src/HOL/simpdata.ML
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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
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*)
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section "Simplifier";
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open Simplifier;
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(*** Addition of rules to simpsets and clasets simultaneously ***)
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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 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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                    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 (AddSIs [zero_var_indexes (th RS iffD2)];  
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                          AddSDs [zero_var_indexes (th RS iffD1)])
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                    else  AddSIs [th]
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              | _ => AddSIs [th];
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       Addsimps [th])
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      handle _ => error ("AddIffs: theorem must be unconditional\n" ^ 
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                         string_of_thm th)
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  fun delIff 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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                    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 Delrules [zero_var_indexes (th RS iffD2),
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                                   make_elim (zero_var_indexes (th RS iffD1))]
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                    else Delrules [th]
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              | _ => Delrules [th];
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       Delsimps [th])
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      handle _ => warning("DelIffs: ignoring conditional theorem\n" ^ 
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                          string_of_thm th)
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in
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val AddIffs = seq addIff
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val DelIffs = seq delIff
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end;
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(** instantiate generic simp procs for `quantifier elimination': **)
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structure Quantifier1 = Quantifier1Fun(
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struct
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  (*abstract syntax*)
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  fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t)
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    | dest_eq _ = None;
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  fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t)
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    | dest_conj _ = None;
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  val conj = HOLogic.conj
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  val imp  = HOLogic.imp
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  (*rules*)
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  val iff_reflection = eq_reflection
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  val iffI = iffI
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  val sym  = sym
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  val conjI= conjI
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  val conjE= conjE
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  val impI = impI
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  val impE = impE
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  val mp   = mp
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  val exI  = exI
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  val exE  = exE
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  val allI = allI
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  val allE = allE
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end);
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local
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  fun prover s = prove_goal HOL.thy s (fn _ => [blast_tac HOL_cs 1]);
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  val P_imp_P_iff_True = prover "P --> (P = True)" RS mp;
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  val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection;
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  val not_P_imp_P_iff_F = prover "~P --> (P = False)" RS mp;
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  val not_P_imp_P_eq_False = not_P_imp_P_iff_F RS eq_reflection;
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  fun atomize pairs =
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    let fun atoms th =
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          (case concl_of th of
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             Const("Trueprop",_) $ p =>
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               (case head_of p of
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                  Const(a,_) =>
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                    (case assoc(pairs,a) of
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                       Some(rls) => flat (map atoms ([th] RL rls))
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                     | None => [th])
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                | _ => [th])
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           | _ => [th])
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    in atoms end;
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  fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th;
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in
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  fun mk_meta_eq r = r RS eq_reflection;
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  fun mk_meta_eq_simp r = case concl_of r of
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          Const("==",_)$_$_ => r
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      |   _$(Const("op =",_)$lhs$rhs) =>
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             (case fst(Logic.rewrite_rule_ok (#sign(rep_thm r)) (prems_of r) lhs rhs) of
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                None => mk_meta_eq r
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              | Some _ => r RS P_imp_P_eq_True)
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      |   _$(Const("Not",_)$_) => r RS not_P_imp_P_eq_False
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      |   _ => r RS P_imp_P_eq_True;
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  (* last 2 lines requires all formulae to be of the from Trueprop(.) *)
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val simp_thms = map prover
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 [ "(x=x) = True",
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   "(~True) = False", "(~False) = True", "(~ ~ P) = P",
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   "(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))",
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   "(True=P) = P", "(P=True) = 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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   "(? x. x=t & P(x)) = P(t)",
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   "(! x. t=x --> P(x)) = P(t)" ];
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(*Add congruence rules for = (instead of ==) *)
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infix 4 addcongs delcongs;
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fun ss addcongs congs = ss addeqcongs (map standard (congs RL [eq_reflection]));
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fun ss delcongs congs = ss deleqcongs (map standard (congs RL [eq_reflection]));
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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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fun mksimps pairs = map mk_meta_eq_simp o atomize pairs o gen_all;
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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 HOL_cs 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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(*** Simplification procedures for turning
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            ? x. ... & x = t & ...
