src/HOL/Nominal/nominal_atoms.ML
author wenzelm
Sat Jul 08 12:54:33 2006 +0200 (2006-07-08)
changeset 20046 9c8909fc5865
parent 19993 e0a5783d708f
child 20097 be2d96bbf39c
permissions -rw-r--r--
Goal.prove_global;
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(*  Title:      HOL/Nominal/nominal_atoms.ML
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    ID:         $Id$
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    Author:     Christian Urban and Stefan Berghofer, TU Muenchen
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Declaration of atom types to be used in nominal datatypes.
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*)
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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
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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_unchecked_i true [((name, def2),[])])
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            |> PrimrecPackage.add_primrec_unchecked_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_unchecked_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_unchecked_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, Goal.prove_global 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 (pt_ax_classes,thy7) =  fold_map (fn (ak_name, T) => fn thy =>
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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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          AxClass.define_class_i (cl_name, ["HOL.type"]) []
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                [((cl_name ^ "1", [Simplifier.simp_add]), [axiom1]),
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                 ((cl_name ^ "2", []), [axiom2]),                           
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                 ((cl_name ^ "3", []), [axiom3])] thy                          
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      end) ak_names_types thy6;
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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, Goal.prove_global 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 (fs_ax_classes,thy11) =  fold_map (fn (ak_name, T) => fn thy =>
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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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        AxClass.define_class_i (cl_name, [pt_name]) [] [((cl_name ^ "1", []), [axiom1])] thy            
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       end) ak_names_types thy8; 
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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);
berghofe@18068
   281
berghofe@18068
   282
         val proof = fn _ => auto_tac (claset(),simp_s);
berghofe@18068
   283
       in 
wenzelm@20046
   284
         ((name, Goal.prove_global thy11 [] [] statement proof), []) 
berghofe@18068
   285
       end) ak_names_types);
berghofe@18068
   286
berghofe@18068
   287
       (* declares for every atom-kind combination an axclass            *)
berghofe@18068
   288
       (* cp_<ak1>_<ak2> giving a composition property                   *)
berghofe@18068
   289
       (* cp_<ak1>_<ak2>1: pi1 o pi2 o x = (pi1 o pi2) o (pi1 o x)       *)
urbanc@18438
   290
        val (_,thy12b) = fold_map (fn (ak_name, T) => fn thy =>
urbanc@18438
   291
	 fold_map (fn (ak_name', T') => fn thy' =>
berghofe@18068
   292
	     let
berghofe@18068
   293
	       val cl_name = "cp_"^ak_name^"_"^ak_name';
berghofe@18068
   294
	       val ty = TFree("'a",["HOL.type"]);
berghofe@18068
   295
               val x   = Free ("x", ty);
berghofe@18068
   296
               val pi1 = Free ("pi1", mk_permT T);
berghofe@18068
   297
	       val pi2 = Free ("pi2", mk_permT T');                  
berghofe@19494
   298
	       val cperm1 = Const ("Nominal.perm", mk_permT T  --> ty --> ty);
berghofe@19494
   299
               val cperm2 = Const ("Nominal.perm", mk_permT T' --> ty --> ty);
berghofe@19494
   300
               val cperm3 = Const ("Nominal.perm", mk_permT T  --> mk_permT T' --> mk_permT T');
berghofe@18068
   301
berghofe@18068
   302
               val ax1   = HOLogic.mk_Trueprop 
berghofe@18068
   303
			   (HOLogic.mk_eq (cperm1 $ pi1 $ (cperm2 $ pi2 $ x), 
berghofe@18068
   304
                                           cperm2 $ (cperm3 $ pi1 $ pi2) $ (cperm1 $ pi1 $ x)));
berghofe@18068
   305
	       in  
wenzelm@19509
   306
		 AxClass.define_class_i (cl_name, ["HOL.type"]) [] [((cl_name ^ "1", []), [ax1])] thy'  
urbanc@18438
   307
	       end) ak_names_types thy) ak_names_types thy12;
berghofe@18068
   308
berghofe@18068
   309
        (* proves for every <ak>-combination a cp_<ak1>_<ak2>_inst theorem;     *)
berghofe@18068
   310
        (* lemma cp_<ak1>_<ak2>_inst:                                           *)
berghofe@18068
   311
        (* cp TYPE('a::cp_<ak1>_<ak2>) TYPE(<ak1>) TYPE(<ak2>)                  *)
urbanc@18381
   312
        val (cp_thms,thy12c) = fold_map (fn (ak_name, T) => fn thy =>
urbanc@18381
   313
	 fold_map (fn (ak_name', T') => fn thy' =>
berghofe@18068
   314
