src/Pure/Isar/class_target.ML

codified comment

(*  Title:      Pure/Isar/class_target.ML
    Author:     Florian Haftmann, TU Muenchen

Type classes derived from primitive axclasses and locales - mechanisms.
*)

signature CLASS_TARGET =
sig
  (*classes*)
  val register: class -> class list -> ((string * typ) * (string * typ)) list
    -> sort -> morphism -> morphism -> thm option -> thm option -> thm
    -> theory -> theory

  val is_class: theory -> class -> bool
  val base_sort: theory -> class -> sort
  val rules: theory -> class -> thm option * thm
  val these_params: theory -> sort -> (string * (class * (string * typ))) list
  val these_defs: theory -> sort -> thm list
  val these_operations: theory -> sort
    -> (string * (class * (typ * term))) list
  val print_classes: theory -> unit

  val begin: class list -> sort -> Proof.context -> Proof.context
  val init: class -> theory -> Proof.context
  val declare: class -> (binding * mixfix) * (term list * term) -> theory -> theory
  val abbrev: class -> Syntax.mode -> (binding * mixfix) * term -> theory -> theory
  val class_prefix: string -> string
  val refresh_syntax: class -> Proof.context -> Proof.context
  val redeclare_operations: theory -> sort -> Proof.context -> Proof.context

  (*instances*)
  val init_instantiation: string list * (string * sort) list * sort
    -> theory -> Proof.context
  val instance_arity_cmd: xstring list * xstring list * xstring -> theory -> Proof.state
  val instantiation_instance: (local_theory -> local_theory)
    -> local_theory -> Proof.state
  val prove_instantiation_instance: (Proof.context -> tactic)
    -> local_theory -> local_theory
  val prove_instantiation_exit: (Proof.context -> tactic)
    -> local_theory -> theory
  val prove_instantiation_exit_result: (morphism -> 'a -> 'b)
    -> (Proof.context -> 'b -> tactic) -> 'a -> local_theory -> 'b * theory
  val conclude_instantiation: local_theory -> local_theory
  val instantiation_param: local_theory -> binding -> string option
  val confirm_declaration: binding -> local_theory -> local_theory
  val pretty_instantiation: local_theory -> Pretty.T
  val read_multi_arity: theory -> xstring list * xstring list * xstring
    -> string list * (string * sort) list * sort
  val type_name: string -> string

  (*subclasses*)
  val register_subclass: class * class -> morphism option -> Element.witness option
    -> morphism -> theory -> theory
  val classrel: class * class -> theory -> Proof.state
  val classrel_cmd: xstring * xstring -> theory -> Proof.state

  (*tactics*)
  val intro_classes_tac: thm list -> tactic
  val default_intro_tac: Proof.context -> thm list -> tactic
end;

structure Class_Target : CLASS_TARGET =
struct

(** class data **)

datatype class_data = ClassData of {

  (* static part *)
  consts: (string * string) list
    (*locale parameter ~> constant name*),
  base_sort: sort,
  base_morph: morphism
    (*static part of canonical morphism*),
  export_morph: morphism,
  assm_intro: thm option,
  of_class: thm,
  axiom: thm option,
  
  (* dynamic part *)
  defs: thm list,
  operations: (string * (class * (typ * term))) list

};

fun make_class_data ((consts, base_sort, base_morph, export_morph, assm_intro, of_class, axiom),
    (defs, operations)) =
  ClassData { consts = consts, base_sort = base_sort,
    base_morph = base_morph, export_morph = export_morph, assm_intro = assm_intro,
    of_class = of_class, axiom = axiom, defs = defs, operations = operations };
fun map_class_data f (ClassData { consts, base_sort, base_morph, export_morph, assm_intro,
    of_class, axiom, defs, operations }) =
  make_class_data (f ((consts, base_sort, base_morph, export_morph, assm_intro, of_class, axiom),
    (defs, operations)));
fun merge_class_data _ (ClassData { consts = consts,
    base_sort = base_sort, base_morph = base_morph, export_morph = export_morph, assm_intro = assm_intro,
    of_class = of_class, axiom = axiom, defs = defs1, operations = operations1 },
  ClassData { consts = _, base_sort = _, base_morph = _, export_morph = _, assm_intro = _,
    of_class = _, axiom = _, defs = defs2, operations = operations2 }) =
  make_class_data ((consts, base_sort, base_morph, export_morph, assm_intro, of_class, axiom),
    (Thm.merge_thms (defs1, defs2),
      AList.merge (op =) (K true) (operations1, operations2)));

structure ClassData = Theory_Data
(
  type T = class_data Graph.T
  val empty = Graph.empty;
  val extend = I;
  val merge = Graph.join merge_class_data;
);


