author | wenzelm |
Thu, 07 Apr 2005 09:27:33 +0200 | |
changeset 15670 | 963cd3f7976c |
parent 15574 | b1d1b5bfc464 |
child 15798 | 016f3be5a5ec |
permissions | -rw-r--r-- |
10781 | 1 |
(* Title: TFL/rules.ML |
10769 | 2 |
ID: $Id$ |
3 |
Author: Konrad Slind, Cambridge University Computer Laboratory |
|
4 |
Copyright 1997 University of Cambridge |
|
5 |
||
6 |
Emulation of HOL inference rules for TFL |
|
7 |
*) |
|
8 |
||
9 |
signature RULES = |
|
10 |
sig |
|
11 |
val dest_thm : thm -> term list * term |
|
12 |
||
13 |
(* Inference rules *) |
|
14 |
val REFL :cterm -> thm |
|
15 |
val ASSUME :cterm -> thm |
|
16 |
val MP :thm -> thm -> thm |
|
17 |
val MATCH_MP :thm -> thm -> thm |
|
18 |
val CONJUNCT1 :thm -> thm |
|
19 |
val CONJUNCT2 :thm -> thm |
|
20 |
val CONJUNCTS :thm -> thm list |
|
21 |
val DISCH :cterm -> thm -> thm |
|
22 |
val UNDISCH :thm -> thm |
|
23 |
val SPEC :cterm -> thm -> thm |
|
24 |
val ISPEC :cterm -> thm -> thm |
|
25 |
val ISPECL :cterm list -> thm -> thm |
|
26 |
val GEN :cterm -> thm -> thm |
|
27 |
val GENL :cterm list -> thm -> thm |
|
28 |
val LIST_CONJ :thm list -> thm |
|
29 |
||
30 |
val SYM : thm -> thm |
|
31 |
val DISCH_ALL : thm -> thm |
|
32 |
val FILTER_DISCH_ALL : (term -> bool) -> thm -> thm |
|
33 |
val SPEC_ALL : thm -> thm |
|
34 |
val GEN_ALL : thm -> thm |
|
35 |
val IMP_TRANS : thm -> thm -> thm |
|
36 |
val PROVE_HYP : thm -> thm -> thm |
|
37 |
||
38 |
val CHOOSE : cterm * thm -> thm -> thm |
|
39 |
val EXISTS : cterm * cterm -> thm -> thm |
|
40 |
val EXISTL : cterm list -> thm -> thm |
|
41 |
val IT_EXISTS : (cterm*cterm) list -> thm -> thm |
|
42 |
||
43 |
val EVEN_ORS : thm list -> thm list |
|
44 |
val DISJ_CASESL : thm -> thm list -> thm |
|
45 |
||
46 |
val list_beta_conv : cterm -> cterm list -> thm |
|
47 |
val SUBS : thm list -> thm -> thm |
|
48 |
val simpl_conv : simpset -> thm list -> cterm -> thm |
|
49 |
||
50 |
val rbeta : thm -> thm |
|
51 |
(* For debugging my isabelle solver in the conditional rewriter *) |
|
52 |
val term_ref : term list ref |
|
53 |
val thm_ref : thm list ref |
|
15021 | 54 |
val ss_ref : simpset list ref |
10769 | 55 |
val tracing : bool ref |
56 |
val CONTEXT_REWRITE_RULE : term * term list * thm * thm list |
|
57 |
-> thm -> thm * term list |
|
58 |
val RIGHT_ASSOC : thm -> thm |
|
59 |
||
11632 | 60 |
val prove : bool -> cterm * tactic -> thm |
10769 | 61 |
end; |
62 |
||
63 |
structure Rules: RULES = |
|
64 |
struct |
|
65 |
||
66 |
structure S = USyntax; |
|
67 |
structure U = Utils; |
|
68 |
structure D = Dcterm; |
|
69 |
||
70 |
||
71 |
fun RULES_ERR func mesg = U.ERR {module = "Rules", func = func, mesg = mesg}; |
|
72 |
||
73 |
||
74 |
fun cconcl thm = D.drop_prop (#prop (Thm.crep_thm thm)); |
|
75 |
fun chyps thm = map D.drop_prop (#hyps (Thm.crep_thm thm)); |
|
76 |
||
77 |
fun dest_thm thm = |
|
78 |
let val {prop,hyps,...} = Thm.rep_thm thm |
|
79 |
in (map HOLogic.dest_Trueprop hyps, HOLogic.dest_Trueprop prop) end |
|
80 |
handle TERM _ => raise RULES_ERR "dest_thm" "missing Trueprop"; |
|
81 |
||
82 |
||
83 |
(* Inference rules *) |
|
84 |
||
85 |
(*--------------------------------------------------------------------------- |
|
86 |
* Equality (one step) |
|
87 |
*---------------------------------------------------------------------------*) |
|
88 |
||
89 |
fun REFL tm = Thm.reflexive tm RS meta_eq_to_obj_eq |
|
90 |
handle THM (msg, _, _) => raise RULES_ERR "REFL" msg; |
|
91 |
||
92 |
fun SYM thm = thm RS sym |
|
93 |
handle THM (msg, _, _) => raise RULES_ERR "SYM" msg; |
|
94 |
||
95 |
fun ALPHA thm ctm1 = |
|
96 |
let |
|
97 |
val ctm2 = Thm.cprop_of thm; |
|
98 |
val ctm2_eq = Thm.reflexive ctm2; |
|
99 |
val ctm1_eq = Thm.reflexive ctm1; |
|
100 |
in Thm.equal_elim (Thm.transitive ctm2_eq ctm1_eq) thm end |
|
101 |
handle THM (msg, _, _) => raise RULES_ERR "ALPHA" msg; |
|
102 |
||
103 |
fun rbeta th = |
|
104 |
(case D.strip_comb (cconcl th) of |
|
105 |
(_, [l, r]) => Thm.transitive th (Thm.beta_conversion false r) |
|
106 |
| _ => raise RULES_ERR "rbeta" ""); |
|
107 |
||
108 |
||
109 |
(*---------------------------------------------------------------------------- |
|
110 |
* Implication and the assumption list |
|
111 |
* |
|
112 |
* Assumptions get stuck on the meta-language assumption list. Implications |
|
113 |