           let
berghofe@18068
   315
             val ak_name_qu  = Sign.full_name (sign_of thy') (ak_name);
berghofe@18068
   316
	     val ak_name_qu' = Sign.full_name (sign_of thy') (ak_name');
berghofe@18068
   317
             val cp_name_qu  = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
berghofe@18068
   318
             val i_type0 = TFree("'a",[cp_name_qu]);
berghofe@18068
   319
             val i_type1 = Type(ak_name_qu,[]);
berghofe@18068
   320
             val i_type2 = Type(ak_name_qu',[]);
berghofe@19494
   321
	     val ccp = Const ("Nominal.cp",
berghofe@18068
   322
                             (Term.itselfT i_type0)-->(Term.itselfT i_type1)-->
berghofe@18068
   323
                                                      (Term.itselfT i_type2)-->HOLogic.boolT);
berghofe@18068
   324
             val at_type  = Logic.mk_type i_type1;
berghofe@18068
   325
             val at_type' = Logic.mk_type i_type2;
berghofe@18068
   326
	     val cp_type  = Logic.mk_type i_type0;
berghofe@18068
   327
             val simp_s   = HOL_basic_ss addsimps PureThy.get_thmss thy' [(Name "cp_def")];
berghofe@18068
   328
	     val cp1      = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"1"));
berghofe@18068
   329
berghofe@18068
   330
	     val name = "cp_"^ak_name^ "_"^ak_name'^"_inst";
berghofe@18068
   331
             val statement = HOLogic.mk_Trueprop (ccp $ cp_type $ at_type $ at_type');
berghofe@18068
   332
berghofe@18068
   333
             val proof = fn _ => EVERY [auto_tac (claset(),simp_s), rtac cp1 1];
berghofe@18068
   334
	   in
wenzelm@20046
   335
	     PureThy.add_thms [((name, Goal.prove_global thy' [] [] statement proof), [])] thy'
berghofe@18068
   336
	   end) 
urbanc@18381
   337
           ak_names_types thy) ak_names_types thy12b;
berghofe@18068
   338
       
berghofe@18068
   339
        (* proves for every non-trivial <ak>-combination a disjointness   *)
berghofe@18068
   340
        (* theorem; i.e. <ak1> != <ak2>                                   *)
berghofe@18068
   341
        (* lemma ds_<ak1>_<ak2>:                                          *)
berghofe@18068
   342
        (* dj TYPE(<ak1>) TYPE(<ak2>)                                     *)
urbanc@18381
   343
        val (dj_thms, thy12d) = fold_map (fn (ak_name,T) => fn thy =>
urbanc@18381
   344
	  fold_map (fn (ak_name',T') => fn thy' =>
berghofe@18068
   345
          (if not (ak_name = ak_name') 
berghofe@18068
   346
           then 
berghofe@18068
   347
	       let
berghofe@18068
   348
		 val ak_name_qu  = Sign.full_name (sign_of thy') (ak_name);
berghofe@18068
   349
	         val ak_name_qu' = Sign.full_name (sign_of thy') (ak_name');
berghofe@18068
   350
                 val i_type1 = Type(ak_name_qu,[]);
berghofe@18068
   351
                 val i_type2 = Type(ak_name_qu',[]);
berghofe@19494
   352
	         val cdj = Const ("Nominal.disjoint",
berghofe@18068
   353
                           (Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
berghofe@18068
   354
                 val at_type  = Logic.mk_type i_type1;
berghofe@18068
   355
                 val at_type' = Logic.mk_type i_type2;
berghofe@18068
   356
                 val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy' 
berghofe@18068
   357
					   [Name "disjoint_def",
berghofe@18068
   358
                                            Name (ak_name^"_prm_"^ak_name'^"_def"),
berghofe@18068
   359
                                            Name (ak_name'^"_prm_"^ak_name^"_def")];
berghofe@18068
   360
berghofe@18068
   361
	         val name = "dj_"^ak_name^"_"^ak_name';
berghofe@18068
   362
                 val statement = HOLogic.mk_Trueprop (cdj $ at_type $ at_type');
berghofe@18068
   363
berghofe@18068
   364
                 val proof = fn _ => auto_tac (claset(),simp_s);
berghofe@18068
   365
	       in
wenzelm@20046
   366
		PureThy.add_thms [((name, Goal.prove_global thy' [] [] statement proof), [])] thy'
berghofe@18068
   367
	       end
berghofe@18068
   368
           else 
urbanc@18381
   369
            ([],thy')))  (* do nothing branch, if ak_name = ak_name' *) 
urbanc@18381
   370
	    ak_names_types thy) ak_names_types thy12c;
berghofe@18068
   371
berghofe@18068
   372
     (*<<<<<<<  pt_<ak> class instances  >>>>>>>*)
berghofe@18068
   373
     (*=========================================*)
urbanc@18279
   374
     (* some abbreviations for theorems *)
urbanc@18279
   375
      val pt1           = thm "pt1";
urbanc@18279
   376
      val pt2           = thm "pt2";
urbanc@18279
   377
      val pt3           = thm "pt3";
urbanc@18279
   378
      val at_pt_inst    = thm "at_pt_inst";
urbanc@18279
   379
      val pt_set_inst   = thm "pt_set_inst"; 
urbanc@18279
   380
      val pt_unit_inst  = thm "pt_unit_inst";
urbanc@18279
   381
      val pt_prod_inst  = thm "pt_prod_inst"; 
urbanc@18600
   382
      val pt_nprod_inst = thm "pt_nprod_inst"; 
urbanc@18279
   383
      val pt_list_inst  = thm "pt_list_inst";   
urbanc@18279
   384
      val pt_optn_inst  = thm "pt_option_inst";   
urbanc@18279
   385
      val pt_noptn_inst = thm "pt_noption_inst";   
urbanc@18279
   386
      val pt_fun_inst   = thm "pt_fun_inst";     
