author  paulson 
Thu, 10 Sep 1998 17:33:09 +0200  
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parent 5411  7a43b484f6d2 
child 5481  c41956742c2e 
permissions  rwrr 
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(* Title: Provers/blast.ML 
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ID: $Id$ 
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory 

3083  4 
Copyright 1997 University of Cambridge 
2894  5 

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Generic tableau prover with proof reconstruction 

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SKOLEMIZES ReplaceI WRONGLY: allow new vars in prems, or forbid such rules?? 
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Needs explicit instantiation of assumptions? 
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Blast_tac is often more powerful than fast_tac, but has some limitations. 
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Blast_tac... 
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* ignores wrappers (addss, addbefore, addafter, addWrapper, ...); 
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this restriction is intrinsic 

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

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* ignores types, which can make HOL proofs fail 

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* rules must not require higherorder unification, e.g. apply_type in ZF 
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+ message "Function Var's argument not a bound variable" relates to this 
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* its proof strategy is more general but can actually be slower 
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Known problems: 

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"Recursive" chains of rules can sometimes exclude other unsafe formulae 
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from expansion. This happens because newlycreated formulae always 
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have priority over existing ones. But obviously recursive rules 
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such as transitivity are treated specially to prevent this. Sometimes 
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the formulae get into the wrong order (see WRONG below). 
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With overloading: 
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Calls to Blast.overloaded (see HOL/Set.ML for examples) are needed 
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to tell Blast_tac when to retain some type information. Make sure 
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you know the constant's internal name, which might be "op <=" or 
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"Relation.op ^^". 
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With substition for equalities (hyp_subst_tac): 
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When substitution affects a haz formula or literal, it is moved 
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back to the list of safe formulae. 
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But there's no way of putting it in the right place. A "moved" or 
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"no DETERM" flag would prevent proofs failing here. 
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*) 
42 

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(*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 
*) 

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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 

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val hyp_subst_tac : bool ref > int > tactic 
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val claset : unit > claset 
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val rep_cs : (* dependent on classical.ML *) 
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claset > {safeIs: thm list, safeEs: thm list, 
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hazIs: thm list, hazEs: thm list, 

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swrappers: (string * wrapper) list, 
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uwrappers: (string * wrapper) list, 

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safe0_netpair: netpair, safep_netpair: netpair, 
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haz_netpair: netpair, dup_netpair: netpair} 

69 
end; 

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signature BLAST = 

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sig 

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type claset 
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exception TRANS of string (*reports translation errors*) 
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datatype term = 
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Const of string 
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 TConst of string * term 
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 Skolem of string * term option ref list 
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 Free of string 
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 Var of term option ref 
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 Bound of int 
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 Abs of string*term 
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 $ of term*term; 
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type branch 
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val depth_tac : claset > int > int > tactic 
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val blast_tac : claset > int > tactic 

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val Blast_tac : int > tactic 

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val overloaded : string * (Term.typ > Term.typ) > unit 
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(*debugging tools*) 
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val stats : bool ref 
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val trace : bool ref 
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val fullTrace : branch list list ref 
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val fromType : (indexname * term) list ref > Term.typ > term 
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val fromTerm : Term.term > term 

96 
val fromSubgoal : Term.term > term 

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val instVars : term > (unit > unit) 

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val toTerm : int > term > Term.term 
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val readGoal : Sign.sg > string > term 
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val tryInThy : theory > int > string > 
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(int>tactic) list * branch list list * (int*int*exn) list 
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val trygl : claset > int > int > 
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(int>tactic) list * branch list list * (int*int*exn) list 
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val Trygl : int > int > 

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

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val normBr : branch > branch 
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end; 
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109 

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functor BlastFun(Data: BLAST_DATA) : BLAST = 
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struct 
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type claset = Data.claset; 

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val trace = ref false 
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and stats = ref false; (*for runtime and search statistics*) 
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datatype term = 

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Const of string 
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 TConst of string * term (*type of overloaded constantas a term!*) 
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 Skolem of string * term option ref list 
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 Free of string 
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 Var of term option ref 
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 Bound of int 
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 Abs of string*term 
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 $ of term*term; 
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128 

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(** 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 

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(*** Dealing with overloaded constants ***) 
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(*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) 

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185 
local 

4065  186 
val overloads = ref ([]: (string * (Term.typ > Term.typ)) list) 
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in 
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fun overloaded arg = (overloads := arg :: (!overloads)); 
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(*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 

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handle Match => error 
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("Blast_tac: unexpected type for overloaded constant " ^ a) 
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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 
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 (Skolem (a,_)) aconv (Skolem (b,_)) = a=b (*arglists must then be equal*) 
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 (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 
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 (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) 

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 add_term_vars (TConst (_,t), vars) = add_term_vars(t,vars) 
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 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 

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(*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 

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(*Normalize...but not the bodies of ABSTRACTIONS*) 
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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) 
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 (Var (ref None)) => t 
295 
 (Var (ref (Some u))) => norm u 

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

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Abs(_,body) => norm (subst_bound (u, body)) 
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 nf => nf $ norm u) 
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 _ => 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)) 
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 _ => t 
318 
and wkNorm t = case head_of t of 

319 
Const _ => t 

4065  320 
 TConst _ => t 
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 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
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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 

