author  wenzelm 
Wed, 25 Nov 1998 14:04:28 +0100  
changeset 5963  94709c11601e 
parent 4271  3a82492e70c5 
child 6969  441393b452c7 
permissions  rwrr 
0  1 
(* Title: FOLP/simp 
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ID: $Id$ 

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Author: Tobias Nipkow 

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Copyright 1993 University of Cambridge 

5 

6 
FOLP version of... 

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Generic simplifier, suitable for most logics. (from Provers) 

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10 
This version allows instantiation of Vars in the subgoal, since the proof 

11 
term must change. 

12 
*) 

13 

14 
signature SIMP_DATA = 

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sig 

16 
val case_splits : (thm * string) list 

17 
val dest_red : term > term * term * term 

18 
val mk_rew_rules : thm > thm list 

19 
val norm_thms : (thm*thm) list (* [(?x>>norm(?x), norm(?x)>>?x), ...] *) 

20 
val red1 : thm (* ?P>>?Q ==> ?P ==> ?Q *) 

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val red2 : thm (* ?P>>?Q ==> ?Q ==> ?P *) 

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val refl_thms : thm list 

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val subst_thms : thm list (* [ ?a>>?b ==> ?P(?a) ==> ?P(?b), ...] *) 

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val trans_thms : thm list 

25 
end; 

26 

27 

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infix 4 addrews addcongs delrews delcongs setauto; 

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signature SIMP = 

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sig 

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type simpset 

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val empty_ss : simpset 

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val addcongs : simpset * thm list > simpset 

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val addrews : simpset * thm list > simpset 

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val delcongs : simpset * thm list > simpset 

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val delrews : simpset * thm list > simpset 

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val dest_ss : simpset > thm list * thm list 

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val print_ss : simpset > unit 

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val setauto : simpset * (int > tactic) > simpset 

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val ASM_SIMP_CASE_TAC : simpset > int > tactic 

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val ASM_SIMP_TAC : simpset > int > tactic 

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val CASE_TAC : simpset > int > tactic 

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val SIMP_CASE2_TAC : simpset > int > tactic 

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val SIMP_THM : simpset > thm > thm 

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val SIMP_TAC : simpset > int > tactic 

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val SIMP_CASE_TAC : simpset > int > tactic 

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val mk_congs : theory > string list > thm list 

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val mk_typed_congs : theory > (string * string) list > thm list 

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(* temporarily disabled: 

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val extract_free_congs : unit > thm list 

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*) 

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val tracing : bool ref 

54 
end; 

55 

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functor SimpFun (Simp_data: SIMP_DATA) : SIMP = 

57 
struct 

58 

59 
local open Simp_data Logic in 

60 

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(*For taking apart reductions into left, right hand sides*) 

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val lhs_of = #2 o dest_red; 

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val rhs_of = #3 o dest_red; 

64 

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(*** Indexing and filtering of theorems ***) 

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fun eq_brl ((b1,th1),(b2,th2)) = b1=b2 andalso eq_thm(th1,th2); 

68 

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(*insert a thm in a discrimination net by its lhs*) 

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fun lhs_insert_thm (th,net) = 

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Net.insert_term((lhs_of (concl_of th), (false,th)), net, eq_brl) 

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handle Net.INSERT => net; 

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(*match subgoal i against possible theorems in the net. 

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Similar to match_from_nat_tac, but the net does not contain numbers; 

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rewrite rules are not ordered.*) 

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fun net_tac net = 

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SUBGOAL(fn (prem,i) => 

1459  79 
resolve_tac (Net.unify_term net (strip_assums_concl prem)) i); 
0  80 

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(*match subgoal i against possible theorems indexed by lhs in the net*) 

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fun lhs_net_tac net = 

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SUBGOAL(fn (prem,i) => 

1459  84 
biresolve_tac (Net.unify_term net 
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(lhs_of (strip_assums_concl prem))) i); 

0  86 

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fun nth_subgoal i thm = nth_elem(i1,prems_of thm); 

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fun goal_concl i thm = strip_assums_concl(nth_subgoal i thm); 

