author  ballarin 
Wed, 19 Jul 2006 19:25:58 +0200  
changeset 20168  ed7bced29e1b 
parent 18708  4b3dadb4fe33 
child 20223  89d2758ecddf 
permissions  rwrr 
9889  1 
(* Title: FOL/simpdata.ML 
0  2 
ID: $Id$ 
1459  3 
Author: Lawrence C Paulson, Cambridge University Computer Laboratory 
282  4 
Copyright 1994 University of Cambridge 
0  5 

9889  6 
Simplification data for FOL. 
0  7 
*) 
8 

9300  9 

5496  10 
(* Elimination of True from asumptions: *) 
11 

12038  12 
bind_thm ("True_implies_equals", prove_goal IFOL.thy 
5496  13 
"(True ==> PROP P) == PROP P" 
14 
(K [rtac equal_intr_rule 1, atac 2, 

15 
METAHYPS (fn prems => resolve_tac prems 1) 1, 

12038  16 
rtac TrueI 1])); 
5496  17 

18 

0  19 
(*** Rewrite rules ***) 
20 

10431  21 
fun int_prove_fun s = 
22 
(writeln s; 

282  23 
prove_goal IFOL.thy s 
10431  24 
(fn prems => [ (cut_facts_tac prems 1), 
2601
b301958c465d
Renamed structure Int (intuitionistic prover) to IntPr to prevent clash
paulson
parents:
2469
diff
changeset

25 
(IntPr.fast_tac 1) ])); 
0  26 

12038  27 
bind_thms ("conj_simps", map int_prove_fun 
1459  28 
["P & True <> P", "True & P <> P", 
0  29 
"P & False <> False", "False & P <> False", 
2801  30 
"P & P <> P", "P & P & Q <> P & Q", 
1459  31 
"P & ~P <> False", "~P & P <> False", 
12038  32 
"(P & Q) & R <> P & (Q & R)"]); 
0  33 

12038  34 
bind_thms ("disj_simps", map int_prove_fun 
1459  35 
["P  True <> True", "True  P <> True", 
36 
"P  False <> P", "False  P <> P", 

2801  37 
"P  P <> P", "P  P  Q <> P  Q", 
12038  38 
"(P  Q)  R <> P  (Q  R)"]); 
0  39 

12038  40 
bind_thms ("not_simps", map int_prove_fun 
282  41 
["~(PQ) <> ~P & ~Q", 
12038  42 
"~ False <> True", "~ True <> False"]); 
0  43 

12038  44 
bind_thms ("imp_simps", map int_prove_fun 
1459  45 
["(P > False) <> ~P", "(P > True) <> True", 
10431  46 
"(False > P) <> True", "(True > P) <> P", 
12038  47 
"(P > P) <> True", "(P > ~P) <> ~P"]); 
0  48 

12038  49 
bind_thms ("iff_simps", map int_prove_fun 
1459  50 
["(True <> P) <> P", "(P <> True) <> P", 
0  51 
"(P <> P) <> True", 
12038  52 
"(False <> P) <> ~P", "(P <> False) <> ~P"]); 
0  53 

4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

54 
(*The x=t versions are needed for the simplification procedures*) 
12038  55 
bind_thms ("quant_simps", map int_prove_fun 
10431  56 
["(ALL x. P) <> P", 
4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

57 
"(ALL x. x=t > P(x)) <> P(t)", 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

58 
"(ALL x. t=x > P(x)) <> P(t)", 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

59 
"(EX x. P) <> P", 
13149
773657d466cb
better simplification of trivial existential equalities
paulson
parents:
12825
diff
changeset

60 
"EX x. x=t", "EX x. t=x", 
10431  61 
"(EX x. x=t & P(x)) <> P(t)", 
12038  62 
"(EX x. t=x & P(x)) <> P(t)"]); 
0  63 

64 
(*These are NOT supplied by default!*) 

