src/FOL/simpdata.ML
author clasohm
Fri, 13 Oct 1995 11:48:40 +0100
changeset 1280 909079af97b7
parent 1088 fc4fb6e8a636
child 1459 d12da312eff4
permissions -rw-r--r--
corrected spelling of title
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     1
(*  Title: 	FOL/simpdata
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     2
    ID:         $Id$
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     3
    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
     4
    Copyright   1994  University of Cambridge
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     5
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     6
Simplification data for FOL
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     7
*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     8
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     9
(*** Rewrite rules ***)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    10
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    11
fun int_prove_fun s = 
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    12
 (writeln s;  
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    13
  prove_goal IFOL.thy s
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    14
   (fn prems => [ (cut_facts_tac prems 1), 
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    15
		  (Int.fast_tac 1) ]));
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    16
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    17
val conj_rews = map int_prove_fun
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    18
 ["P & True <-> P", 	 "True & P <-> P",
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    19
  "P & False <-> False", "False & P <-> False",
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    20
  "P & P <-> P",
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    21
  "P & ~P <-> False", 	 "~P & P <-> False",
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    22
  "(P & Q) & R <-> P & (Q & R)"];
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    23
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    24
val disj_rews = map int_prove_fun
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    25
 ["P | True <-> True", 	"True | P <-> True",
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    26
  "P | False <-> P", 	"False | P <-> P",
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    27
  "P | P <-> P",
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    28
  "(P | Q) | R <-> P | (Q | R)"];
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    29
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    30
val not_rews = map int_prove_fun
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    31
 ["~(P|Q)  <-> ~P & ~Q",
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    32
  "~ False <-> True",	"~ True <-> False"];
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    33
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    34
val imp_rews = map int_prove_fun
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    35
 ["(P --> False) <-> ~P",	"(P --> True) <-> True",
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    36
  "(False --> P) <-> True",	"(True --> P) <-> P", 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    37
  "(P --> P) <-> True",		"(P --> ~P) <-> ~P"];
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    38
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    39
val iff_rews = map int_prove_fun
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    40
 ["(True <-> P) <-> P", 	"(P <-> True) <-> P",
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    41
  "(P <-> P) <-> True",
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    42
  "(False <-> P) <-> ~P", 	"(P <-> False) <-> ~P"];
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    43
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    44
val quant_rews = map int_prove_fun
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    45
 ["(ALL x.P) <-> P",	"(EX x.P) <-> P"];
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    46
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    47
(*These are NOT supplied by default!*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    48
val distrib_rews  = map int_prove_fun
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    49
 ["P & (Q | R) <-> P&Q | P&R", 
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    50
  "(Q | R) & P <-> Q&P | R&P",
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    51
  "(P | Q --> R) <-> (P --> R) & (Q --> R)"];
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    52
784
b5adfdad0663 conj_commute,disj_commute: new
lcp
parents: 756
diff changeset
    53
bind_thm("conj_commute", int_prove_fun "P&Q <-> Q&P");
b5adfdad0663 conj_commute,disj_commute: new
lcp
parents: 756
diff changeset
    54
bind_thm("disj_commute", int_prove_fun "P|Q <-> Q|P");
b5adfdad0663 conj_commute,disj_commute: new
lcp
parents: 756
diff changeset
    55
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    56
(** Conversion into rewrite rules **)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    57
53
f8f37a9a31dc Added gen_all to simpdata.ML.
nipkow
parents: 3
diff changeset
    58
fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th;
f8f37a9a31dc Added gen_all to simpdata.ML.
