src/HOL/simpdata.ML
author wenzelm
Thu Aug 26 19:04:19 1999 +0200 (1999-08-26)
changeset 7369 2d2110cda81e
parent 7357 d0e16da40ea2
child 7570 a9391550eea1
permissions -rw-r--r--
iff_attrib_setup;
     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 (* "iff" attribute *)
    61 
    62 local
    63   fun change_global_css f (thy, th) =
    64     let
    65       val cs_ref = Classical.claset_ref_of thy;
    66       val ss_ref = Simplifier.simpset_ref_of thy;
    67       val (cs', ss') = f ((! cs_ref, ! ss_ref), [th]);
    68     in cs_ref := cs'; ss_ref := ss'; (thy, th) end;
    69 
    70   fun change_local_css f (ctxt, th) =
    71     let
    72       val cs = Classical.get_local_claset ctxt;
    73       val ss = Simplifier.get_local_simpset ctxt;
    74       val (cs', ss') = f ((cs, ss), [th]);
    75       val ctxt' =
    76         ctxt
    77         |> Classical.put_local_claset cs'
    78         |> Simplifier.put_local_simpset ss';
    79     in (ctxt', th) end;
    80 in
    81 
    82 val iff_add_global = change_global_css (op addIffs);
    83 val iff_add_local = change_local_css (op addIffs);
    84 
    85 val iff_attrib_setup =
    86   [Attrib.add_attributes [("iff", (Attrib.no_args iff_add_global, Attrib.no_args iff_add_local),
    87     "add rules to simpset and claset simultaneously")]];
    88 
    89 end;
    90 
    91 
    92 val [prem] = goal (the_context ()) "x==y ==> x=y";
    93 by (rewtac prem);
    94 by (rtac refl 1);
    95 qed "meta_eq_to_obj_eq";
    96 
    97 local
    98 
    99   fun prover s = prove_goal (the_context ()) s (fn _ => [(Blast_tac 1)]);
   100 
   101 in
   102 
   103 (*Make meta-equalities.  The operator below is Trueprop*)
   104 
   105 fun mk_meta_eq r = r RS eq_reflection;
   106 
   107 val Eq_TrueI  = mk_meta_eq(prover  "P --> (P = True)"  RS mp);
   108 val Eq_FalseI = mk_meta_eq(prover "~P --> (P = False)" RS mp);
   109 
   110 fun mk_eq th = case concl_of th of
   111         Const("==",_)$_$_       => th
   112     |   _$(Const("op =",_)$_$_) => mk_meta_eq th
   113     |   _$(Const("Not",_)$_)    => th RS Eq_FalseI
   114     |   _                       => th RS Eq_TrueI;
   115 (* last 2 lines requires all formulae to be of the from Trueprop(.) *)
   116 
   117 fun mk_eq_True r = Some(r RS meta_eq_to_obj_eq RS Eq_TrueI);
   118 
   119 fun mk_meta_cong rl =
   120   standard(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl))
   121   handle THM _ =>
   122   error("Premises and conclusion of congruence rules must be =-equalities");
   123 
   124 val not_not = prover "(~ ~ P) = P";
   125 
   126 val simp_thms = [not_not] @ map prover
   127  [ "(x=x) = True",
   128    "(~True) = False", "(~False) = True",
   129    "(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))",
   130    "(True=P) = P", "(P=True) = P", "(False=P) = (~P)", "(P=False) = (~P)",
   131    "(True --> P) = P", "(False --> P) = True", 
   132    "(P --> True) = True", "(P --> P) = True",
   133    "(P --> False) = (~P)", "(P --> ~P) = (~P)",
   134    "(P & True) = P", "(True & P) = P", 
   135    "(P & False) = False", "(False & P) = False",
   136    "(P & P) = P", "(P & (P & Q)) = (P & Q)",
   137    "(P & ~P) = False",    "(~P & P) = False",
   138    "(P | True) = True", "(True | P) = True", 
   139    "(P | False) = P", "(False | P) = P",
   140    "(P | P) = P", "(P | (P | Q)) = (P | Q)",
   141    "(P | ~P) = True",    "(~P | P) = True",
   142    "((~P) = (~Q)) = (P=Q)",
   143    "(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x", 
   144 (*two needed for the one-point-rule quantifier simplification procs*)
   145    "(? x. x=t & P(x)) = P(t)",		(*essential for termination!!*)
   146    "(! x. t=x --> P(x)) = P(t)" ];      (*covers a stray case*)
   147 
   148 (* Add congruence rules for = (instead of ==) *)
   149 
   150 (* ###FIXME: Move to simplifier, 
   151    taking mk_meta_cong as input, eliminating addeqcongs and deleqcongs *)
