(*  Title:      Pure/Isar/class.ML

    ID:         $Id$

    Author:     Florian Haftmann, TU Muenchen

Type classes derived from primitive axclasses and locales.

*)

signature CLASS =

sig

  (*classes*)

  val class: bstring -> class list -> Element.context_i Locale.element list

    -> string list -> theory -> string * Proof.context

  val class_cmd: bstring -> xstring list -> Element.context Locale.element list

    -> xstring list -> theory -> string * Proof.context

  val is_class: theory -> class -> bool

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

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

  val add_logical_const: string -> Markup.property list

    -> (string * mixfix) * term -> theory -> theory

  val add_syntactic_const: string -> Syntax.mode -> Markup.property list

    -> (string * mixfix) * term -> theory -> theory

  val refresh_syntax: class -> Proof.context -> Proof.context

  val intro_classes_tac: thm list -> tactic

  val default_intro_classes_tac: thm list -> tactic

  val prove_subclass: class * class -> thm list -> Proof.context

    -> theory -> theory

  val print_classes: theory -> unit

  val class_prefix: string -> string

  (*instances*)

  val declare_overloaded: string * typ * mixfix -> theory -> term * theory

  val define_overloaded: string -> string * term -> theory -> thm * theory

  val unoverload: theory -> conv

  val overload: theory -> conv

  val unoverload_const: theory -> string * typ -> string

  val inst_const: theory -> string * string -> string

  val param_const: theory -> string -> (string * string) option

  val instantiation: arity list -> theory -> local_theory

  val proof_instantiation: (local_theory -> local_theory) -> local_theory -> Proof.state

  val prove_instantiation: (Proof.context -> tactic) -> local_theory -> local_theory

  val conclude_instantiation: local_theory -> local_theory

  val end_instantiation: local_theory -> Proof.context

  val instantiation_const: Proof.context -> string -> string option

  (*old axclass layer*)

  val axclass_cmd: bstring * xstring list

    -> ((bstring * Attrib.src list) * string list) list

    -> theory -> class * theory

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

  (*old instance layer*)

  val instance_arity: (theory -> theory) -> arity list -> theory -> Proof.state

  val instance: arity list -> ((bstring * Attrib.src list) * term) list

    -> (thm list -> theory -> theory)

    -> theory -> Proof.state

  val instance_cmd: (bstring * xstring list * xstring) list

    -> ((bstring * Attrib.src list) * xstring) list

    -> (thm list -> theory -> theory)

    -> theory -> Proof.state

  val prove_instance: tactic -> arity list

    -> ((bstring * Attrib.src list) * term) list

    -> theory -> thm list * theory

end;

structure Class : CLASS =

struct

(** auxiliary **)

val classN = "class";

val introN = "intro";

fun prove_interpretation tac prfx_atts expr inst =

  Locale.interpretation_i I prfx_atts expr inst

  #> Proof.global_terminal_proof

      (Method.Basic (K (Method.SIMPLE_METHOD tac), Position.none), NONE)

  #> ProofContext.theory_of;

fun prove_interpretation_in tac after_qed (name, expr) =

  Locale.interpretation_in_locale

      (ProofContext.theory after_qed) (name, expr)

  #> Proof.global_terminal_proof

      (Method.Basic (K (Method.SIMPLE_METHOD tac), Position.none), NONE)

  #> ProofContext.theory_of;

fun OF_LAST thm1 thm2 = thm1 RSN (Thm.nprems_of thm2, thm2);

fun strip_all_ofclass thy sort =

  let

    val typ = TVar ((Name.aT, 0), sort);

    fun prem_inclass t =

      case Logic.strip_imp_prems t

       of ofcls :: _ => try Logic.dest_inclass ofcls

        | [] => NONE;

    fun strip_ofclass class thm =

      thm OF (fst o AxClass.of_sort thy (typ, [class])) AxClass.cache;

    fun strip thm = case (prem_inclass o Thm.prop_of) thm

     of SOME (_, class) => thm |> strip_ofclass class |> strip

      | NONE => thm;

  in strip end;

fun get_remove_global_constraint c thy =

  let

    val ty = Sign.the_const_constraint thy c;

  in

    thy

    |> Sign.add_const_constraint (c, NONE)

    |> pair (c, Logic.unvarifyT ty)

  end;

(** axclass command **)

fun axclass_cmd (class, raw_superclasses) raw_specs thy =

  let

    val ctxt = ProofContext.init thy;

    val superclasses = map (Sign.read_class thy) raw_superclasses;

    val name_atts = map ((apsnd o map) (Attrib.attribute thy) o fst)

      raw_specs;

    val axiomss = ProofContext.read_propp (ctxt, map (map (rpair []) o snd)

          raw_specs)

      |> snd

      |> (map o map) fst;

  in

    AxClass.define_class (class, superclasses) []

