6498

1 
(* Title: TFL/rules


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 


10 
structure Rules : Rules_sig =


11 
struct


12 


13 
open Utils;


14 


15 
structure USyntax = USyntax;


16 
structure S = USyntax;


17 
structure U = Utils;


18 
structure D = Dcterm;


19 


20 


21 
fun RULES_ERR{func,mesg} = Utils.ERR{module = "Rules",func=func,mesg=mesg};


22 


23 


24 
fun cconcl thm = D.drop_prop(#prop(crep_thm thm));


25 
fun chyps thm = map D.drop_prop(#hyps(crep_thm thm));


26 


27 
fun dest_thm thm =


28 
let val {prop,hyps,...} = rep_thm thm


29 
in (map HOLogic.dest_Trueprop hyps, HOLogic.dest_Trueprop prop)


30 
end;


31 


32 


33 


34 
(* Inference rules *)


35 


36 
(*


37 
* Equality (one step)


38 
**)


39 
fun REFL tm = Thm.reflexive tm RS meta_eq_to_obj_eq;


40 
fun SYM thm = thm RS sym;


41 


42 
fun ALPHA thm ctm1 =


43 
let val ctm2 = cprop_of thm


44 
val ctm2_eq = reflexive ctm2


45 
val ctm1_eq = reflexive ctm1


46 
in equal_elim (transitive ctm2_eq ctm1_eq) thm


47 
end;


48 


49 


50 
(*


51 
* typ instantiation


52 
**)


53 
fun INST_TYPE blist thm =


54 
let val {sign,...} = rep_thm thm


55 
val blist' = map (fn (TVar(idx,_), B) => (idx, ctyp_of sign B)) blist


56 
in Thm.instantiate (blist',[]) thm


57 
end


58 
handle _ => raise RULES_ERR{func = "INST_TYPE", mesg = ""};


59 


60 


61 
(*


62 
* Implication and the assumption list


63 
*


64 
* Assumptions get stuck on the metalanguage assumption list. Implications


65 
* are in the object language, so discharging an assumption "A" from theorem


66 
* "B" results in something that looks like "A > B".


67 
**)


68 
fun ASSUME ctm = Thm.assume (D.mk_prop ctm);


69 


70 


71 
(*


72 
* Implication in TFL is >. Metalanguage implication (==>) is only used


73 
* in the implementation of some of the inference rules below.


74 
**)


75 
fun MP th1 th2 = th2 RS (th1 RS mp);


76 


77 
(*forces the first argument to be a proposition if necessary*)


78 
fun DISCH tm thm = Thm.implies_intr (D.mk_prop tm) thm COMP impI;


79 


80 
fun DISCH_ALL thm = Utils.itlist DISCH (#hyps (crep_thm thm)) thm;


81 


82 


83 
fun FILTER_DISCH_ALL P thm =


84 
let fun check tm = U.holds P (#t(rep_cterm tm))


85 
in foldr (fn (tm,th) => if (check tm) then DISCH tm th else th)


86 
(chyps thm, thm)


87 
end;


88 


89 
(* freezeT expensive! *)


90 
fun UNDISCH thm =


91 
let val tm = D.mk_prop(#1(D.dest_imp(cconcl (freezeT thm))))


92 
in implies_elim (thm RS mp) (ASSUME tm)


93 
end


94 
handle _ => raise RULES_ERR{func = "UNDISCH", mesg = ""};


95 


96 
fun PROVE_HYP ath bth = MP (DISCH (cconcl ath) bth) ath;


97 


98 
local val [p1,p2] = goal HOL.thy "(A>B) ==> (B > C) ==> (A>C)"


99 
val dummy = by (rtac impI 1)


100 
val dummy = by (rtac (p2 RS mp) 1)


101 
val dummy = by (rtac (p1 RS mp) 1)


102 
val dummy = by (assume_tac 1)


103 
val imp_trans = result()


104 
in


105 
fun IMP_TRANS th1 th2 = th2 RS (th1 RS imp_trans)


106 
end;


107 


108 
(*


109 
* Conjunction


110 
**)


111 
fun CONJUNCT1 thm = (thm RS conjunct1)


112 
fun CONJUNCT2 thm = (thm RS conjunct2);


