src/FOLP/simpdata.ML
author haftmann
Tue Sep 20 08:21:49 2005 +0200 (2005-09-20)
changeset 17496 26535df536ae
parent 17480 fd19f77dcf60
child 26322 eaf634e975fa
permissions -rw-r--r--
slight adaptions to library changes
clasohm@1463
     1
(*  Title:      FOLP/simpdata.ML
clasohm@0
     2
    ID:         $Id$
clasohm@1459
     3
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
clasohm@0
     4
    Copyright   1991  University of Cambridge
clasohm@0
     5
wenzelm@17480
     6
Simplification data for FOLP.
clasohm@0
     7
*)
clasohm@0
     8
clasohm@0
     9
(*** Rewrite rules ***)
clasohm@0
    10
wenzelm@17480
    11
fun int_prove_fun_raw s =
wenzelm@17480
    12
    (writeln s;  prove_goal (the_context ()) s
paulson@2603
    13
       (fn prems => [ (cut_facts_tac prems 1), (IntPr.fast_tac 1) ]));
clasohm@0
    14
clasohm@0
    15
fun int_prove_fun s = int_prove_fun_raw ("?p : "^s);
clasohm@0
    16
clasohm@0
    17
val conj_rews = map int_prove_fun
clasohm@1459
    18
 ["P & True <-> P",     "True & P <-> P",
clasohm@0
    19
  "P & False <-> False", "False & P <-> False",
clasohm@0
    20
  "P & P <-> P",
clasohm@1459
    21
  "P & ~P <-> False",   "~P & P <-> False",
clasohm@0
    22
  "(P & Q) & R <-> P & (Q & R)"];
clasohm@0
    23
clasohm@0
    24
val disj_rews = map int_prove_fun
clasohm@1459
    25
 ["P | True <-> True",  "True | P <-> True",
clasohm@1459
    26
  "P | False <-> P",    "False | P <-> P",
clasohm@0
    27
  "P | P <-> P",
clasohm@0
    28
  "(P | Q) | R <-> P | (Q | R)"];
clasohm@0
    29
clasohm@0
    30
val not_rews = map int_prove_fun
clasohm@1459
    31
 ["~ False <-> True",   "~ True <-> False"];
clasohm@0
    32
clasohm@0
    33
val imp_rews = map int_prove_fun
clasohm@1459
    34
 ["(P --> False) <-> ~P",       "(P --> True) <-> True",
wenzelm@17480
    35
  "(False --> P) <-> True",     "(True --> P) <-> P",
clasohm@1459
    36
  "(P --> P) <-> True",         "(P --> ~P) <-> ~P"];
clasohm@0
    37
clasohm@0
    38
val iff_rews = map int_prove_fun
clasohm@1459
    39
 ["(True <-> P) <-> P",         "(P <-> True) <-> P",
clasohm@0
    40
  "(P <-> P) <-> True",
clasohm@1459
    41
  "(False <-> P) <-> ~P",       "(P <-> False) <-> ~P"];
clasohm@0
    42
clasohm@0
    43
val quant_rews = map int_prove_fun
wenzelm@3836
    44
 ["(ALL x. P) <-> P",    "(EX x. P) <-> P"];
clasohm@0
    45
clasohm@0
    46
(*These are NOT supplied by default!*)
clasohm@0
    47
val distrib_rews  = map int_prove_fun
clasohm@0
    48
 ["~(P|Q) <-> ~P & ~Q",
clasohm@0
    49
  "P & (Q | R) <-> P&Q | P&R", "(Q | R) & P <-> Q&P | R&P",
clasohm@0
    50
  "(P | Q --> R) <-> (P --> R) & (Q --> R)",
wenzelm@3836
    51
  "~(EX x. NORM(P(x))) <-> (ALL x. ~NORM(P(x)))",
wenzelm@3836
    52
  "((EX x. NORM(P(x))) --> Q) <-> (ALL x. NORM(P(x)) --> Q)",
wenzelm@3836
    53
  "(EX x. NORM(P(x))) & NORM(Q) <-> (EX x. NORM(P(x)) & NORM(Q))",
wenzelm@3836
    54
  "NORM(Q) & (EX x. NORM(P(x))) <-> (EX x. NORM(Q) & NORM(P(x)))"];
clasohm@0
    55
clasohm@0
    56
val P_Imp_P_iff_T = int_prove_fun_raw "p:P ==> ?p:(P <-> True)";
clasohm@0
    57
clasohm@0
    58
fun make_iff_T th = th RS P_Imp_P_iff_T;
clasohm@0
    59
clasohm@0
    60
val refl_iff_T = make_iff_T refl;
clasohm@0
    61
clasohm@0
    62
val norm_thms = [(norm_eq RS sym, norm_eq),
clasohm@1459
    63
                 (NORM_iff RS iff_sym, NORM_iff)];
clasohm@0
    64
clasohm@0
    65
clasohm@0
    66
(* Conversion into rewrite rules *)
clasohm@0
    67
clasohm@0
    68
val not_P_imp_P_iff_F = int_prove_fun_raw "p:~P ==> ?p:(P <-> False)";
