(*  Title:      Pure/Isar/class.ML

    ID:         $Id$

    Author:     Florian Haftmann, TU Muenchen

Type classes derived from primitive axclasses and locales.

*)

signature CLASS =

sig

  val fork_mixfix: bool -> string option -> mixfix -> mixfix * mixfix

  val axclass_cmd: bstring * xstring list

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

    -> theory -> class * theory

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

  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 add_const_in_class: string -> (string * term) * Syntax.mixfix

    -> theory -> theory

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

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

  val prove_interpretation_in_class: tactic -> class * class -> theory -> theory

  val intro_classes_tac: thm list -> tactic

  val default_intro_classes_tac: thm list -> tactic

  val class_of_locale: theory -> string -> class option

  val print_classes: theory -> unit

  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

  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 params_of_sort: theory -> sort -> (string * (string * typ)) list

  (*experimental*)

  val init_ref: (class -> Proof.context -> (theory -> theory) * Proof.context) ref

  val init: class -> Proof.context -> (theory -> theory) * Proof.context;

  val init_default: class -> Proof.context -> (theory -> theory) * Proof.context;

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

  val class_term_check: theory -> class -> term list -> Proof.context -> term list * Proof.context

  val local_param: theory -> class -> string -> (term * (class * int)) option

end;

structure Class : CLASS =

struct

(** auxiliary **)

fun fork_mixfix is_loc some_class mx =

  let

    val mx' = Syntax.unlocalize_mixfix mx;

    val mx_global = if is_some some_class orelse (is_loc andalso mx = mx')

      then NoSyn else mx';

    val mx_local = if is_loc then mx else NoSyn;

  in (mx_global, mx_local) end;

fun prove_interpretation tac prfx_atts expr insts =

  Locale.interpretation_i I prfx_atts expr insts

  #> 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 =

  let

    val n = (length o Logic.strip_imp_prems o prop_of) thm2;

  in (thm1 RSN (n, thm2)) end;

fun strip_all_ofclass thy sort =

  let

    val typ = TVar ((AxClass.param_tyvarname, 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_contraint c thy =

  let

    val ty = Sign.the_const_constraint thy c;

  in

    thy

    |> Sign.add_const_constraint_i (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*)

(** explicit constants for overloaded definitions **)

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));

);

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

    (InstData.get thy) [];

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 false (inst_thms I thy);

fun overload thy = MetaSimplifier.rewrite false (inst_thms symmetric thy);

fun inst_const thy (c, tyco) =

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

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

  case AxClass.class_of_param thy c

   of SOME class => (case Sign.const_typargs thy c_ty

       of [Type (tyco, _)] => (case Symtab.lookup

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

             of SOME (c, _) => c

              | NONE => c)

        | [_] => c)

    | NONE => c;

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

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

  let

    val tyco_base = NameSpace.base tyco;

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

    val c_inst_base = NameSpace.base c ^ "_" ^ tyco_base;

  in

    thy

    |> Sign.sticky_prefix name_inst

    |> PureThy.simple_def ("", [])

         (((c_inst_base, ty, Syntax.NoSyn), []), Const (c, ty))

    |-> (fn (c_inst, thm) => add_inst (c, tyco) (c_inst, 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;

    fun (*add_inst' def ([], (Const (c_inst, ty))) =

          if forall (fn TFree _ => true | _ => false) (Sign.const_typargs thy (c_inst, ty))

          then add_inst (c, tyco) (c_inst, def)

          else add_inst_def (class, tyco) (c, ty)

      |*) add_inst' _ t = add_inst_def (class, tyco) (c, ty);

  in

    thy

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

    |-> (fn [def] => add_inst' def (args, rhs) #> 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 (Sign.pp thy) 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 o map quote) dupl_tycos);

    val super_sort =

      (Graph.all_succs o #classes o Sorts.rep_algebra o Sign.classes_of) theory;

    fun get_consts_class tyco ty class =

      let

        val cs = (these o Option.map snd o try (AxClass.params_of_class 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 "'a" asorts))

      in maps (get_consts_class tyco ty) (super_sort 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_i (map (apsnd SOME) cs)

