- completed the list of thms for supp_atm
- cleaned up the way how thms are collected under single names
(* $Id$ *)
signature NOMINAL_PACKAGE =
sig
val create_nom_typedecls : string list -> theory -> theory
val add_nominal_datatype : bool -> string list -> (string list * bstring * mixfix *
(bstring * string list * mixfix) list) list -> theory -> theory *
{distinct : thm list list,
inject : thm list list,
exhaustion : thm list,
rec_thms : thm list,
case_thms : thm list list,
split_thms : (thm * thm) list,
induction : thm,
size : thm list,
simps : thm list}
val setup : (theory -> theory) list
end
structure NominalPackage (*: NOMINAL_PACKAGE *) =
struct
open DatatypeAux;
(* data kind 'HOL/nominal' *)
structure NominalArgs =
struct
val name = "HOL/nominal";
type T = unit Symtab.table;
val empty = Symtab.empty;
val copy = I;
val extend = I;
fun merge _ x = Symtab.merge (K true) x;
fun print sg tab = ();
end;
structure NominalData = TheoryDataFun(NominalArgs);
fun atoms_of thy = map fst (Symtab.dest (NominalData.get thy));
(* FIXME: add to hologic.ML ? *)
fun mk_listT T = Type ("List.list", [T]);
fun mk_permT T = mk_listT (HOLogic.mk_prodT (T, T));
fun mk_Cons x xs =
let val T = fastype_of x
in Const ("List.list.Cons", T --> mk_listT T --> mk_listT T) $ x $ xs end;
(* FIXME: should be a library function *)
fun cprod ([], ys) = []
| cprod (x :: xs, ys) = map (pair x) ys @ cprod (xs, ys);
(* this function sets up all matters related to atom- *)
(* kinds; the user specifies a list of atom-kind names *)
(* atom_decl <ak1> ... <akn> *)
fun create_nom_typedecls ak_names thy =
let
(* declares a type-decl for every atom-kind: *)
(* that is typedecl <ak> *)
val thy1 = TypedefPackage.add_typedecls (map (fn x => (x,[],NoSyn)) ak_names) thy;
(* produces a list consisting of pairs: *)
(* fst component is the atom-kind name *)
(* snd component is its type *)
val full_ak_names = map (Sign.intern_type (sign_of thy1)) ak_names;
val ak_names_types = ak_names ~~ map (Type o rpair []) full_ak_names;
(* adds for every atom-kind an axiom *)
(* <ak>_infinite: infinite (UNIV::<ak_type> set) *)
val (thy2,inf_axs) = PureThy.add_axioms_i (map (fn (ak_name, T) =>
let
val name = ak_name ^ "_infinite"
val axiom = HOLogic.mk_Trueprop (HOLogic.mk_not
(HOLogic.mk_mem (HOLogic.mk_UNIV T,
Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT T)))))
in
((name, axiom), [])
end) ak_names_types) thy1;
(* declares a swapping function for every atom-kind, it is *)
(* const swap_<ak> :: <akT> * <akT> => <akT> => <akT> *)
(* swap_<ak> (a,b) c = (if a=c then b (else if b=c then a else c)) *)
(* overloades then the general swap-function *)
val (thy3, swap_eqs) = foldl_map (fn (thy, (ak_name, T)) =>
let
val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
val swap_name = Sign.full_name (sign_of thy) ("swap_" ^ ak_name);
val a = Free ("a", T);
val b = Free ("b", T);
val c = Free ("c", T);
val ab = Free ("ab", HOLogic.mk_prodT (T, T))
val cif = Const ("HOL.If", HOLogic.boolT --> T --> T --> T);
val cswap_akname = Const (swap_name, swapT);
val cswap = Const ("nominal.swap", swapT)
val name = "swap_"^ak_name^"_def";
val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq
(cswap_akname $ HOLogic.mk_prod (a,b) $ c,
cif $ HOLogic.mk_eq (a,c) $ b $ (cif $ HOLogic.mk_eq (b,c) $ a $ c)))
val def2 = Logic.mk_equals (cswap $ ab $ c, cswap_akname $ ab $ c)
in
thy |> Theory.add_consts_i [("swap_" ^ ak_name, swapT, NoSyn)]
|> (#1 o PureThy.add_defs_i true [((name, def2),[])])
|> PrimrecPackage.add_primrec_i "" [(("", def1),[])]
end) (thy2, ak_names_types);
(* declares a permutation function for every atom-kind acting *)
(* on such atoms *)
(* const <ak>_prm_<ak> :: (<akT> * <akT>)list => akT => akT *)
(* <ak>_prm_<ak> [] a = a *)
(* <ak>_prm_<ak> (x#xs) a = swap_<ak> x (perm xs a) *)
val (thy4, prm_eqs) = foldl_map (fn (thy, (ak_name, T)) =>
let
val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
val swap_name = Sign.full_name (sign_of thy) ("swap_" ^ ak_name)
val prmT = mk_permT T --> T --> T;
val prm_name = ak_name ^ "_prm_" ^ ak_name;
val qu_prm_name = Sign.full_name (sign_of thy) prm_name;
val x = Free ("x", HOLogic.mk_prodT (T, T));
val xs = Free ("xs", mk_permT T);
val a = Free ("a", T) ;
val cnil = Const ("List.list.Nil", mk_permT T);
val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq (Const (qu_prm_name, prmT) $ cnil $ a, a));
val def2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
(Const (qu_prm_name, prmT) $ mk_Cons x xs $ a,
Const (swap_name, swapT) $ x $ (Const (qu_prm_name, prmT) $ xs $ a)));
in
thy |> Theory.add_consts_i [(prm_name, mk_permT T --> T --> T, NoSyn)]
|> PrimrecPackage.add_primrec_i "" [(("", def1), []),(("", def2), [])]
end) (thy3, ak_names_types);
(* defines permutation functions for all combinations of atom-kinds; *)
(* there are a trivial cases and non-trivial cases *)
(* non-trivial case: *)
(* <ak>_prm_<ak>_def: perm pi a == <ak>_prm_<ak> pi a *)
(* trivial case with <ak> != <ak'> *)
(* <ak>_prm<ak'>_def[simp]: perm pi a == a *)
(* *)
(* the trivial cases are added to the simplifier, while the non- *)
(* have their own rules proved below *)
val (thy5, perm_defs) = foldl_map (fn (thy, (ak_name, T)) =>
foldl_map (fn (thy', (ak_name', T')) =>
let
val perm_def_name = ak_name ^ "_prm_" ^ ak_name';
val pi = Free ("pi", mk_permT T);
val a = Free ("a", T');
val cperm = Const ("nominal.perm", mk_permT T --> T' --> T');
val cperm_def = Const (Sign.full_name (sign_of thy') perm_def_name, mk_permT T --> T' --> T');
val name = ak_name ^ "_prm_" ^ ak_name' ^ "_def";
val def = Logic.mk_equals
(cperm $ pi $ a, if ak_name = ak_name' then cperm_def $ pi $ a else a)
in
thy' |> PureThy.add_defs_i true [((name, def),[])]
end) (thy, ak_names_types)) (thy4, ak_names_types);
(* proves that every atom-kind is an instance of at *)
(* lemma at_<ak>_inst: *)
(* at TYPE(<ak>) *)
val (thy6, prm_cons_thms) =
thy5 |> PureThy.add_thms (map (fn (ak_name, T) =>
let
val ak_name_qu = Sign.full_name (sign_of thy5) (ak_name);
val i_type = Type(ak_name_qu,[]);
val cat = Const ("nominal.at",(Term.itselfT i_type) --> HOLogic.boolT);
val at_type = Logic.mk_type i_type;
val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy5
[Name "at_def",
Name (ak_name ^ "_prm_" ^ ak_name ^ "_def"),
Name (ak_name ^ "_prm_" ^ ak_name ^ ".simps"),
Name ("swap_" ^ ak_name ^ "_def"),
Name ("swap_" ^ ak_name ^ ".simps"),
Name (ak_name ^ "_infinite")]
val name = "at_"^ak_name^ "_inst";
val statement = HOLogic.mk_Trueprop (cat $ at_type);
val proof = fn _ => auto_tac (claset(),simp_s);
in
((name, standard (Goal.prove thy5 [] [] statement proof)), [])
end) ak_names_types);
(* declares a perm-axclass for every atom-kind *)
(* axclass pt_<ak> *)
(* pt_<ak>1[simp]: perm [] x = x *)
(* pt_<ak>2: perm (pi1@pi2) x = perm pi1 (perm pi2 x) *)
(* pt_<ak>3: pi1 ~ pi2 ==> perm pi1 x = perm pi2 x *)
val (thy7, pt_ax_classes) = foldl_map (fn (thy, (ak_name, T)) =>
let
val cl_name = "pt_"^ak_name;
val ty = TFree("'a",["HOL.type"]);
val x = Free ("x", ty);
val pi1 = Free ("pi1", mk_permT T);
val pi2 = Free ("pi2", mk_permT T);
val cperm = Const ("nominal.perm", mk_permT T --> ty --> ty);
val cnil = Const ("List.list.Nil", mk_permT T);
val cappend = Const ("List.op @",mk_permT T --> mk_permT T --> mk_permT T);
val cprm_eq = Const ("nominal.prm_eq",mk_permT T --> mk_permT T --> HOLogic.boolT);
(* nil axiom *)
val axiom1 = HOLogic.mk_Trueprop (HOLogic.mk_eq
(cperm $ cnil $ x, x));
(* append axiom *)
val axiom2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
(cperm $ (cappend $ pi1 $ pi2) $ x, cperm $ pi1 $ (cperm $ pi2 $ x)));
(* perm-eq axiom *)
val axiom3 = Logic.mk_implies
(HOLogic.mk_Trueprop (cprm_eq $ pi1 $ pi2),
HOLogic.mk_Trueprop (HOLogic.mk_eq (cperm $ pi1 $ x, cperm $ pi2 $ x)));
in
thy |> AxClass.add_axclass_i (cl_name, ["HOL.type"])
[((cl_name^"1", axiom1),[Simplifier.simp_add_global]),
((cl_name^"2", axiom2),[]),
((cl_name^"3", axiom3),[])]
end) (thy6,ak_names_types);
(* proves that every pt_<ak>-type together with <ak>-type *)
(* instance of pt *)
(* lemma pt_<ak>_inst: *)
(* pt TYPE('x::pt_<ak>) TYPE(<ak>) *)
val (thy8, prm_inst_thms) =
thy7 |> PureThy.add_thms (map (fn (ak_name, T) =>
let
val ak_name_qu = Sign.full_name (sign_of thy7) (ak_name);
val pt_name_qu = Sign.full_name (sign_of thy7) ("pt_"^ak_name);
val i_type1 = TFree("'x",[pt_name_qu]);
val i_type2 = Type(ak_name_qu,[]);
val cpt = Const ("nominal.pt",(Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
val pt_type = Logic.mk_type i_type1;
val at_type = Logic.mk_type i_type2;
val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy7
[Name "pt_def",
Name ("pt_" ^ ak_name ^ "1"),
Name ("pt_" ^ ak_name ^ "2"),
Name ("pt_" ^ ak_name ^ "3")];
val name = "pt_"^ak_name^ "_inst";
val statement = HOLogic.mk_Trueprop (cpt $ pt_type $ at_type);
val proof = fn _ => auto_tac (claset(),simp_s);
in
((name, standard (Goal.prove thy7 [] [] statement proof)), [])
end) ak_names_types);
(* declares an fs-axclass for every atom-kind *)
(* axclass fs_<ak> *)
(* fs_<ak>1: finite ((supp x)::<ak> set) *)
val (thy11, fs_ax_classes) = foldl_map (fn (thy, (ak_name, T)) =>
let
val cl_name = "fs_"^ak_name;
val pt_name = Sign.full_name (sign_of thy) ("pt_"^ak_name);
val ty = TFree("'a",["HOL.type"]);