(* queries *)

fun lookup_class_data thy class = case try (Graph.get_node (ClassData.get thy)) class
 of SOME (ClassData data) => SOME data
  | NONE => NONE;

fun the_class_data thy class = case lookup_class_data thy class
 of NONE => error ("Undeclared class " ^ quote class)
  | SOME data => data;

val is_class = is_some oo lookup_class_data;

val ancestry = Graph.all_succs o ClassData.get;
val heritage = Graph.all_preds o ClassData.get;

fun these_params thy =
  let
    fun params class =
      let
        val const_typs = (#params o AxClass.get_info thy) class;
        val const_names = (#consts o the_class_data thy) class;
      in
        (map o apsnd)
          (fn c => (class, (c, (the o AList.lookup (op =) const_typs) c))) const_names
      end;
  in maps params o ancestry thy end;

val base_sort = #base_sort oo the_class_data;

fun rules thy class =
  let val { axiom, of_class, ... } = the_class_data thy class
  in (axiom, of_class) end;

fun all_assm_intros thy =
  Graph.fold (fn (_, (ClassData { assm_intro, ... }, _)) => fold (insert Thm.eq_thm)
    (the_list assm_intro)) (ClassData.get thy) [];

fun these_defs thy = maps (#defs o the_class_data thy) o ancestry thy;
fun these_operations thy = maps (#operations o the_class_data thy) o ancestry thy;

val base_morphism = #base_morph oo the_class_data;
fun morphism thy class = base_morphism thy class
  $> Element.eq_morphism thy (these_defs thy [class]);
val export_morphism = #export_morph oo the_class_data;

fun print_classes thy =
  let
    val ctxt = ProofContext.init thy;
    val algebra = Sign.classes_of thy;
    val arities =
      Symtab.empty
      |> Symtab.fold (fn (tyco, arities) => fold (fn (class, _) =>
           Symtab.map_default (class, []) (insert (op =) tyco)) arities)
             (Sorts.arities_of algebra);
    val the_arities = these o Symtab.lookup arities;
    fun mk_arity class tyco =
      let
        val Ss = Sorts.mg_domain algebra tyco [class];
      in Syntax.pretty_arity ctxt (tyco, Ss, [class]) end;
    fun mk_param (c, ty) = Pretty.str (Sign.extern_const thy c ^ " :: "
      ^ setmp_CRITICAL show_sorts false (Syntax.string_of_typ ctxt o Type.strip_sorts) ty);
    fun mk_entry class = (Pretty.block o Pretty.fbreaks o map_filter I) [
      (SOME o Pretty.str) ("class " ^ Sign.extern_class thy class ^ ":"),
      (SOME o Pretty.block) [Pretty.str "supersort: ",
        (Syntax.pretty_sort ctxt o Sign.minimize_sort thy o Sign.super_classes thy) class],
      ((fn [] => NONE | ps => (SOME o Pretty.block o Pretty.fbreaks)
          (Pretty.str "parameters:" :: ps)) o map mk_param
        o these o Option.map #params o try (AxClass.get_info thy)) class,
      (SOME o Pretty.block o Pretty.breaks) [
        Pretty.str "instances:",
        Pretty.list "" "" (map (mk_arity class) (the_arities class))
      ]
    ]
  in
    (Pretty.writeln o Pretty.chunks o separate (Pretty.str "")
      o map mk_entry o Sorts.all_classes) algebra
  end;


(* updaters *)

fun register class sups params base_sort base_morph export_morph
    axiom assm_intro of_class thy =
  let
    val operations = map (fn (v_ty as (_, ty), (c, _)) =>
      (c, (class, (ty, Free v_ty)))) params;
    val add_class = Graph.new_node (class,
        make_class_data (((map o pairself) fst params, base_sort,
          base_morph, export_morph, assm_intro, of_class, axiom), ([], operations)))
      #> fold (curry Graph.add_edge class) sups;
  in ClassData.map add_class thy end;

fun activate_defs class thms thy =
  let
    val eq_morph = Element.eq_morphism thy thms;
    fun amend cls thy = Locale.amend_registration (cls, base_morphism thy cls)
      (eq_morph, true) (export_morphism thy cls) thy;
  in fold amend (heritage thy [class]) thy end;

