src/Pure/axclass.ML
author berghofe
Mon Jan 24 17:59:48 2005 +0100 (2005-01-24 ago)
changeset 15457 1fbd4aba46e3
parent 14981 e73f8140af78
child 15531 08c8dad8e399
permissions -rw-r--r--
Adapted to modified interface of PureThy.get_thm(s).
     1 (*  Title:      Pure/axclass.ML
     2     ID:         $Id$
     3     Author:     Markus Wenzel, TU Muenchen
     4 
     5 Axiomatic type class package.
     6 *)
     7 
     8 signature AX_CLASS =
     9 sig
    10   val quiet_mode: bool ref
    11   val print_axclasses: theory -> unit
    12   val add_classrel_thms: thm list -> theory -> theory
    13   val add_arity_thms: thm list -> theory -> theory
    14   val add_axclass: bclass * xclass list -> ((bstring * string) * Args.src list) list
    15     -> theory -> theory * {intro: thm, axioms: thm list}
    16   val add_axclass_i: bclass * class list -> ((bstring * term) * theory attribute list) list
    17     -> theory -> theory * {intro: thm, axioms: thm list}
    18   val add_inst_subclass_x: xclass * xclass -> string list -> thm list
    19     -> tactic option -> theory -> theory
    20   val add_inst_subclass: xclass * xclass -> tactic -> theory -> theory
    21   val add_inst_subclass_i: class * class -> tactic -> theory -> theory
    22   val add_inst_arity_x: xstring * string list * string -> string list
    23     -> thm list -> tactic option -> theory -> theory
    24   val add_inst_arity: xstring * string list * string -> tactic -> theory -> theory
    25   val add_inst_arity_i: string * sort list * sort -> tactic -> theory -> theory
    26   val default_intro_classes_tac: thm list -> tactic
    27   val axclass_tac: thm list -> tactic
    28   val instance_subclass_proof: xclass * xclass -> bool -> theory -> ProofHistory.T
    29   val instance_subclass_proof_i: class * class -> bool -> theory -> ProofHistory.T
    30   val instance_arity_proof: xstring * string list * string -> bool -> theory -> ProofHistory.T
    31   val instance_arity_proof_i: string * sort list * sort -> bool -> theory -> ProofHistory.T
    32   val setup: (theory -> theory) list
    33 end;
    34 
    35 structure AxClass : AX_CLASS =
    36 struct
    37 
    38 
    39 (** utilities **)
    40 
    41 (* messages *)
    42 
    43 val quiet_mode = ref false;
    44 fun message s = if ! quiet_mode then () else writeln s;
    45 
    46 
    47 (* type vars *)
    48 
    49 fun map_typ_frees f (Type (t, tys)) = Type (t, map (map_typ_frees f) tys)
    50   | map_typ_frees f (TFree a) = f a
    51   | map_typ_frees _ a = a;
    52 
    53 val map_term_tfrees = map_term_types o map_typ_frees;
    54 
    55 fun aT S = TFree ("'a", S);
    56 
    57 fun dest_varT (TFree (x, S)) = ((x, ~1), S)
    58   | dest_varT (TVar xi_S) = xi_S
    59   | dest_varT T = raise TYPE ("dest_varT", [T], []);
    60 
    61 
    62 (* get axioms and theorems *)
    63 
    64 val is_def = Logic.is_equals o #prop o rep_thm;
    65 
    66 fun witnesses thy names thms =
    67   PureThy.get_thmss thy (map (rpair None) names) @ thms @ filter is_def (map snd (axioms_of thy));
    68 
    69 
    70 
    71 (** abstract syntax operations **)
    72 
    73 (* names *)
    74 
    75 fun intro_name c = c ^ "I";
    76 val introN = "intro";
    77 val axiomsN = "axioms";
    78 
    79 
    80 (* subclass relations as terms *)
    81 
    82 fun mk_classrel (c1, c2) = Logic.mk_inclass (aT [c1], c2);
    83 
    84 fun dest_classrel tm =
    85   let
    86     fun err () = raise TERM ("dest_classrel", [tm]);
    87 
