src/Pure/simplifier.ML
author haftmann
Tue Sep 06 08:30:43 2005 +0200 (2005-09-06)
changeset 17271 2756a73f63a5
parent 17004 6a0d8ecf65f1
child 17723 ee5b42e3cbb4
permissions -rw-r--r--
introduced some new-style AList operations
     1 (*  Title:      Pure/simplifier.ML
     2     ID:         $Id$
     3     Author:     Tobias Nipkow and Markus Wenzel, TU Muenchen
     4 
     5 Generic simplifier, suitable for most logics (see also
     6 meta_simplifier.ML for the actual meta-level rewriting engine).
     7 *)
     8 
     9 signature BASIC_SIMPLIFIER =
    10 sig
    11   include BASIC_META_SIMPLIFIER
    12   type context_solver
    13   val mk_context_solver: string -> (Proof.context -> thm list -> int -> tactic)
    14     -> context_solver
    15   type context_simproc
    16   val mk_context_simproc: string -> cterm list ->
    17     (Proof.context -> simpset -> term -> thm option) -> context_simproc
    18   val print_simpset: theory -> unit
    19   val simpset_ref_of_sg: theory -> simpset ref    (*obsolete*)
    20   val simpset_ref_of: theory -> simpset ref
    21   val simpset_of_sg: theory -> simpset            (*obsolete*)
    22   val simpset_of: theory -> simpset
    23   val SIMPSET: (simpset -> tactic) -> tactic
    24   val SIMPSET': (simpset -> 'a -> tactic) -> 'a -> tactic
    25   val simpset: unit -> simpset
    26   val simpset_ref: unit -> simpset ref
    27   val Addsimps: thm list -> unit
    28   val Delsimps: thm list -> unit
    29   val Addsimprocs: simproc list -> unit
    30   val Delsimprocs: simproc list -> unit
    31   val Addcongs: thm list -> unit
    32   val Delcongs: thm list -> unit
    33   val local_simpset_of: Proof.context -> simpset
    34   val safe_asm_full_simp_tac: simpset -> int -> tactic
    35   val               simp_tac: simpset -> int -> tactic
    36   val           asm_simp_tac: simpset -> int -> tactic
    37   val          full_simp_tac: simpset -> int -> tactic
    38   val        asm_lr_simp_tac: simpset -> int -> tactic
    39   val      asm_full_simp_tac: simpset -> int -> tactic
    40   val               Simp_tac:            int -> tactic
    41   val           Asm_simp_tac:            int -> tactic
    42   val          Full_simp_tac:            int -> tactic
    43   val        Asm_lr_simp_tac:            int -> tactic
    44   val      Asm_full_simp_tac:            int -> tactic
    45   val          simplify: simpset -> thm -> thm
    46   val      asm_simplify: simpset -> thm -> thm
    47   val     full_simplify: simpset -> thm -> thm
    48   val   asm_lr_simplify: simpset -> thm -> thm
    49   val asm_full_simplify: simpset -> thm -> thm
    50 end;
    51 
    52 signature SIMPLIFIER =
    53 sig
    54   include BASIC_SIMPLIFIER
    55   val clear_ss: simpset -> simpset
    56   val inherit_bounds: simpset -> simpset -> simpset
    57   val simproc_i: theory -> string -> term list
    58     -> (theory -> simpset -> term -> thm option) -> simproc
    59   val simproc: theory -> string -> string list
    60     -> (theory -> simpset -> term -> thm option) -> simproc
    61   val context_simproc_i: theory -> string -> term list
    62     -> (Proof.context -> simpset -> term -> thm option) -> context_simproc
    63   val context_simproc: theory -> string -> string list
    64     -> (Proof.context -> simpset -> term -> thm option) -> context_simproc
    65   val          rewrite: simpset -> cterm -> thm
    66   val      asm_rewrite: simpset -> cterm -> thm
    67   val     full_rewrite: simpset -> cterm -> thm
    68   val   asm_lr_rewrite: simpset -> cterm -> thm
    69   val asm_full_rewrite: simpset -> cterm -> thm
