src/HOL/Nominal/nominal_atoms.ML
author urbanc
Mon Dec 19 12:09:56 2005 +0100 (2005-12-19)
changeset 18435 318d2c271040
parent 18432 0b596274ba4f
child 18436 9649e24bc10e
permissions -rw-r--r--
tuned one comment
berghofe@18068
     1
(* $Id$ *)
berghofe@18068
     2
berghofe@18068
     3
signature NOMINAL_ATOMS =
berghofe@18068
     4
sig
berghofe@18068
     5
  val create_nom_typedecls : string list -> theory -> theory
berghofe@18068
     6
  val atoms_of : theory -> string list
berghofe@18068
     7
  val mk_permT : typ -> typ
berghofe@18068
     8
  val setup : (theory -> theory) list
berghofe@18068
     9
end
berghofe@18068
    10
berghofe@18068
    11
structure NominalAtoms : NOMINAL_ATOMS =
berghofe@18068
    12
struct
berghofe@18068
    13
berghofe@18068
    14
(* data kind 'HOL/nominal' *)
berghofe@18068
    15
berghofe@18068
    16
structure NominalArgs =
berghofe@18068
    17
struct
berghofe@18068
    18
  val name = "HOL/nominal";
berghofe@18068
    19
  type T = unit Symtab.table;
berghofe@18068
    20
berghofe@18068
    21
  val empty = Symtab.empty;
berghofe@18068
    22
  val copy = I;
berghofe@18068
    23
  val extend = I;
berghofe@18068
    24
  fun merge _ x = Symtab.merge (K true) x;
berghofe@18068
    25
berghofe@18068
    26
  fun print sg tab = ();
berghofe@18068
    27
end;
berghofe@18068
    28
berghofe@18068
    29
structure NominalData = TheoryDataFun(NominalArgs);
berghofe@18068
    30
berghofe@18068
    31
fun atoms_of thy = map fst (Symtab.dest (NominalData.get thy));
berghofe@18068
    32
berghofe@18068
    33
(* FIXME: add to hologic.ML ? *)
berghofe@18068
    34
fun mk_listT T = Type ("List.list", [T]);
berghofe@18068
    35
fun mk_permT T = mk_listT (HOLogic.mk_prodT (T, T));
berghofe@18068
    36
berghofe@18068
    37
fun mk_Cons x xs =
berghofe@18068
    38
  let val T = fastype_of x
berghofe@18068
    39
  in Const ("List.list.Cons", T --> mk_listT T --> mk_listT T) $ x $ xs end;
berghofe@18068
    40
berghofe@18068
    41
berghofe@18068
    42
(* this function sets up all matters related to atom-  *)
berghofe@18068
    43
(* kinds; the user specifies a list of atom-kind names *)
berghofe@18068
    44
(* atom_decl <ak1> ... <akn>                           *)
berghofe@18068
    45
fun create_nom_typedecls ak_names thy =
berghofe@18068
    46
  let
berghofe@18068
    47
    (* declares a type-decl for every atom-kind: *) 
berghofe@18068
    48
    (* that is typedecl <ak>                     *)
berghofe@18068
    49
    val thy1 = TypedefPackage.add_typedecls (map (fn x => (x,[],NoSyn)) ak_names) thy;
berghofe@18068
    50
    
berghofe@18068
    51
    (* produces a list consisting of pairs:         *)
berghofe@18068
    52
    (*  fst component is the atom-kind name         *)
berghofe@18068
    53
    (*  snd component is its type                   *)
berghofe@18068
    54
    val full_ak_names = map (Sign.intern_type (sign_of thy1)) ak_names;
berghofe@18068
    55
    val ak_names_types = ak_names ~~ map (Type o rpair []) full_ak_names;
berghofe@18068
    56
     
berghofe@18068
    57
    (* adds for every atom-kind an axiom             *)
berghofe@18068
    58
    (* <ak>_infinite: infinite (UNIV::<ak_type> set) *)
urbanc@18381
    59
    val (inf_axs,thy2) = PureThy.add_axioms_i (map (fn (ak_name, T) =>
berghofe@18068
    60
      let 
berghofe@18068
    61
	val name = ak_name ^ "_infinite"
berghofe@18068
    62
        val axiom = HOLogic.mk_Trueprop (HOLogic.mk_not
berghofe@18068
    63
                    (HOLogic.mk_mem (HOLogic.mk_UNIV T,
berghofe@18068
    64
                     Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT T)))))
berghofe@18068
    65
      in
berghofe@18068
    66
	((name, axiom), []) 
berghofe@18068
    67
      end) ak_names_types) thy1;
berghofe@18068
    68
    
berghofe@18068
    69
    (* declares a swapping function for every atom-kind, it is         *)
berghofe@18068
    70
    (* const swap_<ak> :: <akT> * <akT> => <akT> => <akT>              *)
berghofe@18068
    71
    (* swap_<ak> (a,b) c = (if a=c then b (else if b=c then a else c)) *)
berghofe@18068
    72
    (* overloades then the general swap-function                       *) 
berghofe@18068
    73
    val (thy3, swap_eqs) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
    74
      let
berghofe@18068
    75
        val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
berghofe@18068
    76
        val swap_name = Sign.full_name (sign_of thy) ("swap_" ^ ak_name);
berghofe@18068
    77
        val a = Free ("a", T);
berghofe@18068
    78
        val b = Free ("b", T);
berghofe@18068
    79
        val c = Free ("c", T);
berghofe@18068
    80
        val ab = Free ("ab", HOLogic.mk_prodT (T, T))
berghofe@18068
    81
        val cif = Const ("HOL.If", HOLogic.boolT --> T --> T --> T);
berghofe@18068
    82
        val cswap_akname = Const (swap_name, swapT);
berghofe@18068
    83
        val cswap = Const ("nominal.swap", swapT)
berghofe@18068
    84
berghofe@18068
    85
        val name = "swap_"^ak_name^"_def";
berghofe@18068
    86
        val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@18068
    87
		   (cswap_akname $ HOLogic.mk_prod (a,b) $ c,
berghofe@18068
    88
                    cif $ HOLogic.mk_eq (a,c) $ b $ (cif $ HOLogic.mk_eq (b,c) $ a $ c)))
berghofe@18068
    89
        val def2 = Logic.mk_equals (cswap $ ab $ c, cswap_akname $ ab $ c)
berghofe@18068
    90
      in
berghofe@18068
    91
        thy |> Theory.add_consts_i [("swap_" ^ ak_name, swapT, NoSyn)] 
berghofe@18366
    92
            |> (#2 o PureThy.add_defs_i true [((name, def2),[])])
berghofe@18068
    93
            |> PrimrecPackage.add_primrec_i "" [(("", def1),[])]            
berghofe@18068
    94
      end) (thy2, ak_names_types);
berghofe@18068
    95
    
berghofe@18068
    96
    (* declares a permutation function for every atom-kind acting  *)
berghofe@18068
    97
    (* on such atoms                                               *)
berghofe@18068
    98
    (* const <ak>_prm_<ak> :: (<akT> * <akT>)list => akT => akT    *)
berghofe@18068
    99
    (* <ak>_prm_<ak> []     a = a                                  *)
berghofe@18068
   100
    (* <ak>_prm_<ak> (x#xs) a = swap_<ak> x (perm xs a)            *)
berghofe@18068
   101
    val (thy4, prm_eqs) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   102
      let
berghofe@18068
   103
        val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
berghofe@18068
   104
        val swap_name = Sign.full_name (sign_of thy) ("swap_" ^ ak_name)
berghofe@18068
   105
        val prmT = mk_permT T --> T --> T;
berghofe@18068
   106
        val prm_name = ak_name ^ "_prm_" ^ ak_name;
berghofe@18068
   107
        val qu_prm_name = Sign.full_name (sign_of thy) prm_name;
berghofe@18068
   108
        val x  = Free ("x", HOLogic.mk_prodT (T, T));
berghofe@18068
   109
        val xs = Free ("xs", mk_permT T);
berghofe@18068
   110
        val a  = Free ("a", T) ;
berghofe@18068
   111
berghofe@18068
   112
        val cnil  = Const ("List.list.Nil", mk_permT T);
berghofe@18068
   113
        