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     into   ? x. x = t & ... & ...
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     where the `? x. x = t &' in the latter formula is eliminated
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           by ordinary simplification. 
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     and   ! x. (... & x = t & ...) --> P x
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     into  ! x. x = t --> (... & ...) --> P x
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     where the `!x. x=t -->' in the latter formula is eliminated
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           by ordinary simplification.
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NB Simproc is only triggered by "!x. P(x) & P'(x) --> Q(x)"
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   "!x. x=t --> P(x)" and "!x. t=x --> P(x)"
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   must be taken care of by ordinary rewrite rules.
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local
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fun def(eq as (c as Const("op =",_)) $ s $ t) =
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      if s = Bound 0 andalso not(loose_bvar1(t,0)) then Some eq else
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      if t = Bound 0 andalso not(loose_bvar1(s,0)) then Some(c$t$s)
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      else None
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  | def _ = None;
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fun extract(Const("op &",_) $ P $ Q) =
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      (case def P of
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         Some eq => Some(eq,Q)
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       | None => (case def Q of
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                   Some eq => Some(eq,P)
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                 | None =>
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       (case extract P of
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         Some(eq,P') => Some(eq, HOLogic.conj $ P' $ Q)
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       | None => (case extract Q of
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                   Some(eq,Q') => Some(eq,HOLogic.conj $ P $ Q')
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                 | None => None))))
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  | extract _ = None;
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fun prove_ex_eq(ceqt) =
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  let val tac = rtac eq_reflection 1 THEN rtac iffI 1 THEN
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                ALLGOALS(EVERY'[etac exE, REPEAT o (etac conjE),
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                 rtac exI, REPEAT o (ares_tac [conjI] ORELSE' etac sym)])
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  in rule_by_tactic tac (trivial ceqt) end;
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fun rearrange_ex sg _ (F as ex $ Abs(x,T,P)) =
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     (case extract P of
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        None => None
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      | Some(eq,Q) =>
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          let val ceqt = cterm_of sg
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                       (Logic.mk_equals(F,ex $ Abs(x,T,HOLogic.conj$eq$Q)))
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          in Some(prove_ex_eq ceqt) end)
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  | rearrange_ex _ _ _ = None;
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val ex_pattern =
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  read_cterm (sign_of HOL.thy) ("? x. P(x) & Q(x)",HOLogic.boolT)
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fun prove_all_eq(ceqt) =
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  let fun tac _ = [EVERY1[rtac eq_reflection, rtac iffI,
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                       rtac allI, etac allE, rtac impI, rtac impI, etac mp,
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                          REPEAT o (etac conjE),
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                          REPEAT o (ares_tac [conjI] ORELSE' etac sym),
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                       rtac allI, etac allE, rtac impI, REPEAT o (etac conjE),
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                          etac impE, atac ORELSE' etac sym, etac mp,
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                          REPEAT o (ares_tac [conjI])]]
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  in prove_goalw_cterm [] ceqt tac end;
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fun rearrange_all sg _ (F as all $ Abs(x,T,Const("op -->",_)$P$Q)) =
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     (case extract P of
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        None => None
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      | Some(eq,P') =>
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          let val R = HOLogic.imp $ eq $ (HOLogic.imp $ P' $ Q)
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              val ceqt = cterm_of sg (Logic.mk_equals(F,all$Abs(x,T,R)))
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          in Some(prove_all_eq ceqt) end)