    70   val add_context_simprocs: context_simproc list -> theory -> theory
    71   val del_context_simprocs: context_simproc list -> theory -> theory
    72   val set_context_subgoaler: (Proof.context -> simpset -> int -> tactic) -> theory -> theory
    73   val reset_context_subgoaler: theory -> theory
    74   val add_context_looper: string * (Proof.context -> int -> Tactical.tactic) ->
    75     theory -> theory
    76   val del_context_looper: string -> theory -> theory
    77   val add_context_unsafe_solver: context_solver -> theory -> theory
    78   val add_context_safe_solver: context_solver -> theory -> theory
    79   val print_local_simpset: Proof.context -> unit
    80   val get_local_simpset: Proof.context -> simpset
    81   val put_local_simpset: simpset -> Proof.context -> Proof.context
    82   val change_global_ss: (simpset * thm list -> simpset) -> theory attribute
    83   val change_local_ss: (simpset * thm list -> simpset) -> Proof.context attribute
    84   val simp_add_global: theory attribute
    85   val simp_del_global: theory attribute
    86   val simp_add_local: Proof.context attribute
    87   val simp_del_local: Proof.context attribute
    88   val cong_add_global: theory attribute
    89   val cong_del_global: theory attribute
    90   val cong_add_local: Proof.context attribute
    91   val cong_del_local: Proof.context attribute
    92   val change_simpset_of: (simpset * 'a -> simpset) -> 'a -> theory -> theory
    93   val simp_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list
    94   val method_setup: (Args.T list -> (Method.modifier * Args.T list)) list
    95     -> (theory -> theory) list
    96   val easy_setup: thm -> thm list -> (theory -> theory) list
    97 end;
    98 
    99 structure Simplifier: SIMPLIFIER =
   100 struct
   101 
   102 open MetaSimplifier;
   103 
   104 
   105 (** context dependent simpset components **)
   106 
   107 (* datatype context_solver *)
   108 
   109 datatype context_solver =
   110   ContextSolver of (string * (Proof.context -> thm list -> int -> tactic)) * stamp;
   111 
   112 fun mk_context_solver name f = ContextSolver ((name, f), stamp ());
   113 fun eq_context_solver (ContextSolver (_, id1), ContextSolver (_, id2)) = (id1 = id2);
   114 val merge_context_solvers = gen_merge_lists eq_context_solver;
   115 
   116 
   117 (* datatype context_simproc *)
   118 
   119 datatype context_simproc = ContextSimproc of
   120   (string * cterm list * (Proof.context -> simpset -> term -> thm option)) * stamp;
   121 
   122 fun mk_context_simproc name lhss f = ContextSimproc ((name, lhss, f), stamp ());
   123 fun eq_context_simproc (ContextSimproc (_, id1), ContextSimproc (_, id2)) = (id1 = id2);
   124 val merge_context_simprocs = gen_merge_lists eq_context_simproc;
   125 
   126 fun context_simproc_i thy name =
   127   mk_context_simproc name o map (Thm.cterm_of thy o Logic.varify);
   128 
   129 fun context_simproc thy name =
   130   context_simproc_i thy name o map (Sign.read_term thy);
   131 
   132 
   133 (* datatype context_ss *)
   134 
   135 datatype context_ss = ContextSS of
   136  {simprocs: context_simproc list,
   137   subgoal_tac: (Proof.context -> simpset -> int -> tactic) option,
   138   loop_tacs: (string * (Proof.context -> int -> tactic)) list,
   139   unsafe_solvers: context_solver list,
   140   solvers: context_solver list};
   141 
   142 fun context_ss ctxt ss ctxt_ss =
   143   let
   144     val ContextSS {simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers} = ctxt_ss;
   145     fun prep_simproc (ContextSimproc ((name, lhss, f), _)) =