113 
fun CONJUNCTS th = (CONJUNCTS (CONJUNCT1 th) @ CONJUNCTS (CONJUNCT2 th))


114 
handle _ => [th];


115 


116 
fun LIST_CONJ [] = raise RULES_ERR{func = "LIST_CONJ", mesg = "empty list"}


117 
 LIST_CONJ [th] = th


118 
 LIST_CONJ (th::rst) = MP(MP(conjI COMP (impI RS impI)) th) (LIST_CONJ rst);


119 


120 


121 
(*


122 
* Disjunction


123 
**)


124 
local val {prop,sign,...} = rep_thm disjI1


125 
val [P,Q] = term_vars prop


126 
val disj1 = forall_intr (cterm_of sign Q) disjI1


127 
in


128 
fun DISJ1 thm tm = thm RS (forall_elim (D.drop_prop tm) disj1)


129 
end;


130 


131 
local val {prop,sign,...} = rep_thm disjI2


132 
val [P,Q] = term_vars prop


133 
val disj2 = forall_intr (cterm_of sign P) disjI2


134 
in


135 
fun DISJ2 tm thm = thm RS (forall_elim (D.drop_prop tm) disj2)


136 
end;


137 


138 


139 
(*


140 
*


141 
* A1  M1, ..., An  Mn


142 
* 


143 
* [A1  M1 \/ ... \/ Mn, ..., An  M1 \/ ... \/ Mn]


144 
*


145 
**)


146 


147 


148 
fun EVEN_ORS thms =


149 
let fun blue ldisjs [] _ = []


150 
 blue ldisjs (th::rst) rdisjs =


151 
let val tail = tl rdisjs


152 
val rdisj_tl = D.list_mk_disj tail


153 
in itlist DISJ2 ldisjs (DISJ1 th rdisj_tl)


154 
:: blue (ldisjs@[cconcl th]) rst tail


155 
end handle _ => [itlist DISJ2 ldisjs th]


156 
in


157 
blue [] thms (map cconcl thms)


158 
end;


159 


160 


161 
(*


162 
*


163 
* A  P \/ Q B,P  R C,Q  R


164 
* 


165 
* A U B U C  R


166 
*


167 
**)


168 
local val [p1,p2,p3] = goal HOL.thy "(P  Q) ==> (P > R) ==> (Q > R) ==> R"


169 
val dummy = by (rtac (p1 RS disjE) 1)


170 
val dummy = by (rtac (p2 RS mp) 1)


171 
val dummy = by (assume_tac 1)


172 
val dummy = by (rtac (p3 RS mp) 1)


173 
val dummy = by (assume_tac 1)


174 
val tfl_exE = result()


175 
in


176 
fun DISJ_CASES th1 th2 th3 =


177 
let val c = D.drop_prop(cconcl th1)


178 
val (disj1,disj2) = D.dest_disj c


179 
val th2' = DISCH disj1 th2


180 
val th3' = DISCH disj2 th3


181 
in


182 
th3' RS (th2' RS (th1 RS tfl_exE))


183 
end


184 
end;


185 


186 


187 
(*


188 
*


189 
*  A1 \/ ... \/ An [A1  M, ..., An  M]


190 
* 


191 
*  M


192 
*


193 
* Note. The list of theorems may be all jumbled up, so we have to


194 
* first organize it to align with the first argument (the disjunctive


195 
* theorem).


196 
**)


197 


198 
fun organize eq = (* a bit slow  analogous to insertion sort *)


199 
let fun extract a alist =


200 
let fun ex (_,[]) = raise RULES_ERR{func = "organize",


201 
mesg = "not a permutation.1"}


202 
 ex(left,h::t) = if (eq h a) then (h,rev left@t) else ex(h::left,t)


203 
in ex ([],alist)


204 
end


205 
fun place [] [] = []


206 
 place (a::rst) alist =


207 
let val (item,next) = extract a alist


208 
in item::place rst next


209 
end


210 
 place _ _ = raise RULES_ERR{func = "organize",


211 
mesg = "not a permutation.2"}


212 
in place


213 
end;


214 
(* freezeT expensive! *)


215 
fun DISJ_CASESL disjth thl =


216 
let val c = cconcl disjth


217 
fun eq th atm = exists (fn t => HOLogic.dest_Trueprop t


218 
aconv term_of atm)


