author  wenzelm 
Sat, 10 Jul 1999 21:48:27 +0200  
changeset 6968  7f2977e96a5c 
parent 6915  4ab8e31a8421 
child 7031  972b5f62f476 
permissions  rwrr 
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(* Title: HOL/simpdata.ML 
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ID: $Id$ 
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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"; 
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6514  11 
(*** Addition of rules to simpsets and clasets simultaneously ***) (* FIXME move to Provers/clasimp.ML? *) 
1984  12 

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infix 4 addIffs delIffs; 
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1984  15 
(*Takes UNCONDITIONAL theorems of the form A<>B to 
2031  16 
the Safe Intr rule B==>A and 
17 
the Safe Destruct rule A==>B. 

1984  18 
Also ~A goes to the Safe Elim rule A ==> ?R 
19 
Failing other cases, A is added as a Safe Intr rule*) 

20 
local 

21 
val iff_const = HOLogic.eq_const HOLogic.boolT; 

22 

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fun addIff ((cla, simp), th) = 
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(case HOLogic.dest_Trueprop (#prop (rep_thm th)) of 
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(Const("Not", _) $ A) => 
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cla addSEs [zero_var_indexes (th RS notE)] 
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 (con $ _ $ _) => 
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if con = iff_const 
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then cla addSIs [zero_var_indexes (th RS iffD2)] 
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addSDs [zero_var_indexes (th RS iffD1)] 
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else cla addSIs [th] 
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 _ => cla addSIs [th], 
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simp addsimps [th]) 
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handle TERM _ => error ("AddIffs: theorem must be unconditional\n" ^ 
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string_of_thm th); 
1984  36 

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fun delIff ((cla, simp), th) = 
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(case HOLogic.dest_Trueprop (#prop (rep_thm th)) of 
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(Const ("Not", _) $ A) => 
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cla delrules [zero_var_indexes (th RS notE)] 
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 (con $ _ $ _) => 
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if con = iff_const 
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then cla delrules [zero_var_indexes (th RS iffD2), 
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make_elim (zero_var_indexes (th RS iffD1))] 
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else cla delrules [th] 
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 _ => cla delrules [th], 
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simp delsimps [th]) 
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handle TERM _ => (warning("DelIffs: ignoring conditional theorem\n" ^ 
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string_of_thm th); (cla, simp)); 
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fun store_clasimp (cla, simp) = (claset_ref () := cla; simpset_ref () := simp) 
1984  52 
in 
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val op addIffs = foldl addIff; 
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val op delIffs = foldl delIff; 
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fun AddIffs thms = store_clasimp ((claset (), simpset ()) addIffs thms); 
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fun DelIffs thms = store_clasimp ((claset (), simpset ()) delIffs thms); 
1984  57 
end; 
58 

5304  59 

6514  60 
(* "iff" attribute *) 
61 

62 
local 

63 
fun change_global_css f (thy, th) = 

64 
let 

65 
val cs_ref = Classical.claset_ref_of thy; 

66 
val ss_ref = Simplifier.simpset_ref_of thy; 

67 
val (cs', ss') = f ((! cs_ref, ! ss_ref), [th]); 

68 
in cs_ref := cs'; ss_ref := ss'; (thy, th) end; 

69 

70 
fun change_local_css f (ctxt, th) = 

71 
let 

72 
val cs = Classical.get_local_claset ctxt; 

73 
val ss = Simplifier.get_local_simpset ctxt; 

74 
val (cs', ss') = f ((cs, ss), [th]); 

75 
val ctxt' = 

76 
ctxt 

77 
> Classical.put_local_claset cs' 

78 
> Simplifier.put_local_simpset ss'; 

79 
in (ctxt', th) end; 

80 
in 

81 

82 
val iff_add_global = change_global_css (op addIffs); 

83 
val iff_add_local = change_local_css (op addIffs); 

84 

85 
val simpdata_setup = 

86 
[Attrib.add_attributes [("iff", (Attrib.no_args iff_add_global, Attrib.no_args iff_add_local), 

87 
"add rules to simpset and claset simultaneously")]]; 

88 

89 
end; 

90 

91 

4640  92 
qed_goal "meta_eq_to_obj_eq" HOL.thy "x==y ==> x=y" 
93 
(fn [prem] => [rewtac prem, rtac refl 1]); 

94 

923  95 
local 
96 

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fun prover s = prove_goal HOL.thy s (K [Blast_tac 1]); 
923  98 

