src/HOL/Nominal/nominal_atoms.ML
author narboux
Wed Apr 25 21:29:14 2007 +0200 (2007-04-25 ago)
changeset 22794 d0f483fd57dd
parent 22786 d8d7a53ffb63
child 22846 fb79144af9a3
permissions -rw-r--r--
add the lemma supp_eqvt and put the right attribute
     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   val setup : theory -> theory
    17 end
    18 
    19 structure NominalAtoms : NOMINAL_ATOMS =
    20 struct
    21 
    22 val finite_emptyI = thm "finite.emptyI";
    23 val Collect_const = thm "Collect_const";
    24 
    25 
    26 (* data kind 'HOL/nominal' *)
    27 
    28 type atom_info =
    29   {pt_class : string,
    30    fs_class : string,
    31    cp_classes : (string * string) list};
    32 
    33 structure NominalArgs =
    34 struct
    35   val name = "HOL/nominal";
    36   type T = atom_info Symtab.table;
    37 
    38   val empty = Symtab.empty;
    39   val copy = I;
    40   val extend = I;
    41   fun merge _ x = Symtab.merge (K true) x;
    42 
    43   fun print sg tab = ();
    44 end;
    45 
    46 structure NominalData = TheoryDataFun(NominalArgs);
    47 
    48 fun make_atom_info ((pt_class, fs_class), cp_classes) =
    49   {pt_class = pt_class,
    50    fs_class = fs_class,
    51    cp_classes = cp_classes};
    52 
    53 val get_atom_infos = NominalData.get;
    54 val get_atom_info = Symtab.lookup o NominalData.get;
    55 
    56 fun atoms_of thy = map fst (Symtab.dest (NominalData.get thy));
    57 
    58 fun mk_permT T = HOLogic.listT (HOLogic.mk_prodT (T, T));
    59 
    60 fun mk_Cons x xs =
    61   let val T = fastype_of x
    62   in Const ("List.list.Cons", T --> HOLogic.listT T --> HOLogic.listT T) $ x $ xs end;
    63 
    64 
    65 (* this function sets up all matters related to atom-  *)
    66 (* kinds; the user specifies a list of atom-kind names *)
    67 (* atom_decl <ak1> ... <akn>                           *)
    68 fun create_nom_typedecls ak_names thy =
    69   let
    70     (* declares a type-decl for every atom-kind: *) 
    71     (* that is typedecl <ak>                     *)
    72     val thy1 = TypedefPackage.add_typedecls (map (fn x => (x,[],NoSyn)) ak_names) thy;
    73     
    74     (* produces a list consisting of pairs:         *)
    75     (*  fst component is the atom-kind name         *)
    76     (*  snd component is its type                   *)
    77     val full_ak_names = map (Sign.intern_type thy1) ak_names;
    78     val ak_names_types = ak_names ~~ map (Type o rpair []) full_ak_names;
    79      
    80     (* adds for every atom-kind an axiom             *)
    81     (* <ak>_infinite: infinite (UNIV::<ak_type> set) *)
    82     val (inf_axs,thy2) = PureThy.add_axioms_i (map (fn (ak_name, T) =>
    83       let 
    84     val name = ak_name ^ "_infinite"
    85         val axiom = HOLogic.mk_Trueprop (HOLogic.mk_not
    86                     (Const ("Finite_Set.finite", HOLogic.mk_setT T --> HOLogic.boolT) $
    87                        HOLogic.mk_UNIV T))
    88       in
    89         ((name, axiom), []) 
    90       end) ak_names_types) thy1;
    91     
    92     (* declares a swapping function for every atom-kind, it is         *)
    93     (* const swap_<ak> :: <akT> * <akT> => <akT> => <akT>              *)
    94     (* swap_<ak> (a,b) c = (if a=c then b (else if b=c then a else c)) *)
    95     (* overloades then the general swap-function                       *) 
    96     val (swap_eqs, thy3) = fold_map (fn (ak_name, T) => fn thy =>
    97       let
    98         val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
    99         val swap_name = Sign.full_name thy ("swap_" ^ ak_name);
   100         val a = Free ("a", T);
   101         val b = Free ("b", T);
   102         val c = Free ("c", T);
   103         val ab = Free ("ab", HOLogic.mk_prodT (T, T))
   104         val cif = Const ("HOL.If", HOLogic.boolT --> T --> T --> T);
   105         val cswap_akname = Const (swap_name, swapT);
   106         val cswap = Const ("Nominal.swap", swapT)
   107 
   108         val name = "swap_"^ak_name^"_def";
   109         val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq
   110                 (cswap_akname $ HOLogic.mk_prod (a,b) $ c,
   111                     cif $ HOLogic.mk_eq (a,c) $ b $ (cif $ HOLogic.mk_eq (b,c) $ a $ c)))
   112         val def2 = Logic.mk_equals (cswap $ ab $ c, cswap_akname $ ab $ c)
   113       in
   114         thy |> Theory.add_consts_i [("swap_" ^ ak_name, swapT, NoSyn)] 
   115             |> PureThy.add_defs_unchecked_i true [((name, def2),[])]
   116             |> snd
   117             |> PrimrecPackage.add_primrec_unchecked_i "" [(("", def1),[])]
   118       end) ak_names_types thy2;
   119     
   120     (* declares a permutation function for every atom-kind acting  *)
   121     (* on such atoms                                               *)
   122     (* const <ak>_prm_<ak> :: (<akT> * <akT>)list => akT => akT    *)
   123     (* <ak>_prm_<ak> []     a = a                                  *)
   124     (* <ak>_prm_<ak> (x#xs) a = swap_<ak> x (perm xs a)            *)
   125     val (prm_eqs, thy4) = fold_map (fn (ak_name, T) => fn thy =>
   126       let
   127         val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
   128         val swap_name = Sign.full_name thy ("swap_" ^ ak_name)