* are in the object language, so discharging an assumption "A" from theorem |
|
114 |
* "B" results in something that looks like "A --> B". |
|
115 |
*---------------------------------------------------------------------------*) |
|
116 |
||
117 |
fun ASSUME ctm = Thm.assume (D.mk_prop ctm); |
|
118 |
||
119 |
||
120 |
(*--------------------------------------------------------------------------- |
|
121 |
* Implication in TFL is -->. Meta-language implication (==>) is only used |
|
122 |
* in the implementation of some of the inference rules below. |
|
123 |
*---------------------------------------------------------------------------*) |
|
124 |
fun MP th1 th2 = th2 RS (th1 RS mp) |
|
125 |
handle THM (msg, _, _) => raise RULES_ERR "MP" msg; |
|
126 |
||
127 |
(*forces the first argument to be a proposition if necessary*) |
|
128 |
fun DISCH tm thm = Thm.implies_intr (D.mk_prop tm) thm COMP impI |
|
129 |
handle THM (msg, _, _) => raise RULES_ERR "DISCH" msg; |
|
130 |
||
131 |
fun DISCH_ALL thm = U.itlist DISCH (#hyps (Thm.crep_thm thm)) thm; |
|
132 |
||
133 |
||
134 |
fun FILTER_DISCH_ALL P thm = |
|
135 |
let fun check tm = P (#t (Thm.rep_cterm tm)) |
|
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
136 |
in foldr (fn (tm,th) => if check tm then DISCH tm th else th) |
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
137 |
thm (chyps thm) |
10769 | 138 |
end; |
139 |
||
140 |
(* freezeT expensive! *) |
|
141 |
fun UNDISCH thm = |
|
142 |
let val tm = D.mk_prop (#1 (D.dest_imp (cconcl (Thm.freezeT thm)))) |
|
143 |
in Thm.implies_elim (thm RS mp) (ASSUME tm) end |
|
144 |
handle U.ERR _ => raise RULES_ERR "UNDISCH" "" |
|
145 |
| THM _ => raise RULES_ERR "UNDISCH" ""; |
|
146 |
||
147 |
fun PROVE_HYP ath bth = MP (DISCH (cconcl ath) bth) ath; |
|
148 |
||
149 |
fun IMP_TRANS th1 th2 = th2 RS (th1 RS Thms.imp_trans) |
|
150 |
handle THM (msg, _, _) => raise RULES_ERR "IMP_TRANS" msg; |
|
151 |
||
152 |
||
153 |
(*---------------------------------------------------------------------------- |
|
154 |
* Conjunction |
|
155 |
*---------------------------------------------------------------------------*) |
|
156 |
||
157 |
fun CONJUNCT1 thm = thm RS conjunct1 |
|
158 |
handle THM (msg, _, _) => raise RULES_ERR "CONJUNCT1" msg; |
|
159 |
||
160 |
fun CONJUNCT2 thm = thm RS conjunct2 |
|
161 |
handle THM (msg, _, _) => raise RULES_ERR "CONJUNCT2" msg; |
|
162 |
||
163 |
fun CONJUNCTS th = CONJUNCTS (CONJUNCT1 th) @ CONJUNCTS (CONJUNCT2 th) handle U.ERR _ => [th]; |
|
164 |
||
165 |
fun LIST_CONJ [] = raise RULES_ERR "LIST_CONJ" "empty list" |
|
166 |
| LIST_CONJ [th] = th |
|
167 |
| LIST_CONJ (th :: rst) = MP (MP (conjI COMP (impI RS impI)) th) (LIST_CONJ rst) |
|
168 |
handle THM (msg, _, _) => raise RULES_ERR "LIST_CONJ" msg; |
|
169 |
||
170 |
||
171 |
(*---------------------------------------------------------------------------- |
|
172 |
* Disjunction |
|
173 |
*---------------------------------------------------------------------------*) |
|
174 |
local val {prop,sign,...} = rep_thm disjI1 |
|
175 |
val [P,Q] = term_vars prop |
|
176 |
val disj1 = Thm.forall_intr (Thm.cterm_of sign Q) disjI1 |
|
177 |
in |
|
178 |
fun DISJ1 thm tm = thm RS (forall_elim (D.drop_prop tm) disj1) |
|
179 |
handle THM (msg, _, _) => raise RULES_ERR "DISJ1" msg; |
|
180 |
end; |
|
181 |
||
182 |
local val {prop,sign,...} = rep_thm disjI2 |
|
183 |
val [P,Q] = term_vars prop |
|
184 |
val disj2 = Thm.forall_intr (Thm.cterm_of sign P) disjI2 |
|
185 |
in |
|
186 |
fun DISJ2 tm thm = thm RS (forall_elim (D.drop_prop tm) disj2) |
|
187 |
handle THM (msg, _, _) => raise RULES_ERR "DISJ2" msg; |
|
188 |
end; |
|
189 |
||
190 |
||
191 |
(*---------------------------------------------------------------------------- |
|
192 |
* |
|
193 |
* A1 |- M1, ..., An |- Mn |
|
194 |
* --------------------------------------------------- |
|
195 |
* [A1 |- M1 \/ ... \/ Mn, ..., An |- M1 \/ ... \/ Mn] |
|
196 |
* |
|
197 |
*---------------------------------------------------------------------------*) |
|
198 |
||
199 |
||
200 |
fun EVEN_ORS thms = |
|
201 |
let fun blue ldisjs [] _ = [] |
|
202 |
| blue ldisjs (th::rst) rdisjs = |
|
203 |
let val tail = tl rdisjs |
|
204 |
val rdisj_tl = D.list_mk_disj tail |
|
205 |
in U.itlist DISJ2 ldisjs (DISJ1 th rdisj_tl) |
|
206 |
:: blue (ldisjs @ [cconcl th]) rst tail |
|
207 |
