|
(* Title: HOL/Nominal/nominal_atoms.ML
Author: Christian Urban and Stefan Berghofer, TU Muenchen
Declaration of atom types to be used in nominal datatypes.
*)
signature NOMINAL_ATOMS =
sig
val create_nom_typedecls : string list -> theory -> theory
type atom_info
val get_atom_infos : theory -> atom_info Symtab.table
val get_atom_info : theory -> string -> atom_info option
val the_atom_info : theory -> string -> atom_info
val fs_class_of : theory -> string -> string
val pt_class_of : theory -> string -> string
val cp_class_of : theory -> string -> string -> string
val at_inst_of : theory -> string -> thm
val pt_inst_of : theory -> string -> thm
val cp_inst_of : theory -> string -> string -> thm
val dj_thm_of : theory -> string -> string -> thm
val atoms_of : theory -> string list
val mk_permT : typ -> typ
end
structure NominalAtoms : NOMINAL_ATOMS =
struct
val finite_emptyI = @{thm "finite.emptyI"};
val Collect_const = @{thm "Collect_const"};
val inductive_forall_def = @{thm HOL.induct_forall_def};
(* theory data *)
type atom_info =
{pt_class : string,
fs_class : string,
cp_classes : string Symtab.table,
at_inst : thm,
pt_inst : thm,
cp_inst : thm Symtab.table,
dj_thms : thm Symtab.table};
structure NominalData = Theory_Data
(
type T = atom_info Symtab.table;
val empty = Symtab.empty;
val extend = I;
fun merge data = Symtab.merge (K true) data;
);
fun make_atom_info ((((((pt_class, fs_class), cp_classes), at_inst), pt_inst), cp_inst), dj_thms) =
{pt_class = pt_class,
fs_class = fs_class,
cp_classes = cp_classes,
at_inst = at_inst,
pt_inst = pt_inst,
cp_inst = cp_inst,
dj_thms = dj_thms};
val get_atom_infos = NominalData.get;
val get_atom_info = Symtab.lookup o NominalData.get;
fun gen_lookup lookup name = case lookup name of
SOME info => info
| NONE => error ("Unknown atom type " ^ quote name);
fun the_atom_info thy = gen_lookup (get_atom_info thy);
fun gen_lookup' f thy = the_atom_info thy #> f;
fun gen_lookup'' f thy =
gen_lookup' (f #> Symtab.lookup #> gen_lookup) thy;
val fs_class_of = gen_lookup' #fs_class;
val pt_class_of = gen_lookup' #pt_class;
val at_inst_of = gen_lookup' #at_inst;
val pt_inst_of = gen_lookup' #pt_inst;
val cp_class_of = gen_lookup'' #cp_classes;
val cp_inst_of = gen_lookup'' #cp_inst;
val dj_thm_of = gen_lookup'' #dj_thms;
fun atoms_of thy = map fst (Symtab.dest (NominalData.get thy));
fun mk_permT T = HOLogic.listT (HOLogic.mk_prodT (T, T));
fun mk_Cons x xs =
let val T = fastype_of x
in Const (\<^const_name>\<open>Cons\<close>, T --> HOLogic.listT T --> HOLogic.listT T) $ x $ xs end;
fun add_thms_string args = Global_Theory.add_thms ((map o apfst o apfst) Binding.name args);
fun add_thmss_string args = Global_Theory.add_thmss ((map o apfst o apfst) Binding.name args);
(* 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
val (_,thy1) =
fold_map (fn ak => fn thy =>
let val dt = ((Binding.name ak, [], NoSyn), [(Binding.name ak, [\<^typ>\<open>nat\<close>], NoSyn)])
val (dt_names, thy1) = BNF_LFP_Compat.add_datatype [BNF_LFP_Compat.Kill_Type_Args] [dt] thy;
val injects = maps (#inject o BNF_LFP_Compat.the_info thy1 []) dt_names;
val ak_type = Type (Sign.intern_type thy1 ak,[])
val ak_sign = Sign.intern_const thy1 ak
val inj_type = \<^typ>\<open>nat\<close> --> ak_type
val inj_on_type = inj_type --> \<^typ>\<open>nat set\<close> --> \<^typ>\<open>bool\<close>
(* first statement *)
val stmnt1 = HOLogic.mk_Trueprop
(Const (\<^const_name>\<open>inj_on\<close>,inj_on_type) $
Const (ak_sign,inj_type) $ HOLogic.mk_UNIV \<^typ>\<open>nat\<close>)
val simp1 = @{thm inj_on_def} :: injects;
fun proof1 ctxt = EVERY [simp_tac (put_simpset HOL_basic_ss ctxt addsimps simp1) 1,
resolve_tac ctxt @{thms ballI} 1,
resolve_tac ctxt @{thms ballI} 1,
resolve_tac ctxt @{thms impI} 1,
assume_tac ctxt 1]
val (inj_thm,thy2) =
add_thms_string [((ak^"_inj",Goal.prove_global thy1 [] [] stmnt1 (proof1 o #context)), [])] thy1
(* second statement *)
val y = Free ("y",ak_type)
val stmnt2 = HOLogic.mk_Trueprop
(HOLogic.mk_exists ("x",\<^typ>\<open>nat\<close>,HOLogic.mk_eq (y,Const (ak_sign,inj_type) $ Bound 0)))
val proof2 = fn {prems, context = ctxt} =>
Induct_Tacs.case_tac ctxt "y" [] NONE 1 THEN
asm_simp_tac (put_simpset HOL_basic_ss ctxt addsimps simp1) 1 THEN
resolve_tac ctxt @{thms exI} 1 THEN
resolve_tac ctxt @{thms refl} 1
(* third statement *)
val (inject_thm,thy3) =
add_thms_string [((ak^"_injection",Goal.prove_global thy2 [] [] stmnt2 proof2), [])] thy2
val stmnt3 = HOLogic.mk_Trueprop
(HOLogic.mk_not
(Const (\<^const_name>\<open>finite\<close>, HOLogic.mk_setT ak_type --> HOLogic.boolT) $
HOLogic.mk_UNIV ak_type))
val simp2 = [@{thm image_def},@{thm bex_UNIV}]@inject_thm
val simp3 = [@{thm UNIV_def}]
fun proof3 ctxt = EVERY [cut_facts_tac inj_thm 1,