5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

472 
fun rot_tac [] i st = Seq.single 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*) 

5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

565 
type branch = 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

566 
{pairs: ((term*bool) list * (*safe formulae on this level*) 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

567 
(term*bool) list) list, (*haz formulae on this level*) 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

568 
lits: term list, (*literals: irreducible formulae*) 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

569 
vars: term option ref list, (*variables occurring in branch*) 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

570 
lim: int}; (*resource limit*) 
3092  571 

572 
val fullTrace = ref[] : branch list list ref; 

573 

574 
(*Normalize a branchfor tracing*) 

575 
fun norm2 (G,md) = (norm G, md); 

576 

577 
fun normLev (Gs,Hs) = (map norm2 Gs, map norm2 Hs); 

578 

5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

579 
fun normBr {pairs, lits, vars, lim} = 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

580 
{pairs = map normLev pairs, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

581 
lits = map norm lits, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

582 
vars = vars, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

583 
lim = lim}; 
3092  584 

585 

4065  586 
val dummyTVar = Term.TVar(("a",0), []); 
3092  587 
val dummyVar2 = Term.Var(("var",0), dummyT); 
588 

4065  589 
(*convert Blast_tac's type representation to real types for tracing*) 
590 
fun showType (Free a) = Term.TFree (a,[]) 

591 
 showType (Var _) = dummyTVar 

592 
 showType t = 

593 
(case strip_comb t of 

594 
(Const a, us) => Term.Type(a, map showType us) 

595 
 _ => dummyT); 

596 

597 
(*Display toplevel overloading if any*) 

598 
fun topType (TConst(a,t)) = Some (showType t) 

599 
 topType (Abs(a,t)) = topType t 

600 
 topType (f $ u) = (case topType f of 

601 
None => topType u 

602 
 some => some) 

603 
 topType _ = None; 

604 

605 

3092  606 
(*Convert from prototerms to ordinary terms with dummy types for tracing*) 
607 
fun showTerm d (Const a) = Term.Const (a,dummyT) 

4065  608 
 showTerm d (TConst(a,_)) = Term.Const (a,dummyT) 
3092  609 
 showTerm d (Skolem(a,_)) = Term.Const (a,dummyT) 
610 
 showTerm d (Free a) = Term.Free (a,dummyT) 

611 
 showTerm d (Bound i) = Term.Bound i 

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

612 
 showTerm d (Var(ref(Some u))) = showTerm d u 
e8a92f497295
Again "norm" DOES NOT normalize bodies of abstractions
paulson
parents:
3092
diff
changeset

613 
 showTerm d (Var(ref None)) = dummyVar2 
3092  614 
 showTerm d (Abs(a,t)) = if d=0 then dummyVar 
615 
else Term.Abs(a, dummyT, showTerm (d1) t) 

616 
 showTerm d (f $ u) = if d=0 then dummyVar 

617 
else Term.$ (showTerm d f, showTerm (d1) u); 

618 

4065  619 
fun string_of sign d t = Sign.string_of_term sign (showTerm d t); 
3092  620 

4065  621 
fun traceTerm sign t = 
622 
let val t' = norm t 

623 
val stm = string_of sign 8 t' 

624 
in 

625 
case topType t' of 

626 
None => stm (*no type to attach*) 

627 
 Some T => stm ^ "\t:: " ^ Sign.string_of_typ sign T 

628 
end; 

3092  629 

630 

631 
(*Print tracing information at each iteration of prover*) 

632 
fun tracing sign brs = 

633 
let fun printPairs (((G,_)::_,_)::_) = prs(traceTerm sign G) 

634 
 printPairs (([],(H,_)::_)::_) = prs(traceTerm sign H ^ "\t (Unsafe)") 

635 
 printPairs _ = () 

5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

636 
fun printBrs (brs0 as {pairs, lits, lim, ...} :: brs) = 
3092  637 
(fullTrace := brs0 :: !fullTrace; 
638 
seq (fn _ => prs "+") brs; 

639 
prs (" [" ^ Int.toString lim ^ "] "); 

640 
printPairs pairs; 

641 
writeln"") 

642 
in if !trace then printBrs (map normBr brs) else () 

643 
end; 

644 

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

645 
fun traceMsg s = if !trace then writeln s else (); 
4065  646 

3092  647 
(*Tracing: variables updated in the last branch operation?*) 
4065  648 
fun traceVars sign ntrl = 
649 
if !trace then 

650 
(case !ntrailntrl of 

651 
0 => () 

652 
 1 => prs"\t1 variable UPDATED:" 

653 
 n => prs("\t" ^ Int.toString n ^ " variables UPDATED:"); 

654 
(*display the instantiations themselves, though no variable names*) 

655 
seq (fn v => prs(" " ^ string_of sign 4 (the (!v)))) 

656 
(List.take(!trail, !ntrailntrl)); 

657 
writeln"") 

3092  658 
else (); 
659 

660 
(*Tracing: how many new branches are created?*) 

661 
fun traceNew prems = 

662 
if !trace then 

663 
case length prems of 

664 
0 => prs"branch closed by rule" 

665 
 1 => prs"branch extended (1 new subgoal)" 

666 
 n => prs("branch split: "^ Int.toString n ^ " new subgoals") 

