author  paulson 
Fri, 07 Jan 2000 11:06:03 +0100  
changeset 8114  09a7a180cc99 
parent 7711  4dae7a4fceaf 
child 8473  2798d2f71ec2 
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 

6514  11 
(*** Addition of rules to simpsets and clasets simultaneously ***) (* FIXME move to Provers/clasimp.ML? *) 
1984  12 

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

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

20 
local 

21 
val iff_const = HOLogic.eq_const HOLogic.boolT; 

22 

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fun addIff ((cla, simp), th) = 
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(case HOLogic.dest_Trueprop (#prop (rep_thm th)) of 
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(Const("Not", _) $ A) => 
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cla addSEs [zero_var_indexes (th RS notE)] 
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 (con $ _ $ _) => 
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if con = iff_const 
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then cla addSIs [zero_var_indexes (th RS iffD2)] 
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addSDs [zero_var_indexes (th RS iffD1)] 
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else cla addSIs [th] 
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 _ => cla addSIs [th], 
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simp addsimps [th]) 
6968  34 
handle TERM _ => error ("AddIffs: theorem must be unconditional\n" ^ 
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string_of_thm th); 
1984  36 

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fun delIff ((cla, simp), th) = 
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(case HOLogic.dest_Trueprop (#prop (rep_thm th)) of 
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(Const ("Not", _) $ A) => 
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cla delrules [zero_var_indexes (th RS notE)] 
2031  41 
 (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]) 
6968  48 
handle TERM _ => (warning("DelIffs: ignoring conditional theorem\n" ^ 
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string_of_thm th); (cla, simp)); 
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fun store_clasimp (cla, simp) = (claset_ref () := cla; simpset_ref () := simp) 
1984  52 
in 
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val op addIffs = foldl addIff; 
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val op delIffs = foldl delIff; 
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fun AddIffs thms = store_clasimp ((claset (), simpset ()) addIffs thms); 
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fun DelIffs thms = store_clasimp ((claset (), simpset ()) delIffs thms); 
1984  57 
end; 
58 

5304  59 

6514  60 
(* "iff" attribute *) 
61 

62 
local 

63 
fun change_global_css f (thy, th) = 

64 
let 

65 
val cs_ref = Classical.claset_ref_of thy; 

66 
val ss_ref = Simplifier.simpset_ref_of thy; 

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

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

69 

70 
fun change_local_css f (ctxt, th) = 

71 
let 

72 
val cs = Classical.get_local_claset ctxt; 

73 
val ss = Simplifier.get_local_simpset ctxt; 

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

75 
val ctxt' = 

76 
ctxt 

77 
> Classical.put_local_claset cs' 

78 
> Simplifier.put_local_simpset ss'; 

79 
in (ctxt', th) end; 

80 
in 

81 

82 
val iff_add_global = change_global_css (op addIffs); 

83 
val iff_add_local = change_local_css (op addIffs); 

84 

7369  85 
val iff_attrib_setup = 
6514  86 
[Attrib.add_attributes [("iff", (Attrib.no_args iff_add_global, Attrib.no_args iff_add_local), 
87 
"add rules to simpset and claset simultaneously")]]; 

88 

89 
end; 

90 

91 

7357  92 
val [prem] = goal (the_context ()) "x==y ==> x=y"; 
7031  93 
by (rewtac prem); 
94 
by (rtac refl 1); 

95 
qed "meta_eq_to_obj_eq"; 

4640  96 

923  97 
local 
98 

7357  99 
fun prover s = prove_goal (the_context ()) s (fn _ => [(Blast_tac 1)]); 
923  100 

2134  101 
in 
102 

5552  103 
(*Make metaequalities. The operator below is Trueprop*) 
104 

6128  105 
fun mk_meta_eq r = r RS eq_reflection; 
106 

107 
val Eq_TrueI = mk_meta_eq(prover "P > (P = True)" RS mp); 

108 
val Eq_FalseI = mk_meta_eq(prover "~P > (P = False)" RS mp); 

5304  109 

6128  110 
fun mk_eq th = case concl_of th of 
111 
Const("==",_)$_$_ => th 

112 
 _$(Const("op =",_)$_$_) => mk_meta_eq th 

113 
 _$(Const("Not",_)$_) => th RS Eq_FalseI 

114 
 _ => th RS Eq_TrueI; 

115 
(* last 2 lines requires all formulae to be of the from Trueprop(.) *) 