dresolve_tac ctxt @{thms range_inj_infinite} 1,
asm_full_simp_tac (put_simpset HOL_basic_ss ctxt addsimps simp2) 1,
simp_tac (put_simpset HOL_basic_ss ctxt addsimps simp3) 1]
val (inf_thm,thy4) =
add_thms_string [((ak^"_infinite",Goal.prove_global thy3 [] [] stmnt3 (proof3 o #context)), [])] thy3
in
((inj_thm,inject_thm,inf_thm),thy4)
end) 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 thy1) ak_names;
val ak_names_types = ak_names ~~ map (Type o rpair []) full_ak_names;
(* 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 (swap_eqs, thy3) = fold_map (fn (ak_name, T) => fn thy =>
let
val thy' = Sign.add_path "rec" thy;
val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
val swap_name = "swap_" ^ ak_name;
val full_swap_name = Sign.full_bname thy' swap_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 (\<^const_name>\<open>If\<close>, HOLogic.boolT --> T --> T --> T);
val cswap_akname = Const (full_swap_name, swapT);
val cswap = Const (\<^const_name>\<open>Nominal.swap\<close>, swapT)
val name = swap_name ^ "_def";
val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq
(Free (swap_name, swapT) $ 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' |>
BNF_LFP_Compat.primrec_global
[(Binding.name swap_name, SOME swapT, NoSyn)]
[((Binding.empty_atts, def1), [], [])] ||>
Sign.parent_path ||>>
Global_Theory.add_defs_unchecked true
[((Binding.name name, def2), [])] |>> (snd o fst)
end) ak_names_types thy1;
(* 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 (prm_eqs, thy4) = fold_map (fn (ak_name, T) => fn thy =>
let
val thy' = Sign.add_path "rec" thy;
val swapT = HOLogic.mk_prodT (T, T) --> T --> T;
val swap_name = Sign.full_bname thy' ("swap_" ^ ak_name)
val prmT = mk_permT T --> T --> T;
val prm_name = ak_name ^ "_prm_" ^ ak_name;
val prm = Free (prm_name, prmT);
val x = Free ("x", HOLogic.mk_prodT (T, T));
val xs = Free ("xs", mk_permT T);
val a = Free ("a", T) ;
val cnil = Const (\<^const_name>\<open>Nil\<close>, mk_permT T);
val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq (prm $ cnil $ a, a));
val def2 = HOLogic.mk_Trueprop (HOLogic.mk_eq
(prm $ mk_Cons x xs $ a,
Const (swap_name, swapT) $ x $ (prm $ xs $ a)));
in
thy' |>
BNF_LFP_Compat.primrec_global
[(Binding.name prm_name, SOME prmT, NoSyn)]
(map (fn def => ((Binding.empty_atts, def), [], [])) [def1, def2]) ||>
Sign.parent_path
end) ak_names_types thy3;
(* 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 (perm_defs, thy5) = fold_map (fn (ak_name, T) => fn thy =>
fold_map (fn (ak_name', T') => fn thy' =>
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 (\<^const_name>\<open>Nominal.perm\<close>, mk_permT T --> T' --> T');
val thy'' = Sign.add_path "rec" thy'
val cperm_def = Const (Sign.full_bname thy'' perm_def_name, mk_permT T --> T' --> T');
val thy''' = Sign.parent_path thy'';
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
Global_Theory.add_defs_unchecked true [((Binding.name name, def), [])] thy'''
end) ak_names_types thy) ak_names_types thy4;
(* proves that every atom-kind is an instance of at *)
(* lemma at_<ak>_inst: *)
(* at TYPE(<ak>) *)
val (prm_cons_thms,thy6) =
thy5 |> add_thms_string (map (fn (ak_name, T) =>
let
val ak_name_qu = Sign.full_bname thy5 (ak_name);
val i_type = Type(ak_name_qu,[]);
val cat = Const (\<^const_name>\<open>Nominal.at\<close>, Term.itselfT i_type --> HOLogic.boolT);
val at_type = Logic.mk_type i_type;
fun proof ctxt =
simp_tac (put_simpset HOL_ss ctxt
addsimps maps (Global_Theory.get_thms thy5)
["at_def",
ak_name ^ "_prm_" ^ ak_name ^ "_def",
ak_name ^ "_prm_" ^ ak_name ^ ".simps",
"swap_" ^ ak_name ^ "_def",
"swap_" ^ ak_name ^ ".simps",
ak_name ^ "_infinite"]) 1;
val name = "at_"^ak_name^ "_inst";
val statement = HOLogic.mk_Trueprop (cat $ at_type);
in
((name, Goal.prove_global thy5 [] [] statement (proof o #context)), [])
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 (pt_ax_classes,thy7) = fold_map (fn (ak_name, T) => fn thy =>
let
val cl_name = "pt_"^ak_name;
val ty = TFree("'a", \<^sort>\<open>type\<close>);
val x = Free ("x", ty);
val pi1 = Free ("pi1", mk_permT T);
val pi2 = Free ("pi2", mk_permT T);
val cperm = Const (\<^const_name>\<open>Nominal.perm\<close>, mk_permT T --> ty --> ty);
val cnil = Const (\<^const_name>\<open>Nil\<close>, mk_permT T);
val cappend = Const (\<^const_name>\<open>append\<close>, mk_permT T --> mk_permT T --> mk_permT T);
val cprm_eq = Const (\<^const_name>\<open>Nominal.prm_eq\<close>, 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
Axclass.define_class (Binding.name cl_name, \<^sort>\<open>type\<close>) []
[((Binding.name (cl_name ^ "1"), [Simplifier.simp_add]), [axiom1]),
((Binding.name (cl_name ^ "2"), []), [axiom2]),
((Binding.name (cl_name ^ "3"), []), [axiom3])] thy
end) ak_names_types thy6;
