src/Pure/axclass.ML
author wenzelm
Fri Oct 24 17:11:48 1997 +0200 (1997-10-24)
changeset 3988 6ff1a1e2bd21
parent 3956 d59fe4579004
child 4015 92874142156b
permissions -rw-r--r--
removed add_thms_as_axms;
     1 (*  Title:      Pure/axclass.ML
     2     ID:         $Id$
     3     Author:     Markus Wenzel, TU Muenchen
     4 
     5 User interfaces for axiomatic type classes.
     6 *)
     7 
     8 signature AX_CLASS =
     9 sig
    10   val add_classrel_thms: thm list -> theory -> theory
    11   val add_arity_thms: thm list -> theory -> theory
    12   val add_axclass: bclass * xclass list -> (string * string) list
    13     -> theory -> theory
    14   val add_axclass_i: bclass * class list -> (string * term) list
    15     -> theory -> theory
    16   val add_inst_subclass: xclass * xclass -> string list -> thm list
    17     -> tactic option -> theory -> theory
    18   val add_inst_subclass_i: class * class -> string list -> thm list
    19     -> tactic option -> theory -> theory
    20   val add_inst_arity: xstring * xsort list * xclass list -> string list
    21     -> thm list -> tactic option -> theory -> theory
    22   val add_inst_arity_i: string * sort list * class list -> string list
    23     -> thm list -> tactic option -> theory -> theory
    24   val axclass_tac: theory -> thm list -> tactic
    25   val prove_subclass: theory -> class * class -> thm list
    26     -> tactic option -> thm
    27   val prove_arity: theory -> string * sort list * class -> thm list
    28     -> tactic option -> thm
    29   val goal_subclass: theory -> xclass * xclass -> thm list
    30   val goal_arity: theory -> xstring * xsort list * xclass -> thm list
    31 end;
    32 
    33 structure AxClass : AX_CLASS =
    34 struct
    35 
    36 (** utilities **)
    37 
    38 (* type vars *)
    39 
    40 fun map_typ_frees f (Type (t, tys)) = Type (t, map (map_typ_frees f) tys)
    41   | map_typ_frees f (TFree a) = f a
    42   | map_typ_frees _ a = a;
    43 
    44 val map_term_tfrees = map_term_types o map_typ_frees;
    45 
    46 fun aT S = TFree ("'a", S);
    47 
    48 fun dest_varT (TFree (x, S)) = ((x, ~1), S)
    49   | dest_varT (TVar xi_S) = xi_S
    50   | dest_varT T = raise TYPE ("dest_varT", [T], []);
    51 
    52 
    53 (* get axioms and theorems *)
    54 
    55 fun get_ax thy name =
    56   Some (get_axiom thy name) handle THEORY _ => None;
    57 
    58 val get_axioms = mapfilter o get_ax;
    59 
    60 val is_def = Logic.is_equals o #prop o rep_thm;
    61 
    62 fun witnesses thy axms thms =
    63   map (get_axiom thy) axms @ thms @ filter is_def (map snd (axioms_of thy));
    64 
    65 
    66 
    67 (** abstract syntax operations **)
    68 
    69 (* subclass relations as terms *)
    70 
    71 fun mk_classrel (c1, c2) = Logic.mk_inclass (aT [c1], c2);
    72 
    73 fun dest_classrel tm =
    74   let
    75     fun err () = raise TERM ("dest_classrel", [tm]);
    76 
    77     val (ty, c2) = Logic.dest_inclass tm handle TERM _ => err ();
    78     val c1 = (case dest_varT ty of (_, [c]) => c | _ => err ())
    79       handle TYPE _ => err ();
    80   in
    81     (c1, c2)
    82   end;
    83 
    84 
    85 (* arities as terms *)
    86 
    87 fun mk_arity (t, ss, c) =
    88   let
    89     val names = tl (variantlist (replicate (length ss + 1) "'", []));
    90     val tfrees = ListPair.map TFree (names, ss);
    91   in
    92     Logic.mk_inclass (Type (t, tfrees), c)
    93   end;
    94 
    95 fun dest_arity tm =
    96   let
    97     fun err () = raise TERM ("dest_arity", [tm]);
    98 
    99     val (ty, c) = Logic.dest_inclass tm handle TERM _ => err ();
   100     val (t, tvars) =
   101       (case ty of
   102         Type (t, tys) => (t, map dest_varT tys handle TYPE _ => err ())
   103       | _ => err ());
   104     val ss =
   105       if null (gen_duplicates eq_fst tvars)
