author  nipkow 
Fri, 24 Nov 2000 16:49:27 +0100  
changeset 10519  ade64af4c57c 
parent 10231  178a272bceeb 
child 11003  ee0838d89deb 
permissions  rwrr 
1465  1 
(* Title: HOL/simpdata.ML 
923  2 
ID: $Id$ 
1465  3 
Author: Tobias Nipkow 
923  4 
Copyright 1991 University of Cambridge 
5 

5304  6 
Instantiation of the generic simplifier for HOL. 
923  7 
*) 
8 

1984  9 
section "Simplifier"; 
10 

7357  11 
val [prem] = goal (the_context ()) "x==y ==> x=y"; 
7031  12 
by (rewtac prem); 
13 
by (rtac refl 1); 

14 
qed "meta_eq_to_obj_eq"; 

4640  15 

9023  16 
Goal "(%s. f s) = f"; 
17 
br refl 1; 

18 
qed "eta_contract_eq"; 

19 

923  20 
local 
21 

7357  22 
fun prover s = prove_goal (the_context ()) s (fn _ => [(Blast_tac 1)]); 
923  23 

2134  24 
in 
25 

5552  26 
(*Make metaequalities. The operator below is Trueprop*) 
27 

6128  28 
fun mk_meta_eq r = r RS eq_reflection; 
9832  29 
fun safe_mk_meta_eq r = mk_meta_eq r handle Thm.THM _ => r; 
6128  30 

31 
val Eq_TrueI = mk_meta_eq(prover "P > (P = True)" RS mp); 

32 
val Eq_FalseI = mk_meta_eq(prover "~P > (P = False)" RS mp); 

5304  33 

6128  34 
fun mk_eq th = case concl_of th of 
35 
Const("==",_)$_$_ => th 

36 
 _$(Const("op =",_)$_$_) => mk_meta_eq th 

37 
 _$(Const("Not",_)$_) => th RS Eq_FalseI 

38 
 _ => th RS Eq_TrueI; 

39 
(* last 2 lines requires all formulae to be of the from Trueprop(.) *) 

5304  40 

6128  41 
fun mk_eq_True r = Some(r RS meta_eq_to_obj_eq RS Eq_TrueI); 
5552  42 

9713  43 
(*Congruence rules for = (instead of ==)*) 
6128  44 
fun mk_meta_cong rl = 
45 
standard(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl)) 

46 
handle THM _ => 

47 
error("Premises and conclusion of congruence rules must be =equalities"); 

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val not_not = prover "(~ ~ P) = P"; 
923  50 

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val simp_thms = [not_not] @ map prover 
2082  52 
[ "(x=x) = True", 
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"(~True) = False", "(~False) = True", 
2082  54 
"(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))", 
4640  55 
"(True=P) = P", "(P=True) = P", "(False=P) = (~P)", "(P=False) = (~P)", 
9713  56 
"(True > P) = P", "(False > P) = True", 
2082  57 
"(P > True) = True", "(P > P) = True", 
58 
"(P > False) = (~P)", "(P > ~P) = (~P)", 

9713  59 
"(P & True) = P", "(True & P) = P", 
2800  60 
"(P & False) = False", "(False & P) = False", 
61 
"(P & P) = P", "(P & (P & Q)) = (P & Q)", 

3913  62 
"(P & ~P) = False", "(~P & P) = False", 
9713  63 
"(P  True) = True", "(True  P) = True", 
2800  64 
"(P  False) = P", "(False  P) = P", 
65 
"(P  P) = P", "(P  (P  Q)) = (P  Q)", 

3913  66 
"(P  ~P) = True", "(~P  P) = True", 
2082  67 
"((~P) = (~Q)) = (P=Q)", 
9713  68 
"(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x", 
4351  69 
(*two needed for the onepointrule quantifier simplification procs*) 
9713  70 
"(? x. x=t & P(x)) = P(t)", (*essential for termination!!*) 
4351  71 
"(! x. t=x > P(x)) = P(t)" ]; (*covers a stray case*) 
923  72 

