src/HOL/simpdata.ML
author paulson
Mon Jul 19 15:24:35 1999 +0200 (1999-07-19 ago)
changeset 7031 972b5f62f476
parent 6968 7f2977e96a5c
child 7127 48e235179ffb
permissions -rw-r--r--
getting rid of qed_goal
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(*  Title:      HOL/simpdata.ML
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    ID:         $Id$
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    Author:     Tobias Nipkow
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    Copyright   1991  University of Cambridge
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Instantiation of the generic simplifier for HOL.
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*)
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section "Simplifier";
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(*** Addition of rules to simpsets and clasets simultaneously ***)	(* FIXME move to Provers/clasimp.ML? *)
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infix 4 addIffs delIffs;
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(*Takes UNCONDITIONAL theorems of the form A<->B to 
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        the Safe Intr     rule B==>A and 
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        the Safe Destruct rule A==>B.
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  Also ~A goes to the Safe Elim rule A ==> ?R
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  Failing other cases, A is added as a Safe Intr rule*)
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local
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  val iff_const = HOLogic.eq_const HOLogic.boolT;
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  fun addIff ((cla, simp), th) = 
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      (case HOLogic.dest_Trueprop (#prop (rep_thm th)) of
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                (Const("Not", _) $ A) =>
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                    cla addSEs [zero_var_indexes (th RS notE)]
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              | (con $ _ $ _) =>
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                    if con = iff_const
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                    then cla addSIs [zero_var_indexes (th RS iffD2)]  
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                              addSDs [zero_var_indexes (th RS iffD1)]
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                    else  cla addSIs [th]
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              | _ => cla addSIs [th],
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       simp addsimps [th])
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      handle TERM _ => error ("AddIffs: theorem must be unconditional\n" ^ 
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                         string_of_thm th);
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  fun delIff ((cla, simp), th) = 
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      (case HOLogic.dest_Trueprop (#prop (rep_thm th)) of
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                (Const ("Not", _) $ A) =>
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                    cla delrules [zero_var_indexes (th RS notE)]
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              | (con $ _ $ _) =>
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                    if con = iff_const
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                    then cla delrules [zero_var_indexes (th RS iffD2),
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                                       make_elim (zero_var_indexes (th RS iffD1))]
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                    else cla delrules [th]
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              | _ => cla delrules [th],
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       simp delsimps [th])
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      handle TERM _ => (warning("DelIffs: ignoring conditional theorem\n" ^ 
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                          string_of_thm th); (cla, simp));
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  fun store_clasimp (cla, simp) = (claset_ref () := cla; simpset_ref () := simp)
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in
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val op addIffs = foldl addIff;
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val op delIffs = foldl delIff;
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fun AddIffs thms = store_clasimp ((claset (), simpset ()) addIffs thms);
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fun DelIffs thms = store_clasimp ((claset (), simpset ()) delIffs thms);
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end;
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(* "iff" attribute *)
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local
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  fun change_global_css f (thy, th) =
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    let
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      val cs_ref = Classical.claset_ref_of thy;
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      val ss_ref = Simplifier.simpset_ref_of thy;
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      val (cs', ss') = f ((! cs_ref, ! ss_ref), [th]);
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    in cs_ref := cs'; ss_ref := ss'; (thy, th) end;
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  fun change_local_css f (ctxt, th) =
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    let
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      val cs = Classical.get_local_claset ctxt;
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      val ss = Simplifier.get_local_simpset ctxt;
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      val (cs', ss') = f ((cs, ss), [th]);
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      val ctxt' =
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        ctxt
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        |> Classical.put_local_claset cs'
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        |> Simplifier.put_local_simpset ss';
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    in (ctxt', th) end;
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in
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val iff_add_global = change_global_css (op addIffs);
