src/HOL/simpdata.ML
author wenzelm
Tue Aug 29 00:55:31 2000 +0200 (2000-08-29)
changeset 9713 2c5b42311eb0
parent 9511 bb029080ff8b
child 9736 332fab43628f
permissions -rw-r--r--
cong setup now part of Simplifier;
     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 for HOL.
     7 *)
     8 
     9 section "Simplifier";
    10 
    11 (*** Addition of rules to simpsets and clasets simultaneously ***)      (* FIXME move to Provers/clasimp.ML? *)
    12 
    13 infix 4 addIffs delIffs;
    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 ((cla, simp), th) =
    24       (case HOLogic.dest_Trueprop (#prop (rep_thm th)) of
    25                 (Const("Not", _) $ A) =>
    26                     cla addSEs [zero_var_indexes (th RS notE)]
    27               | (con $ _ $ _) =>
    28                     if con = iff_const
    29                     then cla addSIs [zero_var_indexes (th RS iffD2)]
    30                               addSDs [zero_var_indexes (th RS iffD1)]
    31                     else  cla addSIs [th]
    32               | _ => cla addSIs [th],
    33        simp addsimps [th])
    34       handle TERM _ => error ("AddIffs: theorem must be unconditional\n" ^
    35                          string_of_thm th);
    36 
    37   fun delIff ((cla, simp), th) =
    38       (case HOLogic.dest_Trueprop (#prop (rep_thm th)) of
    39            (Const ("Not", _) $ A) =>
    40                cla delrules [zero_var_indexes (th RS notE)]
    41          | (con $ _ $ _) =>
    42                if con = iff_const
    43                then cla delrules
    44                         [zero_var_indexes (th RS iffD2),
    45                          cla_make_elim (zero_var_indexes (th RS iffD1))]
    46                else cla delrules [th]
    47          | _ => cla delrules [th],
    48        simp delsimps [th])
    49       handle TERM _ => (warning("DelIffs: ignoring conditional theorem\n" ^
    50                                 string_of_thm th); (cla, simp));
    51 
    52   fun store_clasimp (cla, simp) = (claset_ref () := cla; simpset_ref () := simp)
    53 in
    54 val op addIffs = foldl addIff;
    55 val op delIffs = foldl delIff;
    56 fun AddIffs thms = store_clasimp ((claset (), simpset ()) addIffs thms);
    57 fun DelIffs thms = store_clasimp ((claset (), simpset ()) delIffs thms);
    58 end;
    59 
    60 
    61 val [prem] = goal (the_context ()) "x==y ==> x=y";
    62 by (rewtac prem);
    63 by (rtac refl 1);
    64 qed "meta_eq_to_obj_eq";
    65 
    66 Goal "(%s. f s) = f";
    67 br refl 1;
    68 qed "eta_contract_eq";
    69 
    70 local
    71 
    72   fun prover s = prove_goal (the_context ()) s (fn _ => [(Blast_tac 1)]);
    73 
    74 in
    75 
    76 (*Make meta-equalities.  The operator below is Trueprop*)
    77 
    78 fun mk_meta_eq r = r RS eq_reflection;
    79 
    80 val Eq_TrueI  = mk_meta_eq(prover  "P --> (P = True)"  RS mp);
    81 val Eq_FalseI = mk_meta_eq(prover "~P --> (P = False)" RS mp);
    82 
    83 fun mk_eq th = case concl_of th of
    84         Const("==",_)$_$_       => th
    85     |   _$(Const("op =",_)$_$_) => mk_meta_eq th
    86     |   _$(Const("Not",_)$_)    => th RS Eq_FalseI
    87     |   _                       => th RS Eq_TrueI;