nipkow
parents: 3
diff changeset
    59
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    60
(*Make atomic rewrite rules*)
429
888bbb4119f8 atomize: borrowed HOL version, which checks for both Trueprop
lcp
parents: 394
diff changeset
    61
fun atomize r =
888bbb4119f8 atomize: borrowed HOL version, which checks for both Trueprop
lcp
parents: 394
diff changeset
    62
  case concl_of r of
888bbb4119f8 atomize: borrowed HOL version, which checks for both Trueprop
lcp
parents: 394
diff changeset
    63
    Const("Trueprop",_) $ p =>
888bbb4119f8 atomize: borrowed HOL version, which checks for both Trueprop
lcp
parents: 394
diff changeset
    64
      (case p of
888bbb4119f8 atomize: borrowed HOL version, which checks for both Trueprop
lcp
parents: 394
diff changeset
    65
	 Const("op -->",_)$_$_ => atomize(r RS mp)
888bbb4119f8 atomize: borrowed HOL version, which checks for both Trueprop
lcp
parents: 394
diff changeset
    66
       | Const("op &",_)$_$_   => atomize(r RS conjunct1) @
888bbb4119f8 atomize: borrowed HOL version, which checks for both Trueprop
lcp
parents: 394
diff changeset
    67
	  		          atomize(r RS conjunct2)
888bbb4119f8 atomize: borrowed HOL version, which checks for both Trueprop
lcp
parents: 394
diff changeset
    68
       | Const("All",_)$_      => atomize(r RS spec)
888bbb4119f8 atomize: borrowed HOL version, which checks for both Trueprop
lcp
parents: 394
diff changeset
    69
       | Const("True",_)       => []	(*True is DELETED*)
888bbb4119f8 atomize: borrowed HOL version, which checks for both Trueprop
lcp
parents: 394
diff changeset
    70
       | Const("False",_)      => []	(*should False do something?*)
888bbb4119f8 atomize: borrowed HOL version, which checks for both Trueprop
lcp
parents: 394
diff changeset
    71
       | _                     => [r])
888bbb4119f8 atomize: borrowed HOL version, which checks for both Trueprop
lcp
parents: 394
diff changeset
    72
  | _ => [r];
888bbb4119f8 atomize: borrowed HOL version, which checks for both Trueprop
lcp
parents: 394
diff changeset
    73
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    74
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    75
val P_iff_F = int_prove_fun "~P ==> (P <-> False)";
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    76
val iff_reflection_F = P_iff_F RS iff_reflection;
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    77
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    78
val P_iff_T = int_prove_fun "P ==> (P <-> True)";
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    79
val iff_reflection_T = P_iff_T RS iff_reflection;
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    80
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    81
(*Make meta-equalities.  The operator below is Trueprop*)
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    82
fun mk_meta_eq th = case concl_of th of
394
432bb9995893 Modified mk_meta_eq to leave meta-equlities on unchanged.
nipkow
parents: 371
diff changeset
    83
    Const("==",_)$_$_           => th
432bb9995893 Modified mk_meta_eq to leave meta-equlities on unchanged.
nipkow
parents: 371
diff changeset
    84
  | _ $ (Const("op =",_)$_$_)   => th RS eq_reflection
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    85
  | _ $ (Const("op <->",_)$_$_) => th RS iff_reflection
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    86
  | _ $ (Const("Not",_)$_)      => th RS iff_reflection_F
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    87
  | _                           => th RS iff_reflection_T;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    88
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    89
structure Induction = InductionFun(struct val spec=IFOL.spec end);
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    90
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    91
open Simplifier Induction;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    92
981
864370666a24 Defined addss to perform simplification in a claset.
lcp
parents: 942
diff changeset
    93
(*Add congruence rules for = or <-> (instead of ==) *)
864370666a24 Defined addss to perform simplification in a claset.
lcp
parents: 942
diff changeset
    94
infix 4 addcongs;
3
5f77582e3a89 defined local addcongs
nipkow
parents: 0
diff changeset
    95
fun ss addcongs congs =
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    96
    ss addeqcongs (congs RL [eq_reflection,iff_reflection]);
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
    97
981
864370666a24 Defined addss to perform simplification in a claset.
lcp
parents: 942
diff changeset
    98
(*Add a simpset to a classical set!*)
864370666a24 Defined addss to perform simplification in a claset.
lcp
parents: 942
diff changeset
    99
infix 4 addss;
864370666a24 Defined addss to perform simplification in a claset.
lcp
parents: 942
diff changeset
   100
fun cs addss ss = cs addbefore asm_full_simp_tac ss 1;
864370666a24 Defined addss to perform simplification in a claset.
lcp
parents: 942
diff changeset
   101
864370666a24 Defined addss to perform simplification in a claset.