val x = Free ("x", ty);
val csupp = Const ("nominal.supp", ty --> HOLogic.mk_setT T);
val cfinites = Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT T))
val axiom1 = HOLogic.mk_Trueprop (HOLogic.mk_mem (csupp $ x, cfinites));
in
thy |> AxClass.add_axclass_i (cl_name, [pt_name]) [((cl_name^"1", axiom1),[])]
end) (thy8,ak_names_types);
(* proves that every fs_<ak>-type together with <ak>-type *)
(* instance of fs-type *)
(* lemma abst_<ak>_inst: *)
(* fs TYPE('x::pt_<ak>) TYPE (<ak>) *)
val (thy12, fs_inst_thms) =
thy11 |> PureThy.add_thms (map (fn (ak_name, T) =>
let
val ak_name_qu = Sign.full_name (sign_of thy11) (ak_name);
val fs_name_qu = Sign.full_name (sign_of thy11) ("fs_"^ak_name);
val i_type1 = TFree("'x",[fs_name_qu]);
val i_type2 = Type(ak_name_qu,[]);
val cfs = Const ("nominal.fs",
(Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
val fs_type = Logic.mk_type i_type1;
val at_type = Logic.mk_type i_type2;
val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy11
[Name "fs_def",
Name ("fs_" ^ ak_name ^ "1")];
val name = "fs_"^ak_name^ "_inst";
val statement = HOLogic.mk_Trueprop (cfs $ fs_type $ at_type);
val proof = fn _ => auto_tac (claset(),simp_s);
in
((name, standard (Goal.prove thy11 [] [] statement proof)), [])
end) ak_names_types);
(* declares for every atom-kind combination an axclass *)
(* cp_<ak1>_<ak2> giving a composition property *)
(* cp_<ak1>_<ak2>1: pi1 o pi2 o x = (pi1 o pi2) o (pi1 o x) *)
val (thy12b,_) = foldl_map (fn (thy, (ak_name, T)) =>
foldl_map (fn (thy', (ak_name', T')) =>
let
val cl_name = "cp_"^ak_name^"_"^ak_name';
val ty = TFree("'a",["HOL.type"]);
val x = Free ("x", ty);
val pi1 = Free ("pi1", mk_permT T);
val pi2 = Free ("pi2", mk_permT T');
val cperm1 = Const ("nominal.perm", mk_permT T --> ty --> ty);
val cperm2 = Const ("nominal.perm", mk_permT T' --> ty --> ty);
val cperm3 = Const ("nominal.perm", mk_permT T --> mk_permT T' --> mk_permT T');
val ax1 = HOLogic.mk_Trueprop
(HOLogic.mk_eq (cperm1 $ pi1 $ (cperm2 $ pi2 $ x),
cperm2 $ (cperm3 $ pi1 $ pi2) $ (cperm1 $ pi1 $ x)));
in
(fst (AxClass.add_axclass_i (cl_name, ["HOL.type"]) [((cl_name^"1", ax1),[])] thy'),())
end)
(thy, ak_names_types)) (thy12, ak_names_types)
(* proves for every <ak>-combination a cp_<ak1>_<ak2>_inst theorem; *)
(* lemma cp_<ak1>_<ak2>_inst: *)
(* cp TYPE('a::cp_<ak1>_<ak2>) TYPE(<ak1>) TYPE(<ak2>) *)
val (thy12c, cp_thms) = foldl_map (fn (thy, (ak_name, T)) =>
foldl_map (fn (thy', (ak_name', T')) =>
let
val ak_name_qu = Sign.full_name (sign_of thy') (ak_name);
val ak_name_qu' = Sign.full_name (sign_of thy') (ak_name');
val cp_name_qu = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
val i_type0 = TFree("'a",[cp_name_qu]);
val i_type1 = Type(ak_name_qu,[]);
val i_type2 = Type(ak_name_qu',[]);
val ccp = Const ("nominal.cp",
(Term.itselfT i_type0)-->(Term.itselfT i_type1)-->
(Term.itselfT i_type2)-->HOLogic.boolT);
val at_type = Logic.mk_type i_type1;
val at_type' = Logic.mk_type i_type2;
val cp_type = Logic.mk_type i_type0;
val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy' [(Name "cp_def")];
val cp1 = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"1"));
val name = "cp_"^ak_name^ "_"^ak_name'^"_inst";
val statement = HOLogic.mk_Trueprop (ccp $ cp_type $ at_type $ at_type');
val proof = fn _ => EVERY [auto_tac (claset(),simp_s), rtac cp1 1];
in
thy' |> PureThy.add_thms
[((name, standard (Goal.prove thy' [] [] statement proof)), [])]
end)
(thy, ak_names_types)) (thy12b, ak_names_types);
(* proves for every non-trivial <ak>-combination a disjointness *)
(* theorem; i.e. <ak1> != <ak2> *)
(* lemma ds_<ak1>_<ak2>: *)
(* dj TYPE(<ak1>) TYPE(<ak2>) *)
val (thy12d, dj_thms) = foldl_map (fn (thy, (ak_name, T)) =>
foldl_map (fn (thy', (ak_name', T')) =>
(if not (ak_name = ak_name')
then
let
val ak_name_qu = Sign.full_name (sign_of thy') (ak_name);
val ak_name_qu' = Sign.full_name (sign_of thy') (ak_name');
val i_type1 = Type(ak_name_qu,[]);
val i_type2 = Type(ak_name_qu',[]);
val cdj = Const ("nominal.disjoint",
(Term.itselfT i_type1)-->(Term.itselfT i_type2)-->HOLogic.boolT);
val at_type = Logic.mk_type i_type1;
val at_type' = Logic.mk_type i_type2;
val simp_s = HOL_basic_ss addsimps PureThy.get_thmss thy'
[Name "disjoint_def",
Name (ak_name^"_prm_"^ak_name'^"_def"),
Name (ak_name'^"_prm_"^ak_name^"_def")];
val name = "dj_"^ak_name^"_"^ak_name';
val statement = HOLogic.mk_Trueprop (cdj $ at_type $ at_type');
val proof = fn _ => auto_tac (claset(),simp_s);
in
thy' |> PureThy.add_thms
[((name, standard (Goal.prove thy' [] [] statement proof)), []) ]
end
else
(thy',[]))) (* do nothing branch, if ak_name = ak_name' *)
(thy, ak_names_types)) (thy12c, ak_names_types);
(*<<<<<<< pt_<ak> class instances >>>>>>>*)
(*=========================================*)
(* some frequently used theorems *)
val pt1 = PureThy.get_thm thy12c (Name "pt1");
val pt2 = PureThy.get_thm thy12c (Name "pt2");
val pt3 = PureThy.get_thm thy12c (Name "pt3");
val at_pt_inst = PureThy.get_thm thy12c (Name "at_pt_inst");
val pt_bool_inst = PureThy.get_thm thy12c (Name "pt_bool_inst");
val pt_set_inst = PureThy.get_thm thy12c (Name "pt_set_inst");
val pt_unit_inst = PureThy.get_thm thy12c (Name "pt_unit_inst");
val pt_prod_inst = PureThy.get_thm thy12c (Name "pt_prod_inst");
val pt_list_inst = PureThy.get_thm thy12c (Name "pt_list_inst");
val pt_optn_inst = PureThy.get_thm thy12c (Name "pt_option_inst");
val pt_noptn_inst = PureThy.get_thm thy12c (Name "pt_noption_inst");
val pt_fun_inst = PureThy.get_thm thy12c (Name "pt_fun_inst");
(* for all atom-kind combination shows that *)
(* every <ak> is an instance of pt_<ai> *)
val (thy13,_) = foldl_map (fn (thy, (ak_name, T)) =>
foldl_map (fn (thy', (ak_name', T')) =>
(if ak_name = ak_name'
then
let
val qu_name = Sign.full_name (sign_of thy') ak_name;
val qu_class = Sign.full_name (sign_of thy') ("pt_"^ak_name);
val at_inst = PureThy.get_thm thy' (Name ("at_"^ak_name ^"_inst"));
val proof = EVERY [AxClass.intro_classes_tac [],
rtac ((at_inst RS at_pt_inst) RS pt1) 1,
rtac ((at_inst RS at_pt_inst) RS pt2) 1,
rtac ((at_inst RS at_pt_inst) RS pt3) 1,
atac 1];
in
(AxClass.add_inst_arity_i (qu_name,[],[qu_class]) proof thy',())
end
else
let
val qu_name' = Sign.full_name (sign_of thy') ak_name';
val qu_class = Sign.full_name (sign_of thy') ("pt_"^ak_name);
val simp_s = HOL_basic_ss addsimps
PureThy.get_thmss thy' [Name (ak_name^"_prm_"^ak_name'^"_def")];
val proof = EVERY [AxClass.intro_classes_tac [], auto_tac (claset(),simp_s)];
in
(AxClass.add_inst_arity_i (qu_name',[],[qu_class]) proof thy',())
end))
(thy, ak_names_types)) (thy12c, ak_names_types);
(* shows that bool is an instance of pt_<ak> *)
(* uses the theorem pt_bool_inst *)
val (thy14,_) = foldl_map (fn (thy, (ak_name, T)) =>
let
val qu_class = Sign.full_name (sign_of thy) ("pt_"^ak_name);
val proof = EVERY [AxClass.intro_classes_tac [],
rtac (pt_bool_inst RS pt1) 1,
rtac (pt_bool_inst RS pt2) 1,
rtac (pt_bool_inst RS pt3) 1,
atac 1];
in
(AxClass.add_inst_arity_i ("bool",[],[qu_class]) proof thy,())
end) (thy13,ak_names_types);
(* shows that set(pt_<ak>) is an instance of pt_<ak> *)
(* unfolds the permutation definition and applies pt_<ak>i *)
val (thy15,_) = foldl_map (fn (thy, (ak_name, T)) =>
let
val qu_class = Sign.full_name (sign_of thy) ("pt_"^ak_name);
val pt_inst = PureThy.get_thm thy (Name ("pt_"^ak_name^"_inst"));
val proof = EVERY [AxClass.intro_classes_tac [],
rtac ((pt_inst RS pt_set_inst) RS pt1) 1,
rtac ((pt_inst RS pt_set_inst) RS pt2) 1,
rtac ((pt_inst RS pt_set_inst) RS pt3) 1,
atac 1];
in
(AxClass.add_inst_arity_i ("set",[[qu_class]],[qu_class]) proof thy,())
end) (thy14,ak_names_types);
(* shows that unit is an instance of pt_<ak> *)
val (thy16,_) = foldl_map (fn (thy, (ak_name, T)) =>
let
val qu_class = Sign.full_name (sign_of thy) ("pt_"^ak_name);
val proof = EVERY [AxClass.intro_classes_tac [],
rtac (pt_unit_inst RS pt1) 1,
rtac (pt_unit_inst RS pt2) 1,
rtac (pt_unit_inst RS pt3) 1,
atac 1];
in
(AxClass.add_inst_arity_i ("Product_Type.unit",[],[qu_class]) proof thy,())
end) (thy15,ak_names_types);
(* shows that *(pt_<ak>,pt_<ak>) is an instance of pt_<ak> *)
(* uses the theorem pt_prod_inst and pt_<ak>_inst *)
val (thy17,_) = foldl_map (fn (thy, (ak_name, T)) =>
let
val qu_class = Sign.full_name (sign_of thy) ("pt_"^ak_name);
val pt_inst = PureThy.get_thm thy (Name ("pt_"^ak_name^"_inst"));
val proof = EVERY [AxClass.intro_classes_tac [],
rtac ((pt_inst RS (pt_inst RS pt_prod_inst)) RS pt1) 1,
rtac ((pt_inst RS (pt_inst RS pt_prod_inst)) RS pt2) 1,
rtac ((pt_inst RS (pt_inst RS pt_prod_inst)) RS pt3) 1,
atac 1];
in
(AxClass.add_inst_arity_i ("*",[[qu_class],[qu_class]],[qu_class]) proof thy,())
end) (thy16,ak_names_types);
(* shows that list(pt_<ak>) is an instance of pt_<ak> *)
(* uses the theorem pt_list_inst and pt_<ak>_inst *)
val (thy18,_) = foldl_map (fn (thy, (ak_name, T)) =>
let
val qu_class = Sign.full_name (sign_of thy) ("pt_"^ak_name);
val pt_inst = PureThy.get_thm thy (Name ("pt_"^ak_name^"_inst"));
val proof = EVERY [AxClass.intro_classes_tac [],
rtac ((pt_inst RS pt_list_inst) RS pt1) 1,
rtac ((pt_inst RS pt_list_inst) RS pt2) 1,
rtac ((pt_inst RS pt_list_inst) RS pt3) 1,
atac 1];
in
(AxClass.add_inst_arity_i ("List.list",[[qu_class]],[qu_class]) proof thy,())
