author  oheimb 
Thu, 24 Sep 1998 17:16:06 +0200  
changeset 5552  dcd3e7711cac 
parent 5447  df03d330aeab 
child 5975  cd19eaa90f45 
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 

5190
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

13 
infix 4 addIffs delIffs; 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

14 

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 

5190
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

23 
fun addIff ((cla, simp), th) = 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

24 
(case HOLogic.dest_Trueprop (#prop (rep_thm th)) of 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

25 
(Const("Not", _) $ A) => 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

26 
cla addSEs [zero_var_indexes (th RS notE)] 
2031  27 
 (con $ _ $ _) => 
5190
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

28 
if con = iff_const 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

29 
then cla addSIs [zero_var_indexes (th RS iffD2)] 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

30 
addSDs [zero_var_indexes (th RS iffD1)] 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

31 
else cla addSIs [th] 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

32 
 _ => cla addSIs [th], 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

33 
simp addsimps [th]) 
1984  34 
handle _ => error ("AddIffs: theorem must be unconditional\n" ^ 
5190
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

35 
string_of_thm th); 
1984  36 

5190
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

37 
fun delIff ((cla, simp), th) = 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

38 
(case HOLogic.dest_Trueprop (#prop (rep_thm th)) of 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

39 
(Const ("Not", _) $ A) => 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

40 
cla delrules [zero_var_indexes (th RS notE)] 
2031  41 
 (con $ _ $ _) => 
5190
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

42 
if con = iff_const 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

43 
then cla delrules [zero_var_indexes (th RS iffD2), 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

44 
make_elim (zero_var_indexes (th RS iffD1))] 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

45 
else cla delrules [th] 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

46 
 _ => cla delrules [th], 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

47 
simp delsimps [th]) 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

48 
handle _ => (warning("DelIffs: ignoring conditional theorem\n" ^ 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

49 
string_of_thm th); (cla, simp)); 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

50 

4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

51 
fun store_clasimp (cla, simp) = (claset_ref () := cla; simpset_ref () := simp) 
1984  52 
in 
5190
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

53 
val op addIffs = foldl addIff; 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

54 
val op delIffs = foldl delIff; 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

55 
fun AddIffs thms = store_clasimp ((claset (), simpset ()) addIffs thms); 
4ae031622592
Added functions addIffs and delIffs which operate on clasimpsets.
berghofe
parents:
4930
diff
changeset

56 
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 

4769
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

65 
fun prover s = prove_goal HOL.thy s (K [Blast_tac 1]); 
923  66 

1922  67 
val P_imp_P_iff_True = prover "P > (P = True)" RS mp; 
68 
val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection; 

923  69 

1922  70 
val not_P_imp_P_iff_F = prover "~P > (P = False)" RS mp; 
71 
val not_P_imp_P_eq_False = not_P_imp_P_iff_F RS eq_reflection; 

923  72 

2134  73 
in 
74 

5552  75 
(*Make metaequalities. The operator below is Trueprop*) 
76 

77 
fun mk_meta_eq r = r RS eq_reflection; 

5304  78 

5552  79 
fun mk_eq th = case concl_of th of 
5304  80 
Const("==",_)$_$_ => th 
5552  81 
 _$(Const("op =",_)$_$_) => mk_meta_eq th 
5304  82 
 _$(Const("Not",_)$_) => th RS not_P_imp_P_eq_False 
83 
 _ => th RS P_imp_P_eq_True; 

84 
(* last 2 lines requires all formulae to be of the from Trueprop(.) *) 

85 

5552  86 
fun mk_eq_True r = Some(r RS meta_eq_to_obj_eq RS P_imp_P_eq_True); 
87 

88 
fun mk_meta_cong rl = 

89 
standard(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl)) 

90 
handle THM _ => 

91 
error("Premises and conclusion of congruence rules must be =equalities"); 

3896
ee8ebb74ec00
Various new lemmas. Improved conversion of equations to rewrite rules:
nipkow
parents:
3842
diff
changeset

92 

923  93 

2082  94 
val simp_thms = map prover 
95 
[ "(x=x) = True", 

96 
"(~True) = False", "(~False) = True", "(~ ~ P) = P", 

97 
"(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))", 

4640  98 
"(True=P) = P", "(P=True) = P", "(False=P) = (~P)", "(P=False) = (~P)", 
2082  99 
"(True > P) = P", "(False > P) = True", 
100 
"(P > True) = True", "(P > P) = True", 

