(*  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: bool -> bstring -> class list -> Element.context_i Locale.element list

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

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

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

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

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

     -> theory -> string * theory

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

     -> theory -> string * theory

   val remove_constraint: sort -> string -> Proof.context -> Proof.context

   val intro_classes_tac: thm list -> tactic

   val default_intro_classes_tac: thm list -> tactic

   val class_of_locale: theory -> string -> class option

   val locale_of_class: theory -> class -> string

   val local_syntax: theory -> class -> bool

   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

 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 not is_loc orelse (is_some some_class andalso not (mx = mx'))

       then mx' else NoSyn;

     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 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 ((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;

 (** 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);

     fun get_remove_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;

     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 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_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 {

   locale: string,

   consts: (string * string) list

     (*locale parameter ~> constant name*),

   local_sort: sort,

   inst: typ Symtab.table * term Symtab.table

     (*canonical interpretation*),

   intro: thm,

   local_syntax: bool,

   defs: thm list,

   operations: (string * (term * int) option) list,

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

   constraints: (string * typ) list

 };

 fun rep_class_data (ClassData d) = d;

 fun mk_class_data ((locale, consts, local_sort, inst, intro, local_syntax),

     (defs, (operations, constraints))) =

   ClassData { locale = locale, consts = consts, local_sort = local_sort, inst = inst,

     intro = intro, local_syntax = local_syntax, defs = defs, operations = operations,

     constraints = constraints };

 fun map_class_data f (ClassData { locale, consts, local_sort, inst, intro,

     local_syntax, defs, operations, constraints }) =

   mk_class_data (f ((locale, consts, local_sort, inst, intro, local_syntax),

     (defs, (operations, constraints))));

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

     local_sort = local_sort, inst = inst, intro = intro, local_syntax = local_syntax,

     defs = defs1, operations = operations1, constraints = constraints1 },

   ClassData { locale = _, consts = _, local_sort = _, inst = _, intro = _, local_syntax = _,

     defs = defs2, operations = operations2, constraints = constraints2 }) =

   mk_class_data ((locale, consts, local_sort, inst, intro, local_syntax),

     (Thm.merge_thms (defs1, defs2),

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

       AList.merge (op =) (K true) (constraints1, constraints2))));

 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 locale_of_class = #locale oo the_class_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_operations thy =

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

 fun these_constraints thy =

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

 fun local_operation thy = Option.join oo AList.lookup (op =) o these_operations thy;

 fun sups_local_sort thy sort =

   let

     val sups = filter (is_some o lookup_class_data thy) sort

       |> Sign.minimize_sort thy;

     val local_sort = case sups

      of sup :: _ => #local_sort (the_class_data thy sup)

       | [] => sort;

   in (sups, local_sort) end;

 fun local_syntax thy = #local_syntax o the_class_data 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 " ^ class ^ ":"),

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

         (Syntax.pretty_sort ctxt o Sign.minimize_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, local_sort, inst, intro, local_syntax)) =

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

     gr

     |> Graph.new_node (class, mk_class_data ((locale, (map o pairself) fst consts,

         local_sort, inst, intro, local_syntax),

           ([], (map (apfst fst o apsnd (SOME o rpair 0 o Free) o swap) consts, map snd consts))))

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

     tab

     |> Symtab.update (locale, class)

   ));

 fun register_const class (entry, def) =

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

     (fn (defs, (operations, constraints)) =>

       (def :: defs, (apsnd (SOME o snd) entry :: operations, apsnd fst entry :: constraints)));

 fun register_abbrev class (abbrev, ty) =

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

     (fn (operations, constraints) => ((abbrev, NONE) :: operations, (abbrev, ty) :: constraints));

 (** 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 ((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 { 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 (Name.aT, [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 context initialization *)

 fun remove_constraint local_sort c ctxt =

   let

     val ty = ProofContext.the_const_constraint ctxt c;

     val ty' = map_atyps (fn ty as TFree (v, _) => if v = Name.aT

       then TFree (v, local_sort) else ty | ty => ty) ty;

   in

     ctxt

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

   end;

 fun sort_term_check sups local_sort ts ctxt =

   let

     val thy = ProofContext.theory_of ctxt;

     val local_operation = local_operation thy sups;

     val constraints = these_constraints thy sups;

     val consts = ProofContext.consts_of ctxt;

     fun check_typ (c, ty) (t', idx) = case nth (Consts.typargs consts (c, ty)) idx

      of TFree (v, _) => if v = Name.aT

           then apfst (AList.update (op =) ((c, ty), t')) else I

       | TVar (vi, _) => if TypeInfer.is_param vi

           then apfst (AList.update (op =) ((c, ty), t'))