end handle U.ERR _ => [U.itlist DISJ2 ldisjs th] |
|
208 |
in blue [] thms (map cconcl thms) end; |
|
209 |
||
210 |
||
211 |
(*---------------------------------------------------------------------------- |
|
212 |
* |
|
213 |
* A |- P \/ Q B,P |- R C,Q |- R |
|
214 |
* --------------------------------------------------- |
|
215 |
* A U B U C |- R |
|
216 |
* |
|
217 |
*---------------------------------------------------------------------------*) |
|
218 |
||
219 |
fun DISJ_CASES th1 th2 th3 = |
|
220 |
let |
|
221 |
val c = D.drop_prop (cconcl th1); |
|
222 |
val (disj1, disj2) = D.dest_disj c; |
|
223 |
val th2' = DISCH disj1 th2; |
|
224 |
val th3' = DISCH disj2 th3; |
|
225 |
in |
|
226 |
th3' RS (th2' RS (th1 RS Thms.tfl_disjE)) |
|
227 |
handle THM (msg, _, _) => raise RULES_ERR "DISJ_CASES" msg |
|
228 |
end; |
|
229 |
||
230 |
||
231 |
(*----------------------------------------------------------------------------- |
|
232 |
* |
|
233 |
* |- A1 \/ ... \/ An [A1 |- M, ..., An |- M] |
|
234 |
* --------------------------------------------------- |
|
235 |
* |- M |
|
236 |
* |
|
237 |
* Note. The list of theorems may be all jumbled up, so we have to |
|
238 |
* first organize it to align with the first argument (the disjunctive |
|
239 |
* theorem). |
|
240 |
*---------------------------------------------------------------------------*) |
|
241 |
||
242 |
fun organize eq = (* a bit slow - analogous to insertion sort *) |
|
243 |
let fun extract a alist = |
|
244 |
let fun ex (_,[]) = raise RULES_ERR "organize" "not a permutation.1" |
|
245 |
| ex(left,h::t) = if (eq h a) then (h,rev left@t) else ex(h::left,t) |
|
246 |
in ex ([],alist) |
|
247 |
end |
|
248 |
fun place [] [] = [] |
|
249 |
| place (a::rst) alist = |
|
250 |
let val (item,next) = extract a alist |
|
251 |
in item::place rst next |
|
252 |
end |
|
253 |
| place _ _ = raise RULES_ERR "organize" "not a permutation.2" |
|
254 |
in place |
|
255 |
end; |
|
256 |
(* freezeT expensive! *) |
|
257 |
fun DISJ_CASESL disjth thl = |
|
258 |
let val c = cconcl disjth |
|
259 |
fun eq th atm = exists (fn t => HOLogic.dest_Trueprop t |
|
260 |
aconv term_of atm) |
|
261 |
(#hyps(rep_thm th)) |
|
262 |
val tml = D.strip_disj c |
|
263 |
fun DL th [] = raise RULES_ERR "DISJ_CASESL" "no cases" |
|
264 |
| DL th [th1] = PROVE_HYP th th1 |
|
265 |
| DL th [th1,th2] = DISJ_CASES th th1 th2 |
|
266 |
| DL th (th1::rst) = |
|
267 |
let val tm = #2(D.dest_disj(D.drop_prop(cconcl th))) |
|
268 |
in DISJ_CASES th th1 (DL (ASSUME tm) rst) end |
|
269 |
in DL (freezeT disjth) (organize eq tml thl) |
|
270 |
end; |
|
271 |
||
272 |
||
273 |
(*---------------------------------------------------------------------------- |
|
274 |
* Universals |
|
275 |
*---------------------------------------------------------------------------*) |
|
276 |
local (* this is fragile *) |
|
277 |
val {prop,sign,...} = rep_thm spec |
|
278 |
val x = hd (tl (term_vars prop)) |
|
279 |
val (TVar (indx,_)) = type_of x |
|
280 |
val gspec = forall_intr (cterm_of sign x) spec |
|
281 |
in |
|
282 |
fun SPEC tm thm = |
|
283 |
let val {sign,T,...} = rep_cterm tm |
|
284 |
val gspec' = instantiate([(indx,ctyp_of sign T)],[]) gspec |
|
285 |
in |
|
286 |
thm RS (forall_elim tm gspec') |
|
287 |
end |
|
288 |
end; |
|
289 |
||
290 |
fun SPEC_ALL thm = U.rev_itlist SPEC (#1(D.strip_forall(cconcl thm))) thm; |
|
291 |
||
292 |
val ISPEC = SPEC |
|
293 |
val ISPECL = U.rev_itlist ISPEC; |
|
294 |
||
295 |
(* Not optimized! Too complicated. *) |
|
296 |
local val {prop,sign,...} = rep_thm allI |
|
297 |
val [P] = add_term_vars (prop, []) |
|
298 |
fun cty_theta s = map (fn (i,ty) => (i, ctyp_of s ty)) |
|
299 |
fun ctm_theta s = map (fn (i,tm2) => |
|
300 |
let val ctm2 = cterm_of s tm2 |
|
301 |
in (cterm_of s (Var(i,#T(rep_cterm ctm2))), ctm2) |
|
302 |
end) |
|
303 |
fun certify s (ty_theta,tm_theta) = (cty_theta s ty_theta, |
|
304 |
ctm_theta s tm_theta) |
|
305 |
in |
|
306 |
fun GEN v th = |
|
307 |
let val gth = forall_intr v th |
|
308 |
val {prop=Const("all",_)$Abs(x,ty,rst),sign,...} = rep_thm gth |
|
309 |
val P' = Abs(x,ty, HOLogic.dest_Trueprop rst) (* get rid of trueprop *) |
|
14643 | 310 |
val tsig = Sign.tsig_of sign |
10769 | 311 |
val theta = Pattern.match tsig (P,P') |
312 |
val allI2 = instantiate (certify sign theta) allI |
|
313 |
