author  paulson 
Wed, 19 Aug 1998 10:49:30 +0200  
changeset 5343  871b77df79a0 
parent 4653  d60f76680bf4 
child 5411  7a43b484f6d2 
permissions  rwrr 
4078  1 
(* Title: Provers/blast.ML 
2894  2 
ID: $Id$ 
3 
Author: Lawrence C Paulson, Cambridge University Computer Laboratory 

3083  4 
Copyright 1997 University of Cambridge 
2894  5 

6 
Generic tableau prover with proof reconstruction 

7 

2854  8 
SKOLEMIZES ReplaceI WRONGLY: allow new vars in prems, or forbid such rules?? 
2894  9 
Needs explicit instantiation of assumptions? 
10 

11 

2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

12 
Blast_tac is often more powerful than fast_tac, but has some limitations. 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

13 
Blast_tac... 
4651  14 
* ignores wrappers (addss, addbefore, addafter, addWrapper, ...); 
15 
this restriction is intrinsic 

2894  16 
* ignores elimination rules that don't have the correct format 
17 
(conclusion must be a formula variable) 

18 
* ignores types, which can make HOL proofs fail 

2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

19 
* rules must not require higherorder unification, e.g. apply_type in ZF 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

20 
+ message "Function Var's argument not a bound variable" relates to this 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

21 
* its proof strategy is more general but can actually be slower 
2894  22 

23 
Known problems: 

3092  24 
"Recursive" chains of rules can sometimes exclude other unsafe formulae 
3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset

25 
from expansion. This happens because newlycreated formulae always 
3092  26 
have priority over existing ones. But obviously recursive rules 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

27 
such as transitivity are treated specially to prevent this. Sometimes 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

28 
the formulae get into the wrong order (see WRONG below). 
3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset

29 

2952  30 
With overloading: 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

31 
Calls to Blast.overloaded (see HOL/Set.ML for examples) are needed 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

32 
to tell Blast_tac when to retain some type information. Make sure 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

33 
you know the constant's internal name, which might be "op <=" or 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

34 
"Relation.op ^^". 
2952  35 

2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

36 
With substition for equalities (hyp_subst_tac): 
3092  37 
When substitution affects a haz formula or literal, it is moved 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

38 
back to the list of safe formulae. 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

39 
But there's no way of putting it in the right place. A "moved" or 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

40 
"no DETERM" flag would prevent proofs failing here. 
2854  41 
*) 
42 

43 
(*Should be a type abbreviation?*) 

44 
type netpair = (int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net; 

45 

46 

47 
(*Assumptions about constants: 

48 
The negation symbol is "Not" 

49 
The equality symbol is "op =" 

50 
The istrue judgement symbol is "Trueprop" 

51 
There are no constants named "*Goal* or "*False*" 

52 
*) 

53 
signature BLAST_DATA = 

54 
sig 

55 
type claset 

56 
val notE : thm (* [ ~P; P ] ==> R *) 

57 
val ccontr : thm 

58 
val contr_tac : int > tactic 

59 
val dup_intr : thm > thm 

4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

60 
val hyp_subst_tac : bool ref > int > tactic 
4078  61 
val claset : unit > claset 
4653  62 
val rep_cs : (* dependent on classical.ML *) 
2854  63 
claset > {safeIs: thm list, safeEs: thm list, 
64 
hazIs: thm list, hazEs: thm list, 

4651  65 
swrappers: (string * wrapper) list, 
66 
uwrappers: (string * wrapper) list, 

2854  67 
safe0_netpair: netpair, safep_netpair: netpair, 
68 
haz_netpair: netpair, dup_netpair: netpair} 

69 
end; 

70 

71 

72 
signature BLAST = 

73 
sig 

2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

74 
type claset 
4233
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

75 
exception TRANS of string (*reports translation errors*) 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

76 
datatype term = 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

77 
Const of string 
4065  78 
 TConst of string * term 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

79 
 Skolem of string * term option ref list 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

80 
 Free of string 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

81 
 Var of term option ref 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

82 
 Bound of int 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

83 
 Abs of string*term 
3030  84 
 $ of term*term; 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

85 
type branch 
2883  86 
val depth_tac : claset > int > int > tactic 
87 
val blast_tac : claset > int > tactic 

88 
val Blast_tac : int > tactic 

4240
8ba60a4cd380
Renamed "overload" to "overloaded" for sml/nj compatibility
paulson
parents:
4233
diff
changeset

89 
val overloaded : string * (Term.typ > Term.typ) > unit 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

90 
(*debugging tools*) 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

91 
val stats : bool ref 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

92 
val trace : bool ref 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

93 
val fullTrace : branch list list ref 
4065  94 
val fromType : (indexname * term) list ref > Term.typ > term 
95 
val fromTerm : Term.term > term 

96 
val fromSubgoal : Term.term > term 

97 
val instVars : term > (unit > unit) 

2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

98 
val toTerm : int > term > Term.term 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

99 
val readGoal : Sign.sg > string > term 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

100 
val tryInThy : theory > int > string > 
3083  101 
(int>tactic) list * branch list list * (int*int*exn) list 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

102 
val trygl : claset > int > int > 
3083  103 
(int>tactic) list * branch list list * (int*int*exn) list 
104 
val Trygl : int > int > 

105 
(int>tactic) list * branch list list * (int*int*exn) list 

2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

106 
val normBr : branch > branch 
2854  107 
end; 
108 

109 

3092  110 
functor BlastFun(Data: BLAST_DATA) : BLAST = 
2854  111 
struct 
112 

113 
type claset = Data.claset; 

114 

4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

115 
val trace = ref false 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

116 
and stats = ref false; (*for runtime and search statistics*) 
2854  117 

118 
datatype term = 

5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

119 
Const of string 
4065  120 
 TConst of string * term (*type of overloaded constantas a term!*) 
2854  121 
 Skolem of string * term option ref list 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

122 
 Free of string 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

123 
 Var of term option ref 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

124 
 Bound of int 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

125 
 Abs of string*term 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

126 
 $ of term*term; 
2854  127 

128 

129 
(** Basic syntactic operations **) 

130 

131 
fun is_Var (Var _) = true 

132 
 is_Var _ = false; 

133 

134 
fun dest_Var (Var x) = x; 

135 

136 

137 
fun rand (f$x) = x; 

138 

139 
(* maps (f, [t1,...,tn]) to f(t1,...,tn) *) 

140 
val list_comb : term * term list > term = foldl (op $); 

141 

142 

143 
(* maps f(t1,...,tn) to (f, [t1,...,tn]) ; naturally tailrecursive*) 

144 
fun strip_comb u : term * term list = 

145 
let fun stripc (f$t, ts) = stripc (f, t::ts) 

146 
 stripc x = x 

147 
in stripc(u,[]) end; 

148 

149 

150 
(* maps f(t1,...,tn) to f , which is never a combination *) 

151 
fun head_of (f$t) = head_of f 

152 
 head_of u = u; 

153 

154 

155 
(** Particular constants **) 

156 

157 
fun negate P = Const"Not" $ P; 

158 

159 
fun mkGoal P = Const"*Goal*" $ P; 

160 

161 
fun isGoal (Const"*Goal*" $ _) = true 

162 
 isGoal _ = false; 

163 

164 
val Trueprop = Term.Const("Trueprop", Type("o",[])>propT); 

165 
fun mk_tprop P = Term.$ (Trueprop, P); 

166 

167 
fun isTrueprop (Term.Const("Trueprop",_)) = true 

168 
 isTrueprop _ = false; 

169 

170 

4065  171 
(*** Dealing with overloaded constants ***) 
2854  172 

4065  173 
(*alist is a map from TVar names to Vars. We need to unify the TVars 
174 
faithfully in order to track overloading*) 

175 
fun fromType alist (Term.Type(a,Ts)) = list_comb (Const a, 

176 
map (fromType alist) Ts) 

177 
 fromType alist (Term.TFree(a,_)) = Free a 

178 
 fromType alist (Term.TVar (ixn,_)) = 

179 
(case (assoc_string_int(!alist,ixn)) of 

180 
None => let val t' = Var(ref None) 

181 
in alist := (ixn, t') :: !alist; t' 

182 
end 

183 
 Some v => v) 

2854  184 

185 
local 

4065  186 
val overloads = ref ([]: (string * (Term.typ > Term.typ)) list) 
2854  187 
in 
188 

4240
8ba60a4cd380
Renamed "overload" to "overloaded" for sml/nj compatibility
paulson
parents:
4233
diff
changeset

