author  wenzelm 
Wed, 14 Nov 2001 23:22:15 +0100  
changeset 12193  b269a927c137 
parent 11632  6fc8de600f58 
child 12902  a23dc0b7566f 
permissions  rwrr 
10769  1 
(* Title: TFL/tfl.ML 
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ID: $Id$ 

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Author: Konrad Slind, Cambridge University Computer Laboratory 

4 
Copyright 1997 University of Cambridge 

5 

6 
First part of main module. 

7 
*) 

8 

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signature PRIM = 

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sig 

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val trace: bool ref 

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type pattern 

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val mk_functional: theory > term list > {functional: term, pats: pattern list} 

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

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

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{theory: theory, 

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rules: thm, 

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rows: int list, 

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TCs: term list list, 

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full_pats_TCs: (term * term list) list} 

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

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{WFR: term, 

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SV: term list, 

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proto_def: term, 

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extracta: (thm * term list) list, 

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pats: pattern list} 

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

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{theory: theory, 

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rules: thm, 

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R: term, 

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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 > 

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

11632  36 
val postprocess: bool > {wf_tac: tactic, terminator: tactic, simplifier: cterm > thm} 
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> theory > {rules: thm, induction: thm, TCs: term list list} 

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

10769  39 
end; 
40 

41 
structure Prim: PRIM = 

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struct 

43 

44 
val trace = ref false; 

45 

46 
open BasisLibrary; 

47 

48 
structure R = Rules; 

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structure S = USyntax; 

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structure U = Utils; 

51 

52 

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

54 

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val concl = #2 o R.dest_thm; 

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val hyp = #1 o R.dest_thm; 

57 

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

59 

60 
fun enumerate xs = ListPair.zip(xs, 0 upto (length xs  1)); 

61 

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

63 
 front_last [x] = ([],x) 

64 
 front_last (h::t) = 

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let val (pref,x) = front_last t 

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in 

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(h::pref,x) 

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end; 

69 

70 

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(* 

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* The next function is common to patternmatch translation and 

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* proof of completeness of cases for the induction theorem. 

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* 

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

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

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

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* function contains embedded refs! 

79 
**) 

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fun gvvariant names = 

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let val slist = ref names 

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val vname = ref "u" 

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fun new() = 

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if !vname mem_string (!slist) 

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then (vname := bump_string (!vname); new()) 

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else (slist := !vname :: !slist; !vname) 

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in 

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

89 
end; 

90 

91 

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(* 

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

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* partitioning up pattern rows by the leading constructor. 

95 
**) 

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fun ipartition gv (constructors,rows) = 

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

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

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

100 
 part {constrs = _::_, rows = [], A} = pfail"cases missing in defn" 

101 
 part {constrs = c::crst, rows, A} = 

102 
let val (Name,Ty) = dest_Const c 

103 
val L = binder_types Ty 

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val (in_group, not_in_group) = 

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U.itlist (fn (row as (p::rst, rhs)) => 

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fn (in_group,not_in_group) => 

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let val (pc,args) = S.strip_comb p 

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in if (#1(dest_Const pc) = Name) 

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then ((args@rst, rhs)::in_group, not_in_group) 

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else (in_group, row::not_in_group) 

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end) rows ([],[]) 

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

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in 

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part{constrs = crst, rows = not_in_group, 

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A = {constructor = c, 

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new_formals = map gv col_types, 

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group = in_group}::A} 

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end 

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

120 
end; 

121 

122 

123 

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(* 

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

126 
* i is the clause it came from and 

127 
* b=true indicates that clause was given by the user 

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

129 
* b=false > i = ~1 

130 
**) 

131 

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type pattern = term * (int * bool) 

133 

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

135 

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fun pattern_subst theta = pattern_map (subst_free theta); 

137 

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val pat_of = fst; 

139 
fun row_of_pat x = fst (snd x); 

140 
fun given x = snd (snd x); 

141 

142 
(* 

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

144 
**) 

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fun fresh_constr ty_match colty gv c = 

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let val (_,Ty) = dest_Const c 

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val L = binder_types Ty 

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and ty = body_type Ty 

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val ty_theta = ty_match ty colty 

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val c' = S.inst ty_theta c 

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

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in (c', gvars) 

153 
end; 

154 

155 

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(* 

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

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* pattern with constructor = Name. 

159 
**) 

160 
fun mk_group Name rows = 

161 
U.itlist (fn (row as ((prfx, p::rst), rhs)) => 

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fn (in_group,not_in_group) => 

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let val (pc,args) = S.strip_comb p 

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in if ((#1 (Term.dest_Const pc) = Name) handle TERM _ => false) 

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then (((prfx,args@rst), rhs)::in_group, not_in_group) 

166 
else (in_group, row::not_in_group) end) 

167 
rows ([],[]); 

168 

169 
(* 

170 
* Partition the rows. Not efficient: we should use hashing. 

171 
**) 

172 
fun partition _ _ (_,_,_,[]) = raise TFL_ERR "partition" "no rows" 

173 
 partition gv ty_match 

174 
(constructors, colty, res_ty, rows as (((prfx,_),_)::_)) = 

175 
let val fresh = fresh_constr ty_match colty gv 

176 
fun part {constrs = [], rows, A} = rev A 

177 
 part {constrs = c::crst, rows, A} = 

178 
let val (c',gvars) = fresh c 

179 
val (Name,Ty) = dest_Const c' 

180 
val (in_group, not_in_group) = mk_group Name rows 

181 
val in_group' = 

182 
if (null in_group) (* Constructor not given *) 

183 
then [((prfx, #2(fresh c)), (S.ARB res_ty, (~1,false)))] 

184 
else in_group 

185 
in 

186 
part{constrs = crst, 

187 
rows = not_in_group, 

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A = {constructor = c', 

189 
new_formals = gvars, 

190 
group = in_group'}::A} 

191 
end 

192 
in part{constrs=constructors, rows=rows, A=[]} 

193 
end; 

194 

195 
(* 

196 
* Misc. routines used in mk_case 

197 
**) 

198 

199 
fun mk_pat (c,l) = 

200 
let val L = length (binder_types (type_of c)) 

201 
fun build (prfx,tag,plist) = 

202 
let val args = take (L,plist) 

203 
and plist' = drop(L,plist) 

204 
in (prfx,tag,list_comb(c,args)::plist') end 

205 
in map build l end; 

206 

207 
fun v_to_prfx (prfx, v::pats) = (v::prfx,pats) 

208 
 v_to_prfx _ = raise TFL_ERR "mk_case" "v_to_prfx"; 

209 

210 
fun v_to_pats (v::prfx,tag, pats) = (prfx, tag, v::pats) 

211 
 v_to_pats _ = raise TFL_ERR "mk_case" "v_to_pats"; 

212 

213 

214 
(* 

215 
* Translation of pattern terms into nested case expressions. 