90 

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fun lhs_of_eq i thm = lhs_of(goal_concl i thm) 

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and rhs_of_eq i thm = rhs_of(goal_concl i thm); 

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fun var_lhs(thm,i) = 

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let fun var(Var _) = true 

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 var(Abs(_,_,t)) = var t 

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 var(f$_) = var f 

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 var _ = false; 

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in var(lhs_of_eq i thm) end; 

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fun contains_op opns = 

102 
let fun contains(Const(s,_)) = s mem opns  

103 
contains(s$t) = contains s orelse contains t  

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contains(Abs(_,_,t)) = contains t  

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contains _ = false; 

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in contains end; 

107 

108 
fun may_match(match_ops,i) = contains_op match_ops o lhs_of_eq i; 

109 

110 
val (normI_thms,normE_thms) = split_list norm_thms; 

111 

112 
(*Get the norm constants from norm_thms*) 

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val norms = 

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let fun norm thm = 

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case lhs_of(concl_of thm) of 

1459  116 
Const(n,_)$_ => n 
117 
 _ => (prths normE_thms; error"No constant in lhs of a norm_thm") 

0  118 
in map norm normE_thms end; 
119 

120 
fun lhs_is_NORM(thm,i) = case lhs_of_eq i thm of 

1459  121 
Const(s,_)$_ => s mem norms  _ => false; 
0  122 

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val refl_tac = resolve_tac refl_thms; 

124 

125 
fun find_res thms thm = 

126 
let fun find [] = (prths thms; error"Check Simp_Data") 

127 
 find(th::thms) = thm RS th handle _ => find thms 

128 
in find thms end; 

129 

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val mk_trans = find_res trans_thms; 

131 

132 
fun mk_trans2 thm = 

133 
let fun mk[] = error"Check transitivity" 

134 
 mk(t::ts) = (thm RSN (2,t)) handle _ => mk ts 

135 
in mk trans_thms end; 

136 

137 
(*Applies tactic and returns the first resulting state, FAILS if none!*) 

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fun one_result(tac,thm) = case Seq.pull(tac thm) of 
1459  139 
Some(thm',_) => thm' 
0  140 
 None => raise THM("Simplifier: could not continue", 0, [thm]); 
141 

142 
fun res1(thm,thms,i) = one_result(resolve_tac thms i,thm); 

143 

144 

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(**** Adding "NORM" tags ****) 

146 

147 
(*get name of the constant from conclusion of a congruence rule*) 

148 
fun cong_const cong = 

149 
case head_of (lhs_of (concl_of cong)) of 

1459  150 
Const(c,_) => c 
151 
 _ => "" (*a placeholder distinct from const names*); 

0  152 

153 
(*true if the term is an atomic proposition (no ==> signs) *) 

154 
val atomic = null o strip_assums_hyp; 

155 

156 
(*ccs contains the names of the constants possessing congruence rules*) 

157 
fun add_hidden_vars ccs = 

158 
let fun add_hvars(tm,hvars) = case tm of 

1459  159 
Abs(_,_,body) => add_term_vars(body,hvars) 
160 
 _$_ => let val (f,args) = strip_comb tm 

161 
in case f of 

162 
Const(c,T) => 

163 
if c mem ccs 

164 
then foldr add_hvars (args,hvars) 

165 
else add_term_vars(tm,hvars) 

166 
 _ => add_term_vars(tm,hvars) 

167 
end 

168 
 _ => hvars; 

0  169 
in add_hvars end; 
170 

171 
fun add_new_asm_vars new_asms = 

172 
let fun itf((tm,at),vars) = 

1459  173 
if at then vars else add_term_vars(tm,vars) 
174 
fun add_list(tm,al,vars) = let val (_,tml) = strip_comb tm 

175 
in if length(tml)=length(al) 

176 
then foldr itf (tml~~al,vars) 

177 
else vars 

178 
end 

179 
fun add_vars (tm,vars) = case tm of 

180 
Abs (_,_,body) => add_vars(body,vars) 

181 
 r$s => (case head_of tm of 

182 
Const(c,T) => (case assoc(new_asms,c) of 

183 
None => add_vars(r,add_vars(s,vars)) 

184 
 Some(al) => add_list(tm,al,vars)) 

185 
 _ => add_vars(r,add_vars(s,vars))) 