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  | rearrange_all _ _ _ = None;
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val all_pattern =
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  read_cterm (sign_of HOL.thy) ("! x. P(x) & P'(x) --> Q(x)",HOLogic.boolT)
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in
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val defEX_regroup = mk_simproc "defined EX" [ex_pattern] rearrange_ex;
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val defALL_regroup = mk_simproc "defined ALL" [all_pattern] rearrange_all;
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end;
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***)
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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 HOL_cs 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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   286
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   287
prove "disj_commute" "(P|Q) = (Q|P)";
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   288
prove "disj_left_commute" "(P|(Q|R)) = (Q|(P|R))";
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   289
val disj_comms = [disj_commute, disj_left_commute];
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   290
prove "disj_assoc" "((P|Q)|R) = (P|(Q|R))";
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   291
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   292
prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)";
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   293
prove "conj_disj_distribR" "((P|Q)&R) = (P&R | Q&R)";
1485
240cc98b94a7 Added qed_spec_mp to avoid renaming of bound vars in 'th RS spec'
nipkow
parents: 1465
diff changeset
   294
1892
23765bc3e8e2 Added two new distributive laws
paulson
parents: 1874
diff changeset
   295
prove "disj_conj_distribL" "(P|(Q&R)) = ((P|Q) & (P|R))";
23765bc3e8e2 Added two new distributive laws
paulson
parents: 1874
diff changeset
   296
prove "disj_conj_distribR" "((P&Q)|R) = ((P|R) & (Q|R))";
23765bc3e8e2 Added two new distributive laws
paulson
parents: 1874
diff changeset
   297
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   298
prove "imp_conjR" "(P --> (Q&R)) = ((P-->Q) & (P-->R))";
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   299
prove "imp_conjL" "((P&Q) -->R)  = (P --> (Q --> R))";
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   300
prove "imp_disjL" "((P|Q) --> R) = ((P-->R)&(Q-->R))";
1892
23765bc3e8e2 Added two new distributive laws
paulson
parents: 1874
diff changeset
   301
3448
8a79e27ac53b Two new rewrite rules--NOT included by default\!
paulson
parents: 3446
diff changeset
   302
(*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*)
8a79e27ac53b Two new rewrite rules--NOT included by default\!
paulson
parents: 3446
diff changeset
   303
prove "imp_disj_not1" "((P --> Q | R)) = (~Q --> P --> R)";
8a79e27ac53b Two new rewrite rules--NOT included by default\!
paulson
parents: 3446
diff changeset
   304
prove "imp_disj_not2" "((P --> Q | R)) = (~R --> P --> Q)";
8a79e27ac53b Two new rewrite rules--NOT included by default\!
paulson
parents: 3446
diff changeset
   305
3904
c0d56e4c823e New simprules imp_disj1, imp_disj2
paulson
parents: 3896
diff changeset
   306
prove "imp_disj1" "((P-->Q)|R) = (P--> Q|R)";
c0d56e4c823e New simprules imp_disj1, imp_disj2
paulson
parents: 3896
diff changeset
   307
prove "imp_disj2" "(Q|(P-->R)) = (P--> Q|R)";
c0d56e4c823e New simprules imp_disj1, imp_disj2
paulson
parents: 3896
diff changeset
   308
1485
240cc98b94a7 Added qed_spec_mp to avoid renaming of bound vars in 'th RS spec'
nipkow
parents: 1465
diff changeset
   309
prove "de_Morgan_disj" "(~(P | Q)) = (~P & ~Q)";
240cc98b94a7 Added qed_spec_mp to avoid renaming of bound vars in 'th RS spec'
nipkow
parents: 1465
diff changeset
   310
prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)";
3446
a14e5451f613 Addition of not_imp (which pushes negation into implication) as a default
paulson
parents: 3282
diff changeset
   311
prove "not_imp" "(~(P --> Q)) = (P & ~Q)";
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   312
prove "not_iff" "(P~=Q) = (P = (~Q))";
1485
240cc98b94a7 Added qed_spec_mp to avoid renaming of bound vars in 'th RS spec'
nipkow
parents: 1465
diff changeset
   313
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   314
(*Avoids duplication of subgoals after expand_if, when the true and false 
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   315
  cases boil down to the same thing.*) 
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   316
prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   317
3842
b55686a7b22c fixed dots;
wenzelm
parents: 3654
diff changeset
   318
prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))";
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   319
prove "imp_all" "((! x. P x) --> Q) = (? x. P x --> Q)";
3842
b55686a7b22c fixed dots;
wenzelm
parents: 3654
diff changeset
   320
prove "not_ex"  "(~ (? x. P(x))) = (! x.~P(x))";
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   321
prove "imp_ex" "((? x. P x) --> Q) = (! x. P x --> Q)";
1660
8cb42cd97579 *** empty log message ***
oheimb
parents: 1655
diff changeset
   322
1655
5be64540f275 Added a number of lemmas
nipkow
parents: 1548
diff changeset
   323
prove "ex_disj_distrib" "(? x. P(x) | Q(x)) = ((? x. P(x)) | (? x. Q(x)))";
5be64540f275 Added a number of lemmas
nipkow
parents: 1548
diff changeset
   324
prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))";
5be64540f275 Added a number of lemmas
nipkow
parents: 1548
diff changeset
   325
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   326
(* '&' congruence rule: not included by default!
