author  berghofe 
Tue, 29 Nov 2005 12:26:22 +0100  
changeset 18280  45e139675daf 
parent 18261  1318955d57ac 
child 18302  577e5d19b33c 
permissions  rwrr 
17870  1 
(* $Id$ *) 
2 

3 
signature NOMINAL_PACKAGE = 

4 
sig 

5 
val add_nominal_datatype : bool > string list > (string list * bstring * mixfix * 

18068  6 
(bstring * string list * mixfix) list) list > theory > theory 
17870  7 
end 
8 

18068  9 
structure NominalPackage : NOMINAL_PACKAGE = 
17870  10 
struct 
11 

12 
open DatatypeAux; 

18068  13 
open NominalAtoms; 
17870  14 

18016  15 
(** FIXME: DatatypePackage should export this function **) 
16 

17 
local 

18 

19 
fun dt_recs (DtTFree _) = [] 

20 
 dt_recs (DtType (_, dts)) = List.concat (map dt_recs dts) 

21 
 dt_recs (DtRec i) = [i]; 

22 

23 
fun dt_cases (descr: descr) (_, args, constrs) = 

24 
let 

25 
fun the_bname i = Sign.base_name (#1 (valOf (AList.lookup (op =) descr i))); 

26 
val bnames = map the_bname (distinct (List.concat (map dt_recs args))); 

27 
in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end; 

28 

29 

30 
fun induct_cases descr = 

31 
DatatypeProp.indexify_names (List.concat (map (dt_cases descr) (map #2 descr))); 

32 

33 
fun exhaust_cases descr i = dt_cases descr (valOf (AList.lookup (op =) descr i)); 

34 

35 
in 

36 

37 
fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr); 

38 

39 
fun mk_case_names_exhausts descr new = 

40 
map (RuleCases.case_names o exhaust_cases descr o #1) 

41 
(List.filter (fn ((_, (name, _, _))) => name mem_string new) descr); 

42 

43 
end; 

44 

45 
(*******************************) 

46 

17870  47 
val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma); 
48 

49 
fun read_typ sign ((Ts, sorts), str) = 

50 
let 

51 
val T = Type.no_tvars (Sign.read_typ (sign, (AList.lookup op =) 

52 
(map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg 

53 
in (Ts @ [T], add_typ_tfrees (T, sorts)) end; 

54 

55 
(** taken from HOL/Tools/datatype_aux.ML **) 

56 

57 
fun indtac indrule indnames i st = 

58 
let 

59 
val ts = HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule)); 

60 
val ts' = HOLogic.dest_conj (HOLogic.dest_Trueprop 

61 
(Logic.strip_imp_concl (List.nth (prems_of st, i  1)))); 

62 
val getP = if can HOLogic.dest_imp (hd ts) then 

63 
(apfst SOME) o HOLogic.dest_imp else pair NONE; 

64 
fun abstr (t1, t2) = (case t1 of 

65 
NONE => (case filter (fn Free (s, _) => s mem indnames  _ => false) 

66 
(term_frees t2) of 

67 
[Free (s, T)] => absfree (s, T, t2) 

68 
 _ => sys_error "indtac") 

69 
 SOME (_ $ t' $ _) => Abs ("x", fastype_of t', abstract_over (t', t2))) 

70 
val cert = cterm_of (Thm.sign_of_thm st); 

71 
val Ps = map (cert o head_of o snd o getP) ts; 

72 
val indrule' = cterm_instantiate (Ps ~~ 

73 
(map (cert o abstr o getP) ts')) indrule 

74 
in 

75 
rtac indrule' i st 

76 
end; 

77 

78 
fun gen_add_nominal_datatype prep_typ err flat_names new_type_names dts thy = 

79 
let 

80 
(* this theory is used just for parsing *) 

81 

82 
val tmp_thy = thy > 

83 
Theory.copy > 

84 
Theory.add_types (map (fn (tvs, tname, mx, _) => 

85 
(tname, length tvs, mx)) dts); 

86 

87 
val sign = Theory.sign_of tmp_thy; 

88 

89 
val atoms = atoms_of thy; 

90 
val classes = map (NameSpace.map_base (fn s => "pt_" ^ s)) atoms; 

91 
val cp_classes = List.concat (map (fn atom1 => map (fn atom2 => 

92 
Sign.intern_class thy ("cp_" ^ Sign.base_name atom1 ^ "_" ^ 

93 
Sign.base_name atom2)) atoms) atoms); 

94 
fun augment_sort S = S union classes; 

95 
val augment_sort_typ = map_type_tfree (fn (s, S) => TFree (s, augment_sort S)); 

96 

97 
fun prep_constr ((constrs, sorts), (cname, cargs, mx)) = 

98 
let val (cargs', sorts') = Library.foldl (prep_typ sign) (([], sorts), cargs) 

99 
in (constrs @ [(cname, cargs', mx)], sorts') end 

100 

101 
fun prep_dt_spec ((dts, sorts), (tvs, tname, mx, constrs)) = 

102 
let val (constrs', sorts') = Library.foldl prep_constr (([], sorts), constrs) 

103 
in (dts @ [(tvs, tname, mx, constrs')], sorts') end 

104 

105 
val (dts', sorts) = Library.foldl prep_dt_spec (([], []), dts); 

106 
val sorts' = map (apsnd augment_sort) sorts; 

107 
val tyvars = map #1 dts'; 

108 

109 
val types_syntax = map (fn (tvs, tname, mx, constrs) => (tname, mx)) dts'; 

110 
val constr_syntax = map (fn (tvs, tname, mx, constrs) => 

111 
map (fn (cname, cargs, mx) => (cname, mx)) constrs) dts'; 

112 

113 
val ps = map (fn (_, n, _, _) => 

114 
(Sign.full_name sign n, Sign.full_name sign (n ^ "_Rep"))) dts; 

115 
val rps = map Library.swap ps; 

116 

117 
fun replace_types (Type ("nominal.ABS", [T, U])) = 

118 
Type ("fun", [T, Type ("nominal.nOption", [replace_types U])]) 

119 
 replace_types (Type (s, Ts)) = 

120 
Type (getOpt (AList.lookup op = ps s, s), map replace_types Ts) 

121 
 replace_types T = T; 

122 

123 
fun replace_types' (Type (s, Ts)) = 

124 
Type (getOpt (AList.lookup op = rps s, s), map replace_types' Ts) 

125 
 replace_types' T = T; 

126 

127 
val dts'' = map (fn (tvs, tname, mx, constrs) => (tvs, tname ^ "_Rep", NoSyn, 

128 
map (fn (cname, cargs, mx) => (cname, 

129 
map (augment_sort_typ o replace_types) cargs, NoSyn)) constrs)) dts'; 

130 

131 
val new_type_names' = map (fn n => n ^ "_Rep") new_type_names; 

132 
val full_new_type_names' = map (Sign.full_name (sign_of thy)) new_type_names'; 

133 

18045  134 
val ({induction, ...},thy1) = 
17870  135 
DatatypePackage.add_datatype_i err flat_names new_type_names' dts'' thy; 
136 

137 
val SOME {descr, ...} = Symtab.lookup 

138 
(DatatypePackage.get_datatypes thy1) (hd full_new_type_names'); 

18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

139 
fun nth_dtyp i = typ_of_dtyp descr sorts' (DtRec i); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

140 

17870  141 
(**** define permutation functions ****) 
142 

143 
val permT = mk_permT (TFree ("'x", HOLogic.typeS)); 

144 
val pi = Free ("pi", permT); 

145 
val perm_types = map (fn (i, _) => 

146 
let val T = nth_dtyp i 

147 
in permT > T > T end) descr; 

148 
val perm_names = replicate (length new_type_names) "nominal.perm" @ 

149 
DatatypeProp.indexify_names (map (fn i => Sign.full_name (sign_of thy1) 

150 
("perm_" ^ name_of_typ (nth_dtyp i))) 

151 
(length new_type_names upto length descr  1)); 

152 
val perm_names_types = perm_names ~~ perm_types; 

153 

154 
val perm_eqs = List.concat (map (fn (i, (_, _, constrs)) => 

155 
let val T = nth_dtyp i 

156 
in map (fn (cname, dts) => 

157 
let 

18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

158 
val Ts = map (typ_of_dtyp descr sorts') dts; 
17870  159 
val names = DatatypeProp.make_tnames Ts; 
160 
val args = map Free (names ~~ Ts); 

