author  oheimb 
Thu, 12 Mar 1998 13:17:13 +0100  
changeset 4743  b3bfcbd9fb93 
parent 4718  fc2ba9fb2135 
child 4744  4469d498cd48 
permissions  rwrr 
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(* Title: HOL/simpdata.ML 
923  2 
ID: $Id$ 
1465  3 
Author: Tobias Nipkow 
923  4 
Copyright 1991 University of Cambridge 
5 

6 
Instantiation of the generic simplifier 

7 
*) 

8 

1984  9 
section "Simplifier"; 
10 

923  11 
open Simplifier; 
12 

1984  13 
(*** Addition of rules to simpsets and clasets simultaneously ***) 
14 

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 

23 
fun addIff th = 

24 
(case HOLogic.dest_Trueprop (#prop(rep_thm th)) of 

2718  25 
(Const("Not",_) $ A) => 
2031  26 
AddSEs [zero_var_indexes (th RS notE)] 
27 
 (con $ _ $ _) => 

28 
if con=iff_const 

29 
then (AddSIs [zero_var_indexes (th RS iffD2)]; 

30 
AddSDs [zero_var_indexes (th RS iffD1)]) 

31 
else AddSIs [th] 

32 
 _ => AddSIs [th]; 

1984  33 
Addsimps [th]) 
34 
handle _ => error ("AddIffs: theorem must be unconditional\n" ^ 

2031  35 
string_of_thm th) 
1984  36 

37 
fun delIff th = 

38 
(case HOLogic.dest_Trueprop (#prop(rep_thm th)) of 

2718  39 
(Const("Not",_) $ A) => 
2031  40 
Delrules [zero_var_indexes (th RS notE)] 
41 
 (con $ _ $ _) => 

42 
if con=iff_const 

43 
then Delrules [zero_var_indexes (th RS iffD2), 

3518  44 
make_elim (zero_var_indexes (th RS iffD1))] 
2031  45 
else Delrules [th] 
46 
 _ => Delrules [th]; 

1984  47 
Delsimps [th]) 
48 
handle _ => warning("DelIffs: ignoring conditional theorem\n" ^ 

2031  49 
string_of_thm th) 
1984  50 
in 
51 
val AddIffs = seq addIff 

52 
val DelIffs = seq delIff 

53 
end; 

54 

4640  55 
qed_goal "meta_eq_to_obj_eq" HOL.thy "x==y ==> x=y" 
56 
(fn [prem] => [rewtac prem, rtac refl 1]); 

57 

923  58 
local 
59 

4525  60 
fun prover s = prove_goal HOL.thy s (K [blast_tac HOL_cs 1]); 
923  61 

1922  62 
val P_imp_P_iff_True = prover "P > (P = True)" RS mp; 
63 
val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection; 

923  64 

1922  65 
val not_P_imp_P_iff_F = prover "~P > (P = False)" RS mp; 
66 
val not_P_imp_P_eq_False = not_P_imp_P_iff_F RS eq_reflection; 

923  67 

1922  68 
fun atomize pairs = 
69 
let fun atoms th = 

2031  70 
(case concl_of th of 
71 
Const("Trueprop",_) $ p => 

72 
(case head_of p of 

73 
Const(a,_) => 

74 
(case assoc(pairs,a) of 

75 
Some(rls) => flat (map atoms ([th] RL rls)) 

76 
 None => [th]) 

77 
 _ => [th]) 

78 
 _ => [th]) 

1922  79 
in atoms end; 
923  80 

2134  81 
fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th; 
82 

83 
in 

84 

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fun mk_meta_eq r = r RS eq_reflection; 
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fun mk_meta_eq_True r = Some(r RS meta_eq_to_obj_eq RS P_imp_P_eq_True); 
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fun mk_meta_eq_simp r = case concl_of r of 
2031  89 
Const("==",_)$_$_ => r 
4677  90 
 _$(Const("op =",_)$lhs$rhs) => mk_meta_eq r 
2718  91 
 _$(Const("Not",_)$_) => r RS not_P_imp_P_eq_False 
1922  92 
 _ => r RS P_imp_P_eq_True; 
93 
(* last 2 lines requires all formulae to be of the from Trueprop(.) *) 

923  94 

2082  95 
val simp_thms = map prover 
96 
[ "(x=x) = True", 

97 
"(~True) = False", "(~False) = True", "(~ ~ P) = P", 

98 
"(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))", 

4640  99 
"(True=P) = P", "(P=True) = P", "(False=P) = (~P)", "(P=False) = (~P)", 
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"(True > P) = P", "(False > P) = True", 
101 
"(P > True) = True", "(P > P) = True", 