val thm = Thm.implies_elim allI2 gth |
|
314 |
val {prop = tp $ (A $ Abs(_,_,M)),sign,...} = rep_thm thm |
|
315 |
val prop' = tp $ (A $ Abs(x,ty,M)) |
|
316 |
in ALPHA thm (cterm_of sign prop') |
|
317 |
end |
|
318 |
end; |
|
319 |
||
320 |
val GENL = U.itlist GEN; |
|
321 |
||
322 |
fun GEN_ALL thm = |
|
323 |
let val {prop,sign,...} = rep_thm thm |
|
324 |
val tycheck = cterm_of sign |
|
325 |
val vlist = map tycheck (add_term_vars (prop, [])) |
|
326 |
in GENL vlist thm |
|
327 |
end; |
|
328 |
||
329 |
||
330 |
fun MATCH_MP th1 th2 = |
|
331 |
if (D.is_forall (D.drop_prop(cconcl th1))) |
|
332 |
then MATCH_MP (th1 RS spec) th2 |
|
333 |
else MP th1 th2; |
|
334 |
||
335 |
||
336 |
(*---------------------------------------------------------------------------- |
|
337 |
* Existentials |
|
338 |
*---------------------------------------------------------------------------*) |
|
339 |
||
340 |
||
341 |
||
342 |
(*--------------------------------------------------------------------------- |
|
343 |
* Existential elimination |
|
344 |
* |
|
345 |
* A1 |- ?x.t[x] , A2, "t[v]" |- t' |
|
346 |
* ------------------------------------ (variable v occurs nowhere) |
|
347 |
* A1 u A2 |- t' |
|
348 |
* |
|
349 |
*---------------------------------------------------------------------------*) |
|
350 |
||
351 |
fun CHOOSE (fvar, exth) fact = |
|
352 |
let |
|
353 |
val lam = #2 (D.dest_comb (D.drop_prop (cconcl exth))) |
|
354 |
val redex = D.capply lam fvar |
|
355 |
val {sign, t = t$u,...} = Thm.rep_cterm redex |
|
356 |
val residue = Thm.cterm_of sign (betapply (t, u)) |
|
357 |
in |
|
358 |
GEN fvar (DISCH residue fact) RS (exth RS Thms.choose_thm) |
|
359 |
handle THM (msg, _, _) => raise RULES_ERR "CHOOSE" msg |
|
360 |
end; |
|
361 |
||
362 |
local val {prop,sign,...} = rep_thm exI |
|
363 |
val [P,x] = term_vars prop |
|
364 |
in |
|
365 |
fun EXISTS (template,witness) thm = |
|
366 |
let val {prop,sign,...} = rep_thm thm |
|
367 |
val P' = cterm_of sign P |
|
368 |
val x' = cterm_of sign x |
|
369 |
val abstr = #2 (D.dest_comb template) |
|
370 |
in |
|
371 |
thm RS (cterm_instantiate[(P',abstr), (x',witness)] exI) |
|
372 |
handle THM (msg, _, _) => raise RULES_ERR "EXISTS" msg |
|
373 |
end |
|
374 |
end; |
|
375 |
||
376 |
(*---------------------------------------------------------------------------- |
|
377 |
* |
|
378 |
* A |- M |
|
379 |
* ------------------- [v_1,...,v_n] |
|
380 |
* A |- ?v1...v_n. M |
|
381 |
* |
|
382 |
*---------------------------------------------------------------------------*) |
|
383 |
||
384 |
fun EXISTL vlist th = |
|
385 |
U.itlist (fn v => fn thm => EXISTS(D.mk_exists(v,cconcl thm), v) thm) |
|
386 |
vlist th; |
|
387 |
||
388 |
||
389 |
(*---------------------------------------------------------------------------- |
|
390 |
* |
|
391 |
* A |- M[x_1,...,x_n] |
|
392 |
* ---------------------------- [(x |-> y)_1,...,(x |-> y)_n] |
|
393 |
* A |- ?y_1...y_n. M |
|
394 |
* |
|
395 |
*---------------------------------------------------------------------------*) |
|
396 |
(* Could be improved, but needs "subst_free" for certified terms *) |
|
397 |
||
398 |
fun IT_EXISTS blist th = |
|
399 |
let val {sign,...} = rep_thm th |
|
400 |
val tych = cterm_of sign |
|
401 |
val detype = #t o rep_cterm |
|
402 |
val blist' = map (fn (x,y) => (detype x, detype y)) blist |
|
403 |
fun ?v M = cterm_of sign (S.mk_exists{Bvar=v,Body = M}) |
|
404 |
||
405 |
in |
|
406 |
U.itlist (fn (b as (r1,r2)) => fn thm => |
|
407 |
EXISTS(?r2(subst_free[b] |
|
408 |
(HOLogic.dest_Trueprop(#prop(rep_thm thm)))), tych r1) |
|
409 |
thm) |
|
410 |
blist' th |
|
411 |
end; |
|
412 |
||
413 |
(*--------------------------------------------------------------------------- |
|
414 |
* Faster version, that fails for some as yet unknown reason |
|
415 |
* fun IT_EXISTS blist th = |
|
416 |
* let val {sign,...} = rep_thm th |
|
417 |
* val tych = cterm_of sign |
|
418 |
* fun detype (x,y) = ((#t o rep_cterm) x, (#t o rep_cterm) y) |
|
419 |
* in |
|
420 |
* fold (fn (b as (r1,r2), thm) => |
|
421 |
* EXISTS(D.mk_exists(r2, tych(subst_free[detype b](#t(rep_cterm(cconcl thm))))), |
|
422 |
* r1) thm) blist th |
|
423 |
* end; |
|
424 |
*---------------------------------------------------------------------------*) |
|
425 |
||
426 |
(*---------------------------------------------------------------------------- |
