src/HOL/simpdata.ML
author nipkow
Tue Sep 02 17:02:02 1997 +0200 (1997-09-02)
changeset 3654 ebad042c0bba
parent 3615 e5322197cfea
child 3842 b55686a7b22c
permissions -rw-r--r--
Added True_implies_equals
clasohm@1465
     1
(*  Title:      HOL/simpdata.ML
clasohm@923
     2
    ID:         $Id$
clasohm@1465
     3
    Author:     Tobias Nipkow
clasohm@923
     4
    Copyright   1991  University of Cambridge
clasohm@923
     5
clasohm@923
     6
Instantiation of the generic simplifier
clasohm@923
     7
*)
clasohm@923
     8
paulson@1984
     9
section "Simplifier";
paulson@1984
    10
clasohm@923
    11
open Simplifier;
clasohm@923
    12
paulson@1984
    13
(*** Addition of rules to simpsets and clasets simultaneously ***)
paulson@1984
    14
paulson@1984
    15
(*Takes UNCONDITIONAL theorems of the form A<->B to 
paulson@2031
    16
        the Safe Intr     rule B==>A and 
paulson@2031
    17
        the Safe Destruct rule A==>B.
paulson@1984
    18
  Also ~A goes to the Safe Elim rule A ==> ?R
paulson@1984
    19
  Failing other cases, A is added as a Safe Intr rule*)
paulson@1984
    20
local
paulson@1984
    21
  val iff_const = HOLogic.eq_const HOLogic.boolT;
paulson@1984
    22
paulson@1984
    23
  fun addIff th = 
paulson@1984
    24
      (case HOLogic.dest_Trueprop (#prop(rep_thm th)) of
paulson@2718
    25
                (Const("Not",_) $ A) =>
paulson@2031
    26
                    AddSEs [zero_var_indexes (th RS notE)]
paulson@2031
    27
              | (con $ _ $ _) =>
paulson@2031
    28
                    if con=iff_const
paulson@2031
    29
                    then (AddSIs [zero_var_indexes (th RS iffD2)];  
paulson@2031
    30
                          AddSDs [zero_var_indexes (th RS iffD1)])
paulson@2031
    31
                    else  AddSIs [th]
paulson@2031
    32
              | _ => AddSIs [th];
paulson@1984
    33
       Addsimps [th])
paulson@1984
    34
      handle _ => error ("AddIffs: theorem must be unconditional\n" ^ 
paulson@2031
    35
                         string_of_thm th)
paulson@1984
    36
paulson@1984
    37
  fun delIff th = 
paulson@1984
    38
      (case HOLogic.dest_Trueprop (#prop(rep_thm th)) of
paulson@2718
    39
                (Const("Not",_) $ A) =>
paulson@2031
    40
                    Delrules [zero_var_indexes (th RS notE)]
paulson@2031
    41
              | (con $ _ $ _) =>
paulson@2031
    42
                    if con=iff_const
paulson@2031
    43
                    then Delrules [zero_var_indexes (th RS iffD2),
paulson@3518
    44
                                   make_elim (zero_var_indexes (th RS iffD1))]
paulson@2031
    45
                    else Delrules [th]
paulson@2031
    46
              | _ => Delrules [th];
paulson@1984
    47
       Delsimps [th])
paulson@1984
    48
      handle _ => warning("DelIffs: ignoring conditional theorem\n" ^ 
paulson@2031
    49
                          string_of_thm th)
paulson@1984
    50
in
paulson@1984
    51
val AddIffs = seq addIff
paulson@1984
    52
val DelIffs = seq delIff
paulson@1984
    53
end;
paulson@1984
    54
paulson@1984
    55
clasohm@923
    56
local
clasohm@923
    57
paulson@2935
    58
  fun prover s = prove_goal HOL.thy s (fn _ => [blast_tac HOL_cs 1]);
clasohm@923
    59
paulson@1922
    60
  val P_imp_P_iff_True = prover "P --> (P = True)" RS mp;
paulson@1922
    61
  val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection;
clasohm@923
    62
paulson@1922
    63
  val not_P_imp_P_iff_F = prover "~P --> (P = False)" RS mp;
paulson@1922
    64
  val not_P_imp_P_eq_False = not_P_imp_P_iff_F RS eq_reflection;
clasohm@923
    65
paulson@1922
    66
  fun atomize pairs =
paulson@1922
    67
    let fun atoms th =
paulson@2031
    68
          (case concl_of th of
paulson@2031
    69
             Const("Trueprop",_) $ p =>
paulson@2031
    70
               (case head_of p of
paulson@2031
    71
                  Const(a,_) =>
paulson@2031
    72
                    (case assoc(pairs,a) of
paulson@2031
    73
                       Some(rls) => flat (map atoms ([th] RL rls))