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val iff_add_local = change_local_css (op addIffs);
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val simpdata_setup =
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  [Attrib.add_attributes [("iff", (Attrib.no_args iff_add_global, Attrib.no_args iff_add_local),
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    "add rules to simpset and claset simultaneously")]];
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end;
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val [prem] = goal HOL.thy "x==y ==> x=y";
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by (rewtac prem);
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by (rtac refl 1);
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qed "meta_eq_to_obj_eq";
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local
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  fun prover s = prove_goal HOL.thy s (fn _ => [(Blast_tac 1)]);
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in
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(*Make meta-equalities.  The operator below is Trueprop*)
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fun mk_meta_eq r = r RS eq_reflection;
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val Eq_TrueI  = mk_meta_eq(prover  "P --> (P = True)"  RS mp);
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val Eq_FalseI = mk_meta_eq(prover "~P --> (P = False)" RS mp);
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fun mk_eq th = case concl_of th of
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        Const("==",_)$_$_       => th
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    |   _$(Const("op =",_)$_$_) => mk_meta_eq th
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    |   _$(Const("Not",_)$_)    => th RS Eq_FalseI
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    |   _                       => th RS Eq_TrueI;
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(* last 2 lines requires all formulae to be of the from Trueprop(.) *)
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fun mk_eq_True r = Some(r RS meta_eq_to_obj_eq RS Eq_TrueI);
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fun mk_meta_cong rl =
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  standard(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl))
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  handle THM _ =>
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  error("Premises and conclusion of congruence rules must be =-equalities");
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val not_not = prover "(~ ~ P) = P";
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val simp_thms = [not_not] @ map prover
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 [ "(x=x) = True",
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   "(~True) = False", "(~False) = True",
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   "(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))",
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   "(True=P) = P", "(P=True) = P", "(False=P) = (~P)", "(P=False) = (~P)",
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   "(True --> P) = P", "(False --> P) = True", 
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   "(P --> True) = True", "(P --> P) = True",
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   "(P --> False) = (~P)", "(P --> ~P) = (~P)",
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   "(P & True) = P", "(True & P) = P", 
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   "(P & False) = False", "(False & P) = False",
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   "(P & P) = P", "(P & (P & Q)) = (P & Q)",
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   "(P & ~P) = False",    "(~P & P) = False",
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   "(P | True) = True", "(True | P) = True", 
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   "(P | False) = P", "(False | P) = P",
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   "(P | P) = P", "(P | (P | Q)) = (P | Q)",
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   "(P | ~P) = True",    "(~P | P) = True",
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   "((~P) = (~Q)) = (P=Q)",
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   "(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x", 
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(*two needed for the one-point-rule quantifier simplification procs*)
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   "(? x. x=t & P(x)) = P(t)",		(*essential for termination!!*)
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   "(! x. t=x --> P(x)) = P(t)" ];      (*covers a stray case*)
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(* Add congruence rules for = (instead of ==) *)
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(* ###FIXME: Move to simplifier, 
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   taking mk_meta_cong as input, eliminating addeqcongs and deleqcongs *)
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infix 4 addcongs delcongs;
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fun ss addcongs congs = ss addeqcongs (map mk_meta_cong congs);
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fun ss delcongs congs = ss deleqcongs (map mk_meta_cong congs);
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fun Addcongs congs = (simpset_ref() := simpset() addcongs congs);
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fun Delcongs congs = (simpset_ref() := simpset() delcongs congs);
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val imp_cong = impI RSN
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    (2, prove_goal HOL.thy "(P=P')--> (P'--> (Q=Q'))--> ((P-->Q) = (P'-->Q'))"
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        (fn _=> [(Blast_tac 1)]) RS mp RS mp);
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(*Miniscoping: pushing in existential quantifiers*)
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val ex_simps = map prover 
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                ["(EX x. P x & Q)   = ((EX x. P x) & Q)",
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                 "(EX x. P & Q x)   = (P & (EX x. Q x))",
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                 "(EX x. P x | Q)   = ((EX x. P x) | Q)",
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                 "(EX x. P | Q x)   = (P | (EX x. Q x))",
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                 "(EX x. P x --> Q) = ((ALL x. P x) --> Q)",
