src/HOL/Nominal/nominal_atoms.ML
author urbanc
Sun Dec 18 13:38:06 2005 +0100 (2005-12-18 ago)
changeset 18430 46c18c0b52c1
parent 18426 d2303e8654a2
child 18431 a59c79a3544c
permissions -rw-r--r--
improved the code for showing that a type is
in the pt-axclass (I try to slowly overcome
my incompetence with such ML-code).
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(* $Id$ *)
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signature NOMINAL_ATOMS =
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sig
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  val create_nom_typedecls : string list -> theory -> theory
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  val atoms_of : theory -> string list
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  val mk_permT : typ -> typ
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  val setup : (theory -> theory) list
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end
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structure NominalAtoms : NOMINAL_ATOMS =
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struct
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(* data kind 'HOL/nominal' *)
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structure NominalArgs =
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struct
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  val name = "HOL/nominal";
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  type T = unit Symtab.table;
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  val empty = Symtab.empty;
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  val copy = I;
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  val extend = I;
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  fun merge _ x = Symtab.merge (K true) x;
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  fun print sg tab = ();
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end;
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structure NominalData = TheoryDataFun(NominalArgs);
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fun atoms_of thy = map fst (Symtab.dest (NominalData.get thy));
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(* FIXME: add to hologic.ML ? *)
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fun mk_listT T = Type ("List.list", [T]);
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fun mk_permT T = mk_listT (HOLogic.mk_prodT (T, T));
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fun mk_Cons x xs =
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  let val T = fastype_of x
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  in Const ("List.list.Cons", T --> mk_listT T --> mk_listT T) $ x $ xs end;
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(* this function sets up all matters related to atom-  *)
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(* kinds; the user specifies a list of atom-kind names *)
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(* atom_decl <ak1> ... <akn>                           *)
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fun create_nom_typedecls ak_names thy =
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  let
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    (* declares a type-decl for every atom-kind: *) 
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    (* that is typedecl <ak>                     *)
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    val thy1 = TypedefPackage.add_typedecls (map (fn x => (x,[],NoSyn)) ak_names) thy;
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    (* produces a list consisting of pairs:         *)
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    (*  fst component is the atom-kind name         *)
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    (*  snd component is its type                   *)
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    val full_ak_names = map (Sign.intern_type (sign_of thy1)) ak_names;
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    val ak_names_types = ak_names ~~ map (Type o rpair []) full_ak_names;
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    (* adds for every atom-kind an axiom             *)
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    (* <ak>_infinite: infinite (UNIV::<ak_type> set) *)
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    val (inf_axs,thy2) = PureThy.add_axioms_i (map (fn (ak_name, T) =>
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      let 
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	val name = ak_name ^ "_infinite"
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        val axiom = HOLogic.mk_Trueprop (HOLogic.mk_not
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                    (HOLogic.mk_mem (HOLogic.mk_UNIV T,
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                     Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT T)))))
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      in
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	((name, axiom), []) 
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      end) ak_names_types) thy1;
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    (* declares a swapping function for every atom-kind, it is         *)
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    (* const swap_<ak> :: <akT> * <akT> => <akT> => <akT>              *)
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    (* swap_<ak> (a,b) c = (if a=c then b (else if b=c then a else c)) *)
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    (* overloades then the general swap-function                       *) 
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    val (thy3, swap_eqs) = foldl_map (fn (thy, (ak_name, T)) =>
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      let
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        val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
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        val swap_name = Sign.full_name (sign_of thy) ("swap_" ^ ak_name);
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        val a = Free ("a", T);
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        val b = Free ("b", T);
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        val c = Free ("c", T);
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        val ab = Free ("ab", HOLogic.mk_prodT (T, T))
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        val cif = Const ("HOL.If", HOLogic.boolT --> T --> T --> T);
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        val cswap_akname = Const (swap_name, swapT);
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        val cswap = Const ("nominal.swap", swapT)
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        val name = "swap_"^ak_name^"_def";
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        val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq
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		   (cswap_akname $ HOLogic.mk_prod (a,b) $ c,
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                    cif $ HOLogic.mk_eq (a,c) $ b $ (cif $ HOLogic.mk_eq (b,c) $ a $ c)))
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        val def2 = Logic.mk_equals (cswap $ ab $ c, cswap_akname $ ab $ c)
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      in
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        thy |> Theory.add_consts_i [("swap_" ^ ak_name, swapT, NoSyn)] 
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            |> (#2 o PureThy.add_defs_i true [((name, def2),[])])