   129         val prmT = mk_permT T --> T --> T;
   130         val prm_name = ak_name ^ "_prm_" ^ ak_name;
   131         val qu_prm_name = Sign.full_name thy prm_name;
   132         val x  = Free ("x", HOLogic.mk_prodT (T, T));
   133         val xs = Free ("xs", mk_permT T);
   134         val a  = Free ("a", T) ;
   135 
   136         val cnil  = Const ("List.list.Nil", mk_permT T);
   137         
   138         val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq (Const (qu_prm_name, prmT) $ cnil $ a, a));
   139 
   140         val def2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
   141                    (Const (qu_prm_name, prmT) $ mk_Cons x xs $ a,
   142                     Const (swap_name, swapT) $ x $ (Const (qu_prm_name, prmT) $ xs $ a)));
   143       in
   144         thy |> Theory.add_consts_i [(prm_name, mk_permT T --> T --> T, NoSyn)] 
   145             |> PrimrecPackage.add_primrec_unchecked_i "" [(("", def1), []),(("", def2), [])]
   146       end) ak_names_types thy3;
   147     
   148     (* defines permutation functions for all combinations of atom-kinds; *)
   149     (* there are a trivial cases and non-trivial cases                   *)
   150     (* non-trivial case:                                                 *)
   151     (* <ak>_prm_<ak>_def:  perm pi a == <ak>_prm_<ak> pi a               *)
   152     (* trivial case with <ak> != <ak'>                                   *)
   153     (* <ak>_prm<ak'>_def[simp]:  perm pi a == a                          *)
   154     (*                                                                   *)
   155     (* the trivial cases are added to the simplifier, while the non-     *)
   156     (* have their own rules proved below                                 *)  
   157     val (perm_defs, thy5) = fold_map (fn (ak_name, T) => fn thy =>
   158       fold_map (fn (ak_name', T') => fn thy' =>
   159         let
   160           val perm_def_name = ak_name ^ "_prm_" ^ ak_name';
   161           val pi = Free ("pi", mk_permT T);
   162           val a  = Free ("a", T');
   163           val cperm = Const ("Nominal.perm", mk_permT T --> T' --> T');
   164           val cperm_def = Const (Sign.full_name thy' perm_def_name, mk_permT T --> T' --> T');
   165 
   166           val name = ak_name ^ "_prm_" ^ ak_name' ^ "_def";
   167           val def = Logic.mk_equals
   168                     (cperm $ pi $ a, if ak_name = ak_name' then cperm_def $ pi $ a else a)
   169         in
   170           PureThy.add_defs_unchecked_i true [((name, def),[])] thy'
   171         end) ak_names_types thy) ak_names_types thy4;
   172     
   173     (* proves that every atom-kind is an instance of at *)
   174     (* lemma at_<ak>_inst:                              *)
   175     (* at TYPE(<ak>)                                    *)
   176     val (prm_cons_thms,thy6) = 
   177       thy5 |> PureThy.add_thms (map (fn (ak_name, T) =>
   178       let
   179         val ak_name_qu = Sign.full_name thy5 (ak_name);
   180         val i_type = Type(ak_name_qu,[]);
   181 	val cat = Const ("Nominal.at",(Term.itselfT i_type)  --> HOLogic.boolT);
   182         val at_type = Logic.mk_type i_type;
   183         val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy5
   184                                   [Name "at_def",
   185                                    Name (ak_name ^ "_prm_" ^ ak_name ^ "_def"),
   186                                    Name (ak_name ^ "_prm_" ^ ak_name ^ ".simps"),
   187                                    Name ("swap_" ^ ak_name ^ "_def"),
   188                                    Name ("swap_" ^ ak_name ^ ".simps"),
   189                                    Name (ak_name ^ "_infinite")]
   190 	    
   191 	val name = "at_"^ak_name^ "_inst";
   192         val statement = HOLogic.mk_Trueprop (cat $ at_type);
   193 
   194         val proof = fn _ => auto_tac (claset(),simp_s);
   195 
   196       in 
   197         ((name, Goal.prove_global thy5 [] [] statement proof), []) 
   198       end) ak_names_types);
   199 
   200     (* declares a perm-axclass for every atom-kind               *)
   201     (* axclass pt_<ak>                                           *)
   202     (* pt_<ak>1[simp]: perm [] x = x                             *)
   203     (* pt_<ak>2:       perm (pi1@pi2) x = perm pi1 (perm pi2 x)  *)
   204     (* pt_<ak>3:       pi1 ~ pi2 ==> perm pi1 x = perm pi2 x     *)
   205      val (pt_ax_classes,thy7) =  fold_map (fn (ak_name, T) => fn thy =>
   206       let 
   207 	  val cl_name = "pt_"^ak_name;
   208           val ty = TFree("'a",["HOL.type"]);
   209           val x   = Free ("x", ty);
   210           val pi1 = Free ("pi1", mk_permT T);
   211           val pi2 = Free ("pi2", mk_permT T);
   212           val cperm = Const ("Nominal.perm", mk_permT T --> ty --> ty);
   213           val cnil  = Const ("List.list.Nil", mk_permT T);
   214           val cappend = Const ("List.op @",mk_permT T --> mk_permT T --> mk_permT T);
   215           val cprm_eq = Const ("Nominal.prm_eq",mk_permT T --> mk_permT T --> HOLogic.boolT);
   216           (* nil axiom *)
   217           val axiom1 = HOLogic.mk_Trueprop (HOLogic.mk_eq 
   218                        (cperm $ cnil $ x, x));
   219           (* append axiom *)
   220           val axiom2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