berghofe@18068
   114
        val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq (Const (qu_prm_name, prmT) $ cnil $ a, a));
berghofe@18068
   115
berghofe@18068
   116
        val def2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@18068
   117
                   (Const (qu_prm_name, prmT) $ mk_Cons x xs $ a,
berghofe@18068
   118
                    Const (swap_name, swapT) $ x $ (Const (qu_prm_name, prmT) $ xs $ a)));
berghofe@18068
   119
      in
berghofe@18068
   120
        thy |> Theory.add_consts_i [(prm_name, mk_permT T --> T --> T, NoSyn)] 
berghofe@18068
   121
            |> PrimrecPackage.add_primrec_i "" [(("", def1), []),(("", def2), [])]
berghofe@18068
   122
      end) (thy3, ak_names_types);
berghofe@18068
   123
    
berghofe@18068
   124
    (* defines permutation functions for all combinations of atom-kinds; *)
berghofe@18068
   125
    (* there are a trivial cases and non-trivial cases                   *)
berghofe@18068
   126
    (* non-trivial case:                                                 *)
berghofe@18068
   127
    (* <ak>_prm_<ak>_def:  perm pi a == <ak>_prm_<ak> pi a               *)
berghofe@18068
   128
    (* trivial case with <ak> != <ak'>                                   *)
berghofe@18068
   129
    (* <ak>_prm<ak'>_def[simp]:  perm pi a == a                          *)
berghofe@18068
   130
    (*                                                                   *)
berghofe@18068
   131
    (* the trivial cases are added to the simplifier, while the non-     *)
berghofe@18068
   132
    (* have their own rules proved below                                 *)  
berghofe@18366
   133
    val (perm_defs, thy5) = fold_map (fn (ak_name, T) => fn thy =>
berghofe@18366
   134
      fold_map (fn (ak_name', T') => fn thy' =>
berghofe@18068
   135
        let
berghofe@18068
   136
          val perm_def_name = ak_name ^ "_prm_" ^ ak_name';
berghofe@18068
   137
          val pi = Free ("pi", mk_permT T);
berghofe@18068
   138
          val a  = Free ("a", T');
berghofe@18068
   139
          val cperm = Const ("nominal.perm", mk_permT T --> T' --> T');
berghofe@18068
   140
          val cperm_def = Const (Sign.full_name (sign_of thy') perm_def_name, mk_permT T --> T' --> T');
berghofe@18068
   141
berghofe@18068
   142
          val name = ak_name ^ "_prm_" ^ ak_name' ^ "_def";
berghofe@18068
   143
          val def = Logic.mk_equals
berghofe@18068
   144
                    (cperm $ pi $ a, if ak_name = ak_name' then cperm_def $ pi $ a else a)
berghofe@18068
   145
        in
berghofe@18366
   146
          PureThy.add_defs_i true [((name, def),[])] thy'
berghofe@18366
   147
        end) ak_names_types thy) ak_names_types thy4;
berghofe@18068
   148
    
berghofe@18068
   149
    (* proves that every atom-kind is an instance of at *)
berghofe@18068
   150
    (* lemma at_<ak>_inst:                              *)
berghofe@18068
   151
    (* at TYPE(<ak>)                                    *)
urbanc@18381
   152
    val (prm_cons_thms,thy6) = 
berghofe@18068
   153
      thy5 |> PureThy.add_thms (map (fn (ak_name, T) =>
berghofe@18068
   154
      let
berghofe@18068
   155
        val ak_name_qu = Sign.full_name (sign_of thy5) (ak_name);
berghofe@18068
   156
        val i_type = Type(ak_name_qu,[]);
berghofe@18068
   157
	val cat = Const ("nominal.at",(Term.itselfT i_type)  --> HOLogic.boolT);
berghofe@18068
   158
        val at_type = Logic.mk_type i_type;
berghofe@18068
   159
        val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy5
berghofe@18068
   160
                                  [Name "at_def",
berghofe@18068
   161
                                   Name (ak_name ^ "_prm_" ^ ak_name ^ "_def"),
berghofe@18068
   162
                                   Name (ak_name ^ "_prm_" ^ ak_name ^ ".simps"),
berghofe@18068
   163
                                   Name ("swap_" ^ ak_name ^ "_def"),
berghofe@18068
   164
                                   Name ("swap_" ^ ak_name ^ ".simps"),
berghofe@18068
   165
                                   Name (ak_name ^ "_infinite")]
berghofe@18068
   166
	    