paulson@2031
    74
                     | None => [th])
paulson@2031
    75
                | _ => [th])
paulson@2031
    76
           | _ => [th])
paulson@1922
    77
    in atoms end;
clasohm@923
    78
nipkow@2134
    79
  fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th;
nipkow@2134
    80
nipkow@2134
    81
in
nipkow@2134
    82
paulson@1922
    83
  fun mk_meta_eq r = case concl_of r of
paulson@2031
    84
          Const("==",_)$_$_ => r
paulson@1922
    85
      |   _$(Const("op =",_)$_$_) => r RS eq_reflection
paulson@2718
    86
      |   _$(Const("Not",_)$_) => r RS not_P_imp_P_eq_False
paulson@1922
    87
      |   _ => r RS P_imp_P_eq_True;
paulson@1922
    88
  (* last 2 lines requires all formulae to be of the from Trueprop(.) *)
clasohm@923
    89
paulson@2082
    90
val simp_thms = map prover
paulson@2082
    91
 [ "(x=x) = True",
paulson@2082
    92
   "(~True) = False", "(~False) = True", "(~ ~ P) = P",
paulson@2082
    93
   "(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))",
paulson@2082
    94
   "(True=P) = P", "(P=True) = P",
paulson@2082
    95
   "(True --> P) = P", "(False --> P) = True", 
paulson@2082
    96
   "(P --> True) = True", "(P --> P) = True",
paulson@2082
    97
   "(P --> False) = (~P)", "(P --> ~P) = (~P)",
paulson@2082
    98
   "(P & True) = P", "(True & P) = P", 
nipkow@2800
    99
   "(P & False) = False", "(False & P) = False",
nipkow@2800
   100
   "(P & P) = P", "(P & (P & Q)) = (P & Q)",
paulson@2082
   101
   "(P | True) = True", "(True | P) = True", 
nipkow@2800
   102
   "(P | False) = P", "(False | P) = P",
nipkow@2800
   103
   "(P | P) = P", "(P | (P | Q)) = (P | Q)",
paulson@2082
   104
   "((~P) = (~Q)) = (P=Q)",
nipkow@2129
   105
   "(!x.P) = P", "(? x.P) = P", "? x. x=t", "? x. t=x", 
nipkow@3573
   106
   "(? x. x=t & P(x)) = P(t)",
nipkow@3568
   107
   "(! x. t=x --> P(x)) = P(t)" ];
clasohm@923
   108
lcp@988
   109
(*Add congruence rules for = (instead of ==) *)
oheimb@2636
   110
infix 4 addcongs delcongs;
wenzelm@3559
   111
fun ss addcongs congs = ss addeqcongs (map standard (congs RL [eq_reflection]));
wenzelm@3559
   112
fun ss delcongs congs = ss deleqcongs (map standard (congs RL [eq_reflection]));
clasohm@923
   113
clasohm@1264
   114
fun Addcongs congs = (simpset := !simpset addcongs congs);
oheimb@2636
   115
fun Delcongs congs = (simpset := !simpset delcongs congs);
clasohm@1264
   116
clasohm@923
   117
fun mksimps pairs = map mk_meta_eq o atomize pairs o gen_all;
clasohm@923
   118
paulson@1922
   119
val imp_cong = impI RSN
paulson@1922
   120
    (2, prove_goal HOL.thy "(P=P')--> (P'--> (Q=Q'))--> ((P-->Q) = (P'-->Q'))"
paulson@2935
   121
        (fn _=> [blast_tac HOL_cs 1]) RS mp RS mp);
paulson@1922
   122
paulson@1948
   123
(*Miniscoping: pushing in existential quantifiers*)
paulson@1948
   124
val ex_simps = map prover 
paulson@2031
   125
                ["(EX x. P x & Q)   = ((EX x.P x) & Q)",
paulson@2031
   126
                 "(EX x. P & Q x)   = (P & (EX x.Q x))",
paulson@2031
   127
                 "(EX x. P x | Q)   = ((EX x.P x) | Q)",
paulson@2031
   128
                 "(EX x. P | Q x)   = (P | (EX x.Q x))",
paulson@2031
   129
                 "(EX x. P x --> Q) = ((ALL x.P x) --> Q)",
paulson@2031
   130
                 "(EX x. P --> Q x) = (P --> (EX x.Q x))"];
paulson@1948
   131
paulson@1948
   132
(*Miniscoping: pushing in universal quantifiers*)
paulson@1948
   133
val all_simps = map prover
paulson@2031
   134
                ["(ALL x. P x & Q)   = ((ALL x.P x) & Q)",
paulson@2031
   135
                 "(ALL x. P & Q x)   = (P & (ALL x.Q x))",
paulson@2031
   136
                 "(ALL x. P x | Q)   = ((ALL x.P x) | Q)",
paulson@2031
   137
                 "(ALL x. P | Q x)   = (P | (ALL x.Q x))",
paulson@2031
   138
                 "(ALL x. P x --> Q) = ((EX x.P x) --> Q)",
paulson@2031
   139
                 "(ALL x. P --> Q x) = (P --> (ALL x.Q x))"];
paulson@1948
   140
nipkow@3568
   141
(*** Simplification procedure for turning  ? x. ... & x = t & ...