12038  65 
bind_thms ("distrib_simps", map int_prove_fun 
10431  66 
["P & (Q  R) <> P&Q  P&R", 
282  67 
"(Q  R) & P <> Q&P  R&P", 
12038  68 
"(P  Q > R) <> (P > R) & (Q > R)"]); 
0  69 

282  70 
(** Conversion into rewrite rules **) 
0  71 

12038  72 
bind_thm ("P_iff_F", int_prove_fun "~P ==> (P <> False)"); 
73 
bind_thm ("iff_reflection_F", P_iff_F RS iff_reflection); 

282  74 

12038  75 
bind_thm ("P_iff_T", int_prove_fun "P ==> (P <> True)"); 
76 
bind_thm ("iff_reflection_T", P_iff_T RS iff_reflection); 

282  77 

78 
(*Make metaequalities. The operator below is Trueprop*) 

5555  79 

282  80 
fun mk_meta_eq th = case concl_of th of 
5555  81 
_ $ (Const("op =",_)$_$_) => th RS eq_reflection 
82 
 _ $ (Const("op <>",_)$_$_) => th RS iff_reflection 

10431  83 
 _ => 
5555  84 
error("conclusion must be a =equality or <>");; 
85 

86 
fun mk_eq th = case concl_of th of 

394
432bb9995893
Modified mk_meta_eq to leave metaequlities on unchanged.
nipkow
parents:
371
diff
changeset

87 
Const("==",_)$_$_ => th 
5555  88 
 _ $ (Const("op =",_)$_$_) => mk_meta_eq th 
89 
 _ $ (Const("op <>",_)$_$_) => mk_meta_eq th 

282  90 
 _ $ (Const("Not",_)$_) => th RS iff_reflection_F 
91 
 _ => th RS iff_reflection_T; 

0  92 

6114
45958e54d72e
congruence rules finally use == instead of = and <>
paulson
parents:
5555
diff
changeset

93 
(*Replace premises x=y, X<>Y by X==Y*) 
10431  94 
val mk_meta_prems = 
95 
rule_by_tactic 

6114
45958e54d72e
congruence rules finally use == instead of = and <>
paulson
parents:
5555
diff
changeset

96 
(REPEAT_FIRST (resolve_tac [meta_eq_to_obj_eq, def_imp_iff])); 
45958e54d72e
congruence rules finally use == instead of = and <>
paulson
parents:
5555
diff
changeset

97 

9713  98 
(*Congruence rules for = or <> (instead of ==)*) 
6114
45958e54d72e
congruence rules finally use == instead of = and <>
paulson
parents:
5555
diff
changeset

99 
fun mk_meta_cong rl = 
45958e54d72e
congruence rules finally use == instead of = and <>
paulson
parents:
5555
diff
changeset

100 
standard(mk_meta_eq (mk_meta_prems rl)) 
45958e54d72e
congruence rules finally use == instead of = and <>
paulson
parents:
5555
diff
changeset

101 
handle THM _ => 
45958e54d72e
congruence rules finally use == instead of = and <>
paulson
parents:
5555
diff
changeset

102 
error("Premises and conclusion of congruence rules must use =equality or <>"); 
5555  103 

5304  104 
val mksimps_pairs = 
105 
[("op >", [mp]), ("op &", [conjunct1,conjunct2]), 

106 
("All", [spec]), ("True", []), ("False", [])]; 

107 

16019  108 
(* ###FIXME: move to simplifier.ML 
5304  109 
val mk_atomize: (string * thm list) list > thm > thm list 
110 
*) 

16019  111 
(* ###FIXME: move to simplifier.ML *) 
5304  112 
fun mk_atomize pairs = 
113 
let fun atoms th = 

114 
(case concl_of th of 

115 
Const("Trueprop",_) $ p => 

116 
(case head_of p of 

117 
Const(a,_) => 

17325  118 
(case AList.lookup (op =) pairs a of 
15570  119 
SOME(rls) => List.concat (map atoms ([th] RL rls)) 
15531  120 
 NONE => [th]) 
5304  121 
 _ => [th]) 
122 
 _ => [th]) 