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                 "(EX x. P --> Q x) = (P --> (EX x. Q x))"];
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(*Miniscoping: pushing in universal quantifiers*)
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val all_simps = map prover
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                ["(ALL x. P x & Q)   = ((ALL x. P x) & Q)",
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                 "(ALL x. P & Q x)   = (P & (ALL x. Q x))",
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                 "(ALL x. P x | Q)   = ((ALL x. P x) | Q)",
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                 "(ALL x. P | Q x)   = (P | (ALL x. Q x))",
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                 "(ALL x. P x --> Q) = ((EX x. P x) --> Q)",
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                 "(ALL x. P --> Q x) = (P --> (ALL x. Q x))"];
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(* elimination of existential quantifiers in assumptions *)
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val ex_all_equiv =
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  let val lemma1 = prove_goal HOL.thy
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        "(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)"
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        (fn prems => [resolve_tac prems 1, etac exI 1]);
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      val lemma2 = prove_goalw HOL.thy [Ex_def]
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        "(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)"
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        (fn prems => [(REPEAT(resolve_tac prems 1))])
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  in equal_intr lemma1 lemma2 end;
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end;
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(* Elimination of True from asumptions: *)
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val True_implies_equals = prove_goal HOL.thy
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 "(True ==> PROP P) == PROP P"
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(fn _ => [rtac equal_intr_rule 1, atac 2,
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          METAHYPS (fn prems => resolve_tac prems 1) 1,
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          rtac TrueI 1]);
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fun prove nm thm  = qed_goal nm HOL.thy thm (fn _ => [(Blast_tac 1)]);
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prove "conj_commute" "(P&Q) = (Q&P)";
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prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))";
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val conj_comms = [conj_commute, conj_left_commute];
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prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))";
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prove "disj_commute" "(P|Q) = (Q|P)";
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prove "disj_left_commute" "(P|(Q|R)) = (Q|(P|R))";
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val disj_comms = [disj_commute, disj_left_commute];
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prove "disj_assoc" "((P|Q)|R) = (P|(Q|R))";
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prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)";
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prove "conj_disj_distribR" "((P|Q)&R) = (P&R | Q&R)";
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prove "disj_conj_distribL" "(P|(Q&R)) = ((P|Q) & (P|R))";
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prove "disj_conj_distribR" "((P&Q)|R) = ((P|R) & (Q|R))";
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prove "imp_conjR" "(P --> (Q&R)) = ((P-->Q) & (P-->R))";
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prove "imp_conjL" "((P&Q) -->R)  = (P --> (Q --> R))";
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prove "imp_disjL" "((P|Q) --> R) = ((P-->R)&(Q-->R))";
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(*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*)
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prove "imp_disj_not1" "((P --> Q | R)) = (~Q --> P --> R)";
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prove "imp_disj_not2" "((P --> Q | R)) = (~R --> P --> Q)";
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prove "imp_disj1" "((P-->Q)|R) = (P--> Q|R)";
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prove "imp_disj2" "(Q|(P-->R)) = (P--> Q|R)";
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prove "de_Morgan_disj" "(~(P | Q)) = (~P & ~Q)";
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prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)";
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prove "not_imp" "(~(P --> Q)) = (P & ~Q)";
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prove "not_iff" "(P~=Q) = (P = (~Q))";
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prove "disj_not1" "(~P | Q) = (P --> Q)";
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prove "disj_not2" "(P | ~Q) = (Q --> P)"; (* changes orientation :-( *)
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prove "imp_conv_disj" "(P --> Q) = ((~P) | Q)";
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prove "iff_conv_conj_imp" "(P = Q) = ((P --> Q) & (Q --> P))";
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(*Avoids duplication of subgoals after split_if, when the true and false 
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  cases boil down to the same thing.*) 
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prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";
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prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))";
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prove "imp_all" "((! x. P x) --> Q) = (? x. P x --> Q)";
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prove "not_ex"  "(~ (? x. P(x))) = (! x.~P(x))";
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prove "imp_ex" "((? x. P x) --> Q) = (! x. P x --> Q)";
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prove "ex_disj_distrib" "(? x. P(x) | Q(x)) = ((? x. P(x)) | (? x. Q(x)))";
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prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))";
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(* '&' congruence rule: not included by default!