186 
 _ => vars 

0  187 
in add_vars end; 
188 

189 

190 
fun add_norms(congs,ccs,new_asms) thm = 

191 
let val thm' = mk_trans2 thm; 

192 
(* thm': [?z > l; Prems; r > ?t] ==> ?z > ?t *) 

193 
val nops = nprems_of thm' 

194 
val lhs = rhs_of_eq 1 thm' 

195 
val rhs = lhs_of_eq nops thm' 

196 
val asms = tl(rev(tl(prems_of thm'))) 

197 
val hvars = foldr (add_hidden_vars ccs) (lhs::rhs::asms,[]) 

198 
val hvars = add_new_asm_vars new_asms (rhs,hvars) 

199 
fun it_asms (asm,hvars) = 

1459  200 
if atomic asm then add_new_asm_vars new_asms (asm,hvars) 
201 
else add_term_frees(asm,hvars) 

0  202 
val hvars = foldr it_asms (asms,hvars) 
203 
val hvs = map (#1 o dest_Var) hvars 

204 
val refl1_tac = refl_tac 1 

3537  205 
fun norm_step_tac st = st > 
206 
(case head_of(rhs_of_eq 1 st) of 

207 
Var(ixn,_) => if ixn mem hvs then refl1_tac 

208 
else resolve_tac normI_thms 1 ORELSE refl1_tac 

209 
 Const _ => resolve_tac normI_thms 1 ORELSE 

210 
resolve_tac congs 1 ORELSE refl1_tac 

211 
 Free _ => resolve_tac congs 1 ORELSE refl1_tac 

212 
 _ => refl1_tac) 

213 
val add_norm_tac = DEPTH_FIRST (has_fewer_prems nops) norm_step_tac 

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val Some(thm'',_) = Seq.pull(add_norm_tac thm') 
0  215 
in thm'' end; 
216 

217 
fun add_norm_tags congs = 

218 
let val ccs = map cong_const congs 

1459  219 
val new_asms = filter (exists not o #2) 
220 
(ccs ~~ (map (map atomic o prems_of) congs)); 

0  221 
in add_norms(congs,ccs,new_asms) end; 
222 

223 
fun normed_rews congs = 

224 
let val add_norms = add_norm_tags congs; 

225 
in fn thm => map (varifyT o add_norms o mk_trans) (mk_rew_rules(freezeT thm)) 

226 
end; 

227 

1459  228 
fun NORM norm_lhs_tac = EVERY'[rtac red2 , norm_lhs_tac, refl_tac]; 
0  229 

230 
val trans_norms = map mk_trans normE_thms; 

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232 

233 
(* SIMPSET *) 

234 

235 
datatype simpset = 

1459  236 
SS of {auto_tac: int > tactic, 
237 
congs: thm list, 

238 
cong_net: thm Net.net, 

239 
mk_simps: thm > thm list, 

240 
simps: (thm * thm list) list, 

241 
simp_net: thm Net.net} 

0  242 

243 
val empty_ss = SS{auto_tac= K no_tac, congs=[], cong_net=Net.empty, 

1459  244 
mk_simps=normed_rews[], simps=[], simp_net=Net.empty}; 
0  245 

246 
(** Insertion of congruences and rewrites **) 

247 

248 
(*insert a thm in a thm net*) 

249 
fun insert_thm_warn (th,net) = 

250 
Net.insert_term((concl_of th, th), net, eq_thm) 

251 
handle Net.INSERT => 

252 
(writeln"\nDuplicate rewrite or congruence rule:"; print_thm th; 

253 
net); 

254 

255 
val insert_thms = foldr insert_thm_warn; 

256 

257 
fun addrew(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thm) = 

258 
let val thms = mk_simps thm 

259 
in SS{auto_tac=auto_tac,congs=congs, cong_net=cong_net, mk_simps=mk_simps, 

260 
simps = (thm,thms)::simps, simp_net = insert_thms(thms,simp_net)} 

261 
end; 