2134  99 
in 
100 

5552  101 
(*Make metaequalities. The operator below is Trueprop*) 
102 

6128  103 
fun mk_meta_eq r = r RS eq_reflection; 
104 

105 
val Eq_TrueI = mk_meta_eq(prover "P > (P = True)" RS mp); 

106 
val Eq_FalseI = mk_meta_eq(prover "~P > (P = False)" RS mp); 

5304  107 

6128  108 
fun mk_eq th = case concl_of th of 
109 
Const("==",_)$_$_ => th 

110 
 _$(Const("op =",_)$_$_) => mk_meta_eq th 

111 
 _$(Const("Not",_)$_) => th RS Eq_FalseI 

112 
 _ => th RS Eq_TrueI; 

113 
(* last 2 lines requires all formulae to be of the from Trueprop(.) *) 

5304  114 

6128  115 
fun mk_eq_True r = Some(r RS meta_eq_to_obj_eq RS Eq_TrueI); 
5552  116 

6128  117 
fun mk_meta_cong rl = 
118 
standard(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl)) 

119 
handle THM _ => 

120 
error("Premises and conclusion of congruence rules must be =equalities"); 

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val not_not = prover "(~ ~ P) = P"; 
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val simp_thms = [not_not] @ map prover 
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[ "(x=x) = True", 
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"(~True) = False", "(~False) = True", 
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"(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))", 
4640  128 
"(True=P) = P", "(P=True) = P", "(False=P) = (~P)", "(P=False) = (~P)", 
2082  129 
"(True > P) = P", "(False > P) = True", 
130 
"(P > True) = True", "(P > P) = True", 

131 
"(P > False) = (~P)", "(P > ~P) = (~P)", 

132 
"(P & True) = P", "(True & P) = P", 

2800  133 
"(P & False) = False", "(False & P) = False", 
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"(P & P) = P", "(P & (P & Q)) = (P & Q)", 

3913  135 
"(P & ~P) = False", "(~P & P) = False", 
2082  136 
"(P  True) = True", "(True  P) = True", 
2800  137 
"(P  False) = P", "(False  P) = P", 
138 
"(P  P) = P", "(P  (P  Q)) = (P  Q)", 

3913  139 
"(P  ~P) = True", "(~P  P) = True", 
2082  140 
"((~P) = (~Q)) = (P=Q)", 
3842  141 
"(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x", 
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(*two needed for the onepointrule quantifier simplification procs*) 
143 
"(? x. x=t & P(x)) = P(t)", (*essential for termination!!*) 

144 
"(! x. t=x > P(x)) = P(t)" ]; (*covers a stray case*) 

923  145 

5552  146 
(* Add congruence rules for = (instead of ==) *) 
4351  147 

5552  148 
(* ###FIXME: Move to simplifier, 
149 
taking mk_meta_cong as input, eliminating addeqcongs and deleqcongs *) 

150 
infix 4 addcongs delcongs; 

4640  151 
fun ss addcongs congs = ss addeqcongs (map mk_meta_cong congs); 
152 
fun ss delcongs congs = ss deleqcongs (map mk_meta_cong congs); 

4086  153 
fun Addcongs congs = (simpset_ref() := simpset() addcongs congs); 
154 
fun Delcongs congs = (simpset_ref() := simpset() delcongs congs); 

1264  155 

5552  156 

1922  157 
val imp_cong = impI RSN 
158 
(2, prove_goal HOL.thy "(P=P')> (P'> (Q=Q'))> ((P>Q) = (P'>Q'))" 

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(fn _=> [Blast_tac 1]) RS mp RS mp); 
1922  160 

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(*Miniscoping: pushing in existential quantifiers*) 
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val ex_simps = map prover 
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["(EX x. P x & Q) = ((EX x. P x) & Q)", 
164 
"(EX x. P & Q x) = (P & (EX x. Q x))", 

165 
"(EX x. P x  Q) = ((EX x. P x)  Q)", 

166 
"(EX x. P  Q x) = (P  (EX x. Q x))", 

167 
"(EX x. P x > Q) = ((ALL x. P x) > Q)", 

168 
"(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 
3842  172 
["(ALL x. P x & Q) = ((ALL x. P x) & Q)", 
173 
"(ALL x. P & Q x) = (P & (ALL x. Q x))", 