berghofe@18068
   387
urbanc@18435
   388
     (* for all atom-kind combinations <ak>/<ak'> show that        *)
urbanc@18435
   389
     (* every <ak> is an instance of pt_<ak'>; the proof for       *)
urbanc@18435
   390
     (* ak!=ak' is by definition; the case ak=ak' uses at_pt_inst. *)
urbanc@18431
   391
     val thy13 = fold (fn ak_name => fn thy =>
urbanc@18431
   392
	fold (fn ak_name' => fn thy' =>
urbanc@18431
   393
         let
urbanc@18431
   394
           val qu_name =  Sign.full_name (sign_of thy') ak_name';
urbanc@18431
   395
           val cls_name = Sign.full_name (sign_of thy') ("pt_"^ak_name);
urbanc@18431
   396
           val at_inst  = PureThy.get_thm thy' (Name ("at_"^ak_name'^"_inst")); 
urbanc@18431
   397
berghofe@19133
   398
           val proof1 = EVERY [ClassPackage.intro_classes_tac [],
berghofe@18068
   399
                                 rtac ((at_inst RS at_pt_inst) RS pt1) 1,
berghofe@18068
   400
                                 rtac ((at_inst RS at_pt_inst) RS pt2) 1,
berghofe@18068
   401
                                 rtac ((at_inst RS at_pt_inst) RS pt3) 1,
berghofe@18068
   402
                                 atac 1];
urbanc@18431
   403
           val simp_s = HOL_basic_ss addsimps 
urbanc@18431
   404
                        PureThy.get_thmss thy' [Name (ak_name^"_prm_"^ak_name'^"_def")];  
berghofe@19133
   405
           val proof2 = EVERY [ClassPackage.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)];
urbanc@18431
   406
urbanc@18431
   407
         in
urbanc@18431
   408
           thy'
berghofe@19275
   409
           |> AxClass.prove_arity (qu_name,[],[cls_name])
urbanc@18431
   410
              (if ak_name = ak_name' then proof1 else proof2)
urbanc@18431
   411
         end) ak_names thy) ak_names thy12c;
berghofe@18068
   412
urbanc@18430
   413
     (* show that                       *)
urbanc@18430
   414
     (*      fun(pt_<ak>,pt_<ak>)       *)
urbanc@18579
   415
     (*      noption(pt_<ak>)           *)
urbanc@18430
   416
     (*      option(pt_<ak>)            *)
urbanc@18430
   417
     (*      list(pt_<ak>)              *)
urbanc@18430
   418
     (*      *(pt_<ak>,pt_<ak>)         *)
urbanc@18600
   419
     (*      nprod(pt_<ak>,pt_<ak>)     *)
urbanc@18430
   420
     (*      unit                       *)
urbanc@18430
   421
     (*      set(pt_<ak>)               *)
urbanc@18430
   422
     (* are instances of pt_<ak>        *)
urbanc@18431
   423
     val thy18 = 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 = 
berghofe@19133
   430
	      EVERY [ClassPackage.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@18600
   438
          val pt_thm_nprod = pt_inst RS (pt_inst RS pt_nprod_inst);
urbanc@18430
   439
          val pt_thm_unit  = pt_unit_inst;
urbanc@18430
   440
          val pt_thm_set   = pt_inst RS pt_set_inst
berghofe@18068
   441
       in 
urbanc@18430
   442
	thy
berghofe@19275
   443
	|> AxClass.prove_arity ("fun",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_fun)
berghofe@19494
   444
        |> AxClass.prove_arity ("Nominal.noption",[[cls_name]],[cls_name]) (pt_proof pt_thm_noptn) 
berghofe@19275
   445
        |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (pt_proof pt_thm_optn)
berghofe@19275
   446
        |> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (pt_proof pt_thm_list)
berghofe@19275
   447
        |> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_prod)
berghofe@19494
   448
        |> AxClass.prove_arity ("Nominal.nprod",[[cls_name],[cls_name]],[cls_name]) 
urbanc@18600
   449
                                    (pt_proof pt_thm_nprod)
berghofe@19275
   450
        |> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (pt_proof pt_thm_unit)
berghofe@19275
   451
        |> AxClass.prove_arity ("set",[[cls_name]],[cls_name]) (pt_proof pt_thm_set)
urbanc@18430
   452
     end) ak_names thy13; 
berghofe@18068
   453
berghofe@18068
   454
       (*<<<<<<<  fs_<ak> class instances  >>>>>>>*)
berghofe@18068
   455
       (*=========================================*)
urbanc@18279
   456
       (* abbreviations for some lemmas *)
urbanc@18431
   457
       val fs1            = thm "fs1";
urbanc@18431
   458
       val fs_at_inst     = thm "fs_at_inst";
urbanc@18431
   459
       val fs_unit_inst   = thm "fs_unit_inst";
urbanc@18431
   460
       val fs_prod_inst   = thm "fs_prod_inst";
urbanc@18600
   461
       val fs_nprod_inst  = thm "fs_nprod_inst";
urbanc@18431
   462
       val fs_list_inst   = thm "fs_list_inst";
urbanc@18431
   463
       val fs_option_inst = thm "fs_option_inst";
urbanc@18437
   464
       val dj_supp        = thm "dj_supp"
berghofe@18068
   465
berghofe@18068
   466
       (* shows that <ak> is an instance of fs_<ak>     *)
berghofe@18068
   467
       (* uses the theorem at_<ak>_inst                 *)
urbanc@18431
   468
       val thy20 = fold (fn ak_name => fn thy =>
urbanc@18437
   469
	fold (fn ak_name' => fn thy' => 
urbanc@18437
   470
        let
urbanc@18437
   471
           val qu_name =  Sign.full_name (sign_of thy') ak_name';
urbanc@18437
   472
           val qu_class = Sign.full_name (sign_of thy') ("fs_"^ak_name);
urbanc@18437
