src/HOL/simpdata.ML
author berghofe
Tue Oct 05 15:24:58 1999 +0200 (1999-10-05)
changeset 7711 4dae7a4fceaf
parent 7648 8258b93cdd32
child 8114 09a7a180cc99
permissions -rw-r--r--
Rule not_not is now stored in theory (needed by Inductive).
     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 bind_thms ("ex_simps", ex_simps);
   196 bind_thms ("all_simps", all_simps);
   197 bind_thm ("not_not", not_not);
   198 
   199 (* Elimination of True from asumptions: *)
   200 
   201 val True_implies_equals = prove_goal (the_context ())
   202  "(True ==> PROP P) == PROP P"
   203 (fn _ => [rtac equal_intr_rule 1, atac 2,
   204           METAHYPS (fn prems => resolve_tac prems 1) 1,
   205           rtac TrueI 1]);
   206 
   207 fun prove nm thm  = qed_goal nm (the_context ()) thm (fn _ => [(Blast_tac 1)]);
   208 
   209 prove "eq_commute" "(a=b)=(b=a)";
   210 prove "eq_left_commute" "(P=(Q=R)) = (Q=(P=R))";
   211 prove "eq_assoc" "((P=Q)=R) = (P=(Q=R))";
   212 val eq_ac = [eq_commute, eq_left_commute, eq_assoc];
   213 
   214 prove "conj_commute" "(P&Q) = (Q&P)";
   215 prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))";
   216 val conj_comms = [conj_commute, conj_left_commute];
   217 prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))";
   218 
   219 prove "disj_commute" "(P|Q) = (Q|P)";
   220 prove "disj_left_commute" "(P|(Q|R)) = (Q|(P|R))";
   221 val disj_comms = [disj_commute, disj_left_commute];
   222 prove "disj_assoc" "((P|Q)|R) = (P|(Q|R))";
   223 
   224 prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)";
   225 prove "conj_disj_distribR" "((P|Q)&R) = (P&R | Q&R)";
   226 
   227 prove "disj_conj_distribL" "(P|(Q&R)) = ((P|Q) & (P|R))";
   228 prove "disj_conj_distribR" "((P&Q)|R) = ((P|R) & (Q|R))";
   229 
   230 prove "imp_conjR" "(P --> (Q&R)) = ((P-->Q) & (P-->R))";
   231 prove "imp_conjL" "((P&Q) -->R)  = (P --> (Q --> R))";
   232 prove "imp_disjL" "((P|Q) --> R) = ((P-->R)&(Q-->R))";
   233 
   234 (*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*)
   235 prove "imp_disj_not1" "((P --> Q | R)) = (~Q --> P --> R)";
   236 prove "imp_disj_not2" "((P --> Q | R)) = (~R --> P --> Q)";
   237 
   238 prove "imp_disj1" "((P-->Q)|R) = (P--> Q|R)";
   239 prove "imp_disj2" "(Q|(P-->R)) = (P--> Q|R)";
   240 
   241 prove "de_Morgan_disj" "(~(P | Q)) = (~P & ~Q)";
   242 prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)";
   243 prove "not_imp" "(~(P --> Q)) = (P & ~Q)";
   244 prove "not_iff" "(P~=Q) = (P = (~Q))";
   245 prove "disj_not1" "(~P | Q) = (P --> Q)";
   246 prove "disj_not2" "(P | ~Q) = (Q --> P)"; (* changes orientation :-( *)
   247 prove "imp_conv_disj" "(P --> Q) = ((~P) | Q)";
   248 
   249 prove "iff_conv_conj_imp" "(P = Q) = ((P --> Q) & (Q --> P))";
   250 
   251 
   252 (*Avoids duplication of subgoals after split_if, when the true and false 
   253   cases boil down to the same thing.*) 
   254 prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";
   255 
   256 prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))";
   257 prove "imp_all" "((! x. P x) --> Q) = (? x. P x --> Q)";
   258 prove "not_ex"  "(~ (? x. P(x))) = (! x.~P(x))";
   259 prove "imp_ex" "((? x. P x) --> Q) = (! x. P x --> Q)";
   260 
   261 prove "ex_disj_distrib" "(? x. P(x) | Q(x)) = ((? x. P(x)) | (? x. Q(x)))";
   262 prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))";
   263 
   264 (* '&' congruence rule: not included by default!