189 
fun overloaded arg = (overloads := arg :: (!overloads)); 
2854  190 

4065  191 
(*Convert a possibly overloaded Term.Const to a Blast.Const or Blast.TConst, 
192 
converting its type to a Blast.term in the latter case.*) 

193 
fun fromConst alist (a,T) = 

194 
case assoc_string (!overloads, a) of 

195 
None => Const a (*not overloaded*) 

196 
 Some f => 

197 
let val T' = f T 

4233
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

198 
handle Match => error 
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

199 
("Blast_tac: unexpected type for overloaded constant " ^ a) 
4065  200 
in TConst(a, fromType alist T') end; 
201 

2854  202 
end; 
203 

204 

205 
(*Tests whether 2 terms are alphaconvertible; chases instantiations*) 

206 
fun (Const a) aconv (Const b) = a=b 

4065  207 
 (TConst (a,ta)) aconv (TConst (b,tb)) = a=b andalso ta aconv tb 
2854  208 
 (Skolem (a,_)) aconv (Skolem (b,_)) = a=b (*arglists must then be equal*) 
209 
 (Free a) aconv (Free b) = a=b 

210 
 (Var(ref(Some t))) aconv u = t aconv u 

4065  211 
 t aconv (Var(ref(Some u))) = t aconv u 
2854  212 
 (Var v) aconv (Var w) = v=w (*both Vars are unassigned*) 
213 
 (Bound i) aconv (Bound j) = i=j 

214 
 (Abs(_,t)) aconv (Abs(_,u)) = t aconv u 

215 
 (f$t) aconv (g$u) = (f aconv g) andalso (t aconv u) 

216 
 _ aconv _ = false; 

217 

218 

219 
fun mem_term (_, []) = false 

220 
 mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts); 

221 

222 
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts; 

223 

224 
fun mem_var (v: term option ref, []) = false 

225 
 mem_var (v, v'::vs) = v=v' orelse mem_var(v,vs); 

226 

227 
fun ins_var(v,vs) = if mem_var(v,vs) then vs else v :: vs; 

228 

229 

230 
(** Vars **) 

231 

232 
(*Accumulates the Vars in the term, suppressing duplicates*) 

233 
fun add_term_vars (Skolem(a,args), vars) = add_vars_vars(args,vars) 

234 
 add_term_vars (Var (v as ref None), vars) = ins_var (v, vars) 

235 
 add_term_vars (Var (ref (Some u)), vars) = add_term_vars(u,vars) 

4065  236 
 add_term_vars (TConst (_,t), vars) = add_term_vars(t,vars) 
2854  237 
 add_term_vars (Abs (_,body), vars) = add_term_vars(body,vars) 
238 
 add_term_vars (f$t, vars) = add_term_vars (f, add_term_vars(t, vars)) 

239 
 add_term_vars (_, vars) = vars 

240 
(*Term list version. [The fold functionals are slow]*) 

241 
and add_terms_vars ([], vars) = vars 

242 
 add_terms_vars (t::ts, vars) = add_terms_vars (ts, add_term_vars(t,vars)) 

243 
(*Var list version.*) 

244 
and add_vars_vars ([], vars) = vars 

245 
 add_vars_vars (ref (Some u) :: vs, vars) = 

246 
add_vars_vars (vs, add_term_vars(u,vars)) 

247 
 add_vars_vars (v::vs, vars) = (*v must be a ref None*) 

248 
add_vars_vars (vs, ins_var (v, vars)); 

249 

250 

251 
(*Chase assignments in "vars"; return a list of unassigned variables*) 

252 
fun vars_in_vars vars = add_vars_vars(vars,[]); 

253 

254 

255 

256 
(*increment a term's nonlocal bound variables 

257 
inc is increment for bound variables 

258 
lev is level at which a bound variable is considered 'loose'*) 

259 
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u 

260 
 incr_bv (inc, lev, Abs(a,body)) = Abs(a, incr_bv(inc,lev+1,body)) 

261 
 incr_bv (inc, lev, f$t) = incr_bv(inc,lev,f) $ incr_bv(inc,lev,t) 

262 
 incr_bv (inc, lev, u) = u; 

263 

264 
fun incr_boundvars 0 t = t 

265 
 incr_boundvars inc t = incr_bv(inc,0,t); 

266 

267 

268 
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond. 

269 
(Bound 0) is loose at level 0 *) 

270 
fun add_loose_bnos (Bound i, lev, js) = if i<lev then js 

271 
else (ilev) ins_int js 

272 
 add_loose_bnos (Abs (_,t), lev, js) = add_loose_bnos (t, lev+1, js) 

273 
 add_loose_bnos (f$t, lev, js) = 

274 
add_loose_bnos (f, lev, add_loose_bnos (t, lev, js)) 

275 
 add_loose_bnos (_, _, js) = js; 

276 

277 
fun loose_bnos t = add_loose_bnos (t, 0, []); 

278 

279 
fun subst_bound (arg, t) : term = 

280 
let fun subst (t as Bound i, lev) = 

281 
if i<lev then t (*var is locally bound*) 

282 
else if i=lev then incr_boundvars lev arg 

283 
else Bound(i1) (*loose: change it*) 

284 
 subst (Abs(a,body), lev) = Abs(a, subst(body,lev+1)) 

285 
 subst (f$t, lev) = subst(f,lev) $ subst(t,lev) 

286 
 subst (t,lev) = t 

287 
in subst (t,0) end; 

288 

289 

3101
e8a92f497295
Again "norm" DOES NOT normalize bodies of abstractions
paulson
parents:
3092
diff
changeset

290 
(*Normalize...but not the bodies of ABSTRACTIONS*) 
2854  291 
fun norm t = case t of 
2952  292 
Skolem (a,args) => Skolem(a, vars_in_vars args) 
4065  293 
 TConst(a,aT) => TConst(a, norm aT) 
2854  294 
 (Var (ref None)) => t 
295 
 (Var (ref (Some u))) => norm u 

296 
 (f $ u) => (case norm f of 

3101
e8a92f497295
Again "norm" DOES NOT normalize bodies of abstractions
paulson
parents:
3092
diff
changeset

297 
Abs(_,body) => norm (subst_bound (u, body)) 
e8a92f497295
Again "norm" DOES NOT normalize bodies of abstractions
paulson
parents:
3092
diff
changeset

298 
 nf => nf $ norm u) 
2854  299 
 _ => t; 
300 

301 

302 
(*Weak (onelevel) normalize for use in unification*) 

303 
fun wkNormAux t = case t of 

304 
(Var v) => (case !v of 

305 
Some u => wkNorm u 

306 
 None => t) 

307 
 (f $ u) => (case wkNormAux f of 

308 
Abs(_,body) => wkNorm (subst_bound (u, body)) 

309 
 nf => nf $ u) 

2952  310 
 Abs (a,body) => (*etacontract if possible*) 
311 
(case wkNormAux body of 

312 
nb as (f $ t) => 

313 
if (0 mem_int loose_bnos f) orelse wkNorm t <> Bound 0 

314 
then Abs(a,nb) 

315 
else wkNorm (incr_boundvars ~1 f) 

3092  316 
 nb => Abs (a,nb)) 
2854  317 
 _ => t 
318 
and wkNorm t = case head_of t of 

319 
Const _ => t 

4065  320 
 TConst _ => t 
2854  321 
 Skolem(a,args) => t 
322 
 Free _ => t 

323 
 _ => wkNormAux t; 

324 

325 

326 
(*Does variable v occur in u? For unification.*) 

327 
fun varOccur v = 

328 
let fun occL [] = false (*same as (exists occ), but faster*) 

329 
 occL (u::us) = occ u orelse occL us 

330 
and occ (Var w) = 

331 
v=w orelse 

332 
(case !w of None => false 

333 
 Some u => occ u) 

334 
 occ (Skolem(_,args)) = occL (map Var args) 

4065  335 
 occ (TConst(_,u)) = occ u 
2854  336 
 occ (Abs(_,u)) = occ u 
337 
 occ (f$u) = occ u orelse occ f 

338 
 occ (_) = false; 

339 
in occ end; 

340 

341 
exception UNIFY; 

342 

343 
val trail = ref [] : term option ref list ref; 

344 
val ntrail = ref 0; 

345 

346 

347 
(*Restore the trail to some previous state: for backtracking*) 

348 
fun clearTo n = 

3083  349 
while !ntrail<>n do 
2854  350 
(hd(!trail) := None; 
351 
trail := tl (!trail); 

352 
ntrail := !ntrail  1); 

353 

354 

355 
(*Firstorder unification with bound variables. 

