src/HOL/simpdata.ML
author wenzelm
Fri Mar 31 22:00:36 2000 +0200 (2000-03-31)
changeset 8641 978db2870862
parent 8473 2798d2f71ec2
child 8644 c47735e7bd1c
permissions -rw-r--r--
change_global/local_css move to Provers/clasimp.ML;
fixed 'iff' att syntax;
added 'cong' att;
     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 [zero_var_indexes (th RS iffD2),
    44                                        make_elim (zero_var_indexes (th RS iffD1))]
    45                     else cla delrules [th]
    46               | _ => cla delrules [th],
    47        simp delsimps [th])
    48       handle TERM _ => (warning("DelIffs: ignoring conditional theorem\n" ^ 
    49                           string_of_thm th); (cla, simp));
    50 
    51   fun store_clasimp (cla, simp) = (claset_ref () := cla; simpset_ref () := simp)
    52 in
    53 val op addIffs = foldl addIff;
    54 val op delIffs = foldl delIff;
    55 fun AddIffs thms = store_clasimp ((claset (), simpset ()) addIffs thms);
    56 fun DelIffs thms = store_clasimp ((claset (), simpset ()) delIffs thms);
    57 end;
    58 
    59 
    60 val [prem] = goal (the_context ()) "x==y ==> x=y";
    61 by (rewtac prem);
    62 by (rtac refl 1);
    63 qed "meta_eq_to_obj_eq";
    64 
    65 local
    66 
    67   fun prover s = prove_goal (the_context ()) s (fn _ => [(Blast_tac 1)]);
    68 
    69 in
    70 
    71 (*Make meta-equalities.  The operator below is Trueprop*)
    72 
    73 fun mk_meta_eq r = r RS eq_reflection;
    74 
    75 val Eq_TrueI  = mk_meta_eq(prover  "P --> (P = True)"  RS mp);
    76 val Eq_FalseI = mk_meta_eq(prover "~P --> (P = False)" RS mp);
    77 
    78 fun mk_eq th = case concl_of th of
    79         Const("==",_)$_$_       => th
    80     |   _$(Const("op =",_)$_$_) => mk_meta_eq th
    81     |   _$(Const("Not",_)$_)    => th RS Eq_FalseI
    82     |   _                       => th RS Eq_TrueI;
    83 (* last 2 lines requires all formulae to be of the from Trueprop(.) *)
    84 
    85 fun mk_eq_True r = Some(r RS meta_eq_to_obj_eq RS Eq_TrueI);
    86 
    87 fun mk_meta_cong rl =
    88   standard(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl))
    89   handle THM _ =>
    90   error("Premises and conclusion of congruence rules must be =-equalities");
    91 
    92 val not_not = prover "(~ ~ P) = P";
    93 
    94 val simp_thms = [not_not] @ map prover
    95  [ "(x=x) = True",
    96    "(~True) = False", "(~False) = True",
    97    "(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))",
    98    "(True=P) = P", "(P=True) = P", "(False=P) = (~P)", "(P=False) = (~P)",
    99    "(True --> P) = P", "(False --> P) = True", 
   100    "(P --> True) = True", "(P --> P) = True",
   101    "(P --> False) = (~P)", "(P --> ~P) = (~P)",
   102    "(P & True) = P", "(True & P) = P", 
   103    "(P & False) = False", "(False & P) = False",
   104    "(P & P) = P", "(P & (P & Q)) = (P & Q)",
   105    "(P & ~P) = False",    "(~P & P) = False",
   106    "(P | True) = True", "(True | P) = True", 
   107    "(P | False) = P", "(False | P) = P",