   265    May slow rewrite proofs down by as much as 50% *)
   266 
   267 let val th = prove_goal (the_context ()) 
   268                 "(P=P')--> (P'--> (Q=Q'))--> ((P&Q) = (P'&Q'))"
   269                 (fn _=> [(Blast_tac 1)])
   270 in  bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   271 
   272 let val th = prove_goal (the_context ()) 
   273                 "(Q=Q')--> (Q'--> (P=P'))--> ((P&Q) = (P'&Q'))"
   274                 (fn _=> [(Blast_tac 1)])
   275 in  bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   276 
   277 (* '|' congruence rule: not included by default! *)
   278 
   279 let val th = prove_goal (the_context ()) 
   280                 "(P=P')--> (~P'--> (Q=Q'))--> ((P|Q) = (P'|Q'))"
   281                 (fn _=> [(Blast_tac 1)])
   282 in  bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   283 
   284 prove "eq_sym_conv" "(x=y) = (y=x)";
   285 
   286 
   287 (** if-then-else rules **)
   288 
   289 Goalw [if_def] "(if True then x else y) = x";
   290 by (Blast_tac 1);
   291 qed "if_True";
   292 
   293 Goalw [if_def] "(if False then x else y) = y";
   294 by (Blast_tac 1);
   295 qed "if_False";
   296 
   297 Goalw [if_def] "P ==> (if P then x else y) = x";
   298 by (Blast_tac 1);
   299 qed "if_P";
   300 
   301 Goalw [if_def] "~P ==> (if P then x else y) = y";
   302 by (Blast_tac 1);
   303 qed "if_not_P";
   304 
   305 Goal "P(if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))";
   306 by (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1);
   307 by (stac if_P 2);
   308 by (stac if_not_P 1);
   309 by (ALLGOALS (Blast_tac));
   310 qed "split_if";
   311 
   312 (* for backwards compatibility: *)
   313 val expand_if = split_if;
   314 
   315 Goal "P(if Q then x else y) = (~((Q & ~P x) | (~Q & ~P y)))";
   316 by (stac split_if 1);
   317 by (Blast_tac 1);
   318 qed "split_if_asm";
   319 
   320 Goal "(if c then x else x) = x";
   321 by (stac split_if 1);
   322 by (Blast_tac 1);
   323 qed "if_cancel";
   324 
   325 Goal "(if x = y then y else x) = x";
   326 by (stac split_if 1);
   327 by (Blast_tac 1);
   328 qed "if_eq_cancel";
   329 
   330 (*This form is useful for expanding IFs on the RIGHT of the ==> symbol*)
   331 Goal "(if P then Q else R) = ((P-->Q) & (~P-->R))";
   332 by (rtac split_if 1);
   333 qed "if_bool_eq_conj";
   334 
   335 (*And this form is useful for expanding IFs on the LEFT*)
   336 Goal "(if P then Q else R) = ((P&Q) | (~P&R))";
   337 by (stac split_if 1);
   338 by (Blast_tac 1);
   339 qed "if_bool_eq_disj";
   340 
   341 
   342 (*** make simplification procedures for quantifier elimination ***)
   343 
   344 structure Quantifier1 = Quantifier1Fun(
   345 struct
   346   (*abstract syntax*)
   347   fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t)
   348     | dest_eq _ = None;
   349   fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t)
   350     | dest_conj _ = None;
   351   val conj = HOLogic.conj
   352   val imp  = HOLogic.imp
   353   (*rules*)
   354   val iff_reflection = eq_reflection
   355   val iffI = iffI
   356   val sym  = sym
   357   val conjI= conjI
   358   val conjE= conjE
   359   val impI = impI
   360   val impE = impE
   361   val mp   = mp
   362   val exI  = exI
   363   val exE  = exE
   364   val allI = allI
   365   val allE = allE
   366 end);
   367 
   368 local
   369 val ex_pattern =
   370   Thm.read_cterm (Theory.sign_of (the_context ())) ("EX x. P(x) & Q(x)",HOLogic.boolT)
   371 
   372 val all_pattern =
   373   Thm.read_cterm (Theory.sign_of (the_context ())) ("ALL x. P(x) & P'(x) --> Q(x)",HOLogic.boolT)
   374 
   375 in
   376 val defEX_regroup =
   377   mk_simproc "defined EX" [ex_pattern] Quantifier1.rearrange_ex;