   473
           val proof = 
urbanc@18437
   474
	       (if ak_name = ak_name'
urbanc@18437
   475
	        then
urbanc@18437
   476
	          let val at_thm = PureThy.get_thm thy' (Name ("at_"^ak_name^"_inst"));
berghofe@19133
   477
                  in  EVERY [ClassPackage.intro_classes_tac [],
urbanc@18437
   478
                             rtac ((at_thm RS fs_at_inst) RS fs1) 1] end
urbanc@18437
   479
                else
urbanc@18437
   480
		  let val dj_inst = PureThy.get_thm thy' (Name ("dj_"^ak_name'^"_"^ak_name));
urbanc@18437
   481
                      val simp_s = HOL_basic_ss addsimps [dj_inst RS dj_supp, Finites.emptyI]; 
berghofe@19133
   482
                  in EVERY [ClassPackage.intro_classes_tac [], asm_simp_tac simp_s 1] end)      
urbanc@18437
   483
        in 
berghofe@19275
   484
	 AxClass.prove_arity (qu_name,[],[qu_class]) proof thy' 
urbanc@18437
   485
        end) ak_names thy) ak_names thy18;
berghofe@18068
   486
urbanc@18431
   487
       (* shows that                  *)
urbanc@18431
   488
       (*    unit                     *)
urbanc@18431
   489
       (*    *(fs_<ak>,fs_<ak>)       *)
urbanc@18600
   490
       (*    nprod(fs_<ak>,fs_<ak>)   *)
urbanc@18431
   491
       (*    list(fs_<ak>)            *)
urbanc@18431
   492
       (*    option(fs_<ak>)          *) 
urbanc@18431
   493
       (* are instances of fs_<ak>    *)
berghofe@18068
   494
urbanc@18431
   495
       val thy24 = fold (fn ak_name => fn thy => 
urbanc@18431
   496
        let
urbanc@18431
   497
          val cls_name = Sign.full_name (sign_of thy) ("fs_"^ak_name);
berghofe@18068
   498
          val fs_inst  = PureThy.get_thm thy (Name ("fs_"^ak_name^"_inst"));
berghofe@19133
   499
          fun fs_proof thm = EVERY [ClassPackage.intro_classes_tac [], rtac (thm RS fs1) 1];      
berghofe@18068
   500
urbanc@18600
   501
          val fs_thm_unit  = fs_unit_inst;
urbanc@18600
   502
          val fs_thm_prod  = fs_inst RS (fs_inst RS fs_prod_inst);
urbanc@18600
   503
          val fs_thm_nprod = fs_inst RS (fs_inst RS fs_nprod_inst);
urbanc@18600
   504
          val fs_thm_list  = fs_inst RS fs_list_inst;
urbanc@18600
   505
          val fs_thm_optn  = fs_inst RS fs_option_inst;
urbanc@18431
   506
        in 
urbanc@18431
   507
         thy 
berghofe@19275
   508
         |> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (fs_proof fs_thm_unit) 
berghofe@19275
   509
         |> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (fs_proof fs_thm_prod) 
berghofe@19494
   510
         |> AxClass.prove_arity ("Nominal.nprod",[[cls_name],[cls_name]],[cls_name]) 
urbanc@18600
   511
                                     (fs_proof fs_thm_nprod) 
berghofe@19275
   512
         |> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (fs_proof fs_thm_list)
berghofe@19275
   513
         |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (fs_proof fs_thm_optn)
urbanc@18431
   514
        end) ak_names thy20; 
urbanc@18431
   515
berghofe@18068
   516
       (*<<<<<<<  cp_<ak>_<ai> class instances  >>>>>>>*)
berghofe@18068
   517
       (*==============================================*)
urbanc@18279
   518
       (* abbreviations for some lemmas *)
urbanc@18279
   519
       val cp1             = thm "cp1";
urbanc@18279
   520
       val cp_unit_inst    = thm "cp_unit_inst";
urbanc@18279
   521
       val cp_bool_inst    = thm "cp_bool_inst";
urbanc@18279
   522
       val cp_prod_inst    = thm "cp_prod_inst";
urbanc@18279
   523
       val cp_list_inst    = thm "cp_list_inst";
urbanc@18279
   524
       val cp_fun_inst     = thm "cp_fun_inst";
urbanc@18279
   525
       val cp_option_inst  = thm "cp_option_inst";
urbanc@18279
   526
       val cp_noption_inst = thm "cp_noption_inst";
urbanc@18279
   527
       val pt_perm_compose = thm "pt_perm_compose";
urbanc@19477
   528
       
urbanc@18279
   529
       val dj_pp_forget    = thm "dj_perm_perm_forget";
berghofe@18068
   530
berghofe@18068
   531
       (* shows that <aj> is an instance of cp_<ak>_<ai>  *)
urbanc@18432
   532
       (* for every  <ak>/<ai>-combination                *)
urbanc@18432
   533
       val thy25 = fold (fn ak_name => fn thy => 
urbanc@18432
   534
	 fold (fn ak_name' => fn thy' => 
urbanc@18432
   535
          fold (fn ak_name'' => fn thy'' => 
berghofe@18068
   536
            let
urbanc@18432
   537
              val name =  Sign.full_name (sign_of thy'') ak_name;
urbanc@18432
   538
              val cls_name = Sign.full_name (sign_of thy'') ("cp_"^ak_name'^"_"^ak_name'');
berghofe@18068
   539
              val proof =
berghofe@18068
   540
                (if (ak_name'=ak_name'') then 
berghofe@18068
   541
		  (let
berghofe@18068
   542
                    val pt_inst  = PureThy.get_thm thy'' (Name ("pt_"^ak_name''^"_inst"));
berghofe@18068
   543
		    val at_inst  = PureThy.get_thm thy'' (Name ("at_"^ak_name''^"_inst"));
berghofe@18068
   544
                  in 
berghofe@19133
   545
		   EVERY [ClassPackage.intro_classes_tac [], 
berghofe@18068
   546
                          rtac (at_inst RS (pt_inst RS pt_perm_compose)) 1]
berghofe@18068
   547
                  end)
berghofe@18068
   548
		else
