src/HOL/simpdata.ML
author wenzelm
Tue, 29 Aug 2000 00:55:31 +0200
changeset 9713 2c5b42311eb0
parent 9511 bb029080ff8b
child 9736 332fab43628f
permissions -rw-r--r--
cong setup now part of Simplifier;
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
1465
5d7a7e439cec expanded tabs
clasohm
parents: 1264
diff changeset
     1
(*  Title:      HOL/simpdata.ML
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
     2
    ID:         $Id$
1465
5d7a7e439cec expanded tabs
clasohm
parents: 1264
diff changeset
     3
    Author:     Tobias Nipkow
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
     4
    Copyright   1991  University of Cambridge
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
     5
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
     6
Instantiation of the generic simplifier for HOL.
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
     7
*)
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
     8
1984
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
     9
section "Simplifier";
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    10
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    11
(*** Addition of rules to simpsets and clasets simultaneously ***)      (* FIXME move to Provers/clasimp.ML? *)
1984
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    12
5190
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    13
infix 4 addIffs delIffs;
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    14
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    15
(*Takes UNCONDITIONAL theorems of the form A<->B to
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    16
        the Safe Intr     rule B==>A and
2031
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    17
        the Safe Destruct rule A==>B.
1984
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    18
  Also ~A goes to the Safe Elim rule A ==> ?R
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    19
  Failing other cases, A is added as a Safe Intr rule*)
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    20
local
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    21
  val iff_const = HOLogic.eq_const HOLogic.boolT;
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    22
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    23
  fun addIff ((cla, simp), th) =
5190
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    24
      (case HOLogic.dest_Trueprop (#prop (rep_thm th)) of
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    25
                (Const("Not", _) $ A) =>
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    26
                    cla addSEs [zero_var_indexes (th RS notE)]
2031
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    27
              | (con $ _ $ _) =>
5190
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    28
                    if con = iff_const
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    29
                    then cla addSIs [zero_var_indexes (th RS iffD2)]
5190
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    30
                              addSDs [zero_var_indexes (th RS iffD1)]
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    31
                    else  cla addSIs [th]
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    32
              | _ => cla addSIs [th],
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    33
       simp addsimps [th])
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    34
      handle TERM _ => error ("AddIffs: theorem must be unconditional\n" ^
5190
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    35
                         string_of_thm th);
1984
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    36
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    37
  fun delIff ((cla, simp), th) =
5190
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    38
      (case HOLogic.dest_Trueprop (#prop (rep_thm th)) of
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    39
           (Const ("Not", _) $ A) =>
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    40
               cla delrules [zero_var_indexes (th RS notE)]
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    41
         | (con $ _ $ _) =>
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    42
               if con = iff_const
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    43
               then cla delrules
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    44
                        [zero_var_indexes (th RS iffD2),
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    45
                         cla_make_elim (zero_var_indexes (th RS iffD1))]
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    46
               else cla delrules [th]
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    47
         | _ => cla delrules [th],
5190
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    48
       simp delsimps [th])
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    49
      handle TERM _ => (warning("DelIffs: ignoring conditional theorem\n" ^
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    50
                                string_of_thm th); (cla, simp));
5190
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    51
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    52
  fun store_clasimp (cla, simp) = (claset_ref () := cla; simpset_ref () := simp)
1984
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    53
in
5190
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    54
val op addIffs = foldl addIff;
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    55
val op delIffs = foldl delIff;
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    56
fun AddIffs thms = store_clasimp ((claset (), simpset ()) addIffs thms);
4ae031622592 Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents: 4930
diff changeset
    57
fun DelIffs thms = store_clasimp ((claset (), simpset ()) delIffs thms);
1984
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    58
end;
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    59
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
    60
7357
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents: 7213
diff changeset
    61
val [prem] = goal (the_context ()) "x==y ==> x=y";
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
    62
by (rewtac prem);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
    63
by (rtac refl 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
    64
qed "meta_eq_to_obj_eq";
4640
ac6cf9f18653 Congruence rules use == in premises now.