219 
(#hyps(rep_thm th))


220 
val tml = D.strip_disj c


221 
fun DL th [] = raise RULES_ERR{func="DISJ_CASESL",mesg="no cases"}


222 
 DL th [th1] = PROVE_HYP th th1


223 
 DL th [th1,th2] = DISJ_CASES th th1 th2


224 
 DL th (th1::rst) =


225 
let val tm = #2(D.dest_disj(D.drop_prop(cconcl th)))


226 
in DISJ_CASES th th1 (DL (ASSUME tm) rst) end


227 
in DL (freezeT disjth) (organize eq tml thl)


228 
end;


229 


230 


231 
(*


232 
* Universals


233 
**)


234 
local (* this is fragile *)


235 
val {prop,sign,...} = rep_thm spec


236 
val x = hd (tl (term_vars prop))


237 
val (TVar (indx,_)) = type_of x


238 
val gspec = forall_intr (cterm_of sign x) spec


239 
in


240 
fun SPEC tm thm =


241 
let val {sign,T,...} = rep_cterm tm


242 
val gspec' = instantiate([(indx,ctyp_of sign T)],[]) gspec


243 
in


244 
thm RS (forall_elim tm gspec')


245 
end


246 
end;


247 


248 
fun SPEC_ALL thm = rev_itlist SPEC (#1(D.strip_forall(cconcl thm))) thm;


249 


250 
val ISPEC = SPEC


251 
val ISPECL = rev_itlist ISPEC;


252 


253 
(* Not optimized! Too complicated. *)


254 
local val {prop,sign,...} = rep_thm allI


255 
val [P] = add_term_vars (prop, [])


256 
fun cty_theta s = map (fn (i,ty) => (i, ctyp_of s ty))


257 
fun ctm_theta s = map (fn (i,tm2) =>


258 
let val ctm2 = cterm_of s tm2


259 
in (cterm_of s (Var(i,#T(rep_cterm ctm2))), ctm2)


260 
end)


261 
fun certify s (ty_theta,tm_theta) = (cty_theta s ty_theta,


262 
ctm_theta s tm_theta)


263 
in


264 
fun GEN v th =


265 
let val gth = forall_intr v th


266 
val {prop=Const("all",_)$Abs(x,ty,rst),sign,...} = rep_thm gth


267 
val P' = Abs(x,ty, HOLogic.dest_Trueprop rst) (* get rid of trueprop *)


268 
val tsig = #tsig(Sign.rep_sg sign)


269 
val theta = Pattern.match tsig (P,P')


270 
val allI2 = instantiate (certify sign theta) allI


271 
val thm = implies_elim allI2 gth


272 
val {prop = tp $ (A $ Abs(_,_,M)),sign,...} = rep_thm thm


273 
val prop' = tp $ (A $ Abs(x,ty,M))


274 
in ALPHA thm (cterm_of sign prop')


275 
end


276 
end;


277 


278 
val GENL = itlist GEN;


279 


280 
fun GEN_ALL thm =


281 
let val {prop,sign,...} = rep_thm thm


282 
val tycheck = cterm_of sign


283 
val vlist = map tycheck (add_term_vars (prop, []))


284 
in GENL vlist thm


285 
end;


286 


287 


288 
fun MATCH_MP th1 th2 =


289 
if (D.is_forall (D.drop_prop(cconcl th1)))


290 
then MATCH_MP (th1 RS spec) th2


291 
else MP th1 th2;


292 


293 


294 
(*


295 
* Existentials


296 
**)


297 


298 


299 


300 
(*


301 
* Existential elimination


302 
*


303 
* A1  ?x.t[x] , A2, "t[v]"  t'


304 
*  (variable v occurs nowhere)


305 
* A1 u A2  t'


306 
*


307 
**)


308 


309 
local val [p1,p2] = goal HOL.thy "(? x. P x) ==> (!x. P x > Q) ==> Q"


310 
val dummy = by (rtac (p1 RS exE) 1)


311 
val dummy = by (rtac ((p2 RS allE) RS mp) 1)


312 
val dummy = by (assume_tac 2)


313 
val dummy = by (assume_tac 1)


314 
val choose_thm = result()