   221                        (cperm $ (cappend $ pi1 $ pi2) $ x, cperm $ pi1 $ (cperm $ pi2 $ x)));
   222           (* perm-eq axiom *)
   223           val axiom3 = Logic.mk_implies
   224                        (HOLogic.mk_Trueprop (cprm_eq $ pi1 $ pi2),
   225                         HOLogic.mk_Trueprop (HOLogic.mk_eq (cperm $ pi1 $ x, cperm $ pi2 $ x)));
   226       in
   227           AxClass.define_class (cl_name, ["HOL.type"]) []
   228                 [((cl_name ^ "1", [Simplifier.simp_add]), [axiom1]),
   229                  ((cl_name ^ "2", []), [axiom2]),                           
   230                  ((cl_name ^ "3", []), [axiom3])] thy                          
   231       end) ak_names_types thy6;
   232 
   233     (* proves that every pt_<ak>-type together with <ak>-type *)
   234     (* instance of pt                                         *)
   235     (* lemma pt_<ak>_inst:                                    *)
   236     (* pt TYPE('x::pt_<ak>) TYPE(<ak>)                        *)
   237     val (prm_inst_thms,thy8) = 
   238       thy7 |> PureThy.add_thms (map (fn (ak_name, T) =>
   239       let
   240         val ak_name_qu = Sign.full_name thy7 ak_name;
   241         val pt_name_qu = Sign.full_name thy7 ("pt_"^ak_name);
   242         val i_type1 = TFree("'x",[pt_name_qu]);
   243         val i_type2 = Type(ak_name_qu,[]);
   244 	val cpt = Const ("Nominal.pt",(Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
   245         val pt_type = Logic.mk_type i_type1;
   246         val at_type = Logic.mk_type i_type2;
   247         val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy7
   248                                   [Name "pt_def",
   249                                    Name ("pt_" ^ ak_name ^ "1"),
   250                                    Name ("pt_" ^ ak_name ^ "2"),
   251                                    Name ("pt_" ^ ak_name ^ "3")];
   252 
   253 	val name = "pt_"^ak_name^ "_inst";
   254         val statement = HOLogic.mk_Trueprop (cpt $ pt_type $ at_type);
   255 
   256         val proof = fn _ => auto_tac (claset(),simp_s);
   257       in 
   258         ((name, Goal.prove_global thy7 [] [] statement proof), []) 
   259       end) ak_names_types);
   260 
   261      (* declares an fs-axclass for every atom-kind       *)
   262      (* axclass fs_<ak>                                  *)
   263      (* fs_<ak>1: finite ((supp x)::<ak> set)            *)
   264      val (fs_ax_classes,thy11) =  fold_map (fn (ak_name, T) => fn thy =>
   265        let 
   266 	  val cl_name = "fs_"^ak_name;
   267 	  val pt_name = Sign.full_name thy ("pt_"^ak_name);
   268           val ty = TFree("'a",["HOL.type"]);
   269           val x   = Free ("x", ty);
   270           val csupp    = Const ("Nominal.supp", ty --> HOLogic.mk_setT T);
   271           val cfinite  = Const ("Finite_Set.finite", HOLogic.mk_setT T --> HOLogic.boolT)
   272           
   273           val axiom1   = HOLogic.mk_Trueprop (cfinite $ (csupp $ x));
   274 
   275        in  
   276         AxClass.define_class (cl_name, [pt_name]) [] [((cl_name ^ "1", []), [axiom1])] thy            
   277        end) ak_names_types thy8; 
   278 	 
   279      (* proves that every fs_<ak>-type together with <ak>-type   *)
   280      (* instance of fs-type                                      *)
   281      (* lemma abst_<ak>_inst:                                    *)
   282      (* fs TYPE('x::pt_<ak>) TYPE (<ak>)                         *)
   283      val (fs_inst_thms,thy12) = 
   284        thy11 |> PureThy.add_thms (map (fn (ak_name, T) =>
   285        let
   286          val ak_name_qu = Sign.full_name thy11 ak_name;
   287          val fs_name_qu = Sign.full_name thy11 ("fs_"^ak_name);
   288          val i_type1 = TFree("'x",[fs_name_qu]);
   289          val i_type2 = Type(ak_name_qu,[]);
   290  	 val cfs = Const ("Nominal.fs", 
   291                                  (Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
   292          val fs_type = Logic.mk_type i_type1;
   293          val at_type = Logic.mk_type i_type2;
   294 	 val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy11
   295                                    [Name "fs_def",
   296                                     Name ("fs_" ^ ak_name ^ "1")];
   297     
   298 	 val name = "fs_"^ak_name^ "_inst";
   299          val statement = HOLogic.mk_Trueprop (cfs $ fs_type $ at_type);
   300 
   301          val proof = fn _ => auto_tac (claset(),simp_s);
   302        in 
   303          ((name, Goal.prove_global thy11 [] [] statement proof), []) 
   304        end) ak_names_types);
   305 
   306        (* declares for every atom-kind combination an axclass            *)
   307        (* cp_<ak1>_<ak2> giving a composition property                   *)
   308        (* cp_<ak1>_<ak2>1: pi1 o pi2 o x = (pi1 o pi2) o (pi1 o x)       *)
   309         val (cp_ax_classes,thy12b) = fold_map (fn (ak_name, T) => fn thy =>
   310 	 fold_map (fn (ak_name', T') => fn thy' =>
   311 	     let
   312 	       val cl_name = "cp_"^ak_name^"_"^ak_name';
   313 	       val ty = TFree("'a",["HOL.type"]);
   314                val x   = Free ("x", ty);
   315                val pi1 = Free ("pi1", mk_permT T);
   316 	       val pi2 = Free ("pi2", mk_permT T');                  