5304  116 

6128  117 
fun mk_eq_True r = Some(r RS meta_eq_to_obj_eq RS Eq_TrueI); 
5552  118 

6128  119 
fun mk_meta_cong rl = 
120 
standard(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl)) 

121 
handle THM _ => 

122 
error("Premises and conclusion of congruence rules must be =equalities"); 

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val not_not = prover "(~ ~ P) = P"; 
923  125 

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val simp_thms = [not_not] @ map prover 
2082  127 
[ "(x=x) = True", 
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"(~True) = False", "(~False) = True", 
2082  129 
"(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))", 
4640  130 
"(True=P) = P", "(P=True) = P", "(False=P) = (~P)", "(P=False) = (~P)", 
2082  131 
"(True > P) = P", "(False > P) = True", 
132 
"(P > True) = True", "(P > P) = True", 

133 
"(P > False) = (~P)", "(P > ~P) = (~P)", 

134 
"(P & True) = P", "(True & P) = P", 

2800  135 
"(P & False) = False", "(False & P) = False", 
136 
"(P & P) = P", "(P & (P & Q)) = (P & Q)", 

3913  137 
"(P & ~P) = False", "(~P & P) = False", 
2082  138 
"(P  True) = True", "(True  P) = True", 
2800  139 
"(P  False) = P", "(False  P) = P", 
140 
"(P  P) = P", "(P  (P  Q)) = (P  Q)", 

3913  141 
"(P  ~P) = True", "(~P  P) = True", 
2082  142 
"((~P) = (~Q)) = (P=Q)", 
3842  143 
"(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x", 
4351  144 
(*two needed for the onepointrule quantifier simplification procs*) 
145 
"(? x. x=t & P(x)) = P(t)", (*essential for termination!!*) 

146 
"(! x. t=x > P(x)) = P(t)" ]; (*covers a stray case*) 

923  147 

5552  148 
(* Add congruence rules for = (instead of ==) *) 
4351  149 

5552  150 
(* ###FIXME: Move to simplifier, 
151 
taking mk_meta_cong as input, eliminating addeqcongs and deleqcongs *) 

152 
infix 4 addcongs delcongs; 

4640  153 
fun ss addcongs congs = ss addeqcongs (map mk_meta_cong congs); 
154 
fun ss delcongs congs = ss deleqcongs (map mk_meta_cong congs); 

4086  155 
fun Addcongs congs = (simpset_ref() := simpset() addcongs congs); 
156 
fun Delcongs congs = (simpset_ref() := simpset() delcongs congs); 

1264  157 

5552  158 

1922  159 
val imp_cong = impI RSN 
7357  160 
(2, prove_goal (the_context ()) "(P=P')> (P'> (Q=Q'))> ((P>Q) = (P'>Q'))" 
7031  161 
(fn _=> [(Blast_tac 1)]) RS mp RS mp); 
1922  162 

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(*Miniscoping: pushing in existential quantifiers*) 
7648  164 
val ex_simps = map prover 
3842  165 
["(EX x. P x & Q) = ((EX x. P x) & Q)", 
166 
"(EX x. P & Q x) = (P & (EX x. Q x))", 

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

168 
"(EX x. P  Q x) = (P  (EX x. Q x))", 

169 
"(EX x. P x > Q) = ((ALL x. P x) > Q)", 

170 
"(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  174 
["(ALL x. P x & Q) = ((ALL x. P x) & Q)", 
175 
"(ALL x. P & Q x) = (P & (ALL x. Q x))", 

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

177 
"(ALL x. P  Q x) = (P  (ALL x. Q x))", 

178 
"(ALL x. P x > Q) = ((EX x. P x) > Q)", 

179 
"(ALL x. P > Q x) = (P > (ALL x. Q x))"]; 

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180 

923  181 

2022  182 
(* elimination of existential quantifiers in assumptions *) 
923  183 

184 
val ex_all_equiv = 

7357  185 
let val lemma1 = prove_goal (the_context ()) 
923  186 
"(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)" 
187 
(fn prems => [resolve_tac prems 1, etac exI 1]); 

7357  188 
val lemma2 = prove_goalw (the_context ()) [Ex_def] 
923  189 
"(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)" 
7031  190 
(fn prems => [(REPEAT(resolve_tac prems 1))]) 
923  191 
in equal_intr lemma1 lemma2 end; 
192 

193 
end; 

194 

7648  195 
bind_thms ("ex_simps", ex_simps); 
196 
bind_thms ("all_simps", all_simps); 

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bind_thm ("not_not", not_not); 
7648  198 