berghofe@18068
   167
	val name = "at_"^ak_name^ "_inst";
berghofe@18068
   168
        val statement = HOLogic.mk_Trueprop (cat $ at_type);
berghofe@18068
   169
berghofe@18068
   170
        val proof = fn _ => auto_tac (claset(),simp_s);
berghofe@18068
   171
berghofe@18068
   172
      in 
berghofe@18068
   173
        ((name, standard (Goal.prove thy5 [] [] statement proof)), []) 
berghofe@18068
   174
      end) ak_names_types);
berghofe@18068
   175
berghofe@18068
   176
    (* declares a perm-axclass for every atom-kind               *)
berghofe@18068
   177
    (* axclass pt_<ak>                                           *)
berghofe@18068
   178
    (* pt_<ak>1[simp]: perm [] x = x                             *)
berghofe@18068
   179
    (* pt_<ak>2:       perm (pi1@pi2) x = perm pi1 (perm pi2 x)  *)
berghofe@18068
   180
    (* pt_<ak>3:       pi1 ~ pi2 ==> perm pi1 x = perm pi2 x     *)
berghofe@18068
   181
     val (thy7, pt_ax_classes) =  foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   182
      let 
berghofe@18068
   183
	  val cl_name = "pt_"^ak_name;
berghofe@18068
   184
          val ty = TFree("'a",["HOL.type"]);
berghofe@18068
   185
          val x   = Free ("x", ty);
berghofe@18068
   186
          val pi1 = Free ("pi1", mk_permT T);
berghofe@18068
   187
          val pi2 = Free ("pi2", mk_permT T);
berghofe@18068
   188
          val cperm = Const ("nominal.perm", mk_permT T --> ty --> ty);
berghofe@18068
   189
          val cnil  = Const ("List.list.Nil", mk_permT T);
berghofe@18068
   190
          val cappend = Const ("List.op @",mk_permT T --> mk_permT T --> mk_permT T);
berghofe@18068
   191
          val cprm_eq = Const ("nominal.prm_eq",mk_permT T --> mk_permT T --> HOLogic.boolT);
berghofe@18068
   192
          (* nil axiom *)
berghofe@18068
   193
          val axiom1 = HOLogic.mk_Trueprop (HOLogic.mk_eq 
berghofe@18068
   194
                       (cperm $ cnil $ x, x));
berghofe@18068
   195
          (* append axiom *)
berghofe@18068
   196
          val axiom2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@18068
   197
                       (cperm $ (cappend $ pi1 $ pi2) $ x, cperm $ pi1 $ (cperm $ pi2 $ x)));
berghofe@18068
   198
          (* perm-eq axiom *)
berghofe@18068
   199
          val axiom3 = Logic.mk_implies
berghofe@18068
   200
                       (HOLogic.mk_Trueprop (cprm_eq $ pi1 $ pi2),
berghofe@18068
   201
                        HOLogic.mk_Trueprop (HOLogic.mk_eq (cperm $ pi1 $ x, cperm $ pi2 $ x)));
berghofe@18068
   202
      in
berghofe@18068
   203
        thy |> AxClass.add_axclass_i (cl_name, ["HOL.type"])
berghofe@18068
   204
                [((cl_name^"1", axiom1),[Simplifier.simp_add_global]), 
berghofe@18068
   205
                 ((cl_name^"2", axiom2),[]),                           
berghofe@18068
   206
                 ((cl_name^"3", axiom3),[])]                          
berghofe@18068
   207
      end) (thy6,ak_names_types);
berghofe@18068
   208
berghofe@18068
   209
    (* proves that every pt_<ak>-type together with <ak>-type *)
berghofe@18068
   210
    (* instance of pt                                         *)
berghofe@18068
   211
    (* lemma pt_<ak>_inst:                                    *)
berghofe@18068
   212
    (* pt TYPE('x::pt_<ak>) TYPE(<ak>)                        *)
urbanc@18381
   213
    val (prm_inst_thms,thy8) = 
berghofe@18068
   214
      thy7 |> PureThy.add_thms (map (fn (ak_name, T) =>
berghofe@18068
   215
      let
berghofe@18068
   216
        val ak_name_qu = Sign.full_name (sign_of thy7) (ak_name);
berghofe@18068
   217
        val pt_name_qu = Sign.full_name (sign_of thy7) ("pt_"^ak_name);
berghofe@18068
   218
        val i_type1 = TFree("'x",[pt_name_qu]);
berghofe@18068
   219
        val i_type2 = Type(ak_name_qu,[]);
berghofe@18068
   220
	val cpt = Const ("nominal.pt",(Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
berghofe@18068
   221
        val pt_type = Logic.mk_type i_type1;
berghofe@18068
   222
        val at_type = Logic.mk_type i_type2;
berghofe@18068
   223
        val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy7
berghofe@18068
   224
                                  [Name "pt_def",
berghofe@18068
   225
                                   Name ("pt_" ^ ak_name ^ "1"),
berghofe@18068
   226
                                   Name ("pt_" ^ ak_name ^ "2"),
berghofe@18068
   227
                                   Name ("pt_" ^ ak_name ^ "3")];
berghofe@18068
   228
berghofe@18068
   229
	val name = "pt_"^ak_name^ "_inst";
berghofe@18068
   230
        val statement = HOLogic.mk_Trueprop (cpt $ pt_type $ at_type);
berghofe@18068
   231
berghofe@18068
   232
        val proof = fn _ => auto_tac (claset(),simp_s);
berghofe@18068
   233
      in 
berghofe@18068
   234
        ((name, standard (Goal.prove thy7 [] [] statement proof)), []) 
berghofe@18068
   235
      end) ak_names_types);
berghofe@18068
   236
berghofe@18068
   237
     (* declares an fs-axclass for every atom-kind       *)
berghofe@18068
   238
     (* axclass fs_<ak>                                  *)
berghofe@18068
   239
     (* fs_<ak>1: finite ((supp x)::<ak> set)            *)
berghofe@18068
   240
     val (thy11, fs_ax_classes) =  foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   241
       let 
berghofe@18068
   242
	  val cl_name = "fs_"^ak_name;
berghofe@18068
   243
	  val pt_name = Sign.full_name (sign_of thy) ("pt_"^ak_name);
berghofe@18068
   244
          val ty = TFree("'a",["HOL.type"]);
berghofe@18068
   245
          val x   = Free ("x", ty);
berghofe@18068
   246
          val csupp    = Const ("nominal.supp", ty --> HOLogic.mk_setT T);
berghofe@18068
   247
          val cfinites = Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT T))
berghofe@18068
   248
          
berghofe@18068
   249
          val axiom1   = HOLogic.mk_Trueprop (HOLogic.mk_mem (csupp $ x, cfinites));
berghofe@18068
   250
berghofe@18068
   251
       in  
berghofe@18068
   252
        thy |> AxClass.add_axclass_i (cl_name, [pt_name]) [((cl_name^"1", axiom1),[])]            
berghofe@18068
   253
       end) (thy8,ak_names_types); 
berghofe@18068
   254
berghofe@18068
   255
     (* proves that every fs_<ak>-type together with <ak>-type   *)
berghofe@18068
   256
     (* instance of fs-type                                      *)
berghofe@18068
   257
     (* lemma abst_<ak>_inst:                                    *)
berghofe@18068
   258
     (* fs TYPE('x::pt_<ak>) TYPE (<ak>)                         *)
urbanc@18381
   259
     val (fs_inst_thms,thy12) = 
berghofe@18068
   260
       thy11 |> PureThy.add_thms (map (fn (ak_name, T) =>
berghofe@18068
   261
       let
berghofe@18068
   262
         val ak_name_qu = Sign.full_name (sign_of thy11) (ak_name);
berghofe@18068
   263
         val fs_name_qu = Sign.full_name (sign_of thy11) ("fs_"^ak_name);
berghofe@18068
   264
         val i_type1 = TFree("'x",[fs_name_qu]);
berghofe@18068
   265
         val i_type2 = Type(ak_name_qu,[]);
berghofe@18068
   266
 	 val cfs = Const ("nominal.fs", 
berghofe@18068
   267
                                 (Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
berghofe@18068
   268
         val fs_type = Logic.mk_type i_type1;
berghofe@18068
   269
         val at_type = Logic.mk_type i_type2;
berghofe@18068
   270
	 val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy11
berghofe@18068
   271
                                   [Name "fs_def",
berghofe@18068
   272
                                    Name ("fs_" ^ ak_name ^ "1")];
berghofe@18068
   273
    
berghofe@18068
   274
	 val name = "fs_"^ak_name^ "_inst";
berghofe@18068
   275
         val statement = HOLogic.mk_Trueprop (cfs $ fs_type $ at_type);
berghofe@18068
   276
berghofe@18068
   277
         val proof = fn _ => auto_tac (claset(),simp_s);
berghofe@18068
   278
       in 
berghofe@18068
   279
         ((name, standard (Goal.prove thy11 [] [] statement proof)), []) 
berghofe@18068
   280
       end) ak_names_types);
berghofe@18068
   281
berghofe@18068
   282
       (* declares for every atom-kind combination an axclass            *)
berghofe@18068
   283
       (* cp_<ak1>_<ak2> giving a composition property                   *)
berghofe@18068
   284
       (* cp_<ak1>_<ak2>1: pi1 o pi2 o x = (pi1 o pi2) o (pi1 o x)       *)
berghofe@18068
   285
        val (thy12b,_) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   286
	 foldl_map (fn (thy', (ak_name', T')) =>
berghofe@18068
   287
	     let
berghofe@18068
   288
	       val cl_name = "cp_"^ak_name^"_"^ak_name';
berghofe@18068
   289
	       val ty = TFree("'a",["HOL.type"]);
berghofe@18068
   290
               val x   = Free ("x", ty);
berghofe@18068
   291
               val pi1 = Free ("pi1", mk_permT T);
berghofe@18068
   292
	       val pi2 = Free ("pi2", mk_permT T');                  
berghofe@18068
   293
	       val cperm1 = Const ("nominal.perm", mk_permT T  --> ty --> ty);
berghofe@18068
   294
               val cperm2 = Const ("nominal.perm", mk_permT T' --> ty --> ty);
berghofe@18068
   295
               val cperm3 = Const ("nominal.perm", mk_permT T  --> mk_permT T' --> mk_permT T');
berghofe@18068
   296
berghofe@18068
   297
               val ax1   = HOLogic.mk_Trueprop 
berghofe@18068
   298
			   (HOLogic.mk_eq (cperm1 $ pi1 $ (cperm2 $ pi2 $ x), 
berghofe@18068
   299
                                           cperm2 $ (cperm3 $ pi1 $ pi2) $ (cperm1 $ pi1 $ x)));
berghofe@18068
   300
	       in  
berghofe@18068
   301
	       (fst (AxClass.add_axclass_i (cl_name, ["HOL.type"]) [((cl_name^"1", ax1),[])] thy'),())  
berghofe@18068
   302
	       end) 
berghofe@18068
   303
	   (thy, ak_names_types)) (thy12, ak_names_types)
berghofe@18068
   304
berghofe@18068
   305
        (* proves for every <ak>-combination a cp_<ak1>_<ak2>_inst theorem;     *)
berghofe@18068
   306
        (* lemma cp_<ak1>_<ak2>_inst:                                           *)
berghofe@18068
   307
        (* cp TYPE('a::cp_<ak1>_<ak2>) TYPE(<ak1>) TYPE(<ak2>)                  *)
urbanc@18381
   308
        val (cp_thms,thy12c) = fold_map (fn (ak_name, T) => fn thy =>
urbanc@18381
   309
	 fold_map (fn (ak_name', T') => fn thy' =>
berghofe@18068
   310
           let
berghofe@18068
   311
             val ak_name_qu  = Sign.full_name (sign_of thy') (ak_name);
berghofe@18068
   312
	     val ak_name_qu' = Sign.full_name (sign_of thy') (ak_name');
berghofe@18068
   313
             val cp_name_qu  = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
berghofe@18068
   314
             val i_type0 = TFree("'a",[cp_name_qu]);
berghofe@18068
   315
             val i_type1 = Type(ak_name_qu,[]);
berghofe@18068
   316
             val i_type2 = Type(ak_name_qu',[]);
berghofe@18068
   317
	     val ccp = Const ("nominal.cp",
berghofe@18068
   318
                             (Term.itselfT i_type0)-->(Term.itselfT i_type1)-->
berghofe@18068
   319
                                                      (Term.itselfT i_type2)-->HOLogic.boolT);
berghofe@18068
   320
             val at_type  = Logic.mk_type i_type1;
berghofe@18068
   321
             val at_type' = Logic.mk_type i_type2;
berghofe@18068
   322
	     val cp_type  = Logic.mk_type i_type0;
berghofe@18068
   323
             val simp_s   = HOL_basic_ss addsimps PureThy.get_thmss thy' [(Name "cp_def")];
berghofe@18068
   324
	     val cp1      = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"1"));
berghofe@18068
   325
berghofe@18068
   326
	     val name = "cp_"^ak_name^ "_"^ak_name'^"_inst";
berghofe@18068
   327
             val statement = HOLogic.mk_Trueprop (ccp $ cp_type $ at_type $ at_type');
berghofe@18068
   328
berghofe@18068
   329
             val proof = fn _ => EVERY [auto_tac (claset(),simp_s), rtac cp1 1];
berghofe@18068
   330
	   in
urbanc@18381
   331
	     PureThy.add_thms [((name, standard (Goal.prove thy' [] [] statement proof)), [])] thy'
berghofe@18068
   332
	   end) 
urbanc@18381
   333
           ak_names_types thy) ak_names_types thy12b;
berghofe@18068
   334
       