174 
"(ALL x. P x  Q) = ((ALL x. P x)  Q)", 

175 
"(ALL x. P  Q x) = (P  (ALL x. Q x))", 

176 
"(ALL x. P x > Q) = ((EX x. P x) > Q)", 

177 
"(ALL x. P > Q x) = (P > (ALL x. Q x))"]; 

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923  179 

2022  180 
(* elimination of existential quantifiers in assumptions *) 
923  181 

182 
val ex_all_equiv = 

183 
let val lemma1 = prove_goal HOL.thy 

184 
"(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)" 

185 
(fn prems => [resolve_tac prems 1, etac exI 1]); 

186 
val lemma2 = prove_goalw HOL.thy [Ex_def] 

187 
"(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)" 

188 
(fn prems => [REPEAT(resolve_tac prems 1)]) 

189 
in equal_intr lemma1 lemma2 end; 

190 

191 
end; 

192 

3654  193 
(* Elimination of True from asumptions: *) 
194 

195 
val True_implies_equals = prove_goal HOL.thy 

196 
"(True ==> PROP P) == PROP P" 

4525  197 
(K [rtac equal_intr_rule 1, atac 2, 
3654  198 
METAHYPS (fn prems => resolve_tac prems 1) 1, 
199 
rtac TrueI 1]); 

200 

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fun prove nm thm = qed_goal nm HOL.thy thm (K [Blast_tac 1]); 
923  202 

203 
prove "conj_commute" "(P&Q) = (Q&P)"; 

204 
prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))"; 

205 
val conj_comms = [conj_commute, conj_left_commute]; 

2134  206 
prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))"; 
923  207 

1922  208 
prove "disj_commute" "(PQ) = (QP)"; 
209 
prove "disj_left_commute" "(P(QR)) = (Q(PR))"; 

210 
val disj_comms = [disj_commute, disj_left_commute]; 

2134  211 
prove "disj_assoc" "((PQ)R) = (P(QR))"; 
1922  212 

923  213 
prove "conj_disj_distribL" "(P&(QR)) = (P&Q  P&R)"; 
214 
prove "conj_disj_distribR" "((PQ)&R) = (P&R  Q&R)"; 

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1892  216 
prove "disj_conj_distribL" "(P(Q&R)) = ((PQ) & (PR))"; 
217 
prove "disj_conj_distribR" "((P&Q)R) = ((PR) & (QR))"; 

218 

2134  219 
prove "imp_conjR" "(P > (Q&R)) = ((P>Q) & (P>R))"; 
220 
prove "imp_conjL" "((P&Q) >R) = (P > (Q > R))"; 

221 
prove "imp_disjL" "((PQ) > R) = ((P>R)&(Q>R))"; 

1892  222 

3448  223 
(*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*) 
224 
prove "imp_disj_not1" "((P > Q  R)) = (~Q > P > R)"; 

225 
prove "imp_disj_not2" "((P > Q  R)) = (~R > P > Q)"; 

226 

3904  227 
prove "imp_disj1" "((P>Q)R) = (P> QR)"; 
228 
prove "imp_disj2" "(Q(P>R)) = (P> QR)"; 

229 

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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  233 
prove "not_iff" "(P~=Q) = (P = (~Q))"; 
4743  234 
prove "disj_not1" "(~P  Q) = (P > Q)"; 
235 
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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4830  241 
(*Avoids duplication of subgoals after split_if, when the true and false 
2134  242 
cases boil down to the same thing.*) 
243 
prove "cases_simp" "((P > Q) & (~P > Q)) = Q"; 

244 

3842  245 
prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))"; 
1922  246 
prove "imp_all" "((! x. P x) > Q) = (? x. P x > Q)"; 
3842  247 
prove "not_ex" "(~ (? x. P(x))) = (! x.~P(x))"; 
1922  248 
prove "imp_ex" "((? x. P x) > Q) = (! x. P x > Q)"; 
1660  249 

1655  250 
prove "ex_disj_distrib" "(? x. P(x)  Q(x)) = ((? x. P(x))  (? x. Q(x)))"; 
251 
prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))"; 

252 

2134  253 
(* '&' congruence rule: not included by default! 
254 
May slow rewrite proofs down by as much as 50% *) 

255 

256 
let val th = prove_goal HOL.thy 

257 
"(P=P')> (P'> (Q=Q'))> ((P&Q) = (P'&Q'))" 

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(fn _=> [Blast_tac 1]) 
2134  259 
in bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
260 

261 
let val th = prove_goal HOL.thy 

262 
"(Q=Q')> (Q'> (P=P'))> ((P&Q) = (P'&Q'))" 