216 
* 

217 
* This performs the translation and also builds the full set of patterns. 

218 
* Thus it supports the construction of induction theorems even when an 

219 
* incomplete set of patterns is given. 

220 
**) 

221 

222 
fun mk_case ty_info ty_match usednames range_ty = 

223 
let 

224 
fun mk_case_fail s = raise TFL_ERR "mk_case" s 

225 
val fresh_var = gvvariant usednames 

226 
val divide = partition fresh_var ty_match 

227 
fun expand constructors ty ((_,[]), _) = mk_case_fail"expand_var_row" 

228 
 expand constructors ty (row as ((prfx, p::rst), rhs)) = 

229 
if (is_Free p) 

230 
then let val fresh = fresh_constr ty_match ty fresh_var 

231 
fun expnd (c,gvs) = 

232 
let val capp = list_comb(c,gvs) 

233 
in ((prfx, capp::rst), pattern_subst[(p,capp)] rhs) 

234 
end 

235 
in map expnd (map fresh constructors) end 

236 
else [row] 

237 
fun mk{rows=[],...} = mk_case_fail"no rows" 

238 
 mk{path=[], rows = ((prfx, []), (tm,tag))::_} = (* Done *) 

239 
([(prfx,tag,[])], tm) 

240 
 mk{path=[], rows = _::_} = mk_case_fail"blunder" 

241 
 mk{path as u::rstp, rows as ((prfx, []), rhs)::rst} = 

242 
mk{path = path, 

243 
rows = ((prfx, [fresh_var(type_of u)]), rhs)::rst} 

244 
 mk{path = u::rstp, rows as ((_, p::_), _)::_} = 

245 
let val (pat_rectangle,rights) = ListPair.unzip rows 

246 
val col0 = map(hd o #2) pat_rectangle 

247 
in 

248 
if (forall is_Free col0) 

249 
then let val rights' = map (fn(v,e) => pattern_subst[(v,u)] e) 

250 
(ListPair.zip (col0, rights)) 

251 
val pat_rectangle' = map v_to_prfx pat_rectangle 

252 
val (pref_patl,tm) = mk{path = rstp, 

253 
rows = ListPair.zip (pat_rectangle', 

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rights')} 

255 
in (map v_to_pats pref_patl, tm) 

256 
end 

257 
else 

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

259 
in 

260 
case (ty_info ty_name) 

261 
of None => mk_case_fail("Not a known datatype: "^ty_name) 

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 Some{case_const,constructors} => 

263 
let 

264 
val case_const_name = #1(dest_Const case_const) 

265 
val nrows = List.concat (map (expand constructors pty) rows) 

266 
val subproblems = divide(constructors, pty, range_ty, nrows) 

267 
val groups = map #group subproblems 

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and new_formals = map #new_formals subproblems 

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and constructors' = map #constructor subproblems 

270 
val news = map (fn (nf,rows) => {path = nf@rstp, rows=rows}) 

271 
(ListPair.zip (new_formals, groups)) 

272 
val rec_calls = map mk news 

273 
val (pat_rect,dtrees) = ListPair.unzip rec_calls 

274 
val case_functions = map S.list_mk_abs 

275 
(ListPair.zip (new_formals, dtrees)) 

276 
val types = map type_of (case_functions@[u]) @ [range_ty] 

277 
val case_const' = Const(case_const_name, list_mk_type types) 

278 
val tree = list_comb(case_const', case_functions@[u]) 

279 
val pat_rect1 = List.concat 

280 
(ListPair.map mk_pat (constructors', pat_rect)) 

281 
in (pat_rect1,tree) 

282 
end 

283 
end end 

284 
in mk 

285 
end; 

286 

287 

288 
(* Repeated variable occurrences in a pattern are not allowed. *) 

289 
fun FV_multiset tm = 

290 
case (S.dest_term tm) 

291 
of S.VAR{Name,Ty} => [Free(Name,Ty)] 

292 
 S.CONST _ => [] 

293 
 S.COMB{Rator, Rand} => FV_multiset Rator @ FV_multiset Rand 

294 
 S.LAMB _ => raise TFL_ERR "FV_multiset" "lambda"; 

295 

296 
fun no_repeat_vars thy pat = 

297 
let fun check [] = true 

298 
 check (v::rst) = 

299 
if mem_term (v,rst) then 

300 
raise TFL_ERR "no_repeat_vars" 

301 
(quote (#1 (dest_Free v)) ^ 

302 
" occurs repeatedly in the pattern " ^ 

303 
quote (string_of_cterm (Thry.typecheck thy pat))) 

304 
else check rst 

305 
in check (FV_multiset pat) 

306 
end; 

307 

308 
fun dest_atom (Free p) = p 

309 
 dest_atom (Const p) = p 

310 
 dest_atom _ = raise TFL_ERR "dest_atom" "function name not an identifier"; 

311 

312 
fun same_name (p,q) = #1(dest_atom p) = #1(dest_atom q); 

313 

314 
local fun mk_functional_err s = raise TFL_ERR "mk_functional" s 

315 
fun single [_$_] = 

316 
mk_functional_err "recdef does not allow currying" 