berghofe@18068
   335
        (* proves for every non-trivial <ak>-combination a disjointness   *)
berghofe@18068
   336
        (* theorem; i.e. <ak1> != <ak2>                                   *)
berghofe@18068
   337
        (* lemma ds_<ak1>_<ak2>:                                          *)
berghofe@18068
   338
        (* dj TYPE(<ak1>) TYPE(<ak2>)                                     *)
urbanc@18381
   339
        val (dj_thms, thy12d) = fold_map (fn (ak_name,T) => fn thy =>
urbanc@18381
   340
	  fold_map (fn (ak_name',T') => fn thy' =>
berghofe@18068
   341
          (if not (ak_name = ak_name') 
berghofe@18068
   342
           then 
berghofe@18068
   343
	       let
berghofe@18068
   344
		 val ak_name_qu  = Sign.full_name (sign_of thy') (ak_name);
berghofe@18068
   345
	         val ak_name_qu' = Sign.full_name (sign_of thy') (ak_name');
berghofe@18068
   346
                 val i_type1 = Type(ak_name_qu,[]);
berghofe@18068
   347
                 val i_type2 = Type(ak_name_qu',[]);
berghofe@18068
   348
	         val cdj = Const ("nominal.disjoint",
berghofe@18068
   349
                           (Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
berghofe@18068
   350
                 val at_type  = Logic.mk_type i_type1;
berghofe@18068
   351
                 val at_type' = Logic.mk_type i_type2;
berghofe@18068
   352
                 val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy' 
berghofe@18068
   353
					   [Name "disjoint_def",
berghofe@18068
   354
                                            Name (ak_name^"_prm_"^ak_name'^"_def"),
berghofe@18068
   355
                                            Name (ak_name'^"_prm_"^ak_name^"_def")];
berghofe@18068
   356
berghofe@18068
   357
	         val name = "dj_"^ak_name^"_"^ak_name';
berghofe@18068
   358
                 val statement = HOLogic.mk_Trueprop (cdj $ at_type $ at_type');
berghofe@18068
   359
berghofe@18068
   360
                 val proof = fn _ => auto_tac (claset(),simp_s);
berghofe@18068
   361
	       in
urbanc@18381
   362
		PureThy.add_thms [((name, standard (Goal.prove thy' [] [] statement proof)), [])] thy'
berghofe@18068
   363
	       end
berghofe@18068
   364
           else 
urbanc@18381
   365
            ([],thy')))  (* do nothing branch, if ak_name = ak_name' *) 
urbanc@18381
   366
	    ak_names_types thy) ak_names_types thy12c;
berghofe@18068
   367
berghofe@18068
   368
     (*<<<<<<<  pt_<ak> class instances  >>>>>>>*)
berghofe@18068
   369
     (*=========================================*)
urbanc@18279
   370
     (* some abbreviations for theorems *)
urbanc@18279
   371
      val pt1           = thm "pt1";
urbanc@18279
   372
      val pt2           = thm "pt2";
urbanc@18279
   373
      val pt3           = thm "pt3";
urbanc@18279
   374
      val at_pt_inst    = thm "at_pt_inst";
urbanc@18279
   375
      val pt_set_inst   = thm "pt_set_inst"; 
urbanc@18279
   376
      val pt_unit_inst  = thm "pt_unit_inst";
urbanc@18279
   377
      val pt_prod_inst  = thm "pt_prod_inst"; 
urbanc@18279
   378
      val pt_list_inst  = thm "pt_list_inst";   
urbanc@18279
   379
      val pt_optn_inst  = thm "pt_option_inst";   
urbanc@18279
   380
      val pt_noptn_inst = thm "pt_noption_inst";   
urbanc@18279
   381
      val pt_fun_inst   = thm "pt_fun_inst";     
berghofe@18068
   382
urbanc@18435
   383
     (* for all atom-kind combinations <ak>/<ak'> show that        *)
urbanc@18435
   384
     (* every <ak> is an instance of pt_<ak'>; the proof for       *)
urbanc@18435
   385
     (* ak!=ak' is by definition; the case ak=ak' uses at_pt_inst. *)
urbanc@18431
   386
     val thy13 = fold (fn ak_name => fn thy =>
urbanc@18431
   387
	fold (fn ak_name' => fn thy' =>
urbanc@18431
   388
         let
urbanc@18431
   389
           val qu_name =  Sign.full_name (sign_of thy') ak_name';
urbanc@18431
   390
           val cls_name = Sign.full_name (sign_of thy') ("pt_"^ak_name);
urbanc@18431
   391
           val at_inst  = PureThy.get_thm thy' (Name ("at_"^ak_name'^"_inst")); 
urbanc@18431
   392
urbanc@18431
   393
           val proof1 = EVERY [AxClass.intro_classes_tac [],
berghofe@18068
   394
                                 rtac ((at_inst RS at_pt_inst) RS pt1) 1,
berghofe@18068
   395
                                 rtac ((at_inst RS at_pt_inst) RS pt2) 1,
berghofe@18068
   396
                                 rtac ((at_inst RS at_pt_inst) RS pt3) 1,
berghofe@18068
   397
                                 atac 1];
urbanc@18431
   398
           val simp_s = HOL_basic_ss addsimps 
urbanc@18431
   399
                        PureThy.get_thmss thy' [Name (ak_name^"_prm_"^ak_name'^"_def")];  
urbanc@18431
   400
           val proof2 = EVERY [AxClass.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)];
urbanc@18431
   401
urbanc@18431
   402
         in
urbanc@18431
   403
           thy'
urbanc@18431
   404
           |> AxClass.add_inst_arity_i (qu_name,[],[cls_name])
urbanc@18431
   405
              (if ak_name = ak_name' then proof1 else proof2)
urbanc@18431
   406
         end) ak_names thy) ak_names thy12c;
berghofe@18068
   407
urbanc@18430
   408
     (* show that                       *)
urbanc@18430
   409
     (*      fun(pt_<ak>,pt_<ak>)       *)
urbanc@18430
   410
     (*      nOption(pt_<ak>)           *)
urbanc@18430
   411
     (*      option(pt_<ak>)            *)
urbanc@18430
   412
     (*      list(pt_<ak>)              *)
urbanc@18430
   413
     (*      *(pt_<ak>,pt_<ak>)         *)
urbanc@18430
   414
     (*      unit                       *)
urbanc@18430
   415
     (*      set(pt_<ak>)               *)
urbanc@18430
   416
     (* are instances of pt_<ak>        *)
urbanc@18431
   417
     val thy18 = fold (fn ak_name => fn thy =>
berghofe@18068
   418
       let
urbanc@18430
   419
          val cls_name = Sign.full_name (sign_of thy) ("pt_"^ak_name);
berghofe@18068
   420
          val at_thm   = PureThy.get_thm thy (Name ("at_"^ak_name^"_inst"));
berghofe@18068
   421
          val pt_inst  = PureThy.get_thm thy (Name ("pt_"^ak_name^"_inst"));
urbanc@18430
   422
          