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   327
   May slow rewrite proofs down by as much as 50% *)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   328
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   329
let val th = prove_goal HOL.thy 
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   330
                "(P=P')--> (P'--> (Q=Q'))--> ((P&Q) = (P'&Q'))"
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   331
                (fn _=> [blast_tac HOL_cs 1])
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   332
in  bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   333
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   334
let val th = prove_goal HOL.thy 
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   335
                "(Q=Q')--> (Q'--> (P=P'))--> ((P&Q) = (P'&Q'))"
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   336
                (fn _=> [blast_tac HOL_cs 1])
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   337
in  bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   338
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   339
(* '|' congruence rule: not included by default! *)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   340
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   341
let val th = prove_goal HOL.thy 
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   342
                "(P=P')--> (~P'--> (Q=Q'))--> ((P|Q) = (P'|Q'))"
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   343
                (fn _=> [blast_tac HOL_cs 1])
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   344
in  bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   345
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   346
prove "eq_sym_conv" "(x=y) = (y=x)";
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   347
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   348
qed_goalw "o_apply" HOL.thy [o_def] "(f o g) x = f (g x)"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   349
 (fn _ => [rtac refl 1]);
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   350
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   351
qed_goal "meta_eq_to_obj_eq" HOL.thy "x==y ==> x=y"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   352
  (fn [prem] => [rewtac prem, rtac refl 1]);
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   353
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   354
qed_goalw "if_True" HOL.thy [if_def] "(if True then x else y) = x"
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   355
 (fn _=>[blast_tac (HOL_cs addIs [select_equality]) 1]);
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   356
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   357
qed_goalw "if_False" HOL.thy [if_def] "(if False then x else y) = y"
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   358
 (fn _=>[blast_tac (HOL_cs addIs [select_equality]) 1]);
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   359
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   360
qed_goal "if_P" HOL.thy "P ==> (if P then x else y) = x"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   361
 (fn [prem] => [ stac (prem RS eqTrueI) 1, rtac if_True 1 ]);
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   362
(*
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   363
qed_goal "if_not_P" HOL.thy "~P ==> (if P then x else y) = y"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   364
 (fn [prem] => [ stac (prem RS not_P_imp_P_iff_F) 1, rtac if_False 1 ]);
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   365
*)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   366
qed_goalw "if_not_P" HOL.thy [if_def] "!!P. ~P ==> (if P then x else y) = y"
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   367
 (fn _ => [blast_tac (HOL_cs addIs [select_equality]) 1]);
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   368
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   369
qed_goal "expand_if" HOL.thy
4205
96632970d203 simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents: 4189
diff changeset
   370
    "P(if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))" (K [
96632970d203 simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents: 4189
diff changeset
   371
	res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1,
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   372
         stac if_P 2,
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   373
         stac if_not_P 1,
4205
96632970d203 simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents: 4189
diff changeset
   374
         ALLGOALS (blast_tac HOL_cs)]);
96632970d203 simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents: 4189
diff changeset
   375
96632970d203 simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents: 4189
diff changeset
   376
qed_goal "split_if_asm" HOL.thy
