thmss thy5
   180                                   [Name "at_def",
   181                                    Name (ak_name ^ "_prm_" ^ ak_name ^ "_def"),
   182                                    Name (ak_name ^ "_prm_" ^ ak_name ^ ".simps"),
   183                                    Name ("swap_" ^ ak_name ^ "_def"),
   184                                    Name ("swap_" ^ ak_name ^ ".simps"),
   185                                    Name (ak_name ^ "_infinite")]
   186 	    
   187 	val name = "at_"^ak_name^ "_inst";
   188         val statement = HOLogic.mk_Trueprop (cat $ at_type);
   189 
   190         val proof = fn _ => simp_tac simp_s 1
   191 
   192       in 
   193         ((name, Goal.prove_global thy5 [] [] statement proof), []) 
   194       end) ak_names_types);
   195 
   196     (* declares a perm-axclass for every atom-kind               *)
   197     (* axclass pt_<ak>                                           *)
   198     (* pt_<ak>1[simp]: perm [] x = x                             *)
   199     (* pt_<ak>2:       perm (pi1@pi2) x = perm pi1 (perm pi2 x)  *)
   200     (* pt_<ak>3:       pi1 ~ pi2 ==> perm pi1 x = perm pi2 x     *)
   201      val (pt_ax_classes,thy7) =  fold_map (fn (ak_name, T) => fn thy =>
   202       let 
   203 	  val cl_name = "pt_"^ak_name;
   204           val ty = TFree("'a",["HOL.type"]);
   205           val x   = Free ("x", ty);
   206           val pi1 = Free ("pi1", mk_permT T);
   207           val pi2 = Free ("pi2", mk_permT T);
   208           val cperm = Const ("Nominal.perm", mk_permT T --> ty --> ty);
   209           val cnil  = Const ("List.list.Nil", mk_permT T);
   210           val cappend = Const ("List.append",mk_permT T --> mk_permT T --> mk_permT T);
   211           val cprm_eq = Const ("Nominal.prm_eq",mk_permT T --> mk_permT T --> HOLogic.boolT);
   212           (* nil axiom *)
   213           val axiom1 = HOLogic.mk_Trueprop (HOLogic.mk_eq 
   214                        (cperm $ cnil $ x, x));
   215           (* append axiom *)
   216           val axiom2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
   217                        (cperm $ (cappend $ pi1 $ pi2) $ x, cperm $ pi1 $ (cperm $ pi2 $ x)));
   218           (* perm-eq axiom *)
   219           val axiom3 = Logic.mk_implies
   220                        (HOLogic.mk_Trueprop (cprm_eq $ pi1 $ pi2),
   221                         HOLogic.mk_Trueprop (HOLogic.mk_eq (cperm $ pi1 $ x, cperm $ pi2 $ x)));
   222       in
   223           AxClass.define_class (cl_name, ["HOL.type"]) []
   224                 [((cl_name ^ "1", [Simplifier.simp_add]), [axiom1]),
   225                  ((cl_name ^ "2", []), [axiom2]),                           
   226                  ((cl_name ^ "3", []), [axiom3])] thy                          
   227       end) ak_names_types thy6;
   228 
   229     (* proves that every pt_<ak>-type together with <ak>-type *)
   230     (* instance of pt                                         *)
   231     (* lemma pt_<ak>_inst:                                    *)
   232     (* pt TYPE('x::pt_<ak>) TYPE(<ak>)                        *)
   233     val (prm_inst_thms,thy8) = 
   234       thy7 |> PureThy.add_thms (map (fn (ak_name, T) =>
   235       let
   236         val ak_name_qu = Sign.full_name thy7 ak_name;
   237         val pt_name_qu = Sign.full_name thy7 ("pt_"^ak_name);
   238         val i_type1 = TFree("'x",[pt_name_qu]);
   239         val i_type2 = Type(ak_name_qu,[]);
   240 	val cpt = Const ("Nominal.pt",(Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
   241         val pt_type = Logic.mk_type i_type1;
   242         val at_type = Logic.mk_type i_type2;
   243         val simp_s = HOL_ss addsimps PureThy.get_thmss thy7
   244                                   [Name "pt_def",
   245                                    Name ("pt_" ^ ak_name ^ "1"),
   246                                    Name ("pt_" ^ ak_name ^ "2"),
   247                                    Name ("pt_" ^ ak_name ^ "3")];
   248 
   249 	val name = "pt_"^ak_name^ "_inst";
   250         val statement = HOLogic.mk_Trueprop (cpt $ pt_type $ at_type);
   251 
   252         val proof = fn _ => simp_tac simp_s 1;
   253       in 
   254         ((name, Goal.prove_global thy7 [] [] statement proof), []) 
   255       end) ak_names_types);
   256 
   257      (* declares an fs-axclass for every atom-kind       *)
   258      (* axclass fs_<ak>                                  *)
   259      (* fs_<ak>1: finite ((supp x)::<ak> set)            *)
   260      val (fs_ax_classes,thy11) =  fold_map (fn (ak_name, T) => fn thy =>
   261        let 
   262 	  val cl_name = "fs_"^ak_name;
   263 	  val pt_name = Sign.full_name thy ("pt_"^ak_name);
   264           val ty = TFree("'a",["HOL.type"]);
   265           val x   = Free ("x", ty);
   266           val csupp    = Const ("Nominal.supp", ty --> HOLogic.mk_setT T);
   267           val cfinite  = Const ("Finite_Set.finite", HOLogic.mk_setT T --> HOLogic.boolT)
   268           
   269           val axiom1   = HOLogic.mk_Trueprop (cfinite $ (csupp $ x));
   270 
   271        in  
   272         AxClass.define_class (cl_name, [pt_name]) [] [((cl_name ^ "1", []), [axiom1])] thy            
   273        end) ak_names_types thy8; 
