author  wenzelm 
Sat, 08 Jul 2006 12:54:50 +0200  
changeset 20062  60de4603e645 
parent 19927  9286e99b2808 
child 20088  bffda4cd0f79 
permissions  rwrr 
10769  1 
(* Title: TFL/tfl.ML 
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ID: $Id$ 

3 
Author: Konrad Slind, Cambridge University Computer Laboratory 

4 
Copyright 1997 University of Cambridge 

5 

6 
First part of main module. 

7 
*) 

8 

9 
signature PRIM = 

10 
sig 

11 
val trace: bool ref 

14240  12 
val trace_thms: string > thm list > unit 
13 
val trace_cterms: string > cterm list > unit 

10769  14 
type pattern 
15 
val mk_functional: theory > term list > {functional: term, pats: pattern list} 

16 
val wfrec_definition0: theory > string > term > term > theory * thm 

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val post_definition: thm list > theory * (thm * pattern list) > 

20062  18 
{rules: thm, 
10769  19 
rows: int list, 
20 
TCs: term list list, 

21 
full_pats_TCs: (term * term list) list} 

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val wfrec_eqns: theory > xstring > thm list > term list > 

23 
{WFR: term, 

24 
SV: term list, 

25 
proto_def: term, 

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extracta: (thm * term list) list, 

27 
pats: pattern list} 

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val lazyR_def: theory > xstring > thm list > term list > 

29 
{theory: theory, 

30 
rules: thm, 

31 
R: term, 

32 
SV: term list, 

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full_pats_TCs: (term * term list) list, 

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patterns : pattern list} 

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val mk_induction: theory > 

36 
{fconst: term, R: term, SV: term list, pat_TCs_list: (term * term list) list} > thm 

11632  37 
val postprocess: bool > {wf_tac: tactic, terminator: tactic, simplifier: cterm > thm} 
38 
> theory > {rules: thm, induction: thm, TCs: term list list} 

39 
> {rules: thm, induction: thm, nested_tcs: thm list} 

10769  40 
end; 
41 

42 
structure Prim: PRIM = 

43 
struct 

44 

45 
val trace = ref false; 

46 

47 
structure R = Rules; 

48 
structure S = USyntax; 

49 
structure U = Utils; 

50 

51 

52 
fun TFL_ERR func mesg = U.ERR {module = "Tfl", func = func, mesg = mesg}; 

53 

54 
val concl = #2 o R.dest_thm; 

55 
val hyp = #1 o R.dest_thm; 

56 

57 
val list_mk_type = U.end_itlist (curry (op >)); 

58 

59 
fun enumerate xs = ListPair.zip(xs, 0 upto (length xs  1)); 

60 

61 
fun front_last [] = raise TFL_ERR "front_last" "empty list" 

62 
 front_last [x] = ([],x) 

63 
 front_last (h::t) = 

64 
let val (pref,x) = front_last t 

65 
in 

66 
(h::pref,x) 

67 
end; 

68 

69 

70 
(* 

71 
* The next function is common to patternmatch translation and 

72 
* proof of completeness of cases for the induction theorem. 

73 
* 

74 
* The curried function "gvvariant" returns a function to generate distinct 

75 
* variables that are guaranteed not to be in names. The names of 

76 
* the variables go u, v, ..., z, aa, ..., az, ... The returned 

77 
* function contains embedded refs! 

78 
**) 

79 
fun gvvariant names = 

80 
let val slist = ref names 

81 
val vname = ref "u" 

82 
fun new() = 

83 
if !vname mem_string (!slist) 

12902  84 
then (vname := Symbol.bump_string (!vname); new()) 
10769  85 
else (slist := !vname :: !slist; !vname) 
86 
in 

87 
fn ty => Free(new(), ty) 

88 
end; 

89 

90 

91 
(* 

92 
* Used in induction theorem production. This is the simple case of 

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* partitioning up pattern rows by the leading constructor. 

94 
**) 

95 
fun ipartition gv (constructors,rows) = 

96 
let fun pfail s = raise TFL_ERR "partition.part" s 

97 
fun part {constrs = [], rows = [], A} = rev A 

98 
 part {constrs = [], rows = _::_, A} = pfail"extra cases in defn" 

99 
 part {constrs = _::_, rows = [], A} = pfail"cases missing in defn" 

100 
 part {constrs = c::crst, rows, A} = 

16505  101 
let val (c, T) = dest_Const c 
102 
val L = binder_types T 

10769  103 
val (in_group, not_in_group) = 
16853  104 
fold_rev (fn (row as (p::rst, rhs)) => 
10769  105 
fn (in_group,not_in_group) => 
106 
let val (pc,args) = S.strip_comb p 

16505  107 
in if (#1(dest_Const pc) = c) 
10769  108 
then ((args@rst, rhs)::in_group, not_in_group) 
109 
else (in_group, row::not_in_group) 

110 
end) rows ([],[]) 

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val col_types = U.take type_of (length L, #1(hd in_group)) 

112 
in 

113 
part{constrs = crst, rows = not_in_group, 

114 
A = {constructor = c, 

115 
new_formals = map gv col_types, 

116 
group = in_group}::A} 

117 
end 

118 
in part{constrs = constructors, rows = rows, A = []} 

119 
end; 

120 

121 

122 

123 
(* 

124 
* Each pattern carries with it a tag (i,b) where 

125 
* i is the clause it came from and 

126 
* b=true indicates that clause was given by the user 

127 
* (or is an instantiation of a user supplied pattern) 

128 
* b=false > i = ~1 

129 
**) 

130 

131 
type pattern = term * (int * bool) 

132 

133 
fun pattern_map f (tm,x) = (f tm, x); 

134 

135 
fun pattern_subst theta = pattern_map (subst_free theta); 

136 

137 
val pat_of = fst; 

138 
fun row_of_pat x = fst (snd x); 

139 
fun given x = snd (snd x); 

140 

141 
(* 

142 
* Produce an instance of a constructor, plus genvars for its arguments. 