lcp
parents: 942
diff changeset
   102
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   103
val IFOL_rews =
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   104
   [refl RS P_iff_T] @ conj_rews @ disj_rews @ not_rews @ 
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   105
    imp_rews @ iff_rews @ quant_rews;
3
5f77582e3a89 defined local addcongs
nipkow
parents: 0
diff changeset
   106
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   107
val notFalseI = int_prove_fun "~False";
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   108
val triv_rls = [TrueI,refl,iff_refl,notFalseI];
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   109
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   110
val IFOL_ss = 
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   111
  empty_ss 
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   112
  setmksimps (map mk_meta_eq o atomize o gen_all)
371
3a853818f1d2 FOL/simpdata: added etac FalseE in setsolver call. Toby: "now that the
lcp
parents: 282
diff changeset
   113
  setsolver  (fn prems => resolve_tac (triv_rls@prems) 
3a853818f1d2 FOL/simpdata: added etac FalseE in setsolver call. Toby: "now that the
lcp
parents: 282
diff changeset
   114
	                  ORELSE' assume_tac
3a853818f1d2 FOL/simpdata: added etac FalseE in setsolver call. Toby: "now that the
lcp
parents: 282
diff changeset
   115
	                  ORELSE' etac FalseE)
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   116
  setsubgoaler asm_simp_tac
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   117
  addsimps IFOL_rews
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   118
  addcongs [imp_cong];
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   119
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   120
(*Classical version...*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   121
fun prove_fun s = 
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   122
 (writeln s;  
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   123
  prove_goal FOL.thy s
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   124
   (fn prems => [ (cut_facts_tac prems 1), 
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   125
		  (Cla.fast_tac FOL_cs 1) ]));
745
45a789407806 added blank line
lcp
parents: 429
diff changeset
   126
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   127
val cla_rews = map prove_fun
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   128
 ["~(P&Q)  <-> ~P | ~Q",
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   129
  "P | ~P", 		"~P | P",
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   130
  "~ ~ P <-> P",	"(~P --> P) <-> P"];
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   131
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   132
val FOL_ss = IFOL_ss addsimps cla_rews;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   133
1088
fc4fb6e8a636 Imported meta_eq_to_obj_eq from HOL for use with 'split'.
lcp
parents: 981
diff changeset
   134
(*Used in ZF, perhaps elsewhere?*)
fc4fb6e8a636 Imported meta_eq_to_obj_eq from HOL for use with 'split'.
lcp
parents: 981
diff changeset
   135
val meta_eq_to_obj_eq = prove_goal IFOL.thy "x==y ==> x=y"
fc4fb6e8a636 Imported meta_eq_to_obj_eq from HOL for use with 'split'.
lcp
parents: 981
diff changeset
   136
  (fn [prem] => [rewtac prem, rtac refl 1]);
fc4fb6e8a636 Imported meta_eq_to_obj_eq from HOL for use with 'split'.
lcp
parents: 981
diff changeset
   137
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   138
(*** case splitting ***)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   139
1088
fc4fb6e8a636 Imported meta_eq_to_obj_eq from HOL for use with 'split'.
lcp
parents: 981
diff changeset
   140
qed_goal "meta_iffD" IFOL.thy "[| P==Q; Q |] ==> P"
756
e0e5c1581e4c added qed_goal for meta_iffD
clasohm
parents: 745
diff changeset
   141
        (fn [prem1,prem2] => [rewtac prem1, rtac prem2 1]);
282
731b27c90d2f FOL/simpdata: tidied
lcp
parents: 215
diff changeset
   142
942
d9edeb96b51c Enforced partial evaluation of mk_case_split_tac.
nipkow
parents: 784
diff changeset
   143
local val mktac = mk_case_split_tac meta_iffD
d9edeb96b51c Enforced partial evaluation of mk_case_split_tac.
nipkow
parents: 784
diff changeset
   144
in
d9edeb96b51c Enforced partial evaluation of mk_case_split_tac.
nipkow
parents: 784
diff changeset
   145
fun split_tac splits = mktac (map mk_meta_eq splits)
d9edeb96b51c Enforced partial evaluation of mk_case_split_tac.
nipkow
parents: 784
diff changeset
   146
end;