(* 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 (prm_inst_thms,thy8) =
thy7 |> add_thms_string (map (fn (ak_name, T) =>
let
val ak_name_qu = Sign.full_bname thy7 ak_name;
val pt_name_qu = Sign.full_bname thy7 ("pt_"^ak_name);
val i_type1 = TFree("'x",[pt_name_qu]);
val i_type2 = Type(ak_name_qu,[]);
val cpt =
Const (\<^const_name>\<open>Nominal.pt\<close>, (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;
fun proof ctxt =
simp_tac (put_simpset HOL_ss ctxt addsimps maps (Global_Theory.get_thms thy7)
["pt_def",
"pt_" ^ ak_name ^ "1",
"pt_" ^ ak_name ^ "2",
"pt_" ^ ak_name ^ "3"]) 1;
val name = "pt_"^ak_name^ "_inst";
val statement = HOLogic.mk_Trueprop (cpt $ pt_type $ at_type);
in
((name, Goal.prove_global thy7 [] [] statement (proof o #context)), [])
end) ak_names_types);
(* declares an fs-axclass for every atom-kind *)
(* axclass fs_<ak> *)
(* fs_<ak>1: finite ((supp x)::<ak> set) *)
val (fs_ax_classes,thy11) = fold_map (fn (ak_name, T) => fn thy =>
let
val cl_name = "fs_"^ak_name;
val pt_name = Sign.full_bname thy ("pt_"^ak_name);
val ty = TFree("'a",\<^sort>\<open>type\<close>);
val x = Free ("x", ty);
val csupp = Const (\<^const_name>\<open>Nominal.supp\<close>, ty --> HOLogic.mk_setT T);
val cfinite = Const (\<^const_name>\<open>finite\<close>, HOLogic.mk_setT T --> HOLogic.boolT)
val axiom1 = HOLogic.mk_Trueprop (cfinite $ (csupp $ x));
in
Axclass.define_class (Binding.name cl_name, [pt_name]) []
[((Binding.name (cl_name ^ "1"), []), [axiom1])] thy
end) ak_names_types thy8;
(* 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 (fs_inst_thms,thy12) =
thy11 |> add_thms_string (map (fn (ak_name, T) =>
let
val ak_name_qu = Sign.full_bname thy11 ak_name;
val fs_name_qu = Sign.full_bname thy11 ("fs_"^ak_name);
val i_type1 = TFree("'x",[fs_name_qu]);
val i_type2 = Type(ak_name_qu,[]);
val cfs = Const (\<^const_name>\<open>Nominal.fs\<close>,
(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;
fun proof ctxt =
simp_tac (put_simpset HOL_ss ctxt addsimps maps (Global_Theory.get_thms thy11)
["fs_def",
"fs_" ^ ak_name ^ "1"]) 1;
val name = "fs_"^ak_name^ "_inst";
val statement = HOLogic.mk_Trueprop (cfs $ fs_type $ at_type);
in
((name, Goal.prove_global thy11 [] [] statement (proof o #context)), [])
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 (cp_ax_classes,thy12b) = fold_map (fn (ak_name, T) => fn thy =>
fold_map (fn (ak_name', T') => fn thy' =>
let
val cl_name = "cp_"^ak_name^"_"^ak_name';
val ty = TFree("'a",\<^sort>\<open>type\<close>);
val x = Free ("x", ty);
val pi1 = Free ("pi1", mk_permT T);
val pi2 = Free ("pi2", mk_permT T');
val cperm1 = Const (\<^const_name>\<open>Nominal.perm\<close>, mk_permT T --> ty --> ty);
val cperm2 = Const (\<^const_name>\<open>Nominal.perm\<close>, mk_permT T' --> ty --> ty);
val cperm3 = Const (\<^const_name>\<open>Nominal.perm\<close>, 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
Axclass.define_class (Binding.name cl_name, \<^sort>\<open>type\<close>) []
[((Binding.name (cl_name ^ "1"), []), [ax1])] thy'
end) ak_names_types thy) ak_names_types thy12;
(* 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 (cp_thms,thy12c) = fold_map (fn (ak_name, T) => fn thy =>
fold_map (fn (ak_name', T') => fn thy' =>
let
val ak_name_qu = Sign.full_bname thy' (ak_name);
val ak_name_qu' = Sign.full_bname thy' (ak_name');
val cp_name_qu = Sign.full_bname 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 (\<^const_name>\<open>Nominal.cp\<close>,
(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 cp1 = Global_Theory.get_thm thy' ("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');
fun proof ctxt =
simp_tac (put_simpset HOL_basic_ss ctxt
addsimps maps (Global_Theory.get_thms thy') ["cp_def"]) 1
THEN EVERY [resolve_tac ctxt [allI] 1,
resolve_tac ctxt [allI] 1,
resolve_tac ctxt [allI] 1,
resolve_tac ctxt [cp1] 1];
in
yield_singleton add_thms_string ((name,
Goal.prove_global thy' [] [] statement (proof o #context)), []) thy'
end)
ak_names_types thy) ak_names_types thy12b;
(* proves for every non-trivial <ak>-combination a disjointness *)
(* theorem; i.e. <ak1> != <ak2> *)
(* lemma ds_<ak1>_<ak2>: *)
(* dj TYPE(<ak1>) TYPE(<ak2>) *)
val (dj_thms, thy12d) = fold_map (fn (ak_name,T) => fn thy =>
fold_map (fn (ak_name',T') => fn thy' =>
(if not (ak_name = ak_name')
then
let
val ak_name_qu = Sign.full_bname thy' ak_name;
val ak_name_qu' = Sign.full_bname thy' ak_name';
val i_type1 = Type(ak_name_qu,[]);
val i_type2 = Type(ak_name_qu',[]);
val cdj = Const (\<^const_name>\<open>Nominal.disjoint\<close>,
(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;
fun proof ctxt =
simp_tac (put_simpset HOL_ss ctxt
addsimps maps (Global_Theory.get_thms thy')
["disjoint_def",
ak_name ^ "_prm_" ^ ak_name' ^ "_def",