3654  199 
(* Elimination of True from asumptions: *) 
200 

7357  201 
val True_implies_equals = prove_goal (the_context ()) 
3654  202 
"(True ==> PROP P) == PROP P" 
7031  203 
(fn _ => [rtac equal_intr_rule 1, atac 2, 
3654  204 
METAHYPS (fn prems => resolve_tac prems 1) 1, 
205 
rtac TrueI 1]); 

206 

7357  207 
fun prove nm thm = qed_goal nm (the_context ()) thm (fn _ => [(Blast_tac 1)]); 
923  208 

7623  209 
prove "eq_commute" "(a=b)=(b=a)"; 
210 
prove "eq_left_commute" "(P=(Q=R)) = (Q=(P=R))"; 

211 
prove "eq_assoc" "((P=Q)=R) = (P=(Q=R))"; 

212 
val eq_ac = [eq_commute, eq_left_commute, eq_assoc]; 

213 

923  214 
prove "conj_commute" "(P&Q) = (Q&P)"; 
215 
prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))"; 

216 
val conj_comms = [conj_commute, conj_left_commute]; 

2134  217 
prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))"; 
923  218 

1922  219 
prove "disj_commute" "(PQ) = (QP)"; 
220 
prove "disj_left_commute" "(P(QR)) = (Q(PR))"; 

221 
val disj_comms = [disj_commute, disj_left_commute]; 

2134  222 
prove "disj_assoc" "((PQ)R) = (P(QR))"; 
1922  223 

923  224 
prove "conj_disj_distribL" "(P&(QR)) = (P&Q  P&R)"; 
225 
prove "conj_disj_distribR" "((PQ)&R) = (P&R  Q&R)"; 

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1892  227 
prove "disj_conj_distribL" "(P(Q&R)) = ((PQ) & (PR))"; 
228 
prove "disj_conj_distribR" "((P&Q)R) = ((PR) & (QR))"; 

229 

2134  230 
prove "imp_conjR" "(P > (Q&R)) = ((P>Q) & (P>R))"; 
231 
prove "imp_conjL" "((P&Q) >R) = (P > (Q > R))"; 

232 
prove "imp_disjL" "((PQ) > R) = ((P>R)&(Q>R))"; 

1892  233 

3448  234 
(*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*) 
8114  235 
prove "imp_disj_not1" "(P > Q  R) = (~Q > P > R)"; 
236 
prove "imp_disj_not2" "(P > Q  R) = (~R > P > Q)"; 

3448  237 

3904  238 
prove "imp_disj1" "((P>Q)R) = (P> QR)"; 
239 
prove "imp_disj2" "(Q(P>R)) = (P> QR)"; 

240 

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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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243 
prove "not_imp" "(~(P > Q)) = (P & ~Q)"; 
1922  244 
prove "not_iff" "(P~=Q) = (P = (~Q))"; 
4743  245 
prove "disj_not1" "(~P  Q) = (P > Q)"; 
246 
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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248 

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prove "iff_conv_conj_imp" "(P = Q) = ((P > Q) & (Q > P))"; 
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250 

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251 

4830  252 
(*Avoids duplication of subgoals after split_if, when the true and false 
2134  253 
cases boil down to the same thing.*) 
254 
prove "cases_simp" "((P > Q) & (~P > Q)) = Q"; 

255 

3842  256 
prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))"; 
1922  257 
prove "imp_all" "((! x. P x) > Q) = (? x. P x > Q)"; 
3842  258 
prove "not_ex" "(~ (? x. P(x))) = (! x.~P(x))"; 
1922  259 
prove "imp_ex" "((? x. P x) > Q) = (! x. P x > Q)"; 
1660  260 

1655  261 
prove "ex_disj_distrib" "(? x. P(x)  Q(x)) = ((? x. P(x))  (? x. Q(x)))"; 
262 
prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))"; 

263 

2134  264 
(* '&' congruence rule: not included by default! 
265 
May slow rewrite proofs down by as much as 50% *) 

266 

7357  267 
let val th = prove_goal (the_context ()) 
2134  268 
"(P=P')> (P'> (Q=Q'))> ((P&Q) = (P'&Q'))" 
7031  269 
(fn _=> [(Blast_tac 1)]) 
2134  270 
in bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
271 

7357  272 
let val th = prove_goal (the_context ()) 
2134  273 
"(Q=Q')> (Q'> (P=P'))> ((P&Q) = (P'&Q'))" 
7031  274 
(fn _=> [(Blast_tac 1)]) 
2134  275 
in bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
276 