   317 	       val cperm1 = Const ("Nominal.perm", mk_permT T  --> ty --> ty);
   318                val cperm2 = Const ("Nominal.perm", mk_permT T' --> ty --> ty);
   319                val cperm3 = Const ("Nominal.perm", mk_permT T  --> mk_permT T' --> mk_permT T');
   320 
   321                val ax1   = HOLogic.mk_Trueprop 
   322 			   (HOLogic.mk_eq (cperm1 $ pi1 $ (cperm2 $ pi2 $ x), 
   323                                            cperm2 $ (cperm3 $ pi1 $ pi2) $ (cperm1 $ pi1 $ x)));
   324 	       in  
   325 		 AxClass.define_class (cl_name, ["HOL.type"]) [] [((cl_name ^ "1", []), [ax1])] thy'  
   326 	       end) ak_names_types thy) ak_names_types thy12;
   327 
   328         (* proves for every <ak>-combination a cp_<ak1>_<ak2>_inst theorem;     *)
   329         (* lemma cp_<ak1>_<ak2>_inst:                                           *)
   330         (* cp TYPE('a::cp_<ak1>_<ak2>) TYPE(<ak1>) TYPE(<ak2>)                  *)
   331         val (cp_thms,thy12c) = fold_map (fn (ak_name, T) => fn thy =>
   332 	 fold_map (fn (ak_name', T') => fn thy' =>
   333            let
   334              val ak_name_qu  = Sign.full_name thy' (ak_name);
   335 	     val ak_name_qu' = Sign.full_name thy' (ak_name');
   336              val cp_name_qu  = Sign.full_name thy' ("cp_"^ak_name^"_"^ak_name');
   337              val i_type0 = TFree("'a",[cp_name_qu]);
   338              val i_type1 = Type(ak_name_qu,[]);
   339              val i_type2 = Type(ak_name_qu',[]);
   340 	     val ccp = Const ("Nominal.cp",
   341                              (Term.itselfT i_type0)-->(Term.itselfT i_type1)-->
   342                                                       (Term.itselfT i_type2)-->HOLogic.boolT);
   343              val at_type  = Logic.mk_type i_type1;
   344              val at_type' = Logic.mk_type i_type2;
   345 	     val cp_type  = Logic.mk_type i_type0;
   346              val simp_s   = HOL_basic_ss addsimps PureThy.get_thmss thy' [(Name "cp_def")];
   347 	     val cp1      = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"1"));
   348 
   349 	     val name = "cp_"^ak_name^ "_"^ak_name'^"_inst";
   350              val statement = HOLogic.mk_Trueprop (ccp $ cp_type $ at_type $ at_type');
   351 
   352              val proof = fn _ => EVERY [auto_tac (claset(),simp_s), rtac cp1 1];
   353 	   in
   354 	     PureThy.add_thms [((name, Goal.prove_global thy' [] [] statement proof), [])] thy'
   355 	   end) 
   356            ak_names_types thy) ak_names_types thy12b;
   357        
   358         (* proves for every non-trivial <ak>-combination a disjointness   *)
   359         (* theorem; i.e. <ak1> != <ak2>                                   *)
   360         (* lemma ds_<ak1>_<ak2>:                                          *)
   361         (* dj TYPE(<ak1>) TYPE(<ak2>)                                     *)
   362         val (dj_thms, thy12d) = fold_map (fn (ak_name,T) => fn thy =>
   363 	  fold_map (fn (ak_name',T') => fn thy' =>
   364           (if not (ak_name = ak_name') 
   365            then 
   366 	       let
   367 		 val ak_name_qu  = Sign.full_name thy' ak_name;
   368 	         val ak_name_qu' = Sign.full_name thy' ak_name';
   369                  val i_type1 = Type(ak_name_qu,[]);
   370                  val i_type2 = Type(ak_name_qu',[]);
   371 	         val cdj = Const ("Nominal.disjoint",
   372                            (Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
   373                  val at_type  = Logic.mk_type i_type1;
   374                  val at_type' = Logic.mk_type i_type2;
   375                  val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy' 
   376 					   [Name "disjoint_def",
   377                                             Name (ak_name^"_prm_"^ak_name'^"_def"),
   378                                             Name (ak_name'^"_prm_"^ak_name^"_def")];
   379 
   380 	         val name = "dj_"^ak_name^"_"^ak_name';
   381                  val statement = HOLogic.mk_Trueprop (cdj $ at_type $ at_type');
   382 
   383                  val proof = fn _ => auto_tac (claset(),simp_s);
   384 	       in
   385 		PureThy.add_thms [((name, Goal.prove_global thy' [] [] statement proof), [])] thy'
   386 	       end
   387            else 
   388             ([],thy')))  (* do nothing branch, if ak_name = ak_name' *) 
   389 	    ak_names_types thy) ak_names_types thy12c;
   390 
   391      (********  pt_<ak> class instances  ********)
   392      (*=========================================*)
   393      (* some abbreviations for theorems *)
   394       val pt1           = thm "pt1";
   395       val pt2           = thm "pt2";
   396       val pt3           = thm "pt3";
   397       val at_pt_inst    = thm "at_pt_inst";
   398       val pt_set_inst   = thm "pt_set_inst"; 
   399       val pt_unit_inst  = thm "pt_unit_inst";
   400       val pt_prod_inst  = thm "pt_prod_inst"; 
   401       val pt_nprod_inst = thm "pt_nprod_inst"; 
   402       val pt_list_inst  = thm "pt_list_inst";   
   403       val pt_optn_inst  = thm "pt_option_inst";   
   404       val pt_noptn_inst = thm "pt_noption_inst";   
   405       val pt_fun_inst   = thm "pt_fun_inst";     
   406 
   407      (* for all atom-kind combinations <ak>/<ak'> show that        *)
   408      (* every <ak> is an instance of pt_<ak'>; the proof for       *)