123 
in atoms end; 

124 

12725  125 
fun mksimps pairs = (map mk_eq o mk_atomize pairs o gen_all); 
981  126 

2074
30a65172e003
Added the de Morgan laws (incl quantifier versions) to basic simpset
paulson
parents:
2065
diff
changeset

127 
(*** Classical laws ***) 
282  128 

10431  129 
fun prove_fun s = 
130 
(writeln s; 

7355
4c43090659ca
proper bootstrap of IFOL/FOL theories and packages;
wenzelm
parents:
6391
diff
changeset

131 
prove_goal (the_context ()) s 
10431  132 
(fn prems => [ (cut_facts_tac prems 1), 
1459  133 
(Cla.fast_tac FOL_cs 1) ])); 
745  134 

10431  135 
(*Avoids duplication of subgoals after expand_if, when the true and false 
136 
cases boil down to the same thing.*) 

12038  137 
bind_thm ("cases_simp", prove_fun "(P > Q) & (~P > Q) <> Q"); 
1953  138 

4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

139 

50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

140 
(*** Miniscoping: pushing quantifiers in 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

141 
We do NOT distribute of ALL over &, or dually that of EX over  
10431  142 
Baaz and Leitsch, On Skolemization and Proof Complexity (1994) 
4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

143 
show that this step can increase proof length! 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

144 
***) 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

145 

50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

146 
(*existential miniscoping*) 
12038  147 
bind_thms ("int_ex_simps", map int_prove_fun 
148 
["(EX x. P(x) & Q) <> (EX x. P(x)) & Q", 

149 
"(EX x. P & Q(x)) <> P & (EX x. Q(x))", 

150 
"(EX x. P(x)  Q) <> (EX x. P(x))  Q", 

151 
"(EX x. P  Q(x)) <> P  (EX x. Q(x))"]); 

4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

152 

50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

153 
(*classical rules*) 
12038  154 
bind_thms ("cla_ex_simps", map prove_fun 
155 
["(EX x. P(x) > Q) <> (ALL x. P(x)) > Q", 

156 
"(EX x. P > Q(x)) <> P > (EX x. Q(x))"]); 

0  157 

12038  158 
bind_thms ("ex_simps", int_ex_simps @ cla_ex_simps); 
4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

159 

50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

160 
(*universal miniscoping*) 
12038  161 
bind_thms ("int_all_simps", map int_prove_fun 
162 
["(ALL x. P(x) & Q) <> (ALL x. P(x)) & Q", 

163 
"(ALL x. P & Q(x)) <> P & (ALL x. Q(x))", 

164 
"(ALL x. P(x) > Q) <> (EX x. P(x)) > Q", 

165 
"(ALL x. P > Q(x)) <> P > (ALL x. Q(x))"]); 

1953  166 

4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

167 
(*classical rules*) 
12038  168 
bind_thms ("cla_all_simps", map prove_fun 
169 
["(ALL x. P(x)  Q) <> (ALL x. P(x))  Q", 

170 
"(ALL x. P  Q(x)) <> P  (ALL x. Q(x))"]); 

4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

171 

12038  172 
bind_thms ("all_simps", int_all_simps @ cla_all_simps); 
4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

173 

50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

174 

50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

175 
(*** Named rewrite rules proved for IFOL ***) 
1953  176 

1914  177 
fun int_prove nm thm = qed_goal nm IFOL.thy thm 
10431  178 
(fn prems => [ (cut_facts_tac prems 1), 
2601
b301958c465d
Renamed structure Int (intuitionistic prover) to IntPr to prevent clash
paulson
parents:
2469
diff
changeset

179 
(IntPr.fast_tac 1) ]); 
1914  180 

7355
4c43090659ca
proper bootstrap of IFOL/FOL theories and packages;
wenzelm
parents:
6391
diff
changeset