277 
(* '' congruence rule: not included by default! *) 

278 

7357  279 
let val th = prove_goal (the_context ()) 
2134  280 
"(P=P')> (~P'> (Q=Q'))> ((PQ) = (P'Q'))" 
7031  281 
(fn _=> [(Blast_tac 1)]) 
2134  282 
in bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp))) end; 
283 

284 
prove "eq_sym_conv" "(x=y) = (y=x)"; 

285 

5278  286 

287 
(** ifthenelse rules **) 

288 

7031  289 
Goalw [if_def] "(if True then x else y) = x"; 
290 
by (Blast_tac 1); 

291 
qed "if_True"; 

2134  292 

7031  293 
Goalw [if_def] "(if False then x else y) = y"; 
294 
by (Blast_tac 1); 

295 
qed "if_False"; 

2134  296 

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diff
changeset

297 
Goalw [if_def] "P ==> (if P then x else y) = x"; 
7031  298 
by (Blast_tac 1); 
299 
qed "if_P"; 

5304  300 

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301 
Goalw [if_def] "~P ==> (if P then x else y) = y"; 
7031  302 
by (Blast_tac 1); 
303 
qed "if_not_P"; 

2134  304 

7031  305 
Goal "P(if Q then x else y) = ((Q > P(x)) & (~Q > P(y)))"; 
306 
by (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1); 

307 
by (stac if_P 2); 

308 
by (stac if_not_P 1); 

309 
by (ALLGOALS (Blast_tac)); 

310 
qed "split_if"; 

311 

4830  312 
(* for backwards compatibility: *) 
313 
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

314 

7031  315 
Goal "P(if Q then x else y) = (~((Q & ~P x)  (~Q & ~P y)))"; 
316 
by (stac split_if 1); 

317 
by (Blast_tac 1); 

318 
qed "split_if_asm"; 

2134  319 

7031  320 
Goal "(if c then x else x) = x"; 
321 
by (stac split_if 1); 

322 
by (Blast_tac 1); 

323 
qed "if_cancel"; 

5304  324 

7031  325 
Goal "(if x = y then y else x) = x"; 
326 
by (stac split_if 1); 

327 
by (Blast_tac 1); 

328 
qed "if_eq_cancel"; 

5304  329 

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

330 
(*This form is useful for expanding IFs on the RIGHT of the ==> symbol*) 
7127
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7031
diff
changeset

331 
Goal "(if P then Q else R) = ((P>Q) & (~P>R))"; 
7031  332 
by (rtac split_if 1); 
333 
qed "if_bool_eq_conj"; 

4769
bb60149fe21b
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paulson
parents:
4744
diff
changeset

334 

bb60149fe21b
changed if_bool_eq to if_bool_eq_conj and added if_bool_eq_disj
paulson
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diff
changeset

335 
(*And this form is useful for expanding IFs on the LEFT*) 
7031  336 
Goal "(if P then Q else R) = ((P&Q)  (~P&R))"; 
337 
by (stac split_if 1); 

338 
by (Blast_tac 1); 

339 
qed "if_bool_eq_disj"; 

2134  340 

4351  341 

342 
(*** make simplification procedures for quantifier elimination ***) 

343 

344 
structure Quantifier1 = Quantifier1Fun( 

345 
struct 

346 
(*abstract syntax*) 

347 
fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t) 

348 
 dest_eq _ = None; 

349 
fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t) 

350 
 dest_conj _ = None; 

351 
val conj = HOLogic.conj 

352 
val imp = HOLogic.imp 

353 
(*rules*) 

354 
val iff_reflection = eq_reflection 

355 
val iffI = iffI 

356 
val sym = sym 

357 
val conjI= conjI 

358 
val conjE= conjE 

359 
val impI = impI 

360 
val impE = impE 

361 
val mp = mp 

362 
val exI = exI 

363 
val exE = exE 

364 
val allI = allI 

365 
val allE = allE 

366 
end); 

367 

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

368 
local 
24d9e6639cd4
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diff
changeset

369 
val ex_pattern = 
7357  370 
Thm.read_cterm (Theory.sign_of (the_context ())) ("EX x. P(x) & Q(x)",HOLogic.boolT) 
3913  371 

4320
24d9e6639cd4
Moved the quantifier elimination simp procs into Provers.
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changeset

372 
val all_pattern = 
7357  373 
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.
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changeset