   409      (* ak!=ak' is by definition; the case ak=ak' uses at_pt_inst. *)
   410      val thy13 = fold (fn ak_name => fn thy =>
   411 	fold (fn ak_name' => fn thy' =>
   412          let
   413            val qu_name =  Sign.full_name thy' ak_name';
   414            val cls_name = Sign.full_name thy' ("pt_"^ak_name);
   415            val at_inst  = PureThy.get_thm thy' (Name ("at_"^ak_name'^"_inst")); 
   416 
   417            val proof1 = EVERY [ClassPackage.intro_classes_tac [],
   418                                  rtac ((at_inst RS at_pt_inst) RS pt1) 1,
   419                                  rtac ((at_inst RS at_pt_inst) RS pt2) 1,
   420                                  rtac ((at_inst RS at_pt_inst) RS pt3) 1,
   421                                  atac 1];
   422            val simp_s = HOL_basic_ss addsimps 
   423                         PureThy.get_thmss thy' [Name (ak_name^"_prm_"^ak_name'^"_def")];  
   424            val proof2 = EVERY [ClassPackage.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)];
   425 
   426          in
   427            thy'
   428            |> AxClass.prove_arity (qu_name,[],[cls_name])
   429               (if ak_name = ak_name' then proof1 else proof2)
   430          end) ak_names thy) ak_names thy12c;
   431 
   432      (* show that                       *)
   433      (*      fun(pt_<ak>,pt_<ak>)       *)
   434      (*      noption(pt_<ak>)           *)
   435      (*      option(pt_<ak>)            *)
   436      (*      list(pt_<ak>)              *)
   437      (*      *(pt_<ak>,pt_<ak>)         *)
   438      (*      nprod(pt_<ak>,pt_<ak>)     *)
   439      (*      unit                       *)
   440      (*      set(pt_<ak>)               *)
   441      (* are instances of pt_<ak>        *)
   442      val thy18 = fold (fn ak_name => fn thy =>
   443        let
   444           val cls_name = Sign.full_name thy ("pt_"^ak_name);
   445           val at_thm   = PureThy.get_thm thy (Name ("at_"^ak_name^"_inst"));
   446           val pt_inst  = PureThy.get_thm thy (Name ("pt_"^ak_name^"_inst"));
   447 
   448           fun pt_proof thm = 
   449               EVERY [ClassPackage.intro_classes_tac [],
   450                      rtac (thm RS pt1) 1, rtac (thm RS pt2) 1, rtac (thm RS pt3) 1, atac 1];
   451 
   452           val pt_thm_fun   = at_thm RS (pt_inst RS (pt_inst RS pt_fun_inst));
   453           val pt_thm_noptn = pt_inst RS pt_noptn_inst; 
   454           val pt_thm_optn  = pt_inst RS pt_optn_inst; 
   455           val pt_thm_list  = pt_inst RS pt_list_inst;
   456           val pt_thm_prod  = pt_inst RS (pt_inst RS pt_prod_inst);
   457           val pt_thm_nprod = pt_inst RS (pt_inst RS pt_nprod_inst);
   458           val pt_thm_unit  = pt_unit_inst;
   459           val pt_thm_set   = pt_inst RS pt_set_inst
   460        in
   461         thy
   462         |> AxClass.prove_arity ("fun",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_fun)
   463         |> AxClass.prove_arity ("Nominal.noption",[[cls_name]],[cls_name]) (pt_proof pt_thm_noptn) 
   464         |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (pt_proof pt_thm_optn)
   465         |> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (pt_proof pt_thm_list)
   466         |> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_prod)
   467         |> AxClass.prove_arity ("Nominal.nprod",[[cls_name],[cls_name]],[cls_name]) 
   468                                     (pt_proof pt_thm_nprod)
   469         |> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (pt_proof pt_thm_unit)
   470         |> AxClass.prove_arity ("set",[[cls_name]],[cls_name]) (pt_proof pt_thm_set)
   471      end) ak_names thy13; 
   472 
   473        (********  fs_<ak> class instances  ********)
   474        (*=========================================*)
   475        (* abbreviations for some lemmas *)
   476        val fs1            = thm "fs1";
   477        val fs_at_inst     = thm "fs_at_inst";
   478        val fs_unit_inst   = thm "fs_unit_inst";
   479        val fs_prod_inst   = thm "fs_prod_inst";
   480        val fs_nprod_inst  = thm "fs_nprod_inst";
   481        val fs_list_inst   = thm "fs_list_inst";
   482        val fs_option_inst = thm "fs_option_inst";
   483        val dj_supp        = thm "dj_supp"
   484 
   485        (* shows that <ak> is an instance of fs_<ak>     *)
   486        (* uses the theorem at_<ak>_inst                 *)
   487        val thy20 = fold (fn ak_name => fn thy =>
   488         fold (fn ak_name' => fn thy' =>
   489         let
   490            val qu_name =  Sign.full_name thy' ak_name';
   491            val qu_class = Sign.full_name thy' ("fs_"^ak_name);
   492            val proof =
   493                (if ak_name = ak_name'
   494                 then
   495                   let val at_thm = PureThy.get_thm thy' (Name ("at_"^ak_name^"_inst"));
   496                   in  EVERY [ClassPackage.intro_classes_tac [],
   497                              rtac ((at_thm RS fs_at_inst) RS fs1) 1] end
   498                 else
   499                   let val dj_inst = PureThy.get_thm thy' (Name ("dj_"^ak_name'^"_"^ak_name));
   500                       val simp_s = HOL_basic_ss addsimps [dj_inst RS dj_supp, finite_emptyI];
   501                   in EVERY [ClassPackage.intro_classes_tac [], asm_simp_tac simp_s 1] end)