317 
 single [f] = f 

318 
 single fs = 

319 
(*multiple function names?*) 

320 
if length (gen_distinct same_name fs) < length fs 

321 
then mk_functional_err 

322 
"The function being declared appears with multiple types" 

323 
else mk_functional_err 

324 
(Int.toString (length fs) ^ 

325 
" distinct function names being declared") 

326 
in 

327 
fun mk_functional thy clauses = 

328 
let val (L,R) = ListPair.unzip (map HOLogic.dest_eq clauses 

329 
handle TERM _ => raise TFL_ERR "mk_functional" 

330 
"recursion equations must use the = relation") 

331 
val (funcs,pats) = ListPair.unzip (map (fn (t$u) =>(t,u)) L) 

332 
val atom = single (gen_distinct (op aconv) funcs) 

333 
val (fname,ftype) = dest_atom atom 

334 
val dummy = map (no_repeat_vars thy) pats 

335 
val rows = ListPair.zip (map (fn x => ([]:term list,[x])) pats, 

336 
map (fn (t,i) => (t,(i,true))) (enumerate R)) 

337 
val names = foldr add_term_names (R,[]) 

338 
val atype = type_of(hd pats) 

339 
and aname = variant names "a" 

340 
val a = Free(aname,atype) 

341 
val ty_info = Thry.match_info thy 

342 
val ty_match = Thry.match_type thy 

343 
val range_ty = type_of (hd R) 

344 
val (patts, case_tm) = mk_case ty_info ty_match (aname::names) range_ty 

345 
{path=[a], rows=rows} 

346 
val patts1 = map (fn (_,tag,[pat]) => (pat,tag)) patts 

347 
handle Match => mk_functional_err "error in patternmatch translation" 

348 
val patts2 = Library.sort (Library.int_ord o Library.pairself row_of_pat) patts1 

349 
val finals = map row_of_pat patts2 

350 
val originals = map (row_of_pat o #2) rows 

351 
val dummy = case (originals\\finals) 

352 
of [] => () 

353 
 L => mk_functional_err 

354 
("The following clauses are redundant (covered by preceding clauses): " ^ 

355 
commas (map (fn i => Int.toString (i + 1)) L)) 

356 
in {functional = Abs(Sign.base_name fname, ftype, 

357 
abstract_over (atom, 

358 
absfree(aname,atype, case_tm))), 

359 
pats = patts2} 

360 
end end; 

361 

362 

363 
(* 

364 
* 

365 
* PRINCIPLES OF DEFINITION 

366 
* 

367 
**) 

368 

369 

370 
(*For Isabelle, the lhs of a definition must be a constant.*) 

371 
fun mk_const_def sign (Name, Ty, rhs) = 

372 
Sign.infer_types sign (K None) (K None) [] false 

373 
([Const("==",dummyT) $ Const(Name,Ty) $ rhs], propT) 

374 
> #1; 

375 

376 
(*Make all TVars available for instantiation by adding a ? to the front*) 

377 
fun poly_tvars (Type(a,Ts)) = Type(a, map (poly_tvars) Ts) 

378 
 poly_tvars (TFree (a,sort)) = TVar (("?" ^ a, 0), sort) 

379 
 poly_tvars (TVar ((a,i),sort)) = TVar (("?" ^ a, i+1), sort); 

380 

381 
local val f_eq_wfrec_R_M = 

382 
#ant(S.dest_imp(#2(S.strip_forall (concl Thms.WFREC_COROLLARY)))) 

383 
val {lhs=f, rhs} = S.dest_eq f_eq_wfrec_R_M 

384 
val (fname,_) = dest_Free f 

385 
val (wfrec,_) = S.strip_comb rhs 

386 
in 

387 
fun wfrec_definition0 thy fid R (functional as Abs(Name, Ty, _)) = 

388 
let val def_name = if Name<>fid then 

389 
raise TFL_ERR "wfrec_definition0" 

390 
("Expected a definition of " ^ 

391 
quote fid ^ " but found one of " ^ 

392 
quote Name) 

393 
else Name ^ "_def" 

394 
val wfrec_R_M = map_term_types poly_tvars 

395 
(wfrec $ map_term_types poly_tvars R) 

396 
$ functional 

397 
val def_term = mk_const_def (Theory.sign_of thy) (Name, Ty, wfrec_R_M) 

398 
val (thy', [def]) = PureThy.add_defs_i false [Thm.no_attributes (def_name, def_term)] thy 

399 
in (thy', def) end; 

400 
end; 

401 

402 

403 

404 
(* 

405 
* This structure keeps track of congruence rules that aren't derived 

406 
* from a datatype definition. 

407 
**) 

408 
fun extraction_thms thy = 

409 
let val {case_rewrites,case_congs} = Thry.extract_info thy 

410 
in (case_rewrites, case_congs) 

411 
end; 

412 

413 

414 
(* 

415 
* Pair patterns with termination conditions. The full list of patterns for 

416 
* a definition is merged with the TCs arising from the usergiven clauses. 

417 
* There can be fewer clauses than the full list, if the user omitted some 

418 
* cases. This routine is used to prepare input for mk_induction. 