   152 infix 4 addcongs delcongs;
   153 fun ss addcongs congs = ss addeqcongs (map mk_meta_cong congs);
   154 fun ss delcongs congs = ss deleqcongs (map mk_meta_cong congs);
   155 fun Addcongs congs = (simpset_ref() := simpset() addcongs congs);
   156 fun Delcongs congs = (simpset_ref() := simpset() delcongs congs);
   157 
   158 
   159 val imp_cong = impI RSN
   160     (2, prove_goal (the_context ()) "(P=P')--> (P'--> (Q=Q'))--> ((P-->Q) = (P'-->Q'))"
   161         (fn _=> [(Blast_tac 1)]) RS mp RS mp);
   162 
   163 (*Miniscoping: pushing in existential quantifiers*)
   164 val ex_simps = map prover 
   165                 ["(EX x. P x & Q)   = ((EX x. P x) & Q)",
   166                  "(EX x. P & Q x)   = (P & (EX x. Q x))",
   167                  "(EX x. P x | Q)   = ((EX x. P x) | Q)",
   168                  "(EX x. P | Q x)   = (P | (EX x. Q x))",
   169                  "(EX x. P x --> Q) = ((ALL x. P x) --> Q)",
   170                  "(EX x. P --> Q x) = (P --> (EX x. Q x))"];
   171 
   172 (*Miniscoping: pushing in universal quantifiers*)
   173 val all_simps = map prover
   174                 ["(ALL x. P x & Q)   = ((ALL x. P x) & Q)",
   175                  "(ALL x. P & Q x)   = (P & (ALL x. Q x))",
   176                  "(ALL x. P x | Q)   = ((ALL x. P x) | Q)",
   177                  "(ALL x. P | Q x)   = (P | (ALL x. Q x))",
   178                  "(ALL x. P x --> Q) = ((EX x. P x) --> Q)",
   179                  "(ALL x. P --> Q x) = (P --> (ALL x. Q x))"];
   180 
   181 
   182 (* elimination of existential quantifiers in assumptions *)
   183 
   184 val ex_all_equiv =
   185   let val lemma1 = prove_goal (the_context ())
   186         "(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)"
   187         (fn prems => [resolve_tac prems 1, etac exI 1]);
   188       val lemma2 = prove_goalw (the_context ()) [Ex_def]
   189         "(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)"
   190         (fn prems => [(REPEAT(resolve_tac prems 1))])
   191   in equal_intr lemma1 lemma2 end;
   192 
   193 end;
   194 
   195 (* Elimination of True from asumptions: *)
   196 
   197 val True_implies_equals = prove_goal (the_context ())
   198  "(True ==> PROP P) == PROP P"
   199 (fn _ => [rtac equal_intr_rule 1, atac 2,
   200           METAHYPS (fn prems => resolve_tac prems 1) 1,
   201           rtac TrueI 1]);
   202 
   203 fun prove nm thm  = qed_goal nm (the_context ()) thm (fn _ => [(Blast_tac 1)]);
   204 
   205 prove "conj_commute" "(P&Q) = (Q&P)";
   206 prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))";
   207 val conj_comms = [conj_commute, conj_left_commute];
   208 prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))";
   209 
   210 prove "disj_commute" "(P|Q) = (Q|P)";
   211 prove "disj_left_commute" "(P|(Q|R)) = (Q|(P|R))";
   212 val disj_comms = [disj_commute, disj_left_commute];
   213 prove "disj_assoc" "((P|Q)|R) = (P|(Q|R))";
   214 
   215 prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)";
   216 prove "conj_disj_distribR" "((P|Q)&R) = (P&R | Q&R)";
   217 
   218 prove "disj_conj_distribL" "(P|(Q&R)) = ((P|Q) & (P|R))";
   219 prove "disj_conj_distribR" "((P&Q)|R) = ((P|R) & (Q|R))";
   220 
   221 prove "imp_conjR" "(P --> (Q&R)) = ((P-->Q) & (P-->R))";
   222 prove "imp_conjL" "((P&Q) -->R)  = (P --> (Q --> R))";
   223 prove "imp_disjL" "((P|Q) --> R) = ((P-->R)&(Q-->R))";
   224 
   225 (*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*)
   226 prove "imp_disj_not1" "((P --> Q | R)) = (~Q --> P --> R)";
   227 prove "imp_disj_not2" "((P --> Q | R)) = (~R --> P --> Q)";
   228 
   229 prove "imp_disj1" "((P-->Q)|R) = (P--> Q|R)";
   230 prove "imp_disj2" "(Q|(P-->R)) = (P--> Q|R)";
   231 
   232 prove "de_Morgan_disj" "(~(P | Q)) = (~P & ~Q)";
   233 prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)";
   234 prove "not_imp" "(~(P --> Q)) = (P & ~Q)";