   378 val defALL_regroup =
   379   mk_simproc "defined ALL" [all_pattern] Quantifier1.rearrange_all;
   380 end;
   381 
   382 
   383 (*** Case splitting ***)
   384 
   385 structure SplitterData =
   386   struct
   387   structure Simplifier = Simplifier
   388   val mk_eq          = mk_eq
   389   val meta_eq_to_iff = meta_eq_to_obj_eq
   390   val iffD           = iffD2
   391   val disjE          = disjE
   392   val conjE          = conjE
   393   val exE            = exE
   394   val contrapos      = contrapos
   395   val contrapos2     = contrapos2
   396   val notnotD        = notnotD
   397   end;
   398 
   399 structure Splitter = SplitterFun(SplitterData);
   400 
   401 val split_tac        = Splitter.split_tac;
   402 val split_inside_tac = Splitter.split_inside_tac;
   403 val split_asm_tac    = Splitter.split_asm_tac;
   404 val op addsplits     = Splitter.addsplits;
   405 val op delsplits     = Splitter.delsplits;
   406 val Addsplits        = Splitter.Addsplits;
   407 val Delsplits        = Splitter.Delsplits;
   408 
   409 (*In general it seems wrong to add distributive laws by default: they
   410   might cause exponential blow-up.  But imp_disjL has been in for a while
   411   and cannot be removed without affecting existing proofs.  Moreover, 
   412   rewriting by "(P|Q --> R) = ((P-->R)&(Q-->R))" might be justified on the
   413   grounds that it allows simplification of R in the two cases.*)
   414 
   415 fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th;
   416 
   417 val mksimps_pairs =
   418   [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
   419    ("All", [spec]), ("True", []), ("False", []),
   420    ("If", [if_bool_eq_conj RS iffD1])];
   421 
   422 (* ###FIXME: move to Provers/simplifier.ML
   423 val mk_atomize:      (string * thm list) list -> thm -> thm list
   424 *)
   425 (* ###FIXME: move to Provers/simplifier.ML *)
   426 fun mk_atomize pairs =
   427   let fun atoms th =
   428         (case concl_of th of
   429            Const("Trueprop",_) $ p =>
   430              (case head_of p of
   431                 Const(a,_) =>
   432                   (case assoc(pairs,a) of
   433                      Some(rls) => flat (map atoms ([th] RL rls))
   434                    | None => [th])
   435               | _ => [th])
   436          | _ => [th])
   437   in atoms end;
   438 
   439 fun mksimps pairs = (map mk_eq o mk_atomize pairs o gen_all);
   440 
   441 fun unsafe_solver_tac prems =
   442   FIRST'[resolve_tac(reflexive_thm::TrueI::refl::prems), atac, etac FalseE];
   443 val unsafe_solver = mk_solver "HOL unsafe" unsafe_solver_tac;
   444 
   445 (*No premature instantiation of variables during simplification*)
   446 fun safe_solver_tac prems =
   447   FIRST'[match_tac(reflexive_thm::TrueI::refl::prems),
   448          eq_assume_tac, ematch_tac [FalseE]];
   449 val safe_solver = mk_solver "HOL safe" safe_solver_tac;
   450 
   451 val HOL_basic_ss = empty_ss setsubgoaler asm_simp_tac
   452 			    setSSolver safe_solver
   453 			    setSolver  unsafe_solver
   454 			    setmksimps (mksimps mksimps_pairs)
   455 			    setmkeqTrue mk_eq_True;
   456 
   457 val HOL_ss = 
   458     HOL_basic_ss addsimps 
   459      ([triv_forall_equality, (* prunes params *)
   460        True_implies_equals, (* prune asms `True' *)
   461        if_True, if_False, if_cancel, if_eq_cancel,
   462        imp_disjL, conj_assoc, disj_assoc,
   463        de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp,
   464        disj_not1, not_all, not_ex, cases_simp, Eps_eq, Eps_sym_eq]
   465      @ ex_simps @ all_simps @ simp_thms)
   466      addsimprocs [defALL_regroup,defEX_regroup]
   467      addcongs [imp_cong]