   274 	 
   275      (* proves that every fs_<ak>-type together with <ak>-type   *)
   276      (* instance of fs-type                                      *)
   277      (* lemma abst_<ak>_inst:                                    *)
   278      (* fs TYPE('x::pt_<ak>) TYPE (<ak>)                         *)
   279      val (fs_inst_thms,thy12) = 
   280        thy11 |> PureThy.add_thms (map (fn (ak_name, T) =>
   281        let
   282          val ak_name_qu = Sign.full_name thy11 ak_name;
   283          val fs_name_qu = Sign.full_name thy11 ("fs_"^ak_name);
   284          val i_type1 = TFree("'x",[fs_name_qu]);
   285          val i_type2 = Type(ak_name_qu,[]);
   286  	 val cfs = Const ("Nominal.fs", 
   287                                  (Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
   288          val fs_type = Logic.mk_type i_type1;
   289          val at_type = Logic.mk_type i_type2;
   290 	 val simp_s = HOL_ss addsimps PureThy.get_thmss thy11
   291                                    [Name "fs_def",
   292                                     Name ("fs_" ^ ak_name ^ "1")];
   293     
   294 	 val name = "fs_"^ak_name^ "_inst";
   295          val statement = HOLogic.mk_Trueprop (cfs $ fs_type $ at_type);
   296 
   297          val proof = fn _ => simp_tac simp_s 1;
   298        in 
   299          ((name, Goal.prove_global thy11 [] [] statement proof), []) 
   300        end) ak_names_types);
   301 
   302        (* declares for every atom-kind combination an axclass            *)
   303        (* cp_<ak1>_<ak2> giving a composition property                   *)
   304        (* cp_<ak1>_<ak2>1: pi1 o pi2 o x = (pi1 o pi2) o (pi1 o x)       *)
   305         val (cp_ax_classes,thy12b) = fold_map (fn (ak_name, T) => fn thy =>
   306 	 fold_map (fn (ak_name', T') => fn thy' =>
   307 	     let
   308 	       val cl_name = "cp_"^ak_name^"_"^ak_name';
   309 	       val ty = TFree("'a",["HOL.type"]);
   310                val x   = Free ("x", ty);
   311                val pi1 = Free ("pi1", mk_permT T);
   312 	       val pi2 = Free ("pi2", mk_permT T');                  
   313 	       val cperm1 = Const ("Nominal.perm", mk_permT T  --> ty --> ty);
   314                val cperm2 = Const ("Nominal.perm", mk_permT T' --> ty --> ty);
   315                val cperm3 = Const ("Nominal.perm", mk_permT T  --> mk_permT T' --> mk_permT T');
   316 
   317                val ax1   = HOLogic.mk_Trueprop 
   318 			   (HOLogic.mk_eq (cperm1 $ pi1 $ (cperm2 $ pi2 $ x), 
   319                                            cperm2 $ (cperm3 $ pi1 $ pi2) $ (cperm1 $ pi1 $ x)));
   320 	       in  
   321 		 AxClass.define_class (cl_name, ["HOL.type"]) [] [((cl_name ^ "1", []), [ax1])] thy'  
   322 	       end) ak_names_types thy) ak_names_types thy12;
   323 
   324         (* proves for every <ak>-combination a cp_<ak1>_<ak2>_inst theorem;     *)
   325         (* lemma cp_<ak1>_<ak2>_inst:                                           *)
   326         (* cp TYPE('a::cp_<ak1>_<ak2>) TYPE(<ak1>) TYPE(<ak2>)                  *)
   327         val (cp_thms,thy12c) = fold_map (fn (ak_name, T) => fn thy =>
   328 	 fold_map (fn (ak_name', T') => fn thy' =>
   329            let
   330              val ak_name_qu  = Sign.full_name thy' (ak_name);
   331 	     val ak_name_qu' = Sign.full_name thy' (ak_name');
   332              val cp_name_qu  = Sign.full_name thy' ("cp_"^ak_name^"_"^ak_name');
   333              val i_type0 = TFree("'a",[cp_name_qu]);
   334              val i_type1 = Type(ak_name_qu,[]);
   335              val i_type2 = Type(ak_name_qu',[]);
   336 	     val ccp = Const ("Nominal.cp",
   337                              (Term.itselfT i_type0)-->(Term.itselfT i_type1)-->
   338                                                       (Term.itselfT i_type2)-->HOLogic.boolT);
   339              val at_type  = Logic.mk_type i_type1;
   340              val at_type' = Logic.mk_type i_type2;
   341 	     val cp_type  = Logic.mk_type i_type0;
   342              val simp_s   = HOL_basic_ss addsimps PureThy.get_thmss thy' [(Name "cp_def")];
   343 	     val cp1      = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"1"));
   344 
   345 	     val name = "cp_"^ak_name^ "_"^ak_name'^"_inst";
   346              val statement = HOLogic.mk_Trueprop (ccp $ cp_type $ at_type $ at_type');
   347 
   348              val proof = fn _ => EVERY [simp_tac simp_s 1, 
   349                                         rtac allI 1, rtac allI 1, rtac allI 1,
   350                                         rtac cp1 1];
   351 	   in
   352 	     PureThy.add_thms [((name, Goal.prove_global thy' [] [] statement proof), [])] thy'
   353 	   end) 
   354            ak_names_types thy) ak_names_types thy12b;
   355        
   356         (* proves for every non-trivial <ak>-combination a disjointness   *)
   357         (* theorem; i.e. <ak1> != <ak2>                                   *)
   358         (* lemma ds_<ak1>_<ak2>:                                          *)
   359         (* dj TYPE(<ak1>) TYPE(<ak2>)                                     *)
   360         val (dj_thms, thy12d) = fold_map (fn (ak_name,T) => fn thy =>
   361 	  fold_map (fn (ak_name',T') => fn thy' =>
   362           (if not (ak_name = ak_name') 