   235 prove "not_iff" "(P~=Q) = (P = (~Q))";
   236 prove "disj_not1" "(~P | Q) = (P --> Q)";
   237 prove "disj_not2" "(P | ~Q) = (Q --> P)"; (* changes orientation :-( *)
   238 prove "imp_conv_disj" "(P --> Q) = ((~P) | Q)";
   239 
   240 prove "iff_conv_conj_imp" "(P = Q) = ((P --> Q) & (Q --> P))";
   241 
   242 
   243 (*Avoids duplication of subgoals after split_if, when the true and false 
   244   cases boil down to the same thing.*) 
   245 prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";
   246 
   247 prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))";
   248 prove "imp_all" "((! x. P x) --> Q) = (? x. P x --> Q)";
   249 prove "not_ex"  "(~ (? x. P(x))) = (! x.~P(x))";
   250 prove "imp_ex" "((? x. P x) --> Q) = (! x. P x --> Q)";
   251 
   252 prove "ex_disj_distrib" "(? x. P(x) | Q(x)) = ((? x. P(x)) | (? x. Q(x)))";
   253 prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))";
   254 
   255 (* '&' congruence rule: not included by default!
   256    May slow rewrite proofs down by as much as 50% *)
   257 
   258 let val th = prove_goal (the_context ()) 
   259                 "(P=P')--> (P'--> (Q=Q'))--> ((P&Q) = (P'&Q'))"
   260                 (fn _=> [(Blast_tac 1)])
   261 in  bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   262 
   263 let val th = prove_goal (the_context ()) 
   264                 "(Q=Q')--> (Q'--> (P=P'))--> ((P&Q) = (P'&Q'))"
   265                 (fn _=> [(Blast_tac 1)])
   266 in  bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   267 
   268 (* '|' congruence rule: not included by default! *)
   269 
   270 let val th = prove_goal (the_context ()) 
   271                 "(P=P')--> (~P'--> (Q=Q'))--> ((P|Q) = (P'|Q'))"
   272                 (fn _=> [(Blast_tac 1)])
   273 in  bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   274 
   275 prove "eq_sym_conv" "(x=y) = (y=x)";
   276 
   277 
   278 (** if-then-else rules **)
   279 
   280 Goalw [if_def] "(if True then x else y) = x";
   281 by (Blast_tac 1);
   282 qed "if_True";
   283 
   284 Goalw [if_def] "(if False then x else y) = y";
   285 by (Blast_tac 1);
   286 qed "if_False";
   287 
   288 Goalw [if_def] "P ==> (if P then x else y) = x";
   289 by (Blast_tac 1);
   290 qed "if_P";
   291 
   292 Goalw [if_def] "~P ==> (if P then x else y) = y";
   293 by (Blast_tac 1);
   294 qed "if_not_P";
   295 
   296 Goal "P(if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))";
   297 by (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1);
   298 by (stac if_P 2);
   299 by (stac if_not_P 1);
   300 by (ALLGOALS (Blast_tac));
   301 qed "split_if";
   302 
   303 (* for backwards compatibility: *)
   304 val expand_if = split_if;
   305 
   306 Goal "P(if Q then x else y) = (~((Q & ~P x) | (~Q & ~P y)))";
   307 by (stac split_if 1);
   308 by (Blast_tac 1);
   309 qed "split_if_asm";
   310 
   311 Goal "(if c then x else x) = x";
   312 by (stac split_if 1);
   313 by (Blast_tac 1);
   314 qed "if_cancel";
   315 
   316 Goal "(if x = y then y else x) = x";
   317 by (stac split_if 1);
   318 by (Blast_tac 1);
   319 qed "if_eq_cancel";
   320 
   321 (*This form is useful for expanding IFs on the RIGHT of the ==> symbol*)
   322 Goal "(if P then Q else R) = ((P-->Q) & (~P-->R))";
   323 by (rtac split_if 1);
   324 qed "if_bool_eq_conj";
   325 
   326 (*And this form is useful for expanding IFs on the LEFT*)
   327 Goal "(if P then Q else R) = ((P&Q) | (~P&R))";
   328 by (stac split_if 1);
   329 by (Blast_tac 1);
   330 qed "if_bool_eq_disj";
   331 
   332 
   333 (*** make simplification procedures for quantifier elimination ***)
   334 
   335 structure Quantifier1 = Quantifier1Fun(
   336 struct
   337   (*abstract syntax*)
   338   fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t)
   339     | dest_eq _ = None;
   340   fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t)
   341     | dest_conj _ = None;
   342   val conj = HOLogic.conj