    88 (* last 2 lines requires all formulae to be of the from Trueprop(.) *)
    89 
    90 fun mk_eq_True r = Some(r RS meta_eq_to_obj_eq RS Eq_TrueI);
    91 
    92 (*Congruence rules for = (instead of ==)*)
    93 fun mk_meta_cong rl =
    94   standard(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl))
    95   handle THM _ =>
    96   error("Premises and conclusion of congruence rules must be =-equalities");
    97 
    98 val not_not = prover "(~ ~ P) = P";
    99 
   100 val simp_thms = [not_not] @ map prover
   101  [ "(x=x) = True",
   102    "(~True) = False", "(~False) = True",
   103    "(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))",
   104    "(True=P) = P", "(P=True) = P", "(False=P) = (~P)", "(P=False) = (~P)",
   105    "(True --> P) = P", "(False --> P) = True",
   106    "(P --> True) = True", "(P --> P) = True",
   107    "(P --> False) = (~P)", "(P --> ~P) = (~P)",
   108    "(P & True) = P", "(True & P) = P",
   109    "(P & False) = False", "(False & P) = False",
   110    "(P & P) = P", "(P & (P & Q)) = (P & Q)",
   111    "(P & ~P) = False",    "(~P & P) = False",
   112    "(P | True) = True", "(True | P) = True",
   113    "(P | False) = P", "(False | P) = P",
   114    "(P | P) = P", "(P | (P | Q)) = (P | Q)",
   115    "(P | ~P) = True",    "(~P | P) = True",
   116    "((~P) = (~Q)) = (P=Q)",
   117    "(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x",
   118 (*two needed for the one-point-rule quantifier simplification procs*)
   119    "(? x. x=t & P(x)) = P(t)",          (*essential for termination!!*)
   120    "(! x. t=x --> P(x)) = P(t)" ];      (*covers a stray case*)
   121 
   122 val imp_cong = impI RSN
   123     (2, prove_goal (the_context ()) "(P=P')--> (P'--> (Q=Q'))--> ((P-->Q) = (P'-->Q'))"
   124         (fn _=> [(Blast_tac 1)]) RS mp RS mp);
   125 
   126 (*Miniscoping: pushing in existential quantifiers*)
   127 val ex_simps = map prover
   128                 ["(EX x. P x & Q)   = ((EX x. P x) & Q)",
   129                  "(EX x. P & Q x)   = (P & (EX x. Q x))",
   130                  "(EX x. P x | Q)   = ((EX x. P x) | Q)",
   131                  "(EX x. P | Q x)   = (P | (EX x. Q x))",
   132                  "(EX x. P x --> Q) = ((ALL x. P x) --> Q)",
   133                  "(EX x. P --> Q x) = (P --> (EX x. Q x))"];
   134 
   135 (*Miniscoping: pushing in universal quantifiers*)
   136 val all_simps = map prover
   137                 ["(ALL x. P x & Q)   = ((ALL x. P x) & Q)",
   138                  "(ALL x. P & Q x)   = (P & (ALL x. Q x))",
   139                  "(ALL x. P x | Q)   = ((ALL x. P x) | Q)",
   140                  "(ALL x. P | Q x)   = (P | (ALL x. Q x))",
   141                  "(ALL x. P x --> Q) = ((EX x. P x) --> Q)",
   142                  "(ALL x. P --> Q x) = (P --> (ALL x. Q x))"];
   143 
   144 
   145 (* elimination of existential quantifiers in assumptions *)
   146 
   147 val ex_all_equiv =
   148   let val lemma1 = prove_goal (the_context ())
   149         "(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)"
   150         (fn prems => [resolve_tac prems 1, etac exI 1]);
   151       val lemma2 = prove_goalw (the_context ()) [Ex_def]
   152         "(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)"
   153         (fn prems => [(REPEAT(resolve_tac prems 1))])
