author  wenzelm 
Tue, 29 Aug 2000 00:55:31 +0200  
changeset 9713  2c5b42311eb0 
parent 9511  bb029080ff8b 
child 9736  332fab43628f 
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 

9713  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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9713  15 
(*Takes UNCONDITIONAL theorems of the form A<>B to 
16 
the Safe Intr rule B==>A and 

2031  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 

9713  23 
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 
9713  29 
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]) 
9713  34 
handle TERM _ => error ("AddIffs: theorem must be unconditional\n" ^ 
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string_of_thm th); 
1984  36 

9713  37 
fun delIff ((cla, simp), th) = 
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(case HOLogic.dest_Trueprop (#prop (rep_thm th)) of 
9713  39 
(Const ("Not", _) $ A) => 
40 
cla delrules [zero_var_indexes (th RS notE)] 

41 
 (con $ _ $ _) => 

42 
if con = iff_const 

43 
then cla delrules 

44 
[zero_var_indexes (th RS iffD2), 

45 
cla_make_elim (zero_var_indexes (th RS iffD1))] 

46 
else cla delrules [th] 

47 
 _ => cla delrules [th], 

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simp delsimps [th]) 
9713  49 
handle TERM _ => (warning("DelIffs: ignoring conditional theorem\n" ^ 
50 
string_of_thm th); (cla, simp)); 

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fun store_clasimp (cla, simp) = (claset_ref () := cla; simpset_ref () := simp) 
1984  53 
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  58 
end; 
59 

5304  60 

7357  61 
val [prem] = goal (the_context ()) "x==y ==> x=y"; 
7031  62 
by (rewtac prem); 
63 
by (rtac refl 1); 

64 
qed "meta_eq_to_obj_eq"; 

4640  65 

9023  66 
Goal "(%s. f s) = f"; 
67 
br refl 1; 

68 
qed "eta_contract_eq"; 

69 

923  70 
local 
71 

7357  72 
fun prover s = prove_goal (the_context ()) s (fn _ => [(Blast_tac 1)]); 
923  73 

2134  74 
in 
75 

5552  76 
(*Make metaequalities. The operator below is Trueprop*) 
77 

6128  78 
fun mk_meta_eq r = r RS eq_reflection; 
79 

80 
val Eq_TrueI = mk_meta_eq(prover "P > (P = True)" RS mp); 

81 
val Eq_FalseI = mk_meta_eq(prover "~P > (P = False)" RS mp); 

5304  82 

6128  83 
fun mk_eq th = case concl_of th of 
84 
Const("==",_)$_$_ => th 

85 
 _$(Const("op =",_)$_$_) => mk_meta_eq th 

86 
 _$(Const("Not",_)$_) => th RS Eq_FalseI 

87 
 _ => th RS Eq_TrueI; 

88 
(* last 2 lines requires all formulae to be of the from Trueprop(.) *) 

5304  89 

6128  90 
fun mk_eq_True r = Some(r RS meta_eq_to_obj_eq RS Eq_TrueI); 
5552  91 

9713  92 
(*Congruence rules for = (instead of ==)*) 
6128  93 
fun mk_meta_cong rl = 
94 
standard(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl)) 

95 
handle THM _ => 

96 
error("Premises and conclusion of congruence rules must be =equalities"); 

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val not_not = prover "(~ ~ P) = P"; 
923  99 

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val simp_thms = [not_not] @ map prover 
2082  101 
[ "(x=x) = True", 
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"(~True) = False", "(~False) = True", 
2082  103 
"(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))", 
4640  104 
"(True=P) = P", "(P=True) = P", "(False=P) = (~P)", "(P=False) = (~P)", 
9713  105 
"(True > P) = P", "(False > P) = True", 
2082  106 
"(P > True) = True", "(P > P) = True", 
107 
"(P > False) = (~P)", "(P > ~P) = (~P)", 

9713  108 
"(P & True) = P", "(True & P) = P", 
2800  109 
"(P & False) = False", "(False & P) = False", 
110 
"(P & P) = P", "(P & (P & Q)) = (P & Q)", 

3913  111 
"(P & ~P) = False", "(~P & P) = False", 
9713  112 
"(P  True) = True", "(True  P) = True", 
2800  113 
"(P  False) = P", "(False  P) = P", 
114 
"(P  P) = P", "(P  (P  Q)) = (P  Q)", 