315 
in


316 
fun CHOOSE(fvar,exth) fact =


317 
let val lam = #2(dest_comb(D.drop_prop(cconcl exth)))


318 
val redex = capply lam fvar


319 
val {sign, t = t$u,...} = rep_cterm redex


320 
val residue = cterm_of sign (betapply(t,u))


321 
in GEN fvar (DISCH residue fact) RS (exth RS choose_thm)


322 
end


323 
end;


324 


325 


326 
local val {prop,sign,...} = rep_thm exI


327 
val [P,x] = term_vars prop


328 
in


329 
fun EXISTS (template,witness) thm =


330 
let val {prop,sign,...} = rep_thm thm


331 
val P' = cterm_of sign P


332 
val x' = cterm_of sign x


333 
val abstr = #2(dest_comb template)


334 
in


335 
thm RS (cterm_instantiate[(P',abstr), (x',witness)] exI)


336 
end


337 
end;


338 


339 
(*


340 
*


341 
* A  M


342 
*  [v_1,...,v_n]


343 
* A  ?v1...v_n. M


344 
*


345 
**)


346 


347 
fun EXISTL vlist th =


348 
U.itlist (fn v => fn thm => EXISTS(D.mk_exists(v,cconcl thm), v) thm)


349 
vlist th;


350 


351 


352 
(*


353 
*


354 
* A  M[x_1,...,x_n]


355 
*  [(x > y)_1,...,(x > y)_n]


356 
* A  ?y_1...y_n. M


357 
*


358 
**)


359 
(* Could be improved, but needs "subst_free" for certified terms *)


360 


361 
fun IT_EXISTS blist th =


362 
let val {sign,...} = rep_thm th


363 
val tych = cterm_of sign


364 
val detype = #t o rep_cterm


365 
val blist' = map (fn (x,y) => (detype x, detype y)) blist


366 
fun ?v M = cterm_of sign (S.mk_exists{Bvar=v,Body = M})


367 


368 
in


369 
U.itlist (fn (b as (r1,r2)) => fn thm =>


370 
EXISTS(?r2(subst_free[b]


371 
(HOLogic.dest_Trueprop(#prop(rep_thm thm)))), tych r1)


372 
thm)


373 
blist' th


374 
end;


375 


376 
(*


377 
* Faster version, that fails for some as yet unknown reason


378 
* fun IT_EXISTS blist th =


379 
* let val {sign,...} = rep_thm th


380 
* val tych = cterm_of sign


381 
* fun detype (x,y) = ((#t o rep_cterm) x, (#t o rep_cterm) y)


382 
* in


383 
* fold (fn (b as (r1,r2), thm) =>


384 
* EXISTS(D.mk_exists(r2, tych(subst_free[detype b](#t(rep_cterm(cconcl thm))))),


385 
* r1) thm) blist th


386 
* end;


387 
**)


388 


389 
(*


390 
* Rewriting


391 
**)


392 


393 
fun SUBS thl =


394 
rewrite_rule (map (fn th => (th RS eq_reflection) handle _ => th) thl);


395 


396 
local fun rew_conv mss = Thm.rewrite_cterm (true,false,false) mss (K(K None))


397 
in


398 
fun simpl_conv ss thl ctm =


399 
rew_conv (Thm.mss_of (#simps (Thm.dest_mss (#mss (rep_ss ss))) @ thl)) ctm


400 
RS meta_eq_to_obj_eq


401 
end;


402 


403 
local fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1])


404 
in


405 
val RIGHT_ASSOC = rewrite_rule [prover"((ab)c) = (a(bc))" RS eq_reflection]


406 
val ASM = refl RS iffD1


407 
end;


408 


409 


410 


411 


412 
(*


413 
* TERMINATION CONDITION EXTRACTION


414 
**)


415 


416 


417 
(* Object language quantifier, i.e., "!" *)


418 
fun Forall v M = S.mk_forall{Bvar=v, Body=M};


419 


420 


421 
(* Fragile: it's a cong if it is not "R y x ==> cut f R x y = f y" *)


422 
fun is_cong thm =


423 
let val {prop, ...} = rep_thm thm


424 
in case prop


425 
of (Const("==>",_)$(Const("Trueprop",_)$ _) $


426 
(Const("==",_) $ (Const ("cut",_) $ f $ R $ a $ x) $ _)) => false


427 
 _ => true


428 
end;


