src/HOL/simpdata.ML
author paulson
Fri, 11 Apr 1997 15:21:36 +0200
changeset 2935 998cb95fdd43
parent 2805 6e5b2d6503eb
child 2948 f18035b1d531
permissions -rw-r--r--
Yet more fast_tac->blast_tac, and other tidying
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
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
     6
Instantiation of the generic simplifier
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
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
    11
open Simplifier;
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
    12
1984
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    13
(*** Addition of rules to simpsets and clasets simultaneously ***)
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    14
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    15
(*Takes UNCONDITIONAL theorems of the form A<->B to 
2031
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    16
        the Safe Intr     rule B==>A and 
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
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    23
  fun addIff th = 
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    24
      (case HOLogic.dest_Trueprop (#prop(rep_thm th)) of
2718
460fd0f8d478 Renamed constant "not" to "Not"
paulson
parents: 2636
diff changeset
    25
                (Const("Not",_) $ A) =>
2031
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    26
                    AddSEs [zero_var_indexes (th RS notE)]
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    27
              | (con $ _ $ _) =>
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    28
                    if con=iff_const
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    29
                    then (AddSIs [zero_var_indexes (th RS iffD2)];  
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    30
                          AddSDs [zero_var_indexes (th RS iffD1)])
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    31
                    else  AddSIs [th]
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    32
              | _ => AddSIs [th];
1984
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    33
       Addsimps [th])
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    34
      handle _ => error ("AddIffs: theorem must be unconditional\n" ^ 
2031
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    35
                         string_of_thm th)
1984
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    36
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    37
  fun delIff th = 
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    38
      (case HOLogic.dest_Trueprop (#prop(rep_thm th)) of
2718
460fd0f8d478 Renamed constant "not" to "Not"
paulson
parents: 2636
diff changeset
    39
                (Const("Not",_) $ A) =>
2031
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    40
                    Delrules [zero_var_indexes (th RS notE)]
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    41
              | (con $ _ $ _) =>
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    42
                    if con=iff_const
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    43
                    then Delrules [zero_var_indexes (th RS iffD2),
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    44
                                   zero_var_indexes (th RS iffD1)]
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    45
                    else Delrules [th]
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    46
              | _ => Delrules [th];
1984
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    47
       Delsimps [th])
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    48
      handle _ => warning("DelIffs: ignoring conditional theorem\n" ^ 
2031
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    49
                          string_of_thm th)
1984
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    50
in
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    51
val AddIffs = seq addIff
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    52
val DelIffs = seq delIff
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    53
end;
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    54
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
    55
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
    56
local
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
    57
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
    58
  fun prover s = prove_goal HOL.thy s (fn _ => [blast_tac HOL_cs 1]);
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
    59
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
    60
  val P_imp_P_iff_True = prover "P --> (P = True)" RS mp;
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
    61
  val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection;
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
    62
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
    63
  val not_P_imp_P_iff_F = prover "~P --> (P = False)" RS mp;
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
    64
  val not_P_imp_P_eq_False = not_P_imp_P_iff_F RS eq_reflection;
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
    65
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
    66
  fun atomize pairs =
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
    67
    let fun atoms th =
2031
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    68
          (case concl_of th of
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    69
             Const("Trueprop",_) $ p =>
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    70
               (case head_of p of
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    71
                  Const(a,_) =>
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    72
                    (case assoc(pairs,a) of
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    73
                       Some(rls) => flat (map atoms ([th] RL rls))
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    74
                     | None => [th])
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    75
                | _ => [th])
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    76
           | _ => [th])
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
    77
    in atoms end;
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
    78
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
    79
  fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th;
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
    80
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
    81
in
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
    82
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
    83
  fun mk_meta_eq r = case concl_of r of
2031
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
    84
          Const("==",_)$_$_ => r
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
    85
      |   _$(Const("op =",_)$_$_) => r RS eq_reflection
2718
460fd0f8d478 Renamed constant "not" to "Not"
paulson
parents: 2636
diff changeset
    86
      |   _$(Const("Not",_)$_) => r RS not_P_imp_P_eq_False
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
    87
      |   _ => r RS P_imp_P_eq_True;
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
    88
  (* last 2 lines requires all formulae to be of the from Trueprop(.) *)
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
    89
2082
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
    90
val simp_thms = map prover
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
    91
 [ "(x=x) = True",
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
    92
   "(~True) = False", "(~False) = True", "(~ ~ P) = P",
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
    93
   "(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))",
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
    94
   "(True=P) = P", "(P=True) = P",
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
    95
   "(True --> P) = P", "(False --> P) = True", 
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
    96
   "(P --> True) = True", "(P --> P) = True",
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
    97
   "(P --> False) = (~P)", "(P --> ~P) = (~P)",
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
    98
   "(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
    99
   "(P & False) = False", "(False & P) = False",
9741c4c6b62b Added P&P&Q = P&Q and P|P|Q = P|Q.