berghofe@18068
   549
		  (let 
berghofe@18068
   550
                     val dj_inst  = PureThy.get_thm thy'' (Name ("dj_"^ak_name''^"_"^ak_name'));
berghofe@18068
   551
		     val simp_s = HOL_basic_ss addsimps 
berghofe@18068
   552
                                        ((dj_inst RS dj_pp_forget)::
berghofe@18068
   553
                                         (PureThy.get_thmss thy'' 
berghofe@18068
   554
					   [Name (ak_name' ^"_prm_"^ak_name^"_def"),
berghofe@18068
   555
                                            Name (ak_name''^"_prm_"^ak_name^"_def")]));  
berghofe@18068
   556
		  in 
berghofe@19133
   557
                    EVERY [ClassPackage.intro_classes_tac [], simp_tac simp_s 1]
berghofe@18068
   558
                  end))
berghofe@18068
   559
	      in
berghofe@19275
   560
                AxClass.prove_arity (name,[],[cls_name]) proof thy''
urbanc@18432
   561
	      end) ak_names thy') ak_names thy) ak_names thy24;
berghofe@18068
   562
      
urbanc@18432
   563
       (* shows that                                                    *) 
urbanc@18432
   564
       (*      units                                                    *) 
urbanc@18432
   565
       (*      products                                                 *)
urbanc@18432
   566
       (*      lists                                                    *)
urbanc@18432
   567
       (*      functions                                                *)
urbanc@18432
   568
       (*      options                                                  *)
urbanc@18432
   569
       (*      noptions                                                 *)
urbanc@18432
   570
       (* are instances of cp_<ak>_<ai> for every <ak>/<ai>-combination *)
urbanc@18432
   571
       val thy26 = fold (fn ak_name => fn thy =>
urbanc@18432
   572
	fold (fn ak_name' => fn thy' =>
urbanc@18432
   573
        let
urbanc@18432
   574
            val cls_name = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
berghofe@18068
   575
            val cp_inst  = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
berghofe@18068
   576
            val pt_inst  = PureThy.get_thm thy' (Name ("pt_"^ak_name^"_inst"));
berghofe@18068
   577
            val at_inst  = PureThy.get_thm thy' (Name ("at_"^ak_name^"_inst"));
urbanc@18432
   578
berghofe@19133
   579
            fun cp_proof thm  = EVERY [ClassPackage.intro_classes_tac [],rtac (thm RS cp1) 1];     
urbanc@18432
   580
	  
urbanc@18432
   581
            val cp_thm_unit = cp_unit_inst;
urbanc@18432
   582
            val cp_thm_prod = cp_inst RS (cp_inst RS cp_prod_inst);
urbanc@18432
   583
            val cp_thm_list = cp_inst RS cp_list_inst;
urbanc@18432
   584
            val cp_thm_fun  = at_inst RS (pt_inst RS (cp_inst RS (cp_inst RS cp_fun_inst)));
urbanc@18432
   585
            val cp_thm_optn = cp_inst RS cp_option_inst;
urbanc@18432
   586
            val cp_thm_noptn = cp_inst RS cp_noption_inst;
urbanc@18432
   587
        in
urbanc@18432
   588
         thy'
berghofe@19275
   589
         |> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (cp_proof cp_thm_unit)
berghofe@19275
   590
	 |> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_prod)
berghofe@19275
   591
         |> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (cp_proof cp_thm_list)
berghofe@19275
   592
         |> AxClass.prove_arity ("fun",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_fun)
berghofe@19275
   593
         |> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (cp_proof cp_thm_optn)
berghofe@19494
   594
         |> AxClass.prove_arity ("Nominal.noption",[[cls_name]],[cls_name]) (cp_proof cp_thm_noptn)
urbanc@18432
   595
        end) ak_names thy) ak_names thy25;
urbanc@18432
   596
       
urbanc@18432
   597
     (* show that discrete nominal types are permutation types, finitely     *) 
urbanc@18432
   598
     (* supported and have the commutation property                          *)
urbanc@18432
   599
     (* discrete types have a permutation operation defined as pi o x = x;   *)
urbanc@18432
   600
     (* which renders the proofs to be simple "simp_all"-proofs.             *)            
urbanc@18432
   601
     val thy32 =
urbanc@18432
   602
        let 
urbanc@18432
   603
	  fun discrete_pt_inst discrete_ty defn = 
urbanc@18432
   604
	     fold (fn ak_name => fn thy =>
urbanc@18432
   605
	     let
urbanc@18432
   606
	       val qu_class = Sign.full_name (sign_of thy) ("pt_"^ak_name);
urbanc@18432
   607
	       val simp_s = HOL_basic_ss addsimps [defn];
berghofe@19133
   608
               val proof = EVERY [ClassPackage.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)];      
urbanc@18432
   609
             in  
berghofe@19275
   610
	       AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
urbanc@18432
   611
             end) ak_names;
berghofe@18068
   612
urbanc@18432
   613
          fun discrete_fs_inst discrete_ty defn = 
urbanc@18432
   614
	     fold (fn ak_name => fn thy =>
urbanc@18432
   615
	     let
urbanc@18432
   616
	       val qu_class = Sign.full_name (sign_of thy) ("fs_"^ak_name);
berghofe@19494
   617
	       val supp_def = thm "Nominal.supp_def";