   363            then 
   364 	       let
   365 		 val ak_name_qu  = Sign.full_name thy' ak_name;
   366 	         val ak_name_qu' = Sign.full_name thy' ak_name';
   367                  val i_type1 = Type(ak_name_qu,[]);
   368                  val i_type2 = Type(ak_name_qu',[]);
   369 	         val cdj = Const ("Nominal.disjoint",
   370                            (Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
   371                  val at_type  = Logic.mk_type i_type1;
   372                  val at_type' = Logic.mk_type i_type2;
   373                  val simp_s = HOL_ss addsimps PureThy.get_thmss thy' 
   374 					   [Name "disjoint_def",
   375                                             Name (ak_name^"_prm_"^ak_name'^"_def"),
   376                                             Name (ak_name'^"_prm_"^ak_name^"_def")];
   377 
   378 	         val name = "dj_"^ak_name^"_"^ak_name';
   379                  val statement = HOLogic.mk_Trueprop (cdj $ at_type $ at_type');
   380 
   381                  val proof = fn _ => simp_tac simp_s 1;
   382 	       in
   383 		PureThy.add_thms [((name, Goal.prove_global thy' [] [] statement proof), [])] thy'
   384 	       end
   385            else 
   386             ([],thy')))  (* do nothing branch, if ak_name = ak_name' *) 
   387 	    ak_names_types thy) ak_names_types thy12c;
   388 
   389      (********  pt_<ak> class instances  ********)
   390      (*=========================================*)
   391      (* some abbreviations for theorems *)
   392       val pt1           = @{thm "pt1"};
   393       val pt2           = @{thm "pt2"};
   394       val pt3           = @{thm "pt3"};
   395       val at_pt_inst    = @{thm "at_pt_inst"};
   396       val pt_set_inst   = @{thm "pt_set_inst"}; 
   397       val pt_unit_inst  = @{thm "pt_unit_inst"};
   398       val pt_prod_inst  = @{thm "pt_prod_inst"}; 
   399       val pt_nprod_inst = @{thm "pt_nprod_inst"}; 
   400       val pt_list_inst  = @{thm "pt_list_inst"};
   401       val pt_optn_inst  = @{thm "pt_option_inst"};
   402       val pt_noptn_inst = @{thm "pt_noption_inst"};
   403       val pt_fun_inst   = @{thm "pt_fun_inst"};
   404 
   405      (* for all atom-kind combinations <ak>/<ak'> show that        *)
   406      (* every <ak> is an instance of pt_<ak'>; the proof for       *)
   407      (* ak!=ak' is by definition; the case ak=ak' uses at_pt_inst. *)
   408      val thy13 = fold (fn ak_name => fn thy =>
   409 	fold (fn ak_name' => fn thy' =>
   410          let
   411            val qu_name =  Sign.full_name thy' ak_name';
   412            val cls_name = Sign.full_name thy' ("pt_"^ak_name);
   413            val at_inst  = PureThy.get_thm thy' (Name ("at_"^ak_name'^"_inst")); 
   414 
   415            val proof1 = EVERY [Class.intro_classes_tac [],
   416                                  rtac ((at_inst RS at_pt_inst) RS pt1) 1,
   417                                  rtac ((at_inst RS at_pt_inst) RS pt2) 1,
   418                                  rtac ((at_inst RS at_pt_inst) RS pt3) 1,
   419                                  atac 1];
   420            val simp_s = HOL_basic_ss addsimps 
   421                         PureThy.get_thmss thy' [Name (ak_name^"_prm_"^ak_name'^"_def")];  
   422            val proof2 = EVERY [Class.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)];
   423 
   424          in
   425            thy'
   426            |> AxClass.prove_arity (qu_name,[],[cls_name])
   427               (if ak_name = ak_name' then proof1 else proof2)
   428          end) ak_names thy) ak_names thy12c;
   429 
   430      (* show that                       *)
   431      (*      fun(pt_<ak>,pt_<ak>)       *)
   432      (*      noption(pt_<ak>)           *)
   433      (*      option(pt_<ak>)            *)
   434      (*      list(pt_<ak>)              *)
   435      (*      *(pt_<ak>,pt_<ak>)         *)
   436      (*      nprod(pt_<ak>,pt_<ak>)     *)
   437      (*      unit                       *)
   438      (*      set(pt_<ak>)               *)
   439      (* are instances of pt_<ak>        *)
   440      val thy18 = fold (fn ak_name => fn thy =>
   441        let
   442           val cls_name = Sign.full_name thy ("pt_"^ak_name);
   443           val at_thm   = PureThy.get_thm thy (Name ("at_"^ak_name^"_inst"));
   444           val pt_inst  = PureThy.get_thm thy (Name ("pt_"^ak_name^"_inst"));
   445 
   446           fun pt_proof thm = 
   447               EVERY [Class.intro_classes_tac [],
   448                      rtac (thm RS pt1) 1, rtac (thm RS pt2) 1, rtac (thm RS pt3) 1, atac 1];
   449 
   450           val pt_thm_fun   = at_thm RS (pt_inst RS (pt_inst RS pt_fun_inst));
   451           val pt_thm_noptn = pt_inst RS pt_noptn_inst; 
   452           val pt_thm_optn  = pt_inst RS pt_optn_inst; 
   453           val pt_thm_list  = pt_inst RS pt_list_inst;
   454           val pt_thm_prod  = pt_inst RS (pt_inst RS pt_prod_inst);
   455           val pt_thm_nprod = pt_inst RS (pt_inst RS pt_nprod_inst);
   456           val pt_thm_unit  = pt_unit_inst;
   457           val pt_thm_set   = pt_inst RS pt_set_inst
   458        in
   459         thy
   460         |> AxClass.prove_arity ("fun",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_fun)