urbanc@18430
   423
          fun pt_proof thm = 
urbanc@18430
   424
	      EVERY [AxClass.intro_classes_tac [],
urbanc@18430
   425
                     rtac (thm RS pt1) 1, rtac (thm RS pt2) 1, rtac (thm RS pt3) 1, atac 1];
urbanc@18430
   426
urbanc@18430
   427
          val pt_thm_fun   = at_thm RS (pt_inst RS (pt_inst RS pt_fun_inst));
urbanc@18430
   428
          val pt_thm_noptn = pt_inst RS pt_noptn_inst; 
urbanc@18430
   429
          val pt_thm_optn  = pt_inst RS pt_optn_inst; 
urbanc@18430
   430
          val pt_thm_list  = pt_inst RS pt_list_inst;
urbanc@18430
   431
          val pt_thm_prod  = pt_inst RS (pt_inst RS pt_prod_inst);
urbanc@18430
   432
          val pt_thm_unit  = pt_unit_inst;
urbanc@18430
   433
          val pt_thm_set   = pt_inst RS pt_set_inst
berghofe@18068
   434
       in 
urbanc@18430
   435
	thy
urbanc@18430
   436
	|> AxClass.add_inst_arity_i ("fun",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_fun)
urbanc@18430
   437
        |> AxClass.add_inst_arity_i ("nominal.nOption",[[cls_name]],[cls_name]) (pt_proof pt_thm_noptn) 
urbanc@18430
   438
        |> AxClass.add_inst_arity_i ("Datatype.option",[[cls_name]],[cls_name]) (pt_proof pt_thm_optn)
urbanc@18430
   439
        |> AxClass.add_inst_arity_i ("List.list",[[cls_name]],[cls_name]) (pt_proof pt_thm_list)
urbanc@18430
   440
        |> AxClass.add_inst_arity_i ("*",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_prod)
urbanc@18430
   441
        |> AxClass.add_inst_arity_i ("Product_Type.unit",[],[cls_name]) (pt_proof pt_thm_unit)
urbanc@18430
   442
        |> AxClass.add_inst_arity_i ("set",[[cls_name]],[cls_name]) (pt_proof pt_thm_set)
urbanc@18430
   443
     end) ak_names thy13; 
berghofe@18068
   444
berghofe@18068
   445
       (*<<<<<<<  fs_<ak> class instances  >>>>>>>*)
berghofe@18068
   446
       (*=========================================*)
urbanc@18279
   447
       (* abbreviations for some lemmas *)
urbanc@18431
   448
       val fs1            = thm "fs1";
urbanc@18431
   449
       val fs_at_inst     = thm "fs_at_inst";
urbanc@18431
   450
       val fs_unit_inst   = thm "fs_unit_inst";
urbanc@18431
   451
       val fs_prod_inst   = thm "fs_prod_inst";
urbanc@18431
   452
       val fs_list_inst   = thm "fs_list_inst";
urbanc@18431
   453
       val fs_option_inst = thm "fs_option_inst";
berghofe@18068
   454
berghofe@18068
   455
       (* shows that <ak> is an instance of fs_<ak>     *)
berghofe@18068
   456
       (* uses the theorem at_<ak>_inst                 *)
urbanc@18432
   457
       (* FIXME -- needs to be done for all ak-combinations, or not? *) 
urbanc@18431
   458
       val thy20 = fold (fn ak_name => fn thy =>
berghofe@18068
   459
       let
berghofe@18068
   460
          val qu_name =  Sign.full_name (sign_of thy) ak_name;
berghofe@18068
   461
          val qu_class = Sign.full_name (sign_of thy) ("fs_"^ak_name);
urbanc@18307
   462
          val at_thm = PureThy.get_thm thy (Name ("at_"^ak_name^"_inst"));
berghofe@18068
   463
          val proof = EVERY [AxClass.intro_classes_tac [],
berghofe@18068
   464
                             rtac ((at_thm RS fs_at_inst) RS fs1) 1];      
berghofe@18068
   465
       in 
urbanc@18431
   466
	 AxClass.add_inst_arity_i (qu_name,[],[qu_class]) proof thy 
urbanc@18432
   467
       end) ak_names thy18;
berghofe@18068
   468
urbanc@18431
   469
       (* shows that                  *)
urbanc@18431
   470
       (*    unit                     *)
urbanc@18431
   471
       (*    *(fs_<ak>,fs_<ak>)       *)
urbanc@18431
   472
       (*    list(fs_<ak>)            *)
urbanc@18431
   473
       (*    option(fs_<ak>)          *) 
urbanc@18431
   474
       (* are instances of fs_<ak>    *)
berghofe@18068
   475
urbanc@18431
   476
       val thy24 = fold (fn ak_name => fn thy => 
urbanc@18431
   477
        let
urbanc@18431
   478
          val cls_name = Sign.full_name (sign_of thy) ("fs_"^ak_name);
berghofe@18068
   479
          val fs_inst  = PureThy.get_thm thy (Name ("fs_"^ak_name^"_inst"));
urbanc@18431
   480
          fun fs_proof thm = EVERY [AxClass.intro_classes_tac [], rtac (thm RS fs1) 1];      
berghofe@18068
   481
urbanc@18431
   482
          val fs_thm_unit = fs_unit_inst;
urbanc@18431
   483
          val fs_thm_prod = fs_inst RS (fs_inst RS fs_prod_inst);
urbanc@18431
   484
          val fs_thm_list = fs_inst RS fs_list_inst;
urbanc@18431
   485
          val fs_thm_optn = fs_inst RS fs_option_inst;
urbanc@18431
   486
        in 
urbanc@18431
   487
         thy 
urbanc@18431
   488
         |> AxClass.add_inst_arity_i ("Product_Type.unit",[],[cls_name]) (fs_proof fs_thm_unit) 
urbanc@18431
   489
         |> AxClass.add_inst_arity_i ("*",[[cls_name],[cls_name]],[cls_name]) (fs_proof fs_thm_prod)    
urbanc@18431
   490
         |> AxClass.add_inst_arity_i ("List.list",[[cls_name]],[cls_name]) (fs_proof fs_thm_list)
urbanc@18431
   491
         |> AxClass.add_inst_arity_i ("Datatype.option",[[cls_name]],[cls_name]) (fs_proof fs_thm_optn)
urbanc@18431
   492
        end) ak_names thy20; 
urbanc@18431
   493
berghofe@18068
   494
       (*<<<<<<<  cp_<ak>_<ai> class instances  >>>>>>>*)
berghofe@18068
   495
       (*==============================================*)
urbanc@18279
   496
       (* abbreviations for some lemmas *)
urbanc@18279
   497
       val cp1             = thm "cp1";
urbanc@18279
   498
       val cp_unit_inst    = thm "cp_unit_inst";
urbanc@18279
   499
       val cp_bool_inst    = thm "cp_bool_inst";
urbanc@18279
   500
       val cp_prod_inst    = thm "cp_prod_inst";
urbanc@18279
   501
       val cp_list_inst    = thm "cp_list_inst";
urbanc@18279
   502
       val cp_fun_inst     = thm "cp_fun_inst";
urbanc@18279
   503
       val cp_option_inst  = thm "cp_option_inst";
urbanc@18279
   504
       val cp_noption_inst = thm "cp_noption_inst";
urbanc@18279
   505
       val pt_perm_compose = thm "pt_perm_compose";
urbanc@18279
   506
       val dj_pp_forget    = thm "dj_perm_perm_forget";
berghofe@18068
   507
berghofe@18068
   508
       (* shows that <aj> is an instance of cp_<ak>_<ai>  *)
urbanc@18432
   509
       (* for every  <ak>/<ai>-combination                *)
urbanc@18432
   510
       val thy25 = fold (fn ak_name => fn thy => 
urbanc@18432
   511
	 fold (fn ak_name' => fn thy' => 
urbanc@18432
   512
          fold (fn ak_name'' => fn thy'' => 
berghofe@18068
   513
            let
urbanc@18432
   514
              val name =  Sign.full_name (sign_of thy'') ak_name;
urbanc@18432
   515
              val cls_name = Sign.full_name (sign_of thy'') ("cp_"^ak_name'^"_"^ak_name'');
berghofe@18068
   516
              val proof =
berghofe@18068
   517
                (if (ak_name'=ak_name'') then 
berghofe@18068
   518
		  (let
berghofe@18068
   519
                    val pt_inst  = PureThy.get_thm thy'' (Name ("pt_"^ak_name''^"_inst"));
berghofe@18068
   520
		    val at_inst  = PureThy.get_thm thy'' (Name ("at_"^ak_name''^"_inst"));
berghofe@18068
   521
                  in 
berghofe@18068
   522
		   EVERY [AxClass.intro_classes_tac [], 
berghofe@18068
   523
                          rtac (at_inst RS (pt_inst RS pt_perm_compose)) 1]
berghofe@18068
   524
                  end)
berghofe@18068
   525
		else
berghofe@18068
   526
		  (let 
berghofe@18068
   527
                     val dj_inst  = PureThy.get_thm thy'' (Name ("dj_"^ak_name''^"_"^ak_name'));
berghofe@18068
   528
		     val simp_s = HOL_basic_ss addsimps 
berghofe@18068
   529
                                        ((dj_inst RS dj_pp_forget)::
berghofe@18068
   530
                                         (PureThy.get_thmss thy'' 
berghofe@18068
   531
					   [Name (ak_name' ^"_prm_"^ak_name^"_def"),
berghofe@18068
   532
                                            Name (ak_name''^"_prm_"^ak_name^"_def")]));  
berghofe@18068
   533
		  in 
berghofe@18068
   534
                    EVERY [AxClass.intro_classes_tac [], simp_tac simp_s 1]
berghofe@18068
   535
                  end))
berghofe@18068
   536
	      in
urbanc@18432
   537
                AxClass.add_inst_arity_i (name,[],[cls_name]) proof thy''
urbanc@18432
   538
	      end) ak_names thy') ak_names thy) ak_names thy24;
berghofe@18068
   539
      