nipkow@3568
   142
     into                                  ? x. x = t & ... & ...
nipkow@3568
   143
     where the latter can be rewritten via (? x. x = t & P(x)) = P(t)
nipkow@3568
   144
 ***)
nipkow@3568
   145
nipkow@3568
   146
local
nipkow@3568
   147
nipkow@3568
   148
fun def(eq as (c as Const("op =",_)) $ s $ t) =
nipkow@3568
   149
      if s = Bound 0 andalso not(loose_bvar1(t,0)) then Some eq else
nipkow@3568
   150
      if t = Bound 0 andalso not(loose_bvar1(s,0)) then Some(c$t$s)
nipkow@3568
   151
      else None
nipkow@3568
   152
  | def _ = None;
nipkow@3568
   153
nipkow@3568
   154
fun extract(Const("op &",_) $ P $ Q) =
nipkow@3568
   155
      (case def P of
nipkow@3568
   156
         Some eq => Some(eq,Q)
nipkow@3568
   157
       | None => (case def Q of
nipkow@3568
   158
                   Some eq => Some(eq,P)
nipkow@3568
   159
                 | None =>
nipkow@3568
   160
       (case extract P of
nipkow@3568
   161
         Some(eq,P') => Some(eq, HOLogic.conj $ P' $ Q)
nipkow@3568
   162
       | None => (case extract Q of
nipkow@3568
   163
                   Some(eq,Q') => Some(eq,HOLogic.conj $ P $ Q')
nipkow@3568
   164
                 | None => None))))
nipkow@3568
   165
  | extract _ = None;
nipkow@3568
   166
nipkow@3568
   167
fun prove_eq(ceqt) =
nipkow@3568
   168
  let val tac = rtac eq_reflection 1 THEN rtac iffI 1 THEN
nipkow@3568
   169
                ALLGOALS(EVERY'[etac exE, REPEAT o (etac conjE),
nipkow@3568
   170
                 rtac exI, REPEAT o (ares_tac [conjI] ORELSE' etac sym)])
nipkow@3568
   171
  in rule_by_tactic tac (trivial ceqt) end;
nipkow@3568
   172
wenzelm@3577
   173
fun rearrange sg _ (F as ex $ Abs(x,T,P)) =
nipkow@3568
   174
     (case extract P of
nipkow@3568
   175
        None => None
nipkow@3568
   176
      | Some(eq,Q) =>
nipkow@3568
   177
          let val ceqt = cterm_of sg
nipkow@3568
   178
                       (Logic.mk_equals(F,ex $ Abs(x,T,HOLogic.conj$eq$Q)))
nipkow@3568
   179
          in Some(prove_eq ceqt) end)
wenzelm@3577
   180
  | rearrange _ _ _ = None;
nipkow@3568
   181
nipkow@3568
   182
val pattern = read_cterm (sign_of HOL.thy) ("? x.P(x) & Q(x)",HOLogic.boolT)
nipkow@3568
   183
nipkow@3568
   184
in
nipkow@3568
   185
val defEX_regroup = mk_simproc "defined EX" [pattern] rearrange;
nipkow@3568
   186
end;
berghofe@1722
   187
clasohm@923
   188
paulson@2022
   189
(* elimination of existential quantifiers in assumptions *)
clasohm@923
   190
clasohm@923
   191
val ex_all_equiv =
clasohm@923
   192
  let val lemma1 = prove_goal HOL.thy
clasohm@923
   193
        "(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)"
clasohm@923
   194
        (fn prems => [resolve_tac prems 1, etac exI 1]);
clasohm@923
   195
      val lemma2 = prove_goalw HOL.thy [Ex_def]
clasohm@923
   196
        "(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)"
clasohm@923
   197
        (fn prems => [REPEAT(resolve_tac prems 1)])
clasohm@923
   198
  in equal_intr lemma1 lemma2 end;
clasohm@923
   199
clasohm@923
   200