|
427 |
* Rewriting |
|
428 |
*---------------------------------------------------------------------------*) |
|
429 |
||
430 |
fun SUBS thl = |
|
431 |
rewrite_rule (map (fn th => th RS eq_reflection handle THM _ => th) thl); |
|
432 |
||
15531 | 433 |
val rew_conv = MetaSimplifier.rewrite_cterm (true, false, false) (K (K NONE)); |
15021 | 434 |
|
10769 | 435 |
fun simpl_conv ss thl ctm = |
15021 | 436 |
rew_conv (ss addsimps thl) ctm RS meta_eq_to_obj_eq; |
437 |
||
10769 | 438 |
|
439 |
val RIGHT_ASSOC = rewrite_rule [Thms.disj_assoc]; |
|
440 |
||
441 |
||
442 |
||
443 |
(*--------------------------------------------------------------------------- |
|
444 |
* TERMINATION CONDITION EXTRACTION |
|
445 |
*---------------------------------------------------------------------------*) |
|
446 |
||
447 |
||
448 |
(* Object language quantifier, i.e., "!" *) |
|
449 |
fun Forall v M = S.mk_forall{Bvar=v, Body=M}; |
|
450 |
||
451 |
||
452 |
(* Fragile: it's a cong if it is not "R y x ==> cut f R x y = f y" *) |
|
453 |
fun is_cong thm = |
|
454 |
let val {prop, ...} = rep_thm thm |
|
455 |
in case prop |
|
456 |
of (Const("==>",_)$(Const("Trueprop",_)$ _) $ |
|
457 |
(Const("==",_) $ (Const ("Wellfounded_Recursion.cut",_) $ f $ R $ a $ x) $ _)) => false |
|
458 |
| _ => true |
|
459 |
end; |
|
460 |
||
461 |
||
462 |
||
463 |
fun dest_equal(Const ("==",_) $ |
|
464 |
(Const ("Trueprop",_) $ lhs) |
|
465 |
$ (Const ("Trueprop",_) $ rhs)) = {lhs=lhs, rhs=rhs} |
|
466 |
| dest_equal(Const ("==",_) $ lhs $ rhs) = {lhs=lhs, rhs=rhs} |
|
467 |
| dest_equal tm = S.dest_eq tm; |
|
468 |
||
469 |
fun get_lhs tm = #lhs(dest_equal (HOLogic.dest_Trueprop tm)); |
|
470 |
||
471 |
fun dest_all used (Const("all",_) $ (a as Abs _)) = S.dest_abs used a |
|
472 |
| dest_all _ _ = raise RULES_ERR "dest_all" "not a !!"; |
|
473 |
||
474 |
val is_all = can (dest_all []); |
|
475 |
||
476 |
fun strip_all used fm = |
|
477 |
if (is_all fm) |
|
478 |
then let val ({Bvar, Body}, used') = dest_all used fm |
|
479 |
val (bvs, core, used'') = strip_all used' Body |
|
480 |
in ((Bvar::bvs), core, used'') |
|
481 |
end |
|
482 |
else ([], fm, used); |
|
483 |
||
484 |
fun break_all(Const("all",_) $ Abs (_,_,body)) = body |
|
485 |
| break_all _ = raise RULES_ERR "break_all" "not a !!"; |
|
486 |
||
487 |
fun list_break_all(Const("all",_) $ Abs (s,ty,body)) = |
|
488 |
let val (L,core) = list_break_all body |
|
489 |
in ((s,ty)::L, core) |
|
490 |
end |
|
491 |
| list_break_all tm = ([],tm); |
|
492 |
||
493 |
(*--------------------------------------------------------------------------- |
|
494 |
* Rename a term of the form |
|
495 |
* |
|
496 |
* !!x1 ...xn. x1=M1 ==> ... ==> xn=Mn |
|
497 |
* ==> ((%v1...vn. Q) x1 ... xn = g x1 ... xn. |
|
498 |
* to one of |
|
499 |
* |
|
500 |
* !!v1 ... vn. v1=M1 ==> ... ==> vn=Mn |
|
501 |
* ==> ((%v1...vn. Q) v1 ... vn = g v1 ... vn. |
|
502 |
* |
|
503 |
* This prevents name problems in extraction, and helps the result to read |
|
504 |
* better. There is a problem with varstructs, since they can introduce more |
|
505 |
* than n variables, and some extra reasoning needs to be done. |
|
506 |
*---------------------------------------------------------------------------*) |
|
507 |
||
508 |
fun get ([],_,L) = rev L |
|
509 |
| get (ant::rst,n,L) = |
|
510 |
case (list_break_all ant) |
|
511 |
of ([],_) => get (rst, n+1,L) |
|
512 |
| (vlist,body) => |
|
513 |
let val eq = Logic.strip_imp_concl body |
|
514 |
val (f,args) = S.strip_comb (get_lhs eq) |
|
515 |
val (vstrl,_) = S.strip_abs f |
|
516 |
val names = variantlist (map (#1 o dest_Free) vstrl, |
|
517 |
add_term_names(body, [])) |
|
518 |
in get (rst, n+1, (names,n)::L) end |
|
519 |
handle TERM _ => get (rst, n+1, L) |
|
520 |
| U.ERR _ => get (rst, n+1, L); |
|
521 |
||
522 |
(* Note: rename_params_rule counts from 1, not 0 *) |
|
523 |
fun rename thm = |
|
524 |
let val {prop,sign,...} = rep_thm thm |
|
525 |
val tych = cterm_of sign |
|
526 |
val ants = Logic.strip_imp_prems prop |
|
527 |
val news = get (ants,1,[]) |
|
528 |
in |
|
529 |
U.rev_itlist rename_params_rule news thm |
|
530 |
end; |
|
531 |
||
532 |
||
533 |
(*--------------------------------------------------------------------------- |
|
534 |
* Beta-conversion to the rhs of an equation (taken from hol90/drule.sml) |