262 

263 
val op addrews = foldl addrew; 

264 

265 
fun op addcongs(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thms) = 

266 
let val congs' = thms @ congs; 

267 
in SS{auto_tac=auto_tac, congs= congs', 

268 
cong_net= insert_thms (map mk_trans thms,cong_net), 

269 
mk_simps= normed_rews congs', simps=simps, simp_net=simp_net} 

270 
end; 

271 

272 
(** Deletion of congruences and rewrites **) 

273 

274 
(*delete a thm from a thm net*) 

275 
fun delete_thm_warn (th,net) = 

276 
Net.delete_term((concl_of th, th), net, eq_thm) 

277 
handle Net.DELETE => 

278 
(writeln"\nNo such rewrite or congruence rule:"; print_thm th; 

279 
net); 

280 

281 
val delete_thms = foldr delete_thm_warn; 

282 

283 
fun op delcongs(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thms) = 

284 
let val congs' = foldl (gen_rem eq_thm) (congs,thms) 

285 
in SS{auto_tac=auto_tac, congs= congs', 

286 
cong_net= delete_thms(map mk_trans thms,cong_net), 

287 
mk_simps= normed_rews congs', simps=simps, simp_net=simp_net} 

288 
end; 

289 

290 
fun delrew(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thm) = 

291 
let fun find((p as (th,ths))::ps',ps) = 

1459  292 
if eq_thm(thm,th) then (ths,ps@ps') else find(ps',p::ps) 
0  293 
 find([],simps') = (writeln"\nNo such rewrite or congruence rule:"; 
1459  294 
print_thm thm; 
295 
([],simps')) 

0  296 
val (thms,simps') = find(simps,[]) 
297 
in SS{auto_tac=auto_tac, congs=congs, cong_net=cong_net, mk_simps=mk_simps, 

298 
simps = simps', simp_net = delete_thms(thms,simp_net)} 

299 
end; 

300 

301 
val op delrews = foldl delrew; 

302 

303 

304 
fun op setauto(SS{congs,cong_net,mk_simps,simps,simp_net,...}, auto_tac) = 

305 
SS{auto_tac=auto_tac, congs=congs, cong_net=cong_net, mk_simps=mk_simps, 

306 
simps=simps, simp_net=simp_net}; 

307 

308 

309 
(** Inspection of a simpset **) 

310 

311 
fun dest_ss(SS{congs,simps,...}) = (congs, map #1 simps); 

312 

313 
fun print_ss(SS{congs,simps,...}) = 

1459  314 
(writeln"Congruences:"; prths congs; 
315 
writeln"Rewrite Rules:"; prths (map #1 simps); ()); 

0  316 

317 

318 
(* Rewriting with conditionals *) 

319 

320 
val (case_thms,case_consts) = split_list case_splits; 

321 
val case_rews = map mk_trans case_thms; 

322 

323 
fun if_rewritable ifc i thm = 

324 
let val tm = goal_concl i thm 

1459  325 
fun nobound(Abs(_,_,tm),j,k) = nobound(tm,j,k+1) 
326 
 nobound(s$t,j,k) = nobound(s,j,k) andalso nobound(t,j,k) 

327 
 nobound(Bound n,j,k) = n < k orelse k+j <= n 

328 
 nobound(_) = true; 

329 
fun check_args(al,j) = forall (fn t => nobound(t,j,0)) al 

330 
fun find_if(Abs(_,_,tm),j) = find_if(tm,j+1) 

331 
 find_if(tm as s$t,j) = let val (f,al) = strip_comb tm in 

332 
case f of Const(c,_) => if c=ifc then check_args(al,j) 

333 
else find_if(s,j) orelse find_if(t,j) 

334 
 _ => find_if(s,j) orelse find_if(t,j) end 

335 
 find_if(_) = false; 

0  336 
in find_if(tm,0) end; 
337 

338 
fun IF1_TAC cong_tac i = 

1512  339 
let fun seq_try (ifth::ifths,ifc::ifcs) thm = 
340 
(COND (if_rewritable ifc i) (DETERM(rtac ifth i)) 