102 
"(P > False) = (~P)", "(P > ~P) = (~P)", 

103 
"(P & True) = P", "(True & P) = P", 

2800  104 
"(P & False) = False", "(False & P) = False", 
105 
"(P & P) = P", "(P & (P & Q)) = (P & Q)", 

3913  106 
"(P & ~P) = False", "(~P & P) = False", 
2082  107 
"(P  True) = True", "(True  P) = True", 
2800  108 
"(P  False) = P", "(False  P) = P", 
109 
"(P  P) = P", "(P  (P  Q)) = (P  Q)", 

3913  110 
"(P  ~P) = True", "(~P  P) = True", 
2082  111 
"((~P) = (~Q)) = (P=Q)", 
3842  112 
"(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x", 
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(*two needed for the onepointrule quantifier simplification procs*) 
114 
"(? x. x=t & P(x)) = P(t)", (*essential for termination!!*) 

115 
"(! x. t=x > P(x)) = P(t)" ]; (*covers a stray case*) 

923  116 

988  117 
(*Add congruence rules for = (instead of ==) *) 
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infix 4 addcongs delcongs; 
4351  119 

4640  120 
fun mk_meta_cong rl = 
121 
standard(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl)) 

122 
handle THM _ => 

123 
error("Premises and conclusion of congruence rules must be =equalities"); 

124 

125 
fun ss addcongs congs = ss addeqcongs (map mk_meta_cong congs); 

126 

127 
fun ss delcongs congs = ss deleqcongs (map mk_meta_cong congs); 

923  128 

4086  129 
fun Addcongs congs = (simpset_ref() := simpset() addcongs congs); 
130 
fun Delcongs congs = (simpset_ref() := simpset() delcongs congs); 

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fun mksimps pairs = map mk_meta_eq_simp o atomize pairs o gen_all; 
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1922  134 
val imp_cong = impI RSN 
135 
(2, prove_goal HOL.thy "(P=P')> (P'> (Q=Q'))> ((P>Q) = (P'>Q'))" 

2935  136 
(fn _=> [blast_tac HOL_cs 1]) RS mp RS mp); 
1922  137 

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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)", 
141 
"(EX x. P & Q x) = (P & (EX x. Q x))", 

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

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

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

145 
"(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)", 
150 
"(ALL x. P & Q x) = (P & (ALL x. Q x))", 

151 
"(ALL x. P x  Q) = ((ALL x. P x)  Q)", 

152 
"(ALL x. P  Q x) = (P  (ALL x. Q x))", 

153 
"(ALL x. P x > Q) = ((EX x. P x) > Q)", 

154 
"(ALL x. P > Q x) = (P > (ALL x. Q x))"]; 

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923  156 

2022  157 
(* elimination of existential quantifiers in assumptions *) 
923  158 

159 
val ex_all_equiv = 

160 
let val lemma1 = prove_goal HOL.thy 

161 
"(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)" 

162 
(fn prems => [resolve_tac prems 1, etac exI 1]); 

163 
val lemma2 = prove_goalw HOL.thy [Ex_def] 

164 
"(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)" 

165 
(fn prems => [REPEAT(resolve_tac prems 1)]) 

166 
in equal_intr lemma1 lemma2 end; 

167 

168 
end; 

169 

3654  170 
(* Elimination of True from asumptions: *) 
171 

172 
val True_implies_equals = prove_goal HOL.thy 

173 
"(True ==> PROP P) == PROP P" 

4525  174 
(K [rtac equal_intr_rule 1, atac 2, 
3654  175 
METAHYPS (fn prems => resolve_tac prems 1) 1, 
176 
rtac TrueI 1]); 

177 

4525  178 
fun prove nm thm = qed_goal nm HOL.thy thm (K [blast_tac HOL_cs 1]); 
923  179 

180 
prove "conj_commute" "(P&Q) = (Q&P)"; 

181 
prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))"; 

182 
val conj_comms = [conj_commute, conj_left_commute]; 

2134  183 
prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))"; 
923  184 

1922  185 
prove "disj_commute" "(PQ) = (QP)"; 
186 
prove "disj_left_commute" "(P(QR)) = (Q(PR))"; 

187 
val disj_comms = [disj_commute, disj_left_commute]; 

2134  188 
prove "disj_assoc" "((PQ)R) = (P(QR))"; 
1922  189 

923  190 
prove "conj_disj_distribL" "(P&(QR)) = (P&Q  P&R)"; 
191 
prove "conj_disj_distribR" "((PQ)&R) = (P&R  Q&R)"; 