(*fun activate_defs class thms thy = Locale.amend_registration (class, base_morphism thy class)
  (Element.eq_morphism thy thms, true) (export_morphism thy class) thy;*)

fun register_operation class (c, (t, some_def)) thy =
  let
    val base_sort = base_sort thy class;
    val prep_typ = map_type_tfree
      (fn (v, sort) => if Name.aT = v
        then TFree (v, base_sort) else TVar ((v, 0), sort));
    val t' = map_types prep_typ t;
    val ty' = Term.fastype_of t';
  in
    thy
    |> (ClassData.map o Graph.map_node class o map_class_data o apsnd)
      (fn (defs, operations) =>
        (fold cons (the_list some_def) defs,
          (c, (class, (ty', t'))) :: operations))
    |> is_some some_def ? activate_defs class (the_list some_def)
  end;

fun register_subclass (sub, sup) some_dep_morph some_wit export thy =
  let
    val intros = (snd o rules thy) sup :: map_filter I
      [Option.map (Drule.export_without_context_open o Element.conclude_witness) some_wit,
        (fst o rules thy) sub];
    val tac = EVERY (map (TRYALL o Tactic.rtac) intros);
    val classrel = Skip_Proof.prove_global thy [] [] (Logic.mk_classrel (sub, sup))
      (K tac);
    val diff_sort = Sign.complete_sort thy [sup]
      |> subtract (op =) (Sign.complete_sort thy [sub])
      |> filter (is_class thy);
    val add_dependency = case some_dep_morph
     of SOME dep_morph => Locale.add_dependency sub
          (sup, dep_morph $> Element.satisfy_morphism (the_list some_wit)) export
      | NONE => I
  in
    thy
    |> AxClass.add_classrel classrel
    |> ClassData.map (Graph.add_edge (sub, sup))
    |> activate_defs sub (these_defs thy diff_sort)
    |> add_dependency
  end;


(** classes and class target **)

(* class context syntax *)

fun these_unchecks thy = map (fn (c, (_, (ty, t))) => (t, Const (c, ty)))
  o these_operations thy;

fun redeclare_const thy c =
  let val b = Long_Name.base_name c
  in Sign.intern_const thy b = c ? Variable.declare_const (b, c) end;

fun synchronize_class_syntax sort base_sort ctxt =
  let
    val thy = ProofContext.theory_of ctxt;
    val algebra = Sign.classes_of thy;
    val operations = these_operations thy sort;
    fun subst_class_typ sort = map_type_tfree (K (TVar ((Name.aT, 0), sort)));
    val primary_constraints =
      (map o apsnd) (subst_class_typ base_sort o fst o snd) operations;
    val secondary_constraints =
      (map o apsnd) (fn (class, (ty, _)) => subst_class_typ [class] ty) operations;
    fun improve (c, ty) = (case AList.lookup (op =) primary_constraints c
     of SOME ty' => (case try (Type.raw_match (ty', ty)) Vartab.empty
         of SOME tyenv => (case Vartab.lookup tyenv (Name.aT, 0)
             of SOME (_, ty' as TVar (vi, sort)) =>
                  if TypeInfer.is_param vi
                    andalso Sorts.sort_le algebra (base_sort, sort)
                      then SOME (ty', TFree (Name.aT, base_sort))
                      else NONE
              | _ => NONE)
          | NONE => NONE)
      | NONE => NONE)
    fun subst (c, ty) = Option.map snd (AList.lookup (op =) operations c);
    val unchecks = these_unchecks thy sort;
  in
    ctxt
    |> fold (redeclare_const thy o fst) primary_constraints
    |> Overloading.map_improvable_syntax (K (((primary_constraints, secondary_constraints),
        (((improve, subst), true), unchecks)), false))
    |> Overloading.set_primary_constraints
  end;

fun refresh_syntax class ctxt =
  let
    val thy = ProofContext.theory_of ctxt;
    val base_sort = base_sort thy class;
  in synchronize_class_syntax [class] base_sort ctxt end;

fun redeclare_operations thy sort =
  fold (redeclare_const thy o fst) (these_operations thy sort);

fun begin sort base_sort ctxt =
  ctxt
  |> Variable.declare_term
      (Logic.mk_type (TFree (Name.aT, base_sort)))
  |> synchronize_class_syntax sort base_sort
  |> Overloading.add_improvable_syntax;

fun init class thy =
  thy
  |> Locale.init class
  |> begin [class] (base_sort thy class);


