src/Pure/Isar/class.ML
author wenzelm
Thu Sep 16 15:37:12 2010 +0200 (2010-09-16 ago)
changeset 39438 c5ece2a7a86e
parent 39378 df86b1b4ce10
child 39557 fe5722fce758
permissions -rw-r--r--
Isar "default" step needs to fail for solved problems, for clear distinction of '.' and '..' for example -- amending lapse introduced in 9de4d64eee3b (April 2004);
     1 (*  Title:      Pure/Isar/class.ML
     2     Author:     Florian Haftmann, TU Muenchen
     3 
     4 Type classes derived from primitive axclasses and locales.
     5 *)
     6 
     7 signature CLASS =
     8 sig
     9   (*classes*)
    10   val is_class: theory -> class -> bool
    11   val these_params: theory -> sort -> (string * (class * (string * typ))) list
    12   val base_sort: theory -> class -> sort
    13   val rules: theory -> class -> thm option * thm
    14   val these_defs: theory -> sort -> thm list
    15   val these_operations: theory -> sort
    16     -> (string * (class * (typ * term))) list
    17   val print_classes: theory -> unit
    18   val init: class -> theory -> Proof.context
    19   val begin: class list -> sort -> Proof.context -> Proof.context
    20   val const: class -> (binding * mixfix) * (term list * term) -> local_theory -> local_theory
    21   val abbrev: class -> Syntax.mode -> (binding * mixfix) * term -> local_theory -> local_theory
    22   val redeclare_operations: theory -> sort -> Proof.context -> Proof.context
    23   val class_prefix: string -> string
    24   val register: class -> class list -> ((string * typ) * (string * typ)) list
    25     -> sort -> morphism -> morphism -> thm option -> thm option -> thm
    26     -> theory -> theory
    27 
    28   (*instances*)
    29   val instantiation: string list * (string * sort) list * sort -> theory -> local_theory
    30   val instantiation_instance: (local_theory -> local_theory)
    31     -> local_theory -> Proof.state
    32   val prove_instantiation_instance: (Proof.context -> tactic)
    33     -> local_theory -> local_theory
    34   val prove_instantiation_exit: (Proof.context -> tactic)
    35     -> local_theory -> theory
    36   val prove_instantiation_exit_result: (morphism -> 'a -> 'b)
    37     -> (Proof.context -> 'b -> tactic) -> 'a -> local_theory -> 'b * theory
    38   val read_multi_arity: theory -> xstring list * xstring list * xstring
    39     -> string list * (string * sort) list * sort
    40   val type_name: string -> string
    41   val instantiation_cmd: xstring list * xstring list * xstring -> theory -> local_theory
    42   val instance_arity_cmd: xstring list * xstring list * xstring -> theory -> Proof.state
    43 
    44   (*subclasses*)
    45   val classrel: class * class -> theory -> Proof.state
    46   val classrel_cmd: xstring * xstring -> theory -> Proof.state
    47   val register_subclass: class * class -> morphism option -> Element.witness option
    48     -> morphism -> theory -> theory
    49 
    50   (*tactics*)
    51   val intro_classes_tac: thm list -> tactic
    52   val default_intro_tac: Proof.context -> thm list -> tactic
    53 end;
    54 
    55 structure Class: CLASS =
    56 struct
    57 
    58 (** class data **)
    59 
    60 datatype class_data = ClassData of {
    61 
    62   (* static part *)
    63   consts: (string * string) list
    64     (*locale parameter ~> constant name*),
    65   base_sort: sort,
    66   base_morph: morphism
    67     (*static part of canonical morphism*),
    68   export_morph: morphism,
    69   assm_intro: thm option,
    70   of_class: thm,
    71   axiom: thm option,
    72   
    73   (* dynamic part *)
    74   defs: thm list,