101 
"(P > False) = (~P)", "(P > ~P) = (~P)", 

102 
"(P & True) = P", "(True & P) = P", 

2800  103 
"(P & False) = False", "(False & P) = False", 
104 
"(P & P) = P", "(P & (P & Q)) = (P & Q)", 

3913  105 
"(P & ~P) = False", "(~P & P) = False", 
2082  106 
"(P  True) = True", "(True  P) = True", 
2800  107 
"(P  False) = P", "(False  P) = P", 
108 
"(P  P) = P", "(P  (P  Q)) = (P  Q)", 

3913  109 
"(P  ~P) = True", "(~P  P) = True", 
2082  110 
"((~P) = (~Q)) = (P=Q)", 
3842  111 
"(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x", 
4351  112 
(*two needed for the onepointrule quantifier simplification procs*) 
113 
"(? x. x=t & P(x)) = P(t)", (*essential for termination!!*) 

114 
"(! x. t=x > P(x)) = P(t)" ]; (*covers a stray case*) 

923  115 

5552  116 
(* Add congruence rules for = (instead of ==) *) 
4351  117 

5552  118 
(* ###FIXME: Move to simplifier, 
119 
taking mk_meta_cong as input, eliminating addeqcongs and deleqcongs *) 

120 
infix 4 addcongs delcongs; 

4640  121 
fun ss addcongs congs = ss addeqcongs (map mk_meta_cong congs); 
122 
fun ss delcongs congs = ss deleqcongs (map mk_meta_cong congs); 

4086  123 
fun Addcongs congs = (simpset_ref() := simpset() addcongs congs); 
124 
fun Delcongs congs = (simpset_ref() := simpset() delcongs congs); 

1264  125 

5552  126 

1922  127 
val imp_cong = impI RSN 
128 
(2, prove_goal HOL.thy "(P=P')> (P'> (Q=Q'))> ((P>Q) = (P'>Q'))" 

4769
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

129 
(fn _=> [Blast_tac 1]) RS mp RS mp); 
1922  130 

1948
78e5bfcbc1e9
Added miniscoping to the simplifier: quantifiers are now pushed in
paulson
parents:
1922
diff
changeset

131 
(*Miniscoping: pushing in existential quantifiers*) 
78e5bfcbc1e9
Added miniscoping to the simplifier: quantifiers are now pushed in
paulson
parents:
1922
diff
changeset

132 
val ex_simps = map prover 
3842  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) = ((EX x. P x)  Q)", 

136 
"(EX x. P  Q x) = (P  (EX x. Q x))", 

137 
"(EX x. P x > Q) = ((ALL x. P x) > Q)", 

138 
"(EX x. P > Q x) = (P > (EX x. Q x))"]; 

1948
78e5bfcbc1e9
Added miniscoping to the simplifier: quantifiers are now pushed in
paulson
parents:
1922
diff
changeset

139 

78e5bfcbc1e9
Added miniscoping to the simplifier: quantifiers are now pushed in
paulson
parents:
1922
diff
changeset

140 
(*Miniscoping: pushing in universal quantifiers*) 
78e5bfcbc1e9
Added miniscoping to the simplifier: quantifiers are now pushed in
paulson
parents:
1922
diff
changeset

141 
val all_simps = map prover 
3842  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) = ((ALL x. P x)  Q)", 

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

146 
"(ALL x. P x > Q) = ((EX x. P x) > Q)", 

147 
"(ALL x. P > Q x) = (P > (ALL x. Q x))"]; 

1948
78e5bfcbc1e9
Added miniscoping to the simplifier: quantifiers are now pushed in
paulson
parents:
1922
diff
changeset

148 

923  149 

2022  150 
(* elimination of existential quantifiers in assumptions *) 
923  151 

152 
val ex_all_equiv = 

153 
let val lemma1 = prove_goal HOL.thy 

154 
"(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)" 

155 
(fn prems => [resolve_tac prems 1, etac exI 1]); 

156 
val lemma2 = prove_goalw HOL.thy [Ex_def] 

157 
"(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)" 

158 
(fn prems => [REPEAT(resolve_tac prems 1)]) 

159 
in equal_intr lemma1 lemma2 end; 

160 

161 
end; 