667 
else (); 

668 

669 

670 

2854  671 
(*** Code for handling equality: naive substitution, like hyp_subst_tac ***) 
672 

673 
(*Replace the ATOMIC term "old" by "new" in t*) 

674 
fun subst_atomic (old,new) t = 

675 
let fun subst (Var(ref(Some u))) = subst u 

676 
 subst (Abs(a,body)) = Abs(a, subst body) 

677 
 subst (f$t) = subst f $ subst t 

678 
 subst t = if t aconv old then new else t 

679 
in subst t end; 

680 

681 
(*Etacontract a term from outside: just enough to reduce it to an atom*) 

682 
fun eta_contract_atom (t0 as Abs(a, body)) = 

683 
(case eta_contract2 body of 

684 
f $ Bound 0 => if (0 mem_int loose_bnos f) then t0 

685 
else eta_contract_atom (incr_boundvars ~1 f) 

686 
 _ => t0) 

687 
 eta_contract_atom t = t 

688 
and eta_contract2 (f$t) = f $ eta_contract_atom t 

689 
 eta_contract2 t = eta_contract_atom t; 

690 

691 

692 
(*When can we safely delete the equality? 

693 
Not if it equates two constants; consider 0=1. 

694 
Not if it resembles x=t[x], since substitution does not eliminate x. 

695 
Not if it resembles ?x=0; another goal could instantiate ?x to Suc(i) 

696 
Prefer to eliminate Bound variables if possible. 

697 
Result: true = use as is, false = reorient first *) 

698 

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

699 
(*Can t occur in u? For substitution. 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

700 
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

701 
REFLEXIVE because hyp_subst_tac fails on x=x.*) 
2854  702 
fun substOccur t = 
4354
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

703 
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

704 
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

705 
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

706 
could be instantiated to Suc(x).*) 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

707 
val vars = case t of 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

708 
Skolem(_,vars) => vars 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

709 
 _ => [] 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

710 
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

711 
and occ (Var(ref(Some u))) = occEq u 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

712 
 occ (Var v) = not (mem_var (v, vars)) 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

713 
 occ (Abs(_,u)) = occEq u 
2854  714 
 occ (f$u) = occEq u orelse occEq f 
715 
 occ (_) = false; 

716 
in occEq end; 

717 

3092  718 
exception DEST_EQ; 
719 

720 
(*Take apart an equality (plain or overloaded). NO constant Trueprop*) 

721 
fun dest_eq (Const "op =" $ t $ u) = 

722 
(eta_contract_atom t, eta_contract_atom u) 

4065  723 
 dest_eq (TConst("op =",_) $ t $ u) = 
3092  724 
(eta_contract_atom t, eta_contract_atom u) 
725 
 dest_eq _ = raise DEST_EQ; 

726 

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

727 
(*Reject the equality if u occurs in (or equals!) t*) 
2854  728 
fun check (t,u,v) = if substOccur t u then raise DEST_EQ else v; 
729 

730 
(*IF the goal is an equality with a substitutable variable 

731 
THEN orient that equality ELSE raise exception DEST_EQ*) 

3092  732 
fun orientGoal (t,u) = case (t,u) of 
2854  733 
(Skolem _, _) => check(t,u,(t,u)) (*eliminates t*) 
734 
 (_, Skolem _) => check(u,t,(u,t)) (*eliminates u*) 

735 
 (Free _, _) => check(t,u,(t,u)) (*eliminates t*) 

736 
 (_, Free _) => check(u,t,(u,t)) (*eliminates u*) 

737 
 _ => raise DEST_EQ; 

738 

2894  739 
(*Substitute through the branch if an equality goal (else raise DEST_EQ). 
740 
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

741 
they should go: this could make proofs fail.*) 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

742 
fun equalSubst sign (G, {pairs, lits, vars, lim}) = 
3092  743 
let val (t,u) = orientGoal(dest_eq G) 
744 
val subst = subst_atomic (t,u) 

2854  745 
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

746 
(*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

747 
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

748 
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

749 
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

750 
else ((nG,md)::changed, pairs) 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

751 
end 
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

752 
(*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

753 
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

754 
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

755 
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

756 
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

757 
(*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

758 
fun subLit (lit, (changed, nlits)) = 
2854  759 
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

760 
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

761 
else ((nlit,true)::changed, nlits) 
2854  762 
end 
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

763 
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

764 
val (changed', pairs') = foldr subFrame (pairs, (changed, [])) 
3092  765 
in if !trace then writeln ("Substituting " ^ traceTerm sign u ^ 
766 
" for " ^ traceTerm sign t ^ " in branch" ) 

767 
else (); 

5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

768 
{pairs = (changed',[])::pairs', (*affected formulas, and others*) 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

769 
lits = lits', (*unaffected literals*) 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

770 
vars = vars, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

771 
lim = lim} 
2854  772 
end; 
773 

774 

775 
exception NEWBRANCHES and CLOSEF; 

776 

777 
exception PROVE; 

778 

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

779 
(*Trying eq_contr_tac first INCREASES the effort, slowing reconstruction*) 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

780 
val contr_tac = ematch_tac [Data.notE] THEN' 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