161 
val c = Const (cname, Ts > T); 

162 
fun perm_arg (dt, x) = 

163 
let val T = type_of x 

164 
in if is_rec_type dt then 

165 
let val (Us, _) = strip_type T 

166 
in list_abs (map (pair "x") Us, 

167 
Const (List.nth (perm_names_types, body_index dt)) $ pi $ 

168 
list_comb (x, map (fn (i, U) => 

169 
Const ("nominal.perm", permT > U > U) $ 

170 
(Const ("List.rev", permT > permT) $ pi) $ 

171 
Bound i) ((length Us  1 downto 0) ~~ Us))) 

172 
end 

173 
else Const ("nominal.perm", permT > T > T) $ pi $ x 

174 
end; 

175 
in 

176 
(("", HOLogic.mk_Trueprop (HOLogic.mk_eq 

177 
(Const (List.nth (perm_names_types, i)) $ 

178 
Free ("pi", mk_permT (TFree ("'x", HOLogic.typeS))) $ 

179 
list_comb (c, args), 

180 
list_comb (c, map perm_arg (dts ~~ args))))), []) 

181 
end) constrs 

182 
end) descr); 

183 

184 
val (thy2, perm_simps) = thy1 > 

185 
Theory.add_consts_i (map (fn (s, T) => (Sign.base_name s, T, NoSyn)) 

186 
(List.drop (perm_names_types, length new_type_names))) > 

187 
PrimrecPackage.add_primrec_i "" perm_eqs; 

188 

189 
(**** prove that permutation functions introduced by unfolding are ****) 

190 
(**** equivalent to already existing permutation functions ****) 

191 

192 
val _ = warning ("length descr: " ^ string_of_int (length descr)); 

193 
val _ = warning ("length new_type_names: " ^ string_of_int (length new_type_names)); 

194 

195 
val perm_indnames = DatatypeProp.make_tnames (map body_type perm_types); 

196 
val perm_fun_def = PureThy.get_thm thy2 (Name "perm_fun_def"); 

197 

198 
val unfolded_perm_eq_thms = 

199 
if length descr = length new_type_names then [] 

200 
else map standard (List.drop (split_conj_thm 

18010  201 
(Goal.prove thy2 [] [] 
17870  202 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 
203 
(map (fn (c as (s, T), x) => 

204 
let val [T1, T2] = binder_types T 

205 
in HOLogic.mk_eq (Const c $ pi $ Free (x, T2), 

206 
Const ("nominal.perm", T) $ pi $ Free (x, T2)) 

207 
end) 

18010  208 
(perm_names_types ~~ perm_indnames)))) 
209 
(fn _ => EVERY [indtac induction perm_indnames 1, 

17870  210 
ALLGOALS (asm_full_simp_tac 
211 
(simpset_of thy2 addsimps [perm_fun_def]))])), 

212 
length new_type_names)); 

213 

214 
(**** prove [] \<bullet> t = t ****) 

215 

216 
val _ = warning "perm_empty_thms"; 

217 

218 
val perm_empty_thms = List.concat (map (fn a => 

219 
let val permT = mk_permT (Type (a, [])) 

220 
in map standard (List.take (split_conj_thm 

18010  221 
(Goal.prove thy2 [] [] 
17870  222 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 
223 
(map (fn ((s, T), x) => HOLogic.mk_eq 

224 
(Const (s, permT > T > T) $ 

225 
Const ("List.list.Nil", permT) $ Free (x, T), 

226 
Free (x, T))) 

227 
(perm_names ~~ 

18010  228 
map body_type perm_types ~~ perm_indnames)))) 
229 
(fn _ => EVERY [indtac induction perm_indnames 1, 

17870  230 
ALLGOALS (asm_full_simp_tac (simpset_of thy2))])), 
231 
length new_type_names)) 

232 
end) 

233 
atoms); 

234 

235 
(**** prove (pi1 @ pi2) \<bullet> t = pi1 \<bullet> (pi2 \<bullet> t) ****) 

236 

237 
val _ = warning "perm_append_thms"; 

238 

239 
(*FIXME: these should be looked up statically*) 

240 
val at_pt_inst = PureThy.get_thm thy2 (Name "at_pt_inst"); 

241 
val pt2 = PureThy.get_thm thy2 (Name "pt2"); 

242 

243 
val perm_append_thms = List.concat (map (fn a => 

244 
let 

245 
val permT = mk_permT (Type (a, [])); 

246 
val pi1 = Free ("pi1", permT); 

247 
val pi2 = Free ("pi2", permT); 

248 
val pt_inst = PureThy.get_thm thy2 (Name ("pt_" ^ Sign.base_name a ^ "_inst")); 

249 
val pt2' = pt_inst RS pt2; 

250 
val pt2_ax = PureThy.get_thm thy2 

251 
(Name (NameSpace.map_base (fn s => "pt_" ^ s ^ "2") a)); 

252 
in List.take (map standard (split_conj_thm 

18010  253 
(Goal.prove thy2 [] [] 
17870  254 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 
255 
(map (fn ((s, T), x) => 

256 
let val perm = Const (s, permT > T > T) 

257 
in HOLogic.mk_eq 

258 
(perm $ (Const ("List.op @", permT > permT > permT) $ 

259 
pi1 $ pi2) $ Free (x, T), 

260 
perm $ pi1 $ (perm $ pi2 $ Free (x, T))) 

261 
end) 

262 
(perm_names ~~ 

18010  263 
map body_type perm_types ~~ perm_indnames)))) 
264 
(fn _ => EVERY [indtac induction perm_indnames 1, 

17870  265 
ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt2', pt2_ax]))]))), 
266 
length new_type_names) 

267 
end) atoms); 

268 

269 
(**** prove pi1 ~ pi2 ==> pi1 \<bullet> t = pi2 \<bullet> t ****) 

270 

271 
val _ = warning "perm_eq_thms"; 

272 

273 
val pt3 = PureThy.get_thm thy2 (Name "pt3"); 

274 
val pt3_rev = PureThy.get_thm thy2 (Name "pt3_rev"); 

275 

276 
val perm_eq_thms = List.concat (map (fn a => 

277 
let 

278 
val permT = mk_permT (Type (a, [])); 

279 
val pi1 = Free ("pi1", permT); 

280 
val pi2 = Free ("pi2", permT); 

281 
(*FIXME: not robust  better access these theorems using NominalData?*) 

282 
val at_inst = PureThy.get_thm thy2 (Name ("at_" ^ Sign.base_name a ^ "_inst")); 

283 
val pt_inst = PureThy.get_thm thy2 (Name ("pt_" ^ Sign.base_name a ^ "_inst")); 

284 
val pt3' = pt_inst RS pt3; 

285 
val pt3_rev' = at_inst RS (pt_inst RS pt3_rev); 

286 
val pt3_ax = PureThy.get_thm thy2 

287 
(Name (NameSpace.map_base (fn s => "pt_" ^ s ^ "3") a)); 

288 
in List.take (map standard (split_conj_thm 

18010  289 
(Goal.prove thy2 [] [] (Logic.mk_implies 
17870  290 
(HOLogic.mk_Trueprop (Const ("nominal.prm_eq", 
291 
permT > permT > HOLogic.boolT) $ pi1 $ pi2), 

292 
HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 

293 
(map (fn ((s, T), x) => 

294 
let val perm = Const (s, permT > T > T) 

295 
in HOLogic.mk_eq 

296 
(perm $ pi1 $ Free (x, T), 

297 
perm $ pi2 $ Free (x, T)) 

298 
end) 

299 
(perm_names ~~ 

18010  300 
map body_type perm_types ~~ perm_indnames))))) 
301 
(fn _ => EVERY [indtac induction perm_indnames 1, 

17870  302 
ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt3', pt3_rev', pt3_ax]))]))), 
303 
length new_type_names) 

304 
end) atoms); 

305 

306 
(**** prove pi1 \<bullet> (pi2 \<bullet> t) = (pi1 \<bullet> pi2) \<bullet> (pi1 \<bullet> t) ****) 

307 

308 
val cp1 = PureThy.get_thm thy2 (Name "cp1"); 

