src/Pure/axclass.ML
author wenzelm
Wed Apr 28 13:32:00 2010 +0200 (2010-04-28 ago)
changeset 36456 9fd0f1eacd35
parent 36430 0a7fdd584391
child 36610 bafd82950e24
permissions -rw-r--r--
made SML/NJ happy;
     1 (*  Title:      Pure/axclass.ML
     2     Author:     Markus Wenzel, TU Muenchen
     3 
     4 Type classes defined as predicates, associated with a record of
     5 parameters.  Proven class relations and type arities.
     6 *)
     7 
     8 signature AX_CLASS =
     9 sig
    10   type info = {def: thm, intro: thm, axioms: thm list, params: (string * typ) list}
    11   val get_info: theory -> class -> info
    12   val class_of_param: theory -> string -> class option
    13   val instance_name: string * class -> string
    14   val thynames_of_arity: theory -> class * string -> string list
    15   val param_of_inst: theory -> string * string -> string
    16   val inst_of_param: theory -> string -> (string * string) option
    17   val unoverload: theory -> thm -> thm
    18   val overload: theory -> thm -> thm
    19   val unoverload_conv: theory -> conv
    20   val overload_conv: theory -> conv
    21   val lookup_inst_param: Consts.T -> ((string * string) * 'a) list -> string * typ -> 'a option
    22   val unoverload_const: theory -> string * typ -> string
    23   val cert_classrel: theory -> class * class -> class * class
    24   val read_classrel: theory -> xstring * xstring -> class * class
    25   val declare_overloaded: string * typ -> theory -> term * theory
    26   val define_overloaded: binding -> string * term -> theory -> thm * theory
    27   val add_classrel: thm -> theory -> theory
    28   val add_arity: thm -> theory -> theory
    29   val prove_classrel: class * class -> tactic -> theory -> theory
    30   val prove_arity: string * sort list * sort -> tactic -> theory -> theory
    31   val define_class: binding * class list -> string list ->
    32     (Thm.binding * term list) list -> theory -> class * theory
    33   val axiomatize_class: binding * class list -> theory -> theory
    34   val axiomatize_class_cmd: binding * xstring list -> theory -> theory
    35   val axiomatize_classrel: (class * class) list -> theory -> theory
    36   val axiomatize_classrel_cmd: (xstring * xstring) list -> theory -> theory
    37   val axiomatize_arity: arity -> theory -> theory
    38   val axiomatize_arity_cmd: xstring * string list * string -> theory -> theory
    39 end;
    40 
    41 structure AxClass: AX_CLASS =
    42 struct
    43 
    44 (** theory data **)
    45 
    46 (* axclass info *)
    47 
    48 type info =
    49  {def: thm,
    50   intro: thm,
    51   axioms: thm list,
    52   params: (string * typ) list};
    53 
    54 fun make_axclass (def, intro, axioms, params): info =
    55   {def = def, intro = intro, axioms = axioms, params = params};
    56 
    57 
    58 (* class parameters (canonical order) *)
    59 
    60 type param = string * class;
    61 
    62 fun add_param pp ((x, c): param) params =
    63   (case AList.lookup (op =) params x of
    64     NONE => (x, c) :: params
    65   | SOME c' => error ("Duplicate class parameter " ^ quote x ^
    66       " for " ^ Pretty.string_of_sort pp [c] ^
    67       (if c = c' then "" else " and " ^ Pretty.string_of_sort pp [c'])));
    68 
    69 
    70 (* setup data *)
    71 
    72 datatype data = Data of
    73  {axclasses: info Symtab.table,
    74   params: param list,
    75   proven_classrels: thm Symreltab.table,