    75   operations: (string * (class * (typ * term))) list
    76 
    77 };
    78 
    79 fun make_class_data ((consts, base_sort, base_morph, export_morph, assm_intro, of_class, axiom),
    80     (defs, operations)) =
    81   ClassData { consts = consts, base_sort = base_sort,
    82     base_morph = base_morph, export_morph = export_morph, assm_intro = assm_intro,
    83     of_class = of_class, axiom = axiom, defs = defs, operations = operations };
    84 fun map_class_data f (ClassData { consts, base_sort, base_morph, export_morph, assm_intro,
    85     of_class, axiom, defs, operations }) =
    86   make_class_data (f ((consts, base_sort, base_morph, export_morph, assm_intro, of_class, axiom),
    87     (defs, operations)));
    88 fun merge_class_data _ (ClassData { consts = consts,
    89     base_sort = base_sort, base_morph = base_morph, export_morph = export_morph, assm_intro = assm_intro,
    90     of_class = of_class, axiom = axiom, defs = defs1, operations = operations1 },
    91   ClassData { consts = _, base_sort = _, base_morph = _, export_morph = _, assm_intro = _,
    92     of_class = _, axiom = _, defs = defs2, operations = operations2 }) =
    93   make_class_data ((consts, base_sort, base_morph, export_morph, assm_intro, of_class, axiom),
    94     (Thm.merge_thms (defs1, defs2),
    95       AList.merge (op =) (K true) (operations1, operations2)));
    96 
    97 structure ClassData = Theory_Data
    98 (
    99   type T = class_data Graph.T
   100   val empty = Graph.empty;
   101   val extend = I;
   102   val merge = Graph.join merge_class_data;
   103 );
   104 
   105 
   106 (* queries *)
   107 
   108 fun lookup_class_data thy class = case try (Graph.get_node (ClassData.get thy)) class
   109  of SOME (ClassData data) => SOME data
   110   | NONE => NONE;
   111 
   112 fun the_class_data thy class = case lookup_class_data thy class
   113  of NONE => error ("Undeclared class " ^ quote class)
   114   | SOME data => data;
   115 
   116 val is_class = is_some oo lookup_class_data;
   117 
   118 val ancestry = Graph.all_succs o ClassData.get;
   119 val heritage = Graph.all_preds o ClassData.get;
   120 
   121 fun these_params thy =
   122   let
   123     fun params class =
   124       let
   125         val const_typs = (#params o AxClass.get_info thy) class;
   126         val const_names = (#consts o the_class_data thy) class;
   127       in
   128         (map o apsnd)
   129           (fn c => (class, (c, (the o AList.lookup (op =) const_typs) c))) const_names
   130       end;
   131   in maps params o ancestry thy end;
   132 
   133 val base_sort = #base_sort oo the_class_data;
   134 
   135 fun rules thy class =
   136   let val { axiom, of_class, ... } = the_class_data thy class
   137   in (axiom, of_class) end;
   138 
   139 fun all_assm_intros thy =
   140   Graph.fold (fn (_, (ClassData { assm_intro, ... }, _)) => fold (insert Thm.eq_thm)
   141     (the_list assm_intro)) (ClassData.get thy) [];
   142 
   143 fun these_defs thy = maps (#defs o the_class_data thy) o ancestry thy;
   144 fun these_operations thy = maps (#operations o the_class_data thy) o ancestry thy;
   145 
   146 val base_morphism = #base_morph oo the_class_data;
   147 fun morphism thy class = case Element.eq_morphism thy (these_defs thy [class])
   148  of SOME eq_morph => base_morphism thy class $> eq_morph
   149   | NONE => base_morphism thy class;
   150 val export_morphism = #export_morph oo the_class_data;
   151 
   152 fun print_classes thy =
   153   let
   154     val ctxt = ProofContext.init_global thy;
   155     val algebra = Sign.classes_of thy;
   156     val arities =
