src/HOL/simpdata.ML
author oheimb
Fri Nov 07 18:02:15 1997 +0100 (1997-11-07)
changeset 4188 1025a27b08f9
parent 4119 de6e388f3d86
child 4189 b8c7a6bc6c16
permissions -rw-r--r--
changed libraray function find to find_index_eq, currying it
     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 = r RS eq_reflection;
    84 
    85   fun mk_meta_eq_simp r = case concl_of r of
    86           Const("==",_)$_$_ => r
    87       |   _$(Const("op =",_)$lhs$rhs) =>
    88              (case fst(Logic.rewrite_rule_ok (#sign(rep_thm r)) (prems_of r) lhs rhs) of
    89                 None => mk_meta_eq r
    90               | Some _ => r RS P_imp_P_eq_True)
    91       |   _$(Const("Not",_)$_) => r RS not_P_imp_P_eq_False
    92       |   _ => r RS P_imp_P_eq_True;
    93   (* last 2 lines requires all formulae to be of the from Trueprop(.) *)
    94 
    95 val simp_thms = map prover
    96  [ "(x=x) = True",
    97    "(~True) = False", "(~False) = True", "(~ ~ P) = P",
    98    "(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))",
    99    "(True=P) = P", "(P=True) = P",
   100    "(True --> P) = P", "(False --> P) = True", 
   101    "(P --> True) = True", "(P --> P) = True",
   102    "(P --> False) = (~P)", "(P --> ~P) = (~P)",
   103    "(P & True) = P", "(True & P) = P", 
   104    "(P & False) = False", "(False & P) = False",
   105    "(P & P) = P", "(P & (P & Q)) = (P & Q)",
   106    "(P & ~P) = False",    "(~P & P) = False",
   107    "(P | True) = True", "(True | P) = True", 
   108    "(P | False) = P", "(False | P) = P",
   109    "(P | P) = P", "(P | (P | Q)) = (P | Q)",
   110    "(P | ~P) = True",    "(~P | P) = True",
   111    "((~P) = (~Q)) = (P=Q)",
   112    "(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x", 
   113    "(? x. x=t & P(x)) = P(t)",
   114    "(! x. t=x --> P(x)) = P(t)" ];
   115 
   116 (*Add congruence rules for = (instead of ==) *)
   117 infix 4 addcongs delcongs;
   118 fun ss addcongs congs = ss addeqcongs (map standard (congs RL [eq_reflection]));
   119 fun ss delcongs congs = ss deleqcongs (map standard (congs RL [eq_reflection]));
   120 
   121 fun Addcongs congs = (simpset_ref() := simpset() addcongs congs);
   122 fun Delcongs congs = (simpset_ref() := simpset() delcongs congs);
   123 
   124 fun mksimps pairs = map mk_meta_eq_simp o atomize pairs o gen_all;
   125 
   126 val imp_cong = impI RSN
   127     (2, prove_goal HOL.thy "(P=P')--> (P'--> (Q=Q'))--> ((P-->Q) = (P'-->Q'))"
   128         (fn _=> [blast_tac HOL_cs 1]) RS mp RS mp);
   129 
   130 (*Miniscoping: pushing in existential quantifiers*)
   131 val ex_simps = map prover 
   132                 ["(EX x. P x & Q)   = ((EX x. P x) & Q)",
   133                  "(EX x. P & Q x)   = (P & (EX x. Q x))",
   134                  "(EX x. P x | Q)   = ((EX x. P x) | Q)",
   135                  "(EX x. P | Q x)   = (P | (EX x. Q x))",
   136                  "(EX x. P x --> Q) = ((ALL x. P x) --> Q)",
   137                  "(EX x. P --> Q x) = (P --> (EX x. Q x))"];
   138 
   139 (*Miniscoping: pushing in universal quantifiers*)
   140 val all_simps = map prover
   141                 ["(ALL x. P x & Q)   = ((ALL x. P x) & Q)",
   142                  "(ALL x. P & Q x)   = (P & (ALL x. Q x))",
   143                  "(ALL x. P x | Q)   = ((ALL x. P x) | Q)",
   144                  "(ALL x. P | Q x)   = (P | (ALL x. Q x))",
   145                  "(ALL x. P x --> Q) = ((EX x. P x) --> Q)",
   146                  "(ALL x. P --> Q x) = (P --> (ALL x. Q x))"];
   147 
   148 (*** Simplification procedures for turning
   149 
   150             ? x. ... & x = t & ...