429 


430 


431 


432 
fun dest_equal(Const ("==",_) $


433 
(Const ("Trueprop",_) $ lhs)


434 
$ (Const ("Trueprop",_) $ rhs)) = {lhs=lhs, rhs=rhs}


435 
 dest_equal(Const ("==",_) $ lhs $ rhs) = {lhs=lhs, rhs=rhs}


436 
 dest_equal tm = S.dest_eq tm;


437 


438 
fun get_lhs tm = #lhs(dest_equal (HOLogic.dest_Trueprop tm));


439 


440 
fun dest_all(Const("all",_) $ (a as Abs _)) = S.dest_abs a


441 
 dest_all _ = raise RULES_ERR{func = "dest_all", mesg = "not a !!"};


442 


443 
val is_all = Utils.can dest_all;


444 


445 
fun strip_all fm =


446 
if (is_all fm)


447 
then let val {Bvar,Body} = dest_all fm


448 
val (bvs,core) = strip_all Body


449 
in ((Bvar::bvs), core)


450 
end


451 
else ([],fm);


452 


453 
fun break_all(Const("all",_) $ Abs (_,_,body)) = body


454 
 break_all _ = raise RULES_ERR{func = "break_all", mesg = "not a !!"};


455 


456 
fun list_break_all(Const("all",_) $ Abs (s,ty,body)) =


457 
let val (L,core) = list_break_all body


458 
in ((s,ty)::L, core)


459 
end


460 
 list_break_all tm = ([],tm);


461 


462 
(*


463 
* Rename a term of the form


464 
*


465 
* !!x1 ...xn. x1=M1 ==> ... ==> xn=Mn


466 
* ==> ((%v1...vn. Q) x1 ... xn = g x1 ... xn.


467 
* to one of


468 
*


469 
* !!v1 ... vn. v1=M1 ==> ... ==> vn=Mn


470 
* ==> ((%v1...vn. Q) v1 ... vn = g v1 ... vn.


471 
*


472 
* This prevents name problems in extraction, and helps the result to read


473 
* better. There is a problem with varstructs, since they can introduce more


474 
* than n variables, and some extra reasoning needs to be done.


475 
**)


476 


477 
fun get ([],_,L) = rev L


478 
 get (ant::rst,n,L) =


479 
case (list_break_all ant)


480 
of ([],_) => get (rst, n+1,L)


481 
 (vlist,body) =>


482 
let val eq = Logic.strip_imp_concl body


483 
val (f,args) = S.strip_comb (get_lhs eq)


484 
val (vstrl,_) = S.strip_abs f


485 
val names = variantlist (map (#1 o dest_Free) vstrl,


486 
add_term_names(body, []))


487 
in get (rst, n+1, (names,n)::L)


488 
end handle _ => get (rst, n+1, L);


489 


490 
(* Note: rename_params_rule counts from 1, not 0 *)


491 
fun rename thm =


492 
let val {prop,sign,...} = rep_thm thm


493 
val tych = cterm_of sign


494 
val ants = Logic.strip_imp_prems prop


495 
val news = get (ants,1,[])


496 
in


497 
U.rev_itlist rename_params_rule news thm


498 
end;


499 


500 


501 
(*


502 
* Betaconversion to the rhs of an equation (taken from hol90/drule.sml)


503 
**)


504 


505 
fun list_beta_conv tm =


506 
let fun rbeta th = transitive th (beta_conversion(#2(D.dest_eq(cconcl th))))


507 
fun iter [] = reflexive tm


508 
 iter (v::rst) = rbeta (combination(iter rst) (reflexive v))


509 
in iter end;


510 


511 


512 
(*


513 
* Trace information for the rewriter


514 
**)


515 
val term_ref = ref[] : term list ref


516 
val mss_ref = ref [] : meta_simpset list ref;


517 
val thm_ref = ref [] : thm list ref;


518 
val tracing = ref false;


519 


520 
fun say s = if !tracing then writeln s else ();


521 


522 
fun print_thms s L =


523 
say (cat_lines (s :: map string_of_thm L));


524 


525 
fun print_cterms s L =


526 
say (cat_lines (s :: map string_of_cterm L));


527 


528 


529 
(*


530 
* General abstraction handlers, should probably go in USyntax.