   157       Symtab.empty
   158       |> Symtab.fold (fn (tyco, arities) => fold (fn (class, _) =>
   159            Symtab.map_default (class, []) (insert (op =) tyco)) arities)
   160              (Sorts.arities_of algebra);
   161     val the_arities = these o Symtab.lookup arities;
   162     fun mk_arity class tyco =
   163       let
   164         val Ss = Sorts.mg_domain algebra tyco [class];
   165       in Syntax.pretty_arity ctxt (tyco, Ss, [class]) end;
   166     fun mk_param (c, ty) = Pretty.str (Sign.extern_const thy c ^ " :: "
   167       ^ (Syntax.string_of_typ (Config.put show_sorts false ctxt) o Type.strip_sorts) ty);
   168     fun mk_entry class = (Pretty.block o Pretty.fbreaks o map_filter I) [
   169       (SOME o Pretty.str) ("class " ^ Sign.extern_class thy class ^ ":"),
   170       (SOME o Pretty.block) [Pretty.str "supersort: ",
   171         (Syntax.pretty_sort ctxt o Sign.minimize_sort thy o Sign.super_classes thy) class],
   172       ((fn [] => NONE | ps => (SOME o Pretty.block o Pretty.fbreaks)
   173           (Pretty.str "parameters:" :: ps)) o map mk_param
   174         o these o Option.map #params o try (AxClass.get_info thy)) class,
   175       (SOME o Pretty.block o Pretty.breaks) [
   176         Pretty.str "instances:",
   177         Pretty.list "" "" (map (mk_arity class) (the_arities class))
   178       ]
   179     ]
   180   in
   181     (Pretty.writeln o Pretty.chunks o separate (Pretty.str "")
   182       o map mk_entry o Sorts.all_classes) algebra
   183   end;
   184 
   185 
   186 (* updaters *)
   187 
   188 fun register class sups params base_sort base_morph export_morph
   189     axiom assm_intro of_class thy =
   190   let
   191     val operations = map (fn (v_ty as (_, ty), (c, _)) =>
   192       (c, (class, (ty, Free v_ty)))) params;
   193     val add_class = Graph.new_node (class,
   194         make_class_data (((map o pairself) fst params, base_sort,
   195           base_morph, export_morph, assm_intro, of_class, axiom), ([], operations)))
   196       #> fold (curry Graph.add_edge class) sups;
   197   in ClassData.map add_class thy end;
   198 
   199 fun activate_defs class thms thy = case Element.eq_morphism thy thms
   200  of SOME eq_morph => fold (fn cls => fn thy =>
   201       Context.theory_map (Locale.amend_registration (cls, base_morphism thy cls)
   202         (eq_morph, true) (export_morphism thy cls)) thy) (heritage thy [class]) thy
   203   | NONE => thy;
   204 
   205 fun register_operation class (c, (t, some_def)) thy =
   206   let
   207     val base_sort = base_sort thy class;
   208     val prep_typ = map_type_tfree
   209       (fn (v, sort) => if Name.aT = v
   210         then TFree (v, base_sort) else TVar ((v, 0), sort));
   211     val t' = map_types prep_typ t;
   212     val ty' = Term.fastype_of t';
   213   in
   214     thy
   215     |> (ClassData.map o Graph.map_node class o map_class_data o apsnd)
   216       (fn (defs, operations) =>
   217         (fold cons (the_list some_def) defs,
   218           (c, (class, (ty', t'))) :: operations))
   219     |> activate_defs class (the_list some_def)
   220   end;
   221 
   222 fun register_subclass (sub, sup) some_dep_morph some_wit export thy =
   223   let
   224     val intros = (snd o rules thy) sup :: map_filter I
   225       [Option.map (Drule.export_without_context_open o Element.conclude_witness) some_wit,
   226         (fst o rules thy) sub];
   227     val tac = EVERY (map (TRYALL o Tactic.rtac) intros);
   228     val classrel = Skip_Proof.prove_global thy [] [] (Logic.mk_classrel (sub, sup))
   229       (K tac);
   230     val diff_sort = Sign.complete_sort thy [sup]
