src/Pure/axclass.ML
author wenzelm
Wed Mar 17 13:44:43 1999 +0100 (1999-03-17)
changeset 6379 2b17ff28a6cc
parent 6084 842b059e023f
child 6390 5d58c100ca3f
permissions -rw-r--r--
theory data;
attributes for class axioms;
instance_subclass/arity_proof(_i);
expand_classes proof method;
'axclass' / 'instance' outer syntax;
     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: xclass * xclass -> string list -> thm list
    19     -> tactic option -> theory -> theory
    20   val add_inst_subclass_i: class * class -> string list -> thm list
    21     -> tactic option -> theory -> theory
    22   val add_inst_arity: xstring * xsort list * xclass list -> string list
    23     -> thm list -> tactic option -> theory -> theory
    24   val add_inst_arity_i: string * sort list * class list -> string list
    25     -> thm list -> tactic option -> theory -> theory
    26   val axclass_tac: thm list -> tactic
    27   val prove_subclass: theory -> class * class -> thm list
    28     -> tactic option -> thm
    29   val prove_arity: theory -> string * sort list * class -> thm list
    30     -> tactic option -> thm
    31   val goal_subclass: theory -> xclass * xclass -> thm list
    32   val goal_arity: theory -> xstring * xsort list * xclass -> thm list
    33   val instance_subclass_proof: xclass * xclass -> theory -> ProofHistory.T
    34   val instance_subclass_proof_i: class * class -> theory -> ProofHistory.T
    35   val instance_arity_proof: xstring * xsort list * xclass -> theory -> ProofHistory.T
    36   val instance_arity_proof_i: string * sort list * class -> theory -> ProofHistory.T
    37   val setup: (theory -> theory) list
    38 end;
    39 
    40 structure AxClass : AX_CLASS =
    41 struct
    42 
    43 
    44 (** utilities **)
    45 
    46 (* messages *)
    47 
    48 val quiet_mode = ref false;
    49 fun message s = if ! quiet_mode then () else writeln s;
    50 
    51 
    52 (* type vars *)
    53 
    54 fun map_typ_frees f (Type (t, tys)) = Type (t, map (map_typ_frees f) tys)
    55   | map_typ_frees f (TFree a) = f a
    56   | map_typ_frees _ a = a;
    57 
    58 val map_term_tfrees = map_term_types o map_typ_frees;
    59 
    60 fun aT S = TFree ("'a", S);
    61 
    62 fun dest_varT (TFree (x, S)) = ((x, ~1), S)
    63   | dest_varT (TVar xi_S) = xi_S
    64   | dest_varT T = raise TYPE ("dest_varT", [T], []);
    65 
    66 
    67 (* get axioms and theorems *)
    68 
    69 val is_def = Logic.is_equals o #prop o rep_thm;
    70 
    71 fun witnesses thy names thms =
    72   PureThy.get_thmss thy names @ thms @ filter is_def (map snd (axioms_of thy));
    73 
    74 
    75 
    76 (** abstract syntax operations **)
    77 
    78 (* names *)
    79 
    80 fun intro_name c = c ^ "I";
    81 val introN = "intro";
    82 val axiomsN = "axioms";
    83 
    84 
    85 (* subclass relations as terms *)
    86 
    87 fun mk_classrel (c1, c2) = Logic.mk_inclass (aT [c1], c2);
    88 
    89 fun dest_classrel tm =
    90   let
    91     fun err () = raise TERM ("dest_classrel", [tm]);
    92 
    93     val (ty, c2) = Logic.dest_inclass tm handle TERM _ => err ();
    94     val c1 = (case dest_varT ty of (_, [c]) => c | _ => err ())
    95       handle TYPE _ => err ();
    96   in (c1, c2) end;
    97 
    98 
    99 (* arities as terms *)
   100 
   101 fun mk_arity (t, ss, c) =
   102   let
   103     val names = tl (variantlist (replicate (length ss + 1) "'", []));
   104     val tfrees = ListPair.map TFree (names, ss);
   105   in Logic.mk_inclass (Type (t, tfrees), c) end;
   106 
   107 fun dest_arity tm =
   108   let
   109     fun err () = raise TERM ("dest_arity", [tm]);
   110 
   111     val (ty, c) = Logic.dest_inclass tm handle TERM _ => err ();
   112     val (t, tvars) =
   113       (case ty of
   114         Type (t, tys) => (t, map dest_varT tys handle TYPE _ => err ())
   115       | _ => err ());
   116     val ss =
   117       if null (gen_duplicates eq_fst tvars)
   118       then map snd tvars else err ();