   108    "(P | P) = P", "(P | (P | Q)) = (P | Q)",
   109    "(P | ~P) = True",    "(~P | P) = True",
   110    "((~P) = (~Q)) = (P=Q)",
   111    "(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x", 
   112 (*two needed for the one-point-rule quantifier simplification procs*)
   113    "(? x. x=t & P(x)) = P(t)",		(*essential for termination!!*)
   114    "(! x. t=x --> P(x)) = P(t)" ];      (*covers a stray case*)
   115 
   116 (* Add congruence rules for = (instead of ==) *)
   117 
   118 (* ###FIXME: Move to simplifier, 
   119    taking mk_meta_cong as input, eliminating addeqcongs and deleqcongs *)
   120 infix 4 addcongs delcongs;
   121 fun ss addcongs congs = ss addeqcongs (map mk_meta_cong congs);
   122 fun ss delcongs congs = ss deleqcongs (map mk_meta_cong congs);
   123 fun Addcongs congs = (simpset_ref() := simpset() addcongs congs);
   124 fun Delcongs congs = (simpset_ref() := simpset() delcongs congs);
   125 
   126 val cong_add_global = Simplifier.change_global_ss (op addcongs);
   127 val cong_add_local = Simplifier.change_local_ss (op addcongs);
   128 
   129 val cong_attrib_setup =
   130   [Attrib.add_attributes [("cong", (Attrib.no_args cong_add_global, Attrib.no_args cong_add_local),
   131     "add rules to simpset and claset simultaneously")]];
   132 
   133 
   134 val imp_cong = impI RSN
   135     (2, prove_goal (the_context ()) "(P=P')--> (P'--> (Q=Q'))--> ((P-->Q) = (P'-->Q'))"
   136         (fn _=> [(Blast_tac 1)]) RS mp RS mp);
   137 
   138 (*Miniscoping: pushing in existential quantifiers*)
   139 val ex_simps = map prover
   140                 ["(EX x. P x & Q)   = ((EX x. P x) & Q)",
   141                  "(EX x. P & Q x)   = (P & (EX x. Q x))",
   142                  "(EX x. P x | Q)   = ((EX x. P x) | Q)",
   143                  "(EX x. P | Q x)   = (P | (EX x. Q x))",
   144                  "(EX x. P x --> Q) = ((ALL x. P x) --> Q)",
   145                  "(EX x. P --> Q x) = (P --> (EX x. Q x))"];
   146 
   147 (*Miniscoping: pushing in universal quantifiers*)
   148 val all_simps = map prover
   149                 ["(ALL x. P x & Q)   = ((ALL x. P x) & Q)",
   150                  "(ALL x. P & Q x)   = (P & (ALL x. Q x))",
   151                  "(ALL x. P x | Q)   = ((ALL x. P x) | Q)",
   152                  "(ALL x. P | Q x)   = (P | (ALL x. Q x))",
   153                  "(ALL x. P x --> Q) = ((EX x. P x) --> Q)",
   154                  "(ALL x. P --> Q x) = (P --> (ALL x. Q x))"];
   155 
   156 
   157 (* elimination of existential quantifiers in assumptions *)
   158 
   159 val ex_all_equiv =
   160   let val lemma1 = prove_goal (the_context ())
   161         "(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)"
   162         (fn prems => [resolve_tac prems 1, etac exI 1]);
   163       val lemma2 = prove_goalw (the_context ()) [Ex_def]
   164         "(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)"
   165         (fn prems => [(REPEAT(resolve_tac prems 1))])
   166   in equal_intr lemma1 lemma2 end;
   167 
   168 end;
   169 
   170 bind_thms ("ex_simps", ex_simps);