143 
**) 

144 
fun fresh_constr ty_match colty gv c = 

145 
let val (_,Ty) = dest_Const c 

146 
val L = binder_types Ty 

147 
and ty = body_type Ty 

148 
val ty_theta = ty_match ty colty 

149 
val c' = S.inst ty_theta c 

150 
val gvars = map (S.inst ty_theta o gv) L 

151 
in (c', gvars) 

152 
end; 

153 

154 

155 
(* 

156 
* Goes through a list of rows and picks out the ones beginning with a 

16505  157 
* pattern with constructor = name. 
10769  158 
**) 
16505  159 
fun mk_group name rows = 
16853  160 
fold_rev (fn (row as ((prfx, p::rst), rhs)) => 
10769  161 
fn (in_group,not_in_group) => 
162 
let val (pc,args) = S.strip_comb p 

16505  163 
in if ((#1 (Term.dest_Const pc) = name) handle TERM _ => false) 
10769  164 
then (((prfx,args@rst), rhs)::in_group, not_in_group) 
165 
else (in_group, row::not_in_group) end) 

166 
rows ([],[]); 

167 

168 
(* 

169 
* Partition the rows. Not efficient: we should use hashing. 

170 
**) 

171 
fun partition _ _ (_,_,_,[]) = raise TFL_ERR "partition" "no rows" 

172 
 partition gv ty_match 

173 
(constructors, colty, res_ty, rows as (((prfx,_),_)::_)) = 

174 
let val fresh = fresh_constr ty_match colty gv 

175 
fun part {constrs = [], rows, A} = rev A 

176 
 part {constrs = c::crst, rows, A} = 

177 
let val (c',gvars) = fresh c 

16505  178 
val (in_group, not_in_group) = mk_group (#1 (dest_Const c')) rows 
10769  179 
val in_group' = 
180 
if (null in_group) (* Constructor not given *) 

181 
then [((prfx, #2(fresh c)), (S.ARB res_ty, (~1,false)))] 

182 
else in_group 

183 
in 

184 
part{constrs = crst, 

185 
rows = not_in_group, 

186 
A = {constructor = c', 

187 
new_formals = gvars, 

188 
group = in_group'}::A} 

189 
end 

190 
in part{constrs=constructors, rows=rows, A=[]} 

191 
end; 

192 

193 
(* 

194 
* Misc. routines used in mk_case 

195 
**) 

196 

197 
fun mk_pat (c,l) = 

198 
let val L = length (binder_types (type_of c)) 

199 
fun build (prfx,tag,plist) = 

15570  200 
let val args = Library.take (L,plist) 
201 
and plist' = Library.drop(L,plist) 

10769  202 
in (prfx,tag,list_comb(c,args)::plist') end 
203 
in map build l end; 

204 

205 
fun v_to_prfx (prfx, v::pats) = (v::prfx,pats) 

206 
 v_to_prfx _ = raise TFL_ERR "mk_case" "v_to_prfx"; 

207 

208 
fun v_to_pats (v::prfx,tag, pats) = (prfx, tag, v::pats) 

209 
 v_to_pats _ = raise TFL_ERR "mk_case" "v_to_pats"; 

210 

211 

212 
(* 

213 
* Translation of pattern terms into nested case expressions. 

214 
* 

215 
* This performs the translation and also builds the full set of patterns. 

216 
* Thus it supports the construction of induction theorems even when an 

217 
* incomplete set of patterns is given. 

218 
**) 

219 

220 
fun mk_case ty_info ty_match usednames range_ty = 

221 
let 

222 
fun mk_case_fail s = raise TFL_ERR "mk_case" s 

223 
val fresh_var = gvvariant usednames 

224 
val divide = partition fresh_var ty_match 

225 
fun expand constructors ty ((_,[]), _) = mk_case_fail"expand_var_row" 

226 
 expand constructors ty (row as ((prfx, p::rst), rhs)) = 

227 
if (is_Free p) 

228 
then let val fresh = fresh_constr ty_match ty fresh_var 

229 
fun expnd (c,gvs) = 

230 
let val capp = list_comb(c,gvs) 

231 
in ((prfx, capp::rst), pattern_subst[(p,capp)] rhs) 

232 
end 

233 
in map expnd (map fresh constructors) end 

234 
else [row] 

235 
fun mk{rows=[],...} = mk_case_fail"no rows" 

236 
 mk{path=[], rows = ((prfx, []), (tm,tag))::_} = (* Done *) 

237 
([(prfx,tag,[])], tm) 

238 
 mk{path=[], rows = _::_} = mk_case_fail"blunder" 

239 
 mk{path as u::rstp, rows as ((prfx, []), rhs)::rst} = 

240 
mk{path = path, 

241 
rows = ((prfx, [fresh_var(type_of u)]), rhs)::rst} 

242 
 mk{path = u::rstp, rows as ((_, p::_), _)::_} = 

243 
let val (pat_rectangle,rights) = ListPair.unzip rows 

244 
val col0 = map(hd o #2) pat_rectangle 

245 
in 

246 
if (forall is_Free col0) 

247 
then let val rights' = map (fn(v,e) => pattern_subst[(v,u)] e) 

248 
(ListPair.zip (col0, rights)) 

249 
val pat_rectangle' = map v_to_prfx pat_rectangle 

250 
val (pref_patl,tm) = mk{path = rstp, 

251 
rows = ListPair.zip (pat_rectangle', 

252 
rights')} 

253 
in (map v_to_pats pref_patl, tm) 

254 
end 

255 
else 

256 
let val pty as Type (ty_name,_) = type_of p 

257 
in 

258 
case (ty_info ty_name) 

15531  259 
of NONE => mk_case_fail("Not a known datatype: "^ty_name) 
260 
 SOME{case_const,constructors} => 

10769  261 
let 
262 
val case_const_name = #1(dest_Const case_const) 

263 
val nrows = List.concat (map (expand constructors pty) rows) 

264 
val subproblems = divide(constructors, pty, range_ty, nrows) 

265 
val groups = map #group subproblems 

266 
and new_formals = map #new_formals subproblems 

267 
and constructors' = map #constructor subproblems 

268 
val news = map (fn (nf,rows) => {path = nf@rstp, rows=rows}) 

269 
(ListPair.zip (new_formals, groups)) 

270 
val rec_calls = map mk news 

271 
val (pat_rect,dtrees) = ListPair.unzip rec_calls 

272 
val case_functions = map S.list_mk_abs 

273 
(ListPair.zip (new_formals, dtrees)) 

274 
val types = map type_of (case_functions@[u]) @ [range_ty] 

275 
val case_const' = Const(case_const_name, list_mk_type types) 

276 
val tree = list_comb(case_const', case_functions@[u]) 

277 
val pat_rect1 = List.concat 

278 
(ListPair.map mk_pat (constructors', pat_rect)) 

279 
in (pat_rect1,tree) 

280 
end 

281 
end end 

282 
in mk 

283 
end; 

284 

285 

286 
(* Repeated variable occurrences in a pattern are not allowed. *) 

287 
fun FV_multiset tm = 

288 
case (S.dest_term tm) 