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            |> PrimrecPackage.add_primrec_i "" [(("", def1),[])]            
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      end) (thy2, ak_names_types);
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    (* declares a permutation function for every atom-kind acting  *)
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    (* on such atoms                                               *)
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    (* const <ak>_prm_<ak> :: (<akT> * <akT>)list => akT => akT    *)
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    (* <ak>_prm_<ak> []     a = a                                  *)
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    (* <ak>_prm_<ak> (x#xs) a = swap_<ak> x (perm xs a)            *)
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    val (thy4, prm_eqs) = foldl_map (fn (thy, (ak_name, T)) =>
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      let
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        val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
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        val swap_name = Sign.full_name (sign_of thy) ("swap_" ^ ak_name)
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        val prmT = mk_permT T --> T --> T;
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        val prm_name = ak_name ^ "_prm_" ^ ak_name;
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        val qu_prm_name = Sign.full_name (sign_of thy) prm_name;
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        val x  = Free ("x", HOLogic.mk_prodT (T, T));
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        val xs = Free ("xs", mk_permT T);
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        val a  = Free ("a", T) ;
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        val cnil  = Const ("List.list.Nil", mk_permT T);
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        val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq (Const (qu_prm_name, prmT) $ cnil $ a, a));
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        val def2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
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                   (Const (qu_prm_name, prmT) $ mk_Cons x xs $ a,
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                    Const (swap_name, swapT) $ x $ (Const (qu_prm_name, prmT) $ xs $ a)));
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      in
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        thy |> Theory.add_consts_i [(prm_name, mk_permT T --> T --> T, NoSyn)] 
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            |> PrimrecPackage.add_primrec_i "" [(("", def1), []),(("", def2), [])]
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      end) (thy3, ak_names_types);
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    (* defines permutation functions for all combinations of atom-kinds; *)
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    (* there are a trivial cases and non-trivial cases                   *)
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    (* non-trivial case:                                                 *)
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    (* <ak>_prm_<ak>_def:  perm pi a == <ak>_prm_<ak> pi a               *)
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    (* trivial case with <ak> != <ak'>                                   *)
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    (* <ak>_prm<ak'>_def[simp]:  perm pi a == a                          *)
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    (*                                                                   *)
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    (* the trivial cases are added to the simplifier, while the non-     *)
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    (* have their own rules proved below                                 *)  
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    val (perm_defs, thy5) = fold_map (fn (ak_name, T) => fn thy =>
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      fold_map (fn (ak_name', T') => fn thy' =>
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        let
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          val perm_def_name = ak_name ^ "_prm_" ^ ak_name';
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          val pi = Free ("pi", mk_permT T);
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          val a  = Free ("a", T');
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          val cperm = Const ("nominal.perm", mk_permT T --> T' --> T');
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          val cperm_def = Const (Sign.full_name (sign_of thy') perm_def_name, mk_permT T --> T' --> T');
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          val name = ak_name ^ "_prm_" ^ ak_name' ^ "_def";
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          val def = Logic.mk_equals
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                    (cperm $ pi $ a, if ak_name = ak_name' then cperm_def $ pi $ a else a)
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        in
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          PureThy.add_defs_i true [((name, def),[])] thy'
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        end) ak_names_types thy) ak_names_types thy4;
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    (* proves that every atom-kind is an instance of at *)
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    (* lemma at_<ak>_inst:                              *)
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    (* at TYPE(<ak>)                                    *)
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    val (prm_cons_thms,thy6) = 
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      thy5 |> PureThy.add_thms (map (fn (ak_name, T) =>
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      let
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        val ak_name_qu = Sign.full_name (sign_of thy5) (ak_name);
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        val i_type = Type(ak_name_qu,[]);
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	val cat = Const ("nominal.at",(Term.itselfT i_type)  --> HOLogic.boolT);
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        val at_type = Logic.mk_type i_type;
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        val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy5
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                                  [Name "at_def",
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                                   Name (ak_name ^ "_prm_" ^ ak_name ^ "_def"),
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                                   Name (ak_name ^ "_prm_" ^ ak_name ^ ".simps"),
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                                   Name ("swap_" ^ ak_name ^ "_def"),
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                                   Name ("swap_" ^ ak_name ^ ".simps"),
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                                   Name (ak_name ^ "_infinite")]
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	val name = "at_"^ak_name^ "_inst";
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        val statement = HOLogic.mk_Trueprop (cat $ at_type);