309 
val dj_cp = PureThy.get_thm thy2 (Name "dj_cp"); 

310 
val pt_perm_compose = PureThy.get_thm thy2 (Name "pt_perm_compose"); 

311 
val pt_perm_compose_rev = PureThy.get_thm thy2 (Name "pt_perm_compose_rev"); 

312 
val dj_perm_perm_forget = PureThy.get_thm thy2 (Name "dj_perm_perm_forget"); 

313 

314 
fun composition_instance name1 name2 thy = 

315 
let 

316 
val name1' = Sign.base_name name1; 

317 
val name2' = Sign.base_name name2; 

318 
val cp_class = Sign.intern_class thy ("cp_" ^ name1' ^ "_" ^ name2'); 

319 
val permT1 = mk_permT (Type (name1, [])); 

320 
val permT2 = mk_permT (Type (name2, [])); 

321 
val augment = map_type_tfree 

322 
(fn (x, S) => TFree (x, cp_class :: S)); 

323 
val Ts = map (augment o body_type) perm_types; 

324 
val cp_inst = PureThy.get_thm thy 

325 
(Name ("cp_" ^ name1' ^ "_" ^ name2' ^ "_inst")); 

326 
val simps = simpset_of thy addsimps (perm_fun_def :: 

327 
(if name1 <> name2 then 

328 
let val dj = PureThy.get_thm thy (Name ("dj_" ^ name2' ^ "_" ^ name1')) 

329 
in [dj RS (cp_inst RS dj_cp), dj RS dj_perm_perm_forget] end 

330 
else 

331 
let 

332 
val at_inst = PureThy.get_thm thy (Name ("at_" ^ name1' ^ "_inst")); 

333 
val pt_inst = PureThy.get_thm thy (Name ("pt_" ^ name1' ^ "_inst")) 

334 
in 

335 
[cp_inst RS cp1 RS sym, 

336 
at_inst RS (pt_inst RS pt_perm_compose) RS sym, 

337 
at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym] 

338 
end)) 

18010  339 
val thms = split_conj_thm (standard (Goal.prove thy [] [] 
17870  340 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj 
341 
(map (fn ((s, T), x) => 

342 
let 

343 
val pi1 = Free ("pi1", permT1); 

344 
val pi2 = Free ("pi2", permT2); 

345 
val perm1 = Const (s, permT1 > T > T); 

346 
val perm2 = Const (s, permT2 > T > T); 

347 
val perm3 = Const ("nominal.perm", permT1 > permT2 > permT2) 

348 
in HOLogic.mk_eq 

349 
(perm1 $ pi1 $ (perm2 $ pi2 $ Free (x, T)), 

350 
perm2 $ (perm3 $ pi1 $ pi2) $ (perm1 $ pi1 $ Free (x, T))) 

351 
end) 

18010  352 
(perm_names ~~ Ts ~~ perm_indnames)))) 
353 
(fn _ => EVERY [indtac induction perm_indnames 1, 

354 
ALLGOALS (asm_full_simp_tac simps)]))) 

17870  355 
in 
356 
foldl (fn ((s, tvs), thy) => AxClass.add_inst_arity_i 

357 
(s, replicate (length tvs) (cp_class :: classes), [cp_class]) 

358 
(AxClass.intro_classes_tac [] THEN ALLGOALS (resolve_tac thms)) thy) 

359 
thy (full_new_type_names' ~~ tyvars) 

360 
end; 

361 

362 
val (thy3, perm_thmss) = thy2 > 

363 
fold (fn name1 => fold (composition_instance name1) atoms) atoms > 

364 
curry (Library.foldr (fn ((i, (tyname, args, _)), thy) => 

365 
AxClass.add_inst_arity_i (tyname, replicate (length args) classes, classes) 

366 
(AxClass.intro_classes_tac [] THEN REPEAT (EVERY 

367 
[resolve_tac perm_empty_thms 1, 

368 
resolve_tac perm_append_thms 1, 

369 
resolve_tac perm_eq_thms 1, assume_tac 1])) thy)) 

370 
(List.take (descr, length new_type_names)) > 

371 
PureThy.add_thmss 

372 
[((space_implode "_" new_type_names ^ "_unfolded_perm_eq", 

373 
unfolded_perm_eq_thms), [Simplifier.simp_add_global]), 

374 
((space_implode "_" new_type_names ^ "_perm_empty", 

375 
perm_empty_thms), [Simplifier.simp_add_global]), 

376 
((space_implode "_" new_type_names ^ "_perm_append", 

377 
perm_append_thms), [Simplifier.simp_add_global]), 

378 
((space_implode "_" new_type_names ^ "_perm_eq", 

379 
perm_eq_thms), [Simplifier.simp_add_global])]; 

380 

381 
(**** Define representing sets ****) 

382 

383 
val _ = warning "representing sets"; 

384 

385 
val rep_set_names = map (Sign.full_name thy3) (DatatypeProp.indexify_names 

386 
(map (fn (i, _) => name_of_typ (nth_dtyp i) ^ "_set") descr)); 

387 
val big_rep_name = 

388 
space_implode "_" (DatatypeProp.indexify_names (List.mapPartial 

389 
(fn (i, ("nominal.nOption", _, _)) => NONE 

390 
 (i, _) => SOME (name_of_typ (nth_dtyp i))) descr)) ^ "_set"; 

391 
val _ = warning ("big_rep_name: " ^ big_rep_name); 

392 

393 
fun strip_option (dtf as DtType ("fun", [dt, DtRec i])) = 

394 
(case AList.lookup op = descr i of 

395 
SOME ("nominal.nOption", _, [(_, [dt']), _]) => 

396 
apfst (cons dt) (strip_option dt') 

397 
 _ => ([], dtf)) 

18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

398 
 strip_option (DtType ("fun", [dt, DtType ("nominal.nOption", [dt'])])) = 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

399 
apfst (cons dt) (strip_option dt') 
17870  400 
 strip_option dt = ([], dt); 
401 

18280
45e139675daf
Corrected atom class constraints in strong induction rule.
berghofe
parents:
18261
diff
changeset

402 
val dt_atomTs = distinct (map (typ_of_dtyp descr sorts') 
45e139675daf
Corrected atom class constraints in strong induction rule.
berghofe
parents:
18261
diff
changeset

403 
(List.concat (map (fn (_, (_, _, cs)) => List.concat 
45e139675daf
Corrected atom class constraints in strong induction rule.
berghofe
parents:
18261
diff
changeset

404 
(map (List.concat o map (fst o strip_option) o snd) cs)) descr))); 
45e139675daf
Corrected atom class constraints in strong induction rule.
berghofe
parents:
18261
diff
changeset

405 

17870  406 
fun make_intr s T (cname, cargs) = 
407 
let 

408 
fun mk_prem (dt, (j, j', prems, ts)) = 

409 
let 

410 
val (dts, dt') = strip_option dt; 

411 
val (dts', dt'') = strip_dtyp dt'; 

18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

412 
val Ts = map (typ_of_dtyp descr sorts') dts; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

413 
val Us = map (typ_of_dtyp descr sorts') dts'; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

414 
val T = typ_of_dtyp descr sorts' dt''; 
17870  415 
val free = mk_Free "x" (Us > T) j; 
416 
val free' = app_bnds free (length Us); 

417 
fun mk_abs_fun (T, (i, t)) = 

418 
let val U = fastype_of t 

419 
in (i + 1, Const ("nominal.abs_fun", [T, U, T] > 

420 
Type ("nominal.nOption", [U])) $ mk_Free "y" T i $ t) 

421 
end 

422 
in (j + 1, j' + length Ts, 

423 
case dt'' of 

424 
DtRec k => list_all (map (pair "x") Us, 

425 
HOLogic.mk_Trueprop (HOLogic.mk_mem (free', 

426 
Const (List.nth (rep_set_names, k), 

427 
HOLogic.mk_setT T)))) :: prems 

428 
 _ => prems, 

429 
snd (foldr mk_abs_fun (j', free) Ts) :: ts) 

430 
end; 

431 

432 
val (_, _, prems, ts) = foldr mk_prem (1, 1, [], []) cargs; 