781 
(eq_assume_tac ORELSE' assume_tac); 
2854  782 

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

783 
val eContr_tac = TRACE Data.notE contr_tac; 
2854  784 
val eAssume_tac = TRACE asm_rl (eq_assume_tac ORELSE' assume_tac); 
785 

786 
(*Try to unify complementary literals and return the corresponding tactic. *) 

3083  787 
fun tryClose (Const"*Goal*" $ G, L) = 
4065  788 
if unify([],G,L) then Some eAssume_tac else None 
3083  789 
 tryClose (G, Const"*Goal*" $ L) = 
4065  790 
if unify([],G,L) then Some eAssume_tac else None 
3083  791 
 tryClose (Const"Not" $ G, L) = 
4065  792 
if unify([],G,L) then Some eContr_tac else None 
3083  793 
 tryClose (G, Const"Not" $ L) = 
4065  794 
if unify([],G,L) then Some eContr_tac else None 
3083  795 
 tryClose _ = None; 
2854  796 

797 

798 
(*Were there Skolem terms in the premise? Must NOT chase Vars*) 

799 
fun hasSkolem (Skolem _) = true 

800 
 hasSkolem (Abs (_,body)) = hasSkolem body 

801 
 hasSkolem (f$t) = hasSkolem f orelse hasSkolem t 

802 
 hasSkolem _ = false; 

803 

804 
(*Attach the right "may duplicate" flag to new formulae: if they contain 

805 
Skolem terms then allow duplication.*) 

806 
fun joinMd md [] = [] 

807 
 joinMd md (G::Gs) = (G, hasSkolem G orelse md) :: joinMd md Gs; 

808 

2894  809 
(*Convert a Goal to an ordinary Not. Used also in dup_intr, where a goal like 
810 
Ex(P) is duplicated as the assumption ~Ex(P). *) 

811 
fun negOfGoal (Const"*Goal*" $ G) = negate G 

812 
 negOfGoal G = G; 

813 

814 
fun negOfGoal2 (G,md) = (negOfGoal G, md); 

815 

816 
(*Converts all Goals to Nots in the safe parts of a branch. They could 

817 
have been moved there from the literals list after substitution (equalSubst). 

818 
There can be at most onethis function could be made more efficient.*) 

819 
fun negOfGoals pairs = map (fn (Gs,haz) => (map negOfGoal2 Gs, haz)) pairs; 

820 

821 
(*Tactic. Convert *Goal* to negated assumption in FIRST position*) 

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

822 
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

823 
rotate_tac ~1 i; 
2894  824 

2854  825 

826 
(** Backtracking and Pruning **) 

827 

828 
(*clashVar vars (n,trail) determines whether any of the last n elements 

829 
of "trail" occur in "vars" OR in their instantiations*) 

830 
fun clashVar [] = (fn _ => false) 

831 
 clashVar vars = 

832 
let fun clash (0, _) = false 

833 
 clash (_, []) = false 

834 
 clash (n, v::vs) = exists (varOccur v) vars orelse clash(n1,vs) 

835 
in clash end; 

836 

837 

838 
(*nbrs = # of branches just prior to closing this one. Delete choice points 

839 
for goals proved by the latest inference, provided NO variables in the 

840 
next branch have been updated.*) 

841 
fun prune (1, nxtVars, choices) = choices (*DON'T prune at very end: allow 

842 
backtracking over bad proofs*) 

843 
 prune (nbrs, nxtVars, choices) = 

844 
let fun traceIt last = 

845 
let val ll = length last 

846 
and lc = length choices 

847 
in if !trace andalso ll<lc then 

3083  848 
(writeln("Pruning " ^ Int.toString(lcll) ^ " levels"); 
2854  849 
last) 
850 
else last 

851 
end 

852 
fun pruneAux (last, _, _, []) = last 

3083  853 
 pruneAux (last, ntrl, trl, (ntrl',nbrs',exn) :: choices) = 
2854  854 
if nbrs' < nbrs 
855 
then last (*don't backtrack beyond first solution of goal*) 

856 
else if nbrs' > nbrs then pruneAux (last, ntrl, trl, choices) 

857 
else (* nbrs'=nbrs *) 

858 
if clashVar nxtVars (ntrlntrl', trl) then last 

859 
else (*no clashes: can go back at least this far!*) 

860 
pruneAux(choices, ntrl', List.drop(trl, ntrlntrl'), 

861 
choices) 

862 
in traceIt (pruneAux (choices, !ntrail, !trail, choices)) end; 

863 

5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

864 
fun nextVars ({pairs, lits, vars, lim} :: _) = map Var vars 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

865 
 nextVars [] = []; 
2854  866 

3083  867 
fun backtrack (choices as (ntrl, nbrs, exn)::_) = 
868 
(if !trace then (writeln ("Backtracking; now there are " ^ 

869 
Int.toString nbrs ^ " branches")) 

870 
else (); 

871 
raise exn) 

872 
 backtrack _ = raise PROVE; 

2854  873 

2894  874 
(*Add the literal G, handling *Goal* and detecting duplicates.*) 
875 
fun addLit (Const "*Goal*" $ G, lits) = 

876 
(*New literal is a *Goal*, so change all other Goals to Nots*) 

2854  877 
let fun bad (Const"*Goal*" $ _) = true 
878 
 bad (Const"Not" $ G') = G aconv G' 