16505  289 
of S.VAR{Name = c, Ty = T} => [Free(c, T)] 
10769  290 
 S.CONST _ => [] 
291 
 S.COMB{Rator, Rand} => FV_multiset Rator @ FV_multiset Rand 

292 
 S.LAMB _ => raise TFL_ERR "FV_multiset" "lambda"; 

293 

294 
fun no_repeat_vars thy pat = 

295 
let fun check [] = true 

296 
 check (v::rst) = 

297 
if mem_term (v,rst) then 

298 
raise TFL_ERR "no_repeat_vars" 

299 
(quote (#1 (dest_Free v)) ^ 

300 
" occurs repeatedly in the pattern " ^ 

301 
quote (string_of_cterm (Thry.typecheck thy pat))) 

302 
else check rst 

303 
in check (FV_multiset pat) 

304 
end; 

305 

306 
fun dest_atom (Free p) = p 

307 
 dest_atom (Const p) = p 

308 
 dest_atom _ = raise TFL_ERR "dest_atom" "function name not an identifier"; 

309 

310 
fun same_name (p,q) = #1(dest_atom p) = #1(dest_atom q); 

311 

312 
local fun mk_functional_err s = raise TFL_ERR "mk_functional" s 

313 
fun single [_$_] = 

314 
mk_functional_err "recdef does not allow currying" 

315 
 single [f] = f 

316 
 single fs = 

317 
(*multiple function names?*) 

19046
bc5c6c9b114e
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wenzelm
parents:
18972
diff
changeset

318 
if length (distinct same_name fs) < length fs 
10769  319 
then mk_functional_err 
320 
"The function being declared appears with multiple types" 

321 
else mk_functional_err 

322 
(Int.toString (length fs) ^ 

323 
" distinct function names being declared") 

324 
in 

325 
fun mk_functional thy clauses = 

326 
let val (L,R) = ListPair.unzip (map HOLogic.dest_eq clauses 

327 
handle TERM _ => raise TFL_ERR "mk_functional" 

328 
"recursion equations must use the = relation") 

329 
val (funcs,pats) = ListPair.unzip (map (fn (t$u) =>(t,u)) L) 

19046
bc5c6c9b114e
removed distinct, renamed gen_distinct to distinct;
wenzelm
parents:
18972
diff
changeset

330 
val atom = single (distinct (op aconv) funcs) 
10769  331 
val (fname,ftype) = dest_atom atom 
332 
val dummy = map (no_repeat_vars thy) pats 

333 
val rows = ListPair.zip (map (fn x => ([]:term list,[x])) pats, 

334 
map (fn (t,i) => (t,(i,true))) (enumerate R)) 

15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset

335 
val names = foldr add_term_names [] R 
10769  336 
val atype = type_of(hd pats) 
337 
and aname = variant names "a" 

338 
val a = Free(aname,atype) 

339 
val ty_info = Thry.match_info thy 

340 
val ty_match = Thry.match_type thy 

341 
val range_ty = type_of (hd R) 

342 
val (patts, case_tm) = mk_case ty_info ty_match (aname::names) range_ty 

343 
{path=[a], rows=rows} 

344 
val patts1 = map (fn (_,tag,[pat]) => (pat,tag)) patts 

345 
handle Match => mk_functional_err "error in patternmatch translation" 

346 
val patts2 = Library.sort (Library.int_ord o Library.pairself row_of_pat) patts1 

347 
val finals = map row_of_pat patts2 

348 
val originals = map (row_of_pat o #2) rows 

349 
val dummy = case (originals\\finals) 

350 
of [] => () 

351 
 L => mk_functional_err 

352 
("The following clauses are redundant (covered by preceding clauses): " ^ 

353 
commas (map (fn i => Int.toString (i + 1)) L)) 

354 
in {functional = Abs(Sign.base_name fname, ftype, 

355 
abstract_over (atom, 

356 
absfree(aname,atype, case_tm))), 

357 
pats = patts2} 

358 
end end; 

359 

360 

361 
(* 

362 
* 

363 
* PRINCIPLES OF DEFINITION 

364 
* 

365 
**) 

366 

367 

368 
(*For Isabelle, the lhs of a definition must be a constant.*) 

16505  369 
fun mk_const_def sign (c, Ty, rhs) = 
18972  370 
Sign.infer_types (Sign.pp sign) sign (Sign.consts_of sign) (K NONE) (K NONE) [] false 
16505  371 
([Const("==",dummyT) $ Const(c,Ty) $ rhs], propT) 
10769  372 
> #1; 
373 

374 
(*Make all TVars available for instantiation by adding a ? to the front*) 

375 
fun poly_tvars (Type(a,Ts)) = Type(a, map (poly_tvars) Ts) 

376 
 poly_tvars (TFree (a,sort)) = TVar (("?" ^ a, 0), sort) 

377 
 poly_tvars (TVar ((a,i),sort)) = TVar (("?" ^ a, i+1), sort); 

378 

379 
local val f_eq_wfrec_R_M = 

380 
#ant(S.dest_imp(#2(S.strip_forall (concl Thms.WFREC_COROLLARY)))) 

381 
val {lhs=f, rhs} = S.dest_eq f_eq_wfrec_R_M 

382 
val (fname,_) = dest_Free f 

383 
val (wfrec,_) = S.strip_comb rhs 

384 
in 

16505  385 
fun wfrec_definition0 thy fid R (functional as Abs(x, Ty, _)) = 
386 
let val def_name = if x<>fid then 

10769  387 
raise TFL_ERR "wfrec_definition0" 
388 
("Expected a definition of " ^ 

389 
quote fid ^ " but found one of " ^ 

16505  390 
quote x) 
391 
else x ^ "_def" 

10769  392 
val wfrec_R_M = map_term_types poly_tvars 
393 
(wfrec $ map_term_types poly_tvars R) 

394 
$ functional 

16505  395 
val def_term = mk_const_def (Theory.sign_of thy) (x, Ty, wfrec_R_M) 
18358  396 
val ([def], thy') = PureThy.add_defs_i false [Thm.no_attributes (def_name, def_term)] thy 
10769  397 
in (thy', def) end; 
398 
end; 

399 

400 

401 

402 
(* 

403 
* This structure keeps track of congruence rules that aren't derived 

404 
* from a datatype definition. 

405 
**) 

406 
fun extraction_thms thy = 

407 
let val {case_rewrites,case_congs} = Thry.extract_info thy 

408 
in (case_rewrites, case_congs) 

409 
end; 

410 

411 

412 
(* 

413 
* Pair patterns with termination conditions. The full list of patterns for 

414 
* a definition is merged with the TCs arising from the usergiven clauses. 