   502         in
   503          AxClass.prove_arity (qu_name,[],[qu_class]) proof thy'
   504         end) ak_names thy) ak_names thy18;
   505 
   506        (* shows that                  *)
   507        (*    unit                     *)
   508        (*    *(fs_<ak>,fs_<ak>)       *)
   509        (*    nprod(fs_<ak>,fs_<ak>)   *)
   510        (*    list(fs_<ak>)            *)
   511        (*    option(fs_<ak>)          *) 
   512        (* are instances of fs_<ak>    *)
   513 
   514        val thy24 = fold (fn ak_name => fn thy => 
   515         let
   516           val cls_name = Sign.full_name thy ("fs_"^ak_name);
   517           val fs_inst  = PureThy.get_thm thy (Name ("fs_"^ak_name^"_inst"));
   518           fun fs_proof thm = EVERY [ClassPackage.intro_classes_tac [], rtac (thm RS fs1) 1];
   519 
   520           val fs_thm_unit  = fs_unit_inst;
   521           val fs_thm_prod  = fs_inst RS (fs_inst RS fs_prod_inst);
   522           val fs_thm_nprod = fs_inst RS (fs_inst RS fs_nprod_inst);
   523           val fs_thm_list  = fs_inst RS fs_list_inst;
   524           val fs_thm_optn  = fs_inst RS fs_option_inst;
   525         in 
   526          thy
   527          |> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (fs_proof fs_thm_unit) 
   528          |> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (fs_proof fs_thm_prod) 
   529          |> AxClass.prove_arity ("Nominal.nprod",[[cls_name],[cls_name]],[cls_name]) 
   530                                      (fs_proof fs_thm_nprod) 
   531          |> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (fs_proof fs_thm_list)
   532          |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (fs_proof fs_thm_optn)
   533         end) ak_names thy20;
   534 
   535        (********  cp_<ak>_<ai> class instances  ********)
   536        (*==============================================*)
   537        (* abbreviations for some lemmas *)
   538        val cp1             = thm "cp1";
   539        val cp_unit_inst    = thm "cp_unit_inst";
   540        val cp_bool_inst    = thm "cp_bool_inst";
   541        val cp_prod_inst    = thm "cp_prod_inst";
   542        val cp_list_inst    = thm "cp_list_inst";
   543        val cp_fun_inst     = thm "cp_fun_inst";
   544        val cp_option_inst  = thm "cp_option_inst";
   545        val cp_noption_inst = thm "cp_noption_inst";
   546        val cp_set_inst     = thm "cp_set_inst";
   547        val pt_perm_compose = thm "pt_perm_compose";
   548 
   549        val dj_pp_forget    = thm "dj_perm_perm_forget";
   550 
   551        (* shows that <aj> is an instance of cp_<ak>_<ai>  *)
   552        (* for every  <ak>/<ai>-combination                *)
   553        val thy25 = fold (fn ak_name => fn thy =>
   554          fold (fn ak_name' => fn thy' =>
   555           fold (fn ak_name'' => fn thy'' =>
   556             let
   557               val name =  Sign.full_name thy'' ak_name;
   558               val cls_name = Sign.full_name thy'' ("cp_"^ak_name'^"_"^ak_name'');
   559               val proof =
   560                 (if (ak_name'=ak_name'') then 
   561                   (let
   562                     val pt_inst  = PureThy.get_thm thy'' (Name ("pt_"^ak_name''^"_inst"));
   563                     val at_inst  = PureThy.get_thm thy'' (Name ("at_"^ak_name''^"_inst"));
   564                   in
   565 		   EVERY [ClassPackage.intro_classes_tac [],
   566                           rtac (at_inst RS (pt_inst RS pt_perm_compose)) 1]
   567                   end)
   568 		else
   569 		  (let
   570                      val dj_inst  = PureThy.get_thm thy'' (Name ("dj_"^ak_name''^"_"^ak_name'));
   571 		     val simp_s = HOL_basic_ss addsimps
   572                                         ((dj_inst RS dj_pp_forget)::
   573                                          (PureThy.get_thmss thy''
   574                                            [Name (ak_name' ^"_prm_"^ak_name^"_def"),
   575                                             Name (ak_name''^"_prm_"^ak_name^"_def")]));
   576                   in
   577                     EVERY [ClassPackage.intro_classes_tac [], simp_tac simp_s 1]
   578                   end))
   579               in
   580                 AxClass.prove_arity (name,[],[cls_name]) proof thy''
   581               end) ak_names thy') ak_names thy) ak_names thy24;
   582 
   583        (* shows that                                                    *) 
   584        (*      units                                                    *) 
   585        (*      products                                                 *)
   586        (*      lists                                                    *)
   587        (*      functions                                                *)
   588        (*      options                                                  *)
   589        (*      noptions                                                 *)
   590        (*      sets                                                     *)
   591        (* are instances of cp_<ak>_<ai> for every <ak>/<ai>-combination *)
   592        val thy26 = fold (fn ak_name => fn thy =>
   593 	fold (fn ak_name' => fn thy' =>
   594         let
   595             val cls_name = Sign.full_name thy' ("cp_"^ak_name^"_"^ak_name');