531 
**)


532 
fun mk_aabs(vstr,body) = S.mk_abs{Bvar=vstr,Body=body}


533 
handle _ => S.mk_pabs{varstruct = vstr, body = body};


534 


535 
fun list_mk_aabs (vstrl,tm) =


536 
U.itlist (fn vstr => fn tm => mk_aabs(vstr,tm)) vstrl tm;


537 


538 
fun dest_aabs tm =


539 
let val {Bvar,Body} = S.dest_abs tm


540 
in (Bvar,Body)


541 
end handle _ => let val {varstruct,body} = S.dest_pabs tm


542 
in (varstruct,body)


543 
end;


544 


545 
fun strip_aabs tm =


546 
let val (vstr,body) = dest_aabs tm


547 
val (bvs, core) = strip_aabs body


548 
in (vstr::bvs, core)


549 
end


550 
handle _ => ([],tm);


551 


552 
fun dest_combn tm 0 = (tm,[])


553 
 dest_combn tm n =


554 
let val {Rator,Rand} = S.dest_comb tm


555 
val (f,rands) = dest_combn Rator (n1)


556 
in (f,Rand::rands)


557 
end;


558 


559 


560 


561 


562 
local fun dest_pair M = let val {fst,snd} = S.dest_pair M in (fst,snd) end


563 
fun mk_fst tm =


564 
let val ty as Type("*", [fty,sty]) = type_of tm


565 
in Const ("fst", ty > fty) $ tm end


566 
fun mk_snd tm =


567 
let val ty as Type("*", [fty,sty]) = type_of tm


568 
in Const ("snd", ty > sty) $ tm end


569 
in


570 
fun XFILL tych x vstruct =


571 
let fun traverse p xocc L =


572 
if (is_Free p)


573 
then tych xocc::L


574 
else let val (p1,p2) = dest_pair p


575 
in traverse p1 (mk_fst xocc) (traverse p2 (mk_snd xocc) L)


576 
end


577 
in


578 
traverse vstruct x []


579 
end end;


580 


581 
(*


582 
* Replace a free tuple (vstr) by a universally quantified variable (a).


583 
* Note that the notion of "freeness" for a tuple is different than for a


584 
* variable: if variables in the tuple also occur in any other place than


585 
* an occurrences of the tuple, they aren't "free" (which is thus probably


586 
* the wrong word to use).


587 
**)


588 


589 
fun VSTRUCT_ELIM tych a vstr th =


590 
let val L = S.free_vars_lr vstr


591 
val bind1 = tych (HOLogic.mk_Trueprop (HOLogic.mk_eq(a,vstr)))


592 
val thm1 = implies_intr bind1 (SUBS [SYM(assume bind1)] th)


593 
val thm2 = forall_intr_list (map tych L) thm1


594 
val thm3 = forall_elim_list (XFILL tych a vstr) thm2


595 
in refl RS


596 
rewrite_rule[symmetric (surjective_pairing RS eq_reflection)] thm3


597 
end;


598 


599 
fun PGEN tych a vstr th =


600 
let val a1 = tych a


601 
val vstr1 = tych vstr


602 
in


603 
forall_intr a1


604 
(if (is_Free vstr)


605 
then cterm_instantiate [(vstr1,a1)] th


606 
else VSTRUCT_ELIM tych a vstr th)


607 
end;


608 


609 


610 
(*


611 
* Takes apart a paired betaredex, looking like "(\(x,y).N) vstr", into


612 
*


613 
* (([x,y],N),vstr)


614 
**)


615 
fun dest_pbeta_redex M n =


616 
let val (f,args) = dest_combn M n


617 
val dummy = dest_aabs f


618 
in (strip_aabs f,args)


619 
end;


620 


621 
fun pbeta_redex M n = U.can (U.C dest_pbeta_redex n) M;


622 


623 
fun dest_impl tm =


624 
let val ants = Logic.strip_imp_prems tm


625 
val eq = Logic.strip_imp_concl tm


626 
in (ants,get_lhs eq)


627 
end;