9875  73 
val imp_cong = standard(impI RSN 
7357  74 
(2, prove_goal (the_context ()) "(P=P')> (P'> (Q=Q'))> ((P>Q) = (P'>Q'))" 
9875  75 
(fn _=> [(Blast_tac 1)]) RS mp RS mp)); 
1922  76 

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(*Miniscoping: pushing in existential quantifiers*) 
7648  78 
val ex_simps = map prover 
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["(EX x. P x & Q) = ((EX x. P x) & Q)", 
80 
"(EX x. P & Q x) = (P & (EX x. Q x))", 

81 
"(EX x. P x  Q) = ((EX x. P x)  Q)", 

82 
"(EX x. P  Q x) = (P  (EX x. Q x))", 

83 
"(EX x. P x > Q) = ((ALL x. P x) > Q)", 

84 
"(EX x. P > Q x) = (P > (EX x. Q x))"]; 

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(*Miniscoping: pushing in universal quantifiers*) 
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val all_simps = map prover 
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["(ALL x. P x & Q) = ((ALL x. P x) & Q)", 
89 
"(ALL x. P & Q x) = (P & (ALL x. Q x))", 

90 
"(ALL x. P x  Q) = ((ALL x. P x)  Q)", 

91 
"(ALL x. P  Q x) = (P  (ALL x. Q x))", 

92 
"(ALL x. P x > Q) = ((EX x. P x) > Q)", 

93 
"(ALL x. P > Q x) = (P > (ALL x. Q x))"]; 

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923  95 

2022  96 
(* elimination of existential quantifiers in assumptions *) 
923  97 

98 
val ex_all_equiv = 

7357  99 
let val lemma1 = prove_goal (the_context ()) 
923  100 
"(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)" 
101 
(fn prems => [resolve_tac prems 1, etac exI 1]); 

7357  102 
val lemma2 = prove_goalw (the_context ()) [Ex_def] 
923  103 
"(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)" 
7031  104 
(fn prems => [(REPEAT(resolve_tac prems 1))]) 
923  105 
in equal_intr lemma1 lemma2 end; 
106 

107 
end; 

108 

7648  109 
bind_thms ("ex_simps", ex_simps); 
110 
bind_thms ("all_simps", all_simps); 

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bind_thm ("not_not", not_not); 
9875  112 
bind_thm ("imp_cong", imp_cong); 
7648  113 

3654  114 
(* Elimination of True from asumptions: *) 
115 

7357  116 
val True_implies_equals = prove_goal (the_context ()) 
3654  117 
"(True ==> PROP P) == PROP P" 
7031  118 
(fn _ => [rtac equal_intr_rule 1, atac 2, 
3654  119 
METAHYPS (fn prems => resolve_tac prems 1) 1, 
120 
rtac TrueI 1]); 

121 

7357  122 
fun prove nm thm = qed_goal nm (the_context ()) thm (fn _ => [(Blast_tac 1)]); 
923  123 

9511  124 
prove "eq_commute" "(a=b) = (b=a)"; 
7623  125 
prove "eq_left_commute" "(P=(Q=R)) = (Q=(P=R))"; 
126 
prove "eq_assoc" "((P=Q)=R) = (P=(Q=R))"; 

127 
val eq_ac = [eq_commute, eq_left_commute, eq_assoc]; 

128 

9511  129 
prove "neq_commute" "(a~=b) = (b~=a)"; 
130 

923  131 
prove "conj_commute" "(P&Q) = (Q&P)"; 
132 
prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))"; 

133 
val conj_comms = [conj_commute, conj_left_commute]; 

2134  134 
prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))"; 
923  135 

1922  136 
prove "disj_commute" "(PQ) = (QP)"; 
137 
prove "disj_left_commute" "(P(QR)) = (Q(PR))"; 