nipkow
parents: 2748
diff changeset
   100
   "(P & P) = P", "(P & (P & Q)) = (P & Q)",
2082
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
   101
   "(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
   102
   "(P | False) = P", "(False | P) = P",
9741c4c6b62b Added P&P&Q = P&Q and P|P|Q = P|Q.
nipkow
parents: 2748
diff changeset
   103
   "(P | P) = P", "(P | (P | Q)) = (P | Q)",
2082
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
   104
   "((~P) = (~Q)) = (P=Q)",
2129
2ffe6e24f38d Added (? x. t=x) = True
nipkow
parents: 2098
diff changeset
   105
   "(!x.P) = P", "(? x.P) = P", "? x. x=t", "? x. t=x", 
2082
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
   106
   "(? x. x=t & P(x)) = P(t)", "(? x. t=x & P(x)) = P(t)", 
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
   107
   "(! x. x=t --> P(x)) = P(t)", "(! x. t=x --> P(x)) = P(t)" ];
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   108
988
8317adb1c444 Defined addss to perform simplification in a claset.
lcp
parents: 965
diff changeset
   109
(*Add congruence rules for = (instead of ==) *)
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   110
infix 4 addcongs delcongs;
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   111
fun ss addcongs congs = ss addeqcongs (congs RL [eq_reflection]);
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   112
fun ss delcongs congs = ss deleqcongs (congs RL [eq_reflection]);
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   113
1264
3eb91524b938 added local simpsets; removed IOA from 'make test'
clasohm
parents: 988
diff changeset
   114
fun Addcongs congs = (simpset := !simpset addcongs congs);
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   115
fun Delcongs congs = (simpset := !simpset delcongs congs);
1264
3eb91524b938 added local simpsets; removed IOA from 'make test'
clasohm
parents: 988
diff changeset
   116
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   117
fun mksimps pairs = map mk_meta_eq o atomize pairs o gen_all;
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   118
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   119
val imp_cong = impI RSN
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   120
    (2, prove_goal HOL.thy "(P=P')--> (P'--> (Q=Q'))--> ((P-->Q) = (P'-->Q'))"
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   121
        (fn _=> [blast_tac HOL_cs 1]) RS mp RS mp);
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   122
1948
78e5bfcbc1e9 Added miniscoping to the simplifier: quantifiers are now pushed in
paulson
parents: 1922
diff changeset
   123
(*Miniscoping: pushing in existential quantifiers*)
78e5bfcbc1e9 Added miniscoping to the simplifier: quantifiers are now pushed in
paulson
parents: 1922
diff changeset
   124
val ex_simps = map prover 
2031
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
   125
                ["(EX x. P x & Q)   = ((EX x.P x) & Q)",
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
   126
                 "(EX x. P & Q x)   = (P & (EX x.Q x))",
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
   127
                 "(EX x. P x | Q)   = ((EX x.P x) | Q)",
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
   128
                 "(EX x. P | Q x)   = (P | (EX x.Q x))",
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
   129
                 "(EX x. P x --> Q) = ((ALL x.P x) --> Q)",
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
   130
                 "(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
   131
78e5bfcbc1e9 Added miniscoping to the simplifier: quantifiers are now pushed in
paulson
parents: 1922
diff changeset
   132
(*Miniscoping: pushing in universal quantifiers*)
78e5bfcbc1e9 Added miniscoping to the simplifier: quantifiers are now pushed in
paulson
parents: 1922
diff changeset
   133
val all_simps = map prover
2031
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
   134
                ["(ALL x. P x & Q)   = ((ALL x.P x) & Q)",
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
   135
                 "(ALL x. P & Q x)   = (P & (ALL x.Q x))",
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
   136
                 "(ALL x. P x | Q)   = ((ALL x.P x) | Q)",
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
   137
                 "(ALL x. P | Q x)   = (P | (ALL x.Q x))",
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
   138
                 "(ALL x. P x --> Q) = ((EX x.P x) --> Q)",
03a843f0f447 Ran expandshort
paulson
parents: 2022
diff changeset
   139
                 "(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
   140
1722
bb326972ede6 Added split_inside_tac.