end) (thy17,ak_names_types);
(* shows that option(pt_<ak>) is an instance of pt_<ak> *)
(* uses the theorem pt_option_inst and pt_<ak>_inst *)
val (thy18a,_) = foldl_map (fn (thy, (ak_name, T)) =>
let
val qu_class = Sign.full_name (sign_of thy) ("pt_"^ak_name);
val pt_inst = PureThy.get_thm thy (Name ("pt_"^ak_name^"_inst"));
val proof = EVERY [AxClass.intro_classes_tac [],
rtac ((pt_inst RS pt_optn_inst) RS pt1) 1,
rtac ((pt_inst RS pt_optn_inst) RS pt2) 1,
rtac ((pt_inst RS pt_optn_inst) RS pt3) 1,
atac 1];
in
(AxClass.add_inst_arity_i ("Datatype.option",[[qu_class]],[qu_class]) proof thy,())
end) (thy18,ak_names_types);
(* shows that nOption(pt_<ak>) is an instance of pt_<ak> *)
(* uses the theorem pt_option_inst and pt_<ak>_inst *)
val (thy18b,_) = foldl_map (fn (thy, (ak_name, T)) =>
let
val qu_class = Sign.full_name (sign_of thy) ("pt_"^ak_name);
val pt_inst = PureThy.get_thm thy (Name ("pt_"^ak_name^"_inst"));
val proof = EVERY [AxClass.intro_classes_tac [],
rtac ((pt_inst RS pt_noptn_inst) RS pt1) 1,
rtac ((pt_inst RS pt_noptn_inst) RS pt2) 1,
rtac ((pt_inst RS pt_noptn_inst) RS pt3) 1,
atac 1];
in
(AxClass.add_inst_arity_i ("nominal.nOption",[[qu_class]],[qu_class]) proof thy,())
end) (thy18a,ak_names_types);
(* shows that fun(pt_<ak>,pt_<ak>) is an instance of pt_<ak> *)
(* uses the theorem pt_list_inst and pt_<ak>_inst *)
val (thy19,_) = foldl_map (fn (thy, (ak_name, T)) =>
let
val qu_class = Sign.full_name (sign_of thy) ("pt_"^ak_name);
val at_thm = PureThy.get_thm thy (Name ("at_"^ak_name^"_inst"));
val pt_inst = PureThy.get_thm thy (Name ("pt_"^ak_name^"_inst"));
val proof = EVERY [AxClass.intro_classes_tac [],
rtac ((at_thm RS (pt_inst RS (pt_inst RS pt_fun_inst))) RS pt1) 1,
rtac ((at_thm RS (pt_inst RS (pt_inst RS pt_fun_inst))) RS pt2) 1,
rtac ((at_thm RS (pt_inst RS (pt_inst RS pt_fun_inst))) RS pt3) 1,
atac 1];
in
(AxClass.add_inst_arity_i ("fun",[[qu_class],[qu_class]],[qu_class]) proof thy,())
end) (thy18b,ak_names_types);
(*<<<<<<< fs_<ak> class instances >>>>>>>*)
(*=========================================*)
val fs1 = PureThy.get_thm thy19 (Name "fs1");
val fs_at_inst = PureThy.get_thm thy19 (Name "fs_at_inst");
val fs_unit_inst = PureThy.get_thm thy19 (Name "fs_unit_inst");
val fs_bool_inst = PureThy.get_thm thy19 (Name "fs_bool_inst");
val fs_prod_inst = PureThy.get_thm thy19 (Name "fs_prod_inst");
val fs_list_inst = PureThy.get_thm thy19 (Name "fs_list_inst");
(* shows that <ak> is an instance of fs_<ak> *)
(* uses the theorem at_<ak>_inst *)
val (thy20,_) = foldl_map (fn (thy, (ak_name, T)) =>
let
val qu_name = Sign.full_name (sign_of thy) ak_name;
val qu_class = Sign.full_name (sign_of thy) ("fs_"^ak_name);
val at_thm = PureThy.get_thm thy (Name ("at_"^ak_name^"_inst"));
val proof = EVERY [AxClass.intro_classes_tac [],
rtac ((at_thm RS fs_at_inst) RS fs1) 1];
in
(AxClass.add_inst_arity_i (qu_name,[],[qu_class]) proof thy,())
end) (thy19,ak_names_types);
(* shows that unit is an instance of fs_<ak> *)
(* uses the theorem fs_unit_inst *)
val (thy21,_) = foldl_map (fn (thy, (ak_name, T)) =>
let
val qu_class = Sign.full_name (sign_of thy) ("fs_"^ak_name);
val proof = EVERY [AxClass.intro_classes_tac [],
rtac (fs_unit_inst RS fs1) 1];
in
(AxClass.add_inst_arity_i ("Product_Type.unit",[],[qu_class]) proof thy,())
end) (thy20,ak_names_types);
(* shows that bool is an instance of fs_<ak> *)
(* uses the theorem fs_bool_inst *)
val (thy22,_) = foldl_map (fn (thy, (ak_name, T)) =>
let
val qu_class = Sign.full_name (sign_of thy) ("fs_"^ak_name);
val proof = EVERY [AxClass.intro_classes_tac [],
rtac (fs_bool_inst RS fs1) 1];
in
(AxClass.add_inst_arity_i ("bool",[],[qu_class]) proof thy,())
end) (thy21,ak_names_types);
(* shows that *(fs_<ak>,fs_<ak>) is an instance of fs_<ak> *)
(* uses the theorem fs_prod_inst *)
val (thy23,_) = foldl_map (fn (thy, (ak_name, T)) =>
let
val qu_class = Sign.full_name (sign_of thy) ("fs_"^ak_name);
val fs_inst = PureThy.get_thm thy (Name ("fs_"^ak_name^"_inst"));
val proof = EVERY [AxClass.intro_classes_tac [],
rtac ((fs_inst RS (fs_inst RS fs_prod_inst)) RS fs1) 1];
in
(AxClass.add_inst_arity_i ("*",[[qu_class],[qu_class]],[qu_class]) proof thy,())
end) (thy22,ak_names_types);
(* shows that list(fs_<ak>) is an instance of fs_<ak> *)
(* uses the theorem fs_list_inst *)
val (thy24,_) = foldl_map (fn (thy, (ak_name, T)) =>
let
val qu_class = Sign.full_name (sign_of thy) ("fs_"^ak_name);
val fs_inst = PureThy.get_thm thy (Name ("fs_"^ak_name^"_inst"));
val proof = EVERY [AxClass.intro_classes_tac [],
rtac ((fs_inst RS fs_list_inst) RS fs1) 1];
in
(AxClass.add_inst_arity_i ("List.list",[[qu_class]],[qu_class]) proof thy,())
end) (thy23,ak_names_types);
(*<<<<<<< cp_<ak>_<ai> class instances >>>>>>>*)
(*==============================================*)
val cp1 = PureThy.get_thm thy24 (Name "cp1");
val cp_unit_inst = PureThy.get_thm thy24 (Name "cp_unit_inst");
val cp_bool_inst = PureThy.get_thm thy24 (Name "cp_bool_inst");
val cp_prod_inst = PureThy.get_thm thy24 (Name "cp_prod_inst");
val cp_list_inst = PureThy.get_thm thy24 (Name "cp_list_inst");
val cp_fun_inst = PureThy.get_thm thy24 (Name "cp_fun_inst");
val cp_option_inst = PureThy.get_thm thy24 (Name "cp_option_inst");
val cp_noption_inst = PureThy.get_thm thy24 (Name "cp_noption_inst");
val pt_perm_compose = PureThy.get_thm thy24 (Name "pt_perm_compose");
val dj_pp_forget = PureThy.get_thm thy24 (Name "dj_perm_perm_forget");
(* shows that <aj> is an instance of cp_<ak>_<ai> *)
(* that needs a three-nested loop *)
val (thy25,_) = foldl_map (fn (thy, (ak_name, T)) =>
foldl_map (fn (thy', (ak_name', T')) =>
foldl_map (fn (thy'', (ak_name'', T'')) =>
let
val qu_name = Sign.full_name (sign_of thy'') ak_name;
val qu_class = Sign.full_name (sign_of thy'') ("cp_"^ak_name'^"_"^ak_name'');
val proof =
(if (ak_name'=ak_name'') then
(let
val pt_inst = PureThy.get_thm thy'' (Name ("pt_"^ak_name''^"_inst"));
val at_inst = PureThy.get_thm thy'' (Name ("at_"^ak_name''^"_inst"));
in
EVERY [AxClass.intro_classes_tac [],
rtac (at_inst RS (pt_inst RS pt_perm_compose)) 1]
end)
else
(let
val dj_inst = PureThy.get_thm thy'' (Name ("dj_"^ak_name''^"_"^ak_name'));
val simp_s = HOL_basic_ss addsimps
((dj_inst RS dj_pp_forget)::
(PureThy.get_thmss thy''
[Name (ak_name' ^"_prm_"^ak_name^"_def"),
Name (ak_name''^"_prm_"^ak_name^"_def")]));
in
EVERY [AxClass.intro_classes_tac [], simp_tac simp_s 1]
end))
in
(AxClass.add_inst_arity_i (qu_name,[],[qu_class]) proof thy'',())
end)
(thy', ak_names_types)) (thy, ak_names_types)) (thy24, ak_names_types);
(* shows that unit is an instance of cp_<ak>_<ai> *)
(* for every <ak>-combination *)
val (thy26,_) = foldl_map (fn (thy, (ak_name, T)) =>
foldl_map (fn (thy', (ak_name', T')) =>
let
val qu_class = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
val proof = EVERY [AxClass.intro_classes_tac [],rtac (cp_unit_inst RS cp1) 1];
in
(AxClass.add_inst_arity_i ("Product_Type.unit",[],[qu_class]) proof thy',())
end)
(thy, ak_names_types)) (thy25, ak_names_types);
(* shows that bool is an instance of cp_<ak>_<ai> *)
(* for every <ak>-combination *)
val (thy27,_) = foldl_map (fn (thy, (ak_name, T)) =>
foldl_map (fn (thy', (ak_name', T')) =>
let
val qu_class = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
val proof = EVERY [AxClass.intro_classes_tac [], rtac (cp_bool_inst RS cp1) 1];
in
(AxClass.add_inst_arity_i ("bool",[],[qu_class]) proof thy',())
end)
(thy, ak_names_types)) (thy26, ak_names_types);
(* shows that prod is an instance of cp_<ak>_<ai> *)
(* for every <ak>-combination *)
val (thy28,_) = foldl_map (fn (thy, (ak_name, T)) =>
foldl_map (fn (thy', (ak_name', T')) =>
let
val qu_class = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
val cp_inst = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
val proof = EVERY [AxClass.intro_classes_tac [],
rtac ((cp_inst RS (cp_inst RS cp_prod_inst)) RS cp1) 1];
in
(AxClass.add_inst_arity_i ("*",[[qu_class],[qu_class]],[qu_class]) proof thy',())
end)
(thy, ak_names_types)) (thy27, ak_names_types);
(* shows that list is an instance of cp_<ak>_<ai> *)
(* for every <ak>-combination *)
val (thy29,_) = foldl_map (fn (thy, (ak_name, T)) =>
foldl_map (fn (thy', (ak_name', T')) =>
let
val qu_class = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
val cp_inst = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
val proof = EVERY [AxClass.intro_classes_tac [],
rtac ((cp_inst RS cp_list_inst) RS cp1) 1];
in
(AxClass.add_inst_arity_i ("List.list",[[qu_class]],[qu_class]) proof thy',())
end)
(thy, ak_names_types)) (thy28, ak_names_types);
(* shows that function is an instance of cp_<ak>_<ai> *)
(* for every <ak>-combination *)
val (thy30,_) = foldl_map (fn (thy, (ak_name, T)) =>
foldl_map (fn (thy', (ak_name', T')) =>
let
val qu_class = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
val cp_inst = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
val pt_inst = PureThy.get_thm thy' (Name ("pt_"^ak_name^"_inst"));
val at_inst = PureThy.get_thm thy' (Name ("at_"^ak_name^"_inst"));
val proof = EVERY [AxClass.intro_classes_tac [],
rtac ((at_inst RS (pt_inst RS (cp_inst RS (cp_inst RS cp_fun_inst)))) RS cp1) 1];
in
(AxClass.add_inst_arity_i ("fun",[[qu_class],[qu_class]],[qu_class]) proof thy',())