162 

3654  163 
(* Elimination of True from asumptions: *) 
164 

165 
val True_implies_equals = prove_goal HOL.thy 

166 
"(True ==> PROP P) == PROP P" 

4525  167 
(K [rtac equal_intr_rule 1, atac 2, 
3654  168 
METAHYPS (fn prems => resolve_tac prems 1) 1, 
169 
rtac TrueI 1]); 

170 

4769
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

171 
fun prove nm thm = qed_goal nm HOL.thy thm (K [Blast_tac 1]); 
923  172 

173 
prove "conj_commute" "(P&Q) = (Q&P)"; 

174 
prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))"; 

175 
val conj_comms = [conj_commute, conj_left_commute]; 

2134  176 
prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))"; 
923  177 

1922  178 
prove "disj_commute" "(PQ) = (QP)"; 
179 
prove "disj_left_commute" "(P(QR)) = (Q(PR))"; 

180 
val disj_comms = [disj_commute, disj_left_commute]; 

2134  181 
prove "disj_assoc" "((PQ)R) = (P(QR))"; 
1922  182 

923  183 
prove "conj_disj_distribL" "(P&(QR)) = (P&Q  P&R)"; 
184 
prove "conj_disj_distribR" "((PQ)&R) = (P&R  Q&R)"; 

1485
240cc98b94a7
Added qed_spec_mp to avoid renaming of bound vars in 'th RS spec'
nipkow
parents:
1465
diff
changeset

185 

1892  186 
prove "disj_conj_distribL" "(P(Q&R)) = ((PQ) & (PR))"; 
187 
prove "disj_conj_distribR" "((P&Q)R) = ((PR) & (QR))"; 

188 

2134  189 
prove "imp_conjR" "(P > (Q&R)) = ((P>Q) & (P>R))"; 
190 
prove "imp_conjL" "((P&Q) >R) = (P > (Q > R))"; 

191 
prove "imp_disjL" "((PQ) > R) = ((P>R)&(Q>R))"; 

1892  192 

3448  193 
(*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*) 
194 
prove "imp_disj_not1" "((P > Q  R)) = (~Q > P > R)"; 

195 
prove "imp_disj_not2" "((P > Q  R)) = (~R > P > Q)"; 

196 

3904  197 
prove "imp_disj1" "((P>Q)R) = (P> QR)"; 
198 
prove "imp_disj2" "(Q(P>R)) = (P> QR)"; 

199 

1485
240cc98b94a7
Added qed_spec_mp to avoid renaming of bound vars in 'th RS spec'
nipkow
parents:
1465
diff
changeset

200 
prove "de_Morgan_disj" "(~(P  Q)) = (~P & ~Q)"; 
240cc98b94a7
Added qed_spec_mp to avoid renaming of bound vars in 'th RS spec'
nipkow
parents:
1465
diff
changeset

201 
prove "de_Morgan_conj" "(~(P & Q)) = (~P  ~Q)"; 
3446
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

202 
prove "not_imp" "(~(P > Q)) = (P & ~Q)"; 
1922  203 
prove "not_iff" "(P~=Q) = (P = (~Q))"; 
4743  204 
prove "disj_not1" "(~P  Q) = (P > Q)"; 
205 
prove "disj_not2" "(P  ~Q) = (Q > P)"; (* changes orientation :( *) 

1485
240cc98b94a7
Added qed_spec_mp to avoid renaming of bound vars in 'th RS spec'
nipkow
parents:
1465
diff
changeset

206 

4830  207 
(*Avoids duplication of subgoals after split_if, when the true and false 
2134  208 
cases boil down to the same thing.*) 
209 
prove "cases_simp" "((P > Q) & (~P > Q)) = Q"; 

210 

3842  211 
prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))"; 
1922  212 
prove "imp_all" "((! x. P x) > Q) = (? x. P x > Q)"; 
3842  213 
prove "not_ex" "(~ (? x. P(x))) = (! x.~P(x))"; 
1922  214 
prove "imp_ex" "((? x. P x) > Q) = (! x. P x > Q)"; 
1660  215 

1655  216 
prove "ex_disj_distrib" "(? x. P(x)  Q(x)) = ((? x. P(x))  (? x. Q(x)))"; 
217 
prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))"; 

218 

2134  219 
(* '&' congruence rule: not included by default! 
220 
May slow rewrite proofs down by as much as 50% *) 

