src/HOL/simpdata.ML
author wenzelm
Fri Jul 25 13:18:09 1997 +0200 (1997-07-25)
changeset 3577 9715b6e3ec5f
parent 3573 7544c866315c
child 3615 e5322197cfea
permissions -rw-r--r--
added prems argument to simplification procedures;
     1 (*  Title:      HOL/simpdata.ML
     2     ID:         $Id$
     3     Author:     Tobias Nipkow
     4     Copyright   1991  University of Cambridge
     5 
     6 Instantiation of the generic simplifier
     7 *)
     8 
     9 section "Simplifier";
    10 
    11 open Simplifier;
    12 
    13 (*** Addition of rules to simpsets and clasets simultaneously ***)
    14 
    15 (*Takes UNCONDITIONAL theorems of the form A<->B to 
    16         the Safe Intr     rule B==>A and 
    17         the Safe Destruct rule A==>B.
    18   Also ~A goes to the Safe Elim rule A ==> ?R
    19   Failing other cases, A is added as a Safe Intr rule*)
    20 local
    21   val iff_const = HOLogic.eq_const HOLogic.boolT;
    22 
    23   fun addIff th = 
    24       (case HOLogic.dest_Trueprop (#prop(rep_thm th)) of
    25                 (Const("Not",_) $ A) =>
    26                     AddSEs [zero_var_indexes (th RS notE)]
    27               | (con $ _ $ _) =>
    28                     if con=iff_const
    29                     then (AddSIs [zero_var_indexes (th RS iffD2)];  
    30                           AddSDs [zero_var_indexes (th RS iffD1)])
    31                     else  AddSIs [th]
    32               | _ => AddSIs [th];
    33        Addsimps [th])
    34       handle _ => error ("AddIffs: theorem must be unconditional\n" ^ 
    35                          string_of_thm th)
    36 
    37   fun delIff th = 
    38       (case HOLogic.dest_Trueprop (#prop(rep_thm th)) of
    39                 (Const("Not",_) $ A) =>
    40                     Delrules [zero_var_indexes (th RS notE)]
    41               | (con $ _ $ _) =>
    42                     if con=iff_const
    43                     then Delrules [zero_var_indexes (th RS iffD2),
    44                                    make_elim (zero_var_indexes (th RS iffD1))]
    45                     else Delrules [th]
    46               | _ => Delrules [th];
    47        Delsimps [th])
    48       handle _ => warning("DelIffs: ignoring conditional theorem\n" ^ 
    49                           string_of_thm th)
    50 in
    51 val AddIffs = seq addIff
    52 val DelIffs = seq delIff
    53 end;
    54 
    55 
    56 local
    57 
    58   fun prover s = prove_goal HOL.thy s (fn _ => [blast_tac HOL_cs 1]);
    59 
    60   val P_imp_P_iff_True = prover "P --> (P = True)" RS mp;
    61   val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection;
    62 
    63   val not_P_imp_P_iff_F = prover "~P --> (P = False)" RS mp;
    64   val not_P_imp_P_eq_False = not_P_imp_P_iff_F RS eq_reflection;
    65 
    66   fun atomize pairs =
    67     let fun atoms th =
    68           (case concl_of th of
    69              Const("Trueprop",_) $ p =>
    70                (case head_of p of
    71                   Const(a,_) =>
    72                     (case assoc(pairs,a) of
    73                        Some(rls) => flat (map atoms ([th] RL rls))
    74                      | None => [th])