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        val proof = fn _ => auto_tac (claset(),simp_s);
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      in 
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        ((name, standard (Goal.prove thy5 [] [] statement proof)), []) 
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      end) ak_names_types);
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    (* declares a perm-axclass for every atom-kind               *)
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    (* axclass pt_<ak>                                           *)
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    (* pt_<ak>1[simp]: perm [] x = x                             *)
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    (* pt_<ak>2:       perm (pi1@pi2) x = perm pi1 (perm pi2 x)  *)
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    (* pt_<ak>3:       pi1 ~ pi2 ==> perm pi1 x = perm pi2 x     *)
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     val (thy7, pt_ax_classes) =  foldl_map (fn (thy, (ak_name, T)) =>
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      let 
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	  val cl_name = "pt_"^ak_name;
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          val ty = TFree("'a",["HOL.type"]);
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          val x   = Free ("x", ty);
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          val pi1 = Free ("pi1", mk_permT T);
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          val pi2 = Free ("pi2", mk_permT T);
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          val cperm = Const ("nominal.perm", mk_permT T --> ty --> ty);
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          val cnil  = Const ("List.list.Nil", mk_permT T);
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          val cappend = Const ("List.op @",mk_permT T --> mk_permT T --> mk_permT T);
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          val cprm_eq = Const ("nominal.prm_eq",mk_permT T --> mk_permT T --> HOLogic.boolT);
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          (* nil axiom *)
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          val axiom1 = HOLogic.mk_Trueprop (HOLogic.mk_eq 
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                       (cperm $ cnil $ x, x));
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          (* append axiom *)
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          val axiom2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
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                       (cperm $ (cappend $ pi1 $ pi2) $ x, cperm $ pi1 $ (cperm $ pi2 $ x)));
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          (* perm-eq axiom *)
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          val axiom3 = Logic.mk_implies
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                       (HOLogic.mk_Trueprop (cprm_eq $ pi1 $ pi2),
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                        HOLogic.mk_Trueprop (HOLogic.mk_eq (cperm $ pi1 $ x, cperm $ pi2 $ x)));
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      in
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        thy |> AxClass.add_axclass_i (cl_name, ["HOL.type"])
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                [((cl_name^"1", axiom1),[Simplifier.simp_add_global]), 
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                 ((cl_name^"2", axiom2),[]),                           
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                 ((cl_name^"3", axiom3),[])]                          
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      end) (thy6,ak_names_types);
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    (* proves that every pt_<ak>-type together with <ak>-type *)
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    (* instance of pt                                         *)
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    (* lemma pt_<ak>_inst:                                    *)
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    (* pt TYPE('x::pt_<ak>) TYPE(<ak>)                        *)
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    val (prm_inst_thms,thy8) = 
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      thy7 |> PureThy.add_thms (map (fn (ak_name, T) =>
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      let
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        val ak_name_qu = Sign.full_name (sign_of thy7) (ak_name);
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        val pt_name_qu = Sign.full_name (sign_of thy7) ("pt_"^ak_name);
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        val i_type1 = TFree("'x",[pt_name_qu]);
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        val i_type2 = Type(ak_name_qu,[]);
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	val cpt = Const ("nominal.pt",(Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
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        val pt_type = Logic.mk_type i_type1;
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        val at_type = Logic.mk_type i_type2;
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        val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy7
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                                  [Name "pt_def",
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                                   Name ("pt_" ^ ak_name ^ "1"),
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                                   Name ("pt_" ^ ak_name ^ "2"),
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                                   Name ("pt_" ^ ak_name ^ "3")];
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	val name = "pt_"^ak_name^ "_inst";
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        val statement = HOLogic.mk_Trueprop (cpt $ pt_type $ at_type);
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        val proof = fn _ => auto_tac (claset(),simp_s);
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      in 
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        ((name, standard (Goal.prove thy7 [] [] statement proof)), []) 
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      end) ak_names_types);
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     (* declares an fs-axclass for every atom-kind       *)
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     (* axclass fs_<ak>                                  *)
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     (* fs_<ak>1: finite ((supp x)::<ak> set)            *)
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     val (thy11, fs_ax_classes) =  foldl_map (fn (thy, (ak_name, T)) =>
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       let 
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	  val cl_name = "fs_"^ak_name;
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	  val pt_name = Sign.full_name (sign_of thy) ("pt_"^ak_name);
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          val ty = TFree("'a",["HOL.type"]);
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          val x   = Free ("x", ty);
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          val csupp    = Const ("nominal.supp", ty --> HOLogic.mk_setT T);