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   May slow rewrite proofs down by as much as 50% *)
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let val th = prove_goal HOL.thy 
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                "(P=P')--> (P'--> (Q=Q'))--> ((P&Q) = (P'&Q'))"
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                (fn _=> [(Blast_tac 1)])
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in  bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
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let val th = prove_goal HOL.thy 
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                "(Q=Q')--> (Q'--> (P=P'))--> ((P&Q) = (P'&Q'))"
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                (fn _=> [(Blast_tac 1)])
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in  bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
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(* '|' congruence rule: not included by default! *)
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let val th = prove_goal HOL.thy 
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                "(P=P')--> (~P'--> (Q=Q'))--> ((P|Q) = (P'|Q'))"
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                (fn _=> [(Blast_tac 1)])
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in  bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
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prove "eq_sym_conv" "(x=y) = (y=x)";
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(** if-then-else rules **)
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Goalw [if_def] "(if True then x else y) = x";
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by (Blast_tac 1);
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qed "if_True";
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Goalw [if_def] "(if False then x else y) = y";
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by (Blast_tac 1);
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qed "if_False";
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Goalw [if_def] "!!P. P ==> (if P then x else y) = x";
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by (Blast_tac 1);
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qed "if_P";
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Goalw [if_def] "!!P. ~P ==> (if P then x else y) = y";
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by (Blast_tac 1);
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qed "if_not_P";
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Goal "P(if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))";
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by (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1);
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by (stac if_P 2);
paulson@7031
   299
by (stac if_not_P 1);
paulson@7031
   300
by (ALLGOALS (Blast_tac));
paulson@7031
   301
qed "split_if";
paulson@7031
   302
nipkow@4830
   303
(* for backwards compatibility: *)
nipkow@4830
   304
val expand_if = split_if;
oheimb@4205
   305
paulson@7031
   306
Goal "P(if Q then x else y) = (~((Q & ~P x) | (~Q & ~P y)))";
paulson@7031
   307
by (stac split_if 1);
paulson@7031
   308
by (Blast_tac 1);
paulson@7031
   309
qed "split_if_asm";
nipkow@2134
   310
paulson@7031
   311
Goal "(if c then x else x) = x";
paulson@7031
   312
by (stac split_if 1);
paulson@7031
   313
by (Blast_tac 1);
paulson@7031
   314
qed "if_cancel";
oheimb@5304
   315
paulson@7031
   316
Goal "(if x = y then y else x) = x";
paulson@7031
   317
by (stac split_if 1);
paulson@7031
   318
by (Blast_tac 1);
paulson@7031
   319
qed "if_eq_cancel";
oheimb@5304
   320
paulson@4769
   321
(*This form is useful for expanding IFs on the RIGHT of the ==> symbol*)