urbanc@18432
   618
               val simp_s = HOL_ss addsimps [supp_def,Collect_const,Finites.emptyI,defn];
berghofe@19133
   619
               val proof = EVERY [ClassPackage.intro_classes_tac [], asm_simp_tac simp_s 1];      
urbanc@18432
   620
             in  
berghofe@19275
   621
	       AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
urbanc@18432
   622
             end) ak_names;  
berghofe@18068
   623
urbanc@18432
   624
          fun discrete_cp_inst discrete_ty defn = 
urbanc@18432
   625
	     fold (fn ak_name' => (fold (fn ak_name => fn thy =>
urbanc@18432
   626
	     let
urbanc@18432
   627
	       val qu_class = Sign.full_name (sign_of thy) ("cp_"^ak_name^"_"^ak_name');
berghofe@19494
   628
	       val supp_def = thm "Nominal.supp_def";
urbanc@18432
   629
               val simp_s = HOL_ss addsimps [defn];
berghofe@19133
   630
               val proof = EVERY [ClassPackage.intro_classes_tac [], asm_simp_tac simp_s 1];      
urbanc@18432
   631
             in  
berghofe@19275
   632
	       AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy
urbanc@18432
   633
             end) ak_names)) ak_names;  
urbanc@18432
   634
          
urbanc@18432
   635
        in
urbanc@18432
   636
         thy26
urbanc@18432
   637
         |> discrete_pt_inst "nat"  (thm "perm_nat_def")
urbanc@18432
   638
         |> discrete_fs_inst "nat"  (thm "perm_nat_def") 
urbanc@18432
   639
         |> discrete_cp_inst "nat"  (thm "perm_nat_def") 
urbanc@18432
   640
         |> discrete_pt_inst "bool" (thm "perm_bool")
urbanc@18432
   641
         |> discrete_fs_inst "bool" (thm "perm_bool")
urbanc@18432
   642
         |> discrete_cp_inst "bool" (thm "perm_bool")
urbanc@18432
   643
         |> discrete_pt_inst "IntDef.int" (thm "perm_int_def")
urbanc@18432
   644
         |> discrete_fs_inst "IntDef.int" (thm "perm_int_def") 
urbanc@18432
   645
         |> discrete_cp_inst "IntDef.int" (thm "perm_int_def") 
urbanc@18432
   646
         |> discrete_pt_inst "List.char" (thm "perm_char_def")
urbanc@18432
   647
         |> discrete_fs_inst "List.char" (thm "perm_char_def")
urbanc@18432
   648
         |> discrete_cp_inst "List.char" (thm "perm_char_def")
urbanc@18432
   649
        end;
urbanc@18432
   650
urbanc@19562
   651
 
urbanc@18262
   652
       (* abbreviations for some lemmas *)
urbanc@18262
   653
       (*===============================*)
berghofe@19494
   654
       val abs_fun_pi          = thm "Nominal.abs_fun_pi";
berghofe@19494
   655
       val abs_fun_pi_ineq     = thm "Nominal.abs_fun_pi_ineq";
berghofe@19494
   656
       val abs_fun_eq          = thm "Nominal.abs_fun_eq";
urbanc@19562
   657
       val abs_fun_eq'         = thm "Nominal.abs_fun_eq'";
berghofe@19494
   658
       val dj_perm_forget      = thm "Nominal.dj_perm_forget";
berghofe@19494
   659
       val dj_pp_forget        = thm "Nominal.dj_perm_perm_forget";
berghofe@19494
   660
       val fresh_iff           = thm "Nominal.fresh_abs_fun_iff";
berghofe@19494
   661
       val fresh_iff_ineq      = thm "Nominal.fresh_abs_fun_iff_ineq";
berghofe@19494
   662
       val abs_fun_supp        = thm "Nominal.abs_fun_supp";
berghofe@19494
   663
       val abs_fun_supp_ineq   = thm "Nominal.abs_fun_supp_ineq";
berghofe@19494
   664
       val pt_swap_bij         = thm "Nominal.pt_swap_bij";
berghofe@19494
   665
       val pt_fresh_fresh      = thm "Nominal.pt_fresh_fresh";
berghofe@19494
   666
       val pt_bij              = thm "Nominal.pt_bij";
berghofe@19494
   667
       val pt_perm_compose     = thm "Nominal.pt_perm_compose";
berghofe@19494
   668
       val pt_perm_compose'    = thm "Nominal.pt_perm_compose'";
berghofe@19494
   669
       val perm_app            = thm "Nominal.pt_fun_app_eq";
berghofe@19494
   670
       val at_fresh            = thm "Nominal.at_fresh";
urbanc@19972
   671
       val at_fresh_ineq       = thm "Nominal.at_fresh_ineq";
berghofe@19494
   672
       val at_calc             = thms "Nominal.at_calc";
berghofe@19494
   673
       val at_supp             = thm "Nominal.at_supp";
berghofe@19494
   674
       val dj_supp             = thm "Nominal.dj_supp";
berghofe@19494
   675
       val fresh_left_ineq     = thm "Nominal.pt_fresh_left_ineq";
berghofe@19494
   676
       val fresh_left          = thm "Nominal.pt_fresh_left";
urbanc@19548
   677
       val fresh_right_ineq    = thm "Nominal.pt_fresh_right_ineq";
urbanc@19548
   678
       val fresh_right         = thm "Nominal.pt_fresh_right";
berghofe@19494
   679
       val fresh_bij_ineq      = thm "Nominal.pt_fresh_bij_ineq";
berghofe@19494
   680
       val fresh_bij           = thm "Nominal.pt_fresh_bij";
urbanc@19638
   681
       val fresh_aux_ineq      = thm "Nominal.pt_fresh_aux_ineq";
urbanc@19638
   682
       val fresh_aux           = thm "Nominal.pt_fresh_aux";
urbanc@19972
   683
       val fresh_eqvt          = thm "Nominal.pt_fresh_eqvt";
urbanc@19972
   684
       val all_eqvt            = thm "Nominal.pt_all_eqvt";
berghofe@19494
   685
       val pt_pi_rev           = thm "Nominal.pt_pi_rev";
berghofe@19494
   686
       val pt_rev_pi           = thm "Nominal.pt_rev_pi";
urbanc@19972
   687