   154   in equal_intr lemma1 lemma2 end;
   155 
   156 end;
   157 
   158 bind_thms ("ex_simps", ex_simps);
   159 bind_thms ("all_simps", all_simps);
   160 bind_thm ("not_not", not_not);
   161 
   162 (* Elimination of True from asumptions: *)
   163 
   164 val True_implies_equals = prove_goal (the_context ())
   165  "(True ==> PROP P) == PROP P"
   166 (fn _ => [rtac equal_intr_rule 1, atac 2,
   167           METAHYPS (fn prems => resolve_tac prems 1) 1,
   168           rtac TrueI 1]);
   169 
   170 fun prove nm thm  = qed_goal nm (the_context ()) thm (fn _ => [(Blast_tac 1)]);
   171 
   172 prove "eq_commute" "(a=b) = (b=a)";
   173 prove "eq_left_commute" "(P=(Q=R)) = (Q=(P=R))";
   174 prove "eq_assoc" "((P=Q)=R) = (P=(Q=R))";
   175 val eq_ac = [eq_commute, eq_left_commute, eq_assoc];
   176 
   177 prove "neq_commute" "(a~=b) = (b~=a)";
   178 
   179 prove "conj_commute" "(P&Q) = (Q&P)";
   180 prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))";
   181 val conj_comms = [conj_commute, conj_left_commute];
   182 prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))";
   183 
   184 prove "disj_commute" "(P|Q) = (Q|P)";
   185 prove "disj_left_commute" "(P|(Q|R)) = (Q|(P|R))";
   186 val disj_comms = [disj_commute, disj_left_commute];
   187 prove "disj_assoc" "((P|Q)|R) = (P|(Q|R))";
   188 
   189 prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)";
   190 prove "conj_disj_distribR" "((P|Q)&R) = (P&R | Q&R)";
   191 
   192 prove "disj_conj_distribL" "(P|(Q&R)) = ((P|Q) & (P|R))";
   193 prove "disj_conj_distribR" "((P&Q)|R) = ((P|R) & (Q|R))";
   194 
   195 prove "imp_conjR" "(P --> (Q&R)) = ((P-->Q) & (P-->R))";
   196 prove "imp_conjL" "((P&Q) -->R)  = (P --> (Q --> R))";
   197 prove "imp_disjL" "((P|Q) --> R) = ((P-->R)&(Q-->R))";
   198 
   199 (*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*)
   200 prove "imp_disj_not1" "(P --> Q | R) = (~Q --> P --> R)";
   201 prove "imp_disj_not2" "(P --> Q | R) = (~R --> P --> Q)";
   202 
   203 prove "imp_disj1" "((P-->Q)|R) = (P--> Q|R)";
   204 prove "imp_disj2" "(Q|(P-->R)) = (P--> Q|R)";
   205 
   206 prove "de_Morgan_disj" "(~(P | Q)) = (~P & ~Q)";
   207 prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)";
   208 prove "not_imp" "(~(P --> Q)) = (P & ~Q)";
   209 prove "not_iff" "(P~=Q) = (P = (~Q))";
   210 prove "disj_not1" "(~P | Q) = (P --> Q)";
   211 prove "disj_not2" "(P | ~Q) = (Q --> P)"; (* changes orientation :-( *)
   212 prove "imp_conv_disj" "(P --> Q) = ((~P) | Q)";
   213 
   214 prove "iff_conv_conj_imp" "(P = Q) = ((P --> Q) & (Q --> P))";
   215 
   216 
   217 (*Avoids duplication of subgoals after split_if, when the true and false
   218   cases boil down to the same thing.*)
   219 prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";
   220 
   221 prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))";
   222 prove "imp_all" "((! x. P x) --> Q) = (? x. P x --> Q)";
   223 prove "not_ex"  "(~ (? x. P(x))) = (! x.~P(x))";
   224 prove "imp_ex" "((? x. P x) --> Q) = (! x. P x --> Q)";
   225 
   226 prove "ex_disj_distrib" "(? x. P(x) | Q(x)) = ((? x. P(x)) | (? x. Q(x)))";
   227 prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))";
   228 
   229 (* '&' congruence rule: not included by default!