end)
(thy, ak_names_types)) (thy29, ak_names_types);
(* shows that option is an instance of cp_<ak>_<ai> *)
(* for every <ak>-combination *)
val (thy31,_) = foldl_map (fn (thy, (ak_name, T)) =>
foldl_map (fn (thy', (ak_name', T')) =>
let
val qu_class = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
val cp_inst = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
val proof = EVERY [AxClass.intro_classes_tac [],
rtac ((cp_inst RS cp_option_inst) RS cp1) 1];
in
(AxClass.add_inst_arity_i ("Datatype.option",[[qu_class]],[qu_class]) proof thy',())
end)
(thy, ak_names_types)) (thy30, ak_names_types);
(* shows that nOption is an instance of cp_<ak>_<ai> *)
(* for every <ak>-combination *)
val (thy32,_) = foldl_map (fn (thy, (ak_name, T)) =>
foldl_map (fn (thy', (ak_name', T')) =>
let
val qu_class = Sign.full_name (sign_of thy') ("cp_"^ak_name^"_"^ak_name');
val cp_inst = PureThy.get_thm thy' (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
val proof = EVERY [AxClass.intro_classes_tac [],
rtac ((cp_inst RS cp_noption_inst) RS cp1) 1];
in
(AxClass.add_inst_arity_i ("nominal.nOption",[[qu_class]],[qu_class]) proof thy',())
end)
(thy, ak_names_types)) (thy31, ak_names_types);
(* abbreviations for some collection of rules *)
(*============================================*)
val abs_fun_pi = PureThy.get_thm thy32 (Name ("nominal.abs_fun_pi"));
val abs_fun_pi_ineq = PureThy.get_thm thy32 (Name ("nominal.abs_fun_pi_ineq"));
val abs_fun_eq = PureThy.get_thm thy32 (Name ("nominal.abs_fun_eq"));
val dj_perm_forget = PureThy.get_thm thy32 (Name ("nominal.dj_perm_forget"));
val dj_pp_forget = PureThy.get_thm thy32 (Name ("nominal.dj_perm_perm_forget"));
val fresh_iff = PureThy.get_thm thy32 (Name ("nominal.fresh_abs_fun_iff"));
val fresh_iff_ineq = PureThy.get_thm thy32 (Name ("nominal.fresh_abs_fun_iff_ineq"));
val abs_fun_supp = PureThy.get_thm thy32 (Name ("nominal.abs_fun_supp"));
val abs_fun_supp_ineq = PureThy.get_thm thy32 (Name ("nominal.abs_fun_supp_ineq"));
val pt_swap_bij = PureThy.get_thm thy32 (Name ("nominal.pt_swap_bij"));
val pt_fresh_fresh = PureThy.get_thm thy32 (Name ("nominal.pt_fresh_fresh"));
val pt_bij = PureThy.get_thm thy32 (Name ("nominal.pt_bij"));
val pt_perm_compose = PureThy.get_thm thy32 (Name ("nominal.pt_perm_compose"));
val perm_eq_app = PureThy.get_thm thy32 (Name ("nominal.perm_eq_app"));
val at_fresh = PureThy.get_thm thy32 (Name ("nominal.at_fresh"));
val at_calc = PureThy.get_thms thy32 (Name ("nominal.at_calc"));
val at_supp = PureThy.get_thm thy32 (Name ("nominal.at_supp"));
val dj_supp = PureThy.get_thm thy32 (Name ("nominal.dj_supp"));
(* abs_perm collects all lemmas for simplifying a permutation *)
(* in front of an abs_fun *)
val (thy33,_) =
let
val name = "abs_perm"
val thm_list = Library.flat (map (fn (ak_name, T) =>
let
val at_inst = PureThy.get_thm thy32 (Name ("at_"^ak_name^"_inst"));
val pt_inst = PureThy.get_thm thy32 (Name ("pt_"^ak_name^"_inst"));
val thm = [pt_inst, at_inst] MRS abs_fun_pi
val thm_list = map (fn (ak_name', T') =>
let
val cp_inst = PureThy.get_thm thy32 (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
in
[pt_inst, pt_inst, at_inst, cp_inst] MRS abs_fun_pi_ineq
end) ak_names_types;
in thm::thm_list end) (ak_names_types))
in
(PureThy.add_thmss [((name, thm_list),[])] thy32)
end;
val (thy34,_) =
let
(* takes a theorem and a list of theorems *)
(* produces a list of theorems of the form *)
(* [t1 RS thm,..,tn RS thm] where t1..tn in thms *)
fun instantiate thm thms = map (fn ti => ti RS thm) thms;
(* takes two theorem lists (hopefully of the same length) *)
(* produces a list of theorems of the form *)
(* [t1 RS m1,..,tn RS mn] where t1..tn in thms1 and m1..mn in thms2 *)
fun instantiate_zip thms1 thms2 =
map (fn (t1,t2) => t1 RS t2) (thms1 ~~ thms2);
(* list of all at_inst-theorems *)
val ats = map (fn ak => PureThy.get_thm thy33 (Name ("at_"^ak^"_inst"))) ak_names
(* list of all pt_inst-theorems *)
val pts = map (fn ak => PureThy.get_thm thy33 (Name ("pt_"^ak^"_inst"))) ak_names
(* list of all cp_inst-theorems *)
val cps =
let fun cps_fun (ak1,ak2) = PureThy.get_thm thy33 (Name ("cp_"^ak1^"_"^ak2^"_inst"))
in map cps_fun (cprod (ak_names,ak_names)) end;
(* list of all dj_inst-theorems *)
val djs =
let fun djs_fun (ak1,ak2) =
if ak1=ak2
then NONE
else SOME(PureThy.get_thm thy33 (Name ("dj_"^ak1^"_"^ak2)))
in List.mapPartial I (map djs_fun (cprod (ak_names,ak_names))) end;
fun inst_pt thms = Library.flat (map (fn ti => instantiate ti pts) thms);
fun inst_at thms = Library.flat (map (fn ti => instantiate ti ats) thms);
fun inst_pt_at thms = instantiate_zip ats (inst_pt thms);
fun inst_dj thms = Library.flat (map (fn ti => instantiate ti djs) thms);
in
thy33
|> PureThy.add_thmss [(("alpha", inst_pt_at [abs_fun_eq]),[])]
|>>> PureThy.add_thmss [(("perm_swap", inst_pt_at [pt_swap_bij]),[])]
|>>> PureThy.add_thmss [(("perm_fresh_fresh", inst_pt_at [pt_fresh_fresh]),[])]
|>>> PureThy.add_thmss [(("perm_bij", inst_pt_at [pt_bij]),[])]
|>>> PureThy.add_thmss [(("perm_compose", inst_pt_at [pt_perm_compose]),[])]
|>>> PureThy.add_thmss [(("perm_app_eq", inst_pt_at [perm_eq_app]),[])]
|>>> PureThy.add_thmss [(("supp_atm", (inst_at [at_supp]) @ (inst_dj [dj_supp])),[])]
|>>> PureThy.add_thmss [(("fresh_atm", inst_at [at_fresh]),[])]
|>>> PureThy.add_thmss [(("calc_atm", inst_at at_calc),[])]
end;
(* perm_dj collects all lemmas that forget an permutation *)
(* when it acts on an atom of different type *)
val (thy35,_) =
let
val name = "perm_dj"
val thm_list = Library.flat (map (fn (ak_name, T) =>
Library.flat (map (fn (ak_name', T') =>
if not (ak_name = ak_name')
then
let
val dj_inst = PureThy.get_thm thy34 (Name ("dj_"^ak_name^"_"^ak_name'));
in
[dj_inst RS dj_perm_forget, dj_inst RS dj_pp_forget]
end
else []) ak_names_types)) ak_names_types)
in
(PureThy.add_thmss [((name, thm_list),[])] thy34)
end;
(* abs_fresh collects all lemmas for simplifying a freshness *)
(* proposition involving an abs_fun *)
val (thy36,_) =
let
val name = "abs_fresh"
val thm_list = Library.flat (map (fn (ak_name, T) =>
let
val at_inst = PureThy.get_thm thy35 (Name ("at_"^ak_name^"_inst"));
val pt_inst = PureThy.get_thm thy35 (Name ("pt_"^ak_name^"_inst"));
val fs_inst = PureThy.get_thm thy35 (Name ("fs_"^ak_name^"_inst"));
val thm = [pt_inst, at_inst, (fs_inst RS fs1)] MRS fresh_iff
val thm_list = Library.flat (map (fn (ak_name', T') =>
(if (not (ak_name = ak_name'))
then
let
val cp_inst = PureThy.get_thm thy35 (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
val dj_inst = PureThy.get_thm thy35 (Name ("dj_"^ak_name'^"_"^ak_name));
in
[[pt_inst, pt_inst, at_inst, cp_inst, dj_inst] MRS fresh_iff_ineq]
end
else [])) ak_names_types);
in thm::thm_list end) (ak_names_types))
in
(PureThy.add_thmss [((name, thm_list),[])] thy35)
end;
(* abs_supp collects all lemmas for simplifying *)
(* support proposition involving an abs_fun *)
val (thy37,_) =
let
val name = "abs_supp"
val thm_list = Library.flat (map (fn (ak_name, T) =>
let
val at_inst = PureThy.get_thm thy36 (Name ("at_"^ak_name^"_inst"));
val pt_inst = PureThy.get_thm thy36 (Name ("pt_"^ak_name^"_inst"));
val fs_inst = PureThy.get_thm thy36 (Name ("fs_"^ak_name^"_inst"));
val thm1 = [pt_inst, at_inst, (fs_inst RS fs1)] MRS abs_fun_supp
val thm2 = [pt_inst, at_inst] MRS abs_fun_supp
val thm_list = Library.flat (map (fn (ak_name', T') =>
(if (not (ak_name = ak_name'))
then
let
val cp_inst = PureThy.get_thm thy36 (Name ("cp_"^ak_name^"_"^ak_name'^"_inst"));
val dj_inst = PureThy.get_thm thy36 (Name ("dj_"^ak_name'^"_"^ak_name));
in
[[pt_inst, pt_inst, at_inst, cp_inst, dj_inst] MRS abs_fun_supp_ineq]
end
else [])) ak_names_types);
in thm1::thm2::thm_list end) (ak_names_types))
in
(PureThy.add_thmss [((name, thm_list),[])] thy36)
end;
in NominalData.put (fold Symtab.update (map (rpair ()) full_ak_names)
(NominalData.get thy11)) thy37
end;
(* syntax und parsing *)
structure P = OuterParse and K = OuterKeyword;
val atom_declP =
OuterSyntax.command "atom_decl" "Declare new kinds of atoms" K.thy_decl
(Scan.repeat1 P.name >> (Toplevel.theory o create_nom_typedecls));
val _ = OuterSyntax.add_parsers [atom_declP];
val setup = [NominalData.init];
(*=======================================================================*)
(** FIXME: DatatypePackage should export this function **)
local
fun dt_recs (DtTFree _) = []
| dt_recs (DtType (_, dts)) = List.concat (map dt_recs dts)
| dt_recs (DtRec i) = [i];
fun dt_cases (descr: descr) (_, args, constrs) =
let
fun the_bname i = Sign.base_name (#1 (valOf (AList.lookup (op =) descr i)));
val bnames = map the_bname (distinct (List.concat (map dt_recs args)));
in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end;
fun induct_cases descr =
DatatypeProp.indexify_names (List.concat (map (dt_cases descr) (map #2 descr)));
fun exhaust_cases descr i = dt_cases descr (valOf (AList.lookup (op =) descr i));
in
fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);
fun mk_case_names_exhausts descr new =
map (RuleCases.case_names o exhaust_cases descr o #1)
(List.filter (fn ((_, (name, _, _))) => name mem_string new) descr);
end;
(*******************************)
val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma);
fun read_typ sign ((Ts, sorts), str) =
let
