src/Pure/axclass.ML
author wenzelm
Tue Feb 12 20:28:27 2002 +0100 (2002-02-12 ago)
changeset 12876 a70df1e5bf10
parent 12694 9950c1ce9d24
child 14605 9de4d64eee3b
permissions -rw-r--r--
got rid of explicit marginal comments (now stripped earlier from input);
     1 (*  Title:      Pure/axclass.ML
     2     ID:         $Id$
     3     Author:     Markus Wenzel, TU Muenchen
     4     License:    GPL (GNU GENERAL PUBLIC LICENSE)
     5 
     6 Axiomatic type class package.
     7 *)
     8 
     9 signature AX_CLASS =
    10 sig
    11   val quiet_mode: bool ref
    12   val print_axclasses: theory -> unit
    13   val add_classrel_thms: thm list -> theory -> theory
    14   val add_arity_thms: thm list -> theory -> theory
    15   val add_axclass: bclass * xclass list -> ((bstring * string) * Args.src list) list
    16     -> theory -> theory * {intro: thm, axioms: thm list}
    17   val add_axclass_i: bclass * class list -> ((bstring * term) * theory attribute list) list
    18     -> theory -> theory * {intro: thm, axioms: thm list}
    19   val add_inst_subclass_x: xclass * xclass -> string list -> thm list
    20     -> tactic option -> theory -> theory
    21   val add_inst_subclass: xclass * xclass -> tactic -> theory -> theory
    22   val add_inst_subclass_i: class * class -> tactic -> theory -> theory
    23   val add_inst_arity_x: xstring * string list * string -> string list
    24     -> thm list -> tactic option -> theory -> theory
    25   val add_inst_arity: xstring * string list * string -> tactic -> theory -> theory
    26   val add_inst_arity_i: string * sort list * sort -> tactic -> theory -> theory
    27   val default_intro_classes_tac: thm list -> int -> tactic
    28   val axclass_tac: thm list -> tactic
    29   val instance_subclass_proof: xclass * xclass -> bool -> theory -> ProofHistory.T
    30   val instance_subclass_proof_i: class * class -> bool -> theory -> ProofHistory.T
    31   val instance_arity_proof: xstring * string list * xclass -> bool -> theory -> ProofHistory.T
    32   val instance_arity_proof_i: string * sort list * class -> bool -> theory -> ProofHistory.T
    33   val setup: (theory -> theory) list
    34 end;
    35 
    36 structure AxClass : AX_CLASS =
    37 struct
    38 
    39 
    40 (** utilities **)
    41 
    42 (* messages *)
    43 
    44 val quiet_mode = ref false;
    45 fun message s = if ! quiet_mode then () else writeln s;
    46 
    47 
    48 (* type vars *)
    49 
    50 fun map_typ_frees f (Type (t, tys)) = Type (t, map (map_typ_frees f) tys)
    51   | map_typ_frees f (TFree a) = f a
    52   | map_typ_frees _ a = a;
    53 
    54 val map_term_tfrees = map_term_types o map_typ_frees;
    55 
    56 fun aT S = TFree ("'a", S);
    57 
    58 fun dest_varT (TFree (x, S)) = ((x, ~1), S)
    59   | dest_varT (TVar xi_S) = xi_S
    60   | dest_varT T = raise TYPE ("dest_varT", [T], []);
    61 
    62 
    63 (* get axioms and theorems *)
    64 
    65 val is_def = Logic.is_equals o #prop o rep_thm;
    66 
    67 fun witnesses thy names thms =
    68   PureThy.get_thmss thy names @ thms @ filter is_def (map snd (axioms_of thy));
    69 
    70 
    71 
    72 (** abstract syntax operations **)
    73 
    74 (* names *)
    75 
    76 fun intro_name c = c ^ "I";
    77 val introN = "intro";
    78 val axiomsN = "axioms";
    79 
    80 
    81 (* subclass relations as terms *)
    82 
    83 fun mk_classrel (c1, c2) = Logic.mk_inclass (aT [c1], c2);
    84 
    85 fun dest_classrel tm =
    86   let
    87     fun err () = raise TERM ("dest_classrel", [tm]);
    88 
    89     val (ty, c2) = Logic.dest_inclass tm handle TERM _ => err ();