   230    May slow rewrite proofs down by as much as 50% *)
   231 
   232 let val th = prove_goal (the_context ())
   233                 "(P=P')--> (P'--> (Q=Q'))--> ((P&Q) = (P'&Q'))"
   234                 (fn _=> [(Blast_tac 1)])
   235 in  bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   236 
   237 let val th = prove_goal (the_context ())
   238                 "(Q=Q')--> (Q'--> (P=P'))--> ((P&Q) = (P'&Q'))"
   239                 (fn _=> [(Blast_tac 1)])
   240 in  bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   241 
   242 (* '|' congruence rule: not included by default! *)
   243 
   244 let val th = prove_goal (the_context ())
   245                 "(P=P')--> (~P'--> (Q=Q'))--> ((P|Q) = (P'|Q'))"
   246                 (fn _=> [(Blast_tac 1)])
   247 in  bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   248 
   249 prove "eq_sym_conv" "(x=y) = (y=x)";
   250 
   251 
   252 (** if-then-else rules **)
   253 
   254 Goalw [if_def] "(if True then x else y) = x";
   255 by (Blast_tac 1);
   256 qed "if_True";
   257 
   258 Goalw [if_def] "(if False then x else y) = y";
   259 by (Blast_tac 1);
   260 qed "if_False";
   261 
   262 Goalw [if_def] "P ==> (if P then x else y) = x";
   263 by (Blast_tac 1);
   264 qed "if_P";
   265 
   266 Goalw [if_def] "~P ==> (if P then x else y) = y";
   267 by (Blast_tac 1);
   268 qed "if_not_P";
   269 
   270 Goal "P(if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))";
   271 by (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1);
   272 by (stac if_P 2);
   273 by (stac if_not_P 1);
   274 by (ALLGOALS (Blast_tac));
   275 qed "split_if";
   276 
   277 Goal "P(if Q then x else y) = (~((Q & ~P x) | (~Q & ~P y)))";
   278 by (stac split_if 1);
   279 by (Blast_tac 1);
   280 qed "split_if_asm";
   281 
   282 bind_thms ("if_splits", [split_if, split_if_asm]);
   283 
   284 Goal "(if c then x else x) = x";
   285 by (stac split_if 1);
   286 by (Blast_tac 1);
   287 qed "if_cancel";
   288 
   289 Goal "(if x = y then y else x) = x";
   290 by (stac split_if 1);
   291 by (Blast_tac 1);
   292 qed "if_eq_cancel";
   293 
   294 (*This form is useful for expanding IFs on the RIGHT of the ==> symbol*)
   295 Goal "(if P then Q else R) = ((P-->Q) & (~P-->R))";
   296 by (rtac split_if 1);
   297 qed "if_bool_eq_conj";
   298 
   299 (*And this form is useful for expanding IFs on the LEFT*)
   300 Goal "(if P then Q else R) = ((P&Q) | (~P&R))";
   301 by (stac split_if 1);
   302 by (Blast_tac 1);
   303 qed "if_bool_eq_disj";
   304 
   305 
   306 (*** make simplification procedures for quantifier elimination ***)
   307 
   308 structure Quantifier1 = Quantifier1Fun(
   309 struct
   310   (*abstract syntax*)
   311   fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t)
   312     | dest_eq _ = None;
   313   fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t)
   314     | dest_conj _ = None;
   315   val conj = HOLogic.conj
   316   val imp  = HOLogic.imp
   317   (*rules*)
   318   val iff_reflection = eq_reflection
   319   val iffI = iffI
   320   val sym  = sym
   321   val conjI= conjI
   322   val conjE= conjE
   323   val impI = impI
   324   val impE = impE
   325   val mp   = mp
   326   val exI  = exI
   327   val exE  = exE
   328   val allI = allI
   329   val allE = allE
   330 end);
   331 
   332 local
   333 val ex_pattern =
   334   Thm.read_cterm (Theory.sign_of (the_context ())) ("EX x. P(x) & Q(x)",HOLogic.boolT)
   335 
   336 val all_pattern =
   337   Thm.read_cterm (Theory.sign_of (the_context ())) ("ALL x. P(x) & P'(x) --> Q(x)",HOLogic.boolT)
   338 
   339 in
   340 val defEX_regroup =
   341   mk_simproc "defined EX" [ex_pattern] Quantifier1.rearrange_ex;
   342 val defALL_regroup =
   343   mk_simproc "defined ALL" [all_pattern] Quantifier1.rearrange_all;
   344 end;
   345 
   346 
   347 (*** Case splitting ***)
   348 
   349 structure SplitterData =