   596             val cp_inst  = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
   597             val pt_inst  = PureThy.get_thm thy' (Name ("pt_"^ak_name^"_inst"));
   598             val at_inst  = PureThy.get_thm thy' (Name ("at_"^ak_name^"_inst"));
   599 
   600             fun cp_proof thm  = EVERY [ClassPackage.intro_classes_tac [],rtac (thm RS cp1) 1];
   601 	  
   602             val cp_thm_unit = cp_unit_inst;
   603             val cp_thm_prod = cp_inst RS (cp_inst RS cp_prod_inst);
   604             val cp_thm_list = cp_inst RS cp_list_inst;
   605             val cp_thm_fun  = at_inst RS (pt_inst RS (cp_inst RS (cp_inst RS cp_fun_inst)));
   606             val cp_thm_optn = cp_inst RS cp_option_inst;
   607             val cp_thm_noptn = cp_inst RS cp_noption_inst;
   608             val cp_thm_set = cp_inst RS cp_set_inst;
   609         in
   610          thy'
   611          |> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (cp_proof cp_thm_unit)
   612 	 |> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_prod)
   613          |> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (cp_proof cp_thm_list)
   614          |> AxClass.prove_arity ("fun",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_fun)
   615          |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (cp_proof cp_thm_optn)
   616          |> AxClass.prove_arity ("Nominal.noption",[[cls_name]],[cls_name]) (cp_proof cp_thm_noptn)
   617          |> AxClass.prove_arity ("set",[[cls_name]],[cls_name]) (cp_proof cp_thm_set)
   618         end) ak_names thy) ak_names thy25;
   619 
   620      (* show that discrete nominal types are permutation types, finitely     *)
   621      (* supported and have the commutation property                          *)
   622      (* discrete types have a permutation operation defined as pi o x = x;   *)
   623      (* which renders the proofs to be simple "simp_all"-proofs.             *)
   624      val thy32 =
   625         let
   626 	  fun discrete_pt_inst discrete_ty defn =
   627 	     fold (fn ak_name => fn thy =>
   628 	     let
   629 	       val qu_class = Sign.full_name thy ("pt_"^ak_name);
   630 	       val simp_s = HOL_basic_ss addsimps [defn];
   631                val proof = EVERY [ClassPackage.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)];
   632              in 
   633 	       AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
   634              end) ak_names;
   635 
   636           fun discrete_fs_inst discrete_ty defn = 
   637 	     fold (fn ak_name => fn thy =>
   638 	     let
   639 	       val qu_class = Sign.full_name thy ("fs_"^ak_name);
   640 	       val supp_def = thm "Nominal.supp_def";
   641                val simp_s = HOL_ss addsimps [supp_def,Collect_const,finite_emptyI,defn];
   642                val proof = EVERY [ClassPackage.intro_classes_tac [], asm_simp_tac simp_s 1];
   643              in 
   644 	       AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
   645              end) ak_names;
   646 
   647           fun discrete_cp_inst discrete_ty defn = 
   648 	     fold (fn ak_name' => (fold (fn ak_name => fn thy =>
   649 	     let
   650 	       val qu_class = Sign.full_name thy ("cp_"^ak_name^"_"^ak_name');
   651 	       val supp_def = thm "Nominal.supp_def";
   652                val simp_s = HOL_ss addsimps [defn];
   653                val proof = EVERY [ClassPackage.intro_classes_tac [], asm_simp_tac simp_s 1];
   654              in
   655 	       AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
   656              end) ak_names)) ak_names;
   657 
   658         in
   659          thy26
   660          |> discrete_pt_inst "nat"  (thm "perm_nat_def")
   661          |> discrete_fs_inst "nat"  (thm "perm_nat_def") 
   662          |> discrete_cp_inst "nat"  (thm "perm_nat_def") 
   663          |> discrete_pt_inst "bool" (thm "perm_bool")
   664          |> discrete_fs_inst "bool" (thm "perm_bool")
   665          |> discrete_cp_inst "bool" (thm "perm_bool")
   666          |> discrete_pt_inst "IntDef.int" (thm "perm_int_def")
   667          |> discrete_fs_inst "IntDef.int" (thm "perm_int_def") 
   668          |> discrete_cp_inst "IntDef.int" (thm "perm_int_def") 
   669          |> discrete_pt_inst "List.char" (thm "perm_char_def")
   670          |> discrete_fs_inst "List.char" (thm "perm_char_def")
   671          |> discrete_cp_inst "List.char" (thm "perm_char_def")
   672         end;
   673 
   674 
   675        (* abbreviations for some lemmas *)
   676        (*===============================*)
   677        val abs_fun_pi          = thm "Nominal.abs_fun_pi";
   678        val abs_fun_pi_ineq     = thm "Nominal.abs_fun_pi_ineq";
   679        val abs_fun_eq          = thm "Nominal.abs_fun_eq";
   680        val abs_fun_eq'         = thm "Nominal.abs_fun_eq'";
   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 [(("perm_swap", inst_pt_at [pt_swap_bij] @ inst_pt_at [pt_swap_bij']),[])]
   790             ||>> PureThy.add_thmss [(("swap_simps", inst_at at_swap_simps),[])]	 
   791             ||>> PureThy.add_thmss 
   792 	      let val thms1 = inst_pt_at [pt_pi_rev];
   793 		  val thms2 = inst_pt_at [pt_rev_pi];
   794               in [(("perm_pi_simp",thms1 @ thms2),[])] end
   795             ||>> PureThy.add_thmss [(("perm_fresh_fresh", inst_pt_at [pt_fresh_fresh]),[])]