      (name_atts ~~ axiomss) thy

  end;

local

fun gen_instance mk_prop add_thm after_qed insts thy =

  let

    fun after_qed' results =

      ProofContext.theory ((fold o fold) add_thm results #> after_qed);

  in

    thy

    |> ProofContext.init

    |> Proof.theorem_i NONE after_qed' ((map (fn t => [(t, [])])

        o maps (mk_prop thy)) insts)

  end;

in

val instance_arity =

  gen_instance (Logic.mk_arities oo Sign.cert_arity) AxClass.add_arity;

val classrel =

  gen_instance (single oo (Logic.mk_classrel oo AxClass.cert_classrel))

    AxClass.add_classrel I o single;

val classrel_cmd =

  gen_instance (single oo (Logic.mk_classrel oo AxClass.read_classrel))

    AxClass.add_classrel I o single;

end; (*local*)

(** basic overloading **)

(* bookkeeping *)

structure InstData = TheoryDataFun

(

  type T = (string * thm) Symtab.table Symtab.table * (string * string) Symtab.table;

    (*constant name ~> type constructor ~> (constant name, equation),

        constant name ~> (constant name, type constructor)*)

  val empty = (Symtab.empty, Symtab.empty);

  val copy = I;

  val extend = I;

  fun merge _ ((taba1, tabb1), (taba2, tabb2)) =

    (Symtab.join (K (Symtab.merge (K true))) (taba1, taba2),

      Symtab.merge (K true) (tabb1, tabb2));

);

val inst_tyco = Option.map fst o try (dest_Type o the_single) oo Sign.const_typargs;

fun inst thy (c, tyco) =

  (the o Symtab.lookup ((the o Symtab.lookup (fst (InstData.get thy))) c)) tyco;

val inst_const = fst oo inst;

fun inst_thms thy = (Symtab.fold (Symtab.fold (cons o snd o snd) o snd) o fst)

  (InstData.get thy) [];

val param_const = Symtab.lookup o snd o InstData.get;

fun add_inst (c, tyco) inst = (InstData.map o apfst

      o Symtab.map_default (c, Symtab.empty)) (Symtab.update_new (tyco, inst))

  #> (InstData.map o apsnd) (Symtab.update_new (fst inst, (c, tyco)));

fun unoverload thy = MetaSimplifier.rewrite true (inst_thms thy);

fun overload thy = MetaSimplifier.rewrite true (map Thm.symmetric (inst_thms thy));

fun unoverload_const thy (c_ty as (c, _)) =

  case AxClass.class_of_param thy c

   of SOME class => (case inst_tyco thy c_ty

       of SOME tyco => (case try (inst thy) (c, tyco)

             of SOME (c, _) => c

              | NONE => c)

        | NONE => c)

    | NONE => c;

(* declaration and definition of instances of overloaded constants *)

fun primitive_note kind (name, thm) =

  PureThy.note_thmss_i kind [((name, []), [([thm], [])])]

  #>> (fn [(_, [thm])] => thm);

fun declare_overloaded (c, ty, mx) thy =

  let

    val SOME class = AxClass.class_of_param thy c;

    val SOME tyco = inst_tyco thy (c, ty);

    val name_inst = NameSpace.base class ^ "_" ^ NameSpace.base tyco ^ "_inst";

    val c' = NameSpace.base c;

    val ty' = Type.strip_sorts ty;

  in

    thy

    |> Sign.sticky_prefix name_inst

    |> Sign.no_base_names

    |> Sign.notation true Syntax.mode_default [(Const (c, ty), mx)]

    |> Sign.declare_const [] (c', ty', NoSyn)

    |-> (fn const' as Const (c'', _) => Thm.add_def true

          (Thm.def_name c', Logic.mk_equals (Const (c, ty'), const'))

    #>> Thm.varifyT

    #-> (fn thm => add_inst (c, tyco) (c'', thm)

    #> primitive_note Thm.internalK (c', thm)

    #> snd

    #> Sign.restore_naming thy

    #> pair (Const (c, ty))))

  end;

fun define_overloaded name (c, t) thy =

  let

    val ty = Term.fastype_of t;

    val SOME tyco = inst_tyco thy (c, ty);

    val (c', eq) = inst thy (c, tyco);

    val [Type (_, tys)] = Sign.const_typargs thy (c, ty);

    val eq' = eq

      |> Drule.instantiate' (map (SOME o Thm.ctyp_of thy) tys) [];

          (*FIXME proper recover_sort mechanism*)

    val prop = Logic.mk_equals (Const (c', ty), t);

    val name' = if name = "" then

      Thm.def_name (NameSpace.base c ^ "_" ^ NameSpace.base tyco) else name;

  in

    thy

    |> Thm.add_def false (name', prop)

    |>> (fn thm => Thm.transitive eq' thm)

  end;