879 
 bad _ = false; 

880 
fun change [] = [] 

881 
 change (Const"*Goal*" $ G' :: lits) = 

882 
if G aconv G' then change lits 

883 
else Const"Not" $ G' :: change lits 

884 
 change (Const"Not" $ G' :: lits) = 

885 
if G aconv G' then change lits 

886 
else Const"Not" $ G' :: change lits 

887 
 change (lit::lits) = lit :: change lits 

888 
in 

889 
Const "*Goal*" $ G :: (if exists bad lits then change lits else lits) 

890 
end 

891 
 addLit (G,lits) = ins_term(G, lits) 

892 

893 

2952  894 
(*For calculating the "penalty" to assess on a branching factor of n 
895 
log2 seems a little too severe*) 

3083  896 
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

897 

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

898 

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

899 
(*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

900 
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

901 
fun match (Var _) u = true 
4065  902 
 match (Const"*Goal*") (Const"Not") = true 
903 
 match (Const"Not") (Const"*Goal*") = true 

904 
 match (Const a) (Const b) = (a=b) 

905 
 match (TConst (a,ta)) (TConst (b,tb)) = a=b andalso match ta tb 

906 
 match (Free a) (Free b) = (a=b) 

907 
 match (Bound i) (Bound j) = (i=j) 

908 
 match (Abs(_,t)) (Abs(_,u)) = match t u 

909 
 match (f$t) (g$u) = match f g andalso match t u 

910 
 match t u = false; 

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

911 

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

912 

4300  913 
(*Branches closed: number of branches closed during the search 
914 
Branches tried: number of branches created by splitting (counting from 1)*) 

915 
val nclosed = ref 0 

916 
and ntried = ref 1; 

917 

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

918 
fun printStats (b, start, tacs) = 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

919 
if b then 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

920 
writeln (endTiming start ^ " for search. Closed: " 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

921 
^ Int.toString (!nclosed) ^ 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

922 
" tried: " ^ Int.toString (!ntried) ^ 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

923 
" tactics: " ^ Int.toString (length tacs)) 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

924 
else (); 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

925 

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

926 

2854  927 
(*Tableau prover based on leanTaP. Argument is a list of branches. Each 
928 
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

929 
bound on unsafe expansions. 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

930 
"start" is CPU time at start, for printing search time 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

931 
*) 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

932 
fun prove (sign, start, cs, brs, cont) = 
4653  933 
let val {safe0_netpair, safep_netpair, haz_netpair, ...} = Data.rep_cs cs 
2854  934 
val safeList = [safe0_netpair, safep_netpair] 
935 
and hazList = [haz_netpair] 

4065  936 
fun prv (tacs, trs, choices, []) = 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

937 
(printStats (!trace orelse !stats, start, tacs); 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

938 
cont (tacs, trs, choices)) (*all branches closed!*) 
2854  939 
 prv (tacs, trs, choices, 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

940 
brs0 as {pairs = ((G,md)::br, haz)::pairs, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

941 
lits, vars, lim} :: brs) = 
3917  942 
(*apply a safe rule only (possibly allowing instantiation); 
943 
defer any haz formulae*) 

2854  944 
let exception PRV (*backtrack to precisely this recursion!*) 
945 
val ntrl = !ntrail 

946 
val nbrs = length brs0 

947 
val nxtVars = nextVars brs 

948 
val G = norm G 

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

949 
val rules = netMkRules G vars safeList 
2854  950 
(*Make a new branch, decrementing "lim" if instantiations occur*) 
2894  951 
fun newBr (vars',lim') prems = 
952 
map (fn prem => 

953 
if (exists isGoal prem) 

5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

954 
then {pairs = ((joinMd md prem, []) :: 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

955 
negOfGoals ((br, haz)::pairs)), 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

956 
lits = map negOfGoal lits, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

957 
vars = vars', 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

958 
lim = lim'} 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

959 
else {pairs = ((joinMd md prem, []) :: 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

960 
(br, haz) :: pairs), 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

961 
lits = lits, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

962 
vars = vars', 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

963 
lim = lim'}) 
2854  964 
prems @ 
965 
brs 

966 
(*Seek a matching rule. If unifiable then add new premises 

967 
to branch.*) 

968 
fun deeper [] = raise NEWBRANCHES 

969 
 deeper (((P,prems),tac)::grls) = 

4065  970 
if unify(add_term_vars(P,[]), P, G) 
3083  971 
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

972 
let val updated = ntrl < !ntrail (*branch updated*) 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

973 
val lim' = if updated 
3083  974 
then lim  (1+log(length rules)) 
975 
else lim (*discourage branching updates*) 

976 
val vars = vars_in_vars vars 

977 
val vars' = foldr add_terms_vars (prems, vars) 

978 
val choices' = (ntrl, nbrs, PRV) :: choices 

5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

979 
val tacs' = (tac(updated,false,true)) 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

980 
:: tacs (*no duplication; rotate*) 
3083  981 
in 
4065  982 
traceNew prems; traceVars sign ntrl; 
3083  983 
(if null prems then (*closed the branch: prune!*) 
4300  984 
(nclosed := !nclosed + 1; 
985 
prv(tacs', brs0::trs, 

986 
prune (nbrs, nxtVars, choices'), 

987 
brs)) 