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          val cfinites = Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT T))
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          val axiom1   = HOLogic.mk_Trueprop (HOLogic.mk_mem (csupp $ x, cfinites));
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       in  
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        thy |> AxClass.add_axclass_i (cl_name, [pt_name]) [((cl_name^"1", axiom1),[])]            
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       end) (thy8,ak_names_types); 
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     (* proves that every fs_<ak>-type together with <ak>-type   *)
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     (* instance of fs-type                                      *)
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     (* lemma abst_<ak>_inst:                                    *)
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     (* fs TYPE('x::pt_<ak>) TYPE (<ak>)                         *)
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     val (fs_inst_thms,thy12) = 
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       thy11 |> PureThy.add_thms (map (fn (ak_name, T) =>
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       let
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         val ak_name_qu = Sign.full_name (sign_of thy11) (ak_name);
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         val fs_name_qu = Sign.full_name (sign_of thy11) ("fs_"^ak_name);
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         val i_type1 = TFree("'x",[fs_name_qu]);
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         val i_type2 = Type(ak_name_qu,[]);
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 	 val cfs = Const ("nominal.fs", 
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                                 (Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
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         val fs_type = Logic.mk_type i_type1;
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         val at_type = Logic.mk_type i_type2;
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	 val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy11
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                                   [Name "fs_def",
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                                    Name ("fs_" ^ ak_name ^ "1")];
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	 val name = "fs_"^ak_name^ "_inst";
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         val statement = HOLogic.mk_Trueprop (cfs $ fs_type $ at_type);
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         val proof = fn _ => auto_tac (claset(),simp_s);
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       in 
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   279
         ((name, standard (Goal.prove thy11 [] [] statement proof)), []) 
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   280
       end) ak_names_types);
berghofe@18068
   281
berghofe@18068
   282
       (* declares for every atom-kind combination an axclass            *)
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   283
       (* cp_<ak1>_<ak2> giving a composition property                   *)
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   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)) =>
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   286
	 foldl_map (fn (thy', (ak_name', T')) =>
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   287
	     let
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   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);
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   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)));
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   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;     *)
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   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_bool_inst  = thm "pt_bool_inst";
urbanc@18279
   376
      val pt_set_inst   = thm "pt_set_inst"; 
urbanc@18279
   377
      val pt_unit_inst  = thm "pt_unit_inst";
urbanc@18279
   378
      val pt_prod_inst  = thm "pt_prod_inst"; 
urbanc@18279
   379
      val pt_list_inst  = thm "pt_list_inst";   
urbanc@18279
   380
      val pt_optn_inst  = thm "pt_option_inst";   
urbanc@18279
   381
      val pt_noptn_inst = thm "pt_noption_inst";   
urbanc@18279
   382
      val pt_fun_inst   = thm "pt_fun_inst";     
berghofe@18068
   383
berghofe@18068
   384
     (* for all atom-kind combination shows that         *)
berghofe@18068
   385
     (* every <ak> is an instance of pt_<ai>             *)
berghofe@18068
   386
     val (thy13,_) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   387
	 foldl_map (fn (thy', (ak_name', T')) =>
berghofe@18068
   388
          (if ak_name = ak_name'
berghofe@18068
   389
	   then
berghofe@18068
   390
	     let
berghofe@18068
   391
	      val qu_name =  Sign.full_name (sign_of thy') ak_name;
berghofe@18068
   392
              val qu_class = Sign.full_name (sign_of thy') ("pt_"^ak_name);
berghofe@18068
   393
              val at_inst  = PureThy.get_thm thy' (Name ("at_"^ak_name ^"_inst"));
berghofe@18068
   394
              val proof = EVERY [AxClass.intro_classes_tac [],
berghofe@18068
   395
                                 rtac ((at_inst RS at_pt_inst) RS pt1) 1,
berghofe@18068
   396
                                 rtac ((at_inst RS at_pt_inst) RS pt2) 1,
berghofe@18068
   397
                                 rtac ((at_inst RS at_pt_inst) RS pt3) 1,
berghofe@18068
   398
                                 atac 1];
berghofe@18068
   399
             in 
berghofe@18068
   400
	      (AxClass.add_inst_arity_i (qu_name,[],[qu_class]) proof thy',()) 
berghofe@18068
   401
             end
berghofe@18068
   402
           else 
berghofe@18068
   403
             let
berghofe@18068
   404
	      val qu_name' = Sign.full_name (sign_of thy') ak_name';
berghofe@18068
   405
              val qu_class = Sign.full_name (sign_of thy') ("pt_"^ak_name);
berghofe@18068
   406
              val simp_s = HOL_basic_ss addsimps 
berghofe@18068
   407
                           PureThy.get_thmss thy' [Name (ak_name^"_prm_"^ak_name'^"_def")];  
berghofe@18068
   408
              val proof = EVERY [AxClass.intro_classes_tac [], auto_tac (claset(),simp_s)];
berghofe@18068
   409
             in 
berghofe@18068
   410
	      (AxClass.add_inst_arity_i (qu_name',[],[qu_class]) proof thy',()) 
berghofe@18068
   411
             end)) 
berghofe@18068
   412
	     (thy, ak_names_types)) (thy12c, ak_names_types);
berghofe@18068
   413
urbanc@18430
   414
     (* show that                       *)
urbanc@18430
   415
     (*      fun(pt_<ak>,pt_<ak>)       *)
urbanc@18430
   416
     (*      nOption(pt_<ak>)           *)
urbanc@18430
   417
     (*      option(pt_<ak>)            *)
urbanc@18430
   418
     (*      list(pt_<ak>)              *)
urbanc@18430
   419
     (*      *(pt_<ak>,pt_<ak>)         *)
urbanc@18430
   420
     (*      unit                       *)
urbanc@18430
   421
     (*      set(pt_<ak>)               *)
urbanc@18430
   422
     (* are instances of pt_<ak>        *)
urbanc@18430
   423
     val thy19 = fold (fn ak_name => fn thy =>
berghofe@18068
   424
       let
urbanc@18430
   425
          val cls_name = Sign.full_name (sign_of thy) ("pt_"^ak_name);
berghofe@18068
   426
          val at_thm   = PureThy.get_thm thy (Name ("at_"^ak_name^"_inst"));
berghofe@18068
   427