356 
"vars" is a list of variables local to the rule and NOT to be put 

357 
on the trail (no point in doing so) 

358 
*) 

4065  359 
fun unify(vars,t,u) = 
2854  360 
let val n = !ntrail 
361 
fun update (t as Var v, u) = 

362 
if t aconv u then () 

363 
else if varOccur v u then raise UNIFY 

364 
else if mem_var(v, vars) then v := Some u 

365 
else (*avoid updating Vars in the branch if possible!*) 

366 
if is_Var u andalso mem_var(dest_Var u, vars) 

367 
then dest_Var u := Some t 

368 
else (v := Some u; 

369 
trail := v :: !trail; ntrail := !ntrail + 1) 

370 
fun unifyAux (t,u) = 

371 
case (wkNorm t, wkNorm u) of 

372 
(nt as Var v, nu) => update(nt,nu) 

373 
 (nu, nt as Var v) => update(nt,nu) 

4065  374 
 (TConst(a,at), TConst(b,bt)) => if a=b then unifyAux(at,bt) 
375 
else raise UNIFY 

2854  376 
 (Abs(_,t'), Abs(_,u')) => unifyAux(t',u') 
377 
(*NB: can yield unifiers having dangling Bound vars!*) 

378 
 (f$t', g$u') => (unifyAux(f,g); unifyAux(t',u')) 

379 
 (nt, nu) => if nt aconv nu then () else raise UNIFY 

3083  380 
in (unifyAux(t,u); true) handle UNIFY => (clearTo n; false) 
2854  381 
end; 
382 

383 

4065  384 
(*Convert from "real" terms to prototerms; etacontract 
385 
Code is duplicated with fromSubgoal. Correct this?*) 

386 
fun fromTerm t = 

387 
let val alistVar = ref [] 

388 
and alistTVar = ref [] 

389 
fun from (Term.Const aT) = fromConst alistTVar aT 

2854  390 
 from (Term.Free (a,_)) = Free a 
391 
 from (Term.Bound i) = Bound i 

392 
 from (Term.Var (ixn,T)) = 

4065  393 
(case (assoc_string_int(!alistVar,ixn)) of 
2854  394 
None => let val t' = Var(ref None) 
4065  395 
in alistVar := (ixn, t') :: !alistVar; t' 
2854  396 
end 
4065  397 
 Some v => v) 
2854  398 
 from (Term.Abs (a,_,u)) = 
399 
(case from u of 

400 
u' as (f $ Bound 0) => 

401 
if (0 mem_int loose_bnos f) then Abs(a,u') 

402 
else incr_boundvars ~1 f 

403 
 u' => Abs(a,u')) 

404 
 from (Term.$ (f,u)) = from f $ from u 

405 
in from t end; 

406 

4065  407 
(*A debugging function: replaces all Vars by dummy Frees for visual inspection 
408 
of whether they are distinct. Function revert undoes the assignments.*) 

409 
fun instVars t = 

410 
let val name = ref "A" 

411 
val updated = ref [] 

412 
fun inst (TConst(a,t)) = inst t 

413 
 inst (Var(v as ref None)) = (updated := v :: (!updated); 

414 
v := Some (Free ("?" ^ !name)); 

415 
name := bump_string (!name)) 

416 
 inst (Abs(a,t)) = inst t 

417 
 inst (f $ u) = (inst f; inst u) 

418 
 inst _ = () 

419 
fun revert() = seq (fn v => v:=None) (!updated) 

420 
in inst t; revert end; 

421 

422 

2854  423 
(* A1==>...An==>B goes to [A1,...,An], where B is not an implication *) 
424 
fun strip_imp_prems (Const"==>" $ (Const"Trueprop" $ A) $ B) = 

425 
A :: strip_imp_prems B 

426 
 strip_imp_prems (Const"==>" $ A $ B) = A :: strip_imp_prems B 

427 
 strip_imp_prems _ = []; 

428 

429 
(* A1==>...An==>B goes to B, where B is not an implication *) 

430 
fun strip_imp_concl (Const"==>" $ A $ B) = strip_imp_concl B 

431 
 strip_imp_concl (Const"Trueprop" $ A) = A 

432 
 strip_imp_concl A = A : term; 

433 

434 

435 
(*** Conversion of Elimination Rules to Tableau Operations ***) 

436 

437 
(*The conclusion becomes the goal/negated assumption *False*: delete it!*) 

438 
fun squash_nots [] = [] 

439 
 squash_nots (Const "*Goal*" $ (Var (ref (Some (Const"*False*")))) :: Ps) = 

440 
squash_nots Ps 

441 
 squash_nots (Const "Not" $ (Var (ref (Some (Const"*False*")))) :: Ps) = 

442 
squash_nots Ps 

443 
 squash_nots (P::Ps) = P :: squash_nots Ps; 

444 

445 
fun skoPrem vars (Const "all" $ Abs (_, P)) = 

446 
skoPrem vars (subst_bound (Skolem (gensym "S_", vars), P)) 

447 
 skoPrem vars P = P; 

448 

449 
fun convertPrem t = 

450 
squash_nots (mkGoal (strip_imp_concl t) :: strip_imp_prems t); 

451 

452 
(*Expects elimination rules to have a formula variable as conclusion*) 

453 
fun convertRule vars t = 

454 
let val (P::Ps) = strip_imp_prems t 

455 
val Var v = strip_imp_concl t 

456 
in v := Some (Const"*False*"); 

457 
(P, map (convertPrem o skoPrem vars) Ps) 

458 
end; 

459 

460 

461 
(*Like dup_elim, but puts the duplicated major premise FIRST*) 

4271
3a82492e70c5
changed Pure/Sequence interface  isatool fixseq;
wenzelm
parents:
4240
diff
changeset

462 
fun rev_dup_elim th = th RSN (2, revcut_rl) > assumption 2 > Seq.hd; 
2854  463 

464 

4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

465 
(*Rotate the assumptions in all new subgoals for the LIFO discipline*) 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

466 
local 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

467 
(*Count new hyps so that they can be rotated*) 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

468 
fun nNewHyps [] = 0 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

469 
 nNewHyps (Const "*Goal*" $ _ :: Ps) = nNewHyps Ps 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

470 
 nNewHyps (P::Ps) = 1 + nNewHyps Ps; 
2854  471 

4511
93a84eb6c522
Blast_tac now squashes flexflex pairs immediately
paulson
parents:
4466
diff
changeset

472 
fun rot_tac [] i st = Seq.single (Seq.hd (flexflex_rule st)) 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

473 
 rot_tac (0::ks) i st = rot_tac ks (i+1) st 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

474 
 rot_tac (k::ks) i st = rot_tac ks (i+1) (rotate_rule (~k) i st); 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

475 
in 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

476 
fun rot_subgoals_tac (rot, rl) = 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

477 
rot_tac (if rot then map nNewHyps rl else []) 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

478 
end; 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

479 

2854  480 

2999
fad7cc426242
Penalty for branching instantiations reduced from log3 to log4.
paulson
parents:
2952
diff
changeset

481 
fun TRACE rl tac st i = if !trace then (prth rl; tac st i) else tac st i; 
2854  482 

5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

483 
(*Resolution/matching tactics: if upd then the proof state may be updated. 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

484 
Matching makes the tactics more deterministic in the presence of Vars.*) 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

485 
fun emtac upd rl = TRACE rl (if upd then etac rl else ematch_tac [rl]); 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

486 
fun rmtac upd rl = TRACE rl (if upd then rtac rl else match_tac [rl]); 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

487 

871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

488 
(*Tableau rule from elimination rule. 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

489 
Flag "upd" says that the inference updated the branch. 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

490 
Flag "dup" requests duplication of the affected formula.*) 
2854  491 
fun fromRule vars rl = 
4065  492 
let val trl = rl > rep_thm > #prop > fromTerm > convertRule vars 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

493 
fun tac (upd, dup,rot) i = 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

494 
emtac upd (if dup then rev_dup_elim rl else rl) i 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

495 
THEN 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

496 
rot_subgoals_tac (rot, #2 trl) i 
3244
71b760618f30
Basis library version of type "option" now resides in its own structure Option
paulson
parents:
3101
diff
changeset

497 
in Option.SOME (trl, tac) end 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