   151      into   ? x. x = t & ... & ...
   152      where the `? x. x = t &' in the latter formula is eliminated
   153            by ordinary simplification. 
   154 
   155      and   ! x. (... & x = t & ...) --> P x
   156      into  ! x. x = t --> (... & ...) --> P x
   157      where the `!x. x=t -->' in the latter formula is eliminated
   158            by ordinary simplification.
   159 
   160 NB Simproc is only triggered by "!x. P(x) & P'(x) --> Q(x)"
   161    "!x. x=t --> P(x)" and "!x. t=x --> P(x)"
   162    must be taken care of by ordinary rewrite rules.
   163 ***)
   164 
   165 local
   166 
   167 fun def(eq as (c as Const("op =",_)) $ s $ t) =
   168       if s = Bound 0 andalso not(loose_bvar1(t,0)) then Some eq else
   169       if t = Bound 0 andalso not(loose_bvar1(s,0)) then Some(c$t$s)
   170       else None
   171   | def _ = None;
   172 
   173 fun extract(Const("op &",_) $ P $ Q) =
   174       (case def P of
   175          Some eq => Some(eq,Q)
   176        | None => (case def Q of
   177                    Some eq => Some(eq,P)
   178                  | None =>
   179        (case extract P of
   180          Some(eq,P') => Some(eq, HOLogic.conj $ P' $ Q)
   181        | None => (case extract Q of
   182                    Some(eq,Q') => Some(eq,HOLogic.conj $ P $ Q')
   183                  | None => None))))
   184   | extract _ = None;
   185 
   186 fun prove_ex_eq(ceqt) =
   187   let val tac = rtac eq_reflection 1 THEN rtac iffI 1 THEN
   188                 ALLGOALS(EVERY'[etac exE, REPEAT o (etac conjE),
   189                  rtac exI, REPEAT o (ares_tac [conjI] ORELSE' etac sym)])
   190   in rule_by_tactic tac (trivial ceqt) end;
   191 
   192 fun rearrange_ex sg _ (F as ex $ Abs(x,T,P)) =
   193      (case extract P of
   194         None => None
   195       | Some(eq,Q) =>
   196           let val ceqt = cterm_of sg
   197                        (Logic.mk_equals(F,ex $ Abs(x,T,HOLogic.conj$eq$Q)))
   198           in Some(prove_ex_eq ceqt) end)
   199   | rearrange_ex _ _ _ = None;
   200 
   201 val ex_pattern =
   202   read_cterm (sign_of HOL.thy) ("? x. P(x) & Q(x)",HOLogic.boolT)
   203 
   204 fun prove_all_eq(ceqt) =
   205   let fun tac _ = [EVERY1[rtac eq_reflection, rtac iffI,
   206                        rtac allI, etac allE, rtac impI, rtac impI, etac mp,
   207                           REPEAT o (etac conjE),
   208                           REPEAT o (ares_tac [conjI] ORELSE' etac sym),
   209                        rtac allI, etac allE, rtac impI, REPEAT o (etac conjE),
   210                           etac impE, atac ORELSE' etac sym, etac mp,
   211                           REPEAT o (ares_tac [conjI])]]
   212   in prove_goalw_cterm [] ceqt tac end;
   213 
   214 fun rearrange_all sg _ (F as all $ Abs(x,T,Const("op -->",_)$P$Q)) =
   215      (case extract P of
   216         None => None
   217       | Some(eq,P') =>
   218           let val R = HOLogic.imp $ eq $ (HOLogic.imp $ P' $ Q)
   219               val ceqt = cterm_of sg (Logic.mk_equals(F,all$Abs(x,T,R)))
   220           in Some(prove_all_eq ceqt) end)
   221   | rearrange_all _ _ _ = None;
   222 
   223 val all_pattern =
   224   read_cterm (sign_of HOL.thy) ("! x. P(x) & P'(x) --> Q(x)",HOLogic.boolT)