   171 bind_thms ("all_simps", all_simps);
   172 bind_thm ("not_not", not_not);
   173 
   174 (* Elimination of True from asumptions: *)
   175 
   176 val True_implies_equals = prove_goal (the_context ())
   177  "(True ==> PROP P) == PROP P"
   178 (fn _ => [rtac equal_intr_rule 1, atac 2,
   179           METAHYPS (fn prems => resolve_tac prems 1) 1,
   180           rtac TrueI 1]);
   181 
   182 fun prove nm thm  = qed_goal nm (the_context ()) thm (fn _ => [(Blast_tac 1)]);
   183 
   184 prove "eq_commute" "(a=b)=(b=a)";
   185 prove "eq_left_commute" "(P=(Q=R)) = (Q=(P=R))";
   186 prove "eq_assoc" "((P=Q)=R) = (P=(Q=R))";
   187 val eq_ac = [eq_commute, eq_left_commute, eq_assoc];
   188 
   189 prove "conj_commute" "(P&Q) = (Q&P)";
   190 prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))";
   191 val conj_comms = [conj_commute, conj_left_commute];
   192 prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))";
   193 
   194 prove "disj_commute" "(P|Q) = (Q|P)";
   195 prove "disj_left_commute" "(P|(Q|R)) = (Q|(P|R))";
   196 val disj_comms = [disj_commute, disj_left_commute];
   197 prove "disj_assoc" "((P|Q)|R) = (P|(Q|R))";
   198 
   199 prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)";
   200 prove "conj_disj_distribR" "((P|Q)&R) = (P&R | Q&R)";
   201 
   202 prove "disj_conj_distribL" "(P|(Q&R)) = ((P|Q) & (P|R))";
   203 prove "disj_conj_distribR" "((P&Q)|R) = ((P|R) & (Q|R))";
   204 
   205 prove "imp_conjR" "(P --> (Q&R)) = ((P-->Q) & (P-->R))";
   206 prove "imp_conjL" "((P&Q) -->R)  = (P --> (Q --> R))";
   207 prove "imp_disjL" "((P|Q) --> R) = ((P-->R)&(Q-->R))";
   208 
   209 (*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*)
   210 prove "imp_disj_not1" "(P --> Q | R) = (~Q --> P --> R)";
   211 prove "imp_disj_not2" "(P --> Q | R) = (~R --> P --> Q)";
   212 
   213 prove "imp_disj1" "((P-->Q)|R) = (P--> Q|R)";
   214 prove "imp_disj2" "(Q|(P-->R)) = (P--> Q|R)";
   215 
   216 prove "de_Morgan_disj" "(~(P | Q)) = (~P & ~Q)";
   217 prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)";
   218 prove "not_imp" "(~(P --> Q)) = (P & ~Q)";
   219 prove "not_iff" "(P~=Q) = (P = (~Q))";
   220 prove "disj_not1" "(~P | Q) = (P --> Q)";
   221 prove "disj_not2" "(P | ~Q) = (Q --> P)"; (* changes orientation :-( *)
   222 prove "imp_conv_disj" "(P --> Q) = ((~P) | Q)";
   223 
   224 prove "iff_conv_conj_imp" "(P = Q) = ((P --> Q) & (Q --> P))";
   225 
   226 
   227 (*Avoids duplication of subgoals after split_if, when the true and false 
   228   cases boil down to the same thing.*) 
   229 prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";
   230 
   231 prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))";
   232 prove "imp_all" "((! x. P x) --> Q) = (? x. P x --> Q)";
   233 prove "not_ex"  "(~ (? x. P(x))) = (! x.~P(x))";
   234 prove "imp_ex" "((? x. P x) --> Q) = (! x. P x --> Q)";
   235 
   236 prove "ex_disj_distrib" "(? x. P(x) | Q(x)) = ((? x. P(x)) | (? x. Q(x)))";
   237 prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))";
   238 
   239 (* '&' congruence rule: not included by default!
