author  paulson 
Mon, 01 Mar 1999 18:37:23 +0100  
changeset 6293  2a4357301973 
parent 6128  2acc5d36610c 
child 6301  08245f5a436d 
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 

11 
(*** Addition of rules to simpsets and clasets simultaneously ***) 

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)] 
2031  27 
 (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]) 
1984  34 
handle _ => 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 _ => (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 

4640  60 
qed_goal "meta_eq_to_obj_eq" HOL.thy "x==y ==> x=y" 
61 
(fn [prem] => [rewtac prem, rtac refl 1]); 

62 

923  63 
local 
64 

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fun prover s = prove_goal HOL.thy s (K [Blast_tac 1]); 
923  66 

2134  67 
in 
68 

5552  69 
(*Make metaequalities. The operator below is Trueprop*) 
70 

6128  71 
fun mk_meta_eq r = r RS eq_reflection; 
72 

73 
val Eq_TrueI = mk_meta_eq(prover "P > (P = True)" RS mp); 

74 
val Eq_FalseI = mk_meta_eq(prover "~P > (P = False)" RS mp); 

5304  75 

6128  76 
fun mk_eq th = case concl_of th of 
77 
Const("==",_)$_$_ => th 

78 
 _$(Const("op =",_)$_$_) => mk_meta_eq th 

79 
 _$(Const("Not",_)$_) => th RS Eq_FalseI 

80 
 _ => th RS Eq_TrueI; 

81 
(* last 2 lines requires all formulae to be of the from Trueprop(.) *) 

5304  82 

6128  83 
fun mk_eq_True r = Some(r RS meta_eq_to_obj_eq RS Eq_TrueI); 
5552  84 

6128  85 
fun mk_meta_cong rl = 
86 
standard(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl)) 

87 
handle THM _ => 

88 
error("Premises and conclusion of congruence rules must be =equalities"); 

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val not_not = prover "(~ ~ P) = P"; 
923  91 

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val simp_thms = [not_not] @ map prover 
2082  93 
[ "(x=x) = True", 
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"(~True) = False", "(~False) = True", 
2082  95 
"(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))", 
4640  96 
"(True=P) = P", "(P=True) = P", "(False=P) = (~P)", "(P=False) = (~P)", 
2082  97 
"(True > P) = P", "(False > P) = True", 
98 
"(P > True) = True", "(P > P) = True", 

99 
"(P > False) = (~P)", "(P > ~P) = (~P)", 

100 
"(P & True) = P", "(True & P) = P", 

2800  101 
"(P & False) = False", "(False & P) = False", 
102 
"(P & P) = P", "(P & (P & Q)) = (P & Q)", 

3913  103 
"(P & ~P) = False", "(~P & P) = False", 
2082  104 
"(P  True) = True", "(True  P) = True", 
2800  105 
"(P  False) = P", "(False  P) = P", 
106 
"(P  P) = P", "(P  (P  Q)) = (P  Q)", 

3913  107 
"(P  ~P) = True", "(~P  P) = True", 
2082  108 
"((~P) = (~Q)) = (P=Q)", 
3842  109 
"(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x", 
4351  110 
(*two needed for the onepointrule quantifier simplification procs*) 
111 
"(? x. x=t & P(x)) = P(t)", (*essential for termination!!*) 

112 
"(! x. t=x > P(x)) = P(t)" ]; (*covers a stray case*) 

923  113 

5552  114 
(* Add congruence rules for = (instead of ==) *) 
4351  115 

5552  116 
(* ###FIXME: Move to simplifier, 
117 
taking mk_meta_cong as input, eliminating addeqcongs and deleqcongs *) 

118 
infix 4 addcongs delcongs; 

4640  119 
fun ss addcongs congs = ss addeqcongs (map mk_meta_cong congs); 
120 
fun ss delcongs congs = ss deleqcongs (map mk_meta_cong congs); 

4086  121 
fun Addcongs congs = (simpset_ref() := simpset() addcongs congs); 
122 
fun Delcongs congs = (simpset_ref() := simpset() delcongs congs); 

1264  123 

5552  124 

1922  125 
val imp_cong = impI RSN 
126 
(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); 
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(*Miniscoping: pushing in existential quantifiers*) 
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val ex_simps = map prover 
3842  131 
["(EX x. P x & Q) = ((EX x. P x) & Q)", 
132 
"(EX x. P & Q x) = (P & (EX x. Q x))", 