   119   in (t, ss, c) end;
   120 
   121 
   122 
   123 (** add theorems as axioms **)
   124 
   125 fun prep_thm_axm thy thm =
   126   let
   127     fun err msg = raise THM ("prep_thm_axm: " ^ msg, 0, [thm]);
   128 
   129     val {sign, hyps, prop, ...} = rep_thm thm;
   130   in
   131     if not (Sign.subsig (sign, sign_of thy)) then
   132       err "theorem not of same theory"
   133     else if not (null (extra_shyps thm)) orelse not (null hyps) then
   134       err "theorem may not contain hypotheses"
   135     else prop
   136   end;
   137 
   138 (*theorems expressing class relations*)
   139 fun add_classrel_thms thms thy =
   140   let
   141     fun prep_thm thm =
   142       let
   143         val prop = prep_thm_axm thy thm;
   144         val (c1, c2) = dest_classrel prop handle TERM _ =>
   145           raise THM ("add_classrel_thms: theorem is not a class relation", 0, [thm]);
   146       in (c1, c2) end;
   147   in Theory.add_classrel (map prep_thm thms) thy end;
   148 
   149 (*theorems expressing arities*)
   150 fun add_arity_thms thms thy =
   151   let
   152     fun prep_thm thm =
   153       let
   154         val prop = prep_thm_axm thy thm;
   155         val (t, ss, c) = dest_arity prop handle TERM _ =>
   156           raise THM ("add_arity_thms: theorem is not an arity", 0, [thm]);
   157       in (t, ss, [c]) end;
   158   in Theory.add_arities (map prep_thm thms) thy end;
   159 
   160 
   161 
   162 (** axclass info **)
   163 
   164 (* data kind 'Pure/axclasses' *)
   165 
   166 type axclass_info =
   167   {super_classes: class list,
   168     intro: thm,
   169     axioms: thm list};
   170 
   171 structure AxclassesArgs =
   172 struct
   173   val name = "Pure/axclasses";
   174   type T = axclass_info Symtab.table;
   175 
   176   val empty = Symtab.empty;
   177   val prep_ext = I;
   178   fun merge (tab1, tab2) = Symtab.merge (K true) (tab1, tab2);
   179 
   180   fun print sg tab =
   181     let
   182       val ext_class = Sign.cond_extern sg Sign.classK;
   183       val ext_thm = PureThy.cond_extern_thm_sg sg;
   184 
   185       fun pretty_class c cs = Pretty.block
   186         (Pretty.str (ext_class c) :: Pretty.str " <" :: Pretty.brk 1 ::
   187           Pretty.breaks (map (Pretty.str o ext_class) cs));
   188 
   189       fun pretty_thms name thms = Pretty.big_list (name ^ ":") (map Display.pretty_thm thms);
   190 
   191       fun pretty_axclass (name, {super_classes, intro, axioms}) = Pretty.block (Pretty.fbreaks
   192         [pretty_class name super_classes, pretty_thms introN [intro], pretty_thms axiomsN axioms]);
   193     in seq (Pretty.writeln o pretty_axclass) (Symtab.dest tab) end;
   194 end;
   195 
   196 structure AxclassesData = TheoryDataFun(AxclassesArgs);
   197 val print_axclasses = AxclassesData.print;
   198 
   199 
   200 (* get and put data *)
   201 
   202 fun lookup_axclass_info_sg sg c = Symtab.lookup (AxclassesData.get_sg sg, c);
   203 
   204 fun get_axclass_info thy c =
   205   (case lookup_axclass_info_sg (Theory.sign_of thy) c of
   206     None => error ("Unknown axclass " ^ quote c)
   207   | Some info => info);
   208 
   209 fun put_axclass_info c info thy =
   210   thy |> AxclassesData.put (Symtab.update ((c, info), AxclassesData.get thy));
   211 
   212 
   213 
   214 (** add axiomatic type classes **)
   215 
   216 (* errors *)
   217 
   218 fun err_not_logic c =
   219   error ("Axiomatic class " ^ quote c ^ " not subclass of " ^ quote logicC);
   220 
   221 fun err_bad_axsort ax c =
   222   error ("Sort constraint in axiom " ^ quote ax ^ " not supersort of " ^ quote c);
   223 
   224 fun err_bad_tfrees ax =
   225   error ("More than one type variable in axiom " ^ quote ax);
   226 
   227 
   228 (* ext_axclass *)
   229 
   230 fun ext_axclass prep_class prep_axm prep_att (bclass, raw_super_classes) raw_axioms_atts thy =
   231   let
   232     val sign = Theory.sign_of thy;
   233 
   234     val class = Sign.full_name sign bclass;