   240    May slow rewrite proofs down by as much as 50% *)
   241 
   242 let val th = prove_goal (the_context ()) 
   243                 "(P=P')--> (P'--> (Q=Q'))--> ((P&Q) = (P'&Q'))"
   244                 (fn _=> [(Blast_tac 1)])
   245 in  bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   246 
   247 let val th = prove_goal (the_context ()) 
   248                 "(Q=Q')--> (Q'--> (P=P'))--> ((P&Q) = (P'&Q'))"
   249                 (fn _=> [(Blast_tac 1)])
   250 in  bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   251 
   252 (* '|' congruence rule: not included by default! *)
   253 
   254 let val th = prove_goal (the_context ()) 
   255                 "(P=P')--> (~P'--> (Q=Q'))--> ((P|Q) = (P'|Q'))"
   256                 (fn _=> [(Blast_tac 1)])
   257 in  bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   258 
   259 prove "eq_sym_conv" "(x=y) = (y=x)";
   260 
   261 
   262 (** if-then-else rules **)
   263 
   264 Goalw [if_def] "(if True then x else y) = x";
   265 by (Blast_tac 1);
   266 qed "if_True";
   267 
   268 Goalw [if_def] "(if False then x else y) = y";
   269 by (Blast_tac 1);
   270 qed "if_False";
   271 
   272 Goalw [if_def] "P ==> (if P then x else y) = x";
   273 by (Blast_tac 1);
   274 qed "if_P";
   275 
   276 Goalw [if_def] "~P ==> (if P then x else y) = y";
   277 by (Blast_tac 1);
   278 qed "if_not_P";
   279 
   280 Goal "P(if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))";
   281 by (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1);
   282 by (stac if_P 2);
   283 by (stac if_not_P 1);
   284 by (ALLGOALS (Blast_tac));
   285 qed "split_if";
   286 
   287 (* for backwards compatibility: *)
   288 val expand_if = split_if;
   289 
   290 Goal "P(if Q then x else y) = (~((Q & ~P x) | (~Q & ~P y)))";
   291 by (stac split_if 1);
   292 by (Blast_tac 1);
   293 qed "split_if_asm";
   294 
   295 Goal "(if c then x else x) = x";
   296 by (stac split_if 1);
   297 by (Blast_tac 1);
   298 qed "if_cancel";
   299 
   300 Goal "(if x = y then y else x) = x";
   301 by (stac split_if 1);
   302 by (Blast_tac 1);
   303 qed "if_eq_cancel";
   304 
   305 (*This form is useful for expanding IFs on the RIGHT of the ==> symbol*)
   306 Goal "(if P then Q else R) = ((P-->Q) & (~P-->R))";
   307 by (rtac split_if 1);
   308 qed "if_bool_eq_conj";
   309 
   310 (*And this form is useful for expanding IFs on the LEFT*)
   311 Goal "(if P then Q else R) = ((P&Q) | (~P&R))";
   312 by (stac split_if 1);
   313 by (Blast_tac 1);
   314 qed "if_bool_eq_disj";
   315 
   316 
   317 (*** make simplification procedures for quantifier elimination ***)
   318 
   319 structure Quantifier1 = Quantifier1Fun(
   320 struct
   321   (*abstract syntax*)
   322   fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t)
   323     | dest_eq _ = None;
   324   fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t)
   325     | dest_conj _ = None;
   326   val conj = HOLogic.conj
   327   val imp  = HOLogic.imp
   328   (*rules*)
   329   val iff_reflection = eq_reflection
   330   val iffI = iffI
   331   val sym  = sym
   332   val conjI= conjI
   333   val conjE= conjE
   334   val impI = impI
   335   val impE = impE
   336   val mp   = mp
   337   val exI  = exI
   338   val exE  = exE
   339   val allI = allI
   340   val allE = allE
   341 end);
   342 
   343 local
   344 val ex_pattern =
   345   Thm.read_cterm (Theory.sign_of (the_context ())) ("EX x. P(x) & Q(x)",HOLogic.boolT)
   346 
   347 val all_pattern =
   348   Thm.read_cterm (Theory.sign_of (the_context ())) ("ALL x. P(x) & P'(x) --> Q(x)",HOLogic.boolT)
   349 
   350 in
   351 val defEX_regroup =
   352   mk_simproc "defined EX" [ex_pattern] Quantifier1.rearrange_ex;
   353 val defALL_regroup =
   354   mk_simproc "defined ALL" [all_pattern] Quantifier1.rearrange_all;
   355 end;
   356 
   357 