133 
"(EX x. P x  Q) = ((EX x. P x)  Q)", 

134 
"(EX x. P  Q x) = (P  (EX x. Q x))", 

135 
"(EX x. P x > Q) = ((ALL x. P x) > Q)", 

136 
"(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  140 
["(ALL x. P x & Q) = ((ALL x. P x) & Q)", 
141 
"(ALL x. P & Q x) = (P & (ALL x. Q x))", 

142 
"(ALL x. P x  Q) = ((ALL x. P x)  Q)", 

143 
"(ALL x. P  Q x) = (P  (ALL x. Q x))", 

144 
"(ALL x. P x > Q) = ((EX x. P x) > Q)", 

145 
"(ALL x. P > Q x) = (P > (ALL x. Q x))"]; 

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923  147 

2022  148 
(* elimination of existential quantifiers in assumptions *) 
923  149 

150 
val ex_all_equiv = 

151 
let val lemma1 = prove_goal HOL.thy 

152 
"(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)" 

153 
(fn prems => [resolve_tac prems 1, etac exI 1]); 

154 
val lemma2 = prove_goalw HOL.thy [Ex_def] 

155 
"(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)" 

156 
(fn prems => [REPEAT(resolve_tac prems 1)]) 

157 
in equal_intr lemma1 lemma2 end; 

158 

159 
end; 

160 

3654  161 
(* Elimination of True from asumptions: *) 
162 

163 
val True_implies_equals = prove_goal HOL.thy 

164 
"(True ==> PROP P) == PROP P" 

4525  165 
(K [rtac equal_intr_rule 1, atac 2, 
3654  166 
METAHYPS (fn prems => resolve_tac prems 1) 1, 
167 
rtac TrueI 1]); 

168 

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fun prove nm thm = qed_goal nm HOL.thy thm (K [Blast_tac 1]); 
923  170 

171 
prove "conj_commute" "(P&Q) = (Q&P)"; 

172 
prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))"; 

173 
val conj_comms = [conj_commute, conj_left_commute]; 

2134  174 
prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))"; 
923  175 

1922  176 
prove "disj_commute" "(PQ) = (QP)"; 
177 
prove "disj_left_commute" "(P(QR)) = (Q(PR))"; 

178 
val disj_comms = [disj_commute, disj_left_commute]; 

2134  179 
prove "disj_assoc" "((PQ)R) = (P(QR))"; 
1922  180 

923  181 
prove "conj_disj_distribL" "(P&(QR)) = (P&Q  P&R)"; 
182 
prove "conj_disj_distribR" "((PQ)&R) = (P&R  Q&R)"; 

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1892  184 
prove "disj_conj_distribL" "(P(Q&R)) = ((PQ) & (PR))"; 
185 
prove "disj_conj_distribR" "((P&Q)R) = ((PR) & (QR))"; 

186 

2134  187 
prove "imp_conjR" "(P > (Q&R)) = ((P>Q) & (P>R))"; 
188 
prove "imp_conjL" "((P&Q) >R) = (P > (Q > R))"; 

189 
prove "imp_disjL" "((PQ) > R) = ((P>R)&(Q>R))"; 

1892  190 

3448  191 
(*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*) 
192 
prove "imp_disj_not1" "((P > Q  R)) = (~Q > P > R)"; 

193 
prove "imp_disj_not2" "((P > Q  R)) = (~R > P > Q)"; 

194 

3904  195 
prove "imp_disj1" "((P>Q)R) = (P> QR)"; 
196 
prove "imp_disj2" "(Q(P>R)) = (P> QR)"; 

197 

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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  201 
prove "not_iff" "(P~=Q) = (P = (~Q))"; 
4743  202 
prove "disj_not1" "(~P  Q) = (P > Q)"; 
203 
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  209 
(*Avoids duplication of subgoals after split_if, when the true and false 
2134  210 
cases boil down to the same thing.*) 
211 
prove "cases_simp" "((P > Q) & (~P > Q)) = Q"; 

212 

3842  213 
prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))"; 
1922  214 
prove "imp_all" "((! x. P x) > Q) = (? x. P x > Q)"; 
3842  215 
prove "not_ex" "(~ (? x. P(x))) = (! x.~P(x))"; 
1922  216 
prove "imp_ex" "((? x. P x) > Q) = (! x. P x > Q)"; 
1660  217 