       val at_exists_fresh     = thm "Nominal.at_exists_fresh";
urbanc@19638
   688
  
berghofe@18068
   689
urbanc@18262
   690
       (* Now we collect and instantiate some lemmas w.r.t. all atom      *)
urbanc@18262
   691
       (* types; this allows for example to use abs_perm (which is a      *)
urbanc@18262
   692
       (* collection of theorems) instead of thm abs_fun_pi with explicit *)
urbanc@18262
   693
       (* instantiations.                                                 *)
urbanc@18381
   694
       val (_,thy33) = 
urbanc@18262
   695
	 let 
urbanc@18651
   696
             
urbanc@18651
   697
urbanc@18279
   698
             (* takes a theorem thm and a list of theorems [t1,..,tn]            *)
urbanc@18279
   699
             (* produces a list of theorems of the form [t1 RS thm,..,tn RS thm] *) 
urbanc@18262
   700
             fun instR thm thms = map (fn ti => ti RS thm) thms;
berghofe@18068
   701
urbanc@18262
   702
             (* takes two theorem lists (hopefully of the same length ;o)                *)
urbanc@18262
   703
             (* produces a list of theorems of the form                                  *)
urbanc@18262
   704
             (* [t1 RS m1,..,tn RS mn] where [t1,..,tn] is thms1 and [m1,..,mn] is thms2 *) 
urbanc@18279
   705
             fun inst_zip thms1 thms2 = map (fn (t1,t2) => t1 RS t2) (thms1 ~~ thms2);
berghofe@18068
   706
urbanc@18262
   707
             (* takes a theorem list of the form [l1,...,ln]              *)
urbanc@18262
   708
             (* and a list of theorem lists of the form                   *)
urbanc@18262
   709
             (* [[h11,...,h1m],....,[hk1,....,hkm]                        *)
urbanc@18262
   710
             (* produces the list of theorem lists                        *)
urbanc@18262
   711
             (* [[l1 RS h11,...,l1 RS h1m],...,[ln RS hk1,...,ln RS hkm]] *)
urbanc@18279
   712
             fun inst_mult thms thmss = map (fn (t,ts) => instR t ts) (thms ~~ thmss);
urbanc@18279
   713
urbanc@18279
   714
             (* FIXME: these lists do not need to be created dynamically again *)
urbanc@18262
   715
berghofe@18068
   716
             (* list of all at_inst-theorems *)
urbanc@18262
   717
             val ats = map (fn ak => PureThy.get_thm thy32 (Name ("at_"^ak^"_inst"))) ak_names
berghofe@18068
   718
             (* list of all pt_inst-theorems *)
urbanc@18262
   719
             val pts = map (fn ak => PureThy.get_thm thy32 (Name ("pt_"^ak^"_inst"))) ak_names
urbanc@18262
   720
             (* list of all cp_inst-theorems as a collection of lists*)
berghofe@18068
   721
             val cps = 
urbanc@18262
   722
		 let fun cps_fun ak1 ak2 = PureThy.get_thm thy32 (Name ("cp_"^ak1^"_"^ak2^"_inst"))
urbanc@18262
   723
		 in map (fn aki => (map (cps_fun aki) ak_names)) ak_names end; 
urbanc@18262
   724
             (* list of all cp_inst-theorems that have different atom types *)
urbanc@18262
   725
             val cps' = 
urbanc@18262
   726
		let fun cps'_fun ak1 ak2 = 
urbanc@18262
   727
		if ak1=ak2 then NONE else SOME(PureThy.get_thm thy32 (Name ("cp_"^ak1^"_"^ak2^"_inst")))
urbanc@18262
   728
		in map (fn aki => (List.mapPartial I (map (cps'_fun aki) ak_names))) ak_names end;
berghofe@18068
   729
             (* list of all dj_inst-theorems *)
berghofe@18068
   730
             val djs = 
berghofe@18068
   731
	       let fun djs_fun (ak1,ak2) = 
urbanc@18262
   732
		     if ak1=ak2 then NONE else SOME(PureThy.get_thm thy32 (Name ("dj_"^ak2^"_"^ak1)))
urbanc@18262
   733
	       in List.mapPartial I (map djs_fun (Library.product ak_names ak_names)) end;
urbanc@18262
   734
             (* list of all fs_inst-theorems *)
urbanc@18262
   735
             val fss = map (fn ak => PureThy.get_thm thy32 (Name ("fs_"^ak^"_inst"))) ak_names
urbanc@18651
   736
              
urbanc@18262
   737
             fun inst_pt thms = Library.flat (map (fn ti => instR ti pts) thms); 
urbanc@18262
   738
             fun inst_at thms = Library.flat (map (fn ti => instR ti ats) thms);               
urbanc@18262
   739
             fun inst_fs thms = Library.flat (map (fn ti => instR ti fss) thms);
urbanc@18436
   740
             fun inst_cp thms cps = Library.flat (inst_mult thms cps); 
urbanc@18262
   741
	     fun inst_pt_at thms = inst_zip ats (inst_pt thms);			
urbanc@18262
   742
             fun inst_dj thms = Library.flat (map (fn ti => instR ti djs) thms);  
urbanc@18436
   743
	     fun inst_pt_pt_at_cp thms = inst_cp (inst_zip ats (inst_zip pts (inst_pt thms))) cps;
urbanc@18262
   744
             fun inst_pt_at_fs thms = inst_zip (inst_fs [fs1]) (inst_zip ats (inst_pt thms));
urbanc@18396
   745
	     fun inst_pt_pt_at_cp thms = 
urbanc@18279
   746
		 let val i_pt_pt_at = inst_zip ats (inst_zip pts (inst_pt thms));
urbanc@18436
   747
                     val i_pt_pt_at_cp = inst_cp i_pt_pt_at cps';
urbanc@18396
   748
		 in i_pt_pt_at_cp end;
urbanc@18396
   749
             fun inst_pt_pt_at_cp_dj thms = inst_zip djs (inst_pt_pt_at_cp thms);
berghofe@18068
   750
           in
urbanc@18262
   751
            thy32 
urbanc@18652
   752
	    |>   PureThy.add_thmss [(("alpha", inst_pt_at [abs_fun_eq]),[])]
urbanc@19562
   753