      #> after_qed defs;

  in

    theory

    |> fold_map get_remove_contraint (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 {

  locale: string,

  consts: (string * string) list

    (*locale parameter ~> theory constant name*),

  v: string,

  inst: typ Symtab.table * term Symtab.table

    (*canonical interpretation*),

  intro: thm,

  defs: thm list,

  localized: (string * (term * (class * int))) list

    (*theory constant name ~> (locale parameter, (class, instantiaton index of class typ))*)

};

fun rep_class_data (ClassData d) = d;

fun mk_class_data ((locale, consts, v, inst, intro), (defs, localized)) =

  ClassData { locale = locale, consts = consts, v = v, inst = inst, intro = intro,

    defs = defs, localized = localized };

fun map_class_data f (ClassData { locale, consts, v, inst, intro, defs, localized }) =

  mk_class_data (f ((locale, consts, v, inst, intro), (defs, localized)))

fun merge_class_data _ (ClassData { locale = locale, consts = consts, v = v, inst = inst,

    intro = intro, defs = defs1, localized = localized1 },

  ClassData { locale = _, consts = _, v = _, inst = _, intro = _,

    defs = defs2, localized = localized2 }) =

  mk_class_data ((locale, consts, v, inst, intro),

    (Thm.merge_thms (defs1, defs2), AList.merge (op =) (K true) (localized1, localized2)));

fun merge_pair f1 f2 ((x1, y1), (x2, y2)) = (f1 (x1, x2), f2 (y1, y2));

structure ClassData = TheoryDataFun

(

  type T = class_data Graph.T * class Symtab.table

    (*locale name ~> class name*);

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

  val copy = I;

  val extend = I;

  fun merge _ = merge_pair (Graph.join merge_class_data) (Symtab.merge (K true));

);

(* queries *)

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

  o fst o ClassData.get;

fun class_of_locale thy = Symtab.lookup ((snd o ClassData.get) thy);

fun the_class_data thy class = case lookup_class_data thy class

 of NONE => error ("undeclared class " ^ quote class)

  | SOME data => data;

val ancestry = Graph.all_succs o fst o ClassData.get;

fun params_of_sort thy =

  let

    fun params class =

      let

        val const_typs = (#params o AxClass.get_definition 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 these_intros thy =

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

    ((fst o ClassData.get) thy) [];

fun these_localized thy class =

  maps (#localized o the_class_data thy) (ancestry thy [class]);

fun local_param thy = AList.lookup (op =) o these_localized thy;

fun print_classes thy =

  let

    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 Sign.pretty_arity thy (tyco, Ss, [class]) end;

    fun mk_param (c, ty) = Pretty.str (Sign.extern_const thy c ^ " :: "

      ^ setmp show_sorts false (Sign.string_of_typ thy o Type.strip_sorts) ty);

    fun mk_entry class = (Pretty.block o Pretty.fbreaks o map_filter I) [

      (SOME o Pretty.str) ("class " ^ class ^ ":"),

      (SOME o Pretty.block) [Pretty.str "supersort: ",

        (Sign.pretty_sort thy o Sign.certify_sort thy o Sign.super_classes thy) class],

      Option.map (Pretty.str o prefix "locale: " o #locale) (lookup_class_data 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_definition 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), (locale, consts, v, inst, intro)) =

  ClassData.map (fn (gr, tab) => (

    gr

    |> Graph.new_node (class, mk_class_data ((locale, (map o apfst) fst consts, v, inst, intro),

         ([], map (apsnd (rpair (class, 0) o Free) o swap) consts)))

    |> fold (curry Graph.add_edge class) superclasses,

    tab

    |> Symtab.update (locale, class)

  ));

fun add_class_const_def (class, (entry, def)) =

  (ClassData.map o apfst o Graph.map_node class o map_class_data o apsnd)

    (fn (defs, localized) => (def :: defs, (apsnd o apsnd) (pair class) entry :: localized));