   225 
   226 in
   227 val defEX_regroup = mk_simproc "defined EX" [ex_pattern] rearrange_ex;
   228 val defALL_regroup = mk_simproc "defined ALL" [all_pattern] rearrange_all;
   229 end;
   230 
   231 
   232 (* elimination of existential quantifiers in assumptions *)
   233 
   234 val ex_all_equiv =
   235   let val lemma1 = prove_goal HOL.thy
   236         "(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)"
   237         (fn prems => [resolve_tac prems 1, etac exI 1]);
   238       val lemma2 = prove_goalw HOL.thy [Ex_def]
   239         "(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)"
   240         (fn prems => [REPEAT(resolve_tac prems 1)])
   241   in equal_intr lemma1 lemma2 end;
   242 
   243 end;
   244 
   245 (* Elimination of True from asumptions: *)
   246 
   247 val True_implies_equals = prove_goal HOL.thy
   248  "(True ==> PROP P) == PROP P"
   249 (fn _ => [rtac equal_intr_rule 1, atac 2,
   250           METAHYPS (fn prems => resolve_tac prems 1) 1,
   251           rtac TrueI 1]);
   252 
   253 fun prove nm thm  = qed_goal nm HOL.thy thm (fn _ => [blast_tac HOL_cs 1]);
   254 
   255 prove "conj_commute" "(P&Q) = (Q&P)";
   256 prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))";
   257 val conj_comms = [conj_commute, conj_left_commute];
   258 prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))";
   259 
   260 prove "disj_commute" "(P|Q) = (Q|P)";
   261 prove "disj_left_commute" "(P|(Q|R)) = (Q|(P|R))";
   262 val disj_comms = [disj_commute, disj_left_commute];
   263 prove "disj_assoc" "((P|Q)|R) = (P|(Q|R))";
   264 
   265 prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)";
   266 prove "conj_disj_distribR" "((P|Q)&R) = (P&R | Q&R)";
   267 
   268 prove "disj_conj_distribL" "(P|(Q&R)) = ((P|Q) & (P|R))";
   269 prove "disj_conj_distribR" "((P&Q)|R) = ((P|R) & (Q|R))";
   270 
   271 prove "imp_conjR" "(P --> (Q&R)) = ((P-->Q) & (P-->R))";
   272 prove "imp_conjL" "((P&Q) -->R)  = (P --> (Q --> R))";
   273 prove "imp_disjL" "((P|Q) --> R) = ((P-->R)&(Q-->R))";
   274 
   275 (*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*)
   276 prove "imp_disj_not1" "((P --> Q | R)) = (~Q --> P --> R)";
   277 prove "imp_disj_not2" "((P --> Q | R)) = (~R --> P --> Q)";
   278 
   279 prove "imp_disj1" "((P-->Q)|R) = (P--> Q|R)";
   280 prove "imp_disj2" "(Q|(P-->R)) = (P--> Q|R)";
   281 
   282 prove "de_Morgan_disj" "(~(P | Q)) = (~P & ~Q)";
   283 prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)";
   284 prove "not_imp" "(~(P --> Q)) = (P & ~Q)";
   285 prove "not_iff" "(P~=Q) = (P = (~Q))";
   286 
   287 (*Avoids duplication of subgoals after expand_if, when the true and false 
   288   cases boil down to the same thing.*) 
   289 prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";
   290 
   291 prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))";
   292 prove "imp_all" "((! x. P x) --> Q) = (? x. P x --> Q)";
   293 prove "not_ex"  "(~ (? x. P(x))) = (! x.~P(x))";
   294 prove "imp_ex" "((? x. P x) --> Q) = (! x. P x --> Q)";
   295 
   296 prove "ex_disj_distrib" "(? x. P(x) | Q(x)) = ((? x. P(x)) | (? x. Q(x)))";
   297 prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))";
   298 
   299 (* '&' congruence rule: not included by default!