(* class target *)

val class_prefix = Logic.const_of_class o Long_Name.base_name;

fun declare class ((c, mx), (type_params, dict)) thy =
  let
    val morph = morphism thy class;
    val b = Morphism.binding morph c;
    val b_def = Morphism.binding morph (Binding.suffix_name "_dict" b);
    val c' = Sign.full_name thy b;
    val dict' = Morphism.term morph dict;
    val ty' = map Term.fastype_of type_params ---> Term.fastype_of dict';
    val def_eq = Logic.mk_equals (list_comb (Const (c', ty'), type_params), dict')
      |> map_types Type.strip_sorts;
  in
    thy
    |> Sign.declare_const ((b, Type.strip_sorts ty'), mx)
    |> snd
    |> Thm.add_def false false (b_def, def_eq)
    |>> apsnd Thm.varifyT_global
    |-> (fn (_, def_thm) => PureThy.store_thm (b_def, def_thm)
      #> snd
      #> null type_params ? register_operation class (c', (dict', SOME (Thm.symmetric def_thm))))
    |> Sign.add_const_constraint (c', SOME ty')
  end;

fun abbrev class prmode ((c, mx), rhs) thy =
  let
    val morph = morphism thy class;
    val unchecks = these_unchecks thy [class];
    val b = Morphism.binding morph c;
    val c' = Sign.full_name thy b;
    val rhs' = Pattern.rewrite_term thy unchecks [] rhs;
    val ty' = Term.fastype_of rhs';
    val rhs'' = map_types Logic.varifyT_global rhs';
  in
    thy
    |> Sign.add_abbrev (#1 prmode) (b, rhs'')
    |> snd
    |> Sign.add_const_constraint (c', SOME ty')
    |> Sign.notation true prmode [(Const (c', ty'), mx)]
    |> not (#1 prmode = PrintMode.input) ? register_operation class (c', (rhs', NONE))
  end;


(* simple subclasses *)

local

fun gen_classrel mk_prop classrel thy =
  let
    fun after_qed results =
      ProofContext.theory ((fold o fold) AxClass.add_classrel results);
  in
    thy
    |> ProofContext.init
    |> Proof.theorem NONE after_qed [[(mk_prop thy classrel, [])]]
  end;

in

val classrel =
  gen_classrel (Logic.mk_classrel oo AxClass.cert_classrel);
val classrel_cmd =
  gen_classrel (Logic.mk_classrel oo AxClass.read_classrel);

end; (*local*)


(** instantiation target **)

(* bookkeeping *)

datatype instantiation = Instantiation of {
  arities: string list * (string * sort) list * sort,
  params: ((string * string) * (string * typ)) list
    (*(instantiation parameter, type constructor), (local instantiation parameter, typ)*)
}

structure Instantiation = Proof_Data
(
  type T = instantiation
  fun init _ = Instantiation { arities = ([], [], []), params = [] };
);

fun mk_instantiation (arities, params) =
  Instantiation { arities = arities, params = params };
fun get_instantiation lthy = case Instantiation.get (Local_Theory.target_of lthy)
 of Instantiation data => data;
fun map_instantiation f = (Local_Theory.target o Instantiation.map)
  (fn Instantiation { arities, params } => mk_instantiation (f (arities, params)));

fun the_instantiation lthy = case get_instantiation lthy
 of { arities = ([], [], []), ... } => error "No instantiation target"
  | data => data;

val instantiation_params = #params o get_instantiation;

fun instantiation_param lthy b = instantiation_params lthy
  |> find_first (fn (_, (v, _)) => Binding.name_of b = v)
  |> Option.map (fst o fst);

fun read_multi_arity thy (raw_tycos, raw_sorts, raw_sort) =
  let
    val ctxt = ProofContext.init thy;
    val all_arities = map (fn raw_tyco => ProofContext.read_arity ctxt
      (raw_tyco, raw_sorts, raw_sort)) raw_tycos;
    val tycos = map #1 all_arities;
    val (_, sorts, sort) = hd all_arities;
    val vs = Name.names Name.context Name.aT sorts;
  in (tycos, vs, sort) end;