    76   proven_arities: ((class * sort list) * (thm * string)) list Symtab.table,
    77     (*arity theorems with theory name*)
    78   inst_params:
    79     (string * thm) Symtab.table Symtab.table *
    80       (*constant name ~> type constructor ~> (constant name, equation)*)
    81     (string * string) Symtab.table (*constant name ~> (constant name, type constructor)*),
    82   diff_classrels: (class * class) list};
    83 
    84 fun make_data
    85     (axclasses, params, proven_classrels, proven_arities, inst_params, diff_classrels) =
    86   Data {axclasses = axclasses, params = params, proven_classrels = proven_classrels,
    87     proven_arities = proven_arities, inst_params = inst_params,
    88     diff_classrels = diff_classrels};
    89 
    90 fun diff_table tab1 tab2 =
    91   Symreltab.fold (fn (x, _) => if Symreltab.defined tab2 x then I else cons x) tab1 [];
    92 
    93 structure Data = Theory_Data_PP
    94 (
    95   type T = data;
    96   val empty =
    97     make_data (Symtab.empty, [], Symreltab.empty, Symtab.empty, (Symtab.empty, Symtab.empty), []);
    98   val extend = I;
    99   fun merge pp
   100       (Data {axclasses = axclasses1, params = params1, proven_classrels = proven_classrels1,
   101         proven_arities = proven_arities1, inst_params = inst_params1,
   102         diff_classrels = diff_classrels1},
   103        Data {axclasses = axclasses2, params = params2, proven_classrels = proven_classrels2,
   104         proven_arities = proven_arities2, inst_params = inst_params2,
   105         diff_classrels = diff_classrels2}) =
   106     let
   107       val axclasses' = Symtab.merge (K true) (axclasses1, axclasses2);
   108       val params' =
   109         if null params1 then params2
   110         else fold_rev (fn p => if member (op =) params1 p then I else add_param pp p) params2 params1;
   111 
   112       (*transitive closure of classrels and arity completion is done in Theory.at_begin hook*)
   113       val proven_classrels' = Symreltab.join (K #1) (proven_classrels1, proven_classrels2);
   114       val proven_arities' =
   115         Symtab.join (K (Library.merge (eq_fst op =))) (proven_arities1, proven_arities2);
   116 
   117       val diff_classrels' =
   118         diff_table proven_classrels1 proven_classrels2 @
   119         diff_table proven_classrels2 proven_classrels1 @
   120         diff_classrels1 @ diff_classrels2;
   121 
   122       val inst_params' =
   123         (Symtab.join (K (Symtab.merge (K true))) (#1 inst_params1, #1 inst_params2),
   124           Symtab.merge (K true) (#2 inst_params1, #2 inst_params2));
   125     in
   126       make_data
   127         (axclasses', params', proven_classrels', proven_arities', inst_params', diff_classrels')
   128     end;
   129 );
   130 
   131 fun map_data f =
   132   Data.map (fn Data {axclasses, params, proven_classrels, proven_arities, inst_params, diff_classrels} =>
   133     make_data (f (axclasses, params, proven_classrels, proven_arities, inst_params, diff_classrels)));
   134 
   135 fun map_axclasses f =
   136   map_data (fn (axclasses, params, proven_classrels, proven_arities, inst_params, diff_classrels) =>
   137     (f axclasses, params, proven_classrels, proven_arities, inst_params, diff_classrels));
   138 
   139 fun map_params f =
   140   map_data (fn (axclasses, params, proven_classrels, proven_arities, inst_params, diff_classrels) =>
   141     (axclasses, f params, proven_classrels, proven_arities, inst_params, diff_classrels));
   142 