          val pt_inst  = PureThy.get_thm thy (Name ("pt_"^ak_name^"_inst"));
urbanc@18430
   428
          
urbanc@18430
   429
          fun pt_proof thm = 
urbanc@18430
   430
	      EVERY [AxClass.intro_classes_tac [],
urbanc@18430
   431
                     rtac (thm RS pt1) 1, rtac (thm RS pt2) 1, rtac (thm RS pt3) 1, atac 1];
urbanc@18430
   432
urbanc@18430
   433
          val pt_thm_fun   = at_thm RS (pt_inst RS (pt_inst RS pt_fun_inst));
urbanc@18430
   434
          val pt_thm_noptn = pt_inst RS pt_noptn_inst; 
urbanc@18430
   435
          val pt_thm_optn  = pt_inst RS pt_optn_inst; 
urbanc@18430
   436
          val pt_thm_list  = pt_inst RS pt_list_inst;
urbanc@18430
   437
          val pt_thm_prod  = pt_inst RS (pt_inst RS pt_prod_inst);
urbanc@18430
   438
          val pt_thm_unit  = pt_unit_inst;
urbanc@18430
   439
          val pt_thm_set   = pt_inst RS pt_set_inst
berghofe@18068
   440
       in 
urbanc@18430
   441
	thy
urbanc@18430
   442
	|> AxClass.add_inst_arity_i ("fun",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_fun)
urbanc@18430
   443
        |> AxClass.add_inst_arity_i ("nominal.nOption",[[cls_name]],[cls_name]) (pt_proof pt_thm_noptn) 
urbanc@18430
   444
        |> AxClass.add_inst_arity_i ("Datatype.option",[[cls_name]],[cls_name]) (pt_proof pt_thm_optn)
urbanc@18430
   445
        |> AxClass.add_inst_arity_i ("List.list",[[cls_name]],[cls_name]) (pt_proof pt_thm_list)
urbanc@18430
   446
        |> AxClass.add_inst_arity_i ("*",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_prod)
urbanc@18430
   447
        |> AxClass.add_inst_arity_i ("Product_Type.unit",[],[cls_name]) (pt_proof pt_thm_unit)
urbanc@18430
   448
        |> AxClass.add_inst_arity_i ("set",[[cls_name]],[cls_name]) (pt_proof pt_thm_set)
urbanc@18430
   449
     end) ak_names thy13; 
berghofe@18068
   450
urbanc@18430
   451
     (* show that discrete types are permutation types and finitely supported *)
urbanc@18430
   452
     (* discrete types have a permutation operation defined as pi o x = x;    *)
urbanc@18430
   453
     (* which renders the proofs to be simple "simp_all"-proofs.              *)            
urbanc@18430
   454
     val thy19 =
urbanc@18279
   455
        let 
urbanc@18307
   456
	  fun discrete_pt_inst discrete_ty defn = 
urbanc@18307
   457
	     fold (fn ak_name => fn thy =>
urbanc@18307
   458
	     let
urbanc@18279
   459
	       val qu_class = Sign.full_name (sign_of thy) ("pt_"^ak_name);
urbanc@18307
   460
	       val simp_s = HOL_basic_ss addsimps [defn];
urbanc@18307
   461
               val proof = EVERY [AxClass.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)];      
urbanc@18279
   462
             in  
urbanc@18307
   463
	       AxClass.add_inst_arity_i (discrete_ty,[],[qu_class]) proof thy
urbanc@18307
   464
             end) ak_names;
urbanc@18307
   465
urbanc@18307
   466
          fun discrete_fs_inst discrete_ty defn = 
urbanc@18307
   467
	     fold (fn ak_name => fn thy =>
urbanc@18307
   468
	     let
urbanc@18307
   469
	       val qu_class = Sign.full_name (sign_of thy) ("fs_"^ak_name);
urbanc@18307
   470
	       val supp_def = thm "nominal.supp_def";
urbanc@18307
   471
               val simp_s = HOL_ss addsimps [supp_def,if_False,Collect_const,Finites.emptyI,defn];
urbanc@18307
   472
               val proof = EVERY [AxClass.intro_classes_tac [], asm_simp_tac simp_s 1];      
urbanc@18307
   473
             in  
urbanc@18307
   474
	       AxClass.add_inst_arity_i (discrete_ty,[],[qu_class]) proof thy
urbanc@18307
   475
             end) ak_names;  
urbanc@18355
   476
urbanc@18355
   477
          fun discrete_cp_inst discrete_ty defn = 
urbanc@18355
   478
	     fold (fn ak_name' => (fold (fn ak_name => fn thy =>
urbanc@18355
   479
	     let
urbanc@18355
   480
	       val qu_class = Sign.full_name (sign_of thy) ("cp_"^ak_name^"_"^ak_name');
urbanc@18355
   481
	       val supp_def = thm "nominal.supp_def";
urbanc@18355
   482
               val simp_s = HOL_ss addsimps [defn];
urbanc@18355
   483
               val proof = EVERY [AxClass.intro_classes_tac [], asm_simp_tac simp_s 1];      
urbanc@18355
   484
             in  
urbanc@18355
   485
	       AxClass.add_inst_arity_i (discrete_ty,[],[qu_class]) proof thy
urbanc@18355
   486
             end) ak_names)) ak_names;  
urbanc@18307
   487
          
urbanc@18279
   488
        in
urbanc@18430
   489
         thy19
urbanc@18307
   490
         |> discrete_pt_inst "nat"  (thm "perm_nat_def")
urbanc@18355
   491
         |> discrete_fs_inst "nat"  (thm "perm_nat_def") 
urbanc@18355
   492
         |> discrete_cp_inst "nat"  (thm "perm_nat_def") 
urbanc@18307
   493
         |> discrete_pt_inst "bool" (thm "perm_bool")
urbanc@18307
   494
         |> discrete_fs_inst "bool" (thm "perm_bool")
urbanc@18355
   495
         |> discrete_cp_inst "bool" (thm "perm_bool")
urbanc@18307
   496
         |> discrete_pt_inst "IntDef.int" (thm "perm_int_def")
urbanc@18355
   497
         |> discrete_fs_inst "IntDef.int" (thm "perm_int_def") 
urbanc@18355
   498
         |> discrete_cp_inst "IntDef.int" (thm "perm_int_def") 
urbanc@18307
   499
         |> discrete_pt_inst "List.char" (thm "perm_char_def")
urbanc@18307
   500
         |> discrete_fs_inst "List.char" (thm "perm_char_def")
urbanc@18355
   501
         |> discrete_cp_inst "List.char" (thm "perm_char_def")
urbanc@18279
   502
        end;
urbanc@18307
   503
urbanc@18279
   504
berghofe@18068
   505
       (*<<<<<<<  fs_<ak> class instances  >>>>>>>*)
berghofe@18068
   506
       (*=========================================*)
urbanc@18279
   507
       (* abbreviations for some lemmas *)
urbanc@18279
   508
       val fs1          = thm "fs1";
urbanc@18279
   509
       val fs_at_inst   = thm "fs_at_inst";
urbanc@18279
   510
       val fs_unit_inst = thm "fs_unit_inst";
urbanc@18279
   511
       val fs_bool_inst = thm "fs_bool_inst";
urbanc@18279
   512
       val fs_prod_inst = thm "fs_prod_inst";
urbanc@18279
   513
       val fs_list_inst = thm "fs_list_inst";
berghofe@18068
   514
berghofe@18068
   515
       (* shows that <ak> is an instance of fs_<ak>     *)
berghofe@18068
   516
       (* uses the theorem at_<ak>_inst                 *)
berghofe@18068
   517
       val (thy20,_) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   518
       let
berghofe@18068
   519
          val qu_name =  Sign.full_name (sign_of thy) ak_name;
berghofe@18068
   520
          val qu_class = Sign.full_name (sign_of thy) ("fs_"^ak_name);
urbanc@18307
   521
          val at_thm = PureThy.get_thm thy (Name ("at_"^ak_name^"_inst"));
berghofe@18068
   522
          val proof = EVERY [AxClass.intro_classes_tac [],
berghofe@18068
   523
                             rtac ((at_thm RS fs_at_inst) RS fs1) 1];      
berghofe@18068
   524
       in 
berghofe@18068
   525
	 (AxClass.add_inst_arity_i (qu_name,[],[qu_class]) proof thy,()) 
berghofe@18068
   526
       end) (thy19,ak_names_types);  
berghofe@18068
   527
berghofe@18068
   528
       (* shows that unit is an instance of fs_<ak>     *)
berghofe@18068
   529
       (* uses the theorem fs_unit_inst                 *)
berghofe@18068
   530
       val (thy21,_) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   531
       let
berghofe@18068
   532
          val qu_class = Sign.full_name (sign_of thy) ("fs_"^ak_name);
berghofe@18068
   533
          val proof = EVERY [AxClass.intro_classes_tac [],
berghofe@18068
   534
                             rtac (fs_unit_inst RS fs1) 1];      
berghofe@18068
   535
       in 
berghofe@18068
   536
	 (AxClass.add_inst_arity_i ("Product_Type.unit",[],[qu_class]) proof thy,()) 
berghofe@18068