138 
val disj_comms = [disj_commute, disj_left_commute]; 

2134  139 
prove "disj_assoc" "((PQ)R) = (P(QR))"; 
1922  140 

923  141 
prove "conj_disj_distribL" "(P&(QR)) = (P&Q  P&R)"; 
142 
prove "conj_disj_distribR" "((PQ)&R) = (P&R  Q&R)"; 

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1892  144 
prove "disj_conj_distribL" "(P(Q&R)) = ((PQ) & (PR))"; 
145 
prove "disj_conj_distribR" "((P&Q)R) = ((PR) & (QR))"; 

146 

2134  147 
prove "imp_conjR" "(P > (Q&R)) = ((P>Q) & (P>R))"; 
148 
prove "imp_conjL" "((P&Q) >R) = (P > (Q > R))"; 

149 
prove "imp_disjL" "((PQ) > R) = ((P>R)&(Q>R))"; 

1892  150 

3448  151 
(*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*) 
8114  152 
prove "imp_disj_not1" "(P > Q  R) = (~Q > P > R)"; 
153 
prove "imp_disj_not2" "(P > Q  R) = (~R > P > Q)"; 

3448  154 

3904  155 
prove "imp_disj1" "((P>Q)R) = (P> QR)"; 
156 
prove "imp_disj2" "(Q(P>R)) = (P> QR)"; 

157 

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prove "de_Morgan_disj" "(~(P  Q)) = (~P & ~Q)"; 
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prove "de_Morgan_conj" "(~(P & Q)) = (~P  ~Q)"; 
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prove "not_imp" "(~(P > Q)) = (P & ~Q)"; 
1922  161 
prove "not_iff" "(P~=Q) = (P = (~Q))"; 
4743  162 
prove "disj_not1" "(~P  Q) = (P > Q)"; 
163 
prove "disj_not2" "(P  ~Q) = (Q > P)"; (* changes orientation :( *) 

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prove "imp_conv_disj" "(P > Q) = ((~P)  Q)"; 
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prove "iff_conv_conj_imp" "(P = Q) = ((P > Q) & (Q > P))"; 
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9713  169 
(*Avoids duplication of subgoals after split_if, when the true and false 
170 
cases boil down to the same thing.*) 

2134  171 
prove "cases_simp" "((P > Q) & (~P > Q)) = Q"; 
172 

3842  173 
prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))"; 
1922  174 
prove "imp_all" "((! x. P x) > Q) = (? x. P x > Q)"; 
3842  175 
prove "not_ex" "(~ (? x. P(x))) = (! x.~P(x))"; 
1922  176 
prove "imp_ex" "((? x. P x) > Q) = (! x. P x > Q)"; 
1660  177 

1655  178 
prove "ex_disj_distrib" "(? x. P(x)  Q(x)) = ((? x. P(x))  (? x. Q(x)))"; 
179 
prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))"; 

180 

2134  181 
(* '&' congruence rule: not included by default! 
182 
May slow rewrite proofs down by as much as 50% *) 

183 

9713  184 
let val th = prove_goal (the_context ()) 
2134  185 
"(P=P')> (P'> (Q=Q'))> ((P&Q) = (P'&Q'))" 
7031  186 
(fn _=> [(Blast_tac 1)]) 
2134  187 
in bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
188 

9713  189 
let val th = prove_goal (the_context ()) 
2134  190 
"(Q=Q')> (Q'> (P=P'))> ((P&Q) = (P'&Q'))" 
7031  191 
(fn _=> [(Blast_tac 1)]) 
2134  192 
in bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
193 

194 
(* '' congruence rule: not included by default! *) 

195 

9713  196 
let val th = prove_goal (the_context ()) 
2134  197 
"(P=P')> (~P'> (Q=Q'))> ((PQ) = (P'Q'))" 
7031  198 
(fn _=> [(Blast_tac 1)]) 
2134  199 
in bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
200 

