src/Pure/axclass.ML
author wenzelm
Fri May 21 11:36:02 1999 +0200 (1999-05-21)
changeset 6679 7c1630496e21
parent 6546 995a66249a9b
child 6719 7c2dafc8e801
permissions -rw-r--r--
improved errors;
     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 -> bool -> theory -> ProofHistory.T
    34   val instance_subclass_proof_i: class * class -> bool -> theory -> ProofHistory.T
    35   val instance_arity_proof: xstring * xsort list * xclass -> bool -> theory -> ProofHistory.T
    36   val instance_arity_proof_i: string * sort list * class -> bool -> 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, Theory.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 copy = I;
   178   val prep_ext = I;
   179   fun merge (tab1, tab2) = Symtab.merge (K true) (tab1, tab2);
   180 
   181   fun print sg tab =
   182     let
   183       val ext_class = Sign.cond_extern sg Sign.classK;
   184       val ext_thm = PureThy.cond_extern_thm_sg sg;
   185 
   186       fun pretty_class c cs = Pretty.block
   187         (Pretty.str (ext_class c) :: Pretty.str " <" :: Pretty.brk 1 ::
   188           Pretty.breaks (map (Pretty.str o ext_class) cs));
   189 
   190       fun pretty_thms name thms = Pretty.big_list (name ^ ":") (map Display.pretty_thm thms);
   191 
   192       fun pretty_axclass (name, {super_classes, intro, axioms}) = Pretty.block (Pretty.fbreaks
   193         [pretty_class name super_classes, pretty_thms introN [intro], pretty_thms axiomsN axioms]);
   194     in seq (Pretty.writeln o pretty_axclass) (Symtab.dest tab) end;
   195 end;
   196 
   197 structure AxclassesData = TheoryDataFun(AxclassesArgs);
   198 val print_axclasses = AxclassesData.print;
   199 
   200 
   201 (* get and put data *)
   202 
   203 fun lookup_axclass_info_sg sg c = Symtab.lookup (AxclassesData.get_sg sg, c);
   204 
   205 fun get_axclass_info thy c =
   206   (case lookup_axclass_info_sg (Theory.sign_of thy) c of
   207     None => error ("Unknown axclass " ^ quote c)
   208   | Some info => info);
   209 
   210 fun put_axclass_info c info thy =
   211   thy |> AxclassesData.put (Symtab.update ((c, info), AxclassesData.get thy));
   212 
   213 
   214 
   215 (** add axiomatic type classes **)
   216 
   217 (* errors *)
   218 
   219 fun err_not_logic c =
   220   error ("Axiomatic class " ^ quote c ^ " not subclass of " ^ quote logicC);
   221 
   222 fun err_bad_axsort ax c =
   223   error ("Sort constraint in axiom " ^ quote ax ^ " not supersort of " ^ quote c);
   224 
   225 fun err_bad_tfrees ax =
   226   error ("More than one type variable in axiom " ^ quote ax);
   227 
   228 
   229 (* ext_axclass *)
   230 
   231 fun ext_axclass prep_class prep_axm prep_att (bclass, raw_super_classes) raw_axioms_atts thy =
   232   let
   233     val sign = Theory.sign_of thy;
   234 
   235     val class = Sign.full_name sign bclass;
   236     val super_classes = map (prep_class sign) raw_super_classes;
   237     val axms = map (prep_axm sign o fst) raw_axioms_atts;
   238     val atts = map (map (prep_att thy) o snd) raw_axioms_atts;
   239 
   240     (*declare class*)
   241     val class_thy =
   242       thy |> Theory.add_classes_i [(bclass, super_classes)];
   243     val class_sign = Theory.sign_of class_thy;
   244 
   245     (*prepare abstract axioms*)
   246     fun abs_axm ax =
   247       if null (term_tfrees ax) then
   248         Logic.mk_implies (Logic.mk_inclass (aT logicS, class), ax)
   249       else map_term_tfrees (K (aT [class])) ax;
   250     val abs_axms = map (abs_axm o #2) axms;
   251 
   252     (*prepare introduction rule*)
   253     val _ = if Sign.subsort class_sign ([class], logicS) then () else err_not_logic class;