end;
clasohm@923
   201
nipkow@3654
   202
(* Elimination of True from asumptions: *)
nipkow@3654
   203
nipkow@3654
   204
val True_implies_equals = prove_goal HOL.thy
nipkow@3654
   205
 "(True ==> PROP P) == PROP P"
nipkow@3654
   206
(fn _ => [rtac equal_intr_rule 1, atac 2,
nipkow@3654
   207
          METAHYPS (fn prems => resolve_tac prems 1) 1,
nipkow@3654
   208
          rtac TrueI 1]);
nipkow@3654
   209
paulson@2935
   210
fun prove nm thm  = qed_goal nm HOL.thy thm (fn _ => [blast_tac HOL_cs 1]);
clasohm@923
   211
clasohm@923
   212
prove "conj_commute" "(P&Q) = (Q&P)";
clasohm@923
   213
prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))";
clasohm@923
   214
val conj_comms = [conj_commute, conj_left_commute];
nipkow@2134
   215
prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))";
clasohm@923
   216
paulson@1922
   217
prove "disj_commute" "(P|Q) = (Q|P)";
paulson@1922
   218
prove "disj_left_commute" "(P|(Q|R)) = (Q|(P|R))";
paulson@1922
   219
val disj_comms = [disj_commute, disj_left_commute];
nipkow@2134
   220
prove "disj_assoc" "((P|Q)|R) = (P|(Q|R))";
paulson@1922
   221
clasohm@923
   222
prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)";
clasohm@923
   223
prove "conj_disj_distribR" "((P|Q)&R) = (P&R | Q&R)";
nipkow@1485
   224
paulson@1892
   225
prove "disj_conj_distribL" "(P|(Q&R)) = ((P|Q) & (P|R))";
paulson@1892
   226
prove "disj_conj_distribR" "((P&Q)|R) = ((P|R) & (Q|R))";
paulson@1892
   227
nipkow@2134
   228
prove "imp_conjR" "(P --> (Q&R)) = ((P-->Q) & (P-->R))";
nipkow@2134
   229
prove "imp_conjL" "((P&Q) -->R)  = (P --> (Q --> R))";
nipkow@2134
   230
prove "imp_disjL" "((P|Q) --> R) = ((P-->R)&(Q-->R))";
paulson@1892
   231
paulson@3448
   232
(*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*)
paulson@3448
   233
prove "imp_disj_not1" "((P --> Q | R)) = (~Q --> P --> R)";
paulson@3448
   234
prove "imp_disj_not2" "((P --> Q | R)) = (~R --> P --> Q)";
paulson@3448
   235
nipkow@1485
   236
prove "de_Morgan_disj" "(~(P | Q)) = (~P & ~Q)";
nipkow@1485
   237
prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)";
paulson@3446
   238
prove "not_imp" "(~(P --> Q)) = (P & ~Q)";
paulson@1922
   239
prove "not_iff" "(P~=Q) = (P = (~Q))";
nipkow@1485
   240
nipkow@2134
   241
(*Avoids duplication of subgoals after expand_if, when the true and false 
nipkow@2134
   242
  cases boil down to the same thing.*) 
nipkow@2134
   243
prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";
nipkow@2134
   244
oheimb@1660
   245
prove "not_all" "(~ (! x.P(x))) = (? x.~P(x))";
paulson@1922
   246
prove "imp_all" "((! x. P x) --> Q) = (? x. P x --> Q)";
oheimb@1660
   247
prove "not_ex"  "(~ (? x.P(x))) = (! x.~P(x))";
paulson@1922
   248
prove "imp_ex" "((? x. P x) --> Q) = (! x. P x --> Q)";
oheimb@1660
   249
nipkow@1655
   250
prove "ex_disj_distrib" "(? x. P(x) | Q(x)) = ((? x. P(x)) | (? x. Q(x)))";
nipkow@1655
   251
prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))";
nipkow@1655
   252
nipkow@2134
   253
(* '&' congruence rule: not included by default!