   146       mk_simproc name lhss (K (f ctxt));
   147     fun add_loop (name, f) simpset = simpset addloop (name, f ctxt);
   148     fun add_solver add (ContextSolver ((name, f), _)) simpset =
   149       add (simpset, mk_solver name (f ctxt));
   150   in
   151     ((case subgoal_tac of NONE => ss | SOME tac => ss setsubgoaler tac ctxt)
   152       addsimprocs map prep_simproc simprocs)
   153     |> fold_rev add_loop loop_tacs
   154     |> fold_rev (add_solver (op addSolver)) unsafe_solvers
   155     |> fold_rev (add_solver (op addSSolver)) solvers
   156   end;
   157 
   158 fun make_context_ss (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) =
   159   ContextSS {simprocs = simprocs, subgoal_tac = subgoal_tac, loop_tacs = loop_tacs,
   160     unsafe_solvers = unsafe_solvers, solvers = solvers};
   161 
   162 val empty_context_ss = make_context_ss ([], NONE, [], [], []);
   163 
   164 fun merge_context_ss (ctxt_ss1, ctxt_ss2) =
   165   let
   166     val ContextSS {simprocs = simprocs1, subgoal_tac = subgoal_tac1, loop_tacs = loop_tacs1,
   167       unsafe_solvers = unsafe_solvers1, solvers = solvers1} = ctxt_ss1;
   168     val ContextSS {simprocs = simprocs2, subgoal_tac = subgoal_tac2, loop_tacs = loop_tacs2,
   169       unsafe_solvers = unsafe_solvers2, solvers = solvers2} = ctxt_ss2;
   170 
   171     val simprocs' = merge_context_simprocs simprocs1 simprocs2;
   172     val subgoal_tac' = (case subgoal_tac1 of NONE => subgoal_tac2 | some => some);
   173     val loop_tacs' = merge_alists loop_tacs1 loop_tacs2;
   174     val unsafe_solvers' = merge_context_solvers unsafe_solvers1 unsafe_solvers2;
   175     val solvers' = merge_context_solvers solvers1 solvers2;
   176   in make_context_ss (simprocs', subgoal_tac', loop_tacs', unsafe_solvers', solvers') end;
   177 
   178 
   179 
   180 (** global and local simpset data **)
   181 
   182 (* theory data kind 'Pure/simpset' *)
   183 
   184 structure GlobalSimpset = TheoryDataFun
   185 (struct
   186   val name = "Pure/simpset";
   187   type T = simpset ref * context_ss;
   188 
   189   val empty = (ref empty_ss, empty_context_ss);
   190   fun copy (ref ss, ctxt_ss) = (ref ss, ctxt_ss): T;            (*create new reference!*)
   191   val extend = copy;
   192   fun merge _ ((ref ss1, ctxt_ss1), (ref ss2, ctxt_ss2)) =
   193     (ref (merge_ss (ss1, ss2)), merge_context_ss (ctxt_ss1, ctxt_ss2));
   194   fun print _ (ref ss, _) = print_ss ss;
   195 end);
   196 
   197 val _ = Context.add_setup [GlobalSimpset.init];
   198 val print_simpset = GlobalSimpset.print;
   199 
   200 val simpset_ref_of = #1 o GlobalSimpset.get;
   201 val simpset_ref_of_sg = simpset_ref_of;
   202 val get_context_ss = #2 o GlobalSimpset.get o ProofContext.theory_of;
   203 
   204 fun map_context_ss f = GlobalSimpset.map (apsnd
   205   (fn ContextSS {simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers} =>
   206     make_context_ss (f (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers))));
   207 
   208 
   209 (* access global simpset *)
   210 
   211 val simpset_of = ! o simpset_ref_of;
   212 val simpset_of_sg = simpset_of;
   213 
   214 fun SIMPSET tacf state = tacf (simpset_of (Thm.theory_of_thm state)) state;
   215 fun SIMPSET' tacf i state = tacf (simpset_of (Thm.theory_of_thm state)) i state;
   216 
   217 val simpset = simpset_of o Context.the_context;
   218 val simpset_ref = simpset_ref_of o Context.the_context;
   219 
   220 
   221 (* change global simpset *)
   222 
   223 fun change_simpset_of f x thy =
   224   let val r = simpset_ref_of thy
   225   in r := f (! r, x); thy end;
   226 