1655  218 
prove "ex_disj_distrib" "(? x. P(x)  Q(x)) = ((? x. P(x))  (? x. Q(x)))"; 
219 
prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))"; 

220 

2134  221 
(* '&' congruence rule: not included by default! 
222 
May slow rewrite proofs down by as much as 50% *) 

223 

224 
let val th = prove_goal HOL.thy 

225 
"(P=P')> (P'> (Q=Q'))> ((P&Q) = (P'&Q'))" 

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(fn _=> [Blast_tac 1]) 
2134  227 
in bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
228 

229 
let val th = prove_goal HOL.thy 

230 
"(Q=Q')> (Q'> (P=P'))> ((P&Q) = (P'&Q'))" 

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231 
(fn _=> [Blast_tac 1]) 
2134  232 
in bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
233 

234 
(* '' congruence rule: not included by default! *) 

235 

236 
let val th = prove_goal HOL.thy 

237 
"(P=P')> (~P'> (Q=Q'))> ((PQ) = (P'Q'))" 

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(fn _=> [Blast_tac 1]) 
2134  239 
in bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
240 

241 
prove "eq_sym_conv" "(x=y) = (y=x)"; 

242 

5278  243 

244 
(** ifthenelse rules **) 

245 

2134  246 
qed_goalw "if_True" HOL.thy [if_def] "(if True then x else y) = x" 
4525  247 
(K [Blast_tac 1]); 
2134  248 

249 
qed_goalw "if_False" HOL.thy [if_def] "(if False then x else y) = y" 

4525  250 
(K [Blast_tac 1]); 
2134  251 

5304  252 
qed_goalw "if_P" HOL.thy [if_def] "!!P. P ==> (if P then x else y) = x" 
253 
(K [Blast_tac 1]); 

254 

2134  255 
qed_goalw "if_not_P" HOL.thy [if_def] "!!P. ~P ==> (if P then x else y) = y" 
4525  256 
(K [Blast_tac 1]); 
2134  257 

4830  258 
qed_goal "split_if" HOL.thy 
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"P(if Q then x else y) = ((Q > P(x)) & (~Q > P(y)))" (K [ 
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260 
res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1, 
2134  261 
stac if_P 2, 
262 
stac if_not_P 1, 

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263 
ALLGOALS (Blast_tac)]); 
4830  264 
(* for backwards compatibility: *) 
265 
val expand_if = split_if; 

4205
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266 

96632970d203
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267 
qed_goal "split_if_asm" HOL.thy 
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268 
"P(if Q then x else y) = (~((Q & ~P x)  (~Q & ~P y)))" 
4830  269 
(K [stac split_if 1, 
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270 
Blast_tac 1]); 
2134  271 

5304  272 
qed_goal "if_cancel" HOL.thy "(if c then x else x) = x" 
273 
(K [stac split_if 1, Blast_tac 1]); 

274 

275 
qed_goal "if_eq_cancel" HOL.thy "(if x = y then y else x) = x" 

276 
(K [stac split_if 1, Blast_tac 1]); 

277 

4769
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278 
(*This form is useful for expanding IFs on the RIGHT of the ==> symbol*) 
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279 
qed_goal "if_bool_eq_conj" HOL.thy 
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280 
"(if P then Q else R) = ((P>Q) & (~P>R))" 
4830  281 
(K [rtac split_if 1]); 
4769
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282 

bb60149fe21b
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283 
(*And this form is useful for expanding IFs on the LEFT*) 
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284 
qed_goal "if_bool_eq_disj" HOL.thy 
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285 
"(if P then Q else R) = ((P&Q)  (~P&R))" 
4830  286 
(K [stac split_if 1, 
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287 
Blast_tac 1]); 
2134  288 

4351  289 

290 
(*** make simplification procedures for quantifier elimination ***) 

291 

292 
structure Quantifier1 = Quantifier1Fun( 

293 
struct 

294 
(*abstract syntax*) 

295 
fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t) 

296 
 dest_eq _ = None; 

297 
fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t) 

298 
 dest_conj _ = None; 

299 
val conj = HOLogic.conj 

300 
val imp = HOLogic.imp 

301 
(*rules*) 