nipkow@2134
   254
   May slow rewrite proofs down by as much as 50% *)
nipkow@2134
   255
nipkow@2134
   256
let val th = prove_goal HOL.thy 
nipkow@2134
   257
                "(P=P')--> (P'--> (Q=Q'))--> ((P&Q) = (P'&Q'))"
paulson@2935
   258
                (fn _=> [blast_tac HOL_cs 1])
nipkow@2134
   259
in  bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
nipkow@2134
   260
nipkow@2134
   261
let val th = prove_goal HOL.thy 
nipkow@2134
   262
                "(Q=Q')--> (Q'--> (P=P'))--> ((P&Q) = (P'&Q'))"
paulson@2935
   263
                (fn _=> [blast_tac HOL_cs 1])
nipkow@2134
   264
in  bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
nipkow@2134
   265
nipkow@2134
   266
(* '|' congruence rule: not included by default! *)
nipkow@2134
   267
nipkow@2134
   268
let val th = prove_goal HOL.thy 
nipkow@2134
   269
                "(P=P')--> (~P'--> (Q=Q'))--> ((P|Q) = (P'|Q'))"
paulson@2935
   270
                (fn _=> [blast_tac HOL_cs 1])
nipkow@2134
   271
in  bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
nipkow@2134
   272
nipkow@2134
   273
prove "eq_sym_conv" "(x=y) = (y=x)";
nipkow@2134
   274
nipkow@2134
   275
qed_goalw "o_apply" HOL.thy [o_def] "(f o g) x = f (g x)"
nipkow@2134
   276
 (fn _ => [rtac refl 1]);
nipkow@2134
   277
nipkow@2134
   278
qed_goal "meta_eq_to_obj_eq" HOL.thy "x==y ==> x=y"
nipkow@2134
   279
  (fn [prem] => [rewtac prem, rtac refl 1]);
nipkow@2134
   280
nipkow@2134
   281
qed_goalw "if_True" HOL.thy [if_def] "(if True then x else y) = x"
paulson@2935
   282
 (fn _=>[blast_tac (HOL_cs addIs [select_equality]) 1]);
nipkow@2134
   283
nipkow@2134
   284
qed_goalw "if_False" HOL.thy [if_def] "(if False then x else y) = y"
paulson@2935
   285
 (fn _=>[blast_tac (HOL_cs addIs [select_equality]) 1]);
nipkow@2134
   286
nipkow@2134
   287
qed_goal "if_P" HOL.thy "P ==> (if P then x else y) = x"
nipkow@2134
   288
 (fn [prem] => [ stac (prem RS eqTrueI) 1, rtac if_True 1 ]);
nipkow@2134
   289
(*
nipkow@2134
   290
qed_goal "if_not_P" HOL.thy "~P ==> (if P then x else y) = y"
nipkow@2134
   291
 (fn [prem] => [ stac (prem RS not_P_imp_P_iff_F) 1, rtac if_False 1 ]);
nipkow@2134
   292
*)
nipkow@2134
   293
qed_goalw "if_not_P" HOL.thy [if_def] "!!P. ~P ==> (if P then x else y) = y"
paulson@2935
   294
 (fn _ => [blast_tac (HOL_cs addIs [select_equality]) 1]);
nipkow@2134
   295
nipkow@2134
   296
qed_goal "expand_if" HOL.thy
nipkow@2134
   297
    "P(if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))"
nipkow@2134
   298
 (fn _=> [ (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1),
nipkow@2134
   299
         stac if_P 2,
nipkow@2134
   300
         stac if_not_P 1,
paulson@2935
   301
         REPEAT(blast_tac HOL_cs 1) ]);
nipkow@2134
   302
nipkow@2134
   303
qed_goal "if_bool_eq" HOL.thy
nipkow@2134
   304
                   "(if P then Q else R) = ((P-->Q) & (~P-->R))"
nipkow@2134
   305
                   (fn _ => [rtac expand_if 1]);
nipkow@2134
   306
oheimb@2263
   307
local val mktac = mk_case_split_tac (meta_eq_to_obj_eq RS iffD2)
oheimb@2263
   308
in
oheimb@2263
   309
fun split_tac splits = mktac (map mk_meta_eq splits)
oheimb@2263
   310
end;
oheimb@2263
   311
oheimb@2263
   312
local val mktac = mk_case_split_inside_tac (meta_eq_to_obj_eq RS iffD2)
oheimb@2263
   313
in
oheimb@2263
   314
fun split_inside_tac splits = mktac (map mk_meta_eq splits)
oheimb@2263
   315
end;
oheimb@2263
   316
oheimb@2263
   317
oheimb@2251
   318
qed_goal "if_cancel" HOL.thy "(if c then x else x) = x"
paulson@2935
   319
  (fn _ => [split_tac [expand_if] 1, blast_tac HOL_cs 1]);
oheimb@2251
   320
nipkow@2134
   321
(** 'if' congruence rules: neither included by default! *)
