(*  Title:      Pure/Isar/class.ML

    ID:         $Id$

    Author:     Florian Haftmann, TU Muenchen

Type classes derived from primitive axclasses and locales.

*)

signature CLASS =

sig

  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 is_class: theory -> class -> bool

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

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

  val add_logical_const: string -> (string * mixfix) * term

    -> theory -> string * theory

  val add_syntactic_const: string -> Syntax.mode -> (string * mixfix) * term

    -> theory -> string * 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 print_classes: theory -> unit

  val uncheck: bool ref

  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

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 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*)

(** 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 thy = (Symtab.fold (Symtab.fold (cons 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 true (inst_thms thy);

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

    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_i 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 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 * ((term * typ) * (typ * int))) list

    (*constant name ~> (locale term & typ,

        (constant constraint, instantiaton index of class typ))*)

};

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 local_operation thy = AList.lookup (op =) o these_operations thy;

fun sups_base_sort thy sort =

  let

    val sups = filter (is_class thy) sort

      |> Sign.minimize_sort thy;

    val base_sort = case sups

     of _ :: _ => maps (#base_sort o the_class_data thy) sups

          |> Sign.minimize_sort thy

      | [] => sort;

  in (sups, base_sort) end;

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, insttab, phi, intro)) thy =

  let

    val inst = map

      (SOME o the o Symtab.lookup insttab o fst o fst)

        (Locale.parameters_of_expr thy (Locale.Locale class));

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

      (c, ((Free v_ty, ty'), (Logic.varifyT ty, 0)))) cs;

    val cs = (map o pairself) fst cs;

    val add_class = Graph.new_node (class,

        mk_class_data ((cs, base_sort, inst, phi, intro), ([], operations)))

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

  in

    ClassData.map add_class thy

  end;

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

  let

    val ty = Sign.the_const_constraint thy c;

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

    val typidx = find_index (fn TVar ((v, _), _) => Name.aT = v | _ => false) typargs;

    val ty' = Term.fastype_of rhs;

  in

    thy

    |> (ClassData.map o Graph.map_node class o map_class_data o apsnd)

      (fn (defs, operations) =>

        (case some_def of NONE => defs | SOME def => def :: defs,

          (c, ((rhs, ty'), (ty, typidx))) :: 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.identity

    $> 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

    (ALLGOALS (Method.insert_tac facts THEN'

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

    THEN Tactic.distinct_subgoals_tac) 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")]);

(** classes and class target **)

(* class context syntax *)

structure ClassSyntax = ProofDataFun(

  type T = {

    constraints: (string * typ) list,

    base_sort: sort,

    local_operation: string * typ -> (typ * term) option,

    rews: (term * term) list,

    passed: bool

  } option;

  fun init _ = NONE;

);

fun synchronize_syntax thy sups base_sort ctxt =

  let

    val operations = these_operations thy sups;

    (* constraints *)

    fun local_constraint (c, (_, (ty, _))) =

      let

        val ty' = ty

          |> map_atyps (fn ty as TVar ((v, 0), _) =>

               if v = Name.aT then TVar ((v, 0), base_sort) else ty)

          |> SOME;

      in (c, ty') end

    val constraints = (map o apsnd) (fst o snd) operations;

    (* check phase *)

    val typargs = Consts.typargs (ProofContext.consts_of ctxt);

    fun check_const (c, ty) ((t, _), (_, idx)) =

      ((nth (typargs (c, ty)) idx), t);

    fun local_operation (c_ty as (c, _)) = AList.lookup (op =) operations c

      |> Option.map (check_const c_ty);

    (* uncheck phase *)

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

    fun rew_app f (t1 $ t2) = rew_app f t1 $ f t2

      | rew_app f t = t;

    val rews = (map o apfst o rew_app)

      (Pattern.rewrite_term thy proto_rews []) proto_rews;

  in

    ctxt

    |> fold (ProofContext.add_const_constraint o local_constraint) operations

    |> ClassSyntax.map (K (SOME {

        constraints = constraints,

        base_sort = base_sort,

        local_operation = local_operation,

        rews = rews,

        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 thy [class] base_sort ctxt end;

val mark_passed = (ClassSyntax.map o Option.map)