   300    May slow rewrite proofs down by as much as 50% *)
   301 
   302 let val th = prove_goal HOL.thy 
   303                 "(P=P')--> (P'--> (Q=Q'))--> ((P&Q) = (P'&Q'))"
   304                 (fn _=> [blast_tac HOL_cs 1])
   305 in  bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   306 
   307 let val th = prove_goal HOL.thy 
   308                 "(Q=Q')--> (Q'--> (P=P'))--> ((P&Q) = (P'&Q'))"
   309                 (fn _=> [blast_tac HOL_cs 1])
   310 in  bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   311 
   312 (* '|' congruence rule: not included by default! *)
   313 
   314 let val th = prove_goal HOL.thy 
   315                 "(P=P')--> (~P'--> (Q=Q'))--> ((P|Q) = (P'|Q'))"
   316                 (fn _=> [blast_tac HOL_cs 1])
   317 in  bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   318 
   319 prove "eq_sym_conv" "(x=y) = (y=x)";
   320 
   321 qed_goalw "o_apply" HOL.thy [o_def] "(f o g) x = f (g x)"
   322  (fn _ => [rtac refl 1]);
   323 
   324 qed_goal "meta_eq_to_obj_eq" HOL.thy "x==y ==> x=y"
   325   (fn [prem] => [rewtac prem, rtac refl 1]);
   326 
   327 qed_goalw "if_True" HOL.thy [if_def] "(if True then x else y) = x"
   328  (fn _=>[blast_tac (HOL_cs addIs [select_equality]) 1]);
   329 
   330 qed_goalw "if_False" HOL.thy [if_def] "(if False then x else y) = y"
   331  (fn _=>[blast_tac (HOL_cs addIs [select_equality]) 1]);
   332 
   333 qed_goal "if_P" HOL.thy "P ==> (if P then x else y) = x"
   334  (fn [prem] => [ stac (prem RS eqTrueI) 1, rtac if_True 1 ]);
   335 (*
   336 qed_goal "if_not_P" HOL.thy "~P ==> (if P then x else y) = y"
   337  (fn [prem] => [ stac (prem RS not_P_imp_P_iff_F) 1, rtac if_False 1 ]);
   338 *)
   339 qed_goalw "if_not_P" HOL.thy [if_def] "!!P. ~P ==> (if P then x else y) = y"
   340  (fn _ => [blast_tac (HOL_cs addIs [select_equality]) 1]);
   341 
   342 qed_goal "expand_if" HOL.thy
   343     "P(if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))"
   344  (fn _=> [ (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1),
   345          stac if_P 2,
   346          stac if_not_P 1,
   347          REPEAT(blast_tac HOL_cs 1) ]);
   348 
   349 qed_goal "if_bool_eq" HOL.thy
   350                    "(if P then Q else R) = ((P-->Q) & (~P-->R))"
   351                    (fn _ => [rtac expand_if 1]);
   352 
   353 
   354 
   355 (** Case splitting **)
   356 
   357 local val mktac = mk_case_split_tac (meta_eq_to_obj_eq RS iffD2)
   358 in
   359 fun split_tac splits = mktac (map mk_meta_eq splits)
   360 end;
   361 
   362 local val mktac = mk_case_split_inside_tac (meta_eq_to_obj_eq RS iffD2)
   363 in
   364 fun split_inside_tac splits = mktac (map mk_meta_eq splits)
   365 end;
   366 
   367 infix 4 addsplits;
   368 fun ss addsplits splits = ss addloop (split_tac splits);
   369 
   370 
   371 qed_goal "if_cancel" HOL.thy "(if c then x else x) = x"
   372   (fn _ => [split_tac [expand_if] 1, blast_tac HOL_cs 1]);