201 
prove "eq_sym_conv" "(x=y) = (y=x)"; 

202 

5278  203 

204 
(** ifthenelse rules **) 

205 

7031  206 
Goalw [if_def] "(if True then x else y) = x"; 
207 
by (Blast_tac 1); 

208 
qed "if_True"; 

2134  209 

7031  210 
Goalw [if_def] "(if False then x else y) = y"; 
211 
by (Blast_tac 1); 

212 
qed "if_False"; 

2134  213 

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Goalw [if_def] "P ==> (if P then x else y) = x"; 
7031  215 
by (Blast_tac 1); 
216 
qed "if_P"; 

5304  217 

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Goalw [if_def] "~P ==> (if P then x else y) = y"; 
7031  219 
by (Blast_tac 1); 
220 
qed "if_not_P"; 

2134  221 

7031  222 
Goal "P(if Q then x else y) = ((Q > P(x)) & (~Q > P(y)))"; 
223 
by (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1); 

224 
by (stac if_P 2); 

225 
by (stac if_not_P 1); 

226 
by (ALLGOALS (Blast_tac)); 

227 
qed "split_if"; 

228 

229 
Goal "P(if Q then x else y) = (~((Q & ~P x)  (~Q & ~P y)))"; 

230 
by (stac split_if 1); 

231 
by (Blast_tac 1); 

232 
qed "split_if_asm"; 

2134  233 

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bind_thms ("if_splits", [split_if, split_if_asm]); 
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7031  236 
Goal "(if c then x else x) = x"; 
237 
by (stac split_if 1); 

238 
by (Blast_tac 1); 

239 
qed "if_cancel"; 

5304  240 

7031  241 
Goal "(if x = y then y else x) = x"; 
242 
by (stac split_if 1); 

243 
by (Blast_tac 1); 

244 
qed "if_eq_cancel"; 

5304  245 

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(*This form is useful for expanding IFs on the RIGHT of the ==> symbol*) 
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Goal "(if P then Q else R) = ((P>Q) & (~P>R))"; 
7031  248 
by (rtac split_if 1); 
249 
qed "if_bool_eq_conj"; 

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(*And this form is useful for expanding IFs on the LEFT*) 
7031  252 
Goal "(if P then Q else R) = ((P&Q)  (~P&R))"; 
253 
by (stac split_if 1); 

254 
by (Blast_tac 1); 

255 
qed "if_bool_eq_disj"; 

2134  256 

4351  257 

258 
(*** make simplification procedures for quantifier elimination ***) 

259 

9851  260 
structure Quantifier1 = Quantifier1Fun 
261 
(struct 

4351  262 
(*abstract syntax*) 
263 
fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t) 

264 
 dest_eq _ = None; 

265 
fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t) 

266 
 dest_conj _ = None; 

267 
val conj = HOLogic.conj 

268 
val imp = HOLogic.imp 

269 
(*rules*) 

270 
val iff_reflection = eq_reflection 

271 
val iffI = iffI 

272 
val sym = sym 

273 
val conjI= conjI 

274 
val conjE= conjE 

275 
val impI = impI 

276 
val impE = impE 

277 
val mp = mp 

278 
val exI = exI 

279 
val exE = exE 

280 
val allI = allI 

281 
val allE = allE 

282 
end); 

283 

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local 
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val ex_pattern = 
7357  286 
Thm.read_cterm (Theory.sign_of (the_context ())) ("EX x. P(x) & Q(x)",HOLogic.boolT) 
3913  287 

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val all_pattern = 
7357  289 
Thm.read_cterm (Theory.sign_of (the_context ())) ("ALL x. P(x) & P'(x) > Q(x)",HOLogic.boolT) 
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in 
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val defEX_regroup = 
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mk_simproc "defined EX" [ex_pattern] Quantifier1.rearrange_ex; 
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val defALL_regroup = 
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mk_simproc "defined ALL" [all_pattern] Quantifier1.rearrange_all; 
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end; 
3913  297 