nipkow
parents: 4633
diff changeset
    65
9023
09d02e7365c1 added eta_contract_eq, also to simpset
oheimb
parents: 8955
diff changeset
    66
Goal "(%s. f s) = f";
09d02e7365c1 added eta_contract_eq, also to simpset
oheimb
parents: 8955
diff changeset
    67
br refl 1;
09d02e7365c1 added eta_contract_eq, also to simpset
oheimb
parents: 8955
diff changeset
    68
qed "eta_contract_eq";
09d02e7365c1 added eta_contract_eq, also to simpset
oheimb
parents: 8955
diff changeset
    69
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
    70
local
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
    71
7357
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents: 7213
diff changeset
    72
  fun prover s = prove_goal (the_context ()) s (fn _ => [(Blast_tac 1)]);
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
    73
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
    74
in
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
    75
5552
dcd3e7711cac simplified CLASIMP_DATA
oheimb
parents: 5447
diff changeset
    76
(*Make meta-equalities.  The operator below is Trueprop*)
dcd3e7711cac simplified CLASIMP_DATA
oheimb
parents: 5447
diff changeset
    77
6128
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
    78
fun mk_meta_eq r = r RS eq_reflection;
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
    79
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
    80
val Eq_TrueI  = mk_meta_eq(prover  "P --> (P = True)"  RS mp);
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
    81
val Eq_FalseI = mk_meta_eq(prover "~P --> (P = False)" RS mp);
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
    82
6128
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
    83
fun mk_eq th = case concl_of th of
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
    84
        Const("==",_)$_$_       => th
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
    85
    |   _$(Const("op =",_)$_$_) => mk_meta_eq th
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
    86
    |   _$(Const("Not",_)$_)    => th RS Eq_FalseI
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
    87
    |   _                       => th RS Eq_TrueI;
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
    88
(* last 2 lines requires all formulae to be of the from Trueprop(.) *)
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
    89
6128
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
    90
fun mk_eq_True r = Some(r RS meta_eq_to_obj_eq RS Eq_TrueI);
5552
dcd3e7711cac simplified CLASIMP_DATA
oheimb
parents: 5447
diff changeset
    91
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
    92
(*Congruence rules for = (instead of ==)*)
6128
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
    93
fun mk_meta_cong rl =
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
    94
  standard(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl))
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
    95
  handle THM _ =>
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
    96
  error("Premises and conclusion of congruence rules must be =-equalities");
3896
ee8ebb74ec00 Various new lemmas. Improved conversion of equations to rewrite rules:
nipkow
parents: 3842
diff changeset
    97
5975
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
    98
val not_not = prover "(~ ~ P) = P";
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
    99
5975
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   100
val simp_thms = [not_not] @ map prover
2082
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
   101
 [ "(x=x) = True",
5975
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   102
   "(~True) = False", "(~False) = True",
2082
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
   103
   "(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))",
4640
ac6cf9f18653 Congruence rules use == in premises now.
nipkow
parents: 4633
diff changeset
   104
   "(True=P) = P", "(P=True) = P", "(False=P) = (~P)", "(P=False) = (~P)",
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   105
   "(True --> P) = P", "(False --> P) = True",
2082
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
   106
   "(P --> True) = True", "(P --> P) = True",
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
   107
   "(P --> False) = (~P)", "(P --> ~P) = (~P)",
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   108
   "(P & True) = P", "(True & P) = P",
2800
9741c4c6b62b Added P&P&Q = P&Q and P|P|Q = P|Q.
nipkow
parents: 2748
diff changeset
   109
   "(P & False) = False", "(False & P) = False",
9741c4c6b62b Added P&P&Q = P&Q and P|P|Q = P|Q.
nipkow
parents: 2748
diff changeset
   110
   "(P & P) = P", "(P & (P & Q)) = (P & Q)",
3913
96e28b16861c New trivial rewrites
paulson
parents: 3904
diff changeset
   111
   "(P & ~P) = False",    "(~P & P) = False",
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   112
   "(P | True) = True", "(True | P) = True",
2800
9741c4c6b62b Added P&P&Q = P&Q and P|P|Q = P|Q.
nipkow
parents: 2748
diff changeset
   113
   "(P | False) = P", "(False | P) = P",
9741c4c6b62b Added P&P&Q = P&Q and P|P|Q = P|Q.
nipkow
parents: 2748
diff changeset
   114
   "(P | P) = P", "(P | (P | Q)) = (P | Q)",
3913
96e28b16861c New trivial rewrites
paulson
parents: 3904
diff changeset
   115
   "(P | ~P) = True",    "(~P | P) = True",
2082
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
   116
   "((~P) = (~Q)) = (P=Q)",
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   117
   "(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x",
4351
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   118
(*two needed for the one-point-rule quantifier simplification procs*)
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   119
   "(? x. x=t & P(x)) = P(t)",          (*essential for termination!!*)
4351
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   120
   "(! x. t=x --> P(x)) = P(t)" ];      (*covers a stray case*)
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   121