            ||>> PureThy.add_thmss [(("alpha'", inst_pt_at [abs_fun_eq']),[])]
urbanc@18381
   754
            ||>> PureThy.add_thmss [(("perm_swap", inst_pt_at [pt_swap_bij]),[])]
urbanc@19139
   755
            ||>> PureThy.add_thmss 
urbanc@19139
   756
	      let val thms1 = inst_pt_at [pt_pi_rev];
urbanc@19139
   757
		  val thms2 = inst_pt_at [pt_rev_pi];
urbanc@19139
   758
              in [(("perm_pi_simp",thms1 @ thms2),[])] end
urbanc@18381
   759
            ||>> PureThy.add_thmss [(("perm_fresh_fresh", inst_pt_at [pt_fresh_fresh]),[])]
urbanc@18381
   760
            ||>> PureThy.add_thmss [(("perm_bij", inst_pt_at [pt_bij]),[])]
urbanc@18436
   761
            ||>> PureThy.add_thmss 
urbanc@18436
   762
	      let val thms1 = inst_pt_at [pt_perm_compose];
urbanc@18436
   763
		  val thms2 = instR cp1 (Library.flat cps');
urbanc@18436
   764
              in [(("perm_compose",thms1 @ thms2),[])] end
urbanc@19139
   765
            ||>> PureThy.add_thmss [(("perm_compose'",inst_pt_at [pt_perm_compose']),[])] 
urbanc@19139
   766
            ||>> PureThy.add_thmss [(("perm_app", inst_pt_at [perm_app]),[])]
urbanc@18381
   767
            ||>> PureThy.add_thmss [(("supp_atm", (inst_at [at_supp]) @ (inst_dj [dj_supp])),[])]
urbanc@19972
   768
            ||>> PureThy.add_thmss [(("exists_fresh", inst_at [at_exists_fresh]),[])]
urbanc@19972
   769
            ||>> PureThy.add_thmss [(("all_eqvt", inst_pt_at [all_eqvt]),[])]
urbanc@19972
   770
            ||>> PureThy.add_thmss 
urbanc@19972
   771
	      let val thms1 = inst_at [at_fresh]
urbanc@19972
   772
		  val thms2 = inst_dj [at_fresh_ineq]
urbanc@19972
   773
	      in [(("fresh_atm", thms1 @ thms2),[])] end
urbanc@19992
   774
            ||>> PureThy.add_thmss
urbanc@19992
   775
	      let val thms1 = List.concat (List.concat perm_defs)
urbanc@19993
   776
              in [(("calc_atm", (inst_at at_calc) @ thms1),[])] end
urbanc@18381
   777
            ||>> PureThy.add_thmss
urbanc@18279
   778
	      let val thms1 = inst_pt_at [abs_fun_pi]
urbanc@18279
   779
		  and thms2 = inst_pt_pt_at_cp [abs_fun_pi_ineq]
urbanc@18279
   780
	      in [(("abs_perm", thms1 @ thms2),[])] end
urbanc@18381
   781
            ||>> PureThy.add_thmss
urbanc@18279
   782
	      let val thms1 = inst_dj [dj_perm_forget]
urbanc@18279
   783
		  and thms2 = inst_dj [dj_pp_forget]
urbanc@18279
   784
              in [(("perm_dj", thms1 @ thms2),[])] end
urbanc@18381
   785
            ||>> PureThy.add_thmss
urbanc@18279
   786
	      let val thms1 = inst_pt_at_fs [fresh_iff]
urbanc@18626
   787
                  and thms2 = inst_pt_at [fresh_iff]
urbanc@18626
   788
		  and thms3 = inst_pt_pt_at_cp_dj [fresh_iff_ineq]
urbanc@18626
   789
	    in [(("abs_fresh", thms1 @ thms2 @ thms3),[])] end
urbanc@18381
   790
	    ||>> PureThy.add_thmss
urbanc@18279
   791
	      let val thms1 = inst_pt_at [abs_fun_supp]
urbanc@18279
   792
		  and thms2 = inst_pt_at_fs [abs_fun_supp]
urbanc@18279
   793
		  and thms3 = inst_pt_pt_at_cp_dj [abs_fun_supp_ineq]
urbanc@18279
   794
	      in [(("abs_supp", thms1 @ thms2 @ thms3),[])] end
urbanc@18396
   795
            ||>> PureThy.add_thmss
urbanc@18396
   796
	      let val thms1 = inst_pt_at [fresh_left]
urbanc@18396
   797
		  and thms2 = inst_pt_pt_at_cp [fresh_left_ineq]
urbanc@18396
   798
	      in [(("fresh_left", thms1 @ thms2),[])] end
urbanc@18426
   799
            ||>> PureThy.add_thmss
urbanc@19548
   800
	      let val thms1 = inst_pt_at [fresh_right]
urbanc@19548
   801
		  and thms2 = inst_pt_pt_at_cp [fresh_right_ineq]
urbanc@19548
   802
	      in [(("fresh_right", thms1 @ thms2),[])] end
urbanc@19548
   803
            ||>> PureThy.add_thmss
urbanc@18426
   804
	      let val thms1 = inst_pt_at [fresh_bij]
urbanc@18426
   805
		  and thms2 = inst_pt_pt_at_cp [fresh_bij_ineq]
urbanc@19972
   806
	      in [(("fresh_bij", thms1 @ thms2),[])] end
urbanc@19972
   807
            ||>> PureThy.add_thmss
urbanc@19972
   808
	      let val thms1 = inst_pt_at [fresh_eqvt]
urbanc@19972
   809
	      in [(("fresh_eqvt", thms1),[])] end
urbanc@19638
   810
            ||>> PureThy.add_thmss
urbanc@19638
   811
	      let val thms1 = inst_pt_at [fresh_aux]
urbanc@19638
   812
		  and thms2 = inst_pt_pt_at_cp_dj [fresh_aux_ineq]
urbanc@19638
   813
	      in [(("fresh_aux", thms1 @ thms2),[])] end
berghofe@18068
   814
	   end;
berghofe@18068
   815
berghofe@18068
   816
    in NominalData.put (fold Symtab.update (map (rpair ()) full_ak_names)
urbanc@18262
   817
      (NominalData.get thy11)) thy33
berghofe@18068
   818
    end;
berghofe@18068
   819
berghofe@18068
   820
berghofe@18068
   821
(* syntax und parsing *)
berghofe@18068
   822
structure P = OuterParse and K = OuterKeyword;
berghofe@18068
   823
berghofe@18068
   824
val atom_declP =
berghofe@18068
   825
  OuterSyntax.command "atom_decl" "Declare new kinds of atoms" K.thy_decl
berghofe@18068
   826
    (Scan.repeat1 P.name >> (Toplevel.theory o create_nom_typedecls));
berghofe@18068
   827
berghofe@18068
   828
val _ = OuterSyntax.add_parsers [atom_declP];
berghofe@18068
   829
urbanc@18746
   830
val setup = NominalData.init;
berghofe@18068
   831
berghofe@18068
   832
end;