   461         |> AxClass.prove_arity ("Nominal.noption",[[cls_name]],[cls_name]) (pt_proof pt_thm_noptn) 
   462         |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (pt_proof pt_thm_optn)
   463         |> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (pt_proof pt_thm_list)
   464         |> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_prod)
   465         |> AxClass.prove_arity ("Nominal.nprod",[[cls_name],[cls_name]],[cls_name]) 
   466                                     (pt_proof pt_thm_nprod)
   467         |> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (pt_proof pt_thm_unit)
   468         |> AxClass.prove_arity ("set",[[cls_name]],[cls_name]) (pt_proof pt_thm_set)
   469      end) ak_names thy13; 
   470 
   471        (********  fs_<ak> class instances  ********)
   472        (*=========================================*)
   473        (* abbreviations for some lemmas *)
   474        val fs1            = @{thm "fs1"};
   475        val fs_at_inst     = @{thm "fs_at_inst"};
   476        val fs_unit_inst   = @{thm "fs_unit_inst"};
   477        val fs_prod_inst   = @{thm "fs_prod_inst"};
   478        val fs_nprod_inst  = @{thm "fs_nprod_inst"};
   479        val fs_list_inst   = @{thm "fs_list_inst"};
   480        val fs_option_inst = @{thm "fs_option_inst"};
   481        val dj_supp        = @{thm "dj_supp"};
   482 
   483        (* shows that <ak> is an instance of fs_<ak>     *)
   484        (* uses the theorem at_<ak>_inst                 *)
   485        val thy20 = fold (fn ak_name => fn thy =>
   486         fold (fn ak_name' => fn thy' =>
   487         let
   488            val qu_name =  Sign.full_name thy' ak_name';
   489            val qu_class = Sign.full_name thy' ("fs_"^ak_name);
   490            val proof =
   491                (if ak_name = ak_name'
   492                 then
   493                   let val at_thm = PureThy.get_thm thy' (Name ("at_"^ak_name^"_inst"));
   494                   in  EVERY [Class.intro_classes_tac [],
   495                              rtac ((at_thm RS fs_at_inst) RS fs1) 1] end
   496                 else
   497                   let val dj_inst = PureThy.get_thm thy' (Name ("dj_"^ak_name'^"_"^ak_name));
   498                       val simp_s = HOL_basic_ss addsimps [dj_inst RS dj_supp, finite_emptyI];
   499                   in EVERY [Class.intro_classes_tac [], asm_simp_tac simp_s 1] end)
   500         in
   501          AxClass.prove_arity (qu_name,[],[qu_class]) proof thy'
   502         end) ak_names thy) ak_names thy18;
   503 
   504        (* shows that                  *)
   505        (*    unit                     *)
   506        (*    *(fs_<ak>,fs_<ak>)       *)
   507        (*    nprod(fs_<ak>,fs_<ak>)   *)
   508        (*    list(fs_<ak>)            *)
   509        (*    option(fs_<ak>)          *) 
   510        (* are instances of fs_<ak>    *)
   511 
   512        val thy24 = fold (fn ak_name => fn thy => 
   513         let
   514           val cls_name = Sign.full_name thy ("fs_"^ak_name);
   515           val fs_inst  = PureThy.get_thm thy (Name ("fs_"^ak_name^"_inst"));
   516           fun fs_proof thm = EVERY [Class.intro_classes_tac [], rtac (thm RS fs1) 1];
   517 
   518           val fs_thm_unit  = fs_unit_inst;
   519           val fs_thm_prod  = fs_inst RS (fs_inst RS fs_prod_inst);
   520           val fs_thm_nprod = fs_inst RS (fs_inst RS fs_nprod_inst);
   521           val fs_thm_list  = fs_inst RS fs_list_inst;
   522           val fs_thm_optn  = fs_inst RS fs_option_inst;
   523         in 
   524          thy
   525          |> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (fs_proof fs_thm_unit) 
   526          |> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (fs_proof fs_thm_prod) 
   527          |> AxClass.prove_arity ("Nominal.nprod",[[cls_name],[cls_name]],[cls_name]) 
   528                                      (fs_proof fs_thm_nprod) 
   529          |> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (fs_proof fs_thm_list)
   530          |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (fs_proof fs_thm_optn)
   531         end) ak_names thy20;
   532 
   533        (********  cp_<ak>_<ai> class instances  ********)
   534        (*==============================================*)
   535        (* abbreviations for some lemmas *)
   536        val cp1             = @{thm "cp1"};
   537        val cp_unit_inst    = @{thm "cp_unit_inst"};
   538        val cp_bool_inst    = @{thm "cp_bool_inst"};
   539        val cp_prod_inst    = @{thm "cp_prod_inst"};
   540        val cp_list_inst    = @{thm "cp_list_inst"};
   541        val cp_fun_inst     = @{thm "cp_fun_inst"};
   542        val cp_option_inst  = @{thm "cp_option_inst"};
   543        val cp_noption_inst = @{thm "cp_noption_inst"};
   544        val cp_set_inst     = @{thm "cp_set_inst"};
   545        val pt_perm_compose = @{thm "pt_perm_compose"};
   546 
   547        val dj_pp_forget    = @{thm "dj_perm_perm_forget"};
   548 
   549        (* shows that <aj> is an instance of cp_<ak>_<ai>  *)
   550        (* for every  <ak>/<ai>-combination                *)
   551        val thy25 = fold (fn ak_name => fn thy =>
   552          fold (fn ak_name' => fn thy' =>
