src/Pure/Isar/class.ML
author haftmann
Tue Sep 25 12:16:13 2007 +0200 (2007-09-25)
changeset 24701 f8bfd592a6dc
parent 24657 185502d54c3d
child 24707 dfeb98f84e93
permissions -rw-r--r--
no cleverness for instance parameters
     1 (*  Title:      Pure/Isar/class.ML
     2     ID:         $Id$
     3     Author:     Florian Haftmann, TU Muenchen
     4 
     5 Type classes derived from primitive axclasses and locales.
     6 *)
     7 
     8 signature CLASS =
     9 sig
    10   val fork_mixfix: bool -> string option -> mixfix -> mixfix * mixfix
    11 
    12   val axclass_cmd: bstring * xstring list
    13     -> ((bstring * Attrib.src list) * string list) list
    14     -> theory -> class * theory
    15   val classrel_cmd: xstring * xstring -> theory -> Proof.state
    16   val class: bstring -> class list -> Element.context_i Locale.element list
    17     -> string list -> theory -> string * Proof.context
    18   val class_cmd: bstring -> xstring list -> Element.context Locale.element list
    19     -> xstring list -> theory -> string * Proof.context
    20   val add_const_in_class: string -> (string * term) * Syntax.mixfix
    21     -> theory -> theory
    22   val interpretation_in_class: class * class -> theory -> Proof.state
    23   val interpretation_in_class_cmd: xstring * xstring -> theory -> Proof.state
    24   val prove_interpretation_in_class: tactic -> class * class -> theory -> theory
    25   val intro_classes_tac: thm list -> tactic
    26   val default_intro_classes_tac: thm list -> tactic
    27   val class_of_locale: theory -> string -> class option
    28   val print_classes: theory -> unit
    29 
    30   val instance_arity: (theory -> theory) -> arity list -> theory -> Proof.state
    31   val instance: arity list -> ((bstring * Attrib.src list) * term) list
    32     -> (thm list -> theory -> theory)
    33     -> theory -> Proof.state
    34   val instance_cmd: (bstring * xstring list * xstring) list
    35     -> ((bstring * Attrib.src list) * xstring) list
    36     -> (thm list -> theory -> theory)
    37     -> theory -> Proof.state
    38   val prove_instance: tactic -> arity list
    39     -> ((bstring * Attrib.src list) * term) list
    40     -> theory -> thm list * theory
    41   val unoverload: theory -> conv
    42   val overload: theory -> conv
    43   val unoverload_const: theory -> string * typ -> string
    44   val inst_const: theory -> string * string -> string
    45   val param_const: theory -> string -> (string * string) option
    46   val params_of_sort: theory -> sort -> (string * (string * typ)) list
    47 
    48   (*experimental*)
    49   val init_ref: (class -> Proof.context -> (theory -> theory) * Proof.context) ref
    50   val init: class -> Proof.context -> (theory -> theory) * Proof.context;
    51   val init_default: class -> Proof.context -> (theory -> theory) * Proof.context;
    52   val remove_constraints: class -> theory -> (string * typ) list * theory
    53   val class_term_check: theory -> class -> term list -> Proof.context -> term list * Proof.context
    54   val local_param: theory -> class -> string -> (term * (class * int)) option
    55 end;
    56 
    57 structure Class : CLASS =
    58 struct
    59 
    60 (** auxiliary **)
    61 
    62 fun fork_mixfix is_loc some_class mx =
    63   let
    64     val mx' = Syntax.unlocalize_mixfix mx;
    65     val mx_global = if is_some some_class orelse (is_loc andalso mx = mx')
    66       then NoSyn else mx';
    67     val mx_local = if is_loc then mx else NoSyn;
    68   in (mx_global, mx_local) end;
    69 
    70 fun prove_interpretation tac prfx_atts expr insts =
    71   Locale.interpretation_i I prfx_atts expr insts
    72   #> Proof.global_terminal_proof
    73       (Method.Basic (K (Method.SIMPLE_METHOD tac), Position.none), NONE)
    74   #> ProofContext.theory_of;
    75 
    76 fun prove_interpretation_in tac after_qed (name, expr) =
    77   Locale.interpretation_in_locale
    78       (ProofContext.theory after_qed) (name, expr)
    79   #> Proof.global_terminal_proof
    80       (Method.Basic (K (Method.SIMPLE_METHOD tac), Position.none), NONE)
    81   #> ProofContext.theory_of;
    82 
    83 fun OF_LAST thm1 thm2 =
    84   let
    85     val n = (length o Logic.strip_imp_prems o prop_of) thm2;
    86   in (thm1 RSN (n, thm2)) end;
    87 
    88 fun strip_all_ofclass thy sort =
    89   let
    90     val typ = TVar ((AxClass.param_tyvarname, 0), sort);
    91     fun prem_inclass t =
    92       case Logic.strip_imp_prems t