   350   struct
   351   structure Simplifier = Simplifier
   352   val mk_eq          = mk_eq
   353   val meta_eq_to_iff = meta_eq_to_obj_eq
   354   val iffD           = iffD2
   355   val disjE          = disjE
   356   val conjE          = conjE
   357   val exE            = exE
   358   val contrapos      = contrapos
   359   val contrapos2     = contrapos2
   360   val notnotD        = notnotD
   361   end;
   362 
   363 structure Splitter = SplitterFun(SplitterData);
   364 
   365 val split_tac        = Splitter.split_tac;
   366 val split_inside_tac = Splitter.split_inside_tac;
   367 val split_asm_tac    = Splitter.split_asm_tac;
   368 val op addsplits     = Splitter.addsplits;
   369 val op delsplits     = Splitter.delsplits;
   370 val Addsplits        = Splitter.Addsplits;
   371 val Delsplits        = Splitter.Delsplits;
   372 
   373 (*In general it seems wrong to add distributive laws by default: they
   374   might cause exponential blow-up.  But imp_disjL has been in for a while
   375   and cannot be removed without affecting existing proofs.  Moreover,
   376   rewriting by "(P|Q --> R) = ((P-->R)&(Q-->R))" might be justified on the
   377   grounds that it allows simplification of R in the two cases.*)
   378 
   379 fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th;
   380 
   381 val mksimps_pairs =
   382   [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
   383    ("All", [spec]), ("True", []), ("False", []),
   384    ("If", [if_bool_eq_conj RS iffD1])];
   385 
   386 (* ###FIXME: move to Provers/simplifier.ML
   387 val mk_atomize:      (string * thm list) list -> thm -> thm list
   388 *)
   389 (* ###FIXME: move to Provers/simplifier.ML *)
   390 fun mk_atomize pairs =
   391   let fun atoms th =
   392         (case concl_of th of
   393            Const("Trueprop",_) $ p =>
   394              (case head_of p of
   395                 Const(a,_) =>
   396                   (case assoc(pairs,a) of
   397                      Some(rls) => flat (map atoms ([th] RL rls))
   398                    | None => [th])
   399               | _ => [th])
   400          | _ => [th])
   401   in atoms end;
   402 
   403 fun mksimps pairs = (map mk_eq o mk_atomize pairs o gen_all);
   404 
   405 fun unsafe_solver_tac prems =
   406   FIRST'[resolve_tac(reflexive_thm::TrueI::refl::prems), atac, etac FalseE];
   407 val unsafe_solver = mk_solver "HOL unsafe" unsafe_solver_tac;
   408 
   409 (*No premature instantiation of variables during simplification*)
   410 fun safe_solver_tac prems =
   411   FIRST'[match_tac(reflexive_thm::TrueI::refl::prems),
   412          eq_assume_tac, ematch_tac [FalseE]];
   413 val safe_solver = mk_solver "HOL safe" safe_solver_tac;
   414 
   415 val HOL_basic_ss =
   416   empty_ss setsubgoaler asm_simp_tac
   417     setSSolver safe_solver
   418     setSolver unsafe_solver
   419     setmksimps (mksimps mksimps_pairs)
   420     setmkeqTrue mk_eq_True
   421     setmkcong mk_meta_cong;
   422 
   423 val HOL_ss =
   424     HOL_basic_ss addsimps
   425      ([triv_forall_equality, (* prunes params *)
   426        True_implies_equals, (* prune asms `True' *)
   427        eta_contract_eq, (* prunes eta-expansions *)
   428        if_True, if_False, if_cancel, if_eq_cancel,
   429        imp_disjL, conj_assoc, disj_assoc,
   430        de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp,
   431        disj_not1, not_all, not_ex, cases_simp, Eps_eq, Eps_sym_eq,
   432        thm"plus_ac0.zero", thm"plus_ac0_zero_right"]
   433      @ ex_simps @ all_simps @ simp_thms)
   434      addsimprocs [defALL_regroup,defEX_regroup]
   435      addcongs [imp_cong]
   436      addsplits [split_if];
   437 
   438 (*Simplifies x assuming c and y assuming ~c*)
   439 val prems = Goalw [if_def]
   440   "[| b=c; c ==> x=u; ~c ==> y=v |] ==> \
   441 \  (if b then x else y) = (if c then u else v)";