181 
fun prove nm thm = qed_goal nm (the_context ()) thm (fn _ => [Blast_tac 1]); 
1914  182 

183 
int_prove "conj_commute" "P&Q <> Q&P"; 

184 
int_prove "conj_left_commute" "P&(Q&R) <> Q&(P&R)"; 

12038  185 
bind_thms ("conj_comms", [conj_commute, conj_left_commute]); 
1914  186 

187 
int_prove "disj_commute" "PQ <> QP"; 

188 
int_prove "disj_left_commute" "P(QR) <> Q(PR)"; 

12038  189 
bind_thms ("disj_comms", [disj_commute, disj_left_commute]); 
1914  190 

191 
int_prove "conj_disj_distribL" "P&(QR) <> (P&Q  P&R)"; 

192 
int_prove "conj_disj_distribR" "(PQ)&R <> (P&R  Q&R)"; 

193 

194 
int_prove "disj_conj_distribL" "P(Q&R) <> (PQ) & (PR)"; 

195 
int_prove "disj_conj_distribR" "(P&Q)R <> (PR) & (QR)"; 

196 

197 
int_prove "imp_conj_distrib" "(P > (Q&R)) <> (P>Q) & (P>R)"; 

198 
int_prove "imp_conj" "((P&Q)>R) <> (P > (Q > R))"; 

199 
int_prove "imp_disj" "(PQ > R) <> (P>R) & (Q>R)"; 

200 

3910  201 
prove "imp_disj1" "(P>Q)  R <> (P>Q  R)"; 
202 
prove "imp_disj2" "Q  (P>R) <> (P>Q  R)"; 

203 

1914  204 
int_prove "de_Morgan_disj" "(~(P  Q)) <> (~P & ~Q)"; 
205 
prove "de_Morgan_conj" "(~(P & Q)) <> (~P  ~Q)"; 

206 

12765  207 
prove "not_imp" "~(P > Q) <> (P & ~Q)"; 
1914  208 
prove "not_iff" "~(P <> Q) <> (P <> ~Q)"; 
209 

3835  210 
prove "not_all" "(~ (ALL x. P(x))) <> (EX x.~P(x))"; 
211 
prove "imp_all" "((ALL x. P(x)) > Q) <> (EX x. P(x) > Q)"; 

212 
int_prove "not_ex" "(~ (EX x. P(x))) <> (ALL x.~P(x))"; 

1914  213 
int_prove "imp_ex" "((EX x. P(x)) > Q) <> (ALL x. P(x) > Q)"; 
214 

215 
int_prove "ex_disj_distrib" 

216 
"(EX x. P(x)  Q(x)) <> ((EX x. P(x))  (EX x. Q(x)))"; 

217 
int_prove "all_conj_distrib" 

218 
"(ALL x. P(x) & Q(x)) <> ((ALL x. P(x)) & (ALL x. Q(x)))"; 

219 

220 

11232  221 
local 
222 
val uncurry = prove_goal (the_context()) "P > Q > R ==> P & Q > R" 

223 
(fn prems => [cut_facts_tac prems 1, Blast_tac 1]); 

224 

225 
val iff_allI = allI RS 

226 
prove_goal (the_context()) "ALL x. P(x) <> Q(x) ==> (ALL x. P(x)) <> (ALL x. Q(x))" 

227 
(fn prems => [cut_facts_tac prems 1, Blast_tac 1]) 

12526
1b9db2581fe2
mods due to changed 1point simprocs (quantifier1).
nipkow
parents:
12038
diff
changeset

228 
val iff_exI = allI RS 
1b9db2581fe2
mods due to changed 1point simprocs (quantifier1).
nipkow
parents:
12038
diff
changeset

229 
prove_goal (the_context()) "ALL x. P(x) <> Q(x) ==> (EX x. P(x)) <> (EX x. Q(x))" 
1b9db2581fe2
mods due to changed 1point simprocs (quantifier1).
nipkow
parents:
12038
diff
changeset