4351  298 

299 
(*** Case splitting ***) 

3913  300 

5304  301 
structure SplitterData = 
302 
struct 

303 
structure Simplifier = Simplifier 

5552  304 
val mk_eq = mk_eq 
5304  305 
val meta_eq_to_iff = meta_eq_to_obj_eq 
306 
val iffD = iffD2 

307 
val disjE = disjE 

308 
val conjE = conjE 

309 
val exE = exE 

10231  310 
val contrapos = contrapos_nn 
311 
val contrapos2 = contrapos_pp 

5304  312 
val notnotD = notnotD 
313 
end; 

4681  314 

5304  315 
structure Splitter = SplitterFun(SplitterData); 
2263  316 

5304  317 
val split_tac = Splitter.split_tac; 
318 
val split_inside_tac = Splitter.split_inside_tac; 

319 
val split_asm_tac = Splitter.split_asm_tac; 

5307  320 
val op addsplits = Splitter.addsplits; 
321 
val op delsplits = Splitter.delsplits; 

5304  322 
val Addsplits = Splitter.Addsplits; 
323 
val Delsplits = Splitter.Delsplits; 

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324 

2134  325 
(*In general it seems wrong to add distributive laws by default: they 
326 
might cause exponential blowup. But imp_disjL has been in for a while 

9713  327 
and cannot be removed without affecting existing proofs. Moreover, 
2134  328 
rewriting by "(PQ > R) = ((P>R)&(Q>R))" might be justified on the 
329 
grounds that it allows simplification of R in the two cases.*) 

330 

5304  331 
fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th; 
332 

2134  333 
val mksimps_pairs = 
334 
[("op >", [mp]), ("op &", [conjunct1,conjunct2]), 

335 
("All", [spec]), ("True", []), ("False", []), 

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336 
("If", [if_bool_eq_conj RS iffD1])]; 
1758  337 

5552  338 
(* ###FIXME: move to Provers/simplifier.ML 
5304  339 
val mk_atomize: (string * thm list) list > thm > thm list 
340 
*) 

5552  341 
(* ###FIXME: move to Provers/simplifier.ML *) 
5304  342 
fun mk_atomize pairs = 
343 
let fun atoms th = 

344 
(case concl_of th of 

345 
Const("Trueprop",_) $ p => 

346 
(case head_of p of 

347 
Const(a,_) => 

348 
(case assoc(pairs,a) of 

349 
Some(rls) => flat (map atoms ([th] RL rls)) 

350 
 None => [th]) 

351 
 _ => [th]) 

352 
 _ => [th]) 

353 
in atoms end; 

354 

5552  355 
fun mksimps pairs = (map mk_eq o mk_atomize pairs o gen_all); 
5304  356 

7570  357 
fun unsafe_solver_tac prems = 
358 
FIRST'[resolve_tac(reflexive_thm::TrueI::refl::prems), atac, etac FalseE]; 

359 
val unsafe_solver = mk_solver "HOL unsafe" unsafe_solver_tac; 

360 

2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
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361 
(*No premature instantiation of variables during simplification*) 
7570  362 
fun safe_solver_tac prems = 
363 
FIRST'[match_tac(reflexive_thm::TrueI::refl::prems), 

364 
eq_assume_tac, ematch_tac [FalseE]]; 

365 
val safe_solver = mk_solver "HOL safe" safe_solver_tac; 

2443
a81d4c219c3c
factored out HOL_base_ss and val HOL_min_ss, added HOL_safe_min_ss
oheimb
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diff
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366 

9713  367 
val HOL_basic_ss = 
368 
empty_ss setsubgoaler asm_simp_tac 

369 
setSSolver safe_solver 

370 
setSolver unsafe_solver 

371 
setmksimps (mksimps mksimps_pairs) 