   231       |> subtract (op =) (Sign.complete_sort thy [sub])
   232       |> filter (is_class thy);
   233     val add_dependency = case some_dep_morph
   234      of SOME dep_morph => Locale.add_dependency sub
   235           (sup, dep_morph $> Element.satisfy_morphism (the_list some_wit)) export
   236       | NONE => I
   237   in
   238     thy
   239     |> AxClass.add_classrel classrel
   240     |> ClassData.map (Graph.add_edge (sub, sup))
   241     |> activate_defs sub (these_defs thy diff_sort)
   242     |> add_dependency
   243   end;
   244 
   245 
   246 (** classes and class target **)
   247 
   248 (* class context syntax *)
   249 
   250 fun these_unchecks thy = map (fn (c, (_, (ty, t))) => (t, Const (c, ty)))
   251   o these_operations thy;
   252 
   253 fun redeclare_const thy c =
   254   let val b = Long_Name.base_name c
   255   in Sign.intern_const thy b = c ? Variable.declare_const (b, c) end;
   256 
   257 fun synchronize_class_syntax sort base_sort ctxt =
   258   let
   259     val thy = ProofContext.theory_of ctxt;
   260     val algebra = Sign.classes_of thy;
   261     val operations = these_operations thy sort;
   262     fun subst_class_typ sort = map_type_tfree (K (TVar ((Name.aT, 0), sort)));
   263     val primary_constraints =
   264       (map o apsnd) (subst_class_typ base_sort o fst o snd) operations;
   265     val secondary_constraints =
   266       (map o apsnd) (fn (class, (ty, _)) => subst_class_typ [class] ty) operations;
   267     fun improve (c, ty) = (case AList.lookup (op =) primary_constraints c
   268      of SOME ty' => (case try (Type.raw_match (ty', ty)) Vartab.empty
   269          of SOME tyenv => (case Vartab.lookup tyenv (Name.aT, 0)
   270              of SOME (_, ty' as TVar (vi, sort)) =>
   271                   if Type_Infer.is_param vi
   272                     andalso Sorts.sort_le algebra (base_sort, sort)
   273                       then SOME (ty', TFree (Name.aT, base_sort))
   274                       else NONE
   275               | _ => NONE)
   276           | NONE => NONE)
   277       | NONE => NONE)
   278     fun subst (c, ty) = Option.map snd (AList.lookup (op =) operations c);
   279     val unchecks = these_unchecks thy sort;
   280   in
   281     ctxt
   282     |> fold (redeclare_const thy o fst) primary_constraints
   283     |> Overloading.map_improvable_syntax (K (((primary_constraints, secondary_constraints),
   284         (((improve, subst), true), unchecks)), false))
   285     |> Overloading.set_primary_constraints
   286   end;
   287 
   288 fun redeclare_operations thy sort =
   289   fold (redeclare_const thy o fst) (these_operations thy sort);
   290 
   291 fun begin sort base_sort ctxt =
   292   ctxt
   293   |> Variable.declare_term
   294       (Logic.mk_type (TFree (Name.aT, base_sort)))
   295   |> synchronize_class_syntax sort base_sort
   296   |> Overloading.activate_improvable_syntax;
   297 
   298 fun init class thy =
   299   thy
   300   |> Locale.init class
   301   |> begin [class] (base_sort thy class);
   302 
   303 
   304 (* class target *)
   305 
   306 val class_prefix = Logic.const_of_class o Long_Name.base_name;
   307 
   308 fun target_extension f class lthy =
   309   lthy
   310   |> Local_Theory.raw_theory f
   311   |> Local_Theory.target (synchronize_class_syntax [class]
   312       (base_sort (ProofContext.theory_of lthy) class));
   313 
   314 local
   315 
   316 fun target_const class ((c, mx), (type_params, dict)) thy =
   317   let
   318     val morph = morphism thy class;
   319     val b = Morphism.binding morph c;