   343   val imp  = HOLogic.imp
   344   (*rules*)
   345   val iff_reflection = eq_reflection
   346   val iffI = iffI
   347   val sym  = sym
   348   val conjI= conjI
   349   val conjE= conjE
   350   val impI = impI
   351   val impE = impE
   352   val mp   = mp
   353   val exI  = exI
   354   val exE  = exE
   355   val allI = allI
   356   val allE = allE
   357 end);
   358 
   359 local
   360 val ex_pattern =
   361   Thm.read_cterm (Theory.sign_of (the_context ())) ("EX x. P(x) & Q(x)",HOLogic.boolT)
   362 
   363 val all_pattern =
   364   Thm.read_cterm (Theory.sign_of (the_context ())) ("ALL x. P(x) & P'(x) --> Q(x)",HOLogic.boolT)
   365 
   366 in
   367 val defEX_regroup =
   368   mk_simproc "defined EX" [ex_pattern] Quantifier1.rearrange_ex;
   369 val defALL_regroup =
   370   mk_simproc "defined ALL" [all_pattern] Quantifier1.rearrange_all;
   371 end;
   372 
   373 
   374 (*** Case splitting ***)
   375 
   376 structure SplitterData =
   377   struct
   378   structure Simplifier = Simplifier
   379   val mk_eq          = mk_eq
   380   val meta_eq_to_iff = meta_eq_to_obj_eq
   381   val iffD           = iffD2
   382   val disjE          = disjE
   383   val conjE          = conjE
   384   val exE            = exE
   385   val contrapos      = contrapos
   386   val contrapos2     = contrapos2
   387   val notnotD        = notnotD
   388   end;
   389 
   390 structure Splitter = SplitterFun(SplitterData);
   391 
   392 val split_tac        = Splitter.split_tac;
   393 val split_inside_tac = Splitter.split_inside_tac;
   394 val split_asm_tac    = Splitter.split_asm_tac;
   395 val op addsplits     = Splitter.addsplits;
   396 val op delsplits     = Splitter.delsplits;
   397 val Addsplits        = Splitter.Addsplits;
   398 val Delsplits        = Splitter.Delsplits;
   399 
   400 (*In general it seems wrong to add distributive laws by default: they
   401   might cause exponential blow-up.  But imp_disjL has been in for a while
   402   and cannot be removed without affecting existing proofs.  Moreover, 
   403   rewriting by "(P|Q --> R) = ((P-->R)&(Q-->R))" might be justified on the
   404   grounds that it allows simplification of R in the two cases.*)
   405 
   406 fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th;
   407 
   408 val mksimps_pairs =
   409   [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
   410    ("All", [spec]), ("True", []), ("False", []),
   411    ("If", [if_bool_eq_conj RS iffD1])];
   412 
   413 (* ###FIXME: move to Provers/simplifier.ML
   414 val mk_atomize:      (string * thm list) list -> thm -> thm list
   415 *)
   416 (* ###FIXME: move to Provers/simplifier.ML *)
   417 fun mk_atomize pairs =
   418   let fun atoms th =
   419         (case concl_of th of
   420            Const("Trueprop",_) $ p =>
   421              (case head_of p of
   422                 Const(a,_) =>
   423                   (case assoc(pairs,a) of
   424                      Some(rls) => flat (map atoms ([th] RL rls))
   425                    | None => [th])
   426               | _ => [th])
   427          | _ => [th])
   428   in atoms end;
   429 
   430 fun mksimps pairs = (map mk_eq o mk_atomize pairs o gen_all);
   431 
   432 fun unsafe_solver prems = FIRST'[resolve_tac(reflexive_thm::TrueI::refl::prems),
   433 				 atac         ,       etac  FalseE ];
   434 (*No premature instantiation of variables during simplification*)
   435 fun   safe_solver prems = FIRST'[  match_tac(reflexive_thm::TrueI::refl::prems),
   436 				 eq_assume_tac, ematch_tac [FalseE]];
   437 
   438 val HOL_basic_ss = empty_ss setsubgoaler asm_simp_tac
   439 			    setSSolver   safe_solver
   440 			    setSolver  unsafe_solver
   441 			    setmksimps (mksimps mksimps_pairs)
   442 			    setmkeqTrue mk_eq_True;
   443 
   444 val HOL_ss = 
   445     HOL_basic_ss addsimps 
   446      ([triv_forall_equality, (* prunes params *)