ak_name' ^ "_prm_" ^ ak_name ^ "_def"]) 1;
val name = "dj_"^ak_name^"_"^ak_name';
val statement = HOLogic.mk_Trueprop (cdj $ at_type $ at_type');
in
add_thms_string [((name, Goal.prove_global thy' [] [] statement (proof o #context)), [])] thy'
end
else
([],thy'))) (* do nothing branch, if ak_name = ak_name' *)
ak_names_types thy) ak_names_types thy12c;
(******** pt_<ak> class instances ********)
(*=========================================*)
(* some abbreviations for theorems *)
val pt1 = @{thm "pt1"};
val pt2 = @{thm "pt2"};
val pt3 = @{thm "pt3"};
val at_pt_inst = @{thm "at_pt_inst"};
val pt_unit_inst = @{thm "pt_unit_inst"};
val pt_prod_inst = @{thm "pt_prod_inst"};
val pt_nprod_inst = @{thm "pt_nprod_inst"};
val pt_list_inst = @{thm "pt_list_inst"};
val pt_optn_inst = @{thm "pt_option_inst"};
val pt_noptn_inst = @{thm "pt_noption_inst"};
val pt_fun_inst = @{thm "pt_fun_inst"};
val pt_set_inst = @{thm "pt_set_inst"};
(* for all atom-kind combinations <ak>/<ak'> show that *)
(* every <ak> is an instance of pt_<ak'>; the proof for *)
(* ak!=ak' is by definition; the case ak=ak' uses at_pt_inst. *)
val thy13 = fold (fn ak_name => fn thy =>
fold (fn ak_name' => fn thy' =>
let
val qu_name = Sign.full_bname thy' ak_name';
val cls_name = Sign.full_bname thy' ("pt_"^ak_name);
val at_inst = Global_Theory.get_thm thy' ("at_" ^ ak_name' ^ "_inst");
fun proof1 ctxt = EVERY [Class.intro_classes_tac ctxt [],
resolve_tac ctxt [(at_inst RS at_pt_inst) RS pt1] 1,
resolve_tac ctxt [(at_inst RS at_pt_inst) RS pt2] 1,
resolve_tac ctxt [(at_inst RS at_pt_inst) RS pt3] 1,
assume_tac ctxt 1];
fun proof2 ctxt =
Class.intro_classes_tac ctxt [] THEN
REPEAT (asm_simp_tac
(put_simpset HOL_basic_ss ctxt addsimps
maps (Global_Theory.get_thms thy') [ak_name ^ "_prm_" ^ ak_name' ^ "_def"]) 1);
in
thy'
|> Axclass.prove_arity (qu_name,[],[cls_name])
(fn ctxt => if ak_name = ak_name' then proof1 ctxt else proof2 ctxt)
end) ak_names thy) ak_names thy12d;
(* show that *)
(* fun(pt_<ak>,pt_<ak>) *)
(* noption(pt_<ak>) *)
(* option(pt_<ak>) *)
(* list(pt_<ak>) *)
(* *(pt_<ak>,pt_<ak>) *)
(* nprod(pt_<ak>,pt_<ak>) *)
(* unit *)
(* set(pt_<ak>) *)
(* are instances of pt_<ak> *)
val thy18 = fold (fn ak_name => fn thy =>
let
val cls_name = Sign.full_bname thy ("pt_"^ak_name);
val at_thm = Global_Theory.get_thm thy ("at_"^ak_name^"_inst");
val pt_inst = Global_Theory.get_thm thy ("pt_"^ak_name^"_inst");
fun pt_proof thm ctxt =
EVERY [Class.intro_classes_tac ctxt [],
resolve_tac ctxt [thm RS pt1] 1,
resolve_tac ctxt [thm RS pt2] 1,
resolve_tac ctxt [thm RS pt3] 1,
assume_tac ctxt 1];
val pt_thm_fun = at_thm RS (pt_inst RS (pt_inst RS pt_fun_inst));
val pt_thm_set = pt_inst RS pt_set_inst;
val pt_thm_noptn = pt_inst RS pt_noptn_inst;
val pt_thm_optn = pt_inst RS pt_optn_inst;
val pt_thm_list = pt_inst RS pt_list_inst;
val pt_thm_prod = pt_inst RS (pt_inst RS pt_prod_inst);
val pt_thm_nprod = pt_inst RS (pt_inst RS pt_nprod_inst);
val pt_thm_unit = pt_unit_inst;
in
thy
|> Axclass.prove_arity (\<^type_name>\<open>fun\<close>,[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_fun)
|> Axclass.prove_arity (\<^type_name>\<open>set\<close>,[[cls_name]],[cls_name]) (pt_proof pt_thm_set)
|> Axclass.prove_arity (\<^type_name>\<open>noption\<close>,[[cls_name]],[cls_name]) (pt_proof pt_thm_noptn)
|> Axclass.prove_arity (\<^type_name>\<open>option\<close>,[[cls_name]],[cls_name]) (pt_proof pt_thm_optn)
|> Axclass.prove_arity (\<^type_name>\<open>list\<close>,[[cls_name]],[cls_name]) (pt_proof pt_thm_list)
|> Axclass.prove_arity (\<^type_name>\<open>prod\<close>,[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_prod)
|> Axclass.prove_arity (\<^type_name>\<open>nprod\<close>,[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_nprod)
|> Axclass.prove_arity (\<^type_name>\<open>unit\<close>,[],[cls_name]) (pt_proof pt_thm_unit)
end) ak_names thy13;
(******** fs_<ak> class instances ********)
(*=========================================*)
(* abbreviations for some lemmas *)
val fs1 = @{thm "fs1"};
val fs_at_inst = @{thm "fs_at_inst"};
val fs_unit_inst = @{thm "fs_unit_inst"};
val fs_prod_inst = @{thm "fs_prod_inst"};
val fs_nprod_inst = @{thm "fs_nprod_inst"};
val fs_list_inst = @{thm "fs_list_inst"};
val fs_option_inst = @{thm "fs_option_inst"};
val dj_supp = @{thm "dj_supp"};
(* shows that <ak> is an instance of fs_<ak> *)
(* uses the theorem at_<ak>_inst *)
val thy20 = fold (fn ak_name => fn thy =>
fold (fn ak_name' => fn thy' =>
let
val qu_name = Sign.full_bname thy' ak_name';
val qu_class = Sign.full_bname thy' ("fs_"^ak_name);
fun proof ctxt =
(if ak_name = ak_name'
then
let val at_thm = Global_Theory.get_thm thy' ("at_"^ak_name^"_inst") in
EVERY [Class.intro_classes_tac ctxt [],
resolve_tac ctxt [(at_thm RS fs_at_inst) RS fs1] 1]