498 
handle Bind => (*reject: conclusion is not just a variable*) 
3533  499 
(if !trace then (warning ("ignoring illformed elimination rule\n" ^ 
500 
string_of_thm rl)) 

2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

501 
else (); 
3244
71b760618f30
Basis library version of type "option" now resides in its own structure Option
paulson
parents:
3101
diff
changeset

502 
Option.NONE); 
2854  503 

504 

3101
e8a92f497295
Again "norm" DOES NOT normalize bodies of abstractions
paulson
parents:
3092
diff
changeset

505 
(*** Conversion of Introduction Rules ***) 
2854  506 

507 
fun convertIntrPrem t = mkGoal (strip_imp_concl t) :: strip_imp_prems t; 

508 

509 
fun convertIntrRule vars t = 

510 
let val Ps = strip_imp_prems t 

511 
val P = strip_imp_concl t 

512 
in (mkGoal P, map (convertIntrPrem o skoPrem vars) Ps) 

513 
end; 

514 

5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

515 
(*Tableau rule from introduction rule. 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

516 
Flag "upd" says that the inference updated the branch. 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

517 
Flag "dup" requests duplication of the affected formula. 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

518 
Since haz rules are now delayed, "dup" is always FALSE for 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

519 
introduction rules.*) 
2854  520 
fun fromIntrRule vars rl = 
4065  521 
let val trl = rl > rep_thm > #prop > fromTerm > convertIntrRule vars 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

522 
fun tac (upd,dup,rot) i = 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

523 
rmtac upd (if dup then Data.dup_intr rl else rl) i 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

524 
THEN 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

525 
rot_subgoals_tac (rot, #2 trl) i 
2854  526 
in (trl, tac) end; 
527 

528 

3030  529 
val dummyVar = Term.Var (("etc",0), dummyT); 
2854  530 

531 
(*Convert from prototerms to ordinary terms with dummy types 

2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

532 
Ignore abstractions; identify all Vars; STOP at given depth*) 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

533 
fun toTerm 0 _ = dummyVar 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

534 
 toTerm d (Const a) = Term.Const (a,dummyT) 
4065  535 
 toTerm d (TConst(a,_)) = Term.Const (a,dummyT) (*no need to convert type*) 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

536 
 toTerm d (Skolem(a,_)) = Term.Const (a,dummyT) 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

537 
 toTerm d (Free a) = Term.Free (a,dummyT) 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

538 
 toTerm d (Bound i) = Term.Bound i 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

539 
 toTerm d (Var _) = dummyVar 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

540 
 toTerm d (Abs(a,_)) = dummyVar 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

541 
 toTerm d (f $ u) = Term.$ (toTerm d f, toTerm (d1) u); 
2854  542 

543 

544 
fun netMkRules P vars (nps: netpair list) = 

545 
case P of 

546 
(Const "*Goal*" $ G) => 

2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

547 
let val pG = mk_tprop (toTerm 2 G) 
2854  548 
val intrs = List.concat 
549 
(map (fn (inet,_) => Net.unify_term inet pG) 

550 
nps) 

551 
in map (fromIntrRule vars o #2) (orderlist intrs) end 

552 
 _ => 

2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

553 
let val pP = mk_tprop (toTerm 3 P) 
2854  554 
val elims = List.concat 
555 
(map (fn (_,enet) => Net.unify_term enet pP) 

556 
nps) 

557 
in List.mapPartial (fromRule vars o #2) (orderlist elims) end; 

558 

559 
(** 

560 
end; 

561 
**) 

562 

3092  563 

564 
(*Pending formulae carry md (may duplicate) flags*) 

565 
type branch = ((term*bool) list * (*safe formulae on this level*) 

566 
(term*bool) list) list * (*haz formulae on this level*) 

567 
term list * (*literals: irreducible formulae*) 

568 
term option ref list * (*variables occurring in branch*) 

569 
int; (*resource limit*) 

570 

571 
val fullTrace = ref[] : branch list list ref; 

572 

573 
(*Normalize a branchfor tracing*) 

574 
fun norm2 (G,md) = (norm G, md); 

575 

576 
fun normLev (Gs,Hs) = (map norm2 Gs, map norm2 Hs); 

577 

578 
fun normBr (br, lits, vars, lim) = 

579 
(map normLev br, map norm lits, vars, lim); 

580 

581 

4065  582 
val dummyTVar = Term.TVar(("a",0), []); 
3092  583 
val dummyVar2 = Term.Var(("var",0), dummyT); 
584 

4065  585 
(*convert Blast_tac's type representation to real types for tracing*) 
586 
fun showType (Free a) = Term.TFree (a,[]) 

587 
 showType (Var _) = dummyTVar 

588 
 showType t = 

589 
(case strip_comb t of 

590 
(Const a, us) => Term.Type(a, map showType us) 

591 
 _ => dummyT); 

592 

593 
(*Display toplevel overloading if any*) 

594 
fun topType (TConst(a,t)) = Some (showType t) 

595 
 topType (Abs(a,t)) = topType t 

596 
 topType (f $ u) = (case topType f of 

597 
None => topType u 

598 
 some => some) 

599 
 topType _ = None; 

600 

601 

3092  602 
(*Convert from prototerms to ordinary terms with dummy types for tracing*) 
603 
fun showTerm d (Const a) = Term.Const (a,dummyT) 

4065  604 
 showTerm d (TConst(a,_)) = Term.Const (a,dummyT) 
3092  605 
 showTerm d (Skolem(a,_)) = Term.Const (a,dummyT) 
606 
 showTerm d (Free a) = Term.Free (a,dummyT) 

607 
 showTerm d (Bound i) = Term.Bound i 

3101
e8a92f497295
Again "norm" DOES NOT normalize bodies of abstractions
paulson
parents:
3092
diff
changeset

608 
 showTerm d (Var(ref(Some u))) = showTerm d u 
e8a92f497295
Again "norm" DOES NOT normalize bodies of abstractions
paulson
parents:
3092
diff
changeset

609 
 showTerm d (Var(ref None)) = dummyVar2 
3092  610 
 showTerm d (Abs(a,t)) = if d=0 then dummyVar 
611 
else Term.Abs(a, dummyT, showTerm (d1) t) 

612 
 showTerm d (f $ u) = if d=0 then dummyVar 

613 
else Term.$ (showTerm d f, showTerm (d1) u); 

614 

4065  615 
fun string_of sign d t = Sign.string_of_term sign (showTerm d t); 
3092  616 

4065  617 
fun traceTerm sign t = 
618 
let val t' = norm t 

619 
val stm = string_of sign 8 t' 

620 
in 

621 
case topType t' of 

622 
None => stm (*no type to attach*) 

623 
 Some T => stm ^ "\t:: " ^ Sign.string_of_typ sign T 

624 
end; 

3092  625 

626 

627 
(*Print tracing information at each iteration of prover*) 

628 
fun tracing sign brs = 

629 
let fun printPairs (((G,_)::_,_)::_) = prs(traceTerm sign G) 

630 
 printPairs (([],(H,_)::_)::_) = prs(traceTerm sign H ^ "\t (Unsafe)") 

631 
 printPairs _ = () 

632 
fun printBrs (brs0 as (pairs, lits, _, lim) :: brs) = 

633 
(fullTrace := brs0 :: !fullTrace; 

634 
seq (fn _ => prs "+") brs; 

635 
prs (" [" ^ Int.toString lim ^ "] "); 

636 
printPairs pairs; 

637 
writeln"") 

638 
in if !trace then printBrs (map normBr brs) else () 

639 
end; 

640 

5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

641 
fun traceMsg s = if !trace then writeln s else (); 
4065  642 

3092  643 
(*Tracing: variables updated in the last branch operation?*) 
4065  644 
fun traceVars sign ntrl = 
645 
if !trace then 

646 
(case !ntrailntrl of 

647 
0 => () 

648 
 1 => prs"\t1 variable UPDATED:" 

649 
 n => prs("\t" ^ Int.toString n ^ " variables UPDATED:"); 

650 
(*display the instantiations themselves, though no variable names*) 

651 
seq (fn v => prs(" " ^ string_of sign 4 (the (!v)))) 

652 
(List.take(!trail, !ntrailntrl)); 

653 
writeln"") 

3092  654 
else (); 
655 

656 
(*Tracing: how many new branches are created?*) 

657 
fun traceNew prems = 

658 
if !trace then 

659 
case length prems of 

660 
0 => prs"branch closed by rule" 

661 
 1 => prs"branch extended (1 new subgoal)" 