415 
* There can be fewer clauses than the full list, if the user omitted some 

416 
* cases. This routine is used to prepare input for mk_induction. 

417 
**) 

418 
fun merge full_pats TCs = 

419 
let fun insert (p,TCs) = 

420 
let fun insrt ((x as (h,[]))::rst) = 

421 
if (p aconv h) then (p,TCs)::rst else x::insrt rst 

422 
 insrt (x::rst) = x::insrt rst 

423 
 insrt[] = raise TFL_ERR "merge.insert" "pattern not found" 

424 
in insrt end 

425 
fun pass ([],ptcl_final) = ptcl_final 

426 
 pass (ptcs::tcl, ptcl) = pass(tcl, insert ptcs ptcl) 

427 
in 

428 
pass (TCs, map (fn p => (p,[])) full_pats) 

429 
end; 

430 

431 

15570  432 
fun givens pats = map pat_of (List.filter given pats); 
10769  433 

434 
fun post_definition meta_tflCongs (theory, (def, pats)) = 

435 
let val tych = Thry.typecheck theory 

436 
val f = #lhs(S.dest_eq(concl def)) 

437 
val corollary = R.MATCH_MP Thms.WFREC_COROLLARY def 

15570  438 
val pats' = List.filter given pats 
10769  439 
val given_pats = map pat_of pats' 
440 
val rows = map row_of_pat pats' 

441 
val WFR = #ant(S.dest_imp(concl corollary)) 

442 
val R = #Rand(S.dest_comb WFR) 

443 
val corollary' = R.UNDISCH corollary (* put WF R on assums *) 

444 
val corollaries = map (fn pat => R.SPEC (tych pat) corollary') 

445 
given_pats 

446 
val (case_rewrites,context_congs) = extraction_thms theory 

14219  447 
(*case_ss causes minimal simplification: bodies of case expressions are 
16505  448 
not simplified. Otherwise large examples (RedBlack trees) are too 
14219  449 
slow.*) 
20062  450 
val case_ss = Simplifier.theory_context theory 
451 
(HOL_basic_ss addcongs 

452 
(map (#weak_case_cong o snd) o Symtab.dest o DatatypePackage.get_datatypes) theory addsimps case_rewrites) 

14217
9f5679e97eac
Fixed inefficiency in post_definition by adding weak case congruence
berghofe
parents:
12902
diff
changeset

453 
val corollaries' = map (Simplifier.simplify case_ss) corollaries 
10769  454 
val extract = R.CONTEXT_REWRITE_RULE 
455 
(f, [R], cut_apply, meta_tflCongs@context_congs) 

456 
val (rules, TCs) = ListPair.unzip (map extract corollaries') 

457 
val rules0 = map (rewrite_rule [Thms.CUT_DEF]) rules 

458 
val mk_cond_rule = R.FILTER_DISCH_ALL(not o curry (op aconv) WFR) 

459 
val rules1 = R.LIST_CONJ(map mk_cond_rule rules0) 

460 
in 

20062  461 
{rules = rules1, 
10769  462 
rows = rows, 
463 
full_pats_TCs = merge (map pat_of pats) (ListPair.zip (given_pats, TCs)), 

464 
TCs = TCs} 

465 
end; 

466 

467 

468 
(* 

469 
* Perform the extraction without making the definition. Definition and 

470 
* extraction commute for the nonnested case. (Deferred recdefs) 

471 
* 

472 
* The purpose of wfrec_eqns is merely to instantiate the recursion theorem 

473 
* and extract termination conditions: no definition is made. 

474 
**) 

475 

476 
fun wfrec_eqns thy fid tflCongs eqns = 

477 
let val {lhs,rhs} = S.dest_eq (hd eqns) 

478 
val (f,args) = S.strip_comb lhs 

479 
val (fname,fty) = dest_atom f 

480 
val (SV,a) = front_last args (* SV = schematic variables *) 

481 
val g = list_comb(f,SV) 

482 
val h = Free(fname,type_of g) 

483 
val eqns1 = map (subst_free[(g,h)]) eqns 

16505  484 
val {functional as Abs(x, Ty, _), pats} = mk_functional thy eqns1 
10769  485 
val given_pats = givens pats 
16505  486 
(* val f = Free(x,Ty) *) 
10769  487 
val Type("fun", [f_dty, f_rty]) = Ty 
16505  488 
val dummy = if x<>fid then 
10769  489 
raise TFL_ERR "wfrec_eqns" 
490 
("Expected a definition of " ^ 

491 
quote fid ^ " but found one of " ^ 

16505  492 
quote x) 
10769  493 
else () 
494 
val (case_rewrites,context_congs) = extraction_thms thy 

495 
val tych = Thry.typecheck thy 

496 
val WFREC_THM0 = R.ISPEC (tych functional) Thms.WFREC_COROLLARY 

497 
val Const("All",_) $ Abs(Rname,Rtype,_) = concl WFREC_THM0 

15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset

498 
val R = Free (variant (foldr add_term_names [] eqns) Rname, 
10769  499 
Rtype) 
500 
val WFREC_THM = R.ISPECL [tych R, tych g] WFREC_THM0 

501 
val ([proto_def, WFR],_) = S.strip_imp(concl WFREC_THM) 

502 
val dummy = 

503 
if !trace then 

504 
writeln ("ORIGINAL PROTO_DEF: " ^ 

505 
Sign.string_of_term (Theory.sign_of thy) proto_def) 

506 
else () 

507 
val R1 = S.rand WFR 

508 
val corollary' = R.UNDISCH(R.UNDISCH WFREC_THM) 

509 
val corollaries = map (fn pat => R.SPEC (tych pat) corollary') given_pats 

510 
val corollaries' = map (rewrite_rule case_rewrites) corollaries 

511 
fun extract X = R.CONTEXT_REWRITE_RULE 

512 
(f, R1::SV, cut_apply, tflCongs@context_congs) X 

513 
in {proto_def = proto_def, 

514 
SV=SV, 

515 
WFR=WFR, 

516 
pats=pats, 

517 
extracta = map extract corollaries'} 

518 
end; 

519 

520 

521 
(* 

522 
* Define the constant after extracting the termination conditions. The 

523 
* wellfounded relation used in the definition is computed by using the 

524 
* choice operator on the extracted conditions (plus the condition that 

525 
* such a relation must be wellfounded). 