urbanc@18432
   540
       (* shows that                                                    *) 
urbanc@18432
   541
       (*      units                                                    *) 
urbanc@18432
   542
       (*      products                                                 *)
urbanc@18432
   543
       (*      lists                                                    *)
urbanc@18432
   544
       (*      functions                                                *)
urbanc@18432
   545
       (*      options                                                  *)
urbanc@18432
   546
       (*      noptions                                                 *)
urbanc@18432
   547
       (* are instances of cp_<ak>_<ai> for every <ak>/<ai>-combination *)
urbanc@18432
   548
       val thy26 = fold (fn ak_name => fn thy =>
urbanc@18432
   549
	fold (fn ak_name' => fn thy' =>
urbanc@18432
   550
        let
urbanc@18432
   551
            val cls_name = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
berghofe@18068
   552
            val cp_inst  = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
berghofe@18068
   553
            val pt_inst  = PureThy.get_thm thy' (Name ("pt_"^ak_name^"_inst"));
berghofe@18068
   554
            val at_inst  = PureThy.get_thm thy' (Name ("at_"^ak_name^"_inst"));
urbanc@18432
   555
urbanc@18432
   556
            fun cp_proof thm  = EVERY [AxClass.intro_classes_tac [],rtac (thm RS cp1) 1];     
urbanc@18432
   557
	  
urbanc@18432
   558
            val cp_thm_unit = cp_unit_inst;
urbanc@18432
   559
            val cp_thm_prod = cp_inst RS (cp_inst RS cp_prod_inst);
urbanc@18432
   560
            val cp_thm_list = cp_inst RS cp_list_inst;
urbanc@18432
   561
            val cp_thm_fun  = at_inst RS (pt_inst RS (cp_inst RS (cp_inst RS cp_fun_inst)));
urbanc@18432
   562
            val cp_thm_optn = cp_inst RS cp_option_inst;
urbanc@18432
   563
            val cp_thm_noptn = cp_inst RS cp_noption_inst;
urbanc@18432
   564
        in
urbanc@18432
   565
         thy'
urbanc@18432
   566
         |> AxClass.add_inst_arity_i ("Product_Type.unit",[],[cls_name]) (cp_proof cp_thm_unit)
urbanc@18432
   567
	 |> AxClass.add_inst_arity_i ("*",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_prod)
urbanc@18432
   568
         |> AxClass.add_inst_arity_i ("List.list",[[cls_name]],[cls_name]) (cp_proof cp_thm_list)
urbanc@18432
   569
         |> AxClass.add_inst_arity_i ("fun",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_fun)
urbanc@18432
   570
         |> AxClass.add_inst_arity_i ("Datatype.option",[[cls_name]],[cls_name]) (cp_proof cp_thm_optn)
urbanc@18432
   571
         |> AxClass.add_inst_arity_i ("nominal.nOption",[[cls_name]],[cls_name]) (cp_proof cp_thm_noptn)
urbanc@18432
   572
        end) ak_names thy) ak_names thy25;
urbanc@18432
   573
       