   106       then map snd tvars else err ();
   107   in
   108     (t, ss, c)
   109   end;
   110 
   111 
   112 
   113 (** add theorems as axioms **)
   114 
   115 fun prep_thm_axm thy thm =
   116   let
   117     fun err msg = raise THM ("prep_thm_axm: " ^ msg, 0, [thm]);
   118 
   119     val {sign, hyps, prop, ...} = rep_thm thm;
   120   in
   121     if not (Sign.subsig (sign, sign_of thy)) then
   122       err "theorem not of same theory"
   123     else if not (null (extra_shyps thm)) orelse not (null hyps) then
   124       err "theorem may not contain hypotheses"
   125     else prop
   126   end;
   127 
   128 (*theorems expressing class relations*)
   129 fun add_classrel_thms thms thy =
   130   let
   131     fun prep_thm thm =
   132       let
   133         val prop = prep_thm_axm thy thm;
   134         val (c1, c2) = dest_classrel prop handle TERM _ =>
   135           raise THM ("add_classrel_thms: theorem is not a class relation", 0, [thm]);
   136       in (c1, c2) end;
   137   in
   138     Theory.add_classrel (map prep_thm thms) thy
   139   end;
   140 
   141 (*theorems expressing arities*)
   142 fun add_arity_thms thms thy =
   143   let
   144     fun prep_thm thm =
   145       let
   146         val prop = prep_thm_axm thy thm;
   147         val (t, ss, c) = dest_arity prop handle TERM _ =>
   148           raise THM ("add_arity_thms: theorem is not an arity", 0, [thm]);
   149       in (t, ss, [c]) end;
   150   in
   151     Theory.add_arities (map prep_thm thms) thy
   152   end;
   153 
   154 
   155 
   156 (** add axiomatic type classes **)
   157 
   158 (* errors *)
   159 
   160 fun err_not_logic c =
   161   error ("Axiomatic class " ^ quote c ^ " not subclass of \"logic\"");
   162 
   163 fun err_bad_axsort ax c =
   164   error ("Sort constraint in axiom " ^ quote ax ^ " not supersort of " ^ quote c);
   165 
   166 fun err_bad_tfrees ax =
   167   error ("More than one type variable in axiom " ^ quote ax);
   168 
   169 
   170 (* ext_axclass *)
   171 
   172 fun ext_axclass int prep_axm (raw_class, raw_super_classes) raw_axioms old_thy =
   173   let
   174     val old_sign = sign_of old_thy;
   175     val axioms = map (prep_axm old_sign) raw_axioms;
   176     val class = Sign.full_name old_sign raw_class;
   177 
   178     val thy =
   179       (if int then Theory.add_classes else Theory.add_classes_i)
   180         [(raw_class, raw_super_classes)] old_thy;
   181     val sign = sign_of thy;
   182     val super_classes =
   183       if int then map (Sign.intern_class sign) raw_super_classes
   184       else raw_super_classes;
   185 
   186 
   187     (* prepare abstract axioms *)
   188 
   189     fun abs_axm ax =
   190       if null (term_tfrees ax) then
   191         Logic.mk_implies (Logic.mk_inclass (aT logicS, class), ax)
   192       else map_term_tfrees (K (aT [class])) ax;
   193 
   194     val abs_axioms = map (apsnd abs_axm) axioms;
   195 
   196 
   197     (* prepare introduction orule *)
   198 
   199     val _ =
   200       if Sign.subsort sign ([class], logicS) then ()
   201       else err_not_logic class;
   202 
   203     fun axm_sort (name, ax) =
   204       (case term_tfrees ax of
   205         [] => []
   206       | [(_, S)] =>
   207           if Sign.subsort sign ([class], S) then S
   208           else err_bad_axsort name class
   209       | _ => err_bad_tfrees name);
   210 
   211     val axS = Sign.norm_sort sign (logicC :: flat (map axm_sort axioms))
   212 
   213     val int_axm = Logic.close_form o map_term_tfrees (K (aT axS));
   214     fun inclass c = Logic.mk_inclass (aT axS, c);
   215 
   216     val intro_axm = Logic.list_implies
   217       (map inclass super_classes @ map (int_axm o snd) axioms, inclass class);
   218   in
   219     Theory.add_axioms_i ((raw_class ^ "I", intro_axm) :: abs_axioms) thy
   220   end;
   221 
   222 