526 
**) 

527 

528 
fun lazyR_def thy fid tflCongs eqns = 

529 
let val {proto_def,WFR,pats,extracta,SV} = 

530 
wfrec_eqns thy fid tflCongs eqns 

531 
val R1 = S.rand WFR 

532 
val f = #lhs(S.dest_eq proto_def) 

533 
val (extractants,TCl) = ListPair.unzip extracta 

534 
val dummy = if !trace 

535 
then (writeln "Extractants = "; 

536 
prths extractants; 

537 
()) 

538 
else () 

15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset

539 
val TCs = foldr (gen_union (op aconv)) [] TCl 
10769  540 
val full_rqt = WFR::TCs 
541 
val R' = S.mk_select{Bvar=R1, Body=S.list_mk_conj full_rqt} 

542 
val R'abs = S.rand R' 

543 
val proto_def' = subst_free[(R1,R')] proto_def 

544 
val dummy = if !trace then writeln ("proto_def' = " ^ 

545 
Sign.string_of_term 

546 
(Theory.sign_of thy) proto_def') 

547 
else () 

548 
val {lhs,rhs} = S.dest_eq proto_def' 

549 
val (c,args) = S.strip_comb lhs 

16505  550 
val (name,Ty) = dest_atom c 
10769  551 
val defn = mk_const_def (Theory.sign_of thy) 
16505  552 
(name, Ty, S.list_mk_abs (args,rhs)) 
18358  553 
val ([def0], theory) = 
10769  554 
thy 
555 
> PureThy.add_defs_i false 

556 
[Thm.no_attributes (fid ^ "_def", defn)] 

19927
9286e99b2808
refrain from reforming TFL  back to previous revision;
wenzelm
parents:
19925
diff
changeset

557 
val def = Thm.freezeT def0; 
10769  558 
val dummy = if !trace then writeln ("DEF = " ^ string_of_thm def) 
559 
else () 

560 
(* val fconst = #lhs(S.dest_eq(concl def)) *) 

561 
val tych = Thry.typecheck theory 

562 
val full_rqt_prop = map (Dcterm.mk_prop o tych) full_rqt 

563 
(*lcp: a lot of objectlogic inference to remove*) 

564 
val baz = R.DISCH_ALL 

16853  565 
(fold_rev R.DISCH full_rqt_prop 
10769  566 
(R.LIST_CONJ extractants)) 
567 
val dum = if !trace then writeln ("baz = " ^ string_of_thm baz) 

568 
else () 

569 
val f_free = Free (fid, fastype_of f) (*'cos f is a Const*) 

570 
val SV' = map tych SV; 

571 
val SVrefls = map reflexive SV' 

16853  572 
val def0 = (fold (fn x => fn th => R.rbeta(combination th x)) 
10769  573 
SVrefls def) 
574 
RS meta_eq_to_obj_eq 

575 
val def' = R.MP (R.SPEC (tych R') (R.GEN (tych R1) baz)) def0 

576 
val body_th = R.LIST_CONJ (map R.ASSUME full_rqt_prop) 

11455
e07927b980ec
defer_recdef (lazyR_def) now looks for theorem Hilbert_Choice.tfl_some
paulson
parents:
10769
diff
changeset

577 
val SELECT_AX = (*in this way we hope to avoid a STATIC dependence upon 
e07927b980ec
defer_recdef (lazyR_def) now looks for theorem Hilbert_Choice.tfl_some
paulson
parents:
10769
diff
changeset

578 
theory Hilbert_Choice*) 
16505  579 
thm "Hilbert_Choice.tfl_some" 
18678  580 
handle ERROR msg => cat_error msg 
11455
e07927b980ec
defer_recdef (lazyR_def) now looks for theorem Hilbert_Choice.tfl_some
paulson
parents:
10769
diff
changeset

581 
"defer_recdef requires theory Main or at least Hilbert_Choice as parent" 
e07927b980ec
defer_recdef (lazyR_def) now looks for theorem Hilbert_Choice.tfl_some
paulson
parents:
10769
diff
changeset

582 
val bar = R.MP (R.ISPECL[tych R'abs, tych R1] SELECT_AX) body_th 
10769  583 
in {theory = theory, R=R1, SV=SV, 
16853  584 
rules = fold (U.C R.MP) (R.CONJUNCTS bar) def', 
10769  585 
full_pats_TCs = merge (map pat_of pats) (ListPair.zip (givens pats, TCl)), 
586 
patterns = pats} 

587 
end; 

588 

589 

590 

591 
(* 

592 
* 

593 
* INDUCTION THEOREM 

594 
* 

595 
**) 

596 

597 

598 
(* Miscellaneous function  

599 
* 

600 
* [x_1,...,x_n] ?v_1...v_n. M[v_1,...,v_n] 

601 
*  

602 
* ( M[x_1,...,x_n], [(x_i,?v_1...v_n. M[v_1,...,v_n]), 

603 
* ... 

604 
* (x_j,?v_n. M[x_1,...,x_(n1),v_n])] ) 

605 
* 

606 
* This function is totally ad hoc. Used in the production of the induction 

607 
* theorem. The nchotomy theorem can have clauses that look like 

608 
* 

609 
* ?v1..vn. z = C vn..v1 

610 
* 

611 
* in which the order of quantification is not the order of occurrence of the 

612 
* quantified variables as arguments to C. Since we have no control over this 

613 
* aspect of the nchotomy theorem, we make the correspondence explicit by 

614 
* pairing the incoming new variable with the term it gets betareduced into. 

615 
**) 

616 

617 
fun alpha_ex_unroll (xlist, tm) = 

618 
let val (qvars,body) = S.strip_exists tm 

619 
val vlist = #2(S.strip_comb (S.rhs body)) 

620 
val plist = ListPair.zip (vlist, xlist) 

17314  621 
val args = map (the o AList.lookup (op aconv) plist) qvars 
15531  622 
handle Option => sys_error 
10769  623 
"TFL fault [alpha_ex_unroll]: no correspondence" 
624 
fun build ex [] = [] 

625 
 build (_$rex) (v::rst) = 

18176  626 
let val ex1 = Term.betapply(rex, v) 
10769  627 
in ex1 :: build ex1 rst 
628 
end 

629 
val (nex::exl) = rev (tm::build tm args) 

630 
in 

631 
(nex, ListPair.zip (args, rev exl)) 

632 
end; 

633 

634 

635 

636 
(* 

637 
* 

638 
* PROVING COMPLETENESS OF PATTERNS 

639 
* 

640 
**) 

641 

642 
fun mk_case ty_info usednames thy = 

643 
let 

644 
val divide = ipartition (gvvariant usednames) 