628 


629 
fun restricted t = is_some (S.find_term


630 
(fn (Const("cut",_)) =>true  _ => false)


631 
t)


632 


633 
fun CONTEXT_REWRITE_RULE (func, G, cut_lemma, congs) th =


634 
let val globals = func::G


635 
val pbeta_reduce = simpl_conv empty_ss [split RS eq_reflection];


636 
val tc_list = ref[]: term list ref


637 
val dummy = term_ref := []


638 
val dummy = thm_ref := []


639 
val dummy = mss_ref := []


640 
val cut_lemma' = cut_lemma RS eq_reflection


641 
fun prover mss thm =


642 
let fun cong_prover mss thm =


643 
let val dummy = say "cong_prover:"


644 
val cntxt = prems_of_mss mss


645 
val dummy = print_thms "cntxt:" cntxt


646 
val dummy = say "cong rule:"


647 
val dummy = say (string_of_thm thm)


648 
val dummy = thm_ref := (thm :: !thm_ref)


649 
val dummy = mss_ref := (mss :: !mss_ref)


650 
(* Unquantified eliminate *)


651 
fun uq_eliminate (thm,imp,sign) =


652 
let val tych = cterm_of sign


653 
val dummy = print_cterms "To eliminate:" [tych imp]


654 
val ants = map tych (Logic.strip_imp_prems imp)


655 
val eq = Logic.strip_imp_concl imp


656 
val lhs = tych(get_lhs eq)


657 
val mss' = add_prems(mss, map ASSUME ants)


658 
val lhs_eq_lhs1 = Thm.rewrite_cterm(false,true,false)mss' prover lhs


659 
handle _ => reflexive lhs


660 
val dummy = print_thms "proven:" [lhs_eq_lhs1]


661 
val lhs_eq_lhs2 = implies_intr_list ants lhs_eq_lhs1


662 
val lhs_eeq_lhs2 = lhs_eq_lhs2 RS meta_eq_to_obj_eq


663 
in


664 
lhs_eeq_lhs2 COMP thm


665 
end


666 
fun pq_eliminate (thm,sign,vlist,imp_body,lhs_eq) =


667 
let val ((vstrl,_),args) = dest_pbeta_redex lhs_eq(length vlist)


668 
val dummy = assert (forall (op aconv)


669 
(ListPair.zip (vlist, args)))


670 
"assertion failed in CONTEXT_REWRITE_RULE"


671 
val imp_body1 = subst_free (ListPair.zip (args, vstrl))


672 
imp_body


673 
val tych = cterm_of sign


674 
val ants1 = map tych (Logic.strip_imp_prems imp_body1)


675 
val eq1 = Logic.strip_imp_concl imp_body1


676 
val Q = get_lhs eq1


677 
val QeqQ1 = pbeta_reduce (tych Q)


678 
val Q1 = #2(D.dest_eq(cconcl QeqQ1))


679 
val mss' = add_prems(mss, map ASSUME ants1)


680 
val Q1eeqQ2 = Thm.rewrite_cterm (false,true,false) mss' prover Q1


681 
handle _ => reflexive Q1


682 
val Q2 = #2 (Logic.dest_equals (#prop(rep_thm Q1eeqQ2)))


683 
val Q3 = tych(list_comb(list_mk_aabs(vstrl,Q2),vstrl))


684 
val Q2eeqQ3 = symmetric(pbeta_reduce Q3 RS eq_reflection)


685 
val thA = transitive(QeqQ1 RS eq_reflection) Q1eeqQ2


686 
val QeeqQ3 = transitive thA Q2eeqQ3 handle _ =>


687 
((Q2eeqQ3 RS meta_eq_to_obj_eq)


688 
RS ((thA RS meta_eq_to_obj_eq) RS trans))


689 
RS eq_reflection


690 
val impth = implies_intr_list ants1 QeeqQ3


691 
val impth1 = impth RS meta_eq_to_obj_eq


692 
(* Need to abstract *)


693 
val ant_th = U.itlist2 (PGEN tych) args vstrl impth1


694 
in ant_th COMP thm


695 
end


696 
fun q_eliminate (thm,imp,sign) =


697 
let val (vlist,imp_body) = strip_all imp


698 
val (ants,Q) = dest_impl imp_body


699 
in if (pbeta_redex Q) (length vlist)