(* syntax *)

fun synchronize_inst_syntax ctxt =
  let
    val Instantiation { params, ... } = Instantiation.get ctxt;

    val lookup_inst_param = AxClass.lookup_inst_param
      (Sign.consts_of (ProofContext.theory_of ctxt)) params;
    fun subst (c, ty) = case lookup_inst_param (c, ty)
     of SOME (v_ty as (_, ty)) => SOME (ty, Free v_ty)
      | NONE => NONE;
    val unchecks =
      map (fn ((c, _), v_ty as (_, ty)) => (Free v_ty, Const (c, ty))) params;
  in
    ctxt
    |> Overloading.map_improvable_syntax
         (fn (((primary_constraints, _), (((improve, _), _), _)), _) =>
            (((primary_constraints, []), (((improve, subst), false), unchecks)), false))
  end;


(* target *)

val sanatize_name = (*FIXME*)
  let
    fun is_valid s = Symbol.is_ascii_letter s orelse Symbol.is_ascii_digit s
      orelse s = "'" orelse s = "_";
    val is_junk = not o is_valid andf Symbol.is_regular;
    val junk = Scan.many is_junk;
    val scan_valids = Symbol.scanner "Malformed input"
      ((junk |--
        (Scan.optional (Scan.one Symbol.is_ascii_letter) "x" ^^ (Scan.many is_valid >> implode)
        --| junk))
      ::: Scan.repeat ((Scan.many1 is_valid >> implode) --| junk));
  in
    explode #> scan_valids #> implode
  end;

fun type_name "*" = "prod"
  | type_name "+" = "sum"
  | type_name s = sanatize_name (Long_Name.base_name s);

fun resort_terms pp algebra consts constraints ts =
  let
    fun matchings (Const (c_ty as (c, _))) = (case constraints c
         of NONE => I
          | SOME sorts => fold2 (curry (Sorts.meet_sort algebra))
              (Consts.typargs consts c_ty) sorts)
      | matchings _ = I
    val tvartab = (fold o fold_aterms) matchings ts Vartab.empty
      handle Sorts.CLASS_ERROR e => error (Sorts.class_error pp e);
    val inst = map_type_tvar
      (fn (vi, sort) => TVar (vi, the_default sort (Vartab.lookup tvartab vi)));
  in if Vartab.is_empty tvartab then NONE else SOME ((map o map_types) inst ts) end;

fun init_instantiation (tycos, vs, sort) thy =
  let
    val _ = if null tycos then error "At least one arity must be given" else ();
    val class_params = these_params thy (filter (can (AxClass.get_info thy)) sort);
    fun get_param tyco (param, (_, (c, ty))) =
      if can (AxClass.param_of_inst thy) (c, tyco)
      then NONE else SOME ((c, tyco),
        (param ^ "_" ^ type_name tyco, map_atyps (K (Type (tyco, map TFree vs))) ty));
    val params = map_product get_param tycos class_params |> map_filter I;
    val primary_constraints = map (apsnd
      (map_atyps (K (TVar ((Name.aT, 0), [])))) o snd o snd) class_params;
    val pp = Syntax.pp_global thy;
    val algebra = Sign.classes_of thy
      |> fold (fn tyco => Sorts.add_arities pp
            (tyco, map (fn class => (class, map snd vs)) sort)) tycos;
    val consts = Sign.consts_of thy;
    val improve_constraints = AList.lookup (op =)
      (map (fn (_, (class, (c, _))) => (c, [[class]])) class_params);
    fun resort_check ts ctxt = case resort_terms (Syntax.pp ctxt) algebra consts improve_constraints ts
     of NONE => NONE
      | SOME ts' => SOME (ts', ctxt);
    val lookup_inst_param = AxClass.lookup_inst_param consts params;
    val typ_instance = Type.typ_instance (Sign.tsig_of thy);
    fun improve (c, ty) = case lookup_inst_param (c, ty)
     of SOME (_, ty') => if typ_instance (ty', ty) then SOME (ty, ty') else NONE
      | NONE => NONE;
  in
    thy
    |> Theory.checkpoint
    |> ProofContext.init
    |> Instantiation.put (mk_instantiation ((tycos, vs, sort), params))
    |> fold (Variable.declare_typ o TFree) vs
    |> fold (Variable.declare_names o Free o snd) params
    |> (Overloading.map_improvable_syntax o apfst)
         (K ((primary_constraints, []), (((improve, K NONE), false), [])))
    |> Overloading.add_improvable_syntax
    |> Context.proof_map (Syntax.add_term_check 0 "resorting" resort_check)
    |> synchronize_inst_syntax
  end;