   235     val super_classes = map (prep_class sign) raw_super_classes;
   236     val axms = map (prep_axm sign o fst) raw_axioms_atts;
   237     val atts = map (map (prep_att thy) o snd) raw_axioms_atts;
   238 
   239     (*declare class*)
   240     val class_thy =
   241       thy |> Theory.add_classes_i [(bclass, super_classes)];
   242     val class_sign = Theory.sign_of class_thy;
   243 
   244     (*prepare abstract axioms*)
   245     fun abs_axm ax =
   246       if null (term_tfrees ax) then
   247         Logic.mk_implies (Logic.mk_inclass (aT logicS, class), ax)
   248       else map_term_tfrees (K (aT [class])) ax;
   249     val abs_axms = map (abs_axm o #2) axms;
   250 
   251     (*prepare introduction rule*)
   252     val _ = if Sign.subsort class_sign ([class], logicS) then () else err_not_logic class;
   253 
   254     fun axm_sort (name, ax) =
   255       (case term_tfrees ax of
   256         [] => []
   257       | [(_, S)] => if Sign.subsort class_sign ([class], S) then S else err_bad_axsort name class
   258       | _ => err_bad_tfrees name);
   259     val axS = Sign.norm_sort class_sign (logicC :: flat (map axm_sort axms));
   260 
   261     val int_axm = Logic.close_form o map_term_tfrees (K (aT axS));
   262     fun inclass c = Logic.mk_inclass (aT axS, c);
   263 
   264     val intro_axm = Logic.list_implies
   265       (map inclass super_classes @ map (int_axm o #2) axms, inclass class);
   266 
   267     (*declare axioms and rule*)
   268     val axms_thy =
   269       class_thy
   270       |> Theory.add_path bclass
   271       |> PureThy.add_axioms_i [Thm.no_attributes (introN, intro_axm)]
   272       |> PureThy.add_axiomss_i [Thm.no_attributes (axiomsN, abs_axms)];
   273 
   274     val intro = PureThy.get_thm axms_thy introN;
   275     val axioms = PureThy.get_thms axms_thy axiomsN;
   276     val info = {super_classes = super_classes, intro = intro, axioms = axioms};
   277 
   278     (*store info*)
   279     val final_thy =
   280       axms_thy
   281       |> PureThy.add_thms ((map #1 axms ~~ axioms) ~~ atts)
   282       |> Theory.parent_path
   283       |> PureThy.add_thms [Thm.no_attributes (intro_name bclass, intro)]
   284       |> put_axclass_info class info;
   285   in (final_thy, {intro = intro, axioms = axioms}) end;
   286 
   287 
   288 (* external interfaces *)
   289 
   290 val add_axclass = ext_axclass Sign.intern_class read_axm Attrib.global_attribute;
   291 val add_axclass_i = ext_axclass (K I) cert_axm (K I);
   292 
   293 
   294 
   295 (** prove class relations and type arities **)
   296 
   297 (* class_axms *)
   298 
   299 fun class_axms sign =
   300   let val classes = Sign.classes sign in
   301     map (Thm.class_triv sign) classes @
   302     mapfilter (apsome #intro o lookup_axclass_info_sg sign) classes
   303   end;
   304 
   305 
   306 (* expand classes *)
   307 
   308 fun expand_classes_tac st =
   309   TRY (REPEAT_FIRST (resolve_tac (class_axms (Thm.sign_of_thm st)))) st;
   310 
   311 val expand_classes_method =
   312   ("expand_classes", Method.no_args (Method.METHOD0 expand_classes_tac),
   313     "expand axiomatic type classes");
   314 
   315 
   316 (* axclass_tac *)
   317 
   318 (*(1) repeatedly resolve goals of form "OFCLASS(ty, c_class)",
   319       try class_trivs first, then "cI" axioms
   320   (2) rewrite goals using user supplied definitions
   321   (3) repeatedly resolve goals with user supplied non-definitions*)
   322 
   323 fun axclass_tac thms =
   324   let
   325     val defs = filter is_def thms;
   326     val non_defs = filter_out is_def thms;
   327   in
   328     expand_classes_tac THEN
   329     TRY (rewrite_goals_tac defs) THEN
   330     TRY (REPEAT_FIRST (fn i => assume_tac i ORELSE resolve_tac non_defs i))
   331   end;
   332 
   333 
   334 (* provers *)
   335 
   336 fun prove mk_prop str_of thy sig_prop thms usr_tac =
   337   let
   338     val sign = sign_of thy;
   339     val goal = Thm.cterm_of sign (mk_prop sig_prop);