end
else
let val dj_inst = Global_Theory.get_thm thy' ("dj_"^ak_name'^"_"^ak_name);
val simp_s =
put_simpset HOL_basic_ss ctxt addsimps [dj_inst RS dj_supp, finite_emptyI];
in EVERY [Class.intro_classes_tac ctxt [], asm_simp_tac simp_s 1] end)
in
Axclass.prove_arity (qu_name,[],[qu_class]) proof thy'
end) ak_names thy) ak_names thy18;
(* shows that *)
(* unit *)
(* *(fs_<ak>,fs_<ak>) *)
(* nprod(fs_<ak>,fs_<ak>) *)
(* list(fs_<ak>) *)
(* option(fs_<ak>) *)
(* are instances of fs_<ak> *)
val thy24 = fold (fn ak_name => fn thy =>
let
val cls_name = Sign.full_bname thy ("fs_"^ak_name);
val fs_inst = Global_Theory.get_thm thy ("fs_"^ak_name^"_inst");
fun fs_proof thm ctxt =
EVERY [Class.intro_classes_tac ctxt [], resolve_tac ctxt [thm RS fs1] 1];
val fs_thm_unit = fs_unit_inst;
val fs_thm_prod = fs_inst RS (fs_inst RS fs_prod_inst);
val fs_thm_nprod = fs_inst RS (fs_inst RS fs_nprod_inst);
val fs_thm_list = fs_inst RS fs_list_inst;
val fs_thm_optn = fs_inst RS fs_option_inst;
in
thy
|> Axclass.prove_arity (\<^type_name>\<open>unit\<close>,[],[cls_name]) (fs_proof fs_thm_unit)
|> Axclass.prove_arity (\<^type_name>\<open>prod\<close>,[[cls_name],[cls_name]],[cls_name]) (fs_proof fs_thm_prod)
|> Axclass.prove_arity (\<^type_name>\<open>nprod\<close>,[[cls_name],[cls_name]],[cls_name]) (fs_proof fs_thm_nprod)
|> Axclass.prove_arity (\<^type_name>\<open>list\<close>,[[cls_name]],[cls_name]) (fs_proof fs_thm_list)
|> Axclass.prove_arity (\<^type_name>\<open>option\<close>,[[cls_name]],[cls_name]) (fs_proof fs_thm_optn)
end) ak_names thy20;
(******** cp_<ak>_<ai> class instances ********)
(*==============================================*)
(* abbreviations for some lemmas *)
val cp1 = @{thm "cp1"};
val cp_unit_inst = @{thm "cp_unit_inst"};
val cp_bool_inst = @{thm "cp_bool_inst"};
val cp_prod_inst = @{thm "cp_prod_inst"};
val cp_list_inst = @{thm "cp_list_inst"};
val cp_fun_inst = @{thm "cp_fun_inst"};
val cp_option_inst = @{thm "cp_option_inst"};
val cp_noption_inst = @{thm "cp_noption_inst"};
val cp_set_inst = @{thm "cp_set_inst"};
val pt_perm_compose = @{thm "pt_perm_compose"};
val dj_pp_forget = @{thm "dj_perm_perm_forget"};
(* shows that <aj> is an instance of cp_<ak>_<ai> *)
(* for every <ak>/<ai>-combination *)
val thy25 = fold (fn ak_name => fn thy =>
fold (fn ak_name' => fn thy' =>
fold (fn ak_name'' => fn thy'' =>
let
val name = Sign.full_bname thy'' ak_name;
val cls_name = Sign.full_bname thy'' ("cp_"^ak_name'^"_"^ak_name'');
fun proof ctxt =
(if (ak_name'=ak_name'') then
(let
val pt_inst = Global_Theory.get_thm thy'' ("pt_"^ak_name''^"_inst");
val at_inst = Global_Theory.get_thm thy'' ("at_"^ak_name''^"_inst");
in
EVERY [Class.intro_classes_tac ctxt [],
resolve_tac ctxt [at_inst RS (pt_inst RS pt_perm_compose)] 1]
end)
else
(let
val dj_inst = Global_Theory.get_thm thy'' ("dj_"^ak_name''^"_"^ak_name');
val simp_s = put_simpset HOL_basic_ss ctxt addsimps
((dj_inst RS dj_pp_forget)::
(maps (Global_Theory.get_thms thy'')
[ak_name' ^"_prm_"^ak_name^"_def",
ak_name''^"_prm_"^ak_name^"_def"]));
in
EVERY [Class.intro_classes_tac ctxt [], simp_tac simp_s 1]
end))
in
Axclass.prove_arity (name,[],[cls_name]) proof thy''
end) ak_names thy') ak_names thy) ak_names thy24;
(* shows that *)
(* units *)
(* products *)
(* lists *)
(* functions *)
(* options *)
(* noptions *)
(* sets *)
(* are instances of cp_<ak>_<ai> for every <ak>/<ai>-combination *)
val thy26 = fold (fn ak_name => fn thy =>
fold (fn ak_name' => fn thy' =>
let
val cls_name = Sign.full_bname thy' ("cp_"^ak_name^"_"^ak_name');
val cp_inst = Global_Theory.get_thm thy' ("cp_"^ak_name^"_"^ak_name'^"_inst");
val pt_inst = Global_Theory.get_thm thy' ("pt_"^ak_name^"_inst");
val at_inst = Global_Theory.get_thm thy' ("at_"^ak_name^"_inst");
fun cp_proof thm ctxt =
EVERY [Class.intro_classes_tac ctxt [], resolve_tac ctxt [thm RS cp1] 1];
val cp_thm_unit = cp_unit_inst;
val cp_thm_prod = cp_inst RS (cp_inst RS cp_prod_inst);
val cp_thm_list = cp_inst RS cp_list_inst;
val cp_thm_fun = at_inst RS (pt_inst RS (cp_inst RS (cp_inst RS cp_fun_inst)));
val cp_thm_optn = cp_inst RS cp_option_inst;
val cp_thm_noptn = cp_inst RS cp_noption_inst;
val cp_thm_set = cp_inst RS cp_set_inst;
in
thy'
|> Axclass.prove_arity (\<^type_name>\<open>unit\<close>,[],[cls_name]) (cp_proof cp_thm_unit)
|> Axclass.prove_arity (\<^type_name>\<open>Product_Type.prod\<close>, [[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_prod)
|> Axclass.prove_arity (\<^type_name>\<open>list\<close>,[[cls_name]],[cls_name]) (cp_proof cp_thm_list)
|> Axclass.prove_arity (\<^type_name>\<open>fun\<close>,[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_fun)
|> Axclass.prove_arity (\<^type_name>\<open>option\<close>,[[cls_name]],[cls_name]) (cp_proof cp_thm_optn)