berghofe
parents: 1660
diff changeset
   141
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   142
2022
9d47e2962edd Fixed spelling error in comment
paulson
parents: 1984
diff changeset
   143
(* elimination of existential quantifiers in assumptions *)
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   144
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   145
val ex_all_equiv =
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   146
  let val lemma1 = prove_goal HOL.thy
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   147
        "(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)"
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   148
        (fn prems => [resolve_tac prems 1, etac exI 1]);
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   149
      val lemma2 = prove_goalw HOL.thy [Ex_def]
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   150
        "(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)"
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   151
        (fn prems => [REPEAT(resolve_tac prems 1)])
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   152
  in equal_intr lemma1 lemma2 end;
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   153
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   154
end;
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   155
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   156
fun prove nm thm  = qed_goal nm HOL.thy thm (fn _ => [blast_tac HOL_cs 1]);
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   157
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   158
prove "conj_commute" "(P&Q) = (Q&P)";
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   159
prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))";
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   160
val conj_comms = [conj_commute, conj_left_commute];
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   161
prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))";
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   162
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   163
prove "disj_commute" "(P|Q) = (Q|P)";
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   164
prove "disj_left_commute" "(P|(Q|R)) = (Q|(P|R))";
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   165
val disj_comms = [disj_commute, disj_left_commute];
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   166
prove "disj_assoc" "((P|Q)|R) = (P|(Q|R))";
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   167
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   168
prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)";
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   169
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
   170
1892
23765bc3e8e2 Added two new distributive laws
paulson
parents: 1874
diff changeset
   171
prove "disj_conj_distribL" "(P|(Q&R)) = ((P|Q) & (P|R))";
23765bc3e8e2 Added two new distributive laws
paulson
parents: 1874
diff changeset
   172
prove "disj_conj_distribR" "((P&Q)|R) = ((P|R) & (Q|R))";
23765bc3e8e2 Added two new distributive laws
paulson
parents: 1874
diff changeset
   173
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   174
prove "imp_conjR" "(P --> (Q&R)) = ((P-->Q) & (P-->R))";
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   175
prove "imp_conjL" "((P&Q) -->R)  = (P --> (Q --> R))";
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   176
prove "imp_disjL" "((P|Q) --> R) = ((P-->R)&(Q-->R))";
1892
23765bc3e8e2 Added two new distributive laws
paulson
parents: 1874
diff changeset
   177
1485
240cc98b94a7 Added qed_spec_mp to avoid renaming of bound vars in 'th RS spec'
nipkow
parents: 1465
diff changeset
   178
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
   179
prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)";
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   180
prove "not_iff" "(P~=Q) = (P = (~Q))";
1485
240cc98b94a7 Added qed_spec_mp to avoid renaming of bound vars in 'th RS spec'
nipkow
parents: 1465
diff changeset
   181
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   182
(*Avoids duplication of subgoals after expand_if, when the true and false 
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   183
  cases boil down to the same thing.*) 
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   184
prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   185
1660
8cb42cd97579 *** empty log message ***
oheimb
parents: 1655
diff changeset
   186
prove "not_all" "(~ (! x.P(x))) = (? x.~P(x))";
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   187
prove "imp_all" "((! x. P x) --> Q) = (? x. P x --> Q)";
1660
8cb42cd97579 *** empty log message ***
oheimb
parents: 1655
diff changeset
   188
prove "not_ex"  "(~ (? x.P(x))) = (! x.~P(x))";
1922
ce495557ac33 Installation of auto_tac; re-organization
paulson
parents: 1892
diff changeset
   189
prove "imp_ex" "((? x. P x) --> Q) = (! x. P x --> Q)";
1660
8cb42cd97579 *** empty log message ***
oheimb
parents: 1655
diff changeset
   190
1655
5be64540f275 Added a number of lemmas
nipkow
parents: 1548
diff changeset
   191
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
   192
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
   193
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   194
(* '&' congruence rule: not included by default!
