src/HOL/Nominal/nominal_atoms.ML
author haftmann
Fri Aug 10 17:04:24 2007 +0200 (2007-08-10 ago)
changeset 24218 fbf1646b267c
parent 24194 96013f81faef
child 24527 888d56a8d9d3
permissions -rw-r--r--
ClassPackage renamed to Class
     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 
    25 (* theory data *)
    26 
    27 type atom_info =
    28   {pt_class : string,
    29    fs_class : string,
    30    cp_classes : (string * string) list};
    31 
    32 structure NominalData = TheoryDataFun
    33 (
    34   type T = atom_info Symtab.table;
    35   val empty = Symtab.empty;
    36   val copy = I;
    37   val extend = I;
    38   fun merge _ x = Symtab.merge (K true) x;
    39 );
    40 
    41 fun make_atom_info ((pt_class, fs_class), cp_classes) =
    42   {pt_class = pt_class,
    43    fs_class = fs_class,
    44    cp_classes = cp_classes};
    45 
    46 val get_atom_infos = NominalData.get;
    47 val get_atom_info = Symtab.lookup o NominalData.get;
    48 
    49 fun atoms_of thy = map fst (Symtab.dest (NominalData.get thy));
    50 
    51 fun mk_permT T = HOLogic.listT (HOLogic.mk_prodT (T, T));
    52 
    53 fun mk_Cons x xs =
    54   let val T = fastype_of x
    55   in Const ("List.list.Cons", T --> HOLogic.listT T --> HOLogic.listT T) $ x $ xs end;
    56 
    57 
    58 (* this function sets up all matters related to atom-  *)
    59 (* kinds; the user specifies a list of atom-kind names *)
    60 (* atom_decl <ak1> ... <akn>                           *)
    61 fun create_nom_typedecls ak_names thy =
    62   let
    63     val cla_s = claset_of thy;
    64 
    65     (* declares a type-decl for every atom-kind: *) 
    66     (* that is typedecl <ak>                     *)
    67     val thy1 = TypedefPackage.add_typedecls (map (fn x => (x,[],NoSyn)) ak_names) thy;
    68     
    69     (* produces a list consisting of pairs:         *)
    70     (*  fst component is the atom-kind name         *)
    71     (*  snd component is its type                   *)
    72     val full_ak_names = map (Sign.intern_type thy1) ak_names;
    73     val ak_names_types = ak_names ~~ map (Type o rpair []) full_ak_names;
    74      
    75     (* adds for every atom-kind an axiom             *)
    76     (* <ak>_infinite: infinite (UNIV::<ak_type> set) *)
    77     val (inf_axs,thy2) = PureThy.add_axioms_i (map (fn (ak_name, T) =>
    78       let 
    79     val name = ak_name ^ "_infinite"
    80         val axiom = HOLogic.mk_Trueprop (HOLogic.mk_not
    81                     (Const ("Finite_Set.finite", HOLogic.mk_setT T --> HOLogic.boolT) $
    82                        HOLogic.mk_UNIV T))
    83       in
    84         ((name, axiom), []) 
    85       end) ak_names_types) thy1;
    86     
    87     (* declares a swapping function for every atom-kind, it is         *)
    88     (* const swap_<ak> :: <akT> * <akT> => <akT> => <akT>              *)
    89     (* swap_<ak> (a,b) c = (if a=c then b (else if b=c then a else c)) *)
    90     (* overloades then the general swap-function                       *) 
    91     val (swap_eqs, thy3) = fold_map (fn (ak_name, T) => fn thy =>
    92       let
    93         val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
    94         val swap_name = Sign.full_name thy ("swap_" ^ ak_name);
    95         val a = Free ("a", T);
    96         val b = Free ("b", T);
    97         val c = Free ("c", T);
    98         val ab = Free ("ab", HOLogic.mk_prodT (T, T))
    99         val cif = Const ("HOL.If", HOLogic.boolT --> T --> T --> T);
   100         val cswap_akname = Const (swap_name, swapT);
   101         val cswap = Const ("Nominal.swap", swapT)
   102 
   103         val name = "swap_"^ak_name^"_def";
   104         val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq
   105                 (cswap_akname $ HOLogic.mk_prod (a,b) $ c,
   106                     cif $ HOLogic.mk_eq (a,c) $ b $ (cif $ HOLogic.mk_eq (b,c) $ a $ c)))
   107         val def2 = Logic.mk_equals (cswap $ ab $ c, cswap_akname $ ab $ c)
   108       in
   109         thy |> Theory.add_consts_i [("swap_" ^ ak_name, swapT, NoSyn)] 
   110             |> PureThy.add_defs_unchecked_i true [((name, def2),[])]
   111             |> snd
   112             |> PrimrecPackage.add_primrec_unchecked_i "" [(("", def1),[])]
   113       end) ak_names_types thy2;
   114     
   115     (* declares a permutation function for every atom-kind acting  *)
   116     (* on such atoms                                               *)
   117     (* const <ak>_prm_<ak> :: (<akT> * <akT>)list => akT => akT    *)
   118     (* <ak>_prm_<ak> []     a = a                                  *)
   119     (* <ak>_prm_<ak> (x#xs) a = swap_<ak> x (perm xs a)            *)
   120     val (prm_eqs, thy4) = fold_map (fn (ak_name, T) => fn thy =>
   121       let
   122         val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
   123         val swap_name = Sign.full_name thy ("swap_" ^ ak_name)
   124         val prmT = mk_permT T --> T --> T;
   125         val prm_name = ak_name ^ "_prm_" ^ ak_name;
   126         val qu_prm_name = Sign.full_name thy prm_name;
   127         val x  = Free ("x", HOLogic.mk_prodT (T, T));
   128         val xs = Free ("xs", mk_permT T);
   129         val a  = Free ("a", T) ;
   130 
   131         val cnil  = Const ("List.list.Nil", mk_permT T);
   132         
   133         val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq (Const (qu_prm_name, prmT) $ cnil $ a, a));
   134 
   135         val def2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
   136                    (Const (qu_prm_name, prmT) $ mk_Cons x xs $ a,
   137                     Const (swap_name, swapT) $ x $ (Const (qu_prm_name, prmT) $ xs $ a)));
   138       in
   139         thy |> Theory.add_consts_i [(prm_name, mk_permT T --> T --> T, NoSyn)] 
   140             |> PrimrecPackage.add_primrec_unchecked_i "" [(("", def1), []),(("", def2), [])]
   141       end) ak_names_types thy3;
   142     
   143     (* defines permutation functions for all combinations of atom-kinds; *)
   144     (* there are a trivial cases and non-trivial cases                   *)
   145     (* non-trivial case:                                                 *)