230 
(fn prems => [cut_facts_tac prems 1, Blast_tac 1]) 
1b9db2581fe2
mods due to changed 1point simprocs (quantifier1).
nipkow
parents:
12038
diff
changeset

231 

1b9db2581fe2
mods due to changed 1point simprocs (quantifier1).
nipkow
parents:
12038
diff
changeset

232 
val all_comm = prove_goal (the_context()) "(ALL x y. P(x,y)) <> (ALL y x. P(x,y))" 
1b9db2581fe2
mods due to changed 1point simprocs (quantifier1).
nipkow
parents:
12038
diff
changeset

233 
(fn _ => [Blast_tac 1]) 
1b9db2581fe2
mods due to changed 1point simprocs (quantifier1).
nipkow
parents:
12038
diff
changeset

234 
val ex_comm = prove_goal (the_context()) "(EX x y. P(x,y)) <> (EX y x. P(x,y))" 
1b9db2581fe2
mods due to changed 1point simprocs (quantifier1).
nipkow
parents:
12038
diff
changeset

235 
(fn _ => [Blast_tac 1]) 
11232  236 
in 
237 

4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

238 
(** make simplification procedures for quantifier elimination **) 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

239 
structure Quantifier1 = Quantifier1Fun( 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

240 
struct 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

241 
(*abstract syntax*) 
15531  242 
fun dest_eq((c as Const("op =",_)) $ s $ t) = SOME(c,s,t) 
243 
 dest_eq _ = NONE; 

244 
fun dest_conj((c as Const("op &",_)) $ s $ t) = SOME(c,s,t) 

245 
 dest_conj _ = NONE; 

246 
fun dest_imp((c as Const("op >",_)) $ s $ t) = SOME(c,s,t) 

247 
 dest_imp _ = NONE; 

4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

248 
val conj = FOLogic.conj 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

249 
val imp = FOLogic.imp 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

250 
(*rules*) 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

251 
val iff_reflection = iff_reflection 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

252 
val iffI = iffI 
12526
1b9db2581fe2
mods due to changed 1point simprocs (quantifier1).
nipkow
parents:
12038
diff
changeset

253 
val iff_trans = iff_trans 
4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

254 
val conjI= conjI 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

255 
val conjE= conjE 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

256 
val impI = impI 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

257 
val mp = mp 
11232  258 
val uncurry = uncurry 
4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

259 
val exI = exI 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

260 
val exE = exE 
11232  261 
val iff_allI = iff_allI 
12526
1b9db2581fe2
mods due to changed 1point simprocs (quantifier1).
nipkow
parents:
12038
diff
changeset

262 
val iff_exI = iff_exI 
1b9db2581fe2
mods due to changed 1point simprocs (quantifier1).
nipkow
parents:
12038
diff
changeset

263 
val all_comm = all_comm 
1b9db2581fe2
mods due to changed 1point simprocs (quantifier1).
nipkow
parents:
12038
diff
changeset

264 
val ex_comm = ex_comm 
4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

265 
end); 
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

266 

11232  267 
end; 
268 

13462  269 
val defEX_regroup = 
17002  270 
Simplifier.simproc (the_context ()) 
13462  271 
"defined EX" ["EX x. P(x)"] Quantifier1.rearrange_ex; 
4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

272 

50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

273 
val defALL_regroup = 
17002  274 
Simplifier.simproc (the_context ()) 
13462  275 
"defined ALL" ["ALL x. P(x)"] Quantifier1.rearrange_all; 
4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

276 

50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

277 

50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

278 
(*** Case splitting ***) 
0  279 

12038  280 
bind_thm ("meta_eq_to_iff", prove_goal IFOL.thy "x==y ==> x<>y" 
281 
(fn [prem] => [rewtac prem, rtac iffI 1, atac 1, atac 1])); 

1722  282 

5304  283 
structure SplitterData = 
284 
struct 

285 
structure Simplifier = Simplifier 

5555  286 
val mk_eq = mk_eq 
5304  287 
val meta_eq_to_iff = meta_eq_to_iff 
288 
val iffD = iffD2 