nipkow@2134
   322
nipkow@2134
   323
(*Simplifies x assuming c and y assuming ~c*)
nipkow@2134
   324
qed_goal "if_cong" HOL.thy
nipkow@2134
   325
  "[| b=c; c ==> x=u; ~c ==> y=v |] ==>\
nipkow@2134
   326
\  (if b then x else y) = (if c then u else v)"
nipkow@2134
   327
  (fn rew::prems =>
nipkow@2134
   328
   [stac rew 1, stac expand_if 1, stac expand_if 1,
paulson@2935
   329
    blast_tac (HOL_cs addDs prems) 1]);
nipkow@2134
   330
nipkow@2134
   331
(*Prevents simplification of x and y: much faster*)
nipkow@2134
   332
qed_goal "if_weak_cong" HOL.thy
nipkow@2134
   333
  "b=c ==> (if b then x else y) = (if c then x else y)"
nipkow@2134
   334
  (fn [prem] => [rtac (prem RS arg_cong) 1]);
nipkow@2134
   335
nipkow@2134
   336
(*Prevents simplification of t: much faster*)
nipkow@2134
   337
qed_goal "let_weak_cong" HOL.thy
nipkow@2134
   338
  "a = b ==> (let x=a in t(x)) = (let x=b in t(x))"
nipkow@2134
   339
  (fn [prem] => [rtac (prem RS arg_cong) 1]);
nipkow@2134
   340
nipkow@2134
   341
(*In general it seems wrong to add distributive laws by default: they
nipkow@2134
   342
  might cause exponential blow-up.  But imp_disjL has been in for a while
nipkow@2134
   343
  and cannot be removed without affecting existing proofs.  Moreover, 
nipkow@2134
   344
  rewriting by "(P|Q --> R) = ((P-->R)&(Q-->R))" might be justified on the
nipkow@2134
   345
  grounds that it allows simplification of R in the two cases.*)
nipkow@2134
   346
nipkow@2134
   347
val mksimps_pairs =
nipkow@2134
   348
  [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
nipkow@2134
   349
   ("All", [spec]), ("True", []), ("False", []),
nipkow@2134
   350
   ("If", [if_bool_eq RS iffD1])];
nipkow@1758
   351
oheimb@2636
   352
fun unsafe_solver prems = FIRST'[resolve_tac (TrueI::refl::prems),
oheimb@2636
   353
				 atac, etac FalseE];
oheimb@2636
   354
(*No premature instantiation of variables during simplification*)
oheimb@2636
   355
fun   safe_solver prems = FIRST'[match_tac (TrueI::refl::prems),
oheimb@2636
   356
				 eq_assume_tac, ematch_tac [FalseE]];
oheimb@2443
   357
oheimb@2636
   358
val HOL_basic_ss = empty_ss setsubgoaler asm_simp_tac
oheimb@2636
   359
			    setSSolver   safe_solver
oheimb@2636
   360
			    setSolver  unsafe_solver
oheimb@2636
   361
			    setmksimps (mksimps mksimps_pairs);
oheimb@2443
   362
paulson@3446
   363
val HOL_ss = 
paulson@3446
   364
    HOL_basic_ss addsimps 
paulson@3446
   365
     ([triv_forall_equality, (* prunes params *)
nipkow@3654
   366
       True_implies_equals, (* prune asms `True' *)
paulson@3446
   367
       if_True, if_False, if_cancel,
paulson@3446
   368
       o_apply, imp_disjL, conj_assoc, disj_assoc,
paulson@3446
   369
       de_Morgan_conj, de_Morgan_disj, not_imp,
paulson@3446
   370
       not_all, not_ex, cases_simp]
paulson@3446
   371
     @ ex_simps @ all_simps @ simp_thms)
nipkow@3568
   372
     addsimprocs [defEX_regroup]
paulson@3446
   373
     addcongs [imp_cong];
paulson@2082
   374
nipkow@1655
   375
qed_goal "if_distrib" HOL.thy
nipkow@1655
   376
  "f(if c then x else y) = (if c then f x else f y)" 
nipkow@1655
   377
  (fn _ => [simp_tac (HOL_ss setloop (split_tac [expand_if])) 1]);
nipkow@1655
   378
oheimb@2097
   379
qed_goalw "o_assoc" HOL.thy [o_def] "f o (g o h) = f o g o h"
oheimb@2098
   380
  (fn _ => [rtac ext 1, rtac refl 1]);
paulson@1984
   381
paulson@1984
   382
paulson@2948
   383
val prems = goal HOL.thy "[| P ==> Q(True); ~P ==> Q(False) |] ==> Q(P)";
paulson@2948
   384
by (case_tac "P" 1);
paulson@2948
   385
by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems)));
paulson@2948
   386