   553           fold (fn ak_name'' => fn thy'' =>
   554             let
   555               val name =  Sign.full_name thy'' ak_name;
   556               val cls_name = Sign.full_name thy'' ("cp_"^ak_name'^"_"^ak_name'');
   557               val proof =
   558                 (if (ak_name'=ak_name'') then 
   559                   (let
   560                     val pt_inst  = PureThy.get_thm thy'' (Name ("pt_"^ak_name''^"_inst"));
   561                     val at_inst  = PureThy.get_thm thy'' (Name ("at_"^ak_name''^"_inst"));
   562                   in
   563 		   EVERY [Class.intro_classes_tac [],
   564                           rtac (at_inst RS (pt_inst RS pt_perm_compose)) 1]
   565                   end)
   566 		else
   567 		  (let
   568                      val dj_inst  = PureThy.get_thm thy'' (Name ("dj_"^ak_name''^"_"^ak_name'));
   569 		     val simp_s = HOL_basic_ss addsimps
   570                                         ((dj_inst RS dj_pp_forget)::
   571                                          (PureThy.get_thmss thy''
   572                                            [Name (ak_name' ^"_prm_"^ak_name^"_def"),
   573                                             Name (ak_name''^"_prm_"^ak_name^"_def")]));
   574                   in
   575                     EVERY [Class.intro_classes_tac [], simp_tac simp_s 1]
   576                   end))
   577               in
   578                 AxClass.prove_arity (name,[],[cls_name]) proof thy''
   579               end) ak_names thy') ak_names thy) ak_names thy24;
   580 
   581        (* shows that                                                    *) 
   582        (*      units                                                    *) 
   583        (*      products                                                 *)
   584        (*      lists                                                    *)
   585        (*      functions                                                *)
   586        (*      options                                                  *)
   587        (*      noptions                                                 *)
   588        (*      sets                                                     *)
   589        (* are instances of cp_<ak>_<ai> for every <ak>/<ai>-combination *)
   590        val thy26 = fold (fn ak_name => fn thy =>
   591 	fold (fn ak_name' => fn thy' =>
   592         let
   593             val cls_name = Sign.full_name thy' ("cp_"^ak_name^"_"^ak_name');
   594             val cp_inst  = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
   595             val pt_inst  = PureThy.get_thm thy' (Name ("pt_"^ak_name^"_inst"));
   596             val at_inst  = PureThy.get_thm thy' (Name ("at_"^ak_name^"_inst"));
   597 
   598             fun cp_proof thm  = EVERY [Class.intro_classes_tac [],rtac (thm RS cp1) 1];
   599 	  
   600             val cp_thm_unit = cp_unit_inst;
   601             val cp_thm_prod = cp_inst RS (cp_inst RS cp_prod_inst);
   602             val cp_thm_list = cp_inst RS cp_list_inst;
   603             val cp_thm_fun  = at_inst RS (pt_inst RS (cp_inst RS (cp_inst RS cp_fun_inst)));
   604             val cp_thm_optn = cp_inst RS cp_option_inst;
   605             val cp_thm_noptn = cp_inst RS cp_noption_inst;
   606             val cp_thm_set = cp_inst RS cp_set_inst;
   607         in
   608          thy'
   609          |> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (cp_proof cp_thm_unit)
   610 	 |> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_prod)
   611          |> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (cp_proof cp_thm_list)
   612          |> AxClass.prove_arity ("fun",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_fun)
   613          |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (cp_proof cp_thm_optn)
   614          |> AxClass.prove_arity ("Nominal.noption",[[cls_name]],[cls_name]) (cp_proof cp_thm_noptn)
   615          |> AxClass.prove_arity ("set",[[cls_name]],[cls_name]) (cp_proof cp_thm_set)
   616         end) ak_names thy) ak_names thy25;
   617 
   618      (* show that discrete nominal types are permutation types, finitely     *)
   619      (* supported and have the commutation property                          *)
   620      (* discrete types have a permutation operation defined as pi o x = x;   *)
   621      (* which renders the proofs to be simple "simp_all"-proofs.             *)
   622      val thy32 =
   623         let
   624 	  fun discrete_pt_inst discrete_ty defn =
   625 	     fold (fn ak_name => fn thy =>
   626 	     let
   627 	       val qu_class = Sign.full_name thy ("pt_"^ak_name);
   628 	       val simp_s = HOL_basic_ss addsimps [defn];
   629                val proof = EVERY [Class.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)];
   630              in 
   631 	       AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
   632              end) ak_names;
   633 
   634           fun discrete_fs_inst discrete_ty defn = 
   635 	     fold (fn ak_name => fn thy =>
   636 	     let
   637 	       val qu_class = Sign.full_name thy ("fs_"^ak_name);
   638 	       val supp_def = @{thm "Nominal.supp_def"};
   639                val simp_s = HOL_ss addsimps [supp_def,Collect_const,finite_emptyI,defn];