    93        of ofcls :: _ => try Logic.dest_inclass ofcls
    94         | [] => NONE;
    95     fun strip_ofclass class thm =
    96       thm OF (fst o AxClass.of_sort thy (typ, [class])) AxClass.cache;
    97     fun strip thm = case (prem_inclass o Thm.prop_of) thm
    98      of SOME (_, class) => thm |> strip_ofclass class |> strip
    99       | NONE => thm;
   100   in strip end;
   101 
   102 fun get_remove_contraint c thy =
   103   let
   104     val ty = Sign.the_const_constraint thy c;
   105   in
   106     thy
   107     |> Sign.add_const_constraint_i (c, NONE)
   108     |> pair (c, Logic.unvarifyT ty)
   109   end;
   110 
   111 
   112 (** axclass command **)
   113 
   114 fun axclass_cmd (class, raw_superclasses) raw_specs thy =
   115   let
   116     val ctxt = ProofContext.init thy;
   117     val superclasses = map (Sign.read_class thy) raw_superclasses;
   118     val name_atts = map ((apsnd o map) (Attrib.attribute thy) o fst)
   119       raw_specs;
   120     val axiomss = ProofContext.read_propp (ctxt, map (map (rpair []) o snd)
   121           raw_specs)
   122       |> snd
   123       |> (map o map) fst;
   124   in
   125     AxClass.define_class (class, superclasses) []
   126       (name_atts ~~ axiomss) thy
   127   end;
   128 
   129 local
   130 
   131 fun gen_instance mk_prop add_thm after_qed insts thy =
   132   let
   133     fun after_qed' results =
   134       ProofContext.theory ((fold o fold) add_thm results #> after_qed);
   135   in
   136     thy
   137     |> ProofContext.init
   138     |> Proof.theorem_i NONE after_qed' ((map (fn t => [(t, [])])
   139         o maps (mk_prop thy)) insts)
   140   end;
   141 
   142 in
   143 
   144 val instance_arity =
   145   gen_instance (Logic.mk_arities oo Sign.cert_arity) AxClass.add_arity;
   146 val classrel =
   147   gen_instance (single oo (Logic.mk_classrel oo AxClass.cert_classrel))
   148     AxClass.add_classrel I o single;
   149 val classrel_cmd =
   150   gen_instance (single oo (Logic.mk_classrel oo AxClass.read_classrel))
   151     AxClass.add_classrel I o single;
   152 
   153 end; (*local*)
   154 
   155 
   156 (** explicit constants for overloaded definitions **)
   157 
   158 structure InstData = TheoryDataFun
   159 (
   160   type T = (string * thm) Symtab.table Symtab.table * (string * string) Symtab.table;
   161     (*constant name ~> type constructor ~> (constant name, equation),
   162         constant name ~> (constant name, type constructor)*)
   163   val empty = (Symtab.empty, Symtab.empty);
   164   val copy = I;
   165   val extend = I;
   166   fun merge _ ((taba1, tabb1), (taba2, tabb2)) =
   167     (Symtab.join (K (Symtab.merge (K true))) (taba1, taba2),
   168       Symtab.merge (K true) (tabb1, tabb2));
   169 );
   170 
   171 fun inst_thms f thy = (Symtab.fold (Symtab.fold (cons o f o snd o snd) o snd) o fst)
   172     (InstData.get thy) [];
   173 fun add_inst (c, tyco) inst = (InstData.map o apfst
   174       o Symtab.map_default (c, Symtab.empty)) (Symtab.update_new (tyco, inst))
   175   #> (InstData.map o apsnd) (Symtab.update_new (fst inst, (c, tyco)));
   176 
   177 fun unoverload thy = MetaSimplifier.rewrite false (inst_thms I thy);
   178 fun overload thy = MetaSimplifier.rewrite false (inst_thms symmetric thy);
   179 
   180 fun inst_const thy (c, tyco) =
   181   (fst o the o Symtab.lookup ((the o Symtab.lookup (fst (InstData.get thy))) c)) tyco;
   182 fun unoverload_const thy (c_ty as (c, _)) =
   183   case AxClass.class_of_param thy c
   184    of SOME class => (case Sign.const_typargs thy c_ty
   185        of [Type (tyco, _)] => (case Symtab.lookup
   186            ((the o Symtab.lookup (fst (InstData.get thy))) c) tyco
   187              of SOME (c, _) => c
   188               | NONE => c)
   189         | [_] => c)
   190     | NONE => c;
   191 
   192 val param_const = Symtab.lookup o snd o InstData.get;
   193 
   194 fun add_inst_def (class, tyco) (c, ty) thy =
   195   let
   196     val tyco_base = NameSpace.base tyco;
   197     val name_inst = NameSpace.base class ^ "_" ^ tyco_base ^ "_inst";
   198     val c_inst_base = NameSpace.base c ^ "_" ^ tyco_base;
   199   in
   200     thy
   201     |> Sign.sticky_prefix name_inst
   202     |> PureThy.simple_def ("", [])
   203          (((c_inst_base, ty, Syntax.NoSyn), []), Const (c, ty))
   204     |-> (fn (c_inst, thm) => add_inst (c, tyco) (c_inst, symmetric thm))
   205     |> Sign.restore_naming thy
   206   end;
   207 
   208 fun add_inst_def' (class, tyco) (c, ty) thy =