clasohm@0
    69
clasohm@0
    70
fun mk_eq th = case concl_of th of
clasohm@0
    71
      _ $ (Const("op <->",_)$_$_) $ _ => th
clasohm@0
    72
    | _ $ (Const("op =",_)$_$_) $ _ => th
wenzelm@17480
    73
    | _ $ (Const("Not",_)$_) $ _ => th RS not_P_imp_P_iff_F
clasohm@0
    74
    | _ => make_iff_T th;
clasohm@0
    75
oheimb@5304
    76
oheimb@5304
    77
val mksimps_pairs =
oheimb@5304
    78
  [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
oheimb@5304
    79
   ("All", [spec]), ("True", []), ("False", [])];
clasohm@0
    80
oheimb@5304
    81
fun mk_atomize pairs =
oheimb@5304
    82
  let fun atoms th =
oheimb@5304
    83
        (case concl_of th of
oheimb@5304
    84
           Const("Trueprop",_) $ p =>
oheimb@5304
    85
             (case head_of p of
oheimb@5304
    86
                Const(a,_) =>
haftmann@17325
    87
                  (case AList.lookup (op =) pairs a of
skalberg@15570
    88
                     SOME(rls) => List.concat (map atoms ([th] RL rls))
skalberg@15531
    89
                   | NONE => [th])
oheimb@5304
    90
              | _ => [th])
oheimb@5304
    91
         | _ => [th])
oheimb@5304
    92
  in atoms end;
oheimb@5304
    93
oheimb@5304
    94
fun mk_rew_rules th = map mk_eq (mk_atomize mksimps_pairs th);
clasohm@0
    95
clasohm@0
    96
(*destruct function for analysing equations*)
clasohm@0
    97
fun dest_red(_ $ (red $ lhs $ rhs) $ _) = (red,lhs,rhs)
clasohm@0
    98
  | dest_red t = raise TERM("FOL/dest_red", [t]);
clasohm@0
    99
clasohm@0
   100
structure FOLP_SimpData : SIMP_DATA =
clasohm@0
   101
  struct
clasohm@1459
   102
  val refl_thms         = [refl, iff_refl]
clasohm@1459
   103
  val trans_thms        = [trans, iff_trans]
clasohm@1459
   104
  val red1              = iffD1
clasohm@1459
   105
  val red2              = iffD2
clasohm@1459
   106
  val mk_rew_rules      = mk_rew_rules
clasohm@1459
   107
  val case_splits       = []         (*NO IF'S!*)
clasohm@1459
   108
  val norm_thms         = norm_thms
clasohm@1459
   109
  val subst_thms        = [subst];
clasohm@1459
   110
  val dest_red          = dest_red
clasohm@0
   111
  end;
clasohm@0
   112
clasohm@0
   113
structure FOLP_Simp = SimpFun(FOLP_SimpData);
clasohm@0
   114
clasohm@0
   115
(*not a component of SIMP_DATA, but an argument of SIMP_TAC *)
wenzelm@17480
   116
val FOLP_congs =
clasohm@0
   117
   [all_cong,ex_cong,eq_cong,
clasohm@0
   118
    conj_cong,disj_cong,imp_cong,iff_cong,not_cong] @ pred_congs;
clasohm@0
   119
clasohm@0
   120
val IFOLP_rews =
wenzelm@17480
   121
   [refl_iff_T] @ conj_rews @ disj_rews @ not_rews @
clasohm@0
   122
    imp_rews @ iff_rews @ quant_rews;
clasohm@0
   123
lcp@1009
   124
open FOLP_Simp;
clasohm@0
   125
clasohm@0
   126
val auto_ss = empty_ss setauto ares_tac [TrueI];
clasohm@0
   127
clasohm@0
   128
val IFOLP_ss = auto_ss addcongs FOLP_congs addrews IFOLP_rews;
clasohm@0
   129
clasohm@0
   130
(*Classical version...*)
wenzelm@17480
   131
fun prove_fun s =
wenzelm@17480
   132
    (writeln s;  prove_goal (the_context ()) s
clasohm@0
   133
       (fn prems => [ (cut_facts_tac prems 1), (Cla.fast_tac FOLP_cs 1) ]));
clasohm@0
   134
clasohm@0
   135
val cla_rews = map prove_fun
clasohm@1459
   136
 ["?p:P | ~P",          "?p:~P | P",
clasohm@1459
   137
  "?p:~ ~ P <-> P",     "?p:(~P --> P) <-> P"];
clasohm@0
   138
clasohm@0
   139
val FOLP_rews = IFOLP_rews@cla_rews;
clasohm@0
   140
clasohm@0
   141
val FOLP_ss = auto_ss addcongs FOLP_congs addrews FOLP_rews;