433 
val concl = HOLogic.mk_Trueprop (HOLogic.mk_mem 

434 
(list_comb (Const (cname, map fastype_of ts > T), ts), 

435 
Const (s, HOLogic.mk_setT T))) 

436 
in Logic.list_implies (prems, concl) 

437 
end; 

438 

439 
val (intr_ts, ind_consts) = 

440 
apfst List.concat (ListPair.unzip (List.mapPartial 

441 
(fn ((_, ("nominal.nOption", _, _)), _) => NONE 

442 
 ((i, (_, _, constrs)), rep_set_name) => 

443 
let val T = nth_dtyp i 

444 
in SOME (map (make_intr rep_set_name T) constrs, 

445 
Const (rep_set_name, HOLogic.mk_setT T)) 

446 
end) 

447 
(descr ~~ rep_set_names))); 

448 

449 
val (thy4, {raw_induct = rep_induct, intrs = rep_intrs, ...}) = 

450 
setmp InductivePackage.quiet_mode false 

451 
(InductivePackage.add_inductive_i false true big_rep_name false true false 

452 
ind_consts (map (fn x => (("", x), [])) intr_ts) []) thy3; 

453 

454 
(**** Prove that representing set is closed under permutation ****) 

455 

456 
val _ = warning "proving closure under permutation..."; 

457 

458 
val perm_indnames' = List.mapPartial 

459 
(fn (x, (_, ("nominal.nOption", _, _))) => NONE  (x, _) => SOME x) 

460 
(perm_indnames ~~ descr); 

461 

462 
fun mk_perm_closed name = map (fn th => standard (th RS mp)) 

18010  463 
(List.take (split_conj_thm (Goal.prove thy4 [] [] 
17870  464 
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map 
465 
(fn (S, x) => 

466 
let 

467 
val S = map_term_types (map_type_tfree 

468 
(fn (s, cs) => TFree (s, cs union cp_classes))) S; 

469 
val T = HOLogic.dest_setT (fastype_of S); 

470 
val permT = mk_permT (Type (name, [])) 

471 
in HOLogic.mk_imp (HOLogic.mk_mem (Free (x, T), S), 

472 
HOLogic.mk_mem (Const ("nominal.perm", permT > T > T) $ 

473 
Free ("pi", permT) $ Free (x, T), S)) 

18010  474 
end) (ind_consts ~~ perm_indnames')))) 
475 
(fn _ => EVERY (* CU: added perm_fun_def in the final tactic in order to deal with funs *) 

17870  476 
[indtac rep_induct [] 1, 
477 
ALLGOALS (simp_tac (simpset_of thy4 addsimps 

478 
(symmetric perm_fun_def :: PureThy.get_thms thy4 (Name ("abs_perm"))))), 

479 
ALLGOALS (resolve_tac rep_intrs 

480 
THEN_ALL_NEW (asm_full_simp_tac (simpset_of thy4 addsimps [perm_fun_def])))])), 

481 
length new_type_names)); 

482 

483 
(* FIXME: theorems are stored in database for testing only *) 

484 
val perm_closed_thmss = map mk_perm_closed atoms; 

485 
val (thy5, _) = PureThy.add_thmss [(("perm_closed", 

486 
List.concat perm_closed_thmss), [])] thy4; 

487 

488 
(**** typedef ****) 

489 

490 
val _ = warning "defining type..."; 

491 

492 
val (thy6, typedefs) = 

493 
foldl_map (fn (thy, ((((name, mx), tvs), c), name')) => 

494 
setmp TypedefPackage.quiet_mode true 

495 
(TypedefPackage.add_typedef_i false (SOME name') (name, tvs, mx) c NONE 

496 
(rtac exI 1 THEN 

497 
QUIET_BREADTH_FIRST (has_fewer_prems 1) 

498 
(resolve_tac rep_intrs 1))) thy > (fn (thy, r) => 

499 
let 

500 
val permT = mk_permT (TFree (variant tvs "'a", HOLogic.typeS)); 

501 
val pi = Free ("pi", permT); 

502 
val tvs' = map (fn s => TFree (s, the (AList.lookup op = sorts' s))) tvs; 

503 
val T = Type (Sign.intern_type thy name, tvs'); 

504 
val Const (_, Type (_, [U])) = c 

505 
in apsnd (pair r o hd) 

506 
(PureThy.add_defs_i true [(("prm_" ^ name ^ "_def", Logic.mk_equals 

507 
(Const ("nominal.perm", permT > T > T) $ pi $ Free ("x", T), 

508 
Const (Sign.intern_const thy ("Abs_" ^ name), U > T) $ 

509 
(Const ("nominal.perm", permT > U > U) $ pi $ 

510 
(Const (Sign.intern_const thy ("Rep_" ^ name), T > U) $ 

511 
Free ("x", T))))), [])] thy) 

512 
end)) 

513 
(thy5, types_syntax ~~ tyvars ~~ 

514 
(List.take (ind_consts, length new_type_names)) ~~ new_type_names); 

515 

516 
val perm_defs = map snd typedefs; 

517 
val Abs_inverse_thms = map (#Abs_inverse o fst) typedefs; 

18016  518 
val Rep_inverse_thms = map (#Rep_inverse o fst) typedefs; 
17870  519 
val Rep_thms = map (#Rep o fst) typedefs; 
520 

18016  521 
val big_name = space_implode "_" new_type_names; 
522 

523 

17870  524 
(** prove that new types are in class pt_<name> **) 
525 

526 
val _ = warning "prove that new types are in class pt_<name> ..."; 

527 

528 
fun pt_instance ((class, atom), perm_closed_thms) = 

529 
fold (fn (((({Abs_inverse, Rep_inverse, Rep, ...}, 

530 
perm_def), name), tvs), perm_closed) => fn thy => 

531 
AxClass.add_inst_arity_i 

532 
(Sign.intern_type thy name, 

533 
replicate (length tvs) (classes @ cp_classes), [class]) 

534 
(EVERY [AxClass.intro_classes_tac [], 

535 
rewrite_goals_tac [perm_def], 

536 
asm_full_simp_tac (simpset_of thy addsimps [Rep_inverse]) 1, 

537 
asm_full_simp_tac (simpset_of thy addsimps 

538 
[Rep RS perm_closed RS Abs_inverse]) 1, 

539 
asm_full_simp_tac (HOL_basic_ss addsimps [PureThy.get_thm thy 

540 
(Name ("pt_" ^ Sign.base_name atom ^ "3"))]) 1]) thy) 

541 
(typedefs ~~ new_type_names ~~ tyvars ~~ perm_closed_thms); 

542 

543 

544 
(** prove that new types are in class cp_<name1>_<name2> **) 

545 

546 
val _ = warning "prove that new types are in class cp_<name1>_<name2> ..."; 

547 

548 
fun cp_instance (atom1, perm_closed_thms1) (atom2, perm_closed_thms2) thy = 

549 
let 

550 
val name = "cp_" ^ Sign.base_name atom1 ^ "_" ^ Sign.base_name atom2; 

551 
val class = Sign.intern_class thy name; 

552 
val cp1' = PureThy.get_thm thy (Name (name ^ "_inst")) RS cp1 

553 
in fold (fn ((((({Abs_inverse, Rep_inverse, Rep, ...}, 

554 
perm_def), name), tvs), perm_closed1), perm_closed2) => fn thy => 

555 
AxClass.add_inst_arity_i 

556 
(Sign.intern_type thy name, 

557 
replicate (length tvs) (classes @ cp_classes), [class]) 

558 
(EVERY [AxClass.intro_classes_tac [], 

559 
rewrite_goals_tac [perm_def], 

560 
asm_full_simp_tac (simpset_of thy addsimps 

561 
((Rep RS perm_closed1 RS Abs_inverse) :: 

562 
(if atom1 = atom2 then [] 

563 
else [Rep RS perm_closed2 RS Abs_inverse]))) 1, 

18016  564 
cong_tac 1, 
17870  565 
rtac refl 1, 
566 
rtac cp1' 1]) thy) 

567 
(typedefs ~~ new_type_names ~~ tyvars ~~ perm_closed_thms1 ~~ 

568 
perm_closed_thms2) thy 

569 
end; 

570 

571 
val thy7 = fold (fn x => fn thy => thy > 

572 
pt_instance x > 

573 
fold (cp_instance (apfst snd x)) (atoms ~~ perm_closed_thmss)) 