   796             ||>> PureThy.add_thmss [(("perm_bij", inst_pt_at [pt_bij]),[])]
   797             ||>> PureThy.add_thmss 
   798 	      let val thms1 = inst_pt_at [pt_perm_compose];
   799 		  val thms2 = instR cp1 (Library.flat cps');
   800               in [(("perm_compose",thms1 @ thms2),[])] end
   801             ||>> PureThy.add_thmss [(("perm_compose'",inst_pt_at [pt_perm_compose']),[])] 
   802             ||>> PureThy.add_thmss [(("perm_app", inst_pt_at [perm_app]),[])]
   803             ||>> PureThy.add_thmss [(("supp_atm", (inst_at [at_supp]) @ (inst_dj [dj_supp])),[])]
   804             ||>> PureThy.add_thmss [(("exists_fresh", inst_at [at_exists_fresh]),[])]
   805             ||>> PureThy.add_thmss [(("exists_fresh'", inst_at [at_exists_fresh']),[])]
   806             ||>> PureThy.add_thmss [(("all_eqvt", inst_pt_at [all_eqvt]),[NominalThmDecls.eqvt_force_add])] 
   807             ||>> PureThy.add_thmss [(("ex_eqvt", inst_pt_at [ex_eqvt]),[NominalThmDecls.eqvt_force_add])]
   808             ||>> PureThy.add_thmss 
   809 	      let val thms1 = inst_at [at_fresh]
   810 		  val thms2 = inst_dj [at_fresh_ineq]
   811 	      in [(("fresh_atm", thms1 @ thms2),[])] end
   812             ||>> PureThy.add_thmss
   813 	      let val thms1 = filter
   814                 (fn th => case prop_of th of _ $ _ $ Var _ => true | _ => false)
   815                 (List.concat (List.concat perm_defs))
   816               in [(("calc_atm", (inst_at at_calc) @ thms1),[])] end
   817             ||>> PureThy.add_thmss
   818 	      let val thms1 = inst_pt_at [abs_fun_pi]
   819 		  and thms2 = inst_pt_pt_at_cp [abs_fun_pi_ineq]
   820 	      in [(("abs_perm", thms1 @ thms2),[NominalThmDecls.eqvt_add])] end
   821             ||>> PureThy.add_thmss
   822 	      let val thms1 = inst_dj [dj_perm_forget]
   823 		  and thms2 = inst_dj [dj_pp_forget]
   824               in [(("perm_dj", thms1 @ thms2),[])] end
   825             ||>> PureThy.add_thmss
   826 	      let val thms1 = inst_pt_at_fs [fresh_iff]
   827                   and thms2 = inst_pt_at [fresh_iff]
   828 		  and thms3 = inst_pt_pt_at_cp_dj [fresh_iff_ineq]
   829 	    in [(("abs_fresh", thms1 @ thms2 @ thms3),[])] end
   830 	    ||>> PureThy.add_thmss
   831 	      let val thms1 = inst_pt_at [abs_fun_supp]
   832 		  and thms2 = inst_pt_at_fs [abs_fun_supp]
   833 		  and thms3 = inst_pt_pt_at_cp_dj [abs_fun_supp_ineq]
   834 	      in [(("abs_supp", thms1 @ thms2 @ thms3),[])] end
   835             ||>> PureThy.add_thmss
   836 	      let val thms1 = inst_pt_at [fresh_left]
   837 		  and thms2 = inst_pt_pt_at_cp [fresh_left_ineq]
   838 	      in [(("fresh_left", thms1 @ thms2),[])] end
   839             ||>> PureThy.add_thmss
   840 	      let val thms1 = inst_pt_at [fresh_right]
   841 		  and thms2 = inst_pt_pt_at_cp [fresh_right_ineq]
   842 	      in [(("fresh_right", thms1 @ thms2),[])] end
   843             ||>> PureThy.add_thmss
   844 	      let val thms1 = inst_pt_at [fresh_bij]
   845  		  and thms2 = inst_pt_pt_at_cp [fresh_bij_ineq]
   846 	      in [(("fresh_bij", thms1 @ thms2),[])] end
   847             ||>> PureThy.add_thmss
   848 	      let val thms1 = inst_pt_at [fresh_eqvt]
   849                   and thms2 = inst_pt_pt_at_cp_dj [fresh_eqvt_ineq]
   850 	      in [(("fresh_eqvt", thms1 @ thms2),[NominalThmDecls.eqvt_add])] end
   851             ||>> PureThy.add_thmss
   852 	      let val thms1 = inst_pt_at [in_eqvt]
   853 	      in [(("in_eqvt", thms1),[NominalThmDecls.eqvt_add])] end
   854   	    ||>> PureThy.add_thmss
   855 	      let val thms1 = inst_pt_at [eq_eqvt]
   856 	      in [(("eq_eqvt", thms1),[NominalThmDecls.eqvt_add])] end
   857 	    ||>> PureThy.add_thmss
   858 	      let val thms1 = inst_pt_at [set_diff_eqvt]
   859 	      in [(("set_diff_eqvt", thms1),[NominalThmDecls.eqvt_add])] end
   860             ||>> PureThy.add_thmss
   861 	      let val thms1 = inst_pt_at [fresh_aux]
   862 		  and thms2 = inst_pt_pt_at_cp_dj [fresh_perm_app_ineq] 
   863 	      in  [(("fresh_aux", thms1 @ thms2),[])] end  
   864             ||>> PureThy.add_thmss
   865 	      let val thms1 = inst_pt_at [fresh_perm_app]
   866 		  and thms2 = inst_pt_pt_at_cp_dj [fresh_perm_app_ineq] 
   867 	      in  [(("fresh_perm_app", thms1 @ thms2),[])] end 
   868             ||>> PureThy.add_thmss
   869 	      let val thms1 = inst_pt_at [pt_perm_supp]
   870 		  and thms2 = inst_pt_pt_at_cp [pt_perm_supp_ineq] 
   871 	      in  [(("supp_eqvt", thms1 @ thms2),[NominalThmDecls.eqvt_add])] end  
   872             ||>> PureThy.add_thmss [(("fin_supp",fs_axs),[])]
   873 	   end;
   874 
   875     in 
   876       NominalData.map (fold Symtab.update (full_ak_names ~~ map make_atom_info
   877         (pt_ax_classes ~~
   878          fs_ax_classes ~~
   879          map (fn cls => full_ak_names ~~ cls) cp_ax_classes))) thy33
   880     end;
   881 
   882 
   883 (* syntax und parsing *)
   884 structure P = OuterParse and K = OuterKeyword;
   885 
   886 val atom_declP =
   887   OuterSyntax.command "atom_decl" "Declare new kinds of atoms" K.thy_decl
   888     (Scan.repeat1 P.name >> (Toplevel.theory o create_nom_typedecls));
   889 
   890 val _ = OuterSyntax.add_parsers [atom_declP];
   891 
   892 val setup = NominalData.init;
   893 
   894 end;