   146     (* <ak>_prm_<ak>_def:  perm pi a == <ak>_prm_<ak> pi a               *)
   147     (* trivial case with <ak> != <ak'>                                   *)
   148     (* <ak>_prm<ak'>_def[simp]:  perm pi a == a                          *)
   149     (*                                                                   *)
   150     (* the trivial cases are added to the simplifier, while the non-     *)
   151     (* have their own rules proved below                                 *)  
   152     val (perm_defs, thy5) = fold_map (fn (ak_name, T) => fn thy =>
   153       fold_map (fn (ak_name', T') => fn thy' =>
   154         let
   155           val perm_def_name = ak_name ^ "_prm_" ^ ak_name';
   156           val pi = Free ("pi", mk_permT T);
   157           val a  = Free ("a", T');
   158           val cperm = Const ("Nominal.perm", mk_permT T --> T' --> T');
   159           val cperm_def = Const (Sign.full_name thy' perm_def_name, mk_permT T --> T' --> T');
   160 
   161           val name = ak_name ^ "_prm_" ^ ak_name' ^ "_def";
   162           val def = Logic.mk_equals
   163                     (cperm $ pi $ a, if ak_name = ak_name' then cperm_def $ pi $ a else a)
   164         in
   165           PureThy.add_defs_unchecked_i true [((name, def),[])] thy'
   166         end) ak_names_types thy) ak_names_types thy4;
   167     
   168     (* proves that every atom-kind is an instance of at *)
   169     (* lemma at_<ak>_inst:                              *)
   170     (* at TYPE(<ak>)                                    *)
   171     val (prm_cons_thms,thy6) = 
   172       thy5 |> PureThy.add_thms (map (fn (ak_name, T) =>
   173       let
   174         val ak_name_qu = Sign.full_name thy5 (ak_name);
   175         val i_type = Type(ak_name_qu,[]);
   176 	val cat = Const ("Nominal.at",(Term.itselfT i_type)  --> HOLogic.boolT);
   177         val at_type = Logic.mk_type i_type;
   178         val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy5
   179                                   [Name "at_def",
   180                                    Name (ak_name ^ "_prm_" ^ ak_name ^ "_def"),
   181                                    Name (ak_name ^ "_prm_" ^ ak_name ^ ".simps"),
   182                                    Name ("swap_" ^ ak_name ^ "_def"),
   183                                    Name ("swap_" ^ ak_name ^ ".simps"),
   184                                    Name (ak_name ^ "_infinite")]
   185 	    
   186 	val name = "at_"^ak_name^ "_inst";
   187         val statement = HOLogic.mk_Trueprop (cat $ at_type);
   188 
   189         val proof = fn _ => auto_tac (cla_s,simp_s);
   190 
   191       in 
   192         ((name, Goal.prove_global thy5 [] [] statement proof), []) 
   193       end) ak_names_types);
   194 
   195     (* declares a perm-axclass for every atom-kind               *)
   196     (* axclass pt_<ak>                                           *)
   197     (* pt_<ak>1[simp]: perm [] x = x                             *)
   198     (* pt_<ak>2:       perm (pi1@pi2) x = perm pi1 (perm pi2 x)  *)
   199     (* pt_<ak>3:       pi1 ~ pi2 ==> perm pi1 x = perm pi2 x     *)
   200      val (pt_ax_classes,thy7) =  fold_map (fn (ak_name, T) => fn thy =>
   201       let 
   202 	  val cl_name = "pt_"^ak_name;
   203           val ty = TFree("'a",["HOL.type"]);
   204           val x   = Free ("x", ty);
   205           val pi1 = Free ("pi1", mk_permT T);
   206           val pi2 = Free ("pi2", mk_permT T);
   207           val cperm = Const ("Nominal.perm", mk_permT T --> ty --> ty);
   208           val cnil  = Const ("List.list.Nil", mk_permT T);
   209           val cappend = Const ("List.append",mk_permT T --> mk_permT T --> mk_permT T);
   210           val cprm_eq = Const ("Nominal.prm_eq",mk_permT T --> mk_permT T --> HOLogic.boolT);
   211           (* nil axiom *)
   212           val axiom1 = HOLogic.mk_Trueprop (HOLogic.mk_eq 
   213                        (cperm $ cnil $ x, x));
   214           (* append axiom *)
   215           val axiom2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
   216                        (cperm $ (cappend $ pi1 $ pi2) $ x, cperm $ pi1 $ (cperm $ pi2 $ x)));
   217           (* perm-eq axiom *)
   218           val axiom3 = Logic.mk_implies
   219                        (HOLogic.mk_Trueprop (cprm_eq $ pi1 $ pi2),
   220                         HOLogic.mk_Trueprop (HOLogic.mk_eq (cperm $ pi1 $ x, cperm $ pi2 $ x)));
   221       in
   222           AxClass.define_class (cl_name, ["HOL.type"]) []
   223                 [((cl_name ^ "1", [Simplifier.simp_add]), [axiom1]),
   224                  ((cl_name ^ "2", []), [axiom2]),                           
   225                  ((cl_name ^ "3", []), [axiom3])] thy                          
   226       end) ak_names_types thy6;
   227 
   228     (* proves that every pt_<ak>-type together with <ak>-type *)
   229     (* instance of pt                                         *)
   230     (* lemma pt_<ak>_inst:                                    *)
   231     (* pt TYPE('x::pt_<ak>) TYPE(<ak>)                        *)
   232     val (prm_inst_thms,thy8) = 
   233       thy7 |> PureThy.add_thms (map (fn (ak_name, T) =>
   234       let
   235         val ak_name_qu = Sign.full_name thy7 ak_name;
   236         val pt_name_qu = Sign.full_name thy7 ("pt_"^ak_name);
   237         val i_type1 = TFree("'x",[pt_name_qu]);
   238         val i_type2 = Type(ak_name_qu,[]);
   239 	val cpt = Const ("Nominal.pt",(Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
   240         val pt_type = Logic.mk_type i_type1;
   241         val at_type = Logic.mk_type i_type2;
   242         val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy7
   243                                   [Name "pt_def",
   244                                    Name ("pt_" ^ ak_name ^ "1"),
   245                                    Name ("pt_" ^ ak_name ^ "2"),
   246                                    Name ("pt_" ^ ak_name ^ "3")];
   247 
   248 	val name = "pt_"^ak_name^ "_inst";
   249         val statement = HOLogic.mk_Trueprop (cpt $ pt_type $ at_type);
   250 
   251         val proof = fn _ => auto_tac (cla_s,simp_s);
   252       in 
   253         ((name, Goal.prove_global thy7 [] [] statement proof), []) 