(* legacy *)

fun add_inst_def (class, tyco) (c, ty) thy =

  let

    val tyco_base = Sign.base_name tyco;

    val name_inst = Sign.base_name class ^ "_" ^ tyco_base ^ "_inst";

    val c_inst_base = Sign.base_name c ^ "_" ^ tyco_base;

  in

    thy

    |> Sign.sticky_prefix name_inst

    |> Sign.declare_const [] (c_inst_base, ty, NoSyn)

    |-> (fn const as Const (c_inst, _) =>

      PureThy.add_defs_i false

        [((Thm.def_name c_inst_base, Logic.mk_equals (const, Const (c, ty))), [])]

      #-> (fn [thm] => add_inst (c, tyco) (c_inst, Thm.symmetric thm)))

    |> Sign.restore_naming thy

  end;

fun add_inst_def' (class, tyco) (c, ty) thy =

  if case Symtab.lookup (fst (InstData.get thy)) c

   of NONE => true

    | SOME tab => is_none (Symtab.lookup tab tyco)

  then add_inst_def (class, tyco) (c, Logic.unvarifyT ty) thy

  else thy;

fun add_def ((class, tyco), ((name, prop), atts)) thy =

  let

    val ((lhs as Const (c, ty), args), rhs) =

      (apfst Term.strip_comb o Logic.dest_equals) prop;

  in

    thy

    |> PureThy.add_defs_i true [((name, prop), map (Attrib.attribute_i thy) atts)]

    |-> (fn [def] => add_inst_def (class, tyco) (c, ty) #> pair def)

  end;

(** instances with implicit parameter handling **)

local

fun gen_read_def thy prep_att parse_prop ((raw_name, raw_atts), raw_t) =

  let

    val ctxt = ProofContext.init thy;

    val t = parse_prop ctxt raw_t |> Syntax.check_prop ctxt;

    val ((c, ty), _) = Sign.cert_def ctxt t;

    val atts = map (prep_att thy) raw_atts;

    val insts = Consts.typargs (Sign.consts_of thy) (c, ty);

    val name = case raw_name

     of "" => NONE

      | _ => SOME raw_name;

  in (c, (insts, ((name, t), atts))) end;

fun read_def_cmd thy = gen_read_def thy Attrib.intern_src Syntax.parse_prop;

fun read_def thy = gen_read_def thy (K I) (K I);

fun gen_instance prep_arity read_def do_proof raw_arities raw_defs after_qed theory =

  let

    val arities = map (prep_arity theory) raw_arities;

    val _ = if null arities then error "At least one arity must be given" else ();

    val _ = case (duplicates (op =) o map #1) arities

     of [] => ()

      | dupl_tycos => error ("Type constructors occur more than once in arities: "

          ^ commas_quote dupl_tycos);

    fun get_consts_class tyco ty class =

      let

        val cs = (these o try (#params o AxClass.get_info theory)) class;

        val subst_ty = map_type_tfree (K ty);

      in

        map (fn (c, ty) => (c, ((class, tyco), subst_ty ty))) cs

      end;

    fun get_consts_sort (tyco, asorts, sort) =

      let

        val ty = Type (tyco, map (fn (v, sort) => TVar ((v, 0), sort))

          (Name.names Name.context Name.aT asorts))

      in maps (get_consts_class tyco ty) (Sign.complete_sort theory sort) end;

    val cs = maps get_consts_sort arities;

    fun mk_typnorm thy (ty, ty_sc) =

      case try (Sign.typ_match thy (Logic.varifyT ty_sc, ty)) Vartab.empty

       of SOME env => SOME (Logic.varifyT #> Envir.typ_subst_TVars env #> Logic.unvarifyT)

        | NONE => NONE;

    fun read_defs defs cs thy_read =

      let

        fun read raw_def cs =

          let

            val (c, (inst, ((name_opt, t), atts))) = read_def thy_read raw_def;

            val ty = Consts.instance (Sign.consts_of thy_read) (c, inst);

            val ((class, tyco), ty') = case AList.lookup (op =) cs c

             of NONE => error ("Illegal definition for constant " ^ quote c)

              | SOME class_ty => class_ty;

            val name = case name_opt

             of NONE => Thm.def_name (Logic.name_arity (tyco, [], c))

              | SOME name => name;

            val t' = case mk_typnorm thy_read (ty', ty)

             of NONE => error ("Illegal definition for constant " ^

                  quote (c ^ "::" ^ setmp show_sorts true

                    (Sign.string_of_typ thy_read) ty))

              | SOME norm => map_types norm t

          in (((class, tyco), ((name, t'), atts)), AList.delete (op =) c cs) end;

      in fold_map read defs cs end;

    val (defs, other_cs) = read_defs raw_defs cs

      (fold Sign.primitive_arity arities (Theory.copy theory));

    fun after_qed' cs defs =

      fold Sign.add_const_constraint (map (apsnd SOME) cs)