302 
val iff_reflection = eq_reflection 

303 
val iffI = iffI 

304 
val sym = sym 

305 
val conjI= conjI 

306 
val conjE= conjE 

307 
val impI = impI 

308 
val impE = impE 

309 
val mp = mp 

310 
val exI = exI 

311 
val exE = exE 

312 
val allI = allI 

313 
val allE = allE 

314 
end); 

315 

4320
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316 
local 
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317 
val ex_pattern = 
4351  318 
read_cterm (sign_of HOL.thy) ("EX x. P(x) & Q(x)",HOLogic.boolT) 
3913  319 

4320
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320 
val all_pattern = 
4351  321 
read_cterm (sign_of HOL.thy) ("ALL x. P(x) & P'(x) > Q(x)",HOLogic.boolT) 
4320
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322 

24d9e6639cd4
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323 
in 
24d9e6639cd4
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324 
val defEX_regroup = 
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325 
mk_simproc "defined EX" [ex_pattern] Quantifier1.rearrange_ex; 
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326 
val defALL_regroup = 
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327 
mk_simproc "defined ALL" [all_pattern] Quantifier1.rearrange_all; 
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328 
end; 
3913  329 

4351  330 

331 
(*** Case splitting ***) 

3913  332 

5304  333 
structure SplitterData = 
334 
struct 

335 
structure Simplifier = Simplifier 

5552  336 
val mk_eq = mk_eq 
5304  337 
val meta_eq_to_iff = meta_eq_to_obj_eq 
338 
val iffD = iffD2 

339 
val disjE = disjE 

340 
val conjE = conjE 

341 
val exE = exE 

342 
val contrapos = contrapos 

343 
val contrapos2 = contrapos2 

344 
val notnotD = notnotD 

345 
end; 

4681  346 

5304  347 
structure Splitter = SplitterFun(SplitterData); 
2263  348 

5304  349 
val split_tac = Splitter.split_tac; 
350 
val split_inside_tac = Splitter.split_inside_tac; 

351 
val split_asm_tac = Splitter.split_asm_tac; 

5307  352 
val op addsplits = Splitter.addsplits; 
353 
val op delsplits = Splitter.delsplits; 

5304  354 
val Addsplits = Splitter.Addsplits; 
355 
val Delsplits = Splitter.Delsplits; 

4718
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oheimb
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changeset

356 

2134  357 
(** 'if' congruence rules: neither included by default! *) 
358 

359 
(*In general it seems wrong to add distributive laws by default: they 

360 
might cause exponential blowup. But imp_disjL has been in for a while 

361 
and cannot be removed without affecting existing proofs. Moreover, 

362 
rewriting by "(PQ > R) = ((P>R)&(Q>R))" might be justified on the 

363 
grounds that it allows simplification of R in the two cases.*) 

364 

5304  365 
fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th; 
366 

2134  367 
val mksimps_pairs = 
368 
[("op >", [mp]), ("op &", [conjunct1,conjunct2]), 

369 
("All", [spec]), ("True", []), ("False", []), 

4769
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370 
("If", [if_bool_eq_conj RS iffD1])]; 
1758  371 

5552  372 
(* ###FIXME: move to Provers/simplifier.ML 
5304  373 
val mk_atomize: (string * thm list) list > thm > thm list 
374 
*) 

5552  375 
(* ###FIXME: move to Provers/simplifier.ML *) 
5304  376 
fun mk_atomize pairs = 
377 
let fun atoms th = 

378 
(case concl_of th of 

379 
Const("Trueprop",_) $ p => 

380 
(case head_of p of 

381 
Const(a,_) => 

382 
(case assoc(pairs,a) of 

383 
Some(rls) => flat (map atoms ([th] RL rls)) 

384 
 None => [th]) 

385 
 _ => [th]) 

386 
 _ => [th]) 

387 
in atoms end; 

388 

5552  389 
fun mksimps pairs = (map mk_eq o mk_atomize pairs o gen_all); 
5304  390 

4640  391 
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:
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diff
changeset

392 
atac, etac FalseE]; 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
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changeset

393 
(*No premature instantiation of variables during simplification*) 
4640  394 
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:
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diff
changeset

395 
eq_assume_tac, ematch_tac [FalseE]]; 
2443
a81d4c219c3c
factored out HOL_base_ss and val HOL_min_ss, added HOL_safe_min_ss
oheimb
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2263
diff
changeset

396 

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

397 
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

398 
setSSolver safe_solver 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