221 

222 
let val th = prove_goal HOL.thy 

223 
"(P=P')> (P'> (Q=Q'))> ((P&Q) = (P'&Q'))" 

4769
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

224 
(fn _=> [Blast_tac 1]) 
2134  225 
in bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
226 

227 
let val th = prove_goal HOL.thy 

228 
"(Q=Q')> (Q'> (P=P'))> ((P&Q) = (P'&Q'))" 

4769
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

229 
(fn _=> [Blast_tac 1]) 
2134  230 
in bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
231 

232 
(* '' congruence rule: not included by default! *) 

233 

234 
let val th = prove_goal HOL.thy 

235 
"(P=P')> (~P'> (Q=Q'))> ((PQ) = (P'Q'))" 

4769
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

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

239 
prove "eq_sym_conv" "(x=y) = (y=x)"; 

240 

5278  241 

242 
(** ifthenelse rules **) 

243 

2134  244 
qed_goalw "if_True" HOL.thy [if_def] "(if True then x else y) = x" 
4525  245 
(K [Blast_tac 1]); 
2134  246 

247 
qed_goalw "if_False" HOL.thy [if_def] "(if False then x else y) = y" 

4525  248 
(K [Blast_tac 1]); 
2134  249 

5304  250 
qed_goalw "if_P" HOL.thy [if_def] "!!P. P ==> (if P then x else y) = x" 
251 
(K [Blast_tac 1]); 

252 

2134  253 
qed_goalw "if_not_P" HOL.thy [if_def] "!!P. ~P ==> (if P then x else y) = y" 
4525  254 
(K [Blast_tac 1]); 
2134  255 

4830  256 
qed_goal "split_if" HOL.thy 
4205
96632970d203
simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents:
4189
diff
changeset

257 
"P(if Q then x else y) = ((Q > P(x)) & (~Q > P(y)))" (K [ 
96632970d203
simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents:
4189
diff
changeset

258 
res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1, 
2134  259 
stac if_P 2, 
260 
stac if_not_P 1, 

4769
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

261 
ALLGOALS (Blast_tac)]); 
4830  262 
(* for backwards compatibility: *) 
263 
val expand_if = split_if; 

4205
96632970d203
simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents:
4189
diff
changeset

264 

96632970d203
simpdata.ML: renamed split_prem_tac to split_asm_tac, added split_if_asm
oheimb
parents:
4189
diff
changeset

265 
qed_goal "split_if_asm" HOL.thy 
4769
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

266 
"P(if Q then x else y) = (~((Q & ~P x)  (~Q & ~P y)))" 
4830  267 
(K [stac split_if 1, 
4769
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

268 
Blast_tac 1]); 
2134  269 

5304  270 
qed_goal "if_cancel" HOL.thy "(if c then x else x) = x" 
271 
(K [stac split_if 1, Blast_tac 1]); 

272 

273 
qed_goal "if_eq_cancel" HOL.thy "(if x = y then y else x) = x" 

274 
(K [stac split_if 1, Blast_tac 1]); 

275 

4769
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

276 
(*This form is useful for expanding IFs on the RIGHT of the ==> symbol*) 
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

277 
qed_goal "if_bool_eq_conj" HOL.thy 
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

278 
"(if P then Q else R) = ((P>Q) & (~P>R))" 
4830  279 
(K [rtac split_if 1]); 
4769
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

280 

bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

281 
(*And this form is useful for expanding IFs on the LEFT*) 
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

282 
qed_goal "if_bool_eq_disj" HOL.thy 
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

283 
"(if P then Q else R) = ((P&Q)  (~P&R))" 
4830  284 
(K [stac split_if 1, 
4769
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

285 
Blast_tac 1]); 
2134  286 

4351  287 

288 
(*** make simplification procedures for quantifier elimination ***) 

289 

290 
structure Quantifier1 = Quantifier1Fun( 

291 
struct 

292 
(*abstract syntax*) 

293 
fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t) 

294 
 dest_eq _ = None; 

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

296 
 dest_conj _ = None; 

297 
val conj = HOLogic.conj 

298 
val imp = HOLogic.imp 

299 
(*rules*) 

300 
val iff_reflection = eq_reflection 

301 
val iffI = iffI 

302 
val sym = sym 

303 
val conjI= conjI 

304 
val conjE= conjE 

305 
val impI = impI 

306 
val impE = impE 

307 
val mp = mp 

308 
val exI = exI 

309 
val exE = exE 

310 
val allI = allI 

311 
val allE = allE 

312 
end); 