    75                 | _ => [th])
    76            | _ => [th])
    77     in atoms end;
    78 
    79   fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th;
    80 
    81 in
    82 
    83   fun mk_meta_eq r = case concl_of r of
    84           Const("==",_)$_$_ => r
    85       |   _$(Const("op =",_)$_$_) => r RS eq_reflection
    86       |   _$(Const("Not",_)$_) => r RS not_P_imp_P_eq_False
    87       |   _ => r RS P_imp_P_eq_True;
    88   (* last 2 lines requires all formulae to be of the from Trueprop(.) *)
    89 
    90 val simp_thms = map prover
    91  [ "(x=x) = True",
    92    "(~True) = False", "(~False) = True", "(~ ~ P) = P",
    93    "(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))",
    94    "(True=P) = P", "(P=True) = P",
    95    "(True --> P) = P", "(False --> P) = True", 
    96    "(P --> True) = True", "(P --> P) = True",
    97    "(P --> False) = (~P)", "(P --> ~P) = (~P)",
    98    "(P & True) = P", "(True & P) = P", 
    99    "(P & False) = False", "(False & P) = False",
   100    "(P & P) = P", "(P & (P & Q)) = (P & Q)",
   101    "(P | True) = True", "(True | P) = True", 
   102    "(P | False) = P", "(False | P) = P",
   103    "(P | P) = P", "(P | (P | Q)) = (P | Q)",
   104    "((~P) = (~Q)) = (P=Q)",
   105    "(!x.P) = P", "(? x.P) = P", "? x. x=t", "? x. t=x", 
   106    "(? x. x=t & P(x)) = P(t)",
   107    "(! x. t=x --> P(x)) = P(t)" ];
   108 
   109 (*Add congruence rules for = (instead of ==) *)
   110 infix 4 addcongs delcongs;
   111 fun ss addcongs congs = ss addeqcongs (map standard (congs RL [eq_reflection]));
   112 fun ss delcongs congs = ss deleqcongs (map standard (congs RL [eq_reflection]));
   113 
   114 fun Addcongs congs = (simpset := !simpset addcongs congs);
   115 fun Delcongs congs = (simpset := !simpset delcongs congs);
   116 
   117 fun mksimps pairs = map mk_meta_eq o atomize pairs o gen_all;
   118 
   119 val imp_cong = impI RSN
   120     (2, prove_goal HOL.thy "(P=P')--> (P'--> (Q=Q'))--> ((P-->Q) = (P'-->Q'))"
   121         (fn _=> [blast_tac HOL_cs 1]) RS mp RS mp);
   122 
   123 (*Miniscoping: pushing in existential quantifiers*)
   124 val ex_simps = map prover 
   125                 ["(EX x. P x & Q)   = ((EX x.P x) & Q)",
   126                  "(EX x. P & Q x)   = (P & (EX x.Q x))",
   127                  "(EX x. P x | Q)   = ((EX x.P x) | Q)",
   128                  "(EX x. P | Q x)   = (P | (EX x.Q x))",
   129                  "(EX x. P x --> Q) = ((ALL x.P x) --> Q)",
   130                  "(EX x. P --> Q x) = (P --> (EX x.Q x))"];
   131 
   132 (*Miniscoping: pushing in universal quantifiers*)
   133 val all_simps = map prover
   134                 ["(ALL x. P x & Q)   = ((ALL x.P x) & Q)",
   135                  "(ALL x. P & Q x)   = (P & (ALL x.Q x))",
   136                  "(ALL x. P x | Q)   = ((ALL x.P x) | Q)",
   137                  "(ALL x. P | Q x)   = (P | (ALL x.Q x))",
   138                  "(ALL x. P x --> Q) = ((EX x.P x) --> Q)",
   139                  "(ALL x. P --> Q x) = (P --> (ALL x.Q x))"];
   140 
   141 (*** Simplification procedure for turning  ? x. ... & x = t & ...
   142      into                                  ? x. x = t & ... & ...