399 
setSolver unsafe_solver 
4677  400 
setmksimps (mksimps mksimps_pairs) 
5552  401 
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

402 

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

403 
val HOL_ss = 
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

404 
HOL_basic_ss addsimps 
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

405 
([triv_forall_equality, (* prunes params *) 
3654  406 
True_implies_equals, (* prune asms `True' *) 
4718
fc2ba9fb2135
new rewrite rules not1_or, not2_or, and if_eq_cancel
oheimb
parents:
4681
diff
changeset

407 
if_True, if_False, if_cancel, if_eq_cancel, 
5304  408 
imp_disjL, conj_assoc, disj_assoc, 
3904  409 
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

410 
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

411 
@ 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

412 
addsimprocs [defALL_regroup,defEX_regroup] 
4744
4469d498cd48
moved addsplits [expand_if] from HOL_basic_ss to HOL_ss;
wenzelm
parents:
4743
diff
changeset

413 
addcongs [imp_cong] 
4830  414 
addsplits [split_if]; 
2082  415 

6293  416 
(*Simplifies x assuming c and y assuming ~c*) 
417 
val prems = Goalw [if_def] 

418 
"[ b=c; c ==> x=u; ~c ==> y=v ] ==> \ 

419 
\ (if b then x else y) = (if c then u else v)"; 

420 
by (asm_simp_tac (HOL_ss addsimps prems) 1); 

421 
qed "if_cong"; 

422 

423 
(*Prevents simplification of x and y: much faster*) 

424 
qed_goal "if_weak_cong" HOL.thy 

425 
"b=c ==> (if b then x else y) = (if c then x else y)" 

426 
(fn [prem] => [rtac (prem RS arg_cong) 1]); 

427 

428 
(*Prevents simplification of t: much faster*) 

429 
qed_goal "let_weak_cong" HOL.thy 

430 
"a = b ==> (let x=a in t(x)) = (let x=b in t(x))" 

431 
(fn [prem] => [rtac (prem RS arg_cong) 1]); 

432 

1655  433 
qed_goal "if_distrib" HOL.thy 
434 
"f(if c then x else y) = (if c then f x else f y)" 

4830  435 
(K [simp_tac (HOL_ss setloop (split_tac [split_if])) 1]); 
1655  436 

1984  437 

4327  438 
(*For expand_case_tac*) 
2948
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

439 
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

440 
by (case_tac "P" 1); 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

441 
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

442 
val expand_case = result(); 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

443 

4327  444 
(*Used in Auth proofs. Typically P contains Vars that become instantiated 
445 
during unification.*) 

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

446 
fun expand_case_tac P i = 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

447 
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

448 
Simp_tac (i+1) THEN 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

449 
Simp_tac i; 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

450 

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

451 

4119  452 
(* install implicit simpset *) 
1984  453 

4086  454 
simpset_ref() := HOL_ss; 
1984  455 

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

456 

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

457 

5219  458 
(*** integration of simplifier with classical reasoner ***) 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

459 

5219  460 
structure Clasimp = ClasimpFun 
5552  461 
(structure Simplifier = Simplifier 
462 
and Classical = Classical 

463 
and Blast = Blast); 

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

464 
open Clasimp; 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

465 

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

466 
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

467 

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

468 

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

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

472 

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

473 
test: term > bool 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

474 
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

475 
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

476 
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

477 

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

478 
prep_tac: int > tactic 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

479 
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

480 
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

481 

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

482 
ref_tac: int > tactic 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

483 
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

484 
[ A1; ...; An ] ==> False 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

485 
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

486 
*) 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

487 

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

488 
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

489 
let val nnf_simps = 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

490 
[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

491 
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

492 
val nnf_simpset = 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

493 
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

494 
setmksimps (mksimps mksimps_pairs) 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

495 
addsimps nnf_simps; 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

496 
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

497 

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

498 
val refute_prems_tac = 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
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parents:
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diff
changeset

499 
REPEAT(eresolve_tac [conjE, exE] 1 ORELSE 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
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parents:
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diff
changeset

500 
filter_prems_tac test 1 ORELSE 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
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diff
changeset

501 
eresolve_tac [disjE] 1) THEN 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
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diff
changeset

502 
ref_tac 1; 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
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parents:
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diff
changeset

503 
in EVERY'[TRY o filter_prems_tac test, 
6128  504 
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

505 
SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)] 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
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parents:
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diff
changeset

506 
end; 