341 
(seq_try(ifths,ifcs))) thm 

342 
 seq_try([],_) thm = no_tac thm 

343 
and try_rew thm = (seq_try(case_rews,case_consts) ORELSE one_subt) thm 

1459  344 
and one_subt thm = 
345 
let val test = has_fewer_prems (nprems_of thm + 1) 

1512  346 
fun loop thm = 
347 
COND test no_tac 

348 
((try_rew THEN DEPTH_FIRST test (refl_tac i)) 

349 
ORELSE (refl_tac i THEN loop)) thm 

350 
in (cong_tac THEN loop) thm end 

351 
in COND (may_match(case_consts,i)) try_rew no_tac end; 

0  352 

353 
fun CASE_TAC (SS{cong_net,...}) i = 

354 
let val cong_tac = net_tac cong_net i 

355 
in NORM (IF1_TAC cong_tac) i end; 

356 

357 
(* Rewriting Automaton *) 

358 

359 
datatype cntrl = STOP  MK_EQ  ASMS of int  SIMP_LHS  REW  REFL  TRUE 

1459  360 
 PROVE  POP_CS  POP_ARTR  IF; 
0  361 
(* 
5963  362 
fun pr_cntrl c = case c of STOP => std_output("STOP")  MK_EQ => std_output("MK_EQ")  
363 
ASMS i => print_int i  POP_ARTR => std_output("POP_ARTR")  

364 
SIMP_LHS => std_output("SIMP_LHS")  REW => std_output("REW")  REFL => std_output("REFL")  

365 
TRUE => std_output("TRUE")  PROVE => std_output("PROVE")  POP_CS => std_output("POP_CS")  IF 

366 
=> std_output("IF"); 

0  367 
*) 
368 
fun simp_refl([],_,ss) = ss 

369 
 simp_refl(a'::ns,a,ss) = if a'=a then simp_refl(ns,a,SIMP_LHS::REFL::ss) 

1459  370 
else simp_refl(ns,a,ASMS(a)::SIMP_LHS::REFL::POP_ARTR::ss); 
0  371 

372 
(** Tracing **) 

373 

374 
val tracing = ref false; 

375 

376 
(*Replace parameters by Free variables in P*) 

377 
fun variants_abs ([],P) = P 

378 
 variants_abs ((a,T)::aTs, P) = 

379 
variants_abs (aTs, #2 (variant_abs(a,T,P))); 

380 

381 
(*Select subgoal i from proof state; substitute parameters, for printing*) 

382 
fun prepare_goal i st = 

383 
let val subgi = nth_subgoal i st 

1459  384 
val params = rev(strip_params subgi) 
0  385 
in variants_abs (params, strip_assums_concl subgi) end; 
386 

387 
(*print lhs of conclusion of subgoal i*) 

388 
fun pr_goal_lhs i st = 

389 
writeln (Sign.string_of_term (#sign(rep_thm st)) 

1459  390 
(lhs_of (prepare_goal i st))); 
0  391 

392 
(*print conclusion of subgoal i*) 

393 
fun pr_goal_concl i st = 

394 
writeln (Sign.string_of_term (#sign(rep_thm st)) (prepare_goal i st)) 

395 

396 
(*print subgoals i to j (inclusive)*) 

397 
fun pr_goals (i,j) st = 

398 
if i>j then () 

399 
else (pr_goal_concl i st; pr_goals (i+1,j) st); 

400 

401 
(*Print rewrite for tracing; i=subgoal#, n=number of new subgoals, 

402 
thm=old state, thm'=new state *) 

403 
fun pr_rew (i,n,thm,thm',not_asms) = 

404 
if !tracing 

405 
then (if not_asms then () else writeln"Assumption used in"; 

406 
pr_goal_lhs i thm; writeln">"; pr_goal_lhs (i+n) thm'; 

1459  407 
if n>0 then (writeln"Conditions:"; pr_goals (i, i+n1) thm') 
0  408 
else (); 
409 
writeln"" ) 

410 
else (); 