val T = Type.no_tvars (Sign.read_typ (sign, (AList.lookup op =)
(map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg
in (Ts @ [T], add_typ_tfrees (T, sorts)) end;
(** taken from HOL/Tools/datatype_aux.ML **)
fun indtac indrule indnames i st =
let
val ts = HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule));
val ts' = HOLogic.dest_conj (HOLogic.dest_Trueprop
(Logic.strip_imp_concl (List.nth (prems_of st, i - 1))));
val getP = if can HOLogic.dest_imp (hd ts) then
(apfst SOME) o HOLogic.dest_imp else pair NONE;
fun abstr (t1, t2) = (case t1 of
NONE => (case filter (fn Free (s, _) => s mem indnames | _ => false)
(term_frees t2) of
[Free (s, T)] => absfree (s, T, t2)
| _ => sys_error "indtac")
| SOME (_ $ t' $ _) => Abs ("x", fastype_of t', abstract_over (t', t2)))
val cert = cterm_of (Thm.sign_of_thm st);
val Ps = map (cert o head_of o snd o getP) ts;
val indrule' = cterm_instantiate (Ps ~~
(map (cert o abstr o getP) ts')) indrule
in
rtac indrule' i st
end;
fun gen_add_nominal_datatype prep_typ err flat_names new_type_names dts thy =
let
(* this theory is used just for parsing *)
val tmp_thy = thy |>
Theory.copy |>
Theory.add_types (map (fn (tvs, tname, mx, _) =>
(tname, length tvs, mx)) dts);
val sign = Theory.sign_of tmp_thy;
val atoms = atoms_of thy;
val classes = map (NameSpace.map_base (fn s => "pt_" ^ s)) atoms;
val cp_classes = List.concat (map (fn atom1 => map (fn atom2 =>
Sign.intern_class thy ("cp_" ^ Sign.base_name atom1 ^ "_" ^
Sign.base_name atom2)) atoms) atoms);
fun augment_sort S = S union classes;
val augment_sort_typ = map_type_tfree (fn (s, S) => TFree (s, augment_sort S));
fun prep_constr ((constrs, sorts), (cname, cargs, mx)) =
let val (cargs', sorts') = Library.foldl (prep_typ sign) (([], sorts), cargs)
in (constrs @ [(cname, cargs', mx)], sorts') end
fun prep_dt_spec ((dts, sorts), (tvs, tname, mx, constrs)) =
let val (constrs', sorts') = Library.foldl prep_constr (([], sorts), constrs)
in (dts @ [(tvs, tname, mx, constrs')], sorts') end
val (dts', sorts) = Library.foldl prep_dt_spec (([], []), dts);
val sorts' = map (apsnd augment_sort) sorts;
val tyvars = map #1 dts';
val types_syntax = map (fn (tvs, tname, mx, constrs) => (tname, mx)) dts';
val constr_syntax = map (fn (tvs, tname, mx, constrs) =>
map (fn (cname, cargs, mx) => (cname, mx)) constrs) dts';
val ps = map (fn (_, n, _, _) =>
(Sign.full_name sign n, Sign.full_name sign (n ^ "_Rep"))) dts;
val rps = map Library.swap ps;
fun replace_types (Type ("nominal.ABS", [T, U])) =
Type ("fun", [T, Type ("nominal.nOption", [replace_types U])])
| replace_types (Type (s, Ts)) =
Type (getOpt (AList.lookup op = ps s, s), map replace_types Ts)
| replace_types T = T;
fun replace_types' (Type (s, Ts)) =
Type (getOpt (AList.lookup op = rps s, s), map replace_types' Ts)
| replace_types' T = T;
val dts'' = map (fn (tvs, tname, mx, constrs) => (tvs, tname ^ "_Rep", NoSyn,
map (fn (cname, cargs, mx) => (cname,
map (augment_sort_typ o replace_types) cargs, NoSyn)) constrs)) dts';
val new_type_names' = map (fn n => n ^ "_Rep") new_type_names;
val full_new_type_names' = map (Sign.full_name (sign_of thy)) new_type_names';
val ({induction, ...},thy1) =
DatatypePackage.add_datatype_i err flat_names new_type_names' dts'' thy;
val SOME {descr, ...} = Symtab.lookup
(DatatypePackage.get_datatypes thy1) (hd full_new_type_names');
val typ_of_dtyp = typ_of_dtyp descr sorts';
fun nth_dtyp i = typ_of_dtyp (DtRec i);
(**** define permutation functions ****)
val permT = mk_permT (TFree ("'x", HOLogic.typeS));
val pi = Free ("pi", permT);
val perm_types = map (fn (i, _) =>
let val T = nth_dtyp i
in permT --> T --> T end) descr;
val perm_names = replicate (length new_type_names) "nominal.perm" @
DatatypeProp.indexify_names (map (fn i => Sign.full_name (sign_of thy1)
("perm_" ^ name_of_typ (nth_dtyp i)))
(length new_type_names upto length descr - 1));
val perm_names_types = perm_names ~~ perm_types;
val perm_eqs = List.concat (map (fn (i, (_, _, constrs)) =>
let val T = nth_dtyp i
in map (fn (cname, dts) =>
let
val Ts = map typ_of_dtyp dts;
val names = DatatypeProp.make_tnames Ts;
val args = map Free (names ~~ Ts);
val c = Const (cname, Ts ---> T);
fun perm_arg (dt, x) =
let val T = type_of x
in if is_rec_type dt then
let val (Us, _) = strip_type T
in list_abs (map (pair "x") Us,
Const (List.nth (perm_names_types, body_index dt)) $ pi $
list_comb (x, map (fn (i, U) =>
Const ("nominal.perm", permT --> U --> U) $
(Const ("List.rev", permT --> permT) $ pi) $
Bound i) ((length Us - 1 downto 0) ~~ Us)))
end
else Const ("nominal.perm", permT --> T --> T) $ pi $ x
end;
in
(("", HOLogic.mk_Trueprop (HOLogic.mk_eq
(Const (List.nth (perm_names_types, i)) $
Free ("pi", mk_permT (TFree ("'x", HOLogic.typeS))) $
list_comb (c, args),
list_comb (c, map perm_arg (dts ~~ args))))), [])
end) constrs
end) descr);
val (thy2, perm_simps) = thy1 |>
Theory.add_consts_i (map (fn (s, T) => (Sign.base_name s, T, NoSyn))
(List.drop (perm_names_types, length new_type_names))) |>
PrimrecPackage.add_primrec_i "" perm_eqs;
(**** prove that permutation functions introduced by unfolding are ****)
(**** equivalent to already existing permutation functions ****)
val _ = warning ("length descr: " ^ string_of_int (length descr));
val _ = warning ("length new_type_names: " ^ string_of_int (length new_type_names));
val perm_indnames = DatatypeProp.make_tnames (map body_type perm_types);
val perm_fun_def = PureThy.get_thm thy2 (Name "perm_fun_def");
val unfolded_perm_eq_thms =
if length descr = length new_type_names then []
else map standard (List.drop (split_conj_thm
(Goal.prove thy2 [] []
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
(map (fn (c as (s, T), x) =>
let val [T1, T2] = binder_types T
in HOLogic.mk_eq (Const c $ pi $ Free (x, T2),
Const ("nominal.perm", T) $ pi $ Free (x, T2))
end)
(perm_names_types ~~ perm_indnames))))
(fn _ => EVERY [indtac induction perm_indnames 1,
ALLGOALS (asm_full_simp_tac
(simpset_of thy2 addsimps [perm_fun_def]))])),
length new_type_names));
(**** prove [] \<bullet> t = t ****)
val _ = warning "perm_empty_thms";
val perm_empty_thms = List.concat (map (fn a =>
let val permT = mk_permT (Type (a, []))
in map standard (List.take (split_conj_thm
(Goal.prove thy2 [] []
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
(map (fn ((s, T), x) => HOLogic.mk_eq
(Const (s, permT --> T --> T) $
Const ("List.list.Nil", permT) $ Free (x, T),
Free (x, T)))
(perm_names ~~
map body_type perm_types ~~ perm_indnames))))
(fn _ => EVERY [indtac induction perm_indnames 1,
ALLGOALS (asm_full_simp_tac (simpset_of thy2))])),
length new_type_names))
end)
atoms);
(**** prove (pi1 @ pi2) \<bullet> t = pi1 \<bullet> (pi2 \<bullet> t) ****)
val _ = warning "perm_append_thms";
(*FIXME: these should be looked up statically*)
val at_pt_inst = PureThy.get_thm thy2 (Name "at_pt_inst");
val pt2 = PureThy.get_thm thy2 (Name "pt2");
val perm_append_thms = List.concat (map (fn a =>
let
val permT = mk_permT (Type (a, []));
val pi1 = Free ("pi1", permT);
val pi2 = Free ("pi2", permT);
val pt_inst = PureThy.get_thm thy2 (Name ("pt_" ^ Sign.base_name a ^ "_inst"));
val pt2' = pt_inst RS pt2;
val pt2_ax = PureThy.get_thm thy2
(Name (NameSpace.map_base (fn s => "pt_" ^ s ^ "2") a));
in List.take (map standard (split_conj_thm
(Goal.prove thy2 [] []
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
(map (fn ((s, T), x) =>
let val perm = Const (s, permT --> T --> T)
in HOLogic.mk_eq
(perm $ (Const ("List.op @", permT --> permT --> permT) $
pi1 $ pi2) $ Free (x, T),
perm $ pi1 $ (perm $ pi2 $ Free (x, T)))
end)
(perm_names ~~
map body_type perm_types ~~ perm_indnames))))
(fn _ => EVERY [indtac induction perm_indnames 1,
ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt2', pt2_ax]))]))),
length new_type_names)
end) atoms);
(**** prove pi1 ~ pi2 ==> pi1 \<bullet> t = pi2 \<bullet> t ****)
val _ = warning "perm_eq_thms";
val pt3 = PureThy.get_thm thy2 (Name "pt3");
val pt3_rev = PureThy.get_thm thy2 (Name "pt3_rev");
val perm_eq_thms = List.concat (map (fn a =>
let
val permT = mk_permT (Type (a, []));
val pi1 = Free ("pi1", permT);
val pi2 = Free ("pi2", permT);
(*FIXME: not robust - better access these theorems using NominalData?*)
val at_inst = PureThy.get_thm thy2 (Name ("at_" ^ Sign.base_name a ^ "_inst"));
val pt_inst = PureThy.get_thm thy2 (Name ("pt_" ^ Sign.base_name a ^ "_inst"));
val pt3' = pt_inst RS pt3;
val pt3_rev' = at_inst RS (pt_inst RS pt3_rev);
val pt3_ax = PureThy.get_thm thy2
(Name (NameSpace.map_base (fn s => "pt_" ^ s ^ "3") a));
in List.take (map standard (split_conj_thm
(Goal.prove thy2 [] [] (Logic.mk_implies
(HOLogic.mk_Trueprop (Const ("nominal.prm_eq",
permT --> permT --> HOLogic.boolT) $ pi1 $ pi2),
HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
(map (fn ((s, T), x) =>
let val perm = Const (s, permT --> T --> T)
in HOLogic.mk_eq
(perm $ pi1 $ Free (x, T),
perm $ pi2 $ Free (x, T))
end)
(perm_names ~~
map body_type perm_types ~~ perm_indnames)))))
(fn _ => EVERY [indtac induction perm_indnames 1,
ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt3', pt3_rev', pt3_ax]))]))),
length new_type_names)
end) atoms);
(**** prove pi1 \<bullet> (pi2 \<bullet> t) = (pi1 \<bullet> pi2) \<bullet> (pi1 \<bullet> t) ****)