419 
**) 

420 
fun merge full_pats TCs = 

421 
let fun insert (p,TCs) = 

422 
let fun insrt ((x as (h,[]))::rst) = 

423 
if (p aconv h) then (p,TCs)::rst else x::insrt rst 

424 
 insrt (x::rst) = x::insrt rst 

425 
 insrt[] = raise TFL_ERR "merge.insert" "pattern not found" 

426 
in insrt end 

427 
fun pass ([],ptcl_final) = ptcl_final 

428 
 pass (ptcs::tcl, ptcl) = pass(tcl, insert ptcs ptcl) 

429 
in 

430 
pass (TCs, map (fn p => (p,[])) full_pats) 

431 
end; 

432 

433 

434 
fun givens pats = map pat_of (filter given pats); 

435 

436 
fun post_definition meta_tflCongs (theory, (def, pats)) = 

437 
let val tych = Thry.typecheck theory 

438 
val f = #lhs(S.dest_eq(concl def)) 

439 
val corollary = R.MATCH_MP Thms.WFREC_COROLLARY def 

440 
val pats' = filter given pats 

441 
val given_pats = map pat_of pats' 

442 
val rows = map row_of_pat pats' 

443 
val WFR = #ant(S.dest_imp(concl corollary)) 

444 
val R = #Rand(S.dest_comb WFR) 

445 
val corollary' = R.UNDISCH corollary (* put WF R on assums *) 

446 
val corollaries = map (fn pat => R.SPEC (tych pat) corollary') 

447 
given_pats 

448 
val (case_rewrites,context_congs) = extraction_thms theory 

449 
val corollaries' = map(rewrite_rule case_rewrites) corollaries 

450 
val extract = R.CONTEXT_REWRITE_RULE 

451 
(f, [R], cut_apply, meta_tflCongs@context_congs) 

452 
val (rules, TCs) = ListPair.unzip (map extract corollaries') 

453 
val rules0 = map (rewrite_rule [Thms.CUT_DEF]) rules 

454 
val mk_cond_rule = R.FILTER_DISCH_ALL(not o curry (op aconv) WFR) 

455 
val rules1 = R.LIST_CONJ(map mk_cond_rule rules0) 

456 
in 

457 
{theory = theory, 

458 
rules = rules1, 

459 
rows = rows, 

460 
full_pats_TCs = merge (map pat_of pats) (ListPair.zip (given_pats, TCs)), 

461 
TCs = TCs} 

462 
end; 

463 

464 

465 
(* 

466 
* Perform the extraction without making the definition. Definition and 

467 
* extraction commute for the nonnested case. (Deferred recdefs) 

468 
* 

469 
* The purpose of wfrec_eqns is merely to instantiate the recursion theorem 

470 
* and extract termination conditions: no definition is made. 

471 
**) 

472 

473 
fun wfrec_eqns thy fid tflCongs eqns = 

474 
let val {lhs,rhs} = S.dest_eq (hd eqns) 

475 
val (f,args) = S.strip_comb lhs 

476 
val (fname,fty) = dest_atom f 

477 
val (SV,a) = front_last args (* SV = schematic variables *) 

478 
val g = list_comb(f,SV) 

479 
val h = Free(fname,type_of g) 

480 
val eqns1 = map (subst_free[(g,h)]) eqns 

481 
val {functional as Abs(Name, Ty, _), pats} = mk_functional thy eqns1 

482 
val given_pats = givens pats 

483 
(* val f = Free(Name,Ty) *) 

484 
val Type("fun", [f_dty, f_rty]) = Ty 

485 
val dummy = if Name<>fid then 

486 
raise TFL_ERR "wfrec_eqns" 

487 
("Expected a definition of " ^ 

488 
quote fid ^ " but found one of " ^ 

489 
quote Name) 

490 
else () 

491 
val (case_rewrites,context_congs) = extraction_thms thy 

492 
val tych = Thry.typecheck thy 

493 
val WFREC_THM0 = R.ISPEC (tych functional) Thms.WFREC_COROLLARY 

494 
val Const("All",_) $ Abs(Rname,Rtype,_) = concl WFREC_THM0 

495 
val R = Free (variant (foldr add_term_names (eqns,[])) Rname, 

496 
Rtype) 

497 
val WFREC_THM = R.ISPECL [tych R, tych g] WFREC_THM0 

498 
val ([proto_def, WFR],_) = S.strip_imp(concl WFREC_THM) 

499 
val dummy = 

500 
if !trace then 

501 
writeln ("ORIGINAL PROTO_DEF: " ^ 

502 
Sign.string_of_term (Theory.sign_of thy) proto_def) 

503 
else () 

504 
val R1 = S.rand WFR 

505 
val corollary' = R.UNDISCH(R.UNDISCH WFREC_THM) 

506 
val corollaries = map (fn pat => R.SPEC (tych pat) corollary') given_pats 

507 
val corollaries' = map (rewrite_rule case_rewrites) corollaries 

508 
fun extract X = R.CONTEXT_REWRITE_RULE 

509 
(f, R1::SV, cut_apply, tflCongs@context_congs) X 

510 
in {proto_def = proto_def, 

511 
SV=SV, 

512 
WFR=WFR, 

513 
pats=pats, 

514 
extracta = map extract corollaries'} 

515 
end; 

516 

517 

518 
(* 

519 
* Define the constant after extracting the termination conditions. The 

520 
* wellfounded relation used in the definition is computed by using the 

521 
* choice operator on the extracted conditions (plus the condition that 

522 
* such a relation must be wellfounded). 

523 
**) 

524 

525 
fun lazyR_def thy fid tflCongs eqns = 

526 
let val {proto_def,WFR,pats,extracta,SV} = 

527 
wfrec_eqns thy fid tflCongs eqns 

528 
val R1 = S.rand WFR 

529 
val f = #lhs(S.dest_eq proto_def) 

530 
val (extractants,TCl) = ListPair.unzip extracta 

531 
val dummy = if !trace 

532 
then (writeln "Extractants = "; 

533 
prths extractants; 

534 
()) 

535 
else () 

536 
val TCs = foldr (gen_union (op aconv)) (TCl, []) 

537 
val full_rqt = WFR::TCs 

538 
val R' = S.mk_select{Bvar=R1, Body=S.list_mk_conj full_rqt} 

539 
val R'abs = S.rand R' 

540 
val proto_def' = subst_free[(R1,R')] proto_def 

541 
val dummy = if !trace then writeln ("proto_def' = " ^ 

542 
Sign.string_of_term 

543 
(Theory.sign_of thy) proto_def') 

544 
else () 

545 
val {lhs,rhs} = S.dest_eq proto_def' 

546 
val (c,args) = S.strip_comb lhs 

547 
val (Name,Ty) = dest_atom c 

548 
val defn = mk_const_def (Theory.sign_of thy) 