   320     val b_def = Morphism.binding morph (Binding.suffix_name "_dict" b);
   321     val c' = Sign.full_name thy b;
   322     val dict' = Morphism.term morph dict;
   323     val ty' = map Term.fastype_of type_params ---> Term.fastype_of dict';
   324     val def_eq = Logic.mk_equals (list_comb (Const (c', ty'), type_params), dict')
   325       |> map_types Type.strip_sorts;
   326   in
   327     thy
   328     |> Sign.declare_const ((b, Type.strip_sorts ty'), mx)
   329     |> snd
   330     |> Thm.add_def false false (b_def, def_eq)
   331     |>> apsnd Thm.varifyT_global
   332     |-> (fn (_, def_thm) => PureThy.store_thm (b_def, def_thm)
   333       #> snd
   334       #> null type_params ? register_operation class (c', (dict', SOME (Thm.symmetric def_thm))))
   335     |> Sign.add_const_constraint (c', SOME ty')
   336   end;
   337 
   338 fun target_abbrev class prmode ((c, mx), rhs) thy =
   339   let
   340     val morph = morphism thy class;
   341     val unchecks = these_unchecks thy [class];
   342     val b = Morphism.binding morph c;
   343     val c' = Sign.full_name thy b;
   344     val rhs' = Pattern.rewrite_term thy unchecks [] rhs;
   345     val ty' = Term.fastype_of rhs';
   346     val rhs'' = map_types Logic.varifyT_global rhs';
   347   in
   348     thy
   349     |> Sign.add_abbrev (#1 prmode) (b, rhs'')
   350     |> snd
   351     |> Sign.add_const_constraint (c', SOME ty')
   352     |> Sign.notation true prmode [(Const (c', ty'), mx)]
   353     |> not (#1 prmode = Print_Mode.input) ? register_operation class (c', (rhs', NONE))
   354   end;
   355 
   356 in
   357 
   358 fun const class arg = target_extension (target_const class arg) class;
   359 fun abbrev class prmode arg = target_extension (target_abbrev class prmode arg) class;
   360 
   361 end;
   362 
   363 
   364 (* simple subclasses *)
   365 
   366 local
   367 
   368 fun gen_classrel mk_prop classrel thy =
   369   let
   370     fun after_qed results =
   371       ProofContext.background_theory ((fold o fold) AxClass.add_classrel results);
   372   in
   373     thy
   374     |> ProofContext.init_global
   375     |> Proof.theorem NONE after_qed [[(mk_prop thy classrel, [])]]
   376   end;
   377 
   378 in
   379 
   380 val classrel =
   381   gen_classrel (Logic.mk_classrel oo AxClass.cert_classrel);
   382 val classrel_cmd =
   383   gen_classrel (Logic.mk_classrel oo AxClass.read_classrel);
   384 
   385 end; (*local*)
   386 
   387 
   388 (** instantiation target **)
   389 
   390 (* bookkeeping *)
   391 
   392 datatype instantiation = Instantiation of {
   393   arities: string list * (string * sort) list * sort,
   394   params: ((string * string) * (string * typ)) list
   395     (*(instantiation parameter, type constructor), (local instantiation parameter, typ)*)
   396 }
   397 
   398 structure Instantiation = Proof_Data
   399 (
   400   type T = instantiation
   401   fun init _ = Instantiation { arities = ([], [], []), params = [] };
   402 );
   403 
   404 fun mk_instantiation (arities, params) =
   405   Instantiation { arities = arities, params = params };
   406 fun get_instantiation lthy = case Instantiation.get (Local_Theory.target_of lthy)
   407  of Instantiation data => data;
   408 fun map_instantiation f = (Local_Theory.target o Instantiation.map)
   409   (fn Instantiation { arities, params } => mk_instantiation (f (arities, params)));
   410 
   411 fun the_instantiation lthy = case get_instantiation lthy
   412  of { arities = ([], [], []), ... } => error "No instantiation target"
   413   | data => data;
   414 
   415 val instantiation_params = #params o get_instantiation;