662 
 n => prs("branch split: "^ Int.toString n ^ " new subgoals") 

663 
else (); 

664 

665 

666 

2854  667 
(*** Code for handling equality: naive substitution, like hyp_subst_tac ***) 
668 

669 
(*Replace the ATOMIC term "old" by "new" in t*) 

670 
fun subst_atomic (old,new) t = 

671 
let fun subst (Var(ref(Some u))) = subst u 

672 
 subst (Abs(a,body)) = Abs(a, subst body) 

673 
 subst (f$t) = subst f $ subst t 

674 
 subst t = if t aconv old then new else t 

675 
in subst t end; 

676 

677 
(*Etacontract a term from outside: just enough to reduce it to an atom*) 

678 
fun eta_contract_atom (t0 as Abs(a, body)) = 

679 
(case eta_contract2 body of 

680 
f $ Bound 0 => if (0 mem_int loose_bnos f) then t0 

681 
else eta_contract_atom (incr_boundvars ~1 f) 

682 
 _ => t0) 

683 
 eta_contract_atom t = t 

684 
and eta_contract2 (f$t) = f $ eta_contract_atom t 

685 
 eta_contract2 t = eta_contract_atom t; 

686 

687 

688 
(*When can we safely delete the equality? 

689 
Not if it equates two constants; consider 0=1. 

690 
Not if it resembles x=t[x], since substitution does not eliminate x. 

691 
Not if it resembles ?x=0; another goal could instantiate ?x to Suc(i) 

692 
Prefer to eliminate Bound variables if possible. 

693 
Result: true = use as is, false = reorient first *) 

694 

4354
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

695 
(*Can t occur in u? For substitution. 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

696 
Does NOT examine the args of Skolem terms: substitution does not affect them. 
4196
9953c0995b79
Now applies "map negOfGoal" to lits when expanding haz rules.
paulson
parents:
4149
diff
changeset

697 
REFLEXIVE because hyp_subst_tac fails on x=x.*) 
2854  698 
fun substOccur t = 
4354
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

699 
let (*NO vars are permitted in u except the arguments of t, if it is 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

700 
a Skolem term. This ensures that no equations are deleted that could 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

701 
be instantiated to a cycle. For example, x=?a is rejected because ?a 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

702 
could be instantiated to Suc(x).*) 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

703 
val vars = case t of 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

704 
Skolem(_,vars) => vars 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

705 
 _ => [] 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

706 
fun occEq u = (t aconv u) orelse occ u 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

707 
and occ (Var(ref(Some u))) = occEq u 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

708 
 occ (Var v) = not (mem_var (v, vars)) 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

709 
 occ (Abs(_,u)) = occEq u 
2854  710 
 occ (f$u) = occEq u orelse occEq f 
711 
 occ (_) = false; 

712 
in occEq end; 

713 

3092  714 
exception DEST_EQ; 
715 

716 
(*Take apart an equality (plain or overloaded). NO constant Trueprop*) 

717 
fun dest_eq (Const "op =" $ t $ u) = 

718 
(eta_contract_atom t, eta_contract_atom u) 

4065  719 
 dest_eq (TConst("op =",_) $ t $ u) = 
3092  720 
(eta_contract_atom t, eta_contract_atom u) 
721 
 dest_eq _ = raise DEST_EQ; 

722 

4196
9953c0995b79
Now applies "map negOfGoal" to lits when expanding haz rules.
paulson
parents:
4149
diff
changeset

723 
(*Reject the equality if u occurs in (or equals!) t*) 
2854  724 
fun check (t,u,v) = if substOccur t u then raise DEST_EQ else v; 
725 

726 
(*IF the goal is an equality with a substitutable variable 

727 
THEN orient that equality ELSE raise exception DEST_EQ*) 

3092  728 
fun orientGoal (t,u) = case (t,u) of 
2854  729 
(Skolem _, _) => check(t,u,(t,u)) (*eliminates t*) 
730 
 (_, Skolem _) => check(u,t,(u,t)) (*eliminates u*) 

731 
 (Free _, _) => check(t,u,(t,u)) (*eliminates t*) 

732 
 (_, Free _) => check(u,t,(u,t)) (*eliminates u*) 

733 
 _ => raise DEST_EQ; 

734 

2894  735 
(*Substitute through the branch if an equality goal (else raise DEST_EQ). 
736 
Moves affected literals back into the branch, but it is not clear where 

4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

737 
they should go: this could make proofs fail.*) 
3092  738 
fun equalSubst sign (G, pairs, lits, vars, lim) = 
739 
let val (t,u) = orientGoal(dest_eq G) 

740 
val subst = subst_atomic (t,u) 

2854  741 
fun subst2(G,md) = (subst G, md) 
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

742 
(*substitute throughout list; extract affected formulae*) 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

743 
fun subForm ((G,md), (changed, pairs)) = 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

744 
let val nG = subst G 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

745 
in if nG aconv G then (changed, (G,md)::pairs) 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

746 
else ((nG,md)::changed, pairs) 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

747 
end 
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

748 
(*substitute throughout "stack frame"; extract affected formulae*) 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

749 
fun subFrame ((Gs,Hs), (changed, frames)) = 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

750 
let val (changed', Gs') = foldr subForm (Gs, (changed, [])) 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

751 
val (changed'', Hs') = foldr subForm (Hs, (changed', [])) 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

752 
in (changed'', (Gs',Hs')::frames) end 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

753 
(*substitute throughout literals; extract affected ones*) 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

754 
fun subLit (lit, (changed, nlits)) = 
2854  755 
let val nlit = subst lit 
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

756 
in if nlit aconv lit then (changed, nlit::nlits) 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

757 
else ((nlit,true)::changed, nlits) 
2854  758 
end 
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

759 
val (changed, lits') = foldr subLit (lits, ([], [])) 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

760 
val (changed', pairs') = foldr subFrame (pairs, (changed, [])) 
3092  761 
in if !trace then writeln ("Substituting " ^ traceTerm sign u ^ 
762 
" for " ^ traceTerm sign t ^ " in branch" ) 

763 
else (); 

4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

764 
((changed',[])::pairs', (*affected formulas, and others*) 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

765 
lits', (*unaffected literals*) 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

766 
vars, lim) 
2854  767 
end; 
768 

769 

770 
exception NEWBRANCHES and CLOSEF; 

771 

772 
exception PROVE; 

773 

4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

774 
(*Trying eq_contr_tac first INCREASES the effort, slowing reconstruction*) 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

775 
val contr_tac = ematch_tac [Data.notE] THEN' 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

776 
(eq_assume_tac ORELSE' assume_tac); 
2854  777 

4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

778 
val eContr_tac = TRACE Data.notE contr_tac; 
2854  779 
val eAssume_tac = TRACE asm_rl (eq_assume_tac ORELSE' assume_tac); 
780 

781 
(*Try to unify complementary literals and return the corresponding tactic. *) 

3083  782 
fun tryClose (Const"*Goal*" $ G, L) = 
4065  783 
if unify([],G,L) then Some eAssume_tac else None 
3083  784 
 tryClose (G, Const"*Goal*" $ L) = 
4065  785 
if unify([],G,L) then Some eAssume_tac else None 
3083  786 
 tryClose (Const"Not" $ G, L) = 
4065  787 
if unify([],G,L) then Some eContr_tac else None 
3083  788 
 tryClose (G, Const"Not" $ L) = 
4065  789 
if unify([],G,L) then Some eContr_tac else None 
3083  790 
 tryClose _ = None; 
2854  791 

792 

793 
(*Were there Skolem terms in the premise? Must NOT chase Vars*) 

794 
fun hasSkolem (Skolem _) = true 

795 
 hasSkolem (Abs (_,body)) = hasSkolem body 

796 
 hasSkolem (f$t) = hasSkolem f orelse hasSkolem t 

797 
 hasSkolem _ = false; 

798 

799 
(*Attach the right "may duplicate" flag to new formulae: if they contain 

800 
Skolem terms then allow duplication.*) 

801 
fun joinMd md [] = [] 

802 
 joinMd md (G::Gs) = (G, hasSkolem G orelse md) :: joinMd md Gs; 

803 

2894  804 
(*Convert a Goal to an ordinary Not. Used also in dup_intr, where a goal like 
805 
Ex(P) is duplicated as the assumption ~Ex(P). *) 

806 
fun negOfGoal (Const"*Goal*" $ G) = negate G 

807 
 negOfGoal G = G; 

808 

809 
fun negOfGoal2 (G,md) = (negOfGoal G, md); 

810 

811 
(*Converts all Goals to Nots in the safe parts of a branch. They could 

812 
have been moved there from the literals list after substitution (equalSubst). 