   143 fun map_proven_classrels f =
   144   map_data (fn (axclasses, params, proven_classrels, proven_arities, inst_params, diff_classrels) =>
   145     (axclasses, params, f proven_classrels, proven_arities, inst_params, diff_classrels));
   146 
   147 fun map_proven_arities f =
   148   map_data (fn (axclasses, params, proven_classrels, proven_arities, inst_params, diff_classrels) =>
   149     (axclasses, params, proven_classrels, f proven_arities, inst_params, diff_classrels));
   150 
   151 fun map_inst_params f =
   152   map_data (fn (axclasses, params, proven_classrels, proven_arities, inst_params, diff_classrels) =>
   153     (axclasses, params, proven_classrels, proven_arities, f inst_params, diff_classrels));
   154 
   155 val clear_diff_classrels =
   156   map_data (fn (axclasses, params, proven_classrels, proven_arities, inst_params, _) =>
   157     (axclasses, params, proven_classrels, proven_arities, inst_params, []));
   158 
   159 val rep_data = Data.get #> (fn Data args => args);
   160 
   161 val axclasses_of = #axclasses o rep_data;
   162 val params_of = #params o rep_data;
   163 val proven_classrels_of = #proven_classrels o rep_data;
   164 val proven_arities_of = #proven_arities o rep_data;
   165 val inst_params_of = #inst_params o rep_data;
   166 val diff_classrels_of = #diff_classrels o rep_data;
   167 
   168 
   169 (* axclasses with parameters *)
   170 
   171 fun get_info thy c =
   172   (case Symtab.lookup (axclasses_of thy) c of
   173     SOME info => info
   174   | NONE => error ("No such axclass: " ^ quote c));
   175 
   176 fun all_params_of thy S =
   177   let val params = params_of thy;
   178   in fold (fn (x, c) => if Sign.subsort thy (S, [c]) then cons x else I) params [] end;
   179 
   180 fun class_of_param thy = AList.lookup (op =) (params_of thy);
   181 
   182 
   183 (* maintain instances *)
   184 
   185 val classrel_prefix = "classrel_";
   186 val arity_prefix = "arity_";
   187 
   188 fun instance_name (a, c) = Long_Name.base_name c ^ "_" ^ Long_Name.base_name a;
   189 
   190 
   191 infix 0 RSO;
   192 
   193 fun (SOME a) RSO (SOME b) = SOME (a RS b)
   194   | x RSO NONE = x
   195   | NONE RSO y = y;
   196 
   197 fun the_classrel thy (c1, c2) =
   198   (case Symreltab.lookup (proven_classrels_of thy) (c1, c2) of
   199     SOME thm => Thm.transfer thy thm
   200   | NONE => error ("Unproven class relation " ^
   201       Syntax.string_of_classrel (ProofContext.init thy) [c1, c2]));
   202 
   203 fun put_trancl_classrel ((c1, c2), th) thy =
   204   let
   205     val classes = Sorts.classes_of (Sign.classes_of thy);
   206     val classrels = proven_classrels_of thy;
   207 
   208     fun reflcl_classrel (c1', c2') =
   209       if c1' = c2' then NONE else SOME (the_classrel thy (c1', c2'));
   210     fun gen_classrel (c1_pred, c2_succ) =
   211       let
   212         val th' =
   213           the ((reflcl_classrel (c1_pred, c1) RSO SOME th) RSO reflcl_classrel (c2, c2_succ))
   214           |> Drule.instantiate' [SOME (ctyp_of thy (TVar ((Name.aT, 0), [])))] []
   215           |> Thm.close_derivation;
   216       in ((c1_pred, c2_succ), th') end;
   217 
   218     val new_classrels =
   219       Library.map_product pair (c1 :: Graph.imm_preds classes c1) (c2 :: Graph.imm_succs classes c2)
   220       |> filter_out ((op =) orf Symreltab.defined classrels)
   221       |> map gen_classrel;
   222     val needed = not (null new_classrels);
   223   in
   224     (needed,