val cp1 = PureThy.get_thm thy2 (Name "cp1");
val dj_cp = PureThy.get_thm thy2 (Name "dj_cp");
val pt_perm_compose = PureThy.get_thm thy2 (Name "pt_perm_compose");
val pt_perm_compose_rev = PureThy.get_thm thy2 (Name "pt_perm_compose_rev");
val dj_perm_perm_forget = PureThy.get_thm thy2 (Name "dj_perm_perm_forget");
fun composition_instance name1 name2 thy =
let
val name1' = Sign.base_name name1;
val name2' = Sign.base_name name2;
val cp_class = Sign.intern_class thy ("cp_" ^ name1' ^ "_" ^ name2');
val permT1 = mk_permT (Type (name1, []));
val permT2 = mk_permT (Type (name2, []));
val augment = map_type_tfree
(fn (x, S) => TFree (x, cp_class :: S));
val Ts = map (augment o body_type) perm_types;
val cp_inst = PureThy.get_thm thy
(Name ("cp_" ^ name1' ^ "_" ^ name2' ^ "_inst"));
val simps = simpset_of thy addsimps (perm_fun_def ::
(if name1 <> name2 then
let val dj = PureThy.get_thm thy (Name ("dj_" ^ name2' ^ "_" ^ name1'))
in [dj RS (cp_inst RS dj_cp), dj RS dj_perm_perm_forget] end
else
let
val at_inst = PureThy.get_thm thy (Name ("at_" ^ name1' ^ "_inst"));
val pt_inst = PureThy.get_thm thy (Name ("pt_" ^ name1' ^ "_inst"))
in
[cp_inst RS cp1 RS sym,
at_inst RS (pt_inst RS pt_perm_compose) RS sym,
at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym]
end))
val thms = split_conj_thm (standard (Goal.prove thy [] []
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
(map (fn ((s, T), x) =>
let
val pi1 = Free ("pi1", permT1);
val pi2 = Free ("pi2", permT2);
val perm1 = Const (s, permT1 --> T --> T);
val perm2 = Const (s, permT2 --> T --> T);
val perm3 = Const ("nominal.perm", permT1 --> permT2 --> permT2)
in HOLogic.mk_eq
(perm1 $ pi1 $ (perm2 $ pi2 $ Free (x, T)),
perm2 $ (perm3 $ pi1 $ pi2) $ (perm1 $ pi1 $ Free (x, T)))
end)
(perm_names ~~ Ts ~~ perm_indnames))))
(fn _ => EVERY [indtac induction perm_indnames 1,
ALLGOALS (asm_full_simp_tac simps)])))
in
foldl (fn ((s, tvs), thy) => AxClass.add_inst_arity_i
(s, replicate (length tvs) (cp_class :: classes), [cp_class])
(AxClass.intro_classes_tac [] THEN ALLGOALS (resolve_tac thms)) thy)
thy (full_new_type_names' ~~ tyvars)
end;
val (thy3, perm_thmss) = thy2 |>
fold (fn name1 => fold (composition_instance name1) atoms) atoms |>
curry (Library.foldr (fn ((i, (tyname, args, _)), thy) =>
AxClass.add_inst_arity_i (tyname, replicate (length args) classes, classes)
(AxClass.intro_classes_tac [] THEN REPEAT (EVERY
[resolve_tac perm_empty_thms 1,
resolve_tac perm_append_thms 1,
resolve_tac perm_eq_thms 1, assume_tac 1])) thy))
(List.take (descr, length new_type_names)) |>
PureThy.add_thmss
[((space_implode "_" new_type_names ^ "_unfolded_perm_eq",
unfolded_perm_eq_thms), [Simplifier.simp_add_global]),
((space_implode "_" new_type_names ^ "_perm_empty",
perm_empty_thms), [Simplifier.simp_add_global]),
((space_implode "_" new_type_names ^ "_perm_append",
perm_append_thms), [Simplifier.simp_add_global]),
((space_implode "_" new_type_names ^ "_perm_eq",
perm_eq_thms), [Simplifier.simp_add_global])];
(**** Define representing sets ****)
val _ = warning "representing sets";
val rep_set_names = map (Sign.full_name thy3) (DatatypeProp.indexify_names
(map (fn (i, _) => name_of_typ (nth_dtyp i) ^ "_set") descr));
val big_rep_name =
space_implode "_" (DatatypeProp.indexify_names (List.mapPartial
(fn (i, ("nominal.nOption", _, _)) => NONE
| (i, _) => SOME (name_of_typ (nth_dtyp i))) descr)) ^ "_set";
val _ = warning ("big_rep_name: " ^ big_rep_name);
fun strip_option (dtf as DtType ("fun", [dt, DtRec i])) =
(case AList.lookup op = descr i of
SOME ("nominal.nOption", _, [(_, [dt']), _]) =>
apfst (cons dt) (strip_option dt')
| _ => ([], dtf))
| strip_option dt = ([], dt);
fun make_intr s T (cname, cargs) =
let
fun mk_prem (dt, (j, j', prems, ts)) =
let
val (dts, dt') = strip_option dt;
val (dts', dt'') = strip_dtyp dt';
val Ts = map typ_of_dtyp dts;
val Us = map typ_of_dtyp dts';
val T = typ_of_dtyp dt'';
val free = mk_Free "x" (Us ---> T) j;
val free' = app_bnds free (length Us);
fun mk_abs_fun (T, (i, t)) =
let val U = fastype_of t
in (i + 1, Const ("nominal.abs_fun", [T, U, T] --->
Type ("nominal.nOption", [U])) $ mk_Free "y" T i $ t)
end
in (j + 1, j' + length Ts,
case dt'' of
DtRec k => list_all (map (pair "x") Us,
HOLogic.mk_Trueprop (HOLogic.mk_mem (free',
Const (List.nth (rep_set_names, k),
HOLogic.mk_setT T)))) :: prems
| _ => prems,
snd (foldr mk_abs_fun (j', free) Ts) :: ts)
end;
val (_, _, prems, ts) = foldr mk_prem (1, 1, [], []) cargs;
val concl = HOLogic.mk_Trueprop (HOLogic.mk_mem
(list_comb (Const (cname, map fastype_of ts ---> T), ts),
Const (s, HOLogic.mk_setT T)))
in Logic.list_implies (prems, concl)
end;
val (intr_ts, ind_consts) =
apfst List.concat (ListPair.unzip (List.mapPartial
(fn ((_, ("nominal.nOption", _, _)), _) => NONE
| ((i, (_, _, constrs)), rep_set_name) =>
let val T = nth_dtyp i
in SOME (map (make_intr rep_set_name T) constrs,
Const (rep_set_name, HOLogic.mk_setT T))
end)
(descr ~~ rep_set_names)));
val (thy4, {raw_induct = rep_induct, intrs = rep_intrs, ...}) =
setmp InductivePackage.quiet_mode false
(InductivePackage.add_inductive_i false true big_rep_name false true false
ind_consts (map (fn x => (("", x), [])) intr_ts) []) thy3;
(**** Prove that representing set is closed under permutation ****)
val _ = warning "proving closure under permutation...";
val perm_indnames' = List.mapPartial
(fn (x, (_, ("nominal.nOption", _, _))) => NONE | (x, _) => SOME x)
(perm_indnames ~~ descr);
fun mk_perm_closed name = map (fn th => standard (th RS mp))
(List.take (split_conj_thm (Goal.prove thy4 [] []
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map
(fn (S, x) =>
let
val S = map_term_types (map_type_tfree
(fn (s, cs) => TFree (s, cs union cp_classes))) S;
val T = HOLogic.dest_setT (fastype_of S);
val permT = mk_permT (Type (name, []))
in HOLogic.mk_imp (HOLogic.mk_mem (Free (x, T), S),
HOLogic.mk_mem (Const ("nominal.perm", permT --> T --> T) $
Free ("pi", permT) $ Free (x, T), S))
end) (ind_consts ~~ perm_indnames'))))
(fn _ => EVERY (* CU: added perm_fun_def in the final tactic in order to deal with funs *)
[indtac rep_induct [] 1,
ALLGOALS (simp_tac (simpset_of thy4 addsimps
(symmetric perm_fun_def :: PureThy.get_thms thy4 (Name ("abs_perm"))))),
ALLGOALS (resolve_tac rep_intrs
THEN_ALL_NEW (asm_full_simp_tac (simpset_of thy4 addsimps [perm_fun_def])))])),
length new_type_names));
(* FIXME: theorems are stored in database for testing only *)
val perm_closed_thmss = map mk_perm_closed atoms;
val (thy5, _) = PureThy.add_thmss [(("perm_closed",
List.concat perm_closed_thmss), [])] thy4;
(**** typedef ****)
val _ = warning "defining type...";
val (thy6, typedefs) =
foldl_map (fn (thy, ((((name, mx), tvs), c), name')) =>
setmp TypedefPackage.quiet_mode true
(TypedefPackage.add_typedef_i false (SOME name') (name, tvs, mx) c NONE
(rtac exI 1 THEN
QUIET_BREADTH_FIRST (has_fewer_prems 1)
(resolve_tac rep_intrs 1))) thy |> (fn (thy, r) =>
let
val permT = mk_permT (TFree (variant tvs "'a", HOLogic.typeS));
val pi = Free ("pi", permT);
val tvs' = map (fn s => TFree (s, the (AList.lookup op = sorts' s))) tvs;
val T = Type (Sign.intern_type thy name, tvs');
val Const (_, Type (_, [U])) = c
in apsnd (pair r o hd)
(PureThy.add_defs_i true [(("prm_" ^ name ^ "_def", Logic.mk_equals
(Const ("nominal.perm", permT --> T --> T) $ pi $ Free ("x", T),
Const (Sign.intern_const thy ("Abs_" ^ name), U --> T) $
(Const ("nominal.perm", permT --> U --> U) $ pi $
(Const (Sign.intern_const thy ("Rep_" ^ name), T --> U) $
Free ("x", T))))), [])] thy)
end))
(thy5, types_syntax ~~ tyvars ~~
(List.take (ind_consts, length new_type_names)) ~~ new_type_names);
val perm_defs = map snd typedefs;
val Abs_inverse_thms = map (#Abs_inverse o fst) typedefs;
val Rep_inverse_thms = map (#Rep_inverse o fst) typedefs;
val Rep_thms = map (#Rep o fst) typedefs;
val big_name = space_implode "_" new_type_names;
(** prove that new types are in class pt_<name> **)
val _ = warning "prove that new types are in class pt_<name> ...";
fun pt_instance ((class, atom), perm_closed_thms) =
fold (fn (((({Abs_inverse, Rep_inverse, Rep, ...},
perm_def), name), tvs), perm_closed) => fn thy =>
AxClass.add_inst_arity_i
(Sign.intern_type thy name,
replicate (length tvs) (classes @ cp_classes), [class])
(EVERY [AxClass.intro_classes_tac [],
rewrite_goals_tac [perm_def],
asm_full_simp_tac (simpset_of thy addsimps [Rep_inverse]) 1,
asm_full_simp_tac (simpset_of thy addsimps
[Rep RS perm_closed RS Abs_inverse]) 1,
asm_full_simp_tac (HOL_basic_ss addsimps [PureThy.get_thm thy
(Name ("pt_" ^ Sign.base_name atom ^ "3"))]) 1]) thy)
(typedefs ~~ new_type_names ~~ tyvars ~~ perm_closed_thms);
(** prove that new types are in class cp_<name1>_<name2> **)
val _ = warning "prove that new types are in class cp_<name1>_<name2> ...";
fun cp_instance (atom1, perm_closed_thms1) (atom2, perm_closed_thms2) thy =
let
val name = "cp_" ^ Sign.base_name atom1 ^ "_" ^ Sign.base_name atom2;
val class = Sign.intern_class thy name;
val cp1' = PureThy.get_thm thy (Name (name ^ "_inst")) RS cp1
in fold (fn ((((({Abs_inverse, Rep_inverse, Rep, ...},
perm_def), name), tvs), perm_closed1), perm_closed2) => fn thy =>
AxClass.add_inst_arity_i
(Sign.intern_type thy name,
replicate (length tvs) (classes @ cp_classes), [class])