988 
else (*prems nonnull*) 

3083  989 
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

990 
then (traceMsg"Excessive branching: KILLED"; 
4065  991 
clearTo ntrl; raise NEWBRANCHES) 
3083  992 
else 
4300  993 
(ntried := !ntried + length prems  1; 
994 
prv(tacs', brs0::trs, choices', 

995 
newBr (vars',lim') prems))) 

3083  996 
handle PRV => 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

997 
if updated then 
3083  998 
(*Backtrack at this level. 
999 
Reset Vars and try another rule*) 

1000 
(clearTo ntrl; deeper grls) 

1001 
else (*backtrack to previous level*) 

1002 
backtrack choices 

1003 
end 

1004 
else deeper grls 

2854  1005 
(*Try to close branch by unifying with head goal*) 
1006 
fun closeF [] = raise CLOSEF 

1007 
 closeF (L::Ls) = 

3083  1008 
case tryClose(G,L) of 
1009 
None => closeF Ls 

1010 
 Some tac => 

1011 
let val choices' = 

3092  1012 
(if !trace then (prs"branch closed"; 
4065  1013 
traceVars sign ntrl) 
3083  1014 
else (); 
1015 
prune (nbrs, nxtVars, 

1016 
(ntrl, nbrs, PRV) :: choices)) 

4300  1017 
in nclosed := !nclosed + 1; 
1018 
prv (tac::tacs, brs0::trs, choices', brs) 

3083  1019 
handle PRV => 
1020 
(*reset Vars and try another literal 

1021 
[this handler is pruned if possible!]*) 

1022 
(clearTo ntrl; closeF Ls) 

1023 
end 

2894  1024 
fun closeFl [] = raise CLOSEF 
1025 
 closeFl ((br, haz)::pairs) = 

1026 
closeF (map fst br) 

1027 
handle CLOSEF => closeF (map fst haz) 

1028 
handle CLOSEF => closeFl pairs 

3083  1029 
in tracing sign brs0; 
4065  1030 
if lim<0 then (traceMsg "Limit reached. "; backtrack choices) 
2854  1031 
else 
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

1032 
prv (Data.hyp_subst_tac trace :: tacs, 
2854  1033 
brs0::trs, choices, 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1034 
equalSubst sign 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1035 
(G, {pairs = (br,haz)::pairs, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1036 
lits = lits, vars = vars, lim = lim}) 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1037 
:: brs) 
4065  1038 
handle DEST_EQ => closeF lits 
1039 
handle CLOSEF => closeFl ((br,haz)::pairs) 

1040 
handle CLOSEF => deeper rules 

2894  1041 
handle NEWBRANCHES => 
1042 
(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

1043 
[] => (*there are no plausible haz rules*) 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1044 
(traceMsg "moving formula to literals"; 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1045 
prv (tacs, brs0::trs, choices, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1046 
{pairs = (br,haz)::pairs, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1047 
lits = addLit(G,lits), 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1048 
vars = vars, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1049 
lim = lim} :: brs)) 
2894  1050 
 _ => (*G admits some haz rules: try later*) 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1051 
(traceMsg "moving formula to haz list"; 
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

1052 
prv (if isGoal G then negOfGoal_tac :: tacs 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1053 
else tacs, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1054 
brs0::trs, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1055 
choices, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1056 
{pairs = (br, haz@[(negOfGoal G, md)])::pairs, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1057 
lits = lits, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1058 
vars = vars, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1059 
lim = lim} :: brs))) 
2854  1060 
end 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1061 
 prv (tacs, trs, choices, 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1062 
{pairs = ([],haz)::(Gs,haz')::pairs, lits, vars, lim} :: brs) = 
2894  1063 
(*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

1064 
prv (tacs, trs, choices, 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1065 
{pairs = (Gs,haz@haz')::pairs, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1066 
lits = lits, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1067 
vars = vars, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1068 
lim = lim} :: brs) 
2854  1069 
 prv (tacs, trs, choices, 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1070 
brs0 as {pairs = [([], (H,md)::Hs)], 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1071 
lits, vars, lim} :: brs) = 
2894  1072 
(*no safe steps possible at any level: apply a haz rule*) 
2854  1073 
let exception PRV (*backtrack to precisely this recursion!*) 
2894  1074 
val H = norm H 
2854  1075 
val ntrl = !ntrail 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1076 
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

1077 
(*new premises of haz rules may NOT be duplicated*) 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1078 
fun newPrem (vars,P,dup,lim') prem = 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1079 
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

1080 
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

1081 
and lits' = if (exists isGoal prem) 
9953c0995b79
Now applies "map negOfGoal" to lits when expanding haz rules.
paulson
parents:
4149
diff
changeset

1082 
then map negOfGoal lits 
9953c0995b79
Now applies "map negOfGoal" to lits when expanding haz rules.
paulson
parents:
4149
diff
changeset

1083 
else lits 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1084 
in {pairs = if exists (match P) prem then [(Gs',Hs')] 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1085 
(*Recursive in this premise. Don't make new 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1086 
"stack frame". New haz premises will end up 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1087 
at the BACK of the queue, preventing 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1088 
exclusion of others*) 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1089 
else [(Gs',[]), ([],Hs')], 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1090 
lits = lits', 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1091 
vars = vars, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1092 
lim = lim'} 
3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset

1093 
end 
2854  1094 
fun newBr x prems = map (newPrem x) prems @ brs 
1095 
(*Seek a matching rule. If unifiable then add new premises 

1096 
to branch.*) 

1097 
fun deeper [] = raise NEWBRANCHES 

1098 
 deeper (((P,prems),tac)::grls) = 

4065  1099 
if unify(add_term_vars(P,[]), P, H) 
3083  1100 
then 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

1101 
let val updated = ntrl < !ntrail (*branch updated*) 
3083  1102 
val vars = vars_in_vars vars 
1103 
val vars' = foldr add_terms_vars (prems, vars) 

1104 
(*duplicate H if md and the subgoal has new vars*) 

1105 
val dup = md andalso vars' <> vars 

5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1106 
(*any instances of P in the subgoals? 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1107 
NB: this boolean affects tracing only!*) 
3083  1108 
and recur = exists (exists (match P)) prems 
1109 
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

1110 
if updated then lim  (1+log(length rules)) 
3083  1111 
else lim1 
1112 
(*It is tempting to leave "lim" UNCHANGED if 

1113 
both dup and recur are false. Proofs are 

1114 
found at shallower depths, but looping 

1115 
occurs too often...*) 

3917  1116 
val mayUndo = 
1117 
(*Allowing backtracking from a rule application 

1118 
if other matching rules exist, if the rule 

1119 
updated variables, or if the rule did not 

1120 
introduce new variables. This latter condition 

1121 
means it is not a standard "gammarule" but 

1122 
some other form of unsafe rule. Aim is to 

1123 
emulate Fast_tac, which allows all unsafe steps 

1124 
to be undone.*) 

1125 
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

1126 
orelse updated 
3917  1127 
orelse vars=vars' (*no new Vars?*) 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

1128 
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

1129 
else DETERM o tac(updated, dup, true) 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1130 
(*if recur then perhaps shouldn't call rotate_tac: new 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1131 
formulae should be last, but that's WRONG if the new 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1132 
formulae are Goals, since they remain in the first 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1133 
position*) 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1134 

3083  1135 
in 
1136 
if lim'<0 andalso not (null prems) 

1137 
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

1138 
(traceMsg"Excessive branching: KILLED"; 
4065  1139 
clearTo ntrl; raise NEWBRANCHES) 
3083  1140 
else 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1141 
traceNew prems; 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1142 
if !trace andalso recur then prs" (recursive)" 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1143 
else (); 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1144 
traceVars sign ntrl; 
4300  1145 
if null prems then nclosed := !nclosed + 1 
1146 
else ntried := !ntried + length prems  1; 

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

1147 
prv(tac' :: tacs, 
3083  1148 
brs0::trs, 
1149 
(ntrl, length brs0, PRV) :: choices, 

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

1150 
newBr (vars', P, dup, lim') prems) 
3083  1151 
handle PRV => 
1152 
if mayUndo 

1153 
then (*reset Vars and try another rule*) 

1154 
(clearTo ntrl; deeper grls) 

1155 
else (*backtrack to previous level*) 

1156 
backtrack choices 

1157 
end 

1158 
else deeper grls 

1159 
in tracing sign brs0; 

4065  1160 
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

1161 
else deeper rules 
2854  1162 
handle NEWBRANCHES => 
2894  1163 
(*cannot close branch: move H to literals*) 
2854  1164 
prv (tacs, brs0::trs, choices, 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1165 
{pairs = [([], Hs)], 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1166 
lits = H::lits, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1167 
vars = vars, 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1168 
lim = lim} :: brs) 
2854  1169 
end 
1170 
 prv (tacs, trs, choices, _ :: brs) = backtrack choices 

4065  1171 
in init_gensym(); 
1172 
prv ([], [], [(!ntrail, length brs, PROVE)], brs) 

1173 
end; 

2854  1174 

1175 

2883  1176 
(*Construct an initial branch.*) 
2854  1177 
fun initBranch (ts,lim) = 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1178 
{pairs = [(map (fn t => (t,true)) ts, [])], 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1179 
lits = [], 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1180 
vars = add_terms_vars (ts,[]), 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1181 
lim = lim}; 
2854  1182 

1183 

1184 
(*** Conversion & Skolemization of the Isabelle proof state ***) 

1185 

1186 
(*Make a list of all the parameters in a subgoal, even if nested*) 

1187 
local open Term 

1188 
in 

1189 
fun discard_foralls (Const("all",_)$Abs(a,T,t)) = discard_foralls t 

1190 
 discard_foralls t = t; 

1191 
end; 

1192 

1193 

1194 
(*List of variables not appearing as arguments to the given parameter*) 

1195 
fun getVars [] i = [] 

1196 
 getVars ((_,(v,is))::alist) i = 

1197 
if i mem is then getVars alist i 

1198 
else v :: getVars alist i; 

1199 

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

1200 
exception TRANS of string; 
2854  1201 

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

1202 
(*Translation of a subgoal: Skolemize all parameters*) 
4065  1203 
fun fromSubgoal t = 
1204 
let val alistVar = ref [] 

1205 
and alistTVar = ref [] 