   537
       end) (thy20,ak_names_types);  
berghofe@18068
   538
berghofe@18068
   539
       (* shows that bool is an instance of fs_<ak>     *)
berghofe@18068
   540
       (* uses the theorem fs_bool_inst                 *)
berghofe@18068
   541
       val (thy22,_) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   542
       let
berghofe@18068
   543
          val qu_class = Sign.full_name (sign_of thy) ("fs_"^ak_name);
berghofe@18068
   544
          val proof = EVERY [AxClass.intro_classes_tac [],
berghofe@18068
   545
                             rtac (fs_bool_inst RS fs1) 1];      
berghofe@18068
   546
       in 
berghofe@18068
   547
	 (AxClass.add_inst_arity_i ("bool",[],[qu_class]) proof thy,()) 
berghofe@18068
   548
       end) (thy21,ak_names_types);  
berghofe@18068
   549
berghofe@18068
   550
       (* shows that *(fs_<ak>,fs_<ak>) is an instance of fs_<ak>     *)
berghofe@18068
   551
       (* uses the theorem fs_prod_inst                               *)
berghofe@18068
   552
       val (thy23,_) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   553
       let
berghofe@18068
   554
          val qu_class = Sign.full_name (sign_of thy) ("fs_"^ak_name);
berghofe@18068
   555
          val fs_inst  = PureThy.get_thm thy (Name ("fs_"^ak_name^"_inst"));
berghofe@18068
   556
          val proof = EVERY [AxClass.intro_classes_tac [],
berghofe@18068
   557
                             rtac ((fs_inst RS (fs_inst RS fs_prod_inst)) RS fs1) 1];      
berghofe@18068
   558
       in 
berghofe@18068
   559
	 (AxClass.add_inst_arity_i ("*",[[qu_class],[qu_class]],[qu_class]) proof thy,()) 
berghofe@18068
   560
       end) (thy22,ak_names_types);  
berghofe@18068
   561
berghofe@18068
   562
       (* shows that list(fs_<ak>) is an instance of fs_<ak>     *)
berghofe@18068
   563
       (* uses the theorem fs_list_inst                          *)
berghofe@18068
   564
       val (thy24,_) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   565
       let
berghofe@18068
   566
          val qu_class = Sign.full_name (sign_of thy) ("fs_"^ak_name);
berghofe@18068
   567
          val fs_inst  = PureThy.get_thm thy (Name ("fs_"^ak_name^"_inst"));
berghofe@18068
   568
          val proof = EVERY [AxClass.intro_classes_tac [],
berghofe@18068
   569
                              rtac ((fs_inst RS fs_list_inst) RS fs1) 1];      
berghofe@18068
   570
       in 
berghofe@18068
   571
	 (AxClass.add_inst_arity_i ("List.list",[[qu_class]],[qu_class]) proof thy,()) 
berghofe@18068
   572
       end) (thy23,ak_names_types);  
berghofe@18068
   573
	   
berghofe@18068
   574
       (*<<<<<<<  cp_<ak>_<ai> class instances  >>>>>>>*)
berghofe@18068
   575
       (*==============================================*)
urbanc@18279
   576
       (* abbreviations for some lemmas *)
urbanc@18279
   577
       val cp1             = thm "cp1";
urbanc@18279
   578
       val cp_unit_inst    = thm "cp_unit_inst";
urbanc@18279
   579
       val cp_bool_inst    = thm "cp_bool_inst";
urbanc@18279
   580
       val cp_prod_inst    = thm "cp_prod_inst";
urbanc@18279
   581
       val cp_list_inst    = thm "cp_list_inst";
urbanc@18279
   582
       val cp_fun_inst     = thm "cp_fun_inst";
urbanc@18279
   583
       val cp_option_inst  = thm "cp_option_inst";
urbanc@18279
   584
       val cp_noption_inst = thm "cp_noption_inst";
urbanc@18279
   585
       val pt_perm_compose = thm "pt_perm_compose";
urbanc@18279
   586
       val dj_pp_forget    = thm "dj_perm_perm_forget";
berghofe@18068
   587
berghofe@18068
   588
       (* shows that <aj> is an instance of cp_<ak>_<ai>  *)
berghofe@18068
   589
       (* that needs a three-nested loop *)
berghofe@18068
   590
       val (thy25,_) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   591
	 foldl_map (fn (thy', (ak_name', T')) =>
berghofe@18068
   592
          foldl_map (fn (thy'', (ak_name'', T'')) =>
berghofe@18068
   593
            let
berghofe@18068
   594
              val qu_name =  Sign.full_name (sign_of thy'') ak_name;
berghofe@18068
   595
              val qu_class = Sign.full_name (sign_of thy'') ("cp_"^ak_name'^"_"^ak_name'');
berghofe@18068
   596
              val proof =
berghofe@18068
   597
                (if (ak_name'=ak_name'') then 
berghofe@18068
   598
		  (let
berghofe@18068
   599
                    val pt_inst  = PureThy.get_thm thy'' (Name ("pt_"^ak_name''^"_inst"));
berghofe@18068
   600
		    val at_inst  = PureThy.get_thm thy'' (Name ("at_"^ak_name''^"_inst"));
berghofe@18068
   601
                  in 
berghofe@18068
   602
		   EVERY [AxClass.intro_classes_tac [], 
berghofe@18068
   603
                          rtac (at_inst RS (pt_inst RS pt_perm_compose)) 1]
berghofe@18068
   604
                  end)
berghofe@18068
   605
		else
berghofe@18068
   606
		  (let 
berghofe@18068
   607
                     val dj_inst  = PureThy.get_thm thy'' (Name ("dj_"^ak_name''^"_"^ak_name'));
berghofe@18068
   608
		     val simp_s = HOL_basic_ss addsimps 
berghofe@18068
   609
                                        ((dj_inst RS dj_pp_forget)::
berghofe@18068
   610
                                         (PureThy.get_thmss thy'' 
berghofe@18068
   611
					   [Name (ak_name' ^"_prm_"^ak_name^"_def"),
berghofe@18068
   612
                                            Name (ak_name''^"_prm_"^ak_name^"_def")]));  
berghofe@18068
   613
		  in 
berghofe@18068
   614
                    EVERY [AxClass.intro_classes_tac [], simp_tac simp_s 1]
berghofe@18068
   615
                  end))
berghofe@18068
   616
	      in
berghofe@18068
   617
                (AxClass.add_inst_arity_i (qu_name,[],[qu_class]) proof thy'',())
berghofe@18068
   618
	      end)
berghofe@18068
   619
	   (thy', ak_names_types)) (thy, ak_names_types)) (thy24, ak_names_types);
berghofe@18068
   620
      
berghofe@18068
   621
       (* shows that unit is an instance of cp_<ak>_<ai>     *)
berghofe@18068
   622
       (* for every <ak>-combination                         *)
berghofe@18068
   623
       val (thy26,_) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   624
	 foldl_map (fn (thy', (ak_name', T')) =>
berghofe@18068
   625
          let
berghofe@18068
   626
            val qu_class = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
berghofe@18068
   627
            val proof = EVERY [AxClass.intro_classes_tac [],rtac (cp_unit_inst RS cp1) 1];     
berghofe@18068
   628
	  in
berghofe@18068
   629
            (AxClass.add_inst_arity_i ("Product_Type.unit",[],[qu_class]) proof thy',())
berghofe@18068
   630
	  end) 
berghofe@18068
   631
	   (thy, ak_names_types)) (thy25, ak_names_types);
berghofe@18068
   632
       
berghofe@18068
   633
       (* shows that bool is an instance of cp_<ak>_<ai>     *)
berghofe@18068
   634
       (* for every <ak>-combination                         *)
berghofe@18068
   635
       val (thy27,_) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   636
	 foldl_map (fn (thy', (ak_name', T')) =>
berghofe@18068
   637
           let
berghofe@18068
   638
	     val qu_class = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
berghofe@18068
   639
             val proof = EVERY [AxClass.intro_classes_tac [], rtac (cp_bool_inst RS cp1) 1];     
berghofe@18068
   640
	   in
berghofe@18068
   641
             (AxClass.add_inst_arity_i ("bool",[],[qu_class]) proof thy',())
berghofe@18068
   642
	   end) 
berghofe@18068
   643
	   (thy, ak_names_types)) (thy26, ak_names_types);
berghofe@18068
   644
berghofe@18068
   645
       (* shows that prod is an instance of cp_<ak>_<ai>     *)
berghofe@18068
   646
       (* for every <ak>-combination                         *)