3913  115 
"(P  ~P) = True", "(~P  P) = True", 
2082  116 
"((~P) = (~Q)) = (P=Q)", 
9713  117 
"(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x", 
4351  118 
(*two needed for the onepointrule quantifier simplification procs*) 
9713  119 
"(? x. x=t & P(x)) = P(t)", (*essential for termination!!*) 
4351  120 
"(! x. t=x > P(x)) = P(t)" ]; (*covers a stray case*) 
923  121 

1922  122 
val imp_cong = impI RSN 
7357  123 
(2, prove_goal (the_context ()) "(P=P')> (P'> (Q=Q'))> ((P>Q) = (P'>Q'))" 
7031  124 
(fn _=> [(Blast_tac 1)]) RS mp RS mp); 
1922  125 

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(*Miniscoping: pushing in existential quantifiers*) 
7648  127 
val ex_simps = map prover 
3842  128 
["(EX x. P x & Q) = ((EX x. P x) & Q)", 
129 
"(EX x. P & Q x) = (P & (EX x. Q x))", 

130 
"(EX x. P x  Q) = ((EX x. P x)  Q)", 

131 
"(EX x. P  Q x) = (P  (EX x. Q x))", 

132 
"(EX x. P x > Q) = ((ALL x. P x) > Q)", 

133 
"(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  137 
["(ALL x. P x & Q) = ((ALL x. P x) & Q)", 
138 
"(ALL x. P & Q x) = (P & (ALL x. Q x))", 

139 
"(ALL x. P x  Q) = ((ALL x. P x)  Q)", 

140 
"(ALL x. P  Q x) = (P  (ALL x. Q x))", 

141 
"(ALL x. P x > Q) = ((EX x. P x) > Q)", 

142 
"(ALL x. P > Q x) = (P > (ALL x. Q x))"]; 

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923  144 

2022  145 
(* elimination of existential quantifiers in assumptions *) 
923  146 

147 
val ex_all_equiv = 

7357  148 
let val lemma1 = prove_goal (the_context ()) 
923  149 
"(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)" 
150 
(fn prems => [resolve_tac prems 1, etac exI 1]); 

7357  151 
val lemma2 = prove_goalw (the_context ()) [Ex_def] 
923  152 
"(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)" 
7031  153 
(fn prems => [(REPEAT(resolve_tac prems 1))]) 
923  154 
in equal_intr lemma1 lemma2 end; 
155 

156 
end; 

157 

7648  158 
bind_thms ("ex_simps", ex_simps); 
159 
bind_thms ("all_simps", all_simps); 

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bind_thm ("not_not", not_not); 
7648  161 

3654  162 
(* Elimination of True from asumptions: *) 
163 

7357  164 
val True_implies_equals = prove_goal (the_context ()) 
3654  165 
"(True ==> PROP P) == PROP P" 
7031  166 
(fn _ => [rtac equal_intr_rule 1, atac 2, 
3654  167 
METAHYPS (fn prems => resolve_tac prems 1) 1, 
168 
rtac TrueI 1]); 

169 

7357  170 
fun prove nm thm = qed_goal nm (the_context ()) thm (fn _ => [(Blast_tac 1)]); 
923  171 

9511  172 
prove "eq_commute" "(a=b) = (b=a)"; 
7623  173 
prove "eq_left_commute" "(P=(Q=R)) = (Q=(P=R))"; 
174 
prove "eq_assoc" "((P=Q)=R) = (P=(Q=R))"; 

175 
val eq_ac = [eq_commute, eq_left_commute, eq_assoc]; 

176 

9511  177 
prove "neq_commute" "(a~=b) = (b~=a)"; 
178 

923  179 
prove "conj_commute" "(P&Q) = (Q&P)"; 
180 
prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))"; 

181 
val conj_comms = [conj_commute, conj_left_commute]; 

2134  182 
prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))"; 
923  183 

1922  184 
prove "disj_commute" "(PQ) = (QP)"; 
185 
prove "disj_left_commute" "(P(QR)) = (Q(PR))"; 

186 
val disj_comms = [disj_commute, disj_left_commute]; 

2134  187 
prove "disj_assoc" "((PQ)R) = (P(QR))"; 
1922  188 

923  189 
prove "conj_disj_distribL" "(P&(QR)) = (P&Q  P&R)"; 
190 
prove "conj_disj_distribR" "((PQ)&R) = (P&R  Q&R)"; 