   254 
   255     fun axm_sort (name, ax) =
   256       (case term_tfrees ax of
   257         [] => []
   258       | [(_, S)] => if Sign.subsort class_sign ([class], S) then S else err_bad_axsort name class
   259       | _ => err_bad_tfrees name);
   260     val axS = Sign.norm_sort class_sign (logicC :: flat (map axm_sort axms));
   261 
   262     val int_axm = Logic.close_form o map_term_tfrees (K (aT axS));
   263     fun inclass c = Logic.mk_inclass (aT axS, c);
   264 
   265     val intro_axm = Logic.list_implies
   266       (map inclass super_classes @ map (int_axm o #2) axms, inclass class);
   267 
   268     (*declare axioms and rule*)
   269     val axms_thy =
   270       class_thy
   271       |> Theory.add_path bclass
   272       |> PureThy.add_axioms_i [Thm.no_attributes (introN, intro_axm)]
   273       |> PureThy.add_axiomss_i [Thm.no_attributes (axiomsN, abs_axms)];
   274 
   275     val intro = PureThy.get_thm axms_thy introN;
   276     val axioms = PureThy.get_thms axms_thy axiomsN;
   277     val info = {super_classes = super_classes, intro = intro, axioms = axioms};
   278 
   279     (*store info*)
   280     val final_thy =
   281       axms_thy
   282       |> PureThy.add_thms ((map #1 axms ~~ axioms) ~~ atts)
   283       |> Theory.parent_path
   284       |> PureThy.add_thms [Thm.no_attributes (intro_name bclass, intro)]
   285       |> put_axclass_info class info;
   286   in (final_thy, {intro = intro, axioms = axioms}) end;
   287 
   288 
   289 (* external interfaces *)
   290 
   291 val add_axclass = ext_axclass Sign.intern_class Theory.read_axm Attrib.global_attribute;
   292 val add_axclass_i = ext_axclass (K I) Theory.cert_axm (K I);
   293 
   294 
   295 
   296 (** prove class relations and type arities **)
   297 
   298 (* class_axms *)
   299 
   300 fun class_axms sign =
   301   let val classes = Sign.classes sign in
   302     map (Thm.class_triv sign) classes @
   303     mapfilter (apsome #intro o lookup_axclass_info_sg sign) classes
   304   end;
   305 
   306 
   307 (* expand classes *)
   308 
   309 fun expand_classes_tac st =
   310   TRY (REPEAT_FIRST (resolve_tac (class_axms (Thm.sign_of_thm st)))) st;
   311 
   312 val expand_classes_method =
   313   ("expand_classes", Method.no_args (Method.METHOD0 expand_classes_tac),
   314     "expand axiomatic type classes");
   315 
   316 
   317 (* axclass_tac *)
   318 
   319 (*(1) repeatedly resolve goals of form "OFCLASS(ty, c_class)",
   320       try class_trivs first, then "cI" axioms
   321   (2) rewrite goals using user supplied definitions
   322   (3) repeatedly resolve goals with user supplied non-definitions*)
   323 
   324 fun axclass_tac thms =
   325   let
   326     val defs = filter is_def thms;
   327     val non_defs = filter_out is_def thms;
   328   in
   329     expand_classes_tac THEN
   330     TRY (rewrite_goals_tac defs) THEN
   331     TRY (REPEAT_FIRST (fn i => assume_tac i ORELSE resolve_tac non_defs i))
   332   end;
   333 
   334 
   335 (* provers *)
   336 
   337 fun prove mk_prop str_of thy sig_prop thms usr_tac =
   338   let
   339     val sign = Theory.sign_of thy;
   340     val goal = Thm.cterm_of sign (mk_prop sig_prop)
   341       handle TERM (msg, _) => error msg
   342         | TYPE (msg, _, _) => error msg;
   343     val tac = axclass_tac thms THEN (if_none usr_tac all_tac);
   344   in
   345     prove_goalw_cterm [] goal (K [tac])
   346   end
   347   handle ERROR => error ("The error(s) above occurred while trying to prove "
   348     ^ quote (str_of (Theory.sign_of thy, sig_prop)));
   349 
   350 val prove_subclass =
   351   prove mk_classrel (fn (sg, c1_c2) => Sign.str_of_classrel sg c1_c2);