(EVERY [AxClass.intro_classes_tac [],
rewrite_goals_tac [perm_def],
asm_full_simp_tac (simpset_of thy addsimps
((Rep RS perm_closed1 RS Abs_inverse) ::
(if atom1 = atom2 then []
else [Rep RS perm_closed2 RS Abs_inverse]))) 1,
cong_tac 1,
rtac refl 1,
rtac cp1' 1]) thy)
(typedefs ~~ new_type_names ~~ tyvars ~~ perm_closed_thms1 ~~
perm_closed_thms2) thy
end;
val thy7 = fold (fn x => fn thy => thy |>
pt_instance x |>
fold (cp_instance (apfst snd x)) (atoms ~~ perm_closed_thmss))
(classes ~~ atoms ~~ perm_closed_thmss) thy6;
(**** constructors ****)
fun mk_abs_fun (x, t) =
let
val T = fastype_of x;
val U = fastype_of t
in
Const ("nominal.abs_fun", T --> U --> T -->
Type ("nominal.nOption", [U])) $ x $ t
end;
val (ty_idxs, _) = foldl
(fn ((i, ("nominal.nOption", _, _)), p) => p
| ((i, _), (ty_idxs, j)) => (ty_idxs @ [(i, j)], j + 1)) ([], 0) descr;
fun reindex (DtType (s, dts)) = DtType (s, map reindex dts)
| reindex (DtRec i) = DtRec (the (AList.lookup op = ty_idxs i))
| reindex dt = dt;
fun strip_suffix i s = implode (List.take (explode s, size s - i));
(** strips the "_Rep" in type names *)
fun strip_nth_name i s =
let val xs = NameSpace.unpack s;
in NameSpace.pack (Library.nth_map (length xs - i) (strip_suffix 4) xs) end;
val descr'' = List.mapPartial
(fn (i, ("nominal.nOption", _, _)) => NONE
| (i, (s, dts, constrs)) => SOME (the (AList.lookup op = ty_idxs i),
(strip_nth_name 1 s, map reindex dts,
map (fn (cname, cargs) =>
(strip_nth_name 2 cname,
foldl (fn (dt, dts) =>
let val (dts', dt') = strip_option dt
in (dts @ dts' @ [reindex dt']) end) [] cargs)) constrs))) descr;
val (descr1, descr2) = splitAt (length new_type_names, descr'');
val descr' = [descr1, descr2];
val typ_of_dtyp' = replace_types' o typ_of_dtyp;
val rep_names = map (fn s =>
Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names;
val abs_names = map (fn s =>
Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names;
val recTs' = List.mapPartial
(fn ((_, ("nominal.nOption", _, _)), T) => NONE
| (_, T) => SOME T) (descr ~~ get_rec_types descr sorts');
val recTs = get_rec_types (List.concat descr') sorts';
val newTs' = Library.take (length new_type_names, recTs');
val newTs = Library.take (length new_type_names, recTs);
val full_new_type_names = map (Sign.full_name (sign_of thy)) new_type_names;
fun make_constr_def tname T T' ((thy, defs, eqns), ((cname, cargs), (cname', mx))) =
let
fun constr_arg (dt, (j, l_args, r_args)) =
let
val x' = mk_Free "x" (typ_of_dtyp' dt) j;
val (dts, dt') = strip_option dt;
val xs = map (fn (dt, i) => mk_Free "x" (typ_of_dtyp' dt) i)
(dts ~~ (j upto j + length dts - 1))
val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts)
val (dts', dt'') = strip_dtyp dt'
in case dt'' of
DtRec k => if k < length new_type_names then
(j + length dts + 1,
xs @ x :: l_args,
foldr mk_abs_fun
(list_abs (map (pair "z" o typ_of_dtyp') dts',
Const (List.nth (rep_names, k), typ_of_dtyp' dt'' -->
typ_of_dtyp dt'') $ app_bnds x (length dts')))
xs :: r_args)
else error "nested recursion not (yet) supported"
| _ => (j + 1, x' :: l_args, x' :: r_args)
end
val (_, l_args, r_args) = foldr constr_arg (1, [], []) cargs;
val abs_name = Sign.intern_const (Theory.sign_of thy) ("Abs_" ^ tname);
val rep_name = Sign.intern_const (Theory.sign_of thy) ("Rep_" ^ tname);
val constrT = map fastype_of l_args ---> T;
val lhs = list_comb (Const (Sign.full_name thy (Sign.base_name cname),
constrT), l_args);
val rhs = list_comb (Const (cname, map fastype_of r_args ---> T'), r_args);
val def = Logic.mk_equals (lhs, Const (abs_name, T' --> T) $ rhs);
val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq
(Const (rep_name, T --> T') $ lhs, rhs));
val def_name = (Sign.base_name cname) ^ "_def";
val (thy', [def_thm]) = thy |>
Theory.add_consts_i [(cname', constrT, mx)] |>
(PureThy.add_defs_i false o map Thm.no_attributes) [(def_name, def)]
in (thy', defs @ [def_thm], eqns @ [eqn]) end;
fun dt_constr_defs ((thy, defs, eqns, dist_lemmas),
(((((_, (_, _, constrs)), tname), T), T'), constr_syntax)) =
let
val rep_const = cterm_of thy
(Const (Sign.intern_const thy ("Rep_" ^ tname), T --> T'));
val dist = standard (cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma);
val (thy', defs', eqns') = Library.foldl (make_constr_def tname T T')
((Theory.add_path tname thy, defs, []), constrs ~~ constr_syntax)
in
(parent_path flat_names thy', defs', eqns @ [eqns'], dist_lemmas @ [dist])
end;
val (thy8, constr_defs, constr_rep_eqns, dist_lemmas) = Library.foldl dt_constr_defs
((thy7, [], [], []), List.take (descr, length new_type_names) ~~
new_type_names ~~ newTs ~~ newTs' ~~ constr_syntax);
val abs_inject_thms = map (fn tname =>
PureThy.get_thm thy8 (Name ("Abs_" ^ tname ^ "_inject"))) new_type_names;
val rep_inject_thms = map (fn tname =>
PureThy.get_thm thy8 (Name ("Rep_" ^ tname ^ "_inject"))) new_type_names;
val rep_thms = map (fn tname =>
PureThy.get_thm thy8 (Name ("Rep_" ^ tname))) new_type_names;
val rep_inverse_thms = map (fn tname =>
PureThy.get_thm thy8 (Name ("Rep_" ^ tname ^ "_inverse"))) new_type_names;
(* prove theorem Rep_i (Constr_j ...) = Constr'_j ... *)
fun prove_constr_rep_thm eqn =
let
val inj_thms = map (fn r => r RS iffD1) abs_inject_thms;
val rewrites = constr_defs @ map mk_meta_eq rep_inverse_thms
in standard (Goal.prove thy8 [] [] eqn (fn _ => EVERY
[resolve_tac inj_thms 1,
rewrite_goals_tac rewrites,
rtac refl 3,
resolve_tac rep_intrs 2,
REPEAT (resolve_tac rep_thms 1)]))
end;
val constr_rep_thmss = map (map prove_constr_rep_thm) constr_rep_eqns;
(* prove theorem pi \<bullet> Rep_i x = Rep_i (pi \<bullet> x) *)
fun prove_perm_rep_perm (atom, perm_closed_thms) = map (fn th =>
let
val _ $ (_ $ (Rep $ x) $ _) = Logic.unvarify (prop_of th);
val Type ("fun", [T, U]) = fastype_of Rep;
val permT = mk_permT (Type (atom, []));
val pi = Free ("pi", permT);
in
standard (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
(Const ("nominal.perm", permT --> U --> U) $ pi $ (Rep $ x),
Rep $ (Const ("nominal.perm", permT --> T --> T) $ pi $ x))))
(fn _ => simp_tac (HOL_basic_ss addsimps (perm_defs @ Abs_inverse_thms @
perm_closed_thms @ Rep_thms)) 1))
end) Rep_thms;
val perm_rep_perm_thms = List.concat (map prove_perm_rep_perm
(atoms ~~ perm_closed_thmss));
(* prove distinctness theorems *)
val distinct_props = setmp DatatypeProp.dtK 1000
(DatatypeProp.make_distincts new_type_names descr' sorts') thy8;
val dist_rewrites = map (fn (rep_thms, dist_lemma) =>
dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0]))
(constr_rep_thmss ~~ dist_lemmas);
fun prove_distinct_thms (_, []) = []
| prove_distinct_thms (p as (rep_thms, dist_lemma), t::ts) =
let
val dist_thm = standard (Goal.prove thy8 [] [] t (fn _ =>
simp_tac (simpset_of thy8 addsimps (dist_lemma :: rep_thms)) 1))
in dist_thm::(standard (dist_thm RS not_sym))::
(prove_distinct_thms (p, ts))
end;
val distinct_thms = map prove_distinct_thms
(constr_rep_thmss ~~ dist_lemmas ~~ distinct_props);
(** prove equations for permutation functions **)
val abs_perm = PureThy.get_thms thy8 (Name "abs_perm"); (* FIXME *)
val perm_simps' = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
let val T = replace_types' (nth_dtyp i)
in List.concat (map (fn (atom, perm_closed_thms) =>
map (fn ((cname, dts), constr_rep_thm) =>
let
val cname = Sign.intern_const thy8
(NameSpace.append tname (Sign.base_name cname));
val permT = mk_permT (Type (atom, []));
val pi = Free ("pi", permT);
fun perm t =
let val T = fastype_of t
in Const ("nominal.perm", permT --> T --> T) $ pi $ t end;
fun constr_arg (dt, (j, l_args, r_args)) =
let
val x' = mk_Free "x" (typ_of_dtyp' dt) j;
val (dts, dt') = strip_option dt;
val Ts = map typ_of_dtyp' dts;
val xs = map (fn (T, i) => mk_Free "x" T i)
(Ts ~~ (j upto j + length dts - 1))
val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts);
val (dts', dt'') = strip_dtyp dt';
in case dt'' of
DtRec k => if k < length new_type_names then
(j + length dts + 1,
xs @ x :: l_args,
map perm (xs @ [x]) @ r_args)
else error "nested recursion not (yet) supported"
| _ => (j + 1, x' :: l_args, perm x' :: r_args)
end
val (_, l_args, r_args) = foldr constr_arg (1, [], []) dts;
val c = Const (cname, map fastype_of l_args ---> T)
in
standard (Goal.prove thy8 [] []
(HOLogic.mk_Trueprop (HOLogic.mk_eq
(perm (list_comb (c, l_args)), list_comb (c, r_args))))
(fn _ => EVERY
[simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: perm_defs)) 1,
simp_tac (HOL_basic_ss addsimps (Rep_thms @ Abs_inverse_thms @
constr_defs @ perm_closed_thms)) 1,
TRY (simp_tac (HOL_basic_ss addsimps
(symmetric perm_fun_def :: abs_perm)) 1),
TRY (simp_tac (HOL_basic_ss addsimps
(perm_fun_def :: perm_defs @ Rep_thms @ Abs_inverse_thms @
perm_closed_thms)) 1)]))
end) (constrs ~~ constr_rep_thms)) (atoms ~~ perm_closed_thmss))
end) (List.take (descr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
(** prove injectivity of constructors **)
val rep_inject_thms' = map (fn th => th RS sym) rep_inject_thms;
val alpha = PureThy.get_thms thy8 (Name "alpha");
val abs_fresh = PureThy.get_thms thy8 (Name "abs_fresh");
val fresh_def = PureThy.get_thm thy8 (Name "fresh_def");
val supp_def = PureThy.get_thm thy8 (Name "supp_def");
val inject_thms = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