    88     val (ty, c2) = Logic.dest_inclass tm handle TERM _ => err ();
    89     val c1 = (case dest_varT ty of (_, [c]) => c | _ => err ())
    90       handle TYPE _ => err ();
    91   in (c1, c2) end;
    92 
    93 
    94 (* arities as terms *)
    95 
    96 fun mk_arity (t, Ss, c) =
    97   let
    98     val tfrees = ListPair.map TFree (Term.invent_names [] "'a" (length Ss), Ss);
    99   in Logic.mk_inclass (Type (t, tfrees), c) end;
   100 
   101 fun mk_arities (t, Ss, S) = map (fn c => mk_arity (t, Ss, c)) S;
   102 
   103 fun dest_arity tm =
   104   let
   105     fun err () = raise TERM ("dest_arity", [tm]);
   106 
   107     val (ty, c) = Logic.dest_inclass tm handle TERM _ => err ();
   108     val (t, tvars) =
   109       (case ty of
   110         Type (t, tys) => (t, map dest_varT tys handle TYPE _ => err ())
   111       | _ => err ());
   112     val ss =
   113       if null (gen_duplicates eq_fst tvars)
   114       then map snd tvars else err ();
   115   in (t, ss, c) end;
   116 
   117 
   118 
   119 (** add theorems as axioms **)
   120 
   121 fun prep_thm_axm thy thm =
   122   let
   123     fun err msg = raise THM ("prep_thm_axm: " ^ msg, 0, [thm]);
   124 
   125     val {sign, hyps, prop, ...} = rep_thm thm;
   126   in
   127     if not (Sign.subsig (sign, Theory.sign_of thy)) then
   128       err "theorem not of same theory"
   129     else if not (null (extra_shyps thm)) orelse not (null hyps) then
   130       err "theorem may not contain hypotheses"
   131     else prop
   132   end;
   133 
   134 (*theorems expressing class relations*)
   135 fun add_classrel_thms thms thy =
   136   let
   137     fun prep_thm thm =
   138       let
   139         val prop = prep_thm_axm thy thm;
   140         val (c1, c2) = dest_classrel prop handle TERM _ =>
   141           raise THM ("add_classrel_thms: theorem is not a class relation", 0, [thm]);
   142       in (c1, c2) end;
   143   in Theory.add_classrel_i (map prep_thm thms) thy end;
   144 
   145 (*theorems expressing arities*)
   146 fun add_arity_thms thms thy =
   147   let
   148     fun prep_thm thm =
   149       let
   150         val prop = prep_thm_axm thy thm;
   151         val (t, ss, c) = dest_arity prop handle TERM _ =>
   152           raise THM ("add_arity_thms: theorem is not an arity", 0, [thm]);
   153       in (t, ss, [c]) end;
   154   in Theory.add_arities_i (map prep_thm thms) thy end;
   155 
   156 
   157 
   158 (** axclass info **)
   159 
   160 (* data kind 'Pure/axclasses' *)
   161 
   162 type axclass_info =
   163   {super_classes: class list,
   164     intro: thm,
   165     axioms: thm list};
   166 
   167 structure AxclassesArgs =
   168 struct
   169   val name = "Pure/axclasses";
   170   type T = axclass_info Symtab.table;
   171 
   172   val empty = Symtab.empty;
   173   val copy = I;
   174   val prep_ext = I;
   175   fun merge (tab1, tab2) = Symtab.merge (K true) (tab1, tab2);
   176 
   177   fun print sg tab =
   178     let
   179       val ext_class = Sign.cond_extern sg Sign.classK;
   180       val ext_thm = PureThy.cond_extern_thm_sg sg;
   181 
   182       fun pretty_class c cs = Pretty.block
   183         (Pretty.str (ext_class c) :: Pretty.str " <" :: Pretty.brk 1 ::
   184           Pretty.breaks (map (Pretty.str o ext_class) cs));
   185 
   186       fun pretty_thms name thms = Pretty.big_list (name ^ ":")
   187         (map (Display.pretty_thm_sg sg) thms);
   188 
   189       fun pretty_axclass (name, {super_classes, intro, axioms}) = Pretty.block (Pretty.fbreaks