   358 (*** Case splitting ***)
   359 
   360 structure SplitterData =
   361   struct
   362   structure Simplifier = Simplifier
   363   val mk_eq          = mk_eq
   364   val meta_eq_to_iff = meta_eq_to_obj_eq
   365   val iffD           = iffD2
   366   val disjE          = disjE
   367   val conjE          = conjE
   368   val exE            = exE
   369   val contrapos      = contrapos
   370   val contrapos2     = contrapos2
   371   val notnotD        = notnotD
   372   end;
   373 
   374 structure Splitter = SplitterFun(SplitterData);
   375 
   376 val split_tac        = Splitter.split_tac;
   377 val split_inside_tac = Splitter.split_inside_tac;
   378 val split_asm_tac    = Splitter.split_asm_tac;
   379 val op addsplits     = Splitter.addsplits;
   380 val op delsplits     = Splitter.delsplits;
   381 val Addsplits        = Splitter.Addsplits;
   382 val Delsplits        = Splitter.Delsplits;
   383 
   384 (*In general it seems wrong to add distributive laws by default: they
   385   might cause exponential blow-up.  But imp_disjL has been in for a while
   386   and cannot be removed without affecting existing proofs.  Moreover, 
   387   rewriting by "(P|Q --> R) = ((P-->R)&(Q-->R))" might be justified on the
   388   grounds that it allows simplification of R in the two cases.*)
   389 
   390 fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th;
   391 
   392 val mksimps_pairs =
   393   [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
   394    ("All", [spec]), ("True", []), ("False", []),
   395    ("If", [if_bool_eq_conj RS iffD1])];
   396 
   397 (* ###FIXME: move to Provers/simplifier.ML
   398 val mk_atomize:      (string * thm list) list -> thm -> thm list
   399 *)
   400 (* ###FIXME: move to Provers/simplifier.ML *)
   401 fun mk_atomize pairs =
   402   let fun atoms th =
   403         (case concl_of th of
   404            Const("Trueprop",_) $ p =>
   405              (case head_of p of
   406                 Const(a,_) =>
   407                   (case assoc(pairs,a) of
   408                      Some(rls) => flat (map atoms ([th] RL rls))
   409                    | None => [th])
   410               | _ => [th])
   411          | _ => [th])
   412   in atoms end;
   413 
   414 fun mksimps pairs = (map mk_eq o mk_atomize pairs o gen_all);
   415 
   416 fun unsafe_solver_tac prems =
   417   FIRST'[resolve_tac(reflexive_thm::TrueI::refl::prems), atac, etac FalseE];
   418 val unsafe_solver = mk_solver "HOL unsafe" unsafe_solver_tac;
   419 
   420 (*No premature instantiation of variables during simplification*)
   421 fun safe_solver_tac prems =
   422   FIRST'[match_tac(reflexive_thm::TrueI::refl::prems),
   423          eq_assume_tac, ematch_tac [FalseE]];
   424 val safe_solver = mk_solver "HOL safe" safe_solver_tac;
   425 
   426 val HOL_basic_ss = empty_ss setsubgoaler asm_simp_tac
   427 			    setSSolver safe_solver
   428 			    setSolver  unsafe_solver
   429 			    setmksimps (mksimps mksimps_pairs)
   430 			    setmkeqTrue mk_eq_True;
   431 
   432 val HOL_ss = 
   433     HOL_basic_ss addsimps 
   434      ([triv_forall_equality, (* prunes params *)
   435        True_implies_equals, (* prune asms `True' *)
   436        if_True, if_False, if_cancel, if_eq_cancel,
   437        imp_disjL, conj_assoc, disj_assoc,
   438        de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp,
   439        disj_not1, not_all, not_ex, cases_simp, Eps_eq, Eps_sym_eq]
   440      @ ex_simps @ all_simps @ simp_thms)
   441      addsimprocs [defALL_regroup,defEX_regroup]
   442      addcongs [imp_cong]
   443      addsplits [split_if];
   444 
   445 (*Simplifies x assuming c and y assuming ~c*)
   446 val prems = Goalw [if_def]
   447   "[| b=c; c ==> x=u; ~c ==> y=v |] ==> \
   448 \  (if b then x else y) = (if c then u else v)";
   449 by (asm_simp_tac (HOL_ss addsimps prems) 1);