   254       end) ak_names_types);
   255 
   256      (* declares an fs-axclass for every atom-kind       *)
   257      (* axclass fs_<ak>                                  *)
   258      (* fs_<ak>1: finite ((supp x)::<ak> set)            *)
   259      val (fs_ax_classes,thy11) =  fold_map (fn (ak_name, T) => fn thy =>
   260        let 
   261 	  val cl_name = "fs_"^ak_name;
   262 	  val pt_name = Sign.full_name thy ("pt_"^ak_name);
   263           val ty = TFree("'a",["HOL.type"]);
   264           val x   = Free ("x", ty);
   265           val csupp    = Const ("Nominal.supp", ty --> HOLogic.mk_setT T);
   266           val cfinite  = Const ("Finite_Set.finite", HOLogic.mk_setT T --> HOLogic.boolT)
   267           
   268           val axiom1   = HOLogic.mk_Trueprop (cfinite $ (csupp $ x));
   269 
   270        in  
   271         AxClass.define_class (cl_name, [pt_name]) [] [((cl_name ^ "1", []), [axiom1])] thy            
   272        end) ak_names_types thy8; 
   273 	 
   274      (* proves that every fs_<ak>-type together with <ak>-type   *)
   275      (* instance of fs-type                                      *)
   276      (* lemma abst_<ak>_inst:                                    *)
   277      (* fs TYPE('x::pt_<ak>) TYPE (<ak>)                         *)
   278      val (fs_inst_thms,thy12) = 
   279        thy11 |> PureThy.add_thms (map (fn (ak_name, T) =>
   280        let
   281          val ak_name_qu = Sign.full_name thy11 ak_name;
   282          val fs_name_qu = Sign.full_name thy11 ("fs_"^ak_name);
   283          val i_type1 = TFree("'x",[fs_name_qu]);
   284          val i_type2 = Type(ak_name_qu,[]);
   285  	 val cfs = Const ("Nominal.fs", 
   286                                  (Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
   287          val fs_type = Logic.mk_type i_type1;
   288          val at_type = Logic.mk_type i_type2;
   289 	 val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy11
   290                                    [Name "fs_def",
   291                                     Name ("fs_" ^ ak_name ^ "1")];
   292     
   293 	 val name = "fs_"^ak_name^ "_inst";
   294          val statement = HOLogic.mk_Trueprop (cfs $ fs_type $ at_type);
   295 
   296          val proof = fn _ => auto_tac (cla_s,simp_s);
   297        in 
   298          ((name, Goal.prove_global thy11 [] [] statement proof), []) 
   299        end) ak_names_types);
   300 
   301        (* declares for every atom-kind combination an axclass            *)
   302        (* cp_<ak1>_<ak2> giving a composition property                   *)
   303        (* cp_<ak1>_<ak2>1: pi1 o pi2 o x = (pi1 o pi2) o (pi1 o x)       *)
   304         val (cp_ax_classes,thy12b) = fold_map (fn (ak_name, T) => fn thy =>
   305 	 fold_map (fn (ak_name', T') => fn thy' =>
   306 	     let
   307 	       val cl_name = "cp_"^ak_name^"_"^ak_name';
   308 	       val ty = TFree("'a",["HOL.type"]);
   309                val x   = Free ("x", ty);
   310                val pi1 = Free ("pi1", mk_permT T);
   311 	       val pi2 = Free ("pi2", mk_permT T');                  
   312 	       val cperm1 = Const ("Nominal.perm", mk_permT T  --> ty --> ty);
   313                val cperm2 = Const ("Nominal.perm", mk_permT T' --> ty --> ty);
   314                val cperm3 = Const ("Nominal.perm", mk_permT T  --> mk_permT T' --> mk_permT T');
   315 
   316                val ax1   = HOLogic.mk_Trueprop 
   317 			   (HOLogic.mk_eq (cperm1 $ pi1 $ (cperm2 $ pi2 $ x), 
   318                                            cperm2 $ (cperm3 $ pi1 $ pi2) $ (cperm1 $ pi1 $ x)));
   319 	       in  
   320 		 AxClass.define_class (cl_name, ["HOL.type"]) [] [((cl_name ^ "1", []), [ax1])] thy'  
   321 	       end) ak_names_types thy) ak_names_types thy12;
   322 
   323         (* proves for every <ak>-combination a cp_<ak1>_<ak2>_inst theorem;     *)
   324         (* lemma cp_<ak1>_<ak2>_inst:                                           *)
   325         (* cp TYPE('a::cp_<ak1>_<ak2>) TYPE(<ak1>) TYPE(<ak2>)                  *)
   326         val (cp_thms,thy12c) = fold_map (fn (ak_name, T) => fn thy =>
   327 	 fold_map (fn (ak_name', T') => fn thy' =>
   328            let
   329              val ak_name_qu  = Sign.full_name thy' (ak_name);
   330 	     val ak_name_qu' = Sign.full_name thy' (ak_name');
   331              val cp_name_qu  = Sign.full_name thy' ("cp_"^ak_name^"_"^ak_name');
   332              val i_type0 = TFree("'a",[cp_name_qu]);
   333              val i_type1 = Type(ak_name_qu,[]);
   334              val i_type2 = Type(ak_name_qu',[]);
   335 	     val ccp = Const ("Nominal.cp",
   336                              (Term.itselfT i_type0)-->(Term.itselfT i_type1)-->
   337                                                       (Term.itselfT i_type2)-->HOLogic.boolT);
   338              val at_type  = Logic.mk_type i_type1;
   339              val at_type' = Logic.mk_type i_type2;
   340 	     val cp_type  = Logic.mk_type i_type0;
   341              val simp_s   = HOL_basic_ss addsimps PureThy.get_thmss thy' [(Name "cp_def")];
   342 	     val cp1      = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"1"));
   343 
   344 	     val name = "cp_"^ak_name^ "_"^ak_name'^"_inst";
   345              val statement = HOLogic.mk_Trueprop (ccp $ cp_type $ at_type $ at_type');
   346 
   347              val proof = fn _ => EVERY [auto_tac (cla_s,simp_s), rtac cp1 1];
   348 	   in
   349 	     PureThy.add_thms [((name, Goal.prove_global thy' [] [] statement proof), [])] thy'
   350 	   end) 
   351            ak_names_types thy) ak_names_types thy12b;
   352        
   353         (* proves for every non-trivial <ak>-combination a disjointness   *)
   354         (* theorem; i.e. <ak1> != <ak2>                                   *)
   355         (* lemma ds_<ak1>_<ak2>:                                          *)
   356         (* dj TYPE(<ak1>) TYPE(<ak2>)                                     *)
   357         val (dj_thms, thy12d) = fold_map (fn (ak_name,T) => fn thy =>
   358 	  fold_map (fn (ak_name',T') => fn thy' =>
   359           (if not (ak_name = ak_name') 
   360            then 
   361 	       let
   362 		 val ak_name_qu  = Sign.full_name thy' ak_name;