   143      where the latter can be rewritten via (? x. x = t & P(x)) = P(t)
   144  ***)
   145 
   146 local
   147 
   148 fun def(eq as (c as Const("op =",_)) $ s $ t) =
   149       if s = Bound 0 andalso not(loose_bvar1(t,0)) then Some eq else
   150       if t = Bound 0 andalso not(loose_bvar1(s,0)) then Some(c$t$s)
   151       else None
   152   | def _ = None;
   153 
   154 fun extract(Const("op &",_) $ P $ Q) =
   155       (case def P of
   156          Some eq => Some(eq,Q)
   157        | None => (case def Q of
   158                    Some eq => Some(eq,P)
   159                  | None =>
   160        (case extract P of
   161          Some(eq,P') => Some(eq, HOLogic.conj $ P' $ Q)
   162        | None => (case extract Q of
   163                    Some(eq,Q') => Some(eq,HOLogic.conj $ P $ Q')
   164                  | None => None))))
   165   | extract _ = None;
   166 
   167 fun prove_eq(ceqt) =
   168   let val tac = rtac eq_reflection 1 THEN rtac iffI 1 THEN
   169                 ALLGOALS(EVERY'[etac exE, REPEAT o (etac conjE),
   170                  rtac exI, REPEAT o (ares_tac [conjI] ORELSE' etac sym)])
   171   in rule_by_tactic tac (trivial ceqt) end;
   172 
   173 fun rearrange sg _ (F as ex $ Abs(x,T,P)) =
   174      (case extract P of
   175         None => None
   176       | Some(eq,Q) =>
   177           let val ceqt = cterm_of sg
   178                        (Logic.mk_equals(F,ex $ Abs(x,T,HOLogic.conj$eq$Q)))
   179           in Some(prove_eq ceqt) end)
   180   | rearrange _ _ _ = None;
   181 
   182 val pattern = read_cterm (sign_of HOL.thy) ("? x.P(x) & Q(x)",HOLogic.boolT)
   183 
   184 in
   185 val defEX_regroup = mk_simproc "defined EX" [pattern] rearrange;
   186 end;
   187 
   188 
   189 (* elimination of existential quantifiers in assumptions *)
   190 
   191 val ex_all_equiv =
   192   let val lemma1 = prove_goal HOL.thy
   193         "(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)"
   194         (fn prems => [resolve_tac prems 1, etac exI 1]);
   195       val lemma2 = prove_goalw HOL.thy [Ex_def]
   196         "(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)"
   197         (fn prems => [REPEAT(resolve_tac prems 1)])
   198   in equal_intr lemma1 lemma2 end;
   199 
   200 end;
   201 
   202 fun prove nm thm  = qed_goal nm HOL.thy thm (fn _ => [blast_tac HOL_cs 1]);
   203 
   204 prove "conj_commute" "(P&Q) = (Q&P)";
   205 prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))";
   206 val conj_comms = [conj_commute, conj_left_commute];
   207 prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))";
   208 
   209 prove "disj_commute" "(P|Q) = (Q|P)";
   210 prove "disj_left_commute" "(P|(Q|R)) = (Q|(P|R))";
   211 val disj_comms = [disj_commute, disj_left_commute];
   212 prove "disj_assoc" "((P|Q)|R) = (P|(Q|R))";
   213 
   214 prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)";
   215 prove "conj_disj_distribR" "((P|Q)&R) = (P&R | Q&R)";
   216 
   217 prove "disj_conj_distribL" "(P|(Q&R)) = ((P|Q) & (P|R))";
   218 prove "disj_conj_distribR" "((P&Q)|R) = ((P|R) & (Q|R))";
   219 
   220 prove "imp_conjR" "(P --> (Q&R)) = ((P-->Q) & (P-->R))";
   221 prove "imp_conjL" "((P&Q) -->R)  = (P --> (Q --> R))";
   222 prove "imp_disjL" "((P|Q) --> R) = ((P-->R)&(Q-->R))";
   223 
   224 (*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*)
   225 prove "imp_disj_not1" "((P --> Q | R)) = (~Q --> P --> R)";
   226 prove "imp_disj_not2" "((P --> Q | R)) = (~R --> P --> Q)";
   227 
   228 prove "de_Morgan_disj" "(~(P | Q)) = (~P & ~Q)";
   229 prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)";
   230 prove "not_imp" "(~(P --> Q)) = (P & ~Q)";
   231 prove "not_iff" "(P~=Q) = (P = (~Q))";
   232 
   233 (*Avoids duplication of subgoals after expand_if, when the true and false 
   234   cases boil down to the same thing.*) 
   235 prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";
   236 
   237 prove "not_all" "(~ (! x.P(x))) = (? x.~P(x))";
   238 prove "imp_all" "((! x. P x) --> Q) = (? x. P x --> Q)";
   239 prove "not_ex"  "(~ (? x.P(x))) = (! x.~P(x))";
   240 prove "imp_ex" "((? x. P x) --> Q) = (! x. P x --> Q)";
   241 
   242 prove "ex_disj_distrib" "(? x. P(x) | Q(x)) = ((? x. P(x)) | (? x. Q(x)))";
   243 prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))";
   244 
   245 (* '&' congruence rule: not included by default!