berghofe@18068
   647
       val (thy28,_) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   648
	 foldl_map (fn (thy', (ak_name', T')) =>
berghofe@18068
   649
          let
berghofe@18068
   650
	    val qu_class = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
berghofe@18068
   651
            val cp_inst  = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
berghofe@18068
   652
            val proof = EVERY [AxClass.intro_classes_tac [],
berghofe@18068
   653
                               rtac ((cp_inst RS (cp_inst RS cp_prod_inst)) RS cp1) 1];     
berghofe@18068
   654
	  in
berghofe@18068
   655
            (AxClass.add_inst_arity_i ("*",[[qu_class],[qu_class]],[qu_class]) proof thy',())
berghofe@18068
   656
	  end)  
berghofe@18068
   657
	  (thy, ak_names_types)) (thy27, ak_names_types);
berghofe@18068
   658
berghofe@18068
   659
       (* shows that list is an instance of cp_<ak>_<ai>     *)
berghofe@18068
   660
       (* for every <ak>-combination                         *)
berghofe@18068
   661
       val (thy29,_) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   662
	 foldl_map (fn (thy', (ak_name', T')) =>
berghofe@18068
   663
           let
berghofe@18068
   664
	     val qu_class = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
berghofe@18068
   665
             val cp_inst  = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
berghofe@18068
   666
             val proof = EVERY [AxClass.intro_classes_tac [],
berghofe@18068
   667
                                rtac ((cp_inst RS cp_list_inst) RS cp1) 1];     
berghofe@18068
   668
	   in
berghofe@18068
   669
            (AxClass.add_inst_arity_i ("List.list",[[qu_class]],[qu_class]) proof thy',())
berghofe@18068
   670
	   end) 
berghofe@18068
   671
	   (thy, ak_names_types)) (thy28, ak_names_types);
berghofe@18068
   672
berghofe@18068
   673
       (* shows that function is an instance of cp_<ak>_<ai>     *)
berghofe@18068
   674
       (* for every <ak>-combination                             *)
berghofe@18068
   675
       val (thy30,_) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   676
	 foldl_map (fn (thy', (ak_name', T')) =>
berghofe@18068
   677
          let
berghofe@18068
   678
	    val qu_class = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
berghofe@18068
   679
            val cp_inst  = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
berghofe@18068
   680
            val pt_inst  = PureThy.get_thm thy' (Name ("pt_"^ak_name^"_inst"));
berghofe@18068
   681
            val at_inst  = PureThy.get_thm thy' (Name ("at_"^ak_name^"_inst"));
berghofe@18068
   682
            val proof = EVERY [AxClass.intro_classes_tac [],
berghofe@18068
   683
                    rtac ((at_inst RS (pt_inst RS (cp_inst RS (cp_inst RS cp_fun_inst)))) RS cp1) 1];  
berghofe@18068
   684
	  in
berghofe@18068
   685
            (AxClass.add_inst_arity_i ("fun",[[qu_class],[qu_class]],[qu_class]) proof thy',())
berghofe@18068
   686
	  end) 
berghofe@18068
   687
	  (thy, ak_names_types)) (thy29, ak_names_types);
berghofe@18068
   688
berghofe@18068
   689
       (* shows that option is an instance of cp_<ak>_<ai>     *)
berghofe@18068
   690
       (* for every <ak>-combination                           *)
berghofe@18068
   691
       val (thy31,_) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   692
	 foldl_map (fn (thy', (ak_name', T')) =>
berghofe@18068
   693
          let
berghofe@18068
   694
	    val qu_class = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
berghofe@18068
   695
            val cp_inst  = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
berghofe@18068
   696
            val proof = EVERY [AxClass.intro_classes_tac [],
berghofe@18068
   697
                               rtac ((cp_inst RS cp_option_inst) RS cp1) 1];     
berghofe@18068
   698
	  in
berghofe@18068
   699
            (AxClass.add_inst_arity_i ("Datatype.option",[[qu_class]],[qu_class]) proof thy',())
berghofe@18068
   700
	  end) 
berghofe@18068
   701
	  (thy, ak_names_types)) (thy30, ak_names_types);
berghofe@18068
   702
berghofe@18068
   703
       (* shows that nOption is an instance of cp_<ak>_<ai>     *)
berghofe@18068
   704
       (* for every <ak>-combination                            *)
berghofe@18068
   705
       val (thy32,_) = foldl_map (fn (thy, (ak_name, T)) =>
berghofe@18068
   706
	 foldl_map (fn (thy', (ak_name', T')) =>
berghofe@18068
   707
          let
berghofe@18068
   708
	    val qu_class = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
berghofe@18068
   709
            val cp_inst  = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
berghofe@18068
   710
            val proof = EVERY [AxClass.intro_classes_tac [],
berghofe@18068
   711
                               rtac ((cp_inst RS cp_noption_inst) RS cp1) 1];     
berghofe@18068
   712
	  in
berghofe@18068
   713
           (AxClass.add_inst_arity_i ("nominal.nOption",[[qu_class]],[qu_class]) proof thy',())
berghofe@18068
   714
	  end) 
berghofe@18068
   715
	  (thy, ak_names_types)) (thy31, ak_names_types);
berghofe@18068
   716
urbanc@18262
   717
       (* abbreviations for some lemmas *)
urbanc@18262
   718
       (*===============================*)
urbanc@18279
   719
       val abs_fun_pi        = thm "nominal.abs_fun_pi";
urbanc@18279
   720
       val abs_fun_pi_ineq   = thm "nominal.abs_fun_pi_ineq";
urbanc@18279
   721
       val abs_fun_eq        = thm "nominal.abs_fun_eq";
urbanc@18279
   722
       val dj_perm_forget    = thm "nominal.dj_perm_forget";
urbanc@18279
   723
       val dj_pp_forget      = thm "nominal.dj_perm_perm_forget";
urbanc@18279
   724
       val fresh_iff         = thm "nominal.fresh_abs_fun_iff";
urbanc@18279
   725
       val fresh_iff_ineq    = thm "nominal.fresh_abs_fun_iff_ineq";
urbanc@18279
   726
       val abs_fun_supp      = thm "nominal.abs_fun_supp";
urbanc@18279
   727
       val abs_fun_supp_ineq = thm "nominal.abs_fun_supp_ineq";
urbanc@18279
   728
       val pt_swap_bij       = thm "nominal.pt_swap_bij";
urbanc@18279
   729
       val pt_fresh_fresh    = thm "nominal.pt_fresh_fresh";
urbanc@18279
   730
       val pt_bij            = thm "nominal.pt_bij";
urbanc@18279
   731
       val pt_perm_compose   = thm "nominal.pt_perm_compose";
urbanc@18279
   732
       val perm_eq_app       = thm "nominal.perm_eq_app";
urbanc@18279
   733
       val at_fresh          = thm "nominal.at_fresh";
urbanc@18279
   734
       val at_calc           = thms "nominal.at_calc";
urbanc@18279
   735
       val at_supp           = thm "nominal.at_supp";
urbanc@18279
   736
       val dj_supp           = thm "nominal.dj_supp";
urbanc@18396
   737
       val fresh_left_ineq   = thm "nominal.pt_fresh_left_ineq";
urbanc@18396
   738
       val fresh_left        = thm "nominal.pt_fresh_left";
urbanc@18426
   739
       val fresh_bij_ineq    = thm "nominal.pt_fresh_bij_ineq";
urbanc@18426
   740
       val fresh_bij         = thm "nominal.pt_fresh_bij";
berghofe@18068
   741
urbanc@18262
   742
       (* Now we collect and instantiate some lemmas w.r.t. all atom      *)
urbanc@18262
   743
       (* types; this allows for example to use abs_perm (which is a      *)
urbanc@18262
   744
       (* collection of theorems) instead of thm abs_fun_pi with explicit *)
urbanc@18262
   745
       (* instantiations.                                                 *)
urbanc@18381
   746
       val (_,thy33) = 
urbanc@18262
   747
	 let 
urbanc@18279
   748
             (* takes a theorem thm and a list of theorems [t1,..,tn]            *)
urbanc@18279
   749
             (* produces a list of theorems of the form [t1 RS thm,..,tn RS thm] *) 