val expand_case = result();
paulson@2948
   387
paulson@2948
   388
fun expand_case_tac P i =
paulson@2948
   389
    res_inst_tac [("P",P)] expand_case i THEN
paulson@2948
   390
    Simp_tac (i+1) THEN 
paulson@2948
   391
    Simp_tac i;
paulson@2948
   392
paulson@2948
   393
paulson@1984
   394
paulson@1984
   395
paulson@1984
   396
(*** Install simpsets and datatypes in theory structure ***)
paulson@1984
   397
oheimb@2251
   398
simpset := HOL_ss;
paulson@1984
   399
paulson@1984
   400
exception SS_DATA of simpset;
paulson@1984
   401
paulson@1984
   402
let fun merge [] = SS_DATA empty_ss
paulson@1984
   403
      | merge ss = let val ss = map (fn SS_DATA x => x) ss;
paulson@1984
   404
                   in SS_DATA (foldl merge_ss (hd ss, tl ss)) end;
paulson@1984
   405
paulson@1984
   406
    fun put (SS_DATA ss) = simpset := ss;
paulson@1984
   407
paulson@1984
   408
    fun get () = SS_DATA (!simpset);
paulson@1984
   409
in add_thydata "HOL"
paulson@1984
   410
     ("simpset", ThyMethods {merge = merge, put = put, get = get})
paulson@1984
   411
end;
paulson@1984
   412
berghofe@3615
   413
fun simpset_of tname =
berghofe@3615
   414
  case get_thydata tname "simpset" of
berghofe@3615
   415
      None => empty_ss
berghofe@3615
   416
    | Some (SS_DATA ss) => ss;
berghofe@3615
   417
nipkow@3040
   418
type dtype_info = {case_const:term,
nipkow@3040
   419
                   case_rewrites:thm list,
nipkow@3040
   420
                   constructors:term list,
nipkow@3040
   421
                   induct_tac: string -> int -> tactic,
nipkow@3282
   422
                   nchotomy: thm,
nipkow@3282
   423
                   exhaustion: thm,
nipkow@3282
   424
                   exhaust_tac: string -> int -> tactic,
nipkow@3040
   425
                   case_cong:thm};
paulson@1984
   426
paulson@1984
   427
exception DT_DATA of (string * dtype_info) list;
paulson@1984
   428
val datatypes = ref [] : (string * dtype_info) list ref;
paulson@1984
   429
paulson@1984
   430
let fun merge [] = DT_DATA []
paulson@1984
   431
      | merge ds =
paulson@1984
   432
          let val ds = map (fn DT_DATA x => x) ds;
paulson@1984
   433
          in DT_DATA (foldl (gen_union eq_fst) (hd ds, tl ds)) end;
paulson@1984
   434
paulson@1984
   435
    fun put (DT_DATA ds) = datatypes := ds;
paulson@1984
   436
paulson@1984
   437
    fun get () = DT_DATA (!datatypes);
paulson@1984
   438
in add_thydata "HOL"
paulson@1984
   439
     ("datatypes", ThyMethods {merge = merge, put = put, get = get})
paulson@1984
   440
end;
paulson@1984
   441
paulson@1984
   442
oheimb@2636
   443
oheimb@2636
   444
(*** Integration of simplifier with classical reasoner ***)
oheimb@2636
   445
oheimb@2636
   446
(* rot_eq_tac rotates the first equality premise of subgoal i to the front,
oheimb@2636
   447
   fails if there is no equaliy or if an equality is already at the front *)
paulson@3538
   448
local
paulson@3538
   449
  fun is_eq (Const ("Trueprop", _) $ (Const("op ="  ,_) $ _ $ _)) = true
paulson@3538
   450
    | is_eq _ = false;
paulson@3538
   451
  fun find_eq n [] = None
paulson@3538
   452
    | find_eq n (t :: ts) = if (is_eq t) then Some n 
paulson@3538
   453
			    else find_eq (n + 1) ts;
paulson@3538
   454
in
paulson@3538
   455
val rot_eq_tac = 
paulson@3538
   456
     SUBGOAL (fn (Bi,i) => 
paulson@3538
   457
	      case find_eq 0 (Logic.strip_assums_hyp Bi) of
paulson@2805
   458
		  None   => no_tac
paulson@2805
   459
		| Some 0 => no_tac
paulson@3538
   460
		| Some n => rotate_tac n i)
paulson@3538
   461
end;
oheimb@2636
   462
oheimb@2636
   463
(*an unsatisfactory fix for the incomplete asm_full_simp_tac!