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

fun class_intro thy locale class sups =

  let

    fun class_elim class =

      case (map Drule.unconstrainTs o #axioms o AxClass.get_definition thy) class

       of [thm] => SOME thm

        | [] => NONE;

    val pred_intro = case Locale.intros thy locale

     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_definition 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 ((AxClass.param_tyvarname, 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 { locale, inst, ... } = the_class_data thy class;

    val tac = (ALLGOALS o ProofContext.fact_tac) facts;

    val prfx = Logic.const_of_class (NameSpace.base class);

  in

    prove_interpretation tac ((false, prfx), []) (Locale.Locale locale)

      (inst, defs) thy

  end;

fun interpretation_in_rule thy (class1, class2) =

  let

    fun mk_axioms class =

      let

        val { locale, inst = (_, insttab), ... } = the_class_data thy class;

      in

        Locale.global_asms_of thy locale

        |> maps snd

        |> (map o map_aterms) (fn Free (s, _) => (the o Symtab.lookup insttab) s | t => t)

        |> (map o map_types o map_atyps) (fn TFree _ => TFree ("'a", [class1]) | T => T)

        |> map (ObjectLogic.ensure_propT thy)

      end;

    val (prems, concls) = pairself mk_axioms (class1, class2);

  in

    Goal.prove_global thy [] prems (Logic.mk_conjunction_list concls)

      (Locale.intro_locales_tac true (ProofContext.init thy))

  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;

    fun add_axclass_intro class =

      case try (AxClass.get_definition thy) class of SOME {intro, ...} => cons intro | _ => I;

    val axclass_intros = fold add_axclass_intro classes [];

  in

    st

    |> ((ALLGOALS (Method.insert_tac facts THEN'

          REPEAT_ALL_NEW (resolve_tac (class_trivs @ class_intros @ axclass_intros))))

            THEN Tactic.distinct_subgoals_tac)

  end;

fun default_intro_classes_tac [] = intro_classes_tac []

  | default_intro_classes_tac _ = Tactical.no_tac;    (*no error message!*)

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")]);

(** classes and class target **)

(* class definition *)

local

fun read_param thy raw_t =  (* FIXME ProofContext.read_const (!?) *)

  let

    val t = Syntax.read_term_global thy raw_t

  in case try dest_Const t

   of SOME (c, _) => c

    | NONE => error ("Not a constant: " ^ Sign.string_of_term thy t)

  end;

fun gen_class add_locale prep_class prep_param bname

    raw_supclasses raw_elems raw_other_consts thy =

  let

    fun mk_instT class = Symtab.empty

      |> Symtab.update (AxClass.param_tyvarname, TFree (AxClass.param_tyvarname, [class]));

    fun mk_inst class param_names cs =

      Symtab.empty

      |> fold2 (fn v => fn (c, ty) => Symtab.update (v, Const

           (c, Term.map_type_tfree (fn (v, _) => TFree (v, [class])) ty))) param_names cs;

    (*FIXME need proper concept for reading locale statements*)

    fun subst_classtyvar (_, _) =

          TFree (AxClass.param_tyvarname, [])

      | subst_classtyvar (v, sort) =

          error ("Sort constraint illegal in type class, for type variable "

            ^ v ^ "::" ^ Sign.string_of_sort thy sort);

    (*val subst_classtyvars = Element.map_ctxt {name = I, var = I, term = I,

      typ = Term.map_type_tfree subst_classtyvar, fact = I, attrib = I};*)

    val other_consts = map (prep_param thy) raw_other_consts;

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

      | Locale.Expr i => apsnd (cons i)) raw_elems ([], []);

    val supclasses = map (prep_class thy) raw_supclasses;

    val sups = filter (is_some o lookup_class_data thy) supclasses

      |> Sign.certify_sort thy;

    val supsort = Sign.certify_sort thy supclasses;

    val suplocales = map (Locale.Locale o #locale o the_class_data thy) sups;

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

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

      (Locale.Merge suplocales);

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

      (map fst supparams);

    (*val elems_constrains = map

      (Element.Constrains o apsnd (Term.map_type_tfree subst_classtyvar)) supparams;*)

    fun mk_tyvar (_, sort) = TFree (AxClass.param_tyvarname,

      if Sign.subsort thy (supsort, sort) then sort else error

        ("Sort " ^ Sign.string_of_sort thy sort

          ^ " is less general than permitted least general sort "