|> Axclass.prove_arity (\<^type_name>\<open>noption\<close>,[[cls_name]],[cls_name]) (cp_proof cp_thm_noptn)
|> Axclass.prove_arity (\<^type_name>\<open>set\<close>,[[cls_name]],[cls_name]) (cp_proof cp_thm_set)
end) ak_names thy) ak_names thy25;
(* show that discrete nominal types are permutation types, finitely *)
(* supported and have the commutation property *)
(* discrete types have a permutation operation defined as pi o x = x; *)
(* which renders the proofs to be simple "simp_all"-proofs. *)
val thy32 =
let
fun discrete_pt_inst discrete_ty defn =
fold (fn ak_name => fn thy =>
let
val qu_class = Sign.full_bname thy ("pt_"^ak_name);
fun proof ctxt =
Class.intro_classes_tac ctxt [] THEN
REPEAT (asm_simp_tac (put_simpset HOL_basic_ss ctxt addsimps [Simpdata.mk_eq defn]) 1);
in
Axclass.prove_arity (discrete_ty, [], [qu_class]) proof thy
end) ak_names;
fun discrete_fs_inst discrete_ty defn =
fold (fn ak_name => fn thy =>
let
val qu_class = Sign.full_bname thy ("fs_"^ak_name);
val supp_def = Simpdata.mk_eq @{thm "Nominal.supp_def"};
fun proof ctxt =
Class.intro_classes_tac ctxt [] THEN
asm_simp_tac (put_simpset HOL_ss ctxt
addsimps [supp_def, Collect_const, finite_emptyI, Simpdata.mk_eq defn]) 1;
in
Axclass.prove_arity (discrete_ty, [], [qu_class]) proof thy
end) ak_names;
fun discrete_cp_inst discrete_ty defn =
fold (fn ak_name' => (fold (fn ak_name => fn thy =>
let
val qu_class = Sign.full_bname thy ("cp_"^ak_name^"_"^ak_name');
val supp_def = Simpdata.mk_eq @{thm "Nominal.supp_def"};
fun proof ctxt =
Class.intro_classes_tac ctxt [] THEN
asm_simp_tac (put_simpset HOL_ss ctxt addsimps [Simpdata.mk_eq defn]) 1;
in
Axclass.prove_arity (discrete_ty, [], [qu_class]) proof thy
end) ak_names)) ak_names;
in
thy26
|> discrete_pt_inst \<^type_name>\<open>nat\<close> @{thm perm_nat_def}
|> discrete_fs_inst \<^type_name>\<open>nat\<close> @{thm perm_nat_def}
|> discrete_cp_inst \<^type_name>\<open>nat\<close> @{thm perm_nat_def}
|> discrete_pt_inst \<^type_name>\<open>bool\<close> @{thm perm_bool_def}
|> discrete_fs_inst \<^type_name>\<open>bool\<close> @{thm perm_bool_def}
|> discrete_cp_inst \<^type_name>\<open>bool\<close> @{thm perm_bool_def}
|> discrete_pt_inst \<^type_name>\<open>int\<close> @{thm perm_int_def}
|> discrete_fs_inst \<^type_name>\<open>int\<close> @{thm perm_int_def}
|> discrete_cp_inst \<^type_name>\<open>int\<close> @{thm perm_int_def}
|> discrete_pt_inst \<^type_name>\<open>char\<close> @{thm perm_char_def}
|> discrete_fs_inst \<^type_name>\<open>char\<close> @{thm perm_char_def}
|> discrete_cp_inst \<^type_name>\<open>char\<close> @{thm perm_char_def}
end;
(* abbreviations for some lemmas *)
(*===============================*)
val abs_fun_pi = @{thm "Nominal.abs_fun_pi"};
val abs_fun_pi_ineq = @{thm "Nominal.abs_fun_pi_ineq"};
val abs_fun_eq = @{thm "Nominal.abs_fun_eq"};
val abs_fun_eq' = @{thm "Nominal.abs_fun_eq'"};
val abs_fun_fresh = @{thm "Nominal.abs_fun_fresh"};
val abs_fun_fresh' = @{thm "Nominal.abs_fun_fresh'"};
val dj_perm_forget = @{thm "Nominal.dj_perm_forget"};
val dj_pp_forget = @{thm "Nominal.dj_perm_perm_forget"};
val fresh_iff = @{thm "Nominal.fresh_abs_fun_iff"};
val fresh_iff_ineq = @{thm "Nominal.fresh_abs_fun_iff_ineq"};
val abs_fun_supp = @{thm "Nominal.abs_fun_supp"};
val abs_fun_supp_ineq = @{thm "Nominal.abs_fun_supp_ineq"};
val pt_swap_bij = @{thm "Nominal.pt_swap_bij"};
val pt_swap_bij' = @{thm "Nominal.pt_swap_bij'"};
val pt_fresh_fresh = @{thm "Nominal.pt_fresh_fresh"};
val pt_bij = @{thm "Nominal.pt_bij"};
val pt_perm_compose = @{thm "Nominal.pt_perm_compose"};
val pt_perm_compose' = @{thm "Nominal.pt_perm_compose'"};
val perm_app = @{thm "Nominal.pt_fun_app_eq"};
val at_fresh = @{thm "Nominal.at_fresh"};
val at_fresh_ineq = @{thm "Nominal.at_fresh_ineq"};
val at_calc = @{thms "Nominal.at_calc"};
val at_swap_simps = @{thms "Nominal.at_swap_simps"};
val at_supp = @{thm "Nominal.at_supp"};
val dj_supp = @{thm "Nominal.dj_supp"};
val fresh_left_ineq = @{thm "Nominal.pt_fresh_left_ineq"};
val fresh_left = @{thm "Nominal.pt_fresh_left"};
val fresh_right_ineq = @{thm "Nominal.pt_fresh_right_ineq"};
val fresh_right = @{thm "Nominal.pt_fresh_right"};
val fresh_bij_ineq = @{thm "Nominal.pt_fresh_bij_ineq"};
val fresh_bij = @{thm "Nominal.pt_fresh_bij"};
val fresh_star_bij_ineq = @{thms "Nominal.pt_fresh_star_bij_ineq"};
val fresh_star_bij = @{thms "Nominal.pt_fresh_star_bij"};
val fresh_eqvt = @{thm "Nominal.pt_fresh_eqvt"};
val fresh_eqvt_ineq = @{thm "Nominal.pt_fresh_eqvt_ineq"};
val fresh_star_eqvt = @{thms "Nominal.pt_fresh_star_eqvt"};
val fresh_star_eqvt_ineq= @{thms "Nominal.pt_fresh_star_eqvt_ineq"};
val set_diff_eqvt = @{thm "Nominal.pt_set_diff_eqvt"};
val in_eqvt = @{thm "Nominal.pt_in_eqvt"};