   225       if needed then map_proven_classrels (fold Symreltab.update new_classrels) thy
   226       else thy)
   227   end;
   228 
   229 fun complete_classrels thy =
   230   let
   231     val classrels = proven_classrels_of thy;
   232     val diff_classrels = diff_classrels_of thy;
   233     val (needed, thy') = (false, thy) |>
   234       fold (fn rel => fn (needed, thy) =>
   235           put_trancl_classrel (rel, Symreltab.lookup classrels rel |> the) thy
   236           |>> (fn b => needed orelse b))
   237         diff_classrels;
   238   in
   239     if null diff_classrels then NONE
   240     else SOME (clear_diff_classrels thy')
   241   end;
   242 
   243 
   244 fun the_arity thy a (c, Ss) =
   245   (case AList.lookup (op =) (Symtab.lookup_list (proven_arities_of thy) a) (c, Ss) of
   246     SOME (thm, _) => Thm.transfer thy thm
   247   | NONE => error ("Unproven type arity " ^
   248       Syntax.string_of_arity (ProofContext.init thy) (a, Ss, [c])));
   249 
   250 fun thynames_of_arity thy (c, a) =
   251   Symtab.lookup_list (proven_arities_of thy) a
   252   |> map_filter (fn ((c', _), (_, name)) => if c = c' then SOME name else NONE)
   253   |> rev;
   254 
   255 fun insert_arity_completions thy t ((c, Ss), ((th, thy_name))) (finished, arities) =
   256   let
   257     val algebra = Sign.classes_of thy;
   258     val ars = Symtab.lookup_list arities t;
   259     val super_class_completions =
   260       Sign.super_classes thy c
   261       |> filter_out (fn c1 => exists (fn ((c2, Ss2), _) =>
   262             c1 = c2 andalso Sorts.sorts_le algebra (Ss2, Ss)) ars);
   263 
   264     val names = Name.invents Name.context Name.aT (length Ss);
   265     val std_vars = map (fn a => SOME (ctyp_of thy (TVar ((a, 0), [])))) names;
   266 
   267     val completions = super_class_completions |> map (fn c1 =>
   268       let
   269         val th1 =
   270           (th RS the_classrel thy (c, c1))
   271           |> Drule.instantiate' std_vars []
   272           |> Thm.close_derivation;
   273       in ((th1, thy_name), c1) end);
   274 
   275     val finished' = finished andalso null completions;
   276     val arities' = fold (fn (th, c1) => Symtab.cons_list (t, ((c1, Ss), th))) completions arities;
   277   in (finished', arities') end;
   278 
   279 fun put_arity ((t, Ss, c), th) thy =
   280   let val ar = ((c, Ss), (th, Context.theory_name thy)) in
   281     thy
   282     |> map_proven_arities
   283       (Symtab.insert_list (eq_fst op =) (t, ar) #>
   284        curry (insert_arity_completions thy t ar) true #> #2)
   285   end;
   286 
   287 fun complete_arities thy =
   288   let
   289     val arities = proven_arities_of thy;
   290     val (finished, arities') =
   291       Symtab.fold (fn (t, ars) => fold (insert_arity_completions thy t) ars) arities (true, arities);
   292   in
   293     if finished then NONE
   294     else SOME (map_proven_arities (K arities') thy)
   295   end;
   296 
   297 val _ = Context.>> (Context.map_theory
   298   (Theory.at_begin complete_classrels #> Theory.at_begin complete_arities));
   299 
   300 val the_classrel_prf = Thm.proof_of oo the_classrel;
   301 val the_arity_prf = Thm.proof_of ooo the_arity;
   302 
   303 
   304 (* maintain instance parameters *)
   305 
   306 fun get_inst_param thy (c, tyco) =
   307   (case Symtab.lookup (the_default Symtab.empty (Symtab.lookup (#1 (inst_params_of thy)) c)) tyco of
   308     SOME c' => c'
   309   | NONE => error ("No instance parameter for constant " ^ quote c ^ " on type " ^ quote tyco));