411 

412 
(* Skip the first n hyps of a goal, and return the rest in generalized form *) 

413 
fun strip_varify(Const("==>", _) $ H $ B, n, vs) = 

1459  414 
if n=0 then subst_bounds(vs,H)::strip_varify(B,0,vs) 
415 
else strip_varify(B,n1,vs) 

0  416 
 strip_varify(Const("all",_)$Abs(_,T,t), n, vs) = 
1459  417 
strip_varify(t,n,Var(("?",length vs),T)::vs) 
0  418 
 strip_varify _ = []; 
419 

420 
fun execute(ss,if_fl,auto_tac,cong_tac,net,i,thm) = let 

421 

422 
fun simp_lhs(thm,ss,anet,ats,cs) = 

423 
if var_lhs(thm,i) then (ss,thm,anet,ats,cs) else 

424 
if lhs_is_NORM(thm,i) then (ss, res1(thm,trans_norms,i), anet,ats,cs) 

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425 
else case Seq.pull(cong_tac i thm) of 
1459  426 
Some(thm',_) => 
427 
let val ps = prems_of thm and ps' = prems_of thm'; 

428 
val n = length(ps')length(ps); 

429 
val a = length(strip_assums_hyp(nth_elem(i1,ps))) 

430 
val l = map (fn p => length(strip_assums_hyp(p))) 

431 
(take(n,drop(i1,ps'))); 

432 
in (simp_refl(rev(l),a,REW::ss),thm',anet,ats,cs) end 

433 
 None => (REW::ss,thm,anet,ats,cs); 

0  434 

435 
(*NB: the "Adding rewrites:" trace will look strange because assumptions 

436 
are represented by rules, generalized over their parameters*) 

437 
fun add_asms(ss,thm,a,anet,ats,cs) = 

438 
let val As = strip_varify(nth_subgoal i thm, a, []); 

1459  439 
val thms = map (trivial o cterm_of(#sign(rep_thm(thm))))As; 
440 
val new_rws = flat(map mk_rew_rules thms); 

441 
val rwrls = map mk_trans (flat(map mk_rew_rules thms)); 

442 
val anet' = foldr lhs_insert_thm (rwrls,anet) 

0  443 
in if !tracing andalso not(null new_rws) 
1459  444 
then (writeln"Adding rewrites:"; prths new_rws; ()) 
445 
else (); 

446 
(ss,thm,anet',anet::ats,cs) 

0  447 
end; 
448 

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449 
fun rew(seq,thm,ss,anet,ats,cs, more) = case Seq.pull seq of 
0  450 
Some(thm',seq') => 
1459  451 
let val n = (nprems_of thm')  (nprems_of thm) 
452 
in pr_rew(i,n,thm,thm',more); 

453 
if n=0 then (SIMP_LHS::ss, thm', anet, ats, cs) 

454 
else ((replicate n PROVE) @ (POP_CS::SIMP_LHS::ss), 

455 
thm', anet, ats, (ss,thm,anet,ats,seq',more)::cs) 

456 
end 

0  457 
 None => if more 
1512  458 
then rew((lhs_net_tac anet i THEN assume_tac i) thm, 
1459  459 
thm,ss,anet,ats,cs,false) 
460 
else (ss,thm,anet,ats,cs); 

0  461 

462 
fun try_true(thm,ss,anet,ats,cs) = 

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463 
case Seq.pull(auto_tac i thm) of 
0  464 
Some(thm',_) => (ss,thm',anet,ats,cs) 
465 
 None => let val (ss0,thm0,anet0,ats0,seq,more)::cs0 = cs 

1459  466 
in if !tracing 
467 
then (writeln"*** Failed to prove precondition. Normal form:"; 

468 
pr_goal_concl i thm; writeln"") 

469 
else (); 

470 
rew(seq,thm0,ss0,anet0,ats0,cs0,more) 

471 
end; 

0  472 

473 
fun if_exp(thm,ss,anet,ats,cs) = 

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changeset

474 
case Seq.pull (IF1_TAC (cong_tac i) i thm) of 
1459  475 
Some(thm',_) => (SIMP_LHS::IF::ss,thm',anet,ats,cs) 
476 
 None => (ss,thm,anet,ats,cs); 