      #> after_qed defs;

  in

    theory

    |> fold_map get_remove_global_constraint (map fst cs |> distinct (op =))

    ||>> fold_map add_def defs

    ||> fold (fn (c, ((class, tyco), ty)) => add_inst_def' (class, tyco) (c, ty)) other_cs

    |-> (fn (cs, defs) => do_proof (after_qed' cs defs) arities defs)

  end;

fun tactic_proof tac f arities defs =

  fold (fn arity => AxClass.prove_arity arity tac) arities

  #> f

  #> pair defs;

in

val instance = gen_instance Sign.cert_arity read_def

  (fn f => fn arities => fn defs => instance_arity f arities);

val instance_cmd = gen_instance Sign.read_arity read_def_cmd

  (fn f => fn arities => fn defs => instance_arity f arities);

fun prove_instance tac arities defs =

  gen_instance Sign.cert_arity read_def

    (tactic_proof tac) arities defs (K I);

end; (*local*)

(** class data **)

datatype class_data = ClassData of {

  consts: (string * string) list

    (*locale parameter ~> constant name*),

  base_sort: sort,

  inst: term option list

    (*canonical interpretation*),

  morphism: morphism,

    (*partial morphism of canonical interpretation*)

  intro: thm,

  defs: thm list,

  operations: (string * (class * (typ * term))) list

};

fun rep_class_data (ClassData d) = d;

fun mk_class_data ((consts, base_sort, inst, morphism, intro),

    (defs, operations)) =

  ClassData { consts = consts, base_sort = base_sort, inst = inst,

    morphism = morphism, intro = intro, defs = defs,

    operations = operations };

fun map_class_data f (ClassData { consts, base_sort, inst, morphism, intro,

    defs, operations }) =

  mk_class_data (f ((consts, base_sort, inst, morphism, intro),

    (defs, operations)));

fun merge_class_data _ (ClassData { consts = consts,

    base_sort = base_sort, inst = inst, morphism = morphism, intro = intro,

    defs = defs1, operations = operations1 },

  ClassData { consts = _, base_sort = _, inst = _, morphism = _, intro = _,

    defs = defs2, operations = operations2 }) =

  mk_class_data ((consts, base_sort, inst, morphism, intro),

    (Thm.merge_thms (defs1, defs2),

      AList.merge (op =) (K true) (operations1, operations2)));

structure ClassData = TheoryDataFun

(

  type T = class_data Graph.T

  val empty = Graph.empty;

  val copy = I;

  val extend = I;

  fun merge _ = Graph.join merge_class_data;

);

(* queries *)

val lookup_class_data = Option.map rep_class_data oo try o Graph.get_node o ClassData.get;

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;

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 => (c, (the o AList.lookup (op =) const_typs) c)) const_names

      end;

  in maps params o ancestry thy end;

fun these_defs thy = maps (these o Option.map #defs o lookup_class_data thy) o ancestry thy;

fun morphism thy = #morphism o the_class_data thy;

fun these_intros thy =

  Graph.fold (fn (_, (data, _)) => insert Thm.eq_thm ((#intro o rep_class_data) data))

    (ClassData.get thy) [];

fun these_operations thy =

  maps (#operations o the_class_data thy) o ancestry thy;

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)

             ((#arities o Sorts.rep_algebra) 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 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],

      if is_class thy class then (SOME o Pretty.str)

        ("locale: " ^ Locale.extern thy class) else NONE,

      ((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 add_class_data ((class, superclasses), (cs, base_sort, inst, phi, intro)) thy =

  let

    val operations = map (fn (v_ty as (_, ty), (c, _)) =>

      (c, (class, (ty, Free v_ty)))) cs;

    val cs = (map o pairself) fst cs;

    val add_class = Graph.new_node (class,

        mk_class_data ((cs, base_sort, map (SOME o Const) inst, phi, intro), ([], operations)))

      #> fold (curry Graph.add_edge class) superclasses;

  in

    ClassData.map add_class thy

  end;

fun register_operation class (c, (t, some_def)) thy =

  let

    val base_sort = (#base_sort o the_class_data thy) class;

    val prep_typ = map_atyps

      (fn TVar (vi as (v, _), sort) => if Name.aT = v

        then TFree (v, base_sort) else TVar (vi, 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))

  end;