   416 
   417 fun instantiation_param lthy b = instantiation_params lthy
   418   |> find_first (fn (_, (v, _)) => Binding.name_of b = v)
   419   |> Option.map (fst o fst);
   420 
   421 fun read_multi_arity thy (raw_tycos, raw_sorts, raw_sort) =
   422   let
   423     val ctxt = ProofContext.init_global thy;
   424     val all_arities = map (fn raw_tyco => ProofContext.read_arity ctxt
   425       (raw_tyco, raw_sorts, raw_sort)) raw_tycos;
   426     val tycos = map #1 all_arities;
   427     val (_, sorts, sort) = hd all_arities;
   428     val vs = Name.names Name.context Name.aT sorts;
   429   in (tycos, vs, sort) end;
   430 
   431 
   432 (* syntax *)
   433 
   434 fun synchronize_inst_syntax ctxt =
   435   let
   436     val Instantiation { params, ... } = Instantiation.get ctxt;
   437 
   438     val lookup_inst_param = AxClass.lookup_inst_param
   439       (Sign.consts_of (ProofContext.theory_of ctxt)) params;
   440     fun subst (c, ty) = case lookup_inst_param (c, ty)
   441      of SOME (v_ty as (_, ty)) => SOME (ty, Free v_ty)
   442       | NONE => NONE;
   443     val unchecks =
   444       map (fn ((c, _), v_ty as (_, ty)) => (Free v_ty, Const (c, ty))) params;
   445   in
   446     ctxt
   447     |> Overloading.map_improvable_syntax
   448          (fn (((primary_constraints, _), (((improve, _), _), _)), _) =>
   449             (((primary_constraints, []), (((improve, subst), false), unchecks)), false))
   450   end;
   451 
   452 fun resort_terms pp algebra consts constraints ts =
   453   let
   454     fun matchings (Const (c_ty as (c, _))) = (case constraints c
   455          of NONE => I
   456           | SOME sorts => fold2 (curry (Sorts.meet_sort algebra))
   457               (Consts.typargs consts c_ty) sorts)
   458       | matchings _ = I
   459     val tvartab = (fold o fold_aterms) matchings ts Vartab.empty
   460       handle Sorts.CLASS_ERROR e => error (Sorts.class_error pp e);
   461     val inst = map_type_tvar
   462       (fn (vi, sort) => TVar (vi, the_default sort (Vartab.lookup tvartab vi)));
   463   in if Vartab.is_empty tvartab then NONE else SOME ((map o map_types) inst ts) end;
   464 
   465 
   466 (* target *)
   467 
   468 val sanitize_name = (*necessary as long as "dirty" type identifiers are permitted*)
   469   let
   470     fun is_valid s = Symbol.is_ascii_letter s orelse Symbol.is_ascii_digit s
   471       orelse s = "'" orelse s = "_";
   472     val is_junk = not o is_valid andf Symbol.is_regular;
   473     val junk = Scan.many is_junk;
   474     val scan_valids = Symbol.scanner "Malformed input"
   475       ((junk |--
   476         (Scan.optional (Scan.one Symbol.is_ascii_letter) "x" ^^ (Scan.many is_valid >> implode)
   477         --| junk))
   478       ::: Scan.repeat ((Scan.many1 is_valid >> implode) --| junk));
   479   in
   480     explode #> scan_valids #> implode
   481   end;
   482 
   483 val type_name = sanitize_name o Long_Name.base_name;
   484 
   485 fun define_overloaded (c, U) v (b_def, rhs) = Local_Theory.background_theory_result
   486     (AxClass.declare_overloaded (c, U) ##>> AxClass.define_overloaded b_def (c, rhs))
   487   ##> (map_instantiation o apsnd) (filter_out (fn (_, (v', _)) => v' = v))
   488   ##> Local_Theory.target synchronize_inst_syntax;
   489 
   490 fun foundation (((b, U), mx), (b_def, rhs)) (type_params, term_params) lthy =
   491   case instantiation_param lthy b
   492    of SOME c => if mx <> NoSyn then error ("Illegal mixfix syntax for overloaded constant " ^ quote c)
   493         else lthy |> define_overloaded (c, U) (Binding.name_of b) (b_def, rhs)
   494     | NONE => lthy |>