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   195
   May slow rewrite proofs down by as much as 50% *)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   196
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   197
let val th = prove_goal HOL.thy 
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   198
                "(P=P')--> (P'--> (Q=Q'))--> ((P&Q) = (P'&Q'))"
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   199
                (fn _=> [blast_tac HOL_cs 1])
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   200
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
   201
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   202
let val th = prove_goal HOL.thy 
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   203
                "(Q=Q')--> (Q'--> (P=P'))--> ((P&Q) = (P'&Q'))"
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   204
                (fn _=> [blast_tac HOL_cs 1])
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   205
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
   206
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   207
(* '|' congruence rule: not included by default! *)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   208
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   209
let val th = prove_goal HOL.thy 
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   210
                "(P=P')--> (~P'--> (Q=Q'))--> ((P|Q) = (P'|Q'))"
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   211
                (fn _=> [blast_tac HOL_cs 1])
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   212
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
   213
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   214
prove "eq_sym_conv" "(x=y) = (y=x)";
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   215
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   216
qed_goalw "o_apply" HOL.thy [o_def] "(f o g) x = f (g x)"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   217
 (fn _ => [rtac refl 1]);
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   218
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   219
qed_goal "meta_eq_to_obj_eq" HOL.thy "x==y ==> x=y"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   220
  (fn [prem] => [rewtac prem, rtac refl 1]);
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   221
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   222
qed_goalw "if_True" HOL.thy [if_def] "(if True then x else y) = x"
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   223
 (fn _=>[blast_tac (HOL_cs addIs [select_equality]) 1]);
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   224
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   225
qed_goalw "if_False" HOL.thy [if_def] "(if False then x else y) = y"
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   226
 (fn _=>[blast_tac (HOL_cs addIs [select_equality]) 1]);
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   227
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   228
qed_goal "if_P" HOL.thy "P ==> (if P then x else y) = x"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   229
 (fn [prem] => [ stac (prem RS eqTrueI) 1, rtac if_True 1 ]);
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   230
(*
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   231
qed_goal "if_not_P" HOL.thy "~P ==> (if P then x else y) = y"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   232
 (fn [prem] => [ stac (prem RS not_P_imp_P_iff_F) 1, rtac if_False 1 ]);
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   233
*)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   234
qed_goalw "if_not_P" HOL.thy [if_def] "!!P. ~P ==> (if P then x else y) = y"
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   235
 (fn _ => [blast_tac (HOL_cs addIs [select_equality]) 1]);
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   236
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   237
qed_goal "expand_if" HOL.thy
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   238
    "P(if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   239
 (fn _=> [ (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1),
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   240
         stac if_P 2,
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   241
         stac if_not_P 1,
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   242
         REPEAT(blast_tac HOL_cs 1) ]);
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   243
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   244
qed_goal "if_bool_eq" HOL.thy
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   245
                   "(if P then Q else R) = ((P-->Q) & (~P-->R))"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   246
                   (fn _ => [rtac expand_if 1]);
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   247
2263
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   248
local val mktac = mk_case_split_tac (meta_eq_to_obj_eq RS iffD2)
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   249
in
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   250
fun split_tac splits = mktac (map mk_meta_eq splits)
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   251
end;
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   252
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   253
local val mktac = mk_case_split_inside_tac (meta_eq_to_obj_eq RS iffD2)
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   254
in
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   255
fun split_inside_tac splits = mktac (map mk_meta_eq splits)
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   256
end;
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   257
c741309167bf moved split_tac
oheimb
parents: 2251
diff changeset
   258
2251
e0e3836f333d moved if_cancel to the right place
oheimb
parents: 2250
diff changeset
   259