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(fn _=> [Blast_tac 1]) 
2134  264 
in bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
265 

266 
(* '' congruence rule: not included by default! *) 

267 

268 
let val th = prove_goal HOL.thy 

269 
"(P=P')> (~P'> (Q=Q'))> ((PQ) = (P'Q'))" 

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270 
(fn _=> [Blast_tac 1]) 
2134  271 
in bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
272 

273 
prove "eq_sym_conv" "(x=y) = (y=x)"; 

274 

5278  275 

276 
(** ifthenelse rules **) 

277 

2134  278 
qed_goalw "if_True" HOL.thy [if_def] "(if True then x else y) = x" 
4525  279 
(K [Blast_tac 1]); 
2134  280 

281 
qed_goalw "if_False" HOL.thy [if_def] "(if False then x else y) = y" 

4525  282 
(K [Blast_tac 1]); 
2134  283 

5304  284 
qed_goalw "if_P" HOL.thy [if_def] "!!P. P ==> (if P then x else y) = x" 
285 
(K [Blast_tac 1]); 

286 

2134  287 
qed_goalw "if_not_P" HOL.thy [if_def] "!!P. ~P ==> (if P then x else y) = y" 
4525  288 
(K [Blast_tac 1]); 
2134  289 

4830  290 
qed_goal "split_if" HOL.thy 
4205
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291 
"P(if Q then x else y) = ((Q > P(x)) & (~Q > P(y)))" (K [ 
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292 
res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1, 
2134  293 
stac if_P 2, 
294 
stac if_not_P 1, 

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295 
ALLGOALS (Blast_tac)]); 
4830  296 
(* for backwards compatibility: *) 
297 
val expand_if = split_if; 

4205
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oheimb
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changeset

298 

96632970d203
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299 
qed_goal "split_if_asm" HOL.thy 
4769
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300 
"P(if Q then x else y) = (~((Q & ~P x)  (~Q & ~P y)))" 
4830  301 
(K [stac split_if 1, 
4769
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302 
Blast_tac 1]); 
2134  303 

5304  304 
qed_goal "if_cancel" HOL.thy "(if c then x else x) = x" 
305 
(K [stac split_if 1, Blast_tac 1]); 

306 

307 
qed_goal "if_eq_cancel" HOL.thy "(if x = y then y else x) = x" 

308 
(K [stac split_if 1, Blast_tac 1]); 

309 

4769
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310 
(*This form is useful for expanding IFs on the RIGHT of the ==> symbol*) 
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311 
qed_goal "if_bool_eq_conj" HOL.thy 
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312 
"(if P then Q else R) = ((P>Q) & (~P>R))" 
4830  313 
(K [rtac split_if 1]); 
4769
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314 

bb60149fe21b
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315 
(*And this form is useful for expanding IFs on the LEFT*) 
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316 
qed_goal "if_bool_eq_disj" HOL.thy 
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317 
"(if P then Q else R) = ((P&Q)  (~P&R))" 
4830  318 
(K [stac split_if 1, 
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319 
Blast_tac 1]); 
2134  320 

4351  321 

322 
(*** make simplification procedures for quantifier elimination ***) 

323 

324 
structure Quantifier1 = Quantifier1Fun( 

325 
struct 

326 
(*abstract syntax*) 

327 
fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t) 

328 
 dest_eq _ = None; 

329 
fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t) 

330 
 dest_conj _ = None; 

331 
val conj = HOLogic.conj 

332 
val imp = HOLogic.imp 

333 
(*rules*) 

334 
val iff_reflection = eq_reflection 

335 
val iffI = iffI 

336 
val sym = sym 

337 
val conjI= conjI 

338 
val conjE= conjE 

339 
val impI = impI 

340 
val impE = impE 

341 
val mp = mp 

342 
val exI = exI 

343 
val exE = exE 

344 
val allI = allI 

345 
val allE = allE 

346 
end); 

347 

4320
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348 
local 
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349 
val ex_pattern = 
6394  350 
Thm.read_cterm (Theory.sign_of HOL.thy) ("EX x. P(x) & Q(x)",HOLogic.boolT) 
3913  351 

4320
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352 
val all_pattern = 
6394  353 
Thm.read_cterm (Theory.sign_of HOL.thy) ("ALL x. P(x) & P'(x) > Q(x)",HOLogic.boolT) 
4320
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changeset