    90     val c1 = (case dest_varT ty of (_, [c]) => c | _ => err ())
    91       handle TYPE _ => err ();
    92   in (c1, c2) end;
    93 
    94 
    95 (* arities as terms *)
    96 
    97 fun mk_arity (t, ss, c) =
    98   let
    99     val tfrees = ListPair.map TFree (Term.invent_type_names [] (length ss), ss);
   100   in Logic.mk_inclass (Type (t, tfrees), c) end;
   101 
   102 fun dest_arity tm =
   103   let
   104     fun err () = raise TERM ("dest_arity", [tm]);
   105 
   106     val (ty, c) = Logic.dest_inclass tm handle TERM _ => err ();
   107     val (t, tvars) =
   108       (case ty of
   109         Type (t, tys) => (t, map dest_varT tys handle TYPE _ => err ())
   110       | _ => err ());
   111     val ss =
   112       if null (gen_duplicates eq_fst tvars)
   113       then map snd tvars else err ();
   114   in (t, ss, c) end;
   115 
   116 
   117 
   118 (** add theorems as axioms **)
   119 
   120 fun prep_thm_axm thy thm =
   121   let
   122     fun err msg = raise THM ("prep_thm_axm: " ^ msg, 0, [thm]);
   123 
   124     val {sign, hyps, prop, ...} = rep_thm thm;
   125   in
   126     if not (Sign.subsig (sign, Theory.sign_of thy)) then
   127       err "theorem not of same theory"
   128     else if not (null (extra_shyps thm)) orelse not (null hyps) then
   129       err "theorem may not contain hypotheses"
   130     else prop
   131   end;
   132 
   133 (*theorems expressing class relations*)
   134 fun add_classrel_thms thms thy =
   135   let
   136     fun prep_thm thm =
   137       let
   138         val prop = prep_thm_axm thy thm;
   139         val (c1, c2) = dest_classrel prop handle TERM _ =>
   140           raise THM ("add_classrel_thms: theorem is not a class relation", 0, [thm]);
   141       in (c1, c2) end;
   142   in Theory.add_classrel_i (map prep_thm thms) thy end;
   143 
   144 (*theorems expressing arities*)
   145 fun add_arity_thms thms thy =
   146   let
   147     fun prep_thm thm =
   148       let
   149         val prop = prep_thm_axm thy thm;
   150         val (t, ss, c) = dest_arity prop handle TERM _ =>
   151           raise THM ("add_arity_thms: theorem is not an arity", 0, [thm]);
   152       in (t, ss, [c]) end;
   153   in Theory.add_arities_i (map prep_thm thms) thy end;
   154 
   155 
   156 
   157 (** axclass info **)
   158 
   159 (* data kind 'Pure/axclasses' *)
   160 
   161 type axclass_info =
   162   {super_classes: class list,
   163     intro: thm,
   164     axioms: thm list};
   165 
   166 structure AxclassesArgs =
   167 struct
   168   val name = "Pure/axclasses";
   169   type T = axclass_info Symtab.table;
   170 
   171   val empty = Symtab.empty;
   172   val copy = I;
   173   val prep_ext = I;
   174   fun merge (tab1, tab2) = Symtab.merge (K true) (tab1, tab2);
   175 
   176   fun print sg tab =
   177     let
   178       val ext_class = Sign.cond_extern sg Sign.classK;
   179       val ext_thm = PureThy.cond_extern_thm_sg sg;
   180 
   181       fun pretty_class c cs = Pretty.block
   182         (Pretty.str (ext_class c) :: Pretty.str " <" :: Pretty.brk 1 ::
   183           Pretty.breaks (map (Pretty.str o ext_class) cs));
   184 
   185       fun pretty_thms name thms = Pretty.big_list (name ^ ":")
   186         (map (Display.pretty_thm_sg sg) thms);
   187 
   188       fun pretty_axclass (name, {super_classes, intro, axioms}) = Pretty.block (Pretty.fbreaks
   189         [pretty_class name super_classes, pretty_thms introN [intro], pretty_thms axiomsN axioms]);
   190     in Pretty.writeln (Pretty.chunks (map pretty_axclass (Symtab.dest tab))) end;
   191 end;
   192 