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prove "disj_conj_distribL" "(P(Q&R)) = ((PQ) & (PR))"; 
194 
prove "disj_conj_distribR" "((P&Q)R) = ((PR) & (QR))"; 

195 

2134  196 
prove "imp_conjR" "(P > (Q&R)) = ((P>Q) & (P>R))"; 
197 
prove "imp_conjL" "((P&Q) >R) = (P > (Q > R))"; 

198 
prove "imp_disjL" "((PQ) > R) = ((P>R)&(Q>R))"; 

1892  199 

3448  200 
(*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*) 
201 
prove "imp_disj_not1" "((P > Q  R)) = (~Q > P > R)"; 

202 
prove "imp_disj_not2" "((P > Q  R)) = (~R > P > Q)"; 

203 

3904  204 
prove "imp_disj1" "((P>Q)R) = (P> QR)"; 
205 
prove "imp_disj2" "(Q(P>R)) = (P> QR)"; 

206 

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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  210 
prove "not_iff" "(P~=Q) = (P = (~Q))"; 
4743  211 
prove "disj_not1" "(~P  Q) = (P > Q)"; 
212 
prove "disj_not2" "(P  ~Q) = (Q > P)"; (* changes orientation :( *) 

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2134  214 
(*Avoids duplication of subgoals after expand_if, when the true and false 
215 
cases boil down to the same thing.*) 

216 
prove "cases_simp" "((P > Q) & (~P > Q)) = Q"; 

217 

3842  218 
prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))"; 
1922  219 
prove "imp_all" "((! x. P x) > Q) = (? x. P x > Q)"; 
3842  220 
prove "not_ex" "(~ (? x. P(x))) = (! x.~P(x))"; 
1922  221 
prove "imp_ex" "((? x. P x) > Q) = (! x. P x > Q)"; 
1660  222 

1655  223 
prove "ex_disj_distrib" "(? x. P(x)  Q(x)) = ((? x. P(x))  (? x. Q(x)))"; 
224 
prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))"; 

225 

2134  226 
(* '&' congruence rule: not included by default! 
227 
May slow rewrite proofs down by as much as 50% *) 

228 

229 
let val th = prove_goal HOL.thy 

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

2935  231 
(fn _=> [blast_tac HOL_cs 1]) 
2134  232 
in bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
233 

234 
let val th = prove_goal HOL.thy 

235 
"(Q=Q')> (Q'> (P=P'))> ((P&Q) = (P'&Q'))" 

2935  236 
(fn _=> [blast_tac HOL_cs 1]) 
2134  237 
in bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
238 

239 
(* '' congruence rule: not included by default! *) 

240 

241 
let val th = prove_goal HOL.thy 

242 
"(P=P')> (~P'> (Q=Q'))> ((PQ) = (P'Q'))" 

2935  243 
(fn _=> [blast_tac HOL_cs 1]) 
2134  244 
in bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
245 

246 
prove "eq_sym_conv" "(x=y) = (y=x)"; 

247 

248 
qed_goalw "o_apply" HOL.thy [o_def] "(f o g) x = f (g x)" 

4525  249 
(K [rtac refl 1]); 
2134  250 

251 
qed_goalw "if_True" HOL.thy [if_def] "(if True then x else y) = x" 

4525  252 
(K [Blast_tac 1]); 
2134  253 

254 
qed_goalw "if_False" HOL.thy [if_def] "(if False then x else y) = y" 

4525  255 
(K [Blast_tac 1]); 
2134  256 

257 
qed_goal "if_P" HOL.thy "P ==> (if P then x else y) = x" 

258 
(fn [prem] => [ stac (prem RS eqTrueI) 1, rtac if_True 1 ]); 

259 
(* 

260 
qed_goal "if_not_P" HOL.thy "~P ==> (if P then x else y) = y" 

261 
(fn [prem] => [ stac (prem RS not_P_imp_P_iff_F) 1, rtac if_False 1 ]); 

262 
*) 

263 
qed_goalw "if_not_P" HOL.thy [if_def] "!!P. ~P ==> (if P then x else y) = y" 

4525  264 
(K [Blast_tac 1]); 
2134  265 

266 
qed_goal "expand_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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res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1, 
2134  269 
stac if_P 2, 
270 
stac if_not_P 1, 

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ALLGOALS (blast_tac HOL_cs)]); 
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qed_goal "split_if_asm" HOL.thy 
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"P(if Q then x else y) = (~((Q & ~P x)  (~Q & ~P y)))" (K [ 
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stac expand_if 1, 
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blast_tac HOL_cs 1]); 
2134  277 