   310 
   311 fun add_inst_param (c, tyco) inst =
   312   (map_inst_params o apfst o Symtab.map_default (c, Symtab.empty)) (Symtab.update_new (tyco, inst))
   313   #> (map_inst_params o apsnd) (Symtab.update_new (#1 inst, (c, tyco)));
   314 
   315 val inst_of_param = Symtab.lookup o #2 o inst_params_of;
   316 val param_of_inst = #1 oo get_inst_param;
   317 
   318 fun inst_thms thy =
   319   Symtab.fold (Symtab.fold (cons o #2 o #2) o #2) (#1 (inst_params_of thy)) [];
   320 
   321 fun get_inst_tyco consts = try (#1 o dest_Type o the_single o Consts.typargs consts);
   322 
   323 fun unoverload thy = MetaSimplifier.simplify true (inst_thms thy);
   324 fun overload thy = MetaSimplifier.simplify true (map Thm.symmetric (inst_thms thy));
   325 
   326 fun unoverload_conv thy = MetaSimplifier.rewrite true (inst_thms thy);
   327 fun overload_conv thy = MetaSimplifier.rewrite true (map Thm.symmetric (inst_thms thy));
   328 
   329 fun lookup_inst_param consts params (c, T) =
   330   (case get_inst_tyco consts (c, T) of
   331     SOME tyco => AList.lookup (op =) params (c, tyco)
   332   | NONE => NONE);
   333 
   334 fun unoverload_const thy (c_ty as (c, _)) =
   335   if is_some (class_of_param thy c) then
   336     (case get_inst_tyco (Sign.consts_of thy) c_ty of
   337       SOME tyco => try (param_of_inst thy) (c, tyco) |> the_default c
   338     | NONE => c)
   339   else c;
   340 
   341 
   342 
   343 (** instances **)
   344 
   345 (* class relations *)
   346 
   347 fun cert_classrel thy raw_rel =
   348   let
   349     val string_of_sort = Syntax.string_of_sort_global thy;
   350     val (c1, c2) = pairself (Sign.certify_class thy) raw_rel;
   351     val _ = Sign.primitive_classrel (c1, c2) (Theory.copy thy);
   352     val _ =
   353       (case subtract (op =) (all_params_of thy [c1]) (all_params_of thy [c2]) of
   354         [] => ()
   355       | xs => raise TYPE ("Class " ^ string_of_sort [c1] ^ " lacks parameter(s) " ^
   356           commas_quote xs ^ " of " ^ string_of_sort [c2], [], []));
   357   in (c1, c2) end;
   358 
   359 fun read_classrel thy raw_rel =
   360   cert_classrel thy (pairself (ProofContext.read_class (ProofContext.init thy)) raw_rel)
   361     handle TYPE (msg, _, _) => error msg;
   362 
   363 
   364 (* declaration and definition of instances of overloaded constants *)
   365 
   366 fun inst_tyco_of thy (c, T) =
   367   (case get_inst_tyco (Sign.consts_of thy) (c, T) of
   368     SOME tyco => tyco
   369   | NONE => error ("Illegal type for instantiation of class parameter: " ^
   370       quote (c ^ " :: " ^ Syntax.string_of_typ_global thy T)));
   371 
   372 fun declare_overloaded (c, T) thy =
   373   let
   374     val class =
   375       (case class_of_param thy c of
   376         SOME class => class
   377       | NONE => error ("Not a class parameter: " ^ quote c));
   378     val tyco = inst_tyco_of thy (c, T);
   379     val name_inst = instance_name (tyco, class) ^ "_inst";
   380     val c' = instance_name (tyco, c);
   381     val T' = Type.strip_sorts T;
   382   in
   383     thy
   384     |> Sign.qualified_path true (Binding.name name_inst)
   385     |> Sign.declare_const ((Binding.name c', T'), NoSyn)
   386     |-> (fn const' as Const (c'', _) =>
   387       Thm.add_def false true
   388         (Binding.name (Thm.def_name c'), Logic.mk_equals (Const (c, T'), const'))
   389       #>> apsnd Thm.varifyT_global