urbanc@18432
   574
     (* show that discrete nominal types are permutation types, finitely     *) 
urbanc@18432
   575
     (* supported and have the commutation property                          *)
urbanc@18432
   576
     (* discrete types have a permutation operation defined as pi o x = x;   *)
urbanc@18432
   577
     (* which renders the proofs to be simple "simp_all"-proofs.             *)            
urbanc@18432
   578
     val thy32 =
urbanc@18432
   579
        let 
urbanc@18432
   580
	  fun discrete_pt_inst discrete_ty defn = 
urbanc@18432
   581
	     fold (fn ak_name => fn thy =>
urbanc@18432
   582
	     let
urbanc@18432
   583
	       val qu_class = Sign.full_name (sign_of thy) ("pt_"^ak_name);
urbanc@18432
   584
	       val simp_s = HOL_basic_ss addsimps [defn];
urbanc@18432
   585
               val proof = EVERY [AxClass.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)];      
urbanc@18432
   586
             in  
urbanc@18432
   587
	       AxClass.add_inst_arity_i (discrete_ty,[],[qu_class]) proof thy
urbanc@18432
   588
             end) ak_names;
berghofe@18068
   589
urbanc@18432
   590
          fun discrete_fs_inst discrete_ty defn = 
urbanc@18432
   591
	     fold (fn ak_name => fn thy =>
urbanc@18432
   592
	     let
urbanc@18432
   593
	       val qu_class = Sign.full_name (sign_of thy) ("fs_"^ak_name);
urbanc@18432
   594
	       val supp_def = thm "nominal.supp_def";
urbanc@18432
   595
               val simp_s = HOL_ss addsimps [supp_def,Collect_const,Finites.emptyI,defn];
urbanc@18432
   596
               val proof = EVERY [AxClass.intro_classes_tac [], asm_simp_tac simp_s 1];      
urbanc@18432
   597
             in  
urbanc@18432
   598
	       AxClass.add_inst_arity_i (discrete_ty,[],[qu_class]) proof thy
urbanc@18432
   599
             end) ak_names;  
berghofe@18068
   600
urbanc@18432
   601
          fun discrete_cp_inst discrete_ty defn = 
urbanc@18432
   602
	     fold (fn ak_name' => (fold (fn ak_name => fn thy =>
urbanc@18432
   603
	     let
urbanc@18432
   604
	       val qu_class = Sign.full_name (sign_of thy) ("cp_"^ak_name^"_"^ak_name');
urbanc@18432
   605
	       val supp_def = thm "nominal.supp_def";
urbanc@18432
   606
               val simp_s = HOL_ss addsimps [defn];
urbanc@18432
   607
               val proof = EVERY [AxClass.intro_classes_tac [], asm_simp_tac simp_s 1];      
urbanc@18432
   608
             in  
urbanc@18432
   609
	       AxClass.add_inst_arity_i (discrete_ty,[],[qu_class]) proof thy
urbanc@18432
   610
             end) ak_names)) ak_names;  
urbanc@18432
   611
          