(** rule calculation, tactics and methods **)

val class_prefix = Logic.const_of_class o Sign.base_name;

fun calculate_morphism class cs =

  let

    val subst_typ = Term.map_type_tfree (fn var as (v, sort) =>

      if v = Name.aT then TVar ((v, 0), [class]) else TVar ((v, 0), sort));

    fun subst_aterm (t as Free (v, ty)) = (case AList.lookup (op =) cs v

         of SOME (c, _) => Const (c, ty)

          | NONE => t)

      | subst_aterm t = t;

    val subst_term = map_aterms subst_aterm #> map_types subst_typ;

  in

    Morphism.term_morphism subst_term

    $> Morphism.typ_morphism subst_typ

  end;

fun class_intro thy class sups =

  let

    fun class_elim class =

      case (#axioms o AxClass.get_info thy) class

       of [thm] => SOME (Drule.unconstrainTs thm)

        | [] => NONE;

    val pred_intro = case Locale.intros thy class

     of ([ax_intro], [intro]) => intro |> OF_LAST ax_intro |> SOME

      | ([intro], []) => SOME intro

      | ([], [intro]) => SOME intro

      | _ => NONE;

    val pred_intro' = pred_intro

      |> Option.map (fn intro => intro OF map_filter class_elim sups);

    val class_intro = (#intro o AxClass.get_info thy) class;

    val raw_intro = case pred_intro'

     of SOME pred_intro => class_intro |> OF_LAST pred_intro

      | NONE => class_intro;

    val sort = Sign.super_classes thy class;

    val typ = TVar ((Name.aT, 0), sort);

    val defs = these_defs thy sups;

  in

    raw_intro

    |> Drule.instantiate' [SOME (Thm.ctyp_of thy typ)] []

    |> strip_all_ofclass thy sort

    |> Thm.strip_shyps

    |> MetaSimplifier.rewrite_rule defs

    |> Drule.unconstrainTs

  end;

fun class_interpretation class facts defs thy =

  let

    val params = these_params thy [class];

    val inst = (#inst o the_class_data thy) class;

    val tac = ALLGOALS (ProofContext.fact_tac facts);

    val prfx = class_prefix class;

  in

    thy

    |> fold_map (get_remove_global_constraint o fst o snd) params

    ||> prove_interpretation tac ((false, prfx), []) (Locale.Locale class)

          (inst, map (fn def => (("", []), def)) defs)

    |-> (fn cs => fold (Sign.add_const_constraint o apsnd SOME) cs)

  end;

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 = these_intros thy;

    val axclass_intros = map_filter (try (#intro o AxClass.get_info thy)) classes;

  in

    Method.intros_tac (class_trivs @ class_intros @ axclass_intros) facts st

  end;

fun default_intro_classes_tac [] = intro_classes_tac []

  | default_intro_classes_tac _ = no_tac;

fun default_tac rules ctxt facts =

  HEADGOAL (Method.some_rule_tac rules ctxt facts) ORELSE

    default_intro_classes_tac facts;

val _ = Context.add_setup (Method.add_methods

 [("intro_classes", Method.no_args (Method.METHOD intro_classes_tac),

    "back-chain introduction rules of classes"),

  ("default", Method.thms_ctxt_args (Method.METHOD oo default_tac),

    "apply some intro/elim rule")]);

fun subclass_rule thy (sub, sup) =

  let

    val ctxt = Locale.init sub thy;

    val ctxt_thy = ProofContext.init thy;

    val props =

      Locale.global_asms_of thy sup

      |> maps snd

      |> map (ObjectLogic.ensure_propT thy);

    fun tac { prems, context } =

      Locale.intro_locales_tac true context prems

        ORELSE ALLGOALS assume_tac;

  in

    Goal.prove_multi ctxt [] [] props tac

    |> map (Assumption.export false ctxt ctxt_thy)

    |> Variable.export ctxt ctxt_thy

  end;

fun prove_single_subclass (sub, sup) thms ctxt thy =

  let

    val ctxt_thy = ProofContext.init thy;

    val subclass_rule = Conjunction.intr_balanced thms

      |> Assumption.export false ctxt ctxt_thy

      |> singleton (Variable.export ctxt ctxt_thy);

    val sub_inst = Thm.ctyp_of thy (TVar ((Name.aT, 0), [sub]));

    val sub_ax = #axioms (AxClass.get_info thy sub);

    val classrel =

      #intro (AxClass.get_info thy sup)

      |> Drule.instantiate' [SOME sub_inst] []

      |> OF_LAST (subclass_rule OF sub_ax)

      |> strip_all_ofclass thy (Sign.super_classes thy sup)

      |> Thm.strip_shyps

  in

    thy

    |> AxClass.add_classrel classrel

    |> prove_interpretation_in (ALLGOALS (ProofContext.fact_tac thms))