oheimb@2636
   464
  better: asm_really_full_simp_tac, a yet to be implemented version of
oheimb@2636
   465
			asm_full_simp_tac that applies all equalities in the
oheimb@2636
   466
			premises to all the premises *)
oheimb@2636
   467
fun safe_asm_more_full_simp_tac ss = TRY o rot_eq_tac THEN' 
oheimb@2636
   468
				     safe_asm_full_simp_tac ss;
oheimb@2636
   469
oheimb@2636
   470
(*Add a simpset to a classical set!*)
oheimb@3206
   471
infix 4 addSss addss;
oheimb@3206
   472
fun cs addSss ss = cs addSaltern (CHANGED o (safe_asm_more_full_simp_tac ss));
oheimb@3206
   473
fun cs addss  ss = cs addbefore                        asm_full_simp_tac ss;
oheimb@2636
   474
oheimb@2636
   475
fun Addss ss = (claset := !claset addss ss);
oheimb@2636
   476
oheimb@2636
   477
(*Designed to be idempotent, except if best_tac instantiates variables
oheimb@2636
   478
  in some of the subgoals*)
oheimb@2636
   479
oheimb@2636
   480
type clasimpset = (claset * simpset);
oheimb@2636
   481
oheimb@2636
   482
val HOL_css = (HOL_cs, HOL_ss);
oheimb@2636
   483
oheimb@2636
   484
fun pair_upd1 f ((a,b),x) = (f(a,x), b);
oheimb@2636
   485
fun pair_upd2 f ((a,b),x) = (a, f(b,x));
oheimb@2636
   486
oheimb@2636
   487
infix 4 addSIs2 addSEs2 addSDs2 addIs2 addEs2 addDs2
oheimb@2636
   488
	addsimps2 delsimps2 addcongs2 delcongs2;
paulson@2748
   489
fun op addSIs2   arg = pair_upd1 (op addSIs) arg;
paulson@2748
   490
fun op addSEs2   arg = pair_upd1 (op addSEs) arg;
paulson@2748
   491
fun op addSDs2   arg = pair_upd1 (op addSDs) arg;
paulson@2748
   492
fun op addIs2    arg = pair_upd1 (op addIs ) arg;
paulson@2748
   493
fun op addEs2    arg = pair_upd1 (op addEs ) arg;
paulson@2748
   494
fun op addDs2    arg = pair_upd1 (op addDs ) arg;
paulson@2748
   495
fun op addsimps2 arg = pair_upd2 (op addsimps) arg;
paulson@2748
   496
fun op delsimps2 arg = pair_upd2 (op delsimps) arg;
paulson@2748
   497
fun op addcongs2 arg = pair_upd2 (op addcongs) arg;
paulson@2748
   498
fun op delcongs2 arg = pair_upd2 (op delcongs) arg;
oheimb@2636
   499
paulson@2805
   500
fun auto_tac (cs,ss) = 
paulson@2805
   501
    let val cs' = cs addss ss 
paulson@2805
   502
    in  EVERY [TRY (safe_tac cs'),
paulson@2805
   503
	       REPEAT (FIRSTGOAL (fast_tac cs')),
oheimb@3206
   504
               TRY (safe_tac (cs addSss ss)),
paulson@2805
   505
	       prune_params_tac] 
paulson@2805
   506
    end;
oheimb@2636
   507
oheimb@2636
   508
fun Auto_tac () = auto_tac (!claset, !simpset);
oheimb@2636
   509
oheimb@2636
   510
fun auto () = by (Auto_tac ());