   246    May slow rewrite proofs down by as much as 50% *)
   247 
   248 let val th = prove_goal HOL.thy 
   249                 "(P=P')--> (P'--> (Q=Q'))--> ((P&Q) = (P'&Q'))"
   250                 (fn _=> [blast_tac HOL_cs 1])
   251 in  bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   252 
   253 let val th = prove_goal HOL.thy 
   254                 "(Q=Q')--> (Q'--> (P=P'))--> ((P&Q) = (P'&Q'))"
   255                 (fn _=> [blast_tac HOL_cs 1])
   256 in  bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   257 
   258 (* '|' congruence rule: not included by default! *)
   259 
   260 let val th = prove_goal HOL.thy 
   261                 "(P=P')--> (~P'--> (Q=Q'))--> ((P|Q) = (P'|Q'))"
   262                 (fn _=> [blast_tac HOL_cs 1])
   263 in  bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   264 
   265 prove "eq_sym_conv" "(x=y) = (y=x)";
   266 
   267 qed_goalw "o_apply" HOL.thy [o_def] "(f o g) x = f (g x)"
   268  (fn _ => [rtac refl 1]);
   269 
   270 qed_goal "meta_eq_to_obj_eq" HOL.thy "x==y ==> x=y"
   271   (fn [prem] => [rewtac prem, rtac refl 1]);
   272 
   273 qed_goalw "if_True" HOL.thy [if_def] "(if True then x else y) = x"
   274  (fn _=>[blast_tac (HOL_cs addIs [select_equality]) 1]);
   275 
   276 qed_goalw "if_False" HOL.thy [if_def] "(if False then x else y) = y"
   277  (fn _=>[blast_tac (HOL_cs addIs [select_equality]) 1]);
   278 
   279 qed_goal "if_P" HOL.thy "P ==> (if P then x else y) = x"
   280  (fn [prem] => [ stac (prem RS eqTrueI) 1, rtac if_True 1 ]);
   281 (*
   282 qed_goal "if_not_P" HOL.thy "~P ==> (if P then x else y) = y"
   283  (fn [prem] => [ stac (prem RS not_P_imp_P_iff_F) 1, rtac if_False 1 ]);
   284 *)
   285 qed_goalw "if_not_P" HOL.thy [if_def] "!!P. ~P ==> (if P then x else y) = y"
   286  (fn _ => [blast_tac (HOL_cs addIs [select_equality]) 1]);
   287 
   288 qed_goal "expand_if" HOL.thy
   289     "P(if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))"
   290  (fn _=> [ (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1),
   291          stac if_P 2,
   292          stac if_not_P 1,
   293          REPEAT(blast_tac HOL_cs 1) ]);
   294 
   295 qed_goal "if_bool_eq" HOL.thy
   296                    "(if P then Q else R) = ((P-->Q) & (~P-->R))"
   297                    (fn _ => [rtac expand_if 1]);
   298 
   299 local val mktac = mk_case_split_tac (meta_eq_to_obj_eq RS iffD2)
   300 in
   301 fun split_tac splits = mktac (map mk_meta_eq splits)
   302 end;
   303 
   304 local val mktac = mk_case_split_inside_tac (meta_eq_to_obj_eq RS iffD2)
   305 in
   306 fun split_inside_tac splits = mktac (map mk_meta_eq splits)
   307 end;
   308 
   309 
   310 qed_goal "if_cancel" HOL.thy "(if c then x else x) = x"
   311   (fn _ => [split_tac [expand_if] 1, blast_tac HOL_cs 1]);
   312 
   313 (** 'if' congruence rules: neither included by default! *)
   314 
   315 (*Simplifies x assuming c and y assuming ~c*)
   316 qed_goal "if_cong" HOL.thy
   317   "[| b=c; c ==> x=u; ~c ==> y=v |] ==>\
   318 \  (if b then x else y) = (if c then u else v)"
   319   (fn rew::prems =>
   320    [stac rew 1, stac expand_if 1, stac expand_if 1,
   321     blast_tac (HOL_cs addDs prems) 1]);
   322 
   323 (*Prevents simplification of x and y: much faster*)
   324 qed_goal "if_weak_cong" HOL.thy
   325   "b=c ==> (if b then x else y) = (if c then x else y)"
   326   (fn [prem] => [rtac (prem RS arg_cong) 1]);