         I (sub, Locale.Locale sup)

    |> ClassData.map (Graph.add_edge (sub, sup))

  end;

fun prove_subclass (sub, sup) thms ctxt thy =

  let

    val classes = ClassData.get thy;

    val is_sup = not o null o curry (Graph.irreducible_paths classes) sub;

    val supclasses = Graph.all_succs classes [sup] |> filter_out is_sup;

    fun transform sup' = subclass_rule thy (sup, sup') |> map (fn thm => thm OF thms);

  in

    thy

    |> fold_rev (fn sup' => prove_single_subclass (sub, sup')

         (transform sup') ctxt) supclasses

 end;

(** classes and class target **)

(* class context syntax *)

structure ClassSyntax = ProofDataFun(

  type T = {

    local_constraints: (string * typ) list,

    global_constraints: (string * typ) list,

    base_sort: sort,

    operations: (string * (typ * term)) list,

    unchecks: (term * term) list,

    passed: bool

  };

  fun init _ = {

    local_constraints = [],

    global_constraints = [],

    base_sort = [],

    operations = [],

    unchecks = [],

    passed = true

  };;

);

fun synchronize_syntax sups base_sort ctxt =

  let

    val thy = ProofContext.theory_of ctxt;

    fun subst_class_typ sort = map_atyps

      (fn TFree _ => TVar ((Name.aT, 0), sort) | ty' => ty');

    val operations = these_operations thy sups;

    val local_constraints =

      (map o apsnd) (subst_class_typ base_sort o fst o snd) operations;

    val global_constraints =

      (map o apsnd) (fn (class, (ty, _)) => subst_class_typ [class] ty) operations;

    fun declare_const (c, _) =

      let val b = Sign.base_name c

      in Sign.intern_const thy b = c ? Variable.declare_const (b, c) end;

    val unchecks = map (fn (c, (_, (ty, t))) => (t, Const (c, ty))) operations;

  in

    ctxt

    |> fold declare_const local_constraints

    |> fold (ProofContext.add_const_constraint o apsnd SOME) local_constraints

    |> ClassSyntax.put {

        local_constraints = local_constraints,

        global_constraints = global_constraints,

        base_sort = base_sort,

        operations = (map o apsnd) snd operations,

        unchecks = unchecks,

        passed = false

      }

  end;

fun refresh_syntax class ctxt =

  let

    val thy = ProofContext.theory_of ctxt;

    val base_sort = (#base_sort o the_class_data thy) class;

  in synchronize_syntax [class] base_sort ctxt end;

val mark_passed = ClassSyntax.map

  (fn { local_constraints, global_constraints, base_sort, operations, unchecks, passed } =>

    { local_constraints = local_constraints, global_constraints = global_constraints,

      base_sort = base_sort, operations = operations, unchecks = unchecks, passed = true });

fun sort_term_check ts ctxt =

  let

    val { local_constraints, global_constraints, base_sort, operations, passed, ... } =

      ClassSyntax.get ctxt;

    fun check_improve (Const (c, ty)) = (case AList.lookup (op =) local_constraints c

         of SOME ty0 => (case try (Type.raw_match (ty0, ty)) Vartab.empty

             of SOME tyenv => (case Vartab.lookup tyenv (Name.aT, 0)

                 of SOME (_, TVar (tvar as (vi, _))) =>

                      if TypeInfer.is_param vi then cons tvar else I

                  | _ => I)

              | NONE => I)

          | NONE => I)

      | check_improve _ = I;

    val improvements = (fold o fold_aterms) check_improve ts [];

    val ts' = (map o map_types o map_atyps) (fn ty as TVar tvar =>

        if member (op =) improvements tvar

          then TFree (Name.aT, base_sort) else ty | ty => ty) ts;

    fun check t0 = Envir.expand_term (fn Const (c, ty) => (case AList.lookup (op =) operations c

         of SOME (ty0, t) =>

              if Type.typ_instance (ProofContext.tsig_of ctxt) (ty, ty0)

              then SOME (ty0, check t) else NONE

          | NONE => NONE)

      | _ => NONE) t0;

    val ts'' = map check ts';

  in if eq_list (op aconv) (ts, ts'') andalso passed then NONE

  else

    ctxt

    |> fold (ProofContext.add_const_constraint o apsnd SOME) global_constraints

    |> mark_passed

    |> pair ts''

    |> SOME

  end;

fun sort_term_uncheck ts ctxt =

  let

    val thy = ProofContext.theory_of ctxt;

    val unchecks = (#unchecks o ClassSyntax.get) ctxt;

    val ts' = map (Pattern.rewrite_term thy unchecks []) ts;

  in if eq_list (op aconv) (ts, ts') then NONE else SOME (ts', ctxt) end;

fun init_ctxt sups base_sort ctxt =

  ctxt

  |> Variable.declare_term

      (Logic.mk_type (TFree (Name.aT, base_sort)))

  |> synchronize_syntax sups base_sort

  |> Context.proof_map (

      Syntax.add_term_check 0 "class" sort_term_check

      #> Syntax.add_term_uncheck 0 "class" sort_term_uncheck)

fun init class thy =

  thy

  |> Locale.init class

  |> init_ctxt [class] ((#base_sort o the_class_data thy) class);