   193 structure AxclassesData = TheoryDataFun(AxclassesArgs);
   194 val print_axclasses = AxclassesData.print;
   195 
   196 
   197 (* get and put data *)
   198 
   199 fun lookup_axclass_info_sg sg c = Symtab.lookup (AxclassesData.get_sg sg, c);
   200 
   201 fun get_axclass_info thy c =
   202   (case lookup_axclass_info_sg (Theory.sign_of thy) c of
   203     None => error ("Unknown axclass " ^ quote c)
   204   | Some info => info);
   205 
   206 fun put_axclass_info c info thy =
   207   thy |> AxclassesData.put (Symtab.update ((c, info), AxclassesData.get thy));
   208 
   209 
   210 
   211 (** add axiomatic type classes **)
   212 
   213 (* errors *)
   214 
   215 fun err_not_logic c =
   216   error ("Axiomatic class " ^ quote c ^ " not subclass of " ^ quote logicC);
   217 
   218 fun err_bad_axsort ax c =
   219   error ("Sort constraint in axiom " ^ quote ax ^ " not supersort of " ^ quote c);
   220 
   221 fun err_bad_tfrees ax =
   222   error ("More than one type variable in axiom " ^ quote ax);
   223 
   224 
   225 (* ext_axclass *)
   226 
   227 fun ext_axclass prep_class prep_axm prep_att (bclass, raw_super_classes) raw_axioms_atts thy =
   228   let
   229     val sign = Theory.sign_of thy;
   230 
   231     val class = Sign.full_name sign bclass;
   232     val super_classes = map (prep_class sign) raw_super_classes;
   233     val axms = map (prep_axm sign o fst) raw_axioms_atts;
   234     val atts = map (map (prep_att thy) o snd) raw_axioms_atts;
   235 
   236     (*declare class*)
   237     val class_thy =
   238       thy |> Theory.add_classes_i [(bclass, super_classes)];
   239     val class_sign = Theory.sign_of class_thy;
   240 
   241     (*prepare abstract axioms*)
   242     fun abs_axm ax =
   243       if null (term_tfrees ax) then
   244         Logic.mk_implies (Logic.mk_inclass (aT logicS, class), ax)
   245       else map_term_tfrees (K (aT [class])) ax;
   246     val abs_axms = map (abs_axm o #2) axms;
   247 
   248     (*prepare introduction rule*)
   249     val _ = if Sign.subsort class_sign ([class], logicS) then () else err_not_logic class;
   250 
   251     fun axm_sort (name, ax) =
   252       (case term_tfrees ax of
   253         [] => []
   254       | [(_, S)] => if Sign.subsort class_sign ([class], S) then S else err_bad_axsort name class
   255       | _ => err_bad_tfrees name);
   256     val axS = Sign.norm_sort class_sign (logicC :: flat (map axm_sort axms));
   257 
   258     val int_axm = Logic.close_form o map_term_tfrees (K (aT axS));
   259     fun inclass c = Logic.mk_inclass (aT axS, c);
   260 
   261     val intro_axm = Logic.list_implies
   262       (map inclass super_classes @ map (int_axm o #2) axms, inclass class);
   263 
   264     (*declare axioms and rule*)
   265     val (axms_thy, ([intro], [axioms])) =
   266       class_thy
   267       |> Theory.add_path bclass
   268       |> PureThy.add_axioms_i [Thm.no_attributes (introN, intro_axm)]
   269       |>>> PureThy.add_axiomss_i [Thm.no_attributes (axiomsN, abs_axms)];
   270     val info = {super_classes = super_classes, intro = intro, axioms = axioms};
   271 
   272     (*store info*)
   273     val final_thy =
   274       axms_thy
   275       |> (#1 o PureThy.add_thms ((map #1 axms ~~ axioms) ~~ atts))
   276       |> Theory.parent_path
   277       |> (#1 o PureThy.add_thms [Thm.no_attributes (intro_name bclass, intro)])
   278       |> put_axclass_info class info;
   279   in (final_thy, {intro = intro, axioms = axioms}) end;
   280 
   281 
   282 (* external interfaces *)
   283 
   284 val add_axclass = ext_axclass Sign.intern_class Theory.read_axm Attrib.global_attribute;