   640                val proof = EVERY [Class.intro_classes_tac [], asm_simp_tac simp_s 1];
   641              in 
   642 	       AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
   643              end) ak_names;
   644 
   645           fun discrete_cp_inst discrete_ty defn = 
   646 	     fold (fn ak_name' => (fold (fn ak_name => fn thy =>
   647 	     let
   648 	       val qu_class = Sign.full_name thy ("cp_"^ak_name^"_"^ak_name');
   649 	       val supp_def = @{thm "Nominal.supp_def"};
   650                val simp_s = HOL_ss addsimps [defn];
   651                val proof = EVERY [Class.intro_classes_tac [], asm_simp_tac simp_s 1];
   652              in
   653 	       AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
   654              end) ak_names)) ak_names;
   655 
   656         in
   657          thy26
   658          |> discrete_pt_inst "nat"  @{thm "perm_nat_def"}
   659          |> discrete_fs_inst "nat"  @{thm "perm_nat_def"}
   660          |> discrete_cp_inst "nat"  @{thm "perm_nat_def"}
   661          |> discrete_pt_inst "bool" @{thm "perm_bool"}
   662          |> discrete_fs_inst "bool" @{thm "perm_bool"}
   663          |> discrete_cp_inst "bool" @{thm "perm_bool"}
   664          |> discrete_pt_inst "IntDef.int" @{thm "perm_int_def"}
   665          |> discrete_fs_inst "IntDef.int" @{thm "perm_int_def"}
   666          |> discrete_cp_inst "IntDef.int" @{thm "perm_int_def"}
   667          |> discrete_pt_inst "List.char" @{thm "perm_char_def"}
   668          |> discrete_fs_inst "List.char" @{thm "perm_char_def"}
   669          |> discrete_cp_inst "List.char" @{thm "perm_char_def"}
   670         end;
   671 
   672 
   673        (* abbreviations for some lemmas *)
   674        (*===============================*)
   675        val abs_fun_pi          = @{thm "Nominal.abs_fun_pi"};
   676        val abs_fun_pi_ineq     = @{thm "Nominal.abs_fun_pi_ineq"};
   677        val abs_fun_eq          = @{thm "Nominal.abs_fun_eq"};
   678        val abs_fun_eq'         = @{thm "Nominal.abs_fun_eq'"};
   679        val abs_fun_fresh       = @{thm "Nominal.abs_fun_fresh"};
   680        val abs_fun_fresh'      = @{thm "Nominal.abs_fun_fresh'"};
   681        val dj_perm_forget      = @{thm "Nominal.dj_perm_forget"};
   682        val dj_pp_forget        = @{thm "Nominal.dj_perm_perm_forget"};
   683        val fresh_iff           = @{thm "Nominal.fresh_abs_fun_iff"};
   684        val fresh_iff_ineq      = @{thm "Nominal.fresh_abs_fun_iff_ineq"};
   685        val abs_fun_supp        = @{thm "Nominal.abs_fun_supp"};
   686        val abs_fun_supp_ineq   = @{thm "Nominal.abs_fun_supp_ineq"};
   687        val pt_swap_bij         = @{thm "Nominal.pt_swap_bij"};
   688        val pt_swap_bij'        = @{thm "Nominal.pt_swap_bij'"};
   689        val pt_fresh_fresh      = @{thm "Nominal.pt_fresh_fresh"};
   690        val pt_bij              = @{thm "Nominal.pt_bij"};
   691        val pt_perm_compose     = @{thm "Nominal.pt_perm_compose"};
   692        val pt_perm_compose'    = @{thm "Nominal.pt_perm_compose'"};
   693        val perm_app            = @{thm "Nominal.pt_fun_app_eq"};
   694        val at_fresh            = @{thm "Nominal.at_fresh"};
   695        val at_fresh_ineq       = @{thm "Nominal.at_fresh_ineq"};
   696        val at_calc             = @{thms "Nominal.at_calc"};
   697        val at_swap_simps       = @{thms "Nominal.at_swap_simps"};
   698        val at_supp             = @{thm "Nominal.at_supp"};
   699        val dj_supp             = @{thm "Nominal.dj_supp"};
   700        val fresh_left_ineq     = @{thm "Nominal.pt_fresh_left_ineq"};
   701        val fresh_left          = @{thm "Nominal.pt_fresh_left"};
   702        val fresh_right_ineq    = @{thm "Nominal.pt_fresh_right_ineq"};
   703        val fresh_right         = @{thm "Nominal.pt_fresh_right"};
   704        val fresh_bij_ineq      = @{thm "Nominal.pt_fresh_bij_ineq"};
   705        val fresh_bij           = @{thm "Nominal.pt_fresh_bij"};
   706        val fresh_eqvt          = @{thm "Nominal.pt_fresh_eqvt"};
   707        val fresh_eqvt_ineq     = @{thm "Nominal.pt_fresh_eqvt_ineq"};
   708        val set_diff_eqvt       = @{thm "Nominal.pt_set_diff_eqvt"};
   709        val in_eqvt             = @{thm "Nominal.pt_in_eqvt"};
   710        val eq_eqvt             = @{thm "Nominal.pt_eq_eqvt"};
   711        val all_eqvt            = @{thm "Nominal.pt_all_eqvt"};
   712        val ex_eqvt             = @{thm "Nominal.pt_ex_eqvt"};
   713        val pt_pi_rev           = @{thm "Nominal.pt_pi_rev"};
   714        val pt_rev_pi           = @{thm "Nominal.pt_rev_pi"};
   715        val at_exists_fresh     = @{thm "Nominal.at_exists_fresh"};
   716        val at_exists_fresh'    = @{thm "Nominal.at_exists_fresh'"};
   717        val fresh_perm_app_ineq = @{thm "Nominal.pt_fresh_perm_app_ineq"};
   718        val fresh_perm_app      = @{thm "Nominal.pt_fresh_perm_app"};	
   719        val fresh_aux           = @{thm "Nominal.pt_fresh_aux"};  
   720        val pt_perm_supp_ineq   = @{thm "Nominal.pt_perm_supp_ineq"};
   721        val pt_perm_supp        = @{thm "Nominal.pt_perm_supp"};
   722 
   723        (* Now we collect and instantiate some lemmas w.r.t. all atom      *)