(* class definition *)

local

fun gen_class_spec prep_class prep_expr process_expr thy raw_supclasses raw_includes_elems =

  let

    val supclasses = map (prep_class thy) raw_supclasses;

    val sups = filter (is_class thy) supclasses;

    fun the_base_sort class = lookup_class_data thy class

      |> Option.map #base_sort

      |> the_default [class];

    val base_sort = Sign.minimize_sort thy (maps the_base_sort supclasses);

    val supsort = Sign.minimize_sort thy supclasses;

    val suplocales = map Locale.Locale sups;

    val (raw_elems, includes) = fold_rev (fn Locale.Elem e => apfst (cons e)

      | Locale.Expr i => apsnd (cons (prep_expr thy i))) raw_includes_elems ([], []);

    val supexpr = Locale.Merge suplocales;

    val supparams = (map fst o Locale.parameters_of_expr thy) supexpr;

    val supconsts = AList.make (the o AList.lookup (op =) (these_params thy sups))

      (map fst supparams);

    val mergeexpr = Locale.Merge (suplocales @ includes);

    val constrain = Element.Constrains ((map o apsnd o map_atyps)

      (fn TFree (_, sort) => TFree (Name.aT, sort)) supparams);

  in

    ProofContext.init thy

    |> Locale.cert_expr supexpr [constrain]

    |> snd

    |> init_ctxt sups base_sort

    |> process_expr Locale.empty raw_elems

    |> fst

    |> (fn elems => ((((sups, supconsts), (supsort, base_sort, mergeexpr)),

          (*FIXME*) if null includes then constrain :: elems else elems)))

  end;

val read_class_spec = gen_class_spec Sign.intern_class Locale.intern_expr Locale.read_expr;

val check_class_spec = gen_class_spec (K I) (K I) Locale.cert_expr;

fun define_class_params (name, raw_superclasses) raw_consts raw_dep_axioms other_consts thy =

  let

    val superclasses = map (Sign.certify_class thy) raw_superclasses;

    val consts = (map o apfst o apsnd) (Sign.certify_typ thy) raw_consts;

    fun add_const ((c, ty), syn) =

      Sign.declare_const [] (c, Type.strip_sorts ty, syn) #>> Term.dest_Const;

    fun mk_axioms cs thy =

      raw_dep_axioms thy cs

      |> (map o apsnd o map) (Sign.cert_prop thy)

      |> rpair thy;

    fun constrain_typs class = (map o apsnd o Term.map_type_tfree)

      (fn (v, _) => TFree (v, [class]))

  in

    thy

    |> Sign.add_path (Logic.const_of_class name)

    |> fold_map add_const consts

    ||> Sign.restore_naming thy

    |-> (fn cs => mk_axioms cs

    #-> (fn axioms_prop => AxClass.define_class (name, superclasses)

           (map fst cs @ other_consts) axioms_prop

    #-> (fn class => `(fn _ => constrain_typs class cs)

    #-> (fn cs' => `(fn thy => AxClass.get_info thy class)

    #-> (fn {axioms, ...} => fold (Sign.add_const_constraint o apsnd SOME) cs'

    #> pair (class, (cs', axioms)))))))

  end;

fun gen_class prep_spec prep_param bname

    raw_supclasses raw_includes_elems raw_other_consts thy =

  let

    val class = Sign.full_name thy bname;

    val (((sups, supconsts), (supsort, base_sort, mergeexpr)), elems_syn) =

      prep_spec thy raw_supclasses raw_includes_elems;

    val other_consts = map (tap (Sign.the_const_type thy) o prep_param thy) raw_other_consts;

    fun mk_inst class cs =

      (map o apsnd o Term.map_type_tfree) (fn (v, _) => TFree (v, [class])) cs;

    fun fork_syntax (Element.Fixes xs) =

          fold_map (fn (c, ty, syn) => cons (c, syn) #> pair (c, ty, NoSyn)) xs

          #>> Element.Fixes

      | fork_syntax x = pair x;

    val (elems, global_syn) = fold_map fork_syntax elems_syn [];

    fun globalize (c, ty) =

      ((c, Term.map_type_tfree (K (TFree (Name.aT, base_sort))) ty),

        (the_default NoSyn o AList.lookup (op =) global_syn) c);

    fun extract_params thy =

      let

        val params = map fst (Locale.parameters_of thy class);