574 
(classes ~~ atoms ~~ perm_closed_thmss) thy6; 

575 

576 
(**** constructors ****) 

577 

578 
fun mk_abs_fun (x, t) = 

579 
let 

580 
val T = fastype_of x; 

581 
val U = fastype_of t 

582 
in 

583 
Const ("nominal.abs_fun", T > U > T > 

584 
Type ("nominal.nOption", [U])) $ x $ t 

585 
end; 

586 

18016  587 
val (ty_idxs, _) = foldl 
588 
(fn ((i, ("nominal.nOption", _, _)), p) => p 

589 
 ((i, _), (ty_idxs, j)) => (ty_idxs @ [(i, j)], j + 1)) ([], 0) descr; 

590 

591 
fun reindex (DtType (s, dts)) = DtType (s, map reindex dts) 

592 
 reindex (DtRec i) = DtRec (the (AList.lookup op = ty_idxs i)) 

593 
 reindex dt = dt; 

594 

595 
fun strip_suffix i s = implode (List.take (explode s, size s  i)); 

596 

597 
(** strips the "_Rep" in type names *) 

18045  598 
fun strip_nth_name i s = 
599 
let val xs = NameSpace.unpack s; 

600 
in NameSpace.pack (Library.nth_map (length xs  i) (strip_suffix 4) xs) end; 

18016  601 

18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

602 
val (descr'', ndescr) = ListPair.unzip (List.mapPartial 
18016  603 
(fn (i, ("nominal.nOption", _, _)) => NONE 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

604 
 (i, (s, dts, constrs)) => 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

605 
let 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

606 
val SOME index = AList.lookup op = ty_idxs i; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

607 
val (constrs1, constrs2) = ListPair.unzip 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

608 
(map (fn (cname, cargs) => apfst (pair (strip_nth_name 2 cname)) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

609 
(foldl_map (fn (dts, dt) => 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

610 
let val (dts', dt') = strip_option dt 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

611 
in (dts @ dts' @ [reindex dt'], (length dts, length dts')) end) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

612 
([], cargs))) constrs) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

613 
in SOME ((index, (strip_nth_name 1 s, map reindex dts, constrs1)), 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

614 
(index, constrs2)) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

615 
end) descr); 
18045  616 

18016  617 
val (descr1, descr2) = splitAt (length new_type_names, descr''); 
618 
val descr' = [descr1, descr2]; 

619 

18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

620 
val typ_of_dtyp' = replace_types' o typ_of_dtyp descr sorts'; 
17870  621 

622 
val rep_names = map (fn s => 

623 
Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names; 

624 
val abs_names = map (fn s => 

625 
Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names; 

626 

18016  627 
val recTs' = List.mapPartial 
628 
(fn ((_, ("nominal.nOption", _, _)), T) => NONE 

629 
 (_, T) => SOME T) (descr ~~ get_rec_types descr sorts'); 

18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

630 
val recTs = get_rec_types descr'' sorts'; 
18016  631 
val newTs' = Library.take (length new_type_names, recTs'); 
632 
val newTs = Library.take (length new_type_names, recTs); 

17870  633 

634 
val full_new_type_names = map (Sign.full_name (sign_of thy)) new_type_names; 

635 

636 
fun make_constr_def tname T T' ((thy, defs, eqns), ((cname, cargs), (cname', mx))) = 

637 
let 

638 
fun constr_arg (dt, (j, l_args, r_args)) = 

639 
let 

640 
val x' = mk_Free "x" (typ_of_dtyp' dt) j; 

641 
val (dts, dt') = strip_option dt; 

642 
val xs = map (fn (dt, i) => mk_Free "x" (typ_of_dtyp' dt) i) 

643 
(dts ~~ (j upto j + length dts  1)) 

644 
val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts) 

645 
val (dts', dt'') = strip_dtyp dt' 

18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

646 
in 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

647 
(j + length dts + 1, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

648 
xs @ x :: l_args, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

649 
foldr mk_abs_fun 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

650 
(case dt'' of 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

651 
DtRec k => if k < length new_type_names then 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

652 
list_abs (map (pair "z" o typ_of_dtyp') dts', 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

653 
Const (List.nth (rep_names, k), typ_of_dtyp' dt'' > 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

654 
typ_of_dtyp descr sorts' dt'') $ app_bnds x (length dts')) 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

655 
else error "nested recursion not (yet) supported" 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

656 
 _ => x) xs :: r_args) 
17870  657 
end 
658 

659 
val (_, l_args, r_args) = foldr constr_arg (1, [], []) cargs; 

660 
val abs_name = Sign.intern_const (Theory.sign_of thy) ("Abs_" ^ tname); 

661 
val rep_name = Sign.intern_const (Theory.sign_of thy) ("Rep_" ^ tname); 

662 
val constrT = map fastype_of l_args > T; 

663 
val lhs = list_comb (Const (Sign.full_name thy (Sign.base_name cname), 

664 
constrT), l_args); 

665 
val rhs = list_comb (Const (cname, map fastype_of r_args > T'), r_args); 

666 
val def = Logic.mk_equals (lhs, Const (abs_name, T' > T) $ rhs); 

667 
val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq 

668 
(Const (rep_name, T > T') $ lhs, rhs)); 

669 
val def_name = (Sign.base_name cname) ^ "_def"; 

670 
val (thy', [def_thm]) = thy > 

671 
Theory.add_consts_i [(cname', constrT, mx)] > 

672 
(PureThy.add_defs_i false o map Thm.no_attributes) [(def_name, def)] 

673 
in (thy', defs @ [def_thm], eqns @ [eqn]) end; 

674 

675 
fun dt_constr_defs ((thy, defs, eqns, dist_lemmas), 

676 
(((((_, (_, _, constrs)), tname), T), T'), constr_syntax)) = 

677 
let 

678 
val rep_const = cterm_of thy 

679 
(Const (Sign.intern_const thy ("Rep_" ^ tname), T > T')); 

680 
val dist = standard (cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma); 

681 
val (thy', defs', eqns') = Library.foldl (make_constr_def tname T T') 

682 
((Theory.add_path tname thy, defs, []), constrs ~~ constr_syntax) 

683 
in 

684 
(parent_path flat_names thy', defs', eqns @ [eqns'], dist_lemmas @ [dist]) 

685 
end; 

686 

687 
val (thy8, constr_defs, constr_rep_eqns, dist_lemmas) = Library.foldl dt_constr_defs 

688 
((thy7, [], [], []), List.take (descr, length new_type_names) ~~ 

689 
new_type_names ~~ newTs ~~ newTs' ~~ constr_syntax); 

690 

691 
val abs_inject_thms = map (fn tname => 

692 
PureThy.get_thm thy8 (Name ("Abs_" ^ tname ^ "_inject"))) new_type_names; 

693 

694 
val rep_inject_thms = map (fn tname => 

695 
PureThy.get_thm thy8 (Name ("Rep_" ^ tname ^ "_inject"))) new_type_names; 

696 

697 
val rep_thms = map (fn tname => 

698 
PureThy.get_thm thy8 (Name ("Rep_" ^ tname))) new_type_names; 

699 

700 
val rep_inverse_thms = map (fn tname => 

701 
PureThy.get_thm thy8 (Name ("Rep_" ^ tname ^ "_inverse"))) new_type_names; 

702 

703 
(* prove theorem Rep_i (Constr_j ...) = Constr'_j ... *) 

704 

705 
fun prove_constr_rep_thm eqn = 

706 
let 

707 
val inj_thms = map (fn r => r RS iffD1) abs_inject_thms; 

708 
val rewrites = constr_defs @ map mk_meta_eq rep_inverse_thms 

18010  709 
in standard (Goal.prove thy8 [] [] eqn (fn _ => EVERY 
17870  710 
[resolve_tac inj_thms 1, 
711 
rewrite_goals_tac rewrites, 

712 
rtac refl 3, 

713 
resolve_tac rep_intrs 2, 

18010  714 
REPEAT (resolve_tac rep_thms 1)])) 
17870  715 
end; 
716 

717 
val constr_rep_thmss = map (map prove_constr_rep_thm) constr_rep_eqns; 

718 

719 
(* prove theorem pi \<bullet> Rep_i x = Rep_i (pi \<bullet> x) *) 