96632970d203 simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents: 4189
diff changeset
   377
    "P(if Q then x else y) = (~((Q & ~P x) | (~Q & ~P y)))" (K [
96632970d203 simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents: 4189
diff changeset
   378
	stac expand_if 1,
96632970d203 simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents: 4189
diff changeset
   379
        blast_tac HOL_cs 1]);
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   380
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   381
qed_goal "if_bool_eq" HOL.thy
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   382
                   "(if P then Q else R) = ((P-->Q) & (~P-->R))"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   383
                   (fn _ => [rtac expand_if 1]);
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   384
4320
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   385
(** make simp procs for quantifier elimination **)
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   386
local
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   387
val ex_pattern =
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   388
  read_cterm (sign_of HOL.thy) ("? x. P(x) & Q(x)",HOLogic.boolT)
3913
96e28b16861c New trivial rewrites
paulson
parents: 3904
diff changeset
   389
4320
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   390
val all_pattern =
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   391
  read_cterm (sign_of HOL.thy) ("! x. P(x) & P'(x) --> Q(x)",HOLogic.boolT)
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   392
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   393
in
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   394
val defEX_regroup =
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   395
  mk_simproc "defined EX" [ex_pattern] Quantifier1.rearrange_ex;
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   396
val defALL_regroup =
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   397
  mk_simproc "defined ALL" [all_pattern] Quantifier1.rearrange_all;
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   398
end;
3913
96e28b16861c New trivial rewrites
paulson
parents: 3904
diff changeset
   399
96e28b16861c New trivial rewrites
paulson
parents: 3904
diff changeset
   400
(** Case splitting **)
96e28b16861c New trivial rewrites
paulson
parents: 3904
diff changeset
   401
2263
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   402
local val mktac = mk_case_split_tac (meta_eq_to_obj_eq RS iffD2)
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   403
in
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   404
fun split_tac splits = mktac (map mk_meta_eq splits)
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   405
end;
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   406
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   407
local val mktac = mk_case_split_inside_tac (meta_eq_to_obj_eq RS iffD2)
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   408
in
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   409
fun split_inside_tac splits = mktac (map mk_meta_eq splits)
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   410
end;
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   411
4205
96632970d203 simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents: 4189
diff changeset
   412
val split_asm_tac = mk_case_split_asm_tac split_tac 
96632970d203 simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents: 4189
diff changeset
   413
			(disjE,conjE,exE,contrapos,contrapos2,notnotD);
4189
b8c7a6bc6c16 added split_prem_tac
oheimb
parents: 4188
diff changeset
   414
3919
c036caebfc75 setloop split_tac -> addsplits
nipkow
parents: 3913
diff changeset
   415
infix 4 addsplits;
c036caebfc75 setloop split_tac -> addsplits
nipkow
parents: 3913
diff changeset
   416
fun ss addsplits splits = ss addloop (split_tac splits);
c036caebfc75 setloop split_tac -> addsplits
nipkow
parents: 3913
diff changeset
   417
2263
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   418
2251
e0e3836f333d moved if_cancel to the right place
oheimb
parents: 2250
diff changeset
   419
qed_goal "if_cancel" HOL.thy "(if c then x else x) = x"
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   420
  (fn _ => [split_tac [expand_if] 1, blast_tac HOL_cs 1]);
2251
e0e3836f333d moved if_cancel to the right place
oheimb
parents: 2250
diff changeset
   421
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   422
(** 'if' congruence rules: neither included by default! *)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   423
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   424
(*Simplifies x assuming c and y assuming ~c*)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   425
qed_goal "if_cong" HOL.thy
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   426
  "[| b=c; c ==> x=u; ~c ==> y=v |] ==>\