      in

        (params, (map globalize o snd o chop (length supconsts)) params)

      end;

    fun extract_assumes params thy cs =

      let

        val consts = supconsts @ (map (fst o fst) params ~~ cs);

        fun subst (Free (c, ty)) =

              Const ((fst o the o AList.lookup (op =) consts) c, ty)

          | subst t = t;

        fun prep_asm ((name, atts), ts) =

          ((Sign.base_name name, map (Attrib.attribute_i thy) atts),

            (map o map_aterms) subst ts);

      in

        Locale.global_asms_of thy class

        |> map prep_asm

      end;

  in

    thy

    |> Locale.add_locale_i (SOME "") bname mergeexpr elems

    |> snd

    |> ProofContext.theory_of

    |> `extract_params

    |-> (fn (all_params, params) =>

        define_class_params (bname, supsort) params

          (extract_assumes params) other_consts

      #-> (fn (_, (consts, axioms)) =>

        `(fn thy => class_intro thy class sups)

      #-> (fn class_intro =>

        PureThy.note_thmss_qualified "" (NameSpace.append class classN)

          [((introN, []), [([class_intro], [])])]

      #-> (fn [(_, [class_intro])] =>

        add_class_data ((class, sups),

          (map fst params ~~ consts, base_sort,

            mk_inst class (map snd supconsts @ consts),

              calculate_morphism class (supconsts @ (map (fst o fst) params ~~ consts)), class_intro))

      #> class_interpretation class axioms []

      ))))

    |> init class

    |> pair class

  end;

fun read_const thy = #1 o Term.dest_Const o ProofContext.read_const (ProofContext.init thy);

in

val class_cmd = gen_class read_class_spec read_const;

val class = gen_class check_class_spec (K I);

end; (*local*)

(* definition in class target *)

fun add_logical_const class pos ((c, mx), dict) thy =

  let

    val prfx = class_prefix class;

    val thy' = thy |> Sign.add_path prfx;

    val phi = morphism thy' class;

    val c' = Sign.full_name thy' c;

    val dict' = Morphism.term phi dict;

    val dict_def = map_types Logic.unvarifyT dict';

    val ty' = Term.fastype_of dict_def;

    val ty'' = Type.strip_sorts ty';

    val def_eq = Logic.mk_equals (Const (c', ty'), dict_def);

  in

    thy'

    |> Sign.declare_const pos (c, ty'', mx) |> snd

    |> Thm.add_def false (c, def_eq)    (* FIXME PureThy.add_defs_i *)

    |>> Thm.symmetric

    |-> (fn def => class_interpretation class [def] [Thm.prop_of def]

          #> register_operation class (c', (dict', SOME (Thm.varifyT def))))

    |> Sign.restore_naming thy

    |> Sign.add_const_constraint (c', SOME ty')

  end;

(* abbreviation in class target *)

fun add_syntactic_const class prmode pos ((c, mx), rhs) thy =

  let

    val prfx = class_prefix class;

    val thy' = thy |> Sign.add_path prfx;

    val phi = morphism thy class;

    val c' = Sign.full_name thy' c;

    val rews = map (Logic.dest_equals o Thm.prop_of) (these_defs thy' [class])

    val rhs' = (Pattern.rewrite_term thy rews [] o Morphism.term phi) rhs;

    val ty' = Logic.unvarifyT (Term.fastype_of rhs');

  in

    thy'

    |> Sign.add_abbrev (#1 prmode) pos (c, map_types Type.strip_sorts rhs') |> snd

    |> Sign.add_const_constraint (c', SOME ty')

    |> Sign.notation true prmode [(Const (c', ty'), mx)]

    |> register_operation class (c', (rhs', NONE))

    |> Sign.restore_naming thy

  end;

(** instantiation target **)

(* bookkeeping *)

datatype instantiation = Instantiation of {

  arities: arity list,

  params: ((string * string) * (string * typ)) list

}

structure Instantiation = ProofDataFun

(

  type T = instantiation

  fun init _ = Instantiation { arities = [], params = [] };

);

fun mk_instantiation (arities, params) = Instantiation {

    arities = arities, params = params

  };

fun map_instantiation f (Instantiation { arities, params }) =

  mk_instantiation (f (arities, params));

fun the_instantiation ctxt = case Instantiation.get ctxt

 of Instantiation { arities = [], ... } => error "No instantiation target"

  | Instantiation data => data;

fun init_instantiation arities ctxt =

  let

    val thy = ProofContext.theory_of ctxt;

    val _ = if null arities then error "At least one arity must be given" else ();

    val _ = case (duplicates (op =) o map #1) arities

     of [] => ()

      | dupl_tycos => error ("Type constructors occur more than once in arities: "

          ^ commas_quote dupl_tycos);