720 

721 
fun prove_perm_rep_perm (atom, perm_closed_thms) = map (fn th => 

722 
let 

723 
val _ $ (_ $ (Rep $ x) $ _) = Logic.unvarify (prop_of th); 

724 
val Type ("fun", [T, U]) = fastype_of Rep; 

725 
val permT = mk_permT (Type (atom, [])); 

726 
val pi = Free ("pi", permT); 

727 
in 

18010  728 
standard (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq 
17870  729 
(Const ("nominal.perm", permT > U > U) $ pi $ (Rep $ x), 
18010  730 
Rep $ (Const ("nominal.perm", permT > T > T) $ pi $ x)))) 
731 
(fn _ => simp_tac (HOL_basic_ss addsimps (perm_defs @ Abs_inverse_thms @ 

732 
perm_closed_thms @ Rep_thms)) 1)) 

17870  733 
end) Rep_thms; 
734 

735 
val perm_rep_perm_thms = List.concat (map prove_perm_rep_perm 

736 
(atoms ~~ perm_closed_thmss)); 

737 

738 
(* prove distinctness theorems *) 

739 

18016  740 
val distinct_props = setmp DatatypeProp.dtK 1000 
741 
(DatatypeProp.make_distincts new_type_names descr' sorts') thy8; 

17870  742 

743 
val dist_rewrites = map (fn (rep_thms, dist_lemma) => 

744 
dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0])) 

745 
(constr_rep_thmss ~~ dist_lemmas); 

746 

747 
fun prove_distinct_thms (_, []) = [] 

748 
 prove_distinct_thms (p as (rep_thms, dist_lemma), t::ts) = 

749 
let 

18010  750 
val dist_thm = standard (Goal.prove thy8 [] [] t (fn _ => 
751 
simp_tac (simpset_of thy8 addsimps (dist_lemma :: rep_thms)) 1)) 

17870  752 
in dist_thm::(standard (dist_thm RS not_sym)):: 
753 
(prove_distinct_thms (p, ts)) 

754 
end; 

755 

756 
val distinct_thms = map prove_distinct_thms 

757 
(constr_rep_thmss ~~ dist_lemmas ~~ distinct_props); 

758 

759 
(** prove equations for permutation functions **) 

760 

761 
val abs_perm = PureThy.get_thms thy8 (Name "abs_perm"); (* FIXME *) 

762 

763 
val perm_simps' = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) => 

764 
let val T = replace_types' (nth_dtyp i) 

765 
in List.concat (map (fn (atom, perm_closed_thms) => 

766 
map (fn ((cname, dts), constr_rep_thm) => 

767 
let 

768 
val cname = Sign.intern_const thy8 

769 
(NameSpace.append tname (Sign.base_name cname)); 

770 
val permT = mk_permT (Type (atom, [])); 

771 
val pi = Free ("pi", permT); 

772 

773 
fun perm t = 

774 
let val T = fastype_of t 

775 
in Const ("nominal.perm", permT > T > T) $ pi $ t end; 

776 

777 
fun constr_arg (dt, (j, l_args, r_args)) = 

778 
let 

779 
val x' = mk_Free "x" (typ_of_dtyp' dt) j; 

780 
val (dts, dt') = strip_option dt; 

781 
val Ts = map typ_of_dtyp' dts; 

782 
val xs = map (fn (T, i) => mk_Free "x" T i) 

783 
(Ts ~~ (j upto j + length dts  1)) 

784 
val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts); 

785 
val (dts', dt'') = strip_dtyp dt'; 

18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

786 
in 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

787 
(j + length dts + 1, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

788 
xs @ x :: l_args, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

789 
map perm (xs @ [x]) @ r_args) 
17870  790 
end 
791 

792 
val (_, l_args, r_args) = foldr constr_arg (1, [], []) dts; 

793 
val c = Const (cname, map fastype_of l_args > T) 

794 
in 

18010  795 
standard (Goal.prove thy8 [] [] 
17870  796 
(HOLogic.mk_Trueprop (HOLogic.mk_eq 
18010  797 
(perm (list_comb (c, l_args)), list_comb (c, r_args)))) 
798 
(fn _ => EVERY 

17870  799 
[simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: perm_defs)) 1, 
800 
simp_tac (HOL_basic_ss addsimps (Rep_thms @ Abs_inverse_thms @ 

801 
constr_defs @ perm_closed_thms)) 1, 

802 
TRY (simp_tac (HOL_basic_ss addsimps 

803 
(symmetric perm_fun_def :: abs_perm)) 1), 

804 
TRY (simp_tac (HOL_basic_ss addsimps 

805 
(perm_fun_def :: perm_defs @ Rep_thms @ Abs_inverse_thms @ 

18010  806 
perm_closed_thms)) 1)])) 
17870  807 
end) (constrs ~~ constr_rep_thms)) (atoms ~~ perm_closed_thmss)) 
808 
end) (List.take (descr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss); 

809 

810 
(** prove injectivity of constructors **) 

811 

812 
val rep_inject_thms' = map (fn th => th RS sym) rep_inject_thms; 

813 
val alpha = PureThy.get_thms thy8 (Name "alpha"); 

814 
val abs_fresh = PureThy.get_thms thy8 (Name "abs_fresh"); 

815 
val fresh_def = PureThy.get_thm thy8 (Name "fresh_def"); 

816 
val supp_def = PureThy.get_thm thy8 (Name "supp_def"); 

817 

818 
val inject_thms = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) => 

819 
let val T = replace_types' (nth_dtyp i) 

820 
in List.mapPartial (fn ((cname, dts), constr_rep_thm) => 

821 
if null dts then NONE else SOME 

822 
let 

823 
val cname = Sign.intern_const thy8 

824 
(NameSpace.append tname (Sign.base_name cname)); 

825 

826 
fun make_inj (dt, (j, args1, args2, eqs)) = 

827 
let 

828 
val x' = mk_Free "x" (typ_of_dtyp' dt) j; 

829 
val y' = mk_Free "y" (typ_of_dtyp' dt) j; 

830 
val (dts, dt') = strip_option dt; 

831 
val Ts_idx = map typ_of_dtyp' dts ~~ (j upto j + length dts  1); 

832 
val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx; 

833 
val ys = map (fn (T, i) => mk_Free "y" T i) Ts_idx; 

834 
val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts); 

835 
val y = mk_Free "y" (typ_of_dtyp' dt') (j + length dts); 

836 
val (dts', dt'') = strip_dtyp dt'; 

18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

837 
in 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

838 
(j + length dts + 1, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

839 
xs @ (x :: args1), ys @ (y :: args2), 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

840 
HOLogic.mk_eq 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

841 
(foldr mk_abs_fun x xs, foldr mk_abs_fun y ys) :: eqs) 
17870  842 
end; 
843 

844 
val (_, args1, args2, eqs) = foldr make_inj (1, [], [], []) dts; 

845 
val Ts = map fastype_of args1; 

846 
val c = Const (cname, Ts > T) 

847 
in 

18010  848 
standard (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq 
17870  849 
(HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)), 
18010  850 
foldr1 HOLogic.mk_conj eqs))) 
851 
(fn _ => EVERY 

17870  852 
[asm_full_simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: 
853 
rep_inject_thms')) 1, 

854 
TRY (asm_full_simp_tac (HOL_basic_ss addsimps (fresh_def :: supp_def :: 

855 
alpha @ abs_perm @ abs_fresh @ rep_inject_thms @ 

17874
8be65cf94d2e
Improved proof of injectivity theorems to make it work on
berghofe
parents:
17873
diff
changeset

856 
perm_rep_perm_thms)) 1), 
8be65cf94d2e
Improved proof of injectivity theorems to make it work on
berghofe
parents:
17873
diff
changeset

857 
TRY (asm_full_simp_tac (HOL_basic_ss addsimps (perm_fun_def :: 
18010  858 
expand_fun_eq :: rep_inject_thms @ perm_rep_perm_thms)) 1)])) 
17870  859 
end) (constrs ~~ constr_rep_thms) 
860 
end) (List.take (descr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss); 

861 

17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

862 
(** equations for support and freshness **) 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

863 

f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

864 
val Un_assoc = PureThy.get_thm thy8 (Name "Un_assoc"); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