   468      addsplits [split_if];
   469 
   470 (*Simplifies x assuming c and y assuming ~c*)
   471 val prems = Goalw [if_def]
   472   "[| b=c; c ==> x=u; ~c ==> y=v |] ==> \
   473 \  (if b then x else y) = (if c then u else v)";
   474 by (asm_simp_tac (HOL_ss addsimps prems) 1);
   475 qed "if_cong";
   476 
   477 (*Prevents simplification of x and y: faster and allows the execution
   478   of functional programs. NOW THE DEFAULT.*)
   479 Goal "b=c ==> (if b then x else y) = (if c then x else y)";
   480 by (etac arg_cong 1);
   481 qed "if_weak_cong";
   482 
   483 (*Prevents simplification of t: much faster*)
   484 Goal "a = b ==> (let x=a in t(x)) = (let x=b in t(x))";
   485 by (etac arg_cong 1);
   486 qed "let_weak_cong";
   487 
   488 Goal "f(if c then x else y) = (if c then f x else f y)";
   489 by (simp_tac (HOL_ss setloop (split_tac [split_if])) 1);
   490 qed "if_distrib";
   491 
   492 (*For expand_case_tac*)
   493 val prems = Goal "[| P ==> Q(True); ~P ==> Q(False) |] ==> Q(P)";
   494 by (case_tac "P" 1);
   495 by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems)));
   496 qed "expand_case";
   497 
   498 (*Used in Auth proofs.  Typically P contains Vars that become instantiated
   499   during unification.*)
   500 fun expand_case_tac P i =
   501     res_inst_tac [("P",P)] expand_case i THEN
   502     Simp_tac (i+1) THEN 
   503     Simp_tac i;
   504 
   505 (*This lemma restricts the effect of the rewrite rule u=v to the left-hand
   506   side of an equality.  Used in {Integ,Real}/simproc.ML*)
   507 Goal "x=y ==> (x=z) = (y=z)";
   508 by (asm_simp_tac HOL_ss 1);
   509 qed "restrict_to_left";
   510 
   511 (* default simpset *)
   512 val simpsetup = 
   513     [fn thy => (simpset_ref_of thy := HOL_ss addcongs [if_weak_cong]; 
   514 		thy)];
   515 
   516 
   517 (*** integration of simplifier with classical reasoner ***)
   518 
   519 structure Clasimp = ClasimpFun
   520  (structure Simplifier = Simplifier 
   521         and Classical  = Classical 
   522         and Blast      = Blast);
   523 open Clasimp;
   524 
   525 val HOL_css = (HOL_cs, HOL_ss);
   526 
   527 
   528 (*** A general refutation procedure ***)
   529  
   530 (* Parameters:
   531 
   532    test: term -> bool
   533    tests if a term is at all relevant to the refutation proof;
   534    if not, then it can be discarded. Can improve performance,
   535    esp. if disjunctions can be discarded (no case distinction needed!).
   536 
   537    prep_tac: int -> tactic
   538    A preparation tactic to be applied to the goal once all relevant premises
   539    have been moved to the conclusion.
   540 
   541    ref_tac: int -> tactic
   542    the actual refutation tactic. Should be able to deal with goals
   543    [| A1; ...; An |] ==> False
   544    where the Ai are atomic, i.e. no top-level &, | or ?
   545 *)
   546 
   547 fun refute_tac test prep_tac ref_tac =
   548   let val nnf_simps =
   549         [imp_conv_disj,iff_conv_conj_imp,de_Morgan_disj,de_Morgan_conj,
   550          not_all,not_ex,not_not];
   551       val nnf_simpset =
   552         empty_ss setmkeqTrue mk_eq_True
   553                  setmksimps (mksimps mksimps_pairs)
   554                  addsimps nnf_simps;
   555       val prem_nnf_tac = full_simp_tac nnf_simpset;
   556 
   557       val refute_prems_tac =
   558         REPEAT(eresolve_tac [conjE, exE] 1 ORELSE
   559                filter_prems_tac test 1 ORELSE
   560                etac disjE 1) THEN
   561         ref_tac 1;
   562   in EVERY'[TRY o filter_prems_tac test,
   563             DETERM o REPEAT o etac rev_mp, prep_tac, rtac ccontr, prem_nnf_tac,
   564             SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)]
   565   end;