urbanc@18432
   612
        in
urbanc@18432
   613
         thy26
urbanc@18432
   614
         |> discrete_pt_inst "nat"  (thm "perm_nat_def")
urbanc@18432
   615
         |> discrete_fs_inst "nat"  (thm "perm_nat_def") 
urbanc@18432
   616
         |> discrete_cp_inst "nat"  (thm "perm_nat_def") 
urbanc@18432
   617
         |> discrete_pt_inst "bool" (thm "perm_bool")
urbanc@18432
   618
         |> discrete_fs_inst "bool" (thm "perm_bool")
urbanc@18432
   619
         |> discrete_cp_inst "bool" (thm "perm_bool")
urbanc@18432
   620
         |> discrete_pt_inst "IntDef.int" (thm "perm_int_def")
urbanc@18432
   621
         |> discrete_fs_inst "IntDef.int" (thm "perm_int_def") 
urbanc@18432
   622
         |> discrete_cp_inst "IntDef.int" (thm "perm_int_def") 
urbanc@18432
   623
         |> discrete_pt_inst "List.char" (thm "perm_char_def")
urbanc@18432
   624
         |> discrete_fs_inst "List.char" (thm "perm_char_def")
urbanc@18432
   625
         |> discrete_cp_inst "List.char" (thm "perm_char_def")
urbanc@18432
   626
        end;
urbanc@18432
   627
berghofe@18068
   628
urbanc@18262
   629
       (* abbreviations for some lemmas *)
urbanc@18262
   630
       (*===============================*)
urbanc@18279
   631
       val abs_fun_pi        = thm "nominal.abs_fun_pi";
urbanc@18279
   632
       val abs_fun_pi_ineq   = thm "nominal.abs_fun_pi_ineq";
urbanc@18279
   633
       val abs_fun_eq        = thm "nominal.abs_fun_eq";
urbanc@18279
   634
       val dj_perm_forget    = thm "nominal.dj_perm_forget";
urbanc@18279
   635
       val dj_pp_forget      = thm "nominal.dj_perm_perm_forget";
urbanc@18279
   636
       val fresh_iff         = thm "nominal.fresh_abs_fun_iff";
urbanc@18279
   637
       val fresh_iff_ineq    = thm "nominal.fresh_abs_fun_iff_ineq";
urbanc@18279
   638
       val abs_fun_supp      = thm "nominal.abs_fun_supp";
urbanc@18279
   639
       val abs_fun_supp_ineq = thm "nominal.abs_fun_supp_ineq";
urbanc@18279
   640
       val pt_swap_bij       = thm "nominal.pt_swap_bij";
urbanc@18279
   641
       val pt_fresh_fresh    = thm "nominal.pt_fresh_fresh";
urbanc@18279
   642
       val pt_bij            = thm "nominal.pt_bij";
urbanc@18279
   643
       val pt_perm_compose   = thm "nominal.pt_perm_compose";
urbanc@18279
   644
       val perm_eq_app       = thm "nominal.perm_eq_app";
urbanc@18279
   645
       val at_fresh          = thm "nominal.at_fresh";
urbanc@18279
   646
       val at_calc           = thms "nominal.at_calc";
urbanc@18279
   647
       val at_supp           = thm "nominal.at_supp";
urbanc@18279
   648
       val dj_supp           = thm "nominal.dj_supp";
urbanc@18396
   649
       val fresh_left_ineq   = thm "nominal.pt_fresh_left_ineq";
urbanc@18396
   650
       val fresh_left        = thm "nominal.pt_fresh_left";
urbanc@18426
   651
       val fresh_bij_ineq    = thm "nominal.pt_fresh_bij_ineq";
urbanc@18426
   652
       val fresh_bij         = thm "nominal.pt_fresh_bij";
berghofe@18068
   653
urbanc@18262
   654
       (* Now we collect and instantiate some lemmas w.r.t. all atom      *)
urbanc@18262
   655
       (* types; this allows for example to use abs_perm (which is a      *)
urbanc@18262
   656
       (* collection of theorems) instead of thm abs_fun_pi with explicit *)
urbanc@18262
   657
       (* instantiations.                                                 *)
urbanc@18381
   658
       val (_,thy33) = 
urbanc@18262
   659
	 let 
urbanc@18279
   660
             (* takes a theorem thm and a list of theorems [t1,..,tn]            *)
urbanc@18279
   661
             (* produces a list of theorems of the form [t1 RS thm,..,tn RS thm] *) 
urbanc@18262
   662
             fun instR thm thms = map (fn ti => ti RS thm) thms;
berghofe@18068
   663
urbanc@18262
   664
             (* takes two theorem lists (hopefully of the same length ;o)                *)
urbanc@18262
   665
             (* produces a list of theorems of the form                                  *)
urbanc@18262
   666
             (* [t1 RS m1,..,tn RS mn] where [t1,..,tn] is thms1 and [m1,..,mn] is thms2 *) 
urbanc@18279
   667
             fun inst_zip thms1 thms2 = map (fn (t1,t2) => t1 RS t2) (thms1 ~~ thms2);
berghofe@18068
   668
urbanc@18262
   669
             (* takes a theorem list of the form [l1,...,ln]              *)
urbanc@18262
   670
             (* and a list of theorem lists of the form                   *)
urbanc@18262
   671
             (* [[h11,...,h1m],....,[hk1,....,hkm]                        *)
urbanc@18262
   672
             (* produces the list of theorem lists                        *)
urbanc@18262
   673
             (* [[l1 RS h11,...,l1 RS h1m],...,[ln RS hk1,...,ln RS hkm]] *)
urbanc@18279
   674
             fun inst_mult thms thmss = map (fn (t,ts) => instR t ts) (thms ~~ thmss);
urbanc@18279
   675
urbanc@18279
   676
             (* FIXME: these lists do not need to be created dynamically again *)
urbanc@18262
   677
berghofe@18068
   678
             (* list of all at_inst-theorems *)
urbanc@18262
   679
             val ats = map (fn ak => PureThy.get_thm thy32 (Name ("at_"^ak^"_inst"))) ak_names
berghofe@18068
   680
             (* list of all pt_inst-theorems *)
urbanc@18262
   681
             val pts = map (fn ak => PureThy.get_thm thy32 (Name ("pt_"^ak^"_inst"))) ak_names
urbanc@18262
   682
             (* list of all cp_inst-theorems as a collection of lists*)
berghofe@18068
   683
             val cps = 
urbanc@18262
   684
		 let fun cps_fun ak1 ak2 = PureThy.get_thm thy32 (Name ("cp_"^ak1^"_"^ak2^"_inst"))
urbanc@18262
   685
		 in map (fn aki => (map (cps_fun aki) ak_names)) ak_names end; 
urbanc@18262
   686
             (* list of all cp_inst-theorems that have different atom types *)
urbanc@18262
   687
             val cps' = 
urbanc@18262
   688
		let fun cps'_fun ak1 ak2 = 
urbanc@18262
   689
		if ak1=ak2 then NONE else SOME(PureThy.get_thm thy32 (Name ("cp_"^ak1^"_"^ak2^"_inst")))
urbanc@18262
   690
		in map (fn aki => (List.mapPartial I (map (cps'_fun aki) ak_names))) ak_names end;
berghofe@18068
   691
             (* list of all dj_inst-theorems *)
berghofe@18068
   692
             val djs = 
berghofe@18068
   693
	       let fun djs_fun (ak1,ak2) = 
urbanc@18262
   694
		     if ak1=ak2 then NONE else SOME(PureThy.get_thm thy32 (Name ("dj_"^ak2^"_"^ak1)))
urbanc@18262
   695
	       in List.mapPartial I (map djs_fun (Library.product ak_names ak_names)) end;
urbanc@18262
   696
             (* list of all fs_inst-theorems *)
urbanc@18262
   697
             val fss = map (fn ak => PureThy.get_thm thy32 (Name ("fs_"^ak^"_inst"))) ak_names
berghofe@18068
   698
urbanc@18262
   699
             fun inst_pt thms = Library.flat (map (fn ti => instR ti pts) thms); 
urbanc@18262
   700
             fun inst_at thms = Library.flat (map (fn ti => instR ti ats) thms);               
urbanc@18262
   701
             fun inst_fs thms = Library.flat (map (fn ti => instR ti fss) thms);
urbanc@18262
   702
	     fun inst_pt_at thms = inst_zip ats (inst_pt thms);			
urbanc@18262
   703
             fun inst_dj thms = Library.flat (map (fn ti => instR ti djs) thms);  
urbanc@18262
   704
	     fun inst_pt_pt_at_cp thms = 
urbanc@18262
   705
		 Library.flat (inst_mult (inst_zip ats (inst_zip pts (inst_pt thms))) cps);
urbanc@18262
   706
             fun inst_pt_at_fs thms = inst_zip (inst_fs [fs1]) (inst_zip ats (inst_pt thms));
urbanc@18396
   707
	     fun inst_pt_pt_at_cp thms = 
urbanc@18279
   708
		 let val i_pt_pt_at = inst_zip ats (inst_zip pts (inst_pt thms));
urbanc@18279
   709
                     val i_pt_pt_at_cp = Library.flat (inst_mult i_pt_pt_at cps');
urbanc@18396
   710
		 in i_pt_pt_at_cp end;
urbanc@18396
   711
             fun inst_pt_pt_at_cp_dj thms = inst_zip djs (inst_pt_pt_at_cp thms);
berghofe@18068
   712
           in
urbanc@18262
   713
            thy32 
berghofe@18068
   714
	    |>   PureThy.add_thmss [(("alpha", inst_pt_at [abs_fun_eq]),[])]
urbanc@18381
   715
            ||>> PureThy.add_thmss [(("perm_swap", inst_pt_at [pt_swap_bij]),[])]
urbanc@18381
   716
            ||>> PureThy.add_thmss [(("perm_fresh_fresh", inst_pt_at [pt_fresh_fresh]),[])]
urbanc@18381
   717
            ||>> PureThy.add_thmss [(("perm_bij", inst_pt_at [pt_bij]),[])]
urbanc@18381
   718
            ||>> PureThy.add_thmss [(("perm_compose", inst_pt_at [pt_perm_compose]),[])]
urbanc@18381
   719
            ||>> PureThy.add_thmss [(("perm_app_eq", inst_pt_at [perm_eq_app]),[])]
urbanc@18381
   720
            ||>> PureThy.add_thmss [(("supp_atm", (inst_at [at_supp]) @ (inst_dj [dj_supp])),[])]
urbanc@18381
   721
            ||>> PureThy.add_thmss [(("fresh_atm", inst_at [at_fresh]),[])]
urbanc@18381
   722
            ||>> PureThy.add_thmss [(("calc_atm", inst_at at_calc),[])]
urbanc@18381
   723
            ||>> PureThy.add_thmss
urbanc@18279
   724
	      let val thms1 = inst_pt_at [abs_fun_pi]
urbanc@18279
   725
		  and thms2 = inst_pt_pt_at_cp [abs_fun_pi_ineq]
urbanc@18279
   726
	      in [(("abs_perm", thms1 @ thms2),[])] end
urbanc@18381
   727
            ||>> PureThy.add_thmss
urbanc@18279
   728
	      let val thms1 = inst_dj [dj_perm_forget]
urbanc@18279
   729
		  and thms2 = inst_dj [dj_pp_forget]
urbanc@18279
   730
              in [(("perm_dj", thms1 @ thms2),[])] end
urbanc@18381
   731
            ||>> PureThy.add_thmss
urbanc@18279
   732
	      let val thms1 = inst_pt_at_fs [fresh_iff]
urbanc@18279
   733
		  and thms2 = inst_pt_pt_at_cp_dj [fresh_iff_ineq]
urbanc@18262
   734
	    in [(("abs_fresh", thms1 @ thms2),[])] end
urbanc@18381
   735
	    ||>> PureThy.add_thmss
urbanc@18279
   736
	      let val thms1 = inst_pt_at [abs_fun_supp]
urbanc@18279
   737
		  and thms2 = inst_pt_at_fs [abs_fun_supp]
urbanc@18279
   738
		  and thms3 = inst_pt_pt_at_cp_dj [abs_fun_supp_ineq]
urbanc@18279
   739
	      in [(("abs_supp", thms1 @ thms2 @ thms3),[])] end
urbanc@18396
   740
            ||>> PureThy.add_thmss
urbanc@18396
   741
	      let val thms1 = inst_pt_at [fresh_left]
urbanc@18396
   742
		  and thms2 = inst_pt_pt_at_cp [fresh_left_ineq]
urbanc@18396
   743
	      in [(("fresh_left", thms1 @ thms2),[])] end
urbanc@18426
   744
            ||>> PureThy.add_thmss
urbanc@18426
   745
	      let val thms1 = inst_pt_at [fresh_bij]
urbanc@18426
   746
		  and thms2 = inst_pt_pt_at_cp [fresh_bij_ineq]
urbanc@18426
   747
	      in [(("fresh_eqvt", thms1 @ thms2),[])] end
berghofe@18068
   748
	   end;
berghofe@18068
   749
berghofe@18068
   750
    in NominalData.put (fold Symtab.update (map (rpair ()) full_ak_names)
urbanc@18262
   751
      (NominalData.get thy11)) thy33
berghofe@18068
   752
    end;
berghofe@18068
   753
berghofe@18068
   754
berghofe@18068
   755
(* syntax und parsing *)
berghofe@18068
   756
structure P = OuterParse and K = OuterKeyword;
berghofe@18068
   757
berghofe@18068
   758
val atom_declP =
berghofe@18068
   759
  OuterSyntax.command "atom_decl" "Declare new kinds of atoms" K.thy_decl
berghofe@18068
   760
    (Scan.repeat1 P.name >> (Toplevel.theory o create_nom_typedecls));
berghofe@18068
   761
berghofe@18068
   762
val _ = OuterSyntax.add_parsers [atom_declP];
berghofe@18068
   763
berghofe@18068
   764
val setup = [NominalData.init];
berghofe@18068
   765
berghofe@18068
   766
end;