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   427
\  (if b then x else y) = (if c then u else v)"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   428
  (fn rew::prems =>
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   429
   [stac rew 1, stac expand_if 1, stac expand_if 1,
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   430
    blast_tac (HOL_cs addDs prems) 1]);
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   431
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   432
(*Prevents simplification of x and y: much faster*)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   433
qed_goal "if_weak_cong" HOL.thy
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   434
  "b=c ==> (if b then x else y) = (if c then x else y)"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   435
  (fn [prem] => [rtac (prem RS arg_cong) 1]);
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   436
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   437
(*Prevents simplification of t: much faster*)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   438
qed_goal "let_weak_cong" HOL.thy
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   439
  "a = b ==> (let x=a in t(x)) = (let x=b in t(x))"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   440
  (fn [prem] => [rtac (prem RS arg_cong) 1]);
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   441
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   442
(*In general it seems wrong to add distributive laws by default: they
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   443
  might cause exponential blow-up.  But imp_disjL has been in for a while
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   444
  and cannot be removed without affecting existing proofs.  Moreover, 
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   445
  rewriting by "(P|Q --> R) = ((P-->R)&(Q-->R))" might be justified on the
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   446
  grounds that it allows simplification of R in the two cases.*)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   447
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   448
val mksimps_pairs =
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   449
  [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   450
   ("All", [spec]), ("True", []), ("False", []),
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   451
   ("If", [if_bool_eq RS iffD1])];
1758
60613b065e9b Added ex_imp
nipkow
parents: 1722
diff changeset
   452
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   453
fun unsafe_solver prems = FIRST'[resolve_tac (TrueI::refl::prems),
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   454
				 atac, etac FalseE];
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   455
(*No premature instantiation of variables during simplification*)
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   456
fun   safe_solver prems = FIRST'[match_tac (TrueI::refl::prems),
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   457
				 eq_assume_tac, ematch_tac [FalseE]];
2443
a81d4c219c3c factored out HOL_base_ss and val HOL_min_ss, added HOL_safe_min_ss
oheimb
parents: 2263
diff changeset
   458
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   459
val HOL_basic_ss = empty_ss setsubgoaler asm_simp_tac
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   460
			    setSSolver   safe_solver
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   461
			    setSolver  unsafe_solver
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   462
			    setmksimps (mksimps mksimps_pairs);
2443
a81d4c219c3c factored out HOL_base_ss and val HOL_min_ss, added HOL_safe_min_ss
oheimb
parents: 2263
diff changeset
   463
3446
a14e5451f613 Addition of not_imp (which pushes negation into implication) as a default
paulson
parents: 3282
diff changeset
   464
val HOL_ss = 
a14e5451f613 Addition of not_imp (which pushes negation into implication) as a default
paulson
parents: 3282
diff changeset
   465
    HOL_basic_ss addsimps 
a14e5451f613 Addition of not_imp (which pushes negation into implication) as a default
paulson
parents: 3282
diff changeset
   466
     ([triv_forall_equality, (* prunes params *)
3654
ebad042c0bba Added True_implies_equals
nipkow
parents: 3615
diff changeset
   467
       True_implies_equals, (* prune asms `True' *)
3446
a14e5451f613 Addition of not_imp (which pushes negation into implication) as a default
paulson
parents: 3282
diff changeset
   468
       if_True, if_False, if_cancel,
a14e5451f613 Addition of not_imp (which pushes negation into implication) as a default
paulson
parents: 3282
diff changeset
   469
       o_apply, imp_disjL, conj_assoc, disj_assoc,
3904
c0d56e4c823e New simprules imp_disj1, imp_disj2
paulson
parents: 3896
diff changeset
   470
       de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp,
3446