   327 
   328 (*Prevents simplification of t: much faster*)
   329 qed_goal "let_weak_cong" HOL.thy
   330   "a = b ==> (let x=a in t(x)) = (let x=b in t(x))"
   331   (fn [prem] => [rtac (prem RS arg_cong) 1]);
   332 
   333 (*In general it seems wrong to add distributive laws by default: they
   334   might cause exponential blow-up.  But imp_disjL has been in for a while
   335   and cannot be removed without affecting existing proofs.  Moreover, 
   336   rewriting by "(P|Q --> R) = ((P-->R)&(Q-->R))" might be justified on the
   337   grounds that it allows simplification of R in the two cases.*)
   338 
   339 val mksimps_pairs =
   340   [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
   341    ("All", [spec]), ("True", []), ("False", []),
   342    ("If", [if_bool_eq RS iffD1])];
   343 
   344 fun unsafe_solver prems = FIRST'[resolve_tac (TrueI::refl::prems),
   345 				 atac, etac FalseE];
   346 (*No premature instantiation of variables during simplification*)
   347 fun   safe_solver prems = FIRST'[match_tac (TrueI::refl::prems),
   348 				 eq_assume_tac, ematch_tac [FalseE]];
   349 
   350 val HOL_basic_ss = empty_ss setsubgoaler asm_simp_tac
   351 			    setSSolver   safe_solver
   352 			    setSolver  unsafe_solver
   353 			    setmksimps (mksimps mksimps_pairs);
   354 
   355 val HOL_ss = 
   356     HOL_basic_ss addsimps 
   357      ([triv_forall_equality, (* prunes params *)
   358        if_True, if_False, if_cancel,
   359        o_apply, imp_disjL, conj_assoc, disj_assoc,
   360        de_Morgan_conj, de_Morgan_disj, not_imp,
   361        not_all, not_ex, cases_simp]
   362      @ ex_simps @ all_simps @ simp_thms)
   363      addsimprocs [defEX_regroup]
   364      addcongs [imp_cong];
   365 
   366 qed_goal "if_distrib" HOL.thy
   367   "f(if c then x else y) = (if c then f x else f y)" 
   368   (fn _ => [simp_tac (HOL_ss setloop (split_tac [expand_if])) 1]);
   369 
   370 qed_goalw "o_assoc" HOL.thy [o_def] "f o (g o h) = f o g o h"
   371   (fn _ => [rtac ext 1, rtac refl 1]);
   372 
   373 
   374 val prems = goal HOL.thy "[| P ==> Q(True); ~P ==> Q(False) |] ==> Q(P)";
   375 by (case_tac "P" 1);
   376 by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems)));
   377 val expand_case = result();
   378 
   379 fun expand_case_tac P i =
   380     res_inst_tac [("P",P)] expand_case i THEN
   381     Simp_tac (i+1) THEN 
   382     Simp_tac i;
   383 
   384 
   385 
   386 
   387 (*** Install simpsets and datatypes in theory structure ***)
   388 
   389 simpset := HOL_ss;
   390 
   391 exception SS_DATA of simpset;
   392 
   393 let fun merge [] = SS_DATA empty_ss
   394       | merge ss = let val ss = map (fn SS_DATA x => x) ss;
   395                    in SS_DATA (foldl merge_ss (hd ss, tl ss)) end;
   396 
   397     fun put (SS_DATA ss) = simpset := ss;
   398 
   399     fun get () = SS_DATA (!simpset);
   400 in add_thydata "HOL"
   401      ("simpset", ThyMethods {merge = merge, put = put, get = get})
   402 end;
   403 
   404 type dtype_info = {case_const:term,
   405                    case_rewrites:thm list,
   406                    constructors:term list,
   407                    induct_tac: string -> int -> tactic,
   408                    nchotomy: thm,
   409                    exhaustion: thm,
   410                    exhaust_tac: string -> int -> tactic,
   411                    case_cong:thm};
   412 