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1892  192 
prove "disj_conj_distribL" "(P(Q&R)) = ((PQ) & (PR))"; 
193 
prove "disj_conj_distribR" "((P&Q)R) = ((PR) & (QR))"; 

194 

2134  195 
prove "imp_conjR" "(P > (Q&R)) = ((P>Q) & (P>R))"; 
196 
prove "imp_conjL" "((P&Q) >R) = (P > (Q > R))"; 

197 
prove "imp_disjL" "((PQ) > R) = ((P>R)&(Q>R))"; 

1892  198 

3448  199 
(*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*) 
8114  200 
prove "imp_disj_not1" "(P > Q  R) = (~Q > P > R)"; 
201 
prove "imp_disj_not2" "(P > Q  R) = (~R > P > Q)"; 

3448  202 

3904  203 
prove "imp_disj1" "((P>Q)R) = (P> QR)"; 
204 
prove "imp_disj2" "(Q(P>R)) = (P> QR)"; 

205 

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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  209 
prove "not_iff" "(P~=Q) = (P = (~Q))"; 
4743  210 
prove "disj_not1" "(~P  Q) = (P > Q)"; 
211 
prove "disj_not2" "(P  ~Q) = (Q > P)"; (* changes orientation :( *) 

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prove "imp_conv_disj" "(P > Q) = ((~P)  Q)"; 
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prove "iff_conv_conj_imp" "(P = Q) = ((P > Q) & (Q > P))"; 
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9713  217 
(*Avoids duplication of subgoals after split_if, when the true and false 
218 
cases boil down to the same thing.*) 

2134  219 
prove "cases_simp" "((P > Q) & (~P > Q)) = Q"; 
220 

3842  221 
prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))"; 
1922  222 
prove "imp_all" "((! x. P x) > Q) = (? x. P x > Q)"; 
3842  223 
prove "not_ex" "(~ (? x. P(x))) = (! x.~P(x))"; 
1922  224 
prove "imp_ex" "((? x. P x) > Q) = (! x. P x > Q)"; 
1660  225 

1655  226 
prove "ex_disj_distrib" "(? x. P(x)  Q(x)) = ((? x. P(x))  (? x. Q(x)))"; 
227 
prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))"; 

228 

2134  229 
(* '&' congruence rule: not included by default! 
230 
May slow rewrite proofs down by as much as 50% *) 

231 

9713  232 
let val th = prove_goal (the_context ()) 
2134  233 
"(P=P')> (P'> (Q=Q'))> ((P&Q) = (P'&Q'))" 
7031  234 
(fn _=> [(Blast_tac 1)]) 
2134  235 
in bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
236 

9713  237 
let val th = prove_goal (the_context ()) 
2134  238 
"(Q=Q')> (Q'> (P=P'))> ((P&Q) = (P'&Q'))" 
7031  239 
(fn _=> [(Blast_tac 1)]) 
2134  240 
in bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
241 

242 
(* '' congruence rule: not included by default! *) 

243 

9713  244 
let val th = prove_goal (the_context ()) 
2134  245 
"(P=P')> (~P'> (Q=Q'))> ((PQ) = (P'Q'))" 
7031  246 
(fn _=> [(Blast_tac 1)]) 
2134  247 
in bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
248 

249 
prove "eq_sym_conv" "(x=y) = (y=x)"; 

250 

5278  251 

252 
(** ifthenelse rules **) 

253 

7031  254 
Goalw [if_def] "(if True then x else y) = x"; 
255 
by (Blast_tac 1); 

256 
qed "if_True"; 

2134  257 

7031  258 
Goalw [if_def] "(if False then x else y) = y"; 
259 
by (Blast_tac 1); 

260 
qed "if_False"; 

2134  261 

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Goalw [if_def] "P ==> (if P then x else y) = x"; 
7031  263 
by (Blast_tac 1); 
264 
qed "if_P"; 

5304  265 

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266 
Goalw [if_def] "~P ==> (if P then x else y) = y"; 
7031  267 
by (Blast_tac 1); 
268 
qed "if_not_P"; 

2134  269 

7031  270 
Goal "P(if Q then x else y) = ((Q > P(x)) & (~Q > P(y)))"; 
271 
by (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1); 

272 
by (stac if_P 2); 

273 
by (stac if_not_P 1); 

274 
by (ALLGOALS (Blast_tac)); 

275 
qed "split_if"; 