865 
val de_Morgan_conj = PureThy.get_thm thy8 (Name "de_Morgan_conj"); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

866 
val Collect_disj_eq = PureThy.get_thm thy8 (Name "Collect_disj_eq"); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

867 
val finite_Un = PureThy.get_thm thy8 (Name "finite_Un"); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

868 

f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

869 
val (supp_thms, fresh_thms) = ListPair.unzip (map ListPair.unzip 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

870 
(map (fn ((((i, (_, _, constrs)), tname), inject_thms'), perm_thms') => 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

871 
let val T = replace_types' (nth_dtyp i) 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

872 
in List.concat (map (fn (cname, dts) => map (fn atom => 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

873 
let 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

874 
val cname = Sign.intern_const thy8 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

875 
(NameSpace.append tname (Sign.base_name cname)); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

876 
val atomT = Type (atom, []); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

877 

f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

878 
fun process_constr (dt, (j, args1, args2)) = 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

879 
let 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

880 
val x' = mk_Free "x" (typ_of_dtyp' dt) j; 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

881 
val (dts, dt') = strip_option dt; 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

882 
val Ts_idx = map typ_of_dtyp' dts ~~ (j upto j + length dts  1); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

883 
val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx; 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

884 
val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

885 
val (dts', dt'') = strip_dtyp dt'; 
18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

886 
in 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

887 
(j + length dts + 1, 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

888 
xs @ (x :: args1), foldr mk_abs_fun x xs :: args2) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

889 
end; 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

890 

f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

891 
val (_, args1, args2) = foldr process_constr (1, [], []) dts; 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

892 
val Ts = map fastype_of args1; 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

893 
val c = list_comb (Const (cname, Ts > T), args1); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

894 
fun supp t = 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

895 
Const ("nominal.supp", fastype_of t > HOLogic.mk_setT atomT) $ t; 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

896 
fun fresh t = 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

897 
Const ("nominal.fresh", atomT > fastype_of t > HOLogic.boolT) $ 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

898 
Free ("a", atomT) $ t; 
18010  899 
val supp_thm = standard (Goal.prove thy8 [] [] 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

900 
(HOLogic.mk_Trueprop (HOLogic.mk_eq 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

901 
(supp c, 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

902 
if null dts then Const ("{}", HOLogic.mk_setT atomT) 
18010  903 
else foldr1 (HOLogic.mk_binop "op Un") (map supp args2)))) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

904 
(fn _ => 
18010  905 
simp_tac (HOL_basic_ss addsimps (supp_def :: 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

906 
Un_assoc :: de_Morgan_conj :: Collect_disj_eq :: finite_Un :: 
17874
8be65cf94d2e
Improved proof of injectivity theorems to make it work on
berghofe
parents:
17873
diff
changeset

907 
symmetric empty_def :: Finites.emptyI :: simp_thms @ 
18010  908 
abs_perm @ abs_fresh @ inject_thms' @ perm_thms')) 1)) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

909 
in 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

910 
(supp_thm, 
18010  911 
standard (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

912 
(fresh c, 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

913 
if null dts then HOLogic.true_const 
18010  914 
else foldr1 HOLogic.mk_conj (map fresh args2)))) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

915 
(fn _ => 
18010  916 
simp_tac (simpset_of thy8 addsimps [fresh_def, supp_thm]) 1))) 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

917 
end) atoms) constrs) 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

918 
end) (List.take (descr, length new_type_names) ~~ new_type_names ~~ inject_thms ~~ perm_simps'))); 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

919 

18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

920 
(**** weak induction theorem ****) 
18016  921 

18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

922 
val arities = get_arities descr''; 
18016  923 

924 
fun mk_funs_inv thm = 

925 
let 

926 
val {sign, prop, ...} = rep_thm thm; 

927 
val _ $ (_ $ (Const (_, Type (_, [U, _])) $ _ $ S)) $ 

928 
(_ $ (_ $ (r $ (a $ _)) $ _)) = Type.freeze prop; 

929 
val used = add_term_tfree_names (a, []); 

930 

931 
fun mk_thm i = 

932 
let 

933 
val Ts = map (TFree o rpair HOLogic.typeS) 

934 
(variantlist (replicate i "'t", used)); 

935 
val f = Free ("f", Ts > U) 

936 
in standard (Goal.prove sign [] [] (Logic.mk_implies 

937 
(HOLogic.mk_Trueprop (HOLogic.list_all 

938 
(map (pair "x") Ts, HOLogic.mk_mem (app_bnds f i, S))), 

939 
HOLogic.mk_Trueprop (HOLogic.mk_eq (list_abs (map (pair "x") Ts, 

940 
r $ (a $ app_bnds f i)), f)))) 

941 
(fn _ => EVERY [REPEAT (rtac ext 1), REPEAT (etac allE 1), rtac thm 1, atac 1])) 

942 
end 

943 
in map (fn r => r RS subst) (thm :: map mk_thm arities) end; 

944 

945 
fun mk_indrule_lemma ((prems, concls), (((i, _), T), U)) = 

946 
let 

947 
val Rep_t = Const (List.nth (rep_names, i), T > U) $ 

948 
mk_Free "x" T i; 

949 

950 
val Abs_t = Const (List.nth (abs_names, i), U > T) 

951 

952 
in (prems @ [HOLogic.imp $ HOLogic.mk_mem (Rep_t, 

953 
Const (List.nth (rep_set_names, i), HOLogic.mk_setT U)) $ 

954 
(mk_Free "P" (T > HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))], 

955 
concls @ [mk_Free "P" (T > HOLogic.boolT) (i + 1) $ mk_Free "x" T i]) 

956 
end; 

957 

958 
val (indrule_lemma_prems, indrule_lemma_concls) = 

18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

959 
Library.foldl mk_indrule_lemma (([], []), (descr'' ~~ recTs ~~ recTs')); 
18016  960 

961 
val indrule_lemma = standard (Goal.prove thy8 [] [] 

962 
(Logic.mk_implies 

963 
(HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems), 

964 
HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY 

965 
[REPEAT (etac conjE 1), 

966 
REPEAT (EVERY 

967 
[TRY (rtac conjI 1), full_simp_tac (HOL_basic_ss addsimps Rep_inverse_thms) 1, 

968 
etac mp 1, resolve_tac Rep_thms 1])])); 

969 

970 
val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma))); 

971 
val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else 

972 
map (Free o apfst fst o dest_Var) Ps; 

973 
val indrule_lemma' = cterm_instantiate 

974 
(map (cterm_of thy8) Ps ~~ map (cterm_of thy8) frees) indrule_lemma; 

975 

976 
val Abs_inverse_thms' = List.concat (map mk_funs_inv Abs_inverse_thms); 

977 

978 
val dt_induct_prop = DatatypeProp.make_ind descr' sorts'; 

979 
val dt_induct = standard (Goal.prove thy8 [] 

980 
(Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop) 

981 
(fn prems => EVERY 

982 
[rtac indrule_lemma' 1, 

983 
(DatatypeAux.indtac rep_induct THEN_ALL_NEW ObjectLogic.atomize_tac) 1, 

984 
EVERY (map (fn (prem, r) => (EVERY 

985 
[REPEAT (eresolve_tac Abs_inverse_thms' 1), 

986 
simp_tac (HOL_basic_ss addsimps [symmetric r]) 1, 

987 
DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)])) 

988 
(prems ~~ constr_defs))])); 

989 

18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

990 
val case_names_induct = mk_case_names_induct descr''; 
18016  991 

18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

992 
(**** prove that new datatypes have finite support ****) 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

993 

18246
676d2e625d98
added fsub.thy (poplmark challenge) to the examples
urbanc
parents:
18245
diff
changeset

994 
val _ = warning "proving finite support for the new datatype"; 
676d2e625d98
added fsub.thy (poplmark challenge) to the examples
urbanc
parents:
18245
diff
changeset

995 

18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

996 
val indnames = DatatypeProp.make_tnames recTs; 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