2854  1206 
fun hdvar ((ix,(v,is))::_) = v 
1207 
fun from lev t = 

1208 
let val (ht,ts) = Term.strip_comb t 

1209 
fun apply u = list_comb (u, map (from lev) ts) 

1210 
fun bounds [] = [] 

1211 
 bounds (Term.Bound i::ts) = 

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

1212 
if i<lev then raise TRANS 
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

1213 
"Function unknown's argument not a parameter" 
2854  1214 
else ilev :: bounds ts 
4233
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

1215 
 bounds ts = raise TRANS 
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

1216 
"Function unknown's argument not a bound variable" 
2854  1217 
in 
1218 
case ht of 

4065  1219 
Term.Const aT => apply (fromConst alistTVar aT) 
2854  1220 
 Term.Free (a,_) => apply (Free a) 
1221 
 Term.Bound i => apply (Bound i) 

1222 
 Term.Var (ix,_) => 

4065  1223 
(case (assoc_string_int(!alistVar,ix)) of 
1224 
None => (alistVar := (ix, (ref None, bounds ts)) 

1225 
:: !alistVar; 

1226 
Var (hdvar(!alistVar))) 

2854  1227 
 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

1228 
else raise TRANS 
5411  1229 
("Discrepancy among occurrences of " 
4233
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

1230 
^ Syntax.string_of_vname ix)) 
2854  1231 
 Term.Abs (a,_,body) => 
1232 
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

1233 
else raise TRANS "argument not in normal form" 
2854  1234 
end 
1235 

1236 
val npars = length (Logic.strip_params t) 

1237 

1238 
(*Skolemize a subgoal from a proof state*) 

1239 
fun skoSubgoal i t = 

1240 
if i<npars then 

1241 
skoSubgoal (i+1) 

4065  1242 
(subst_bound (Skolem (gensym "T_", getVars (!alistVar) i), 
2854  1243 
t)) 
1244 
else t 

1245 

1246 
in skoSubgoal 0 (from 0 (discard_foralls t)) end; 

1247 

1248 

4300  1249 
fun initialize() = 
1250 
(fullTrace:=[]; trail := []; ntrail := 0; 

1251 
nclosed := 0; ntried := 1); 

1252 

1253 

2854  1254 
(*Tactic using tableau engine and proof reconstruction. 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1255 
"start" is CPU time at start, for printing SEARCH time 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1256 
(also prints reconstruction time) 
2854  1257 
"lim" is depth limit.*) 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1258 
fun timing_depth_tac start cs lim i st = 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1259 
(initialize(); 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1260 
let val {sign,...} = rep_thm st 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1261 
val skoprem = fromSubgoal (List.nth(prems_of st, i1)) 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1262 
val hyps = strip_imp_prems skoprem 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1263 
and concl = strip_imp_concl skoprem 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1264 
fun cont (tacs,_,choices) = 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1265 
let val start = startTiming() 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1266 
in 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1267 
case Seq.pull(EVERY' (rev tacs) i st) of 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1268 
None => (writeln ("PROOF FAILED for depth " ^ 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1269 
Int.toString lim); 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1270 
if !trace then writeln "************************\n" 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1271 
else (); 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1272 
backtrack choices) 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1273 
 cell => (if (!trace orelse !stats) 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1274 
then writeln (endTiming start ^ " for reconstruction") 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1275 
else (); 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1276 
Seq.make(fn()=> cell)) 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1277 
end 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1278 
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

1279 
end 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1280 
handle PROVE => Seq.empty); 
2854  1281 

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

1282 
(*Public version with fixed depth*) 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1283 
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

1284 

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

1285 
fun blast_tac cs i st = 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1286 
((DEEPEN (1,20) (timing_depth_tac (startTiming()) cs) 0) i 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1287 
THEN flexflex_tac) st 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1288 
handle TRANS s => (warning ("Blast_tac: " ^ s); Seq.empty); 
2854  1289 

4078  1290 
fun Blast_tac i = blast_tac (Data.claset()) i; 
2854  1291 

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

1292 

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

1293 
(*** 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

1294 
the resulting tactics, trace, etc. ***) 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1295 

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

1296 
(*Translate subgoal i from a proof state*) 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1297 
fun trygl cs lim i = 
4300  1298 
(initialize(); 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1299 
let val st = topthm() 
3030  1300 
val {sign,...} = rep_thm st 
4065  1301 
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

1302 
val hyps = strip_imp_prems skoprem 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1303 
and concl = strip_imp_concl skoprem 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1304 
in timeap prove (sign, startTiming(), cs, 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1305 
[initBranch (mkGoal concl :: hyps, lim)], I) 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1306 
end 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1307 
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

1308 

4078  1309 
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

1310 

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

1311 
(*Read a string to make an initial, singleton branch*) 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1312 
fun readGoal sign s = read_cterm sign (s,propT) > 
4065  1313 
term_of > fromTerm > rand > mkGoal; 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1314 

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

1315 
fun tryInThy thy lim s = 
4300  1316 
(initialize(); 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1317 
timeap prove (sign_of thy, 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1318 
startTiming(), 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1319 
Data.claset(), 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1320 
[initBranch ([readGoal (sign_of thy) s], lim)], 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1321 
I)); 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1322 

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

1323 

2854  1324 
end; 