   190         [pretty_class name super_classes, pretty_thms introN [intro], pretty_thms axiomsN axioms]);
   191     in Pretty.writeln (Pretty.chunks (map pretty_axclass (Symtab.dest tab))) end;
   192 end;
   193 
   194 structure AxclassesData = TheoryDataFun(AxclassesArgs);
   195 val print_axclasses = AxclassesData.print;
   196 
   197 
   198 (* get and put data *)
   199 
   200 fun lookup_axclass_info_sg sg c = Symtab.lookup (AxclassesData.get_sg sg, c);
   201 
   202 fun get_axclass_info thy c =
   203   (case lookup_axclass_info_sg (Theory.sign_of thy) c of
   204     None => error ("Unknown axclass " ^ quote c)
   205   | Some info => info);
   206 
   207 fun put_axclass_info c info thy =
   208   thy |> AxclassesData.put (Symtab.update ((c, info), AxclassesData.get thy));
   209 
   210 
   211 
   212 (** add axiomatic type classes **)
   213 
   214 (* errors *)
   215 
   216 fun err_bad_axsort ax c =
   217   error ("Sort constraint in axiom " ^ quote ax ^ " not supersort of " ^ quote c);
   218 
   219 fun err_bad_tfrees ax =
   220   error ("More than one type variable in axiom " ^ quote ax);
   221 
   222 
   223 (* ext_axclass *)
   224 
   225 fun ext_axclass prep_class prep_axm prep_att (bclass, raw_super_classes) raw_axioms_atts thy =
   226   let
   227     val sign = Theory.sign_of thy;
   228 
   229     val class = Sign.full_name sign bclass;
   230     val super_classes = map (prep_class sign) raw_super_classes;
   231     val axms = map (prep_axm sign o fst) raw_axioms_atts;
   232     val atts = map (map (prep_att thy) o snd) raw_axioms_atts;
   233 
   234     (*declare class*)
   235     val class_thy =
   236       thy |> Theory.add_classes_i [(bclass, super_classes)];
   237     val class_sign = Theory.sign_of class_thy;
   238 
   239     (*prepare abstract axioms*)
   240     fun abs_axm ax =
   241       if null (term_tfrees ax) then
   242         Logic.mk_implies (Logic.mk_inclass (aT [], class), ax)
   243       else map_term_tfrees (K (aT [class])) ax;
   244     val abs_axms = map (abs_axm o #2) axms;
   245 
   246     fun axm_sort (name, ax) =
   247       (case term_tfrees ax of
   248         [] => []
   249       | [(_, S)] => if Sign.subsort class_sign ([class], S) then S else err_bad_axsort name class
   250       | _ => err_bad_tfrees name);
   251     val axS = Sign.certify_sort class_sign (flat (map axm_sort axms));
   252 
   253     val int_axm = Logic.close_form o map_term_tfrees (K (aT axS));
   254     fun inclass c = Logic.mk_inclass (aT axS, c);
   255 
   256     val intro_axm = Logic.list_implies
   257       (map inclass super_classes @ map (int_axm o #2) axms, inclass class);
   258 
   259     (*declare axioms and rule*)
   260     val (axms_thy, ([intro], [axioms])) =
   261       class_thy
   262       |> Theory.add_path bclass
   263       |> PureThy.add_axioms_i [Thm.no_attributes (introN, intro_axm)]
   264       |>>> PureThy.add_axiomss_i [Thm.no_attributes (axiomsN, abs_axms)];
   265     val info = {super_classes = super_classes, intro = intro, axioms = axioms};
   266 
   267     (*store info*)
   268     val final_thy =
   269       axms_thy
   270       |> (#1 o PureThy.add_thms ((map #1 axms ~~ axioms) ~~ atts))
   271       |> Theory.parent_path
   272       |> (#1 o PureThy.add_thms [Thm.no_attributes (intro_name bclass, intro)])
   273       |> put_axclass_info class info;
   274   in (final_thy, {intro = intro, axioms = axioms}) end;
   275 
   276 
   277 (* external interfaces *)
   278 