   285 val add_axclass_i = ext_axclass (K I) Theory.cert_axm (K I);
   286 
   287 
   288 
   289 (** prove class relations and type arities **)
   290 
   291 (* class_axms *)
   292 
   293 fun class_axms sign =
   294   let val classes = Sign.classes sign in
   295     map (Thm.class_triv sign) classes @
   296     mapfilter (apsome #intro o lookup_axclass_info_sg sign) classes
   297   end;
   298 
   299 
   300 (* intro_classes *)
   301 
   302 fun intro_classes_tac facts i st =
   303   ((Method.insert_tac facts THEN'
   304     REPEAT_ALL_NEW (resolve_tac (class_axms (Thm.sign_of_thm st)))) i
   305     THEN Tactic.distinct_subgoals_tac) st;    (*affects all subgoals!?*)
   306 
   307 val intro_classes_method =
   308   ("intro_classes", Method.no_args (Method.METHOD (HEADGOAL o intro_classes_tac)),
   309     "back-chain introduction rules of axiomatic type classes");
   310 
   311 
   312 (* default method *)
   313 
   314 fun default_intro_classes_tac [] i = intro_classes_tac [] i
   315   | default_intro_classes_tac _ _ = Tactical.no_tac;    (*no error message!*)
   316 
   317 fun default_tac rules ctxt facts =
   318   HEADGOAL (Method.some_rule_tac rules ctxt facts ORELSE' default_intro_classes_tac facts);
   319 
   320 val default_method =
   321   ("default", Method.thms_ctxt_args (Method.METHOD oo default_tac), "apply some intro/elim rule");
   322 
   323 
   324 (* axclass_tac *)
   325 
   326 (*(1) repeatedly resolve goals of form "OFCLASS(ty, c_class)",
   327       try class_trivs first, then "cI" axioms
   328   (2) rewrite goals using user supplied definitions
   329   (3) repeatedly resolve goals with user supplied non-definitions*)
   330 
   331 fun axclass_tac thms =
   332   let
   333     val defs = filter is_def thms;
   334     val non_defs = filter_out is_def thms;
   335   in
   336     HEADGOAL (intro_classes_tac []) THEN
   337     TRY (rewrite_goals_tac defs) THEN
   338     TRY (REPEAT_FIRST (fn i => assume_tac i ORELSE resolve_tac non_defs i))
   339   end;
   340 
   341 
   342 (* provers *)
   343 
   344 fun prove mk_prop str_of sign prop thms usr_tac =
   345   (Tactic.prove sign [] [] (mk_prop prop) (K (axclass_tac thms THEN (if_none usr_tac all_tac)))
   346     handle ERROR => error ("The error(s) above occurred while trying to prove " ^
   347      quote (str_of sign prop))) |> Drule.standard;
   348 
   349 val prove_subclass =
   350   prove mk_classrel (fn sg => fn c1_c2 => Sign.str_of_classrel sg c1_c2);
   351 
   352 val prove_arity =
   353   prove mk_arity (fn sg => fn (t, Ss, c) => Sign.str_of_arity sg (t, Ss, [c]));
   354 
   355 
   356 
   357 (** add proved subclass relations and arities **)
   358 
   359 (* prepare classes and arities *)
   360 
   361 fun read_class sg c = Sign.certify_class sg (Sign.intern_class sg c);
   362 
   363 fun cert_classrel sg cc = Library.pairself (Sign.certify_class sg) cc;
   364 fun read_classrel sg cc = Library.pairself (read_class sg) cc;
   365 
   366 fun check_tycon sg t =
   367   let val {tycons, abbrs, ...} = Type.rep_tsig (Sign.tsig_of sg) in
   368     if is_some (Symtab.lookup (abbrs, t)) then
   369       error ("Illegal type abbreviation: " ^ quote t)
   370     else if is_none (Symtab.lookup (tycons, t)) then
   371       error ("Undeclared type constructor: " ^ quote t)
   372     else t
   373   end;
   374 
   375 fun prep_arity prep_tycon prep_sort prep_x sg (t, Ss, x) =
   376   (check_tycon sg (prep_tycon sg t), map (prep_sort sg) Ss, prep_x sg x);
   377 
   378 val read_arity = prep_arity Sign.intern_tycon Sign.read_sort Sign.read_sort;
   379 val cert_arity = prep_arity (K I) Sign.certify_sort Sign.certify_sort;