372 
setmkeqTrue mk_eq_True 

373 
setmkcong mk_meta_cong; 

2443
a81d4c219c3c
factored out HOL_base_ss and val HOL_min_ss, added HOL_safe_min_ss
oheimb
parents:
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diff
changeset

374 

9713  375 
val HOL_ss = 
376 
HOL_basic_ss addsimps 

3446
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
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diff
changeset

377 
([triv_forall_equality, (* prunes params *) 
3654  378 
True_implies_equals, (* prune asms `True' *) 
9023  379 
eta_contract_eq, (* prunes etaexpansions *) 
4718
fc2ba9fb2135
new rewrite rules not1_or, not2_or, and if_eq_cancel
oheimb
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diff
changeset

380 
if_True, if_False, if_cancel, if_eq_cancel, 
5304  381 
imp_disjL, conj_assoc, disj_assoc, 
3904  382 
de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp, 
9969  383 
disj_not1, not_all, not_ex, cases_simp, some_eq_trivial, some_sym_eq_trivial, 
8955  384 
thm"plus_ac0.zero", thm"plus_ac0_zero_right"] 
3446
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
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diff
changeset

385 
@ ex_simps @ all_simps @ simp_thms) 
4032
4b1c69d8b767
For each datatype `t' there is now a theorem `split_t_case' of the form
nipkow
parents:
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diff
changeset

386 
addsimprocs [defALL_regroup,defEX_regroup] 
4744
4469d498cd48
moved addsplits [expand_if] from HOL_basic_ss to HOL_ss;
wenzelm
parents:
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diff
changeset

387 
addcongs [imp_cong] 
4830  388 
addsplits [split_if]; 
2082  389 

6293  390 
(*Simplifies x assuming c and y assuming ~c*) 
391 
val prems = Goalw [if_def] 

392 
"[ b=c; c ==> x=u; ~c ==> y=v ] ==> \ 

393 
\ (if b then x else y) = (if c then u else v)"; 

394 
by (asm_simp_tac (HOL_ss addsimps prems) 1); 

395 
qed "if_cong"; 

396 

7127
48e235179ffb
added parentheses to cope with a possible reduction of the precedence of unary
paulson
parents:
7031
diff
changeset

397 
(*Prevents simplification of x and y: faster and allows the execution 
48e235179ffb
added parentheses to cope with a possible reduction of the precedence of unary
paulson
parents:
7031
diff
changeset

398 
of functional programs. NOW THE DEFAULT.*) 
7031  399 
Goal "b=c ==> (if b then x else y) = (if c then x else y)"; 
400 
by (etac arg_cong 1); 

401 
qed "if_weak_cong"; 

6293  402 

403 
(*Prevents simplification of t: much faster*) 

7031  404 
Goal "a = b ==> (let x=a in t(x)) = (let x=b in t(x))"; 
405 
by (etac arg_cong 1); 

406 
qed "let_weak_cong"; 

6293  407 

7031  408 
Goal "f(if c then x else y) = (if c then f x else f y)"; 
409 
by (simp_tac (HOL_ss setloop (split_tac [split_if])) 1); 

410 
qed "if_distrib"; 

1655  411 

4327  412 
(*For expand_case_tac*) 
7584  413 
val prems = Goal "[ P ==> Q(True); ~P ==> Q(False) ] ==> Q(P)"; 
2948
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

414 
by (case_tac "P" 1); 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

415 
by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems))); 
7584  416 
qed "expand_case"; 
2948
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

417 

4327  418 
(*Used in Auth proofs. Typically P contains Vars that become instantiated 
419 
during unification.*) 

2948
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

420 
fun expand_case_tac P i = 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

421 
res_inst_tac [("P",P)] expand_case i THEN 
9713  422 
Simp_tac (i+1) THEN 
2948
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