val eq_eqvt = @{thm "Nominal.pt_eq_eqvt"};
val all_eqvt = @{thm "Nominal.pt_all_eqvt"};
val ex_eqvt = @{thm "Nominal.pt_ex_eqvt"};
val ex1_eqvt = @{thm "Nominal.pt_ex1_eqvt"};
val the_eqvt = @{thm "Nominal.pt_the_eqvt"};
val pt_pi_rev = @{thm "Nominal.pt_pi_rev"};
val pt_rev_pi = @{thm "Nominal.pt_rev_pi"};
val at_exists_fresh = @{thm "Nominal.at_exists_fresh"};
val at_exists_fresh' = @{thm "Nominal.at_exists_fresh'"};
val fresh_perm_app_ineq = @{thm "Nominal.pt_fresh_perm_app_ineq"};
val fresh_perm_app = @{thm "Nominal.pt_fresh_perm_app"};
val fresh_aux = @{thm "Nominal.pt_fresh_aux"};
val pt_perm_supp_ineq = @{thm "Nominal.pt_perm_supp_ineq"};
val pt_perm_supp = @{thm "Nominal.pt_perm_supp"};
val subseteq_eqvt = @{thm "Nominal.pt_subseteq_eqvt"};
(* Now we collect and instantiate some lemmas w.r.t. all atom *)
(* types; this allows for example to use abs_perm (which is a *)
(* collection of theorems) instead of thm abs_fun_pi with explicit *)
(* instantiations. *)
val (_, thy33) =
let
val ctxt32 = Proof_Context.init_global thy32;
(* takes a theorem thm and a list of theorems [t1,..,tn] *)
(* produces a list of theorems of the form [t1 RS thm,..,tn RS thm] *)
fun instR thm thms = map (fn ti => ti RS thm) thms;
(* takes a theorem thm and a list of theorems [(t1,m1),..,(tn,mn)] *)
(* produces a list of theorems of the form [[t1,m1] MRS thm,..,[tn,mn] MRS thm] *)
fun instRR thm thms = map (fn (ti,mi) => [ti,mi] MRS thm) thms;
(* takes two theorem lists (hopefully of the same length ;o) *)
(* produces a list of theorems of the form *)
(* [t1 RS m1,..,tn RS mn] where [t1,..,tn] is thms1 and [m1,..,mn] is thms2 *)
fun inst_zip thms1 thms2 = map (fn (t1,t2) => t1 RS t2) (thms1 ~~ thms2);
(* takes a theorem list of the form [l1,...,ln] *)
(* and a list of theorem lists of the form *)
(* [[h11,...,h1m],....,[hk1,....,hkm] *)
(* produces the list of theorem lists *)
(* [[l1 RS h11,...,l1 RS h1m],...,[ln RS hk1,...,ln RS hkm]] *)
fun inst_mult thms thmss = map (fn (t,ts) => instR t ts) (thms ~~ thmss);
(* FIXME: these lists do not need to be created dynamically again *)
(* list of all at_inst-theorems *)
val ats = map (fn ak => Global_Theory.get_thm thy32 ("at_"^ak^"_inst")) ak_names
(* list of all pt_inst-theorems *)
val pts = map (fn ak => Global_Theory.get_thm thy32 ("pt_"^ak^"_inst")) ak_names
(* list of all cp_inst-theorems as a collection of lists*)
val cps =
let fun cps_fun ak1 ak2 = Global_Theory.get_thm thy32 ("cp_"^ak1^"_"^ak2^"_inst")
in map (fn aki => (map (cps_fun aki) ak_names)) ak_names end;
(* list of all cp_inst-theorems that have different atom types *)
val cps' =
let fun cps'_fun ak1 ak2 =
if ak1=ak2 then NONE else SOME (Global_Theory.get_thm thy32 ("cp_"^ak1^"_"^ak2^"_inst"))
in map (fn aki => (map_filter I (map (cps'_fun aki) 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(Global_Theory.get_thm thy32 ("dj_"^ak2^"_"^ak1))
in map_filter I (map_product djs_fun ak_names ak_names) end;
(* list of all fs_inst-theorems *)
val fss = map (fn ak => Global_Theory.get_thm thy32 ("fs_"^ak^"_inst")) ak_names
(* list of all at_inst-theorems *)
val fs_axs = map (fn ak => Global_Theory.get_thm thy32 ("fs_"^ak^"1")) ak_names
fun inst_pt thms = maps (fn ti => instR ti pts) thms;
fun inst_at thms = maps (fn ti => instR ti ats) thms;
fun inst_fs thms = maps (fn ti => instR ti fss) thms;
fun inst_cp thms cps = flat (inst_mult thms cps);
fun inst_pt_at thms = maps (fn ti => instRR ti (pts ~~ ats)) thms;
fun inst_dj thms = maps (fn ti => instR ti djs) thms;
fun inst_pt_pt_at_cp thms = inst_cp (inst_zip ats (inst_zip pts (inst_pt thms))) cps;
fun inst_pt_at_fs thms = inst_zip (inst_fs [fs1]) (inst_zip ats (inst_pt thms));
fun inst_pt_pt_at_cp thms =
let val i_pt_pt_at = inst_zip ats (inst_zip pts (inst_pt thms));
val i_pt_pt_at_cp = inst_cp i_pt_pt_at cps';
in i_pt_pt_at_cp end;
fun inst_pt_pt_at_cp_dj thms = inst_zip djs (inst_pt_pt_at_cp thms);
in
thy32
|> add_thmss_string [(("alpha", inst_pt_at [abs_fun_eq]),[])]
||>> add_thmss_string [(("alpha'", inst_pt_at [abs_fun_eq']),[])]
||>> add_thmss_string [(("alpha_fresh", inst_pt_at [abs_fun_fresh]),[])]
||>> add_thmss_string [(("alpha_fresh'", inst_pt_at [abs_fun_fresh']),[])]
||>> add_thmss_string [(("perm_swap", inst_pt_at [pt_swap_bij] @ inst_pt_at [pt_swap_bij']),[])]
||>> add_thmss_string
let val thms1 = inst_at at_swap_simps
and thms2 = inst_dj [dj_perm_forget]
in [(("swap_simps", thms1 @ thms2),[])] end
||>> add_thmss_string
let val thms1 = inst_pt_at [pt_pi_rev];
val thms2 = inst_pt_at [pt_rev_pi];
in [(("perm_pi_simp",thms1 @ thms2),[])] end
||>> add_thmss_string [(("perm_fresh_fresh", inst_pt_at [pt_fresh_fresh]),[])]
||>> add_thmss_string [(("perm_bij", inst_pt_at [pt_bij]),[])]
||>> add_thmss_string
let val thms1 = inst_pt_at [pt_perm_compose];