313 

4320
24d9e6639cd4
Moved the quantifier elimination simp procs into Provers.
nipkow
parents:
4205
diff
changeset

314 
local 
24d9e6639cd4
Moved the quantifier elimination simp procs into Provers.
nipkow
parents:
4205
diff
changeset

315 
val ex_pattern = 
4351  316 
read_cterm (sign_of HOL.thy) ("EX x. P(x) & Q(x)",HOLogic.boolT) 
3913  317 

4320
24d9e6639cd4
Moved the quantifier elimination simp procs into Provers.
nipkow
parents:
4205
diff
changeset

318 
val all_pattern = 
4351  319 
read_cterm (sign_of HOL.thy) ("ALL x. P(x) & P'(x) > Q(x)",HOLogic.boolT) 
4320
24d9e6639cd4
Moved the quantifier elimination simp procs into Provers.
nipkow
parents:
4205
diff
changeset

320 

24d9e6639cd4
Moved the quantifier elimination simp procs into Provers.
nipkow
parents:
4205
diff
changeset

321 
in 
24d9e6639cd4
Moved the quantifier elimination simp procs into Provers.
nipkow
parents:
4205
diff
changeset

322 
val defEX_regroup = 
24d9e6639cd4
Moved the quantifier elimination simp procs into Provers.
nipkow
parents:
4205
diff
changeset

323 
mk_simproc "defined EX" [ex_pattern] Quantifier1.rearrange_ex; 
24d9e6639cd4
Moved the quantifier elimination simp procs into Provers.
nipkow
parents:
4205
diff
changeset

324 
val defALL_regroup = 
24d9e6639cd4
Moved the quantifier elimination simp procs into Provers.
nipkow
parents:
4205
diff
changeset

325 
mk_simproc "defined ALL" [all_pattern] Quantifier1.rearrange_all; 
24d9e6639cd4
Moved the quantifier elimination simp procs into Provers.
nipkow
parents:
4205
diff
changeset

326 
end; 
3913  327 

4351  328 

329 
(*** Case splitting ***) 

3913  330 

5304  331 
structure SplitterData = 
332 
struct 

333 
structure Simplifier = Simplifier 

5552  334 
val mk_eq = mk_eq 
5304  335 
val meta_eq_to_iff = meta_eq_to_obj_eq 
336 
val iffD = iffD2 

337 
val disjE = disjE 

338 
val conjE = conjE 

339 
val exE = exE 

340 
val contrapos = contrapos 

341 
val contrapos2 = contrapos2 

342 
val notnotD = notnotD 

343 
end; 

4681  344 

5304  345 
structure Splitter = SplitterFun(SplitterData); 
2263  346 

5304  347 
val split_tac = Splitter.split_tac; 
348 
val split_inside_tac = Splitter.split_inside_tac; 

349 
val split_asm_tac = Splitter.split_asm_tac; 

5307  350 
val op addsplits = Splitter.addsplits; 
351 
val op delsplits = Splitter.delsplits; 

5304  352 
val Addsplits = Splitter.Addsplits; 
353 
val Delsplits = Splitter.Delsplits; 

4718
fc2ba9fb2135
new rewrite rules not1_or, not2_or, and if_eq_cancel
oheimb
parents:
4681
diff
changeset

354 

2134  355 
(** 'if' congruence rules: neither included by default! *) 
356 

357 
(*Simplifies x assuming c and y assuming ~c*) 

358 
qed_goal "if_cong" HOL.thy 

359 
"[ b=c; c ==> x=u; ~c ==> y=v ] ==>\ 

360 
\ (if b then x else y) = (if c then u else v)" 

361 
(fn rew::prems => 

4830  362 
[stac rew 1, stac split_if 1, stac split_if 1, 
2935  363 
blast_tac (HOL_cs addDs prems) 1]); 
2134  364 

365 
(*Prevents simplification of x and y: much faster*) 

366 
qed_goal "if_weak_cong" HOL.thy 

367 
"b=c ==> (if b then x else y) = (if c then x else y)" 

368 
(fn [prem] => [rtac (prem RS arg_cong) 1]); 

369 

370 
(*Prevents simplification of t: much faster*) 