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   122
val imp_cong = impI RSN
7357
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents: 7213
diff changeset
   123
    (2, prove_goal (the_context ()) "(P=P')--> (P'--> (Q=Q'))--> ((P-->Q) = (P'-->Q'))"
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   124
        (fn _=> [(Blast_tac 1)]) RS mp RS mp);
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   125
1948
78e5bfcbc1e9 Added miniscoping to the simplifier: quantifiers are now pushed in
paulson
parents: 1922
diff changeset
   126
(*Miniscoping: pushing in existential quantifiers*)
7648
8258b93cdd32 bind_thms;
wenzelm
parents: 7623
diff changeset
   127
val ex_simps = map prover
3842
b55686a7b22c fixed dots;
wenzelm
parents: 3654
diff changeset
   128
                ["(EX x. P x & Q)   = ((EX x. P x) & Q)",
b55686a7b22c fixed dots;
wenzelm
parents: 3654
diff changeset
   129
                 "(EX x. P & Q x)   = (P & (EX x. Q x))",
b55686a7b22c fixed dots;
wenzelm
parents: 3654
diff changeset
   130
                 "(EX x. P x | Q)   = ((EX x. P x) | Q)",
b55686a7b22c fixed dots;
wenzelm
parents: 3654
diff changeset
   131
                 "(EX x. P | Q x)   = (P | (EX x. Q x))",
b55686a7b22c fixed dots;
wenzelm
parents: 3654
diff changeset
   132
                 "(EX x. P x --> Q) = ((ALL x. P x) --> Q)",
b55686a7b22c fixed dots;
wenzelm
parents: 3654
diff changeset
   133
                 "(EX x. P --> Q x) = (P --> (EX x. Q x))"];
1948
78e5bfcbc1e9 Added miniscoping to the simplifier: quantifiers are now pushed in
paulson
parents: 1922
diff changeset
   134
78e5bfcbc1e9 Added miniscoping to the simplifier: quantifiers are now pushed in
paulson
parents: 1922
diff changeset
   135
(*Miniscoping: pushing in universal quantifiers*)
78e5bfcbc1e9 Added miniscoping to the simplifier: quantifiers are now pushed in
paulson
parents: 1922
diff changeset
   136
val all_simps = map prover
3842
b55686a7b22c fixed dots;
wenzelm
parents: 3654
diff changeset
   137
                ["(ALL x. P x & Q)   = ((ALL x. P x) & Q)",
b55686a7b22c fixed dots;
wenzelm
parents: 3654
diff changeset
   138
                 "(ALL x. P & Q x)   = (P & (ALL x. Q x))",
b55686a7b22c fixed dots;
wenzelm
parents: 3654
diff changeset
   139
                 "(ALL x. P x | Q)   = ((ALL x. P x) | Q)",
b55686a7b22c fixed dots;
wenzelm
parents: 3654
diff changeset
   140
                 "(ALL x. P | Q x)   = (P | (ALL x. Q x))",
b55686a7b22c fixed dots;
wenzelm
parents: 3654
diff changeset
   141
                 "(ALL x. P x --> Q) = ((EX x. P x) --> Q)",
b55686a7b22c fixed dots;
wenzelm
parents: 3654
diff changeset
   142
                 "(ALL x. P --> Q x) = (P --> (ALL x. Q x))"];
1948
78e5bfcbc1e9 Added miniscoping to the simplifier: quantifiers are now pushed in
paulson
parents: 1922
diff changeset
   143
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   144
2022
9d47e2962edd Fixed spelling error in comment
paulson
parents: 1984
diff changeset
   145
(* elimination of existential quantifiers in assumptions *)
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   146
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   147
val ex_all_equiv =
7357
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents: 7213
diff changeset
   148
  let val lemma1 = prove_goal (the_context ())
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   149
        "(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)"
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   150
        (fn prems => [resolve_tac prems 1, etac exI 1]);
7357
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents: 7213
diff changeset
   151
      val lemma2 = prove_goalw (the_context ()) [Ex_def]
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   152
        "(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)"
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   153
        (fn prems => [(REPEAT(resolve_tac prems 1))])
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   154
  in equal_intr lemma1 lemma2 end;
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   155
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   156
end;
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   157
7648
8258b93cdd32 bind_thms;
wenzelm
parents: 7623
diff changeset
   158
bind_thms ("ex_simps", ex_simps);
8258b93cdd32 bind_thms;
wenzelm
parents: 7623
diff changeset
   159
bind_thms ("all_simps", all_simps);
7711
4dae7a4fceaf Rule not_not is now stored in theory (needed by Inductive).
berghofe
parents: 7648
diff changeset
   160
bind_thm ("not_not", not_not);
7648
8258b93cdd32 bind_thms;
wenzelm
parents: 7623
diff changeset
   161
3654
ebad042c0bba Added True_implies_equals
nipkow
parents: 3615
diff changeset
   162
(* Elimination of True from asumptions: *)
ebad042c0bba Added True_implies_equals
nipkow
parents: 3615
diff changeset
   163
7357
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents: 7213
diff changeset
   164
val True_implies_equals = prove_goal (the_context ())
3654
ebad042c0bba Added True_implies_equals
nipkow
parents: 3615
diff changeset
   165
 "(True ==> PROP P) == PROP P"
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   166
(fn _ => [rtac equal_intr_rule 1, atac 2,
3654
ebad042c0bba Added True_implies_equals
nipkow
parents: 3615
diff changeset
   167
          METAHYPS (fn prems => resolve_tac prems 1) 1,
ebad042c0bba Added True_implies_equals
nipkow
parents: 3615
diff changeset
   168
          rtac TrueI 1]);
ebad042c0bba Added True_implies_equals
nipkow
parents: 3615
diff changeset
   169
7357
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents: 7213
diff changeset
   170
fun prove nm thm  = qed_goal nm (the_context ()) thm (fn _ => [(Blast_tac 1)]);
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   171
9511
bb029080ff8b new theorem neq_commute
paulson
parents: 9384
diff changeset
   172
prove "eq_commute" "(a=b) = (b=a)";
7623
23efbb7ab889 AC rules for equality
paulson
parents: 7584
diff changeset