276 

277 
Goal "P(if Q then x else y) = (~((Q & ~P x)  (~Q & ~P y)))"; 

278 
by (stac split_if 1); 

279 
by (Blast_tac 1); 

280 
qed "split_if_asm"; 

2134  281 

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282 
bind_thms ("if_splits", [split_if, split_if_asm]); 
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283 

7031  284 
Goal "(if c then x else x) = x"; 
285 
by (stac split_if 1); 

286 
by (Blast_tac 1); 

287 
qed "if_cancel"; 

5304  288 

7031  289 
Goal "(if x = y then y else x) = x"; 
290 
by (stac split_if 1); 

291 
by (Blast_tac 1); 

292 
qed "if_eq_cancel"; 

5304  293 

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(*This form is useful for expanding IFs on the RIGHT of the ==> symbol*) 
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295 
Goal "(if P then Q else R) = ((P>Q) & (~P>R))"; 
7031  296 
by (rtac split_if 1); 
297 
qed "if_bool_eq_conj"; 

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299 
(*And this form is useful for expanding IFs on the LEFT*) 
7031  300 
Goal "(if P then Q else R) = ((P&Q)  (~P&R))"; 
301 
by (stac split_if 1); 

302 
by (Blast_tac 1); 

303 
qed "if_bool_eq_disj"; 

2134  304 

4351  305 

306 
(*** make simplification procedures for quantifier elimination ***) 

307 

308 
structure Quantifier1 = Quantifier1Fun( 

309 
struct 

310 
(*abstract syntax*) 

311 
fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t) 

312 
 dest_eq _ = None; 

313 
fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t) 

314 
 dest_conj _ = None; 

315 
val conj = HOLogic.conj 

316 
val imp = HOLogic.imp 

317 
(*rules*) 

318 
val iff_reflection = eq_reflection 

319 
val iffI = iffI 

320 
val sym = sym 

321 
val conjI= conjI 

322 
val conjE= conjE 

323 
val impI = impI 

324 
val impE = impE 

325 
val mp = mp 

326 
val exI = exI 

327 
val exE = exE 

328 
val allI = allI 

329 
val allE = allE 

330 
end); 

331 

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

332 
local 
24d9e6639cd4
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diff
changeset

333 
val ex_pattern = 
7357  334 
Thm.read_cterm (Theory.sign_of (the_context ())) ("EX x. P(x) & Q(x)",HOLogic.boolT) 
3913  335 

4320
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Moved the quantifier elimination simp procs into Provers.
nipkow
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diff
changeset

336 
val all_pattern = 
7357  337 
Thm.read_cterm (Theory.sign_of (the_context ())) ("ALL x. P(x) & P'(x) > Q(x)",HOLogic.boolT) 
4320
24d9e6639cd4
Moved the quantifier elimination simp procs into Provers.
nipkow
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4205
diff
changeset

338 

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

339 
in 
24d9e6639cd4
Moved the quantifier elimination simp procs into Provers.
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4205
diff
changeset

340 
val defEX_regroup = 
24d9e6639cd4
Moved the quantifier elimination simp procs into Provers.
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diff
changeset

341 
mk_simproc "defined EX" [ex_pattern] Quantifier1.rearrange_ex; 
24d9e6639cd4
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342 
val defALL_regroup = 
24d9e6639cd4
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nipkow
parents:
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diff
changeset

343 
mk_simproc "defined ALL" [all_pattern] Quantifier1.rearrange_all; 
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344 
end; 
3913  345 

4351  346 

347 
(*** Case splitting ***) 

3913  348 

5304  349 
structure SplitterData = 
350 
struct 

351 
structure Simplifier = Simplifier 

5552  352 
val mk_eq = mk_eq 
5304  353 
val meta_eq_to_iff = meta_eq_to_obj_eq 
354 
val iffD = iffD2 

355 
val disjE = disjE 

356 
val conjE = conjE 

357 
val exE = exE 

358 
val contrapos = contrapos 

359 
val contrapos2 = contrapos2 

360 
val notnotD = notnotD 

361 
end; 

4681  362 

5304  363 
structure Splitter = SplitterFun(SplitterData); 
2263  364 

5304  365 
val split_tac = Splitter.split_tac; 
366 
val split_inside_tac = Splitter.split_inside_tac; 

367 
val split_asm_tac = Splitter.split_asm_tac; 