fun confirm_declaration b = (map_instantiation o apsnd)
  (filter_out (fn (_, (c', _)) => c' = Binding.name_of b))
  #> Local_Theory.target synchronize_inst_syntax

fun gen_instantiation_instance do_proof after_qed lthy =
  let
    val (tycos, vs, sort) = (#arities o the_instantiation) lthy;
    val arities_proof = maps (fn tyco => Logic.mk_arities (tyco, map snd vs, sort)) tycos;
    fun after_qed' results =
      Local_Theory.theory (fold (AxClass.add_arity o Thm.varifyT_global) results)
      #> after_qed;
  in
    lthy
    |> do_proof after_qed' arities_proof
  end;

val instantiation_instance = gen_instantiation_instance (fn after_qed => fn ts =>
  Proof.theorem NONE (after_qed o map the_single) (map (fn t => [(t, [])]) ts));

fun prove_instantiation_instance tac = gen_instantiation_instance (fn after_qed =>
  fn ts => fn lthy => after_qed (map (fn t => Goal.prove lthy [] [] t
    (fn {context, ...} => tac context)) ts) lthy) I;

fun prove_instantiation_exit tac = prove_instantiation_instance tac
  #> Local_Theory.exit_global;

fun prove_instantiation_exit_result f tac x lthy =
  let
    val morph = ProofContext.export_morphism lthy
      (ProofContext.init (ProofContext.theory_of lthy));
    val y = f morph x;
  in
    lthy
    |> prove_instantiation_exit (fn ctxt => tac ctxt y)
    |> pair y
  end;

fun conclude_instantiation lthy =
  let
    val (tycos, vs, sort) = (#arities o the_instantiation) lthy;
    val thy = ProofContext.theory_of lthy;
    val _ = map (fn tyco => if Sign.of_sort thy
        (Type (tyco, map TFree vs), sort)
      then () else error ("Missing instance proof for type " ^ quote (Sign.extern_type thy tyco)))
        tycos;
  in lthy end;

fun pretty_instantiation lthy =
  let
    val { arities = (tycos, vs, sort), params } = the_instantiation lthy;
    val thy = ProofContext.theory_of lthy;
    fun pr_arity tyco = Syntax.pretty_arity lthy (tyco, map snd vs, sort);
    fun pr_param ((c, _), (v, ty)) =
      (Pretty.block o Pretty.breaks) [Pretty.str v, Pretty.str "==",
        (Pretty.str o Sign.extern_const thy) c, Pretty.str "::", Syntax.pretty_typ_global thy ty];
  in
    (Pretty.block o Pretty.fbreaks)
      (Pretty.str "instantiation" :: map pr_arity tycos @ map pr_param params)
  end;


(* simplified instantiation interface with no class parameter *)

fun instance_arity_cmd raw_arities thy =
  let
    val (tycos, vs, sort) = read_multi_arity thy raw_arities;
    val sorts = map snd vs;
    val arities = maps (fn tyco => Logic.mk_arities (tyco, sorts, sort)) tycos;
    fun after_qed results = ProofContext.theory
      ((fold o fold) AxClass.add_arity results);
  in
    thy
    |> ProofContext.init
    |> Proof.theorem NONE after_qed (map (fn t => [(t, [])]) arities)
  end;


(** tactics and methods **)

fun intro_classes_tac facts st =
  let
    val thy = Thm.theory_of_thm st;
    val classes = Sign.all_classes thy;
    val class_trivs = map (Thm.class_triv thy) classes;
    val class_intros = map_filter (try (#intro o AxClass.get_info thy)) classes;
    val assm_intros = all_assm_intros thy;
  in
    Method.intros_tac (class_trivs @ class_intros @ assm_intros) facts st
  end;

fun default_intro_tac ctxt [] =
      intro_classes_tac [] ORELSE Locale.intro_locales_tac true ctxt []
  | default_intro_tac _ _ = no_tac;

fun default_tac rules ctxt facts =
  HEADGOAL (Method.some_rule_tac rules ctxt facts) ORELSE
    default_intro_tac ctxt facts;

val _ = Context.>> (Context.map_theory
 (Method.setup (Binding.name "intro_classes") (Scan.succeed (K (METHOD intro_classes_tac)))
    "back-chain introduction rules of classes" #>
  Method.setup (Binding.name "default") (Attrib.thms >> (METHOD oo default_tac))
    "apply some intro/elim rule"));

end;