   209   if case Symtab.lookup (fst (InstData.get thy)) c
   210    of NONE => true
   211     | SOME tab => is_none (Symtab.lookup tab tyco)
   212   then add_inst_def (class, tyco) (c, Logic.unvarifyT ty) thy
   213   else thy;
   214 
   215 fun add_def ((class, tyco), ((name, prop), atts)) thy =
   216   let
   217     val ((lhs as Const (c, ty), args), rhs) =
   218       (apfst Term.strip_comb o Logic.dest_equals) prop;
   219     fun (*add_inst' def ([], (Const (c_inst, ty))) =
   220           if forall (fn TFree _ => true | _ => false) (Sign.const_typargs thy (c_inst, ty))
   221           then add_inst (c, tyco) (c_inst, def)
   222           else add_inst_def (class, tyco) (c, ty)
   223       |*) add_inst' _ t = add_inst_def (class, tyco) (c, ty);
   224   in
   225     thy
   226     |> PureThy.add_defs_i true [((name, prop), map (Attrib.attribute thy) atts)]
   227     |-> (fn [def] => add_inst' def (args, rhs) #> pair def)
   228   end;
   229 
   230 
   231 (** instances with implicit parameter handling **)
   232 
   233 local
   234 
   235 fun gen_read_def thy prep_att read_def ((raw_name, raw_atts), raw_t) =
   236   let
   237     val (_, t) = read_def thy (raw_name, raw_t);
   238     val ((c, ty), _) = Sign.cert_def (Sign.pp thy) t;
   239     val atts = map (prep_att thy) raw_atts;
   240     val insts = Consts.typargs (Sign.consts_of thy) (c, ty);
   241     val name = case raw_name
   242      of "" => NONE
   243       | _ => SOME raw_name;
   244   in (c, (insts, ((name, t), atts))) end;
   245 
   246 fun read_def_cmd thy = gen_read_def thy Attrib.intern_src Theory.read_axm;
   247 fun read_def thy = gen_read_def thy (K I) (K I);
   248 
   249 fun gen_instance prep_arity read_def do_proof raw_arities raw_defs after_qed theory =
   250   let
   251     val arities = map (prep_arity theory) raw_arities;
   252     val _ = if null arities then error "at least one arity must be given" else ();
   253     val _ = case (duplicates (op =) o map #1) arities
   254      of [] => ()
   255       | dupl_tycos => error ("type constructors occur more than once in arities: "
   256           ^ (commas o map quote) dupl_tycos);
   257     val super_sort =
   258       (Graph.all_succs o #classes o Sorts.rep_algebra o Sign.classes_of) theory;
   259     fun get_consts_class tyco ty class =
   260       let
   261         val cs = (these o Option.map snd o try (AxClass.params_of_class theory)) class;
   262         val subst_ty = map_type_tfree (K ty);
   263       in
   264         map (fn (c, ty) => (c, ((class, tyco), subst_ty ty))) cs
   265       end;
   266     fun get_consts_sort (tyco, asorts, sort) =
   267       let
   268         val ty = Type (tyco, map (fn (v, sort) => TVar ((v, 0), sort))
   269           (Name.names Name.context "'a" asorts))
   270       in maps (get_consts_class tyco ty) (super_sort sort) end;
   271     val cs = maps get_consts_sort arities;
   272     fun mk_typnorm thy (ty, ty_sc) =
   273       case try (Sign.typ_match thy (Logic.varifyT ty_sc, ty)) Vartab.empty
   274        of SOME env => SOME (Logic.varifyT #> Envir.typ_subst_TVars env #> Logic.unvarifyT)
   275         | NONE => NONE;
   276     fun read_defs defs cs thy_read =
   277       let
   278         fun read raw_def cs =
   279           let
   280             val (c, (inst, ((name_opt, t), atts))) = read_def thy_read raw_def;
   281             val ty = Consts.instance (Sign.consts_of thy_read) (c, inst);
   282             val ((class, tyco), ty') = case AList.lookup (op =) cs c
   283              of NONE => error ("illegal definition for constant " ^ quote c)
   284               | SOME class_ty => class_ty;
   285             val name = case name_opt
   286              of NONE => Thm.def_name (Logic.name_arity (tyco, [], c))
   287               | SOME name => name;
   288             val t' = case mk_typnorm thy_read (ty', ty)
   289              of NONE => error ("illegal definition for constant " ^
   290                   quote (c ^ "::" ^ setmp show_sorts true
   291                     (Sign.string_of_typ thy_read) ty))
   292               | SOME norm => map_types norm t
   293           in (((class, tyco), ((name, t'), atts)), AList.delete (op =) c cs) end;
   294       in fold_map read defs cs end;
   295     val (defs, other_cs) = read_defs raw_defs cs
   296       (fold Sign.primitive_arity arities (Theory.copy theory));
   297     fun after_qed' cs defs =
   298       fold Sign.add_const_constraint_i (map (apsnd SOME) cs)
   299       #> after_qed defs;
   300   in