a14e5451f613 Addition of not_imp (which pushes negation into implication) as a default
paulson
parents: 3282
diff changeset
   471
       not_all, not_ex, cases_simp]
a14e5451f613 Addition of not_imp (which pushes negation into implication) as a default
paulson
parents: 3282
diff changeset
   472
     @ ex_simps @ all_simps @ simp_thms)
4032
4b1c69d8b767 For each datatype `t' there is now a theorem `split_t_case' of the form
nipkow
parents: 3919
diff changeset
   473
     addsimprocs [defALL_regroup,defEX_regroup]
3446
a14e5451f613 Addition of not_imp (which pushes negation into implication) as a default
paulson
parents: 3282
diff changeset
   474
     addcongs [imp_cong];
2082
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
   475
1655
5be64540f275 Added a number of lemmas
nipkow
parents: 1548
diff changeset
   476
qed_goal "if_distrib" HOL.thy
5be64540f275 Added a number of lemmas
nipkow
parents: 1548
diff changeset
   477
  "f(if c then x else y) = (if c then f x else f y)" 
5be64540f275 Added a number of lemmas
nipkow
parents: 1548
diff changeset
   478
  (fn _ => [simp_tac (HOL_ss setloop (split_tac [expand_if])) 1]);
5be64540f275 Added a number of lemmas
nipkow
parents: 1548
diff changeset
   479
2097
076a8d2f972b bound o_apply theorem to thy
oheimb
parents: 2082
diff changeset
   480
qed_goalw "o_assoc" HOL.thy [o_def] "f o (g o h) = f o g o h"
2098
2bfc0675c92f corrected `correction` of o_assoc (of version 1.14),
oheimb
parents: 2097
diff changeset
   481
  (fn _ => [rtac ext 1, rtac refl 1]);
1984
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   482
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   483
2948
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   484
val prems = goal HOL.thy "[| P ==> Q(True); ~P ==> Q(False) |] ==> Q(P)";
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   485
by (case_tac "P" 1);
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   486
by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems)));
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   487
val expand_case = result();
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   488
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   489
fun expand_case_tac P i =
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   490
    res_inst_tac [("P",P)] expand_case i THEN
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   491
    Simp_tac (i+1) THEN 
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   492
    Simp_tac i;
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   493
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   494
4119
de6e388f3d86 removed old datatype_info;
wenzelm
parents: 4117
diff changeset
   495
(* install implicit simpset *)
1984
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   496
4086
958806f7e840 adapted to new implicit simpset;
wenzelm
parents: 4032
diff changeset
   497
simpset_ref() := HOL_ss;
1984
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   498
3615
e5322197cfea Moved some functions which used to be part of thy_data.ML
berghofe
parents: 3577
diff changeset
   499
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   500
(*** Integration of simplifier with classical reasoner ***)
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   501
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   502
(* rot_eq_tac rotates the first equality premise of subgoal i to the front,
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   503
   fails if there is no equaliy or if an equality is already at the front *)
3538
ed9de44032e0 Removal of the tactical STATE
paulson
parents: 3518
diff changeset
   504
local
ed9de44032e0 Removal of the tactical STATE
paulson
parents: 3518
diff changeset
   505
  fun is_eq (Const ("Trueprop", _) $ (Const("op ="  ,_) $ _ $ _)) = true
ed9de44032e0 Removal of the tactical STATE
paulson
parents: 3518
diff changeset
   506
    | is_eq _ = false;
4188
1025a27b08f9 changed libraray function find to find_index_eq, currying it
oheimb
parents: 4119
diff changeset
   507
  val find_eq = find_index is_eq;
3538
ed9de44032e0 Removal of the tactical STATE
paulson
parents: 3518
diff changeset
   508
in
ed9de44032e0 Removal of the tactical STATE
paulson
parents: 3518
diff changeset
   509
val rot_eq_tac = 
4188
1025a27b08f9 changed libraray function find to find_index_eq, currying it
oheimb
parents: 4119
diff changeset
   510
     SUBGOAL (fn (Bi,i) => let val n = find_eq (Logic.strip_assums_hyp Bi) in
1025a27b08f9 changed libraray function find to find_index_eq, currying it
oheimb
parents: 4119
diff changeset
   511
		if n>0 then rotate_tac n i else no_tac end)
3538
ed9de44032e0 Removal of the tactical STATE
paulson
parents: 3518
diff changeset
   512
end;
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   513
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   514
(*an unsatisfactory fix for the incomplete asm_full_simp_tac!