paulson@7031
   322
Goal
paulson@7031
   323
    "(if P then Q else R) = ((P-->Q) & (~P-->R))";
paulson@7031
   324
by (rtac split_if 1);
paulson@7031
   325
qed "if_bool_eq_conj";
paulson@4769
   326
paulson@4769
   327
(*And this form is useful for expanding IFs on the LEFT*)
paulson@7031
   328
Goal "(if P then Q else R) = ((P&Q) | (~P&R))";
paulson@7031
   329
by (stac split_if 1);
paulson@7031
   330
by (Blast_tac 1);
paulson@7031
   331
qed "if_bool_eq_disj";
nipkow@2134
   332
paulson@4351
   333
paulson@4351
   334
(*** make simplification procedures for quantifier elimination ***)
paulson@4351
   335
paulson@4351
   336
structure Quantifier1 = Quantifier1Fun(
paulson@4351
   337
struct
paulson@4351
   338
  (*abstract syntax*)
paulson@4351
   339
  fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t)
paulson@4351
   340
    | dest_eq _ = None;
paulson@4351
   341
  fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t)
paulson@4351
   342
    | dest_conj _ = None;
paulson@4351
   343
  val conj = HOLogic.conj
paulson@4351
   344
  val imp  = HOLogic.imp
paulson@4351
   345
  (*rules*)
paulson@4351
   346
  val iff_reflection = eq_reflection
paulson@4351
   347
  val iffI = iffI
paulson@4351
   348
  val sym  = sym
paulson@4351
   349
  val conjI= conjI
paulson@4351
   350
  val conjE= conjE
paulson@4351
   351
  val impI = impI
paulson@4351
   352
  val impE = impE
paulson@4351
   353
  val mp   = mp
paulson@4351
   354
  val exI  = exI
paulson@4351
   355
  val exE  = exE
paulson@4351
   356
  val allI = allI
paulson@4351
   357
  val allE = allE
paulson@4351
   358
end);
paulson@4351
   359
nipkow@4320
   360
local
nipkow@4320
   361
val ex_pattern =
wenzelm@6394
   362
  Thm.read_cterm (Theory.sign_of HOL.thy) ("EX x. P(x) & Q(x)",HOLogic.boolT)
paulson@3913
   363
nipkow@4320
   364
val all_pattern =
wenzelm@6394
   365
  Thm.read_cterm (Theory.sign_of HOL.thy) ("ALL x. P(x) & P'(x) --> Q(x)",HOLogic.boolT)
nipkow@4320
   366
nipkow@4320
   367
in
nipkow@4320
   368
val defEX_regroup =
nipkow@4320
   369
  mk_simproc "defined EX" [ex_pattern] Quantifier1.rearrange_ex;
nipkow@4320
   370
val defALL_regroup =
nipkow@4320
   371
  mk_simproc "defined ALL" [all_pattern] Quantifier1.rearrange_all;
nipkow@4320
   372
end;
paulson@3913
   373
paulson@4351
   374
paulson@4351
   375
(*** Case splitting ***)
paulson@3913
   376
oheimb@5304
   377
structure SplitterData =
oheimb@5304
   378
  struct
oheimb@5304
   379
  structure Simplifier = Simplifier
oheimb@5552
   380
  val mk_eq          = mk_eq
oheimb@5304
   381
  val meta_eq_to_iff = meta_eq_to_obj_eq
oheimb@5304
   382
  val iffD           = iffD2
oheimb@5304
   383
  val disjE          = disjE
oheimb@5304
   384
  val conjE          = conjE
oheimb@5304
   385
  val exE            = exE
oheimb@5304
   386
  val contrapos      = contrapos
oheimb@5304
   387
  val contrapos2     = contrapos2
oheimb@5304
   388
  val notnotD        = notnotD
oheimb@5304
   389
  end;
nipkow@4681
   390
oheimb@5304
   391
structure Splitter = SplitterFun(SplitterData);
oheimb@2263
   392
oheimb@5304
   393
val split_tac        = Splitter.split_tac;
oheimb@5304
   394
val split_inside_tac = Splitter.split_inside_tac;
oheimb@5304
   395
val split_asm_tac    = Splitter.split_asm_tac;
oheimb@5307
   396
val op addsplits     = Splitter.addsplits;
oheimb@5307
   397
val op delsplits     = Splitter.delsplits;
oheimb@5304
   398
val Addsplits        = Splitter.Addsplits;
oheimb@5304
   399
val Delsplits        = Splitter.Delsplits;
oheimb@4718
   400
nipkow@2134
   401
(** 'if' congruence rules: neither included by default! *)
nipkow@2134
   402
nipkow@2134
   403
(*In general it seems wrong to add distributive laws by default: they
nipkow@2134
   404