qed_goal "if_cancel" HOL.thy "(if c then x else x) = x"
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   260
  (fn _ => [split_tac [expand_if] 1, blast_tac HOL_cs 1]);
2251
e0e3836f333d moved if_cancel to the right place
oheimb
parents: 2250
diff changeset
   261
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   262
(** 'if' congruence rules: neither included by default! *)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   263
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   264
(*Simplifies x assuming c and y assuming ~c*)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   265
qed_goal "if_cong" HOL.thy
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   266
  "[| b=c; c ==> x=u; ~c ==> y=v |] ==>\
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   267
\  (if b then x else y) = (if c then u else v)"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   268
  (fn rew::prems =>
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   269
   [stac rew 1, stac expand_if 1, stac expand_if 1,
2935
998cb95fdd43 Yet more fast_tac->blast_tac, and other tidying
paulson
parents: 2805
diff changeset
   270
    blast_tac (HOL_cs addDs prems) 1]);
2134
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   271
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   272
(*Prevents simplification of x and y: much faster*)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   273
qed_goal "if_weak_cong" HOL.thy
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   274
  "b=c ==> (if b then x else y) = (if c then x else y)"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   275
  (fn [prem] => [rtac (prem RS arg_cong) 1]);
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   276
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   277
(*Prevents simplification of t: much faster*)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   278
qed_goal "let_weak_cong" HOL.thy
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   279
  "a = b ==> (let x=a in t(x)) = (let x=b in t(x))"
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   280
  (fn [prem] => [rtac (prem RS arg_cong) 1]);
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   281
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   282
(*In general it seems wrong to add distributive laws by default: they
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   283
  might cause exponential blow-up.  But imp_disjL has been in for a while
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   284
  and cannot be removed without affecting existing proofs.  Moreover, 
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   285
  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
   286
  grounds that it allows simplification of R in the two cases.*)
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   287
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   288
val mksimps_pairs =
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   289
  [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   290
   ("All", [spec]), ("True", []), ("False", []),
04a71407089d Renamed and shuffled a few thms.
nipkow
parents: 2129
diff changeset
   291
   ("If", [if_bool_eq RS iffD1])];
1758
60613b065e9b Added ex_imp
nipkow
parents: 1722
diff changeset
   292
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   293
fun unsafe_solver prems = FIRST'[resolve_tac (TrueI::refl::prems),
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   294
				 atac, etac FalseE];
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   295
(*No premature instantiation of variables during simplification*)
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   296
fun   safe_solver prems = FIRST'[match_tac (TrueI::refl::prems),
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   297
				 eq_assume_tac, ematch_tac [FalseE]];
2443
a81d4c219c3c factored out HOL_base_ss and val HOL_min_ss, added HOL_safe_min_ss
oheimb
parents: 2263
diff changeset
   298
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   299
val HOL_basic_ss = empty_ss setsubgoaler asm_simp_tac
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   300
			    setSSolver   safe_solver
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   301
			    setSolver  unsafe_solver
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   302
			    setmksimps (mksimps mksimps_pairs);
2443
a81d4c219c3c factored out HOL_base_ss and val HOL_min_ss, added HOL_safe_min_ss
oheimb
parents: 2263
diff changeset
   303
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   304
val HOL_ss = HOL_basic_ss addsimps ([triv_forall_equality, (* prunes params *)
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   305
				     if_True, if_False, if_cancel,
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   306
				     o_apply, imp_disjL, conj_assoc, disj_assoc,
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   307
				     de_Morgan_conj, de_Morgan_disj, 
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   308
				     not_all, not_ex, cases_simp]
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   309
				    @ ex_simps @ all_simps @ simp_thms)
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   310
			  addcongs [imp_cong];
2082
8659e3063a30 Addition of de Morgan laws
paulson
parents: 2054
diff changeset
   311
1655
5be64540f275 Added a number of lemmas
nipkow
parents: 1548
diff changeset
   312
qed_goal "if_distrib" HOL.thy
5be64540f275 Added a number of lemmas
nipkow
parents: 1548
diff changeset
   313
  "f(if c then x else y) = (if c then f x else f y)" 
5be64540f275 Added a number of lemmas
nipkow
parents: 1548
diff changeset
   314
  (fn _ => [simp_tac (HOL_ss setloop (split_tac [expand_if])) 1]);
5be64540f275 Added a number of lemmas
nipkow
parents: 1548
diff changeset
   315
2097
076a8d2f972b bound o_apply theorem to thy
oheimb
parents: 2082
diff changeset
   316
qed_goalw "o_assoc" HOL.thy [o_def] "f o (g o h) = f o g o h"