   390       #-> (fn (_, thm) => add_inst_param (c, tyco) (c'', thm)
   391         #> PureThy.add_thm ((Binding.conceal (Binding.name c'), thm), [])
   392         #> #2
   393         #> pair (Const (c, T))))
   394     ||> Sign.restore_naming thy
   395   end;
   396 
   397 fun define_overloaded b (c, t) thy =
   398   let
   399     val T = Term.fastype_of t;
   400     val tyco = inst_tyco_of thy (c, T);
   401     val (c', eq) = get_inst_param thy (c, tyco);
   402     val prop = Logic.mk_equals (Const (c', T), t);
   403     val b' = Thm.def_binding_optional (Binding.name (instance_name (tyco, c))) b;
   404   in
   405     thy
   406     |> Thm.add_def false false (b', prop)
   407     |>> (fn (_, thm) =>  Drule.transitive_thm OF [eq, thm])
   408   end;
   409 
   410 
   411 (* primitive rules *)
   412 
   413 val shyps_topped = forall null o #shyps o Thm.rep_thm;
   414 
   415 fun add_classrel raw_th thy =
   416   let
   417     val th = Thm.strip_shyps (Thm.transfer thy raw_th);
   418     val prop = Thm.plain_prop_of th;
   419     fun err () = raise THM ("add_classrel: malformed class relation", 0, [th]);
   420     val rel = Logic.dest_classrel prop handle TERM _ => err ();
   421     val (c1, c2) = cert_classrel thy rel handle TYPE _ => err ();
   422     val th' = th
   423       |> Drule.instantiate' [SOME (ctyp_of thy (TVar ((Name.aT, 0), [c1])))] []
   424       |> Thm.unconstrain_allTs;
   425     val _ = shyps_topped th' orelse raise Fail "add_classrel: nontop shyps after unconstrain";
   426   in
   427     thy
   428     |> Sign.primitive_classrel (c1, c2)
   429     |> (#2 oo put_trancl_classrel) ((c1, c2), th')
   430     |> perhaps complete_arities
   431   end;
   432 
   433 fun add_arity raw_th thy =
   434   let
   435     val th = Thm.strip_shyps (Thm.transfer thy raw_th);
   436     val prop = Thm.plain_prop_of th;
   437     fun err () = raise THM ("add_arity: malformed type arity", 0, [th]);
   438     val (t, Ss, c) = Logic.dest_arity prop handle TERM _ => err ();
   439 
   440     val args = Name.names Name.context Name.aT Ss;
   441     val T = Type (t, map TFree args);
   442     val std_vars = map (fn (a, S) => SOME (ctyp_of thy (TVar ((a, 0), S)))) args;
   443 
   444     val missing_params = Sign.complete_sort thy [c]
   445       |> maps (these o Option.map #params o try (get_info thy))
   446       |> filter_out (fn (const, _) => can (get_inst_param thy) (const, t))
   447       |> (map o apsnd o map_atyps) (K T);
   448     val th' = th
   449       |> Drule.instantiate' std_vars []
   450       |> Thm.unconstrain_allTs;
   451     val _ = shyps_topped th' orelse raise Fail "add_arity: nontop shyps after unconstrain";
   452   in
   453     thy
   454     |> fold (#2 oo declare_overloaded) missing_params
   455     |> Sign.primitive_arity (t, Ss, [c])
   456     |> put_arity ((t, Ss, c), th')
   457   end;
   458 
   459 
   460 (* tactical proofs *)
   461 
   462 fun prove_classrel raw_rel tac thy =
   463   let
   464     val ctxt = ProofContext.init thy;
   465     val (c1, c2) = cert_classrel thy raw_rel;
   466     val th = Goal.prove ctxt [] [] (Logic.mk_classrel (c1, c2)) (K tac) handle ERROR msg =>
   467       cat_error msg ("The error(s) above occurred while trying to prove class relation " ^
   468         quote (Syntax.string_of_classrel ctxt [c1, c2]));
   469   in
   470     thy
   471     |> PureThy.add_thms [((Binding.name
   472         (prefix classrel_prefix (Logic.name_classrel (c1, c2))), th), [])]
   473     |-> (fn [th'] => add_classrel th')