  might cause exponential blow-up.  But imp_disjL has been in for a while
nipkow@2134
   405
  and cannot be removed without affecting existing proofs.  Moreover, 
nipkow@2134
   406
  rewriting by "(P|Q --> R) = ((P-->R)&(Q-->R))" might be justified on the
nipkow@2134
   407
  grounds that it allows simplification of R in the two cases.*)
nipkow@2134
   408
oheimb@5304
   409
fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th;
oheimb@5304
   410
nipkow@2134
   411
val mksimps_pairs =
nipkow@2134
   412
  [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
nipkow@2134
   413
   ("All", [spec]), ("True", []), ("False", []),
paulson@4769
   414
   ("If", [if_bool_eq_conj RS iffD1])];
nipkow@1758
   415
oheimb@5552
   416
(* ###FIXME: move to Provers/simplifier.ML
oheimb@5304
   417
val mk_atomize:      (string * thm list) list -> thm -> thm list
oheimb@5304
   418
*)
oheimb@5552
   419
(* ###FIXME: move to Provers/simplifier.ML *)
oheimb@5304
   420
fun mk_atomize pairs =
oheimb@5304
   421
  let fun atoms th =
oheimb@5304
   422
        (case concl_of th of
oheimb@5304
   423
           Const("Trueprop",_) $ p =>
oheimb@5304
   424
             (case head_of p of
oheimb@5304
   425
                Const(a,_) =>
oheimb@5304
   426
                  (case assoc(pairs,a) of
oheimb@5304
   427
                     Some(rls) => flat (map atoms ([th] RL rls))
oheimb@5304
   428
                   | None => [th])
oheimb@5304
   429
              | _ => [th])
oheimb@5304
   430
         | _ => [th])
oheimb@5304
   431
  in atoms end;
oheimb@5304
   432
oheimb@5552
   433
fun mksimps pairs = (map mk_eq o mk_atomize pairs o gen_all);
oheimb@5304
   434
nipkow@4640
   435
fun unsafe_solver prems = FIRST'[resolve_tac (reflexive_thm::TrueI::refl::prems),
oheimb@2636
   436
				 atac, etac FalseE];
oheimb@2636
   437
(*No premature instantiation of variables during simplification*)
nipkow@4640
   438
fun   safe_solver prems = FIRST'[match_tac (reflexive_thm::TrueI::prems),
oheimb@2636
   439
				 eq_assume_tac, ematch_tac [FalseE]];
oheimb@2443
   440
oheimb@2636
   441
val HOL_basic_ss = empty_ss setsubgoaler asm_simp_tac
oheimb@2636
   442
			    setSSolver   safe_solver
oheimb@2636
   443
			    setSolver  unsafe_solver
nipkow@4677
   444
			    setmksimps (mksimps mksimps_pairs)
oheimb@5552
   445
			    setmkeqTrue mk_eq_True;
oheimb@2443
   446
paulson@3446
   447
val HOL_ss = 
paulson@3446
   448
    HOL_basic_ss addsimps 
paulson@3446
   449
     ([triv_forall_equality, (* prunes params *)
nipkow@3654
   450
       True_implies_equals, (* prune asms `True' *)
oheimb@4718
   451
       if_True, if_False, if_cancel, if_eq_cancel,
oheimb@5304
   452
       imp_disjL, conj_assoc, disj_assoc,
paulson@3904
   453
       de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp,
nipkow@5447
   454
       disj_not1, not_all, not_ex, cases_simp, Eps_eq, Eps_sym_eq]
paulson@3446
   455
     @ ex_simps @ all_simps @ simp_thms)
nipkow@4032
   456
     addsimprocs [defALL_regroup,defEX_regroup]
wenzelm@4744
   457
     addcongs [imp_cong]
nipkow@4830
   458
     addsplits [split_if];
paulson@2082
   459
paulson@6293
   460
(*Simplifies x assuming c and y assuming ~c*)
paulson@6293
   461
val prems = Goalw [if_def]
paulson@6293
   462
  "[| b=c; c ==> x=u; ~c ==> y=v |] ==> \
paulson@6293
   463
\  (if b then x else y) = (if c then u else v)";
paulson@6293
   464
by (asm_simp_tac (HOL_ss addsimps prems) 1);
paulson@6293
   465
qed "if_cong";
paulson@6293
   466
paulson@6293
   467
(*Prevents simplification of x and y: much faster*)
paulson@7031
   468
Goal "b=c ==> (if b then x else y) = (if c then x else y)";
paulson@7031
   469
by (etac arg_cong 1);
paulson@7031
   470
qed "if_weak_cong";
paulson@6293
   471
paulson@6293
   472
(*Prevents simplification of t: much faster*)