371 
qed_goal "let_weak_cong" HOL.thy 

372 
"a = b ==> (let x=a in t(x)) = (let x=b in t(x))" 

373 
(fn [prem] => [rtac (prem RS arg_cong) 1]); 

374 

375 
(*In general it seems wrong to add distributive laws by default: they 

376 
might cause exponential blowup. But imp_disjL has been in for a while 

377 
and cannot be removed without affecting existing proofs. Moreover, 

378 
rewriting by "(PQ > R) = ((P>R)&(Q>R))" might be justified on the 

379 
grounds that it allows simplification of R in the two cases.*) 

380 

5304  381 
fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th; 
382 

2134  383 
val mksimps_pairs = 
384 
[("op >", [mp]), ("op &", [conjunct1,conjunct2]), 

385 
("All", [spec]), ("True", []), ("False", []), 

4769
bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
parents:
4744
diff
changeset

386 
("If", [if_bool_eq_conj RS iffD1])]; 
1758  387 

5552  388 
(* ###FIXME: move to Provers/simplifier.ML 
5304  389 
val mk_atomize: (string * thm list) list > thm > thm list 
390 
*) 

5552  391 
(* ###FIXME: move to Provers/simplifier.ML *) 
5304  392 
fun mk_atomize pairs = 
393 
let fun atoms th = 

394 
(case concl_of th of 

395 
Const("Trueprop",_) $ p => 

396 
(case head_of p of 

397 
Const(a,_) => 

398 
(case assoc(pairs,a) of 

399 
Some(rls) => flat (map atoms ([th] RL rls)) 

400 
 None => [th]) 

401 
 _ => [th]) 

402 
 _ => [th]) 

403 
in atoms end; 

404 

5552  405 
fun mksimps pairs = (map mk_eq o mk_atomize pairs o gen_all); 
5304  406 

4640  407 
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

408 
atac, etac FalseE]; 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

409 
(*No premature instantiation of variables during simplification*) 
4640  410 
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

411 
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

412 

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

413 
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

414 
setSSolver safe_solver 
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

415 
setSolver unsafe_solver 
4677  416 
setmksimps (mksimps mksimps_pairs) 
5552  417 
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

418 

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

419 
val HOL_ss = 
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

420 
HOL_basic_ss addsimps 
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

421 
([triv_forall_equality, (* prunes params *) 
3654  422 
True_implies_equals, (* prune asms `True' *) 
4718
fc2ba9fb2135
new rewrite rules not1_or, not2_or, and if_eq_cancel
oheimb
parents:
4681
diff
changeset

423 
if_True, if_False, if_cancel, if_eq_cancel, 
5304  424 
imp_disjL, conj_assoc, disj_assoc, 
3904  425 
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

426 
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

427 
@ 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

428 
addsimprocs [defALL_regroup,defEX_regroup] 
4744
4469d498cd48
moved addsplits [expand_if] from HOL_basic_ss to HOL_ss;
wenzelm
parents:
4743
diff
changeset

429 
addcongs [imp_cong] 
4830  430 
addsplits [split_if]; 
2082  431 

1655  432 
qed_goal "if_distrib" HOL.thy 
433 
"f(if c then x else y) = (if c then f x else f y)" 

4830  434 
(K [simp_tac (HOL_ss setloop (split_tac [split_if])) 1]); 
1655  435 

1984  436 

4327  437 
(*For expand_case_tac*) 
2948
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

438 
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

439 
by (case_tac "P" 1); 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

440 
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

441 
val expand_case = result(); 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

442 

4327  443 
(*Used in Auth proofs. Typically P contains Vars that become instantiated 
444 
during unification.*) 

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

445 
fun expand_case_tac P i = 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

446 
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

447 
Simp_tac (i+1) THEN 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

448 
Simp_tac i; 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

449 

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

450 

4119  451 
(* install implicit simpset *) 
1984  452 

4086  453 
simpset_ref() := HOL_ss; 
1984  454 

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

455 

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

456 

5219  457 
(*** integration of simplifier with classical reasoner ***) 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

458 

5219  459 
structure Clasimp = ClasimpFun 
5552  460 
(structure Simplifier = Simplifier 
461 
and Classical = Classical 

462 
and Blast = Blast); 

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

463 
open Clasimp; 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

464 

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

465 
val HOL_css = (HOL_cs, HOL_ss); 