2098
2bfc0675c92f corrected `correction` of o_assoc (of version 1.14),
oheimb
parents: 2097
diff changeset
   317
  (fn _ => [rtac ext 1, rtac refl 1]);
1984
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   318
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   319
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   320
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   321
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   322
(*** Install simpsets and datatypes in theory structure ***)
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   323
2251
e0e3836f333d moved if_cancel to the right place
oheimb
parents: 2250
diff changeset
   324
simpset := HOL_ss;
1984
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   325
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   326
exception SS_DATA of simpset;
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   327
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   328
let fun merge [] = SS_DATA empty_ss
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   329
      | merge ss = let val ss = map (fn SS_DATA x => x) ss;
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   330
                   in SS_DATA (foldl merge_ss (hd ss, tl ss)) end;
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   331
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   332
    fun put (SS_DATA ss) = simpset := ss;
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   333
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   334
    fun get () = SS_DATA (!simpset);
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   335
in add_thydata "HOL"
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   336
     ("simpset", ThyMethods {merge = merge, put = put, get = get})
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   337
end;
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   338
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   339
type dtype_info = {case_const:term, case_rewrites:thm list,
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   340
                   constructors:term list, nchotomy:thm, case_cong:thm};
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   341
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   342
exception DT_DATA of (string * dtype_info) list;
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   343
val datatypes = ref [] : (string * dtype_info) list ref;
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   344
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   345
let fun merge [] = DT_DATA []
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   346
      | merge ds =
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   347
          let val ds = map (fn DT_DATA x => x) ds;
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   348
          in DT_DATA (foldl (gen_union eq_fst) (hd ds, tl ds)) end;
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   349
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   350
    fun put (DT_DATA ds) = datatypes := ds;
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   351
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   352
    fun get () = DT_DATA (!datatypes);
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   353
in add_thydata "HOL"
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   354
     ("datatypes", ThyMethods {merge = merge, put = put, get = get})
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   355
end;
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   356
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   357
5cf82dc3ce67 Installed AddIffs, and some code from HOL.ML
paulson
parents: 1968
diff changeset
   358
add_thy_reader_file "thy_data.ML";
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   359
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   360
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   361
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   362
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   363
(*** Integration of simplifier with classical reasoner ***)
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   364
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   365
(* rot_eq_tac rotates the first equality premise of subgoal i to the front,
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   366
   fails if there is no equaliy or if an equality is already at the front *)
2805
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   367
fun rot_eq_tac i = 
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   368
  let fun is_eq (Const ("Trueprop", _) $ (Const("op =",_) $ _ $ _)) = true
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   369
	| is_eq _ = false;
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   370
      fun find_eq n [] = None
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   371
	| find_eq n (t :: ts) = if (is_eq t) then Some n 
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   372
				else find_eq (n + 1) ts;
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   373
      fun rot_eq state = 
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   374
	  let val (_, _, Bi, _) = dest_state (state, i) 
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   375
	  in  case find_eq 0 (Logic.strip_assums_hyp Bi) of
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   376
		  None   => no_tac
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   377
		| Some 0 => no_tac
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   378
		| Some n => rotate_tac n i
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   379
	  end;
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   380
  in STATE rot_eq end;
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   381
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   382
(*an unsatisfactory fix for the incomplete asm_full_simp_tac!