   173
prove "eq_left_commute" "(P=(Q=R)) = (Q=(P=R))";
23efbb7ab889 AC rules for equality
paulson
parents: 7584
diff changeset
   174
prove "eq_assoc" "((P=Q)=R) = (P=(Q=R))";
23efbb7ab889 AC rules for equality
paulson
parents: 7584
diff changeset
   175
val eq_ac = [eq_commute, eq_left_commute, eq_assoc];
23efbb7ab889 AC rules for equality
paulson
parents: 7584
diff changeset
   176
9511
bb029080ff8b new theorem neq_commute
paulson
parents: 9384
diff changeset
   177
prove "neq_commute" "(a~=b) = (b~=a)";
bb029080ff8b new theorem neq_commute
paulson
parents: 9384
diff changeset
   178
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   179
prove "conj_commute" "(P&Q) = (Q&P)";
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   180
prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))";
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   181
val conj_comms = [conj_commute, conj_left_commute];
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   182
prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))";
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   183
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   184
prove "disj_commute" "(P|Q) = (Q|P)";
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   185
prove "disj_left_commute" "(P|(Q|R)) = (Q|(P|R))";
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   186
val disj_comms = [disj_commute, disj_left_commute];
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   187
prove "disj_assoc" "((P|Q)|R) = (P|(Q|R))";
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   188
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   189
prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)";
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   190
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
   191
1892
23765bc3e8e2 Added two new distributive laws
paulson
parents: 1874
diff changeset
   192
prove "disj_conj_distribL" "(P|(Q&R)) = ((P|Q) & (P|R))";
23765bc3e8e2 Added two new distributive laws
paulson
parents: 1874
diff changeset
   193
prove "disj_conj_distribR" "((P&Q)|R) = ((P|R) & (Q|R))";
23765bc3e8e2 Added two new distributive laws
paulson
parents: 1874
diff changeset
   194
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   195
prove "imp_conjR" "(P --> (Q&R)) = ((P-->Q) & (P-->R))";
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   196
prove "imp_conjL" "((P&Q) -->R)  = (P --> (Q --> R))";
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   197
prove "imp_disjL" "((P|Q) --> R) = ((P-->R)&(Q-->R))";
1892
23765bc3e8e2 Added two new distributive laws
paulson
parents: 1874
diff changeset
   198
3448
8a79e27ac53b Two new rewrite rules--NOT included by default\!
paulson
parents: 3446
diff changeset
   199
(*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*)
8114
09a7a180cc99 tidied parentheses
paulson
parents: 7711
diff changeset
   200
prove "imp_disj_not1" "(P --> Q | R) = (~Q --> P --> R)";
09a7a180cc99 tidied parentheses
paulson
parents: 7711
diff changeset
   201
prove "imp_disj_not2" "(P --> Q | R) = (~R --> P --> Q)";
3448
8a79e27ac53b Two new rewrite rules--NOT included by default\!
paulson
parents: 3446
diff changeset
   202
3904
c0d56e4c823e New simprules imp_disj1, imp_disj2
paulson
parents: 3896
diff changeset
   203
prove "imp_disj1" "((P-->Q)|R) = (P--> Q|R)";
c0d56e4c823e New simprules imp_disj1, imp_disj2
paulson
parents: 3896
diff changeset
   204
prove "imp_disj2" "(Q|(P-->R)) = (P--> Q|R)";
c0d56e4c823e New simprules imp_disj1, imp_disj2
paulson
parents: 3896
diff changeset
   205
1485
240cc98b94a7 Added qed_spec_mp to avoid renaming of bound vars in 'th RS spec'
nipkow
parents: 1465
diff changeset
   206
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
   207
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
   208
prove "not_imp" "(~(P --> Q)) = (P & ~Q)";
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   209
prove "not_iff" "(P~=Q) = (P = (~Q))";
4743
b3bfcbd9fb93 renamed not1_or to disj_not1, not2_or to disj_not2
oheimb
parents: 4718
diff changeset
   210
prove "disj_not1" "(~P | Q) = (P --> Q)";
b3bfcbd9fb93 renamed not1_or to disj_not1, not2_or to disj_not2
oheimb
parents: 4718
diff changeset
   211
prove "disj_not2" "(P | ~Q) = (Q --> P)"; (* changes orientation :-( *)
5975
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   212
prove "imp_conv_disj" "(P --> Q) = ((~P) | Q)";
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   213
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   214
prove "iff_conv_conj_imp" "(P = Q) = ((P --> Q) & (Q --> P))";
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   215
1485
240cc98b94a7 Added qed_spec_mp to avoid renaming of bound vars in 'th RS spec'
nipkow
parents: 1465
diff changeset
   216
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   217
(*Avoids duplication of subgoals after split_if, when the true and false
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   218
  cases boil down to the same thing.*)
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   219
prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   220
3842
b55686a7b22c fixed dots;
wenzelm
parents: 3654
diff changeset
   221
prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))";
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   222
prove "imp_all" "((! x. P x) --> Q) = (? x. P x --> Q)";
3842
b55686a7b22c fixed dots;
wenzelm
parents: 3654
diff changeset
   223
prove "not_ex"  "(~ (? x. P(x))) = (! x.~P(x))";
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   224
prove "imp_ex" "((? x. P x) --> Q) = (! x. P x --> Q)";
1660
8cb42cd97579 *** empty log message ***
oheimb
parents: 1655
diff changeset
   225
1655
5be64540f275 Added a number of lemmas
nipkow
parents: 1548
diff changeset
   226
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
   227
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
   228
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   229
(* '&' congruence rule: not included by default!