354 

24d9e6639cd4
Moved the quantifier elimination simp procs into Provers.
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changeset

355 
in 
24d9e6639cd4
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356 
val defEX_regroup = 
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357 
mk_simproc "defined EX" [ex_pattern] Quantifier1.rearrange_ex; 
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358 
val defALL_regroup = 
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359 
mk_simproc "defined ALL" [all_pattern] Quantifier1.rearrange_all; 
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360 
end; 
3913  361 

4351  362 

363 
(*** Case splitting ***) 

3913  364 

5304  365 
structure SplitterData = 
366 
struct 

367 
structure Simplifier = Simplifier 

5552  368 
val mk_eq = mk_eq 
5304  369 
val meta_eq_to_iff = meta_eq_to_obj_eq 
370 
val iffD = iffD2 

371 
val disjE = disjE 

372 
val conjE = conjE 

373 
val exE = exE 

374 
val contrapos = contrapos 

375 
val contrapos2 = contrapos2 

376 
val notnotD = notnotD 

377 
end; 

4681  378 

5304  379 
structure Splitter = SplitterFun(SplitterData); 
2263  380 

5304  381 
val split_tac = Splitter.split_tac; 
382 
val split_inside_tac = Splitter.split_inside_tac; 

383 
val split_asm_tac = Splitter.split_asm_tac; 

5307  384 
val op addsplits = Splitter.addsplits; 
385 
val op delsplits = Splitter.delsplits; 

5304  386 
val Addsplits = Splitter.Addsplits; 
387 
val Delsplits = Splitter.Delsplits; 

4718
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new rewrite rules not1_or, not2_or, and if_eq_cancel
oheimb
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changeset

388 

2134  389 
(** 'if' congruence rules: neither included by default! *) 
390 

391 
(*In general it seems wrong to add distributive laws by default: they 

392 
might cause exponential blowup. But imp_disjL has been in for a while 

393 
and cannot be removed without affecting existing proofs. Moreover, 

394 
rewriting by "(PQ > R) = ((P>R)&(Q>R))" might be justified on the 

395 
grounds that it allows simplification of R in the two cases.*) 

396 

5304  397 
fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th; 
398 

2134  399 
val mksimps_pairs = 
400 
[("op >", [mp]), ("op &", [conjunct1,conjunct2]), 

401 
("All", [spec]), ("True", []), ("False", []), 

4769
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paulson
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diff
changeset

402 
("If", [if_bool_eq_conj RS iffD1])]; 
1758  403 

5552  404 
(* ###FIXME: move to Provers/simplifier.ML 
5304  405 
val mk_atomize: (string * thm list) list > thm > thm list 
406 
*) 

5552  407 
(* ###FIXME: move to Provers/simplifier.ML *) 
5304  408 
fun mk_atomize pairs = 
409 
let fun atoms th = 

410 
(case concl_of th of 

411 
Const("Trueprop",_) $ p => 

412 
(case head_of p of 

413 
Const(a,_) => 

414 
(case assoc(pairs,a) of 

415 
Some(rls) => flat (map atoms ([th] RL rls)) 

416 
 None => [th]) 

417 
 _ => [th]) 

418 
 _ => [th]) 

419 
in atoms end; 

420 

5552  421 
fun mksimps pairs = (map mk_eq o mk_atomize pairs o gen_all); 
5304  422 

4640  423 
fun unsafe_solver prems = FIRST'[resolve_tac (reflexive_thm::TrueI::refl::prems), 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

424 
atac, etac FalseE]; 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
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diff
changeset

425 
(*No premature instantiation of variables during simplification*) 
4640  426 
fun safe_solver prems = FIRST'[match_tac (reflexive_thm::TrueI::prems), 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

427 
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

428 

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

429 
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

430 
setSSolver safe_solver 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

431 
setSolver unsafe_solver 
4677  432 
setmksimps (mksimps mksimps_pairs) 
5552  433 
setmkeqTrue mk_eq_True; 
2443
a81d4c219c3c
factored out HOL_base_ss and val HOL_min_ss, added HOL_safe_min_ss
oheimb
parents:
2263
diff
changeset

434 

3446
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

435 
val HOL_ss = 
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

436 
HOL_basic_ss addsimps 
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

437 
([triv_forall_equality, (* prunes params *) 
3654  438 
True_implies_equals, (* prune asms `True' *) 
4718
fc2ba9fb2135
new rewrite rules not1_or, not2_or, and if_eq_cancel
oheimb
parents:
4681
diff
changeset