   450 qed "if_cong";
   451 
   452 (*Prevents simplification of x and y: faster and allows the execution
   453   of functional programs. NOW THE DEFAULT.*)
   454 Goal "b=c ==> (if b then x else y) = (if c then x else y)";
   455 by (etac arg_cong 1);
   456 qed "if_weak_cong";
   457 
   458 (*Prevents simplification of t: much faster*)
   459 Goal "a = b ==> (let x=a in t(x)) = (let x=b in t(x))";
   460 by (etac arg_cong 1);
   461 qed "let_weak_cong";
   462 
   463 Goal "f(if c then x else y) = (if c then f x else f y)";
   464 by (simp_tac (HOL_ss setloop (split_tac [split_if])) 1);
   465 qed "if_distrib";
   466 
   467 (*For expand_case_tac*)
   468 val prems = Goal "[| P ==> Q(True); ~P ==> Q(False) |] ==> Q(P)";
   469 by (case_tac "P" 1);
   470 by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems)));
   471 qed "expand_case";
   472 
   473 (*Used in Auth proofs.  Typically P contains Vars that become instantiated
   474   during unification.*)
   475 fun expand_case_tac P i =
   476     res_inst_tac [("P",P)] expand_case i THEN
   477     Simp_tac (i+1) THEN 
   478     Simp_tac i;
   479 
   480 (*This lemma restricts the effect of the rewrite rule u=v to the left-hand
   481   side of an equality.  Used in {Integ,Real}/simproc.ML*)
   482 Goal "x=y ==> (x=z) = (y=z)";
   483 by (asm_simp_tac HOL_ss 1);
   484 qed "restrict_to_left";
   485 
   486 (* default simpset *)
   487 val simpsetup = 
   488     [fn thy => (simpset_ref_of thy := HOL_ss addcongs [if_weak_cong]; 
   489 		thy)];
   490 
   491 
   492 (*** integration of simplifier with classical reasoner ***)
   493 
   494 structure Clasimp = ClasimpFun
   495  (structure Simplifier = Simplifier and Splitter = Splitter
   496    and Classical  = Classical and Blast = Blast);
   497 open Clasimp;
   498 
   499 val HOL_css = (HOL_cs, HOL_ss);
   500 
   501 
   502 (* "iff" attribute *)
   503 
   504 val iff_add_global = Clasimp.change_global_css (op addIffs);
   505 val iff_add_local = Clasimp.change_local_css (op addIffs);
   506 
   507 val iff_attrib_setup =
   508   [Attrib.add_attributes [("iff", (Attrib.no_args iff_add_global, Attrib.no_args iff_add_local),
   509     "add rules to simpset and claset simultaneously")]];
   510 
   511 
   512 
   513 (*** A general refutation procedure ***)
   514  
   515 (* Parameters:
   516 
   517    test: term -> bool
   518    tests if a term is at all relevant to the refutation proof;
   519    if not, then it can be discarded. Can improve performance,
   520    esp. if disjunctions can be discarded (no case distinction needed!).
   521 
   522    prep_tac: int -> tactic
   523    A preparation tactic to be applied to the goal once all relevant premises
   524    have been moved to the conclusion.
   525 
   526    ref_tac: int -> tactic
   527    the actual refutation tactic. Should be able to deal with goals
   528    [| A1; ...; An |] ==> False
   529    where the Ai are atomic, i.e. no top-level &, | or ?
   530 *)
   531 
   532 fun refute_tac test prep_tac ref_tac =
   533   let val nnf_simps =
   534         [imp_conv_disj,iff_conv_conj_imp,de_Morgan_disj,de_Morgan_conj,
   535          not_all,not_ex,not_not];
   536       val nnf_simpset =
   537         empty_ss setmkeqTrue mk_eq_True
   538                  setmksimps (mksimps mksimps_pairs)
   539                  addsimps nnf_simps;
   540       val prem_nnf_tac = full_simp_tac nnf_simpset;
   541 
   542       val refute_prems_tac =
   543         REPEAT(eresolve_tac [conjE, exE] 1 ORELSE
   544                filter_prems_tac test 1 ORELSE
   545                etac disjE 1) THEN
   546         ref_tac 1;
   547   in EVERY'[TRY o filter_prems_tac test,
   548             DETERM o REPEAT o etac rev_mp, prep_tac, rtac ccontr, prem_nnf_tac,
   549             SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)]
   550   end;