   223 (* external interfaces *)
   224 
   225 val add_axclass = ext_axclass true read_axm;
   226 val add_axclass_i = ext_axclass false cert_axm;
   227 
   228 
   229 
   230 (** prove class relations and type arities **)
   231 
   232 (* class_axms *)
   233 
   234 fun class_axms thy =
   235   let
   236     val classes = Sign.classes (sign_of thy);
   237     val intros = map (fn c => c ^ "I") classes;
   238   in
   239     map (class_triv thy) classes @
   240     get_axioms thy intros
   241   end;
   242 
   243 
   244 (* axclass_tac *)
   245 
   246 (*(1) repeatedly resolve goals of form "OFCLASS(ty, c_class)",
   247       try class_trivs first, then "cI" axioms
   248   (2) rewrite goals using user supplied definitions
   249   (3) repeatedly resolve goals with user supplied non-definitions*)
   250 
   251 fun axclass_tac thy thms =
   252   let
   253     val defs = filter is_def thms;
   254     val non_defs = filter_out is_def thms;
   255   in
   256     TRY (REPEAT_FIRST (resolve_tac (class_axms thy))) THEN
   257     TRY (rewrite_goals_tac defs) THEN
   258     TRY (REPEAT_FIRST (fn i => assume_tac i ORELSE resolve_tac non_defs i))
   259   end;
   260 
   261 
   262 (* provers *)
   263 
   264 fun prove term_of str_of thy sig_prop thms usr_tac =
   265   let
   266     val sign = sign_of thy;
   267     val goal = cterm_of sign (term_of sig_prop);
   268     val tac = axclass_tac thy thms THEN (if_none usr_tac all_tac);
   269   in
   270     prove_goalw_cterm [] goal (K [tac])
   271   end
   272   handle ERROR => error ("The error(s) above occurred while trying to prove "
   273     ^ quote (str_of (sign_of thy, sig_prop)));
   274 
   275 val prove_subclass =
   276   prove mk_classrel (fn (sg, c1_c2) => Sign.str_of_classrel sg c1_c2);
   277 
   278 val prove_arity =
   279   prove mk_arity (fn (sg, (t, Ss, c)) => Sign.str_of_arity sg (t, Ss, [c]));
   280 
   281 
   282 
   283 (** add proved subclass relations and arities **)
   284 
   285 fun intrn_classrel sg c1_c2 =
   286   pairself (Sign.intern_class sg) c1_c2;
   287 
   288 fun ext_inst_subclass int raw_c1_c2 axms thms usr_tac thy =
   289   let
   290     val c1_c2 =
   291       if int then intrn_classrel (sign_of thy) raw_c1_c2
   292       else raw_c1_c2;
   293   in
   294     writeln ("Proving class inclusion " ^
   295       quote (Sign.str_of_classrel (sign_of thy) c1_c2) ^ " ...");
   296     add_classrel_thms
   297       [prove_subclass thy c1_c2 (witnesses thy axms thms) usr_tac] thy
   298   end;
   299 
   300 
   301 fun intrn_arity sg intrn (t, Ss, x) =
   302   (Sign.intern_tycon sg t, map (Sign.intern_sort sg) Ss, intrn sg x);
   303 
   304 fun ext_inst_arity int (raw_t, raw_Ss, raw_cs) axms thms usr_tac thy =
   305   let
   306     val sign = sign_of thy;
   307     val (t, Ss, cs) =
   308       if int then intrn_arity sign Sign.intern_sort (raw_t, raw_Ss, raw_cs)
   309       else (raw_t, raw_Ss, raw_cs);
   310     val wthms = witnesses thy axms thms;
   311     fun prove c =
   312      (writeln ("Proving type arity " ^
   313         quote (Sign.str_of_arity sign (t, Ss, [c])) ^ " ...");
   314         prove_arity thy (t, Ss, c) wthms usr_tac);
   315   in
   316     add_arity_thms (map prove cs) thy
   317   end;
   318 
   319 val add_inst_subclass = ext_inst_subclass true;
   320 val add_inst_subclass_i = ext_inst_subclass false;
   321 val add_inst_arity = ext_inst_arity true;
   322 val add_inst_arity_i = ext_inst_arity false;
   323 
   324 
   325 (* make goals (for interactive use) *)
   326 
   327 fun mk_goal term_of thy sig_prop =
   328   goalw_cterm [] (cterm_of (sign_of thy) (term_of sig_prop));
   329 
   330 fun goal_subclass thy =
   331   mk_goal (mk_classrel o intrn_classrel (sign_of thy)) thy;
   332 
   333 fun goal_arity thy =
   334   mk_goal (mk_arity o intrn_arity (sign_of thy) Sign.intern_class) thy;
   335 
   336 
   337 end;