   442 by (asm_simp_tac (HOL_ss addsimps prems) 1);
   443 qed "if_cong";
   444 
   445 (*Prevents simplification of x and y: faster and allows the execution
   446   of functional programs. NOW THE DEFAULT.*)
   447 Goal "b=c ==> (if b then x else y) = (if c then x else y)";
   448 by (etac arg_cong 1);
   449 qed "if_weak_cong";
   450 
   451 (*Prevents simplification of t: much faster*)
   452 Goal "a = b ==> (let x=a in t(x)) = (let x=b in t(x))";
   453 by (etac arg_cong 1);
   454 qed "let_weak_cong";
   455 
   456 Goal "f(if c then x else y) = (if c then f x else f y)";
   457 by (simp_tac (HOL_ss setloop (split_tac [split_if])) 1);
   458 qed "if_distrib";
   459 
   460 (*For expand_case_tac*)
   461 val prems = Goal "[| P ==> Q(True); ~P ==> Q(False) |] ==> Q(P)";
   462 by (case_tac "P" 1);
   463 by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems)));
   464 qed "expand_case";
   465 
   466 (*Used in Auth proofs.  Typically P contains Vars that become instantiated
   467   during unification.*)
   468 fun expand_case_tac P i =
   469     res_inst_tac [("P",P)] expand_case i THEN
   470     Simp_tac (i+1) THEN
   471     Simp_tac i;
   472 
   473 (*This lemma restricts the effect of the rewrite rule u=v to the left-hand
   474   side of an equality.  Used in {Integ,Real}/simproc.ML*)
   475 Goal "x=y ==> (x=z) = (y=z)";
   476 by (asm_simp_tac HOL_ss 1);
   477 qed "restrict_to_left";
   478 
   479 (* default simpset *)
   480 val simpsetup =
   481   [fn thy => (simpset_ref_of thy := HOL_ss addcongs [if_weak_cong]; thy)];
   482 
   483 
   484 (*** integration of simplifier with classical reasoner ***)
   485 
   486 structure Clasimp = ClasimpFun
   487  (structure Simplifier = Simplifier and Splitter = Splitter
   488    and Classical  = Classical and Blast = Blast);
   489 open Clasimp;
   490 
   491 val HOL_css = (HOL_cs, HOL_ss);
   492 
   493 
   494 (* "iff" attribute *)
   495 
   496 val iff_add_global = Clasimp.change_global_css (op addIffs);
   497 val iff_add_local = Clasimp.change_local_css (op addIffs);
   498 
   499 val iff_attrib_setup =
   500   [Attrib.add_attributes [("iff", (Attrib.no_args iff_add_global, Attrib.no_args iff_add_local),
   501     "add rules to simpset and claset simultaneously")]];
   502 
   503 
   504 
   505 (*** A general refutation procedure ***)
   506 
   507 (* Parameters:
   508 
   509    test: term -> bool
   510    tests if a term is at all relevant to the refutation proof;
   511    if not, then it can be discarded. Can improve performance,
   512    esp. if disjunctions can be discarded (no case distinction needed!).
   513 
   514    prep_tac: int -> tactic
   515    A preparation tactic to be applied to the goal once all relevant premises
   516    have been moved to the conclusion.
   517 
   518    ref_tac: int -> tactic
   519    the actual refutation tactic. Should be able to deal with goals
   520    [| A1; ...; An |] ==> False
   521    where the Ai are atomic, i.e. no top-level &, | or ?
   522 *)
   523 
   524 fun refute_tac test prep_tac ref_tac =
   525   let val nnf_simps =
   526         [imp_conv_disj,iff_conv_conj_imp,de_Morgan_disj,de_Morgan_conj,
   527          not_all,not_ex,not_not];
   528       val nnf_simpset =
   529         empty_ss setmkeqTrue mk_eq_True
   530                  setmksimps (mksimps mksimps_pairs)
   531                  addsimps nnf_simps;
   532       val prem_nnf_tac = full_simp_tac nnf_simpset;
   533 
   534       val refute_prems_tac =
   535         REPEAT(eresolve_tac [conjE, exE] 1 ORELSE
   536                filter_prems_tac test 1 ORELSE
   537                etac disjE 1) THEN
   538         ref_tac 1;
   539   in EVERY'[TRY o filter_prems_tac test,
   540             DETERM o REPEAT o etac rev_mp, prep_tac, rtac ccontr, prem_nnf_tac,
   541             SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)]
   542   end;