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

       | _ => I;

     fun add_const (Const (c, ty)) = (case local_operation c

          of SOME (t', idx) => check_typ (c, ty) (t', idx)

           | NONE => I)

       | add_const _ = I;

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

     val ts' = map (map_aterms

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

       #> (map_types o map_type_tvar) (fn var as (vi, _) => if member (op =) typarams vi

            then TFree (Name.aT, local_sort) else TVar var)) ts;

     val ctxt' = fold (ProofContext.add_const_constraint o apsnd SOME) constraints ctxt;

   in (ts', ctxt') end;

 fun init_class_ctxt sups local_sort ctxt =

   let

     val operations = these_operations (ProofContext.theory_of ctxt) sups;

   in

     ctxt

     |> Variable.declare_term

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

     |> fold (remove_constraint local_sort o fst) operations

     |> Context.proof_map (Syntax.add_term_check 50 "class"

         (sort_term_check sups local_sort))

   end;

 fun init class ctxt =

   init_class_ctxt [class]

     ((#local_sort o the_class_data (ProofContext.theory_of ctxt)) class) ctxt;

 (* 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_spec prep_class prep_expr process_expr thy raw_supclasses raw_includes_elems =

   let

     val supclasses = map (prep_class thy) raw_supclasses;

     val (sups, local_sort) = sups_local_sort thy supclasses;

     val supsort = Sign.minimize_sort thy supclasses;

     val suplocales = map (Locale.Locale o #locale o the_class_data thy) 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 =) (params_of_sort 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_class_ctxt sups local_sort

     |> process_expr Locale.empty raw_elems

     |> fst

     |> (fn elems => ((((sups, supconsts), (supsort, local_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 gen_class prep_spec prep_param local_syntax bname

     raw_supclasses raw_includes_elems raw_other_consts thy =

   let

     val (((sups, supconsts), (supsort, local_sort, mergeexpr)), elems) =

       prep_spec thy raw_supclasses raw_includes_elems;

     val other_consts = map (prep_param thy) raw_other_consts;

     fun mk_instT class = Symtab.empty

       |> Symtab.update (Name.aT, TFree (Name.aT, [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;

     fun extract_params thy name_locale =

       let

         val params = Locale.parameters_of thy name_locale;

         val _ = if Sign.subsort thy (supsort, local_sort) then () else error

           ("Sort " ^ Sign.string_of_sort thy local_sort

             ^ " is less general than permitted least general sort "

             ^ Sign.string_of_sort thy supsort);

       in

         (map fst params, params

         |> (map o apfst o apsnd o Term.map_type_tfree) (K (TFree (Name.aT, local_sort)))

         |> (map o apsnd) (fork_mixfix true (SOME "") #> 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

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

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

       `(fn thy => extract_params thy name_locale)

       #-> (fn (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 ~~ consts, local_sort,

             (mk_instT name_axclass, mk_inst name_axclass (map fst globals)

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

       #> note_intro name_axclass class_intro

       #> class_interpretation name_axclass axioms []

       #> pair name_axclass

       )))))

   end;

 in

 val class_cmd = gen_class read_class_spec read_param;

 val class = gen_class check_class_spec (K I);

 end; (*local*)

 (* 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 mk_operation_entry thy (c, rhs) =

   let

     val ty = fastype_of rhs;

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

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

   in (c, (ty, (rhs, typidx))) 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 constrain_sort = curry (Sorts.inter_sort (Sign.classes_of thy)) [class];

     val rhs' = export_fixes thy class rhs;

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

       if w = Name.aT then TFree (w, constrain_sort sort) else TFree var);

     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 (SOME class) syn;

     fun interpret def thy =

       let

         val def' = symmetric def;

         val def_eq = Thm.prop_of def';

         val entry = mk_operation_entry thy (c', rhs);

       in

         thy

         |> class_interpretation class [def'] [def_eq]

         |> register_const class (entry, 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 (c', SOME ty'')

     |> Sign.restore_naming thy

     |> pair c'

   end;

 (* abbreviation in class target *)

 fun add_abbrev_in_class class prmode ((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, prfx, n3] end;

     val c' = mk_name c;

     val rhs' = export_fixes thy class rhs;

     val ty' = fastype_of rhs';

   in

     thy

     |> Sign.add_notation prmode [(Const (c', ty'), syn)]

     |> register_abbrev class (c', ty')

     |> pair c'

   end;

 end;