|
535 |
*---------------------------------------------------------------------------*) |
|
536 |
||
537 |
fun list_beta_conv tm = |
|
538 |
let fun rbeta th = Thm.transitive th (beta_conversion false (#2(D.dest_eq(cconcl th)))) |
|
539 |
fun iter [] = Thm.reflexive tm |
|
540 |
| iter (v::rst) = rbeta (combination(iter rst) (Thm.reflexive v)) |
|
541 |
in iter end; |
|
542 |
||
543 |
||
544 |
(*--------------------------------------------------------------------------- |
|
545 |
* Trace information for the rewriter |
|
546 |
*---------------------------------------------------------------------------*) |
|
547 |
val term_ref = ref[] : term list ref |
|
15021 | 548 |
val ss_ref = ref [] : simpset list ref; |
10769 | 549 |
val thm_ref = ref [] : thm list ref; |
550 |
val tracing = ref false; |
|
551 |
||
552 |
fun say s = if !tracing then writeln s else (); |
|
553 |
||
554 |
fun print_thms s L = |
|
555 |
say (cat_lines (s :: map string_of_thm L)); |
|
556 |
||
557 |
fun print_cterms s L = |
|
558 |
say (cat_lines (s :: map string_of_cterm L)); |
|
559 |
||
560 |
||
561 |
(*--------------------------------------------------------------------------- |
|
562 |
* General abstraction handlers, should probably go in USyntax. |
|
563 |
*---------------------------------------------------------------------------*) |
|
564 |
fun mk_aabs (vstr, body) = |
|
565 |
S.mk_abs {Bvar = vstr, Body = body} |
|
566 |
handle U.ERR _ => S.mk_pabs {varstruct = vstr, body = body}; |
|
567 |
||
568 |
fun list_mk_aabs (vstrl,tm) = |
|
569 |
U.itlist (fn vstr => fn tm => mk_aabs(vstr,tm)) vstrl tm; |
|
570 |
||
571 |
fun dest_aabs used tm = |
|
572 |
let val ({Bvar,Body}, used') = S.dest_abs used tm |
|
573 |
in (Bvar, Body, used') end |
|
574 |
handle U.ERR _ => |
|
575 |
let val {varstruct, body, used} = S.dest_pabs used tm |
|
576 |
in (varstruct, body, used) end; |
|
577 |
||
578 |
fun strip_aabs used tm = |
|
579 |
let val (vstr, body, used') = dest_aabs used tm |
|
580 |
val (bvs, core, used'') = strip_aabs used' body |
|
581 |
in (vstr::bvs, core, used'') end |
|
582 |
handle U.ERR _ => ([], tm, used); |
|
583 |
||
584 |
fun dest_combn tm 0 = (tm,[]) |
|
585 |
| dest_combn tm n = |
|
586 |
let val {Rator,Rand} = S.dest_comb tm |
|
587 |
val (f,rands) = dest_combn Rator (n-1) |
|
588 |
in (f,Rand::rands) |
|
589 |
end; |
|
590 |
||
591 |
||
592 |
||
593 |
||
594 |
local fun dest_pair M = let val {fst,snd} = S.dest_pair M in (fst,snd) end |
|
595 |
fun mk_fst tm = |
|
596 |
let val ty as Type("*", [fty,sty]) = type_of tm |
|
597 |
in Const ("fst", ty --> fty) $ tm end |
|
598 |
fun mk_snd tm = |
|
599 |
let val ty as Type("*", [fty,sty]) = type_of tm |
|
600 |
in Const ("snd", ty --> sty) $ tm end |
|
601 |
in |
|
602 |
fun XFILL tych x vstruct = |
|
603 |
let fun traverse p xocc L = |
|
604 |
if (is_Free p) |
|
605 |
then tych xocc::L |
|
606 |
else let val (p1,p2) = dest_pair p |
|
607 |
in traverse p1 (mk_fst xocc) (traverse p2 (mk_snd xocc) L) |
|
608 |
end |
|
609 |
in |
|
610 |
traverse vstruct x [] |
|
611 |
end end; |
|
612 |
||
613 |
(*--------------------------------------------------------------------------- |
|
614 |
* Replace a free tuple (vstr) by a universally quantified variable (a). |
|
615 |
* Note that the notion of "freeness" for a tuple is different than for a |
|
616 |
* variable: if variables in the tuple also occur in any other place than |
|
617 |
* an occurrences of the tuple, they aren't "free" (which is thus probably |
|
618 |
* the wrong word to use). |
|
619 |
*---------------------------------------------------------------------------*) |
|
620 |
||
621 |
fun VSTRUCT_ELIM tych a vstr th = |
|
622 |
let val L = S.free_vars_lr vstr |
|
623 |
val bind1 = tych (HOLogic.mk_Trueprop (HOLogic.mk_eq(a,vstr))) |
|
624 |
val thm1 = implies_intr bind1 (SUBS [SYM(assume bind1)] th) |
|
625 |
val thm2 = forall_intr_list (map tych L) thm1 |
|
626 |
val thm3 = forall_elim_list (XFILL tych a vstr) thm2 |
|
627 |
in refl RS |
|
628 |
rewrite_rule [Thm.symmetric (surjective_pairing RS eq_reflection)] thm3 |
|
629 |
end; |
|
630 |
||
631 |
fun PGEN tych a vstr th = |
|
632 |
let val a1 = tych a |
|
633 |
val vstr1 = tych vstr |
|
634 |
in |
|
635 |
forall_intr a1 |
|
636 |
(if (is_Free vstr) |
|
637 |
then cterm_instantiate [(vstr1,a1)] th |
|
638 |