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   383
  better: asm_really_full_simp_tac, a yet to be implemented version of
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   384
			asm_full_simp_tac that applies all equalities in the
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   385
			premises to all the premises *)
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   386
fun safe_asm_more_full_simp_tac ss = TRY o rot_eq_tac THEN' 
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   387
				     safe_asm_full_simp_tac ss;
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   388
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   389
(*Add a simpset to a classical set!*)
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   390
infix 4 addss;
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   391
fun cs addss ss = cs addSaltern (CHANGED o (safe_asm_more_full_simp_tac ss));
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   392
(*old version, for compatibility with unstable old proofs*)
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   393
infix 4 unsafe_addss;
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   394
fun cs unsafe_addss ss = cs addbefore asm_full_simp_tac ss;
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   395
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   396
fun Addss ss = (claset := !claset addss ss);
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   397
(*old version, for compatibility with unstable old proofs*)
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   398
fun Unsafe_Addss ss = (claset := !claset unsafe_addss ss);
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   399
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   400
(*Designed to be idempotent, except if best_tac instantiates variables
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   401
  in some of the subgoals*)
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   402
(*old version, for compatibility with unstable old proofs*)
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   403
fun unsafe_auto_tac (cs,ss) = 
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   404
    ALLGOALS (asm_full_simp_tac ss) THEN
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   405
    REPEAT   (safe_tac cs THEN ALLGOALS (asm_full_simp_tac ss)) THEN
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   406
    REPEAT   (FIRSTGOAL (best_tac (cs addss ss))) THEN
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   407
    prune_params_tac;
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   408
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   409
type clasimpset = (claset * simpset);
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   410
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   411
val HOL_css = (HOL_cs, HOL_ss);
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   412
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   413
fun pair_upd1 f ((a,b),x) = (f(a,x), b);
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   414
fun pair_upd2 f ((a,b),x) = (a, f(b,x));
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   415
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   416
infix 4 addSIs2 addSEs2 addSDs2 addIs2 addEs2 addDs2
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   417
	addsimps2 delsimps2 addcongs2 delcongs2;
2748
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   418
fun op addSIs2   arg = pair_upd1 (op addSIs) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   419
fun op addSEs2   arg = pair_upd1 (op addSEs) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   420
fun op addSDs2   arg = pair_upd1 (op addSDs) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   421
fun op addIs2    arg = pair_upd1 (op addIs ) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   422
fun op addEs2    arg = pair_upd1 (op addEs ) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   423
fun op addDs2    arg = pair_upd1 (op addDs ) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   424
fun op addsimps2 arg = pair_upd2 (op addsimps) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   425
fun op delsimps2 arg = pair_upd2 (op delsimps) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   426
fun op addcongs2 arg = pair_upd2 (op addcongs) arg;
3ae9ccdd701e Eta-expanded some declarations for compatibility with value polymorphism
paulson
parents: 2718
diff changeset
   427
fun op delcongs2 arg = pair_upd2 (op delcongs) arg;
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   428
2805
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   429
fun auto_tac (cs,ss) = 
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   430
    let val cs' = cs addss ss 
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   431
    in  EVERY [TRY (safe_tac cs'),
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   432
	       REPEAT (FIRSTGOAL (fast_tac cs')),
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   433
	       prune_params_tac] 
6e5b2d6503eb Made the indentation rational
paulson
parents: 2800
diff changeset
   434
    end;
2636
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   435
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   436
fun Auto_tac () = auto_tac (!claset, !simpset);
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   437
4b30dbe4a020 added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents: 2595
diff changeset
   438
fun auto () = by (Auto_tac ());