let val T = replace_types' (nth_dtyp i)
in List.mapPartial (fn ((cname, dts), constr_rep_thm) =>
if null dts then NONE else SOME
let
val cname = Sign.intern_const thy8
(NameSpace.append tname (Sign.base_name cname));
fun make_inj (dt, (j, args1, args2, eqs)) =
let
val x' = mk_Free "x" (typ_of_dtyp' dt) j;
val y' = mk_Free "y" (typ_of_dtyp' dt) j;
val (dts, dt') = strip_option dt;
val Ts_idx = map typ_of_dtyp' dts ~~ (j upto j + length dts - 1);
val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
val ys = map (fn (T, i) => mk_Free "y" T i) Ts_idx;
val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts);
val y = mk_Free "y" (typ_of_dtyp' dt') (j + length dts);
val (dts', dt'') = strip_dtyp dt';
in case dt'' of
DtRec k => if k < length new_type_names then
(j + length dts + 1,
xs @ (x :: args1), ys @ (y :: args2),
HOLogic.mk_eq
(foldr mk_abs_fun x xs, foldr mk_abs_fun y ys) :: eqs)
else error "nested recursion not (yet) supported"
| _ => (j + 1, x' :: args1, y' :: args2, HOLogic.mk_eq (x', y') :: eqs)
end;
val (_, args1, args2, eqs) = foldr make_inj (1, [], [], []) dts;
val Ts = map fastype_of args1;
val c = Const (cname, Ts ---> T)
in
standard (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
(HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)),
foldr1 HOLogic.mk_conj eqs)))
(fn _ => EVERY
[asm_full_simp_tac (simpset_of thy8 addsimps (constr_rep_thm ::
rep_inject_thms')) 1,
TRY (asm_full_simp_tac (HOL_basic_ss addsimps (fresh_def :: supp_def ::
alpha @ abs_perm @ abs_fresh @ rep_inject_thms @
perm_rep_perm_thms)) 1),
TRY (asm_full_simp_tac (HOL_basic_ss addsimps (perm_fun_def ::
expand_fun_eq :: rep_inject_thms @ perm_rep_perm_thms)) 1)]))
end) (constrs ~~ constr_rep_thms)
end) (List.take (descr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
(** equations for support and freshness **)
val Un_assoc = PureThy.get_thm thy8 (Name "Un_assoc");
val de_Morgan_conj = PureThy.get_thm thy8 (Name "de_Morgan_conj");
val Collect_disj_eq = PureThy.get_thm thy8 (Name "Collect_disj_eq");
val finite_Un = PureThy.get_thm thy8 (Name "finite_Un");
val (supp_thms, fresh_thms) = ListPair.unzip (map ListPair.unzip
(map (fn ((((i, (_, _, constrs)), tname), inject_thms'), perm_thms') =>
let val T = replace_types' (nth_dtyp i)
in List.concat (map (fn (cname, dts) => map (fn atom =>
let
val cname = Sign.intern_const thy8
(NameSpace.append tname (Sign.base_name cname));
val atomT = Type (atom, []);
fun process_constr (dt, (j, args1, args2)) =
let
val x' = mk_Free "x" (typ_of_dtyp' dt) j;
val (dts, dt') = strip_option dt;
val Ts_idx = map typ_of_dtyp' dts ~~ (j upto j + length dts - 1);
val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts);
val (dts', dt'') = strip_dtyp dt';
in case dt'' of
DtRec k => if k < length new_type_names then
(j + length dts + 1,
xs @ (x :: args1), foldr mk_abs_fun x xs :: args2)
else error "nested recursion not (yet) supported"
| _ => (j + 1, x' :: args1, x' :: args2)
end;
val (_, args1, args2) = foldr process_constr (1, [], []) dts;
val Ts = map fastype_of args1;
val c = list_comb (Const (cname, Ts ---> T), args1);
fun supp t =
Const ("nominal.supp", fastype_of t --> HOLogic.mk_setT atomT) $ t;
fun fresh t =
Const ("nominal.fresh", atomT --> fastype_of t --> HOLogic.boolT) $
Free ("a", atomT) $ t;
val supp_thm = standard (Goal.prove thy8 [] []
(HOLogic.mk_Trueprop (HOLogic.mk_eq
(supp c,
if null dts then Const ("{}", HOLogic.mk_setT atomT)
else foldr1 (HOLogic.mk_binop "op Un") (map supp args2))))
(fn _ =>
simp_tac (HOL_basic_ss addsimps (supp_def ::
Un_assoc :: de_Morgan_conj :: Collect_disj_eq :: finite_Un ::
symmetric empty_def :: Finites.emptyI :: simp_thms @
abs_perm @ abs_fresh @ inject_thms' @ perm_thms')) 1))
in
(supp_thm,
standard (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
(fresh c,
if null dts then HOLogic.true_const
else foldr1 HOLogic.mk_conj (map fresh args2))))
(fn _ =>
simp_tac (simpset_of thy8 addsimps [fresh_def, supp_thm]) 1)))
end) atoms) constrs)
end) (List.take (descr, length new_type_names) ~~ new_type_names ~~ inject_thms ~~ perm_simps')));
(**** Induction theorem ****)
val arities = get_arities (List.concat descr');
fun mk_funs_inv thm =
let
val {sign, prop, ...} = rep_thm thm;
val _ $ (_ $ (Const (_, Type (_, [U, _])) $ _ $ S)) $
(_ $ (_ $ (r $ (a $ _)) $ _)) = Type.freeze prop;
val used = add_term_tfree_names (a, []);
fun mk_thm i =
let
val Ts = map (TFree o rpair HOLogic.typeS)
(variantlist (replicate i "'t", used));
val f = Free ("f", Ts ---> U)
in standard (Goal.prove sign [] [] (Logic.mk_implies
(HOLogic.mk_Trueprop (HOLogic.list_all
(map (pair "x") Ts, HOLogic.mk_mem (app_bnds f i, S))),
HOLogic.mk_Trueprop (HOLogic.mk_eq (list_abs (map (pair "x") Ts,
r $ (a $ app_bnds f i)), f))))
(fn _ => EVERY [REPEAT (rtac ext 1), REPEAT (etac allE 1), rtac thm 1, atac 1]))
end
in map (fn r => r RS subst) (thm :: map mk_thm arities) end;
fun mk_indrule_lemma ((prems, concls), (((i, _), T), U)) =
let
val Rep_t = Const (List.nth (rep_names, i), T --> U) $
mk_Free "x" T i;
val Abs_t = Const (List.nth (abs_names, i), U --> T)
in (prems @ [HOLogic.imp $ HOLogic.mk_mem (Rep_t,
Const (List.nth (rep_set_names, i), HOLogic.mk_setT U)) $
(mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))],
concls @ [mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ mk_Free "x" T i])
end;
val (indrule_lemma_prems, indrule_lemma_concls) =
Library.foldl mk_indrule_lemma (([], []), (List.concat descr' ~~ recTs ~~ recTs'));
val indrule_lemma = standard (Goal.prove thy8 [] []
(Logic.mk_implies
(HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems),
HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY
[REPEAT (etac conjE 1),
REPEAT (EVERY
[TRY (rtac conjI 1), full_simp_tac (HOL_basic_ss addsimps Rep_inverse_thms) 1,
etac mp 1, resolve_tac Rep_thms 1])]));
val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma)));
val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else
map (Free o apfst fst o dest_Var) Ps;
val indrule_lemma' = cterm_instantiate
(map (cterm_of thy8) Ps ~~ map (cterm_of thy8) frees) indrule_lemma;
val Abs_inverse_thms' = List.concat (map mk_funs_inv Abs_inverse_thms);
val dt_induct_prop = DatatypeProp.make_ind descr' sorts';
val dt_induct = standard (Goal.prove thy8 []
(Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop)
(fn prems => EVERY
[rtac indrule_lemma' 1,
(DatatypeAux.indtac rep_induct THEN_ALL_NEW ObjectLogic.atomize_tac) 1,
EVERY (map (fn (prem, r) => (EVERY
[REPEAT (eresolve_tac Abs_inverse_thms' 1),
simp_tac (HOL_basic_ss addsimps [symmetric r]) 1,
DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)]))
(prems ~~ constr_defs))]));
val case_names_induct = mk_case_names_induct (List.concat descr');
(**** prove that new datatypes have finite support ****)
val indnames = DatatypeProp.make_tnames recTs;
val abs_supp = PureThy.get_thms thy8 (Name "abs_supp");
val supp_atm = PureThy.get_thms thy8 (Name "supp_atm");
val finite_supp_thms = map (fn atom =>
let val atomT = Type (atom, [])
in map standard (List.take
(split_conj_thm (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop
(foldr1 HOLogic.mk_conj (map (fn (s, T) => HOLogic.mk_mem
(Const ("nominal.supp", T --> HOLogic.mk_setT atomT) $ Free (s, T),
Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT atomT))))
(indnames ~~ recTs))))
(fn _ => indtac dt_induct indnames 1 THEN
ALLGOALS (asm_full_simp_tac (simpset_of thy8 addsimps
(abs_supp @ supp_atm @
PureThy.get_thms thy8 (Name ("fs_" ^ Sign.base_name atom ^ "1")) @
List.concat supp_thms))))),
length new_type_names))
end) atoms;
val (thy9, _) = thy8 |>
Theory.add_path big_name |>
PureThy.add_thms [(("induct_weak", dt_induct), [case_names_induct])] |>>
Theory.parent_path |>>>
DatatypeAux.store_thmss "distinct" new_type_names distinct_thms |>>>
DatatypeAux.store_thmss "constr_rep" new_type_names constr_rep_thmss |>>>
DatatypeAux.store_thmss "perm" new_type_names perm_simps' |>>>
DatatypeAux.store_thmss "inject" new_type_names inject_thms |>>>
DatatypeAux.store_thmss "supp" new_type_names supp_thms |>>>
DatatypeAux.store_thmss "fresh" new_type_names fresh_thms |>>
fold (fn (atom, ths) => fn thy =>
let val class = Sign.intern_class thy ("fs_" ^ Sign.base_name atom)
in fold (fn T => AxClass.add_inst_arity_i
(fst (dest_Type T),
replicate (length sorts) [class], [class])
(AxClass.intro_classes_tac [] THEN resolve_tac ths 1)) newTs thy
end) (atoms ~~ finite_supp_thms);
in
(thy9, perm_eq_thms)
end;
val add_nominal_datatype = gen_add_nominal_datatype read_typ true;
(* FIXME: The following stuff should be exported by DatatypePackage *)
local structure P = OuterParse and K = OuterKeyword in
val datatype_decl =
Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
(P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix));
fun mk_datatype args =
let
val names = map (fn ((((NONE, _), t), _), _) => t | ((((SOME t, _), _), _), _) => t) args;
val specs = map (fn ((((_, vs), t), mx), cons) =>
(vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
in #1 o add_nominal_datatype false names specs end;
val nominal_datatypeP =
OuterSyntax.command "nominal_datatype" "define inductive datatypes" K.thy_decl
(P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
val _ = OuterSyntax.add_parsers [nominal_datatypeP];
end;
end