(*  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 ^ " :: "

       ^ (Syntax.string_of_typ (Config.put show_sorts false 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.activate_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.background_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 algebra = Sign.classes_of thy

       |> fold (fn tyco => Sorts.add_arities (Syntax.pp_global thy)

             (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.activate_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.background_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 [] =

       COND Thm.no_prems no_tac

         (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;