   363 	         val ak_name_qu' = Sign.full_name thy' ak_name';
   364                  val i_type1 = Type(ak_name_qu,[]);
   365                  val i_type2 = Type(ak_name_qu',[]);
   366 	         val cdj = Const ("Nominal.disjoint",
   367                            (Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
   368                  val at_type  = Logic.mk_type i_type1;
   369                  val at_type' = Logic.mk_type i_type2;
   370                  val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy' 
   371 					   [Name "disjoint_def",
   372                                             Name (ak_name^"_prm_"^ak_name'^"_def"),
   373                                             Name (ak_name'^"_prm_"^ak_name^"_def")];
   374 
   375 	         val name = "dj_"^ak_name^"_"^ak_name';
   376                  val statement = HOLogic.mk_Trueprop (cdj $ at_type $ at_type');
   377 
   378                  val proof = fn _ => auto_tac (cla_s,simp_s);
   379 	       in
   380 		PureThy.add_thms [((name, Goal.prove_global thy' [] [] statement proof), [])] thy'
   381 	       end
   382            else 
   383             ([],thy')))  (* do nothing branch, if ak_name = ak_name' *) 
   384 	    ak_names_types thy) ak_names_types thy12c;
   385 
   386      (********  pt_<ak> class instances  ********)
   387      (*=========================================*)
   388      (* some abbreviations for theorems *)
   389       val pt1           = @{thm "pt1"};
   390       val pt2           = @{thm "pt2"};
   391       val pt3           = @{thm "pt3"};
   392       val at_pt_inst    = @{thm "at_pt_inst"};
   393       val pt_set_inst   = @{thm "pt_set_inst"}; 
   394       val pt_unit_inst  = @{thm "pt_unit_inst"};
   395       val pt_prod_inst  = @{thm "pt_prod_inst"}; 
   396       val pt_nprod_inst = @{thm "pt_nprod_inst"}; 
   397       val pt_list_inst  = @{thm "pt_list_inst"};
   398       val pt_optn_inst  = @{thm "pt_option_inst"};
   399       val pt_noptn_inst = @{thm "pt_noption_inst"};
   400       val pt_fun_inst   = @{thm "pt_fun_inst"};
   401 
   402      (* for all atom-kind combinations <ak>/<ak'> show that        *)
   403      (* every <ak> is an instance of pt_<ak'>; the proof for       *)
   404      (* ak!=ak' is by definition; the case ak=ak' uses at_pt_inst. *)
   405      val thy13 = fold (fn ak_name => fn thy =>
   406 	fold (fn ak_name' => fn thy' =>
   407          let
   408            val qu_name =  Sign.full_name thy' ak_name';
   409            val cls_name = Sign.full_name thy' ("pt_"^ak_name);
   410            val at_inst  = PureThy.get_thm thy' (Name ("at_"^ak_name'^"_inst")); 
   411 
   412            val proof1 = EVERY [Class.intro_classes_tac [],
   413                                  rtac ((at_inst RS at_pt_inst) RS pt1) 1,
   414                                  rtac ((at_inst RS at_pt_inst) RS pt2) 1,
   415                                  rtac ((at_inst RS at_pt_inst) RS pt3) 1,
   416                                  atac 1];
   417            val simp_s = HOL_basic_ss addsimps 
   418                         PureThy.get_thmss thy' [Name (ak_name^"_prm_"^ak_name'^"_def")];  
   419            val proof2 = EVERY [Class.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)];
   420 
   421          in
   422            thy'
   423            |> AxClass.prove_arity (qu_name,[],[cls_name])
   424               (if ak_name = ak_name' then proof1 else proof2)
   425          end) ak_names thy) ak_names thy12c;
   426 
   427      (* show that                       *)
   428      (*      fun(pt_<ak>,pt_<ak>)       *)
   429      (*      noption(pt_<ak>)           *)
   430      (*      option(pt_<ak>)            *)
   431      (*      list(pt_<ak>)              *)
   432      (*      *(pt_<ak>,pt_<ak>)         *)
   433      (*      nprod(pt_<ak>,pt_<ak>)     *)
   434      (*      unit                       *)
   435      (*      set(pt_<ak>)               *)
   436      (* are instances of pt_<ak>        *)
   437      val thy18 = fold (fn ak_name => fn thy =>
   438        let
   439           val cls_name = Sign.full_name thy ("pt_"^ak_name);
   440           val at_thm   = PureThy.get_thm thy (Name ("at_"^ak_name^"_inst"));
   441           val pt_inst  = PureThy.get_thm thy (Name ("pt_"^ak_name^"_inst"));
   442 
   443           fun pt_proof thm = 
   444               EVERY [Class.intro_classes_tac [],
   445                      rtac (thm RS pt1) 1, rtac (thm RS pt2) 1, rtac (thm RS pt3) 1, atac 1];
   446 
   447           val pt_thm_fun   = at_thm RS (pt_inst RS (pt_inst RS pt_fun_inst));
   448           val pt_thm_noptn = pt_inst RS pt_noptn_inst; 
   449           val pt_thm_optn  = pt_inst RS pt_optn_inst; 
   450           val pt_thm_list  = pt_inst RS pt_list_inst;
   451           val pt_thm_prod  = pt_inst RS (pt_inst RS pt_prod_inst);
   452           val pt_thm_nprod = pt_inst RS (pt_inst RS pt_nprod_inst);
   453           val pt_thm_unit  = pt_unit_inst;
   454           val pt_thm_set   = pt_inst RS pt_set_inst
   455        in
   456         thy
   457         |> AxClass.prove_arity ("fun",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_fun)
   458         |> AxClass.prove_arity ("Nominal.noption",[[cls_name]],[cls_name]) (pt_proof pt_thm_noptn) 
   459         |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (pt_proof pt_thm_optn)
   460         |> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (pt_proof pt_thm_list)
   461         |> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_prod)
   462         |> AxClass.prove_arity ("Nominal.nprod",[[cls_name],[cls_name]],[cls_name]) 
   463                                     (pt_proof pt_thm_nprod)
   464         |> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (pt_proof pt_thm_unit)
   465         |> AxClass.prove_arity ("set",[[cls_name]],[cls_name]) (pt_proof pt_thm_set)
   466      end) ak_names thy13; 
   467 
   468        (********  fs_<ak> class instances  ********)
   469        (*=========================================*)
   470        (* abbreviations for some lemmas *)
   471        val fs1            = @{thm "fs1"};
   472        val fs_at_inst     = @{thm "fs_at_inst"};
   473        val fs_unit_inst   = @{thm "fs_unit_inst"};