   279 val add_axclass = ext_axclass Sign.intern_class Theory.read_axm Attrib.global_attribute;
   280 val add_axclass_i = ext_axclass (K I) Theory.cert_axm (K I);
   281 
   282 
   283 
   284 (** prove class relations and type arities **)
   285 
   286 (* class_axms *)
   287 
   288 fun class_axms sign =
   289   let val classes = Sign.classes sign in
   290     map (Thm.class_triv sign) classes @
   291     mapfilter (apsome #intro o lookup_axclass_info_sg sign) classes
   292   end;
   293 
   294 
   295 (* intro_classes *)
   296 
   297 fun intro_classes_tac facts st =
   298   (ALLGOALS (Method.insert_tac facts THEN'
   299       REPEAT_ALL_NEW (resolve_tac (class_axms (Thm.sign_of_thm st))))
   300     THEN Tactic.distinct_subgoals_tac) st;
   301 
   302 val intro_classes_method =
   303   ("intro_classes", Method.no_args (Method.METHOD intro_classes_tac),
   304     "back-chain introduction rules of axiomatic type classes");
   305 
   306 
   307 (* default method *)
   308 
   309 fun default_intro_classes_tac [] = intro_classes_tac []
   310   | default_intro_classes_tac _ = Tactical.no_tac;    (*no error message!*)
   311 
   312 fun default_tac rules ctxt facts =
   313   HEADGOAL (Method.some_rule_tac rules ctxt facts) ORELSE
   314     default_intro_classes_tac facts;
   315 
   316 val default_method =
   317   ("default", Method.thms_ctxt_args (Method.METHOD oo default_tac), "apply some intro/elim rule");
   318 
   319 
   320 (* old-style axclass_tac *)
   321 
   322 (*(1) repeatedly resolve goals of form "OFCLASS(ty, c_class)",
   323       try class_trivs first, then "cI" axioms
   324   (2) rewrite goals using user supplied definitions
   325   (3) repeatedly resolve goals with user supplied non-definitions*)
   326 
   327 fun axclass_tac thms =
   328   let
   329     val defs = filter is_def thms;
   330     val non_defs = filter_out is_def thms;
   331   in
   332     intro_classes_tac [] THEN
   333     TRY (rewrite_goals_tac defs) THEN
   334     TRY (REPEAT_FIRST (fn i => assume_tac i ORELSE resolve_tac non_defs i))
   335   end;
   336 
   337 
   338 (* old-style provers *)
   339 
   340 fun prove mk_prop str_of sign prop thms usr_tac =
   341   (Tactic.prove sign [] [] (mk_prop prop) (K (axclass_tac thms THEN (if_none usr_tac all_tac)))
   342     handle ERROR => error ("The error(s) above occurred while trying to prove " ^
   343      quote (str_of sign prop))) |> Drule.standard;
   344 
   345 val prove_subclass = prove mk_classrel (fn sg => fn (c1, c2) =>
   346   Pretty.string_of_classrel (Sign.pp sg) [c1, c2]);
   347 
   348 val prove_arity = prove mk_arity (fn sg => fn (t, Ss, c) =>
   349   Pretty.string_of_arity (Sign.pp sg) (t, Ss, [c]));
   350 
   351 
   352 
   353 (** add proved subclass relations and arities **)
   354 
   355 (* prepare classes and arities *)
   356 
   357 fun read_class sg c = Sign.certify_class sg (Sign.intern_class sg c);
   358 
   359 fun test_classrel sg cc = (Type.add_classrel (Sign.pp sg) [cc] (Sign.tsig_of sg); cc);
   360 fun cert_classrel sg = test_classrel sg o Library.pairself (Sign.certify_class sg);
   361 fun read_classrel sg = test_classrel sg o Library.pairself (read_class sg);
   362 
   363 fun test_arity sg ar = (Type.add_arities (Sign.pp sg) [ar] (Sign.tsig_of sg); ar);
   364 
   365 fun prep_arity prep_tycon prep_sort prep_x sg (t, Ss, x) =
   366   test_arity sg (prep_tycon sg t, map (prep_sort sg) Ss, prep_x sg x);
   367 
   368 val read_arity = prep_arity Sign.intern_tycon Sign.read_sort Sign.read_sort;