   301     theory
   302     |> fold_map get_remove_contraint (map fst cs |> distinct (op =))
   303     ||>> fold_map add_def defs
   304     ||> fold (fn (c, ((class, tyco), ty)) => add_inst_def' (class, tyco) (c, ty)) other_cs
   305     |-> (fn (cs, defs) => do_proof (after_qed' cs defs) arities defs)
   306   end;
   307 
   308 fun tactic_proof tac f arities defs =
   309   fold (fn arity => AxClass.prove_arity arity tac) arities
   310   #> f
   311   #> pair defs;
   312 
   313 in
   314 
   315 val instance = gen_instance Sign.cert_arity read_def
   316   (fn f => fn arities => fn defs => instance_arity f arities);
   317 val instance_cmd = gen_instance Sign.read_arity read_def_cmd
   318   (fn f => fn arities => fn defs => instance_arity f arities);
   319 fun prove_instance tac arities defs =
   320   gen_instance Sign.cert_arity read_def
   321     (tactic_proof tac) arities defs (K I);
   322 
   323 end; (*local*)
   324 
   325 
   326 
   327 (** class data **)
   328 
   329 datatype class_data = ClassData of {
   330   locale: string,
   331   consts: (string * string) list
   332     (*locale parameter ~> theory constant name*),
   333   v: string,
   334   inst: typ Symtab.table * term Symtab.table
   335     (*canonical interpretation*),
   336   intro: thm,
   337   defs: thm list,
   338   localized: (string * (term * (class * int))) list
   339     (*theory constant name ~> (locale parameter, (class, instantiaton index of class typ))*)
   340 };
   341 
   342 fun rep_class_data (ClassData d) = d;
   343 fun mk_class_data ((locale, consts, v, inst, intro), (defs, localized)) =
   344   ClassData { locale = locale, consts = consts, v = v, inst = inst, intro = intro,
   345     defs = defs, localized = localized };
   346 fun map_class_data f (ClassData { locale, consts, v, inst, intro, defs, localized }) =
   347   mk_class_data (f ((locale, consts, v, inst, intro), (defs, localized)))
   348 fun merge_class_data _ (ClassData { locale = locale, consts = consts, v = v, inst = inst,
   349     intro = intro, defs = defs1, localized = localized1 },
   350   ClassData { locale = _, consts = _, v = _, inst = _, intro = _,
   351     defs = defs2, localized = localized2 }) =
   352   mk_class_data ((locale, consts, v, inst, intro),
   353     (Thm.merge_thms (defs1, defs2), AList.merge (op =) (K true) (localized1, localized2)));
   354 
   355 fun merge_pair f1 f2 ((x1, y1), (x2, y2)) = (f1 (x1, x2), f2 (y1, y2));
   356 
   357 structure ClassData = TheoryDataFun
   358 (
   359   type T = class_data Graph.T * class Symtab.table
   360     (*locale name ~> class name*);
   361   val empty = (Graph.empty, Symtab.empty);
   362   val copy = I;
   363   val extend = I;
   364   fun merge _ = merge_pair (Graph.join merge_class_data) (Symtab.merge (K true));
   365 );
   366 
   367 
   368 (* queries *)
   369 
   370 val lookup_class_data = Option.map rep_class_data oo try o Graph.get_node
   371   o fst o ClassData.get;
   372 fun class_of_locale thy = Symtab.lookup ((snd o ClassData.get) thy);
   373 
   374 fun the_class_data thy class = case lookup_class_data thy class
   375  of NONE => error ("undeclared class " ^ quote class)
   376   | SOME data => data;
   377 
   378 val ancestry = Graph.all_succs o fst o ClassData.get;
   379 
   380 fun params_of_sort thy =
   381   let
   382     fun params class =
   383       let
   384         val const_typs = (#params o AxClass.get_definition thy) class;
   385         val const_names = (#consts o the_class_data thy) class;
   386       in
   387         (map o apsnd) (fn c => (c, (the o AList.lookup (op =) const_typs) c)) const_names
   388       end;
   389   in maps params o ancestry thy end;
   390 
   391 fun these_defs thy = maps (these o Option.map #defs o lookup_class_data thy) o ancestry thy;
   392 
   393 fun these_intros thy =
   394   Graph.fold (fn (_, (data, _)) => insert Thm.eq_thm ((#intro o rep_class_data) data))
   395     ((fst o ClassData.get) thy) [];
   396 
   397 fun these_localized thy class =
   398   maps (#localized o the_class_data thy) (ancestry thy [class]);
   399 
   400 fun local_param thy = AList.lookup (op =) o these_localized thy;
   401 
   402 fun print_classes thy =
   403   let
   404     val algebra = Sign.classes_of thy;
   405     val arities =
   406       Symtab.empty
   407       |> Symtab.fold (fn (tyco, arities) => fold (fn (class, _) =>
   408            Symtab.map_default (class, []) (insert (op =) tyco)) arities)
   409              ((#arities o Sorts.rep_algebra) algebra);