   447        True_implies_equals, (* prune asms `True' *)
   448        if_True, if_False, if_cancel, if_eq_cancel,
   449        imp_disjL, conj_assoc, disj_assoc,
   450        de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp,
   451        disj_not1, not_all, not_ex, cases_simp, Eps_eq, Eps_sym_eq]
   452      @ ex_simps @ all_simps @ simp_thms)
   453      addsimprocs [defALL_regroup,defEX_regroup]
   454      addcongs [imp_cong]
   455      addsplits [split_if];
   456 
   457 (*Simplifies x assuming c and y assuming ~c*)
   458 val prems = Goalw [if_def]
   459   "[| b=c; c ==> x=u; ~c ==> y=v |] ==> \
   460 \  (if b then x else y) = (if c then u else v)";
   461 by (asm_simp_tac (HOL_ss addsimps prems) 1);
   462 qed "if_cong";
   463 
   464 (*Prevents simplification of x and y: faster and allows the execution
   465   of functional programs. NOW THE DEFAULT.*)
   466 Goal "b=c ==> (if b then x else y) = (if c then x else y)";
   467 by (etac arg_cong 1);
   468 qed "if_weak_cong";
   469 
   470 (*Prevents simplification of t: much faster*)
   471 Goal "a = b ==> (let x=a in t(x)) = (let x=b in t(x))";
   472 by (etac arg_cong 1);
   473 qed "let_weak_cong";
   474 
   475 Goal "f(if c then x else y) = (if c then f x else f y)";
   476 by (simp_tac (HOL_ss setloop (split_tac [split_if])) 1);
   477 qed "if_distrib";
   478 
   479 
   480 (*For expand_case_tac*)
   481 val prems = goal (the_context ()) "[| P ==> Q(True); ~P ==> Q(False) |] ==> Q(P)";
   482 by (case_tac "P" 1);
   483 by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems)));
   484 val expand_case = result();
   485 
   486 (*Used in Auth proofs.  Typically P contains Vars that become instantiated
   487   during unification.*)
   488 fun expand_case_tac P i =
   489     res_inst_tac [("P",P)] expand_case i THEN
   490     Simp_tac (i+1) THEN 
   491     Simp_tac i;
   492 
   493 
   494 (* default simpset *)
   495 val simpsetup = [fn thy => (simpset_ref_of thy := HOL_ss addcongs [if_weak_cong]; thy)];
   496 
   497 
   498 (*** integration of simplifier with classical reasoner ***)
   499 
   500 structure Clasimp = ClasimpFun
   501  (structure Simplifier = Simplifier 
   502         and Classical  = Classical 
   503         and Blast      = Blast);
   504 open Clasimp;
   505 
   506 val HOL_css = (HOL_cs, HOL_ss);
   507 
   508 
   509 (*** A general refutation procedure ***)
   510  
   511 (* Parameters:
   512 
   513    test: term -> bool
   514    tests if a term is at all relevant to the refutation proof;
   515    if not, then it can be discarded. Can improve performance,
   516    esp. if disjunctions can be discarded (no case distinction needed!).
   517 
   518    prep_tac: int -> tactic
   519    A preparation tactic to be applied to the goal once all relevant premises
   520    have been moved to the conclusion.
   521 
   522    ref_tac: int -> tactic
   523    the actual refutation tactic. Should be able to deal with goals
   524    [| A1; ...; An |] ==> False
   525    where the Ai are atomic, i.e. no top-level &, | or ?
   526 *)
   527 
   528 fun refute_tac test prep_tac ref_tac =
   529   let val nnf_simps =
   530         [imp_conv_disj,iff_conv_conj_imp,de_Morgan_disj,de_Morgan_conj,
   531          not_all,not_ex,not_not];
   532       val nnf_simpset =
   533         empty_ss setmkeqTrue mk_eq_True
   534                  setmksimps (mksimps mksimps_pairs)
   535                  addsimps nnf_simps;
   536       val prem_nnf_tac = full_simp_tac nnf_simpset;
   537 
   538       val refute_prems_tac =
   539         REPEAT(eresolve_tac [conjE, exE] 1 ORELSE
   540                filter_prems_tac test 1 ORELSE
   541                etac disjE 1) THEN
   542         ref_tac 1;
   543   in EVERY'[TRY o filter_prems_tac test,
   544             DETERM o REPEAT o etac rev_mp, prep_tac, rtac ccontr, prem_nnf_tac,
   545             SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)]
   546   end;