278 
qed_goal "if_bool_eq" HOL.thy 

279 
"(if P then Q else R) = ((P>Q) & (~P>R))" 

4525  280 
(K [rtac expand_if 1]); 
2134  281 

4351  282 

283 
(*** make simplification procedures for quantifier elimination ***) 

284 

285 
structure Quantifier1 = Quantifier1Fun( 

286 
struct 

287 
(*abstract syntax*) 

288 
fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t) 

289 
 dest_eq _ = None; 

290 
fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t) 

291 
 dest_conj _ = None; 

292 
val conj = HOLogic.conj 

293 
val imp = HOLogic.imp 

294 
(*rules*) 

295 
val iff_reflection = eq_reflection 

296 
val iffI = iffI 

297 
val sym = sym 

298 
val conjI= conjI 

299 
val conjE= conjE 

300 
val impI = impI 

301 
val impE = impE 

302 
val mp = mp 

303 
val exI = exI 

304 
val exE = exE 

305 
val allI = allI 

306 
val allE = allE 

307 
end); 

308 

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local 
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val ex_pattern = 
4351  311 
read_cterm (sign_of HOL.thy) ("EX x. P(x) & Q(x)",HOLogic.boolT) 
3913  312 

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val all_pattern = 
4351  314 
read_cterm (sign_of HOL.thy) ("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  322 

4351  323 

324 
(*** Case splitting ***) 

3913  325 

2263  326 
local val mktac = mk_case_split_tac (meta_eq_to_obj_eq RS iffD2) 
327 
in 

328 
fun split_tac splits = mktac (map mk_meta_eq splits) 

329 
end; 

330 

331 
local val mktac = mk_case_split_inside_tac (meta_eq_to_obj_eq RS iffD2) 

332 
in 

333 
fun split_inside_tac splits = mktac (map mk_meta_eq splits) 

334 
end; 

335 

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val split_asm_tac = mk_case_split_asm_tac split_tac 
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337 
(disjE,conjE,exE,contrapos,contrapos2,notnotD); 
4189  338 

4681  339 
infix 4 addsplits delsplits; 
340 

4669  341 
fun ss addsplits splits = 
342 
let fun addsplit(ss,split) = 

343 
let val name = "split " ^ const_of_split_thm split 

344 
in ss addloop (name,split_tac [split]) end 

345 
in foldl addsplit (ss,splits) end; 

2263  346 

4681  347 
fun ss delsplits splits = 
348 
let fun delsplit(ss,split) = 

349 
let val name = "split " ^ const_of_split_thm split 

350 
in ss delloop name end 

351 
in foldl delsplit (ss,splits) end; 

352 

353 
fun Addsplits splits = (simpset_ref() := simpset() addsplits splits); 

354 
fun Delsplits splits = (simpset_ref() := simpset() delsplits splits); 

355 

2251  356 
qed_goal "if_cancel" HOL.thy "(if c then x else x) = x" 
4525  357 
(K [split_tac [expand_if] 1, blast_tac HOL_cs 1]); 
2251  358 

4718
fc2ba9fb2135
new rewrite rules not1_or, not2_or, and if_eq_cancel
oheimb
parents:
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diff
changeset

359 
qed_goal "if_eq_cancel" HOL.thy "(if x = y then y else x) = x" 
fc2ba9fb2135
new rewrite rules not1_or, not2_or, and if_eq_cancel
oheimb
parents:
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diff
changeset

360 
(K [split_tac [expand_if] 1, blast_tac HOL_cs 1]); 
fc2ba9fb2135
new rewrite rules not1_or, not2_or, and if_eq_cancel
oheimb
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361 

2134  362 
(** 'if' congruence rules: neither included by default! *) 
363 

364 
(*Simplifies x assuming c and y assuming ~c*) 

365 
qed_goal "if_cong" HOL.thy 

366 
"[ b=c; c ==> x=u; ~c ==> y=v ] ==>\ 

367 
\ (if b then x else y) = (if c then u else v)" 

368 
(fn rew::prems => 

369 
[stac rew 1, stac expand_if 1, stac expand_if 1, 

2935  370 
blast_tac (HOL_cs addDs prems) 1]); 
2134  371 

372 
(*Prevents simplification of x and y: much faster*) 

373 
qed_goal "if_weak_cong" HOL.thy 

374 
"b=c ==> (if b then x else y) = (if c then x else y)" 

375 
(fn [prem] => [rtac (prem RS arg_cong) 1]); 

376 

377 
(*Prevents simplification of t: much faster*) 

378 
qed_goal "let_weak_cong" HOL.thy 

379 
"a = b ==> (let x=a in t(x)) = (let x=b in t(x))" 