   413 exception DT_DATA of (string * dtype_info) list;
   414 val datatypes = ref [] : (string * dtype_info) list ref;
   415 
   416 let fun merge [] = DT_DATA []
   417       | merge ds =
   418           let val ds = map (fn DT_DATA x => x) ds;
   419           in DT_DATA (foldl (gen_union eq_fst) (hd ds, tl ds)) end;
   420 
   421     fun put (DT_DATA ds) = datatypes := ds;
   422 
   423     fun get () = DT_DATA (!datatypes);
   424 in add_thydata "HOL"
   425      ("datatypes", ThyMethods {merge = merge, put = put, get = get})
   426 end;
   427 
   428 
   429 add_thy_reader_file "thy_data.ML";
   430 
   431 
   432 
   433 
   434 (*** Integration of simplifier with classical reasoner ***)
   435 
   436 (* rot_eq_tac rotates the first equality premise of subgoal i to the front,
   437    fails if there is no equaliy or if an equality is already at the front *)
   438 local
   439   fun is_eq (Const ("Trueprop", _) $ (Const("op ="  ,_) $ _ $ _)) = true
   440     | is_eq _ = false;
   441   fun find_eq n [] = None
   442     | find_eq n (t :: ts) = if (is_eq t) then Some n 
   443 			    else find_eq (n + 1) ts;
   444 in
   445 val rot_eq_tac = 
   446      SUBGOAL (fn (Bi,i) => 
   447 	      case find_eq 0 (Logic.strip_assums_hyp Bi) of
   448 		  None   => no_tac
   449 		| Some 0 => no_tac
   450 		| Some n => rotate_tac n i)
   451 end;
   452 
   453 (*an unsatisfactory fix for the incomplete asm_full_simp_tac!
   454   better: asm_really_full_simp_tac, a yet to be implemented version of
   455 			asm_full_simp_tac that applies all equalities in the
   456 			premises to all the premises *)
   457 fun safe_asm_more_full_simp_tac ss = TRY o rot_eq_tac THEN' 
   458 				     safe_asm_full_simp_tac ss;
   459 
   460 (*Add a simpset to a classical set!*)
   461 infix 4 addSss addss;
   462 fun cs addSss ss = cs addSaltern (CHANGED o (safe_asm_more_full_simp_tac ss));
   463 fun cs addss  ss = cs addbefore                        asm_full_simp_tac ss;
   464 
   465 fun Addss ss = (claset := !claset addss ss);
   466 
   467 (*Designed to be idempotent, except if best_tac instantiates variables
   468   in some of the subgoals*)
   469 
   470 type clasimpset = (claset * simpset);
   471 
   472 val HOL_css = (HOL_cs, HOL_ss);
   473 
   474 fun pair_upd1 f ((a,b),x) = (f(a,x), b);
   475 fun pair_upd2 f ((a,b),x) = (a, f(b,x));
   476 
   477 infix 4 addSIs2 addSEs2 addSDs2 addIs2 addEs2 addDs2
   478 	addsimps2 delsimps2 addcongs2 delcongs2;
   479 fun op addSIs2   arg = pair_upd1 (op addSIs) arg;
   480 fun op addSEs2   arg = pair_upd1 (op addSEs) arg;
   481 fun op addSDs2   arg = pair_upd1 (op addSDs) arg;
   482 fun op addIs2    arg = pair_upd1 (op addIs ) arg;
   483 fun op addEs2    arg = pair_upd1 (op addEs ) arg;
   484 fun op addDs2    arg = pair_upd1 (op addDs ) arg;
   485 fun op addsimps2 arg = pair_upd2 (op addsimps) arg;
   486 fun op delsimps2 arg = pair_upd2 (op delsimps) arg;
   487 fun op addcongs2 arg = pair_upd2 (op addcongs) arg;
   488 fun op delcongs2 arg = pair_upd2 (op delcongs) arg;
   489 
   490 fun auto_tac (cs,ss) = 
   491     let val cs' = cs addss ss 
   492     in  EVERY [TRY (safe_tac cs'),
   493 	       REPEAT (FIRSTGOAL (fast_tac cs')),
   494                TRY (safe_tac (cs addSss ss)),
   495 	       prune_params_tac] 
   496     end;
   497 
   498 fun Auto_tac () = auto_tac (!claset, !simpset);
   499 
   500 fun auto () = by (Auto_tac ());