   495         Generic_Target.theory_foundation (((b, U), mx), (b_def, rhs)) (type_params, term_params);
   496 
   497 fun pretty lthy =
   498   let
   499     val { arities = (tycos, vs, sort), params } = the_instantiation lthy;
   500     val thy = ProofContext.theory_of lthy;
   501     fun pr_arity tyco = Syntax.pretty_arity lthy (tyco, map snd vs, sort);
   502     fun pr_param ((c, _), (v, ty)) =
   503       (Pretty.block o Pretty.breaks) [Pretty.str v, Pretty.str "==",
   504         (Pretty.str o Sign.extern_const thy) c, Pretty.str "::", Syntax.pretty_typ_global thy ty];
   505   in Pretty.str "instantiation" :: map pr_arity tycos @ map pr_param params end;
   506 
   507 fun conclude lthy =
   508   let
   509     val (tycos, vs, sort) = (#arities o the_instantiation) lthy;
   510     val thy = ProofContext.theory_of lthy;
   511     val _ = map (fn tyco => if Sign.of_sort thy
   512         (Type (tyco, map TFree vs), sort)
   513       then () else error ("Missing instance proof for type " ^ quote (Sign.extern_type thy tyco)))
   514         tycos;
   515   in lthy end;
   516 
   517 fun instantiation (tycos, vs, sort) thy =
   518   let
   519     val _ = if null tycos then error "At least one arity must be given" else ();
   520     val class_params = these_params thy (filter (can (AxClass.get_info thy)) sort);
   521     fun get_param tyco (param, (_, (c, ty))) =
   522       if can (AxClass.param_of_inst thy) (c, tyco)
   523       then NONE else SOME ((c, tyco),
   524         (param ^ "_" ^ type_name tyco, map_atyps (K (Type (tyco, map TFree vs))) ty));
   525     val params = map_product get_param tycos class_params |> map_filter I;
   526     val primary_constraints = map (apsnd
   527       (map_atyps (K (TVar ((Name.aT, 0), [])))) o snd o snd) class_params;
   528     val algebra = Sign.classes_of thy
   529       |> fold (fn tyco => Sorts.add_arities (Syntax.pp_global thy)
   530             (tyco, map (fn class => (class, map snd vs)) sort)) tycos;
   531     val consts = Sign.consts_of thy;
   532     val improve_constraints = AList.lookup (op =)
   533       (map (fn (_, (class, (c, _))) => (c, [[class]])) class_params);
   534     fun resort_check ts ctxt = case resort_terms (Syntax.pp ctxt) algebra consts improve_constraints ts
   535      of NONE => NONE
   536       | SOME ts' => SOME (ts', ctxt);
   537     val lookup_inst_param = AxClass.lookup_inst_param consts params;
   538     val typ_instance = Type.typ_instance (Sign.tsig_of thy);
   539     fun improve (c, ty) = case lookup_inst_param (c, ty)
   540      of SOME (_, ty') => if typ_instance (ty', ty) then SOME (ty, ty') else NONE
   541       | NONE => NONE;
   542   in
   543     thy
   544     |> Theory.checkpoint
   545     |> ProofContext.init_global
   546     |> Instantiation.put (mk_instantiation ((tycos, vs, sort), params))
   547     |> fold (Variable.declare_typ o TFree) vs
   548     |> fold (Variable.declare_names o Free o snd) params
   549     |> (Overloading.map_improvable_syntax o apfst)
   550          (K ((primary_constraints, []), (((improve, K NONE), false), [])))
   551     |> Overloading.activate_improvable_syntax
   552     |> Context.proof_map (Syntax.add_term_check 0 "resorting" resort_check)
   553     |> synchronize_inst_syntax
   554     |> Local_Theory.init NONE ""
   555        {define = Generic_Target.define foundation,
   556         notes = Generic_Target.notes
   557           (fn kind => fn global_facts => fn _ => Generic_Target.theory_notes kind global_facts),
   558         abbrev = Generic_Target.abbrev
   559           (fn prmode => fn (b, mx) => fn (t, _) => fn _ => Generic_Target.theory_abbrev prmode ((b, mx), t)),