645 
val tych = Thry.typecheck thy 

646 
fun tych_binding(x,y) = (tych x, tych y) 

647 
fun fail s = raise TFL_ERR "mk_case" s 

648 
fun mk{rows=[],...} = fail"no rows" 

649 
 mk{path=[], rows = [([], (thm, bindings))]} = 

650 
R.IT_EXISTS (map tych_binding bindings) thm 

651 
 mk{path = u::rstp, rows as (p::_, _)::_} = 

652 
let val (pat_rectangle,rights) = ListPair.unzip rows 

653 
val col0 = map hd pat_rectangle 

654 
val pat_rectangle' = map tl pat_rectangle 

655 
in 

656 
if (forall is_Free col0) (* column 0 is all variables *) 

657 
then let val rights' = map (fn ((thm,theta),v) => (thm,theta@[(u,v)])) 

658 
(ListPair.zip (rights, col0)) 

659 
in mk{path = rstp, rows = ListPair.zip (pat_rectangle', rights')} 

660 
end 

661 
else (* column 0 is all constructors *) 

662 
let val Type (ty_name,_) = type_of p 

663 
in 

664 
case (ty_info ty_name) 

15531  665 
of NONE => fail("Not a known datatype: "^ty_name) 
666 
 SOME{constructors,nchotomy} => 

10769  667 
let val thm' = R.ISPEC (tych u) nchotomy 
668 
val disjuncts = S.strip_disj (concl thm') 

669 
val subproblems = divide(constructors, rows) 

670 
val groups = map #group subproblems 

671 
and new_formals = map #new_formals subproblems 

672 
val existentials = ListPair.map alpha_ex_unroll 

673 
(new_formals, disjuncts) 

674 
val constraints = map #1 existentials 

675 
val vexl = map #2 existentials 

676 
fun expnd tm (pats,(th,b)) = (pats,(R.SUBS[R.ASSUME(tych tm)]th,b)) 

677 
val news = map (fn (nf,rows,c) => {path = nf@rstp, 

678 
rows = map (expnd c) rows}) 

679 
(U.zip3 new_formals groups constraints) 

680 
val recursive_thms = map mk news 

15570  681 
val build_exists = Library.foldr 
10769  682 
(fn((x,t), th) => 
683 
R.CHOOSE (tych x, R.ASSUME (tych t)) th) 

684 
val thms' = ListPair.map build_exists (vexl, recursive_thms) 

685 
val same_concls = R.EVEN_ORS thms' 

686 
in R.DISJ_CASESL thm' same_concls 

687 
end 

688 
end end 

689 
in mk 

690 
end; 

691 

692 

693 
fun complete_cases thy = 

694 
let val tych = Thry.typecheck thy 

695 
val ty_info = Thry.induct_info thy 

696 
in fn pats => 

15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset

697 
let val names = foldr add_term_names [] pats 
10769  698 
val T = type_of (hd pats) 
699 
val aname = Term.variant names "a" 

700 
val vname = Term.variant (aname::names) "v" 

701 
val a = Free (aname, T) 

702 
val v = Free (vname, T) 

703 
val a_eq_v = HOLogic.mk_eq(a,v) 

704 
val ex_th0 = R.EXISTS (tych (S.mk_exists{Bvar=v,Body=a_eq_v}), tych a) 

705 
(R.REFL (tych a)) 

706 
val th0 = R.ASSUME (tych a_eq_v) 

707 
val rows = map (fn x => ([x], (th0,[]))) pats 

708 
in 

709 
R.GEN (tych a) 

710 
(R.RIGHT_ASSOC 

711 
(R.CHOOSE(tych v, ex_th0) 

712 
(mk_case ty_info (vname::aname::names) 

713 
thy {path=[v], rows=rows}))) 

714 
end end; 

715 

716 

717 
(* 

718 
* Constructing induction hypotheses: one for each recursive call. 

719 
* 

720 
* Note. R will never occur as a variable in the ind_clause, because 

721 
* to do so, it would have to be from a nested definition, and we don't 

722 
* allow nested defns to have R variable. 

723 
* 

724 
* Note. When the context is empty, there can be no local variables. 

725 
**) 

726 
(* 

727 
local infix 5 ==> 

728 
fun (tm1 ==> tm2) = S.mk_imp{ant = tm1, conseq = tm2} 

729 
in 

730 
fun build_ih f P (pat,TCs) = 

731 
let val globals = S.free_vars_lr pat 

15570  732 
fun nested tm = isSome (S.find_term (curry (op aconv) f) tm) 
10769  733 
fun dest_TC tm = 
734 
let val (cntxt,R_y_pat) = S.strip_imp(#2(S.strip_forall tm)) 

735 
val (R,y,_) = S.dest_relation R_y_pat 

736 
val P_y = if (nested tm) then R_y_pat ==> P$y else P$y 

737 
in case cntxt 

738 
of [] => (P_y, (tm,[])) 

739 
 _ => let 

740 
val imp = S.list_mk_conj cntxt ==> P_y 

741 
val lvs = gen_rems (op aconv) (S.free_vars_lr imp, globals) 

742 
val locals = #2(U.pluck (curry (op aconv) P) lvs) handle U.ERR _ => lvs 

743 
in (S.list_mk_forall(locals,imp), (tm,locals)) end 

744 
end 

745 
in case TCs 

746 
of [] => (S.list_mk_forall(globals, P$pat), []) 

747 
 _ => let val (ihs, TCs_locals) = ListPair.unzip(map dest_TC TCs) 

748 
val ind_clause = S.list_mk_conj ihs ==> P$pat 

749 
in (S.list_mk_forall(globals,ind_clause), TCs_locals) 

750 
end 

751 
end 

752 
end; 

753 
*) 

754 

755 
local infix 5 ==> 

756 
fun (tm1 ==> tm2) = S.mk_imp{ant = tm1, conseq = tm2} 

757 
in 

758 
fun build_ih f (P,SV) (pat,TCs) = 

759 
let val pat_vars = S.free_vars_lr pat 

760 
val globals = pat_vars@SV 

15570  761 
fun nested tm = isSome (S.find_term (curry (op aconv) f) tm) 
10769  762 
fun dest_TC tm = 
763 
let val (cntxt,R_y_pat) = S.strip_imp(#2(S.strip_forall tm)) 

764 
val (R,y,_) = S.dest_relation R_y_pat 

765 
val P_y = if (nested tm) then R_y_pat ==> P$y else P$y 

766 
in case cntxt 

767 
of [] => (P_y, (tm,[])) 

768 
 _ => let 

769 
val imp = S.list_mk_conj cntxt ==> P_y 

770 
val lvs = gen_rems (op aconv) (S.free_vars_lr imp, globals) 

771 
val locals = #2(U.pluck (curry (op aconv) P) lvs) handle U.ERR _ => lvs 

772 
in (S.list_mk_forall(locals,imp), (tm,locals)) end 

773 
end 

774 
in case TCs 

775 
of [] => (S.list_mk_forall(pat_vars, P$pat), []) 

776 
 _ => let val (ihs, TCs_locals) = ListPair.unzip(map dest_TC TCs) 

777 
val ind_clause = S.list_mk_conj ihs ==> P$pat 

778 
in (S.list_mk_forall(pat_vars,ind_clause), TCs_locals) 

779 
end 

780 
end 

781 
end; 

782 

783 
(* 

784 
* This function makes good on the promise made in "build_ih". 