5307  368 
val op addsplits = Splitter.addsplits; 
369 
val op delsplits = Splitter.delsplits; 

5304  370 
val Addsplits = Splitter.Addsplits; 
371 
val Delsplits = Splitter.Delsplits; 

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

372 

2134  373 
(*In general it seems wrong to add distributive laws by default: they 
374 
might cause exponential blowup. But imp_disjL has been in for a while 

9713  375 
and cannot be removed without affecting existing proofs. Moreover, 
2134  376 
rewriting by "(PQ > R) = ((P>R)&(Q>R))" might be justified on the 
377 
grounds that it allows simplification of R in the two cases.*) 

378 

5304  379 
fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th; 
380 

2134  381 
val mksimps_pairs = 
382 
[("op >", [mp]), ("op &", [conjunct1,conjunct2]), 

383 
("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

384 
("If", [if_bool_eq_conj RS iffD1])]; 
1758  385 

5552  386 
(* ###FIXME: move to Provers/simplifier.ML 
5304  387 
val mk_atomize: (string * thm list) list > thm > thm list 
388 
*) 

5552  389 
(* ###FIXME: move to Provers/simplifier.ML *) 
5304  390 
fun mk_atomize pairs = 
391 
let fun atoms th = 

392 
(case concl_of th of 

393 
Const("Trueprop",_) $ p => 

394 
(case head_of p of 

395 
Const(a,_) => 

396 
(case assoc(pairs,a) of 

397 
Some(rls) => flat (map atoms ([th] RL rls)) 

398 
 None => [th]) 

399 
 _ => [th]) 

400 
 _ => [th]) 

401 
in atoms end; 

402 

5552  403 
fun mksimps pairs = (map mk_eq o mk_atomize pairs o gen_all); 
5304  404 

7570  405 
fun unsafe_solver_tac prems = 
406 
FIRST'[resolve_tac(reflexive_thm::TrueI::refl::prems), atac, etac FalseE]; 

407 
val unsafe_solver = mk_solver "HOL unsafe" unsafe_solver_tac; 

408 

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

409 
(*No premature instantiation of variables during simplification*) 
7570  410 
fun safe_solver_tac prems = 
411 
FIRST'[match_tac(reflexive_thm::TrueI::refl::prems), 

412 
eq_assume_tac, ematch_tac [FalseE]]; 

413 
val safe_solver = mk_solver "HOL safe" safe_solver_tac; 

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

414 

9713  415 
val HOL_basic_ss = 
416 
empty_ss setsubgoaler asm_simp_tac 

417 
setSSolver safe_solver 

418 
setSolver unsafe_solver 

419 
setmksimps (mksimps mksimps_pairs) 

420 
setmkeqTrue mk_eq_True 

421 
setmkcong mk_meta_cong; 

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

422 

9713  423 
val HOL_ss = 
424 
HOL_basic_ss addsimps 

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

425 
([triv_forall_equality, (* prunes params *) 
3654  426 
True_implies_equals, (* prune asms `True' *) 
9023  427 
eta_contract_eq, (* prunes etaexpansions *) 
4718
fc2ba9fb2135
new rewrite rules not1_or, not2_or, and if_eq_cancel
oheimb
parents:
4681
diff
changeset

428 
if_True, if_False, if_cancel, if_eq_cancel, 
5304  429 
imp_disjL, conj_assoc, disj_assoc, 
3904  430 
de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp, 
8955  431 
disj_not1, not_all, not_ex, cases_simp, Eps_eq, Eps_sym_eq, 
432 
thm"plus_ac0.zero", thm"plus_ac0_zero_right"] 

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

433 
@ 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

434 
addsimprocs [defALL_regroup,defEX_regroup] 
4744
4469d498cd48
moved addsplits [expand_if] from HOL_basic_ss to HOL_ss;
wenzelm
parents:
4743
diff
changeset

435 
addcongs [imp_cong] 
4830  436 
addsplits [split_if]; 
2082  437 

6293  438 
(*Simplifies x assuming c and y assuming ~c*) 
439 
val prems = Goalw [if_def] 

440 
"[ b=c; c ==> x=u; ~c ==> y=v ] ==> \ 

441 
\ (if b then x else y) = (if c then u else v)"; 

442 
by (asm_simp_tac (HOL_ss addsimps prems) 1); 

443 
qed "if_cong"; 