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   230
   May slow rewrite proofs down by as much as 50% *)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   231
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   232
let val th = prove_goal (the_context ())
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   233
                "(P=P')--> (P'--> (Q=Q'))--> ((P&Q) = (P'&Q'))"
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   234
                (fn _=> [(Blast_tac 1)])
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   235
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
   236
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   237
let val th = prove_goal (the_context ())
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   238
                "(Q=Q')--> (Q'--> (P=P'))--> ((P&Q) = (P'&Q'))"
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   239
                (fn _=> [(Blast_tac 1)])
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   240
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
   241
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   242
(* '|' congruence rule: not included by default! *)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   243
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   244
let val th = prove_goal (the_context ())
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   245
                "(P=P')--> (~P'--> (Q=Q'))--> ((P|Q) = (P'|Q'))"
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   246
                (fn _=> [(Blast_tac 1)])
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   247
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
   248
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   249
prove "eq_sym_conv" "(x=y) = (y=x)";
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   250
5278
a903b66822e2 even more tidying of Goal commands
paulson
parents: 5220
diff changeset
   251
a903b66822e2 even more tidying of Goal commands
paulson
parents: 5220
diff changeset
   252
(** if-then-else rules **)
a903b66822e2 even more tidying of Goal commands
paulson
parents: 5220
diff changeset
   253
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   254
Goalw [if_def] "(if True then x else y) = x";
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   255
by (Blast_tac 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   256
qed "if_True";
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   257
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   258
Goalw [if_def] "(if False then x else y) = y";
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   259
by (Blast_tac 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   260
qed "if_False";
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   261
7127
48e235179ffb added parentheses to cope with a possible reduction of the precedence of unary
paulson
parents: 7031
diff changeset
   262
Goalw [if_def] "P ==> (if P then x else y) = x";
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   263
by (Blast_tac 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   264
qed "if_P";
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   265
7127
48e235179ffb added parentheses to cope with a possible reduction of the precedence of unary
paulson
parents: 7031
diff changeset
   266
Goalw [if_def] "~P ==> (if P then x else y) = y";
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   267
by (Blast_tac 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   268
qed "if_not_P";
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   269
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   270
Goal "P(if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))";
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   271
by (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   272
by (stac if_P 2);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   273
by (stac if_not_P 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   274
by (ALLGOALS (Blast_tac));
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   275
qed "split_if";
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   276
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   277
Goal "P(if Q then x else y) = (~((Q & ~P x) | (~Q & ~P y)))";
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   278
by (stac split_if 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   279
by (Blast_tac 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   280
qed "split_if_asm";
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   281
9384
8e8941c491e6 * HOL: removed obsolete expand_if = split_if; theorems if_splits =
wenzelm
parents: 9164
diff changeset
   282
bind_thms ("if_splits", [split_if, split_if_asm]);
8e8941c491e6 * HOL: removed obsolete expand_if = split_if; theorems if_splits =
wenzelm
parents: 9164
diff changeset
   283
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   284
Goal "(if c then x else x) = x";
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   285
by (stac split_if 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   286
by (Blast_tac 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   287
qed "if_cancel";
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   288
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   289
Goal "(if x = y then y else x) = x";
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   290
by (stac split_if 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   291
by (Blast_tac 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   292
qed "if_eq_cancel";
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   293
4769
bb60149fe21b changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents: 4744
diff changeset
   294
(*This form is useful for expanding IFs on the RIGHT of the ==> symbol*)
7127
48e235179ffb added parentheses to cope with a possible reduction of the precedence of unary
paulson
parents: 7031
diff changeset
   295
Goal "(if P then Q else R) = ((P-->Q) & (~P-->R))";
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   296
by (rtac split_if 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   297
qed "if_bool_eq_conj";
4769
bb60149fe21b changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents: 4744
diff changeset
   298
bb60149fe21b changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents: 4744
diff changeset
   299
(*And this form is useful for expanding IFs on the LEFT*)
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   300
Goal "(if P then Q else R) = ((P&Q) | (~P&R))";
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   301
by (stac split_if 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   302
by (Blast_tac 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   303
qed "if_bool_eq_disj";
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   304
4351
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   305
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   306
(*** make simplification procedures for quantifier elimination ***)
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   307
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   308
structure Quantifier1 = Quantifier1Fun(
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   309
struct
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   310
  (*abstract syntax*)
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   311
  fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t)
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   312
    | dest_eq _ = None;
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   313
  fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t)
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   314
    | dest_conj _ = None;
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   315
  val conj = HOLogic.conj
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   316
  val imp  = HOLogic.imp
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   317
  (*rules*)
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   318
  val iff_reflection = eq_reflection
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   319
  val iffI = iffI
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   320
  val sym  = sym
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   321
  val conjI= conjI
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   322
  val conjE= conjE
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   323
  val impI = impI
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   324
  val impE = impE
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   325
  val mp   = mp
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   326
  val exI  = exI
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   327
  val exE  = exE
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   328
  val allI = allI
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   329
  val allE = allE
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   330
end);
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   331
4320
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   332
local
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   333
val ex_pattern =
7357
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents: 7213
diff changeset
   334
  Thm.read_cterm (Theory.sign_of (the_context ())) ("EX x. P(x) & Q(x)",HOLogic.boolT)
3913
96e28b16861c New trivial rewrites
paulson
parents: 3904
diff changeset
   335
4320
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   336
val all_pattern =
7357
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents: 7213
diff changeset
   337
  Thm.read_cterm (Theory.sign_of (the_context ())) ("ALL x. P(x) & P'(x) --> Q(x)",HOLogic.boolT)
4320
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   338
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   339
in
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   340
val defEX_regroup =
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   341
  mk_simproc "defined EX" [ex_pattern] Quantifier1.rearrange_ex;
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   342
val defALL_regroup =
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   343
  mk_simproc "defined ALL" [all_pattern] Quantifier1.rearrange_all;
24d9e6639cd4 Moved the quantifier elimination simp procs into Provers.