439 
if_True, if_False, if_cancel, if_eq_cancel, 
5304  440 
imp_disjL, conj_assoc, disj_assoc, 
3904  441 
de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp, 
5447
df03d330aeab
Proved and added rewrite rule (@x. x=y) = y to simpset.
nipkow
parents:
5307
diff
changeset

442 
disj_not1, not_all, not_ex, cases_simp, Eps_eq, Eps_sym_eq] 
3446
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

443 
@ 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:
3919
diff
changeset

444 
addsimprocs [defALL_regroup,defEX_regroup] 
4744
4469d498cd48
moved addsplits [expand_if] from HOL_basic_ss to HOL_ss;
wenzelm
parents:
4743
diff
changeset

445 
addcongs [imp_cong] 
4830  446 
addsplits [split_if]; 
2082  447 

6293  448 
(*Simplifies x assuming c and y assuming ~c*) 
449 
val prems = Goalw [if_def] 

450 
"[ b=c; c ==> x=u; ~c ==> y=v ] ==> \ 

451 
\ (if b then x else y) = (if c then u else v)"; 

452 
by (asm_simp_tac (HOL_ss addsimps prems) 1); 

453 
qed "if_cong"; 

454 

455 
(*Prevents simplification of x and y: much faster*) 

456 
qed_goal "if_weak_cong" HOL.thy 

457 
"b=c ==> (if b then x else y) = (if c then x else y)" 

458 
(fn [prem] => [rtac (prem RS arg_cong) 1]); 

459 

460 
(*Prevents simplification of t: much faster*) 

461 
qed_goal "let_weak_cong" HOL.thy 

462 
"a = b ==> (let x=a in t(x)) = (let x=b in t(x))" 

463 
(fn [prem] => [rtac (prem RS arg_cong) 1]); 

464 

1655  465 
qed_goal "if_distrib" HOL.thy 
466 
"f(if c then x else y) = (if c then f x else f y)" 

4830  467 
(K [simp_tac (HOL_ss setloop (split_tac [split_if])) 1]); 
1655  468 

1984  469 

4327  470 
(*For expand_case_tac*) 
2948
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

471 
val prems = goal HOL.thy "[ P ==> Q(True); ~P ==> Q(False) ] ==> Q(P)"; 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

472 
by (case_tac "P" 1); 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

473 
by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems))); 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

474 
val expand_case = result(); 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

475 

4327  476 
(*Used in Auth proofs. Typically P contains Vars that become instantiated 
477 
during unification.*) 

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

478 
fun expand_case_tac P i = 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

479 
res_inst_tac [("P",P)] expand_case i THEN 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

480 
Simp_tac (i+1) THEN 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

481 
Simp_tac i; 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

482 

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

483 

4119  484 
(* install implicit simpset *) 
1984  485 

6915  486 
simpset_ref() := HOL_ss addcongs [if_weak_cong]; 
3615
e5322197cfea
Moved some functions which used to be part of thy_data.ML
berghofe
parents:
3577
diff
changeset

487 

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

488 

5219  489 
(*** integration of simplifier with classical reasoner ***) 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

490 

5219  491 
structure Clasimp = ClasimpFun 
5552  492 
(structure Simplifier = Simplifier 
493 
and Classical = Classical 

494 
and Blast = Blast); 

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

495 
open Clasimp; 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

496 

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

497 
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

498 

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

499 

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

500 
(*** A general refutation procedure ***) 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

501 

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

502 
(* Parameters: 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

503 

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

504 
test: term > bool 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

505 
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

506 
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

507 
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

508 

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

509 
prep_tac: int > tactic 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

510 
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

511 
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

512 

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

513 
ref_tac: int > tactic 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

514 
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

515 
[ A1; ...; An ] ==> False 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

516 
where the Ai are atomic, i.e. no toplevel &,  or ? 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

517 
*) 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

518 

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

519 
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

520 
let val nnf_simps = 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

521 
[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

522 
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

523 
val nnf_simpset = 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

524 
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

525 
setmksimps (mksimps mksimps_pairs) 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

526 
addsimps nnf_simps; 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

527 
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

528 

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

529 
val refute_prems_tac = 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

530 
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

531 
filter_prems_tac test 1 ORELSE 
6301  532 
etac disjE 1) THEN 
5975
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

533 
ref_tac 1; 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

534 
in EVERY'[TRY o filter_prems_tac test, 
6128  535 
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

536 
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

537 
end; 