val thms2 = instR cp1 (Library.flat cps');
in [(("perm_compose",thms1 @ thms2),[])] end
||>> add_thmss_string [(("perm_compose'",inst_pt_at [pt_perm_compose']),[])]
||>> add_thmss_string [(("perm_app", inst_pt_at [perm_app]),[])]
||>> add_thmss_string [(("supp_atm", (inst_at [at_supp]) @ (inst_dj [dj_supp])),[])]
||>> add_thmss_string [(("exists_fresh", inst_at [at_exists_fresh]),[])]
||>> add_thmss_string [(("exists_fresh'", inst_at [at_exists_fresh']),[])]
||>> add_thmss_string
let
val thms1 = inst_pt_at [all_eqvt];
val thms2 = map (fold_rule ctxt32 [inductive_forall_def]) thms1
in
[(("all_eqvt", thms1 @ thms2), [NominalThmDecls.eqvt_force_add])]
end
||>> add_thmss_string [(("ex_eqvt", inst_pt_at [ex_eqvt]),[NominalThmDecls.eqvt_force_add])]
||>> add_thmss_string [(("ex1_eqvt", inst_pt_at [ex1_eqvt]),[NominalThmDecls.eqvt_force_add])]
||>> add_thmss_string [(("the_eqvt", inst_pt_at [the_eqvt]),[NominalThmDecls.eqvt_force_add])]
||>> add_thmss_string
let val thms1 = inst_at [at_fresh]
val thms2 = inst_dj [at_fresh_ineq]
in [(("fresh_atm", thms1 @ thms2),[])] end
||>> add_thmss_string
let val thms1 = inst_at at_calc
and thms2 = inst_dj [dj_perm_forget]
in [(("calc_atm", thms1 @ thms2),[])] end
||>> add_thmss_string
let val thms1 = inst_pt_at [abs_fun_pi]
and thms2 = inst_pt_pt_at_cp [abs_fun_pi_ineq]
in [(("abs_perm", thms1 @ thms2),[NominalThmDecls.eqvt_add])] end
||>> add_thmss_string
let val thms1 = inst_dj [dj_perm_forget]
and thms2 = inst_dj [dj_pp_forget]
in [(("perm_dj", thms1 @ thms2),[])] end
||>> add_thmss_string
let val thms1 = inst_pt_at_fs [fresh_iff]
and thms2 = inst_pt_at [fresh_iff]
and thms3 = inst_pt_pt_at_cp_dj [fresh_iff_ineq]
in [(("abs_fresh", thms1 @ thms2 @ thms3),[])] end
||>> add_thmss_string
let val thms1 = inst_pt_at [abs_fun_supp]
and thms2 = inst_pt_at_fs [abs_fun_supp]
and thms3 = inst_pt_pt_at_cp_dj [abs_fun_supp_ineq]
in [(("abs_supp", thms1 @ thms2 @ thms3),[])] end
||>> add_thmss_string
let val thms1 = inst_pt_at [fresh_left]
and thms2 = inst_pt_pt_at_cp [fresh_left_ineq]
in [(("fresh_left", thms1 @ thms2),[])] end
||>> add_thmss_string
let val thms1 = inst_pt_at [fresh_right]
and thms2 = inst_pt_pt_at_cp [fresh_right_ineq]
in [(("fresh_right", thms1 @ thms2),[])] end
||>> add_thmss_string
let val thms1 = inst_pt_at [fresh_bij]
and thms2 = inst_pt_pt_at_cp [fresh_bij_ineq]
in [(("fresh_bij", thms1 @ thms2),[])] end
||>> add_thmss_string
let val thms1 = inst_pt_at fresh_star_bij
and thms2 = maps (fn ti => inst_pt_pt_at_cp [ti]) fresh_star_bij_ineq
in [(("fresh_star_bij", thms1 @ thms2),[])] end
||>> add_thmss_string
let val thms1 = inst_pt_at [fresh_eqvt]
and thms2 = inst_pt_pt_at_cp_dj [fresh_eqvt_ineq]
in [(("fresh_eqvt", thms1 @ thms2),[NominalThmDecls.eqvt_add])] end
||>> add_thmss_string
let val thms1 = inst_pt_at fresh_star_eqvt
and thms2 = maps (fn ti => inst_pt_pt_at_cp_dj [ti]) fresh_star_eqvt_ineq
in [(("fresh_star_eqvt", thms1 @ thms2),[NominalThmDecls.eqvt_add])] end
||>> add_thmss_string
let val thms1 = inst_pt_at [in_eqvt]
in [(("in_eqvt", thms1),[NominalThmDecls.eqvt_add])] end
||>> add_thmss_string
let val thms1 = inst_pt_at [eq_eqvt]
in [(("eq_eqvt", thms1),[NominalThmDecls.eqvt_add])] end
||>> add_thmss_string
let val thms1 = inst_pt_at [set_diff_eqvt]
in [(("set_diff_eqvt", thms1),[NominalThmDecls.eqvt_add])] end
||>> add_thmss_string
let val thms1 = inst_pt_at [subseteq_eqvt]
in [(("subseteq_eqvt", thms1),[NominalThmDecls.eqvt_add])] end
||>> add_thmss_string
let val thms1 = inst_pt_at [fresh_aux]
and thms2 = inst_pt_pt_at_cp_dj [fresh_perm_app_ineq]
in [(("fresh_aux", thms1 @ thms2),[])] end
||>> add_thmss_string
let val thms1 = inst_pt_at [fresh_perm_app]
and thms2 = inst_pt_pt_at_cp_dj [fresh_perm_app_ineq]
in [(("fresh_perm_app", thms1 @ thms2),[])] end
||>> add_thmss_string
let val thms1 = inst_pt_at [pt_perm_supp]
and thms2 = inst_pt_pt_at_cp [pt_perm_supp_ineq]
in [(("supp_eqvt", thms1 @ thms2),[NominalThmDecls.eqvt_add])] end
||>> add_thmss_string [(("fin_supp",fs_axs),[])]
end;
in
NominalData.map (fold Symtab.update (full_ak_names ~~ map make_atom_info
(pt_ax_classes ~~
fs_ax_classes ~~
map (fn cls => Symtab.make (full_ak_names ~~ cls)) cp_ax_classes ~~
prm_cons_thms ~~ prm_inst_thms ~~
map (fn ths => Symtab.make (full_ak_names ~~ ths)) cp_thms ~~
map (fn thss => Symtab.make
(map_filter (fn (s, [th]) => SOME (s, th) | _ => NONE)
(full_ak_names ~~ thss))) dj_thms))) thy33
end;
(* syntax und parsing *)
val _ =
Outer_Syntax.command \<^command_keyword>\<open>atom_decl\<close> "declare new kinds of atoms"
(Scan.repeat1 Parse.name >> (Toplevel.theory o create_nom_typedecls));
end;
¤ Dauer der Verarbeitung: 0.43 Sekunden
(vorverarbeitet)
¤
|
Haftungshinweis
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
|