else VSTRUCT_ELIM tych a vstr th) |
|
639 |
end; |
|
640 |
||
641 |
||
642 |
(*--------------------------------------------------------------------------- |
|
643 |
* Takes apart a paired beta-redex, looking like "(\(x,y).N) vstr", into |
|
644 |
* |
|
645 |
* (([x,y],N),vstr) |
|
646 |
*---------------------------------------------------------------------------*) |
|
647 |
fun dest_pbeta_redex used M n = |
|
648 |
let val (f,args) = dest_combn M n |
|
649 |
val dummy = dest_aabs used f |
|
650 |
in (strip_aabs used f,args) |
|
651 |
end; |
|
652 |
||
653 |
fun pbeta_redex M n = can (U.C (dest_pbeta_redex []) n) M; |
|
654 |
||
655 |
fun dest_impl tm = |
|
656 |
let val ants = Logic.strip_imp_prems tm |
|
657 |
val eq = Logic.strip_imp_concl tm |
|
658 |
in (ants,get_lhs eq) |
|
659 |
end; |
|
660 |
||
15570 | 661 |
fun restricted t = isSome (S.find_term |
10769 | 662 |
(fn (Const("Wellfounded_Recursion.cut",_)) =>true | _ => false) |
663 |
t) |
|
664 |
||
665 |
fun CONTEXT_REWRITE_RULE (func, G, cut_lemma, congs) th = |
|
666 |
let val globals = func::G |
|
10918 | 667 |
val pbeta_reduce = simpl_conv empty_ss [split_conv RS eq_reflection]; |
10769 | 668 |
val tc_list = ref[]: term list ref |
669 |
val dummy = term_ref := [] |
|
670 |
val dummy = thm_ref := [] |
|
15021 | 671 |
val dummy = ss_ref := [] |
10769 | 672 |
val cut_lemma' = cut_lemma RS eq_reflection |
15021 | 673 |
fun prover used ss thm = |
674 |
let fun cong_prover ss thm = |
|
10769 | 675 |
let val dummy = say "cong_prover:" |
15021 | 676 |
val cntxt = MetaSimplifier.prems_of_ss ss |
10769 | 677 |
val dummy = print_thms "cntxt:" cntxt |
678 |
val dummy = say "cong rule:" |
|
679 |
val dummy = say (string_of_thm thm) |
|
680 |
val dummy = thm_ref := (thm :: !thm_ref) |
|
15021 | 681 |
val dummy = ss_ref := (ss :: !ss_ref) |
10769 | 682 |
(* Unquantified eliminate *) |
683 |
fun uq_eliminate (thm,imp,sign) = |
|
684 |
let val tych = cterm_of sign |
|
685 |
val dummy = print_cterms "To eliminate:" [tych imp] |
|
686 |
val ants = map tych (Logic.strip_imp_prems imp) |
|
687 |
val eq = Logic.strip_imp_concl imp |
|
688 |
val lhs = tych(get_lhs eq) |
|
15021 | 689 |
val ss' = MetaSimplifier.add_prems (map ASSUME ants) ss |
690 |
val lhs_eq_lhs1 = MetaSimplifier.rewrite_cterm (false,true,false) (prover used) ss' lhs |
|
10769 | 691 |
handle U.ERR _ => Thm.reflexive lhs |
692 |
val dummy = print_thms "proven:" [lhs_eq_lhs1] |
|
693 |
val lhs_eq_lhs2 = implies_intr_list ants lhs_eq_lhs1 |
|
694 |
val lhs_eeq_lhs2 = lhs_eq_lhs2 RS meta_eq_to_obj_eq |
|
695 |
in |
|
696 |
lhs_eeq_lhs2 COMP thm |
|
697 |
end |
|
698 |
fun pq_eliminate (thm,sign,vlist,imp_body,lhs_eq) = |
|
699 |
let val ((vstrl, _, used'), args) = dest_pbeta_redex used lhs_eq (length vlist) |
|
700 |
val dummy = assert (forall (op aconv) |
|
701 |
(ListPair.zip (vlist, args))) |
|
702 |
"assertion failed in CONTEXT_REWRITE_RULE" |
|
703 |
val imp_body1 = subst_free (ListPair.zip (args, vstrl)) |
|
704 |
imp_body |
|
705 |
val tych = cterm_of sign |
|
706 |
val ants1 = map tych (Logic.strip_imp_prems imp_body1) |
|
707 |
val eq1 = Logic.strip_imp_concl imp_body1 |
|
708 |
val Q = get_lhs eq1 |
|
709 |
val QeqQ1 = pbeta_reduce (tych Q) |
|
710 |
val Q1 = #2(D.dest_eq(cconcl QeqQ1)) |
|
15021 | 711 |
val ss' = MetaSimplifier.add_prems (map ASSUME ants1) ss |
712 |
val Q1eeqQ2 = MetaSimplifier.rewrite_cterm (false,true,false) (prover used') ss' Q1 |
|
10769 | 713 |
handle U.ERR _ => Thm.reflexive Q1 |
14643 | 714 |
val Q2 = #2 (Logic.dest_equals (Thm.prop_of Q1eeqQ2)) |
10769 | 715 |
val Q3 = tych(list_comb(list_mk_aabs(vstrl,Q2),vstrl)) |
716 |
val Q2eeqQ3 = Thm.symmetric(pbeta_reduce Q3 RS eq_reflection) |
|
717 |
val thA = Thm.transitive(QeqQ1 RS eq_reflection) Q1eeqQ2 |
|
718 |
val QeeqQ3 = Thm.transitive thA Q2eeqQ3 handle THM _ => |
|
719 |
((Q2eeqQ3 RS meta_eq_to_obj_eq) |
|
720 |
RS ((thA RS meta_eq_to_obj_eq) RS trans)) |
|
721 |
RS eq_reflection |
|
722 |
val impth = implies_intr_list ants1 QeeqQ3 |
|
723 |
val impth1 = impth RS meta_eq_to_obj_eq |
|
724 |
(* Need to abstract *) |
|
725 |
val ant_th = U.itlist2 (PGEN tych) args vstrl impth1 |
|
726 |
in ant_th COMP thm |
|
727 |
end |
|
728 |
fun q_eliminate (thm,imp,sign) = |
|
729 |
let val (vlist, imp_body, used') = strip_all used imp |
|
730 |
val (ants,Q) = dest_impl imp_body |