813 
There can be at most onethis function could be made more efficient.*) 

814 
fun negOfGoals pairs = map (fn (Gs,haz) => (map negOfGoal2 Gs, haz)) pairs; 

815 

816 
(*Tactic. Convert *Goal* to negated assumption in FIRST position*) 

4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

817 
fun negOfGoal_tac i = TRACE Data.ccontr (rtac Data.ccontr) i THEN 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

818 
rotate_tac ~1 i; 
2894  819 

2854  820 

821 
(** Backtracking and Pruning **) 

822 

823 
(*clashVar vars (n,trail) determines whether any of the last n elements 

824 
of "trail" occur in "vars" OR in their instantiations*) 

825 
fun clashVar [] = (fn _ => false) 

826 
 clashVar vars = 

827 
let fun clash (0, _) = false 

828 
 clash (_, []) = false 

829 
 clash (n, v::vs) = exists (varOccur v) vars orelse clash(n1,vs) 

830 
in clash end; 

831 

832 

833 
(*nbrs = # of branches just prior to closing this one. Delete choice points 

834 
for goals proved by the latest inference, provided NO variables in the 

835 
next branch have been updated.*) 

836 
fun prune (1, nxtVars, choices) = choices (*DON'T prune at very end: allow 

837 
backtracking over bad proofs*) 

838 
 prune (nbrs, nxtVars, choices) = 

839 
let fun traceIt last = 

840 
let val ll = length last 

841 
and lc = length choices 

842 
in if !trace andalso ll<lc then 

3083  843 
(writeln("Pruning " ^ Int.toString(lcll) ^ " levels"); 
2854  844 
last) 
845 
else last 

846 
end 

847 
fun pruneAux (last, _, _, []) = last 

3083  848 
 pruneAux (last, ntrl, trl, (ntrl',nbrs',exn) :: choices) = 
2854  849 
if nbrs' < nbrs 
850 
then last (*don't backtrack beyond first solution of goal*) 

851 
else if nbrs' > nbrs then pruneAux (last, ntrl, trl, choices) 

852 
else (* nbrs'=nbrs *) 

853 
if clashVar nxtVars (ntrlntrl', trl) then last 

854 
else (*no clashes: can go back at least this far!*) 

855 
pruneAux(choices, ntrl', List.drop(trl, ntrlntrl'), 

856 
choices) 

857 
in traceIt (pruneAux (choices, !ntrail, !trail, choices)) end; 

858 

2894  859 
fun nextVars ((br, lits, vars, lim) :: _) = map Var vars 
3083  860 
 nextVars [] = []; 
2854  861 

3083  862 
fun backtrack (choices as (ntrl, nbrs, exn)::_) = 
863 
(if !trace then (writeln ("Backtracking; now there are " ^ 

864 
Int.toString nbrs ^ " branches")) 

865 
else (); 

866 
raise exn) 

867 
 backtrack _ = raise PROVE; 

2854  868 

2894  869 
(*Add the literal G, handling *Goal* and detecting duplicates.*) 
870 
fun addLit (Const "*Goal*" $ G, lits) = 

871 
(*New literal is a *Goal*, so change all other Goals to Nots*) 

2854  872 
let fun bad (Const"*Goal*" $ _) = true 
873 
 bad (Const"Not" $ G') = G aconv G' 

874 
 bad _ = false; 

875 
fun change [] = [] 

876 
 change (Const"*Goal*" $ G' :: lits) = 

877 
if G aconv G' then change lits 

878 
else Const"Not" $ G' :: change lits 

879 
 change (Const"Not" $ G' :: lits) = 

880 
if G aconv G' then change lits 

881 
else Const"Not" $ G' :: change lits 

882 
 change (lit::lits) = lit :: change lits 

883 
in 

884 
Const "*Goal*" $ G :: (if exists bad lits then change lits else lits) 

885 
end 

886 
 addLit (G,lits) = ins_term(G, lits) 

887 

888 

2952  889 
(*For calculating the "penalty" to assess on a branching factor of n 
890 
log2 seems a little too severe*) 

3083  891 
fun log n = if n<4 then 0 else 1 + log(n div 4); 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

892 

af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

893 

3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset

894 
(*match(t,u) says whether the term u might be an instance of the pattern t 
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset

895 
Used to detect "recursive" rules such as transitivity*) 
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset

896 
fun match (Var _) u = true 
4065  897 
 match (Const"*Goal*") (Const"Not") = true 
898 
 match (Const"Not") (Const"*Goal*") = true 

899 
 match (Const a) (Const b) = (a=b) 

900 
 match (TConst (a,ta)) (TConst (b,tb)) = a=b andalso match ta tb 

901 
 match (Free a) (Free b) = (a=b) 

902 
 match (Bound i) (Bound j) = (i=j) 

903 
 match (Abs(_,t)) (Abs(_,u)) = match t u 

904 
 match (f$t) (g$u) = match f g andalso match t u 

905 
 match t u = false; 

3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset

906 

39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset

907 

4300  908 
(*Branches closed: number of branches closed during the search 
909 
Branches tried: number of branches created by splitting (counting from 1)*) 

910 
val nclosed = ref 0 

911 
and ntried = ref 1; 

912 

4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

913 
fun printStats (b, start, tacs) = 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

914 
if b then 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

915 
writeln (endTiming start ^ " for search. Closed: " 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

916 
^ Int.toString (!nclosed) ^ 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

917 
" tried: " ^ Int.toString (!ntried) ^ 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

918 
" tactics: " ^ Int.toString (length tacs)) 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

919 
else (); 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

920 

561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

921 

2854  922 
(*Tableau prover based on leanTaP. Argument is a list of branches. Each 
923 
branch contains a list of unexpanded formulae, a list of literals, and a 

4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

924 
bound on unsafe expansions. 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

925 
"start" is CPU time at start, for printing search time 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

926 
*) 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

927 
fun prove (sign, start, cs, brs, cont) = 
4653  928 
let val {safe0_netpair, safep_netpair, haz_netpair, ...} = Data.rep_cs cs 
2854  929 
val safeList = [safe0_netpair, safep_netpair] 
930 
and hazList = [haz_netpair] 

4065  931 
fun prv (tacs, trs, choices, []) = 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

932 
(printStats (!trace orelse !stats, start, tacs); 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

933 
cont (tacs, trs, choices)) (*all branches closed!*) 
2854  934 
 prv (tacs, trs, choices, 
2894  935 
brs0 as (((G,md)::br, haz)::pairs, lits, vars, lim) :: brs) = 
3917  936 
(*apply a safe rule only (possibly allowing instantiation); 
937 
defer any haz formulae*) 

2854  938 
let exception PRV (*backtrack to precisely this recursion!*) 
939 
val ntrl = !ntrail 

940 
val nbrs = length brs0 

941 
val nxtVars = nextVars brs 

942 
val G = norm G 

2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

943 
val rules = netMkRules G vars safeList 
2854  944 
(*Make a new branch, decrementing "lim" if instantiations occur*) 
2894  945 
fun newBr (vars',lim') prems = 
946 
map (fn prem => 

947 
if (exists isGoal prem) 

948 
then (((joinMd md prem, []) :: 

949 
negOfGoals ((br, haz)::pairs)), 

950 
map negOfGoal lits, 

951 
vars', lim') 

952 
else (((joinMd md prem, []) :: (br, haz) :: pairs), 

953 
lits, vars', lim')) 

2854  954 
prems @ 
955 
brs 

956 
(*Seek a matching rule. If unifiable then add new premises 

957 
to branch.*) 

958 
fun deeper [] = raise NEWBRANCHES 

959 
 deeper (((P,prems),tac)::grls) = 

4065  960 
if unify(add_term_vars(P,[]), P, G) 
3083  961 
then (*P comes from the rule; G comes from the branch.*) 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

962 
let val updated = ntrl < !ntrail (*branch updated*) 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

963 
val lim' = if updated 
3083  964 
then lim  (1+log(length rules)) 
965 
else lim (*discourage branching updates*) 

966 
val vars = vars_in_vars vars 

967 
val vars' = foldr add_terms_vars (prems, vars) 

968 
val choices' = (ntrl, nbrs, PRV) :: choices 

5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

969 
val tacs' = (DETERM o tac(updated,false,true)) 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