paulson@7031
   473
Goal "a = b ==> (let x=a in t(x)) = (let x=b in t(x))";
paulson@7031
   474
by (etac arg_cong 1);
paulson@7031
   475
qed "let_weak_cong";
paulson@6293
   476
paulson@7031
   477
Goal "f(if c then x else y) = (if c then f x else f y)";
paulson@7031
   478
by (simp_tac (HOL_ss setloop (split_tac [split_if])) 1);
paulson@7031
   479
qed "if_distrib";
nipkow@1655
   480
paulson@1984
   481
paulson@4327
   482
(*For expand_case_tac*)
paulson@2948
   483
val prems = goal HOL.thy "[| P ==> Q(True); ~P ==> Q(False) |] ==> Q(P)";
paulson@2948
   484
by (case_tac "P" 1);
paulson@2948
   485
by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems)));
paulson@2948
   486
val expand_case = result();
paulson@2948
   487
paulson@4327
   488
(*Used in Auth proofs.  Typically P contains Vars that become instantiated
paulson@4327
   489
  during unification.*)
paulson@2948
   490
fun expand_case_tac P i =
paulson@2948
   491
    res_inst_tac [("P",P)] expand_case i THEN
paulson@2948
   492
    Simp_tac (i+1) THEN 
paulson@2948
   493
    Simp_tac i;
paulson@2948
   494
paulson@2948
   495
wenzelm@4119
   496
(* install implicit simpset *)
paulson@1984
   497
paulson@6915
   498
simpset_ref() := HOL_ss addcongs [if_weak_cong];
berghofe@3615
   499
oheimb@4652
   500
wenzelm@5219
   501
(*** integration of simplifier with classical reasoner ***)
oheimb@2636
   502
wenzelm@5219
   503
structure Clasimp = ClasimpFun
oheimb@5552
   504
 (structure Simplifier = Simplifier 
oheimb@5552
   505
        and Classical  = Classical 
oheimb@5552
   506
        and Blast      = Blast);
oheimb@4652
   507
open Clasimp;
oheimb@2636
   508
oheimb@2636
   509
val HOL_css = (HOL_cs, HOL_ss);
nipkow@5975
   510
nipkow@5975
   511
nipkow@5975
   512
(*** A general refutation procedure ***)
nipkow@5975
   513
 
nipkow@5975
   514
(* Parameters:
nipkow@5975
   515
nipkow@5975
   516
   test: term -> bool
nipkow@5975
   517
   tests if a term is at all relevant to the refutation proof;
nipkow@5975
   518
   if not, then it can be discarded. Can improve performance,
nipkow@5975
   519
   esp. if disjunctions can be discarded (no case distinction needed!).
nipkow@5975
   520
nipkow@5975
   521
   prep_tac: int -> tactic
nipkow@5975
   522
   A preparation tactic to be applied to the goal once all relevant premises
nipkow@5975
   523
   have been moved to the conclusion.
nipkow@5975
   524
nipkow@5975
   525
   ref_tac: int -> tactic
nipkow@5975
   526
   the actual refutation tactic. Should be able to deal with goals
nipkow@5975
   527
   [| A1; ...; An |] ==> False
nipkow@5975
   528
   where the Ai are atomic, i.e. no top-level &, | or ?
nipkow@5975
   529
*)
nipkow@5975
   530
nipkow@5975
   531
fun refute_tac test prep_tac ref_tac =
nipkow@5975
   532
  let val nnf_simps =
nipkow@5975
   533
        [imp_conv_disj,iff_conv_conj_imp,de_Morgan_disj,de_Morgan_conj,
nipkow@5975
   534
         not_all,not_ex,not_not];
nipkow@5975
   535
      val nnf_simpset =
nipkow@5975
   536
        empty_ss setmkeqTrue mk_eq_True
nipkow@5975
   537
                 setmksimps (mksimps mksimps_pairs)
nipkow@5975
   538
                 addsimps nnf_simps;
nipkow@5975
   539
      val prem_nnf_tac = full_simp_tac nnf_simpset;
nipkow@5975
   540
nipkow@5975
   541
      val refute_prems_tac =
nipkow@5975
   542
        REPEAT(eresolve_tac [conjE, exE] 1 ORELSE
nipkow@5975
   543
               filter_prems_tac test 1 ORELSE
paulson@6301
   544
               etac disjE 1) THEN
nipkow@5975
   545
        ref_tac 1;
nipkow@5975
   546
  in EVERY'[TRY o filter_prems_tac test,
nipkow@6128
   547
            DETERM o REPEAT o etac rev_mp, prep_tac, rtac ccontr, prem_nnf_tac,
nipkow@5975
   548
            SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)]
nipkow@5975
   549
  end;