   352 
   353 val prove_arity =
   354   prove mk_arity (fn (sg, (t, Ss, c)) => Sign.str_of_arity sg (t, Ss, [c]));
   355 
   356 
   357 
   358 (** add proved subclass relations and arities **)
   359 
   360 fun intrn_classrel sg c1_c2 =
   361   pairself (Sign.intern_class sg) c1_c2;
   362 
   363 fun intrn_arity intrn sg (t, Ss, x) =
   364   (Sign.intern_tycon sg t, map (Sign.intern_sort sg) Ss, intrn sg x);
   365 
   366 
   367 fun ext_inst_subclass prep_classrel raw_c1_c2 names thms usr_tac thy =
   368   let val c1_c2 = prep_classrel (Theory.sign_of thy) raw_c1_c2 in
   369     message ("Proving class inclusion " ^
   370       quote (Sign.str_of_classrel (Theory.sign_of thy) c1_c2) ^ " ...");
   371     thy |> add_classrel_thms [prove_subclass thy c1_c2 (witnesses thy names thms) usr_tac]
   372   end;
   373 
   374 fun ext_inst_arity prep_arity (raw_t, raw_Ss, raw_cs) names thms usr_tac thy =
   375   let
   376     val sign = Theory.sign_of thy;
   377     val (t, Ss, cs) = prep_arity sign (raw_t, raw_Ss, raw_cs);
   378     val wthms = witnesses thy names thms;
   379     fun prove c =
   380      (message ("Proving type arity " ^
   381         quote (Sign.str_of_arity sign (t, Ss, [c])) ^ " ...");
   382         prove_arity thy (t, Ss, c) wthms usr_tac);
   383   in add_arity_thms (map prove cs) thy end;
   384 
   385 
   386 val add_inst_subclass = ext_inst_subclass intrn_classrel;
   387 val add_inst_subclass_i = ext_inst_subclass (K I);
   388 val add_inst_arity = ext_inst_arity (intrn_arity Sign.intern_sort);
   389 val add_inst_arity_i = ext_inst_arity (K I);
   390 
   391 
   392 (* make old-style interactive goals *)
   393 
   394 fun mk_goal mk_prop thy sig_prop =
   395   Goals.goalw_cterm [] (Thm.cterm_of (Theory.sign_of thy) (mk_prop (Theory.sign_of thy) sig_prop));
   396 
   397 val goal_subclass = mk_goal (mk_classrel oo intrn_classrel);
   398 val goal_arity = mk_goal (mk_arity oo intrn_arity Sign.intern_class);
   399 
   400 
   401 
   402 (** instance proof interfaces **)
   403 
   404 fun inst_attribute add_thms (thy, thm) = (add_thms [thm] thy, thm);
   405 
   406 fun inst_proof mk_prop add_thms sig_prop int thy =
   407   thy
   408   |> IsarThy.theorem_i "" [inst_attribute add_thms]
   409     (mk_prop (Theory.sign_of thy) sig_prop, []) int;
   410 
   411 val instance_subclass_proof = inst_proof (mk_classrel oo intrn_classrel) add_classrel_thms;
   412 val instance_subclass_proof_i = inst_proof (K mk_classrel) add_classrel_thms;
   413 val instance_arity_proof = inst_proof (mk_arity oo intrn_arity Sign.intern_class) add_arity_thms;
   414 val instance_arity_proof_i = inst_proof (K mk_arity) add_arity_thms;
   415 
   416 
   417 
   418 (** package setup **)
   419 
   420 (* setup theory *)
   421 
   422 val setup =
   423  [AxclassesData.init,
   424   Method.add_methods [expand_classes_method]];
   425 
   426 
   427 (* outer syntax *)
   428 
   429 local open OuterParse in
   430 
   431 val axclassP =
   432   OuterSyntax.command "axclass" "define axiomatic type class"
   433     (name -- Scan.optional ($$$ "<" |-- !!! (list1 xname)) [] -- Scan.repeat spec_name
   434       >> (fn (cls, axs) => Toplevel.theory (#1 o add_axclass cls axs)));
   435 
   436 val instanceP =
   437   OuterSyntax.command "instance" "prove type arity or subclass relation"
   438     ((xname -- ($$$ "<" |-- xname) >> instance_subclass_proof ||
   439       xname -- ($$$ "::" |-- simple_arity) >> (instance_arity_proof o triple2))
   440       >> (Toplevel.print oo Toplevel.theory_to_proof));
   441 
   442 val _ = OuterSyntax.add_parsers [axclassP, instanceP];
   443 
   444 end;
   445 
   446 
   447 end;