   724        (* types; this allows for example to use abs_perm (which is a      *)
   725        (* collection of theorems) instead of thm abs_fun_pi with explicit *)
   726        (* instantiations.                                                 *)
   727        val (_, thy33) =
   728          let
   729 
   730              (* takes a theorem thm and a list of theorems [t1,..,tn]            *)
   731              (* produces a list of theorems of the form [t1 RS thm,..,tn RS thm] *) 
   732              fun instR thm thms = map (fn ti => ti RS thm) thms;
   733 
   734              (* takes two theorem lists (hopefully of the same length ;o)                *)
   735              (* produces a list of theorems of the form                                  *)
   736              (* [t1 RS m1,..,tn RS mn] where [t1,..,tn] is thms1 and [m1,..,mn] is thms2 *) 
   737              fun inst_zip thms1 thms2 = map (fn (t1,t2) => t1 RS t2) (thms1 ~~ thms2);
   738 
   739              (* takes a theorem list of the form [l1,...,ln]              *)
   740              (* and a list of theorem lists of the form                   *)
   741              (* [[h11,...,h1m],....,[hk1,....,hkm]                        *)
   742              (* produces the list of theorem lists                        *)
   743              (* [[l1 RS h11,...,l1 RS h1m],...,[ln RS hk1,...,ln RS hkm]] *)
   744              fun inst_mult thms thmss = map (fn (t,ts) => instR t ts) (thms ~~ thmss);
   745 
   746              (* FIXME: these lists do not need to be created dynamically again *)
   747 
   748              
   749              (* list of all at_inst-theorems *)
   750              val ats = map (fn ak => PureThy.get_thm thy32 (Name ("at_"^ak^"_inst"))) ak_names
   751              (* list of all pt_inst-theorems *)
   752              val pts = map (fn ak => PureThy.get_thm thy32 (Name ("pt_"^ak^"_inst"))) ak_names
   753              (* list of all cp_inst-theorems as a collection of lists*)
   754              val cps = 
   755 		 let fun cps_fun ak1 ak2 = PureThy.get_thm thy32 (Name ("cp_"^ak1^"_"^ak2^"_inst"))
   756 		 in map (fn aki => (map (cps_fun aki) ak_names)) ak_names end; 
   757              (* list of all cp_inst-theorems that have different atom types *)
   758              val cps' = 
   759 		let fun cps'_fun ak1 ak2 = 
   760 		if ak1=ak2 then NONE else SOME(PureThy.get_thm thy32 (Name ("cp_"^ak1^"_"^ak2^"_inst")))
   761 		in map (fn aki => (List.mapPartial I (map (cps'_fun aki) ak_names))) ak_names end;
   762              (* list of all dj_inst-theorems *)
   763              val djs = 
   764 	       let fun djs_fun (ak1,ak2) = 
   765 		     if ak1=ak2 then NONE else SOME(PureThy.get_thm thy32 (Name ("dj_"^ak2^"_"^ak1)))
   766 	       in List.mapPartial I (map djs_fun (Library.product ak_names ak_names)) end;
   767              (* list of all fs_inst-theorems *)
   768              val fss = map (fn ak => PureThy.get_thm thy32 (Name ("fs_"^ak^"_inst"))) ak_names
   769              (* list of all at_inst-theorems *)
   770              val fs_axs = map (fn ak => PureThy.get_thm thy32 (Name ("fs_"^ak^"1"))) ak_names
   771 
   772              fun inst_pt thms = Library.flat (map (fn ti => instR ti pts) thms);
   773              fun inst_at thms = Library.flat (map (fn ti => instR ti ats) thms);
   774              fun inst_fs thms = Library.flat (map (fn ti => instR ti fss) thms);
   775              fun inst_cp thms cps = Library.flat (inst_mult thms cps);
   776 	     fun inst_pt_at thms = inst_zip ats (inst_pt thms);
   777              fun inst_dj thms = Library.flat (map (fn ti => instR ti djs) thms);
   778 	     fun inst_pt_pt_at_cp thms = inst_cp (inst_zip ats (inst_zip pts (inst_pt thms))) cps;
   779              fun inst_pt_at_fs thms = inst_zip (inst_fs [fs1]) (inst_zip ats (inst_pt thms));
   780 	     fun inst_pt_pt_at_cp thms =
   781 		 let val i_pt_pt_at = inst_zip ats (inst_zip pts (inst_pt thms));
   782                      val i_pt_pt_at_cp = inst_cp i_pt_pt_at cps';
   783 		 in i_pt_pt_at_cp end;
   784              fun inst_pt_pt_at_cp_dj thms = inst_zip djs (inst_pt_pt_at_cp thms);
   785            in
   786             thy32 
   787 	    |>   PureThy.add_thmss [(("alpha", inst_pt_at [abs_fun_eq]),[])]
   788             ||>> PureThy.add_thmss [(("alpha'", inst_pt_at [abs_fun_eq']),[])]
   789             ||>> PureThy.add_thmss [(("alpha_fresh", inst_pt_at [abs_fun_fresh]),[])]
   790             ||>> PureThy.add_thmss [(("alpha_fresh'", inst_pt_at [abs_fun_fresh']),[])]
   791             ||>> PureThy.add_thmss [(("perm_swap", inst_pt_at [pt_swap_bij] @ inst_pt_at [pt_swap_bij']),[])]
   792             ||>> PureThy.add_thmss [(("swap_simps", inst_at at_swap_simps),[])]	 
   793             ||>> PureThy.add_thmss 
   794 	      let val thms1 = inst_pt_at [pt_pi_rev];
   795 		  val thms2 = inst_pt_at [pt_rev_pi];
   796               in [(("perm_pi_simp",thms1 @ thms2),[])] end
   797             ||>> PureThy.add_thmss [(("perm_fresh_fresh", inst_pt_at [pt_fresh_fresh]),[])]
   798             ||>> PureThy.add_thmss [(("perm_bij", inst_pt_at [pt_bij]),[])]
   799             ||>> PureThy.add_thmss 
   800 	      let val thms1 = inst_pt_at [pt_perm_compose];
   801 		  val thms2 = instR cp1 (Library.flat cps');