785 
* 

786 
* Input is tm = "(!y. R y pat ==> P y) ==> P pat", 

787 
* TCs = TC_1[pat] ... TC_n[pat] 

788 
* thm = ih1 /\ ... /\ ih_n  ih[pat] 

789 
**) 

790 
fun prove_case f thy (tm,TCs_locals,thm) = 

791 
let val tych = Thry.typecheck thy 

792 
val antc = tych(#ant(S.dest_imp tm)) 

793 
val thm' = R.SPEC_ALL thm 

15570  794 
fun nested tm = isSome (S.find_term (curry (op aconv) f) tm) 
10769  795 
fun get_cntxt TC = tych(#ant(S.dest_imp(#2(S.strip_forall(concl TC))))) 
796 
fun mk_ih ((TC,locals),th2,nested) = 

797 
R.GENL (map tych locals) 

798 
(if nested then R.DISCH (get_cntxt TC) th2 handle U.ERR _ => th2 

799 
else if S.is_imp (concl TC) then R.IMP_TRANS TC th2 

800 
else R.MP th2 TC) 

801 
in 

802 
R.DISCH antc 

803 
(if S.is_imp(concl thm') (* recursive calls in this clause *) 

804 
then let val th1 = R.ASSUME antc 

805 
val TCs = map #1 TCs_locals 

806 
val ylist = map (#2 o S.dest_relation o #2 o S.strip_imp o 

807 
#2 o S.strip_forall) TCs 

808 
val TClist = map (fn(TC,lvs) => (R.SPEC_ALL(R.ASSUME(tych TC)),lvs)) 

809 
TCs_locals 

810 
val th2list = map (U.C R.SPEC th1 o tych) ylist 

811 
val nlist = map nested TCs 

812 
val triples = U.zip3 TClist th2list nlist 

813 
val Pylist = map mk_ih triples 

814 
in R.MP thm' (R.LIST_CONJ Pylist) end 

815 
else thm') 

816 
end; 

817 

818 

819 
(* 

820 
* 

821 
* x = (v1,...,vn)  M[x] 

822 
*  

823 
* ?v1 ... vn. x = (v1,...,vn)  M[x] 

824 
* 

825 
**) 

826 
fun LEFT_ABS_VSTRUCT tych thm = 

827 
let fun CHOOSER v (tm,thm) = 

828 
let val ex_tm = S.mk_exists{Bvar=v,Body=tm} 

829 
in (ex_tm, R.CHOOSE(tych v, R.ASSUME (tych ex_tm)) thm) 

830 
end 

15570  831 
val [veq] = List.filter (can S.dest_eq) (#1 (R.dest_thm thm)) 
10769  832 
val {lhs,rhs} = S.dest_eq veq 
833 
val L = S.free_vars_lr rhs 

16853  834 
in #2 (fold_rev CHOOSER L (veq,thm)) end; 
10769  835 

836 

837 
(* 

838 
* Input : f, R, and [(pat1,TCs1),..., (patn,TCsn)] 

839 
* 

840 
* Instantiates WF_INDUCTION_THM, getting Sinduct and then tries to prove 

841 
* recursion induction (Rinduct) by proving the antecedent of Sinduct from 

842 
* the antecedent of Rinduct. 

843 
**) 

844 
fun mk_induction thy {fconst, R, SV, pat_TCs_list} = 

845 
let val tych = Thry.typecheck thy 

846 
val Sinduction = R.UNDISCH (R.ISPEC (tych R) Thms.WF_INDUCTION_THM) 

847 
val (pats,TCsl) = ListPair.unzip pat_TCs_list 

848 
val case_thm = complete_cases thy pats 

849 
val domain = (type_of o hd) pats 

15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset

850 
val Pname = Term.variant (foldr (Library.foldr add_term_names) 
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset

851 
[] (pats::TCsl)) "P" 
10769  852 
val P = Free(Pname, domain > HOLogic.boolT) 
853 
val Sinduct = R.SPEC (tych P) Sinduction 

854 
val Sinduct_assumf = S.rand ((#ant o S.dest_imp o concl) Sinduct) 

855 
val Rassums_TCl' = map (build_ih fconst (P,SV)) pat_TCs_list 

856 
val (Rassums,TCl') = ListPair.unzip Rassums_TCl' 

857 
val Rinduct_assum = R.ASSUME (tych (S.list_mk_conj Rassums)) 

18176  858 
val cases = map (fn pat => Term.betapply (Sinduct_assumf, pat)) pats 
10769  859 
val tasks = U.zip3 cases TCl' (R.CONJUNCTS Rinduct_assum) 
860 
val proved_cases = map (prove_case fconst thy) tasks 

15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset

861 
val v = Free (variant (foldr add_term_names [] (map concl proved_cases)) 
10769  862 
"v", 
863 
domain) 

864 
val vtyped = tych v 

865 
val substs = map (R.SYM o R.ASSUME o tych o (curry HOLogic.mk_eq v)) pats 

866 
val proved_cases1 = ListPair.map (fn (th,th') => R.SUBS[th]th') 

867 
(substs, proved_cases) 

868 
val abs_cases = map (LEFT_ABS_VSTRUCT tych) proved_cases1 

869 
val dant = R.GEN vtyped (R.DISJ_CASESL (R.ISPEC vtyped case_thm) abs_cases) 

870 
val dc = R.MP Sinduct dant 

871 
val Parg_ty = type_of(#Bvar(S.dest_forall(concl dc))) 

872 
val vars = map (gvvariant[Pname]) (S.strip_prod_type Parg_ty) 