   560         declaration = K Generic_Target.theory_declaration,
   561         syntax_declaration = K Generic_Target.theory_declaration,
   562         pretty = pretty,
   563         exit = Local_Theory.target_of o conclude}
   564   end;
   565 
   566 fun instantiation_cmd arities thy =
   567   instantiation (read_multi_arity thy arities) thy;
   568 
   569 fun gen_instantiation_instance do_proof after_qed lthy =
   570   let
   571     val (tycos, vs, sort) = (#arities o the_instantiation) lthy;
   572     val arities_proof = maps (fn tyco => Logic.mk_arities (tyco, map snd vs, sort)) tycos;
   573     fun after_qed' results =
   574       Local_Theory.background_theory (fold (AxClass.add_arity o Thm.varifyT_global) results)
   575       #> after_qed;
   576   in
   577     lthy
   578     |> do_proof after_qed' arities_proof
   579   end;
   580 
   581 val instantiation_instance = gen_instantiation_instance (fn after_qed => fn ts =>
   582   Proof.theorem NONE (after_qed o map the_single) (map (fn t => [(t, [])]) ts));
   583 
   584 fun prove_instantiation_instance tac = gen_instantiation_instance (fn after_qed =>
   585   fn ts => fn lthy => after_qed (map (fn t => Goal.prove lthy [] [] t
   586     (fn {context, ...} => tac context)) ts) lthy) I;
   587 
   588 fun prove_instantiation_exit tac = prove_instantiation_instance tac
   589   #> Local_Theory.exit_global;
   590 
   591 fun prove_instantiation_exit_result f tac x lthy =
   592   let
   593     val morph = ProofContext.export_morphism lthy
   594       (ProofContext.init_global (ProofContext.theory_of lthy));
   595     val y = f morph x;
   596   in
   597     lthy
   598     |> prove_instantiation_exit (fn ctxt => tac ctxt y)
   599     |> pair y
   600   end;
   601 
   602 
   603 (* simplified instantiation interface with no class parameter *)
   604 
   605 fun instance_arity_cmd raw_arities thy =
   606   let
   607     val (tycos, vs, sort) = read_multi_arity thy raw_arities;
   608     val sorts = map snd vs;
   609     val arities = maps (fn tyco => Logic.mk_arities (tyco, sorts, sort)) tycos;
   610     fun after_qed results = ProofContext.background_theory
   611       ((fold o fold) AxClass.add_arity results);
   612   in
   613     thy
   614     |> ProofContext.init_global
   615     |> Proof.theorem NONE after_qed (map (fn t => [(t, [])]) arities)
   616   end;
   617 
   618 
   619 (** tactics and methods **)
   620 
   621 fun intro_classes_tac facts st =
   622   let
   623     val thy = Thm.theory_of_thm st;
   624     val classes = Sign.all_classes thy;
   625     val class_trivs = map (Thm.class_triv thy) classes;
   626     val class_intros = map_filter (try (#intro o AxClass.get_info thy)) classes;
   627     val assm_intros = all_assm_intros thy;
   628   in
   629     Method.intros_tac (class_trivs @ class_intros @ assm_intros) facts st
   630   end;
   631 
   632 fun default_intro_tac ctxt [] =
   633       COND Thm.no_prems no_tac
   634         (intro_classes_tac [] ORELSE Locale.intro_locales_tac true ctxt [])
   635   | default_intro_tac _ _ = no_tac;
   636 
   637 fun default_tac rules ctxt facts =
   638   HEADGOAL (Method.some_rule_tac rules ctxt facts) ORELSE
   639     default_intro_tac ctxt facts;
   640 
   641 val _ = Context.>> (Context.map_theory
   642  (Method.setup (Binding.name "intro_classes") (Scan.succeed (K (METHOD intro_classes_tac)))
   643     "back-chain introduction rules of classes" #>
   644   Method.setup (Binding.name "default") (Attrib.thms >> (METHOD oo default_tac))
   645     "apply some intro/elim rule"));
   646 
   647 end;
   648