   410     val the_arities = these o Symtab.lookup arities;
   411     fun mk_arity class tyco =
   412       let
   413         val Ss = Sorts.mg_domain algebra tyco [class];
   414       in Sign.pretty_arity thy (tyco, Ss, [class]) end;
   415     fun mk_param (c, ty) = Pretty.str (Sign.extern_const thy c ^ " :: "
   416       ^ setmp show_sorts false (Sign.string_of_typ thy o Type.strip_sorts) ty);
   417     fun mk_entry class = (Pretty.block o Pretty.fbreaks o map_filter I) [
   418       (SOME o Pretty.str) ("class " ^ class ^ ":"),
   419       (SOME o Pretty.block) [Pretty.str "supersort: ",
   420         (Sign.pretty_sort thy o Sign.certify_sort thy o Sign.super_classes thy) class],
   421       Option.map (Pretty.str o prefix "locale: " o #locale) (lookup_class_data thy class),
   422       ((fn [] => NONE | ps => (SOME o Pretty.block o Pretty.fbreaks) (Pretty.str "parameters:" :: ps)) o map mk_param
   423         o these o Option.map #params o try (AxClass.get_definition thy)) class,
   424       (SOME o Pretty.block o Pretty.breaks) [
   425         Pretty.str "instances:",
   426         Pretty.list "" "" (map (mk_arity class) (the_arities class))
   427       ]
   428     ]
   429   in
   430     (Pretty.writeln o Pretty.chunks o separate (Pretty.str "")
   431       o map mk_entry o Sorts.all_classes) algebra
   432   end;
   433 
   434 
   435 (* updaters *)
   436 
   437 fun add_class_data ((class, superclasses), (locale, consts, v, inst, intro)) =
   438   ClassData.map (fn (gr, tab) => (
   439     gr
   440     |> Graph.new_node (class, mk_class_data ((locale, (map o apfst) fst consts, v, inst, intro),
   441          ([], map (apsnd (rpair (class, 0) o Free) o swap) consts)))
   442     |> fold (curry Graph.add_edge class) superclasses,
   443     tab
   444     |> Symtab.update (locale, class)
   445   ));
   446 
   447 fun add_class_const_def (class, (entry, def)) =
   448   (ClassData.map o apfst o Graph.map_node class o map_class_data o apsnd)
   449     (fn (defs, localized) => (def :: defs, (apsnd o apsnd) (pair class) entry :: localized));
   450 
   451 
   452 (** rule calculation, tactics and methods **)
   453 
   454 fun class_intro thy locale class sups =
   455   let
   456     fun class_elim class =
   457       case (map Drule.unconstrainTs o #axioms o AxClass.get_definition thy) class
   458        of [thm] => SOME thm
   459         | [] => NONE;
   460     val pred_intro = case Locale.intros thy locale
   461      of ([ax_intro], [intro]) => intro |> OF_LAST ax_intro |> SOME
   462       | ([intro], []) => SOME intro
   463       | ([], [intro]) => SOME intro
   464       | _ => NONE;
   465     val pred_intro' = pred_intro
   466       |> Option.map (fn intro => intro OF map_filter class_elim sups);
   467     val class_intro = (#intro o AxClass.get_definition thy) class;
   468     val raw_intro = case pred_intro'
   469      of SOME pred_intro => class_intro |> OF_LAST pred_intro
   470       | NONE => class_intro;
   471     val sort = Sign.super_classes thy class;
   472     val typ = TVar ((AxClass.param_tyvarname, 0), sort);
   473     val defs = these_defs thy sups;
   474   in
   475     raw_intro
   476     |> Drule.instantiate' [SOME (Thm.ctyp_of thy typ)] []
   477     |> strip_all_ofclass thy sort
   478     |> Thm.strip_shyps
   479     |> MetaSimplifier.rewrite_rule defs
   480     |> Drule.unconstrainTs
   481   end;
   482 
   483 fun class_interpretation class facts defs thy =
   484   let
   485     val { locale, inst, ... } = the_class_data thy class;
   486     val tac = (ALLGOALS o ProofContext.fact_tac) facts;
   487     val prfx = Logic.const_of_class (NameSpace.base class);
   488   in
   489     prove_interpretation tac ((false, prfx), []) (Locale.Locale locale)
   490       (inst, defs) thy
   491   end;
   492 
   493 fun interpretation_in_rule thy (class1, class2) =
   494   let
   495     fun mk_axioms class =
   496       let
   497         val { locale, inst = (_, insttab), ... } = the_class_data thy class;
   498       in
   499         Locale.global_asms_of thy locale
   500         |> maps snd
   501         |> (map o map_aterms) (fn Free (s, _) => (the o Symtab.lookup insttab) s | t => t)
   502         |> (map o map_types o map_atyps) (fn TFree _ => TFree ("'a", [class1]) | T => T)
   503         |> map (ObjectLogic.ensure_propT thy)
   504       end;
   505     val (prems, concls) = pairself mk_axioms (class1, class2);
   506   in
   507     Goal.prove_global thy [] prems (Logic.mk_conjunction_list concls)