374 

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

375 
in 
24d9e6639cd4
Moved the quantifier elimination simp procs into Provers.
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changeset

376 
val defEX_regroup = 
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changeset

377 
mk_simproc "defined EX" [ex_pattern] Quantifier1.rearrange_ex; 
24d9e6639cd4
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378 
val defALL_regroup = 
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diff
changeset

379 
mk_simproc "defined ALL" [all_pattern] Quantifier1.rearrange_all; 
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changeset

380 
end; 
3913  381 

4351  382 

383 
(*** Case splitting ***) 

3913  384 

5304  385 
structure SplitterData = 
386 
struct 

387 
structure Simplifier = Simplifier 

5552  388 
val mk_eq = mk_eq 
5304  389 
val meta_eq_to_iff = meta_eq_to_obj_eq 
390 
val iffD = iffD2 

391 
val disjE = disjE 

392 
val conjE = conjE 

393 
val exE = exE 

394 
val contrapos = contrapos 

395 
val contrapos2 = contrapos2 

396 
val notnotD = notnotD 

397 
end; 

4681  398 

5304  399 
structure Splitter = SplitterFun(SplitterData); 
2263  400 

5304  401 
val split_tac = Splitter.split_tac; 
402 
val split_inside_tac = Splitter.split_inside_tac; 

403 
val split_asm_tac = Splitter.split_asm_tac; 

5307  404 
val op addsplits = Splitter.addsplits; 
405 
val op delsplits = Splitter.delsplits; 

5304  406 
val Addsplits = Splitter.Addsplits; 
407 
val Delsplits = Splitter.Delsplits; 

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

408 

2134  409 
(*In general it seems wrong to add distributive laws by default: they 
410 
might cause exponential blowup. But imp_disjL has been in for a while 

411 
and cannot be removed without affecting existing proofs. Moreover, 

412 
rewriting by "(PQ > R) = ((P>R)&(Q>R))" might be justified on the 

413 
grounds that it allows simplification of R in the two cases.*) 

414 

5304  415 
fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th; 
416 

2134  417 
val mksimps_pairs = 
418 
[("op >", [mp]), ("op &", [conjunct1,conjunct2]), 

419 
("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

420 
("If", [if_bool_eq_conj RS iffD1])]; 
1758  421 

5552  422 
(* ###FIXME: move to Provers/simplifier.ML 
5304  423 
val mk_atomize: (string * thm list) list > thm > thm list 
424 
*) 

5552  425 
(* ###FIXME: move to Provers/simplifier.ML *) 
5304  426 
fun mk_atomize pairs = 
427 
let fun atoms th = 

428 
(case concl_of th of 

429 
Const("Trueprop",_) $ p => 

430 
(case head_of p of 

431 
Const(a,_) => 

432 
(case assoc(pairs,a) of 

433 
Some(rls) => flat (map atoms ([th] RL rls)) 

434 
 None => [th]) 

435 
 _ => [th]) 

436 
 _ => [th]) 

437 
in atoms end; 

438 

5552  439 
fun mksimps pairs = (map mk_eq o mk_atomize pairs o gen_all); 
5304  440 

7570  441 
fun unsafe_solver_tac prems = 
442 
FIRST'[resolve_tac(reflexive_thm::TrueI::refl::prems), atac, etac FalseE]; 

443 
val unsafe_solver = mk_solver "HOL unsafe" unsafe_solver_tac; 

444 

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

445 
(*No premature instantiation of variables during simplification*) 
7570  446 
fun safe_solver_tac prems = 
447 
FIRST'[match_tac(reflexive_thm::TrueI::refl::prems), 

448 
eq_assume_tac, ematch_tac [FalseE]]; 

449 
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

450 

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

451 
val HOL_basic_ss = empty_ss setsubgoaler asm_simp_tac 
7570  452 
setSSolver safe_solver 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

453 
setSolver unsafe_solver 
4677  454 
setmksimps (mksimps mksimps_pairs) 
5552  455 
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

456 

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

457 
val HOL_ss = 
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

458 
HOL_basic_ss addsimps 
a14e5451f613
Addition of not_imp (which pushes negation into implication) as a default
paulson
parents:
3282
diff
changeset

459 
([triv_forall_equality, (* prunes params *) 
3654  460 
True_implies_equals, (* prune asms `True' *) 
4718
fc2ba9fb2135
new rewrite rules not1_or, not2_or, and if_eq_cancel
oheimb
parents:
4681
diff
changeset