   474   end;
   475 
   476 fun prove_arity raw_arity tac thy =
   477   let
   478     val ctxt = ProofContext.init thy;
   479     val arity = ProofContext.cert_arity ctxt raw_arity;
   480     val names = map (prefix arity_prefix) (Logic.name_arities arity);
   481     val props = Logic.mk_arities arity;
   482     val ths = Goal.prove_multi ctxt [] [] props
   483       (fn _ => Goal.precise_conjunction_tac (length props) 1 THEN tac) handle ERROR msg =>
   484         cat_error msg ("The error(s) above occurred while trying to prove type arity " ^
   485           quote (Syntax.string_of_arity ctxt arity));
   486   in
   487     thy
   488     |> PureThy.add_thms (map (rpair []) (map Binding.name names ~~ ths))
   489     |-> fold add_arity
   490   end;
   491 
   492 
   493 
   494 (** class definitions **)
   495 
   496 fun split_defined n eq =
   497   let
   498     val intro =
   499       (eq RS Drule.equal_elim_rule2)
   500       |> Conjunction.curry_balanced n
   501       |> n = 0 ? Thm.eq_assumption 1;
   502     val dests =
   503       if n = 0 then []
   504       else
   505         (eq RS Drule.equal_elim_rule1)
   506         |> Balanced_Tree.dest (fn th =>
   507           (th RS Conjunction.conjunctionD1, th RS Conjunction.conjunctionD2)) n;
   508   in (intro, dests) end;
   509 
   510 fun define_class (bclass, raw_super) raw_params raw_specs thy =
   511   let
   512     val ctxt = ProofContext.init thy;
   513     val pp = Syntax.pp ctxt;
   514 
   515 
   516     (* class *)
   517 
   518     val bconst = Binding.map_name Logic.const_of_class bclass;
   519     val class = Sign.full_name thy bclass;
   520     val super = Sign.minimize_sort thy (Sign.certify_sort thy raw_super);
   521 
   522     fun check_constraint (a, S) =
   523       if Sign.subsort thy (super, S) then ()
   524       else error ("Sort constraint of type variable " ^
   525         setmp_CRITICAL show_sorts true (Pretty.string_of_typ pp) (TFree (a, S)) ^
   526         " needs to be weaker than " ^ Pretty.string_of_sort pp super);
   527 
   528 
   529     (* params *)
   530 
   531     val params = raw_params |> map (fn p =>
   532       let
   533         val T = Sign.the_const_type thy p;
   534         val _ =
   535           (case Term.add_tvarsT T [] of
   536             [((a, _), S)] => check_constraint (a, S)
   537           | _ => error ("Exactly one type variable expected in class parameter " ^ quote p));
   538         val T' = Term.map_type_tvar (fn _ => TFree (Name.aT, [class])) T;
   539       in (p, T') end);
   540 
   541 
   542     (* axioms *)
   543 
   544     fun prep_axiom t =
   545       (case Term.add_tfrees t [] of
   546         [(a, S)] => check_constraint (a, S)
   547       | [] => ()
   548       | _ => error ("Multiple type variables in class axiom:\n" ^ Pretty.string_of_term pp t);
   549       t
   550       |> Term.map_types (Term.map_atyps (fn TFree _ => Term.aT [] | U => U))
   551       |> Logic.close_form);
   552 
   553     val axiomss = map (map (prep_axiom o Sign.cert_prop thy) o snd) raw_specs;
   554     val name_atts = map fst raw_specs;
   555 
   556 
   557     (* definition *)
   558 
   559     val conjs = Logic.mk_of_sort (Term.aT [], super) @ flat axiomss;
   560     val class_eq =
   561       Logic.mk_equals (Logic.mk_of_class (Term.aT [], class), Logic.mk_conjunction_balanced conjs);
   562 
   563     val ([def], def_thy) =
   564       thy
   565       |> Sign.primitive_class (bclass, super)