   227 fun change_simpset f x = (change_simpset_of f x (Context.the_context ()); ());
   228 
   229 val Addsimps = change_simpset (op addsimps);
   230 val Delsimps = change_simpset (op delsimps);
   231 val Addsimprocs = change_simpset (op addsimprocs);
   232 val Delsimprocs = change_simpset (op delsimprocs);
   233 val Addcongs = change_simpset (op addcongs);
   234 val Delcongs = change_simpset (op delcongs);
   235 
   236 
   237 (* change context dependent components *)
   238 
   239 fun add_context_simprocs procs =
   240   map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) =>
   241     (merge_context_simprocs procs simprocs, subgoal_tac, loop_tacs,
   242       unsafe_solvers, solvers));
   243 
   244 fun del_context_simprocs procs =
   245   map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) =>
   246     (gen_rems eq_context_simproc (simprocs, procs), subgoal_tac, loop_tacs,
   247       unsafe_solvers, solvers));
   248 
   249 fun set_context_subgoaler tac =
   250   map_context_ss (fn (simprocs, _, loop_tacs, unsafe_solvers, solvers) =>
   251     (simprocs, SOME tac, loop_tacs, unsafe_solvers, solvers));
   252 
   253 val reset_context_subgoaler =
   254   map_context_ss (fn (simprocs, _, loop_tacs, unsafe_solvers, solvers) =>
   255     (simprocs, NONE, loop_tacs, unsafe_solvers, solvers));
   256 
   257 fun add_context_looper (name, tac) =
   258   map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) =>
   259     (simprocs, subgoal_tac, merge_alists [(name, tac)] loop_tacs,
   260       unsafe_solvers, solvers));
   261 
   262 fun del_context_looper name =
   263   map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) =>
   264     (simprocs, subgoal_tac, filter_out (equal name o #1) loop_tacs,
   265       unsafe_solvers, solvers));
   266 
   267 fun add_context_unsafe_solver solver =
   268   map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) =>
   269     (simprocs, subgoal_tac, loop_tacs,
   270       merge_context_solvers [solver] unsafe_solvers, solvers));
   271 
   272 fun add_context_safe_solver solver =
   273   map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) =>
   274     (simprocs, subgoal_tac, loop_tacs, unsafe_solvers,
   275       merge_context_solvers [solver] solvers));
   276 
   277 
   278 (* proof data kind 'Pure/simpset' *)
   279 
   280 structure LocalSimpset = ProofDataFun
   281 (struct
   282   val name = "Pure/simpset";
   283   type T = simpset;
   284   val init = simpset_of;
   285   fun print ctxt ss = print_ss (context_ss ctxt ss (get_context_ss ctxt));
   286 end);
   287 
   288 val _ = Context.add_setup [LocalSimpset.init];
   289 val print_local_simpset = LocalSimpset.print;
   290 
   291 val get_local_simpset = LocalSimpset.get;
   292 val put_local_simpset = LocalSimpset.put;
   293 fun map_local_simpset f ctxt = put_local_simpset (f (get_local_simpset ctxt)) ctxt;
   294 
   295 fun local_simpset_of ctxt =
   296   context_ss ctxt (get_local_simpset ctxt) (get_context_ss ctxt);
   297 
   298 
   299 (* attributes *)
   300 
   301 fun change_global_ss f (thy, th) =
   302   let val r = simpset_ref_of thy
   303   in r := f (! r, [th]); (thy, th) end;
   304 
   305 fun change_local_ss f (ctxt, th) =
   306   let val ss = f (get_local_simpset ctxt, [th])
   307   in (put_local_simpset ss ctxt, th) end;
   308 
   309 val simp_add_global = change_global_ss (op addsimps);
   310 val simp_del_global = change_global_ss (op delsimps);
   311 val simp_add_local = change_local_ss (op addsimps);
   312 val simp_del_local = change_local_ss (op delsimps);
   313 
   314 val cong_add_global = change_global_ss (op addcongs);