   508       (Locale.intro_locales_tac true (ProofContext.init thy))
   509   end;
   510 
   511 fun intro_classes_tac facts st =
   512   let
   513     val thy = Thm.theory_of_thm st;
   514     val classes = Sign.all_classes thy;
   515     val class_trivs = map (Thm.class_triv thy) classes;
   516     val class_intros = these_intros thy;
   517     fun add_axclass_intro class =
   518       case try (AxClass.get_definition thy) class of SOME {intro, ...} => cons intro | _ => I;
   519     val axclass_intros = fold add_axclass_intro classes [];
   520   in
   521     st
   522     |> ((ALLGOALS (Method.insert_tac facts THEN'
   523           REPEAT_ALL_NEW (resolve_tac (class_trivs @ class_intros @ axclass_intros))))
   524             THEN Tactic.distinct_subgoals_tac)
   525   end;
   526 
   527 fun default_intro_classes_tac [] = intro_classes_tac []
   528   | default_intro_classes_tac _ = Tactical.no_tac;    (*no error message!*)
   529 
   530 fun default_tac rules ctxt facts =
   531   HEADGOAL (Method.some_rule_tac rules ctxt facts) ORELSE
   532     default_intro_classes_tac facts;
   533 
   534 val _ = Context.add_setup (Method.add_methods
   535  [("intro_classes", Method.no_args (Method.METHOD intro_classes_tac),
   536     "back-chain introduction rules of classes"),
   537   ("default", Method.thms_ctxt_args (Method.METHOD oo default_tac),
   538     "apply some intro/elim rule")]);
   539 
   540 
   541 (** classes and class target **)
   542 
   543 (* class definition *)
   544 
   545 local
   546 
   547 fun read_param thy raw_t =
   548   let
   549     val t = Sign.read_term thy raw_t
   550   in case try dest_Const t
   551    of SOME (c, _) => c
   552     | NONE => error ("Not a constant: " ^ Sign.string_of_term thy t)
   553   end;
   554 
   555 fun gen_class add_locale prep_class prep_param bname
   556     raw_supclasses raw_elems raw_other_consts thy =
   557   let
   558     fun mk_instT class = Symtab.empty
   559       |> Symtab.update (AxClass.param_tyvarname, TFree (AxClass.param_tyvarname, [class]));
   560     fun mk_inst class param_names cs =
   561       Symtab.empty
   562       |> fold2 (fn v => fn (c, ty) => Symtab.update (v, Const
   563            (c, Term.map_type_tfree (fn (v, _) => TFree (v, [class])) ty))) param_names cs;
   564     (*FIXME need proper concept for reading locale statements*)
   565     fun subst_classtyvar (_, _) =
   566           TFree (AxClass.param_tyvarname, [])
   567       | subst_classtyvar (v, sort) =
   568           error ("Sort constraint illegal in type class, for type variable "
   569             ^ v ^ "::" ^ Sign.string_of_sort thy sort);
   570     (*val subst_classtyvars = Element.map_ctxt {name = I, var = I, term = I,
   571       typ = Term.map_type_tfree subst_classtyvar, fact = I, attrib = I};*)
   572     val other_consts = map (prep_param thy) raw_other_consts;
   573     val (elems, includes) = fold_rev (fn Locale.Elem e => apfst (cons e)
   574       | Locale.Expr i => apsnd (cons i)) raw_elems ([], []);
   575     val supclasses = map (prep_class thy) raw_supclasses;
   576     val sups = filter (is_some o lookup_class_data thy) supclasses
   577       |> Sign.certify_sort thy;
   578     val supsort = Sign.certify_sort thy supclasses;
   579     val suplocales = map (Locale.Locale o #locale o the_class_data thy) sups;
   580     val supexpr = Locale.Merge (suplocales @ includes);
   581     val supparams = (map fst o Locale.parameters_of_expr thy)
   582       (Locale.Merge suplocales);
   583     val supconsts = AList.make (the o AList.lookup (op =) (params_of_sort thy sups))
   584       (map fst supparams);
   585     (*val elems_constrains = map
   586       (Element.Constrains o apsnd (Term.map_type_tfree subst_classtyvar)) supparams;*)
   587     fun mk_tyvar (_, sort) = TFree (AxClass.param_tyvarname,
   588       if Sign.subsort thy (supsort, sort) then sort else error
   589         ("Sort " ^ Sign.string_of_sort thy sort
   590           ^ " is less general than permitted least general sort "
   591           ^ Sign.string_of_sort thy supsort));
   592     fun extract_params thy name_locale =
   593       let
   594         val params = Locale.parameters_of thy name_locale;
   595         val v = case (maps typ_tfrees o map (snd o fst)) params
   596          of (v, _) :: _ => v
   597           | [] => AxClass.param_tyvarname;
   598       in
   599         (v, (map fst params, params
   600         |> (map o apfst o apsnd o Term.map_type_tfree) mk_tyvar
   601         |> (map o apsnd) (fork_mixfix true NONE #> fst)