   566       |> PureThy.add_defs false [((Thm.def_binding bconst, class_eq), [])];
   567     val (raw_intro, (raw_classrel, raw_axioms)) =
   568       split_defined (length conjs) def ||> chop (length super);
   569 
   570 
   571     (* facts *)
   572 
   573     val class_triv = Thm.class_triv def_thy class;
   574     val ([(_, [intro]), (_, classrel), (_, axioms)], facts_thy) =
   575       def_thy
   576       |> Sign.qualified_path true bconst
   577       |> PureThy.note_thmss ""
   578         [((Binding.name "intro", []), [([Drule.export_without_context raw_intro], [])]),
   579          ((Binding.name "super", []), [(map Drule.export_without_context raw_classrel, [])]),
   580          ((Binding.name "axioms", []),
   581            [(map (fn th => Drule.export_without_context (class_triv RS th)) raw_axioms, [])])]
   582       ||> Sign.restore_naming def_thy;
   583 
   584 
   585     (* result *)
   586 
   587     val axclass = make_axclass (def, intro, axioms, params);
   588     val result_thy =
   589       facts_thy
   590       |> fold (#2 oo put_trancl_classrel) (map (pair class) super ~~ classrel)
   591       |> Sign.qualified_path false bconst
   592       |> PureThy.note_thmss "" (name_atts ~~ map Thm.simple_fact (unflat axiomss axioms)) |> #2
   593       |> Sign.restore_naming facts_thy
   594       |> map_axclasses (Symtab.update (class, axclass))
   595       |> map_params (fold (fn (x, _) => add_param pp (x, class)) params);
   596 
   597   in (class, result_thy) end;
   598 
   599 
   600 
   601 (** axiomatizations **)
   602 
   603 local
   604 
   605 (*old-style axioms*)
   606 fun add_axiom (b, prop) =
   607   Thm.add_axiom (b, prop) #->
   608   (fn (_, thm) => PureThy.add_thm ((b, Drule.export_without_context thm), []));
   609 
   610 fun axiomatize prep mk name add raw_args thy =
   611   let
   612     val args = prep thy raw_args;
   613     val specs = mk args;
   614     val names = name args;
   615   in
   616     thy
   617     |> fold_map add_axiom (map Binding.name names ~~ specs)
   618     |-> fold add
   619   end;
   620 
   621 fun ax_classrel prep =
   622   axiomatize (map o prep) (map Logic.mk_classrel)
   623     (map (prefix classrel_prefix o Logic.name_classrel)) add_classrel;
   624 
   625 fun ax_arity prep =
   626   axiomatize (prep o ProofContext.init) Logic.mk_arities
   627     (map (prefix arity_prefix) o Logic.name_arities) add_arity;
   628 
   629 fun class_const c =
   630   (Logic.const_of_class c, Term.itselfT (Term.aT []) --> propT);
   631 
   632 fun ax_class prep_class prep_classrel (bclass, raw_super) thy =
   633   let
   634     val class = Sign.full_name thy bclass;
   635     val super = map (prep_class thy) raw_super |> Sign.minimize_sort thy;
   636   in
   637     thy
   638     |> Sign.primitive_class (bclass, super)
   639     |> ax_classrel prep_classrel (map (fn c => (class, c)) super)
   640     |> Theory.add_deps "" (class_const class) (map class_const super)
   641   end;
   642 
   643 in
   644 
   645 val axiomatize_class = ax_class Sign.certify_class cert_classrel;
   646 val axiomatize_class_cmd = ax_class (ProofContext.read_class o ProofContext.init) read_classrel;
   647 val axiomatize_classrel = ax_classrel cert_classrel;
   648 val axiomatize_classrel_cmd = ax_classrel read_classrel;
   649 val axiomatize_arity = ax_arity ProofContext.cert_arity;
   650 val axiomatize_arity_cmd = ax_arity ProofContext.read_arity;
   651 
   652 end;
   653 
   654 end;