289 
val disjE = disjE 

290 
val conjE = conjE 

291 
val exE = exE 

292 
val contrapos = contrapos 

293 
val contrapos2 = contrapos2 

294 
val notnotD = notnotD 

295 
end; 

1722  296 

5304  297 
structure Splitter = SplitterFun(SplitterData); 
1722  298 

5304  299 
val split_tac = Splitter.split_tac; 
300 
val split_inside_tac = Splitter.split_inside_tac; 

301 
val split_asm_tac = Splitter.split_asm_tac; 

5307  302 
val op addsplits = Splitter.addsplits; 
303 
val op delsplits = Splitter.delsplits; 

5304  304 
val Addsplits = Splitter.Addsplits; 
305 
val Delsplits = Splitter.Delsplits; 

4325  306 

307 

2074
30a65172e003
Added the de Morgan laws (incl quantifier versions) to basic simpset
paulson
parents:
2065
diff
changeset

308 
(*** Standard simpsets ***) 
30a65172e003
Added the de Morgan laws (incl quantifier versions) to basic simpset
paulson
parents:
2065
diff
changeset

309 

30a65172e003
Added the de Morgan laws (incl quantifier versions) to basic simpset
paulson
parents:
2065
diff
changeset

310 
structure Induction = InductionFun(struct val spec=IFOL.spec end); 
30a65172e003
Added the de Morgan laws (incl quantifier versions) to basic simpset
paulson
parents:
2065
diff
changeset

311 

4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

312 
open Induction; 
2074
30a65172e003
Added the de Morgan laws (incl quantifier versions) to basic simpset
paulson
parents:
2065
diff
changeset

313 

5555  314 

12038  315 
bind_thms ("meta_simps", 
316 
[triv_forall_equality, (* prunes params *) 

317 
True_implies_equals]); (* prune asms `True' *) 

5496  318 

12038  319 
bind_thms ("IFOL_simps", 
320 
[refl RS P_iff_T] @ conj_simps @ disj_simps @ not_simps @ 

321 
imp_simps @ iff_simps @ quant_simps); 

2074
30a65172e003
Added the de Morgan laws (incl quantifier versions) to basic simpset
paulson
parents:
2065
diff
changeset

322 

12038  323 
bind_thm ("notFalseI", int_prove_fun "~False"); 
324 
bind_thms ("triv_rls", [TrueI,refl,reflexive_thm,iff_refl,notFalseI]); 

2074
30a65172e003
Added the de Morgan laws (incl quantifier versions) to basic simpset
paulson
parents:
2065
diff
changeset

325 

2633
37c0b5a7ee5d
added delcongs, Delcongs, unsafe_solver, safe_solver, FOL_basic_ss,
oheimb
parents:
2601
diff
changeset

326 
fun unsafe_solver prems = FIRST'[resolve_tac (triv_rls@prems), 
9713  327 
atac, etac FalseE]; 
2633
37c0b5a7ee5d
added delcongs, Delcongs, unsafe_solver, safe_solver, FOL_basic_ss,
oheimb
parents:
2601
diff
changeset

328 
(*No premature instantiation of variables during simplification*) 
37c0b5a7ee5d
added delcongs, Delcongs, unsafe_solver, safe_solver, FOL_basic_ss,
oheimb
parents:
2601
diff
changeset

329 
fun safe_solver prems = FIRST'[match_tac (triv_rls@prems), 
9713  330 
eq_assume_tac, ematch_tac [FalseE]]; 
2633
37c0b5a7ee5d
added delcongs, Delcongs, unsafe_solver, safe_solver, FOL_basic_ss,
oheimb
parents:
2601
diff
changeset

331 

3910  332 
(*No simprules, but basic infastructure for simplification*) 
17892  333 
val FOL_basic_ss = 
334 
Simplifier.theory_context (the_context ()) empty_ss 