380 
(fn [prem] => [rtac (prem RS arg_cong) 1]); 

381 

382 
(*In general it seems wrong to add distributive laws by default: they 

383 
might cause exponential blowup. But imp_disjL has been in for a while 

384 
and cannot be removed without affecting existing proofs. Moreover, 

385 
rewriting by "(PQ > R) = ((P>R)&(Q>R))" might be justified on the 

386 
grounds that it allows simplification of R in the two cases.*) 

387 

388 
val mksimps_pairs = 

389 
[("op >", [mp]), ("op &", [conjunct1,conjunct2]), 

390 
("All", [spec]), ("True", []), ("False", []), 

391 
("If", [if_bool_eq RS iffD1])]; 

1758  392 

4640  393 
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

394 
atac, etac FalseE]; 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
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diff
changeset

395 
(*No premature instantiation of variables during simplification*) 
4640  396 
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

397 
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

398 

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

399 
val HOL_basic_ss = empty_ss setsubgoaler asm_simp_tac 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
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diff
changeset

400 
setSSolver safe_solver 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
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diff
changeset

401 
setSolver unsafe_solver 
4677  402 
setmksimps (mksimps mksimps_pairs) 
4681  403 
setmkeqTrue mk_meta_eq_True 
404 
addsplits [expand_if]; 

2443
a81d4c219c3c
factored out HOL_base_ss and val HOL_min_ss, added HOL_safe_min_ss
oheimb
parents:
2263
diff
changeset

405 

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

406 
val HOL_ss = 
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

407 
HOL_basic_ss addsimps 
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

408 
([triv_forall_equality, (* prunes params *) 
3654  409 
True_implies_equals, (* prune asms `True' *) 
4718
fc2ba9fb2135
new rewrite rules not1_or, not2_or, and if_eq_cancel
oheimb
parents:
4681
diff
changeset

410 
if_True, if_False, if_cancel, if_eq_cancel, 
3446
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

411 
o_apply, imp_disjL, conj_assoc, disj_assoc, 
3904  412 
de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp, 
4743  413 
disj_not1, not_all, not_ex, cases_simp] 
3446
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

414 
@ 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

415 
addsimprocs [defALL_regroup,defEX_regroup] 
3446
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

416 
addcongs [imp_cong]; 
2082  417 

1655  418 
qed_goal "if_distrib" HOL.thy 
419 
"f(if c then x else y) = (if c then f x else f y)" 

4525  420 
(K [simp_tac (HOL_ss setloop (split_tac [expand_if])) 1]); 
1655  421 

2097  422 
qed_goalw "o_assoc" HOL.thy [o_def] "f o (g o h) = f o g o h" 
4525  423 
(K [rtac ext 1, rtac refl 1]); 
1984  424 

425 

4327  426 
(*For expand_case_tac*) 
2948
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

427 
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

428 
by (case_tac "P" 1); 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

429 
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

430 
val expand_case = result(); 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

431 

4327  432 
(*Used in Auth proofs. Typically P contains Vars that become instantiated 
433 
during unification.*) 

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

434 
fun expand_case_tac P i = 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

435 
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

436 
Simp_tac (i+1) THEN 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

437 
Simp_tac i; 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

438 

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

439 

4119  440 
(* install implicit simpset *) 
1984  441 

4086  442 
simpset_ref() := HOL_ss; 
1984  443 

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

444 

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

445 

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

446 

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

447 

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

448 

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

449 
(*** Integration of simplifier with classical reasoner ***) 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

450 

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

451 
(* rot_eq_tac rotates the first equality premise of subgoal i to the front, 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

452 
fails if there is no equaliy or if an equality is already at the front *) 
3538  453 
local 
454 
fun is_eq (Const ("Trueprop", _) $ (Const("op =" ,_) $ _ $ _)) = true 

455 
 is_eq _ = false; 

4188
1025a27b08f9
changed libraray function find to find_index_eq, currying it
oheimb
parents:
4119
diff
changeset

456 
val find_eq = find_index is_eq; 
3538  457 
in 
458 
val rot_eq_tac = 

4188
1025a27b08f9
changed libraray function find to find_index_eq, currying it
oheimb
parents:
4119
diff
changeset

459 
SUBGOAL (fn (Bi,i) => let val n = find_eq (Logic.strip_assums_hyp Bi) in 
1025a27b08f9
changed libraray function find to find_index_eq, currying it
oheimb
parents:
4119
diff
changeset

460 
if n>0 then rotate_tac n i else no_tac end) 
3538  461 
end; 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

462 

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

463 
use "$ISABELLE_HOME/src/Provers/clasimp.ML"; 
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); 