444 

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

445 
(*Prevents simplification of x and y: faster and allows the execution 
48e235179ffb
added parentheses to cope with a possible reduction of the precedence of unary
paulson
parents:
7031
diff
changeset

446 
of functional programs. NOW THE DEFAULT.*) 
7031  447 
Goal "b=c ==> (if b then x else y) = (if c then x else y)"; 
448 
by (etac arg_cong 1); 

449 
qed "if_weak_cong"; 

6293  450 

451 
(*Prevents simplification of t: much faster*) 

7031  452 
Goal "a = b ==> (let x=a in t(x)) = (let x=b in t(x))"; 
453 
by (etac arg_cong 1); 

454 
qed "let_weak_cong"; 

6293  455 

7031  456 
Goal "f(if c then x else y) = (if c then f x else f y)"; 
457 
by (simp_tac (HOL_ss setloop (split_tac [split_if])) 1); 

458 
qed "if_distrib"; 

1655  459 

4327  460 
(*For expand_case_tac*) 
7584  461 
val prems = Goal "[ P ==> Q(True); ~P ==> Q(False) ] ==> Q(P)"; 
2948
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

462 
by (case_tac "P" 1); 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

463 
by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems))); 
7584  464 
qed "expand_case"; 
2948
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

465 

4327  466 
(*Used in Auth proofs. Typically P contains Vars that become instantiated 
467 
during unification.*) 

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

468 
fun expand_case_tac P i = 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

469 
res_inst_tac [("P",P)] expand_case i THEN 
9713  470 
Simp_tac (i+1) THEN 
2948
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

471 
Simp_tac i; 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

472 

7584  473 
(*This lemma restricts the effect of the rewrite rule u=v to the lefthand 
474 
side of an equality. Used in {Integ,Real}/simproc.ML*) 

475 
Goal "x=y ==> (x=z) = (y=z)"; 

476 
by (asm_simp_tac HOL_ss 1); 

477 
qed "restrict_to_left"; 

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

478 

7357  479 
(* default simpset *) 
9713  480 
val simpsetup = 
481 
[fn thy => (simpset_ref_of thy := HOL_ss addcongs [if_weak_cong]; thy)]; 

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

482 

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

483 

5219  484 
(*** integration of simplifier with classical reasoner ***) 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

485 

5219  486 
structure Clasimp = ClasimpFun 
8473  487 
(structure Simplifier = Simplifier and Splitter = Splitter 
488 
and Classical = Classical and Blast = Blast); 

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

489 
open Clasimp; 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

490 

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

491 
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

492 

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

493 

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

494 
(* "iff" attribute *) 
978db2870862
change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents:
8473
diff
changeset

495 

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

496 
val iff_add_global = Clasimp.change_global_css (op addIffs); 
978db2870862
change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents:
8473
diff
changeset

497 
val iff_add_local = Clasimp.change_local_css (op addIffs); 
978db2870862
change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents:
8473
diff
changeset

498 

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

499 
val iff_attrib_setup = 
978db2870862
change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents:
8473
diff
changeset

500 
[Attrib.add_attributes [("iff", (Attrib.no_args iff_add_global, Attrib.no_args iff_add_local), 
978db2870862
change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents:
8473
diff
changeset

501 
"add rules to simpset and claset simultaneously")]]; 
978db2870862
change_global/local_css move to Provers/clasimp.ML;
wenzelm
parents:
8473
diff
changeset

502 

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

503 

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

504 

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

505 
(*** A general refutation procedure ***) 
9713  506 

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

507 
(* Parameters: 
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 
test: term > bool 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

510 
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

511 
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

512 
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

513 

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

514 
prep_tac: int > tactic 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

515 
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

516 
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

517 

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

518 
ref_tac: int > tactic 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

519 
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

520 
[ A1; ...; An ] ==> False 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

521 
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

522 
*) 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

523 

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

524 
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

525 
let val nnf_simps = 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

526 
[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

527 
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

528 
val nnf_simpset = 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

529 
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

530 
setmksimps (mksimps mksimps_pairs) 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

531 
addsimps nnf_simps; 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

532 
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

533 

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

534 
val refute_prems_tac = 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

535 
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

536 
filter_prems_tac test 1 ORELSE 
6301  537 
etac disjE 1) THEN 
5975
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

538 
ref_tac 1; 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

539 
in EVERY'[TRY o filter_prems_tac test, 
6128  540 
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

541 
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

542 
end; 