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   515
  better: asm_really_full_simp_tac, a yet to be implemented version of
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   516
			asm_full_simp_tac that applies all equalities in the
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   517
			premises to all the premises *)
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   518
fun safe_asm_more_full_simp_tac ss = TRY o rot_eq_tac THEN' 
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   519
				     safe_asm_full_simp_tac ss;
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   520
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   521
(*Add a simpset to a classical set!*)
3206
a3de7f32728c renamed addss to addSss, unsafe_addss to addss, extended auto_tac
oheimb
parents: 3040
diff changeset
   522
infix 4 addSss addss;
a3de7f32728c renamed addss to addSss, unsafe_addss to addss, extended auto_tac
oheimb
parents: 3040
diff changeset
   523
fun cs addSss ss = cs addSaltern (CHANGED o (safe_asm_more_full_simp_tac ss));
a3de7f32728c renamed addss to addSss, unsafe_addss to addss, extended auto_tac
oheimb
parents: 3040
diff changeset
   524
fun cs addss  ss = cs addbefore                        asm_full_simp_tac ss;
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   525
4086
958806f7e840 adapted to new implicit simpset;
wenzelm
parents: 4032
diff changeset
   526
fun Addss ss = (claset_ref() := claset() addss ss);
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   527
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   528
(*Designed to be idempotent, except if best_tac instantiates variables
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   529
  in some of the subgoals*)
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   530
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   531
type clasimpset = (claset * simpset);
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   532
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   533
val HOL_css = (HOL_cs, HOL_ss);
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   534
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   535
fun pair_upd1 f ((a,b),x) = (f(a,x), b);
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   536
fun pair_upd2 f ((a,b),x) = (a, f(b,x));
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   537
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   538
infix 4 addSIs2 addSEs2 addSDs2 addIs2 addEs2 addDs2
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   539
	addsimps2 delsimps2 addcongs2 delcongs2;
2748
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   540
fun op addSIs2   arg = pair_upd1 (op addSIs) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   541
fun op addSEs2   arg = pair_upd1 (op addSEs) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   542
fun op addSDs2   arg = pair_upd1 (op addSDs) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   543
fun op addIs2    arg = pair_upd1 (op addIs ) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   544
fun op addEs2    arg = pair_upd1 (op addEs ) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   545
fun op addDs2    arg = pair_upd1 (op addDs ) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   546
fun op addsimps2 arg = pair_upd2 (op addsimps) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   547
fun op delsimps2 arg = pair_upd2 (op delsimps) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   548
fun op addcongs2 arg = pair_upd2 (op addcongs) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   549
fun op delcongs2 arg = pair_upd2 (op delcongs) arg;
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   550
2805
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   551
fun auto_tac (cs,ss) = 
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   552
    let val cs' = cs addss ss 
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   553
    in  EVERY [TRY (safe_tac cs'),
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   554
	       REPEAT (FIRSTGOAL (fast_tac cs')),
3206
a3de7f32728c renamed addss to addSss, unsafe_addss to addss, extended auto_tac
oheimb
parents: 3040
diff changeset
   555
               TRY (safe_tac (cs addSss ss)),
2805
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   556
	       prune_params_tac] 
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   557
    end;
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   558
4086
958806f7e840 adapted to new implicit simpset;
wenzelm
parents: 4032
diff changeset
   559
fun Auto_tac () = auto_tac (claset(), simpset());
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   560
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   561
fun auto () = by (Auto_tac ());