970 
:: tacs (*no duplication; rotate*) 
3083  971 
in 
4065  972 
traceNew prems; traceVars sign ntrl; 
3083  973 
(if null prems then (*closed the branch: prune!*) 
4300  974 
(nclosed := !nclosed + 1; 
975 
prv(tacs', brs0::trs, 

976 
prune (nbrs, nxtVars, choices'), 

977 
brs)) 

978 
else (*prems nonnull*) 

3083  979 
if lim'<0 (*faster to kill ALL the alternatives*) 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

980 
then (traceMsg"Excessive branching: KILLED"; 
4065  981 
clearTo ntrl; raise NEWBRANCHES) 
3083  982 
else 
4300  983 
(ntried := !ntried + length prems  1; 
984 
prv(tacs', brs0::trs, choices', 

985 
newBr (vars',lim') prems))) 

3083  986 
handle PRV => 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

987 
if updated then 
3083  988 
(*Backtrack at this level. 
989 
Reset Vars and try another rule*) 

990 
(clearTo ntrl; deeper grls) 

991 
else (*backtrack to previous level*) 

992 
backtrack choices 

993 
end 

994 
else deeper grls 

2854  995 
(*Try to close branch by unifying with head goal*) 
996 
fun closeF [] = raise CLOSEF 

997 
 closeF (L::Ls) = 

3083  998 
case tryClose(G,L) of 
999 
None => closeF Ls 

1000 
 Some tac => 

1001 
let val choices' = 

3092  1002 
(if !trace then (prs"branch closed"; 
4065  1003 
traceVars sign ntrl) 
3083  1004 
else (); 
1005 
prune (nbrs, nxtVars, 

1006 
(ntrl, nbrs, PRV) :: choices)) 

4300  1007 
in nclosed := !nclosed + 1; 
1008 
prv (tac::tacs, brs0::trs, choices', brs) 

3083  1009 
handle PRV => 
1010 
(*reset Vars and try another literal 

1011 
[this handler is pruned if possible!]*) 

1012 
(clearTo ntrl; closeF Ls) 

1013 
end 

2894  1014 
fun closeFl [] = raise CLOSEF 
1015 
 closeFl ((br, haz)::pairs) = 

1016 
closeF (map fst br) 

1017 
handle CLOSEF => closeF (map fst haz) 

1018 
handle CLOSEF => closeFl pairs 

3083  1019 
in tracing sign brs0; 
4065  1020 
if lim<0 then (traceMsg "Limit reached. "; backtrack choices) 
2854  1021 
else 
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

1022 
prv (Data.hyp_subst_tac trace :: tacs, 
2854  1023 
brs0::trs, choices, 
3092  1024 
equalSubst sign (G, (br,haz)::pairs, lits, vars, lim) :: brs) 
4065  1025 
handle DEST_EQ => closeF lits 
1026 
handle CLOSEF => closeFl ((br,haz)::pairs) 

1027 
handle CLOSEF => deeper rules 

2894  1028 
handle NEWBRANCHES => 
1029 
(case netMkRules G vars hazList of 

4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

1030 
[] => (*there are no plausible haz rules*) 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

1031 
(traceMsg "moving goal to literals"; 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

1032 
prv (tacs, brs0::trs, choices, 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

1033 
((br,haz)::pairs, addLit(G,lits), vars, lim) 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

1034 
::brs)) 
2894  1035 
 _ => (*G admits some haz rules: try later*) 
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

1036 
(traceMsg "moving goal to haz list"; 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

1037 
prv (if isGoal G then negOfGoal_tac :: tacs 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

1038 
else tacs, 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

1039 
brs0::trs, choices, 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

1040 
((br, haz@[(negOfGoal G, md)])::pairs, 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

1041 
lits, vars, lim) :: brs))) 
2854  1042 
end 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1043 
 prv (tacs, trs, choices, 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1044 
(([],haz)::(Gs,haz')::pairs, lits, vars, lim) :: brs) = 
2894  1045 
(*no more "safe" formulae: transfer haz down a level*) 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1046 
prv (tacs, trs, choices, 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1047 
((Gs,haz@haz')::pairs, lits, vars, lim) :: brs) 
2854  1048 
 prv (tacs, trs, choices, 
2894  1049 
brs0 as ([([], (H,md)::Hs)], lits, vars, lim) :: brs) = 
1050 
(*no safe steps possible at any level: apply a haz rule*) 

2854  1051 
let exception PRV (*backtrack to precisely this recursion!*) 
2894  1052 
val H = norm H 
2854  1053 
val ntrl = !ntrail 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1054 
val rules = netMkRules H vars hazList 
3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset

1055 
(*new premises of haz rules may NOT be duplicated*) 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1056 
fun newPrem (vars,P,dup,lim') prem = 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1057 
let val Gs' = map (fn Q => (Q,false)) prem 
3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset

1058 
and Hs' = if dup then Hs @ [(negOfGoal H, md)] else Hs 
4196
9953c0995b79
Now applies "map negOfGoal" to lits when expanding haz rules.
paulson
parents:
4149
diff
changeset

1059 
and lits' = if (exists isGoal prem) 
9953c0995b79
Now applies "map negOfGoal" to lits when expanding haz rules.
paulson
parents:
4149
diff
changeset

1060 
then map negOfGoal lits 
9953c0995b79
Now applies "map negOfGoal" to lits when expanding haz rules.
paulson
parents:
4149
diff
changeset

1061 
else lits 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1062 
in (if exists (match P) prem 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1063 
then (*Recursive in this premise. 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1064 
Don't make new "stack frame". 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1065 
New haz premises will end up at the BACK of the 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1066 
queue, preventing exclusion of others*) 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1067 
[(Gs',Hs')] 
4196
9953c0995b79
Now applies "map negOfGoal" to lits when expanding haz rules.
paulson
parents:
4149
diff
changeset

1068 
else [(Gs',[]), ([],Hs')], 
9953c0995b79
Now applies "map negOfGoal" to lits when expanding haz rules.
paulson
parents:
4149
diff
changeset

1069 
lits', vars, lim') 
3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset

1070 
end 
2854  1071 
fun newBr x prems = map (newPrem x) prems @ brs 
1072 
(*Seek a matching rule. If unifiable then add new premises 

1073 
to branch.*) 

1074 
fun deeper [] = raise NEWBRANCHES 

1075 
 deeper (((P,prems),tac)::grls) = 

4065  1076 
if unify(add_term_vars(P,[]), P, H) 
3083  1077 
then 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

1078 
let val updated = ntrl < !ntrail (*branch updated*) 
3083  1079 
val vars = vars_in_vars vars 
1080 
val vars' = foldr add_terms_vars (prems, vars) 

1081 
(*duplicate H if md and the subgoal has new vars*) 

1082 
val dup = md andalso vars' <> vars 

1083 
(*any instances of P in the subgoals?*) 

1084 
and recur = exists (exists (match P)) prems 

1085 
val lim' = (*Decrement "lim" extra if updates occur*) 

5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

1086 
if updated then lim  (1+log(length rules)) 
3083  1087 
else lim1 
1088 
(*It is tempting to leave "lim" UNCHANGED if 

1089 
both dup and recur are false. Proofs are 

1090 
found at shallower depths, but looping 

1091 
occurs too often...*) 

3917  1092 
val mayUndo = 
1093 
(*Allowing backtracking from a rule application 

1094 
if other matching rules exist, if the rule 

1095 
updated variables, or if the rule did not 

1096 
introduce new variables. This latter condition 

1097 
means it is not a standard "gammarule" but 

1098 
some other form of unsafe rule. Aim is to 

1099 
emulate Fast_tac, which allows all unsafe steps 

1100 
to be undone.*) 

1101 
not(null grls) (*other rules to try?*) 

5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

1102 
orelse updated 
3917  1103 
orelse vars=vars' (*no new Vars?*) 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

1104 
val tac' = if mayUndo then tac(updated, dup, true) 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

1105 
else DETERM o tac(updated, dup, true) 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1106 
(*if recur then doesn't call rotate_tac: 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

1107 
new formulae should be last; WRONG 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

1108 
if the new formulae are Goals, since 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

1109 
they remain in the first position*) 
3083  1110 
in 
1111 
if lim'<0 andalso not (null prems) 

1112 
then (*it's faster to kill ALL the alternatives*) 