   369 val cert_arity = prep_arity (K I) Sign.certify_sort Sign.certify_sort;
   370 
   371 
   372 (* old-style instance declarations *)
   373 
   374 fun ext_inst_subclass prep_classrel raw_c1_c2 names thms usr_tac thy =
   375   let
   376     val sign = Theory.sign_of thy;
   377     val (c1, c2) = prep_classrel sign raw_c1_c2;
   378   in
   379     message ("Proving class inclusion " ^ quote (Sign.string_of_classrel sign [c1, c2]) ^ " ...");
   380     thy |> add_classrel_thms [prove_subclass sign (c1, c2) (witnesses thy names thms) usr_tac]
   381   end;
   382 
   383 fun ext_inst_arity prep_arity (raw_t, raw_Ss, raw_cs) names thms usr_tac thy =
   384   let
   385     val sign = Theory.sign_of thy;
   386     val (t, Ss, cs) = prep_arity sign (raw_t, raw_Ss, raw_cs);
   387     val wthms = witnesses thy names thms;
   388     fun prove c =
   389      (message ("Proving type arity " ^
   390         quote (Sign.string_of_arity sign (t, Ss, [c])) ^ " ...");
   391         prove_arity sign (t, Ss, c) wthms usr_tac);
   392   in add_arity_thms (map prove cs) thy end;
   393 
   394 fun sane_inst_subclass prep sub tac = ext_inst_subclass prep sub [] [] (Some tac);
   395 fun sane_inst_arity prep arity tac = ext_inst_arity prep arity [] [] (Some tac);
   396 
   397 val add_inst_subclass_x = ext_inst_subclass read_classrel;
   398 val add_inst_subclass = sane_inst_subclass read_classrel;
   399 val add_inst_subclass_i = sane_inst_subclass cert_classrel;
   400 val add_inst_arity_x = ext_inst_arity read_arity;
   401 val add_inst_arity = sane_inst_arity read_arity;
   402 val add_inst_arity_i = sane_inst_arity cert_arity;
   403 
   404 
   405 
   406 (** instance proof interfaces **)
   407 
   408 fun inst_proof mk_prop add_thms inst int theory =
   409   theory
   410   |> IsarThy.multi_theorem_i Drule.internalK
   411     ("", [fn (thy, th) => (add_thms [th] thy, th)]) []
   412     (map (fn t => (("", []), [(t, ([], []))])) (mk_prop (Theory.sign_of theory) inst)) int;
   413 
   414 val instance_subclass_proof =
   415   inst_proof (single oo (mk_classrel oo read_classrel)) add_classrel_thms;
   416 val instance_subclass_proof_i =
   417   inst_proof (single oo (mk_classrel oo cert_classrel)) add_classrel_thms;
   418 val instance_arity_proof = inst_proof (mk_arities oo read_arity) add_arity_thms;
   419 val instance_arity_proof_i = inst_proof (mk_arities oo cert_arity) add_arity_thms;
   420 
   421 
   422 
   423 (** package setup **)
   424 
   425 (* setup theory *)
   426 
   427 val setup =
   428  [AxclassesData.init,
   429   Method.add_methods [intro_classes_method, default_method]];
   430 
   431 
   432 (* outer syntax *)
   433 
   434 local structure P = OuterParse and K = OuterSyntax.Keyword in
   435 
   436 val axclassP =
   437   OuterSyntax.command "axclass" "define axiomatic type class" K.thy_decl
   438     ((P.name -- Scan.optional ((P.$$$ "\\<subseteq>" || P.$$$ "<") |--
   439         P.!!! (P.list1 P.xname)) []) -- Scan.repeat P.spec_name
   440       >> (fn (cls, axs) => Toplevel.theory (#1 o add_axclass cls axs)));
   441 
   442 val instanceP =
   443   OuterSyntax.command "instance" "prove type arity or subclass relation" K.thy_goal
   444     ((P.xname -- ((P.$$$ "\\<subseteq>" || P.$$$ "<") |-- P.xname) >> instance_subclass_proof ||
   445       (P.xname -- (P.$$$ "::" |-- P.arity) >> P.triple2) >> instance_arity_proof)
   446       >> (Toplevel.print oo Toplevel.theory_to_proof));
   447 
   448 val _ = OuterSyntax.add_parsers [axclassP, instanceP];
   449 
   450 end;
   451 
   452 end;