423 
Simp_tac i; 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

424 

7584  425 
(*This lemma restricts the effect of the rewrite rule u=v to the lefthand 
426 
side of an equality. Used in {Integ,Real}/simproc.ML*) 

427 
Goal "x=y ==> (x=z) = (y=z)"; 

428 
by (asm_simp_tac HOL_ss 1); 

429 
qed "restrict_to_left"; 

2948
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

430 

7357  431 
(* default simpset *) 
9713  432 
val simpsetup = 
433 
[fn thy => (simpset_ref_of thy := HOL_ss addcongs [if_weak_cong]; thy)]; 

3615
e5322197cfea
Moved some functions which used to be part of thy_data.ML
berghofe
parents:
3577
diff
changeset

434 

4652
d24cca140eeb
factored out common code of HOL/simpdata.ML and FOL/simpdata.ML concerning
oheimb
parents:
4651
diff
changeset

435 

5219  436 
(*** integration of simplifier with classical reasoner ***) 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

437 

5219  438 
structure Clasimp = ClasimpFun 
8473  439 
(structure Simplifier = Simplifier and Splitter = Splitter 
9851  440 
and Classical = Classical and Blast = Blast 
441 
val dest_Trueprop = HOLogic.dest_Trueprop 

442 
val iff_const = HOLogic.eq_const HOLogic.boolT 

443 
val not_const = HOLogic.not_const 

444 
val notE = notE val iffD1 = iffD1 val iffD2 = iffD2 

445 
val cla_make_elim = cla_make_elim); 

4652
d24cca140eeb
factored out common code of HOL/simpdata.ML and FOL/simpdata.ML concerning
oheimb
parents:
4651
diff
changeset

446 
open Clasimp; 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

447 

4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

448 
val HOL_css = (HOL_cs, HOL_ss); 
5975
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

449 

cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

450 

8641
978db2870862
change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents:
8473
diff
changeset

451 

5975
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

452 
(*** A general refutation procedure ***) 
9713  453 

5975
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

454 
(* Parameters: 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

455 

cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

456 
test: term > bool 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

457 
tests if a term is at all relevant to the refutation proof; 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

458 
if not, then it can be discarded. Can improve performance, 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

459 
esp. if disjunctions can be discarded (no case distinction needed!). 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

460 

cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

461 
prep_tac: int > tactic 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

462 
A preparation tactic to be applied to the goal once all relevant premises 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

463 
have been moved to the conclusion. 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

464 

cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

465 
ref_tac: int > tactic 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

466 
the actual refutation tactic. Should be able to deal with goals 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

467 
[ A1; ...; An ] ==> False 
9876  468 
where the Ai are atomic, i.e. no toplevel &,  or EX 
5975
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

469 
*) 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

470 

cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

471 
fun refute_tac test prep_tac ref_tac = 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

472 
let val nnf_simps = 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

473 
[imp_conv_disj,iff_conv_conj_imp,de_Morgan_disj,de_Morgan_conj, 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

474 
not_all,not_ex,not_not]; 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

475 
val nnf_simpset = 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

476 
empty_ss setmkeqTrue mk_eq_True 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

477 
setmksimps (mksimps mksimps_pairs) 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

478 
addsimps nnf_simps; 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

479 
val prem_nnf_tac = full_simp_tac nnf_simpset; 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

480 

cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

481 
val refute_prems_tac = 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

482 
REPEAT(eresolve_tac [conjE, exE] 1 ORELSE 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

483 
filter_prems_tac test 1 ORELSE 
6301  484 
etac disjE 1) THEN 
5975
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

485 
ref_tac 1; 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

486 
in EVERY'[TRY o filter_prems_tac test, 
6128  487 
DETERM o REPEAT o etac rev_mp, prep_tac, rtac ccontr, prem_nnf_tac, 
5975
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

488 
SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)] 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

489 
end; 