   315 val cong_del_global = change_global_ss (op delcongs);
   316 val cong_add_local = change_local_ss (op addcongs);
   317 val cong_del_local = change_local_ss (op delcongs);
   318 
   319 
   320 (* tactics *)
   321 
   322 val simp_tac = generic_simp_tac false (false, false, false);
   323 val asm_simp_tac = generic_simp_tac false (false, true, false);
   324 val full_simp_tac = generic_simp_tac false (true, false, false);
   325 val asm_lr_simp_tac = generic_simp_tac false (true, true, false);
   326 val asm_full_simp_tac = generic_simp_tac false (true, true, true);
   327 val safe_asm_full_simp_tac = generic_simp_tac true (true, true, true);
   328 
   329 (*the abstraction over the proof state delays the dereferencing*)
   330 fun          Simp_tac i st =          simp_tac (simpset ()) i st;
   331 fun      Asm_simp_tac i st =      asm_simp_tac (simpset ()) i st;
   332 fun     Full_simp_tac i st =     full_simp_tac (simpset ()) i st;
   333 fun   Asm_lr_simp_tac i st =   asm_lr_simp_tac (simpset ()) i st;
   334 fun Asm_full_simp_tac i st = asm_full_simp_tac (simpset ()) i st;
   335 
   336 
   337 (* conversions *)
   338 
   339 val          simplify = simp_thm (false, false, false);
   340 val      asm_simplify = simp_thm (false, true, false);
   341 val     full_simplify = simp_thm (true, false, false);
   342 val   asm_lr_simplify = simp_thm (true, true, false);
   343 val asm_full_simplify = simp_thm (true, true, true);
   344 
   345 val          rewrite = simp_cterm (false, false, false);
   346 val      asm_rewrite = simp_cterm (false, true, false);
   347 val     full_rewrite = simp_cterm (true, false, false);
   348 val   asm_lr_rewrite = simp_cterm (true, true, false);
   349 val asm_full_rewrite = simp_cterm (true, true, true);
   350 
   351 
   352 
   353 (** concrete syntax of attributes **)
   354 
   355 (* add / del *)
   356 
   357 val simpN = "simp";
   358 val congN = "cong";
   359 val addN = "add";
   360 val delN = "del";
   361 val onlyN = "only";
   362 val no_asmN = "no_asm";
   363 val no_asm_useN = "no_asm_use";
   364 val no_asm_simpN = "no_asm_simp";
   365 val asm_lrN = "asm_lr";
   366 
   367 val simp_attr =
   368  (Attrib.add_del_args simp_add_global simp_del_global,
   369   Attrib.add_del_args simp_add_local simp_del_local);
   370 
   371 val cong_attr =
   372  (Attrib.add_del_args cong_add_global cong_del_global,
   373   Attrib.add_del_args cong_add_local cong_del_local);
   374 
   375 
   376 (* conversions *)
   377 
   378 local
   379 
   380 fun conv_mode x =
   381   ((Args.parens (Args.$$$ no_asmN) >> K simplify ||
   382     Args.parens (Args.$$$ no_asm_simpN) >> K asm_simplify ||
   383     Args.parens (Args.$$$ no_asm_useN) >> K full_simplify ||
   384     Scan.succeed asm_full_simplify) |> Scan.lift) x;
   385 
   386 fun simplified_att get args =
   387   Attrib.syntax (conv_mode -- args >> (fn (f, ths) =>
   388     Drule.rule_attribute (fn x => f ((if null ths then I else clear_ss) (get x) addsimps ths))));
   389 
   390 in
   391 
   392 val simplified_attr =
   393  (simplified_att simpset_of Attrib.global_thmss,
   394   simplified_att local_simpset_of Attrib.local_thmss);
   395 
   396 end;
   397 
   398 
   399 (* setup attributes *)
   400 
   401 val _ = Context.add_setup
   402  [Attrib.add_attributes
   403    [(simpN, simp_attr, "declaration of simplification rule"),
   404     (congN, cong_attr, "declaration of Simplifier congruence rule"),
   405     ("simplified", simplified_attr, "simplified rule")]];
   406 
   407 
   408 
   409 (** proof methods **)
   410 
   411 (* simplification *)
   412 
   413 val simp_options =