nipkow
parents: 4205
diff changeset
   344
end;
3913
96e28b16861c New trivial rewrites
paulson
parents: 3904
diff changeset
   345
4351
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   346
36b28f78ed1b Tidying and some comments
paulson
parents: 4327
diff changeset
   347
(*** Case splitting ***)
3913
96e28b16861c New trivial rewrites
paulson
parents: 3904
diff changeset
   348
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   349
structure SplitterData =
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   350
  struct
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   351
  structure Simplifier = Simplifier
5552
dcd3e7711cac simplified CLASIMP_DATA
oheimb
parents: 5447
diff changeset
   352
  val mk_eq          = mk_eq
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   353
  val meta_eq_to_iff = meta_eq_to_obj_eq
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   354
  val iffD           = iffD2
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   355
  val disjE          = disjE
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   356
  val conjE          = conjE
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   357
  val exE            = exE
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   358
  val contrapos      = contrapos
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   359
  val contrapos2     = contrapos2
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   360
  val notnotD        = notnotD
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   361
  end;
4681
a331c1f5a23e expand_if is now by default part of the simpset.
nipkow
parents: 4677
diff changeset
   362
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   363
structure Splitter = SplitterFun(SplitterData);
2263
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   364
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   365
val split_tac        = Splitter.split_tac;
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   366
val split_inside_tac = Splitter.split_inside_tac;
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   367
val split_asm_tac    = Splitter.split_asm_tac;
5307
6a699d5cdef4 minor adaption for SML/NJ
oheimb
parents: 5304
diff changeset
   368
val op addsplits     = Splitter.addsplits;
6a699d5cdef4 minor adaption for SML/NJ
oheimb
parents: 5304
diff changeset
   369
val op delsplits     = Splitter.delsplits;
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   370
val Addsplits        = Splitter.Addsplits;
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   371
val Delsplits        = Splitter.Delsplits;
4718
fc2ba9fb2135 new rewrite rules not1_or, not2_or, and if_eq_cancel
oheimb
parents: 4681
diff changeset
   372
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   373
(*In general it seems wrong to add distributive laws by default: they
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   374
  might cause exponential blow-up.  But imp_disjL has been in for a while
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   375
  and cannot be removed without affecting existing proofs.  Moreover,
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   376
  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
   377
  grounds that it allows simplification of R in the two cases.*)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   378
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   379
fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th;
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   380
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   381
val mksimps_pairs =
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   382
  [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   383
   ("All", [spec]), ("True", []), ("False", []),
4769
bb60149fe21b changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents: 4744
diff changeset
   384
   ("If", [if_bool_eq_conj RS iffD1])];
1758
60613b065e9b Added ex_imp
nipkow
parents: 1722
diff changeset
   385
5552
dcd3e7711cac simplified CLASIMP_DATA
oheimb
parents: 5447
diff changeset
   386
(* ###FIXME: move to Provers/simplifier.ML
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   387
val mk_atomize:      (string * thm list) list -> thm -> thm list
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   388
*)
5552
dcd3e7711cac simplified CLASIMP_DATA
oheimb
parents: 5447
diff changeset
   389
(* ###FIXME: move to Provers/simplifier.ML *)
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   390
fun mk_atomize pairs =
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   391
  let fun atoms th =
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   392
        (case concl_of th of
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   393
           Const("Trueprop",_) $ p =>
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   394
             (case head_of p of
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   395
                Const(a,_) =>
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   396
                  (case assoc(pairs,a) of
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   397
                     Some(rls) => flat (map atoms ([th] RL rls))
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   398
                   | None => [th])
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   399
              | _ => [th])
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   400
         | _ => [th])
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   401
  in atoms end;
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   402
5552
dcd3e7711cac simplified CLASIMP_DATA
oheimb
parents: 5447
diff changeset
   403
fun mksimps pairs = (map mk_eq o mk_atomize pairs o gen_all);
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   404
7570
a9391550eea1 Mod because of new solver interface.
nipkow
parents: 7369
diff changeset
   405
fun unsafe_solver_tac prems =
a9391550eea1 Mod because of new solver interface.
nipkow
parents: 7369
diff changeset
   406
  FIRST'[resolve_tac(reflexive_thm::TrueI::refl::prems), atac, etac FalseE];
a9391550eea1 Mod because of new solver interface.
nipkow
parents: 7369
diff changeset
   407
val unsafe_solver = mk_solver "HOL unsafe" unsafe_solver_tac;
a9391550eea1 Mod because of new solver interface.
nipkow
parents: 7369
diff changeset
   408
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   409
(*No premature instantiation of variables during simplification*)
7570
a9391550eea1 Mod because of new solver interface.
nipkow
parents: 7369
diff changeset
   410
fun safe_solver_tac prems =
a9391550eea1 Mod because of new solver interface.