   340     val tac = axclass_tac thms THEN (if_none usr_tac all_tac);
   341   in
   342     prove_goalw_cterm [] goal (K [tac])
   343   end
   344   handle ERROR => error ("The error(s) above occurred while trying to prove "
   345     ^ quote (str_of (sign_of thy, sig_prop)));
   346 
   347 val prove_subclass =
   348   prove mk_classrel (fn (sg, c1_c2) => Sign.str_of_classrel sg c1_c2);
   349 
   350 val prove_arity =
   351   prove mk_arity (fn (sg, (t, Ss, c)) => Sign.str_of_arity sg (t, Ss, [c]));
   352 
   353 
   354 
   355 (** add proved subclass relations and arities **)
   356 
   357 fun intrn_classrel sg c1_c2 =
   358   pairself (Sign.intern_class sg) c1_c2;
   359 
   360 fun intrn_arity intrn sg (t, Ss, x) =
   361   (Sign.intern_tycon sg t, map (Sign.intern_sort sg) Ss, intrn sg x);
   362 
   363 
   364 fun ext_inst_subclass prep_classrel raw_c1_c2 names thms usr_tac thy =
   365   let val c1_c2 = prep_classrel (Theory.sign_of thy) raw_c1_c2 in
   366     message ("Proving class inclusion " ^
   367       quote (Sign.str_of_classrel (sign_of thy) c1_c2) ^ " ...");
   368     thy |> add_classrel_thms [prove_subclass thy c1_c2 (witnesses thy names thms) usr_tac]
   369   end;
   370 
   371 fun ext_inst_arity prep_arity (raw_t, raw_Ss, raw_cs) names thms usr_tac thy =
   372   let
   373     val sign = Theory.sign_of thy;
   374     val (t, Ss, cs) = prep_arity sign (raw_t, raw_Ss, raw_cs);
   375     val wthms = witnesses thy names thms;
   376     fun prove c =
   377      (message ("Proving type arity " ^
   378         quote (Sign.str_of_arity sign (t, Ss, [c])) ^ " ...");
   379         prove_arity thy (t, Ss, c) wthms usr_tac);
   380   in add_arity_thms (map prove cs) thy end;
   381 
   382 
   383 val add_inst_subclass = ext_inst_subclass intrn_classrel;
   384 val add_inst_subclass_i = ext_inst_subclass (K I);
   385 val add_inst_arity = ext_inst_arity (intrn_arity Sign.intern_sort);
   386 val add_inst_arity_i = ext_inst_arity (K I);
   387 
   388 
   389 (* make old-style interactive goals *)
   390 
   391 fun mk_goal mk_prop thy sig_prop =
   392   Goals.goalw_cterm [] (Thm.cterm_of (Theory.sign_of thy) (mk_prop (Theory.sign_of thy) sig_prop));
   393 
   394 val goal_subclass = mk_goal (mk_classrel oo intrn_classrel);
   395 val goal_arity = mk_goal (mk_arity oo intrn_arity Sign.intern_class);
   396 
   397 
   398 
   399 (** instance proof interfaces **)
   400 
   401 fun inst_attribute add_thms (thy, thm) = (add_thms [thm] thy, thm);
   402 
   403 fun inst_proof mk_prop add_thms sig_prop thy =
   404   thy
   405   |> IsarThy.theorem_i "" [inst_attribute add_thms]
   406     (mk_prop (Theory.sign_of thy) sig_prop, []);
   407 
   408 val instance_subclass_proof = inst_proof (mk_classrel oo intrn_classrel) add_classrel_thms;
   409 val instance_subclass_proof_i = inst_proof (K mk_classrel) add_classrel_thms;
   410 val instance_arity_proof = inst_proof (mk_arity oo intrn_arity Sign.intern_class) add_arity_thms;
   411 val instance_arity_proof_i = inst_proof (K mk_arity) add_arity_thms;
   412 
   413 
   414 
   415 (** package setup **)
   416 
   417 (* setup theory *)
   418 
   419 val setup =
   420  [AxclassesData.init,
   421   Method.add_methods [expand_classes_method]];
   422 
   423 
   424 (* outer syntax *)
   425 
   426 local open OuterParse in
   427 
   428 val axclassP =
   429   OuterSyntax.command "axclass" "define axiomatic type class"
   430     (name -- Scan.optional ($$$ "<" |-- !!! (list1 xname)) [] -- Scan.repeat spec_name
   431       >> (fn (cls, axs) => Toplevel.theory (#1 o add_axclass cls axs)));
   432 
   433 val instanceP =
   434   OuterSyntax.command "instance" "prove type arity or subclass relation"
   435     ((xname -- ($$$ "<" |-- xname) >> instance_subclass_proof ||
   436       xname -- ($$$ "::" |-- simple_arity) >> (instance_arity_proof o triple2))
   437       >> (Toplevel.print oo Toplevel.theory_to_proof));
   438 
   439 val _ = OuterSyntax.add_parsers [axclassP, instanceP];
   440 
   441 end;
   442 
   443 
   444 end;