997 

d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

998 
val abs_supp = PureThy.get_thms thy8 (Name "abs_supp"); 
18067  999 
val supp_atm = PureThy.get_thms thy8 (Name "supp_atm"); 
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1000 

d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1001 
val finite_supp_thms = map (fn atom => 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1002 
let val atomT = Type (atom, []) 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1003 
in map standard (List.take 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1004 
(split_conj_thm (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1005 
(foldr1 HOLogic.mk_conj (map (fn (s, T) => HOLogic.mk_mem 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1006 
(Const ("nominal.supp", T > HOLogic.mk_setT atomT) $ Free (s, T), 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1007 
Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT atomT)))) 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1008 
(indnames ~~ recTs)))) 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1009 
(fn _ => indtac dt_induct indnames 1 THEN 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1010 
ALLGOALS (asm_full_simp_tac (simpset_of thy8 addsimps 
18067  1011 
(abs_supp @ supp_atm @ 
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1012 
PureThy.get_thms thy8 (Name ("fs_" ^ Sign.base_name atom ^ "1")) @ 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1013 
List.concat supp_thms))))), 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1014 
length new_type_names)) 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1015 
end) atoms; 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1016 

18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1017 
(**** strong induction theorem ****) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1018 

ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1019 
val pnames = if length descr'' = 1 then ["P"] 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1020 
else map (fn i => "P" ^ string_of_int i) (1 upto length descr''); 
18245
65e60434b3c2
Fixed problem with strong induction theorem for datatypes containing
berghofe
parents:
18142
diff
changeset

1021 
val ind_sort = if null dt_atomTs then HOLogic.typeS 
65e60434b3c2
Fixed problem with strong induction theorem for datatypes containing
berghofe
parents:
18142
diff
changeset

1022 
else map (fn T => Sign.intern_class thy8 ("fs_" ^ 
65e60434b3c2
Fixed problem with strong induction theorem for datatypes containing
berghofe
parents:
18142
diff
changeset

1023 
Sign.base_name (fst (dest_Type T)))) dt_atomTs; 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1024 
val fsT = TFree ("'n", ind_sort); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1025 

ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1026 
fun make_pred i T = 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1027 
Free (List.nth (pnames, i), T > fsT > HOLogic.boolT); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1028 

ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1029 
fun make_ind_prem k T ((cname, cargs), idxs) = 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1030 
let 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1031 
val recs = List.filter is_rec_type cargs; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1032 
val Ts = map (typ_of_dtyp descr'' sorts') cargs; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1033 
val recTs' = map (typ_of_dtyp descr'' sorts') recs; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1034 
val tnames = variantlist (DatatypeProp.make_tnames Ts, pnames); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1035 
val rec_tnames = map fst (List.filter (is_rec_type o snd) (tnames ~~ cargs)); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1036 
val frees = tnames ~~ Ts; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1037 
val z = (variant tnames "z", fsT); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1038 

ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1039 
fun mk_prem ((dt, s), T) = 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1040 
let 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1041 
val (Us, U) = strip_type T; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1042 
val l = length Us 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1043 
in list_all (z :: map (pair "x") Us, HOLogic.mk_Trueprop 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1044 
(make_pred (body_index dt) U $ app_bnds (Free (s, T)) l $ Bound l)) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1045 
end; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1046 

ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1047 
val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs'); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1048 
val prems' = map (fn p as (_, T) => HOLogic.mk_Trueprop 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1049 
(Const ("nominal.fresh", T > fsT > HOLogic.boolT) $ 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1050 
Free p $ Free z)) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1051 
(map (curry List.nth frees) (List.concat (map (fn (m, n) => 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1052 
m upto m + n  1) idxs))) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1053 

ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1054 
in list_all_free (z :: frees, Logic.list_implies (prems' @ prems, 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1055 
HOLogic.mk_Trueprop (make_pred k T $ 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1056 
list_comb (Const (cname, Ts > T), map Free frees) $ Free z))) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1057 
end; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1058 

ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1059 
val ind_prems = List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) => 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1060 
map (make_ind_prem i T) (constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs)); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1061 
val tnames = DatatypeProp.make_tnames recTs; 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1062 
val z = (variant tnames "z", fsT); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1063 
val ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &") 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1064 
(map (fn (((i, _), T), tname) => make_pred i T $ Free (tname, T) $ Free z) 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1065 
(descr'' ~~ recTs ~~ tnames))); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1066 
val induct = Logic.list_implies (ind_prems, ind_concl); 
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1067 

18104
dbe58b104cb9
added thms perm, distinct and fresh to the simplifier.
urbanc
parents:
18068
diff
changeset

1068 
val simp_atts = replicate (length new_type_names) [Simplifier.simp_add_global]; 
dbe58b104cb9
added thms perm, distinct and fresh to the simplifier.
urbanc
parents:
18068
diff
changeset

1069 

17870  1070 
val (thy9, _) = thy8 > 
18016  1071 
Theory.add_path big_name > 
18017
f6abeac6dcb5
fixed case names in the weak induction principle and
urbanc
parents:
18016
diff
changeset

1072 
PureThy.add_thms [(("induct_weak", dt_induct), [case_names_induct])] >> 
18016  1073 
Theory.parent_path >>> 
18104
dbe58b104cb9
added thms perm, distinct and fresh to the simplifier.
urbanc
parents:
18068
diff
changeset

1074 
DatatypeAux.store_thmss_atts "distinct" new_type_names simp_atts distinct_thms >>> 
17870  1075 
DatatypeAux.store_thmss "constr_rep" new_type_names constr_rep_thmss >>> 
18104
dbe58b104cb9
added thms perm, distinct and fresh to the simplifier.
urbanc
parents:
18068
diff
changeset

1076 
DatatypeAux.store_thmss_atts "perm" new_type_names simp_atts perm_simps' >>> 
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

1077 
DatatypeAux.store_thmss "inject" new_type_names inject_thms >>> 
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset

1078 
DatatypeAux.store_thmss "supp" new_type_names supp_thms >>> 
18104
dbe58b104cb9
added thms perm, distinct and fresh to the simplifier.
urbanc
parents:
18068
diff
changeset

1079 
DatatypeAux.store_thmss_atts "fresh" new_type_names simp_atts fresh_thms >> 
18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

1080 
fold (fn (atom, ths) => fn thy => 
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1081 
let val class = Sign.intern_class thy ("fs_" ^ Sign.base_name atom) 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1082 
in fold (fn T => AxClass.add_inst_arity_i 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1083 
(fst (dest_Type T), 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1084 
replicate (length sorts) [class], [class]) 
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset

1085 
(AxClass.intro_classes_tac [] THEN resolve_tac ths 1)) newTs thy 
18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

1086 
end) (atoms ~~ finite_supp_thms) >> 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1087 
Theory.add_path big_name >>> 
18142
a51ab4152097
called the induction principle "unsafe" instead of "test".
urbanc
parents:
18107
diff
changeset

1088 
PureThy.add_axioms_i [(("induct_unsafe", induct), [case_names_induct])] >> 
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset

1089 
Theory.parent_path; 
17870  1090 

1091 
in 

18068  1092 
thy9 
17870  1093 
end; 
1094 

1095 
val add_nominal_datatype = gen_add_nominal_datatype read_typ true; 

1096 

1097 

1098 
(* FIXME: The following stuff should be exported by DatatypePackage *) 

1099 

1100 
local structure P = OuterParse and K = OuterKeyword in 

1101 

1102 
val datatype_decl = 

1103 
Scan.option (P.$$$ "("  P.name  P.$$$ ")")  P.type_args  P.name  P.opt_infix  

1104 
(P.$$$ "="  P.enum1 "" (P.name  Scan.repeat P.typ  P.opt_mixfix)); 

1105 

1106 
fun mk_datatype args = 

1107 
let 

1108 
val names = map (fn ((((NONE, _), t), _), _) => t  ((((SOME t, _), _), _), _) => t) args; 

1109 
val specs = map (fn ((((_, vs), t), mx), cons) => 

1110 
(vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args; 

18068  1111 
in add_nominal_datatype false names specs end; 
17870  1112 

1113 
val nominal_datatypeP = 

1114 
OuterSyntax.command "nominal_datatype" "define inductive datatypes" K.thy_decl 

1115 
(P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype)); 

1116 

1117 
val _ = OuterSyntax.add_parsers [nominal_datatypeP]; 

1118 

1119 
end; 

1120 

18261
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

1121 
end 
1318955d57ac
Corrected treatment of nonrecursive abstraction types.
berghofe
parents:
18246
diff
changeset

1122 