nipkow
parents: 7369
diff changeset
   411
  FIRST'[match_tac(reflexive_thm::TrueI::refl::prems),
a9391550eea1 Mod because of new solver interface.
nipkow
parents: 7369
diff changeset
   412
         eq_assume_tac, ematch_tac [FalseE]];
a9391550eea1 Mod because of new solver interface.
nipkow
parents: 7369
diff changeset
   413
val safe_solver = mk_solver "HOL safe" safe_solver_tac;
2443
a81d4c219c3c factored out HOL_base_ss and val HOL_min_ss, added HOL_safe_min_ss
oheimb
parents: 2263
diff changeset
   414
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   415
val HOL_basic_ss =
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   416
  empty_ss setsubgoaler asm_simp_tac
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   417
    setSSolver safe_solver
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   418
    setSolver unsafe_solver
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   419
    setmksimps (mksimps mksimps_pairs)
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   420
    setmkeqTrue mk_eq_True
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   421
    setmkcong mk_meta_cong;
2443
a81d4c219c3c factored out HOL_base_ss and val HOL_min_ss, added HOL_safe_min_ss
oheimb
parents: 2263
diff changeset
   422
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   423
val HOL_ss =
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   424
    HOL_basic_ss addsimps
3446
a14e5451f613 Addition of not_imp (which pushes negation into implication) as a default
paulson
parents: 3282
diff changeset
   425
     ([triv_forall_equality, (* prunes params *)
3654
ebad042c0bba Added True_implies_equals
nipkow
parents: 3615
diff changeset
   426
       True_implies_equals, (* prune asms `True' *)
9023
09d02e7365c1 added eta_contract_eq, also to simpset
oheimb
parents: 8955
diff changeset
   427
       eta_contract_eq, (* prunes eta-expansions *)
4718
fc2ba9fb2135 new rewrite rules not1_or, not2_or, and if_eq_cancel
oheimb
parents: 4681
diff changeset
   428
       if_True, if_False, if_cancel, if_eq_cancel,
5304
c133f16febc7 the splitter is now defined as a functor
oheimb
parents: 5278
diff changeset
   429
       imp_disjL, conj_assoc, disj_assoc,
3904
c0d56e4c823e New simprules imp_disj1, imp_disj2
paulson
parents: 3896
diff changeset
   430
       de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp,
8955
714497ad2348 installing the plus_ac0 simprules
paulson
parents: 8644
diff changeset
   431
       disj_not1, not_all, not_ex, cases_simp, Eps_eq, Eps_sym_eq,
714497ad2348 installing the plus_ac0 simprules
paulson
parents: 8644
diff changeset
   432
       thm"plus_ac0.zero", thm"plus_ac0_zero_right"]
3446
a14e5451f613 Addition of not_imp (which pushes negation into implication) as a default
paulson
parents: 3282
diff changeset
   433
     @ 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
   434
     addsimprocs [defALL_regroup,defEX_regroup]
4744
4469d498cd48 moved addsplits [expand_if] from HOL_basic_ss to HOL_ss;
wenzelm
parents: 4743
diff changeset
   435
     addcongs [imp_cong]
4830
bd73675adbed Added a few lemmas.
nipkow
parents: 4794
diff changeset
   436
     addsplits [split_if];
2082
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
   437
6293
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   438
(*Simplifies x assuming c and y assuming ~c*)
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   439
val prems = Goalw [if_def]
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   440
  "[| b=c; c ==> x=u; ~c ==> y=v |] ==> \
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   441
\  (if b then x else y) = (if c then u else v)";
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   442
by (asm_simp_tac (HOL_ss addsimps prems) 1);
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   443
qed "if_cong";
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   444
7127
48e235179ffb added parentheses to cope with a possible reduction of the precedence of unary
paulson
parents: 7031
diff changeset
   445
(*Prevents simplification of x and y: faster and allows the execution
48e235179ffb added parentheses to cope with a possible reduction of the precedence of unary
paulson
parents: 7031
diff changeset
   446
  of functional programs. NOW THE DEFAULT.*)
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   447
Goal "b=c ==> (if b then x else y) = (if c then x else y)";
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   448
by (etac arg_cong 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   449
qed "if_weak_cong";
6293
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   450
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   451
(*Prevents simplification of t: much faster*)
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   452
Goal "a = b ==> (let x=a in t(x)) = (let x=b in t(x))";
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   453
by (etac arg_cong 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   454
qed "let_weak_cong";
6293
2a4357301973 simpler proofs of congruence rules
paulson
parents: 6128
diff changeset
   455
7031
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   456
Goal "f(if c then x else y) = (if c then f x else f y)";
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   457
by (simp_tac (HOL_ss setloop (split_tac [split_if])) 1);
972b5f62f476 getting rid of qed_goal
paulson
parents: 6968
diff changeset
   458
qed "if_distrib";
1655
5be64540f275 Added a number of lemmas
nipkow
parents: 1548
diff changeset
   459
4327
2335f6584a1b Added comments
paulson
parents: 4321
diff changeset
   460
(*For expand_case_tac*)
7584
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   461
val prems = Goal "[| P ==> Q(True); ~P ==> Q(False) |] ==> Q(P)";
2948
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   462
by (case_tac "P" 1);
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   463
by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems)));
7584
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   464
qed "expand_case";
2948
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   465
4327
2335f6584a1b Added comments
paulson
parents: 4321
diff changeset
   466
(*Used in Auth proofs.  Typically P contains Vars that become instantiated
2335f6584a1b Added comments
paulson
parents: 4321
diff changeset
   467
  during unification.*)
2948
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   468
fun expand_case_tac P i =
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   469
    res_inst_tac [("P",P)] expand_case i THEN
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   470
    Simp_tac (i+1) THEN
2948
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   471
    Simp_tac i;
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   472
7584
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   473
(*This lemma restricts the effect of the rewrite rule u=v to the left-hand