   602         |> chop (length supconsts)
   603         |> snd))
   604       end;
   605     fun extract_assumes name_locale params thy cs =
   606       let
   607         val consts = supconsts @ (map (fst o fst) params ~~ cs);
   608         fun subst (Free (c, ty)) =
   609               Const ((fst o the o AList.lookup (op =) consts) c, ty)
   610           | subst t = t;
   611         fun prep_asm ((name, atts), ts) =
   612           ((NameSpace.base name, map (Attrib.attribute thy) atts),
   613             (map o map_aterms) subst ts);
   614       in
   615         Locale.global_asms_of thy name_locale
   616         |> map prep_asm
   617       end;
   618     fun note_intro name_axclass class_intro =
   619       PureThy.note_thmss_qualified "" ((Logic.const_of_class o NameSpace.base) name_axclass)
   620         [(("intro", []), [([class_intro], [])])]
   621       #> snd
   622   in
   623     thy
   624     |> add_locale (SOME "") bname supexpr ((*elems_constrains @*) elems)
   625     |-> (fn name_locale => ProofContext.theory_result (
   626       `(fn thy => extract_params thy name_locale)
   627       #-> (fn (v, (globals, params)) =>
   628         AxClass.define_class_params (bname, supsort) params
   629           (extract_assumes name_locale params) other_consts
   630       #-> (fn (name_axclass, (consts, axioms)) =>
   631         `(fn thy => class_intro thy name_locale name_axclass sups)
   632       #-> (fn class_intro =>
   633         add_class_data ((name_axclass, sups),
   634           (name_locale, map fst params ~~ map fst consts, v,
   635             (mk_instT name_axclass, mk_inst name_axclass (map fst globals)
   636               (map snd supconsts @ consts)), class_intro))
   637       #> note_intro name_axclass class_intro
   638       #> class_interpretation name_axclass axioms []
   639       #> pair name_axclass
   640       )))))
   641   end;
   642 
   643 in
   644 
   645 val class_cmd = gen_class Locale.add_locale Sign.intern_class read_param;
   646 val class = gen_class Locale.add_locale_i Sign.certify_class (K I);
   647 
   648 end; (*local*)
   649 
   650 
   651 (* class target context *)
   652 
   653 fun remove_constraints class thy =
   654   thy |> fold_map (get_remove_contraint o fst) (these_localized thy class);
   655 
   656 
   657 (* definition in class target *)
   658 
   659 fun export_fixes thy class =
   660   let
   661     val consts = params_of_sort thy [class];
   662     fun subst_aterm (t as Free (v, ty)) = (case AList.lookup (op =) consts v
   663          of SOME (c, _) => Const (c, ty)
   664           | NONE => t)
   665       | subst_aterm t = t;
   666   in Term.map_aterms subst_aterm end;
   667 
   668 fun add_const_in_class class ((c, rhs), syn) thy =
   669   let
   670     val prfx = (Logic.const_of_class o NameSpace.base) class;
   671     fun mk_name c =
   672       let
   673         val n1 = Sign.full_name thy c;
   674         val n2 = NameSpace.qualifier n1;
   675         val n3 = NameSpace.base n1;
   676       in NameSpace.implode [n2, prfx, n3] end;
   677     val v = (#v o the_class_data thy) class;
   678     val constrain_sort = curry (Sorts.inter_sort (Sign.classes_of thy)) [class];
   679     val subst_typ = Term.map_type_tfree (fn var as (w, sort) =>
   680       if w = v then TFree (w, constrain_sort sort) else TFree var);
   681     val rhs' = export_fixes thy class rhs;
   682     val ty' = Term.fastype_of rhs';
   683     val ty'' = subst_typ ty';
   684     val c' = mk_name c;
   685     val def = (c, Logic.mk_equals (Const (c', ty'), rhs'));
   686     val (syn', _) = fork_mixfix true NONE syn;
   687     fun interpret def thy =
   688       let
   689         val def' = symmetric def;
   690         val def_eq = Thm.prop_of def';
   691         val typargs = Sign.const_typargs thy (c', fastype_of rhs);
   692         val typidx = find_index (fn TFree (w, _) => v = w | _ => false) typargs;
   693       in
   694         thy
   695         |> class_interpretation class [def'] [def_eq]
   696         |> add_class_const_def (class, ((c', (rhs, typidx)), def'))
   697       end;
   698   in
   699     thy
   700     |> Sign.add_path prfx
   701     |> Sign.add_consts_authentic [(c, ty', syn')]
   702     |> Sign.parent_path
   703     |> Sign.sticky_prefix prfx
   704     |> PureThy.add_defs_i false [(def, [])]
   705     |-> (fn [def] => interpret def)
   706     |> Sign.add_const_constraint_i (c', SOME ty'')
   707     |> Sign.restore_naming thy
   708   end;