549 
(Name, Ty, S.list_mk_abs (args,rhs)) 

550 
val (theory, [def0]) = 

551 
thy 

552 
> PureThy.add_defs_i false 

553 
[Thm.no_attributes (fid ^ "_def", defn)] 

554 
val def = freezeT def0; 

555 
val dummy = if !trace then writeln ("DEF = " ^ string_of_thm def) 

556 
else () 

557 
(* val fconst = #lhs(S.dest_eq(concl def)) *) 

558 
val tych = Thry.typecheck theory 

559 
val full_rqt_prop = map (Dcterm.mk_prop o tych) full_rqt 

560 
(*lcp: a lot of objectlogic inference to remove*) 

561 
val baz = R.DISCH_ALL 

562 
(U.itlist R.DISCH full_rqt_prop 

563 
(R.LIST_CONJ extractants)) 

564 
val dum = if !trace then writeln ("baz = " ^ string_of_thm baz) 

565 
else () 

566 
val f_free = Free (fid, fastype_of f) (*'cos f is a Const*) 

567 
val SV' = map tych SV; 

568 
val SVrefls = map reflexive SV' 

569 
val def0 = (U.rev_itlist (fn x => fn th => R.rbeta(combination th x)) 

570 
SVrefls def) 

571 
RS meta_eq_to_obj_eq 

572 
val def' = R.MP (R.SPEC (tych R') (R.GEN (tych R1) baz)) def0 

573 
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

574 
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

575 
theory Hilbert_Choice*) 
e07927b980ec
defer_recdef (lazyR_def) now looks for theorem Hilbert_Choice.tfl_some
paulson
parents:
10769
diff
changeset

576 
thm "Hilbert_Choice.tfl_some" 
e07927b980ec
defer_recdef (lazyR_def) now looks for theorem Hilbert_Choice.tfl_some
paulson
parents:
10769
diff
changeset

577 
handle ERROR => error 
e07927b980ec
defer_recdef (lazyR_def) now looks for theorem Hilbert_Choice.tfl_some
paulson
parents:
10769
diff
changeset

578 
"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

579 
val bar = R.MP (R.ISPECL[tych R'abs, tych R1] SELECT_AX) body_th 
10769  580 
in {theory = theory, R=R1, SV=SV, 
581 
rules = U.rev_itlist (U.C R.MP) (R.CONJUNCTS bar) def', 

582 
full_pats_TCs = merge (map pat_of pats) (ListPair.zip (givens pats, TCl)), 

583 
patterns = pats} 

584 
end; 

585 

586 

587 

588 
(* 

589 
* 

590 
* INDUCTION THEOREM 

591 
* 

592 
**) 

593 

594 

595 
(* Miscellaneous function  

596 
* 

597 
* [x_1,...,x_n] ?v_1...v_n. M[v_1,...,v_n] 

598 
*  

599 
* ( M[x_1,...,x_n], [(x_i,?v_1...v_n. M[v_1,...,v_n]), 

600 
* ... 

601 
* (x_j,?v_n. M[x_1,...,x_(n1),v_n])] ) 

602 
* 

603 
* This function is totally ad hoc. Used in the production of the induction 

604 
* theorem. The nchotomy theorem can have clauses that look like 

605 
* 

606 
* ?v1..vn. z = C vn..v1 

607 
* 

608 
* in which the order of quantification is not the order of occurrence of the 

609 
* quantified variables as arguments to C. Since we have no control over this 

610 
* aspect of the nchotomy theorem, we make the correspondence explicit by 

611 
* pairing the incoming new variable with the term it gets betareduced into. 

612 
**) 

613 

614 
fun alpha_ex_unroll (xlist, tm) = 

615 
let val (qvars,body) = S.strip_exists tm 

616 
val vlist = #2(S.strip_comb (S.rhs body)) 

617 
val plist = ListPair.zip (vlist, xlist) 

618 
val args = map (fn qv => the (gen_assoc (op aconv) (plist, qv))) qvars 

619 
handle Library.OPTION => sys_error 

620 
"TFL fault [alpha_ex_unroll]: no correspondence" 

621 
fun build ex [] = [] 

622 
 build (_$rex) (v::rst) = 

623 
let val ex1 = betapply(rex, v) 

624 
in ex1 :: build ex1 rst 

625 
end 

626 
val (nex::exl) = rev (tm::build tm args) 

627 
in 

628 
(nex, ListPair.zip (args, rev exl)) 

629 
end; 

630 

631 

632 

633 
(* 

634 
* 

635 
* PROVING COMPLETENESS OF PATTERNS 

636 
* 

637 
**) 

638 

639 
fun mk_case ty_info usednames thy = 

640 
let 

641 
val divide = ipartition (gvvariant usednames) 

642 
val tych = Thry.typecheck thy 

643 
fun tych_binding(x,y) = (tych x, tych y) 

644 
fun fail s = raise TFL_ERR "mk_case" s 

645 
fun mk{rows=[],...} = fail"no rows" 

646 
 mk{path=[], rows = [([], (thm, bindings))]} = 

647 
R.IT_EXISTS (map tych_binding bindings) thm 

648 
 mk{path = u::rstp, rows as (p::_, _)::_} = 

649 
let val (pat_rectangle,rights) = ListPair.unzip rows 

650 
val col0 = map hd pat_rectangle 

651 
val pat_rectangle' = map tl pat_rectangle 

652 
in 

653 
if (forall is_Free col0) (* column 0 is all variables *) 

654 
then let val rights' = map (fn ((thm,theta),v) => (thm,theta@[(u,v)])) 

655 
(ListPair.zip (rights, col0)) 

656 
in mk{path = rstp, rows = ListPair.zip (pat_rectangle', rights')} 

657 
end 

658 
else (* column 0 is all constructors *) 

659 
let val Type (ty_name,_) = type_of p 

660 
in 

661 
case (ty_info ty_name) 

662 
of None => fail("Not a known datatype: "^ty_name) 