   474        val fs_prod_inst   = @{thm "fs_prod_inst"};
   475        val fs_nprod_inst  = @{thm "fs_nprod_inst"};
   476        val fs_list_inst   = @{thm "fs_list_inst"};
   477        val fs_option_inst = @{thm "fs_option_inst"};
   478        val dj_supp        = @{thm "dj_supp"};
   479 
   480        (* shows that <ak> is an instance of fs_<ak>     *)
   481        (* uses the theorem at_<ak>_inst                 *)
   482        val thy20 = fold (fn ak_name => fn thy =>
   483         fold (fn ak_name' => fn thy' =>
   484         let
   485            val qu_name =  Sign.full_name thy' ak_name';
   486            val qu_class = Sign.full_name thy' ("fs_"^ak_name);
   487            val proof =
   488                (if ak_name = ak_name'
   489                 then
   490                   let val at_thm = PureThy.get_thm thy' (Name ("at_"^ak_name^"_inst"));
   491                   in  EVERY [Class.intro_classes_tac [],
   492                              rtac ((at_thm RS fs_at_inst) RS fs1) 1] end
   493                 else
   494                   let val dj_inst = PureThy.get_thm thy' (Name ("dj_"^ak_name'^"_"^ak_name));
   495                       val simp_s = HOL_basic_ss addsimps [dj_inst RS dj_supp, finite_emptyI];
   496                   in EVERY [Class.intro_classes_tac [], asm_simp_tac simp_s 1] end)
   497         in
   498          AxClass.prove_arity (qu_name,[],[qu_class]) proof thy'
   499         end) ak_names thy) ak_names thy18;
   500 
   501        (* shows that                  *)
   502        (*    unit                     *)
   503        (*    *(fs_<ak>,fs_<ak>)       *)
   504        (*    nprod(fs_<ak>,fs_<ak>)   *)
   505        (*    list(fs_<ak>)            *)
   506        (*    option(fs_<ak>)          *) 
   507        (* are instances of fs_<ak>    *)
   508 
   509        val thy24 = fold (fn ak_name => fn thy => 
   510         let
   511           val cls_name = Sign.full_name thy ("fs_"^ak_name);
   512           val fs_inst  = PureThy.get_thm thy (Name ("fs_"^ak_name^"_inst"));
   513           fun fs_proof thm = EVERY [Class.intro_classes_tac [], rtac (thm RS fs1) 1];
   514 
   515           val fs_thm_unit  = fs_unit_inst;
   516           val fs_thm_prod  = fs_inst RS (fs_inst RS fs_prod_inst);
   517           val fs_thm_nprod = fs_inst RS (fs_inst RS fs_nprod_inst);
   518           val fs_thm_list  = fs_inst RS fs_list_inst;
   519           val fs_thm_optn  = fs_inst RS fs_option_inst;
   520         in 
   521          thy
   522          |> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (fs_proof fs_thm_unit) 
   523          |> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (fs_proof fs_thm_prod) 
   524          |> AxClass.prove_arity ("Nominal.nprod",[[cls_name],[cls_name]],[cls_name]) 
   525                                      (fs_proof fs_thm_nprod) 
   526          |> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (fs_proof fs_thm_list)
   527          |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (fs_proof fs_thm_optn)
   528         end) ak_names thy20;
   529 
   530        (********  cp_<ak>_<ai> class instances  ********)
   531        (*==============================================*)
   532        (* abbreviations for some lemmas *)
   533        val cp1             = @{thm "cp1"};
   534        val cp_unit_inst    = @{thm "cp_unit_inst"};
   535        val cp_bool_inst    = @{thm "cp_bool_inst"};
   536        val cp_prod_inst    = @{thm "cp_prod_inst"};
   537        val cp_list_inst    = @{thm "cp_list_inst"};
   538        val cp_fun_inst     = @{thm "cp_fun_inst"};
   539        val cp_option_inst  = @{thm "cp_option_inst"};
   540        val cp_noption_inst = @{thm "cp_noption_inst"};
   541        val cp_set_inst     = @{thm "cp_set_inst"};
   542        val pt_perm_compose = @{thm "pt_perm_compose"};
   543 
   544        val dj_pp_forget    = @{thm "dj_perm_perm_forget"};
   545 
   546        (* shows that <aj> is an instance of cp_<ak>_<ai>  *)
   547        (* for every  <ak>/<ai>-combination                *)
   548        val thy25 = fold (fn ak_name => fn thy =>
   549          fold (fn ak_name' => fn thy' =>
   550           fold (fn ak_name'' => fn thy'' =>
   551             let
   552               val name =  Sign.full_name thy'' ak_name;
   553               val cls_name = Sign.full_name thy'' ("cp_"^ak_name'^"_"^ak_name'');
   554               val proof =
   555                 (if (ak_name'=ak_name'') then 
   556                   (let
   557                     val pt_inst  = PureThy.get_thm thy'' (Name ("pt_"^ak_name''^"_inst"));
   558                     val at_inst  = PureThy.get_thm thy'' (Name ("at_"^ak_name''^"_inst"));
   559                   in
   560 		   EVERY [Class.intro_classes_tac [],
   561                           rtac (at_inst RS (pt_inst RS pt_perm_compose)) 1]
   562                   end)
   563 		else
   564 		  (let
   565                      val dj_inst  = PureThy.get_thm thy'' (Name ("dj_"^ak_name''^"_"^ak_name'));
   566 		     val simp_s = HOL_basic_ss addsimps
   567                                         ((dj_inst RS dj_pp_forget)::
   568                                          (PureThy.get_thmss thy''
   569                                            [Name (ak_name' ^"_prm_"^ak_name^"_def"),
   570                                             Name (ak_name''^"_prm_"^ak_name^"_def")]));
   571                   in
   572                     EVERY [Class.intro_classes_tac [], simp_tac simp_s 1]
   573                   end))
   574               in
   575                 AxClass.prove_arity (name,[],[cls_name]) proof thy''
   576               end) ak_names thy') ak_names thy) ak_names thy24;
   577 
   578        (* shows that                                                    *) 
   579        (*      units                                                    *) 
   580        (*      products                                                 *)
   581        (*      lists                                                    *)
   582        (*      functions                                                *)
   583        (*      options                                                  *)