700 
then pq_eliminate (thm,sign,vlist,imp_body,Q)


701 
else


702 
let val tych = cterm_of sign


703 
val ants1 = map tych ants


704 
val mss' = add_prems(mss, map ASSUME ants1)


705 
val Q_eeq_Q1 = Thm.rewrite_cterm(false,true,false) mss'


706 
prover (tych Q)


707 
handle _ => reflexive (tych Q)


708 
val lhs_eeq_lhs2 = implies_intr_list ants1 Q_eeq_Q1


709 
val lhs_eq_lhs2 = lhs_eeq_lhs2 RS meta_eq_to_obj_eq


710 
val ant_th = forall_intr_list(map tych vlist)lhs_eq_lhs2


711 
in


712 
ant_th COMP thm


713 
end end


714 


715 
fun eliminate thm =


716 
case (rep_thm thm)


717 
of {prop = (Const("==>",_) $ imp $ _), sign, ...} =>


718 
eliminate


719 
(if not(is_all imp)


720 
then uq_eliminate (thm,imp,sign)


721 
else q_eliminate (thm,imp,sign))


722 
(* Assume that the leading constant is ==, *)


723 
 _ => thm (* if it is not a ==> *)


724 
in Some(eliminate (rename thm))


725 
end handle _ => None


726 


727 
fun restrict_prover mss thm =


728 
let val dummy = say "restrict_prover:"


729 
val cntxt = rev(prems_of_mss mss)


730 
val dummy = print_thms "cntxt:" cntxt


731 
val {prop = Const("==>",_) $ (Const("Trueprop",_) $ A) $ _,


732 
sign,...} = rep_thm thm


733 
fun genl tm = let val vlist = gen_rems (op aconv)


734 
(add_term_frees(tm,[]), globals)


735 
in U.itlist Forall vlist tm


736 
end


737 
(*


738 
* This actually isn't quite right, since it will think that


739 
* notfully applied occs. of "f" in the context mean that the


740 
* current call is nested. The real solution is to pass in a


741 
* term "f v1..vn" which is a pattern that any full application


742 
* of "f" will match.


743 
**)


744 
val func_name = #1(dest_Const func)


745 
fun is_func (Const (name,_)) = (name = func_name)


746 
 is_func _ = false


747 
val rcontext = rev cntxt


748 
val cncl = HOLogic.dest_Trueprop o #prop o rep_thm


749 
val antl = case rcontext of [] => []


750 
 _ => [S.list_mk_conj(map cncl rcontext)]


751 
val TC = genl(S.list_mk_imp(antl, A))


752 
val dummy = print_cterms "func:" [cterm_of sign func]


753 
val dummy = print_cterms "TC:"


754 
[cterm_of sign (HOLogic.mk_Trueprop TC)]


755 
val dummy = tc_list := (TC :: !tc_list)


756 
val nestedp = is_some (S.find_term is_func TC)


757 
val dummy = if nestedp then say "nested" else say "not_nested"


758 
val dummy = term_ref := ([func,TC]@(!term_ref))


759 
val th' = if nestedp then raise RULES_ERR{func = "solver",


760 
mesg = "nested function"}


761 
else let val cTC = cterm_of sign


762 
(HOLogic.mk_Trueprop TC)


763 
in case rcontext of


764 
[] => SPEC_ALL(ASSUME cTC)


765 
 _ => MP (SPEC_ALL (ASSUME cTC))


766 
(LIST_CONJ rcontext)


767 
end


768 
val th'' = th' RS thm


769 
in Some (th'')


770 
end handle _ => None


771 
in


772 
(if (is_cong thm) then cong_prover else restrict_prover) mss thm


773 
end


774 
val ctm = cprop_of th


775 
val th1 = Thm.rewrite_cterm(false,true,false) (add_congs(mss_of [cut_lemma'], congs))


776 
prover ctm


777 
val th2 = equal_elim th1 th


778 
in


779 
(th2, filter (not o restricted) (!tc_list))


780 
end;


781 


782 


783 


784 
fun prove (ptm,tac) =


785 
#1 (freeze_thaw (prove_goalw_cterm [] ptm (fn _ => [tac])));


786 


787 


788 
end; (* Rules *)