          ^ Sign.string_of_sort thy supsort));

    fun extract_params thy name_locale =

      let

        val params = Locale.parameters_of thy name_locale;

        val v = case (maps typ_tfrees o map (snd o fst)) params

         of (v, _) :: _ => v

          | [] => AxClass.param_tyvarname;

      in

        (v, (map fst params, params

        |> (map o apfst o apsnd o Term.map_type_tfree) mk_tyvar

        |> (map o apsnd) (fork_mixfix true NONE #> fst)

        |> chop (length supconsts)

        |> snd))

      end;

    fun extract_assumes name_locale 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) =

          ((NameSpace.base name, map (Attrib.attribute thy) atts),

            (map o map_aterms) subst ts);

      in

        Locale.global_asms_of thy name_locale

        |> map prep_asm

      end;

    fun note_intro name_axclass class_intro =

      PureThy.note_thmss_qualified "" ((Logic.const_of_class o NameSpace.base) name_axclass)

        [(("intro", []), [([class_intro], [])])]

      #> snd

  in

    thy

    |> add_locale (SOME "") bname supexpr ((*elems_constrains @*) elems)

    |-> (fn name_locale => ProofContext.theory_result (

      `(fn thy => extract_params thy name_locale)

      #-> (fn (v, (globals, params)) =>

        AxClass.define_class_params (bname, supsort) params

          (extract_assumes name_locale params) other_consts

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

        `(fn thy => class_intro thy name_locale name_axclass sups)

      #-> (fn class_intro =>

        add_class_data ((name_axclass, sups),

          (name_locale, map fst params ~~ map fst consts, v,

            (mk_instT name_axclass, mk_inst name_axclass (map fst globals)

              (map snd supconsts @ consts)), class_intro))

      #> note_intro name_axclass class_intro

      #> class_interpretation name_axclass axioms []

      #> pair name_axclass

      )))))

  end;

in

val class_cmd = gen_class Locale.add_locale Sign.intern_class read_param;

val class = gen_class Locale.add_locale_i Sign.certify_class (K I);

end; (*local*)

(* class target context *)

fun remove_constraints class thy =

  thy |> fold_map (get_remove_contraint o fst) (these_localized thy class);

(* definition in class target *)

fun export_fixes thy class =

  let

    val consts = params_of_sort thy [class];

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

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

          | NONE => t)

      | subst_aterm t = t;

  in Term.map_aterms subst_aterm end;

fun add_const_in_class class ((c, rhs), syn) thy =

  let

    val prfx = (Logic.const_of_class o NameSpace.base) class;

    fun mk_name c =

      let

        val n1 = Sign.full_name thy c;

        val n2 = NameSpace.qualifier n1;

        val n3 = NameSpace.base n1;

      in NameSpace.implode [n2, prfx, n3] end;

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

    val constrain_sort = curry (Sorts.inter_sort (Sign.classes_of thy)) [class];

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

      if w = v then TFree (w, constrain_sort sort) else TFree var);

    val rhs' = export_fixes thy class rhs;

    val ty' = Term.fastype_of rhs';

    val ty'' = subst_typ ty';

    val c' = mk_name c;

    val def = (c, Logic.mk_equals (Const (c', ty'), rhs'));

    val (syn', _) = fork_mixfix true NONE syn;

    fun interpret def thy =

      let

        val def' = symmetric def;

        val def_eq = Thm.prop_of def';

        val typargs = Sign.const_typargs thy (c', fastype_of rhs);

        val typidx = find_index (fn TFree (w, _) => v = w | _ => false) typargs;

      in

        thy

        |> class_interpretation class [def'] [def_eq]

        |> add_class_const_def (class, ((c', (rhs, typidx)), def'))

      end;

  in

    thy

    |> Sign.add_path prfx

    |> Sign.add_consts_authentic [(c, ty', syn')]

    |> Sign.parent_path

    |> Sign.sticky_prefix prfx

    |> PureThy.add_defs_i false [(def, [])]

    |-> (fn [def] => interpret def)

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

    |> Sign.restore_naming thy

  end;