   584        (*      noptions                                                 *)
   585        (*      sets                                                     *)
   586        (* are instances of cp_<ak>_<ai> for every <ak>/<ai>-combination *)
   587        val thy26 = fold (fn ak_name => fn thy =>
   588 	fold (fn ak_name' => fn thy' =>
   589         let
   590             val cls_name = Sign.full_name thy' ("cp_"^ak_name^"_"^ak_name');
   591             val cp_inst  = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
   592             val pt_inst  = PureThy.get_thm thy' (Name ("pt_"^ak_name^"_inst"));
   593             val at_inst  = PureThy.get_thm thy' (Name ("at_"^ak_name^"_inst"));
   594 
   595             fun cp_proof thm  = EVERY [Class.intro_classes_tac [],rtac (thm RS cp1) 1];
   596 	  
   597             val cp_thm_unit = cp_unit_inst;
   598             val cp_thm_prod = cp_inst RS (cp_inst RS cp_prod_inst);
   599             val cp_thm_list = cp_inst RS cp_list_inst;
   600             val cp_thm_fun  = at_inst RS (pt_inst RS (cp_inst RS (cp_inst RS cp_fun_inst)));
   601             val cp_thm_optn = cp_inst RS cp_option_inst;
   602             val cp_thm_noptn = cp_inst RS cp_noption_inst;
   603             val cp_thm_set = cp_inst RS cp_set_inst;
   604         in
   605          thy'
   606          |> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (cp_proof cp_thm_unit)
   607 	 |> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_prod)
   608          |> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (cp_proof cp_thm_list)
   609          |> AxClass.prove_arity ("fun",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_fun)
   610          |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (cp_proof cp_thm_optn)
   611          |> AxClass.prove_arity ("Nominal.noption",[[cls_name]],[cls_name]) (cp_proof cp_thm_noptn)
   612          |> AxClass.prove_arity ("set",[[cls_name]],[cls_name]) (cp_proof cp_thm_set)
   613         end) ak_names thy) ak_names thy25;
   614 
   615      (* show that discrete nominal types are permutation types, finitely     *)
   616      (* supported and have the commutation property                          *)
   617      (* discrete types have a permutation operation defined as pi o x = x;   *)
   618      (* which renders the proofs to be simple "simp_all"-proofs.             *)
   619      val thy32 =
   620         let
   621 	  fun discrete_pt_inst discrete_ty defn =
   622 	     fold (fn ak_name => fn thy =>
   623 	     let
   624 	       val qu_class = Sign.full_name thy ("pt_"^ak_name);
   625 	       val simp_s = HOL_basic_ss addsimps [defn];
   626                val proof = EVERY [Class.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)];
   627              in 
   628 	       AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
   629              end) ak_names;
   630 
   631           fun discrete_fs_inst discrete_ty defn = 
   632 	     fold (fn ak_name => fn thy =>
   633 	     let
   634 	       val qu_class = Sign.full_name thy ("fs_"^ak_name);
   635 	       val supp_def = @{thm "Nominal.supp_def"};
   636                val simp_s = HOL_ss addsimps [supp_def,Collect_const,finite_emptyI,defn];
   637                val proof = EVERY [Class.intro_classes_tac [], asm_simp_tac simp_s 1];
   638              in 
   639 	       AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
   640              end) ak_names;
   641 
   642           fun discrete_cp_inst discrete_ty defn = 
   643 	     fold (fn ak_name' => (fold (fn ak_name => fn thy =>
   644 	     let
   645 	       val qu_class = Sign.full_name thy ("cp_"^ak_name^"_"^ak_name');
   646 	       val supp_def = @{thm "Nominal.supp_def"};
   647                val simp_s = HOL_ss addsimps [defn];
   648                val proof = EVERY [Class.intro_classes_tac [], asm_simp_tac simp_s 1];
   649              in
   650 	       AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
   651              end) ak_names)) ak_names;
   652 
   653         in
   654          thy26
   655          |> discrete_pt_inst "nat"  @{thm "perm_nat_def"}
   656          |> discrete_fs_inst "nat"  @{thm "perm_nat_def"}
   657          |> discrete_cp_inst "nat"  @{thm "perm_nat_def"}
   658          |> discrete_pt_inst "bool" @{thm "perm_bool"}
   659          |> discrete_fs_inst "bool" @{thm "perm_bool"}
   660          |> discrete_cp_inst "bool" @{thm "perm_bool"}
   661          |> discrete_pt_inst "IntDef.int" @{thm "perm_int_def"}
   662          |> discrete_fs_inst "IntDef.int" @{thm "perm_int_def"}
   663          |> discrete_cp_inst "IntDef.int" @{thm "perm_int_def"}
   664          |> discrete_pt_inst "List.char" @{thm "perm_char_def"}
   665          |> discrete_fs_inst "List.char" @{thm "perm_char_def"}
   666          |> discrete_cp_inst "List.char" @{thm "perm_char_def"}
   667         end;
   668 
   669 
   670        (* abbreviations for some lemmas *)
   671        (*===============================*)
   672        val abs_fun_pi          = @{thm "Nominal.abs_fun_pi"};
   673        val abs_fun_pi_ineq     = @{thm "Nominal.abs_fun_pi_ineq"};
   674        val abs_fun_eq          = @{thm "Nominal.abs_fun_eq"};
   675        val abs_fun_eq'         = @{thm "Nominal.abs_fun_eq'"};
   676        val abs_fun_fresh       = @{thm "Nominal.abs_fun_fresh"};
   677        val abs_fun_fresh'      = @{thm "Nominal.abs_fun_fresh'"};
   678        val dj_perm_forget      = @{thm "Nominal.dj_perm_forget"};
   679        val dj_pp_forget        = @{thm "Nominal.dj_perm_perm_forget"};
   680        val fresh_iff           = @{thm "Nominal.fresh_abs_fun_iff"};
   681        val fresh_iff_ineq      = @{thm "Nominal.fresh_abs_fun_iff_ineq"};
   682        val abs_fun_supp        = @{thm "Nominal.abs_fun_supp"};
   683        val abs_fun_supp_ineq   = @{thm "Nominal.abs_fun_supp_ineq"};
   684        val pt_swap_bij         = @{thm "Nominal.pt_swap_bij"};
   685        val pt_swap_bij'        = @{thm "Nominal.pt_swap_bij'"};
   686        val pt_fresh_fresh      = @{thm "Nominal.pt_fresh_fresh"};
   687        val pt_bij              = @{thm "Nominal.pt_bij"};
   688        val pt_perm_compose     = @{thm "Nominal.pt_perm_compose"};
   689        val pt_perm_compose'    = @{thm "Nominal.pt_perm_compose'"};