|
731 |
in if (pbeta_redex Q) (length vlist) |
|
732 |
then pq_eliminate (thm,sign,vlist,imp_body,Q) |
|
733 |
else |
|
734 |
let val tych = cterm_of sign |
|
735 |
val ants1 = map tych ants |
|
15021 | 736 |
val ss' = MetaSimplifier.add_prems (map ASSUME ants1) ss |
10769 | 737 |
val Q_eeq_Q1 = MetaSimplifier.rewrite_cterm |
15021 | 738 |
(false,true,false) (prover used') ss' (tych Q) |
10769 | 739 |
handle U.ERR _ => Thm.reflexive (tych Q) |
740 |
val lhs_eeq_lhs2 = implies_intr_list ants1 Q_eeq_Q1 |
|
741 |
val lhs_eq_lhs2 = lhs_eeq_lhs2 RS meta_eq_to_obj_eq |
|
742 |
val ant_th = forall_intr_list(map tych vlist)lhs_eq_lhs2 |
|
743 |
in |
|
744 |
ant_th COMP thm |
|
745 |
end end |
|
746 |
||
747 |
fun eliminate thm = |
|
748 |
case (rep_thm thm) |
|
749 |
of {prop = (Const("==>",_) $ imp $ _), sign, ...} => |
|
750 |
eliminate |
|
751 |
(if not(is_all imp) |
|
752 |
then uq_eliminate (thm,imp,sign) |
|
753 |
else q_eliminate (thm,imp,sign)) |
|
754 |
(* Assume that the leading constant is ==, *) |
|
755 |
| _ => thm (* if it is not a ==> *) |
|
15531 | 756 |
in SOME(eliminate (rename thm)) end |
757 |
handle U.ERR _ => NONE (* FIXME handle THM as well?? *) |
|
10769 | 758 |
|
15021 | 759 |
fun restrict_prover ss thm = |
10769 | 760 |
let val dummy = say "restrict_prover:" |
15021 | 761 |
val cntxt = rev(MetaSimplifier.prems_of_ss ss) |
10769 | 762 |
val dummy = print_thms "cntxt:" cntxt |
763 |
val {prop = Const("==>",_) $ (Const("Trueprop",_) $ A) $ _, |
|
764 |
sign,...} = rep_thm thm |
|
765 |
fun genl tm = let val vlist = gen_rems (op aconv) |
|
766 |
(add_term_frees(tm,[]), globals) |
|
767 |
in U.itlist Forall vlist tm |
|
768 |
end |
|
769 |
(*-------------------------------------------------------------- |
|
770 |
* This actually isn't quite right, since it will think that |
|
771 |
* not-fully applied occs. of "f" in the context mean that the |
|
772 |
* current call is nested. The real solution is to pass in a |
|
773 |
* term "f v1..vn" which is a pattern that any full application |
|
774 |
* of "f" will match. |
|
775 |
*-------------------------------------------------------------*) |
|
776 |
val func_name = #1(dest_Const func) |
|
777 |
fun is_func (Const (name,_)) = (name = func_name) |
|
778 |
| is_func _ = false |
|
779 |
val rcontext = rev cntxt |
|
14643 | 780 |
val cncl = HOLogic.dest_Trueprop o Thm.prop_of |
10769 | 781 |
val antl = case rcontext of [] => [] |
782 |
| _ => [S.list_mk_conj(map cncl rcontext)] |
|
783 |
val TC = genl(S.list_mk_imp(antl, A)) |
|
784 |
val dummy = print_cterms "func:" [cterm_of sign func] |
|
785 |
val dummy = print_cterms "TC:" |
|
786 |
[cterm_of sign (HOLogic.mk_Trueprop TC)] |
|
787 |
val dummy = tc_list := (TC :: !tc_list) |
|
15570 | 788 |
val nestedp = isSome (S.find_term is_func TC) |
10769 | 789 |
val dummy = if nestedp then say "nested" else say "not_nested" |
790 |
val dummy = term_ref := ([func,TC]@(!term_ref)) |
|
791 |
val th' = if nestedp then raise RULES_ERR "solver" "nested function" |
|
792 |
else let val cTC = cterm_of sign |
|
793 |
(HOLogic.mk_Trueprop TC) |
|
794 |
in case rcontext of |
|
795 |
[] => SPEC_ALL(ASSUME cTC) |
|
796 |
| _ => MP (SPEC_ALL (ASSUME cTC)) |
|
797 |
(LIST_CONJ rcontext) |
|
798 |
end |
|
799 |
val th'' = th' RS thm |
|
15531 | 800 |
in SOME (th'') |
801 |
end handle U.ERR _ => NONE (* FIXME handle THM as well?? *) |
|
10769 | 802 |
in |
15021 | 803 |
(if (is_cong thm) then cong_prover else restrict_prover) ss thm |
10769 | 804 |
end |
805 |
val ctm = cprop_of th |
|
806 |
val names = add_term_names (term_of ctm, []) |
|
807 |
val th1 = MetaSimplifier.rewrite_cterm(false,true,false) |
|
15021 | 808 |
(prover names) (empty_ss addsimps [cut_lemma'] addeqcongs congs) ctm |
10769 | 809 |
val th2 = equal_elim th1 th |
810 |
in |
|
15570 | 811 |
(th2, List.filter (not o restricted) (!tc_list)) |
10769 | 812 |
end; |
813 |
||
814 |
||
11632 | 815 |
fun prove strict (ptm, tac) = |
10769 | 816 |
let val result = |
11632 | 817 |
if strict then Goals.prove_goalw_cterm [] ptm (fn _ => [tac]) |
818 |
else |
|
14836 | 819 |
transform_error (fn () => |
11632 | 820 |
Goals.prove_goalw_cterm [] ptm (fn _ => [tac])) () |
821 |
handle ERROR_MESSAGE msg => (warning msg; raise RULES_ERR "prove" msg); |
|
10769 | 822 |
in #1 (freeze_thaw result) end; |
823 |
||
824 |
||
825 |
end; |