461 
if_True, if_False, if_cancel, if_eq_cancel, 
5304  462 
imp_disjL, conj_assoc, disj_assoc, 
3904  463 
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

464 
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

465 
@ 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

466 
addsimprocs [defALL_regroup,defEX_regroup] 
4744
4469d498cd48
moved addsplits [expand_if] from HOL_basic_ss to HOL_ss;
wenzelm
parents:
4743
diff
changeset

467 
addcongs [imp_cong] 
4830  468 
addsplits [split_if]; 
2082  469 

6293  470 
(*Simplifies x assuming c and y assuming ~c*) 
471 
val prems = Goalw [if_def] 

472 
"[ b=c; c ==> x=u; ~c ==> y=v ] ==> \ 

473 
\ (if b then x else y) = (if c then u else v)"; 

474 
by (asm_simp_tac (HOL_ss addsimps prems) 1); 

475 
qed "if_cong"; 

476 

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

477 
(*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

478 
of functional programs. NOW THE DEFAULT.*) 
7031  479 
Goal "b=c ==> (if b then x else y) = (if c then x else y)"; 
480 
by (etac arg_cong 1); 

481 
qed "if_weak_cong"; 

6293  482 

483 
(*Prevents simplification of t: much faster*) 

7031  484 
Goal "a = b ==> (let x=a in t(x)) = (let x=b in t(x))"; 
485 
by (etac arg_cong 1); 

486 
qed "let_weak_cong"; 

6293  487 

7031  488 
Goal "f(if c then x else y) = (if c then f x else f y)"; 
489 
by (simp_tac (HOL_ss setloop (split_tac [split_if])) 1); 

490 
qed "if_distrib"; 

1655  491 

4327  492 
(*For expand_case_tac*) 
7584  493 
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

494 
by (case_tac "P" 1); 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

495 
by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems))); 
7584  496 
qed "expand_case"; 
2948
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

497 

4327  498 
(*Used in Auth proofs. Typically P contains Vars that become instantiated 
499 
during unification.*) 

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

500 
fun expand_case_tac P i = 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

501 
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

502 
Simp_tac (i+1) THEN 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

503 
Simp_tac i; 
f18035b1d531
Moved expand_case_tac from Auth/Message.ML to simpdata.ML
paulson
parents:
2935
diff
changeset

504 

7584  505 
(*This lemma restricts the effect of the rewrite rule u=v to the lefthand 
506 
side of an equality. Used in {Integ,Real}/simproc.ML*) 

507 
Goal "x=y ==> (x=z) = (y=z)"; 

508 
by (asm_simp_tac HOL_ss 1); 

509 
qed "restrict_to_left"; 

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

510 

7357  511 
(* default simpset *) 
7584  512 
val simpsetup = 
513 
[fn thy => (simpset_ref_of thy := HOL_ss addcongs [if_weak_cong]; 

514 
thy)]; 

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

515 

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

516 

5219  517 
(*** integration of simplifier with classical reasoner ***) 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

518 

5219  519 
structure Clasimp = ClasimpFun 
5552  520 
(structure Simplifier = Simplifier 
521 
and Classical = Classical 

522 
and Blast = Blast); 

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

523 
open Clasimp; 
2636
4b30dbe4a020
added delcongs, Delcongs, unsafe_solver, safe_solver, HOL_basic_ss,
oheimb
parents:
2595
diff
changeset

524 

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

525 
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

526 

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

527 

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

528 
(*** A general refutation procedure ***) 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

529 

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

530 
(* Parameters: 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

531 

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

532 
test: term > bool 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

533 
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

534 
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

535 
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

536 

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

537 
prep_tac: int > tactic 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

538 
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

539 
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

540 

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

541 
ref_tac: int > tactic 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

542 
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

543 
[ A1; ...; An ] ==> False 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

544 
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

545 
*) 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

546 

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

547 
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

548 
let val nnf_simps = 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

549 
[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

550 
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

551 
val nnf_simpset = 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

552 
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

553 
setmksimps (mksimps mksimps_pairs) 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

554 
addsimps nnf_simps; 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
diff
changeset

555 
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

556 

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

557 
val refute_prems_tac = 
cd19eaa90f45
Added a general refutation tactic which works by putting things into nnf first.
nipkow
parents:
5552
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558 
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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changeset

559 
filter_prems_tac test 1 ORELSE 
6301  560 
etac disjE 1) THEN 
5975
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

561 
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

562 
in EVERY'[TRY o filter_prems_tac test, 
6128  563 
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:
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diff
changeset

564 
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

565 
end; 