5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

1113 
(traceMsg"Excessive branching: KILLED"; 
4065  1114 
clearTo ntrl; raise NEWBRANCHES) 
3083  1115 
else 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1116 
traceNew prems; 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1117 
if !trace andalso recur then prs" (recursive)" 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1118 
else (); 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1119 
traceVars sign ntrl; 
4300  1120 
if null prems then nclosed := !nclosed + 1 
1121 
else ntried := !ntried + length prems  1; 

4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1122 
prv(tac' :: tacs, 
3083  1123 
brs0::trs, 
1124 
(ntrl, length brs0, PRV) :: choices, 

4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1125 
newBr (vars', P, dup, lim') prems) 
3083  1126 
handle PRV => 
1127 
if mayUndo 

1128 
then (*reset Vars and try another rule*) 

1129 
(clearTo ntrl; deeper grls) 

1130 
else (*backtrack to previous level*) 

1131 
backtrack choices 

1132 
end 

1133 
else deeper grls 

1134 
in tracing sign brs0; 

4065  1135 
if lim<1 then (traceMsg "Limit reached. "; backtrack choices) 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1136 
else deeper rules 
2854  1137 
handle NEWBRANCHES => 
2894  1138 
(*cannot close branch: move H to literals*) 
2854  1139 
prv (tacs, brs0::trs, choices, 
2894  1140 
([([], Hs)], H::lits, vars, lim)::brs) 
2854  1141 
end 
1142 
 prv (tacs, trs, choices, _ :: brs) = backtrack choices 

4065  1143 
in init_gensym(); 
1144 
prv ([], [], [(!ntrail, length brs, PROVE)], brs) 

1145 
end; 

2854  1146 

1147 

2883  1148 
(*Construct an initial branch.*) 
2854  1149 
fun initBranch (ts,lim) = 
2894  1150 
([(map (fn t => (t,true)) ts, [])], 
1151 
[], add_terms_vars (ts,[]), lim); 

2854  1152 

1153 

1154 
(*** Conversion & Skolemization of the Isabelle proof state ***) 

1155 

1156 
(*Make a list of all the parameters in a subgoal, even if nested*) 

1157 
local open Term 

1158 
in 

1159 
fun discard_foralls (Const("all",_)$Abs(a,T,t)) = discard_foralls t 

1160 
 discard_foralls t = t; 

1161 
end; 

1162 

1163 

1164 
(*List of variables not appearing as arguments to the given parameter*) 

1165 
fun getVars [] i = [] 

1166 
 getVars ((_,(v,is))::alist) i = 

1167 
if i mem is then getVars alist i 

1168 
else v :: getVars alist i; 

1169 

4233
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

1170 
exception TRANS of string; 
2854  1171 

4233
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

1172 
(*Translation of a subgoal: Skolemize all parameters*) 
4065  1173 
fun fromSubgoal t = 
1174 
let val alistVar = ref [] 

1175 
and alistTVar = ref [] 

2854  1176 
fun hdvar ((ix,(v,is))::_) = v 
1177 
fun from lev t = 

1178 
let val (ht,ts) = Term.strip_comb t 

1179 
fun apply u = list_comb (u, map (from lev) ts) 

1180 
fun bounds [] = [] 

1181 
 bounds (Term.Bound i::ts) = 

4233
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

1182 
if i<lev then raise TRANS 
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

1183 
"Function unknown's argument not a parameter" 
2854  1184 
else ilev :: bounds ts 
4233
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

1185 
 bounds ts = raise TRANS 
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

1186 
"Function unknown's argument not a bound variable" 
2854  1187 
in 
1188 
case ht of 

4065  1189 
Term.Const aT => apply (fromConst alistTVar aT) 
2854  1190 
 Term.Free (a,_) => apply (Free a) 
1191 
 Term.Bound i => apply (Bound i) 

1192 
 Term.Var (ix,_) => 

4065  1193 
(case (assoc_string_int(!alistVar,ix)) of 
1194 
None => (alistVar := (ix, (ref None, bounds ts)) 

1195 
:: !alistVar; 

1196 
Var (hdvar(!alistVar))) 

2854  1197 
 Some(v,is) => if is=bounds ts then Var v 
4233
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

1198 
else raise TRANS 
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

1199 
("Discrepancy among occurrences of ?" 
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

1200 
^ Syntax.string_of_vname ix)) 
2854  1201 
 Term.Abs (a,_,body) => 
1202 
if null ts then Abs(a, from (lev+1) body) 

4233
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

1203 
else raise TRANS "argument not in normal form" 
2854  1204 
end 
1205 

1206 
val npars = length (Logic.strip_params t) 

1207 

1208 
(*Skolemize a subgoal from a proof state*) 

1209 
fun skoSubgoal i t = 

1210 
if i<npars then 

1211 
skoSubgoal (i+1) 

4065  1212 
(subst_bound (Skolem (gensym "T_", getVars (!alistVar) i), 
2854  1213 
t)) 
1214 
else t 

1215 

1216 
in skoSubgoal 0 (from 0 (discard_foralls t)) end; 

1217 

1218 

4300  1219 
fun initialize() = 
1220 
(fullTrace:=[]; trail := []; ntrail := 0; 

1221 
nclosed := 0; ntried := 1); 

1222 

1223 

2854  1224 
(*Tactic using tableau engine and proof reconstruction. 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1225 
"start" is CPU time at start, for printing SEARCH time 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1226 
(also prints reconstruction time) 
2854  1227 
"lim" is depth limit.*) 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1228 
fun timing_depth_tac start cs lim i st = 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1229 
(initialize(); 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1230 
let val {sign,...} = rep_thm st 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1231 
val skoprem = fromSubgoal (List.nth(prems_of st, i1)) 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1232 
val hyps = strip_imp_prems skoprem 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1233 
and concl = strip_imp_concl skoprem 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1234 
fun cont (tacs,_,choices) = 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1235 
let val start = startTiming() 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1236 
in 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1237 
case Seq.pull(EVERY' (rev tacs) i st) of 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1238 
None => (writeln ("PROOF FAILED for depth " ^ 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1239 
Int.toString lim); 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1240 
backtrack choices) 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1241 
 cell => (if (!trace orelse !stats) 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1242 
then writeln (endTiming start ^ " for reconstruction") 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1243 
else (); 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1244 
Seq.make(fn()=> cell)) 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1245 
end 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1246 
in prove (sign, start, cs, [initBranch (mkGoal concl :: hyps, lim)], cont) 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1247 
end 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1248 
handle PROVE => Seq.empty); 
2854  1249 

4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1250 
(*Public version with fixed depth*) 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1251 
fun depth_tac cs lim i st = timing_depth_tac (startTiming()) cs lim i st; 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1252 

cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1253 
fun blast_tac cs i st = 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1254 
(DEEPEN (1,20) (timing_depth_tac (startTiming()) cs) 0) i st 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1255 
handle TRANS s => (warning ("Blast_tac: " ^ s); Seq.empty); 
2854  1256 

4078  1257 
fun Blast_tac i = blast_tac (Data.claset()) i; 
2854  1258 

2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1259 

af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1260 
(*** For debugging: these apply the prover to a subgoal and return 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1261 
the resulting tactics, trace, etc. ***) 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1262 

af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1263 
(*Translate subgoal i from a proof state*) 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1264 
fun trygl cs lim i = 
4300  1265 
(initialize(); 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1266 
let val st = topthm() 
3030  1267 
val {sign,...} = rep_thm st 
4065  1268 
val skoprem = fromSubgoal (List.nth(prems_of st, i1)) 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1269 
val hyps = strip_imp_prems skoprem 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1270 
and concl = strip_imp_concl skoprem 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1271 
in timeap prove (sign, startTiming(), cs, 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1272 
[initBranch (mkGoal concl :: hyps, lim)], I) 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1273 
end 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1274 
handle Subscript => error("There is no subgoal " ^ Int.toString i)); 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1275 

4078  1276 
fun Trygl lim i = trygl (Data.claset()) lim i; 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1277 

af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1278 
(*Read a string to make an initial, singleton branch*) 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1279 
fun readGoal sign s = read_cterm sign (s,propT) > 
4065  1280 
term_of > fromTerm > rand > mkGoal; 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1281 

af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1282 
fun tryInThy thy lim s = 
4300  1283 
(initialize(); 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1284 
timeap prove (sign_of thy, 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1285 
startTiming(), 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1286 
Data.claset(), 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1287 
[initBranch ([readGoal (sign_of thy) s], lim)], 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1288 
I)); 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1289 

af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1290 

2854  1291 
end; 