   380 val read_simple_arity = prep_arity Sign.intern_tycon Sign.read_sort Sign.intern_class;
   381 fun cert_simple_arity arg = prep_arity (K I) Sign.certify_sort (K I) arg;
   382 
   383 
   384 (* old-style instance declarations *)
   385 
   386 fun ext_inst_subclass prep_classrel raw_c1_c2 names thms usr_tac thy =
   387   let
   388     val sign = Theory.sign_of thy;
   389     val c1_c2 = prep_classrel sign raw_c1_c2;
   390   in
   391     message ("Proving class inclusion " ^ quote (Sign.str_of_classrel sign c1_c2) ^ " ...");
   392     thy |> add_classrel_thms [prove_subclass sign c1_c2 (witnesses thy names thms) usr_tac]
   393   end;
   394 
   395 fun ext_inst_arity prep_arity (raw_t, raw_Ss, raw_cs) names thms usr_tac thy =
   396   let
   397     val sign = Theory.sign_of thy;
   398     val (t, Ss, cs) = prep_arity sign (raw_t, raw_Ss, raw_cs);
   399     val wthms = witnesses thy names thms;
   400     fun prove c =
   401      (message ("Proving type arity " ^
   402         quote (Sign.str_of_arity sign (t, Ss, [c])) ^ " ...");
   403         prove_arity sign (t, Ss, c) wthms usr_tac);
   404   in add_arity_thms (map prove cs) thy end;
   405 
   406 fun sane_inst_subclass prep sub tac = ext_inst_subclass prep sub [] [] (Some tac);
   407 fun sane_inst_arity prep arity tac = ext_inst_arity prep arity [] [] (Some tac);
   408 
   409 val add_inst_subclass_x = ext_inst_subclass read_classrel;
   410 val add_inst_subclass = sane_inst_subclass read_classrel;
   411 val add_inst_subclass_i = sane_inst_subclass cert_classrel;
   412 val add_inst_arity_x = ext_inst_arity read_arity;
   413 val add_inst_arity = sane_inst_arity read_arity;
   414 val add_inst_arity_i = sane_inst_arity cert_arity;
   415 
   416 
   417 
   418 (** instance proof interfaces **)
   419 
   420 fun inst_attribute add_thms (thy, thm) = (add_thms [thm] thy, thm);
   421 
   422 fun inst_proof mk_prop add_thms sig_prop int thy =
   423   thy
   424   |> IsarThy.theorem_i Drule.internalK (("", [inst_attribute add_thms]),
   425     (mk_prop (Theory.sign_of thy) sig_prop, ([], []))) int;
   426 
   427 val instance_subclass_proof = inst_proof (mk_classrel oo read_classrel) add_classrel_thms;
   428 val instance_subclass_proof_i = inst_proof (mk_classrel oo cert_classrel) add_classrel_thms;
   429 val instance_arity_proof = inst_proof (mk_arity oo read_simple_arity) add_arity_thms;
   430 val instance_arity_proof_i = inst_proof (mk_arity oo cert_simple_arity) add_arity_thms;
   431 
   432 
   433 
   434 (** package setup **)
   435 
   436 (* setup theory *)
   437 
   438 val setup =
   439  [AxclassesData.init,
   440   Method.add_methods [intro_classes_method, default_method]];
   441 
   442 
   443 (* outer syntax *)
   444 
   445 local structure P = OuterParse and K = OuterSyntax.Keyword in
   446 
   447 val axclassP =
   448   OuterSyntax.command "axclass" "define axiomatic type class" K.thy_decl
   449     ((P.name -- Scan.optional ((P.$$$ "\\<subseteq>" || P.$$$ "<") |--
   450         P.!!! (P.list1 P.xname)) []) -- Scan.repeat P.spec_name
   451       >> (fn (cls, axs) => Toplevel.theory (#1 o add_axclass cls axs)));
   452 
   453 val instanceP =
   454   OuterSyntax.command "instance" "prove type arity or subclass relation" K.thy_goal
   455     ((P.xname -- ((P.$$$ "\\<subseteq>" || P.$$$ "<") |-- P.xname) >> instance_subclass_proof ||
   456       (P.xname -- (P.$$$ "::" |-- P.simple_arity) >> P.triple2) >> instance_arity_proof)
   457       >> (Toplevel.print oo Toplevel.theory_to_proof));
   458 
   459 val _ = OuterSyntax.add_parsers [axclassP, instanceP];
   460 
   461 end;
   462 
   463 end;