16853  873 
val dc' = fold_rev (R.GEN o tych) vars 
10769  874 
(R.SPEC (tych(S.mk_vstruct Parg_ty vars)) dc) 
875 
in 

876 
R.GEN (tych P) (R.DISCH (tych(concl Rinduct_assum)) dc') 

877 
end 

878 
handle U.ERR _ => raise TFL_ERR "mk_induction" "failed derivation"; 

879 

880 

881 

882 

883 
(* 

884 
* 

885 
* POST PROCESSING 

886 
* 

887 
**) 

888 

889 

890 
fun simplify_induction thy hth ind = 

891 
let val tych = Thry.typecheck thy 

892 
val (asl,_) = R.dest_thm ind 

893 
val (_,tc_eq_tc') = R.dest_thm hth 

894 
val tc = S.lhs tc_eq_tc' 

895 
fun loop [] = ind 

896 
 loop (asm::rst) = 

897 
if (can (Thry.match_term thy asm) tc) 

898 
then R.UNDISCH 

899 
(R.MATCH_MP 

900 
(R.MATCH_MP Thms.simp_thm (R.DISCH (tych asm) ind)) 

901 
hth) 

902 
else loop rst 

903 
in loop asl 

904 
end; 

905 

906 

907 
(* 

908 
* The termination condition is an antecedent to the rule, and an 

909 
* assumption to the theorem. 

910 
**) 

911 
fun elim_tc tcthm (rule,induction) = 

912 
(R.MP rule tcthm, R.PROVE_HYP tcthm induction) 

913 

914 

14240  915 
fun trace_thms s L = 
916 
if !trace then writeln (cat_lines (s :: map string_of_thm L)) 

917 
else (); 

918 

919 
fun trace_cterms s L = 

920 
if !trace then writeln (cat_lines (s :: map string_of_cterm L)) 

921 
else ();; 

922 

923 

11632  924 
fun postprocess strict {wf_tac, terminator, simplifier} theory {rules,induction,TCs} = 
10769  925 
let val tych = Thry.typecheck theory 
11632  926 
val prove = R.prove strict; 
10769  927 

928 
(* 

929 
* Attempt to eliminate WF condition. It's the only assumption of rules 

930 
**) 

931 
val (rules1,induction1) = 

11632  932 
let val thm = prove(tych(HOLogic.mk_Trueprop 
10769  933 
(hd(#1(R.dest_thm rules)))), 
934 
wf_tac) 

935 
in (R.PROVE_HYP thm rules, R.PROVE_HYP thm induction) 

936 
end handle U.ERR _ => (rules,induction); 

937 

938 
(* 

939 
* The termination condition (tc) is simplified to  tc = tc' (there 

940 
* might not be a change!) and then 3 attempts are made: 

941 
* 

942 
* 1. if  tc = T, then eliminate it with eqT; otherwise, 

943 
* 2. apply the terminator to tc'. If  tc' = T then eliminate; else 

944 
* 3. replace tc by tc' in both the rules and the induction theorem. 

945 
**) 

946 

947 
fun simplify_tc tc (r,ind) = 

948 
let val tc1 = tych tc 

14240  949 
val _ = trace_cterms "TC before simplification: " [tc1] 
10769  950 
val tc_eq = simplifier tc1 
14240  951 
val _ = trace_thms "result: " [tc_eq] 
10769  952 
in 
953 
elim_tc (R.MATCH_MP Thms.eqT tc_eq) (r,ind) 

954 
handle U.ERR _ => 

955 
(elim_tc (R.MATCH_MP(R.MATCH_MP Thms.rev_eq_mp tc_eq) 

11632  956 
(prove(tych(HOLogic.mk_Trueprop(S.rhs(concl tc_eq))), 
10769  957 
terminator))) 
958 
(r,ind) 

959 
handle U.ERR _ => 

960 
(R.UNDISCH(R.MATCH_MP (R.MATCH_MP Thms.simp_thm r) tc_eq), 

961 
simplify_induction theory tc_eq ind)) 

962 
end 

963 

964 
(* 

965 
* Nested termination conditions are harder to get at, since they are 

966 
* left embedded in the body of the function (and in induction 

967 
* theorem hypotheses). Our "solution" is to simplify them, and try to 

968 
* prove termination, but leave the application of the resulting theorem 

969 
* to a higher level. So things go much as in "simplify_tc": the 

970 
* termination condition (tc) is simplified to  tc = tc' (there might 

971 
* not be a change) and then 2 attempts are made: 

972 
* 

973 
* 1. if  tc = T, then return  tc; otherwise, 

974 
* 2. apply the terminator to tc'. If  tc' = T then return  tc; else 

975 
* 3. return  tc = tc' 

976 
**) 

977 
fun simplify_nested_tc tc = 

978 
let val tc_eq = simplifier (tych (#2 (S.strip_forall tc))) 

979 
in 

980 
R.GEN_ALL 

981 
(R.MATCH_MP Thms.eqT tc_eq 

982 
handle U.ERR _ => 

983 
(R.MATCH_MP(R.MATCH_MP Thms.rev_eq_mp tc_eq) 

11632  984 
(prove(tych(HOLogic.mk_Trueprop (S.rhs(concl tc_eq))), 
10769  985 
terminator)) 
986 
handle U.ERR _ => tc_eq)) 

987 
end 

988 

989 
(* 

990 
* Attempt to simplify the termination conditions in each rule and 

991 
* in the induction theorem. 

992 
**) 

993 
fun strip_imp tm = if S.is_neg tm then ([],tm) else S.strip_imp tm 

994 
fun loop ([],extras,R,ind) = (rev R, ind, extras) 

995 
 loop ((r,ftcs)::rst, nthms, R, ind) = 

996 
let val tcs = #1(strip_imp (concl r)) 

997 
val extra_tcs = gen_rems (op aconv) (ftcs, tcs) 

998 
val extra_tc_thms = map simplify_nested_tc extra_tcs 

16853  999 
val (r1,ind1) = fold simplify_tc tcs (r,ind) 
10769  1000 
val r2 = R.FILTER_DISCH_ALL(not o S.is_WFR) r1 
1001 
in loop(rst, nthms@extra_tc_thms, r2::R, ind1) 

1002 
end 

1003 
val rules_tcs = ListPair.zip (R.CONJUNCTS rules1, TCs) 

1004 
val (rules2,ind2,extras) = loop(rules_tcs,[],[],induction1) 

1005 
in 

1006 
{induction = ind2, rules = R.LIST_CONJ rules2, nested_tcs = extras} 

1007 
end; 

1008 

1009 

1010 
end; 