   414  (Args.parens (Args.$$$ no_asmN) >> K simp_tac ||
   415   Args.parens (Args.$$$ no_asm_simpN) >> K asm_simp_tac ||
   416   Args.parens (Args.$$$ no_asm_useN) >> K full_simp_tac ||
   417   Args.parens (Args.$$$ asm_lrN) >> K asm_lr_simp_tac ||
   418   Scan.succeed asm_full_simp_tac);
   419 
   420 fun simp_flags x = (Scan.repeat
   421   (Args.parens (Args.$$$ "depth_limit" -- Args.colon |-- Args.nat)
   422     >> setmp MetaSimplifier.simp_depth_limit)
   423   >> (curry (Library.foldl op o) I o rev)) x;
   424 
   425 val cong_modifiers =
   426  [Args.$$$ congN -- Args.colon >> K ((I, cong_add_local):Method.modifier),
   427   Args.$$$ congN -- Args.add -- Args.colon >> K (I, cong_add_local),
   428   Args.$$$ congN -- Args.del -- Args.colon >> K (I, cong_del_local)];
   429 
   430 val simp_modifiers =
   431  [Args.$$$ simpN -- Args.colon >> K (I, simp_add_local),
   432   Args.$$$ simpN -- Args.add -- Args.colon >> K (I, simp_add_local),
   433   Args.$$$ simpN -- Args.del -- Args.colon >> K (I, simp_del_local),
   434   Args.$$$ simpN -- Args.$$$ onlyN -- Args.colon >> K (map_local_simpset clear_ss, simp_add_local)]
   435    @ cong_modifiers;
   436 
   437 val simp_modifiers' =
   438  [Args.add -- Args.colon >> K (I, simp_add_local),
   439   Args.del -- Args.colon >> K (I, simp_del_local),
   440   Args.$$$ onlyN -- Args.colon >> K (map_local_simpset clear_ss, simp_add_local)]
   441    @ cong_modifiers;
   442 
   443 fun simp_args more_mods =
   444   Method.sectioned_args (Args.bang_facts -- Scan.lift simp_options -- Scan.lift simp_flags)
   445     (more_mods @ simp_modifiers');
   446 
   447 fun simp_method ((prems, tac), FLAGS) ctxt = Method.METHOD (fn facts =>
   448   ALLGOALS (Method.insert_tac (prems @ facts)) THEN
   449     (FLAGS o CHANGED_PROP o ALLGOALS o tac) (local_simpset_of ctxt));
   450 
   451 fun simp_method' ((prems, tac), FLAGS) ctxt = Method.METHOD (fn facts =>
   452   HEADGOAL (Method.insert_tac (prems @ facts) THEN'
   453       ((FLAGS o CHANGED_PROP) oo tac) (local_simpset_of ctxt)));
   454 
   455 
   456 (* setup methods *)
   457 
   458 fun setup_methods more_mods = Method.add_methods
   459  [(simpN, simp_args more_mods simp_method', "simplification"),
   460   ("simp_all", simp_args more_mods simp_method, "simplification (all goals)")];
   461 
   462 fun method_setup mods = [setup_methods mods];
   463 
   464 
   465 (** easy_setup **)
   466 
   467 fun easy_setup reflect trivs =
   468   let
   469     val trivialities = Drule.reflexive_thm :: trivs;
   470 
   471     fun unsafe_solver_tac prems = FIRST' [resolve_tac (trivialities @ prems), assume_tac];
   472     val unsafe_solver = mk_solver "easy unsafe" unsafe_solver_tac;
   473 
   474     (*no premature instantiation of variables during simplification*)
   475     fun safe_solver_tac prems = FIRST' [match_tac (trivialities @ prems), eq_assume_tac];
   476     val safe_solver = mk_solver "easy safe" safe_solver_tac;
   477 
   478     fun mk_eq thm =
   479       if Logic.is_equals (Thm.concl_of thm) then [thm]
   480       else [thm RS reflect] handle THM _ => [];
   481 
   482     fun mksimps thm = mk_eq (Drule.forall_elim_vars (#maxidx (Thm.rep_thm thm) + 1) thm);
   483 
   484     fun init_ss thy =
   485       (simpset_ref_of thy :=
   486         empty_ss setsubgoaler asm_simp_tac
   487         setSSolver safe_solver
   488         setSolver unsafe_solver
   489         setmksimps mksimps; thy);
   490   in method_setup [] @ [init_ss] end;
   491 
   492 end;
   493 
   494 structure BasicSimplifier: BASIC_SIMPLIFIER = Simplifier;
   495 open BasicSimplifier;