  (fn { constraints, base_sort, local_operation, rews, passed } =>

    { constraints = constraints, base_sort = base_sort,

      local_operation = local_operation, rews = rews, passed = true });

fun sort_term_check ts ctxt =

  let

    val { constraints, base_sort, local_operation, passed, ... } =

      the (ClassSyntax.get ctxt);

    fun check_typ (c, ty) (TFree (v, _), t) = if v = Name.aT

          then apfst (AList.update (op =) ((c, ty), t)) else I

      | check_typ (c, ty) (TVar (vi, _), t) = if TypeInfer.is_param vi

          then apfst (AList.update (op =) ((c, ty), t))

            #> apsnd (insert (op =) vi) else I

      | check_typ _ _ = I;

    fun add_const (Const c_ty) = Option.map (check_typ c_ty) (local_operation c_ty)

          |> the_default I

      | add_const _ = I;

    val (cs, typarams) = (fold o fold_aterms) add_const ts ([], []);

    val subst_typ = map_type_tvar (fn var as (vi, _) =>

      if member (op =) typarams vi then TFree (Name.aT, base_sort) else TVar var);

    val subst_term = map_aterms

        (fn t as Const (c, ty) => the_default t (AList.lookup (op =) cs (c, ty)) | t => t)

          #> map_types subst_typ;

    val ts' = map subst_term ts;

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

  else

    ctxt

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

    |> mark_passed

    |> pair ts'

    |> SOME

  end;

val uncheck = ref true;

fun sort_term_uncheck ts ctxt =

  let

    (*FIXME abbreviations*)

    val thy = ProofContext.theory_of ctxt;

    val rews = (#rews o the o ClassSyntax.get) ctxt;

    val ts' = if ! uncheck

      then map (Pattern.rewrite_term thy rews []) ts else ts;

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

fun init_ctxt thy sups base_sort ctxt =

  ctxt

  |> Variable.declare_term

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

  |> synchronize_syntax thy sups base_sort

  |> Context.proof_map (

      Syntax.add_term_check 0 "class" sort_term_check

      #> Syntax.add_term_uncheck (~10) "class" sort_term_uncheck)

fun init class ctxt =

  let

    val thy = ProofContext.theory_of ctxt;

  in

    init_ctxt thy [class] ((#base_sort o the_class_data thy) class) ctxt

  end;

(* 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, base_sort) = sups_base_sort thy 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 thy 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 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;

    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 (`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 fst all_params) (map snd supconsts @ consts),

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

      #> class_interpretation class axioms []

      )))))

    |> pair class

  end;

in

val class_cmd = gen_class read_class_spec ((#1 o Term.dest_Const) oo Sign.read_const);

val class = gen_class check_class_spec (K I);

end; (*local*)

(* definition in class target *)

fun add_logical_const class ((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' = (map_types Logic.unvarifyT o Morphism.term phi) dict;

    val ty' = Term.fastype_of dict';

    val ty'' = Type.strip_sorts ty';

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

    val c'' = NameSpace.full (Sign.naming_of thy' |> NameSpace.add_path prfx) c;

  in

    thy'

    |> Sign.hide_consts_i false [c'']

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

    |> Sign.parent_path

    |> Sign.sticky_prefix prfx

    |> Thm.add_def false (c, def_eq)

    |>> 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')

    |> pair c'

  end;

(* abbreviation in class target *)

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

  let

    val prfx = class_prefix class;

    val phi = morphism thy class;

    val naming = Sign.naming_of thy |> NameSpace.add_path prfx |> NameSpace.add_path prfx;

      (*FIXME*)

    val c' = NameSpace.full naming c;

    val rhs' = (map_types Logic.unvarifyT o Morphism.term phi) rhs;

    val ty' = Term.fastype_of rhs';

  in

    thy

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

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

    |> pair c'

  end;

end;