0  477 

478 
fun step(s::ss, thm, anet, ats, cs) = case s of 

1459  479 
MK_EQ => (ss, res1(thm,[red2],i), anet, ats, cs) 
480 
 ASMS(a) => add_asms(ss,thm,a,anet,ats,cs) 

481 
 SIMP_LHS => simp_lhs(thm,ss,anet,ats,cs) 

1512  482 
 REW => rew(net_tac net i thm,thm,ss,anet,ats,cs,true) 
1459  483 
 REFL => (ss, res1(thm,refl_thms,i), anet, ats, cs) 
484 
 TRUE => try_true(res1(thm,refl_thms,i),ss,anet,ats,cs) 

485 
 PROVE => (if if_fl then MK_EQ::SIMP_LHS::IF::TRUE::ss 

486 
else MK_EQ::SIMP_LHS::TRUE::ss, thm, anet, ats, cs) 

487 
 POP_ARTR => (ss,thm,hd ats,tl ats,cs) 

488 
 POP_CS => (ss,thm,anet,ats,tl cs) 

489 
 IF => if_exp(thm,ss,anet,ats,cs); 

0  490 

491 
fun exec(state as (s::ss, thm, _, _, _)) = 

1459  492 
if s=STOP then thm else exec(step(state)); 
0  493 

494 
in exec(ss, thm, Net.empty, [], []) end; 

495 

496 

497 
fun EXEC_TAC(ss,fl) (SS{auto_tac,cong_net,simp_net,...}) = 

498 
let val cong_tac = net_tac cong_net 

1512  499 
in fn i => 
500 
(fn thm => 

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changeset

501 
if i <= 0 orelse nprems_of thm < i then Seq.empty 
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changeset

502 
else Seq.single(execute(ss,fl,auto_tac,cong_tac,simp_net,i,thm))) 
1512  503 
THEN TRY(auto_tac i) 
0  504 
end; 
505 

506 
val SIMP_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,REFL,STOP],false); 

507 
val SIMP_CASE_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,IF,REFL,STOP],false); 

508 

509 
val ASM_SIMP_TAC = EXEC_TAC([ASMS(0),MK_EQ,SIMP_LHS,REFL,STOP],false); 

510 
val ASM_SIMP_CASE_TAC = EXEC_TAC([ASMS(0),MK_EQ,SIMP_LHS,IF,REFL,STOP],false); 

511 

512 
val SIMP_CASE2_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,IF,REFL,STOP],true); 

513 

514 
fun REWRITE (ss,fl) (SS{auto_tac,cong_net,simp_net,...}) = 

515 
let val cong_tac = net_tac cong_net 

516 
in fn thm => let val state = thm RSN (2,red1) 

1459  517 
in execute(ss,fl,auto_tac,cong_tac,simp_net,1,state) end 
0  518 
end; 
519 

520 
val SIMP_THM = REWRITE ([ASMS(0),SIMP_LHS,IF,REFL,STOP],false); 

521 

522 

523 
(* Compute Congruence rules for individual constants using the substition 

524 
rules *) 

525 

526 
val subst_thms = map standard subst_thms; 

527 

528 

529 
fun exp_app(0,t) = t 

530 
 exp_app(i,t) = exp_app(i1,t $ Bound (i1)); 

531 

532 
fun exp_abs(Type("fun",[T1,T2]),t,i) = 

1459  533 
Abs("x"^string_of_int i,T1,exp_abs(T2,t,i+1)) 
0  534 
 exp_abs(T,t,i) = exp_app(i,t); 
535 

536 
fun eta_Var(ixn,T) = exp_abs(T,Var(ixn,T),0); 

537 

538 

539 
fun Pinst(f,fT,(eq,eqT),k,i,T,yik,Ts) = 

540 
let fun xn_list(x,n) = 

1459  541 
let val ixs = map (fn i => (x^(radixstring(26,"a",i)),0)) (0 upto n); 
2266  542 
in ListPair.map eta_Var (ixs, take(n+1,Ts)) end 
0  543 
val lhs = list_comb(f,xn_list("X",k1)) 
544 
val rhs = list_comb(f,xn_list("X",i1) @ [Bound 0] @ yik) 