663 
 Some{constructors,nchotomy} => 

664 
let val thm' = R.ISPEC (tych u) nchotomy 

665 
val disjuncts = S.strip_disj (concl thm') 

666 
val subproblems = divide(constructors, rows) 

667 
val groups = map #group subproblems 

668 
and new_formals = map #new_formals subproblems 

669 
val existentials = ListPair.map alpha_ex_unroll 

670 
(new_formals, disjuncts) 

671 
val constraints = map #1 existentials 

672 
val vexl = map #2 existentials 

673 
fun expnd tm (pats,(th,b)) = (pats,(R.SUBS[R.ASSUME(tych tm)]th,b)) 

674 
val news = map (fn (nf,rows,c) => {path = nf@rstp, 

675 
rows = map (expnd c) rows}) 

676 
(U.zip3 new_formals groups constraints) 

677 
val recursive_thms = map mk news 

678 
val build_exists = foldr 

679 
(fn((x,t), th) => 

680 
R.CHOOSE (tych x, R.ASSUME (tych t)) th) 

681 
val thms' = ListPair.map build_exists (vexl, recursive_thms) 

682 
val same_concls = R.EVEN_ORS thms' 

683 
in R.DISJ_CASESL thm' same_concls 

684 
end 

685 
end end 

686 
in mk 

687 
end; 

688 

689 

690 
fun complete_cases thy = 

691 
let val tych = Thry.typecheck thy 

692 
val ty_info = Thry.induct_info thy 

693 
in fn pats => 

694 
let val names = foldr add_term_names (pats,[]) 

695 
val T = type_of (hd pats) 

696 
val aname = Term.variant names "a" 

697 
val vname = Term.variant (aname::names) "v" 

698 
val a = Free (aname, T) 

699 
val v = Free (vname, T) 

700 
val a_eq_v = HOLogic.mk_eq(a,v) 

701 
val ex_th0 = R.EXISTS (tych (S.mk_exists{Bvar=v,Body=a_eq_v}), tych a) 

702 
(R.REFL (tych a)) 

703 
val th0 = R.ASSUME (tych a_eq_v) 

704 
val rows = map (fn x => ([x], (th0,[]))) pats 

705 
in 

706 
R.GEN (tych a) 

707 
(R.RIGHT_ASSOC 

708 
(R.CHOOSE(tych v, ex_th0) 

709 
(mk_case ty_info (vname::aname::names) 

710 
thy {path=[v], rows=rows}))) 

711 
end end; 

712 

713 

714 
(* 

715 
* Constructing induction hypotheses: one for each recursive call. 

716 
* 

717 
* Note. R will never occur as a variable in the ind_clause, because 

718 
* to do so, it would have to be from a nested definition, and we don't 

719 
* allow nested defns to have R variable. 

720 
* 

721 
* Note. When the context is empty, there can be no local variables. 

722 
**) 

723 
(* 

724 
local infix 5 ==> 

725 
fun (tm1 ==> tm2) = S.mk_imp{ant = tm1, conseq = tm2} 

726 
in 

727 
fun build_ih f P (pat,TCs) = 

728 
let val globals = S.free_vars_lr pat 

729 
fun nested tm = is_some (S.find_term (curry (op aconv) f) tm) 

730 
fun dest_TC tm = 

731 
let val (cntxt,R_y_pat) = S.strip_imp(#2(S.strip_forall tm)) 

732 
val (R,y,_) = S.dest_relation R_y_pat 

733 
val P_y = if (nested tm) then R_y_pat ==> P$y else P$y 

734 
in case cntxt 

735 
of [] => (P_y, (tm,[])) 

736 
 _ => let 

737 
val imp = S.list_mk_conj cntxt ==> P_y 

738 
val lvs = gen_rems (op aconv) (S.free_vars_lr imp, globals) 

739 
val locals = #2(U.pluck (curry (op aconv) P) lvs) handle U.ERR _ => lvs 

740 
in (S.list_mk_forall(locals,imp), (tm,locals)) end 

741 
end 

742 
in case TCs 

743 
of [] => (S.list_mk_forall(globals, P$pat), []) 

744 
 _ => let val (ihs, TCs_locals) = ListPair.unzip(map dest_TC TCs) 

745 
val ind_clause = S.list_mk_conj ihs ==> P$pat 

746 
in (S.list_mk_forall(globals,ind_clause), TCs_locals) 

747 
end 

748 
end 

749 
end; 

750 
*) 

751 

752 
local infix 5 ==> 

753 
fun (tm1 ==> tm2) = S.mk_imp{ant = tm1, conseq = tm2} 

754 
in 

755 
fun build_ih f (P,SV) (pat,TCs) = 

756 
let val pat_vars = S.free_vars_lr pat 

757 
val globals = pat_vars@SV 

758 
fun nested tm = is_some (S.find_term (curry (op aconv) f) tm) 

759 
fun dest_TC tm = 

760 
let val (cntxt,R_y_pat) = S.strip_imp(#2(S.strip_forall tm)) 

761 
val (R,y,_) = S.dest_relation R_y_pat 

762 
val P_y = if (nested tm) then R_y_pat ==> P$y else P$y 

763 
in case cntxt 

764 
of [] => (P_y, (tm,[])) 

765 
 _ => let 

766 
val imp = S.list_mk_conj cntxt ==> P_y 

767 
val lvs = gen_rems (op aconv) (S.free_vars_lr imp, globals) 

768 
val locals = #2(U.pluck (curry (op aconv) P) lvs) handle U.ERR _ => lvs 

769 
in (S.list_mk_forall(locals,imp), (tm,locals)) end 

770 
end 

771 
in case TCs 

772 
of [] => (S.list_mk_forall(pat_vars, P$pat), []) 

773 
 _ => let val (ihs, TCs_locals) = ListPair.unzip(map dest_TC TCs) 

774 
val ind_clause = S.list_mk_conj ihs ==> P$pat 

775 
in (S.list_mk_forall(pat_vars,ind_clause), TCs_locals) 

776 
end 

777 
end 

778 
end; 

779 

780 
(* 

781 
* This function makes good on the promise made in "build_ih". 

