(*  Title:      Pure/Isar/class.ML

    Author:     Florian Haftmann, TU Muenchen

Type classes derived from primitive axclasses and locales.

*)

signature CLASS =

sig

  (*classes*)

  val is_class: theory -> class -> bool

  val these_params: theory -> sort -> (string * (class * (string * typ))) list

  val base_sort: theory -> class -> sort

  val rules: theory -> class -> thm option * thm

  val these_defs: theory -> sort -> thm list

  val these_operations: theory -> sort

    -> (string * (class * (typ * term))) list

  val print_classes: theory -> unit

  val init: class -> theory -> Proof.context

  val begin: class list -> sort -> Proof.context -> Proof.context

  val const: class -> (binding * mixfix) * (term list * term) -> local_theory -> local_theory

  val abbrev: class -> Syntax.mode -> (binding * mixfix) * term -> local_theory -> local_theory

  val redeclare_operations: theory -> sort -> Proof.context -> Proof.context

  val class_prefix: string -> string

  val register: class -> class list -> ((string * typ) * (string * typ)) list

    -> sort -> morphism -> morphism -> thm option -> thm option -> thm

    -> theory -> theory

  (*instances*)

  val instantiation: string list * (string * sort) list * sort -> theory -> local_theory

  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 read_multi_arity: theory -> xstring list * xstring list * xstring

    -> string list * (string * sort) list * sort

  val type_name: string -> string

  val instantiation_cmd: xstring list * xstring list * xstring -> theory -> local_theory

  val instance_arity_cmd: xstring list * xstring list * xstring -> theory -> Proof.state

  (*subclasses*)

  val classrel: class * class -> theory -> Proof.state

  val classrel_cmd: xstring * xstring -> theory -> Proof.state

  val register_subclass: class * class -> morphism option -> Element.witness option

    -> morphism -> theory -> theory

  (*tactics*)

  val intro_classes_tac: thm list -> tactic

  val default_intro_tac: Proof.context -> thm list -> tactic

end;

structure Class: CLASS =

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 = case Element.eq_morphism thy (these_defs thy [class])

 of SOME eq_morph => base_morphism thy class $> eq_morph

  | NONE => base_morphism thy class;

val export_morphism = #export_morph oo the_class_data;

fun print_classes thy =

  let

    val ctxt = ProofContext.init_global 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 = case Element.eq_morphism thy thms

 of SOME eq_morph => fold (fn cls => fn thy =>

      Context.theory_map (Locale.amend_registration (cls, base_morphism thy cls)

        (eq_morph, true) (export_morphism thy cls)) thy) (heritage thy [class]) thy

  | NONE => 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))

    |> 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 Type_Infer.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 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 target_extension f class lthy =

  lthy

  |> Local_Theory.raw_theory f

  |> Local_Theory.target (synchronize_class_syntax [class]

      (base_sort (ProofContext.theory_of lthy) class));

local

fun target_const 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 target_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 = Print_Mode.input) ? register_operation class (c', (rhs', NONE))

  end;

in

fun const class arg = target_extension (target_const class arg) class;

fun abbrev class prmode arg = target_extension (target_abbrev class prmode arg) class;

end;

(* simple subclasses *)

local

fun gen_classrel mk_prop classrel thy =

  let

    fun after_qed results =

      ProofContext.background_theory ((fold o fold) AxClass.add_classrel results);

  in

    thy

    |> ProofContext.init_global

    |> 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_global 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;

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;

(* target *)

val sanitize_name = (*necessary as long as "dirty" type identifiers are permitted*)

  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;

val type_name = sanitize_name o Long_Name.base_name;

fun define_overloaded (c, U) v (b_def, rhs) = Local_Theory.theory_result

    (AxClass.declare_overloaded (c, U) ##>> AxClass.define_overloaded b_def (c, rhs))

  ##> (map_instantiation o apsnd) (filter_out (fn (_, (v', _)) => v' = v))

  ##> Local_Theory.target synchronize_inst_syntax;

fun foundation (((b, U), mx), (b_def, rhs)) (type_params, term_params) lthy =

  case instantiation_param lthy b

   of SOME c => if mx <> NoSyn then error ("Illegal mixfix syntax for overloaded constant " ^ quote c)

        else lthy |> define_overloaded (c, U) (Binding.name_of b) (b_def, rhs)

    | NONE => lthy |>

        Generic_Target.theory_foundation (((b, U), mx), (b_def, rhs)) (type_params, term_params);

fun pretty 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.str "instantiation" :: map pr_arity tycos @ map pr_param params end;

fun conclude 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 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_global

    |> 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

    |> Local_Theory.init NONE ""

       {define = Generic_Target.define foundation,

        notes = Generic_Target.notes

          (fn kind => fn global_facts => fn _ => Generic_Target.theory_notes kind global_facts),

        abbrev = Generic_Target.abbrev

          (fn prmode => fn (b, mx) => fn (t, _) => fn _ => Generic_Target.theory_abbrev prmode ((b, mx), t)),

        declaration = K Generic_Target.theory_declaration,

        syntax_declaration = K Generic_Target.theory_declaration,

        pretty = pretty,

        exit = Local_Theory.target_of o conclude}

  end;

fun instantiation_cmd arities thy =

  instantiation (read_multi_arity thy arities) thy;

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_global (ProofContext.theory_of lthy));

    val y = f morph x;

  in

    lthy

    |> prove_instantiation_exit (fn ctxt => tac ctxt y)

    |> pair y

  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.background_theory

      ((fold o fold) AxClass.add_arity results);

  in

    thy

    |> ProofContext.init_global

    |> 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;