545 
in Abs("", T, Const(eq,[fT,fT]>eqT) $ lhs $ rhs) end; 

546 

547 
fun find_subst tsig T = 

548 
let fun find (thm::thms) = 

1459  549 
let val (Const(_,cT), va, vb) = dest_red(hd(prems_of thm)); 
550 
val [P] = add_term_vars(concl_of thm,[]) \\ [va,vb] 

551 
val eqT::_ = binder_types cT 

0  552 
in if Type.typ_instance(tsig,T,eqT) then Some(thm,va,vb,P) 
1459  553 
else find thms 
554 
end 

0  555 
 find [] = None 
556 
in find subst_thms end; 

557 

558 
fun mk_cong sg (f,aTs,rT) (refl,eq) = 

559 
let val tsig = #tsig(Sign.rep_sg sg); 

560 
val k = length aTs; 

561 
fun ri((subst,va as Var(_,Ta),vb as Var(_,Tb),P),i,si,T,yik) = 

1459  562 
let val ca = cterm_of sg va 
563 
and cx = cterm_of sg (eta_Var(("X"^si,0),T)) 

564 
val cb = cterm_of sg vb 

565 
and cy = cterm_of sg (eta_Var(("Y"^si,0),T)) 

566 
val cP = cterm_of sg P 

567 
and cp = cterm_of sg (Pinst(f,rT,eq,k,i,T,yik,aTs)) 

568 
in cterm_instantiate [(ca,cx),(cb,cy),(cP,cp)] subst end; 

0  569 
fun mk(c,T::Ts,i,yik) = 
1459  570 
let val si = radixstring(26,"a",i) 
571 
in case find_subst tsig T of 

572 
None => mk(c,Ts,i1,eta_Var(("X"^si,0),T)::yik) 

573 
 Some s => let val c' = c RSN (2,ri(s,i,si,T,yik)) 

574 
in mk(c',Ts,i1,eta_Var(("Y"^si,0),T)::yik) end 

575 
end 

0  576 
 mk(c,[],_,_) = c; 
577 
in mk(refl,rev aTs,k1,[]) end; 

578 

579 
fun mk_cong_type sg (f,T) = 

580 
let val (aTs,rT) = strip_type T; 

581 
val tsig = #tsig(Sign.rep_sg sg); 

582 
fun find_refl(r::rs) = 

1459  583 
let val (Const(eq,eqT),_,_) = dest_red(concl_of r) 
584 
in if Type.typ_instance(tsig, rT, hd(binder_types eqT)) 

585 
then Some(r,(eq,body_type eqT)) else find_refl rs 

586 
end 

0  587 
 find_refl([]) = None; 
588 
in case find_refl refl_thms of 

589 
None => []  Some(refl) => [mk_cong sg (f,aTs,rT) refl] 

590 
end; 

591 

592 
fun mk_cong_thy thy f = 

593 
let val sg = sign_of thy; 

611  594 
val T = case Sign.const_type sg f of 
1459  595 
None => error(f^" not declared")  Some(T) => T; 
0  596 
val T' = incr_tvar 9 T; 
597 
in mk_cong_type sg (Const(f,T'),T') end; 

598 

599 
fun mk_congs thy = flat o map (mk_cong_thy thy); 

600 

601 
fun mk_typed_congs thy = 

602 
let val sg = sign_of thy; 

603 
val S0 = Type.defaultS(#tsig(Sign.rep_sg sg)) 

604 
fun readfT(f,s) = 

1459  605 
let val T = incr_tvar 9 (Sign.read_typ(sg,K(Some(S0))) s); 
606 
val t = case Sign.const_type sg f of 

607 
Some(_) => Const(f,T)  None => Free(f,T) 

608 
in (t,T) end 

0  609 
in flat o map (mk_cong_type sg o readfT) end; 
610 

611 
end (* local *) 

612 
end (* SIMP *); 