   373 
   374 (** 'if' congruence rules: neither included by default! *)
   375 
   376 (*Simplifies x assuming c and y assuming ~c*)
   377 qed_goal "if_cong" HOL.thy
   378   "[| b=c; c ==> x=u; ~c ==> y=v |] ==>\
   379 \  (if b then x else y) = (if c then u else v)"
   380   (fn rew::prems =>
   381    [stac rew 1, stac expand_if 1, stac expand_if 1,
   382     blast_tac (HOL_cs addDs prems) 1]);
   383 
   384 (*Prevents simplification of x and y: much faster*)
   385 qed_goal "if_weak_cong" HOL.thy
   386   "b=c ==> (if b then x else y) = (if c then x else y)"
   387   (fn [prem] => [rtac (prem RS arg_cong) 1]);
   388 
   389 (*Prevents simplification of t: much faster*)
   390 qed_goal "let_weak_cong" HOL.thy
   391   "a = b ==> (let x=a in t(x)) = (let x=b in t(x))"
   392   (fn [prem] => [rtac (prem RS arg_cong) 1]);
   393 
   394 (*In general it seems wrong to add distributive laws by default: they
   395   might cause exponential blow-up.  But imp_disjL has been in for a while
   396   and cannot be removed without affecting existing proofs.  Moreover, 
   397   rewriting by "(P|Q --> R) = ((P-->R)&(Q-->R))" might be justified on the
   398   grounds that it allows simplification of R in the two cases.*)
   399 
   400 val mksimps_pairs =
   401   [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
   402    ("All", [spec]), ("True", []), ("False", []),
   403    ("If", [if_bool_eq RS iffD1])];
   404 
   405 fun unsafe_solver prems = FIRST'[resolve_tac (TrueI::refl::prems),
   406 				 atac, etac FalseE];
   407 (*No premature instantiation of variables during simplification*)
   408 fun   safe_solver prems = FIRST'[match_tac (TrueI::refl::prems),
   409 				 eq_assume_tac, ematch_tac [FalseE]];
   410 
   411 val HOL_basic_ss = empty_ss setsubgoaler asm_simp_tac
   412 			    setSSolver   safe_solver
   413 			    setSolver  unsafe_solver
   414 			    setmksimps (mksimps mksimps_pairs);
   415 
   416 val HOL_ss = 
   417     HOL_basic_ss addsimps 
   418      ([triv_forall_equality, (* prunes params *)
   419        True_implies_equals, (* prune asms `True' *)
   420        if_True, if_False, if_cancel,
   421        o_apply, imp_disjL, conj_assoc, disj_assoc,
   422        de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp,
   423        not_all, not_ex, cases_simp]
   424      @ ex_simps @ all_simps @ simp_thms)
   425      addsimprocs [defALL_regroup,defEX_regroup]
   426      addcongs [imp_cong];
   427 
   428 qed_goal "if_distrib" HOL.thy
   429   "f(if c then x else y) = (if c then f x else f y)" 
   430   (fn _ => [simp_tac (HOL_ss setloop (split_tac [expand_if])) 1]);
   431 
   432 qed_goalw "o_assoc" HOL.thy [o_def] "f o (g o h) = f o g o h"
   433   (fn _ => [rtac ext 1, rtac refl 1]);
   434 
   435 
   436 val prems = goal HOL.thy "[| P ==> Q(True); ~P ==> Q(False) |] ==> Q(P)";
   437 by (case_tac "P" 1);
   438 by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems)));