   802               in [(("perm_compose",thms1 @ thms2),[])] end
   803             ||>> PureThy.add_thmss [(("perm_compose'",inst_pt_at [pt_perm_compose']),[])] 
   804             ||>> PureThy.add_thmss [(("perm_app", inst_pt_at [perm_app]),[])]
   805             ||>> PureThy.add_thmss [(("supp_atm", (inst_at [at_supp]) @ (inst_dj [dj_supp])),[])]
   806             ||>> PureThy.add_thmss [(("exists_fresh", inst_at [at_exists_fresh]),[])]
   807             ||>> PureThy.add_thmss [(("exists_fresh'", inst_at [at_exists_fresh']),[])]
   808             ||>> PureThy.add_thmss
   809               let
   810                 val thms1 = inst_pt_at [all_eqvt];
   811                 val thms2 = map (fold_rule [inductive_forall_def]) thms1
   812               in
   813                 [(("all_eqvt", thms1 @ thms2), [NominalThmDecls.eqvt_force_add])]
   814               end
   815             ||>> PureThy.add_thmss [(("ex_eqvt", inst_pt_at [ex_eqvt]),[NominalThmDecls.eqvt_force_add])]
   816             ||>> PureThy.add_thmss 
   817 	      let val thms1 = inst_at [at_fresh]
   818 		  val thms2 = inst_dj [at_fresh_ineq]
   819 	      in [(("fresh_atm", thms1 @ thms2),[])] end
   820             ||>> PureThy.add_thmss
   821 	      let val thms1 = filter
   822                 (fn th => case prop_of th of _ $ _ $ Var _ => true | _ => false)
   823                 (List.concat (List.concat perm_defs))
   824               in [(("calc_atm", (inst_at at_calc) @ thms1),[])] end
   825             ||>> PureThy.add_thmss
   826 	      let val thms1 = inst_pt_at [abs_fun_pi]
   827 		  and thms2 = inst_pt_pt_at_cp [abs_fun_pi_ineq]
   828 	      in [(("abs_perm", thms1 @ thms2),[NominalThmDecls.eqvt_add])] end
   829             ||>> PureThy.add_thmss
   830 	      let val thms1 = inst_dj [dj_perm_forget]
   831 		  and thms2 = inst_dj [dj_pp_forget]
   832               in [(("perm_dj", thms1 @ thms2),[])] end
   833             ||>> PureThy.add_thmss
   834 	      let val thms1 = inst_pt_at_fs [fresh_iff]
   835                   and thms2 = inst_pt_at [fresh_iff]
   836 		  and thms3 = inst_pt_pt_at_cp_dj [fresh_iff_ineq]
   837 	    in [(("abs_fresh", thms1 @ thms2 @ thms3),[])] end
   838 	    ||>> PureThy.add_thmss
   839 	      let val thms1 = inst_pt_at [abs_fun_supp]
   840 		  and thms2 = inst_pt_at_fs [abs_fun_supp]
   841 		  and thms3 = inst_pt_pt_at_cp_dj [abs_fun_supp_ineq]
   842 	      in [(("abs_supp", thms1 @ thms2 @ thms3),[])] end
   843             ||>> PureThy.add_thmss
   844 	      let val thms1 = inst_pt_at [fresh_left]
   845 		  and thms2 = inst_pt_pt_at_cp [fresh_left_ineq]
   846 	      in [(("fresh_left", thms1 @ thms2),[])] end
   847             ||>> PureThy.add_thmss
   848 	      let val thms1 = inst_pt_at [fresh_right]
   849 		  and thms2 = inst_pt_pt_at_cp [fresh_right_ineq]
   850 	      in [(("fresh_right", thms1 @ thms2),[])] end
   851             ||>> PureThy.add_thmss
   852 	      let val thms1 = inst_pt_at [fresh_bij]
   853  		  and thms2 = inst_pt_pt_at_cp [fresh_bij_ineq]
   854 	      in [(("fresh_bij", thms1 @ thms2),[])] end
   855             ||>> PureThy.add_thmss
   856 	      let val thms1 = inst_pt_at [fresh_eqvt]
   857                   and thms2 = inst_pt_pt_at_cp_dj [fresh_eqvt_ineq]
   858 	      in [(("fresh_eqvt", thms1 @ thms2),[NominalThmDecls.eqvt_add])] end
   859             ||>> PureThy.add_thmss
   860 	      let val thms1 = inst_pt_at [in_eqvt]
   861 	      in [(("in_eqvt", thms1),[NominalThmDecls.eqvt_add])] end
   862   	    ||>> PureThy.add_thmss
   863 	      let val thms1 = inst_pt_at [eq_eqvt]
   864 	      in [(("eq_eqvt", thms1),[NominalThmDecls.eqvt_add])] end
   865 	    ||>> PureThy.add_thmss
   866 	      let val thms1 = inst_pt_at [set_diff_eqvt]
   867 	      in [(("set_diff_eqvt", thms1),[NominalThmDecls.eqvt_add])] end
   868             ||>> PureThy.add_thmss
   869 	      let val thms1 = inst_pt_at [fresh_aux]
   870 		  and thms2 = inst_pt_pt_at_cp_dj [fresh_perm_app_ineq] 
   871 	      in  [(("fresh_aux", thms1 @ thms2),[])] end  
   872             ||>> PureThy.add_thmss
   873 	      let val thms1 = inst_pt_at [fresh_perm_app]
   874 		  and thms2 = inst_pt_pt_at_cp_dj [fresh_perm_app_ineq] 
   875 	      in  [(("fresh_perm_app", thms1 @ thms2),[])] end 
   876             ||>> PureThy.add_thmss
   877 	      let val thms1 = inst_pt_at [pt_perm_supp]
   878 		  and thms2 = inst_pt_pt_at_cp [pt_perm_supp_ineq] 
   879 	      in  [(("supp_eqvt", thms1 @ thms2),[NominalThmDecls.eqvt_add])] end  
   880             ||>> PureThy.add_thmss [(("fin_supp",fs_axs),[])]
   881 	   end;
   882 
   883     in 
   884       NominalData.map (fold Symtab.update (full_ak_names ~~ map make_atom_info
   885         (pt_ax_classes ~~
   886          fs_ax_classes ~~
   887          map (fn cls => full_ak_names ~~ cls) cp_ax_classes))) thy33
   888     end;
   889 
   890 
   891 (* syntax und parsing *)
   892 structure P = OuterParse and K = OuterKeyword;
   893 
   894 val atom_declP =
   895   OuterSyntax.command "atom_decl" "Declare new kinds of atoms" K.thy_decl
   896     (Scan.repeat1 P.name >> (Toplevel.theory o create_nom_typedecls));
   897 
   898 val _ = OuterSyntax.add_parsers [atom_declP];
   899 
   900 end;