   690        val perm_app            = @{thm "Nominal.pt_fun_app_eq"};
   691        val at_fresh            = @{thm "Nominal.at_fresh"};
   692        val at_fresh_ineq       = @{thm "Nominal.at_fresh_ineq"};
   693        val at_calc             = @{thms "Nominal.at_calc"};
   694        val at_swap_simps       = @{thms "Nominal.at_swap_simps"};
   695        val at_supp             = @{thm "Nominal.at_supp"};
   696        val dj_supp             = @{thm "Nominal.dj_supp"};
   697        val fresh_left_ineq     = @{thm "Nominal.pt_fresh_left_ineq"};
   698        val fresh_left          = @{thm "Nominal.pt_fresh_left"};
   699        val fresh_right_ineq    = @{thm "Nominal.pt_fresh_right_ineq"};
   700        val fresh_right         = @{thm "Nominal.pt_fresh_right"};
   701        val fresh_bij_ineq      = @{thm "Nominal.pt_fresh_bij_ineq"};
   702        val fresh_bij           = @{thm "Nominal.pt_fresh_bij"};
   703        val fresh_eqvt          = @{thm "Nominal.pt_fresh_eqvt"};
   704        val fresh_eqvt_ineq     = @{thm "Nominal.pt_fresh_eqvt_ineq"};
   705        val set_diff_eqvt       = @{thm "Nominal.pt_set_diff_eqvt"};
   706        val in_eqvt             = @{thm "Nominal.pt_in_eqvt"};
   707        val eq_eqvt             = @{thm "Nominal.pt_eq_eqvt"};
   708        val all_eqvt            = @{thm "Nominal.pt_all_eqvt"};
   709        val ex_eqvt             = @{thm "Nominal.pt_ex_eqvt"};
   710        val pt_pi_rev           = @{thm "Nominal.pt_pi_rev"};
   711        val pt_rev_pi           = @{thm "Nominal.pt_rev_pi"};
   712        val at_exists_fresh     = @{thm "Nominal.at_exists_fresh"};
   713        val at_exists_fresh'    = @{thm "Nominal.at_exists_fresh'"};
   714        val fresh_perm_app_ineq = @{thm "Nominal.pt_fresh_perm_app_ineq"};
   715        val fresh_perm_app      = @{thm "Nominal.pt_fresh_perm_app"};	
   716        val fresh_aux           = @{thm "Nominal.pt_fresh_aux"};  
   717        val pt_perm_supp_ineq   = @{thm "Nominal.pt_perm_supp_ineq"};
   718        val pt_perm_supp        = @{thm "Nominal.pt_perm_supp"};
   719 
   720        (* Now we collect and instantiate some lemmas w.r.t. all atom      *)
   721        (* types; this allows for example to use abs_perm (which is a      *)
   722        (* collection of theorems) instead of thm abs_fun_pi with explicit *)
   723        (* instantiations.                                                 *)
   724        val (_, thy33) =
   725          let
   726 
   727              (* takes a theorem thm and a list of theorems [t1,..,tn]            *)
   728              (* produces a list of theorems of the form [t1 RS thm,..,tn RS thm] *) 
   729              fun instR thm thms = map (fn ti => ti RS thm) thms;
   730 
   731              (* takes two theorem lists (hopefully of the same length ;o)                *)
   732              (* produces a list of theorems of the form                                  *)
   733              (* [t1 RS m1,..,tn RS mn] where [t1,..,tn] is thms1 and [m1,..,mn] is thms2 *) 
   734              fun inst_zip thms1 thms2 = map (fn (t1,t2) => t1 RS t2) (thms1 ~~ thms2);
   735 
   736              (* takes a theorem list of the form [l1,...,ln]              *)
   737              (* and a list of theorem lists of the form                   *)
   738              (* [[h11,...,h1m],....,[hk1,....,hkm]                        *)
   739              (* produces the list of theorem lists                        *)
   740              (* [[l1 RS h11,...,l1 RS h1m],...,[ln RS hk1,...,ln RS hkm]] *)
   741              fun inst_mult thms thmss = map (fn (t,ts) => instR t ts) (thms ~~ thmss);
   742 
   743              (* FIXME: these lists do not need to be created dynamically again *)
   744 
   745              
   746              (* list of all at_inst-theorems *)
   747              val ats = map (fn ak => PureThy.get_thm thy32 (Name ("at_"^ak^"_inst"))) ak_names
   748              (* list of all pt_inst-theorems *)
   749              val pts = map (fn ak => PureThy.get_thm thy32 (Name ("pt_"^ak^"_inst"))) ak_names
   750              (* list of all cp_inst-theorems as a collection of lists*)
   751              val cps = 
   752 		 let fun cps_fun ak1 ak2 = PureThy.get_thm thy32 (Name ("cp_"^ak1^"_"^ak2^"_inst"))
   753 		 in map (fn aki => (map (cps_fun aki) ak_names)) ak_names end; 
   754              (* list of all cp_inst-theorems that have different atom types *)
   755              val cps' = 
   756 		let fun cps'_fun ak1 ak2 = 
   757 		if ak1=ak2 then NONE else SOME(PureThy.get_thm thy32 (Name ("cp_"^ak1^"_"^ak2^"_inst")))
   758 		in map (fn aki => (List.mapPartial I (map (cps'_fun aki) ak_names))) ak_names end;
   759              (* list of all dj_inst-theorems *)
   760              val djs = 
   761 	       let fun djs_fun (ak1,ak2) = 
   762 		     if ak1=ak2 then NONE else SOME(PureThy.get_thm thy32 (Name ("dj_"^ak2^"_"^ak1)))
   763 	       in List.mapPartial I (map djs_fun (Library.product ak_names ak_names)) end;
   764              (* list of all fs_inst-theorems *)
   765              val fss = map (fn ak => PureThy.get_thm thy32 (Name ("fs_"^ak^"_inst"))) ak_names
   766              (* list of all at_inst-theorems *)
   767              val fs_axs = map (fn ak => PureThy.get_thm thy32 (Name ("fs_"^ak^"1"))) ak_names
   768 
   769              fun inst_pt thms = Library.flat (map (fn ti => instR ti pts) thms);
   770              fun inst_at thms = Library.flat (map (fn ti => instR ti ats) thms);
   771              fun inst_fs thms = Library.flat (map (fn ti => instR ti fss) thms);
   772              fun inst_cp thms cps = Library.flat (inst_mult thms cps);
   773 	     fun inst_pt_at thms = inst_zip ats (inst_pt thms);
   774              fun inst_dj thms = Library.flat (map (fn ti => instR ti djs) thms);
   775 	     fun inst_pt_pt_at_cp thms = inst_cp (inst_zip ats (inst_zip pts (inst_pt thms))) cps;
   776              fun inst_pt_at_fs thms = inst_zip (inst_fs [fs1]) (inst_zip ats (inst_pt thms));
   777 	     fun inst_pt_pt_at_cp thms =
   778 		 let val i_pt_pt_at = inst_zip ats (inst_zip pts (inst_pt thms));
   779                      val i_pt_pt_at_cp = inst_cp i_pt_pt_at cps';
   780 		 in i_pt_pt_at_cp end;