urbanc@18262
   750
             fun instR thm thms = map (fn ti => ti RS thm) thms;
berghofe@18068
   751
urbanc@18262
   752
             (* takes two theorem lists (hopefully of the same length ;o)                *)
urbanc@18262
   753
             (* produces a list of theorems of the form                                  *)
urbanc@18262
   754
             (* [t1 RS m1,..,tn RS mn] where [t1,..,tn] is thms1 and [m1,..,mn] is thms2 *) 
urbanc@18279
   755
             fun inst_zip thms1 thms2 = map (fn (t1,t2) => t1 RS t2) (thms1 ~~ thms2);
berghofe@18068
   756
urbanc@18262
   757
             (* takes a theorem list of the form [l1,...,ln]              *)
urbanc@18262
   758
             (* and a list of theorem lists of the form                   *)
urbanc@18262
   759
             (* [[h11,...,h1m],....,[hk1,....,hkm]                        *)
urbanc@18262
   760
             (* produces the list of theorem lists                        *)
urbanc@18262
   761
             (* [[l1 RS h11,...,l1 RS h1m],...,[ln RS hk1,...,ln RS hkm]] *)
urbanc@18279
   762
             fun inst_mult thms thmss = map (fn (t,ts) => instR t ts) (thms ~~ thmss);
urbanc@18279
   763
urbanc@18279
   764
             (* FIXME: these lists do not need to be created dynamically again *)
urbanc@18262
   765
berghofe@18068
   766
             (* list of all at_inst-theorems *)
urbanc@18262
   767
             val ats = map (fn ak => PureThy.get_thm thy32 (Name ("at_"^ak^"_inst"))) ak_names
berghofe@18068
   768
             (* list of all pt_inst-theorems *)
urbanc@18262
   769
             val pts = map (fn ak => PureThy.get_thm thy32 (Name ("pt_"^ak^"_inst"))) ak_names
urbanc@18262
   770
             (* list of all cp_inst-theorems as a collection of lists*)
berghofe@18068
   771
             val cps = 
urbanc@18262
   772
		 let fun cps_fun ak1 ak2 = PureThy.get_thm thy32 (Name ("cp_"^ak1^"_"^ak2^"_inst"))
urbanc@18262
   773
		 in map (fn aki => (map (cps_fun aki) ak_names)) ak_names end; 
urbanc@18262
   774
             (* list of all cp_inst-theorems that have different atom types *)
urbanc@18262
   775
             val cps' = 
urbanc@18262
   776
		let fun cps'_fun ak1 ak2 = 
urbanc@18262
   777
		if ak1=ak2 then NONE else SOME(PureThy.get_thm thy32 (Name ("cp_"^ak1^"_"^ak2^"_inst")))
urbanc@18262
   778
		in map (fn aki => (List.mapPartial I (map (cps'_fun aki) ak_names))) ak_names end;
berghofe@18068
   779
             (* list of all dj_inst-theorems *)
berghofe@18068
   780
             val djs = 
berghofe@18068
   781
	       let fun djs_fun (ak1,ak2) = 
urbanc@18262
   782
		     if ak1=ak2 then NONE else SOME(PureThy.get_thm thy32 (Name ("dj_"^ak2^"_"^ak1)))
urbanc@18262
   783
	       in List.mapPartial I (map djs_fun (Library.product ak_names ak_names)) end;
urbanc@18262
   784
             (* list of all fs_inst-theorems *)
urbanc@18262
   785
             val fss = map (fn ak => PureThy.get_thm thy32 (Name ("fs_"^ak^"_inst"))) ak_names
berghofe@18068
   786
urbanc@18262
   787
             fun inst_pt thms = Library.flat (map (fn ti => instR ti pts) thms); 
urbanc@18262
   788
             fun inst_at thms = Library.flat (map (fn ti => instR ti ats) thms);               
urbanc@18262
   789
             fun inst_fs thms = Library.flat (map (fn ti => instR ti fss) thms);
urbanc@18262
   790
	     fun inst_pt_at thms = inst_zip ats (inst_pt thms);			
urbanc@18262
   791
             fun inst_dj thms = Library.flat (map (fn ti => instR ti djs) thms);  
urbanc@18262
   792
	     fun inst_pt_pt_at_cp thms = 
urbanc@18262
   793
		 Library.flat (inst_mult (inst_zip ats (inst_zip pts (inst_pt thms))) cps);
urbanc@18262
   794
             fun inst_pt_at_fs thms = inst_zip (inst_fs [fs1]) (inst_zip ats (inst_pt thms));
urbanc@18396
   795
	     fun inst_pt_pt_at_cp thms = 
urbanc@18279
   796
		 let val i_pt_pt_at = inst_zip ats (inst_zip pts (inst_pt thms));
urbanc@18279
   797
                     val i_pt_pt_at_cp = Library.flat (inst_mult i_pt_pt_at cps');
urbanc@18396
   798
		 in i_pt_pt_at_cp end;
urbanc@18396
   799
             fun inst_pt_pt_at_cp_dj thms = inst_zip djs (inst_pt_pt_at_cp thms);
berghofe@18068
   800
           in
urbanc@18262
   801
            thy32 
berghofe@18068
   802
	    |>   PureThy.add_thmss [(("alpha", inst_pt_at [abs_fun_eq]),[])]
urbanc@18381
   803
            ||>> PureThy.add_thmss [(("perm_swap", inst_pt_at [pt_swap_bij]),[])]
urbanc@18381
   804
            ||>> PureThy.add_thmss [(("perm_fresh_fresh", inst_pt_at [pt_fresh_fresh]),[])]
urbanc@18381
   805
            ||>> PureThy.add_thmss [(("perm_bij", inst_pt_at [pt_bij]),[])]
urbanc@18381
   806
            ||>> PureThy.add_thmss [(("perm_compose", inst_pt_at [pt_perm_compose]),[])]
urbanc@18381
   807
            ||>> PureThy.add_thmss [(("perm_app_eq", inst_pt_at [perm_eq_app]),[])]
urbanc@18381
   808
            ||>> PureThy.add_thmss [(("supp_atm", (inst_at [at_supp]) @ (inst_dj [dj_supp])),[])]
urbanc@18381
   809
            ||>> PureThy.add_thmss [(("fresh_atm", inst_at [at_fresh]),[])]
urbanc@18381
   810
            ||>> PureThy.add_thmss [(("calc_atm", inst_at at_calc),[])]
urbanc@18381
   811
            ||>> PureThy.add_thmss
urbanc@18279
   812
	      let val thms1 = inst_pt_at [abs_fun_pi]
urbanc@18279
   813
		  and thms2 = inst_pt_pt_at_cp [abs_fun_pi_ineq]
urbanc@18279
   814
	      in [(("abs_perm", thms1 @ thms2),[])] end
urbanc@18381
   815
            ||>> PureThy.add_thmss
urbanc@18279
   816
	      let val thms1 = inst_dj [dj_perm_forget]
urbanc@18279
   817
		  and thms2 = inst_dj [dj_pp_forget]
urbanc@18279
   818
              in [(("perm_dj", thms1 @ thms2),[])] end
urbanc@18381
   819
            ||>> PureThy.add_thmss
urbanc@18279
   820
	      let val thms1 = inst_pt_at_fs [fresh_iff]
urbanc@18279
   821
		  and thms2 = inst_pt_pt_at_cp_dj [fresh_iff_ineq]
urbanc@18262
   822
	    in [(("abs_fresh", thms1 @ thms2),[])] end
urbanc@18381
   823
	    ||>> PureThy.add_thmss
urbanc@18279
   824
	      let val thms1 = inst_pt_at [abs_fun_supp]
urbanc@18279
   825
		  and thms2 = inst_pt_at_fs [abs_fun_supp]
urbanc@18279
   826
		  and thms3 = inst_pt_pt_at_cp_dj [abs_fun_supp_ineq]
urbanc@18279
   827
	      in [(("abs_supp", thms1 @ thms2 @ thms3),[])] end
urbanc@18396
   828
            ||>> PureThy.add_thmss
urbanc@18396
   829
	      let val thms1 = inst_pt_at [fresh_left]
urbanc@18396
   830
		  and thms2 = inst_pt_pt_at_cp [fresh_left_ineq]
urbanc@18396
   831
	      in [(("fresh_left", thms1 @ thms2),[])] end
urbanc@18426
   832
            ||>> PureThy.add_thmss
urbanc@18426
   833
	      let val thms1 = inst_pt_at [fresh_bij]
urbanc@18426
   834
		  and thms2 = inst_pt_pt_at_cp [fresh_bij_ineq]
urbanc@18426
   835
	      in [(("fresh_eqvt", thms1 @ thms2),[])] end
berghofe@18068
   836
	   end;
berghofe@18068
   837
berghofe@18068
   838
    in NominalData.put (fold Symtab.update (map (rpair ()) full_ak_names)
urbanc@18262
   839
      (NominalData.get thy11)) thy33
berghofe@18068
   840
    end;
berghofe@18068
   841
berghofe@18068
   842
berghofe@18068
   843
(* syntax und parsing *)
berghofe@18068
   844
structure P = OuterParse and K = OuterKeyword;
berghofe@18068
   845
berghofe@18068
   846
val atom_declP =
berghofe@18068
   847
  OuterSyntax.command "atom_decl" "Declare new kinds of atoms" K.thy_decl
berghofe@18068
   848
    (Scan.repeat1 P.name >> (Toplevel.theory o create_nom_typedecls));
berghofe@18068
   849
berghofe@18068
   850
val _ = OuterSyntax.add_parsers [atom_declP];
berghofe@18068
   851
berghofe@18068
   852
val setup = [NominalData.init];
berghofe@18068
   853
berghofe@18068
   854
end;