782 
* 

783 
* Input is tm = "(!y. R y pat ==> P y) ==> P pat", 

784 
* TCs = TC_1[pat] ... TC_n[pat] 

785 
* thm = ih1 /\ ... /\ ih_n  ih[pat] 

786 
**) 

787 
fun prove_case f thy (tm,TCs_locals,thm) = 

788 
let val tych = Thry.typecheck thy 

789 
val antc = tych(#ant(S.dest_imp tm)) 

790 
val thm' = R.SPEC_ALL thm 

791 
fun nested tm = is_some (S.find_term (curry (op aconv) f) tm) 

792 
fun get_cntxt TC = tych(#ant(S.dest_imp(#2(S.strip_forall(concl TC))))) 

793 
fun mk_ih ((TC,locals),th2,nested) = 

794 
R.GENL (map tych locals) 

795 
(if nested then R.DISCH (get_cntxt TC) th2 handle U.ERR _ => th2 

796 
else if S.is_imp (concl TC) then R.IMP_TRANS TC th2 

797 
else R.MP th2 TC) 

798 
in 

799 
R.DISCH antc 

800 
(if S.is_imp(concl thm') (* recursive calls in this clause *) 

801 
then let val th1 = R.ASSUME antc 

802 
val TCs = map #1 TCs_locals 

803 
val ylist = map (#2 o S.dest_relation o #2 o S.strip_imp o 

804 
#2 o S.strip_forall) TCs 

805 
val TClist = map (fn(TC,lvs) => (R.SPEC_ALL(R.ASSUME(tych TC)),lvs)) 

806 
TCs_locals 

807 
val th2list = map (U.C R.SPEC th1 o tych) ylist 

808 
val nlist = map nested TCs 

809 
val triples = U.zip3 TClist th2list nlist 

810 
val Pylist = map mk_ih triples 

811 
in R.MP thm' (R.LIST_CONJ Pylist) end 

812 
else thm') 

813 
end; 

814 

815 

816 
(* 

817 
* 

818 
* x = (v1,...,vn)  M[x] 

819 
*  

820 
* ?v1 ... vn. x = (v1,...,vn)  M[x] 

821 
* 

822 
**) 

823 
fun LEFT_ABS_VSTRUCT tych thm = 

824 
let fun CHOOSER v (tm,thm) = 

825 
let val ex_tm = S.mk_exists{Bvar=v,Body=tm} 

826 
in (ex_tm, R.CHOOSE(tych v, R.ASSUME (tych ex_tm)) thm) 

827 
end 

828 
val [veq] = filter (can S.dest_eq) (#1 (R.dest_thm thm)) 

829 
val {lhs,rhs} = S.dest_eq veq 

830 
val L = S.free_vars_lr rhs 

831 
in #2 (U.itlist CHOOSER L (veq,thm)) end; 

832 

833 

834 
(* 

835 
* Input : f, R, and [(pat1,TCs1),..., (patn,TCsn)] 

836 
* 

837 
* Instantiates WF_INDUCTION_THM, getting Sinduct and then tries to prove 

838 
* recursion induction (Rinduct) by proving the antecedent of Sinduct from 

839 
* the antecedent of Rinduct. 

840 
**) 

841 
fun mk_induction thy {fconst, R, SV, pat_TCs_list} = 

842 
let val tych = Thry.typecheck thy 

843 
val Sinduction = R.UNDISCH (R.ISPEC (tych R) Thms.WF_INDUCTION_THM) 

844 
val (pats,TCsl) = ListPair.unzip pat_TCs_list 

845 
val case_thm = complete_cases thy pats 

846 
val domain = (type_of o hd) pats 

847 
val Pname = Term.variant (foldr (foldr add_term_names) 

848 
(pats::TCsl, [])) "P" 

849 
val P = Free(Pname, domain > HOLogic.boolT) 

850 
val Sinduct = R.SPEC (tych P) Sinduction 

851 
val Sinduct_assumf = S.rand ((#ant o S.dest_imp o concl) Sinduct) 

852 
val Rassums_TCl' = map (build_ih fconst (P,SV)) pat_TCs_list 

853 
val (Rassums,TCl') = ListPair.unzip Rassums_TCl' 

854 
val Rinduct_assum = R.ASSUME (tych (S.list_mk_conj Rassums)) 

855 
val cases = map (fn pat => betapply (Sinduct_assumf, pat)) pats 

856 
val tasks = U.zip3 cases TCl' (R.CONJUNCTS Rinduct_assum) 

857 
val proved_cases = map (prove_case fconst thy) tasks 

858 
val v = Free (variant (foldr add_term_names (map concl proved_cases, [])) 

859 
"v", 

860 
domain) 

861 
val vtyped = tych v 

862 
val substs = map (R.SYM o R.ASSUME o tych o (curry HOLogic.mk_eq v)) pats 

863 
val proved_cases1 = ListPair.map (fn (th,th') => R.SUBS[th]th') 

864 
(substs, proved_cases) 

865 
val abs_cases = map (LEFT_ABS_VSTRUCT tych) proved_cases1 

866 
val dant = R.GEN vtyped (R.DISJ_CASESL (R.ISPEC vtyped case_thm) abs_cases) 

867 
val dc = R.MP Sinduct dant 

868 
val Parg_ty = type_of(#Bvar(S.dest_forall(concl dc))) 

869 
val vars = map (gvvariant[Pname]) (S.strip_prod_type Parg_ty) 

870 
val dc' = U.itlist (R.GEN o tych) vars 

871 
(R.SPEC (tych(S.mk_vstruct Parg_ty vars)) dc) 

872 
in 

873 
R.GEN (tych P) (R.DISCH (tych(concl Rinduct_assum)) dc') 

874 
end 

875 
handle U.ERR _ => raise TFL_ERR "mk_induction" "failed derivation"; 

876 

877 

878 

879 

880 
(* 

881 
* 

882 
* POST PROCESSING 

883 
* 

884 
**) 

885 

886 

887 
fun simplify_induction thy hth ind = 

888 
let val tych = Thry.typecheck thy 

889 
val (asl,_) = R.dest_thm ind 

890 
val (_,tc_eq_tc') = R.dest_thm hth 

891 
val tc = S.lhs tc_eq_tc' 

892 
fun loop [] = ind 

893 
 loop (asm::rst) = 

894 
if (can (Thry.match_term thy asm) tc) 

895 
then R.UNDISCH 

896 
(R.MATCH_MP 

897 
(R.MATCH_MP Thms.simp_thm (R.DISCH (tych asm) ind)) 

898 
hth) 

899 
else loop rst 

900 
in loop asl 

901 
end; 

902 

903 

904 
(* 

905 
* The termination condition is an antecedent to the rule, and an 

906 
* assumption to the theorem. 