   439 val expand_case = result();
   440 
   441 fun expand_case_tac P i =
   442     res_inst_tac [("P",P)] expand_case i THEN
   443     Simp_tac (i+1) THEN 
   444     Simp_tac i;
   445 
   446 
   447 (* install implicit simpset *)
   448 
   449 simpset_ref() := HOL_ss;
   450 
   451 
   452 (*** Integration of simplifier with classical reasoner ***)
   453 
   454 (* rot_eq_tac rotates the first equality premise of subgoal i to the front,
   455    fails if there is no equaliy or if an equality is already at the front *)
   456 local
   457   fun is_eq (Const ("Trueprop", _) $ (Const("op ="  ,_) $ _ $ _)) = true
   458     | is_eq _ = false;
   459   val find_eq = find_index is_eq;
   460 in
   461 val rot_eq_tac = 
   462      SUBGOAL (fn (Bi,i) => let val n = find_eq (Logic.strip_assums_hyp Bi) in
   463 		if n>0 then rotate_tac n i else no_tac end)
   464 end;
   465 
   466 (*an unsatisfactory fix for the incomplete asm_full_simp_tac!
   467   better: asm_really_full_simp_tac, a yet to be implemented version of
   468 			asm_full_simp_tac that applies all equalities in the
   469 			premises to all the premises *)
   470 fun safe_asm_more_full_simp_tac ss = TRY o rot_eq_tac THEN' 
   471 				     safe_asm_full_simp_tac ss;
   472 
   473 (*Add a simpset to a classical set!*)
   474 infix 4 addSss addss;
   475 fun cs addSss ss = cs addSaltern (CHANGED o (safe_asm_more_full_simp_tac ss));
   476 fun cs addss  ss = cs addbefore                        asm_full_simp_tac ss;
   477 
   478 fun Addss ss = (claset_ref() := claset() addss ss);
   479 
   480 (*Designed to be idempotent, except if best_tac instantiates variables
   481   in some of the subgoals*)
   482 
   483 type clasimpset = (claset * simpset);
   484 
   485 val HOL_css = (HOL_cs, HOL_ss);
   486 
   487 fun pair_upd1 f ((a,b),x) = (f(a,x), b);
   488 fun pair_upd2 f ((a,b),x) = (a, f(b,x));
   489 
   490 infix 4 addSIs2 addSEs2 addSDs2 addIs2 addEs2 addDs2
   491 	addsimps2 delsimps2 addcongs2 delcongs2;
   492 fun op addSIs2   arg = pair_upd1 (op addSIs) arg;
   493 fun op addSEs2   arg = pair_upd1 (op addSEs) arg;
   494 fun op addSDs2   arg = pair_upd1 (op addSDs) arg;
   495 fun op addIs2    arg = pair_upd1 (op addIs ) arg;
   496 fun op addEs2    arg = pair_upd1 (op addEs ) arg;
   497 fun op addDs2    arg = pair_upd1 (op addDs ) arg;
   498 fun op addsimps2 arg = pair_upd2 (op addsimps) arg;
   499 fun op delsimps2 arg = pair_upd2 (op delsimps) arg;
   500 fun op addcongs2 arg = pair_upd2 (op addcongs) arg;
   501 fun op delcongs2 arg = pair_upd2 (op delcongs) arg;
   502 
   503 fun auto_tac (cs,ss) = 
   504     let val cs' = cs addss ss 
   505     in  EVERY [TRY (safe_tac cs'),
   506 	       REPEAT (FIRSTGOAL (fast_tac cs')),
   507                TRY (safe_tac (cs addSss ss)),
   508 	       prune_params_tac] 
   509     end;
   510 
   511 fun Auto_tac () = auto_tac (claset(), simpset());
   512 
   513 fun auto () = by (Auto_tac ());