10431  335 
setsubgoaler asm_simp_tac 
336 
setSSolver (mk_solver "FOL safe" safe_solver) 

337 
setSolver (mk_solver "FOL unsafe" unsafe_solver) 

338 
setmksimps (mksimps mksimps_pairs) 

339 
setmkcong mk_meta_cong; 

5304  340 

18324  341 
fun unfold_tac ths = 
342 
let val ss0 = Simplifier.clear_ss FOL_basic_ss addsimps ths 

343 
in fn ss => ALLGOALS (full_simp_tac (Simplifier.inherit_context ss ss0)) end; 

17002  344 

2633
37c0b5a7ee5d
added delcongs, Delcongs, unsafe_solver, safe_solver, FOL_basic_ss,
oheimb
parents:
2601
diff
changeset

345 

3910  346 
(*intuitionistic simprules only*) 
10431  347 
val IFOL_ss = FOL_basic_ss 
348 
addsimps (meta_simps @ IFOL_simps @ int_ex_simps @ int_all_simps) 

349 
addsimprocs [defALL_regroup, defEX_regroup] 

350 
addcongs [imp_cong]; 

2074
30a65172e003
Added the de Morgan laws (incl quantifier versions) to basic simpset
paulson
parents:
2065
diff
changeset

351 

12038  352 
bind_thms ("cla_simps", 
353 
[de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, 

12825  354 
not_imp, not_all, not_ex, cases_simp] @ 
12038  355 
map prove_fun 
356 
["~(P&Q) <> ~P  ~Q", 

357 
"P  ~P", "~P  P", 

358 
"~ ~ P <> P", "(~P > P) <> P", 

359 
"(~P <> ~Q) <> (P<>Q)"]); 

2074
30a65172e003
Added the de Morgan laws (incl quantifier versions) to basic simpset
paulson
parents:
2065
diff
changeset

360 

3910  361 
(*classical simprules too*) 
4349
50403e5a44c0
Instantiated the onepointrule quantifier simpprocs for FOL
paulson
parents:
4325
diff
changeset

362 
val FOL_ss = IFOL_ss addsimps (cla_simps @ cla_ex_simps @ cla_all_simps); 
2074
30a65172e003
Added the de Morgan laws (incl quantifier versions) to basic simpset
paulson
parents:
2065
diff
changeset

363 

18708  364 
val simpsetup = (fn thy => (change_simpset_of thy (fn _ => FOL_ss); thy)); 
2633
37c0b5a7ee5d
added delcongs, Delcongs, unsafe_solver, safe_solver, FOL_basic_ss,
oheimb
parents:
2601
diff
changeset

365 

37c0b5a7ee5d
added delcongs, Delcongs, unsafe_solver, safe_solver, FOL_basic_ss,
oheimb
parents:
2601
diff
changeset

366 

5219  367 
(*** integration of simplifier with classical reasoner ***) 
2633
37c0b5a7ee5d
added delcongs, Delcongs, unsafe_solver, safe_solver, FOL_basic_ss,
oheimb
parents:
2601
diff
changeset

368 

5219  369 
structure Clasimp = ClasimpFun 
8472  370 
(structure Simplifier = Simplifier and Splitter = Splitter 
9851  371 
and Classical = Cla and Blast = Blast 
18529  372 
val iffD1 = iffD1 val iffD2 = iffD2 val notE = notE); 
4652
d24cca140eeb
factored out common code of HOL/simpdata.ML and FOL/simpdata.ML concerning
oheimb
parents:
4649
diff
changeset

373 
open Clasimp; 
2633
37c0b5a7ee5d
added delcongs, Delcongs, unsafe_solver, safe_solver, FOL_basic_ss,
oheimb
parents:
2601
diff
changeset

374 

37c0b5a7ee5d
added delcongs, Delcongs, unsafe_solver, safe_solver, FOL_basic_ss,
oheimb
parents:
2601
diff
changeset

375 
val FOL_css = (FOL_cs, FOL_ss); 