907 
**) 

908 
fun elim_tc tcthm (rule,induction) = 

909 
(R.MP rule tcthm, R.PROVE_HYP tcthm induction) 

910 

911 

11632  912 
fun postprocess strict {wf_tac, terminator, simplifier} theory {rules,induction,TCs} = 
10769  913 
let val tych = Thry.typecheck theory 
11632  914 
val prove = R.prove strict; 
10769  915 

916 
(* 

917 
* Attempt to eliminate WF condition. It's the only assumption of rules 

918 
**) 

919 
val (rules1,induction1) = 

11632  920 
let val thm = prove(tych(HOLogic.mk_Trueprop 
10769  921 
(hd(#1(R.dest_thm rules)))), 
922 
wf_tac) 

923 
in (R.PROVE_HYP thm rules, R.PROVE_HYP thm induction) 

924 
end handle U.ERR _ => (rules,induction); 

925 

926 
(* 

927 
* The termination condition (tc) is simplified to  tc = tc' (there 

928 
* might not be a change!) and then 3 attempts are made: 

929 
* 

930 
* 1. if  tc = T, then eliminate it with eqT; otherwise, 

931 
* 2. apply the terminator to tc'. If  tc' = T then eliminate; else 

932 
* 3. replace tc by tc' in both the rules and the induction theorem. 

933 
**) 

934 

935 
fun print_thms s L = 

936 
if !trace then writeln (cat_lines (s :: map string_of_thm L)) 

937 
else (); 

938 

939 
fun print_cterms s L = 

940 
if !trace then writeln (cat_lines (s :: map string_of_cterm L)) 

941 
else ();; 

942 

943 
fun simplify_tc tc (r,ind) = 

944 
let val tc1 = tych tc 

945 
val _ = print_cterms "TC before simplification: " [tc1] 

946 
val tc_eq = simplifier tc1 

947 
val _ = print_thms "result: " [tc_eq] 

948 
in 

949 
elim_tc (R.MATCH_MP Thms.eqT tc_eq) (r,ind) 

950 
handle U.ERR _ => 

951 
(elim_tc (R.MATCH_MP(R.MATCH_MP Thms.rev_eq_mp tc_eq) 

11632  952 
(prove(tych(HOLogic.mk_Trueprop(S.rhs(concl tc_eq))), 
10769  953 
terminator))) 
954 
(r,ind) 

955 
handle U.ERR _ => 

956 
(R.UNDISCH(R.MATCH_MP (R.MATCH_MP Thms.simp_thm r) tc_eq), 

957 
simplify_induction theory tc_eq ind)) 

958 
end 

959 

960 
(* 

961 
* Nested termination conditions are harder to get at, since they are 

962 
* left embedded in the body of the function (and in induction 

963 
* theorem hypotheses). Our "solution" is to simplify them, and try to 

964 
* prove termination, but leave the application of the resulting theorem 

965 
* to a higher level. So things go much as in "simplify_tc": the 

966 
* termination condition (tc) is simplified to  tc = tc' (there might 

967 
* not be a change) and then 2 attempts are made: 

968 
* 

969 
* 1. if  tc = T, then return  tc; otherwise, 

970 
* 2. apply the terminator to tc'. If  tc' = T then return  tc; else 

971 
* 3. return  tc = tc' 

972 
**) 

973 
fun simplify_nested_tc tc = 

974 
let val tc_eq = simplifier (tych (#2 (S.strip_forall tc))) 

975 
in 

976 
R.GEN_ALL 

977 
(R.MATCH_MP Thms.eqT tc_eq 

978 
handle U.ERR _ => 

979 
(R.MATCH_MP(R.MATCH_MP Thms.rev_eq_mp tc_eq) 

11632  980 
(prove(tych(HOLogic.mk_Trueprop (S.rhs(concl tc_eq))), 
10769  981 
terminator)) 
982 
handle U.ERR _ => tc_eq)) 

983 
end 

984 

985 
(* 

986 
* Attempt to simplify the termination conditions in each rule and 

987 
* in the induction theorem. 

988 
**) 

989 
fun strip_imp tm = if S.is_neg tm then ([],tm) else S.strip_imp tm 

990 
fun loop ([],extras,R,ind) = (rev R, ind, extras) 

991 
 loop ((r,ftcs)::rst, nthms, R, ind) = 

992 
let val tcs = #1(strip_imp (concl r)) 

993 
val extra_tcs = gen_rems (op aconv) (ftcs, tcs) 

994 
val extra_tc_thms = map simplify_nested_tc extra_tcs 

995 
val (r1,ind1) = U.rev_itlist simplify_tc tcs (r,ind) 

996 
val r2 = R.FILTER_DISCH_ALL(not o S.is_WFR) r1 

997 
in loop(rst, nthms@extra_tc_thms, r2::R, ind1) 

998 
end 

999 
val rules_tcs = ListPair.zip (R.CONJUNCTS rules1, TCs) 

1000 
val (rules2,ind2,extras) = loop(rules_tcs,[],[],induction1) 

1001 
in 

1002 
{induction = ind2, rules = R.LIST_CONJ rules2, nested_tcs = extras} 

1003 
end; 

1004 

1005 

1006 
end; 