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   474
  side of an equality.  Used in {Integ,Real}/simproc.ML*)
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   475
Goal "x=y ==> (x=z) = (y=z)";
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   476
by (asm_simp_tac HOL_ss 1);
5be4bb8e4e3f tidied; added lemma restrict_to_left
paulson
parents: 7570
diff changeset
   477
qed "restrict_to_left";
2948
f18035b1d531 Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents: 2935
diff changeset
   478
7357
d0e16da40ea2 proper bootstrap of HOL theory and packages;
wenzelm
parents: 7213
diff changeset
   479
(* default simpset *)
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   480
val simpsetup =
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   481
  [fn thy => (simpset_ref_of thy := HOL_ss addcongs [if_weak_cong]; thy)];
3615
e5322197cfea Moved some functions which used to be part of thy_data.ML
berghofe
parents: 3577
diff changeset
   482
4652
d24cca140eeb factored out common code of HOL/simpdata.ML and FOL/simpdata.ML concerning
oheimb
parents: 4651
diff changeset
   483
5219
924359415f09 functorized Clasimp module;
wenzelm
parents: 5190
diff changeset
   484
(*** integration of simplifier with classical reasoner ***)
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   485
5219
924359415f09 functorized Clasimp module;
wenzelm
parents: 5190
diff changeset
   486
structure Clasimp = ClasimpFun
8473
2798d2f71ec2 splitter setup;
wenzelm
parents: 8114
diff changeset
   487
 (structure Simplifier = Simplifier and Splitter = Splitter
2798d2f71ec2 splitter setup;
wenzelm
parents: 8114
diff changeset
   488
   and Classical  = Classical and Blast = Blast);
4652
d24cca140eeb factored out common code of HOL/simpdata.ML and FOL/simpdata.ML concerning
oheimb
parents: 4651
diff changeset
   489
open Clasimp;
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   490
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   491
val HOL_css = (HOL_cs, HOL_ss);
5975
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   492
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   493
8641
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   494
(* "iff" attribute *)
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   495
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   496
val iff_add_global = Clasimp.change_global_css (op addIffs);
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   497
val iff_add_local = Clasimp.change_local_css (op addIffs);
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   498
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   499
val iff_attrib_setup =
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   500
  [Attrib.add_attributes [("iff", (Attrib.no_args iff_add_global, Attrib.no_args iff_add_local),
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   501
    "add rules to simpset and claset simultaneously")]];
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   502
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   503
978db2870862 change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents: 8473
diff changeset
   504
5975
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   505
(*** A general refutation procedure ***)
9713
2c5b42311eb0 cong setup now part of Simplifier;
wenzelm
parents: 9511
diff changeset
   506
5975
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   507
(* Parameters:
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   508
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   509
   test: term -> bool
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   510
   tests if a term is at all relevant to the refutation proof;
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   511
   if not, then it can be discarded. Can improve performance,
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   512
   esp. if disjunctions can be discarded (no case distinction needed!).
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   513
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   514
   prep_tac: int -> tactic
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   515
   A preparation tactic to be applied to the goal once all relevant premises
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   516
   have been moved to the conclusion.
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   517
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   518
   ref_tac: int -> tactic
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   519
   the actual refutation tactic. Should be able to deal with goals
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   520
   [| A1; ...; An |] ==> False
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   521
   where the Ai are atomic, i.e. no top-level &, | or ?
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   522
*)
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   523
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   524
fun refute_tac test prep_tac ref_tac =
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   525
  let val nnf_simps =
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   526
        [imp_conv_disj,iff_conv_conj_imp,de_Morgan_disj,de_Morgan_conj,
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   527
         not_all,not_ex,not_not];
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   528
      val nnf_simpset =
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   529
        empty_ss setmkeqTrue mk_eq_True
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   530
                 setmksimps (mksimps mksimps_pairs)
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   531
                 addsimps nnf_simps;
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   532
      val prem_nnf_tac = full_simp_tac nnf_simpset;
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   533
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   534
      val refute_prems_tac =
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   535
        REPEAT(eresolve_tac [conjE, exE] 1 ORELSE
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   536
               filter_prems_tac test 1 ORELSE
6301
08245f5a436d expandshort
paulson
parents: 6293
diff changeset
   537
               etac disjE 1) THEN
5975
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   538
        ref_tac 1;
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   539
  in EVERY'[TRY o filter_prems_tac test,
6128
2acc5d36610c More arith refinements.
nipkow
parents: 5975
diff changeset
   540
            DETERM o REPEAT o etac rev_mp, prep_tac, rtac ccontr, prem_nnf_tac,
5975
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   541
            SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)]
cd19eaa90f45 Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents: 5552
diff changeset
   542
  end;