   781              fun inst_pt_pt_at_cp_dj thms = inst_zip djs (inst_pt_pt_at_cp thms);
   782            in
   783             thy32 
   784 	    |>   PureThy.add_thmss [(("alpha", inst_pt_at [abs_fun_eq]),[])]
   785             ||>> PureThy.add_thmss [(("alpha'", inst_pt_at [abs_fun_eq']),[])]
   786             ||>> PureThy.add_thmss [(("alpha_fresh", inst_pt_at [abs_fun_fresh]),[])]
   787             ||>> PureThy.add_thmss [(("alpha_fresh'", inst_pt_at [abs_fun_fresh']),[])]
   788             ||>> PureThy.add_thmss [(("perm_swap", inst_pt_at [pt_swap_bij] @ inst_pt_at [pt_swap_bij']),[])]
   789             ||>> PureThy.add_thmss [(("swap_simps", inst_at at_swap_simps),[])]	 
   790             ||>> PureThy.add_thmss 
   791 	      let val thms1 = inst_pt_at [pt_pi_rev];
   792 		  val thms2 = inst_pt_at [pt_rev_pi];
   793               in [(("perm_pi_simp",thms1 @ thms2),[])] end
   794             ||>> PureThy.add_thmss [(("perm_fresh_fresh", inst_pt_at [pt_fresh_fresh]),[])]
   795             ||>> PureThy.add_thmss [(("perm_bij", inst_pt_at [pt_bij]),[])]
   796             ||>> PureThy.add_thmss 
   797 	      let val thms1 = inst_pt_at [pt_perm_compose];
   798 		  val thms2 = instR cp1 (Library.flat cps');
   799               in [(("perm_compose",thms1 @ thms2),[])] end
   800             ||>> PureThy.add_thmss [(("perm_compose'",inst_pt_at [pt_perm_compose']),[])] 
   801             ||>> PureThy.add_thmss [(("perm_app", inst_pt_at [perm_app]),[])]
   802             ||>> PureThy.add_thmss [(("supp_atm", (inst_at [at_supp]) @ (inst_dj [dj_supp])),[])]
   803             ||>> PureThy.add_thmss [(("exists_fresh", inst_at [at_exists_fresh]),[])]
   804             ||>> PureThy.add_thmss [(("exists_fresh'", inst_at [at_exists_fresh']),[])]
   805             ||>> PureThy.add_thmss [(("all_eqvt", inst_pt_at [all_eqvt]),[NominalThmDecls.eqvt_force_add])] 
   806             ||>> PureThy.add_thmss [(("ex_eqvt", inst_pt_at [ex_eqvt]),[NominalThmDecls.eqvt_force_add])]
   807             ||>> PureThy.add_thmss 
   808 	      let val thms1 = inst_at [at_fresh]
   809 		  val thms2 = inst_dj [at_fresh_ineq]
   810 	      in [(("fresh_atm", thms1 @ thms2),[])] end
   811             ||>> PureThy.add_thmss
   812 	      let val thms1 = filter
   813                 (fn th => case prop_of th of _ $ _ $ Var _ => true | _ => false)
   814                 (List.concat (List.concat perm_defs))
   815               in [(("calc_atm", (inst_at at_calc) @ thms1),[])] end
   816             ||>> PureThy.add_thmss
   817 	      let val thms1 = inst_pt_at [abs_fun_pi]
   818 		  and thms2 = inst_pt_pt_at_cp [abs_fun_pi_ineq]
   819 	      in [(("abs_perm", thms1 @ thms2),[NominalThmDecls.eqvt_add])] end
   820             ||>> PureThy.add_thmss
   821 	      let val thms1 = inst_dj [dj_perm_forget]
   822 		  and thms2 = inst_dj [dj_pp_forget]
   823               in [(("perm_dj", thms1 @ thms2),[])] end
   824             ||>> PureThy.add_thmss
   825 	      let val thms1 = inst_pt_at_fs [fresh_iff]
   826                   and thms2 = inst_pt_at [fresh_iff]
   827 		  and thms3 = inst_pt_pt_at_cp_dj [fresh_iff_ineq]
   828 	    in [(("abs_fresh", thms1 @ thms2 @ thms3),[])] end
   829 	    ||>> PureThy.add_thmss
   830 	      let val thms1 = inst_pt_at [abs_fun_supp]
   831 		  and thms2 = inst_pt_at_fs [abs_fun_supp]
   832 		  and thms3 = inst_pt_pt_at_cp_dj [abs_fun_supp_ineq]
   833 	      in [(("abs_supp", thms1 @ thms2 @ thms3),[])] end
   834             ||>> PureThy.add_thmss
   835 	      let val thms1 = inst_pt_at [fresh_left]
   836 		  and thms2 = inst_pt_pt_at_cp [fresh_left_ineq]
   837 	      in [(("fresh_left", thms1 @ thms2),[])] end
   838             ||>> PureThy.add_thmss
   839 	      let val thms1 = inst_pt_at [fresh_right]
   840 		  and thms2 = inst_pt_pt_at_cp [fresh_right_ineq]
   841 	      in [(("fresh_right", thms1 @ thms2),[])] end
   842             ||>> PureThy.add_thmss
   843 	      let val thms1 = inst_pt_at [fresh_bij]
   844  		  and thms2 = inst_pt_pt_at_cp [fresh_bij_ineq]
   845 	      in [(("fresh_bij", thms1 @ thms2),[])] end
   846             ||>> PureThy.add_thmss
   847 	      let val thms1 = inst_pt_at [fresh_eqvt]
   848                   and thms2 = inst_pt_pt_at_cp_dj [fresh_eqvt_ineq]
   849 	      in [(("fresh_eqvt", thms1 @ thms2),[NominalThmDecls.eqvt_add])] end
   850             ||>> PureThy.add_thmss
   851 	      let val thms1 = inst_pt_at [in_eqvt]
   852 	      in [(("in_eqvt", thms1),[NominalThmDecls.eqvt_add])] end
   853   	    ||>> PureThy.add_thmss
   854 	      let val thms1 = inst_pt_at [eq_eqvt]
   855 	      in [(("eq_eqvt", thms1),[NominalThmDecls.eqvt_add])] end
   856 	    ||>> PureThy.add_thmss
   857 	      let val thms1 = inst_pt_at [set_diff_eqvt]
   858 	      in [(("set_diff_eqvt", thms1),[NominalThmDecls.eqvt_add])] end
   859             ||>> PureThy.add_thmss
   860 	      let val thms1 = inst_pt_at [fresh_aux]
   861 		  and thms2 = inst_pt_pt_at_cp_dj [fresh_perm_app_ineq] 
   862 	      in  [(("fresh_aux", thms1 @ thms2),[])] end  
   863             ||>> PureThy.add_thmss
   864 	      let val thms1 = inst_pt_at [fresh_perm_app]
   865 		  and thms2 = inst_pt_pt_at_cp_dj [fresh_perm_app_ineq] 
   866 	      in  [(("fresh_perm_app", thms1 @ thms2),[])] end 
   867             ||>> PureThy.add_thmss
   868 	      let val thms1 = inst_pt_at [pt_perm_supp]
   869 		  and thms2 = inst_pt_pt_at_cp [pt_perm_supp_ineq] 
   870 	      in  [(("supp_eqvt", thms1 @ thms2),[NominalThmDecls.eqvt_add])] end  
   871             ||>> PureThy.add_thmss [(("fin_supp",fs_axs),[])]
   872 	   end;
   873 
   874     in 
   875       NominalData.map (fold Symtab.update (full_ak_names ~~ map make_atom_info
   876         (pt_ax_classes ~~
   877          fs_ax_classes ~~
   878          map (fn cls => full_ak_names ~~ cls) cp_ax_classes))) thy33
   879     end;
   880 
   881 
   882 (* syntax und parsing *)
   883 structure P = OuterParse and K = OuterKeyword;
   884 
   885 val atom_declP =
   886   OuterSyntax.command "atom_decl" "Declare new kinds of atoms" K.thy_decl
   887     (Scan.repeat1 P.name >> (Toplevel.theory o create_nom_typedecls));
   888 
   889 val _ = OuterSyntax.add_parsers [atom_declP];
   890 
   891 end;