(* interpretation in class target *)

local

fun gen_interpretation_in_class prep_class do_proof (raw_class, raw_superclass) theory =

  let

    val class = prep_class theory raw_class;

    val superclass = prep_class theory raw_superclass;

    val loc_name = (#locale o the_class_data theory) class;

    val loc_expr = (Locale.Locale o #locale o the_class_data theory) superclass;

    fun prove_classrel (class, superclass) thy =

      let

        val classes = (Graph.all_succs o #classes o Sorts.rep_algebra

              o Sign.classes_of) thy [superclass]

          |> filter_out (fn class' => Sign.subsort thy ([class], [class']));

        fun instance_subclass (class1, class2) thy  =

          let

            val interp = interpretation_in_rule thy (class1, class2);

            val ax = #axioms (AxClass.get_definition thy class1);

            val intro = #intro (AxClass.get_definition thy class2)

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

                  (TVar ((AxClass.param_tyvarname, 0), [class1])))] [];

            val thm = 

              intro

              |> OF_LAST (interp OF ax)

              |> strip_all_ofclass thy (Sign.super_classes thy class2);

          in

            thy |> AxClass.add_classrel thm

          end;

      in

        thy |> fold_rev (curry instance_subclass class) classes

      end;

  in

    theory

    |> do_proof (prove_classrel (class, superclass)) (loc_name, loc_expr)

  end;

in

val interpretation_in_class = gen_interpretation_in_class Sign.certify_class

  (Locale.interpretation_in_locale o ProofContext.theory);

val interpretation_in_class_cmd = gen_interpretation_in_class Sign.read_class

  (Locale.interpretation_in_locale o ProofContext.theory);

val prove_interpretation_in_class = gen_interpretation_in_class Sign.certify_class

  o prove_interpretation_in;

end; (*local*)

(*experimental*)

fun class_term_check thy class =

  let

    val algebra = Sign.classes_of thy;

    val { v, ... } = the_class_data thy class;

    fun add_constrain_classtyp sort' (ty as TFree (v, _)) =

          AList.map_default (op =) (v, []) (curry (Sorts.inter_sort algebra) sort')

      | add_constrain_classtyp sort' (Type (tyco, tys)) = case Sorts.mg_domain algebra tyco sort'

         of sorts => fold2 add_constrain_classtyp sorts tys;

    fun class_arg c idx ty =

      let

        val typargs = Sign.const_typargs thy (c, ty);

        fun classtyp (t as TFree (w, _)) = if w = v then NONE else SOME t

          | classtyp t = SOME t;

      in classtyp (nth typargs idx) end;

    fun add_inst (c, ty) (terminsts, typinsts) = case local_param thy class c

     of NONE => (terminsts, typinsts)

      | SOME (t, (class', idx)) => (case class_arg c idx ty

         of NONE => (((c, ty), t) :: terminsts, typinsts)

          | SOME ty => (terminsts, add_constrain_classtyp [class'] ty typinsts));

  in pair o (fn ts => let

    val cs = (fold o fold_aterms) (fn Const c_ty => insert (op =) c_ty | _ => I) ts [];

    val (terminsts, typinsts) = fold add_inst cs ([], []);

  in

    ts

    |> (map o map_aterms) (fn t as Const c_ty => the_default t (AList.lookup (op =) terminsts c_ty)

         | t => t)

    |> (map o map_types o map_atyps) (fn t as TFree (v, sort) =>

         case AList.lookup (op =) typinsts v

          of SOME sort' => TFree (v, Sorts.inter_sort algebra (sort, sort'))

           | NONE => t)

  end) end;

val init_ref = ref (K (pair I) : class -> Proof.context -> (theory -> theory) * Proof.context);

fun init class = ! init_ref class;

fun init_default class ctxt =

  let

    val thy = ProofContext.theory_of ctxt;

    val term_check = class_term_check thy class;

  in

    ctxt

    (*|> ProofContext.theory_result (remove_constraints class)*)

    |> Context.proof_map (Syntax.add_term_check term_check)

    (*|>> fold (fn (c, ty) => Sign.add_const_constraint_i (c, SOME ty))*)

    |> pair I

  end;

end;