   709 
   710 
   711 (* interpretation in class target *)
   712 
   713 local
   714 
   715 fun gen_interpretation_in_class prep_class do_proof (raw_class, raw_superclass) theory =
   716   let
   717     val class = prep_class theory raw_class;
   718     val superclass = prep_class theory raw_superclass;
   719     val loc_name = (#locale o the_class_data theory) class;
   720     val loc_expr = (Locale.Locale o #locale o the_class_data theory) superclass;
   721     fun prove_classrel (class, superclass) thy =
   722       let
   723         val classes = (Graph.all_succs o #classes o Sorts.rep_algebra
   724               o Sign.classes_of) thy [superclass]
   725           |> filter_out (fn class' => Sign.subsort thy ([class], [class']));
   726         fun instance_subclass (class1, class2) thy  =
   727           let
   728             val interp = interpretation_in_rule thy (class1, class2);
   729             val ax = #axioms (AxClass.get_definition thy class1);
   730             val intro = #intro (AxClass.get_definition thy class2)
   731               |> Drule.instantiate' [SOME (Thm.ctyp_of thy
   732                   (TVar ((AxClass.param_tyvarname, 0), [class1])))] [];
   733             val thm = 
   734               intro
   735               |> OF_LAST (interp OF ax)
   736               |> strip_all_ofclass thy (Sign.super_classes thy class2);
   737           in
   738             thy |> AxClass.add_classrel thm
   739           end;
   740       in
   741         thy |> fold_rev (curry instance_subclass class) classes
   742       end;
   743   in
   744     theory
   745     |> do_proof (prove_classrel (class, superclass)) (loc_name, loc_expr)
   746   end;
   747 
   748 in
   749 
   750 val interpretation_in_class = gen_interpretation_in_class Sign.certify_class
   751   (Locale.interpretation_in_locale o ProofContext.theory);
   752 val interpretation_in_class_cmd = gen_interpretation_in_class Sign.read_class
   753   (Locale.interpretation_in_locale o ProofContext.theory);
   754 val prove_interpretation_in_class = gen_interpretation_in_class Sign.certify_class
   755   o prove_interpretation_in;
   756 
   757 end; (*local*)
   758 
   759 (*experimental*)
   760 fun class_term_check thy class =
   761   let
   762     val algebra = Sign.classes_of thy;
   763     val { v, ... } = the_class_data thy class;
   764     fun add_constrain_classtyp sort' (ty as TFree (v, _)) =
   765           AList.map_default (op =) (v, []) (curry (Sorts.inter_sort algebra) sort')
   766       | add_constrain_classtyp sort' (Type (tyco, tys)) = case Sorts.mg_domain algebra tyco sort'
   767          of sorts => fold2 add_constrain_classtyp sorts tys;
   768     fun class_arg c idx ty =
   769       let
   770         val typargs = Sign.const_typargs thy (c, ty);
   771         fun classtyp (t as TFree (w, _)) = if w = v then NONE else SOME t
   772           | classtyp t = SOME t;
   773       in classtyp (nth typargs idx) end;
   774     fun add_inst (c, ty) (terminsts, typinsts) = case local_param thy class c
   775      of NONE => (terminsts, typinsts)
   776       | SOME (t, (class', idx)) => (case class_arg c idx ty
   777          of NONE => (((c, ty), t) :: terminsts, typinsts)
   778           | SOME ty => (terminsts, add_constrain_classtyp [class'] ty typinsts));
   779   in pair o (fn ts => let
   780     val cs = (fold o fold_aterms) (fn Const c_ty => insert (op =) c_ty | _ => I) ts [];
   781     val (terminsts, typinsts) = fold add_inst cs ([], []);
   782   in
   783     ts
   784     |> (map o map_aterms) (fn t as Const c_ty => the_default t (AList.lookup (op =) terminsts c_ty)
   785          | t => t)
   786     |> (map o map_types o map_atyps) (fn t as TFree (v, sort) =>
   787          case AList.lookup (op =) typinsts v
   788           of SOME sort' => TFree (v, Sorts.inter_sort algebra (sort, sort'))
   789            | NONE => t)
   790   end) end;
   791 
   792 val init_ref = ref (K (pair I) : class -> Proof.context -> (theory -> theory) * Proof.context);
   793 fun init class = ! init_ref class;
   794 
   795 fun init_default class ctxt =
   796   let
   797     val thy = ProofContext.theory_of ctxt;
   798     val term_check = class_term_check thy class;
   799   in
   800     ctxt
   801     (*|> ProofContext.theory_result (remove_constraints class)*)
   802     |> Context.proof_map (Syntax.add_term_check term_check)
   803     (*|>> fold (fn (c, ty) => Sign.add_const_constraint_i (c, SOME ty))*)
   804     |> pair I
   805   end;
   806 
   807 end;